Osmotic pressures of polyelectrolytes

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. 

Before presenting numerical results, it is worth summarizing the main characteristics of the experimental results for the osmotic pressure of polyelectrolyte solutions [9, 17, 18, 57, 107], The measured osmotic coefficients most often exhibit strong negative deviations from ideality. The measured values are a) lower than it was predicted by the cylindrical cell model theory, b) rather (but not completely) insensitive to the nature of the counterions, and c) also insensitive to the polyelectrolyte concentration in a dilute regime and/or for... 

Takahashi A, Kato T, Nagasawa M. The osmotic pressure of polyelectrolyte in neutral salt solutions. J Phys Chem 1970 74 944-946. 

The membranes used to measure the osmotic pressure are impermeable to polyions but permeable to counter-ions. In spite of this, the osmotic pressure of polyelectrolytes in pure water and for rather small concentrations (but in the semi-dilute regime), is huge. Let us assume that the polyelectrolyte has been put in cell I (see Fig. 5.1). It partially ionizes but both cells must remain practically neutral. The counter-ions which, theoretically, can cross the membrane, are retained in cell I and a contact-potential difference appears at the boundary between the cells. Actually, it looks as if the counter-ions contributed like polyions to the osmotic pressure. Let C be the polyion concentration. We may write approximately... 

Wang L, Bloomfield VA (1990) Osmotic pressure of polyelectrolytes without added salt. Macromolecules 23 804-809... 

The osmotic pressures of polyelectrolyte solutions are most often measured in the presence of a membrane permeable to solvent and small ions but not to polyelectrolyte. The chemical potentials of the added electrolyte and solvent on each side of the membrane in this instance match, a condition defining Donnan equilibrium (200). Assuming ideal chain mixing, the quantity measured here is the Donnan osmotic pressure which can be equated to the difference of the osmotic... 

At low salt concentrations, c, y, the ionic contribution to the osmotic pressure/rf dominates over the polymeric contribution throughout the entire semidilute regime. At high salt concentrations, Cs /-c, both ionic and polymeric contributions are much smaller than those at low salt concentrations. However, for the vast majority of the systems studied so far, the ionic contribution dominates the osmotic pressure of polyelertrolj e solutions. Therefore, eqn [151] is a good approximation of the osmotic pressure of polyelectrolyte solutions. 

The osmotic pressure of polyelectrolytes in salt-free solutions exceeds that of neutral polymers at similar polymer concentrations by several orders of magnitude. It increases almost linearly with polymer concentration and is independent of the chain molecular weight in a wide range of polymer concentrations. This almost linear concentration dependence of the osmotic pressure together with its strong dependence on added salt demonstrates that osmotic pressure is mainly due to coimterion and salt ion contribution. 

The particular contribution to the osmotic pressure of polyelectrolyte solutions comes from counterions at low salt concentration [47-49]. 

The osmotic pressure of polyelectrolyte in added salt system is given by the sum of the osmotic pressure of each component, such as... 

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. ... 

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). 

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... 

Conformational Transition in Polyelectrolyte Molecules Influence of Osmotic Pressure of Counterions... 

On the other hand, for a macroscopic polyelectrolyte gel, which is a collection of an infinite number of macromolecules, the swelling is due to the osmotic pressure of counterions remaining within the sample of gel due to the macroscopic electroneutrality condition. The electrostatic interaction between charged units in this case is of secondary importance. 

We would like to stress that the physical reason of the polyelectrolyte gel expansion is the osmotic pressure of counterions, which originates from their translational entropy. Counterions possessing high translational entropy would like to leave the network sample. However, this is forbidden because of the condition of total electroneutrality. So the counterions create osmotic pressure on the sample of the polymer network. 

Strauss UP, Fuoss RM. Polyelectrolytes. V. Osmotic pressures of poly-4-vinyl-V-ra-butylpyridonium bromide in ethanol at 25°. J Polym Sci 1949 4 457-472. 

Pincus [212] has studied polyelectrolyte chains the monomers of which are in 0 solvent conditions, i.e., the excluded volume is zero. This assumption is justified by the fact that most polyelectrolytes are rather hydrophobic and their solubility in water is only due the presence of charges along the chains. The author shows that electroneutrality is locally achieved within the brush, providing that the fraction of charged monomers p and the densities of adsorption points l/d2 are not too low. Actually, the high concentrations of charged monomers and counterions lead to a Debye length much lower than the brush thickness. Consequently, the only relevant electrostatic contribution to the forces within the brush is the osmotic pressure of the counterions, which behave as a constraint ideal gas with a pressure equal to pckT, in the absence of added salt. Hence the equilibrium thickness of the brush results from the balance between the elastic force and the counterions ... 

Fig. 5.11. Measured values of the osmotic pressure of an aqueous solution of sodium polystyrene-sulphonate for various values of the mass concentration p[g/Z] of polyelectrolyte. Molecular mass M = 3.5 x lO5.10...

In reality, a state of equilibrium is reached where the ionic attraction of the counterions by the polyanion is just balanced by diffusion into the external solution, which is driven by the chemical potential gradient, which in turn arises from the difference in counterion concentrations between the two domains. The overall effect closely resembles Donnan membrane equilibria (4) (Figure 3). As a consequence of the difference in counterion concentrations, the osmotic pressure inside the polymer domain exceeds that of the external solution, and the expansion of the polyelectrolyte can be equated to the difference in osmotic pressures of the intramolecular and intermolecular solutions. 

Electrochemical stimulated systems have potential biomedical and micromechanical application. Electrochemical stimuli controlled loading/adsorption onto oppositely charged polyelectrolyte materials on porous microspheres that was previously reported by Malinova and Wandrey. ° Electrochemical stimuli cause an increase in osmotic pressure of the redox-active polyelectrolyte... 

These authors observed that intrinsic viscosities and osmotic pressures of the DVE-MA copolymer when measured in DMF showed unusual slopes, suggestive of polyelectrolyte behavior. Their intrinsic viscosity data are shown in Figure 11 and their osmotic pressure data are shown in Figure 12. 

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