Proc. Nat. Acad. S&. USAVol. 69, No. 4, pp. 829-833, April 1972

Conductance in Water-Poly(vinyl alcohol) Mixtures(viscosity/diffusion-controlled reactions/polymer solutions)

JIRO KOMIYAMA* AND RAYMOND M. FUOSStSterling Chemistry Laboratory, Yale University, New Haven, Connecticut 06520

Contributed by Raymond M. Fuoss, January 17, 1972

ABSTRACT The conductance of 0.02-0.10 N potassiumchloride in poly(vinyl alcohol)-water mixtures at 250decreases by about 50% as the polymer content increasesfrom zero to 20% by weight, while the bulk viscosity in-creases from 0.0089 to over 1000 poises. Further increasesin polymer concentration transform the highly viscousliquid into an elastomeric solid, in which the conductancestill remains relatively high; it decreases significantly onlyafter the glass composition (75% polymer at 25°) is reached.The internal viscosity, which controls-ionic mobility, wasestimated from the conductance data: it ranges from 0.01to about 0.14 over the range 0-55% polymer, similar to theviscosity of many ordinary liquids. Rates of diffusion-controlled processes involving small molecules in macro-molecular media can, therefore, be expected to be similarto those in usual solution.

Transport processes such as electrolytic conductance anddiffusion are described by currents Ji, which are products ofconcentrations ni and velocities vs (Jf = nitv). Rates of diffu-sion-controlled reactions, of course, depend on diffusion con-stants. The velocities depend on the driving forces; when theforces are not too great, velocity is simply proportional tothe force Ki that produces the motion, Vj = wiKi. In diffusion,the (virtual) force is a concentration gradient; in conductance,the driving force is the applied electric field. The coefficient ofproportionality wj (reciprocal friction coefficient) is related tothe diffusion coefficient Di by the Einstein relationship Di =ozikT. For rigid spheres of radius Ri in a continuum of viscosityn that wets them, ,w = 1/6wr-Ri, according to the well-knownStokes equation. The parameter cw that appears in the de-scription of all transport processes in solution depends, for theprimitive model, on the viscosity of the solvent and on theradius of the solute molecule. Walden's rule (the constancy ofthe product of limiting conductance Ao and solvent viscosityX7 for a given electrolyte in different solvents at different tem-peratures) is a direct corollary of the Stokes equation. Electro-lytes with large ions [for example, quaternary ammoniumtetraphenyl-borides in acetonitrile-carbon tetrachloride mix-tures (1)] conform rather well to Walden's rule; for smallerions, especially in hydrogen bonding solvents, the' productAo- may vary by as much as a factor of two. Accascina (2, 3)found a limiting equivalent conductance of 0.275 for potas-sium chloride in glycerol, where the viscosity (-q = 9.45 poise)is over a thousand times that of water (7 = 0.008903) and theproduct A07 = 2.60, as compared to 1.335 in water. Consider-

ing the enormous change in viscosity on going from water toglycerine, the correlation of a microscopic molecular propertyAO with the macroscopic viscosity through Walden's rule reallyis surprisingly good. Furthermore, the macroscopic viscosityof the water-glycerol mixtures gives the observed limitingslopes of the conductance curves.

Solutions of polymers in general show high viscosity, muchhigher than solutions of ordinary molecules at the same vol-ume fraction. As the concentration of polymer increases, theviscosity increases very rapidly; at about 30-40%, the systembecomes a plastic or elastomer, and may eventually becomea glass at high polymer content. The high viscosity in dilutesolution is caused by the expansion of the polymer chain;in more concentrated solutions, the chains become entangled,and the bulk properties of the system resemble those of anelastic solid. Considered on a molecular scale, however, thepolymer molecules are not rigid structures, and there is con-siderable freedom for motion of polymer segments over shortdistances, or for motion of small molecules around and be-tween segments, as long as the system is above its glass transi-tion point. One would, therefore, expect to find the frictioncoefficients that describe molecular processes in polymer sys-tems to be much smaller than those calculated from bulk vis-cosity; the latter should be completely irrelevant. We shallpresent measurements of the conductance of potassium chlo-ride in a mixed solvent of poly(vinyl alcohol) and water andshow that the local viscosity, as measured by ionic mobility,is smaller than the bulk viscosity by many orders of magni-tude and not greatly different from the viscosity of ordinaryliquids. Consequently, the rates of diffusion-controlled pro-cesses involving small molecules in macromolecular systemsshould not differ greatly from the rates observed in aqueoussolutions.

