Colloids and Surfaces A: Physicochemical and Engineering Aspects

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1 Colloids and Surfaces A: Physicochem. Eng. Aspects 364 (2010) 1 6 Contents lists available at ScienceDirect Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: Permeation of a cationic polyelectrolyte into meso-porous silica Part 1. Factors affecting changes in streaming potential Ning Wu a, Martin A. Hubbe a,, Orlando J. Rojas a,b, Sunkyu Park a a North Carolina State University, Department of Forest Biomaterials, Campus Box 8005, Raleigh, NC , USA b Department of Forest Products Technology, Faculty of Chemistry and Materials Sciences, Helsinki University of Technology, P.O. Box 3320, FIN-0215 TKK, Espoo, Finland article info abstract Article history: Received 11 September 2009 Received in revised form 19 November 2009 Accepted 25 November 2009 Available online 2 December 2009 Keywords: Polyelectrolytes Silica gel Permeation Streaming potential Diffusion Porosity A recently developed streaming potential (SP) strategy was used for the first time to investigate factors affecting permeation of the cationic polyelectrolyte poly-(diallyldimethylammonium chloride) from aqueous solution into silica gel particles. Factors affecting cationic polyelectrolyte permeation were considered, including polyelectrolyte dosage, molecular mass, solution ph, and electrical conductivity. Samples were equilibrated for approximately 20 h before testing. The magnitude of change in streaming potential, which was taken as evidence of permeation, increased with increasing polyelectrolyte dosage, with decreasing molecular mass, and with decreasing ph in the range 11 to 3. The ph effect supports a mechanism in which excessively strong electrostatic attraction between the polyelectrolyte and the substrate immobilizes macromolecules at or near the entrances to the pore network, thus inhibiting permeation of like-charged macromolecules. The same mechanism is consistent with observations that permeation increased with increasing electrical conductivity, though the latter observation also could be explained in terms of conformational changes Elsevier B.V. All rights reserved. 1. Introduction Our interest in the permeation of polyelectrolytes into very small spaces has been motivated by both practical and theoretical concerns. An understanding and ability to predict permeation behavior is important when applying polyelectrolyte treatments during enhanced oil recovery [1 3], papermaking [4 8], and biomass hydrolysis [9 11]. Theoretically it has been proposed that kinetic and thermodynamic factors dominate the permeation of macromolecules in confined spaces [8,12 15]. From a colloidal and interfacial perspective, permeation may depend on the factors considered in our research, such as electrostatic forces and the effective size of macromolecules in solution, among others. Experimentally, it has been relatively difficult to obtain direct evidence of polyelectrolyte adsorption within mesoporous substrates (pore size 2 50 nm according to IUPAC). Definitive work related to permeation into pores within this size range has been based on adsorption isotherms [16,17]. For instance, Alince and van de Ven [16] presented some work obtained by J. Day, who measured adsorption isotherms for cationic polyelectrolytes of different molecular mass interacting with silica gel in suspension. Discontinuities in the functions of adsorbed amount vs. the poly- Corresponding author. Tel.: address: hubbe@ncsu.edu (M.A. Hubbe). mer radius (based on solution viscosity) were explained based on geometrical considerations, comparing the sizes of the pores versus the effective size of the polyelectrolytes. Recently, Horvath et al. [7] used a more direct approach based on fluorescently labeled polyelectrolytes and confocal microscopy to study factors affecting the permeation of cationic polyelectrolytes into cellulosic fibers. By using batches of polyelectrolytes labeled with contrasting color tags, they demonstrated that the initial layer of polyelectrolytes adsorbing onto the cellulosic fibers tended to remain near to their outer surfaces, rather than diffusing further into the pore structure. Later-arriving polyelectrolyte molecules had to squeeze past already-adsorbed molecules during specified long-term exposure periods to diffuse further into the fibers. It was proposed that the initially adsorbed polyelectrolyte layers tended to inhibit further permeation due to charge-charge repulsion. Research by the present authors has focused on effects of ionic strength and dosage of commercial high mass cationic polyelectrolytes on the streaming potential of either silica gel or cellulosic fibers in aqueous suspensions [18 21]. It was found that the sign of streaming potential could be changed in a reversible manner between net positive and net negative, just by changing the ionic strength and electrical conductivity of the solution. The effects were explainable in terms of the electrostatic double layer, since their full development at charged surfaces is predicted to be strongly suppressed within pore spaces that are small relative to the Debye Hückel reciprocal length parameter [22 24] /$ see front matter 2009 Elsevier B.V. All rights reserved. doi: /j.colsurfa

