Polyacrylamide adsorption from very dilute solutions

Polyacrylamide adsorption from very dilute solutions

Polyacrylamide Adsorption from Very Dilute Solutions 1 EDWIN R. HENDRICKSON AND RONALD D. NEUMAN 2 Department o f Forest Products, University o f Minn...

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Polyacrylamide Adsorption from Very Dilute Solutions 1 EDWIN R. HENDRICKSON AND RONALD D. NEUMAN 2 Department o f Forest Products, University o f Minnesota, St. Paul, Minnesota 55108 Received November 1, 1984; accepted July 2, 1985 The adsorption of two high-molecular-weight polyacrylamides (anionic Percol 155 and cationic Percol 292) by an unbleached and a bleached hardwood cellulose was studied at very dilute polymer concentrations. The influence of several simple electrolytes on the adsorption behavior of these polymers was investigated. The results were interpreted in terms of Hesselink's statistical-mechanical theory of polyelectrolyte adsorption. Generally, good agreement between Hesselink's theory and experimental results was obtained. However, it appears that an additional nonelectrical contribution to the free energy of adsorption is necessary and may arise from vicinal water effects which have not been considered explicitly in macromolecular adsorption theory. © 1986AcademicPress,Inc. INTRODUCTION

Macromolecular adsorption is influenced by many factors including the solvent, pH, salts, temperature, the adsorbent, and the macromolecule itself. For a review of the literature concerning polymer adsorption refer to the works of Takahashi and Kawaguehi (1), Lipatov and Sergeeva (2), and Kitchener (3). There have also been theoretical attempts to model macromolecular adsorption. Most notable of these are the theories of Simha et al. (4, 5), Hoeve (6-9), Silberberg (10-15), Roe (16), Scheutjens and Fleer (17, 18), and Hesselink (19, 20). Of the above-mentioned theories, only Hesselink considers the adsorption of polyelectrolytes by charged adsorbents. As enlightening as these statistical-mechanical theories are, experimental verification remains elusive especially for very dilute polymer coneentrations. Because of the absence of data concerning polymer adsorption from dilute solutions, this 1Published as Paper No. 14,161 of the Scientific Journal Series of the Minnesota Agricultural Experiment Station on research conducted under Minnesota Agricultural Experiment Station Project No. 43-65, supported by McIntire-Stennis funds. 2 Present address: Department of Chemical Engineering, Auburn University, Auburn, Ala. 36849.

study was undertaken in an effort to gain some insight into polymer adsorption at low concentrations. This was made possible by the recent development in this laboratory of a very sensitive spectrofluorometric method which enabled the quantitative detection of polyacrylamide in aqueous solutions (21). The adsorption of two high-molecular-weight polyacrylamides (one anionic and the other cationic) by unbleached and bleached hardwood kraft pulps was investigated in the presence of salts. Due to the confusion over the role of simple electrolytes on the adsorption of polymers both chloride and sulfate salts of sodium, calcium, and aluminum were studied. EXPERIMENTAL

The extreme accuracy desired in these experiments necessitated an inordinate amount of care to minimize any extraneous contamination. All glassware and Teflon materials were acid cleaned in a Nochromix (Godax Laboratories)-H2SO4 solution after which they were thoroughly rinsed with water that had been passed through a reverse osmosis-deionization water purification system. All other water used in the experiments, unless otherwise stated, was additionally double distilled from an all-Pyrex apparatus incorporating

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Journalof ColloidandInterfaceScience,Vol. 110,No. 1, March 1986

0021-9797/86 $3.00 Copyright© 1986by AcademicPress,Inc. All rightsof reproductionin any formreserved.

