Research and Development Laboratories

of the

Portland Cement Association

RESEARCH DEPARTMENT

Bulletin 154

Physical Properties of Cement Paste

By

T. C. Powers

Reprinted from Chemistry of Cement

Proceedings of the Fourth International Symposium

Washington, D. C., 1960, held at the

National Bureau of Standards (U.S. Department of Commerce)

Monograph 43, Vol. II, Session V, Paper V-1, 577-609

PHYSICAL PROPERTIES OF CEMENT PASTE

By

T. C. Powers

PORTLAND CEMENT ASSOCIATION’

RESEARCH AND DEVELOPMENT LABORATORIES

5420 Old Orchard Road

Skokie, Illinois 60078

Paper V-1. Physical Properties

T. C. Powers

Synopsis

of Cement Paste*

This paper deals mainly with cement paste in terms of its porosity, internal surface area,interaction between solid substance and evaporable water and related properties. Thereare 10 sections as follows: (1) introduction; (2) properties of fresh paste; (3) specific volumeof hydrated cement and porosity of paste; (4) surface area of hydrated cement, and indicatedparticle size; (5) minimum porosity of hydrated paste and specific volume of cement gel;(6) concepts of structure of cement gel and cement paste; (7) mechanical effects of adsorptionand hydrostatic tension~ (8) instability of cement paste; (9) strength; (10) permeability.

Among the subtopics are the following: definition of pore and solid; permeability ofpaste at all stages of hydration; measurement of surface area; specific volume of cement gel;computation of capillary porosity; physical aspects of hydration products; adsorption andcapillary condensation; spontaneous decrease of specific surface area of hydrated cement;irreversible deformations; gel-space ratio vs. strength; theories of permeabilityy; viscosityof water in cement paste; capillary continuity and discontinuity.

A glossary of terms is appended.

R6sum6

Cet expos6 traite principalement de la pate de cirnent en fonotion de sa porosit& de lasurface sp6cifique interne, de l’action r6ciproque entre la substance solide et l’eau r%aporable,et des propri&% qui B]yrapportent, 11y a 10 sections qui sent les suivantes: (1) introduc-tion; (2) propri6t& de la p~te frzdche; (3) volume sptfcifiq”e du ciment hydrat6 et porosit6 dela piite; (4) surface sp6cifique d“ ciment hydrat.$ et indication sur la taille des particles;(5) porositi minimum de la p4te bydratcte et volume spicifique du gel de ciment; (6) conceptsde structure du gel de ciment et de la p$lte de ciment; (7) effets m6caniques de l’adsorptionet de la tension hydrmtatique; (S) instahilit6 de la p~te de ciment; (9) r&istance; (10) per-m6abilit&

Parmi Ies points secondaires, les suivants sent trait6s: definition de pore et de solide;perm&+bilit4 de la pate A to us les stades de l’h ydratation; mesure de la surface sp6cifique;volume spc!cifique du gel de ciment; calcul de la porosit6 capillaire; aspects physiques desproduits d’hydratation~ adsorption et condensation capillaire; diminution spontande de lasurface sp~cifique du mment hvdrat~; deformations irri$versibles; rapport gel-espace versusri$sistance;,thefories de perm&ibilit6; viscosit6 de l’eau dam la p~te de ciment; continuit6 etdiscontinult~ capillaires,

Un Iexique des termes se trouve en appendice,

Zusammenfassung

In dem Vortrag werden hauptsachlich die Porositat, die Groi3e der inneren Oberflache,die Reaktion zwischen festem Kim-perund verdampfbarem Wasser und die damit zusammen-hangenden Eigenschaften der Zementpasten beschrieben, Die zehn Kapitel haben diefolgenden ~berschriften: (1) Einleitung; (2) Eigenschaften der frischen Paste; (3) Dasspezifische Volumen des hydratisierten Zementes und die Pastenporositiit; (4) OberfMche deshydratisierten Zementes und wahrscheinliche Teilchengro13e; (5) Die Minimumporositiit derhydratisierten Paste und das spezifische Volumen des Zementgels; (6) Der Zementgel- undZementpastenstrukturbegriff; (7) Mechanische Effekte der Adsorption und der hydro-statischen Spannung; (8) Unbestandigkeit der Zementpasten; (9) Festigkeit; (10) Permea-bilitat.

. Fourth Internation.] Symposium .n tbe ChemiStrYof cement, Washington, D,c., IWO. Contribution from the Researchand Development Laboratwigsof the Portland Cement Assmiatkm, Skokie, llliImis,

577

Als sekundiire Themen behandelt sind: Definition der Pore und des festen Korpers;Pastenpermeabilitit in allen Hydratationsstufen: Oberflachenmessung; Das spezifischeVolumen des Zementgek; Berechnung der kapillaren Porositat.; Physikalische Eigenschaftender Hydratationsprodukte; Adsorption und KapiUarkondensatlon; Abnahme der spezifischenOberflache des hydratisierten Zementes; Nicht umkehrbare Formverinderung; Die Festig-keit als eine Function des Verhiltnisses gel/space; Permeabilitatstheorien; Die Viskosit itdes Wassers in der Zementpaste; Kapillare Stetigkeit und Unstetigkcit.

Eine Liste der benutzten Worte ist am Ende hinzugefiigt.

1. Introduction

The chemical origins of the substance calledcement paste, and the physico-chemical processesof its formation, are essential elements of the studyof physical properties of cement paste, and theproperties of cement paste are reflected in almostevery aspect of concrete technology. Thus, thestudy of cement paste provides a bridge betweencement chemistry and concrete technology. Asub j ect of such broad scope involves the wholeliterature of cement and concrete, and a completecritical review would have required more time thanwas available. Th erefore, a complete review wasnot attempted.

This review turned out to be an occasion forrevision and reassessment of our own work, andthis entailed introducing some material not pub-lished before. Concepts of structure have beenemphasized, and special attention is paid to a fewpoints that have proved to be somewhat con-troversial. Perhaps the most important of theseis the question of internal surface area: Areinternal surf aces real, and have we measured them?

Little is said about differences in the chemicalcompositions of cements because the physical

2. Properties of

The Dormant Period

During a short period beginning at the time ofcontact between cement and water, relativelyrapid chemical reactions occur. Then follows alonger period of low activity which has been calledthe dormant period, [1, 2].1 It is the time duringwhich paste normally remains plastic, and, atroom temperature, it normally lasts 40 to 120rein, depending on the characteristics of the ce-ment. - -

The initial reaction does not seem to alter thesize and shape of the cement grains very much.This is indicated for example, by the followingdata obtained with a Wagner turbidimeter byErnsberger and France [3].

, Figures in brackets indicate the htemtum refermws at the end of thisPwer.

properties of paste are not much influenced by suchdifferences. Any hydrated portland cement ispredominantly colloidal and this point of similarityoutweighs the points of difference attributable todifferences in chemistry.

The words used for describing hydrated cementare those required for describing a chemically un-identified substance, In 1947 it was not possible,and still in 1960 it is not feasiblej to use muchchemical nomenclature. The ratios CaO: SiO,:H,O for substances in cement paste are not defi-nitely established, to say nothing of other com-ponents. There 1s reason to suspect that uniquemolecular ratios are not characteristic of hydratedcements. So, in this 1960 review it is still neces-sary to refer to grams of “nonevaporable water”,and to “hydrated cement”, instead of conven-tionally designated molecular species, The resultis rather unsatisfactory to chemists and non-chemists alike, since a discussion based on arbi-trary special definitions often becomes confusingif those definitions are overlooked, (A glossaryof terms will be found in appendix 1.) Possibly,after other papers of this symposium have beendigested, terminology will be improved.

Fresh Paste

I i-m;r:sin1meatMaterial

.m%,g

Powers [4] found that the specific surface areacalculated from the rate of bleeding of cementpastes by a modified Kozeny-Carman equation,was about the same for a paste made with keroseneas with water. Steinour [5] measured the bleed-ing rates of one cement in various liquids. Thevalues for specific surface area, calculated from theKozeny-Carman equation [6] were as follows:

578

Name of liquid surfacearea,cm~lg

—

Diorama... . . . . . . . . . . . . . . . . . . . . . 1,08011..71ether. . . . . . . . . . . . . . . . . . . . 1,630Butyl alcohol. . . . . . . . . . . . . . . . . . 1,670Octyl alcohol. . .. . . . . . . . . . . . . . . . 1,680Diethylphthakte. .. .. . . . . . . . . . . 1,675

Average .. . . . . . . . . . . . . . . . . . . . 1,670

water.................. .. ... ... 1,710

These figures indicate that reaction with watercaused a slight increase in specific surface area.

The constancy of the rate of bleeding duringthe dormant period shows that the new productsformed by reactions occurring during the dormantperiod do not effectively alter the surface contoursof the particles, or change the viscosity of theliquid. Possibly, the layer of hydration productsfirst formed, around which water flows duringbleeding, is of loose enough texture to accommo-date the small quantity of material producedduring the dormant period.

Preparation of Pastes

The physical characteristics of a batch offresh paste depend on how the paste is prepared.When mixed by gentle stirring, the paste remainsstiff relative to the consistency produced byvigorous mechanical stirring [7]. Dry cement,which is normally in a flocculated state, isapparently not uniformly dispersed by wettingalone. To produce a homogeneous paste oflowest possible stiffness, a laboratory mixer ableto” produce a high rate of shear is necessary.

Length of mixing period is important. Ifit is of the order 30 sec or lees, the paste becomesfirm soon after mixing stops [8]. Steinour calledthis phenomenon “brief-mix-set” and attributedit to the grains becoming stuck together by gel

recess of forming on grain eurfaces.@i ““

EvenIf t e mlxmg period is long enough to preventbrief-mix-set, which is usually the case, it maybe too short to eliminate false set. In the labora-tory, it is advisable to allow a period of restbetween an initial and final mixing period, thelength of the rest period having been determinedby trial for each cement: Examples of mixingschedules required to elimmate false set are givenin table 1.

With the exception of matters pertaining tofalse set, time effects and mixing procedures areprincipally laboratory problems. Under normalfield conditions, the time of mixing can hardlybe so short as to permit brief-mix-set, and therolling mass of aggregate in a concrete mixer“homogenizes” the paste as effectively as themost vigorous 1aborator.y stirrer.

When a paste is properly prepared, its propertiesare reproducible, and are amenable to quantita-tive study. A considerable amount of such studyhas been done, and it gave information aboutthe structure of fresh paste that is not only

essential to an understanding of the propertiesand behavior of fresh concrete, but also is pertinentto various aspects of mature concrete.

TABI.E 1. Mixing schedulesrequired by different cementsto eliminate fake set

t3peciflcsurfaoe: 1,5S43cm,,g (Wagner Turbidimeter)Tests were on 1:2(b” wt.) mortarsmade with Elrin sand..——

WICis that required for (l+i.oi,)-inih slump, with 6-incone,aftera 1min mixThe first number of the mixi”z scheduleis the Icngth of the flint period o

mixing; the secondk the Deriodof rest; the last is the find mixing pariod.

Condition afterASTM l-rein mix

type Lot No. b;%.Req”in?d Remolding Slu:prnixi”~ effort, jigs

schedule coneR.E. s Slump

—

min15753 0:;: 27 1.05 2+0 25 1T5

i 15706b .852

2-2-2 3315755. .84 :i

1.101.10 2->2

326 1,10

15757. .34 33 .95 >3-24

27 1,0515762b .34 42 .85 Z-&z 22 1,40

,,,. This cementshowed evidence of modera,te falseset,. This cementshowed marked falseset,o Remolding effort, numberof jigs.

The Flocculent State

During the dormant period, properly preparedpaste is a thick suspension of particles in a floccu-lent state. Steinour [9] found that the term“flocculent state” is not to be construed to meanthat the paste consists of a collection of moreor less separate floccules. Instead, the wholebody of paste constitutes a single flo~, the floestructure being a rather uniform reticulum ofcement particles. Because of such structure,fresh paste has some cohesive strength, as shownby its theological properties.

The flocculent state can be modified or destroyedby means of surface-active agents. Such agentshave been studied extensively? prtrticularly in theSoviet Union, but, this being the subject ofanother paper of the Symposium, it will not bedealt with here.

Studies of sedimentation volume indicate thatcement particles in water, though flocculent, arenot normally far from the dispersed (nouflocculent)state [10]. The sedimentation volume of cementin dry alcohol, in which the particles are com-pletely dispereed, is only a little smaller than thesedimentation volume of cement particles inwater, whereas the sedimentation volume in anonpolar liquid, benzene, for example, is nearlytwice that in dry alcohol. The relatively lowintensity of int,erparticle attraction betweencement particles in water is probably due to thehydrophilic nature of cement.

Although the floe structure of cement pastehas some strength and rigidity, the cement parti-cles are nevertheless discrete during the dormantperiod. This was shown by measurements ofhydrostatic pressure [11]. The constancy of therate of bleeding also shows that the particlesremain discrete during the dormant period. Itappears, that where the gel-coated grains arealmoet m contact, they are separated by a thinlayer of water, probably only a few angstrom

579

units thick. The constancy of the bleeding ratesignifies in particular that such thin, separatinglayers of water have no solidity.

This last-mentioned observation seems contraryto what has been reported for some mixtures ofclay and water [12]7 namely, that rigid, ice-likestructures develop m the small spaces betweensolid surfaces. The flocculent state in cementpaste seems explicable in terms of classical theory,viz., the gel-coated grains carry a “solvatedlayer” and they have a positive zeta potential [13].The combined effect of solvated layer and electro-static charge is such as to prevent actual contactbetween adj scent grains. But the grains are con-centrated enough to experience interparticle attrac-tion, at least over parts of their boundaries. Theeffects of repulsion and attraction balance at acertain distance of separation where the potentialenergy of the particles is at a minirnurn. Thecement grains tend to remain in “potentialtroughs”, which are so located as to require spacesbetween the particles.

Solvated surfaces and electrostatic chargeaccount in part for the kind of theological prop-erties exhibited by cement pastes. Other factorsare the size,, shape, and concentration of particles,and the viscosity of the fluid. In pastes ofrelatively stiff consistency, effects of interparticleforces dominate, viscosity playing a minor role [14].At softer consistencies, w/c= 0.4 and above,cement paste is, as Reiner puts it, “ . a firstapproximation to a Bingham body” [15].

Sedimentation (Bleeding)

Because cement particles remain discrete duringthe dormant period, and because the suspendingmedium is viscous, the suspension is not stableunder the pull of gravity; cement paste “bleeds”.Bleeding has been referred to as au aspect ofcoacervation [16] but experimental evidence thatit is something other than gravitational settlementseems lacking:

The initial rate of bleeding remains constantfor a period determined by v~rious factors [1, 2].Although the largest cement particles are a hun-dred or more times the size of the smallest, allsizes are forced to fall at the same rate becauseof the flocculent state, Hence, the fluid appearingabove the solids remains clear and free from finepartitilm. If sedimentation becomes completedwithin the dormant period, physical factors alonedetermine the particle concentration in the finalsediment. When setting arrests bleeding beforethe process is physically complete, the final sedi-ment does not have uniform concentration ofcement grains. At the bottom there may be alayer of completed “sedimentation zone”, but, atthe top, w/c remains at the initial value. Thus,the final composition of a specimen of cementpaste may differ from the initial composition,and the specimen as a whole may become con-siderably less homogeneous than it was at thebeginning.

The lowest possible water content of the com-pleted sediment is higher, the higher the originalwater content of the paste [18]. In contrast tothis, Steinour found that thick suspensions ofemery would always settle to the same final vol-ume, regardless of the initial volume of the suspen-sion, provided the particles were in a nonflocculentstate [19]. Presumably, cement particles woulddo the same were it not for their flocculent state.

The greatest possible amount of water that canbe lost from a paste by bleeding under the force ofgravity alone has been called the ‘[bleeding ca-pacity” [18]. It is a function of the initial watercontent, and it appears to follow a regular law.Steinour’s studies led to several approximations ofit, one of which may be stated as follows:

(1)

Where AH’ is the bleeding capacity expressed assettlement per unit of original height; w is theinitial weight of water; c the weight of cement;p, is the density of the cement, and V is the initialvolume of the paste. The symbols K, and (w/c) n,are empirical constants characteristic of a givencement, and are dependent mostly on the surfacearea of the cement; (w/c) n was interpreted as thewater cement ratio of a “base” paste in which theparticles arc so concentrated that bleeding cannotoccur. It is evaluated by extrapolation of plotteddata, and may be regarded as referring to a hypo-thetical paste.

The values of the constants in eq (1), for a givencement, can be altered by any means that changesthe state of flocculation. Increase of interparticleattraction increases the base water content, andvice versa, Owing, presumably, to the interparti-cle water films, the base volume is larger the finerthe cement.

Permeability of Fresh Paste

Rate of bleeding is related to the coefficient ofpermeability of the (nonsettled) paste as shownin eq (2).

Q= K[(PJPJ)-11(1-c) (2)

Q is the rate of bleeding in cm/see, or ccjcm’ sec;K1 is the coefficient of per,ncability to a specificfluid at a specific temperature, in cm/sec; p. andP~ are densities of cement and fluid respectively,in g/cc; ~is the volume of fluid-filled space per nmtvolume of pastel i.e., the porosity.

The permeabdity of paste made with a givencement depends on temperature and water con-tent. There is a limiting water contenb belowwhich the pastes all maintain continuous floe struc-ture during bleeding, and above which the struc-ture becomes ruptured and [‘channeled bleeding”occurs [20]. Most of the ensuing discussion per-tains to “normal” rather than ‘(channeled”bleeding.

580

The mean size of pores in fresh paste can beestimated from hydraulic radius, that is, the quo-tient of water content and wetted surface area.An example is given in table 2, The figures in thefinal column are based on the assumption that thesection of a typical pore resembles a rectangularslit [21]. At a given water content the pore sizeis smaller the larger the specific surface area of thecement.

TABLE 2, ‘ ‘PoTe” sizes of fresh pastesfor cementhavinga surface area of 6,OOOcm%/cc(1,9oOcm~/g,Wagner)

1,water E&$i:;lic Estimated averagecement f width of pore,ratio micmn~ microns

by wt.

0.25 0::; 1,25 Between 2)4 and 5.40 2.12 Between 4 and 8.50 ,61 2.60 Between 5 and 10.60 .66 3.23 Between 6,%arid 13,70 ,69 3.70 Between 7% and 15

II I

A theoretical equation for the coefficient ofpermeability making use of the hydraulic radius,and based on the Kozeny-Carman concept, is

(,–w,)’,(3)

~’=ko(pcz;~fl –Wt) “ (1–,)2

The corresponding equation for bleeding rate is

(PC–P,)9 _ . (C–’Wi)3,Q=koq(@)’(l-w J (1–.)

(4)

Symbols not already used are defined as follows:2 is the specific surface of the cement grains incm2/g, as determined by a suitable permeabilitymethod ~ ~ is the viscosity of the fluid in poises.Theoretically, w, is related to a fraction of thefluid that remains with the particles during flow.As shown by Steinour’s work [22], the term(1 – WJ of eq (4) must be squared when a specificsurface value is used that is based on sedimenta-tion analysis and calculated by Stokes’ law in theusual way, which does not take account of fluidthat accompanies the particles, The Wf seemsto be composed of three elements, that is,

-+C“=l+a+fm(5)

where a (1—c) is a quantity of fluid held stagnanton the irregular grains, and b~ (1 —c) is a volumeadded to the original cement grains by the ini~ialchemical reaction. The terms a and b~ thereforeoccur because of an augmentation of the solid:,and a diminution of the fluid, so far as flow 1sconcerned. The c in Wt is zero for nonfloccrdatedsuspensions, but always appears when a thicksuspension becomes flocculated. For sphericalparticles, c= 0.1, approximately [23], and a and bare zero. For crushed glassj b is zero and w, is?Pprox?rnately 0.18. Experiments with pulver-ized sdlca m suspensions of lime water with

different concentrations of calcium hydroxideshowed that as long as the floe structure wass hrongenough to give normal bleeding, varying thedegree of flocculation did not influence c [24].(The degree of flocculation does, however, stronglyinfluence the bleeding capacity.) Steinour’s dataon experiments with suspensions of monodisperseemery particles showed that the change from non-flocculated to flocculated state simply increasedw,. Thus c represents the effect of flocculationper se. Perhaps the best explanation of it is thatit represents water in isolated pockets excludedfrom the continuous floe structure, and is there-fore not to be considered when computing thehydraulic radius of the IIoc structure.

