Solute Diffusion in Hydrated Polymer Networks Part 2.-Polyacrylamide, Hydroxyethylcellulose and Cellulose Gels BY WYN BROWN* AND KALUBA CHITUMBO Institute of Physical Chemistry, Uppsala University, P.O. Box 532, 751 21 Uppsala 1, Sweden Received 6th March, 1974 Diffusion measurements on oligomeric solutes (n-alcohols, polyhydric alcohols, oligosaccharides) and polyethylene oxide polymers in sparsely crosslinked, water-swollen, polymer networks are described. Diffusion coefficients in the gel phase are much lower than those in the bulk liquid, which may be expressed as being mainly due to a change in the local viscosity. Diffusion coefficients ranged from 4.8 x (methanol) to 1.4 x lo-' cm2 s-l (polyethylene oxide 4000) in the hydroxy- ethylcellulose gel. The corresponding ratios to the free diffusionvalues are 0.31 and 0.106.Thereduc- tion of D for small solutes is shown to depend on the concentration and polar character of the matrix polymer but not on the degree of crosslinking of the network. Much of the stability of the postulated water structuring is attributed to the inertia of the polymeric component, with a minor contribution from the strength of the polymer-solvent interaction. Estimates of polymer-solvent interaction energies in the gels are obtained from diffusion data at different temperatures. In Part 1 were described measurements of the translational diffusion coefficients of the same solutes as discussed here in a densely crosslinked, water-swollen, cellulose gel C80.I It was found that diffusion coefficients in the gel phase are substantially lower than the free diffusion values.It was concluded that this effect may be expressed as a network-induced increase in the microscopic viscosity of the medium. This paper describes an extension of these investigations to solute diffusion in loosely crosslinked gels of cellulose, hydroxyethylcellulose and polyacrylamide. The purpose was to establish the generality of the findings of Part 1 and furthermore to examine to what extent the " tightness '' (average pore size) of the matrix determines the magnitude of the microscopic solvent viscosity. In contrast to highly crosslinked gels, steric exclusion of the solutes with the gels used here is negligible (that is, there is an insignificant variation in the effective internal volume of the gel with respect to both solute size and temperature), except in the case of the polymeric solutes.EXPERIMENTAL Experiments were made using the apparatus and technique described in Part 1.l The preparation of the cellulose and hydroxyethylcellulose gels, employing epichl oro- For clleu- hydrin as the crosslinking medium, followed the procedure described in Part 1. TABLE 1 .-STRUCTURAL PARAMETERS OF GEL SAMPLES (WATER-SWOLLEN DISCS ; DIAMETER 4 Cm) plolymerl water content effective internal x (wlw) cm3 volume a/cm3 hicknesslcm pol yacrylamide 6.8 3.03 2.05 0.26 hydroxyethylcellulose 5.4 5.22 3.60 0.43 cellulose (C5) 17.0 6.63 5.60 0.60 a volume of gel solvent diluting the bathing solution. 12W. BROWN AND K . CHITUMBO 13 lose ((3, 0.47 g epichlorohydrin per 100 g viscose was used.With hydroxyethylcellulose a large excess of epichlorohydrin was necessary in the reaction : 100 g epichlorohydrin per 5 g polymer was used. The polyacrylamide gel was a gift from Pharmacia Fine Chemicals, UppsaIa, Sweden. Further details concerning the gels are given in table 1. RESULTS AND DISCUSSION The results of the diffusion measurements are summarized in table 2. TABLE 2.