2 2 N. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 364 (2010) 1 6 Table 1 Levels of independent variables and default conditions. Factors Level * Poly-DADMAC dosage, % on dry 0.1, 1, 3, 10, 30 mass of silica gel Molecular mass of High mass as received poly-dadmac Dialyzed high mass Very low mass as received Solution ph 3, 7, 10 Electrical conductivity ( S/cm) 10, 100, 1000, Equilibraton time: h. * Bold font denotes the default condition. Some of the streaming potential tests results in the cited work provided evidence of substantial permeation of the polyelectrolyte into the silica gel permeation, particularly at a very high polymer concentration [18,21]. It was unclear, however, whether the effect was due to the high concentration per se, or mainly due to a sufficient concentration of very-low-mass oligomers (impurities), which were capable of permeating into small spaces at high polyelectrolyte concentrations. These results led us to choose the present experimental conditions, which were designed to answer the above questions, and to look at the factors affecting polyelectrolyte penetration into mesoporous silica gel particles more comprehensively, as shown in Table 1. When considering each of the factors, default variable levels (marked in bold font) of the remaining factors were used. A packed bed cell was used in which the silica gel sample was contained between a pair of 200-mesh stainless steel screens (see Fig. 1). This was a modification to the streaming potential equipment used in the group s past research [25,26], as described earlier [21]. In the original one-screen system, silica gel particles (or, alternatively, fibers of various types) were periodically collected on a screen through which the suspending medium (aqueous solution) passed when high pressure was applied, and a magnetic stirrer was used to keep the silica gel particles suspended when the pressure was released. However, it was found that the magnetic stirring tended to grind the silica gel particles, and this effect eventually would result in a markedly decreased flow rate through a mat of particles forming on the screen. The grinding effect resulted in a loss in accuracy of the method. In addition, the particles tendency to fall away from the screen surface after cessation of the pressure application could be expected to contribute to a sedimentation potential effect, whose magnitude would be difficult to determine. Those problems were overcome by the modified streaming potential setup used in this investigation. 2. Experimental 2.1. Materials The water used in the experiments was deionized with a Pureflow system. Inorganic chemicals were of reagent grade. The cationic polyelectrolytes were linear poly- (diallyldimethylammonium chloride) (poly-dadmac) samples from the Aldrich, catalogue numbers 52,237-6 (very low mass) and 40,903-0 (high mass). The nominal molecular masses of the products are given as 5k 20k and 400k 500k ranges, respectively. The mesoporous silica gel used in the experiments was obtained as catalogue S745-1 from Fisher Scientific (also known as Davisil Silica Gel 150), which was mesh (except where noted) with a nominal pore size of 15 nm. Certain control experiments were also carried out with a non-porous silica powder, having a mesh size of 200 and finer (Fisher Scientific product cat. no. S153-3). See Table 2 for properties of these silica gel particles Dialysis and gel permeation chromatography (GPC) A Spectra/Por Biotech cellulose ester (CE) dialysis membrane was used for separating the poly-dadmac solutions with nominal 400k 500kDa molecular weight into fractions, of which the retained, high-mass fraction was saved. The molecular mass cut-off value was 100,000 Da, and the tube diameter was 10 mm. Dialysis was carried out with initial poly-dadmac concentrations in the range g/l, and the external solution consisted of 0.158% sodium chloride (Fisher). The external solution was replaced at approximately 3, 8.5, and 13 h after the start, and the retained solution was collected after about 24 h. A Waters 2695 GPC system with a Waters 2996 Photodiode Array refractive index detector was equipped with 300 nm-porosity and 30 nm-porosity (particle size 10 m) columns connected in series. The packing material consisted of OH-functionalized methacrylate-copolymer-network. The flow rate was 1.0 ml/min, and the column temperature was maintained at 35 C. The system was calibrated with four broad molecular mass poly-dadmac standards obtained from the supplier of the columns. Results of GPC showed that most of the lower-mass component of the poly- DADMAC was removed by the dialysis Equilibrium of adsorbate and adsorbent Aqueous solutions were prepared with solutions containing 10 4 M sodium bicarbonate (for purposes of buffering the ph near neutral), plus sufficient sodium sulfate to reach the electrical conductivity values (at about 24 C) as specified later in this report. Silica gel was added to each of six beakers, which were stirred (approx. 