The experimentally observed fact that themodified Kozeny-Carman equation representsexperimental results accurately indicates that theproduct kO(l – WJ is a constant that can beidentified with the Kozeny-Carman constant, k.Thus

lc=ko(l-ro,). (6)

Steinour’s findings, expressed in terms of eq (6),but with (1 – w,) squared since w, was determinedby sedimentation analysis, show that for suspen-sions of chemically inert spheres, w~ is zero andLO=4.06. Such a value for spheres is in agreementwith Carman’s statement to the effect that k forfluidized spheres is e ual to 4.0 [25], If theparticles are irregrdar%ut chemically inert, thea in w, is finite and b is zero. In this case k<4.06.Obviously, if a and b are both finite, k may bestill smaller.

Empirically, it was found that the bleedingrates of pastes conformed to eq (7) [26].

(7)

In this equation s is the specific surface area asdetermined according to ASTM designation C115–58. The constant 5 is correct only if thismeasure of surface area is used. The Wt factormust be evaluated empirically for each differentcement by methods that have been described [27].Steinour showed that variation in w, among differ-ent cements was due principally to differences inspecific surface and in the initial chemical reactionswith water [28].

Capillary Forces in Cement Paste

The bleeding rate of concrete is of the sameorder of magnitude as the na~ural rate of evapora-tion from an open surface. Sun and wind togetheroften cause the rate of evaporation to exceed therate of bleeding. When this occurs, the surfaceloses its sheen, signifying that the plane surface ofwatar hw become replaced by myriad curvbdsurf aces, and this signifies that capillary tensionhas been produced. Carman has shown that themaximum possible capillary tension in a water-filled granular bed occurs just as the water level

581

drops below the upper boundary of the bed, andthe meniscuses take on the greatest possiblecurvature, that being limited by the sizes andshapes of the spaces between particles at the topsurface [29]. The approximate value of maxi-mum capillary tension can be calculated from thefollowing relationship adapted from the basicrelationships given by Carman,

(8)

where Ais the surface tension of water in dynes/cm,u is the specific surface area of the cement incm2/cc, and Pc is capillary pressure, a negativequantity. Substitution of appropriate figures intoeq (8) shows that maximum capillary tension willrange from about )( atm upwards depending onthe surface area of the cement.

The reaction to capillary tension is, of course,an equal downward force exerted on the particles

at the top of the bed. Since the downward forceon those particles due to gravitation only is onlyabout 0.001 atm, it is clear that when the rate ofevaporation exceeds the normal rate of bleedingthe force causing subsidence of the surface may begreatly increased. The effects of such an increasehave been measured under controlled conditionsby Klieger [30].

When resistance to consolidation becomes highenough to offset capillary tension, the watersurfaces retreat to the interior, and lateral con-solidation begins. The result is the so-called“plastic shrinkage”, often giving rise to “plastic-shrinkage cracking”. Swayze has expressed theview that a significant and technically importantdegree of compaction of fresh concrete can beproduced by capillary tensions that may developthroughout a period of several hours, and heproposed a procedure for taking advantage ofit [3].

3. The Specific Volume of Hydrated Cement and the Porosityof Hardened Cement Paste

Definition of Pore and Solid

It is undisputed that porosity is a basic propertyof hardened cement paste, but there may bedisagreement as to the detimtion of pores, In thestudies now being reviewed, pores are defined asspaces that can be occupied by water that isevaporable at a constant low external humidity,at a given temperature.’ A change of either thespecified temperature or humidity results in acorresponding change in the apparent ratio ofsolid to void. Thus, the choice of drying condi-tions defines the pore space and the solids, anddoes not assuredly isolate, or precisely establish,the true extent of the solid phases.

Problems of Mensuration

Besides the difficulty of isolating the solidphases, except on an arbitrary basis, the quantita-tive, accurate measurement of sohd volume alsopresents difficult problems. Hydrated cement iemostly colloidal (see glossary) and of the totalnumber of molecules composing the colloidal part,perhaps one-half to two-third. of them are exposedat surfaces. Seen on an atomic scale, the surfacesof the particles, i.e., the boundaries of the pores,are transition zones of vibrating atoms, and thusthe word surface as applied here does not connote~he conventional geometric concept,; the boundary1s neither sharp, smooth, nor static. In regionsof minimum porosity (see sections 5 and 6) theaverage distance between surfaces is about 5oxygen-atom diameters, and in these places therough transition region might constitute a signif-icant fraction of the interparticle space.

$This definition M not intended to include entrained air bubbles and thelike, which are regarded m cavities rather than integral parts of paste.

The porosity of a given specimen is determinedto a small but significant degree by the balancebetween opposing internal forces. To introduce afluid into such a system of particles releasesenergy and alters the balance of forces. Thesurfaces change their relative positions, and theporosity changes too; swelling occurs. (See sec-tion 7). Even the specific gravity of the solidmaterial may change slightly, owing to the changein interracial free energy. The quantity of fluidthat can be accommodated in interstitial spacesthus depends partly on the amount of swelling,accompanying entry of the fluid. It may depend,too, on how the molecules of the fluid “tit” theatomic roughness of the surfaces, and on the sizeof molecule relative to the size of the smallestinterstitial spaces. Swelling produced by wateris much greater than that produced by organicliquids or inert gases, water molecules beingrelatively small and strongly attracted by thesurface.

Fluids that affect interparticle forces are them-selves affected; they are adsorbed. Possibly,strongly adsorbed water molecules penetrate thetransition region of the solid more than weaklyabsorbed molecules do. It is frequently suggestedthat some of the space found by sorbed watermolecules is inside the crystals, but this seemsdoubtful, as will be seen further on. Whether ornot these phenomena occur, it. is probable that theaverage amount of space required per molecule ofwater in the adsorbed state is different from thatrequired in the liquid state, which is to say thatthe average density of water in the adsorbed statemay differ from that in the liquid state. Powersand Brownyard [32] estimated the specific volumeof gel water, most of which is strongly adsorbed,, at0,90 cc/g. But this estimate was based on density

582

of hydrated cement as determined by displacementin helium, and therefore it may not be correct forwater, as was acknowledged at the time, Thusjalthough it is easy to determine the mass of waterrequired to saturate the spaces in cement paste, itis impossible at present to determine a correspond-ing volume exactly.

Experimental Results

A direct approach to the problem of measuringporosity was based on the following expressions:

[ 1m (l+@Jc) $—1 +1~=1— . (10)~+w+

.

c is the porosity; m is the maturity factor (fractionof the original cement that has become hydrated);w. IS the, specific volume of hydrated cement incc/g; w; M the nonevaporable water content ofcompletely hydrated cement in grams; WOis theoriginal water content in grams? corrected forwater displaced by bleeding; c 1s the originalcement content in grams, and v, is the specificvolume of the original cement in cc/g.

All the factors in eqs (9) and (10) are subjectto direct measurement, but with attendant dif-ficulties, especially for v,,. In attempts tomeasure oh,, various liquids were used as displace-ment media with various results [33]. Forexample, waterl acetone, toluene, and heliumgave the following values for Vfi,, based on thenormal density of each fluid: 0.395, 0.408, 0.429,and 0.424. These result$ from preliminary ex-periments were followed by a considerable amountof work with helium. The displacement inhelium of samples prepared by the magnesiumperchlorate method was finally reported, fromwork by Steinour [34], as 0.41 +0.01 cc/g forfour different cements. Since the four cementswere chemically different, and showed similarityin specific volume of hydration products, it wasassumed thah for any cement the approximatedensity of hydrated cement might be estimatedfrom the relationship given in eq (1 1).

v,+v.w:/c‘h’= 1+W;JC

(11)

where V. is the apparent specific volume of thenonevaporable water, cc/g. The values of o. forthe four cements were calculated from theirhelium displacements by means of eq (12).

~ = (v,/c)–Vc.n

wn/c(12)

V, is the volume of the dry sample, indicated by

its displacement of helium, and c the cementcontent of the sample, grams. The mean valueobtained for four different portland cements was0.=1).82. The individual values ranged from0.81 to 0.83.

An advantage of eqs (11) and (12) is that theypermit evaluation of Vfi, from gas displacementdata on samples of paste that contain unhydratedcement.

Weir, Hunt, and Blaine [35] evaluated ~~from experiments based on eq (13).

W?JCv,=++(v n-v,) —l+wn/c’ (13)

In this equation, v. is the specific volume of thesolid material in the sample, cc/g, including un-hydrated cement, if any. Small cylinders 04 x4 in) of cement paste were cured for variousperiods and then dried by the “dry-ice” methodof Copeland and Hayes [36]. Then the speci-mens were immersed in a light petroleum distillate,and the distill aLe and the specimen immersedin it were eubjected to pressures up to 10,000 atm,the primary purpose of the experiment being todetermine the compressibility of the solid phases.After release of preesure, the amount of distillateremaining in the specimen at atmospheric pressurewas determined. Also the overall volume of thedistillate-saturated specimen was measured bydisplacement. The resulting values of v, wereplot~ed ?~ainst . (w./c)/(l + wJc), producing astraight hne having an intercept at v,= o,. Theslope of the line and the corresponding value ofV, giyes, for a portland cement, v.= 0.87, for analummous cement, o.= 0.75, Comparing the re-sult for portland cement with that reported byPowers and Brownyard, 0,82, Weir, Hunt, andBlaine mentioned that their higher result mightbe due to the presence of a little evaporable waterin their specimens, because of incomplete drying.However, calculation shows that even if thespecific volume of the residue of evaporable waterin their specimens was as high as 1.0, the amountwould have had to be about 40 percent of w., toaccount for the difference in question. Therefore,the data eeem to indicate that helium penetratesregions not accessible to the distillate molecules.

The problem of determining the specific volumeof hydrated cement and the specific volume ofevaporable water has been approached by con-sidering a saturated paste to be composed of twocomponents: (1) the solid material and (2) theevaporable water [37]. From a normal procedureof physical chemistry, it follows that,

v~=N~,&+N.Z, (14)

in which o; is the specific volume of the paste, cor-:ected for, any residue of anhydrous cement; N\,IS the weight fraction of hydrated cement; N; isthe corresponding weight fraction of evaporablewater; Z*, and 5, are the “partial specific volumes”

583

of the solid material and evaporable water respec-tively. For example,

(15)

where V is the volume of the paste and w, is theweight fraction of evaporable water. As used inthe present case, 3, pertains to the evaporablewater in a saturated specimen.

Among the many test data, the values of N,varied widely. When the values of specific volumeof the specimen, O; cc/g, were plotted against corre-sponding values of N:, the points conformedclosely to the straight line represented by thefollowing equation.

o;= O.398N:,+0.99N:. (16)

Equation (16) seems to indicate that 0.398 is thespecific volume of hydrated cement, and 0.99 isthat of the evaporable water. However, a linearrelationship such as eq (16) is characteristic ofphysical mixtures of two components that do notinteract either chemically or physically whenthey are brought together. In the present case itis known that when dry hydrated cement andwater are brought together the energy contentof the system decreases, as shown by evolution ofheat, the amount of heat released being over 20cal/g of hydrated cement [38]. In view of this, itdoes not seem likely that the specific volume ofeither component would be the same after mixingas it was before. The following considerationsseem to reconcile the result indicated by eq (16)and the observations just mentioned.

It is known that at humidities up to about 45percent, the amount of water held in the adsorbedstate is proportional to the amount of hydratedcement in the sample, and is independent of thetotal capacity for evaporable water. The amountadsorbed at 45 percent humidity is a little less thantwo molecular layers on the solid surface. This isthe strongly adsorbed part of the evaporable water,as shown by its relatively high heat of adsorption.The rest comprises weakly adsorbed water and, ifany, water free from the effects of adsorption.‘I’he fraction of the total evaporable water in excessof two molecular layers is greater the higher theporosity of the paste, and thus that part does notbear a constant ratio to the amount of hydratedcement.

It follows that if a specimen of saturated cementpaste is to be treated as a two-component system,it is not permissible, a priori, to identify hydratedcement as one of the components, and total evap-orable water as the other, because the propertiesof some of the evaporable water are certainly notindependent of the other component, hydratedcement, although the properties of the rest of thewater might bc. It seems therefore that the sim-plest permissible assumption is that saturated ce-ment paste is made up of three components: hy-drated cement,, adsorbed water, free water. on

this assumption one wouid write in place of eq(14),

v;= N;&+N;Fa+ (N; —N; )om (17)

where N: is the weight fraction of adsorbed waterthat stands in constant ratio to N~C,Z. is its partialspecific volume and v. Is the specific volume offree water. Expressing the proportionality be-tween adsorbed water and the solid material asN:= bN~C, and thereby eliminating N: from eq(17), we obtain

O:= NiC[ZZ,+b(Za—OW)I+WeW.. (18)

On comparing eq (18) with eq (16), we see thatVm=0.99 and 0~,+b(6roW) =0.398. Therefore, theresults obtained from this analysls were:

The linearity of the plot signifies either of twoconclusions: (A) Al 1 the evaporable water has aspecific volume of 0.99 cc/g (for these particularspecimens) whether adsorbed strongly, weakly, ornot at all, in which case vi,= 0.398, or (B) Someof the evaporable water in every specimen has aspecific volume of 0.99, and the rest, an amountproportional to the amount of hydrated cement,might have a different specific volume, in whichcase tbe specific volume of the hydrated cement isnot 0.398 cc/g. Conclusion (B) is probably thecorrect one.

Another analysis [37] was based on the empiricalrelationship

0Z=0.99—0.25 W./Wt (19)

where o, is the apparent specific volume of allthe water in saturated specimens, including w..It would appear that at wJwt= 1.0, o,=v. =0.74, for, if eq (19) 1s vahd over its entire range,the 0.25 is Z,– v.. However, on the basis of thesame observations and reasoning presented inconnection with eqs (16), (17), and (18), (fi.—VJW. may be replaced by (1 +B) (vw—-qJwn,where B 1s the weight fraction of evaporablewater that stands in constant ratio to w., andwhich may have a specific volume different fromthat of the rest of the evaporable water, andv~ is the mean of the specific volumes of thenonevaporable water and the part of the evapora-~l~eater whose density is altered by adsorption.

w,=~l’?—(1 +B)(om—%)(wn/w, ). (20)

On comparing eqs (19) and (2o) it is evident0.25

that (l+ B)(0.99– VJ =0.25, or, o~=0.99– —l+B”

This result presents the same impasse as eq (18).It cannot be solved unless the fraction, B, ofevaporable water having density different fromthat of the rest is known. Indeed, even if B wereknown, the apparent volume of the water in thesolid phase, on, would still be unknown unless themean density of the adsorbed water were knownalso. Only if it is arbitrarily assumed that B= O

584

TABLE ~. Specijic volume of hydratedcement

0,+0.~~“,G.— .

1+;%=specfflc volume of hydrated cemente,= mecfflc volume of orfgimd cemento.= apparent specificvolume of nonevaporablewater

w.< =gr%msof nonevaporablewater per g cement at completehydration

Computed composition—% V*,,Cc/gCy;nt ___ w:

C;g y ‘———.

C8S C,s C,A C,AF C.So, 0“=0,74 u“=0,82 0,, =0,87— .—— _——

157S4 45.0 27.7 13.4 6.7 4.0 0.31916754 45.0

0.246s21,7 13,4 6.7

0.418,4.0

15622 40.2.319

28.6,227

4.40.397 .411

12.80,421

2.7 ,310156LXI 33.0

,176 .37464.2

.386z 3

.3946,8 3.1 ,311

1.5497 so,1 11.9.174 .374

10.3 7.9 3.1.386 .394

.322 .210 .394 .408 .417

. This figure is based on samples prepared by the magnesium perchlom.temethod, All the rest in this column are forsamplesprepared by the dry ice method.

. This figure Is on the magmasimnpwohlorate basis. AS the othersin the last three columnsare m the dry ice b~is, andare subject to limitations mentioned in the text.

and thus that vd= v., do we obtain vn=o.74. Thisis the lowest possible value for v..

Table 3 is a summary of the findings in terms ofexperimental and calculated results for four dif-ferent cements. Specific volume as given in thefirst line corresponds to direct determinations byhelium displacement of samples prepared by themagnesium perchlomte method. The rest of thevalues in the last three columns were calculatedfrom the values of v. at the heads of the columns.Values in the column headed v,= 0.74 are basedon displacement in water (aqueous solution), andare the smallest possible, entailing the assumptionthat all parts of evaporablo water have a specificvolume of 0.99 cc/g. Values reported under” Vm=0.87 represent displacements in petroleum dis-tillate, applied to different cements on the as-sumption that v. is the same for all. Valuesreported under o.= 0.82 represent displacementsin helium, and the same value of v. is assumed toaPPIY to specimens prepared by either of thetwo methods.

There appears to be little theoretical or experi-mental support for an assumption that o.= 0.74,which is to say that the average density of ad-sorbed water is the same as that of the aqueous

solution in fresh paste. The entropy change onadsorption of the strongly adsorbed part [50] issuch as to suggest a considerable change of statefrom that of free liquid. It seems likely thatsuch a change involves a change of density. Ifthere is a change, an increase seems probable,in view of the openness of the structure of liquidwater. The value of Vx obtained from heliummeasurements, 0.82, indicates either that heliumis excluded from some spaces accessible to water,or that when water is used as a displacementmedium, it is densified by adsorption, or thatboth factors are involved. Assuming that thedifference is due to densification only, it comesout that the specific volume of gel-water (w, =3.o Vm; see section 5) is about 0.90 cc/g.

Although the figures for petroleum distillateprobably are valid for that fluid, they do notseem to indicate complete penetration of pores.Calculation on that basis shows that the porosityof cement gel to helium is 7 percent greater thanthe porosity to the distillate.

On the whole, the state of this subject is unsatis-factory. For general purposes it seems that thehelium values give the best estimate of v~,.

4. Surface Area of Hydrated Cement and Indicated Size of Primary Particles

Surface Area From Water-Vapor Adsorption Determination of surface area of hydrated ce-ment is based on water-vapor adsorption inter-

From work reported in 1946 [40] itwas deduced preted in terms of the Brunauer-Emmett-Tellerthat the specific surface area of the solids in ma- theory (BET) [41]. A convenient formula isture cement paste is equivalent to that of a spherehaving a diameter of 140 A, which is 43o m2/cc,or about 180 m2/g of dry paste. Subsequent work

S,,= 3,800 ~fi~~,c) (21)

calls for an upward revision of this figure forsurface area. where L%, is the specific surface area of hydrated

585

cement, m2/g. The numerical coefficient com-prises Avogach-o’s number, the molecular weightof water, and the area covered by a single adsorbedwater molecule. Powers and Brownymd [42] useda lower due, 3,57o, based on a molecular area of10.6 A2/molecule. Recently Brunauor, Kantro,and Copehmd [43] concluded that for adsorptionof water on tobermorite gel the best value is 11.4.The value 3,8oo corresponds to that figure,

Discussion of Eq (21)

BET Surface Factor, V-

Theoretically V,n is the weight of water requiredto cover the surface of solid material with a layer1 molecule thick? and Wfl is water that is a com-ponent of the sohd phase, Actually, there is someuncertainty as to the relations between observedvalues of Vm and w mand the theoretically correctvalues, To obtain the theoretically correct valueof Vm the process of adsorption should begin witha “bare” surface. The practice of outgassingwith heat to assure this initial condition cannot befollowed because the solid tends to decomposewhen heated. It ie necessary to depend on anarbitrarily established drying procedure. Never-theless, the resulting uncertainty is not such as todestroy the practical value of the data, as is shownespecially well by study reported by Tomes, Hunt,and Blaine.