-DIFFUSION COEFFICIENTS IN VARIOUS WATER-SWOLLEN GELS AT 25°C solute polyhydric alcohol ethylene glycol glycerol erythrit ol arabitol mannit 01 n-alcohol methanol ethanol propanol butanol oligosaccharide glucose sucrose raffinose stachyose polyethylene oxide PEG 1000 2000 3000 4000 hydroxyethyl- cellulose D x I06[cmz s-l 3.9, 2.76 2.56 2.32 3-06 4.78 2.50 4-02 2.62 1.98 1.47 1.22 DX 107fcrnZs-1 9.01 3.3 (j 1.41 4.05 cellulose (C5) D x 106/cmz s-l 3.46 2.82 2.57 2.19 1.88 3.88 - - - 2.05 1.51 1.15 0.94 - - - - polyacryl- amide D x 106/cm2 s- 2.12 1.99 1.84 1.72 1.61 - - - - 1.68 1.25 1.12 0.96 DX 107/crn2s-1 3.93 2.26 1.51 0.88 Fig.1 shows diffusion coefficients for some non-ionic solutes in the polyacrylamide gel. The diffusion coefficients are considerably smaller than those characterizing diffusion of these solutes in bulk water, as was observed in similar measurements in a densely crosslinked cellulose ge1.l These findings also apply to the diffusion data for these solutes obtained in sparsely crosslinked cellulose and hydroxyethylcellulose gels (fig. 2 and 3). With the smallest solutes, there is a reduced dependence of D on molecular size with each gel as was noted in Part 1.Diffusion measurements were made on tritiated water in the polyacrylamide, hydroxyethylcellulose and cellulose gels and the results are summarized in table 3(a). In agreement with our earlier findings, we conclude that the reduction in. D, relative to the diffusion coefficients in the bulk liquid, arises from an increased local viscosity of the solvent caused by its interactions with the polymer matrix, i.e. the factor limiting the diffusion coefficients of small solutes in such systems is the mobility of the solvent in the gel.14 DIFFUSION IN POLYMER NETWORKS An alternative viewpoint is provided by the two-phase model developed by Wang in which the diffusing entity is considered to encounter barriers in the form of macro- molecules with a hydration layer surrounding them.From the ratio of the gel and free diffusion coefficients for a given solute, one may estimate the volume of the hyd- rated polymer. The resulting hydrations of the hydroxyethylcellulose and cellulose gels are 6.7 g H20 and 1.7 g H20 per g gel, respectively (cf. the value of 3.4 g H20 per g for agar gels 3). Fig. 4 compares the results for the “ tight ” and “ open ” cellulose gels which have the same polymer concentration but which differ substantially in degree of crosslink- ing. The divergence observed for the larger solutes reflects the greater probability of solute-segment contacts in the more extensively crosslinked network when the solute 0.5 0- n U ?, - \ GEL DIFFUSION 1 I I 1 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 log vm FIG.1.-A comparison of transport in the polyacrylamide gel with free diffusion data. Double logarithmic plot of diffusion coefficients as a function of solute partial molar volume for polyhydric alcohols (0); oligosaccharides ( A) and polyethylene oxide polymers (0). - -A- - - I --.-- GEL DIFFUSION I 1 I I 1 I I I 13 1.5 I .7 1.9 2. I 2.3 2.5 2.7 log iim FIG. 2.-Double logarithmic plots of gel diffusion data (cellulose gel) and free diffusion data as a function of solute partial molar volume. Polyhydric alcohols (0); oligosaccharides (A). Points for methanol (m) and tritiated water (A) are included.W. BROWN AND K . CHITUMBO 15 n - 0 - L -2 2 ,.$ -0.5- % W tQ - - 1.0- size approaches the mean segment-segment dimension.The convergence at small molecular size shows that the increase in local viscosity is the same in both systems, that is, it is a function of the cellulose concentration only. In studies on the perme- ability of polyacrylamide gels, White also observed that the diffusion coefficient is independent of the degree of crosslinking. 1 7 1.0 cn 0.5 \ R E DIFFUSION \\ GEL DIFFUSION O t I I I I I I I I I 1.1 1.3 1.5 I .7 1.9 2 .I 23 2.5 2.7 log Em (4 1 1 I I I I t 2.7 2.9 3.1 33 3.5 3.7 log urn (6) FIG. 3.-(a) Gel diffusion data (hydroxyethylcellulose gel) and free diffusion data in a double logarithmic plot as a function of solute partial molar volume for n-alcohols (m), polyhydric alcohols (0), oligosaccharides (A) and tritiated water (b. (b) An analogous plot for polyethylene oxide polymers.Nishijima and Oster studied the translational diffusion of sucrose in concentrated aqueous solutions of polyvinylpyrolidone using an interference technique. They found that the diffusion coefficient decreased with increasing polymer concentration and reached a minimum asymptotic value of about 4 to 5 times lower than the diffusion16 DIFFUSION I N POLYMER NETWORKS value in water alone. These results were interpreted in terms of a corresponding increase in the local viscosity of the medium. The magnitude of the effect is similar to that found here [table 3(a)]. TABLE 3.