MATERIALS AND METHODSTwo samples of poly(vinyl alcohol) [poly(ViOHl) ] were used.The first, Dupont's Elvanol 50-42, is 88% hydrolyzed poly-(vinyl acetate); it contained a small amount of acid impurity,as shown by a low pH (3.55) and its specific conductance of2.7 X 10-i mho/cm in 4.0% aqueous solution. A 40-g portionwas suspended in 200 ml of methanol and stirred for about 1 hrat 400. The Elvanol was then filtered out, washed with meth-anol on the filter, and dried under vacuum. A 4.0% solution ofthe product had a specific conductance of 1.1 X 10-5. Asecond extraction reduced the conductance to 0.8 X 10-5.The conductance and pH of a 4.0% aqueous solution remainedunchanged for 8 days, showing that further hydrolysis of theremaining acetate groups did not occur at room temperature.For the preparation of the 0.01-0.10 N potassium chloride

829

Abbreviation: poly(ViOH), poly(vinyl alcohol).* Present address: Department of Polymer Science, TokyoInstitute of Technology, O6kayama, Meguro-ku, Tokyo, Japan.t To whom reprint requests may be addressed.

830 Chemistry: Komiyama and Fuoss

solutions containing up to 20% Elvanol 50-42, methanol-extracted material was used; the maximum solvent correctionwas about 3% of the total conductance. For the systems with50% and higher poly(vinyl alcohol), which were molded underpressure at 86-88', Elvanol 72-60 was chosen. It is a com-pletely hydrolyzed poly(vinyl acetate) and, therefore, couldnot produce acid by hydrolysis during the pressing. As re-ceived, it showed a high conductance in solution. Soxhlet ex-traction with 1:1 ethanol-water for 12 hr, followed by wash-ing with acetone and vacuum drying, gave a product whoseconductance in a pressed disc [50% poly(ViOH), 50% waterby weight] was 0.8 X 10-5, about 2% of the conductance of0.02 N potassium chloride in the same plastic.For systems containing up to 20% poly(ViOH), solutions of

potassium chloride of known concentration were added toweighed amounts of polymer, and then the mixture was stirredor rolled until uniform. For higher concentrations of poly-(ViOH), weighed amounts of polymer and potassium chloridesolution were thoroughly mixed at room temperature, andthen held at 750 for 12 hr in a closed container to allow diffu-sion to distribute the water uniformly. Then the moldingpowder was pressed at 2000 lb/in2 at 86-880 for 10 min in aclosed mold; the charge was the amount calculated to give atest piece of the desired thickness. The final concentrations ofpoly(ViOH) and of salt in the disc or strip was calculatedfrom the initial weights and the weight of the molded sample,assuming that the only loss during pressing was water. Sam-ples in the range 50-80% poly(ViOH) were prepared by press-ing. The 40% poly(ViOH) mixture is too soft for pressing;we obtained these samples by putting 50% pieces into a closedcontainer over a dish of water. They slowly absorbed water;when their weights showed that they had reached 40%, theirconductance was measured. Compositions containing morethan 80% poly(ViOH) were too hard to mold; we obtained the90% samples by slowly evaporating water from 80% strips ina vacuum oven at 500.For systems containing more than several percent poly-

(ViOH), the viscosity is too high for the use of conventionalconductance cells because air bubbles become trapped betweenthe electrodes. The conductance cells for systems containingup to 20% poly(ViOH) were simply glass tubes 1.0 or 2.0 cmin diameter, terminated by female spherical ground joints.Hemispheres were turned onto the ends of short stainless steelrods. The tube could be filled bubble-free with solutions ofvery high viscosity; the steel plugs served as stoppers andelectrodes. The assembly was held together by clamps andplaced in a 25.000 thermostat for conductance measurements.