Tomes, Huntj and Blaine [44] investigated theinfluence of various degrees of drying of testsamples on the experimentally determined valuesof Vm and w.. Using the dry ice method describedby Copeland and Hayes [36] they tested samplesof the same material after seven different periodsof drying ranging from 2.6 to 12.1 days, theshortest period giving a value of W* about 25percent greater than that given by the longest.Within the range of these data, Tomes, Huntj andBlaine found that

(Vm),– (Vm),=– 0.354[(w.),– (WJ2]. (22)

Or, in terms of ratios,

(Vm),–=l-”’’’*G%H ’23)(Vm),

The graph of these data indicates that experi-mental data would conform to eqs (22) and (23)even to the ultimate values for the given condi-tion of drying. Thus, if the arbitrary dryingprocedure is too short to remove all the evaporablewater, the difference between the observed valueof Vm and the correct value is proportional to thedifference between the observed nonevaporablewater content and the correct one.

Even if the ultimate values of Vn and w. for agiven procedure of drying are obtained, it may bethat the humidity maintained in the desiccatoris too high to produce a bare surface at the tempera-ture of the experiment. However, inasmuch as

the drying conditions used for the experiments ofeq (22) are probably not very far from the theoreti-cally correct one, It may be expected that a changeto the correct drying condition would result in arelationship like eq (22) with a slightly differentvalue for the numerical constant. Thusj there isreason to assume that the value of Vm obtained bythe arbitrarily chosen drying procedure is notvery much different from the correct value.

The proportionality between Vm and surfacearea depends on two factors: (a) average areacovered by an adsorbed water molecule, and (b)the difference between the observed and thetheoretically correct Vm. The first factor dependsnot only on the size of the water molecule butalso on the structure and composition of thesurface on which it is adsorbed. The secondfactor depends on drying conditions, as justdiscussed. It thus seems clear that Vm must be“calibrated” for a given material and dryingcondition. The calibration involves establishinga value for molecular area. The value now used,11.4 A2, is that which gave the same surface areaby water-vapor adsorption as was obtained bynitrogen adsorption on a laboratory preparationof afwillite. The first estimate of the area of thewater molecule on this basis gave 11,8 AZ [45].This was later revised to 11.4 A’ [43]. Thismethod of establishing the molecular area is notthe most rigorous that might be devised. More-over, there is no way to assess the accuracy ofthe result, other than by the degree to which thecomputed areas contribute to the internal con-sistency of various related data. On this score,the results now appear very good.

The values of w. formerly obtained were about8 percent higher than those obtained now by theCopeland and Hayes method. Present values ofVm are correspondingly different from the oldvalues. The relationship between the values ofVm now obtained and those formerly obtainedmay be shown as follows: Using eq (23), letsubscript 1 denote values obtained by the magne-sium perchlorate method, and Z those obtained bythe dry ice method. For a particular cement (No.15754) experimental values were (wJVJz = 3.23,and (wJJ(wJ2= 1.084. With these figuree, eq(23) gives (VJ, =O.904 (VJ~, and (VJWJI=O.2L58.This value, based on the Tomes, Hunt, and Blaineempirical eq (23), is the sa.ma as that reported byPowers and Brownyard [46] from direct experiment,0.258 + 0.002. The exactness of agreement maybe somewhat fortuitous, since the cements werenot exactly alike.

Maturity Factor, m

This factor is the weight fraction of cementthat has become hydrated, i.e.,

m=ch/c (24)

where c is the original weight of cement and cfi isthe weight of that part which has become hydrated.

586

(This is not the weight of the hydrated cement.)For most cements, apparently all but ASTMType IV, the following relationships may be usedfor any intermediate stage of hydration after thefirst few hours;

Chk ‘U@:= ~7m/V:= AH/AHO

(The degree mark indicates that the quantity isfor completely hydrated cement.) When theabove, equalities exist it follows that AH/wn andVJwn remain practically constant throughout theperiod of hydration at values characteristic of thecement. This means also that the specific surfacearea of the hydrated cement remains practicallyconstant at a value given by the following equa-tion:

(25)

Correction for Calcium Hydroxide

To obtain the surface area of the colloidal partof cement gel (see glossary) it is necessary to makea correction for calcium hydroxide, which hasnegligible surface area.’ Eq (26) maybe used.

[ 1S.o,= l+%.* s,..C+wn

(26)

(CH) is the weight of calcium hydroxide, andSo, denotes surface area of the colloidal part ofcement gel, cm2/g dry weight. (CH) may bedetermined by X-ray analysis, as described byCopeland and Bragg [47].

Experimental Results

Mature Pastes

Data obtained from four different cements aregiven in table 4, and the results of applying eqs(25) and (26) are given in the first four lines oftable 5. In general, the results are the same asthose reported previously [48]: The specific surfaceof cement gel is not affected very much by differ-ences in chemical composition of cement.

The last two lines of table 5 contain dataderived from the data of Brunauer, Kantro, andCopeland on the hydration products of C3S andC*S [43]. The values of W;/c, (CH)/wm, andVJw. were calculated from the data in theirtable 3, and from the assumption that in colloidaltobermorite the ratio of CaO to Si02 is exactly3/2. Thevalues for St, are experimental. Froma comparison of these data with those in theupper part of the table it appears that the specificsurface of the colloldal part of cement gel is from10 to 20 percent lower than that of pure colloidaltobermorite. Brunauer, Kantro, and Copelrmdeuggested that the sheets and ribbons of colloidaltobermorite maybe two o,. three unit cells thick.

$Possibly there are other nonmlloid.1 COUIDOIHWS.,but if SO,we cannotmee-wrethem st present,

TABLE4. Datausedjor computingwrfacea?ea ojh~dratedcement and cement gel

~ ‘“%’Y “c ‘~ ‘“’c ‘

Clinker 16367;Cement 1676* (CH)/w.=1.18; w:/c= .227

B-s-3 . . . . . . . 0,4!-,70 81-541.. . . . 10 I 0.2147B-15. . . . . . . . I 0.304

,35 611. . . . . . . .B-%1 . . . . . . 80-543. . . . . 7;

lXKI .317;~-.65 .2130 ,312

2W. . . . . . . . . . 11w.- . . . . 1 .1670 2s7! 1 1 t

Weighted—

a~erage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311

Cfinkt?r1502$Cement 1575@(CH)/w.=1.3& w~/c=O.174

B-8-3. . . . . . . 0:~-,65 %?-224..... :B-16. . . . . . . .

1

0:+jg:

1

0,347513. . . . . . . . .394

B-2-1. . . . . . .55 ma. .. . . . . .290. . . . . . . . . .

: ,1693 .349.23 11w...... 132S .378

I I I 1

Weightedaverage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3s6

Clinker 1567uCement 1570&(CFf)/w. =0.35&@,/@ O.170

B-3-3. . . . . . . 0:$+.65 315-3W. . . . 4 0,1525 0.40sB-16. . . . . . . . 605.. . . . . . . ,1337B-m-1 . . . . . . .66

.462@xJ. . . . . . . . Ii .1506 .497

m.... . . . . . . .22 11w...... 1 .1210 .424—

Weightedmerage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,413

! 1 , I ,

Cffnker 1649&Cement 1576&(CH)/vJ.=1.2q ta:/c=0,210

B-8-3. . . . . . . 0:$65 25%86S... 4

I

0,2116 0,276B-L . . . . . . . . 613. . . . . . . . 1870 .335B-x-1. . . . . . .55 054. . . . . . . . : .2102m.... . . . . . . .23

2s411yr . . . . . . 1 ,1711 .236—

Weightedavemge.. . . . . . . . . . . . . . . . . . . . . . . . . .292

The calculated specific surface of a sheet two cellsthick is 377 mz/g, and for a thickness of three cells,252 m2/g. On this basis the colloids in cementgel correspond to a three-cell thickness.

Now that more is known about the morphologyof gel particles, it is perhaps pointless to expresssize of particles in terms of spheres. Neverthe-less, for comparison with the earlier figures, it maybe noted that a specific surface of 210 m2/g, orabout 510 m2/cc corresponds to that of a spherehaving a diameter of 6/(5.1 X106)=118 A, the

TABLE 5. Calculated surface ai-eas for cement gels, and forthecollo%dalpartof csmentgels

S.. =mu’faaeareaof hydrated cement. m%

Computed eom.Refee,nce position, 70 to; ~

——. —T w“

0,S C,S C,A C,AF———— — .

15754. . . . . . . . 45.0 25.8 18.3 6.7 0.227 e.31115756. . . . . . . . 48.5 27.9 4.6 12.9 .174 .36516702. . . . . . . . 28.3 57.5 2.2 6.0 .170 .413,F,7a. . ..--.. &4.6 ,,.3 ,0. s 7.8 216 .202

111111.4Vm-nge... . . . . . . . . . . . . . . . . . . . . . . . .

Bulletfn 86.. 1S0 1------1------1.2s0.277Bulletin s6.. . . . . . . 10U . . . . . . . . . . . . ,16S ,458

.-

(Cm s,., s..,,w“ ~,,g ~,,g

— —

1.18 219 2671,36 m 2460,838 227 2561. !25 193 225

G G—

2,439 z &1.344 279 2%

587

“specific surf ace diameter”. This figure is to becompared with 140 A given by Powers and Brown-yard. The same kind of calculation for thecolloidal part only gives a specific-surface diameterof 98 A. The figure for cement 15754, the cementfrom which a great deal of reported data wereobtained, is 92 A.

Intermediate Stages of Hydration

As already indicated, to the degree that c,/c, thematurity factor m= w./w~, and to the degree that~Jwn remains constant during hydration of agwen cement, S,, is the same at all stages of hydra-tion (eq (25)). The degree of constancy ofVJw. has been reported [49]. That early reporthas been verified by later work, except with respectto Type IV compositions for which the ratio ofVm/wn changes appreciably during the course ofhydration. However, even for those composi-tions, all the ratios fall within 10 percent of theaverage. Thus, the specific surface of the hydra-tion products is practically constant so far as thisfactor is concerned. The validity of the equation~ = w~/w; is &cussed in other terms in anotherpaper of the Symposium [50], Such variationsas there are in the specific surface values of thesuccessive increments of hydration products areprobably insignificant in connection with mostconsiderations involving the internal surface areaof cement paste,

Effect of Curing Temperature

Ludwig and Pence [51] reported specific surfaceas measured by water vapor for pastes cured atelevated temperatures. For a Type I cementcured 7 days, the results shown in table 6 wereobtained.

TABLE 6. Eflect of curing temperature on surface area ofhydratedcement

(Ludwig and Pence, 1956)

IllTemperature Surface

Pressure (wn/c)8 ate%,ins/gOf

I

dry Dame~c ~F

Itltm . . . . . . . . . . 27 0.142l.tm- . . . . . . . . . 66 1:: .162

103123

300psi. . . . . . . . . 200 ,152 75300psi. . . . . . . . . 1% 260 .139 30300Phi. . . . . . . . . 160 320 .139 9

Does Water Vapor Adsorption Give RealSurface Area ?

From one point of view, the question is not veryimportant, for that part of the evaporable waterthat is called adsorbed has certain importantphysical effects on the system as it enters or leaveswhether it occupies space in layered crystals orbetween them. From a less pragmatic view, thequestion is important, for a considerable edifice ofreasoning about this material can rest on the ac-cepted answer.

There are reasons to question the reality of sur-face area as it has been measured by water vaporadsorption, For example, Kalousek wrote asfollows: “The very large ‘areas’ of cement pastesobtained by water-vapor adsorption are not trueareas. Water apparently enters the lattice ofsome of the hydrous calclum silicates, perhaps asit does in zeolites or certain clays . . . . Theareas computed from total amounts [of water up-take] are, therefore, fictitious. ” [52] On the otherhand, McConnell [53], Miss Moore [54] andprobably others, while accepting the fact of inter-layer penetration in certain typos of crystals, seemto question the assumption that cement gel pre-sents a like situation. Also, it has been suggestedthat gel water may bc water of crystallization(e.g., see H. zur Strassen [55]) and thus is naturallypresent in fixed ratio to the amount of hydratedcement. There is a great deal of experimentaldata of diverse kinds bearing on these questions,and it is difficult to assess them meanmg. Onemay observe that evaporable water does occupyspace in cement gel, and that such space musthave a boundary, but it is possible that theboundary indicated by evaporable water does notcoincide with the boundaries of the colloidal crys-tals. However, there appears to be no compellingneed to postulate that this possibility is the actualcase. The value for mean distance between par-ticle eurfaces obtained from the assumption thatlattice penetration does not occur is so smallj inrelation to the reach of interparticle attraction,that effects that might be attributed to latticepenetration are easily accounted for without pos-tulating such penetration. There is a considerableamount of experimental evidence that latticepenetration does not occur, as will be seen below.

The suggestion that gel water might be hydratewater is not easy to reconcile with the results ofpermeability tests discussed below and in sec-tion 10.

Particle Size From Permeability to Water

Powers, Mann, and Copeland [56] studied theflow of water through specimens of saturatedpaste in terms of an equation based on the Stokes-hTavier law, and obtained a figure for the size ofthe primary particles (exclusive of calcium hy-droxide) in terms of a sphericity factor o and a‘(volume” diameter, & Tha result was

4’148=201 A.

6 is the diameter of a sphere having the samevolume as an average particle in the specimen,and @ is defined as the ratio of the diameter, d, ofa sphere having the same specific surface as atypical particle in the specimen to the diameter6 of a sphere having the same volume as thetypical particle, That is, d=@. The measuredspecific surface of the hydrated cement, by watervapor adsorption, gave d= 95 A after correctionfor volume of calcium hydroxide. Combiningthese figures gave the value for sphericity factor

588

1#1=0:37and ~=258 &, In section 10 a discussionculmmatmg m a revmon of these figures is given.The revised data give dJ=O.41 and 6=233.

The volume per particle indicated by the valueof ~ is 9.0 X10B or 6.6x108 Aa, for the first andrevised data respectively. If the material weretobermorite gel only, for which the molecularvolume is approximately 195 A3, the averagenumber of molecules per particle would be 49,000,or from the revised datuml 34,OOO.

To illustrate the sigmficance of the valuefound for sphericity factor, let us consider ahypothetical gel in which the average volume perparticle corresponds to 8=233 A, and assume thatthe particles are thin sheets such as are found inthe hydration product of C3S. If the width is a,the length b, and the thickness c, then, approxi-mately,

2ab 2specific surface=fi=~

as was pointed out by Brunauer, Kantro, andCopeland [43]. If the sheets are 3 cells thick,c is about 30X 10-E cm, or if 4 cells thick, c isabout 40 X 10-8 cm, and we obtain specific sur-face= 667 m2/g, or 500 m2/cc. The correspondingspecific-surface diameters are 90 and 120 A.The sphericity factor for the hypothetical sheetis @=90/233=0.39, for the 3-cell thickness,and O= 120/233=0.52 for the 4-cell thickness.The value 4=0.41, indicated by permeability testand water vapor adsorption, thus could indicatethat the hydration products consist principally ofthin bodies containing, on the average, about40~000 molecules and being about 3 moleculesthick.

Perhaps the most significant aspect of theresults from permeability studies is the evidenceof compatibility between the deductions aboutparticle size from two independent methods.Resistance to flow through a saturated specimenof paste seems to be developed by the sameparticles which, when dry, adsorb water vapor.As shown in section 10, the permeability dataseem extraordinarily amenable to analysis, andthe necessa~ assumptions made in the analysisdo not seem to offer enough leeway to invalidatethe figures for particle volume. The indicatedparticle thickness and number of molecules perparticle seem too large to support a conclusionthat lattice penetration occurs.

Specific Surface by X-ray Scattering

According to Copeland [57] a collimated beamof monochromatic X-rays passing through agranular sample is refracted by crystal latticeplanes according to the Bragg law, but if theparticles composing the sample are of colloidaldimensions, there is also a scattering by refractionat the surfaces of the particles that does notdepend on particle shape m crystallinity. Thiseffect is confined to angles less than about 5°from the direction of the primary beam, and it is

therefore referred to as low angle scattering.The scattering due to particle surfaces varies inintensity as a function of scatter-angle as shownin eq (27),

((4m/k) sin .9)=constant/L (27)

1 is the intensity, o is the angle of scatter, and Aie the wavelength of the beam. The specificsurface of the particles composing the sample isgiven by the following relationship:

sS..= ev.Ch41 h’Idh. (28)

The left-hand side of eq (27) is represented by h.Copeland applied this method to a sample of thematerial represented by the first line in table 5.The result was 197 m2/g. This is to be comparedwith 219, the figure obtained by water vaporadsorption. This agreement indicates that watervapor gives a real measure, and a fairly accurateone, of surface area. However, there are notenough X-ray data to make this evidenceconclusive.

Surface Area by Nitrogen Adsorption

Brunauer, KantroZ and Weise [58] caused C,Sand water to react m a ball mill and found thespecific surface area of the product by nitrogenadsorption to be the same as that by wateradsorption, provided that the molecular areas ofthe adsorbates were taken at 16.2 and 11.4 Azrespectively. The specific surface was about 220m2/g. AISO, a laboratory preparation of afwillitehaving a specific surface of about 15 mz/g showedthe same surface area by nitrogen as by wateradsorption [45]. But when C2S and water reactin the form of paste, the specific surface area ofthe product indicated by nitrogen was found to beonly 21 percent of that indicated by water vaporadsorption. Surface area indicated by nitrogenadsorption for the colloidal hydration products ofC,S was only about 50 percent of that indicatedby water adsorption. In various other experi-ments made in this laboratory on hydrated port-land cement, the surface areas indicated by nitro-gen were substantially smaller than those indicatedby water vapor adsorption. The same kind ofresults were reported by Blainc and Valis [59] andby Tomes, Hunt, and Blaine [44]. For example,in the latter report, for neat cement paste,w/c = O.5,–cured 1 week, the nitrogen surface areawas 22 percent of the water vapor surface area.

Emmett and DeWitt [60] reported that theindicated eurface area of anhydrous cement isabout 10 m2/g by nitrogen adsorption, a valuemuch greater than that found by conventionalmethods. The difference is probably due to themolecular roughness of the surface and possiblydue to a very small amoun~ of gel produced byreaction with moieture from the air. Blaine andValis found the surface area of neat cement,w/c =0.25, to be 10 m2/g after 1 day of hydrationand a little less after 6 months of hydration. In

589

pastes of higher water-cement ratio, the nitrogenspecific surface area seems to increase with theprogress of hydration up to a certain point, andthen ceases to increase. Hunt [61] has observedthat, “If one plots water-vapor surface of aninitially dried paste against its non-evaporablewater content, a straight line is obtained, and theconclusion has been drawn that the gel particlesproduced at all stages of hydration are the samesize, If one makes a similar plot of nitrogensurface areas, using a paste of high water-cement

ratio, a curve is obtained which gets steeper withage. It is as if the structural domains measuredby nitrogen are getting smaller as hydrationpi-oceeds.r’

All thlrws considered (and there is much moreto be con~idered than is presented here), it isdifficult to say what feature of paste structurecontrols the uptake of nitrogen by a sample. Itis clear, however, that the features that governthe uptake of nitrogen vapor are not those thatgovern the uptake of water vapor.

5. Minimum Porosity of Hydrated Cement Paste, and Specific Volumeof Cement Gel

Minimum Porosity

If the cement content of a paste is below a cer-tain limit, and if the paste is kept saturated withwater and at normal temperature, all the cementwill eventually become hydrated. But, if thecement content is above that limit, the excess willremain unhydrated, apparently for an unlimitedperiod. When the cement content is at the limitfor complete hydration, the porosity of a com-pletely hydrated specimen is at a minimum. Atany higher cement content, the porosity of thepaste is lower only because of the presence of un-hydrated cement; the porosity of the hydratedpart remains the same.