-DIFFUSION COEFFICIENTS OF TRITIATED WATER IN GELS (a) sparsely crosslinked, water-swollen at 25°C gel gel diffusion self diffusion D g e i X 106/cmz ssi DgX 106/cm2 s-l l?pe1*/10-3 Pa s ~g:/lO-~ Pa s h y drox ye t hylcel lul ose 5.42 24.4 4.0 0.89 cellulose (C5) 4.03 24.4 5.39 0.89 polyacrylamide 2.9, 24.4 7.3 0.89 (b) densely crosslinked cellulose gel (C80) at different temperatures temperaturelac Dgel x 106/cm2 s-l vgel*/10-3 Pa s 10" 3.1 6 6.87 17" 3.48 6.24 25 " 3.87 5.61 35" 5.91 3.67 31" 5.04 4.30 ; see ref (15).D: 3: +?gel = p HTO L 2 !3 0 - M 0 - -05 - I I 13 1.5 1.7 1.9 2.1 2.3 2.5 log urn FIG. 4.-A comparison of gel diffusion data [cellulose gels: (a) = tightly crosslinked, (b) = sparsely crosslinked] in a double logarithmic plot against solute partial molar volume. Polyhydric alcohols (0); oligosaccharides (A). Points for methanol (M) and tritiated water (A) are included. Similarly, Biddle estimated microscopic viscosities in concentrated hydroxyethyl- cellulose solutions by measuring the rotational diffusion of dissolved fluorescein molecules using the fluorescence depolarization technique.' His estimated local viscosities are similar to those given in table 3(a) and he showed that this parameter increased linearly with polymer concentration.The results of Nishijima and Oster and Biddle for concentrated solutions are thus in agreement with the present findings for diffusion in the gel phase. One concludesW . BROWN A N D K . CHITUMBO 17 that the water mobility depends on the nature of the polymer and its concentration, independently of whether it is present as a tightly or loosely crosslinked network or is in true solution. Similar conclusions were reached by Pika1 and Boyd in a study of ion transport in solutions of sodium polystyrenesulphonate and in the crosslinked polyelectrolyte.Taken together, the results suggest that the increased local viscosity attains a limiting value, as found by Nishijima and Oster.6 THE INFLUENCE OF TEMPERATURE I N SPARSELY CROSSLINKED GELS Data for the temperature dependence of the diffusion coefficient of glucose in the gels are summarized in table 4(a) and shown in the Arrhenius plot, fig. 5. Apparent activation energies, calculated from the slopes in the intervals greater and less than 25"C, are given in table 4(b). The following interpretation is put forward. In the low temperature interval ( < 25"C), the apparent activation energy is smaller than that describing transport in the bulk liquid by the quantity of energy characterizing the interactions between solvent and the relatively immobile polymer segments.Above the observed transition temperature of 25"C, at which point the polymer segments acquire a greatly increased freedom, the apparent activation energy will exceed, by a corresponding amount, that characterizing transport in the bulk liquid. 103 KIT FIG. 5.-Arrhenius plots of glucose diffusion data in various gels. Hydroxyethyl cellulose (0): cellulose (0) ; polyacrylamide ( A). Equivalently, one may regard the apparent activation energy in the low temperature interval as reflecting the small scale segmental motion of the polymer and in the higher temperature interval the energy associated with the dynamic motion of large segments of polymer chains.The change in slope is apparently analogous to that found by Kumins et aL8 for a polymer-solvent system at the glass transition temperature of the polymer (i.e. the point of change from a quasi-crystalline state to a liquid-like one). These workers studied the diffusion of water through a vinyl chloride-vinyl acetate copolymer. Such behaviour in polymer-solvent systems is now well-established, see, for example, the discussions of Stannett and William~.