Analysis of the Multilayer Thickness Relationshipfor Water Vapor and Nitrogen Adsorption

Abdul Raoof,*,1 Jean-Pierre Guilbaud,* Henri Van Damme,† Patrice Porion,† and Pierre Levitz†

*LMSGC, 2, alle´e Kepler, 77420 Champs-sur-Marne, France; and†CRMD, 1B Rue de la Fe´rollerie, 45071 Orleans Cedex 2, France

Received October 30, 1996; accepted June 19, 1998

Six silica gels, where each gel had a characteristic calibrated poresize (40–4000 Å), have been characterized both by water vapor andnitrogen adsorption isotherms. From these results, it was concludedthat two-thirds of the silica surface is hydrophobic. The selection ofwide pores (>300 Å) has enabled the determination of both the waterand nitrogen t-curves for porous silica. It was observed that thedevelopment of the multilayer was identical in the wide pores irre-spective of their size between 300 and 4000 Å. The porous silicat-curve for water coincided exactly with the t-curve of nonporousadsorbents provided that their BET C constants were similar. Fornitrogen t-curves, a matching BET C constant ensured similarity onlyin the monolayer region, above which divergence progressively in-creased, becoming important close to saturation. The effect of thet-curve choice on the pore size distribution was established. A t-curvedisplaying reduced adsorption had a tendency to shift the pore-sizedistribution to lower dimensions, toward the micropore region. As aconsequence, the cumulated surface area obtained from the BJHmodel gave increasingly higher values than the BET nitrogen surfacearea. However, the pore-size distribution was shifted to higher poresizes when the selected t-curve was above the natural t-curve. Errorsas much as 25% were detected for the mean pore radius and cumu-lated surface area for certain literature t-curves. A comparison of thewater and the nitrogen t-curves indicated a crossover point when thewater multilayer thickness became greater than the nitrogen thick-ness. Such behavior lends support to the cooperative adsorptionmechanism for water vapor once a fixed number of water molecules(two layers) are present on the surface. © 1998 Academic Press

Key Words: silica gel; adsorption; water vapor; nitrogen; t-curves; pore-size distribution; cooperative adsorption.

1. INTRODUCTION

Adsorption isotherms are useful to characterize the micro-structural properties of materials. The BET model (1, 2) allowsthe assessment of the surface area of a material. The Gurvitsch(3) relationship allows the quantification of the pore volume atsaturation. The pore size distribution may be obtained by usingthe BJH model (4). The pore size distribution is an importantproperty for the characterization and comparison of materials.

Once these microstructural properties have been obtained, theycan then be incorporated into numerical models for the simu-lation and prediction of the macroscopic properties. For exam-ple, it is possible to simulate the wetting and drying behaviorof civil engineering materials and hence their deformationand/or degradation under different environmental exposureconditions.

The BJH model is based on a two-step process in which thedesorption of the capillary condensate is accompanied by areduction of the multilayer thickness. The multilayer is thevapor which is adsorbed on the pore wall before capillarycondensation takes place. The increase in the quantity of vaporadsorbed on the pore wall as a function of the relative pressureis known as at-curve or the multilayer thickness. Thet-curveof a nonporous adsorbent is not only essential for the pore sizedistribution but also for thet-method developed by Lippensand de Boer (5) and theas method proposed by Sing (6, 7). Thet-method enables the calculation of the surface area and thedetection of micropores, from aVa 2 t plot. Where,Va is thevolume of nitrogen adsorbed in cubic centimeters per gram atSTP of adsorbent andt is the thickness of the multilayer.

