Laboratoire Environnement et Minéralurgie, Nancy-Université, UMR7569 CNRS, BP 40-F-54501 Vandoeuvre-lès-Nancy Cedex, France.
Phys Chem Chem Phys. 2011 Jan 21;13(3):1037-53. doi: 10.1039/c004243a. Epub 2010 Nov 11.
We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may dramatically change depending on the interplay between characteristic Debye length, thickness of ion-permeable layers and their respective protolytic features (e.g. location, magnitude and sign of charge density). This formalism extends a recent model by Ohshima which is strictly limited to interaction between soft mono-shell particles within Deryagin and Debye-Hückel approximations under conditions where ionizable sites are completely dissociated.
我们提出了一种用于评估相同或不同的球形软多层（生物）颗粒之间静电相互作用的稳定态理论，例如微凝胶或微生物。这些颗粒通常由一个刚性核心组成，周围是同心的离子可渗透层，这些层在厚度、软物质密度、化学组成和离子基团的离解度方面可能有所不同。该形式主义允许考虑扩散界面，其中一个层到另一个层的离子基团分布取决于位置。该模型适用于相互作用软颗粒核心周围的任意数量的离子可渗透层，并涵盖了相互作用颗粒性质的所有极限情况，即硬、软或完全多孔胶体之间的同相和异相相互作用。该理论基于对非线性化泊松-玻尔兹曼方程的严格数值解，包括相互作用软颗粒内外电场分布的径向和角向变形。静电相互作用的吉布斯能量是从基于 Verwey 和 Overbeek 方法的一般表达式中获得的，该表达式基于适当的电双层充电机制。对于相互作用发生在大小和电荷密度与 Deryagin 处理和 Debye-Hückel 近似一致的软多层颗粒之间的情况，本文提供了原始的解析解。这些情况包括硬颗粒和软颗粒、硬板和软颗粒或软板和软颗粒之间的相互作用。通过讨论几个情况突出了形式主义的灵活性，这些情况清楚地表明，多层颗粒之间的静电相互作用可能部分或主要由最内部层内的电势分布决定。一个主要后果是，吉布斯静电相互作用能量的幅度和符号可能根据特征 Debye 长度、离子可渗透层的厚度及其各自的质子化特征（例如，位置、电荷密度的大小和符号）之间的相互作用而急剧变化。该形式主义扩展了 Ohshima 的最新模型，该模型严格限于在 Deryagin 和 Debye-Hückel 近似下完全离解的可离子化位点的情况下，软单壳颗粒之间的相互作用。