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double traps and packed columns. The first distillation, being from an alkaline permanganate solution, effectively removed organic contaminants. Two polyacrylamides (anionic Percol 155 and cationic Percol 292) with molecular weights of ca. l06 were obtained in granular form from Allied Colloids (Fairfield, N. J.). The polyacrylamides were dissolved in the best quality water and were routinely dialyzed for 10 days at 1-3°C in Spectra/Por 4 membrane tubing (Spectrum Medical Industries). The polyacrylamides were then freeze-dried and stored at 1-3°C until use. Oak kraft pulps~were supplied by the Forest Products Laboratory in Madison, Wisc. Both an unbleached and a bleached pulp (derived from the unbleached pulp) were received at approximately 20% solids and were stored at 1-3°C until use. Since the pulps were to be employed as the adsorbing substrates in the presence of various electrolytes, it was necessary to remove as many of the foreign ions as possible along with any other materials which might have interfered with the adsorption or the detection of the polyacrylamides. This was accomplished by soaking the pulp fibers in 0.1 NHC1 (1.0 g pulp on an O.D. basis/300 ml HC1 solution) for 10 min followed by 2 h in a fresh batch of 0.1 N HC1. The cellulose was then rinsed with reverse osmosis-deionized water until the pH of the rinse water was within _0.01 pH unit of the pH of fresh reverse osmosis-deionized water. Any pulp fines were removed during the rinse procedure by screening on a 100mesh stainless-steel screen followed by repeated dilution of the suspension and decanting of the supernatant (with fines) from the settled pulp suspension. Next, the washed pulp was mixed with absolute ethanol (1.0 g/50.0 ml) and allowed to soak for l0 rain followed by filtration on a coarse glass flit. This step was repeated with a fresh aliquot (1.0 g/50.0 ml) of absolute ethanol. The ethanol extraction removed surace-acfive agents, especially those present in the unbleached cellulose which inJournal of Colloid and lnterface Science, Vol. 110, No. 1, March 1986

terfered with the polyacrylamide detection method. The cellulose was then rinsed 3 more times with fresh reverse osmosis-deionized water. The extracted pulp was then soaked for 1 h in best quality water and then filtered on a coarse glass tilt. Several simple electrolytes were chosen on the basis of their predominance in industrial applications. The electrolytes examined were NaC1, Na2SO4, CaCI/, CaSO4, AIC13, and A12(SO4)3. FeCI3 and Fe2(SO4)3 also were looked at initially, but because of problems encountered in detecting polyacrylamide at ionic strengths of these salts greater than 1 × 10-4 M, no attempt was made to investigate the effect of these salts on polymer adsorption. The salts used were all analytical grade. Any surface-active agents were removed from the salt solutions by extraction with n-hexane (Phillips 99 mole% pure grade) which was purified by distillation, followed by slow percolation through a 4-ft. column containing silica gel, Florisil, and activated alumina, and finally distilled a second time. The purified salt solutions were stored at room temperature until use. Quantification of polyacrylamide in aqueous solution was made possible by a spectrofluorometric detection method (21) where the polyacrylamide was first converted to its amine derivative via the Hofmann rearrangement reaction. In order to enhance the fluorescence, o-phthalaldehyde was added in the presence of 2-mercaptoethanol under alkaline conditions. The fluorescence was measured in a Turner Model 430 spectrofluorometer where the sampling bandwidth was 15 nm and the excitation and emission wavelengths were set to 348 and 458 nm, respectively. The method utilized for measuring polyacrylamide in aqueous solution proved to be quite sensitive. Accuracies, as determined by a propagation-of-error treatment, were found to be _+0.07 and +_0.17 rag/liter for the Percol 155 and Perco1292, respectively. The primary sources of error in the detection method