The first estimate of minimum porosity of thehydration products in cement paste was based onadsorption data, and capacity for evaporablewater [62]. The minimum capacity for evaporablewater was approximately w ,/( Vm)~= 4, w, beingthe weight of evaporable water, and (VJ, theweight required to form a monomolecular layeron the surface of the solid particles, as determinedon samples prepared by the magnesium perchlo-rate method.4 Another estimate was based onspecific volume measurements, and on this basisthe minimum evaporable water content was statedas wJ(wJ8=0.92, or, wJ(VJS=3,6, where (wJ8is the nonevaporable water content as determinedby the magnesium perchlorate method. Thecomputed corresponding figures for specimensprepared by the dry ice method are wJw.= 1.08,and wJV~=3.6, and the helium porosity is about30 percent.

Although these data were obtained mostly fromspecimens that had been water cured about 6months, it was not certain that minimum porosityhad been reached [63]. Therefore, additionalstudies were carried out later by Copeland andHayes [64], Using the lowest value found in agroup of three dense specimens 11 yr old, they

gave w,/wm=O.74, or w./V~=2.3S as minimumevaporable water contents, and the correspondingporosity as 26 percent, these data being on thedry ice basis.

In the course of this review, I considered addi-tional data on minimum porosity as indicated byminimum evaporable water co”ntent, with theresult given in figure 1. The general relationshipit represents is developed from

w Jc = we/c + 0.254mwJc (29)

where m= wfi/w;. The eecond term of the right-hand side is the amount of water that a specimenmust obtain from an outside source during thecourse of hydration in order to remain in the

9

8

7

6

> 5

,

,4

3

2

1

00$234 5678

‘e . evworoblewater, worn, ‘n . “m .Wamr.ble water,grams“JO . Wgm.1.0!,,, !! ‘+ . !0,01 woe,,

t = w,,gh! d cmw”$,wool,

FIGURE 1. Interrelation of total, euaporable, and miginalwater contents for pastes made with a cement for whichwyc=o. %Z7.

590

The general expressions for amount of evapora-ble water are:

we/c= w Jc - mw#c (30)and

w Jc = wO/c—0.746 mw#c. (31)

For the cement represented in figure 1,

wJc=wO/c+O.058m (32)

w,/c=w,/c —O.227m (33)

W,jwc= 1—0.227mwJc. (34)

The plotted points in figure I represent fullymature specimens which should conform to eq(33) with m= 1.0. They do so down to WJC=0.437 and wJc=o.379. At all lower values ofthese two ratios! w,/w, remains constant at 0.482,or nearl so, as indicated by the points along lineO-B. ~he corresponding value of we/V~ is 3.o;that of wJwn is 0.93.

The ratio w,/w,= 0.482 corresponds to a porosityof 28 percent. This is now considered the bestestimate of minimum porosity of dry paste.

When the cement is in excess of that given by

~=0.437, the ultimate value of m is less than 1,0.

The value is given by m=2.28 WJG, or, m=2.63 W,/C.

Is Stoppage of Hydration Virtual or Real?

Any sample alon the line O—B of figure 1$contains both anhy rous cement and chemically

free water, i.e., water able to maintain a relativehumidity of 100 percent. It is a question, there-fore, whether the stoppage of hydration is virtualor real. Czernin [65] carried out two experimentsdesigned to determine whether or not the apparentcessation of hydration in the presence of excesscement is due to the relatively high resistance todiffusion in very dense pastes. If this is the case,the apparent stoppage is not real and is to beexplained in terms of relative rates of diffusion.In his first experiment, Czernin used a portlandcement paste, ‘(PZ 425”, w/c=0,4. The pastewas water cured 28 days and then ground in a ballmill with added dry cement, reducing w/c to 0.19.After 1 day of grinding, w,/w.= 1.06; after 50 days,wJw. =0.59, which seemed to be near a limit.In his second experiment, Czernin used a labora-tory-made “alite cement” (9o percent C,S). Thecement was milled with 15 ercent water without

Ethe initial period of paste ydration used in thefirst experiment. After 11 days of milling,w,/wn reached about 0.61, and seemed to remainconstant thereafter up to 40 days, the end of the

‘x!%~e%e two experiments gave nearly thesame result. Qualitatively, the result agreeswith the data cited above; that is, there is a lowerlimit to the ratio w,/wn. Quantitatively, the

results disagree, the ball-mill experiment giving alower value than any of the values indicated bythe other data. Thevalue w,/wn=0.59 indicatedfor PZ 425 corresponds to a porosity of about 21percent.

The meaning of the quantitative difference isnot entirely clear. It seems unlikely that thecement represented in figure 1 could differ fromPZ425enough toaccount for the difference, sincethere is no indication that the minimum value ofW,IW. is, influenced much by differences in thecomposition of cement. Possibly the data meanthat a porosity of 21 percent would eventually bereached in pastes, if the curing continued muchlonger than 11 yr. Another possibility, perhapsmore probable, is that the quantity of evaporablewater found in the ball-mill experiment is not thesame measure of porosity as thequantity found inpaste experiments. Dense specimens of pastesuch as some of those represented in figure 1 arenearly if not quite saturated after continuouswater storage for 11 yr. Had they been sealed,without access to curing water, their water contentwould have been considerably below the satura-tion point [66, 67]. Perhaps in the ball-millexperiment there was a similar “self-desiccation.’)If the paste samples had been reduced to the samedegree of desiccation before measuring wJwfi, thetwo values of WJW. would have been broughtcloser together, but neither would have indicatedaccurately the capacity of the gel for evaporablewater. It seems likely that ball-milling woulddestroy most if not all the structure defined bycapillary spaces (see section 6), but it is unlikel

rthat it would destroy the structure of cement geTherefore, there is some reason to expect the gelproduced in the ball mill to have the same porosityas the gel produced in paste, but there is reason todoubt that evaporable water content is a correctmeasure of porosity in the ball-mill experiment.

Whether or not hydration in dense pastes actu-ally stops, it is evident that the rate of hydrationafter several years of curing is so low that it is ofno practical interest. If hydration does continue,it does so by an improbable metamorphosis of ex-isting particles! the metamorphosis being suchthat the interetlces among these variously shaped,randomly oriented particles gradually becomefilled with solid material.

Stoppage of the hydration reactions with bothreagents present is not theoretically impossible.The quasi-crystalline hydrates evidently have anaturally restricted growth, possibly due to accu-mulative misfit of contiguous lattice layers, assuggested by Bernal. After atime when all crys-talsina local region have grown as much as theycan, further growth requires forming viable nucleiin the presumably supersaturated solution in thegel pores. But in places as small as gel pores,formation of a nucleus of a new crystal wouldseem a Klghly improbable event, either from thestandpoint of surface energy, or of the size of aunit cell relative to the size of a gel pore. A

591

similar interpretation was advanced recently byTaplin [68].

Specific Volume of Cement Gel

As will be seen in section 6 the massed hydrationproducts in their densest form are called cementgel. The solid matter of the gel together with thecharacteristic porosity constitutes a solid bodyhaving a characteristic specific volume. A gen-eral expression for the specific volume of cementpaste, on the dry-weight basis, but in the swollenstate, is

~ =’%+ (’@)Un 1+ wn/c ‘

(35)

For cement gel, which is composed only of hy-drated cement and gel pore~j w./c = w~/c, andw~/c = w~/c, the last quantity being the total watercontent of saturated cement gel, including thenonevaporable water. Each quantity is expressedas a ratio to the original amount of cement. Then,eliminating u by means of eq (19),, we obtain thefollowing expression for the spccdic volume ofcement gel:

o 0o.+ 0.99 ~—O.25 ~

Vn=vg= o (36)1+:

Complete data for computing the specificvolume of cement gel are available for only onecement, PCA lot No. 15754. For this cement,v.=0.567.

The indications are that corresponding valuesfor other cements are similar. Although thevalues of w~/c vary considerably (see table 5)the value of w~/c, the total water, is found to be

relatively large where the nonevaporable wateris relatively small. For the present, we may usefor all cements the value 0.567, with due cogni-zance of the uncertainty.

Ratio of Volume of Cement Gel to Volume ofCement

The volume of cement gel produced by 1 ccof cement may be called the gel-cement ratio,N. By definition,

N= (1 +W:/C)V,/V,. (37)

For the cement represented in figure 1, N=2.18.Taplin [68] recently advanced a method for

obtaining the gel-cement ratio based on thefollowing relationship:

(38)

where wm./c and wO/(wz). are for tests at dif-ferent water-cement ratios. The wm./c representscomplete hydration at a water-cement ratio highenough to accomplish this. The WO and (wJ urepresent, respectively, the initial amount of waterand the ultimate value of W. for a water-cementratio low enough to assure an excess of cement.Equation (37) should give a more accurateresult than eq (38) because it is based on the totalwater content of a saturated specimen at thetime of analysis rather than on the original watercontent. If the original water content is usedit should be corrected for any decrease duringthe bleeding period, and for increase due toexpansion of the specimen during the curingperiod.

6. Concepts of Structure of Cement Gel and Cement Paste

Evolution of Models showing the particles to be platy, or ribbonlike

Powers and Brownyard [69] used drawingsfibers, were used, in harmony with electron micro-graphs by Grudemo from calcium silicate hydrates

suggesting that dense masses of gel particles form [74] and from cement paste [75] (see fig. 2). Suchin and around the sites of cement grains, and thatthese masses generally do not fill all the space

drawings give a meager outline of a concept of

between the original boundaries of cement grains,structure. Onc may fill in details on the basis of

Later, Powers and Helmuth [70] presented thedata on the size and shape of particles, the space

same idea in greater de~a~l, representing the gelrequired by hydrated cement, and the mode of

particles as spheres. Orlgmally, t% assumptionformation of cement gel. It is necessary to deduce

as to shape was adopted for slrnphclty and con- various details that are not directly observable.

venience, but later [71] some electron micro graphs Such deductions are more or less speculative, andindicated that the particles actually were spheri- it is to be expected that not all will agree on thecall and this was mentioned in the paper referred dividing line between valid deduction and ques-to. In later publications [72, 73] drawings tionable speculation.

592

FIGURE 2. Simplified modelof paste structure.

Massesof randomly oriented gronDsof bkioklines mDre%mtcementgel. 8pw.eslike thosemarked Crepresentcapillary cavities, UDDerdrawing reprmentsmature paste, vf./c=0.5, capillary porositY20%;lower drawing representsnearly mature paste,w./c=0.3,caDillarYDorositY7’%.

Space Requirements the components of hydrated cement, presumably

As shown in section 5, it is known that cementin a state of supersaturated solution, diffuse inthe opposite direction to the outer border of the

gel requires about 2.2 cc of space per cc of cement.This means that 1 cc is formed inside the original

gel layer, where they add on to existing crystals,

boundaries of the cement grains, and 1.2 cc isor start new ones. Approximately 55 percent 1s

formed outside, in the originally water-filled space.transported outward, and 45 percent stays inside.

(Taplin’s paper [68] indicates that he also madeIt is reasoned that since the hydration products

this observation, and developed concepts similarin a specimen of paste containing an excess of

to those described below.)cement (wO/c< 0.38) can eventually produce a gelhaving a porosity of 28 percent, that same degreeof density can be, and is produced locally at

Mode of Gel Formation [76] various places throughout the paste, even whenthe cement is not in excess. The part of the gel

After an initial process peculiar to conditions that is formed by inward growth is producedthat can exist only a short time, the main part of under the greatest possible concentration ofthe h dration process seems to start at the grain

$-reagents. It seems, therefore, that at least 45

boun arles, and cement gel grows outward and percent of the gel in any apctiimen has minimuminward simultaneously] each grain residue being porosity. Also, since every grain of cement incontinuously encased m gel as long as it exists.Water diffuses inward through the gel pores while

the flocculent, fresh paste (see section 2) ispractically in contact at several points on its

593

surface with neighboring grains, the outward-growing gel should reach minimum porosity atthese points early in the process. It is not known,of course, whether the minimum porosity reachedin the outside material is the same as that of theinside material, but whatever the case may be, itmay be assumed that there is a range of poresizes in the gel as a whole. The smallest sizemight be of a monomolecular dimension; thelargest would seem to be that size just smallerthan the smallest in which nucleation is possible.On this basis, it would seem that the overallporosity of any region containing only poreswithin the size range just described (and consistingof approximately equal portions of the “inside”and [‘outside” product ) is the 28 percent men-tioned above. It follows that any region wherethe porosity exceeds 28 percent is also a regionwhere new crystals could nucleate, or alreadyexisting crystals could continue to grow; in otherwords, it is a region where pores exist that arelarger than the largest characteristic of cementgel. During the process of hydration, the com-ponents of hydrated cement that are diffusingoutward from a grain will belikely to redepositedin the first over-gel-size pore encountered. Thusthe “outside gel” tends to achieve characteristicgel porosity as it grows. This idea is expressedln figure 2 by showing the capillary spaces to beorders of magnitude larger than gel pores. How-ever, it is clear that as a given local regiona~p?oaches m~imum porosity, the remainingcapdlary pores m that region will gradually becomeindistinguishable from gel pores, and this idea isrepresented by some areas in the drawing whereonly slight gaps in the gel appear. One sees thepossibility, if not probability, of the gel particlesformed by inward growth having a differentmorphology, and perhaps even a different stoi-chiometry, from the particles formed by outwardgrowth,

Size of Gel Pores

Powers and Brownyard [77] estimated the widthof pores in cement paste from the ratio of porevolume to surface area, i.e., the hydraulic radius.With the data then available, the figure obtainedfor the hydraulic radius was 10 A. This meantthat theaverage width of pore lay between 20 and40 A, probably closer to 20 than to 40. 13Yomdata given in preceding sections we have

Hydraulic radius= 38~w~~6Vm

=2.6 X10-80, #cm=2.60. #A. (39)m m

As shown in section 5, the minimum value ofwJVm is about 3.0, and therefore the hydraulicradius of the gel is 7.80, A. The specific volumeof gel water is not known exactly. On the basisof the specific volume of hydrated cement as

given by helium displacemen~, it is 0.9, and thisfigure gives a hydraulic radius of 7.0 A. Thecorresponding average distance between solidsurfaces in the gel is between 14 and 28 A, 18 Abeing a reasonable estimate. This distance isabout 5 times the diameter of an unbendedoxygen atom, or about 13}f times the diameterof a single-bonded oxygen atom. The unbendeddiameter, 3.6A, is about the same as that of awater molecule,

Size of Capillary Spaces

No systematic attempts to measure the size of;

capillary spaces have been reported. However, Ivarious observations show that they are generallyorders of magnitude larger than gel pores. Whenthere are capillary spaces, reflected light is scat-tered. Such scattering signifies the presence ofrandomly arrayed structural discontinuities severalhundred angstrom units apart. (These are thereasons why mature paste of high quality has adark] bluish-gray cast, whereas paste of lowquahty appears much whiter.) Other directevidence of the relative largeness of capillaryspaces will be found in section 10 which deals withpermeability to water. When the total porosityof cement paste is increased by reducing theamount of gel and increasing the capillary space,the rate of increase in permeability shows thatthe capillary spaces are very much larger thangel pores.

Summary Description of Cement Paste

Although the concept illustrated in figure 2 is inseveral ways oversimplified, it is a useful aidtoward understanding the properties and behaviorof cement paste and concrete, The main featuresof paste structure may be summarized as follows:cement gel is a rigid substance that occupies about2.2 times as much space as the cement from whichit was derived. Its porosity is about 28 percent,and the average width of its pores is about 18 A,which is about 5 times the diameter of a watermolecule. There is evidence that the gel particlesare in contact with each other at many pointsand that some of the points of contact are chemi-cally bonded. The porosity of cement gel is anatural consequence of the growth of irregularp~rlicles in random directions from randomly dis-tributed starting points. Cement gel is mostlycolloidal matter, but, as defined here, it containsnoncolloidal material also, chiefly calcium hy-droxide.

Cement gel is one component of cement paste.The other component is the residue of originall

“{ \water-filled space that has not become filled wltgel. These spaces are called capillaries or capillarycaoit;e.s. When capillary porosity is relatively high,the capillaries are a continuous interconnected net-work through the gel, but at normal paste porosi-ties, capillary spaces are interconnected only bygel pores and afe accordingly called capillary cav-

594

itiee. The properties of cement gel and the degreeto which the gel is “diluted” with capillary spaces,and the effects of water in gel pores and capillariesare factors that determine important characteris-tics of concrete.

Paste may also contain a residue of anhydrouscement.

Computation of Capillary Porosity of Paste

Since the capillary porosity is a significant fac-{ tor, fundamental studies of strength, strees-strain-

time characteristics, permeability, and durabilitycould be facilitated by dealing with it quantita-

) tively. Convenient means of a computation areI

indicated in eqs (4o) and (41).

[ 1.,=l–? l–m+m(l+w:/c) $ (40)c

[ 1.m (l+w~/c) f—l +1~o=l— e (41)

1++,

Here c. is the capillary porosity; v, is the specificvolume of cement gel in cc/g of dry gel. (Seesection 5.)

7. Mechanical Effects of Adsorption and Hydrostatic Tension

This section may be regarded as an extensionof section 6, for a concept of physical structure issterile unless it is combined with some understand-ing of the interaction of the solids and evaporablewater, which is the present subject. Quantita-tive data are few, but thoee given by Powers andBrownyard [78], together with more recent unpub-lished results, provide a basis for discussion.

Adsorbed Water a&dakpillary-Condensed

At temperatures above the freezing point, chem-ically free water molecules preeent in cement pasteat any humidity below 100 percent would be gas-eous and of negligible amount were it not for forcesthat hold nearly all of them in a condensed state.All surfaces are usually covered with water mole-cules, and, except at low humidities, capillary cav-ities contain water. Powers and Brownyard [79]observed that the amount of water held at anyrelative humidity below about 4045 percent (25“C) was proportional to the internal surface area,i.e., the surface area of the gel particles in thespecimen, but at humidities higher than 4045 per-~ent the amount of water tak~n up by a dry .spec-.linen depended on the poroslt y -of the specimen.It was therefore concluded that at humiditiesbelow 40 percent the water was held entirely byadsorption forces, and that most of the watertaken up at humidities well above that limit isheld by capillary condensation.

The theory of nucleation helps us to understandthis observation and deduction [80]. Two differ-ent theories of the nucleation of vapor bubbles inpure water under negative pressure at room tem-perature lead to the result that the “fracturestrength” of water is about – 1200 atm. Thisis the negative pressure giving a probability ofunity for the spontaneous nucleation within aboutI sec of a vapor bubble by thermal fluctuation ofthe water molecules in the liquid [81]. The theo-retical fracture stress based on nucleation occur-ring within 1 yr is about — 1100 atm [82]. Undersuch stress, water molecules are unable to cohere,

and since a meniscus depends upon molecular co-hesion, capillary condensation becomes impossible.It happens that the relationship between the pres-sure in the liquid phase and the correspondingequilibrium vapor pressure gives, as computed byBarkas [83], – 1200 atm at a relative humidity of40 percent, and – 1100 at 45 percent. Thus, theobservation that water in cement paste at humidi-ties below about 40 percent is not subject tocapillary condensation is in agreement with thetheoretical deduction that a meniscus cannot existbelow such a humidity. Perhaps that agreementmay be regarded as strong support to the theoryof nucleation as a means of arriving at the cohe-sive strength of water, although the fact thatwater in cement paste is not” pure injects someuncertainty as to whether the agreement ought,theoretically, to be as close as indicated. Never-theless, it seems justifiable to assume that part ofthe water held in a specimen at humidities above40–45 percent has the ordinary properties of liquidwater. The water held at a humidity of 45 per-cent is somewhat less than enough to make twocomplete molecular layers over the surfaces of thesolid phases, and such a film does not have theproperties of liquid water. Its condensed state isdue to the forces of adsorption.

In a specimen saturated with water. and sur-rounded with water or a water-saturated atmos-phere, there is no hydrostatic tension! and as wehave seen! some of the water contained in thepores exhibits the normal properties of water.The first question to be considered is how capillarywater is lost from the ,specimen during drymg,particularly the first drying.