100 rpm) by impeller to keep the particles suspended. Poly-DADMAC treatment was based on the dry mass percentage relative to silica gel. After approximately h, the streaming potential was measured Packed bed and steaming potential tests Fig. 1. Sample cell for the streaming potential jar (SPJ) apparatus to allow for a packed bed format during semi-automated streaming potential tests. Electrokinetic tests were carried out with Streaming Potential Jar (SPJ) apparatus [25] fitted with the packed bed described above [21], as illustrated in Fig. 1. It consisted of two 200-mesh screens (316L stainless steel) to hold the solid material (silica particles). The metal probes, for detection of the electrical potential differences, were composed of silver alloy wires (45% Ag, 30% Cu, 25% Zn) [see 25]. Before typical measurement of streaming potential, one

3 N. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 364 (2010) Table 2 Characteristics of silica gel particles. Silica type Pore size (nm) Pore volume (cm 3 /g) Particle size ( m and mesh sizes) Surface area (m 2 /g) Fisher chemical silica Non-porous 0 Floated (200 mesh and finer) Davisil m ( mesh) 282 Ground up Davisil Not measured 292 screen at one end of the packed bed fitting was unscrewed, leaving the part with the other screen held in a clamp with a beaker underneath. After the specified equilibration with poly-dadmac solutions (see Section 2.3), the particles in the beaker were allowed to sediment for at least 5 min. Most of the supernatant solution was set aside for use in rinsing, and the respective silica gel particles, having a mesh size of , were agitated so that the concentrated mixture could be poured through the opened packed bed fitting and retained on a 200 mesh screen. Filtrate was collected in a clean beaker. A syringe was filled with some of the supernatant solution and used to ensure nearly quantitative transfer of the filterable solids into the packed bed. Finally, the unscrewed part was assembled again. Immediately before the streaming potential tests, the silica gel in the packed bed was rinsed by passing fresh buffer solution through it. The streaming potential test was performed by carrying out several repeated measurement cycles involving successive application of high pressure, zero (ambient) pressure, and then sufficient vacuum to return the filtrate to the jar at the end of the measurement cycle (see also Ref. [25]). The difference of potential detected by the two electrodes on either side of the screen between high pressure and zero applied pressure was defined as the streaming potential. A high pressure of 207 kpa was applied for at least 8 s (default), except that a 16 s period was used to obtain more stable results in the absence of sodium sulfate. These tests were carried out with the treated silica gel particles freshly resuspended in the default buffer solution (ph 7, 1000 S/cm). 3. Results and discussion 3.1. Repeatability of streaming potential measurements A typical streaming potential test involved five or more cycles of measurement. In each cycle, the SPJ s software automatically recorded one streaming potential value (potential difference sensed by the two electrode on either side of the screen between high pressure and low pressure), as described in more detail elsewhere [21,25]. Results from the first cycle were routinely discarded, since the electrical signals were generally not as stable as for the subsequent tests. The relative difference among the remaining four or more cyclical measurements was typically less than 10% of the mean recorded potential. It is possible that this relative signal difference was related to how well the electrical potential signal was stabilized near the end of the high pressure application and during the period between 6 and 8 s after the pressure had been released to ambient pressure [25]. Five independent replicate experiments (each based on five or more cycles of pressure and vacuum) were carried out at the center point of the experimental conditions (see Table 2), i.e. testing with an electrical conductivity of 1000 S/cm, ph of 7, and an addition level of 1% of very-low-mass poly-dadmac based on silica gel solids. The mean streaming potential obtained under those conditions was 1.30 mv, which was markedly less negative than 13.4 mv, the result obtained under the same conditions in the absence of polyelectrolyte. The standard deviation among the independent replications of the default treated condition was 0.29 mv, which implies a 95% confidence interval for the mean value between 1.66 and 0.94 mv. Occasional larger differences in streaming potential results were tentatively attributed to subtle differences in the pore size of other properties of silica gel samples obtained from different reagent jars Tests with dialyzed, high-mass poly-dadmac Our GPC results showed that the dialysis process removed the smaller component of commercial poly-dadmac, making its polydispersity to decrease considerably. Fig. 2 shows results of tests to compare streaming potential values at various levels of treatment of the silica gel with dialyzed vs. as-received highmass