POLYACRYLAMIDE ADSORPTION

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proved to be the gravimetric and volumetric mental results could possibly be applied to acdeterminations made prior to the spectrofluo- tual papermaking systems. The fiber concenrometric readings. Linear calibration plots tration in the reaction vessels was 0.5 g/100 g were obtained up to 6.0 mg/liter ofpolyacryl- of suspension, and the initial polymer conamide with this procedure. centration was 2.5 mg/liter. The cationic polyacrylamide had a tendency The first step was the weighing of 0.5 g to adsorb onto surfaces of glassware it con- (O.D.) of damp, purified pulp fibers which tacted. In an effort to minimize this adsorption were immediately transferred to one of the rea procedure used by Hawk et al. (22) to reduce action vessels. The reaction vessels were 125the adsorption of proteins and enzymes by ml Erlenmeyer flasks equipped with ground glass filters was utilized. This was accom- glass stoppers. After the pulp fibers were placed plished by soaking all glassware in a 1% so- in the flasks, best quality water was added in lution of polyethylene glycol (Carbowax, an amount sufficient to yield 100 g of suspen15,000-20,000 mol. wt.). After being exposed sion after the salt and polymer were added. to the polyethylene glycol solution for 30 min, Next, the flask was capped and shaken vigthe glassware was thoroughly rinsed in reverse orously to break up the pulp mass. This was followed by the addition of salt solution which osmosis-deionized water. Adsorption experiments were designed to was pipetted into the reaction vessel as the pulp investigate the effect of each salt on the ad- suspension was gently mixed with a Teflonsorption of the polyacrylamides onto both coated magnetic stirrer. The stirring time topulps. Duplicates of each combination of pulp, taled 1 min from the start of the salt addition. polymer, and salt concentration were run in The reaction vessels were then allowed to addition to three known concentrations of the equilibrate for 1.0 h before polymer addition. polymer in best quality water in order to define The polymer was added at a concentration of the calibration curve. From previous work the 50.0 mg/liter thus only 5.0 ml was required to calibration curves were determined to be linear yield an initial polymer concentration of 2.5 over the concentration range examined (21). mg/liter in the reaction vessels. As the polymer A blank was also performed which consisted solution was added via pipet, the suspension of the cellulose and water. The blank was car- was stirred for 1 min. A 24-h equilibration fled out to insure that no materials were pres- period was then allowed for adsorption. ent in the pulps which could cause a backAfter equilibration four 5.0-ml samples of ground fluorescence reading and, hence, result supernatant were taken from each reaction in the polyacrylamide concentration being vessel and placed in borosilicate test tubes with overestimated. Thus, a typical experimental screw caps fitted with Teflon inserts. Those series consisted of 15 reaction vessels: 3 of samples containing pulp fibers were first cenknown polymer concentrations with no salt trifuged for 10 rain at 2,000 rpm in a Sorvall present (the calibration curve); 2 containing GLC-2B centrifuge to obtain supernatant water and pulp; 2 containing water, pulp and samples free of fibers. The procedure for depolymer; and 8 containing water, pulp, poly- tection of the polyacrylamide outlined earlier mer, and salt. Four salt concentrations (in was then followed. terms of ionic strength) were tested: 10 -6, 10 -5, The only difference in the procedures for 10 -4, and 10-3 M. the two polymers was that when Percol 292 In each of the reaction vessels the concen- was used all glassware, including the reaction trations of pulp fibers and polymer were pur- vessels, were first treated with 1% polyethylene posely set to levels representative of those typ- glycol as described earlier. Otherwise, all exicaUy encountered in the headboxes of paper periments were performed in the same manner machines. This was done so that the experi- and at room temperature (22-23°C). Journal of Colloid and lnterJbce Science, Vol. 110, No. 1, March 1986

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HENDRICKSON AND NEUMAN RESULTS

Adsorption Isotherms Adsorption isotherms were determined at room temperature for polyacrylamide adsorption onto the two substrates. Initial polyacrylamide concentrations ranged from zero to 200 mg/liter. The experiments were performed according to the procedures outlined earlier in the "Experimental" section except that it was necessary to dilute the supernatant from some o f the reaction vessels prior to the Hofmann rearrangement step to insure that the polyacrylamide concentration did not exceed 2.5 mg/liter since this was the maximum concentration determined on the calibration curves. Figures 1 and 2 show the adsorption isotherms and, as can be seen, only the isotherms for cationic Perco1292 appear to be similar in shape to the Langmuirian or high-affinity type isotherms typically encountered in polymer research. The adsorption ofPerco1292 by both substrates is very similar. However, there appears to be a noticeable difference in the amount ofPercol 155 that can be adsorbed by the two substrates. One point of particular in-

