Duval Jérôme F L
Laboratory Environment and Mineral Processing, CNRS, Nancy-University, UMR 7569, BP 40 - F-54501 Vandoeuvre-les-Nancy Cedex, France.
J Phys Chem A. 2009 Mar 19;113(11):2275-93. doi: 10.1021/jp809764h.
The theory for metal speciation dynamics in dilute, monodisperse suspensions of spherical core-shell colloidal ligand particles is extended with the impact of the electric double layer (EDL) field and inhomogeneous site distribution inside the particle. The latter is defined by a diffuse, radial distribution for the density of charged polymer segments supporting the ligands L. The site distribution at the scale of the particle suspension and within the colloidal shell results in association/dissociation rate constants (denoted as k(a)* and k(d), respectively) that may significantly differ from their homogeneous solution counterparts (k(a) and k(d)). The differences arise from intertwined kinetics of metal-ligand (ML) complex formation/dissociation in the particle shell and diffusive transport of free metal ions M within/outside the shell in the electric field set up by the EDL at the core-shell/electrolyte interphase. The relationship between k(a,d) and k(a,d) is derived from the numerical evaluation of the spatial, time-dependent distributions of free and bound metal as governed by coupled Nernst-Planck equations corrected by appropriate chemical source term and written in a Kuwabara cell geometry. The average interphasial electrostatic field stemming from the formation of the EDL at the complexing colloidal interphase is obtained from the solution of the nonlinear Poisson-Boltzmann equation. The EDL composition is exclusively governed by ions from indifferent background electrolyte present in large excess over free metal species M. The dependences of k(a,d)* on rate constants k(a,d), geometrical details of particle, particle charge, concentration of indifferent background electrolyte, and ligand distribution within the shell are thoroughly discussed within the context of dynamic features for colloidal complex systems. Examination of the chemical equilibrium regime allows addressing explicitly the impact of electrostatics on colloidal complex stability (polyelectrolyte effect). The numerical study is further supported by an approximate analytical expression based on Donnan partitioning and valid under the quasi-steady-state approximation (nonequilibrium chemical regime). The analysis covers the limiting cases of charged rigid particles where binding sites are located at the very surface of the core (e.g., functionalized latex colloids) and polyelectrolyte particles devoid of a hard core (e.g., polysaccharide macromolecules, gel particles).
针对球形核壳胶体配体颗粒的稀单分散悬浮液中金属形态动力学理论，考虑了双电层（EDL）场和颗粒内部不均匀位点分布的影响进行了扩展。后者由支持配体L的带电聚合物链段密度的扩散径向分布定义。颗粒悬浮液尺度和胶体壳内的位点分布导致缔合/解离速率常数（分别表示为k(a)和k(d)）可能与其均相溶液对应值（k(a)和k(d)）有显著差异。这些差异源于颗粒壳中金属 - 配体（ML）络合物形成/解离的交织动力学以及在核壳/电解质界面处EDL建立的电场中壳内/外自由金属离子M的扩散传输。k(a,d)*与k(a,d)之间的关系是通过对自由和结合金属的空间、时间相关分布进行数值评估得出的，该分布由耦合的能斯特 - 普朗克方程控制，并通过适当的化学源项进行修正，且以桑原单元几何形状表示。在络合胶体界面处形成EDL产生的平均相间静电场是通过非线性泊松 - 玻尔兹曼方程的解获得的。EDL组成完全由大量过量存在的来自惰性背景电解质的离子控制，相对于自由金属物种M而言。在胶体络合物系统的动态特征背景下，深入讨论了k(a,d)*对速率常数k(a,d)、颗粒几何细节、颗粒电荷、惰性背景电解质浓度以及壳内配体分布的依赖性。对化学平衡状态的研究允许明确解决静电对胶体络合物稳定性的影响（聚电解质效应）。数值研究进一步得到基于唐南分配的近似解析表达式的支持，该表达式在准稳态近似（非平衡化学状态）下有效。分析涵盖了带电刚性颗粒的极限情况（其中结合位点位于核的非常表面，例如功能化乳胶胶体）和没有硬核的聚电解质颗粒（例如多糖大分子、凝胶颗粒）。
