Departament de Química, Universitat de Lleida, Av. Rovira Roure, 191 E-25198 Lleida, Spain.
J Phys Chem B. 2009 Nov 19;113(46):15145-55. doi: 10.1021/jp9041815.
The binding of ions or other small molecules to macromolecules and surfaces can be macroscopically characterized by means of the stepwise (or stoichiometric) equilibrium constants, which can be obtained experimentally from coverage versus concentration data. The present work presents a novel, simple, and direct interpretation of the stepwise constants in terms of the microscopic, site-specific, stability constants. This formalism can be applied to the most general case, including the heterogeneity of the sites, interactions among them, multicomponent adsorption, and so forth, and, in particular, to chelate complexation. We show that the stepwise equilibrium constants can be expressed as a product of two factors, (i) the average number of free potential sites (per bound ion) of the microscopic species to be complexed (stoichiometric factor) and (ii) the average of the microscopic stability constants of their free potential sites. The latter factor generalizes the concept of the intrinsic equilibrium constant to systems with chelate complexation and reduces to the standard definition for monodentate binding. However, in the case of heterogeneous multidentate complexation, the stoichiometric factor cannot be known a priori, so that the finding of the intrinsic constants is not trivial. One option is to approximate the stoichiometric factor by the value that would correspond to identical active centers. We investigate the accuracy of this assumption by comparing the resulting approximate intrinsic constants to those obtained by Monte Carlo simulation of several binding models. For the cases investigated, it is found that the assumption is quite accurate when no correlated structures (typical of short-range interactions) are formed along the chain. For adsorption of particles attached to a large number of active centers, the formalism presented here leads to the Widom particle insertion method.
离子或其他小分子与大分子和表面的结合可以通过逐步（或化学计量）平衡常数来宏观地描述，这些平衡常数可以从覆盖度与浓度数据的实验中获得。本工作提出了一种新颖、简单、直接的微观、位特异性、稳定性常数对逐步常数的解释。这种形式主义可以应用于最一般的情况，包括位点的非均一性、它们之间的相互作用、多组分吸附等，特别是螯合络合。我们表明，逐步平衡常数可以表示为两个因素的乘积：（i）待络合的微观物种的自由势能位（每个结合离子）的平均数量（化学计量因子）和（ii）其自由势能位的微观稳定性常数的平均值。后一个因素将内在平衡常数的概念推广到具有螯合络合的系统，并简化为单齿结合的标准定义。然而，在多齿络合的非均相情况下，化学计量因子不能先验地知道，因此内在常数的发现并非微不足道。一种选择是用对应于相同活性中心的值来近似化学计量因子。我们通过将得到的近似固有常数与通过几个结合模型的蒙特卡罗模拟得到的固有常数进行比较，来研究这种假设的准确性。在所研究的情况下，当链上没有形成相关结构（典型的短程相互作用）时，该假设非常准确。对于附着在大量活性中心上的粒子的吸附，本文提出的形式主义导致 Widom 粒子插入法。