~~ lo Values of the total energy involved in the transition, LIET, are included in table 4(b). Note that, in contrast to the18 DIFFUSION I N POLYMER NETWORKS densely crosslinked network (see next section), there is no change in the effective inter- nal volume with temperature change in any of the gels and glucose simply serves as a label reflecting the dependence of the average local viscosity of the medium on temp- erature.The slopes in the two temperature intervals are consistent in that they separately yield identical values of the " excess energy ", AEE, associated with the solvent mobility [table 4(b)]. The excess energy characterising the solvent in the swollen gel is defined here as the difference between the apparent activation energy in the relevant temperature interval and that characterizing the bulk solvent (average value estimated from the present data 20.5 kJ mol-l) and should provide a measure of the stability of the polymer-solvent interaction to thermal fluctuations (i.e. it is essentially a binding energy). It is then to be expected that D will decrease with increasing interaction, as is shown to be the case in fig.6. AEElkJ mol-' FIG. 6.-The dependence of the diffusion coefficient of glucose (25°C) on the excess energy character- izing the water-polymer interactions in the different gels : hydroxethylcellulose (O), cellulose (0) and polyacrylamide (A). It is also to be expected that the magnitude of AEE is related both to the concentra- tion of polymer segments and their chemical nature, the value of AEE increasing with polar character. One observes, however, that there is a large reduction in the D- value for glucose in comparison with free diffusion even when the interaction energy is small as in the case of the hydroxyethylcellulose gel (2.5 kJ mol-l). As pointed out by Fenichel and Horowitz," this must mean that the main contributing factor to the stability of the postulated water structuring is provided, not by the strength of this short-range interaction, but by long-range forces imparted by the great inertia of the macromolecular component. This structuring profoundly influences transport properties.TEMPERATURE DEPENDENCE-DENSELY CROSSLINKED GEL Fig. 7(a, b) show Arrhenius plots of the diffusion data for tritiated water [table 3(b)] and glucose, respectively, in the tightly crosslinked cellulose gel (C80). Appar- ent activation energies in the high and low temperature intervals are included in table Fig. 7(a) has the same symmetry as the curves in fig. 5 and the apparent activation energies and the derived excess energy are identical to the values characterising solvent mobility in the " open " cellulose gel.Since the polymer concentration in the two gels is the same, this is expected. Fig. 7(b) is markedly different. Since in the tight gel glucose is physically excluded to a degree dependent on the temperature,l the slope in the low temperature interval probably reflects the total energy associated with 4(b).W. BROWN AND K . CHITUMBO 0.8 0.7 h I cn - "E -2 0.6 E: X 9 W M 2 05 19 . 32 5- 3.3 3.4 3.5 3.3 3.4 35 103 K/T 103 KIT (4 (6) FIG. 7.-Arrhenius plots of diffusion data for : (a) tritiated water and (b) glucose in a tightly cross- linked cellulose gel. TABLE 4.-(a) DIFFUSION COEFFICIENTS FOR GLUCOSE IN VARIOUS GELS AS A FUNCTION OF TEMPERATURE hydroxyethylcellulose cellulose (C5) polyacrylamide temp./'C D X 106/cm2 s-l temp./"C DX 106/cm2 s-l ternp./OC DX 106/cm2 s-' 10 1.79 10 1.70 10 1.63 15 2.1 6 13 1-76 17 1.67 20 2.28 17 1 .go 21 1.68 25 2.64 25 2.05 25 1.68 30 3 -08 30 2.56 30 2.26 35 3.83 35 3.18 35 2.80 (6) THERMODYNAMIC PARAMETERS CHARACTERIZING POLYMER-WATER INTERACTIONS IN THE GEL PHASE gel apparent activation excess energy/kJ rno1-I energy*/ D25~ 1061 solute >25'C t25'C kJ mol-i kJ mol-I (glucose) - AET/ AEE/ crn2.s1 h ydroxyet hylcel lulose glucose 23.0 18.0 5.0 2.5 2.64 cellulose (C5) glucose 32.2 9.6 22.6 11.3 2.05 pol yacrylamide glucose 38.9 2.1 36.8 18.4 1.68 cellulose (CSO) tri tiated water 3 2.6 9.6 22.6 11.5 - glucose 21.3 32.2 - 10.9 1.55 * relative to the value (20.5 kJ mol-') characterizing bulk water.20 DIFFUSION IN POLYMER NETWORKS solvent mobilization accompanying