On the theory of dilute polyelectrolyte solutions: Extensions,refinements, and experimental tests

We synthesize a quantitative theory for the radius of gyration, second virial coefficient, intrinsic viscosity, and friction coefficient for polyelectroytes in dilute solution from existing treatments of electrostatic and hydrodynamic interactions within and among wormlike chains. Comparison with data for K-PSS demonstrates the importance of accounting for nonlinearities in the electrostatics and the finite diameter of the polymer backbone.     

Effect of NaCl on the self-aggregation of n-octyl beta-D-thioglucopyranoside in aqueous medium

This report investigates the effect of sodium chloride (NaCl) on the micellization, surface activity, and the evolution in the shape and size of n-octyl beta-D-thioglucopyranoside (OTG) aggregates. By using surface tension measurements, information was obtained on both changes in the critical micelle concentration and adsorption behavior in the air-liquid interface with the electrolyte concentration. These data were used to obtain the thermodynamic properties of micellization along with the corresponding adsorption parameters in the air-liquid interface. From extended static and dynamic light scattering measurements, the micelle molecular weight, the mean aggregation number, and the second virial coefficient, the apparent diffusion coefficient and the mean hydrodynamic radius of micelles in a range of NaCl concentrations were obtained. The light scattering data have shown that when the surfactant concentration is lower to 4.5 g/L, only spherical micelles are formed. However, an increase in the surfactant concentration induces an increase in micellar size, suggesting a rodlike growth of the micelles. This deviation of micelle geometry from spherical to rodlike is supported both by the ratio between the hydrodynamic radius and the radius of gyration and by the angular dependence of light scattering. On the other hand, the studies performed in the presence of high NaCl concentration (0.2 and 0.5 M) provide strong support for the view that the micelles may overlap together to form an entangled network above certain crossover concentration.     

Thermodynamic and conformational properties of polystyrene. III. Dilute solution studies on branched polymers

Light-scattering and viscometric measurements on dilute solutions of five branched polystyrene polymers are reported. The data include studies in decalin as a function of temperature, including the theta temperature, and in toluene. The results for the radius of gyration and the second virial coefficient are not in accord with the two parameter random-flight model. Possible causes of this descrepancy are considered. It is shown that the intrinsic viscosity of branched chains is not uniquely determined by the radius of gyration.     

疏水缔合聚丙烯酰胺在盐水中的自组装行为

使用静态光散射、动态光散射以及原子力显微镜(AFM)研究了疏水缔合聚丙烯酰胺(HAPAM)在盐水溶液中的自组装行为.研究了聚合物分子在不同盐浓度中的表观重均分子量(Mw,a),均方根回转半径(),流体力学半径(),第二维里系数(A2)的变化,并根据/的比值得出聚合物分子的聚集形态.实验结果表明:随着盐浓度的增强,聚合物溶液的分子链由舒展变得卷曲.     

Liquid‐like structure of polymer solutions near the overlap concentration

The light scattering structure factor S( q , c) has been measured for a series of concentrations near the overlap value c* for solutions of high molecular weight poly(α‐methyl styrene) in the good solvent toluene. Scattering functions near and above overlap are characterized by a maximum as a function of scattering vector q . Scattering functions have also been calculated for these conditions using the measured second virial coefficient and radius of gyration, as reported previously for dilute solutions. The scattering function is factored into an intramolecular part that is described by a Debye function with no adjustable parameters and an intermolecular part that depends on the coil–coil pair correlation function, as suggested by Flory and Bueche. The pair correlation function is calculated using the Percus–Yevick theory of liquids and the Flory–Krigbaum potential for coil–coil interactions, as suggested by Frank Stillinger. Good agreement is obtained for the most concentrated dilute solutions, but as the overlap concentration is approached significant discrepancies are observed. The thermodynamic value of the scattering function, S(0, c), is overestimated by the theory. This discrepancy is discussed in terms of the importance of three‐body interactions, the failure of the Flory–Krigbaum potential in semidilute solutions and the limited precision of the standard protocol for calculating the measured scattering function in nondilute solutions. The observed maximum in the scattering function near overlap is not quantitatively reproduced by the theory. This discrepancy is discussed in terms of the failure of the shape of the Flory–Krigbaum potential to accurately reflect the energy of overlap for chains separated by distances near twice the radius of gyration. The mean‐field nature of the potential ignores the increased probability of interactions of linear neighboring segments. Well into the overlap region, the calculated scattering function poorly describes the observed results. The failure of the Flory–Bueche approximation in semidilute solutions is discussed as well as the effect of a changing radius of gyration as a function of concentration on the intramolecular scattering function. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 703–710, 2006     