Several relationships exist in the literature indicating theincrease in the thickness of the adsorbed layert as a functionof the relative pressure (p/po). Initially, it was argued that a“universal” t-curve existed for all nonporous materials. It wassuggested that this universalt-curve was independant of thenature of the sample. Later, this idea was revised, andt-curveswere proposed as a function of the physicochemical and ther-modynamical nature of the sample. The nature of the samplewas interpreted in terms of theC constant of the BET equation.It was established that thet-curve was quite sensitive in the lowrelative pressure region to the heat of adsorption of the vaporon the sample surface. Under these circumstances, severalt-curves were advocated with the choice depending upon theCconstant. Hagymassyet al. (8, 9) proposed fivet-curves in thelow-pressure region (p/po , 0.50) and two in the higher-pressure region. Lecloux and Pirard (10) also proposed fivet-curves in the monolayer region (p/po , 0.40) and two athigher relative pressures. In each case, the authors classed thet-curves according to a range of values of theC constant. Thediversity of thet-curve around the monolayer region, which

1 To whom correspondance should be addressed at: Laboratoire des Mate´-riaux et des Structures du Ge´nie Civil (LMSGC), 2, allee Kepler, 77420Champs-sur-Marne, France.

JOURNAL OF COLLOID AND INTERFACE SCIENCE206,1–9 (1998)ARTICLE NO. CS985704

1 0021-9797/98 $25.00Copyright © 1998 by Academic Press

All rights of reproduction in any form reserved.

diminished or disappeared at higher relative pressures, becamewidely accepted.

Most of the t-curves available in the literature have beenmeasured on nonporous materials which were thought to havea similar chemical surface as to the adsorbent in question.Nonporous materials having a similar BETC constant to theporous material in question are still used for microstructureanalysis. Nitrogent-curves on aluminium hydroxides and ox-ides were measured by de Boer (11, 12). Hagymassyet al. (8)were among the first to measure watert-curves for the analysisof the microtexture of cement pastes. Water was employedbecause it was the principal agent which was responsible fordamage to construction materials. However, theset-curveswere also measured on nonporous metallic hydroxides, oxides,and silicas. In using nonporous adsorbents, there is always therisk that a similart-curve will not be obtained within poreswhere the surrounding walls provide overlapping surfaceforces. Girgis (13) derived a single multilayer curve from theadsorption of nitrogen on 26 different samples of silica gel.The drawback of Girgis’ empirical equation is that severalmicroporous silica samples were included. The presence ofmicropores increased the thickness of the multilayer, becauseof micropore filling, in comparison to previoust-curves. Anadded problem is that with certain sizes of nonporous adsor-bents, there is the possibility of interparticle capillary conden-sation. This phenomenon was observed by Hagymassyet al.(8) for certain nonporous silica.

The present research concerns water and nitrogent-curveson silica gels. As there is ever increasing interest in manyindustrial sectors in the behaviour of water (e.g., constructionand chemical engineering industries) more attention has beenpaid to this adsorbate. Whereas the bulk of the previous mea-surements have been on non-porous materials, the presentstudy has chosen porous materials in order to assess the effectof the pore walls on the multilayer thickness. The objective isto compare the presentt-curves with those already existing,

and above all to evaluate the effect of thet-curve choice on thepore size distribution calculation. A comparison will also bemade of the silica gel behaviour with both adsorbates.

2. MATERIALS AND METHODS

Six chromatographic silica gels were obtained from Mercks.a., Darmstadt. Five of these consisted of calibrated monodis-perse spherical particles of 10mm diameter. The dispersion ofthe particle size was small and was confirmed by a lasergranulometric test (Fig. 1). The pore size distribution was quitenarrow in each sample as required in analytical separationprocesses. The pore sizes selected were 60, 100, 300, 1000, and4000 Å, enabling the coverage of a wide range of pores. Thenumerical figure represents the diameter of the pore space asmeasured by nitrogen adsorption or electron microscope ob-servations. This series was sold under the brand name ofLiChrospher, and therefore the series was denoted LS.