Samples containing more than 30% poly(ViOH) will notflow at room temperature; they retain their shape and there-fore require a method that adapts the electrodes to the sam-ple. Dielectric constants were measured at 1 MHz; at thisfrequency, series capacity caused by imperfect contact be-tween flat metal electrodes and molded disc samples presentedno problems. Measurement of conductance must be made inthe low audiofrequency range, so that ac losses are negligiblecompared to the ionic conductance; difficulty was encountereddue to imperfect contact and to surface polarization. Finally,a method was developed that eliminated the problems of thesample-electrode interfaces. Strips of width w and thicknessd were molded, and then clamped between gold-plated brasselectrodes, one pair at each end of the strip. If 1 is the lengthof the strip between the facing edges of the electrodes, E theend resistance, a the specific conductance, and S the surface

resistance, the measured resistance R is given by the sum ofthe end resistances in series with the volume and surface resis-.tances acting in parallel between the edges of the electrodeclamps:

R = E + l/[wdu + 2(w + d)/S] (1)

Measurements on many samples with different values of 1,w, d, and a verified Eq. 1 and, further, showed that (2/So)(w-I + d-l) was negligible compared to unity, due to the verylarge values of surface resistance. This observation simplifiesEq. 1 to

R = E + (l/wd)a-c (2)

from which it is clear that the conductance can be determined,independent of the end effects which depend in an unknownway on the sample-electrode contacts, from the slope of a plotof measured resistance against 1, the distance between elec-trodes for a series of electrode spacings on a sample of fixedcross section. The electrodes were attached to the covers ofthermostated Lucite boxes, so that the samples could be siis-pended above solutions of potassium chloride whose concen-tration matched that of the sample in that box. Without con-trolled humidity in the box, the resistance drifted steadilybecause of loss of water. Preliminary measurements weremade over the range 2-50 kH; the volume conductivity a wasfound to be rather insensitive to frequency, so final measure-

ments were made only at 20 kH.After most of the conductances at 250 had been determined

by the strip method, we discovered that the water-plasticizedpoly(ViOH) adhered quite tightly to silver under pressure.Discs of silver foil (0.05 mm thick) were placed in the mold,one below the charge and one above. If pressure was appliedslowly, smooth-surfaced discs of poly(ViOH) plastic were

obtained with firmly attached electrodes. The resistancemeasured between silver faces was practically independent offrequency, showing that surface capacity and interface polar-ization were negligible. Probably a film of silver chlorideformed on the foil, which then acted as a reversible Ag-AgClelectrode. Volume conductances of the disc samples measureddirectly agreed within a few percent with the conductancedetermined by R-1 slopes on strips of the same composition.(The lack of perfect agreement was due to the practical im-possibility of making two pressings of precisely the same com-

position.) Availability of disc samples with vapor-imperviousfaces made it possible to measure conductance at higher tem-peratures. Two duplicate silver-faced discs were placed sideby side in an air oven in which the temperature was slowlyraised (about 0.50/min). One sample was connected to theconductance bridge. The other had a thermocouple insertedthrough the edge, and served to monitor the average tempera-ture which was assumed to be the same for both samples.

RESULTS AND DISCUSSION

Addition of poly(vinyl alcohol) to water raises the viscosityat a very rapid rate, as shown in the top curve of Fig. 1 andthe second column of Table 1. The viscosity of water at 25°is 0.0089 poise, that of a 1.5%o solution of Elvanol 50 42 isnearly five times that value (0.0439); that of a 10% solutionis 29.2. On going from zero to 12.8%, the viscosity (as mea-

sured by a capillary viscometer in the range below about 25poise, and by a Brookfield rotor viscometer for the higherrange), increases by 104. Extrapolation of a plot (not shown) ofthe logarithm of viscosity v against the logarithm of the per-

Proc. Nat. Acad. Sci. USA 69 (1972)

Conductance in H20-Poly(vinyl alcohol) 831

TABLE 1. Properties of KCl-poly(VzOH)-H20 systems

n Ao (cm2%Poly(ViOH) (poise) D mho/eq.) (poise)

0.0 0.0089 78.3 149.9 0.00891.5 0.0439 75.6 143.0 0.00943.0 0.160 73.9 137.3 0.00994.6 0.76 73.1 129.5 0.01047.2 4.52 74.8 120.3 0.01138.6 11.2 75.6 112.8 0.012210.0 29.2 73.9 108.7 0.013311.4 59 73.1 104.2 0.013812.8 113 74.8 100.0 0.014816.0 (400)* 70.6 90 0.015720.0 (1200)* 68.6 80 0.018140.0 (105)* 58.0 (32)* 0.0554.1 41.0 (12)* 0.1474.8 15.0 (2.6)* -83.8 - 12.5

= viscosity; D = dielectric constant; Ao = limiting con-ductance; p7i = internal viscosity; -, not determined.

