Colloid Vibration Potential and Ion Vibration Potential in a Dilute Suspension of Spherical Colloidal Particles

Abstract

A general electroacoustic theory is presented for the macroscopic electric field in a dilute suspension of spherical colloidal particles in an electrolyte solution, which consists of the colloid vibration potential (CVP) and the ion vibration potential (IVP), induced by an oscillating pressure gradient field due to an applied sound wave. This is a unified theory that unites previous theories for CVP and those for IVP. Approximate analytic expressions are derived for CVP and IVP. The obtained IVP expression agrees with Debye's formula that is corrected by taking into account the force acting on the electrolyte ions as a result of the pressure gradient in the sound wave. The obtained CVP expression is correct to the first order of the particle zeta potential and applicable for arbitrary kappaalpha, where kappa is the Debye-Hückel parameter and alpha is the particle radius. It is found that an Onsager relation holds between CVP and dynamic electrophoretic mobility. It is also shown that the CVP from particles with very small kappaalpha approaches IVP; that is, in the limit of very small kappaalpha a particle behaves like an ion.

Effect of Ionic Surfactants on Ion Vibration Current and Colloid Vibration Current

“…3.1 Effect of alkyl chain length on ultrasonic vibration current For a dilute suspension of spherical colloidal particles in an electrolyte solution, Ohshima derived a theoretical equation of the total vibration current TVI as the sum of IVI and CVI given by 4,5 TVI IVI CVI…”

“…This is the origin of colloid vibration potential CVP and colloid vibration current CVI . Ohshima has derived the theoretical equations for the ultrasonic vibration potential in a dilute suspension of spherical colloidal particles in an electrolyte solution, and proved that the ultrasonic vibration potential is designated as the sum of IVP and CVP 4,5 . Based on this theory, it is of much interest to investigate the electroacoustic phenomenon in the aqueous solution of ionic surfactants, because the surfactant molecules form the micelle in the solution at a critical micelle concentration cmc , that is, the aqueous solution of ionic surfactant behaves like an inorganic elec-trolyte solution below the cmc, while it may be regarded as a kind of dilute colloidal dispersion above the cmc.…”

Study on Colloid Vibration Current in Aqueous Solution of Binary Surfactant Mixtures: Effects of Counterions and Hydrophobic Chains

“…8 in the DTAB -DTAC mixture system. Although the equation of μ ω is very complicated, it is certain that μ ω is proportional to the ζ -potential of charged particles in the solution 7,8 .…”

“…4 that the slope of CVI at X 2 0.5 is almost constant within experimental error, whereas that at X 2 0.5 increases rapidly with increasing the bulk composition. Considering that the slope of CVI is theoretically related to the ζ -potential of micelle particles 7,8 , it is expected that although the distribution of bromide and chloride ions around the micelle particles remains unaltered in the composition regime of X 2 0.5, that distribution is highly changed in the composition regime of X 2 0.5. We subsequently estimated the composition of mixed micelles from the results of CVI measurements.…”

Micelle Formation Effect on Electroacoustics in an Aqueous Surfactant Solution: Colloid Vibration Current and Ion Vibration Current

“…For this problem, Ohshima has derived more general electroacoustic theory for the poten-tial difference caused by a sound wave in a dilute suspension of spherical colloidal particles in an electrolyte solution by considering explicitly the presence of both particles and electrolyte ions 11,12) . This theory first enables us to analyze the vibration potential in the system including both particles and electrolyte ions, i.e., a general colloidal suspension.…”