Another silica gel was selected in order to allow the studyof narrower pore sizes. The narrowest pore size available forthe LS series was 60 Å. A pore size of 40 Å (silica gel,Merck, grade 10180, 70 –230 mesh) was selected and thesample was labeled LP 40. The geometry and granulometrywere much more irregular for this silica than the LiChro-spher series (Fig. 2). The particles were irregular polygonsof diameter ranging from 63 to 200mm. These observationswere confirmed by electron microscope analysis and lasergranulometry experiments.

The wide pore sized silicas (LS 300, LS 1000 and LS 4000)were obtained in order to assess thet-curve on porous solidsinstead of the standard nonporous materials previously used.Interparticle capillary condensation was avoided because thespace between the particles (approximately 3mm) was toolarge for capillary condensation of the vapor. The pore size was

FIG. 1. Distribution of the diameter of the LS 60 spheres as measured bylaser granulometry.

FIG. 2. Distribution of the size of the LP 60 grains as measured by lasergranulometry.

2 RAOOF ET AL.

also too large for capillary condensation; hence, the onlyprocess occurring in these silicas was the development of themultilayer inside the pores.

Adsorption measurements were conducted on a self-con-structed automatic gravimetric apparatus (14, 15). The appa-ratus was used in the quasi-equilibrium mode (i.e., continuousinjection of water vapor), but the possibility of static measure-ments existed. The continuous measurement of the completeadsorption isotherm was initiated by Lange (16) in 1963. Theapparatus constructed for this study was similar to the one builtby Rouque´rol et al. (17, 18), who showed clearly the advan-tages of the continuous method. He was able to detect thechange of phase on the nitrogen/graphite and argon/graphiteisotherms which had not been possible previously with staticadsorption methods. Double distilled water was used for themeasurements, which were conducted at a temperature of23.06 0.1°C. The rate of water vapor injection was 0.278 mLzs21. This rate was checked to ensure that quasiequilibrium wasmaintained during the measurement by repeating the experi-ment at lower injection rates or by closing the injection valve.In general, 130 mg of silica gel were used for each experiment.Approximately, a week was necessary for the measurement ofthe adsorption–desorption isotherm.

Nitrogen isotherms were measured on a volumetric Micro-meritics Autosorb ASAP 2000 apparatus. The liquid nitrogen

temperature was 77.35 K. On average, 45 points were mea-sured on each branch of the isotherm. The average mass of thesamples was 0.50 g. Approximately 15 hours were necessaryfor the measurement of the complete isotherm.

The samples were preheated in an oven at 115°C for 12hours to remove any physically adsorbed water. Higher tem-peratures were not used in order to avoid dehydroxylation ofthe silica surface.

The surface areas were determined by the use of the BETequation. The Gurvitsch volume was also calculated. The poresize distributions were determined by the use of the BJHmodel. Thet-curve employed was as specified in the text.

3. RESULTS AND DISCUSSION

Characterization of the Silica Gels

The water and nitrogen adsorption isotherms of the six silicagels were measured. The results are presented in Tables 1 and2. A striking difference between the results is that the watersurface area is approximately a third of that obtained fromnitrogen. This suggests that the bulk of the silica surface ishydrophobic. The hydrophobic character of certain silica gelsis a common occurrence and has been commented upon bymany authors (19–21). The pore volume at a relative pressure

TABLE 1Microstructural Parameters Obtained from Water Vapor Isotherms

Sample

Water vapor

BET constant,C

BET surface area(m2 g21)

Pore radius(Å)

Pore volume(cm3 g21)

BJH surface area(m2 g21)

BJH pore volume(cm3 g21)

LP 40 14.0 209.6 25.5 0.58 490.9 0.67

LS 60 8.7 257.7 28.0 0.72 567.8 0.81LS 100 11.6 142.5 55.0 1.15 465.3 1.30LS 300 13.1 13.8 — — — —LS 1000 14.7 6.3 — — — —LS 4000 14.9 3.1 — — — —

TABLE 2Microstructural Parameters Obtained from Nitrogen Isotherms

Sample

Nitrogen

BET constant,C

BET surface area(m2 g21)