* Values in parentheses are extrapolated values.

cent of polymer by weight [the plot is concave-up with a slopeof about 5 at 10% poly(VioH) ] gives an estimated viscosityof 1200 for 20% poly(ViOH), over 105 times that of water.Now consider the conductance of potassium chloride in

poly(ViOH) solutions covering the range 0-20% polymer. Theequivalent conductances up to about 0.1 N (open circles)are plotted against square root of concentration in Fig. 2.Also shown are the conductance curves for potassium chloridein 14.9% by weight of glycerine solution (7 = 0.0133) and in30.1% sucrose solution (n = 0.0248). The curves all have thesame shape (concave-up) and are roughly parallel, approach-ing limiting slopes that do not differ greatly from each other.If asked what the curves of Fig. 2 represented, given only theinformation that the salt was the same in all 12 systems, anelectrochemist would unhesitatingly reply that they wereconductance curves for a strong 1-1 electrolyte in a series ofsolvents of high dielectric constant in which the viscosity in-creased by a factor of about two, reading from top to bottom.Obviously, the frictional resistance which opposes ionic motionin the poly(ViOH) systems has zero correlation with thechange of about 105 in bulk viscosity of the polymer solutionsin which the ions are moving. The 11.4% poly(ViOH) solu-tions (X7 = 58.8) have about the same conductance as thosein 14.9% glycerol (q = 0.0133), and the conductance in 30%sucrose solution (v = 0.0248) is distinctly lower than that ofthe 20% poly(ViOH) with an enormously greater I (macro-scopic) 1200 poise. The dielectric constants of the poly-(ViOH) solutions cover the range D = 78.3 for water to 68.6for 20% Elvanol 50-42, a range in which ionic association isslight.Another striking example of the difference between macro-

scopic properties and those effective on a molecular scale isfurnished by the liquid-gel transition. Sodium borate setssolutions of poly(ViOH) to stiff gels by crosslinking. A 0.1 Nsolution of potassium chloride in 5% poly(ViOH) solutionhad a specific conductance of 0.0113. On addition of 0.2%borax, the solution gelled, but the conductance remainedessentially the same, at 0.0118. (The small increase was dueto the conductance of the sodium ions from the borax.)

% Pc y(ViOH)

FIG. 1. Dependence of properties on poly(ViOH) concentra-tion. Top curve (ordinate scale, upper left): logarithm of bulk vis-cosity; middle curve (ordinate scale, lower right): internal viscosity;bottom curve (ordinate scale, lower left): Walden products.

The necessity for introducing the concept of an internalviscosity to describe ionic motion on a molecular scale alsoappears when one attempts to extrapolate the curves of Fig. 2to zero concentration, in order to obtain the limiting conduc-tances. The extrapolation is made (4) by plotting

A' = A(obs.) + Scl/2 Ec log c (3)against concentration; the plots are usually linear and giveunambiguous values of A0. The coefficients S and E are theo-retically predicted; both are made up of two terms. For thelimiting tangent on a plot of A against c,1/2

S = 0.82 X 106 Ao/(DT)'/2 + 82.5/Aq(DT)1/2 (4)

The curves for water and for the glycerol and sucrose systemsextrapolate readily by this method. But the S-term for thepoly(ViOH) systems is much too small if the macroscopicviscosity is inserted in the second term of Eq. 4, as shown bythe curvature of the resulting curves of A' against c. This is

A

I0~~~~~~~~~~~~~1

75

500.0 0.1 0.2

C',

FIG. 2. Equivalent conductance of potassium chloride. 0,from top to bottom: in 0, 1.5, 3.0, 4.6, 7.2, 8.6, 11.4, 12.8, 16.0, and20.0% by weight of poly(ViOH); 9, in 14.9% glycerol; 5, in30% sucrose. Dashed lines are extrapolated curves. C = concen-tration.