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FIG. 2. Adsorption isotherms of Percol 155 on (O) bleached and (e) unbleached oak kraft pulps.

terest is that the anionic Percol 155 adsorbs onto the unbleached pulp quite extensively. In fact, the unbleached pulp adsorbed approximately half as much Percol 155 as Percol 292. Since the unbleached pulp fibers are anionic, the difference in the amount adsorbed might have been expected to be greater. Adsorption did not appear to occur at very low Percol 155 concentrations as shown in Fig. 2. What is not evident is at very low concentrations of the anionic polymer (~<3.0 and ~<6.0 mg/liter for the bleached and unbleached pulps, respectively) negative adsorption occurred. The adsorption data points in the negative adsorption region have been adjusted to correspond to zero adsorption. In other words, the polymer appeared to be concentrated in the bulk solution away from the fiber surfaces.

Influence of Temperature

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FIG. 1. Adsorption isotherms of Percol 292 on (O) bleached and (e) unbleached oak kraft pulps. Journal of Colloid and Interface Science. VoL i 10, No. 1, M a r c h 1986

The amount of the two polyacrylamides adsorbed by the pulps was determined at 20, 25, and 30°C. A concentration of 20.0 mg/ liter of polyacrylamide was chosen because it represented a concentration where less than 100% of the Percol 292 adsorbed while a detectable amount of Percol 155 was adsorbed by both substrates. The adsorption of Percol 155 was not significantly influenced by temperature whereas

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POLYACRYLAMIDE ADSORPTION 100

Percol 292 adsorption was found to be endothermic. These results are in agreement with what other researchers have found regarding polyacrylamide adsorption onto cellulose

(23, 24).

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Before the experiments were started a decision had to be made regarding whether or not an attempt should be made to control the pH of the systems. Due to the relatively low ionic strengths of the salt solutions being investigated (1.0 × 10-6-1.0 × 10-3 M ) even a small amount of acid or base added would contribute significantly to the ionic strength of the solutions. This being a first study investigating dilute polymer concentrations and because of numerous potential problems arising with cellulosic substrates, pH was not controlled. Future investigations will study the influence of pH. At this time, therefore, the re-

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FIG. 4. The influence of chloride salts on the adsorption of Percol 155 and Percol 292 onto unbleached oak kraft pulp.

100

sults can be interpreted only in terms of qualitative differences between the electrolytes, SO O adsorbates, and adsorbents. w nO The influence of simple electrolytes on oc 0 Percol 155 Wlth NoCI 0 polyacrylamide adsorption is shown in Figs. (n [] Percol 155 With CoCI 2 a 3-6. The results are plotted in terms of the < 60 Percol 155 With AICI 3 oc percentage of the 0.25 mg of polyacrylamide • Percol 292 With NoCI uJ >. added which was adsorbed b y the 0.5 g of • Percol 292 With CaCI2 .J 0 A Perco] 292 With A]CI5 hardwood kraft pulp versus the ionic strength o. 40 of salt added. z w Figure 3 shows that A1CI3 was the only U nc w chloride salt tested which increased Percol 155 o. adsorption onto the bleached pulp as the salt 20 concentration increased. Also of interest is the small increase, followed by a decrease, in the percentage of Percol 155 adsorbed which occurs at very low concentrations of some salts. -6 -5 -4 -3 This behavior is noticeable only when adsorpLOG IONIC S T R E N G T H OF S A L T ADDED (M) tion is occurring onto the bleached hardwood FIG. 3. The influenceof chloridesaltson the adsorption kraft pulp (see Figs. 3 and 5) and is evident of Percol 155 and Perco1292 onto bleached oak kraft pulp. for all salts examined except CaC12. Even Journal of Colloid and Interface Science, Vol. 110, No. 1, March 1986