Pore radius(Å)

Pore volume(cm3 g21)

BJH surface area(m2 g21)

BJH pore volume(cm3 g21)

LP 40 67.2 556.8 20.0 0.62 701.9 0.66

LS 60 85.3 526.6 26.0 0.66 630.0 0.76LS 100 103.1 385.1 60.0 1.19 471.4 1.22LS 300 — 50.7 — — — —LS 1000 — 24.5 — — — —LS 4000 102.6 10.0 — — — —

3MULTILAYER THICKNESS WATER NITROGEN ADSORPTION

of 0.95 for the two adsorbates is identical (65%) as predictedby the Gurvitsch rule. The mean pore radii of the samples forboth adsorbates are quite similar, taking into account experi-mental errors.

Water Vapor t-Curves

The monolayer capacity (Xm) was obtained from the BETequation, and this was then used to estimate the number oflayers present on the pore wall surface. Figure 3 shows themultilayer thickness for LS 60, LS 300, LS 1000, and LS 4000.All four curves are identical in the monolayer region. Thisindicates that they all possess a similar physicochemical andthermodynamical nature. The BETC constant for the materials(ranging from 8.7 to 14.9) is quite similar; therefore, suchbehavior is to be expected. Once the monolayer is complete,the LS 60t-curve begins to diverge from the others indicatingthe onset of volume filling/capillary condensation in the nar-rower pores. The divergence begins at a relative pressure of0.40, which corresponds to a Kelvin radius of 12 Å, suggestingthe presence of pores of radii smaller than 12 Å in the LS 60sample. The LS 100t-curve (not illustrated) started to divergefrom the LS 300t-curve at a relative pressure of 0.55, corre-sponding to a Kelvin radius of 20 Å. It is quite possible that inthese narrow pore silica gels (LP 40, LS 60, and LS 100) adistribution of pore sizes, including micropores, exists.

However, thet-curves for the three wide pore sizes (LS 300,LS 1000, LS 4000) are identical in the complete pressureregion. The superposition of the threet-curves indicates thatthe construction of the multilayer occurs in exactly the sameway whether the pore size is 300 or 4000 Å. The proximity oftheset-curves also indicates that no appreciable quantity ofmicro- or mesopores exist within the samples to cause anupward deviation from the standardt-curve. The results also

imply that the physicochemical and thermodynamical nature ofthe three materials is identical.

At saturation, seven water layers are present. This is inagreement with the conclusions of Hagymassyet al. whomeasured six water layers on metallic hydroxides and oxides.Hagymassy conducted his experimental measurements usingthe dessicator method (8, 9) with saturated saline solutions.The exact control of the desired relative pressure is a precari-ous affair, in particular close to saturation. Croneyet al. (22)showed that the effect of temperature gradients between thesample and the saturated saline solution is important aboverelative pressures of 0.93. Therefore, the difference of onelayer may be attributed to the uncertainty of the relative pres-sure of the Hagymassy measurement.

The water t-curve for the silica gels used has also beendetermined. Figure 4 compares thet-curve for LS 4000 withthose available from literature. The Hagymassyt-curve (BETC constant range5 10 to 14.5) is quite similar to the LS 4000one. The difference arises above a relative pressure of 0.85(Kelvin radius5 70 Å). The materials used by Hagymassyetal. varied widely and included silica gels, anatase, bariumsulphate, and quartz. In the higher relative pressure region,Hagymassyet al.(8) propose twot-curves, one for aC constantof 5.2 and the other forC constants between 10 and 200. TheBET C constant for LS 4000 was 14.9. The reduced adsorptionmay be a result of the fact that the Hagymassyet al. t-curve isan average of six of their curves and five from literature and isproposed for a large range of C constants.