The Process of Drying

When a small container made of a bydrophllicmaterial contains both air and water, the boundarybetween the water and. air is a meniscus concavetoward the am. Water m a glass capdlary,bounded at each end by a meniscus, is a familiarexample. When water evaporates from sucha capillary, it seems that evaporation occurs from

595

the meniscuses, and, from Kelvin’s equation, it isunderstandable that tho tendency of water toevaporate is reduced because of the negativepressure in tho water induced by the curvedsurf aces. On the basis of an analogy betweena porous solid and a “bundle” of capillaries, it issometimes assumed that the drying of a specimenof saturated cement paste involves evaporationfrom the meniscuses in the capillaries within thepaste.

We have already seen that the bundle-of-capilhwies concept is hardly compatible withevidence concerning the st,ucture’ of cementpaste. It is safe to say that in all cement pastessome of the capillary spaces are in the form ofcavities isolated by cement gel, and in somecement pastes, perhaps most, all the cavities areso isolated. (See also section 10.) If we are toassume that, during drying, evaporation occursonly from curved surfaces, none of the water inisolated capillary spaces can evaporate until thehumidity drops sufficiently low to cause evapora-tion from the very small gel pores of the sur-rounding gel, Indeed, a theory of adsorption-desorption hysteresis is based on the notion thatsuch a situation is analogous to an ink bottle: theinside communicates with the outside only throughthe neck and therefore the contents of the bottlecannot escape by evaporation until the neck hasbeen emptied.

The amount of water lost from cement pastesat relatively high humidities cannot be accountedfor on the basis of the theory just mentioned.Water in capillary spaces surrounded by gelevidently does escape at high humidities eventhough it is not able to present a liquid surfacefrom which evaporation can occur. A differenttheory that takes into account some consequencesof hydrostatic tension is required to account forthe observed facts.

When water evaporates from the outside surfaceof a body of cement gel enclosing one or morewater-filled capillary spaces, hydrostatic tensiondevelops, as ie shown by the reduction of water-vapor pressure of the water remaining in the body.The magnitude of the tension is limited by therelative humidity of the surroundings. One con-sequence of hydrostatic tension is that if thewater is initially saturated with air, it immediatelybecomes supersaturated, the degree of super-saturation being a function of the hydrostatictension. When the degree of supersaturation issufficiently high, bubbles can develop in thecapillary cavities. The degree of supersaturationand hence the magnitude of hydrostatic tensionrequired to produce bubbles depends on eeveralfactors, as discussed below. The discussion fol-lows that of Bernath [81].

Let us consider first the conditions necessaryfor static equilibrium betwcon a bubble and itssurrounding;, neglecting the force of gravity.The bubble is surrounded by capillary water, andthe capillary water is continuous with the gelwater that permeates the surrounding structure.

The bubble is assumed to be spherical and tocontain n molecules of gas, including moleculesof water vapor. Let P, represent the gas pressurein the bubble, and 47rr3/3 the volume of thebubble, r being the radius. The following “perfectgas” equation gives the free energy content of thebubble, on the left side in terms of the product ofpressure and volume, and on the right side interms of the kinetic energy of the gas molecules.

(42)

T is absolute temperature; k is Boltzman’sconstant (energy per molecule per degree) andno is the number of molecules in the bubble. Thepressure in the bubble is also equal to the pressureexerted on the gas by its surroundings, that is

P,= PC+;. (43)

Pc is the hydrostatic pressure in the capillarywater and 7 is the surface tension. The secondterm on the right-hand side is the capillarypressure due to the spherical meniscus of thebubble. In the present case,

P.=–t (44)

where tis hydrostatic tension. Substituting from ~eqs (43) and (44) into (42), we obtain eq (45):

(2’)G”’’)=”JT(45)

This equation shows that at a given temperaturethe free energy content of a bubble is a functionof the radius of the bubble. The function is suchthat the free energy content of the system in-creases with an increase of r up to a criticalvalue r*, and for larger values of r, the free-energy content decreases. From this it followsthat if a bubble having a radius smaller than r*should develop, it would probably disappear(dissolve) immediately, but if the radius quicklybecomes equal to r*, the bubble is just as likelyto remain as to disappear, Therefore a bubble islikely to be viable if at one instant it can formwith a radius greater than r*. Such a phenom-enon can happen only when the water becomessufficiently supersaturated with dissolved air.When the water is initially saturated with air,bubbles evidently can form with relatively littlehydrostatic tension. This is indicated by thefact that relatively large amounts of evaporablewater are lost at high humidities. However, itseems clear that bubbles can form only in thosecapillary spaces large enough to permit a viablenucleus to form, that is, only in those cavitieshaving a radius greater than r“.

The necessary size of cavity is that which willaccommodate a nucleus having a radius slightly

596

larger than r *, and able to accommodate also alayer of adsorbed water molecules that cannotbecome a part of the meniscus of the bubble. Thethickness of this layer is estimated to be about 5 A.

The value of r’ can be obtained by differentiat-ing eq (45) with respect to r, with l“ constant, andwith t=t*, where t* is the value of tension atwhich nucleation is possible, The derivative isthen equated to zero, and the equation is solvedfor r. The result is

4~=@=. 1.3 t*

(46)

On comparing eq (46) with eq. (43), withPc= –t”, we see that eq (46) is not a statement ofstatic equilibrium. In other words, the nucleationradius, r*, is not the same as the stable radius forstatic equilibrium at the hydrostatic tension t*.The expression for equilibrium is

27—=% when Ph<<t+.

‘s=t*+Pb t*(47)

The value of r,, the size that would be stable attension t*,is not of special interest in the presentconnection, It only indicates that if t*is estab-lished and kept strictly constant, the bubblewould nucleate and the radius would increaseabout 50 percent to establieh equilibrium. Ex-cept when r * is so small that thermal flactua-tions might disturb equilibrium, static equilibriumis quite possible. However, the equilibrium israther unstable in any case, since even the slightestincrease over t* would ermit the bubble to expand

{“”to the limit fixed by t e dimensions of the cavity.The pores in cement paste range in size from

molecular dimensions upwards to perhaps 0.1 p,the up er limit actually being unknown. Table 7

[gives t e calculated nucleation radius for differentlevels of hydrostatic tension and the correspond-ing values of required cavity size, assuming thecavities to be spherical. If, for example, dryinghas occurred at a relative humidity of 96 percent,all cavities having radii greater than about 175 Awould be able to accommodate the nuclei thatcould form at that humidity, and all the cavitiessmaller than that size would remain full of water.When the humidity has dropped to the 50 percentlevel, all cavities having radii greater than about15 A should contain bubbles. However, as notedin the table, at humidities below about 45 percen~,bubbles cannot exist because the hydrostatictension exceeds the fracture strength of water,and therefore phenomena arising from molecularcohesion of water disappear. The formation ofa meniscus is one such phenomenon.

As shown above, at any given humidity all the#capillary cavities below a certain size (table 7)will remain full whereas each of the larger oneswill contain a bubble. Nevertheless the hydro-static tension must be the same in the cavities con-taining bubbles as in those not containing bubbles.Therefore, beginning with the saturated state, the

hydrostatic tension that develops as the specimenis dried to a lower humidity is, after a state ofequilibrium has become established, the samethroughout the capillary space as if all the capil-lary space had remained filled with water whilethe tension developed. Thus shrinkage caused bydrying at humidities above about 45 percent is ahydrostatic compression, and the amount of hydro-static compression depends upon the elastic andinelastic time-dependent deformation character-istics of the paste.

TABLE 7. Computed inscribed diameters of cap;llary cavitiesable to contain spherical bubbles at giuen humidities (eg(46))

Relativehumidity

Pergu

965285

::4540

●ydrostatictension

am28

1::226495963

1,1001,200

Requiredwlll:~ty radius of. Wl@yf

,.+5

A A346 351170 17534 8943 4820 25

15(::P)

* Bubbles cannot9xistat tension.!above the frae.ture strength of water, which is apparently be-tween – 1,1111and –1,200Mm,

Only a few data on the shrinkage of mature ce-ment paste samples dried under suitable conditionsare now available, but there are some, obtainedabout 20 yrs ago, from specimens dried in COZ-free air at four different humidities. An exam leof the results obtained is shown in figure 3. #hechanges in volume for drying at humidities of 75,45, 18, and 1 percent are plotted against the com-puted tensions for those humidities. These data,

I

-AJ

vx10’

/22 -

/~.

..-20 - c : ,8 x ,0-’ .tm,

/“

18

16

14

12

10

8

6

4

2

001 23+5 6

Tenmn in ev.ap.wable wafer, atmospheres n 10”’

Reference 254 -6-0

Wc = 0.525

Gel Cmce.tmlio”. 0.73

FIGURE 3. Shrinkage US.tension

597

considered together with data for various otherspecimens, indicate that a shrinkage-vs.-stresscurve for tensions up to about 1,000 atm resemblesone for mechanical loading. Shrinkage is approxi-mately proportional to stress, departure from line-arity being greater the higher the capillary poros-ity of the prrste. The slope of a line from the ori-gin to a point representing shrinkage at a givcm ten-sion gives the coefficient of compressibility 6for theindicated sust aiued, isotropic tension. The valueindicated in figure 3 k 18 millionths per atm, andthat figure appears to apply to all tensions up toabout 900 atm, but some curvature would prob-ably be seen if more points were available, sincesome of the compression is inelastic, and such de-formation is not usually exactly proportional tostress. A compressibility y of 18 millionths per atmcorresponds to a Young’s Modulus of about 1.5 X10’ psi or 100 kg/cm2, which is reasonable for theratio of stress to strain for such a paste undersustained load.

other data show that when shrinkage stress isreleased by soaking the specimen in water, theamount of expansion per unit change of stressagrees approximately with the modulus of elas-ticity of the paste as determined from the reso-nance-f requency of vibration of a test prism, Thisis one aspect of the stabilization of paste structurediscussed in section 8,

!lrorn the above discussion of the fracturestrength of water, one might expect some sort ofdiscontinuity in the stress-strain diagram at atension of about 1,100 atm. A discontinuity doesseem to be indicated by these data (fig, 3) but thepoints are too few to establish the locus exactly.It is not clear whether the transition should beabrupt or gradual, but an abrupt transition seemsprobable because when the stress in the waterreaches the breaking point, which, for 1 yr of sus-tained stress would be about — 1,100 atm, stressdue to surface tension in the capillary cavitiesshould disappear. This would reduce the effectivearea from unity to 1—AC, where A. is the cross-sec-tional area of capillary spaces that contained bub-bles, per unit overall area. If we assume that thebreak occurred at – 1,150 atm, and that expansionis proportional to the reduction of effective area,the indicated value of A, is about 20 percent, whichis not far from the actual capillary porosity of thespecirn en, After the transition point, further in.creases in tension are accompanied by progressiveemptying of the gel pores and decreasing of thearea factor. Thu~, for the specimen representedby figure 3, one might suppose that the compressi-bility coefficient remains about the same whiletension increases, but the area factor falls off insuch a way as to give the observed diagram.

From this approach, it would seem that as thearea factor approaches zero, cff ective tension ap-proaches zero, and the specimen should expand.This is not the case, however; at the point where all

JAs defined hem,compressibility k ~~.~, where Va is the volume m thesaturatedstate, .

the evaporable water has become lost, and thearea factor has become zero, shrinkage is at themaximum possible for the temperature of the ex-periment. To understand this result, gel struc-ture must be taken into account.

Areas of Obstructed Adsorption

The observed result seems to be due to obstruc-tions that prevent adsorbed water from spreadingevenly over the surfaces of the particles. Theobstructions arc probably in those areas wherecontiguous particles are bonded to each other,the distance of separation being zero, and inareas (presumably adjacent to those spots) wherethe surfaces are separated, but not separatedenough to accommodate as many water moleculesper unit area of surface as could bc held in areasof unobstructed adsorption, The evidence of theexistence of areas ~f obstructed adsorption, is thesame as that indicating the existence of inter-particle bonds, and the nature of shrinking andswelling phenomena itself.

Those water molecules that are excluded fromareas of obstructed adsorption maintain a pres-sure—a film pressure—that tends to separate theobstructing surfaces. This film pressure thuscauses a slight dilation, or swelling. The amountof swelling produced by film prcssureislirnited bytensile force corresponding to stress in the bondsthat hold the gel particles together. Swellingpressure, and trmsile stress in the bonds, is greatestwhen thespecirne nissaturatedand thus when ten-sion in the evaporable water is nil, When tensionin evaporable water appears, swelling pressure iscorrespondingly diminished and tensile stress andstrain in the bonds also. The reduction of swellingpressure is effective in areas of obstructed adsorp-tion only, but, as already shown, when hydrostatictension is less than the fracture strength of water,hydrostatic tension is effective over the wholearea of the paste, and the specimen becomes com-pressed more than can be accounted for by reduc-tion of ewelling pressure only. However, at ten-sions above the fracture strength of watcrj furtherincrease of tension serves only to reduce swellingpressure in areas of obstructed adsorption. Theeffective areas of obstructed adsorption mustbecome smaller as the water content is reduced,reaching zero when all the water has become evapo-rated. Thus, shrinkago in the high-tension rangeis primarily caused by cohesive forces betweenthe solid bodies of which the gel is composed.

During the last stages of removal of evaporablewater, there is enough increase in intorfacial energyat the solid surfaces to cause an increase in specificgravity of ~h~ particles, and corresponding shrink-age, but this rs now beheved to be a minor contri-bution to the total change shown in figure 3.

Effect of External Pressure

Although no direct experimental confirmationcan be cited, the foregoing discussion of internal

598

forces leads directly to conclusions pertaining tothe efects of applying pressure externally. If aspecimen of hardened paste at equilibrium withthe ambient humidity is subjected to an isotropicpressure applied to the external surface, the com-pressive force on the water films in areas of ob-structed adsorption maintained by tensile stressin the solid bonds is thereby augmented. Someof the water is displaced immediately from theareas of obstructed adsorption, and since thewater lost from the loaded areas must ,be gainedby the rest of the area, the internal humldlty rises.A rise of internal humidity produces an increaseof swelling pressure, opposing the external pres-sure and, in effect, the specimen swells. To re-store equilibrium with the ambient humidity,some water eventually evaporates, and the swellingpressure falls to its orlgmal level, with a furthercompression (shrinkage) of the specimen.

If the specimen had been subjected to isotropictension, rather than isotropic compression, theeffect would have been as follows: the compressiveforce on the water films maintained by the cohesivebonds of the gel would have become diminished,and there would have been a concomitant wideningof the spacm in the areas of obstructed adsorption,thus creating a deficiency of water molecules inthose areas. Molecules from the unobstructedareas would diffuse into the areas of obstructedadsorption, but in so doing, the internal humidityis caused to decrease, the film tension to increasecorrespondingly and the specimen is caused toshrink. However, to restore equilibrium with theambient humidity, water molecules from the out-side would be received until the original humiditywas regained, During the time required for thisprocees, the specimen gradually dilates (swells)under the sustained external tension, finallyannulling the shrinkage induced by the applica-tion of the external isotropic force.

If external pressure is a plied uniaxially, as forc!example by loading the en s of a cylinder, a combi-

nation of effects of isotropic compression andisotropic dilation should be present. Spacesbetween surfaces oriented principally normal tothe axis of the cylinder would be reduced, andthose oriented principally parallel to the axiswould be increased. The effect is a temporaryswelling counter to the direction of compression,and shrinking counter to the lateral extension.Establishing a new state of equilibrium requirestransfer of water from the compressed areas to theextended areas, but there may be no appreciablechange in an average internal humidity, and henceno change in weight of the specimen.

The foregoing discussion accounts, at least inpart, for the time-dependent part of elastic re-sponse to an external force which was shownes ecially well by recent data published byG~cklich [84]. In addition to time-dependentelastic response, there is also a time-dependentinelastic response, apparently related to, if nota direct manifestation of, the instability of cementpaste discussed in section 8.

Freezing of Evaporable Water

Followin the pioneer work of von Gronow [85],tPowers an Brownyard [86] studied the freezing

of water m cement paste by means of dilatometry.They showed that at any subfreezing temperaturesome of the evaporated water remains unfrozen,and for temperatures below —6 ‘C the amountunfrozen is proportional to the surface area of thegel. At temperatures between O and –6°, theamount remaining unfrozen at a given tempera-ture is not proportional to the surface area.Recently, Helmuth [87] found that the departurefrom proportionality is due to the presence ofsolutes in the evaporable water, principally sodiumhydroxide and potassium hydroxide. In general,the findings have been as would be ex ected from

Ethe characteristics of the sorption isot erms.Verbeck and Klieger [88] reported the amounts

of ice formed in concrete, as measured by thechange in heat capacity during cooling. Typicalresults are given in table 8. The last column oftable 8 shows the amount of expansion of waterthat must be accommodated by space in the con-crete during freezing, expressed as a percentage ofthe total volumn of concrete. It m clear thatconcrete normally contains more than enoughvoids to accommodate the expansion of watercaused by freezing, and therefore the destructiveeffect of frost is not due to lack of space in theconcrete for expansion of water. Frost action isthe subject of another paper of this Symposium[89], and will not be pursued further here.

TABLE 8. Amount of water frozen at – 800 C (– 4° F) ificoncrete cured 7 days before freezing

(Verbeok and K1leger,196Sj

II I I watWex-

1f:nmm:

I

Amount of ice

I

Percentat—209C(-4~f?), Perwnt cd

frcwenat p~~%~ofW/. lbslyd~ –7.}; (28

concretevol. vol.

0.41 660 3.6 93 0:.22.49 520 4.9 70.72 3s0 8,1 57 .75

8. Instability of Paste StructureSpontaneousReduction of Specific ~he expense of small ones, a substantial reduction

Surface Area m specdic surface area and in specific free energy

Because of its high surface area, cement gel iscontent of the gel would take place. Evidence ofsuch a than e would be a reduction in the ratio

often referred to as a metastable substance on the ‘fVJw., whlc ratio is proportional to the reduc-grounds that if large gel particles were to grow at tlon in specific surface area. Over the years dur-

599

ing which measurements of V. and w. have beencarried on, no reduction in the ratio has occurredfor any specimen kept continuously moist. Thisindication of stability may be accounted for inpart by the morphology of hydrated cement. Ifcement gel is made up of thin sheets or ribbonlikefibers, a substantial reduction of surface area andsurface energy would require more than meregrowth, for if a large sheet became longer aud widerwhile a smaller one changed dimensions oppositely,the resulting reduction in surface energy would bevery small. Any substantial reduction in surfacearea and free energy would require a more pro-found metamorphosis, particularly a strong tend-ency toward isometry along with increase in size.

Under conditions other than continuous moiststorage, the story is quite different. In an auto-clave at temperatures upwards of 100 “C, thekind of metamorphosis mentioned above oc,cursreadily, accompanied by some change in stolclli-ometry. Powers and 13rownyard [90] found thespecific surface area of autoclaved hydrated ce-rneut to be only 5 percent of that of hydrated ce-ment cured in the ordinary way. Ludwig andPence [51] obtained asimihmresult. See table 6of section 4.

Not so widely known is the disco~-cry by Tomes,Hun~, and Blaine [44] that thevery processor de-termlniug thesurfaee area of cement gel by water-vapor adsorption causes a reduction of specificsurface. After drying samples from the saturatedstate to arelative humidity of about 0.00002, theycarried out eight cycles of adsorption and resorp-tion, theadsorption being in four steps as requiredby the BET procedure, and thedesorption in onestep. The range of humidities was from 0.00002to 0.33. Their data, obtained on granulatedsamples, are given in table 9.

TABLE (1. Eeduccion of specific surface area, caused bycycles of resorption and adsorption

(Tomes, lXunt, and Blsine, 1957)

1stadsorption.. . . .2d adsorption. . . . .3d adsorption. . . . .4thadsorptio n....5th ,dso,ptim.6th adsorpti on....7tfI adw,pt,on. .8th .dmrpt,on . . . .

