Donnan osmotic pressure

Adamson (51) proposed a model for W/0 microemulsion formation in terms of a balance between Laplace pressure associated with the interfacial tension at the oil/water interface and the Donnan Osmotic pressure due to the total higher ionic concentration in the interior of aqueous droplets in oil phase. The microemulsion phase can exist in equilibrium with an essentially non-colloidal aqueous second phase provided there is an added electrolyte distributed between droplet s aqueous interior and the external aqueous medium. Both aqueous media contain some alcohol and the total ionic concentration inside the aqueous droplet exceeds that in the external aqueous phase. This model was further modified (52) for W/0 microemulsions to allow for the diffuse double layer in the interior of aqueous droplets. Levine and Robinson (52) proposed a relation governing the equilibrium of the droplet for 1-1 electrolyte, which was based on a balance between the surface tension of the film at the boundary in its charged state and the Maxwell electrostatic stress associated with the electric field in the internal diffuse double layer. 

The Donnan osmotic pressure in Eq. 22 can be expanded to the virial form... 

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... 

N-isopropylacrylamide (NIPA) has both hydrophobic (rectangle) and hydrophilic (circle) components, while methacrylic acid (MAA) is ionizable. Temperature- and pH-dependent ionization state of MAA controls hydropho-bic/hydrophilic balance of NIPA, and ionization of MAA also leads to swelling due to Donnan osmotic pressure. Reproduced from Ref [28] with kind permission of Springer Science and Business Media 2009. 

A second potential player is Ca, which is generated by the marble reaction [112]. This species should also accumulate with time. It also may affect the membrane s swelling properties as a result of favorable Donnan partitioning and reduction in Donnan osmotic pressure. The dynamics and effect of Ca have not... 

For < 1, the expression is cumbersome and will not be given here. Note that Equation (100) is compatible with Equation (99). Again for a 1 1 electrolyte, the Donnan osmotic pressure tid may be shown [46] to be closely related to the diflFerence... 

A semi-permeable membrane, which is unequally permeable to different components and thus may show a potential difference across the membrane. In case (1), a diffusion potential occurs only if there is a difference in mobility between cation and anion. In case (2), we have to deal with the biologically important Donnan equilibrium e.g., a cell membrane may be permeable to small inorganic ions but impermeable to ions derived from high-molecular-weight proteins, so that across the membrane an osmotic pressure occurs in addition to a Donnan potential. The values concerned can be approximately calculated from the equations derived by Donnan35. In case (3), an intermediate situation, there is a combined effect of diffusion and the Donnan potential, so that its calculation becomes uncertain. 

The experimental verification of Gibbs theorem. Since the osmotic pressure of a solution is generally difficult to measure, it is simplest to choose a case such that Raoult s law holds good and the concentration of the solution may be used in place of osmotic pressure. The solution should therefore be dilute and should be a true solution the solute, that is, must be dispersed as simple molecules and not as molecular aggregates like soap micelles. These conditions were obtained by Donnan and Barker Proc. 

The influence of neutral salts as well as of acids and bases on the swelling of gelatine which we have seen can be attributed to an apparent change in the solvation of the gel fibrils and may be interpreted in the light of Donnan s theory of the effect of a non-diffusible ion on the osmotic pressure differences between the two phases, is likewise to be noted in the alteration of the viscosity and alcohol precipitation values of protein solutions. From the considerations already advanced there should exist two well-defined maxima in the viscosity and alcohol precipitation curves when these properties are plotted as functions of the Ph, the maxima coinciding with the points of maximum dissociation of the salts... 

Equilibrium thermodynamics of solutions of colloidal solutes determines the quantitative details of osmotic and Donnan equilibria and occupies our concern in this chapter. In particular, our discussion here centers on the osmotic pressure. 

Elementary and advanced treatments of such cellular functions are available in specialized monographs and textbooks (Bergethon and Simons 1990 Levitan and Kaczmarek 1991 Nossal and Lecar 1991). One of our objectives in this chapter is to develop the concepts necessary for understanding the Donnan equilibrium and osmotic pressure effects. We define osmotic pressures of charged and uncharged solutes, develop the classical and statistical thermodynamic principles needed to quantify them, discuss some quantitative details of the Donnan equilibrium, and outline some applications. 

We conclude the chapter with a discussion of the Donnan equilibrium and the thermodynamic behavior of charged colloids, particularly with respect to osmotic pressure and molecular weight determination (Section 3.5), and some applications of osmotic phenomena (Section 3.6). 

If the gel has ionic groups, a Donnan-type potential due to the presence of the translational entropy of the counter ions also contributes to the osmotic pressure, which is given by... 

The contribution fl>3 corresponds to the difference between the osmotic pressure in the ionized gel and in external solution (mixing of ions with the slovent). From the Donnan equilibrium we obtain... 

Clearly, the results of osmotic pressure measurements on solutions of charged colloidal particles, such as proteins, will be invalid unless precautions are taken either to eliminate or to correct for this Donnan effect. Working at the isoelectric pH of the protein will eliminate the Donnan effect but will probably introduce new errors due to coagulation of the protein. Working with a moderately large salt concentration and a small protein concentration will make the... 

Bell and co-workers84 confirmed the lowering of osmotic pressure in the presence of salts as observed by Oakley and Young.32 These authors suggested that as disaggregation and the Donnan effect were unlikely, an explanation might be that the salt caused a decreased asymmetry in the molecule with a resultant entropy change. 

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