Polyelectrolytes osmotic pressure

These results show more clearly than Fq. (8.126)-of which they are special cases-the effect of charge and indifferent electrolyte concentration on the osmotic pressure of the solution. In terms of the determination of molecular weight of a polyelectrolyte by osmometry. ... 

If 0.6 N lithium bromide is added to the solution of the polyelectrolyte and also to the solvent on the opposite side of the osmometer membrane, the lowermost set of points in Fig. 145 (lower and left scales) is observed. The anion concentration inside and outside the coil is now so similar that there is little tendency for the bromide ions belonging to the polymer to migrate outside the coil. Hence the osmotic pressure behaves normally in the sense that each poly electrolyte molecule contributes essentially only one osmotic unit. The izjc intercept is lower than that for the parent poly-(vinylpyridine) owing to the increase in molecular weight through addition of a molecule of butyl bromide to each unit. 

The precipitation of polyelectrolytes by the addition of multivalent counterions may be explained in these terms. When there are no multivalent ions in solution there is a strong repulsive force between polyions and the osmotic pressure is large. The solubility of polyions is a result of these repulsive forces. 

The nion term is simply an expression for the osmotic pressure generated across a semipermeable membrane effectively, the gel serves as a membrane which restricts the polyelectrolytes to one phase, while small ions can readily redistribute between phases. Assuming that the ions form an ideal solution, the expression for nion becomes simply... 

If salt is present in the solution, counterions as well as co-ions do penetrate into the brush, which leads to additional screening of the Coulomb repulsion inside the brush. The amount of this screening, and the stretching of the polyelectrolyte chains, are now also controlled by the bulk salt concentration. Since the additional salt screening weakens the swelling of the brush caused by the counterion osmotic pressure, salt leads to a brush con-... 

Krigbaum, W.R. and Flory, P.J. 1952. Treatment of osmotic pressure data. J. Polym. ScL, 9 503. Kulichke, W. 2004. Viscometry of Polymers and Polyelectrolytes. Springer, New York. 

Analysis of polyelectrolytes in the semi-dilute regime is even more complicated as a result of inter-molecular interactions. It has been established, via dynamic light-scattering and time-dependent electric birefringence measurements, that the behavior of polyelectrolytes is qualitatively different in dilute and semi-dilute regimes. The qualitative behavior of osmotic pressure has been described by a power-law relationship, but no theory approaching quantitative description is available. 

We present a review of theoretical and experimental results on the swelling behavior and collapse transition in polymer gels obtained by our group at Moscow State University. The main attention is paid to polyelectrolyte networks where the most important factor is additional osmotic pressure created by mobile counter ions. The influence of other factors such as condensation of counter ions, external mechanical force, the mixed nature of low-molecular solvents, interaction of network chains with linear macromolecules and surfactants etc. is also taken into account Experimental results demonstrate a good correlation with theoretical analysis. 

In the polyelectrolyte regime, due to the presence of low-molecular salt, the osmotic pressure of ions becomes less pronounced because the concentration of salt within the network turns out to be less than the concentration of salt in the outer solution n [27]. As the concentration ns grows, the amplitude of the jump of the dependence a(x) decreases and the jump shifts to the region of better solvents (Fig. 2, curve 2). At some critical value of n, the jump on the curve a(x) disappears, i.e. collapse of the network becomes smooth (Fig. 2, curve 3). Under the subsequent increase of n, the curve a(x) becomes closer and closer to the swelling curve of corresponding neutral network (Fig. 2, curves 4). 

Another viable method to compare experiments and theories are simulations of either the cell model with one or more infinite rods present or to take a solution of finite semi-flexible polyelectrolytes. These will of course capture all correlations and ionic finite size effects on the basis of the RPM, and are therefore a good method to check how far simple potentials will suffice to reproduce experimental results. In Sect. 4.2, we shall in particular compare simulations and results obtained with the DHHC local density functional theory to osmotic pressure data. This comparison will demonstrate to what extent the PB cell model, and furthermore the whole coarse grained RPM approach can be expected to hold, and on which level one starts to see solvation effects and other molecular details present under experimental conditions. 