驱油用聚丙烯酰胺分子量测试的光散射研究

利用旋转流变仪分析了超高分子量部分水解聚丙烯酰胺溶液的流变性质,并根据光散射动态模式分析了其在不同浓度和不同盐离子浓度下的尺寸分布.建立了利用多角度激光光散射准确测量驱油用超高分子量聚丙烯酰胺重均分子量(Mw)、均方根回转半径()和第二位力系数值(A2)的方法.准确测量了商品化驱油用超高分子量聚丙烯酰胺FP3630S的这3个参数,分别为Mw=(1.33±0.06)×107,     

Solution properties of ultrahigh molecular weight polymers. VII. Conformational characteristics of poly(butyl methacrylate)

The paper is concerned with light scattering studies on solutions of ultrahigh molecular weight poly(butyl methacrylate). The dependence of the radius of gyration and of the second virial coefficient on the weight-average molecular weight of the polymers was established in methyl ethyl ketone, dimethylformamide, and CCl₄. Short-range and long-range interactions were discussed in terms of the steric factor σ, of the interaction parameter B, and of the interpenetration function ψ(z).     

水溶性高聚物聚丙烯酰胺的稀溶液性质(Ⅰ)

本工作利用光散射和粘度方法,使用辐射聚合聚丙烯酰胺(PAAM)的级分样品,研究了在较宽分子量范围(10~4-10~7)内PAAM的特性粘数,分子尺寸及第二维利系数对重均分子量的依赖性.从实验上得到了PAAM在0.2mol/lNaCl水溶液中的均方旋转半径与均方末端距之间的关系及高分子-溶剂相互作用参数.     

Molecular characterization of a hyperbranched polyester. II. Small‐angle neutron scattering

A series of fractions of a hyperbranched polyester in deutero tetrahydrofuran solution were investigated by small‐angle neutron scattering. Concentrations of polymer from 2 to 5% w/v were used, and the molecular parameters were obtained from Zimm plots of the data. Second virial coefficients were positive, and these values were confirmed by dilute‐solution light scattering on a small number of fractions with deutero tetrahydrofuran as a solvent. The small‐angle neutron scattering data exhibited the general features predicted for the particle scattering functions of nonrandomly branched polymers, but an exact fit of the theoretical equation to the data could not be obtained for all fractions of the hyperbranched polymer, particularly those of high molecular weight. Excluded volume effects were cited as a possible cause for this disagreement. A fractal dimension of ～2.5 was obtained from the scattering vector dependence of the differential scattering cross section of the polymer in deutero tetrahydrofuran solution, which agreed with the scaling exponent for the dependence of the radius of gyration on weight‐average molecular weight. Hydrogenous tetrahydrofuran solutions of the hyperbranched polymer exhibited negative second virial coefficients that were attributed to isotopic influences on the thermodynamic properties of the polymer–solvent combination. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1352–1361, 2003     

The nonlinear change in conformation of polyelectrolyte macromolecules in saltless water-organic solvent

High molecular weight polyelectrolyte: poly(dimethylaminoethyl methacrylate) [PDMAEMA] with molecular weights M_W = 28.0×10⁶, 20.0×10⁶, 15.0×10⁶ was investigated in dilute solution by light scattering, flow birefringence and viscometry (at different rate gradients) in a water-acetone system by varying the weight fraction of acetone r in the mixture. At r=0.76 the polymer undergoes a reversible coil-globule transition accompanied by a drastic decrease in intrinsic viscosity [n], mean-square radius of gyration R²_z^1/2 and second virial coefficient A₂, with no change in molecular weight. The coil asymmetry parameter p (p=2.5 at r=0.50) decreases with increasing r and attains unity (completely symmetrical particle) at the transition point (r=0.76). The anomalous behavior of the viscosity of PDMAEMA-water-acetone solutions, detected near the transition point (r=0.6+0.7), is interpreted by formation of local knots of compactization on the molecular chain under the influence of a hydrodynamic field.     

