Electroacoustic theory for concentrated colloids with overlapped DLs at arbitrary kappa alpha. I. Application to nanocolloids and nonaqueous colloids.
Existing theories of electroacoustic phenomena in concentrated colloids neglect the possibility of double layer overlap and are valid mostly for the "thin double layer," when the double layer thickness is much less than the particle size. In this paper we present a new electroacoustic theory which removes this restriction. This would make this new theory applicable to characterizing a variety of aqueous nanocolloids and of nonaqueous dispersions. There are two versions of the theory leading to the analytical solutions. The first version corresponds to strongly overlapped diffuse layers (so-called quasi-homogeneous model). It yields a simple analytical formula for colloid vibration current (CVI), which is valid for arbitrary ultrasound frequency, but for restricted kappa alpha range. This version of the theory, as well the Smoluchowski theory for microelectrophoresis, is independent of particle shape and polydispersity. This makes it very attractive for practical use, with the hope that it might be as useful as classical Smoluchowski theory. In order to determine the kappa alpha range of the quasi-homogeneous model validity we develop the second version that limits ultrasound frequency, but applies no restriction on kappa alpha. The ultrasound frequency should substantially exceed the Maxwell-Wagner relaxation frequency. This limitation makes active conductivity related current negligible compared to the passive dielectric displacement current. It is possible to derive an expression for CVI in the concentrated dispersion as formulae inhering definite integrals with integrands depending on equilibrium potential distribution. This second version allowed us to estimate the ranges of the applicability of the first, quasi-homogeneous version. It turns out that the quasi-homogeneous model works for kappa alpha values up to almost 1. For instance, at volume fraction 30%, the highest kappa alpha limit of the quasi-homogeneous model is 0.65. Therefore, this version of the electroacoustic theory is valid for almost all nonaqueous dispersions and a wide variety of nanocolloids, especially with sizes under 100 nm.