Donnan equilibrium, polyelectrolyte

For homopolyelectrolyte, we first studied the ellipsometric measurement of the adsorption of sodium poly(acrylate) onto a platinum plate as a function of added sodium bromide concentration (5). We measured the effect of electrolyte on the thickness of the adsorbed layer and the adsorbances of the polyelectrolyte. It was assumed that the Donnan equilibrium existed between the adsorbed layer and the bulk phase. The thickness was larger and the adsorbance of the polyelectrolyte was lower for the lower salt concentration. However, the data on the molecular weight dependence of both the adsorbance and the thickness of the adsorbed polyelectrolyte have been lacking compared with the studies of adsorption of nonionic polymers onto metal surfaces (6-9). 

Since the components in the adsorbed polyelectrolyte layer are considered to be the same as the bulk phase with a three component system which consists of polyelectrolyte, simple salt, and water, we calculate the adsorbances of polyelectrolyte and salt by assuming the Donnan equilibrium between the bulk phase and the adsorbed polyelectrolyte layer, as described previously (5). 

A related phenomenon occurs when the membrane in the above-mentioned experiment is permeable to the solvent and small ions but not to a macroion such as a polyelectrolyte or charged colloidal particles that may be present in a solution. The polyelectrolyte, prevented from moving to the other side, perturbs the concentration distributions of the small ions and gives rise to an ionic equilibrium (with attendant potential differences) that is different from what we would expect in the absence of the polyelectrolyte. The resulting equilibrium is known as the Donnan equilibrium (or, the Gibbs-Donnan equilibrium) and plays an important role in... 

FIG. 3.1 Donnan equilibrium and regulation of ionic concentrations resulting from the presence of a semipermeable membrane (a) conditions in the absence of polyelectrolyte molecules and (b) ionic concentrations and electrical gradients in the presence of the polyelectrolyte. The membrane is permeable to water and K+ and Cl , but not to the polyelectrolyte Pz. ... 

Sukhorukov GB, Brumen M, Donath E, Mohwald H. Hollow polyelectrolyte shells exclusion of polymers and donnan equilibrium. Journal of Physical Chemistry B 1999, 103, 6434-6440. 

Transport of salt and water into a capsule was considered in [3], Osmotic swelling of the capsule was assumed to be due to Donnan equilibrium between the salt solution outside the capsule and the interior solution which also contained polyelectrolyte molecules. The polyelectrolyte was unable to pass through the membrane which formed the wall of the capsule, but salt could pass freely. A model similar to that used for the clay membrane predicts two relaxation rates, only one of which was observed in experiments in which the salt concentration was varied in the external reservoir [4],... 

We now consider a capsule which consists of liquid surrounded by a closed semi-permeable membrane (figure 2) details are provided in [3,4], Water and salt can pass through the membrane from side 1 (inside the capsule) to side 2 (outside), and vice versa, but large polymer molecules cannot. Trapped inside the capsule are n p polyelectrolyte molecules of valence zp and partial molar volume Tip. The resulting Donnan equilibrium is reviewed in [5, 6], Inside the capsule, electroneutrality requires zpn p + z+n + + Z-ri - = 0. We now assume the salt to be monovalent. At equilibrium there is a jump in electrical potential across the membrane inside the capsule x +xi- r X2+X2- x2 with x = (Q =F zpX p) where... 

Note that this treatment inherently takes into account the effect of the Donnan equilibrium. The osmotic coefficient obtained therefore is that of the polyelectrolyte with no further Donnan correction term being necessary. 

Fig. 7 Ionic strength of the micellar polyelectrolyte shell as a function of added salt concentration. The solid line is a fit to a simple Donnan equilibrium as described by Eq. (2) [49]...

Equation (6.148) is the well-known Donnan equilibrium of salt across a membrane in the presence of a polyelectrolyte, to which the membrane is permeable. It demonstrates the characteristic properties of the chemical potentials of neutral salts. 

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. 

Vlachy, V., and Prausnitz, J.M. Donnan equilibrium - hypernetted-chain study of one-component and multicomponent models for aqueous polyelectrolyte solutions. Journal of Physical Chemistry, 1992, 96, No. 15, p. 6465-6469. 

The solvent in this case is a salt solution (solvent with small ions) which is in Donnan equilibrium with the polyelectrolyte solution, the index /xs means that the chemical potentials of all the solutes except that used in differentiation are constant, and K is given as [39]... 

