Donnan pressure

In addition to the repulsive part of the potential given by Eq. (4), a short-range attraction between the macroions may also be present. This attraction is due to the van der Waals forces [17,18], and can be modelled in different ways. The OCF model can be solved for the macroion-macroion pair-distribution function and thermodynamic properties using various statistical-mechanical theories. One of the most popular is the mean spherical approximation (MSA) [40], The OCF model can be applied to the analysis of small-angle scattering data, where the results are obtained in terms of the macroion-macroion structure factor [35], The same approach can also be applied to thermodynamic properties Kalyuzhnyi and coworkers [41] analyzed Donnan pressure measurements for various globular proteins using a modification of this model which permits the protein molecules to form dimers (see Sec. 7). 

Colloid Osmotic Pressure When a colloidal system is separated from its equilibrium liquid by a semipermeable membrane, not permeable to the colloidal species, the colloid osmotic pressure is the pressure difference required to prevent transfer of the dissolved noncolloidal species. Also referred to as the Donnan pressure. The reduced osmotic pressure is the colloid osmotic pressure divided by the concentration of the colloidal species. See also Osmotic Pressure. 

We can now calculate the Donnan contribution to film pressure through the use of Eq. III-113 in the approximate form ... 

At what molecular area should a fatty-acid film spread on 0.05A/ NaOH have a film pressure of 4 dyn/cm, according to the Donnan treatment and to the Gouy treatment Assume the hydrocarbon part of the film to behave as an ideal gas. Assume 20°C. 

Typical SAH are weakly charged flexible networks. A simple theory was proposed to describe these networks, in which the ionic swelling pressure includes only an ideal (Donnan) contribution [4,101], In this approximation, the swelling equilibrium is described by a system of equations including Eq. (3.1) and the... 

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. 

It will be obvious from the description of Lewis s and Donnan and Barker s experiments that equilibrium is assumed to establish itself during the time of contact between the mercury or air surface and the liquid in fact this point was checked by increasing the time and showing that the result was not affected, i.e., that no further quantity of the solute was removed from solution. Experiments to decide this question had, however, been made at an earlier date by Wilhelm Ostwald. The strict definition of an equilibrium requires that it should be independent of the mass of the phases in contact thus, a soluble substance and its concentrated solution are in equilibrium at a given temperature and pressure, and this obviously remains unaffected by altering the quantity of either solid substance or solution. Ostwald placed a quantity of charcoal in a given volume of dilute hydrochloric acid and determined the decrease in concentration after a short time. If, then, a part of either the charcoal or the dilute solution was... 

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... 

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