Department of Applied Physics, School of Sciences, Campus Fuentenueva, University of Granada, 18071 Granada, Spain.
J Colloid Interface Sci. 2010 Mar 15;343(2):564-73. doi: 10.1016/j.jcis.2009.11.063. Epub 2009 Dec 4.
This paper describes an investigation on the electric permittivity of concentrated suspensions of non-spherical particles, specifically prolate spheroids. It is first discussed how the determination of the frequency (omega) dependence of the electric permittivity (a phenomenon traditionally known as LFDD or low-frequency dielectric dispersion) can provide ample information on the properties of the dispersed material (shape, size, state of aggregation, conductivity) and of its interface with the (typically aqueous) medium. The basic quantities are the strength and frequency dependence of the dipole moment induced by the applied field, and its dimensionless counterpart, the dipole coefficient, C()(omega). It is explicitly shown how the (complex) relative permittivity of the suspension, epsilon(r)()(omega), can be calculated from it. Two theoretical models on the polarizability of spheroidal colloidal particles will be used as theoretical starting point; one of them (Model I) explicitly considers two relaxations of the permittivity, each associated to one of the particle axes. The other (Model II) is a semi-analytical theory that yields an LFDD practically independent of the axial ratio of the particles. Both models are aimed to be used if the suspensions are dilute (low volume fraction of solids, phi), and here they are generalized to concentrated systems by means of a previously published approximate evaluation of the permittivity of concentrated suspensions. Experiments are performed in the 1 kHz-1 MHz frequency range on suspensions of elongated goethite particles; the effects of ionic strength, pH, and volume fraction are investigated, and the two models are fitted to the data. In reality, taking into account that the particles are non-uniformly charged (a fact that contributes to their instability), two zeta potentials (roughly representing the lateral surface and the tip of the spheroid) are used as parameters. The results indicate that, when experimental conditions are optimal (high ionic strength and low zeta potential), the suspensions do indeed display two relaxations, that we ascribe to the long axis (and to flocs likely present in suspension) and to the short one. The permittivity increases with ionic strength, a result found with other systems, and compatible with a zeta potential that, on the average, decreases with ionic strength, an equally well known result, consequence of electric double layer compression. Another reasonable finding is the increase of estimated average dimensions and the decrease of electrokinetic potentials when the pH is close to the isoelectric point of goethite (around pH 9). The increase in volume fraction, finally, produces an overall increase in the permittivity, and the approximate model used for the evaluation of volume fraction variations can describe properly these effects, with basically constant zeta potentials and dimensions.
本文介绍了对非球形颗粒（具体为细长椭球体）浓悬浮液介电常数的一项研究。文中首先讨论了如何通过确定介电常数的频率（ω）依赖性（一种传统上被称为 LFDD 或低频介电弥散的现象）来提供关于分散材料（形状、大小、聚集状态、电导率）及其与（通常为水）介质界面的大量信息。基本量是由施加的场感应的偶极矩的强度和频率依赖性，以及其无量纲对应物，偶极系数 C()(ω)。文中明确展示了如何从它计算悬浮液的（复）相对介电常数ε(r)()(ω)。将使用两个关于球形胶体颗粒的极化率的理论模型作为理论起点；其中一个（模型 I）明确考虑了介电常数的两个弛豫，每个弛豫与颗粒的一个轴相关联。另一个（模型 II）是一种半解析理论，它产生的 LFDD 实际上与颗粒的纵横比无关。如果悬浮液是稀的（固体体积分数低，φ），则这两个模型都可用于此，并且此处通过先前发表的关于浓悬浮液介电常数的近似评估，将它们推广到浓体系中。实验在 1 kHz-1 MHz 频率范围内进行，使用拉长的针铁矿颗粒的悬浮液；研究了离子强度、pH 值和体积分数的影响，并将两个模型拟合到数据上。实际上，考虑到颗粒不均匀带电（这一事实导致其不稳定），使用两个 ζ 电位（大致代表椭球体的侧面和尖端）作为参数。结果表明，当实验条件最佳（高离子强度和低 ζ 电位）时，悬浮液确实确实显示出两个弛豫，我们将其归因于长轴（和悬浮液中可能存在的絮体）和短轴。介电常数随离子强度增加而增加，这是在其他系统中发现的结果，并且与 ζ 电位一致， ζ 电位通常随离子强度降低而降低，这是一个众所周知的结果，是电双层压缩的结果。另一个合理的发现是，当 pH 值接近针铁矿的等电点（约 pH 9）时，估计的平均尺寸增加和电动电位降低。最后，体积分数的增加会导致介电常数的整体增加，并且用于评估体积分数变化的近似模型可以很好地描述这些影响，基本上保持 ζ 电位和尺寸不变。
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