Proc. Nat. Acad. Sci. USA 69 (1972)

0.3

832 Chemistry: Komiyama and Fuoss

FIG. 3. Dependence of Walden products on internal viscosity.0, poly(ViOH) solutions, e, 30% sucrose, 0, 14.9 and 24.8%glycerol.

simply another experimental proof that the viscosity that con-

trols the motion of small ions and molecules is not the viscositymeasured in a viscometer. The failure of the extrapolationmethod, however, suggests a method for determination ofthe internal viscosity from conductance data. The secondterm of S, the electrophoretic part, is the consequence of an

average force acting over a volume, and it has been completelyestablished (2) by comparison with experiment that, forordinary liquids, insertion of the macroscopic viscosity inEq. 4 correctly describes the molecular process of transfer ofmomentum between ions and solvent molecules. To a goodapproximation, the conductance of potassium chloride inwater is given by

A = Ao-Sc'/2 + 92c (5)

over the range 0.0-0.1 N. The term 92c lumps the linear andc log c terms together. The range of dielectric constants forthe 0-20% poly(ViOH) solutions is small (78.3 > D > 68.6),so the value 92c should be a fair approximation to the higherterms for all the poly(ViOH) systems of Fig. 2. The conduc-tance function can then be rearranged as follows:

A" = A(obs.) - 92c

= Ao + Sc1/2

(6)

(7)

Plots of A" against square root of concentration were linear,and gave A0 as intercept and S as slope. Then the internal vis-cosity ns can be calculated by Eq. 4; 7j ranged from 0.0094 forthe 1.5% solution to 0.0181 for the 20% solution, as shownin the central curve of Fig. 1. These values are of the order ofmacroscopic viscosities of "ordinary" liquids, and show thatthe ions move easily between the segments of the polymerchains; internal viscosity in polymer solutions depends on

local segment mobility and is independent of the bulk vis-cosity, which is determined by polymer concentration andmolecular weight.Given limiting conductance and internal viscosity, the

Walden products Aont can now be calculated. If ions behavedlike Stokes spheres in a continuum, the product would beconstant. Actually, as shown in the lower curve of Fig. 1, itincreases slowly from 1.33 in water to 1.52 in the 20%o poly-(ViOH) solution. In Fig. 3, Walden products for potassiumchloride in 0-20%0 poly(ViOH) systems and in glycerol andsucrose solutions are plotted against viscosity; for the poly-(ViOH) systems, the internal viscosity -, obtained from theslopes of the plots of A" against c '2 is used, while for the

other three solutions bulk viscosity is used. As stated above,bulk viscosity correctly describes the electrophoretic effectfor liquids with small molecules. Clustering of all the points onthe same line in Fig. 3 argues that our internal viscosity hasreal physical significance. The trend towards higher values ofA0t1 with increasing viscosity is given by

Ao0o - A-qjf0-2 (8)

which is about the same as the rate of increase found for a

variety of electrolytes in sucrose-water(5), mannitol-water(6),and acetonitrile-octacyanoethylsucrose (7) solutions.

Solutions of potassium chloride in poly(ViOH)-water plas-tics containing 40%0 or more polymer were separately preparedfor each salt concentration, because we could not use theusual dilution method to change concentration. The actualwater content of the solutions varied by several percentaround an average value, with the result that the precision ofthe conductance curves for the plastics was rather poor com-

pared to that for the solutions in the 0-20% range. The pointson the plots of A against cl/2 scattered so much that reliableslopes could not be obtained. Plots of the logarithm of the

specific conductance against logarithm of salt concentrationare shown in Fig. 4; the data over the working range for each

average concentration of poly(ViOH) can be approximatedby straight lines with slopes a little less than one. This is the

behavior characteristic of conventional 1-1 salts in solventsof high dielectric constant; the limiting conductances in the

plastics may then be estimated as only a little higher than the

equivalent conductance at the lowest salt concentration.For the40% system, AO z 32 and for the 54% system, AO 12.

Substitution of these values into Eq. 8 gives 0.05 and 0.14,respectively, for the internal viscosities. Extrapolation givesan estimate of about 105 for the bulk viscosity of the 40%poly(ViOH); the conductance data show that the internal

viscosity increases by only a factor of about 20 while the

macroscopic viscosity changes by seven orders of magnitude.Most of the 20-fold increase in wt occurs in the range from 16

% Pody(ViOH)

FIG. 4 (left). Specific conductance of potassium chloride in poly-(ViOH)-H20 solvent. From top to bottom: in 16.0, 40.0, 54.1,74.8, 83.8, and 91.6% poly(ViOH).