89.975,866563.258.s57,536.056,3

10084747065

1:63,

Although the change in surface area producedin this way is much less than that produced in theautoclave, it is substantial and significant withregard to various aspects of ,concrete technology,as well as to laboratory studies, From the trendof the plotted data, it appears tha~, if the reduc-tion in specific surface occurs during resorption,as seems likely, the original surface area was re-duced at least 20 percent before the first adsorp-tion, and thus, by the sixth adsorption only halfthe original surface remained.

Other experiments were made by the sameauthors in which tbe samples were completelysaturated between successive BEr determinations.The second adsorption gave 97 percent of the areaindicated on the first adsorption and the thirdadsorption gave 89 percent. These figures are tobe compared with 84 percent and 74 percent intable 9. Thus, ailowing the material to swell asmuch as possible between surface area de-terminations seems to undo some of the effect ofresorption.

In a recent paper, Hunt, Tomes, and Blaine [91]report additional observations on spontaneous re-ductions of surface area occurring while samplesm-e in storage in sealed containers. Completelydry samples seemed to be stable, but those con-taining small amounts of evaporable water, left inthe samples deliberately, were unstable. Some ofthe data are given in table 10. The maximumrate of spontaneous change was found in samplesthat produced a humidity of about 50 percent inthe sealed containers. (The humidity was deter-mined by direct measurement. ) The samples thatproduced humidities below 1 percent and aboveabout 80 percent seemed to be stable.

TABLE 10. Changes in specific surface area occurring insealed specimens as a fundzon of amount of residualevaporczblewater

(Hunt, Tomes, md Blaine, 1960)u,,= weicht of ev.’Jor.ble water m the samDle.

“ c.=weig fit of ,snited cement.

1V.”,UJ.aft., stomge

1

Relative surfaceareaPeriod indicated after storagenwiod

,0, indicated-T l————

1month21mmths 1month 21rnmths

I 10:0&6 0,300 0,295u 160 98~

.995 ,280 9s 93.06 .265 .243 88 81.10 .262 .230 87.17 .282 .277 K.20 .300 .a66. 1%+ 166.

I. Estimated by extrapolation.

The nature and cause of a reduction in specific

surface under the conditions describccf above

remains a matter for speculation. Collapse of

a layered structure naturally suggests itself, and

Tomes, IIunt, and Blaine offered, tentatively,

such an explanation. Other data that appear

to be incompatible with such an explanation have

already been present ed (section A) and more may

now be introduced. TornsS, IIunt, and J31aine

found that wetting and drying not only reduced

the surface areia as measured by water but also

reduced the values found by nitrogen. For the

specimens that were subjected only to humidity

fluctuations between O and 33 percent, the mtrogen

area was reduced by about the same percentage

as the wat,er area. For the specimens representedin table 10, the nitrogen areas were reducedmuch mm than the water areas, If water vaporactually penetrated the primary particles, primarywith respect to nitrogen adsorption, a reductionof such penetration by water should reduce theindicated water area but not the nitrogen area.

600

Perhaps the most plausible explanation isthat during resorption, gel particles are broughtcloser together than they have ever been before,and new points of contact are produced underconsiderable pressure. (See section 7.) If thisshould create stable chemical bonde between theparticles, the irreversibility would be accountedfor. If the evidence is construed to indicate suchnew bond formation, it indicates also that thebonds have various degrees of strength, Asshown in table 9 not all possibilities for formingnew bonds are exhausted at one time, so thatrepeated cycles are required to eetablish stabilityunder a given set of conditions. Alsoj consideringthe partial reversal caused by complete swellingbetween surface-area determinations, one con-cludes that some of the new bonds that remainintact at low humidities are weak enough to beruptured by film pressure at high humidity.

The explanation just offered suggests that asthe surfaces of adjacent particles are mashedtogether by shrinkage forces, a pa~tial fusionof the surfaces occurs. If this M so, It indicatesthat m much as half of the original surface canbe eliminated in this way, a fraction so high as tocast doubt on the explanation.

Irreversible Deformations of Cement Paste

Drying Shrinkage

It is a familiar fact that the first isothermalshrinkage caused by drying is only partiallyreversible and that subsequent cyc~es of wettingand drying at the same humldlty are verynearly reversible. Data published by Pickett[79], are typical. This phenomenon is apparentlya manifestation of the same instability that wasreported in terms of decrease in specific surfacearea as discussed above. However, most dataon irreversible shrinkage, including Pickett’s,are complicated by the effects of carbonationoccurring during the period of drying.

Carbonation Shrinkage

Cement gel is unstable in the presence ofcarbon dioxide and moisture [92]; it reacts chem-itally, and irreversible shrinkage accompaniesthe reaction. Rate of carbonation depends onratio of surface area to volume of the specimen,permeability of the paste, internal relative hu-midity, and concentration of C02. -Carbonationshrinkage is greatest when the internal humidityis about 50 percent. Practically no carbonationshrinkage occurs when the internal humidity is100 or 25 percent. Carbon dioxide is able toreact with all components of hydrated cement.The surface area per gram of original anhydrouscement appears to be slightly increased by thereaction. The mechanics of carbonation shrinkagehas not yet been explained.

Effect of Externally Applied Force

A specimen of paste when subjected to anexternally induced stress, such as, for example,that produced by sustained compressive force, ora bendin

%moment? shows behavior similar to

that pro uced by internal tension (shrinkage).Experiments of this kind are usually carried outto study plastic deformation and creep, and itis commor to observe the effect of the appliedload at the same time that shrinkage is going on.Experiments done under less complex conditionswere reported recently by Glucklich [84]. Heused sealed specimens of neat cement subjectedto a bending moment. Although a small amountof leakage through the seal, and self-desiccation[66] no doubt resulted in some internal tension,the internal teneion was probably moderate andrelatively constant throughout the experiment.Repeated ioading showed marked permancmtset on the fist loading, and a little on the second,but further repetitions showed reversible visco-elastic deformation. Thus it appears that theexternal force produced the same kind of effectas did the internal stresses induced by drying.

9. Strength

Werner and Giertz-Hedstrom [93] were appar- in which ideas similar to those reviewed aboutently the first to observe that strength of cement were developed [97]. Strength was considered topaste and concrete should be a function of the be a function of 7 such thatconcentration of hydrated cement, although theearlier cement-space ratio of F&et (1897) cer- Chtainly implied such a relationship. Others who ~=c,+we+o’

(48)

dealt with similar ideas were Work and Laeseter(1931), Woods, Steinonr, and Starke (1932), In terms of the notation used in this review,Freyssinet (1933), Eiger (1934), Bogue and Lerch(1934), and Lea and Jonee (1935), all mentioned C,= (c,Co,,/V) X Constant.by Giertz-Hedstrom in his 1938 review [94].In 1947 Shinohara, [95] and Powers and Brown- Thus, C, is the volume of hydrated cement (notyard [96] independently published work based volume of gel) per unit volume ?f sample. W. ison similar ideas, and about the same concepts the volume of evaporable water m a unit volumewere used by Taplin [68] in 1959. In a disserta- of specimen] whether the specimen is saturated ortion published in 1953, Dzulynsky published a not, and v M the air-filled space. The indicatedstudy of strength in relation to cement hydration constant is inserted because the method of deter-

601

mining fixed (nonevaporable) water used byDzulynsky was not the same as that on which c~,is baeed.

From experimental data obtained from testson pastes and mortars, Dzulynsky concluded that

Where R; is the observed strength, and R; and k areempirical constants. Adopting this form of em-pirical equation had the unfortunate consequencethat when y=O, R;= R: inetead of O as it actually

As seen in eq (37), N is the volume of gel producedby I cc of cement. Constants evaluated fromdata published by Powers and Brownyard aregiven in table 11. Calculations for X were basedon values of WZobtained by the magnesium per-chlorate method. When X is based on W. deter-mined by the dry ice method, the values of n comeout about 12 percent higher, averaging about 3.0.

TABLE 11. Compressive strength junctions for mortarsmade with fiuedifferent cements

(Data from reference17,tables 6-1 to 6-6)

,,,is.Powers and Brownyard [96] adopted the term calculated compound camp, %

gel-space ratio analogous in concept to the Feret cementh,.. N of n of f;

cs I CZsI C,A I C4AFI@so4 ‘q(’7) ‘q ’51) ‘b’ha;em&t-space ratio. “They carried out measure-ments that gave compressive strength and factorsproportional to the amount of gel, and arrived atthe following empirical equations that representedthe data very well.

.f,=lf[(vm/wo)–Bl =lkf[k(wn/wo)–B] (50)

where j. is compressive strength; M, B,. and kare constants for a given cement, k being theratio, VJwn, Since the cement gel producedfrom a given cement has a characteristic specificsurface area proportional to VJVE, where Vg isthe volume of cement gel, the quantity of gel m aunit volume of specimen is properly representedby V,,L/VP, where V, is the volume of the paste,The space initially available to gel is proportionalto WO, However, since the ratio of Vm to w, isnot literally proportional to the gel-space ratio,Powers later [98] used the function

x= gel volumegel volume+ capillary space

where X is the gel-space ratio. Another relation-ship was proposed [72] such that

x.= gel volumegel volume + capillary space+ air voids,

Experimental data conformed closely to an equa-tion of the following form:

,fc=j:x” (51)

where j: and n are empirical constants. Since Xis a fraction between O and 1, X“ operates as a re-duction factor on ft. The intrinsic strength of thegel thus seems to be represented by j~, althoughwhen aggregate is present it probably includesother factors.

Different methods of expressing X have beengiven [72,98]. The following is perhaps the mostconvenient expression,

x=—N—

1++. $.: (52)

—1—l—l—l—l —l-—l—l—14!130J...--.. 22.7 558 6,1 9.8 2,64 2.16 2.53 18,50015007J.. . . . . . 48.0 291 6,8 10.5 2.22 2.18 2.86 17,NO15011S..-.... 45.1 29.1 6.7 10,5 2.43 2,18 244 16,96015013J. . . . ..- 390 29.0 14.0 7.0 3,00 2 18 3.08 13,00015365. . . . . . . . 45,0 28.0 18,3 6.7 4.22 2.24 2.68 13,800

,,, ,, ,,,

The figures in the last column considered inconnection with the chemical compositions of thecements indicate that cement gels low in C~A arestronger than those high in C3A. Although thereis such evidence that the strength of cement gel isa function of its chemical composition, there is noevidence that some of the chemical species presentdo not contribute to strength. By means of asimple detnonstration, Czernin made it clear thatthe physical state of the eolid material may beresponsible for strength [99]. He demonstrated(A) that a mixture of 100 g of coarse quartz andzo g of water was without strength, (B) that whenthe quartz was pulverized to “cement fineness”,the same proportions exhibited some strength and(C) that when the quartz was pulverized so as tohave a surface area of 20,000 cm2/g, a cylindermolded with the aid of a press could support morethan a 10 kg load. Czernin remarked that incement paste the surface area is not 20,000 but2,000,000 cm2/g and thus ‘(. the high strengthattained by the cement in time is entirely plaus-ible. ” Such strength is presumably due to theproximity of surfaces and van der Waals forces,as discussed in section 7. Since all the majorcomponents of hydrated cement are found in sub-stances having high specific surface area, all con-tribute to at least the van der Waals source ofstrength. On the other hand, it seems unl~kelythat the strength of cement gel is clue cxcl,uslvelyto physical forces. For reasons already given, Itseems probable that there are many points ofchemical bonding between the particles. Whetheror not all chemical species contribute to thissource of strength cannot be said. As to the rela-tive importance of the two sources of strength,one can only speculate. When a specimen ofcement paste is dried in such a way as to avoidexcessive stresses during drying, the specimenbecomes stronger as its evaporable water M lost;in fact, If some of the chemically combined wateris removed, there is gain in strength. In terms of

602

van der Waals forces, this gain of strength couldbe accounted for in terms of the reduction in aver-a e distance between surfaces in the cement gel.T%ere is evidence also that new chemical bondsmay be formed during the process of drying (seesection 8).

Effect of Temperature of Curing

Ludwig and Pence [51] cured specimens ofcement paste at various temperature, measuredthe nonevaporable water contents, the surfacearea of the solids, and compressive strengths, andobtained the results shown in tab] e 12. Therelationship between gel-space ratio and compres-sive strength for curing temperatures 27, 66, and93 “C conform to eq. (51) with ~~= 12,000 andn= 3. At the two highest temperatures, the

strength is only 30 percent of that to be expectedfrom the calculated gel-space ratio.

TABLE12. Effect of temperature of curing on compressivestrength

Temjmmtureof curing

“F QC

27l% 66Zsn260 1%320 160

(Ludwig and Penoe, 1956)curing time: 7da~$ Nominal WIC=O.46

Cement: ASTM TYPe I

II

1aim... . . . . . 103 0,1421aim ... . . . . . 123 .16210dOpsi. . . . . . .15210Wpsi. . . . . . X .139mm psi. . . . . . s 4 .139

1

. Including u“h~dmtad cement., Cured at 140‘F.

10. Permeability of Saturated Paste to Water

Under proper experimental conditions, it can bedemonstrated that the flow of water through hard-ened cement paste complies with d’Arty’s law.To obtain a correct result, the test specimen mustbe completely saturated, and osmotic pressure de-veloped in the apparatus during the test must bepractically constant [100]. This observation ofcompliance wit,h d’Arty’s law is the beginningpoint of analytical stud~es of permeability,

Theories of Permeability

Powers and Brownyard [101] attempted to dealwith the flow of water through mature cementpastes in terme of the Kozeny-Carman concepts,as had been done previously for fresh pastes.(See section 2.) According to this approach to theproblem

K,=~ ~ cmkec. (53)??o(T)kr2 (1—6,)*

The constant k is the Kozeny-Carman constant,embodying a ‘ ‘tortuosity factor” and a shape fac-tor, and u is specific surface area of the solid par-jicles, cm’/cc. The subscript, e, on porosity, t,indicates that the effective porosity is not neces-sarily equal to all the space occupied by evaporablewater. That ie, it was known from Carman’swork with clay [102], and from the work on freshcement paste, that some of the fluid might be

. “immobile”. Powers and Brownyard assumedthat the quantity of immobile fluid would beproportional to T’m and obtained the followingexpression:

K,=(7.85X10-”)fiks[+-k’~cm/sec

(54)

The numerical coefficient is the reciprocal of thesquare of the proportionality between T’mand eur-

Com-ws~p pressive

8tren@h,(*pproX) P,,

—l—0:g 3825

b6141.76 f ::;.71,71 1;330

face area. k, is the amount of “immobile” eva -orable water, expressed as a multiple of T‘m. lswill be seen further on, there is evidence that allthe evaporable water is mobile.

Powers and Brownyard assumed that the capil-lary space in paste is in the form of an intercon-nected system of capillary channels throughoutthe gel, and that the hydraulic radius of the prin-cipal conduits could therefore not be calculatedfrom the total porosity and total internal surfacearea: Later, Powers and Copeland neverthelessapphed the Kozeny-Ca~man relationship to ma.ture pastes having capdlary porosity, seeminglywith some success, but that approach was eventu-ally abandoned m favor of another based prin-cipally on Steinour’s adaptation of Stokes’ law toconcentrated suspensions, discussed in section 2.Powers, Mann, and Copeland finally arrived ateq (55) [56].

—“exp-[(f-’)(=)l ’55)

c’K’=% “ (1–,)

where

(56)

B is a constant comprising the following factors:the density of the fluid m the specimen, p,; thegravitational constant, g; a function of particleshape, the Stokes diameter,. d,; and the number 27m,hich comprises the numerical constant in Stokes’law for the free fall of spheres, and another func-tion of concentration ~(c) introduced by Hawksley[103] which corresponds to the Kozeny-Carmantortuosity factor. The term qO(1’) is the nor-mal viscosity of water at temperature T. In theexponential term, a/T( (1—6)/e) 1s a correctionterm applied to normal viscosity, and -Y((1– e)/,)was thought of as a temperature-independentfactor of the same kind. The values of the con-

603

stants in eqs (55) and (56), derived from experi-mental data, were reported as follows:

B=(l.36+0,1)X10-’0~=1,242+ 133

‘y==o.7+o.5.

The fit seemed good except that 7 was not sig-mficantly clifferent from zero, Powers, Cop eland,and Mann, being at the time mostly interested inB, did not pursue the analysis further, Actually,the indication that -Y=O.O could only mean thatthe exponenLial term contains nothing that is in-dependent of temperature. A review of the deriva-tion of eq (55) showed that this might have beenanticipated, particularly in the light of Hawksley’streatment. The least-squares analysis was re-peated during the present writing, omitting -r,with the following results:

E=(1,34+ O. 099)X1 O-’”

a=l,4323z22.

The values of t used in the above calculationswere based on the assumption that the meanspecific volume of evaporable water is independentof porosity and equal to 0.99 cc/g. (See section 3.)Based on c~, the porosity to helinm, calculationsgave

B=(1.18+ 0,085 )X10-’D

~=1,250+ 20,

The two pairs of values may be regarded asupper and lower limits. Probably the correctvalues are closer to those based on e~ than tothose based on the assumption that the specificvolume of adsorbed water is 0.99.

With the success of eq (55) established, it isnow clear why a Kozeny-Carman type of expres-sion cannot be applied successfully to the flow ofwater in hardened cement paste. Steinour [22],experimenting with spherical particles of tapiocasuspended in oil at 25 ‘C, showed that t,he Kozeny -Carman constant k is the following function of e.

k=&exP4.19 (1-E). (57)

For values of e between 0.3 and 0.78, this equationgives k=4.06 within +0.06. This constancy,together with the limits on e, accounts for thesuccess of the Kozeny-Carman equation, and forits limitations.

For flow through celnent pastes, the effects ofadsorption produced a function different fromeq (57), Thus, from eq (55) (without ~) andfrom data give above, we have

For T’=298° K, 1,250 /7’=4.19, the same valuefound by Steinour. With c=o.3, 0.5, and 0.7,eq (57) glv~s k=4.02, 4.05, and 4.o7, whereas thecorresponding figures for eq (58) are 3,500, 32,and 14. Thus, for flow through past es, k M farfrom constant, and its magnitude far away fromthat required for the success of the Kozeny-Carman equation.

The agreement between the numerical coeffi-cients in eqs (57) and (58) is significant, and will bediscussed further on.

Viscosity of Water in Saturated Paste

According to the theory of Eyring [104]

~O(T)=AO exp EO/RT (59)

where q~(2’) is the viscosity of water flowing underconditions that produce unperturbed patterns offlow, such as between smooth, parallel plates.EOis the normal energy of activation for such f’IOW,and AO is a temperature-independent constant.Flow of water through hardened paste does notprovide the conditions just stipulated, but, ac-cording to the same principle the viscosity forflow through paste should be given by

q(T,a,m) =Al exp (E,+ Ea+Em)/RT (60)

where E. and En denote parts of the total activa-tion energy for flow dne to adsorption (andsolutes) and to mechanical interference of flowpatterns, respectively. Thns, relative viscosity7* in paste is given by

n*=~(T,a,m)/m(T)= (A/~0) =w (fL+J%)/~~.(61)

The exponential term in eq (55) is an empiricalcorrection factor for normal viscosity such that

~*=exp (a/T) (l —e)/e. (62)

Thus

(A,/AO) exp (E=+ EJ/RT= exp (a/T) (1 – c)/c.(63)

The agreement pointed out earlier between thevalue 4.19 in eq (57), found by Steinour from ex-periments in which adsorption effects were absent,and a/ T=l,250/298=4.19, found for flow incement paste indicates that when &=O,

~~=exp EJl?T=exp (a/T) (l–E) (64)

where q! is the relative viscosity when there is noadsorption effect. Thus the effect clf adsorption isto require the empirical function of porosity to be(l–c)/e instead of (1–c).

Solutions of eqs (62) and (64) are given in table13, showing the total effect of mechanical inter-ference and adsorption, and the mechanical effectalone.