An unusualt-curve is the one from Naonoet al. (23–25).These authors measured the watert-curve on Aerosil-200(Nippon Aerosil Co.), a nonporous silica. The numericalfigure of 200 represents the BET nitrogen specific surfacearea in square meters per gram. The LS 4000 and theHagymassyet al. t-curves show a small knee before mono-

FIG. 4. Comparison with the literaturet-curves using water vapor [LS4000 (—), Naonoet al. (x), Hagymassyet al. (E).

FIG. 3. Comparison of thet-curves using water vapor for the silica gels[LS 60 (—), LS 300 (E), LS 1000 (*), LS 4000 (x)].

4 RAOOF ET AL.

layer completion. However, in the Naonoet al. t-curve, sucha knee is absent, and the isotherm ressembles a type IIIisotherm, according to the BDDT and the IUPAC classifi-cations (26, 27). In the entire pressure region, the Naonoetal. t-curve is significantly lower than the other twot-curves.It is unusual because a monolayer is formed at a relativepressure of 0.65, which seems a little high for monolayercompletion. The shift of thet-curve measured by Naonoetal. may be caused by the determination of the multilayerthickness,t. The authors used the formula

t ~nm! 5 ~Vliq/SBET!1023, [1]

where Vliq is the volume of liquid adsorbate adsorbed by thematerial (cm3 g21), andSBET is the nitrogen surface area (m2 g21).

However, the Aerosil class of silicas appears to be extremelyhydrophobic, even though the manufacturer classes them as“hydrophilic.” An Aerosil-90 nonporous silica was obtainedfrom Degussa s.a., France, as a test case. The Aerosil-90 wasa pyrogenic silica (flame hydrolysis at high temperatures),consisting of spherical particles of 20 nm average diameter.The particle diameter ranged from 8 to 50 nm. The surface wasconsidered as smooth and nonporous. The nitrogen BET sur-face area was given as 906 15 m2 g21 by the manufacturer.A verification of the nitrogen BET surface area was performedby using the three-point BET method. The resulting surfacearea was 906 15 m2 g21. The water surface area was alsomeasured at 23.0°C. The water surface area measured was only1.2 m2 g21. This suggests that 98.6% of the Aerosil-90 surfaceis hydrophobic. Thet-curve resulting from this sample couldnot be used because of the onset of capillary condensation at arelative pressure of 0.42.

The capillary condensation occurred in the interparticle space.The values of the water surface area of Aerosil-90 indicate that it

has a largely hydrophobic surface area; hence, the resultingt-curve is questionable for use with other materials.

Effect of the Water t-Curve on the Pore Size Distribution

The effect of the Hagymassyet al. and Naonoet al. watert-curves on the pore size distribution was evaluated and ispresented in Figs. 5 and 6. Figure 5 shows the effect of theset-curves on the LS 100 sample and figure 6 on the LP 40sample. The numerical parameters obtained from this analysisare presented in Table 3.

For the LS 100 sample there is relatively little difference, asexpected, between the distributions from the use of the Hagy-massyet al. and LS 4000t-curves. However, the use of theNaono et al. t-curve displaces the pore size distribution tosmaller pore sizes. The pore radius peak maximum is displacedfrom 55 to 51 Å. The effect of this displacement on thenumerical parameters is seen to be relatively important.Whereas, for the Hagymassyet al. t-curve, equivalent cumu-lative BJH surface area and volume were obtained, the Noanoet al. t-curve creates significant differences. The Naono cumu-lated surface area is 3% higher, and the cumulated volume is13% lower than the values from the other twot-curves. Thesedifferences arise because the Naonot-curve tends to shift thepore size distribution to smaller pore sizes, in particular towardthe micropore region. In the micropore region, the surface areais increased, and the condensate pore volume is reduced.

The effect on the LP40 sample is similar but more signifi-cant. The Hagymassyt-curve gives numerical values similar tothe LS4000t-curve. The small differences on the order of 3%can be ascribed to experimental error. However, the Naonot-curve once again shows important differences. The pore sizepeak maximum is displaced from 28 to 22 Å. The cumulatedBJH surface area is 25% higher, and the pore volume is 12%lower. In Fig. 6, it is seen that the pore size distribution isdisplaced to smaller pore sizes toward the micropore region.