Analysis of Light Scattering Data on the Calcium Ion Sensitivity of Caseinate Solution Thermodynamics: Relationship to Emulsion Flocculation

We describe the quantitative interrelation between the thermodynamic parameters of caseinate submicelles in the presence of calcium ions (0-14 mM) in aqueous medium and the capacity of the protein to induce depletion flocculation in oil-in-water emulsions at pH 7.0 and ionic strength 0.05 mol dm(-3). Measurements have been made by static and dynamic multiangle laser light scattering of the weight-average molecular weight, the radius of gyration, the hydrodynamic radius, and the second virial coefficient of caseinate submicelles in aqueous solution. Successive thermodynamic approximations with and without consideration of correlations between caseinate submicelles have been used to calculate the osmotic pressure in caseinate aqueous solutions and the free energy of the depletion interaction between droplets in oil-in-water emulsions stabilized by caseinate. Numerical results from both thermodynamic approximations are in reasonably good agreement with experiment, predicting a pronounced decrease in the strength of the depletion attraction at concentrations of Ca(2+) in the range 4-8 mM (with a minimum value at 8 mM). This correlates well with the great enhancement of stability of these emulsions with respect to flocculation in comparison with systems having no added ionic calcium and emulsions with lower (2 mM) or higher (10 mM) Ca(2+) contents. Nevertheless, the allowance for interactive correlations between caseinate submicelles seems to lead to a better prediction of emulsion flocculation on a qualitative level over the whole range of Ca(2+) concentrations studied (2-14 mM). The calculated pronounced decrease in depletion interaction strength is attributable to marked changes in weight-average molecular weight and mean size of aggregates, and to more positive values of the second virial coefficient of caseinate submicelles with increasing Ca(2+) content. Finally, we discuss the part played by the electrical charge on the protein in determining the overall strength of the flocculation-inducing attractive interactions between droplets. Copyright 2001 Academic Press.     

Investigation of the interaction of a polyelectrolyte with low molecular weight electrolytes containing nonidentical counterions by differential refractometry

If the counterion of a polyelectrolyte is not identical with any of the ions of a low molecular weight electrolyte added to the solution, the system may be regarded as a four-component system. Relations for the refractive index increments have been derived which allow the determination of the coefficient of selective sorption of the added electrolyte from the refractive index increments of the components independent of the original counterion of the polyelectrolyte. Equilibrium dialysis and differential refractometry were used to study the interaction of KCl, KBr and NaI with poly[-1(2-hydroxyethyl)pyridiniumbenzenesulfonate methacrylate] or with an analogous polymer containing a toluenesulfonate counterion in aqueous solutions. The coefficient of selective sorption increases in the series Cl^? < Br^? < I^? from strongly negative to strongly positive values; the specific interaction of these counterions with the macroion increases in the same order.     

水溶性高聚物聚丙烯酰胺的稀溶液性质(Ⅰ)

 本工作利用光散射和粘度方法,使用辐射聚合聚丙烯酰胺(PAAM)的级分样品,研究了在较宽分子量范围(10⁴-10⁷)内PAAM的特性粘数,分子尺寸及第二维利系数对重均分子量的依赖性.从实验上得到了PAAM在0.2mol/lNaCl水溶液中的均方旋转半径与均方末端距之间的关系及高分子-溶剂相互作用参数.     