604

TABLE 13. Computed relative viscosity of fluid in satwatedcement pastes, based on eq (63) and (64) wtth A,= AO,and LY/T=4.19

II

1 .,!,,, ,0,, 0,, .0,,, ,, c,m,”,, vfc ,. ,.,” PO,+,

10 !s ,0, ., ,7. ,s, .,, O.s .40, .,, . . ,,,

Factor of vi,coWyincreaw

Hj:w&Iic —W./c . Me:d#cal Total

effectV?, eq 04 v“, ecr 62

—l—l–—1 —l——

A0.38 0.280 7.8 20,5 .47, 664.45 ,346 10 15,5 2,766.!?4 ,895 12 12.6 663.60 .461 16 9.6 134.70 .489 18 85 78

,,~ Th IS is the value for cmnont @.

Magnitude of Activation Energies

Activation energies for flow through differentpastes ranged from 8,160 for e= O.414 to 6,200for ,=0.572, in calories per mole of water. Themean activation energy for flow of water undernormrrl circumstances is about 4,49o cal/mole.Thus, Em+Ec ranges from about 3,7oo to 1,800cal/mole for the range of c given.

General View of Factors Determining Perme-ability of Saturated Paste

Figure 4 is a simplified version of a diagram,published by Powers, Copeland, and Mann [105]showing the principal factors controlling permea-bility to water at constant temperature. Line Erepresents the perineabilities of fresh pastes overthemngeof water-cement ratios indicated by thetop scale, the permeabilities having been deter-mined from bleeding rates. The resistance toflow depends on the size, shape, and concentrationof cement particles, and on the effect on theparticles of the initial chemical reactions (seesection 2). Since the effect of adsorption on theviscosity of water in fresh paste is negligible,the scale of abscissas should have been in terms ofl–c instead of (l–e)/e. However it was notfeasible to combine both functions in the samegraph, and the present plotting serves the purpose.

Line A represents the permeabilit,ies of pastescontaining completely hydrated cement, and fromwhich all alkali had been leached. The resistanceto flow is determinedly the size, shape, and con-centration of the particles composing hydratedcement, and by the effect of adsorption on vis-cosity of water in paste. The marked pointsalong line B represent a sample of paste at variousstages of hydration from the fresh to the fullymature state, the final point being calculated andthe rest experimental. Points along line C arethe same for a different water-cement ratio.The dashed lines are estimated curves for otherwater-cement ratios.

Continuous and Discontinuous Capillaries

The water-filled space in jresh paste constitutesa continuous, interconnected system of capil-

FIGURE 4. Permeability junctions for fresh, hardening,and mature pastes.

laries. Production of cement gel at first con-stricts the capillaries without destroying conti-nuity, but finally may divide them into segmentsthat are interconnected only by gel pores. Thistransition, in terms of changes of permeability,isshown clearly bycurves B and C and by dashedlines for other water-cement ratios. Capillarycontinuity is indicated by any point between Eand A. At some stage of hydration of a givenpaste the point will just fall on line A, and, ifthere is still a reeerve of unhydrated cement,subsequently produced points will follow line A.If the water-cement ratio is too high, completehydr-ation will,no~ produce enough gel to destroycapdlary contmrnty, and the terminal pointsfall above line A, along some such curve as D.For the particular cement represented by thesepoints (ASTM ‘~ype I, 1800 cm’/g, Wagner),capillary continmty does not disappear at fullmaturity if wO/cis greater than 0.7.

Effect of Cement Composition

Differences in chemical composition of cementdo not have much effect if the tests are madewhen the different cements are at comparablestages of hydration [100]. Data given in pre:ceeding sections showing that the quantity andphysical characteristics of cement gels producedby different cements are similar would lead oneto expect this result. At early ages, pastes madewith a slow-hardening cement will of course haverelatively high permeability.

605

Effect of Alkali

Solutes in the evaporable water, particularlyINaOH and KOH, reduce the rate of flow throughpaste by increasing the viscosity of water. Speci-mens from which alkali has been leached show asmuch as six times the permeability of companionspecimens containing a small a,mount of alkali.Whe,n plotted in ,figurc 4, points representingspecimens contammg alkali fall below line A,except for specimens having capillary continuity.Verbeck [106] found that a given cement paste,with w/c= 0.55, was nearly five times as permeableto pure water as to a salt eolution containing 12g/1 NTaC1. The effect was greater the denserthe paste. It seems that the effect here reportedis due to the presence of hydrated cations, theeffect per ion being greater the greater the degreeof hydration of the ion.

Effectof Cement Fineness

The higher the specific surface of the cement,the farther to the left curve D will be, that is,the higher the water-cement ratio at which capil-lary continuity can be “cured out”. This seemsto be the only way in which the fineness of port-land cement, per se, influence the permeabilityof mature paste.

Effect of Curing

As is apparent from figure 4, the change inpermeability accompanying the transition fromfresh to mature states is enormous. For example,at wO/c= O.7, fresh paste is 3 million times aspermeable as mature paste, 2X 10-’ vs. 6X10-”cm/sec.

It is to be expected that if the temperature ofcuring is high enough to increase the size of theprimary particles, permeability to water willthereby be increased. Ludwig and Pence measuredthe permeabilities of pastes cured under waterat elevated temperatures with the result shownin figure 5 [51]. Verbeck repo~ted results of thesame kind [92].

Effect of Drying

If a specimen becomes dry at some time beforea permeability test, its permeability to water isthereby increased. There are not many data onthis point. In one experiment, mature specimenswere dried very gradually to equilibrium with79 percent relative humidity, and then slowlyresaturated~ first in humid air and then in water.The coefficient of permeability was found to beabout 70 times what it would have been had thespecimens not been given the drying and wettingtreatment. This is probably another aspect ofthe structural instability of cement paste discuseedin section 8.

140

130 I

I

10t

Temperature of curing -oF.

FIGURE 5. Effect of temperature of curing on permeabilitiesof water-cured pastes (Ludwig and Pence).

w/c=O.46 (nomimd), cement .4STM Type 1. Afl specimens cured underwater for 7 days at temper.ture Z200”F; the pressureWT.S300Psi.

Permeability of Unsaturated Paste

Not much systematic study of movement ofmoisture through unsaturated paste has beenreported. Powers and Brownyard [101] gave arelationship between the coefficient of permeabilityof a saturated specimen and a “coefficient ofabsorptivity” of a dry specimen, but, as the rela-tionship was stated, it is applicable only to speci-mens containing an interconnected system ofcapillaries. It has been pointed out [105] thatthe “water-vapor permeability” is not ordinarily aprocess of transmitting vapor as such. Oncewater vapor is in cement paste, pr~ctically all ofit is adsorbed and the transmission occurs in theadsorbed or capillary-condensed state. The mo-tive force is not the vapor pressure difference, butthe gradient in film tension dkcussed in section 7

606

Appendix 1

Glossary

To understand some parts of the text, the author’s definitions of a few terms must bekept in mind. These terms are given below. (All terms defined in the glossary are italicized.)

Capillaries, or Capillary spaces: in fresh cement paste, thespace occupied by water; in mature paste, the pore spacein a specimen of paste in excess of about 28 percent ofthe volume of the specimen. These spaces are regardedm diBcontinuities in a mass of cement gel.

Capil~ary catiities: capillary spaces that are isolated bycement get.

Cement: portland cement in the initial, practically anby-drous state.

Cement gel: the cohesive mass of hydrated cement in itsdensest state. It includes gel pores, and has a porosityof about 28 percent. The solid material is composedmostly of coUoids, but noncolloids, articularl calcium

1 & overallhydroxide, are included in this de mtlon.specific volume is about 0.567 cc/g dry weight; whenprepared at room temperature its specific surface areais about 210mZ/g dry weight.

Cement paste: the term is applied at any stage of hydration,As applied to fresh paste, it is the mixture of cement andwater, exclusive of air bubbles, if any; as applied tohardened paste, it is the rigid body produced by cementand water, composed of cement gel, capillary spaces, ifany, and residual cement, if any. When there is neithercapillary space nor residual cement, cement paste andcement get are identical.

CoUoid: a substance in such physical state that its chemicaland physical properties are influenced to a significantdegree by the surface energy of the substance. A solidcolloidal substance may be amorphous or crystalline,but, if crystalline, the crystals are apt to be imperfectlyorganized. A colloid is characterized by a high specificsurface area. In cement gel calcmm hydroxide, andperhaps some other components are not colloidal.

Dry ice method: the method of isothermal drying of samplesof cement paste described by Copeland and Hayes [36];referred to also as the Copeland and Hayes method.

Get: a cohesive mass of colloidal material. (Comparewith cement geL)

Get pores: the pores in cernerzt gel.Hydrated cement: a collective term for all the chemical

species produced by the reactions between cement andwater, except transient products of initial reactions.

Magnesium perchlorate method: the method of isothermaldrying of samples of cement paste described by Powersand Brownyard ([17], pp. 249–336) and by Powers [98],now largely supplanted by the dry ice method.

Pore (in cement paste): space in cement paste that is, or canbe, occupied by evaporable water. Its definition,quantitatively, involves a standard method of dryingthe sample.

Appendix 2

List of RepeatedlyUsed Symbols

c= weight of cement in its original state, grams.ck = weight of original cement that has become hy-

drated.c;= weight of cement after being ignited.h= relative humidity= p/p, where p is the existing

water-vapor pressure and p, is the water-vaporpressure at saturation and same temperature.

In= logarithm to the base e.log= logarithm to the base 10.

m= maturity factor= fraction of cement that hasbecome hydrated.

N= volume of cement gel moduced from 1 cc of~.cement.

P= pressure, either positive or negative.P,s= pressure in capillary water (usually negative).u.= specific volume of cement, cc/g dry weight.U.= SPec~fiC volume of evaporable water, cclg.V,= sPec@ volume of cement gel, cc/g dry weight.

vi,.= specdic volume of hydrated cement, cc/g dryweight.

Ufi= sPecific volume (apparent) of nonevaporablewater, cc/g.

~0= Wlr~tO volume of saturated paste, cc/g saturated

oi= sPe21fiC volume of total water in saturated speci-men, wjg.

v.= specific volume of water under existing pressure,cc/g.

u;= specific volume of water under reference pressure,cc/g.

V= volume of specimen or batch of paste.V~= tbe Brunauer-Emmett-Teller surface-area factor

= weight of water required for a monomolecularadsorbed layer on a sample dried by the dry icemethod of Copeland and Hayes [36]. (Seeglossary).

(VJ,= ditto for a specimen dried by the magnesiumperchlorate method ([17] PP. 249-336).

~ = weightof water in fresh paste.w.= ditto, corr~cted for water displaced by bleeding.wt= the lmmobde water factor.VJ”= non~vaporable water= water retained by a

specimen prepared by the dry ice method ofCopehmd and Hayes [36].

(wJ,= nonevaporable water = water retained by aspecimen of paste prepared by the magnesiumperohlorate method, vapor pressure 8P of mercury.(r171UD. 249-336).

~= p&~~y, ratio of volume of interstices to gross,ove~all volume of a material.

W= capdlary porosity.err= porosity as c~lculated from the volume of the

saturated specimen and the specific volume of thedried solid as determined by displacement ofhelium.

P.= rkns~tyof cement, glee.p.= dens!ty of solid, g/cc.Pf= dens?ty of fluid, g/cc.u= specdic surface area, om2/co.2= specific surface area, om2/g.

References

[1]T. C. Powers, The bleeding of porthmd cement paste,mortar and concrete, Research Lab. Portland

[3] Fred M. Ernsberger and Wesley. G. Fra,nce, Portland

Cement Assoc. Bull. 2, p. 74, (1939).cement dispersion by adsorption of hgnosuIfonate,

[2] H. H. Steinour, Further studies of the bleeding ofInd. Eng. Chem. 37, 598-602, (1945).

[4] Reference [1], p. 43.portland cement paste, Research Lab. PortlandCement Assoc. Bull. 4, (1945).

[5] H. H. Steinour, unpublished laboratory report No.288-1 1–D4, (1941).

607

[6][7][8][9]

[10]

pressures up to 10,000 atmospheres, J. Research,NBS, 56 No. 1, pp. 39-50, (1956).

L. E, Copehlnd and John C. Hayes, The determina-tioll of non-evaporable n%ter in hardened portlandcement paste, ASTM Bull. No. 194, 70–74, Decern.bcr (1953). Research and Develop. Lab. PortlandCement Assoc. Bull. 47 (1953).

L. E. Copeland, Specific volume of evaporable waterin hm’dened portland cement, pastes, Proc, Am.Concrete Inst. 52 863–874 (1956). Research andDevelop. Lab. Portland Cemellt Assoc. Bull. No, 75[1Q%)

[36]

[37]

(1946).Reference [9], p. 34 of Research Lab. Portland Cement[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18][19][20][21][22]

[23]

[24][25]

[26][27][28][29]

[30]

[31]

[32][33][34]

[38][39][40][41]

[42][43]

[44]

,-. .-, .Reference [17], p. 558Ibid.. nu. 571–574.

Assoc. Bull. 3.Ralph E. Grim, Organization of water on clay mineral

surfaces and its implications for the properties ofclay-water systems. In: Water and its conductionin soils, an internatiOn~l sympOSium, edited byHans F. Winterkorn, Highway Research BoardSpecizal Report 40, (1958) Washington, DC. N’at.Acad. Sci. Nat. Research Council, Publ.

H, H. Steinour, Electro-osmosis tests on cementpastes, Private report, February 11, 1946.

T. C. Powers and E. ,M. Wiler, A device for studyingthe workabdlty of cOncrete, Am. SOC. TestingMaterials Proc. 41 1003–1015, (1941), Also, later

Ibid.j ~~ 498.Stephen Brunauer, The Absorption of Gases and

Vapors (Princeton University Press, 1943).Reference [17], pp. 488-489.Stephen Brunauer, D. L. Kantro, and L. E. Copeland,

The stoj~hiometry of t,he hydration ot beta-dical-mum sdlcate and trlcalclum silicate at i-oomtemperature, J. Am. Chem. Sot. 80 761-767 (1958).Also Research and Dmwlop. Lab. Portland CementAssoc., Bull. No. 86 (1958).

L. A. Tomes, C. M. Hunt, and R. L. Blaine, Somefactors atfectimz the surface area of hvdratedunpublished work.

Marcus Reiner. The rheo

[45]

T.” C. Powers and T. L. Bro[46][47]

.- .. . . ..Reference [17], p. 485, fig. 3-7D.L. E. Copeland, and R. H. Bragg, Quantitative X-ray

diffraction analysis, Anal. Chem, 30, 196-201(1958). Research and Develop. Lab, PortlandCement Assoc., Bull. No, 88, (1958).

Reference [17], p. 491.Ibid., p. 482-488.L. E. Copeland, D. L. Kantro, and George Verbeck,

Chemistry of hydration of portland cement, thisSymposium; paper IV–3.

NT,C. Ludwig and S. .4. Pence, Properties of Dortland

[48][49][50]

~a~ination is used in Bullet in 22.R;fe~ence [1], p. 65.Reference [2], p. 17.Reference [1], p. 3.,. -Reference [17], P.Reference [2] and

tion: I nonflocculated suspensions of uniforms~heres: II susnemions of uniform-size anm.dar

~ &.iH. Steinour, Rate of sediment a- [51]cement pa;tes cured at elevated “temperat~res andpressures, Proc. Am. Concrete Inst. 52, 673-687

p“articlei; III co;centr%ted flocculated suspen~ionsof powders. Ind. Eng. Chem. 36 618–624, 840–847, 901–907 (1944). Research Lab. PortlandCement Assoc. Bull. 3, (1944).

H. H. Steinour, Research Lab. Portland CementAssoc. Bull. 3, p. 47, fig. 4, (See reference [22]).

Reference [11. n. 73.

11956),Gee. L. Ktdousek~ Discussion of “Simplified method

for determination of apparent surface area ofconcrete pro ducts,” Ibid. 51, Part 2, 448-7, –8(1!3.5,5).

[52]

[53] D&cari McConnell, Discussion of “An interpretationof some published researches on the alkali-aggregatereaction” by T. C. Powers and H. H. Steinour.Ibid, 51, Part 2, 812-4 (1955).

A. E. Moore (Miss’), Bemerkungen tiber de Hydrata-tion des Zementes, Zement u. Beton No. 16, 19-20,(July 1959) ,,

H. zur Strassen, Uber die Wasserbindung in erharteten

P.”c. Ca(New York Academy Press, 1956.)

Reference [1], p. 2&32.Ibid., pp. 132-155 and reference [2], pp. 81–87.Reference [2], pp. 35–43.P. C, Carman, Capillary rise and capillary movement

of moisture in fine sands, Soil Sci. 52 1–14, (1 !341)Paul Klieger, The effect of atmospheric conditions

during the bleeding period, and tion the scale resistance of concrete, PTOC. ,lm~Concrete Inst. 52 309–326 (1955–1956), Researchand Develop. Lab. Portland Cement Assoc. Bull, 72(1!356)

. .. .reman, Flow of Gases Through Porous Media

[54]

[55]

[56]Zement, Ibid. 36–37 (JdY 1959). -

T. C. Powers. H. M. Mann. and L. E. Co~eland. Theflow of m?,{er in harden~d portland ceinent Paste,Highway Research Board Special Report 40,308–323,

[me of finishing

(1958). Research and Develop. Lab.Portland Cement Assoc., Bull. 106, (1959). Seereference [12] for further description of the HRBpublication.

L. E. Copeland, Unpublished progress report, October21. 1%$6.

.. . . ...hf. A. Swayze, Finishing and curing: A key to

durable concrete, Proc. Am. Concrete Inst. 47317–331 (1950).

Reference [17] p. 696.Ibid,, u, 693,

[57]

[58] Stephen Brunauer, D. L. Kantro, and Chas H. Wei.se,The surface energy of tobermorite, Can. J. Chem.37, 714–724 (1959). Research and Develop. Lab.Portland Cement Assoc., Bull. 105 (1959).

H. H’.LSteinour, Specific volume of non-evaporablewater in cement paste, unpublished laboratoryreport, Series 254, Seutember 7. 1945. [59] R. L. Blaine and H. J. Valis, Surface available to

nitrogen in hydrated portland cements, J. ResearchNBS 42, 257 (1949).

Li5] C. ~. lV&irj C. M. Hun~, and R, ‘L. Blaine, Behaviorof cements and related materials under hydrostatic

[60] P, H. Emmett, and T. DeWitt, Determination of [86][87]

[88]

Reference [17], pp. 932–969.R. A. Helmuth, Unpublished laboratory report,

October, 1958.George Verbeck and Paul Kliege~, Calorimeter-strain

aJ?Paratus for study of freezing and thawing ofconcrete, Highway Research Board Bulletin No.176. Also Research and Develop. Lab, PortlandCement Assoc.j Bull. 95, (1958), (22 pages).

Paul Nerenst, Frost action in concrete, this Sym-

surface areas, Ind. Eng. Ch&n. Anal. Ed. 13,28–33 (1941).

[61][62][63][64]

Chas. hi.’ Hu;t, private communication, 1960,Reference [17], p. 495.Ibid., p. 704.L. E. Copeland and John C. Hayes, Porosit

hardened porthmd cement paste, Proo. Am. 60::crete Inst. 52, 633-640 (1955–1956). Research and~o~~l)op. Lab. Portland Cement Assoc., Bull, 68,

[89]

[90][91]

[92]

posium, paper VI-2.Reference [17], p. 492.C. M. Hunt, L. A, Tomes, and R. L, Blaine, Some

effects of aging on the surface area of portland ce-ment paste, J. Research, NBS 64A (Phys. andChem.) 163-169 (1960)

A. Steopoe, Die Einwirkung der Kohlensiiure auferharteten Zement, Zement 24, 795–797 (1935) ;I. Leber and F. A. Blakey, Some effects of ~ondioxide on mortars and concrete, Proc. Am, Con.crete Inst. 53, 295–308 (1956) : Georee Verbeck,

[65]

[66]

,. ”-”,.

Wolfgang Czernin, Versuche iiber die Reaktionsfahig.keit des Gelwassers, Zement u. Beton No. 16, 35–37(Iawl),. .-”/.