poly-dadmac. Addition of relatively small amounts of the polyelectrolyte (either undialyzed or dialyzed) was sufficient to increase the measured streaming potential from the initial value of 8 mv up to the range 4to 2 mv, which is in agreement with earlier test results of this type [18]. This change has been attributed to progressive build-up of an adsorbed layer of macromolecules on the outer surfaces of the silica gel particles. It was proposed that relatively small amounts of the polyelectrolyte would permeate into the silica gel particles nanopore network (nominal pore size 15 nm) due to the relatively high molecular mass of the poly-dadmac samples (nominally kda). Thus, it is possible to explain a net negative streaming potential in the system after adsorption resulting from the balance of two opposing effects: on one hand flow past the outer surfaces of the gel particles (giving a positive streaming potential contribution), and on the other hand the effect of liquid passing through the particles (giving a negative streaming potential contribution). In agreement with this interpretation, follow-up tests with non-porous silica under the same aqueous conditions yielded strongly positive streaming potential values of mv, compared to 70.1 mv for the non-porous silica in the absence of the polyelectrolyte. Fig. 2 shows streaming potential as a function of high mass poly-dadmac treatment in salt buffer with 1000 s/cm conductivity. The streaming potential vs. treatment level data were fitted to a fourth-order regression model of the type Fig. 2. Results of streaming potential tests at increasing levels of either undyalized (top curves) or dialyzed (bottom curves) high-mass poly-dadmac to silica gel suspensions under the default conditions.

4 4 N. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 364 (2010) 1 6 y = ˇ0 + ˇ1x + ˇ2x 2 + ˇ3x 3 + ˇ4x 4 + ε to give suitable fits with adjusted R 2 values of approximately 0.93 for each of the plotted lines. When comparing the two streaming potential profiles in Fig. 2, the most distinguishing differences corresponding to undialyzed vs. dialyzed samples were at the highest levels of poly-dadmac treatment. In the case of the systems treated with (high molecular mass) dialyzed poly-dadmac, the measured streaming potential remained negative throughout the range of dosages considered. By contrast, positive values of streaming potential were obtained at highest levels of as-received, high-mass poly-dadmac. For example, at an addition level of 10% polymer to SiO 2 solids (log(% poly-dadmac) = 1), the regression lines gave streaming potential values of 2.9 and 1.4 mv, respectively for the undialyzed vs. dialyzed poly-dadmac. This difference was significant at the 95% confidence level. These results support a hypothesis proposed earlier [18 20], namely that low-mass material in the as-received (undialyzed) poly-dadmac [27] could permeate into the silica gel, and would have a significant effect on steaming potential tests carried out at very high concentrations in the bulk solution. Alternative explanations for the observations described above were also considered. For instance, it can be argued that the highmass poly-dadmac molecules in solution adopt coiled shapes that prevent them from efficiently covering 100% of the outer surface of a silica particle. In such a situation, the presence of a lower-mass population of oligomers in the sample might be expected to fill in the uncovered areas, possibly leading to a more positive streaming potential. In contrast, in the case of adsorption onto a silica gel particle, the low-mass oligomers presumably would be able to migrate into the pore structure of the silica gel particles, rendering the outer surfaces of the particles less positive. The suggested effects, however, are unlikely to take place, because it is known that high-mass polymers of moderately high affinity compete for adsorption sites, even to the extent that they tend to displace lowermass polymers of the same type [28,29]. Also, while the average conformation of dissolved polymers could be described as spherical in shape, especially under conditions of low ionic strength, they are expected to adopt flatter conformations in the adsorbed state, especially when interacting with a substrate of opposite charge [14]. An additional reason to reject the explanation give above is that it does not account for the effect of dialysis on results of experiments carried out with just silica gel as the substrate, as in Fig. 2. Another issue that may affect the streaming potential results from systems of mesoporous particles is that the volumetric flow around such particles is typically many factors of ten greater than the flow through the particles. However, it should be noted that streaming potential effects arise due to double-layers that are limited to the region within a few nm of the surfaces. Because the applied pressure can be expected to govern the velocity gradient adjacent to the wetted surfaces, one can expect the contribution to electrokinetic effects to be approximately proportional to the wetted surface area, as long as a continuous