Record M T, Anderson C F
Department of Chemistry, University of Wisconsin-Madison 53706, USA.
Biophys J. 1995 Mar;68(3):786-94. doi: 10.1016/S0006-3495(95)80254-7.
For a three-component system consisting of solvent (1), polymer or polyelectrolyte (2J), and a nonelectrolyte or electrolyte solute (3), a two-domain description is developed to describe thermodynamic effects of interactions between solute components (2J) and (3). Equilibrium dialysis, which for an electrolyte solute produces the Donnan distribution of ions across a semipermeable membrane, provides a fundamental basis for this two-domain description whose applicability is not restricted, however, to systems where dialysis equilibrium is established. Explicit expressions are obtained for the solute-polymer preferential interaction coefficient gamma 3,2J (nonelectrolyte case) and for gamma +,2J and gamma -,2J, which are corresponding coefficients defined for single (univalent) cations and anions, respectively: gamma +,2J = magnitude of ZJ + gamma -,2J = 0.5(magnitude of ZJ + B-,2J + B+,2J) - B1,2Jm3/m1 Here B+,2J, B-,2J, and B1,2J are defined per mole of species J, respectively, as the number of moles of cation, anion, and water included within the local domains that surround isolated molecules of J; ZJ is the charge on J; m3 is the molal concentration of uniunivalent electrolyte, and m1 = 55.5 mol/kg for water. Incorporating this result into a general thermodynamic description(derived by us elsewhere) of the effects of the activity a+ of excess uniunivalent salt on an equilibrium involving two or more charged species J (each of which is dilute in comparison with the salt) yields:SaKobs bS/d a+ A(r+2J r 2j) A(B+2J B-2 2B12Jm3/m1)where KObS is an equilibrium quotient defined in terms of the molar concentrations of the participants, J, and A denotes astoichio metrically weighted combination of terms pertaining to the reactant(s) and product(s). The derivation presented here does not depend on any particular molecular model for salt-polyelectrolyte (or solute-polymer) interactions; it therefore generalizes our earlier (1978) derivation.
对于由溶剂（1）、聚合物或聚电解质（2J）以及非电解质或电解质溶质（3）组成的三元体系，我们发展了一种双域描述方法来描述溶质组分（2J）和（3）之间相互作用的热力学效应。平衡透析对于电解质溶质会使离子在半透膜两侧产生唐南分布，它为这种双域描述提供了一个基本依据，不过，其适用性并不局限于能建立透析平衡的体系。我们得到了溶质 - 聚合物优先相互作用系数γ3,2J（非电解质情况）以及γ +,2J和γ -,2J的显式表达式，γ +,2J和γ -,2J分别是为单个（单价）阳离子和阴离子定义的相应系数：γ +,2J = |ZJ| + ，γ -,2J = 0.5(|ZJ| + B -,2J + B +,2J) - B1,2Jm3/m1 ，这里B +,2J、B -,2J和B1,2J分别是每摩尔J物种定义的，即包围孤立J分子的局部域内包含的阳离子、阴离子和水的摩尔数；ZJ是J上的电荷；m3是单价电解质的质量摩尔浓度，对于水m1 = 55.5 mol/kg。将此结果纳入我们在其他地方推导的关于过量单价盐的活度a + 对涉及两个或更多带电物种J（每个相对于盐都是稀溶液）的平衡的影响的一般热力学描述中，得到：SaKobs bS/d a + A(r + 2J r 2j) A(B + 2J B - 2 2B12Jm3/m1) ，其中KObS是根据参与者J的摩尔浓度定义的平衡商，A表示与反应物和产物相关项的化学计量加权组合。这里给出的推导不依赖于盐 - 聚电解质（或溶质 - 聚合物）相互作用的任何特定分子模型；因此它推广了我们早期（1978年）的推导。