FIG. 5. Effect of the watert-curve choice on the pore size distribution forLS 100 [LS 4000 (— x), Naonoet al. ( z *), and Hagymassyet al. (— z E)].

FIG. 6. Effect of the watert-curve choice on the pore size distribution forLS 40 [LS 4000 (— x), Naonoet al. ( z *), Hagymassyet al. (— z E)].

5MULTILAYER THICKNESS WATER NITROGEN ADSORPTION

The similarity between the results from the Hagymassy andLS 4000t-curves stems from the fact that capillary condensa-tion occurs in these samples at relative pressures where the twocurves are identical. For LS 60, for example, capillary conden-sation occurs at a relative pressure of 0.7. To evaluate furtherthe effect of the Hagymassyt-curve, it is necessary to selectsamples with pore diameters larger than 180 Å because it isonly in this region that differences arise between thet-curves.

The Naono and Hakuman watert-curve appears unsuitablefor general pore size distribution analysis because it has atendency to shift the pore size distribution to smaller sizes.

Nitrogen t-Curves

The nitrogen isotherms were measured for these samplesusing the volumetric apparatus in the static mode. Thet-curveswere once again determined by the calculation of the BETmonolayer capacity, which was then used to determine thenumber of layers adsorbed on the pore walls. In Fig. 7, acomparison is made between thet-curves of LS 4000, de Boer,Girgis (13), and Lecloux and Pirard (10). The Girgist-curve issuperior in the entire pressure range because of the inclusion ofmicroporous silicas in the sample set as mentioned earlier.Hence, the widespread use of the Girgist-curve does notappear reasonable.

The de Boert-curve is similar to the LS 4000 one around themonolayer region. However, an increasing divergence occursabove relative pressures of 0.30. At a relative pressure of 0.70there is a difference of half a layer, which increases to twolayers at a value of 0.93. The Lecloux and Pirardt-curve formaterials with a BETC constant between 100 and 300 is alsoincluded. The nitrogenC constant value of LS 4000 was 103.There is an increased range of similarity between thet-curveproposed by Lecloux and the LS 4000t-curve. Deviation fromthe measured LS 4000t-curve occurs at relative pressuresgreater than 0.60. However, when a relative pressure of 0.95 isreached, two extra layers are present on the Leclouxt-curve.These results suggest that the similarity of the BETC constants

alone is insufficient for agreement of the nitrogent-curves onnonporous and porous adsorbents, as was found for the watert-curves.

Effect of the Nitrogen t-Curve on the Pore Size Distribution

In order to judge the effect of the particlar nature of thet-curve on the pore size distribution, only the Girgis and deBoer t-curves were used. Theset-curves afforded the largestdifference from the LS 4000t-curve and promised thegreatest impact on the pore size distribution. The importantdifferences between the chosent-curves arise in the highrelative pressure range around 0.80. This pressure rangecorresponds to Kelvin pore radii greater than 100 Å. Thepore size distribution results for LS 100 are presented in Fig.8 and the complete set of results is presented in Table 4. InFig. 8, it is observed that the pore size distribution is offsetto higher pore radii as the divergence increases between the

TABLE 3Effect of the Water Vapor t-Curve Choice on the Pore Size Distribution Parameters

Sample t-curvePore radius

(Å) % errorBJH surface area

(m2 g21) % errorBJH volume(cm3 g21) % error

LP 40 LS 4000 28 — 481.0 — 0.67 —LP 40 Hagymassy 28 0 464.6 3 0.65 2LP 40 Naono 22 21 599.6 24 0.59 12

LS 60 LS 4000 25 — 567.8 — 0.81 —LS 60 Hagymassy 25 0 553.5 3 0.80 2LS 60 Naono 20 20 682.3 20 0.71 12

LS 100 LS 4000 55 — 465.3 — 1.29 —LS 100 Hagymassy 54 2 469.8 1 1.30 0LS 100 Naono 51 7 477.3 3 1.14 12

FIG. 7. Comparison of the literature nitrogent-curves (LS 4000 (—),Girgis (— z x), de Boeret al. (E), Leclouxet al. (*).

