Note: Renormalized jellium model for charged colloids revisited.
Note: Renormalized jellium model for charged colloids revisited.
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注意：重新标准化带电胶体的果冻模型。
DOI：
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发表时间：
2010
影响因子：
4.4
通讯作者：
R. Castañeda
中科院分区：
文献类型：
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作者：
J. M. Falcón;R. Castañeda
最近，已经证明，与对称电解质接触的带电胶体之间的静电相互作用可以通过使用由Trizac和Levin提出的所谓的重整化的jelvis（RJ）模型来精确地描述。1该平均场近似基于泊松-玻尔兹曼方程（PBE），要求标记胶体周围的背景电荷自洽地重整化以与胶体有效电荷一致;这样的要求导致精确的热力学性质，即使在高度带电的胶体悬浮液。2 -5在这篇文章中，我们重新审视重整化的jeldom近似，特别是，提供了一个简单的明确的配方，便于重整化过程容易实现在不同的情况下。我们在这里将这样的配方应用于带电球体的情况，并讨论其对带电棒情况的扩展。所考虑的体系是一个体积分数为η的带电胶体悬浮液，显然由半径为a的带电胶体和与浓度为2cs的对称（1：1）盐库接触的抗衡离子组成，cs是正或负盐离子的密度;溶剂通过介电常数e被包含在内。RJ模型假设标记的大离子周围的Nc − 1胶体粒子的电荷在整个悬浮液中被涂抹掉，形成一个带有电荷Zbacke的均匀背景，e是基本电荷。该背景电荷是Zback = Zbare，其中Zbare是胶体裸电荷，并且不是先验已知的，但是它被自洽地确定为等于标记的大离子的有效电荷Zeff。1 RJ模型的非凡优点是Zeff与系统渗透压、筛选参数、和胶体之间的有效对相互作用（当在汤川近似水平上明确考虑时）。1，2然而，由于它是系统状态的显式函数，即，Zeff = Zeff（η，Zbare，cs），其计算取决于系统的具体条件，目前，整个电荷重整化过程是通过迭代过程进行的。6该迭代过程需要构造Zeff = Zeff（Zback，Zbare）形式的函数。自洽条件在函数与直线Zeff = Zback的交点处达到。然而，它仍然是可能的重新制定这一计划，并避免完整的迭代程序，以获得清晰的方式，RJ可以应用和扩展到研究的电荷稳定的胶体悬浮液的物理性质。完整的原始程序可以重新表述如下。我们从一开始就从自我一致性的要求开始。这意味着条件Zback = Zeff必须明确地并入PBE中。我们的主要假设是，存在一个唯一的Zeff对于一个给定的Zbare，这完全避免了Zback的列入，并大大促进了重整化方案。此外，还应该重新表述典型边界条件（BC），以在一点上使用简单的BC求解PBE [见等式2]。(3)和（4）]。为了实现这一点，我们使用的PBE的远场解决方案有一个Yukawa样的形式，依赖于Zeff的事实。因此，在带电球形胶体的情况下，PBE现在读为d2φ dr 2 + 2 r dφ dr = −3η ZeffλB a − ρ+（∞）e−φ + ρ−（∞）e，（1）
Recently, it has been demonstrated that electrostatic interactions between charged colloids in contact with a symmetric electrolyte can accurately be described by using the so-called renormalized jellium (RJ) model proposed by Trizac and Levin.1 This mean-field approximation, based on the Poisson–Boltzmann equation (PBE), requires that the charge of the background around a tagged colloid be renormalized self-consistently to coincide with the colloid effective charge; such a requirement leads to precise thermodynamic properties even in highly charged colloidal suspensions.2–5 In this note, we revisit the renormalized jellium approximation and, in particular, provide a simple explicit recipe that facilitates the renormalization procedure being easy of implementing in different situations. We here apply such recipe in the case of charged spheres and discuss its extension to the case of charged rods. The system under consideration is a charged colloidal suspension of volume fraction η composed of, obviously, charged colloids of radius a, and counter ions in contact with a symmetric (1:1) salt reservoir of concentration 2cs , with cs the density of positive or negative salt ions; the solvent is included through the dielectric constant e. The RJ model assumes that the charge of Nc − 1 colloidal particles around a tagged macroion is smeared out in the whole suspension to form a homogeneous background with charge Zbacke, e being the elementary charge. This background charge is Zback = Zbare, with Zbare the colloidal bare charge, and not known a priori, but it is determined self-consistently to be equal to the effective charge, Zeff, of the tagged macroion.1 An extraordinary advantage of the RJ model is that Zeff is directly associated to the system osmotic pressure, the screening parameter, and the effective pair interaction between colloids (when it is explicitly considered at the level of the Yukawa approximation).1, 2 Nevertheless, since it is an explicit function of the system state, i.e., Zeff = Zeff(η, Zbare, cs), its evaluation depends on the specific conditions of the system and, currently, the entire charge renormalization procedure is carried out through an iterative process.6 This iterative procedure demands the construction of a function of the form Zeff = Zeff(Zback, Zbare). The selfconsistently condition is reached in the intersection of the function with the straight line Zeff = Zback. However, it is still possible to reformulate this scheme and avoid the full iterative procedure to gain clarity in the way in which the RJ can be applied and extended to study the physical properties of charge-stabilized colloidal suspensions. The complete original procedure can then be reformulated as follows. We start with the requirement of selfconsistency from the beginning. This means that the condition Zback = Zeff must be explicitly incorporated into the PBE. Our main assumption is that there exists a unique Zeff for a given Zbare; this avoids completely the inclusion of Zback and facilitates drastically the renormalization scheme. Additionally, one should also rephrase the typical boundary conditions (BCs) to solve the PBE with simple BCs at one point [see Eqs. (3) and (4)]. To achieve this, we use the fact that the farfield solution of the PBE has a Yukawa-like form that depends on Zeff. Therefore, in the case of charged spherical colloids, the PBE now reads d2φ dr2 + 2 r dφ dr = −3η ZeffλB a − ρ+(∞)e−φ + ρ−(∞)e, (1)