Solution properties of poly(acrylamide-co-3,5,5-trimethylhexane methacrylate) and its polyelectrolyte derivative

The physicochemical properties of hydrophobically modified polyacrylamide (HAPAM) containing a small amount of hydrophobic groups (3,5,5-trimethylhexane methacrylate) and its partially hydrolyzed derivative (HAPAM-10N500) were investigated. The ¹³C spectrum was used to establish the degree of hydrolysis of HAPAM-10N500. Small-angle X-ray scattering (SAXS) was employed to highlight the polyelectrolyte character of HAPAM-10N500, estimate the chain conformation in the semidilute regime, and evaluate the influence of the ionic strength and the type of salt. The weight average molecular weight, the second virial coefficient, and radius of gyration were determined by static light scattering (SLS). The polymers showed different rheological properties in aqueous solution, with significant increase in viscosity due to partial hydrolysis of HAPAM, however, with strong dependence on ionic strength of the medium. Results showed that the polymers HAPAM and HAPAM-10N500 are suitable for application in processes of moderate temperatures and salinities.     

Microstructure and depletion forces in polymer-colloid mixtures from an interfacial statistical associating fluid theory

By using a classical density functional theory (interfacial statistical associating fluid theory), we investigate the structure and effective forces in nonadsorbing polymer-colloid mixtures. The theory is tested under a wide range of conditions and performs very well in comparison to simulation data. A comprehensive study is conducted characterizing the role of polymer concentration, particle/polymer-segment size ratio, and polymer chain length on the structure, polymer induced depletion forces, and the colloid-colloid osmotic second virial coefficient. The theory correctly captures a depletion layer on two different length scales, one on the order of the segment diameter (semidilute regime) and the other on the order of the polymer radius of gyration (dilute regime). The particle/polymer-segment size ratio is demonstrated to play a significant role on the polymer structure near the particle surface at low polymer concentrations, but this effect diminishes at higher polymer concentrations. Results for the polymer-mediated mean force between colloidal particles show that increasing the concentration of the polymer solution encourages particle-particle attraction, while decreasing the range of depletion attraction. At intermediate to high concentrations, depletion attraction can be coupled to a midrange repulsion, especially for colloids in solutions of short chains. Colloid-colloid second virial coefficient calculations indicate that the net repulsion between colloids at low polymer densities gives way to net attraction at higher densities, in agreement with available simulation data. Furthermore, the results indicate a higher tendency toward colloidal aggregation for larger colloids in solutions of longer chains.     

Electrostatic correlations in polyelectrolyte solutions

The major attribute of polyelectrolyte solutions is that all chains are strongly correlated both electrostatically and topologically. Even in very dilute solutions such that the chains are not interpenetrating, the chains are still strongly correlated. These correlations are manifest in the measured scattering intensity when such solutions are subjected to light, X-ray, and neutron radiation. The behavior of scattering intensity from polyelectrolyte solutions is qualitatively different from that of solutions of uncharged polymers. Using the technique introduced by Sir Sam Edwards, and extending the earlier work by the author on the thermodynamics of polyelectrolyte solutions, extrapolation formulas are derived for the scattering intensity from polyelectrolyte solutions. The emergence of the polyelectrolyte peak and its concentration dependence are derived. The derived theory shows that there are five regimes. Published experimental data from many laboratories are also collected into a master figure and a comparison between the present theory and experiments is presented.     

Binding of oppositely charged surfactants to spherical polyelectrolyte brushes: a study by cryogenic transmission electron microscopy