network of pores exists. As mentioned earlier, deviations from this rule can be expected when the electrical conductivity is very low [18,22 24], but not in the presence of the default of buffer solution used during the present work. Fig. 3. Effect of dosage of high-mass cationic polymer in the bulk solution during equilibration (relative to the dry mass of silica gel) on the streaming potential measured in the presence of fresh default buffer. Note that the error limits are small relative to the size of the plotted symbols. changes associated just with poly-dadmac adsorption and permeation during a defined period of equilibration. As shown, the degree of permeation tended to increase with increasing cationic p-dadmac treatment during the equilibration period. Fig. 4 shows the results of similar tests with both very-lowmass and high-mass poly-dadmac (as received). In the case of the very-low-mass cationic polymer (upper curve), the observed streaming potential rose almost in direct proportion with the logarithm of polymer dosage. Interestingly, the results for high-mass poly-dadmac showed a somewhat different trend, with a less apparent effect of dosage. These results are tentatively attributed to (a) a relatively strong adsorption of high-mass polyelectrolyte onto the outer surfaces of the gel particles, reaching near-saturation at relatively low treatment levels, and (b) a substantially less tendency to permeate into the mesoporous structure, compared with the very-low-mass poly-dadmac Effects of ph As shown in Fig. 5, the ph at which the system was equilibrated had a large effect on the streaming potential measured. In these tests, again the streaming potential was measured with poly-dadmac-free buffer with 1000 S/cm conductivity, in order 3.3. Effects of polyelectrolyte dosage and molecular mass Fig. 3 shows the results of streaming potential tests carried out within a broader range of poly-dadmac treatment levels during over-night equilibration. Streaming potential was evaluated with fresh buffer solution (poly-dadmac free buffer with 1000 S/cm conductivity), instead of the original liquid with which the silica gel had been equilibrated. By this approach it was possible to observe Fig. 4. Effect of cationic polymer dosage (very low vs. high mass) on the streaming potential of silica gel particles, with tests carried out in the presence of fresh default buffer.

5 N. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 364 (2010) Fig. 5. Effect of ph on the streaming potential of silica gel particles treated with very-low-mass poly-dadmac and evaluated with fresh default buffer solution. The limit bars shown 95% confidence intervals for the observations. to observe changes associated with poly-dadmac adsorption and permeation, not those due to the direct effect of ph on the streaming potential of the substrate itself. As shown, the least change in streaming potential, relative to the 13 mv measured for untreated silica gel under the same electrolyte conditions, was observed at the highest ph of equilibration. The greatest change in streaming potential, even achieving positive SP values, was observed when the equilibration was at ph values below 5. The trends shown in Fig. 5 directly contradict a possible hypothesis that permeation might be favored by increasing strength of electrostatic attraction between the polyelectrolyte and the substrate. It is well known that SiO 2 surfaces become more negative with increasing ph [30 32] and that the charge characteristics of positively charged poly-dadmac are essentially ph-independent [33]. Thus, a stronger electrostatic interaction is expected at high ph, presumably providing a greater driving force favoring eventual permeation into the negatively charged pores. A more successful way to explain the effect of ph is based on the principle of trapped, non-equilibrium states [14,34]. Accordingly, it is reasonable to expect that a relatively strong electrostatic interaction might result in polyelectrolyte molecules becoming essentially immobilized at their positions of first contact with the strongly negative substrate, i.e. on the outer surfaces and at or near the entrances into the porous network within the silica gel. Subsequent movement of the adsorbed polyelectrolytes, either by transient desorption or by reptation [14], would be greatly suppressed due to multiple simultaneous points of attachment. By contrast, at relatively low ph, where the negative charge density of the silica surface is expected to be much weaker [30 32], one would expect polyelectrolytes to be more able to continue their permeation into the pore network, thus allowing additional macromolecules to occupy their recently vacated positions, and so on. This same mechanism also was found to explain many of the effects recently observed by Horvath et al. [7] in their study of cationic polyelectrolyte adsorption into cellulosic fibers. Fig. 6 shows corresponding results obtained for systems treated with high-mass undialized poly-dadmac at the 0.2% level and compared with a control experiment (in the absence of poly- DADMAC). Again, the testing was done with fresh