Interesting peculiarities of mass transfer processes are observed in fine membranes permeable to ions but impermeable to colloidal particles (semipermeable membranes, e.g. collodium film). If such a membrane separates colloidal system or polyelectrolyte solution from pure dispersion medium, some ions pass through the membrane into the dispersion medium. Under the steady-state conditions the so-called Donnan equilibrium is established. By repeatedly replacing the dispersion medium behind the membrane, one can remove electrolytes from a disperse system. This method of purifying disperse systems and polymer solutions from dissolved electrolytes is referred to as the dialysis. 

Effect of Electrolyte, Emulsions stabilized with hydrophobically modified poly(acrylic acid) are sensitive to electrolytes. Upon contact with a brine solution, emulsion stability is immediately lost, and rapid coalescence of the oil droplets ensues (Figure 23). This instability can be understood by consideration of the Donnan equilibrium of counterions in polyelectrolytes (discussed earlier in this chapter). Addition of salt causes collapses of the polyelectrolyte microgels that are adsorbed at the oil-water interface. Shrinkage of the microgels could conceivably lead to immediate loss of stability, as depicted schematically in Figure 24. 

Applying the procedure of the theory of Flory on the expansion factor of a polyelectrolyte in dilute solutions, based on the Donnan equilibrium[19], to the polyion chain between entanglement points, we have... 

In summary, we conclude that the linear viscoelastic properties of entangled-polyelectrolyte solutions in the terminal regions can be well explained by the reptation model taking into account the electrostatic interactions evaluated by the Donnan equilibrium [10,11]. 

For a polyelectrolyte gel, however, the ionic strength or salt concentration in the gel is not known. In diis case, usually we first use linear counterion condensation tiieory to find the counterion concentration, then we use Donnan equilibrium to calculate the sdt concentration. From the counterion concentration and salt concentration we can find the ionic strength. Then the ionic strengA is used to solve the nonlinear Poisson-Boltzmann equation to find the real counterion condensation and effective degree of... 

The Donnan effect is at the basis of the Donnan equilibrium, which describes the equilibrium distribution of small ions in a system containing macro-ions such as polyelectrolytes or charged colloidal particles. The Donnan equilibrium may be best illustrated by considering a system where a macro-ion M P " in a solution containing a low molecular weight electrolyte M+X is separated from a solution of only M+X . The separation is by a membrane that is permeable to the solvent (water) and M+ andX , but not to the macro-ion Figure 9.12 shows a system where a coUoidal... 

A recent model, based on the Donnan equilibrium concept, but with a different approach, is the elastic polyelectrolyte network (EPN) model. In the EPN model (Orsetti, Andrade, and Molina 2010), the HS particles are considered as divided in to two fractions an inner fraction gf, which behaves as a gel in Donnan equilibrium with the bulk solution, and an external fraction 1-g/, which is in equilibrium with the bulk (Figure 13.8) thus, it is assumed that a fraction gf of the total number of sites resides inside the gel phase, whereas a fraction f-g/ resides outside the gel given an affinity spectrum, it applies to the external sites in equilibrium with the bulk solutions, with activity a for ion i, whereas for the internal medium, it is applied the internal activity aP, in Donnan equilibrium with the bulk ... 

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... 

The value of n for a polyelectrolyte solution will generally manifest nonideal chain mixing as well as the Donnan effect. Because of intermolecular electrostatic repulsions, A2 is nearly always positive and large for polyelectrolytes. When A2 0, an approximate expression corresponding to equation 37 for a polyelectrolyte solution in Donnan equilibrium can be written as (33,37)... 

The most distinctive features of polyelectrolyte gels come from the third term, Gosmotic- Because the gel s fixed charges cannot escape the network, polyelectrolyte gels establish Donnan equilibrium with a bathing solution containing... 

Donnan equilibrium in ionic systems requires charge neuttal-ity on both sides of the membrane aaoss which the osmotic pressure rr is measured. The electroneutrality condition leads to the pattitioning of salt ions between the reservoir and the polyelectrolyte solution region... 

Fig. 5.1. Schematic representation of the Donnan equilibrium situation developing in the presence of bulk polymeric acid not capable to penetrate the wall of hollow polyelectrolyte capsule.

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