The formation of a complex between an anionic spherical polyelectrolyte brush (SPB) and the cationic surfactant cetyltrimethylammonium bromide (CTAB) is investigated. The SPB consists of long chains of the strong polyelectrolyte poly(styrene sulfonate) (PSS), which are bound chemically to a solid poly(styrene) core of 56 nm in radius. The SPB are dispersed in water, and the ionic strength is adjusted by addition of NaBr. The resulting complexes are investigated in dilute solution by dynamic light scattering, by electrophoretic light scattering, and by cryogenic transmission electron microscopy (cryo-TEM). The formation of the complex between the SPB and the surfactant can be monitored by a strong shrinking of the surface layer when adding CTAB to dilute suspensions (0.01 wt %) and by a decrease of the effective charge of the complexes. Complex formation starts at CTAB concentrations lower than the critical micelle concentration of this surfactant. If the ratio r of the charges on the SPB to the charge of the added surfactant is exceeding unity, the particles start to flocculate. Cryo-TEM images of the complexes at r = 0.6 measured in salt-free solution show that the surface layer composed of the PSS chains and the adsorbed CTAB molecules is partially collapsed: A part of the chains form a dense surface layer while another part of the chains or aggregates thereof are still sticking out. This can be deduced from the cryo-TEM micrographs as well as from the hydrodynamic radius, which is still of appreciable magnitude. The 1:1 complex (r = 1.0) exhibits a fully collapsed layer formed by the PSS chains and CTAB. If the complex is formed in the presence of 0.05 M NaBr, r = 0.6 leads to globular structures directly attached to the surface of the core particles. All structures seen in the cryo-TEM images can be explained by a collapse transition of the surface layer brought about by the hydrophobic attraction between the polyelectrolyte chains that became partially hydrophobic through adsorption of CTAB.     

Fluorescence correlation spectroscopy studies of diffusion of a weak polyelectrolyte in aqueous solutions

We apply fluorescent correlation spectroscopy (FCS) to investigate solution dynamics of a synthetic polyelectrolyte, i.e., a weak polycarboxylic acid in aqueous solutions. The technique brings single molecule sensitivity and molecular specificity to dynamic measurements of polyelectrolyte solutions. Translational diffusion of Alexa-labeled poly(methacrylic acid), PMAA*, chains was studied in very dilute, 10(-4) mg/ml, solutions as a function of solution pH and ionic strength. The observed changes in diffusion coefficients were consistent with about twofold expansion of PMAA* coils when pH was changed from 5 to 8, and with chain contraction for alkaline metal ion concentrations from 0.01 to 0.1 M. The dependence of the hydrodynamic size of PMAA* chains on the counterion type followed the sequence: Li(+)>Na(+) approximately equal to Cs(+)>K(+). The dependence of translational diffusion on polyacid concentration was weak at the low concentration limit, but chain motions were significantly slower at higher polymer concentrations when PMAA chains overlapped. Finally, measurements of dynamics of PMAA* chains in "salt-free" solutions showed that self-diffusion of PMAA* chains significantly slowed down when PMAA concentration was increased, probably reflecting the sensitivity of PMAA* translational motions to the onset of interchain domain formation. These results illustrate the utility of the FCS technique for studying hydrodynamic sizes of polyelectrolyte coils in response to variation in solution pH or concentration of salt and polyelectrolytes. They also suggest that FCS will be a promising technique for selective observation of the dynamics of polyelectrolyte components in complex polymer mixtures.     

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer's equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer's model (combining a long-range term, based on the Debye–Hückel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid–liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems.     

Entropy- or enthalpy-driven collapse of strongly charged polymer chains in a one-component charged fluid of counterions or coions

We applied a simulation method [T. Sumi and H. Sekino, J. Chem. Phys. 122, 194910 (2005)] to an infinitely dilute polyelectrolyte immersed in one-component charged fluids in order to investigate salt effects on its collapse. In this model system, the degree of freedom of the counterion (or the coion) is considered using a density-functional theory for polymer-solvent admixtures, while the oppositely charged ions are treated as a structureless background having the opposite charge. Results obtained by these simulations show that not only the counterion but also the coion makes the polymer chain collapsed. The effects by the coion are stronger than that by the counterion. Temperature variation of the gyration radius of the polymer chain immersed in the counterion is opposite to that in the coion: while the radius of gyration decreases as the temperature decreases in the case of the counterion, it decreases as the temperature increases in the case of the coion. From these results we conclude that the former is interpreted as an enthalpy-driven collapse caused by the screening effects of the counterion, whereas the latter is interpreted as an entropy-driven one due to the translational entropy of the coion.