buffer solution having a conductivity of 1000 S/cm. It is clear from these results that although the cationic polymer had a large effect on the streaming potential at each of the ph values considered, the sign of potential was not reversed. These results, which agree with previous findings [18], are attributed to the fact that the interior surfaces within mesopores were not covered by cationic polymer, and such Fig. 6. Effect of ph on the streaming potential of silica gel particles treated with high-mass poly-dadmac (0.2% level) and evaluated with fresh default buffer. The control tests were without the presence of poly-dadmac. surfaces can be expected to contribute a negative component to the overall electrokinetic effect Effects of salt concentration Reasons to expect that the concentration of a monomeric electrolyte in the solution might affect permeation of a cationic polyelectrolyte into silica gel include (a) the more condensed conformation of polyelectrolytes [35], and (b) a weakening of the electrostatic interactions between the polyelectrolyte and substrate surfaces with increasing salt levels [14,36]. As shown in Fig. 7, there was only a very modest increase in the positive value of streaming potential with increasing conductivity during the over-night equilibration in the presence of very-low-mass poly- DADMAC. Though this finding is consistent with the mechanism described in the previous subsection, i.e. an expected weakening of the electrostatic attraction between the macromolecules and the substrate with increasing salt, the results suggest that such a mechanism did not have a large effect. An alternative explanation for an effect of electrical conductivity can be based on changes in the radii of gyration of the polyelectrolytes in solution; indeed the tests related to molecular mass (see Figs. 2 and 4) already had established that smaller molecules are more able to permeate into the silica gel. Issues related to geometrical constraints, effects Fig. 7. Effect of electrical conductivity during equilibration (adjusted by sodium sulfate addition) on the streaming potential of silica gel treated with very-lowmass versus high-mass poly-dadmac at the 1% level on SiO 2 solids with evaluation carried out with default buffer.

6 6 N. Wu et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 364 (2010) 1 6 of salt ions, and desorption will be further considered in subsequent articles. One of the unresolved questions from the present work is why the effects of changed conductivity were not more pronounced, especially in light of the more marked changes that resulted from differing ph values during equilibration of the silica gel with poly-dadmac solutions. One might argue, for instance, that a higher electrical conductivity should have had a similar effect to a reduction in ph, since both conditions would tend to decrease electrostatic attraction forces between the polyelectrolyte and the substrate. It is notable, however, that the high end of the salt concentration range in the present work was not as high as that considered in relevant previous studies [36]. Tests at higher salt levels would be helpful in the future to shed more light on these issues. Two further sets of issues that lie beyond the scope of the present article are time-related effects on streaming potential and measurements of adsorbed amounts. These and other effects will be explored more fully in future publications. 4. Conclusions A streaming potential protocol was used for the first time to obtain evidence of different factors affecting cationic polyelectrolyte penetration into silica gel particles from aqueous solutions during a fixed period of equilibration. The tendency for poly-(diallyldimethylammonium chloride) to permeate into silica gel particles increased with increasing bulk concentration and with decreasing molecular mass of the polyelectrolyte. Salt concentration did not have a marked effect on permeation within the range considered. The tendency of the cationic polyelectrolyte to permeate into the silica gel also increased markedly with decreasing ph. These results were attributed to strong immobilization of the polyelectrolyte under conditions favoring strong electrostatic attraction between the polyelectrolyte and the substrate. By contrast, conditions of low ph are expected to weaken the interaction forces, thus favoring easier migration adjacent to oppositely charged surfaces. Acknowledgments The authors wish to acknowledge the support of the graduate student Ning Wu by the Petroleum Research Fund, and the administration of the fund by the National Science Foundation (grant no AC5). References [1] L.M. Zhang, A review of starches and their derivatives for oilfield application in China, Starch-Starke 53 (2001) 401. [2] A.L. Kjoniksen, N. Beheshti, N.K. Kotlar, K.Z. Zhu, B. Nystrom, Modified polysaccharides for use in enhanced oil recovery applications, Eur. Polym. J. 44 (2008) 959. [3] J. Wang, M. Dong, Optimum effective viscosity of polymer solution for improving heavy oil recovery, J. Petrol. Sci. Eng. 67 (2009) 155. [4] J.L. 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