[三元非电解质溶液的 Kedem-Katchalsky 方程的网络形式。5. 聚合物膜的 Nij Peusner 系数的评估]

[Network form of the Kedem-Katchalsky equations for ternary non-electrolyte solutions. 5. Evaluation of Nij Peusner's coefficients for polymeric membrane].

作者信息

Batko Kornelia M, Slęzak-Prochazka Izabella, Slęzak Andrzej

机构信息

Katedra Informatyki ekonomicznej, Uniwersytet ekonomiczny, Katowice, Polska.

Instytut Marketingu, Politechnika Częstochowska, Gliwice, Polska.

出版信息

Polim Med. 2013 Oct-Dec;43(4):257-75.

PMID:24596041

Abstract

BACKGROUND

Peusner Network Thermodynamics (PNT) enables symmetrical and/or hybrid transformation of classical Kedem-Katchalsky (K-K) equations to network forms. For homogenous nonelectrolyte solutions that consist of solvent and two dissolved substances, two symmetrical and six hybrid forms of network K-K equations can be obtained that contain symmetrical (Rij or Lij) or hybrid (Hij, Wij, Nij, Kij, Sij or Pij) Peusner's coefficients.

OBJECTIVES

The aim of this paper is to derive network form of K-K equations for homogenous ternary nonelectrolyte solutions that contains Peusner's coefficients Nij (i, j ∈ {1, 2, 3}). These coefficients form a third degree matrix of Peusner's coefficients [N]. We also aim to calculate dependences of Nij coefficients on average concentration of one component of solution in a membrane (C1) when value of the second one (C2) is fixed and to compare these dependences with appropriate dependences for coefficients Rij, Lij, Hij and Wij presented in 1-4 parts of the paper.

MATERIAL AND METHODS

A cellulose hemodialysis membrane (Nephrophan) of known transport parameters for aqueous glucose and ethanol solutions was a research material. The PNT formalism and classical form of K-K equations for ternary non-electrolyte solutions was a research tool in this paper.

RESULTS

The network form of K-K equations was presented using the hybrid transformation of Peusner's thermodynamic networks for ternary solutions that contain solvent and two dissolved substances. For homogenous solutions, we calculated dependences of Peusner's coefficients Nij (i, j = 1, 2, 3) on average concentration of one component (C1) of the solution in a membrane when value of the second one is fixed (C2). Moreover, we calculated dependences of quotients Nij/Rij, Nij/Lij, Nij/Hij and Nij/Wij on average concentration of one component (C1) of the solution in a membrane when value of the second one is fixed (C2).

CONCLUSIONS

The network form of K-K equations that contain Peusner's coefficients Nij (i, j ∈ {1, 2, 3}) is a novel tool to study membrane transport. Obtained results of calculations showed that coefficients N12, N21, N22 and N32 are sensitive for composition and concentration of solutions separated by a polymer membrane.

摘要

背景

佩斯内尔网络热力学（PNT）能够将经典的 Kedem-Katchalsky（K-K）方程对称和/或混合转化为网络形式。对于由溶剂和两种溶解物质组成的均相非电解质溶液，可以得到两种对称形式和六种混合形式的网络 K-K 方程，这些方程包含对称的（Rij 或 Lij）或混合的（Hij、Wij、Nij、Kij、Sij 或 Pij）佩斯内尔系数。

目的

本文旨在推导包含佩斯内尔系数 Nij（i, j ∈ {1, 2, 3}）的均相三元非电解质溶液的 K-K 方程的网络形式。这些系数构成了佩斯内尔系数的三阶矩阵[N]。我们还旨在计算当溶液中第二种组分的值（C2）固定时，Nij 系数对膜中溶液一种组分的平均浓度（C1）的依赖性，并将这些依赖性与本文 1 - 4 部分中给出的系数 Rij、Lij、Hij 和 Wij 的相应依赖性进行比较。

材料与方法

一种对葡萄糖和乙醇水溶液具有已知传输参数的纤维素血液透析膜（Nephrophan）作为研究材料。本文使用 PNT 形式主义和三元非电解质溶液的 K-K 方程的经典形式作为研究工具。

结果

通过对包含溶剂和两种溶解物质的三元溶液的佩斯内尔热力学网络进行混合变换，给出了 K-K 方程的网络形式。对于均相溶液，我们计算了在第二种组分的值（C2）固定时，佩斯内尔系数 Nij（i, j = 1, 2, 3）对膜中溶液一种组分（C1）的平均浓度的依赖性。此外，我们还计算了在第二种组分的值（C2）固定时 Nij/Rij、Nij/Lij、Nij/Hij 和 Nij/Wij 的商对膜中溶液一种组分（C1）的平均浓度的依赖性。