activation of the polymeric component.Above 25°C the apparent activation energy has decreased by an amount equal to the polymer- solvent interaction energy (i.e. 10.9 kJ mol-l). Such temperature dependences are characteristic for diffusion in water-swollen networks and have been noted, for example, by Shuler et al. for the diffusion of sucrose through collodion membranes and by Boyd and Soldano l3 for the diffusion of sodium ions in cationic exchangers. INFLUENCE OF SOLUTE CHARACTER Diffusion coefficients for some alkali-metal chlorides in the polyacrylamide gel (fig. 8) are compared in table 5 with values in a cellulose gel. The diffusion coefficients in polyacrylamide are exceptionally low and, as shown by the figures for the effective volume fraction, these solutes are partially excluded from the polyacrylamide matrix.As pointed out by Franks, who compared ionic transport in water and ice,14 any factor which promotes water structure will reduce the mobility of alkali-metal ions. The lower D-values in polyacrylamide are thus to be expected owing to the stronger polymer-water interactions in this system. 0 - 0.5 GEL DIFFUSION O t I I I I I I I log vm FIG. 8.-T\ouble logarithmic plot of gel diffusion data (polyacrylamide gel) and free diffusion data for alkali metal chlorides as a function of solute partial molar vo1ume.l 0.7 0.9 1.1 1.3 1.5 1.7 TABLE S.-DIFFUSION COEFFICIENTS FOR ALKALI METAL CHLORIDES AND OTHER SOLUTES IN POLYACRYLAMIDE AND CELLULOSE GELS IN WATER AT 25°C polyacrylamide cellulose free diffusion solute D X 106/cmZ s-l vr* D x 106/cm2 s-l Vf* D x 106/cm2 s-l LiCl 1.22 0.428 3.66 1 .o 13.12 NaCl 1.88 0.373 4.25 1 .o 15.45 a KCI 1.95 0.35, 4.42 1 .o 19.17 butylamine 0.50 0.24, - - - butyric acid 1.77 0.546 - - 9.18 - 10.1 butanol 1.62 0.68 6 - * Vf = effective internal volume expressed as a fraction of the total solvent contained in the gel.a Handbook of Chemistry and Physics (Chemical Rubber Co., Ohio, 1971-72); b ref. (16).W. BROWN AND K . CHITUMBO 21 In addition, the diffusion coefficients of butylamine and butyric acid are compared with the value for butanol in table 5. As expected with the basic amide groups of the polymer, butylamine has a much lower D-value than butanol. Furthermore, butylamine is most excluded from the network.On the other hand, the diffusion coefficient of butyric acid is significantly higher than the value for butane€. Table 2 includes values of the diffusion coefficients for some polyethylene oxide polymers in the hydroxyethylcellulose and polyacrylamide gels. The values decrease rapidly with increasing molecular weight and, furthermore, the values for the effective volume fraction indicate a progressive increase in the steric exclusion as found for a tightly crosslinked cellulose ge1.l This work is part of a research programme financially supported by the Swedish Forest Products Research Laboratory. Financial support from the Swedish National Science Research Council is also gratefully acknowledged. W. Brown and K. Chitumbo, J.C.S. Farau'ay I, 1975,71, 1. J. H. Wang, J. Amer. Chem. SOC., 1954, 76, 4755. A. G. Langdon and H. C. Thomas, J. Phys. Chem., 1971,75,1821. M. L. White, J. Phys. Chem., 1960,64,1563. M . J. Pika1 and G. E. Boyd, J. Phys. Chem., 1973,77,2918. Y . Nishijima and G. Oster, J. Polymer Sci., 1956, 19, 337. ' D. Biddle, Arkiv Kemi, 1968, 29, 553. * C. A. K d s , C. J. Rolle and J. Roteman. J. Phys. Chern., 1957, 61, 1290. V. T. Stannett and J. L. Williams, J. PuZymer Sci. C, 1965, 10, 45. 1968,118,177. lo B. P. Tikhomirov, H. B. Hopfenberg, V. T. Stannett and J. L. Williams, Mukromol. Chem., l 1 R. Fenichel and S. B. Horowitz, Ann. I?. Y. Acad. Sci., 1965, 125, 290. l2 K. E. Shuler, C. A. Dames and K. J. Laidler, J. Chem. Phys., 1949, 17, 860. l3 G. E. Boyd and B. A. Soldano, J. Amer. Chem. SOC., 1953, 75,6091, 6099. l4 F. Franks, Chem. and I d , 1968, 560. l5 J. H. Wang, C. V. Robinson and I. S. Edelman, J. Amer. Chem. SOC., 1953, 75, 466. l6 Landolt-Bornstein, 5 a, Section 2522 (Springer-Verlag, Berlin/Heidelberg, 1969).