Potential distribution around a charged spherical colloidal particle in a medium containing its counterions and a small amount of added salts
Potential distribution around a charged spherical colloidal particle in a medium containing its counterions and a small amount of added salts
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DOI：
10.1007/s00396-004-1072-9
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发表时间：
2004-03
影响因子：
2.4
通讯作者：
H. Ohshima
中科院分区：
文献类型：
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作者：
H. Ohshima
在Imai和Oosawa理论的基础上，建立了在含有反离子(即粒子表面基团解离产生的反离子)和少量添加盐的介质中，带有电离基团的带电球形胶体粒子周围的电势分布理论。对于体积分数为φ≪1的稀相(但不是无限稀相)颗粒悬浮液，得到了κa≪1(其中κ是德拜-胡克尔参数，aA是颗粒半径)的泊松-玻尔兹曼方程的数值解。这里我们考虑了(I)来自颗粒表面团的反离子和(Ii)有限颗粒体积分数的影响。这些在传统的泊松-玻尔兹曼方程中通常被忽略的影响被发现是重要的。结果表明，在完全无盐的情况下，粒子电荷存在一个临界值(与完全无盐的情况相同)。当粒子电荷低于临界值时，势由库仑势给出。如果粒子电荷高于临界值，则反离子聚集在粒子表面附近(反离子凝聚)，电势变得不那么依赖于粒子电荷。如果条件φ≪1和κa≪1都满足，则即使在电解液浓度高于来自粒子表面团的反离子浓度的情况下也可以观察到上述行为。
A theory is developed for the potential distribution around a charged spherical colloidal particle carrying ionized groups on the particle surface in a medium containing its counterions (i.e., counterions produced from dissociation of the particle surface groups) and a small amount of added salts on the basis of the theory of Imai and Oosawa. Numerical solutions to the Poisson–Boltzmann equation for the potential distribution are obtained for the case of dilute (but not infinitely dilute) particle suspensions of volume fractionφ≪1 forκa≪1 (whereκis the Debye–Hückel parameter andais the particle radius). Here we have taken into account the effects of (i) counterions from the particle surface groups, and (ii) the finite particle volume fraction. These effects, which are usually neglected in the conventional Poisson–Boltzmann equation, are found to be important. It is found that, as in the case of completely salt-free media, there is a certain critical value of the particle charge (which is the same as that for the completely salt-free case). When the particle charge is lower than the critical value, the potential is given by a Coulomb potential. If the particle charge is higher than the critical value, then counterions are accumulated in the vicinity of the particle surface (counterion condensation) and the potential becomes less dependent on the particle charge. The above behaviors can be observed even for the case where the electrolyte concentration is higher than the concentration of counterions from the particle surface groups, if the conditionsφ≪1 andκa≪1are both satisfied.