Staverman relation

Instead of the Flory-Huggins combinatorial contribution. Equation [4.4.68], the Staverman relation is used. 

Staverman [165, 166) has shown how a number of transport phenomena across membranes, such as ion migration, hydraulic permeability, and membrane potentials are related to the Lilt s. In general, if there are n components, n [n— I) independent measurements are required to estimate all Lik s. So for a system consisting of 3 components (e.g. sodium ions, chlorine ions and water) 6 independent measurements are necessary. 

Staverman, A. J. Quantitative relations concerning the glass transition point. Kurzmitteilungen, Symposium fiber Macromolckule in Wiesbaden. Sektion I A9. Oct. 1959. 

Definition of terms relating to individual macromolecules, their assemblies, and dilute solution.This document includes the recommended definitions for molecular weight, molecular weight averages, distribution functions, radius of gyration, end-to-end-distance vector, the Flory-Huggins-Staverman theory, solution viscosity, scattering of radiation by polymers and polymer solutions, fractionation, separation techniques, and so on. The document on dispersity is an important extension of this recommendation. 

Two relations have been given by Staverman and SchwarzP relating the values of G at two frequencies coi and a>2 ... 

Parameters related to differences in size and shape and respectively change in internal energy of mixing Entropy correction terms Parameter related to average interaction energy Internal energy of the system Flory s equation of state Flory-Huggins Staverman theory... 

Staverman examined the problem of representing a solution in which the molecules are no longer linear, and therefore a certain amount of the molecule would not be exposed to the molecules of solvent, because they would be isolated inside the molecule of solute. These imprisoned sites receive no molecules of solvent. Figure 3.5 gives a 2D representation of the exclusion of certain sites (shaded) which are no longer able to receive molecules of solvent as near neighbors. This introduces a corrective factor relating to the surface of the molecule. 

The UNIQUAC (Universal Quasi-Chemical) model was introduced by Abrams and Prausnitz (1975), using Guggenheim s quasi-chemical model and applying the concepts of conformation with Staverman s relation and Wilson s local-composition model. 

We shall express the canonical partition function of mixing by using Guggenheim s quasi-chemical method (see section 3.3), applied with Staverman s athermic model as a reference, where the excess entropy is given by relation [3.137],... 

In this Section, it is implicitly assumed that the mass transport resistance at the fluid-membrane interface on either side of the membrane is negligible. Also the following is information that is made available publicly by the membrane manufacturers, when not otherwise noted. As in technical processes, mass transport across semipermeable medical membranes is conveniently related to the concentration and pressme driving forces according to irreversible thermodynamics. Hence, for a two-component mixture the solute and solvent capacity to permeate a semipermeable membrane under an applied pressure and concentration gradient across the membrane can be expressed in terms of the following three parameters Lp, hydraulic permeability Pm, diffusive permeability and a, Staverman reflection coefficient (Kedem and Katchalski, 1958). All of them are more accurately measured experimentally because a limited knowledge of membrane stmcture means that theoretical models provide rather inaccurate predictions. 

The Staverman reflection coefficient, o, measures the extent to which the membrane rejects a given solute purely transported by convection. Solutes fully rejected by the membrane feature o = 1. Solutes freely permeating the membrane feature ct = 0. Membrane rejection toward a given solute is experimentally assessed in the course of pure filtration experiments in terms of its rejection coefficient R, or its sieving coefficient S, with S = —R being the permeate-to-retentate solute concentration ratio. In fact, R is related to a as follows (Spiegler and Kedem, 1996) ... 

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