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HENDRICKSON AND NEUMAN

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LOG IONIC STRENGTH O F S A L T A D D E D ( M )

low salt concentrations. By comparing Figs. 3 and 4, it is seen that the chloride salts had a fairly uniform influence on the adsorption of the cationic polyacrylamide by both celluloses. The influence of sulfate salts on the adsorption of both polyacrylamides by the bleached pulp is shown in Fig. 5. As with the chloride salts, the sulfate salts did not have much of an effect on the adsorption of Percol 155. What was surprising, however, is the near absence of Percol 155 adsorption in the presence of alum. Like Fig. 3, there is also a very slight improvement in Percol 155 adsorption from salt solutions of ionic strength less than approximately 1 × 10-s Mevident in Fig. 5. Percol 292 adsorption by bleached pulp fibers is quite dramatically influenced by the presence of sulfate salts, especially at the highest ionic strength of the salt solutions examined. Alum reduced adsorption the most, followed by Na2SO4 and then CaSO4. It should

FIG. 5. The influence of sulfate salts on the adsorption ofPercol 155 and Perco1292 onto bleached oak kraft pulp.

though the increase in adsorption of the anionic polyacrylamide is quite small at low salt concentrations it occurred often enough that it is believed to be real and not due to experimental error. The chloride salts of sodium, calcium, and aluminum had a more uniform influence on the amount of Percol 292 adsorbed by the bleached pulp. Figure 3 shows that Percol 292 adsorption decreased with increasing chloride salt concentration with the reduction in adsorption being between about 11 and 17% at the highest salt concentration. Figure 4 shows the effect of chloride salts on polyacrylamide adsorption by unbleached hardwood kraft fibers. The general trends are much the same as those encountered in Fig. 3. AIC13 is the only chloride salt tested which increased Percol 155 adsorption by the unbleached pulp. Unlike the bleached pulp, the unbleached pulp does not show a tendency to adsorb small quantities of Percol 155 at very Journal of Colloid andlnterface Science, Vol. 110,No. 1, March 1986

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FIG. 6. The influence of sulfate salts on the adsorption of Percol t 55 and Percot 292 onto unbleached oak kraft pulp.

POLYACRYLAMIDE ADSORPTION

be mentioned that the highest ionic strength at which CaSO4 was tested may have been outside the range over which the polyacrylamide detection method was most accurate (21). Even if the percentage of Percol 292 adsorbed at the highest concentration of CaSO4 is not as accurate, the general trend of reduced adsorption with increasing salt concentration should be correct. A very dramatic improvement in Percol 155 adsorption by the unbleached pulp in the presence of high alum concentrations is shown in Fig. 6. Na2SO4 also increased the percentage ofPercol 155 adsorbed by the unbleached pulp but not to the same extent. On the other hand, CaSO4 did not appear to have any influence on Percol 155 adsorption. The sulfate salts investigated all reduced Perco1292 adsorption by the unbleached pulp with CaSO4 appearing to reduce adsorption slightly more than the sulfate salts of sodium and aluminum. Rather surprising is the fact that the sulfate salts of aluminum and sodium did not reduce adsorption ofPerco1292 by the unbleached pulp to the same degree as observed for the bleached pulp (see Figs. 5 and 6). DISCUSSION The adsorption isotherms indicate that the adsorption of cationic Perco1292 by both substrates is governed, at least initially, by electrostatic interactions. At low concentrations essentially 100% of the Percol 292 was adsorbed, while at higher concentrations the percentage of polymer adsorbed declined, but the total amount adsorbed continued to increase (see Fig. 1). The adsorption isotherms representing the adsorption of the anionic Percol 155 by the two substrates are quite different from those isotherms obtained for the cationic polyacrylamide. At very low concentrations of Percol 155 the experimental results showed that negative adsorption occurred, or in other words, there was more Percol 155 detected than had been added to the system. This

