Theory of semipermeable vesicles and membranes: An integral-equation approach. II. Donnan equilibrium

Journal Article · Thu Dec 01 00:00:00 EST 1988 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.455328· OSTI ID:6748699

Zhou, Y; Stell, G

Integral equations that yield the charge and density profiles are derived for a Donnan system, in which an ionic solution is separated into two regions by a semipermeable membrane (SPM) or a spherical semipermeable vesicle (SPV). These equations are obtained from the Ornstein--Zernike (OZ) equation. We show how quantitative results can be obtained from either the mean spherical approximation (MSA) closure or the hypernetted-chain (HNC) closure for profiles. Use is made of bulk-correlation input obtained by means of the Debye--Hueckel approximation, the MSA approximation, or the HNC approximation. The resulting approximations will be referred as MSA/DH, HNC/DH, MSA/MSA, etc. The system on which we focus contains three charged hard-sphere species: cation, anion, and a large ion (a protein or polymer ion) separated by a plane SPM, through which the large ion cannot pass, and to one side of which all large ions are confined, or a spherical SPV, outside of which the large ions are confined. Analytical expressions for the bulk density ratio between the two sides of a plane membrane as well as the membrane potential in various approximations are obtained. Results obtained from these expresssions are compared with the results obtained by equating electrochemical potentials. A new contact-value theorem is provided for the plane SPM system. Analytical solutions for the charge profile and the potential profile in the MSA/DH approximation are obtained. It turns out that results obtained in the HNC/DH approximation are exactly the same as those obtained by using 1D nonlinear Poisson--Boltzmann equations if the repulsive cores of the macroions are neglected.

• Research Organization: Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794
• OSTI ID: 6748699
• Journal Information: J. Chem. Phys.; (United States), Vol. 89:11
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC
ORGANIC
PHYSICAL AND ANALYTICAL CHEMISTRY
MEMBRANES
INTERACTIONS
PERMEABILITY
SOLUTIONS
HARD-SPHERE MODEL
IONIC COMPOSITION
CHARGE DISTRIBUTION
DENSITY
INTEGRAL EQUATIONS
PERCUS-YEVICK EQUATION
STATISTICAL MECHANICS
DISPERSIONS
EQUATIONS
MECHANICS
MIXTURES
PHYSICAL PROPERTIES
400201* - Chemical & Physicochemical Properties