The osmotic pressure of a solution of non-interacting molecules or ions at the zero concentration limit is determined by the total molar concentration of solute species. In this hypothetical state, a solution of a polyelectrolyte may contain highly charged polyions at concentration c and monovalent counterions at a concentration where c is the molar concentration of the polyelectrolyte and z is the number of counterions per polyion. Since the total molar concentration is c (z +1) c z for z l, the ideal osmotic pressure is... 

The mechanical properties of polyelectrolyte multilayer capsules have been subject of several studies using different methods. Baumler and co-workers [7] have used the micropipette technique and found that PMCs are not conserving their volume if pressure differences are applied between inside and outside of the shell. This is expected, since the shells can only be formed in first place because the membrane is permeable to low molecular weight species, the core dissolution products. They found no deformation up to a critical pressure followed by an irreversible collapse, showing that shells deform not elastically but plastically for large deformations. First quantitative estimates of the Young s modulus of the shell material were obtained by Gao and coworkers, using osmotic pressure differences between inside and outside of the shell [8,9], These authors monitored the onset of the buck-... 

The osmotic pressure ti of a polyelectrolyte solution is complex, since it depends largely on the amount of salt added. In order to determine the molecular weight of the polyelectrolyte by measuring the osmotic pressure it is important to add a small amount of salt and plot nfc against the concentration c at a constant salt concentration. 

Theoretical discussion of the osmotic pressure of polyelectrolytes has been made by two methods, one using the Donnan equilibrium and the other the McMillan and Mayer theory. Both methods are equivalent but in order to obatin explicitly the osmotic pressure we should know in the former case the activities of component systems and in the latter case the potential of average force between the solute molecules. 

Gum arabic (acacia) has been used in pharmacy as an emulsifier. It is a polyelectrolyte whose solutions are highly viscous owing to the branched stmcture of the macromolecular chains its adhesive properties are also believed to be due to, or in some way related to, this branched stmcture. Molecular weights of between 200 000 and 250 000 (MJ have been determined by osmotic pressure, values between 250 000 and 3 x 10 by sedimentation and diffusion, and values of 10 by light scattering, which also points to the shape of the molecules as short stiff spirals with numerous side-chains. Arabic acid prepared from commercial gum arabic by precipitation is a moderately strong acid whose aqueous solutions have a pH of 2.2-2.7. It has a higher viscosity than its salts, but emulsions prepared with arabic acid cream are not as stable as those made with its salts. 

Keywords Polyelectrolytes, globular proteins, osmotic pressure, Poissson-Boltzman theory,... 

The so-called product reactant Ornstein-Zernike approach (PROZA) for these systems was developed by Kalyuzhnyi, Stell, Blum, and others [46-54], The theory is based on Wertheim s multidensity Ornstein-Zernike (WOZ) integral equation formalism [55] and yields the monomer-monomer pair correlation functions, from which the thermodynamic properties of the model fluid can be obtained. Based on the MSA closure an analytical theory has been developed which yields good agreement with computer simulations for short polyelectrolyte chains [44, 56], The theory has been recently compared with experimental data for the osmotic pressure by Zhang and coworkers [57], In the present paper we also show some preliminary results for an extension of this model in which the solvent is now treated explicitly as a separate species. In this first calculation the solvent molecules are modelled as two fused charged hard spheres of unequal radii as shown in Fig. 1 [45],... 

In a recent contribution [87] we studied the catalytic effect in polyelectrolyte-electrolyte mixtures by various theoretical techniques. For an isotropic model where the macroions, co-ions and counterions are pictured as charged hard spheres, we employed the HNC approximation, the modified PB and symmetric PB theories. The results for k/k° were compared with the computer simulations for the same quantity. Note that this quantity is much more sensitive to the details of the model and theory than thermodynamic properties like osmotic pressure studied before. The conclusion was that these theories are not well-suited to treat the problem they were capable of reproducing MC values only qualitatively and even this merely for low-charged macroions. 

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