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negative adsorption was particularly noticeable when unbleached cellulose was utilized as the substrate. Hesselink (20) in his theory concerning polyelectrolyte adsorption predicted that negative adsorption was possible when the substrate and the adsorbing polyelectrolyte have the same electrical charge, thus leading to a slight concentration increase of polymer molecules in the bulk solution due to electrostatic repulsion. This is not to say that positive adsorption cannot occur when both the adsorbent and the adsorbate are similarly charged. As the equilibrium concentration of Percol 155 increased positive adsorption began. From Fig. 2 it is seen that the unbleached pulp is capable of adsorbing significantly more Percol 155 than the bleached pulp. Why the unbleached cellulose, which is accepted to be more electronegative than the bleached cellulose, would adsorb more of the anionic polyelectrolyte than the bleached pulp is difficult to explain unless one considers the nonelectrical contribution t o t h e free energy of adsorption. Hesselink (20) treated the electrical and nonelectrical contributions to the free energy of the adsorption process as separate in order to determine the partition function for the polyelectrolyte molecules adsorbed onto a surface. Hesselink gives the nonelectrical portion of the free energy of adsorption as the sum of (a) the free energy of the conformational change upon adsorption of a random coil in solution into a sequence of trains and loops, (b) the interactions of the adsorbed trains with the adsorbent surface and with each other, and (c) the interactions between the dangling loops and the solvent. What Hesselink has not considered as part of the nonelectrical contribution is the displacement of solvent molecules from the adsorbing surface. Related to this are recent developments concerning the existence of a layer ofvicinal or surface modified water possessing a definite structure and lying adjacent to solid surfaces (25-28). Thus, it seems logical to sugJournal of Colloid and InterfaceScience, VoL 110, No. 1, March 1986

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HENDRICKSON AND NEUMAN

gest that the "breaking" and/or restructuring of the vicinal water resulting from polymer adsorption should also be considered an additional nonelectrical contribution to the free energy change. This breaking and/or restructuring of the vicinal water layer may be the source of the substantial entropy increase which is needed to offset the enthalpy increase commonly observed in polymer adsorption. An additional point of interest regarding the adsorption isotherms is the absence of a horizontal plateau. This absence of a horizontal plateau has been considered by many to be due to an equilibrium concentration of polymer being not high enough to permit the surface of the substrate to become completely covered or the polyacrylamide sample being too polydisperse. Interestingly, however, Hesselink (20) found that the isotherms derived from his theory also never became horizontal. The results of the experiments investigating the influence of simple electrolytes on the adsorption of polyacrylamide by cellulose fibers are shown in Figs. 3-6. As was observed eartier, the general effect of the simple electrolytes is to enhance the adsorption of the anionic polyacrylamide and to reduce the amount of cationic polyacrylamide adsorbed by the fibers. Hesselink (20) concluded from his theoretical analysis that generally an increase in the concentration of salt could be expected to increase polymer adsorption due to a reduction in electrostatic interactions which usually oppose adsorption. When charge interaction is the primary reason for adsorption, the adsorption will decrease according to Hesselink (20). However, if nonionic adsorption energy drives the adsorption, increasing the concentration of the salt will tend to enhance adsorption. Hesselink believed that for very low concentrations (<0.03 M of monovalent salt) his theoretical model was invalid. However, the general trends observed in Figs. 3-6 appear to be supportive of Hesselink's model even at very low concentrations of simple electrolytes. On the other hand, there are several exceptions where our experimental results are inconsistent with the general trends observed Journal of Colloid and Interface Science, VoL 110, No. 1, March 1986

above. One discrepancy is the small "hump" observed in the adsorption ofPercol 155 onto only the bleached pulp at very low electrolyte concentrations. Electrostatic interactions cannot explain this behavior, and at present we do not have an adequate explanation. The most notable of the inconsistencies is observed in Figs. 5 and 6 where a dramatic difference is observed in the amount of Percol 155 adsorbed onto the two substrates in the presence of A12(SO4)3. Electrical interactions, once again, cannot explain this inconsistency. An explanation for this behavior might be found by considering the vicinal water layer adjacent to the adsorbing pulp fiber surface as an energy barrier which must be overcome before adsorption can occur. Since the pH values for the respective salt concentrations are about the same for the bleached and unbleached pulps, there is no indication that pH was a factor in causing the observed difference in adsorption between the two substrates. It is theorized that, since the unbleached pulp surface is more anionic than the bleached pulp surface, the cationic aluminum species can approach the unbleached surface more closely and "break" the vicinal water layer which apparently hinders adsorption. The bleached pulp, being less anionic, does not possess the electrical charge intensity necessary to bring the cationic aluminum species close enough to "break" the vicinal layer, Thus, polymer adsorption does not occur. The near complete adsorption of the cationic Percol 292 by both substrates is not an indication that the vicinal water layer is absent, but rather that the cationic polymer can overcome the vicinal water barrier and adsorb. These vicinal water effects as an additional factor influencing polymer adsorption are discussed in greater detail elsewhere (29). One factor which has not been considered is a change in the surface area of the substrates resulting from the presence of the electrolytes. The influence of available adsorbing surface on the amount of polymer adsorbed is well known and is no doubt a factor in these experiments. However, it is not believed that any