6 RAOOF ET AL.

t-curves. This shift was expected as earlier a shift in theopposite direction was observed when the Naonot-curvewas below the LS 4000 one. Presently, the literaturet-curves are situated above the LS 4000t-curve. The pore sizedistribution obtained from the use of the Girgist-curve isdisplaced approximately 4 Å to higher pore dimensions.

Table 4 shows that there is an increasing difference for theBJH cumulated surface area and pore volume as the pore sizeof the material increases and as thet-curve difference in-creases. For the LP 40 sample, the de Boer cumulated surfacearea is 15% lower; however, for the LS 100 sample, thisdifference increases to 17%. For LS 100, the de Boer cumu-lated surface area is 17% lower, whereas the Girgis surfacearea is 26% lower. These results indicate the importance of thecorrect choice of thet-curve for pore size distribution analysis.

Comparison of the Water and Nitrogen t-Curves

A comparison of thet-curve of the two adsorbates on LS4000 is presented in Fig. 9. This time they-axis is the

thickness of the multilayer (Å) instead of the number oflayers as presented previously. An interesting feature is thecross-over of the two curves at a relative pressure of 0.6.Below this value, the thickness of the nitrogen layer isgreater than that of the water layer. At a relative pressure of0.1, the average thickness of the nitrogen layer is almost 4Å, which implies more than a single layer assuming that thenitrogen molecule has a diameter of 3.5 Å. However, at thispressure value, the water layer is only 2 Å thick, which isless than the diameter of the water molecule (3 Å). Thedifference is the result of the hydrophobic nature of thesilica gel surface. Earlier, it was observed that approxi-mately two thirds of the silica surface was hydrophobic.

The differences between the behavior of the two adsorbatesmay arise from the calculation of the monolayer capacity,Xm

from the original BET equation. This method is prone toinducing errors because the BET theory supposes that themultilayer adsorption goes on parallel (fromp/po 5 0) with the

FIG. 8. Effect of the nitrogent-curve choice on the pore size distribution[LS4000 (—E), de Boeret al. (— z x), and Girgis (*)].

TABLE 4Effect of the Nitrogen t-Curve Choice on the Pore Size Distribution Parameters

Sample t-curvePore radius

(Å) % errorBJH surface area

(m2 g21) % errorBJH volume(cm3 g21) % error

LP 40 LS 4000 20.0 — 474.7 — 0.48 —LP 40 de Boer 20.6 3 403.3 15 0.45 6LP 40 Girgis 22.0 10 363.3 23 0.45 6

LS 60 LS 4000 29.6 — 538.0 — 0.69 —LS 60 de Boer 30.7 4 444.1 17 0.65 6LS 60 Girgis 32.8 11 399.8 26 0.65 6

LS 100 LS 4000 65.0 — 460.7 — 1.21 —LS 100 de Boer 68.7 4 381.4 17 1.17 3LS 100 Girgis 72.5 11 342.1 26 1.18 2

FIG. 9. Comparison of the water and nitrogent-curves measured on LS4000 [nitrogen (E) and water (—)].

7MULTILAYER THICKNESS WATER NITROGEN ADSORPTION

monolayer one. Hence, according to the BET theory, a puremonolayer domain does not exist. However, in practice often apure monolayer domain exists and multilayer adsorption be-gins only at a definite pressure,p/po @ 0. The monolayerdomain in water vapor isotherms is much wider than that innitrogen isotherms; approximatelyp/po ' 0.01 2 0.02 fornitrogen andp/po ' 0.22 0.4 for water vapor. This differencecan introduce errors in the calculation of thet-curves for watervapor. However, for the comparison of thet-curves for the twoadsorbates with those found in the literature, this calculationmethod was unavoidable.