T. C, Powers, A discussion of cement hydration inrelation to the curing of concrete, Proc. HighwayResearch Board 27, 178–188 (1947). ResearchLab. Portland Cement Assoc., Bull. 25 (1948).

L. E. Copeland and R. H. Bragg, Self-desiccation inportland cement pastes, ASTM Bull. No. 204,34–39, February (1955). Research and Develop.Lab. Portland Cement Assoc., Bull. 52 (1955).

,J. H. Taplin, A method for following the hydrationreaction in portland cement paste, Australian J.Appl. Sci, 10, 329-345 (1959).

Reference [17], p. 496, fig. 3-10; p. 585, fig, 4-11.T, C. Powers and R, A. Helmuth, Theory of volume

changes in hardened portland cement paste duringfreezing, Proc. Highway Research Board 32, 285-297 (1953). Research and Develop. Lab. PortlandCement Assoc., Bull. 46 (1953).

R. H. Bogue, Discussion of paper No, 9, “The struc-tures of cement hydration compounds, ” by J. D.Bernal. Proc, Third Int. Symp. on the Chem. ofCement, London 1952, p. 254.

T. C. Powers, The physical structure and engineeringproperties of concrete, Reprint of a lecture presentedat the Institution of Civil Engineers, London(March 1956). Also issued as Research and De-velop. Lab. Portland Cement Assoc., Bull. 90, 28

[67]

Carbonation of hydrated’ portiand c~ment, Am:Sot, Testing Materials Spec. Tech, Pub. No. 205:(1958). Also issued as Research and Develop. Lab.Portland Cement Assoc. Bull. 87 (1958),

D. Werner and S. Giertz-Hedstrom, Die Abhiingigkeitder technisch wichtigen Eigenschaften des Betonsvon den physikalisch-chemischen Eigenschaften desZements. I. Zement 20. 98*987. 1000-1006

[68]

[69][70]

[93]

(1931).[94] S. Giertz-Hedstrom, The physical structure of hy-

drated cement, Proo. of the Symposium on theChemistry of Cements, Stockholm, 1938, pp. 505–534.

[95] Kinji Shinohara, Fundamentals of the strength ofhardened cement pastes, (in Japanese). Reportof the Department of Engineering, Kyushu Uni-versit y, 10 No. 2. 54-.163 (1947).

[96] Reference [17] pp. 845-864.[97] M. Dzulinsky, Relation entre la r&istance et l’hy-

dratation des liants hydrauliques, Bull. Centre.d’Etudes de Recherohes et d’Essais Scientifiques,University of Liege, 6206-226 (1953).

[98] T. C. Powers, The nou-evaporable water content ofhardened portland cement paste—its’ significancefor concrete research and its method of determina-tion”, ASTM Bull. No. 158, pp. 68-76, (May,1949). Research Lab. Portland Cement Assoc.

[71]

[72]

pages (1959).T, C. Powers, Structure and physical properties of

hardened portland cement paste, J. Am, Ceram. Sot.41, 1–6, (1958). Research and Develop, Lab.Portland Cement Assoc. Bull. 94, (1958).

~. Grudemo, An electronographic study of the mor-phology and crystallization properties of calciumsilicate hydrates, Swed. Cement and Concrete Inst.Royal Inst. Tech. Stockholm Proc. No. 26, 103

[73]

[74]

Bull. 29 (1949).[99] W. Czernin, Discussion of principal papers, Sym-

posium on the Hydration of Cement, Vienna.Zement u. Beton, No. 16, 16-19 (1959),

[100] T. C. Powers, L. E. Copehmd, J. C. Hayes, and H.hf. Mann, Permeability of portland cement pastesProc. Am. Concrete Inst. 51,285-298 (1954-1955).Also Research and Develop. Lab. Portland Ce-ment Assoc. Bull. 53 (1955),

[101] Reference [17], pp. 865-880,[102] P. C. Carman, Permeability of saturated sands, soils,

and clays, J. Agri. Sci, 29, 262 (1939).[1031 P. G. W. Hawkslev, The effect of concentration cm

pages (1955).By cooperative arrangement with the Swedish Re-

search and Concrete Institute? Mr. Grudemo was,during 1957, a guest scientist m the laboratories ofthe Portland Cement Association Research andDevelopment Laboratories, Skokie, Illinois, Dur-ing this time he obtained several hundred electronphotographs of cement gel,

T. C. Powers, Some physical aspects of the hydrationof portland cement, J. of PCA Research andDevelop. Labs. 3, No. 1, pp. 47-56 (Jan, 1961).

Reference [17], p. 496–498.Ibid,, pp. 549–602.Ibid,, p. 302 and pp. 476-477,M~2~lmer, Kinetic der Phasenbildung (Steinkopff,

[75]

[76]

[77][78][79][80]

the settling of - suspensions and flow throughporous media, In: Some Aspects of Fluid Flow,7~<1f14-135 (Edward Arnold & Co,, London,

[104]

[105]

H. Ey;ing, Viscosity, plasticity and diffusion asexamples of absolute reaction rates, J. Chem.Phys. 4, 283, (1936),

T. C. Powers, L. E, Copekmd, and H, M. Mann,Capillary continuity or discontinuity in cementpastes, J. of PCA Research and Develop. Labs. 1,No. 2, 3g48 (May 1959).

George Verbeck—Unpublished report (1955).

[81].“- .,.

C. L. Bernath, The theory of bubble formation inliquids, Ind. Eng. Chem. 44, 1310 (1952).

J. C. Fisher, Fracture of liquids: Nucleation theoryapphed tO bubble formation, Sci. Monthly 48, 415–419 (1947)

W. W. Barkas, The Swelling of Wood Under Stress,~~4~)~-39 (His Majesty’s Stationery Office, London,

[82]

[83][106]

84] J. Glucklich, Theological behavior of hardened pasteunder low strem, Froc, Am, Concre$e Inst. 66, 327–337. (1959)

[85] H, Elsnw vo’n Gronow, Die von erhiirtendem Zementgebunden Wassermengen und die Frostbestandigkeitvan Zementmorteln, Zement 26, 485–490 (1936). PCA.R&D.Ser.941-l

609

Bulletins Published by the

Research Department

Research and Development Laboratories

of the

Portland Cement Association

100. “List of Published Bulletins and Papers of the Research Department, ”May, 1959 (Also lists earlier research papers of the Portland CementAssociation).

101. “Determination of the Apparent Density of Hydraulic Cement in WaterUsing a Vacuum Pycnometer,” by C. L. FORD.

Reprinted from ASTM BuUeti?z, No. 231, 81-84 (JuIY, 1958).

102. “Long-Time Study of Cement Performance in Concrete—Chapter 11.

Report on Condition of Three Test Pavements After 15 Years of Serv-ice,” by FRANK H. JACKSON.

Reprinted from Jowmat of the American Conc~ete Institute (June, 1958) ; Pro-ceedings, 54, 1017-1032 (1957-1958).

103. “Effect of Mixing and Curing Temperature on Concrete Strength,” byPAUL KLIEGER.

Reprinted from Journal of the A?ner’ican c?onc~ete Institute (June, 1958); P~o-ceedings, 54, 1063-1081(1957-1958).

104. “The Successive Determination of Manganese, Sodium and PotassiumOxide in Cement by Flame Photometry,” by C. L. FORD.

Reprinted from ASTM Bulletin, No. 233,57-63(October, 1958).

105. “The Surface Energy of Tobermorite,” by STEPHEN BRUNAURR, D. L.KANTRO and C. H. WEISE.

Reprinted from Canadian Jowmat of Clzemistr_y, 37, 714-724(April, 1959).

106. “The F1OW of Water in Hardened po~land Cement paste,~~ bY T, c.POWERS, H. M. MANN and L. E. COPELAND.

Reprinted from iYigJzwayResearch Board ,Speciat Report 40, 308-323 ( 1958).

107. “The Ball-Mill Hydration of Tricalcium Silicate at Room Temperature,”by D. L. KANTRO,STEPHENBRUNAUm and C. H. WEISE.

Reminted from Jou?mat of CoUoid Science, 14, 363-3’76 (1959).

108. “Quantitative Determination of the Four Major Phases of PortlandCement by Combined X-Ray and Chemical Analysis, ” by L. E. CoPE-LAND,STEPHENBRUNAUER,D. L. KANTRO,EDITHG. SCHULZand C. H. WEISE.

Reprintedfrom Analytical Chemistry, 31, 1521-1530 ( September, 1959).

109. “Function of New PCA Fire Research Laboratory, ” by C. C. CARLSON.

Reprinted from the Journal of the PCA Research and Deueloprnent Labora-tories, 1, No. 2, 2-13 (May, 1959).

110. “Capillary Continuity or Discontinuity in Cement Pastes,” by T. C.POWERS, L. E. COPEI,ANDand H. M. MANN.

Reprinted from the Jourrzatof the PCA Research and Development Labora-tories, 1, No. 2, 3848 (May, 1959).

111. “Petrography of Cement and Concrete,” by L. S. BROWN.Reprinted from the Journal of the PCA Research and Development Labora-tories, 1, No. 3, 23-34 (September, 1959).

112. “The Gravimetric Determination of Strontium Oxide in PortlandCement,” by C. L. FORD.

Reprinted from ASTM Bulletin, No. 245, 71-75 (April, 1960).

113. “Quantitative Determination of the Four Major Phases in PortlandCement by X-Ray Analysis,” by STEPHENBRUNAU~, L. E. COPELAND,D. L. KANTRO,C. H. WEISE and EDITH G. SCHULZ.

Reprintedfrom Proceedings of the American Society for Testing Materials, 59,1091-1100(1959).

114. “Long-Time Study of Cement Performance in Concrete—Chapter 12.Concrete Exposed to Sea Water and Fresh Water,” by I. L. TYLER.

Reprinted from Journal of the American Concrete lmtitute (March, 1960);Proceedings, 56, 825-836 (1960).

115. “A Gravimetric Method for the Determination of Barium oxide in Port.land Cement,” by C. L. FORD.

Reprinted from ASTM BuUetin,No. 247, 77-80(July, 1960).

116. “The Thermodynamic Functions for the Solution of Calcium Hydroxidein Water,” by S. A. GREENBERGand L. E. COPELAND.

Reprinted from Journal of PIwsicat Chemistrv, 64, 1057-1059 (August, 1960).

117. “Investigation of Colloidal Hydrated Silicates. I. Volubility Products,”by S. A. GREENBERG,T. N. CHANG and ELAINE ANDERSON.

Reprinted from Jowwat of Physical Chemistiy, 64, 1151-1156(September, 1960).

118. “Some Aspects of Durability and Volume Change of Concrete for Pre-stressing,” by PAUL KLIEGER.

Reprinted from the Jou?’ncctof the PCA Resea~ch a?td Development Labora-tories, 2, No. 3, 2-12 (September, 1960).

119. “Concrete Mix Water—How Impure Can It Be?” by HAROLD H. STEINOUR.Reprinted from the Journal of the PCA Research and Development Labora-tories, 2, No. 3, 32-50 (September, 1960).

120. “Corrosion of Prestressed Wire in Concrete, ” by G. E. MONFOREandG. J. VERBECK.

Reprinted from Jou?wcd of the American Concrete Institute (November, 1960);Proceedings, 57, 491-515 (September, 1960).

121. “Freezing and Thawing Tests of Lightweight Aggregate Concrete,” byPAUL KLIEGERand J. A. HANSON.

Reprinted from Journat of the American Concrete Institute (January, 1961):P~oceedirzgs, 57, 779-796 (1961).

122. “A Cement-Aggregate Reaction That occurs With Certain Sand-GravelAggregates,” by WILLIAM LERCH.

Reprintedfrom the Journal of the PCA Research and Development Laborato-ries, 1, No. 3. 42-50 (September, 1959).

123. “Volume Changes of Concrete Affected by Aggregate Type,” byHAROLD ROPER.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 2, No. 3, 13-19 (September, 1960).

124. “A Short Method for the Flame Photometric Determination of Magne-sium, Manganic, Sodium, and Potassium Oxides in Portland Cement, ”by C. L. FORD.

Reprinted from ASTM BuUetin, No. 2.50, 25-29, (December, 1960).

125. “’Some Physical Aspects of the Hydration of Portland Cement,” byT. C. POWERS.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 3, No. 1, 47-56 (January, 1961).

126. “Influence of Physical Characteristics of Aggregates on Frost Re-

sistance of Concrete, ” by GEORGE VERBECK and ROBERT LANDGREN.

Reprinted from Proceedings of the American Society for Testing Materials, 60,1063-1079 (1980) .

127. “Determination of the Free Calcium Hydroxide Contents of HydratedPortland Cements and Calcium Silicate s,” by E. E. PRESSLER, STEpHEN

BRUNAUER, D. L. KANTRO, and C. H. WEISE.

Reprinted from Analytical Chemkt?w,33, No. 7, 877-882(June, 1961).

128. “An X.ray Diffraction Investigation of Hydrated Portland CementPastes,” by D. L. KANTRO, L. E. COPELAND, and ELAINE R. ANDERSON.

Reprinted from Proceedings of the American Society for Testing Materials, 60,1020-1035 (1960) .

129. “Dimensional Changes of Hardened Portland Cement Pastes Causedby Temperature Changes,” by R. A. HELMUTH.

Reprinted from Highway Research Board Proceedings, 40, 315-336 (1961).

130. “Progress in the Chemistry of Portland Cement, 1887-1960,” by HAROLDH.STEINOUR.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 3, No. 2, 2-11 (May, 1981).

131. “Research on Fire Resistance of Prestressed Concrete,” by HUBERT

WOODS, including discussion by V. PASCHKIS, and author’s closure.

Reprinted from Journal of the Structural Division, Proceedings of the Ameri-can Society of Civil E7Wi?ZeeTS, Proc. Paper 2640, 86, ST 11, 53-64 (November,1960); Discussion, 87, ST 2, 59-80 (February, 1961); Closure, 87, ST 5, 81 (June,1961).

132. “Centralized Control of Test Furnaces in the PCA Fire Research Labo.ratory, ” by PHIL J. TATMAN.

Reprinted from the Journal of the PCA Research and Development Labora-to~ies, 3, No. 2, 22-26 (May, 1961).

133. “A Proposed Simple Test Method for Determining the Permeability of

Concrete, ” by I. L. TYLER and BERNARD ERLIN.Reprinted from the Journal of the PCA Research and Development Labora-tories, 3, No. 3, 2-7 (September, 1981).

134. “The Behavior at High Temperature of Steel Strand for Prestressed

Concrete, ” by M. S. ABRAMS and C. R. CRUZ.Reprinted from the Journal of the PCA Research and Development Labora-tories, 3, No. 3, 8-19 (September, 1961).

135. “Electron optical Investigation of the Hydration Products of CalciumSilicates and Portland Cement,” by L. E. COPELAND and EDITH G. SCHULZ.

Reprinted from the Journal of the PCA Research and Development Labora-to~ies, 4, No. 1, 2-12 (January, 1962).

136. “Soil-Cement Technology—A Resume,” by MILES D. CATTON.Reprinted from the Journal of the PCA Resea?ch and Development Labora-tories 4, No. 1, 13-21 (January, 1962).

137. “Surface Temperature Measurements With Felted Asbestos Pads, ” byM. S. ABRAMS.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 4, No. 1, 22-3o (January. 1962).

138. “Tobermorite Gel—The Heart of Concrete, ” by STEPHEN BRUNAUER.

Reprinted from the American Scientist, 50, No. 1, 210-229 (March, 1962).

139. “Alkali Reactivity of Carbonate Rocks—Expansion and Dedolomitiza-tion,” by DAVID W. HADLEY.

Reprinted from Highway Research Board Proceedings, 40, 462-474 (1961 ).

140. “Development of Surface in the Hydration of Calcium Silicates,” bv

141.

142.

143.

144.

145.

146.

147.

148.

149.

150.

151,

D. L. K&TRO, STEPHEN BRUNAUER, and c. H. WEISSI.. .

Reprinted from Sofid Surfaces and the Gas-Solid Interface, Advances inChemistry Series 33, 199-219 (1961).

“Thermodynamic Theory of Adsorption,” by L. E. COPELAND and T. F.YOUNG.

Reprinted from Sofid Surfaces and the Gas-Solid Interface, Advances inChemistry Series 33, 348-356 (1961),

and“Thermodynamics of Adsorption. Barium Sulphate—Water System,” byY. C. Wu and L. E. COPELAND.

Reprinted from Solid Surfaces and the Gas-Solid lnterfar.e, Advances inChemistry Series 33, 357-368(1961).

“The New Beam Furnace at PCA and Some Experience Gained fromIts Use,” by C. C. CARLSON and PHIL J. TATMAN.

Reprinted from Symposium on Fire Test Methods. ASTM Special TechnicalPublication No. 301, 41-59 (1961).

“New Techniques for Temperature and Humidity Control in X-Ray Dif -fractometry,” by PAUL SELIGMANN and N. R. GREENING.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 4, No. 2, 2-9 (May, 1962).

“An Optical Method for Determining the Elastic Constants of Concrete,”by C. R. CRUZ.

Reprinted from the Journal of the PCA Research and Development Labora-to~ies, 4, No. 2, 24-32 (May, 1962).

“Physical Properties of Concrete at Very Low Temperatures, ” by G. E.MONFOREand A. E. LENTZ.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 4, No. 2, 33-39 (May, 1962).

“A Hypothesis on Carbonation Shrinkage,” by T. C. POWERS.Reprinted from the Journal of the PCA Research and Development Labora-to~ies, 4, No. 2, 40-50 (May, 1962).

“Fire Resistance of Prestressed Concrete Beams. Study A — Influenceof Thickness of Concrete Covering Over Prestressing Steel Strand, ” byC. C. CARLSON,

Published by Portland Cement Association, Research and Development Labora-tories, Skokie, Illinois, (July, 1962).

“Prevention of Frost Damage to Green Concrete,” by T. C. POWERS.

Reprinted from R&inion Intewsationale des Laboratoi?’es d’llssais et de Re-cherches SW’ les Mat&iatsx et les Constructions, RILEM Bulletin 14, 120-124(March, 1962).

“Air Content of Hardened Concrete by a High-Pressure Method,” byBERNARD ERLIN.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 4, No. 3, 24-29 (September, 1962).

“A Direct Current Strain Bridge, ” and “A Biaxial Strain Apparatus forSmall Cylinders, ” by G. E. MONFORE.

Reprinted from the Journal of the PCA Research and Development Labora-tories, 4, No. 3. 2-9 (September, 1962).

“Development of Surface in the Hydration of Calcium Silicates. II. Ex-tension of Investigations to Earlier and Later Stages of Hydration,”by D. L. KANTRO, STEPHEN BRUNAUER, and C. H. WEISE.

~&inted from The Joarnal of PhysicaZ Cizernist?w, 66, No. 10, 1804-9 (October,

152. “The Hydration of Tricalcium Silicate and ,B-Dicalcium Silicate at

Room Temperature, ” by STEPHEN BRUNAUER and S. A. GREENBERG.

Reprinted from Chemistry of Cement, Proceedings of the Fow-tiz InternationalSymposium, Washington, D. C., 1960, held at the National Bureau of Standards(U.S. Department of Commerce), Monograph 43, Vol. I, Session III, PaperIII-1, 135-165.

153. “Chemistry of Hydration of Portland Cement,” by L. E. COPELAND, D. L.

KANTRO, and GEORGE VERBECK.Reprinted from Chemistry of Cement, Proceedings of the Fourth InternationalSymposium, Washington, D. C., 1960, held at the National Bureau of Standards(U.S. Department of Commerce), Monograph 43, Vol. I, Session IV, PaperIV-3, 429-465.

154. “Physical Properties of Cement Paste, ” by T. C. POWERS.Reprinted from Chemistry of Cement, Proceedings of the Fourth IntQTnatiOnaLSymposium, Washington, D. C., 1960, held at the National Bureau of Standards(U.S. Department of Commerce), Monograph 43, Vol. II, Session V, Paperv-1, 577-609.

Printed in U.S.A.