POLYACRYLAMIDE ADSORPTION

differences in the surface areas of the substrates can totally account for the great variations observed in the adsorption behavior of the two adsorbates. REFERENCES 1. Takahashi, A., and Kawaguchi, M., Adv. Polym. Sci. 46, 1 (1982). 2, Lipatov, Yu. S., and Sergeeva, L. M., "Adsorption of Polymers." Wiley, New York, 1974. 3, Kitchener, J. A., Br. Polym. J. 4, 217 (1972). 4. Simha, R., Frisch, H. L., and Eirich, F. R., J. Phys. Chem. 57, 584 (1953). 5. Frisch, H. L., and Simha, R., J. Chem. Phys. 27, 702 (1957). 6. Hoeve, C. A. J., DiMarzio, E. A., and Peyser, P., J. Chem. Phys. 42, 2558 (1965). 7. Hoeve, C. A. J.,J. Chem. Phys. 44, 1505 (1966). 8. Hoeve, C. A. J., J. Polym. Sci. C30, 361 (1970). 9. Hoeve, C. A. J., J. Polym. Sci. C34, 1 (1971). 10. Silberberg, A., J. Phys. Chem. 66, 1872 (1962). 11. Silberberg, A., J. Phys. Chem. 66, 1884 (1962). 12. Silberberg, A., J. Chem. Phys. 46, 1105 (1967). 13. Silberberg, A., Z Chem. Phys. 48, 2835 (1968). 14. Silberberg, A., J. Polym. Sci. C30, 393 (1970). 15. Silberberg, A~,J. ColloidlnterfaceSci. 38, 217 (1972).

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16. Roe, R. J., J. Chem. Phys. 60, 4192 (1974). 17. Scheutjens, J. M. H. M., and Fleer, G. J., J. Phys. Chem. 83, 1619 (1979). 18. Scheutjens, J. M. H. M., and Fleer, G. J., J. Phys. Chem. 84, 178 (1980). 19. Hesselink, F. Th., J. Electroanal. Chem. 37, 317 (1972). 20. Hesselink, F. Th., J. Colloid Interface Sci. 60, 448 (1977). 21. Hendrickson, E. R., and Neuman, R. D., Anal. Chem. 56, 354 (1984). 22. Hawk, G. L., Cameron, J. A., and Dufault, L. B., Prep. Biochem. 2, 193 (1972). 23. Nedelcheva, M. P., and Stoilkov, G. V., Colloid Polym. Sci. 225, 327 (1977). 24. Lindstrrm, T., and Srremark, C., J. Colloidlnterface Sci. 55, 305 (1976). 25. Drost-Hansen, W., Ind. Eng. Chem. 61(11), 10 (1969). 26. Ramiah, M. V., and Goring, D. A, I., J. Polym. Sci. C 11, 27 (1965). 27. Drost-Hansen, W., in "Biophysics of Water: Proceedings of a working conference held at Girton College," Cambridge, June 29-July 3, 1981 (F. Franks, Ed.). Wiley, New York, 1982. 28. Etzler, F. M., and Drost-Hansen, W., Croat. Acta 56, 563 (1983). 29. Hendrickson, E. R., and Neuman, R. D., Tappi J. 68(11), 120 (1985).

Journal of Colloid and Interface Science, Vol. 110, No. 1, March 1986