The difference between the multilayer thickness of the twoadsorbates diminishes as the relative pressure is increased untilapproximately two layers of each adsorbate are adsorbed. Atthis point, the thickness of the water layer becomes greater thanthat of the nitrogen layer. At a relative pressure of 0.95, thewater layer is 3 Å greater than the nitrogen layer. The increasedadsorption of water vapor is probably the result of a coopera-tive adsorption mechanism. Initially, the water molecules arereluctant to adsorb on to the hydrophobic surface and theweakness of the adsorbent–adsorbate interaction. However,once two layers are present on the surface, the adsorbate–adsorbate forces become dominant, and these forces promotethe adsorption of further molecules of water. For nitrogen, thedominant interaction is the adsorbent–adsorbate one, which isparticularly important in the construction of the first layer.With the formation of successive layers, the interaction forcewith the surface diminishes. However, the decrease in theadsorbent–adsorbate forces is not compensated for by a respec-tive increase in the forces between the adsorbate molecules asin the case of water.

Douillard et al. (28) measured the water and nitrogenadsorption isotherms of a nonporous silica sample (Sphero-sil XOB 015 LS, Rhoˆne Poulenc Chemical). In theirt-curvesthe thickness of the nitrogen layer was always superior tothe water layer one. However, the progressive increase ofthe relative pressure diminished the difference between thetwo t-curves, until close to saturation (p/po 5 0.85) wherethe two curves merged together. No cross-over point wasobserved by Douillardet al.,even though their silica surfacewas also hydrophobic.

4. SUMMARY

An analysis of six largely hydrophobic silica gels ofdifferent pore radii (20 –2000 Å) has been effected by themeasurement of water vapor and nitrogen isotherms. Theselection of wide pores (300 – 4000 Å) has enabled themeasurement of thet-curves, for both adsorbates, and al-lowed a comparison with thet-curves for nonporous adsor-bents in the literature. The multilayer growth was identicalirrespective of the pore radius of the wide pore silica gels.Approximately seven layers were present at saturation onthe pore walls. For water vapor, the porous silicat-curves

coincided exactly with thet-curves for nonporous adsor-bents proposed by Hagymassy provided that their BETCconstants were similar. However, for the nitrogent-curves,a matching of the BETC constant ensured similarity only inthe monolayer region, above which divergence progres-sively increased, becoming important close to saturation.

The effect of thet-curve choice on the pore size distributioncalculation by the BJH model was established. At-curvedisplaying reduced adsorption had a tendency to shift the poresize distribution to lower dimensions, toward the microporeregion. As a consequence, the BJH cumulated surface areagave higher values than the BET nitrogen surface area, and theBJH cumulated volume was reduced. The reverse behavior wasobserved when the chosent-curve had a higher multilayerthickness than the naturalt-curve of the silica gels. A greaterdivergence between thet-curves increased the differences be-tween the numerical pore size distribution parameters. Errorsas much as 25% were detected on the selection of certainliteraturet-curves.

Finally, a comparison of the water vapor and the nitrogent-curves indicated a cross-over point when the water multilayerthickness became greater than the nitrogen thickness. Suchbehavior lends support to the cooperative adsorption mecha-nism for water vapor once a fixed number of water molecules(two layers) are present on the surface. However, one must takeinto account the limitations of the original BET theory and theinherent difficulties in the exact determination of the mono-layer domain.

ACKNOWLEDGMENT

The authors thank Herve´ Gaillard (INRA, Orleans, France) for havingkindly carried out the nitrogen adsorption measurements.

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9MULTILAYER THICKNESS WATER NITROGEN ADSORPTION