FIG. 5 (right). Temperature dependence of resistance of 85%poly(ViOH), scales at top and left. TG = glass temperature.Dependence of glass transition on composition, scales at bottom andright. Temperatures in 'K.

3.0 3.1 1000/T 3.33.5

3.0TG

2.0 100

ED90 100

Proc. Nat. Acad. Sci. USA 69 (1972)

b

.wv

Conductance in H20-Poly(vinyl alcohol) 833

to 54% poly(ViOH), as can be seen in Fig. 3. This increaseis due to the decreasing mobility of segments of the polymerchain as they become more tightly packed and impede themotion of the ions.Beyond 50% poly(ViOH) the mobility of polymer seg-

ments, and hence that of the ions located in the mesh, decreasesvery rapidly, as shown by the three decade drop in conductanceat a given salt concentration on going from 54 to 92% poly-(ViOH). The persistence of the slope of about minus oneshows, however, that the electrolyte is still acting like a nor-mal 1-1 salt, but in a medium of very high viscosity. The largeand rapid increase in internal viscosity is the consequence of atransition in the poly(ViOH-water system; at a fixed tempera-ture, polymeric systems change from elastomers to glasseswith decreasing plasticizer content. Conversely, for fixedcomposition, the system changes from glass to elastomer atTG, the glass temperature. Fig. 5 shows how TG may be deter-mined by conductance measurements in the KCl-poly(ViOH)-H20 plastics. The top plot shows the logarithm of the re-sistance of a disc with 85% poly(ViOH) as a function of re-ciprocal absolute temperature. It will be noted that the datacan be represented by two linear segments; their intersectionlocates the glass temperature. The temperature coefficient inthe glass is higher than that in the elastomeric state (activa-tion energies from the slopes are, respectively, 11 and 8 kcal/mol); molecular motion in the glassy state meets very muchmore resistance than in the elastomer. The lower graph inFig. 5 gives the dependence of TG on composition. Systems

with more than 75% poly(ViOH) are glasses at 250. Thesharp change in conductance shown in Fig. 4 exactly parallelsthe glass transition: the conductance at 25° in systems withless than 75% poly(ViOH) is high and not very sensitive tocomposition, while the conductance becomes quite low andvery dependent on water content in the systems with highpolymer percentages.

The authors acknowledge the support of this work by theOffice of Saline Water, U.S. Department of the Interior, underContract no. 14-01-0001-1308.

1. Berns, D. S. & Fuoss, R. M. (1960) "Tetra-alkylammoniumTetraphenylborides in Acetonitrile-Carbon TetrachlorideMixtures at 25°," J. Amer. Chem. Soc. 82, 5585-5588.

2. Accascina, F. (1959) "The Conductance of Potassium Chlo-ride in Water-Glycerol Mixtures at 25°," J. Amer. Chem.Soc. 81, 4995.

3. Accascina, F. & Petrucci, S. (1959) "Conductance and Vis-cosity in the System Potassium Chloride-water-glycerin at250," Ric. Sci. 29, 1640-1648.

4. Fuoss, R. M. & Accascina, F. (1959) in Electrolytic Conduc-tance (Interscience Publishers, Inc., New York, N.Y.), p. 197.

5. Stokes, J. M. & Stokes, R. H. (1956) "The Conductance ofSome Simple Electrolytes in Aqueous Sucrose Solutions at250,)" J. Phys. Chem. 60, 217-220.

6. Stokes, J. M. & Stokes, R. H. (1958) "The Conductances ofSome Electrolytes in Aqueous Sucrose and Mannitol Solu-tions at 250," J. Phys. Chem. 62, 497-498.

7. Treiner, C. & Fuoss, R. M. (1965) 'Electrolyte-SolventInteraction. XVI. Quaternary Salts in Cyanoethylsucrose-Acetonitrile Mixtures," J. Phys. Chem. 69, 2576-2581.

Proc. Nat. Acad. Sci. USA 69 (1972)