scholarly journals The Ohm Law as an Alternative for the Entropy Origin Nonlinearities in Conductivity of Dilute Colloidal Polyelectrolytes

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 225
Author(s):  
Ioulia Chikina ◽  
Valeri Shikin ◽  
Andrey Varlamov
Keyword(s):  
Electric Field ◽  
Linear Function ◽  
Colloidal Particles ◽  
Colloidal Particle ◽  
Effective Conductivity ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Low Concentration ◽  
Multiply Charged ◽  
Experimental Findings

We discuss the peculiarities of the Ohm law in dilute polyelectrolytes containing a relatively low concentration n ⊙ of multiply charged colloidal particles. It is demonstrated that in these conditions, the effective conductivity of polyelectrolyte is the linear function of n ⊙ . This happens due to the change of the electric field in the polyelectrolyte under the effect of colloidal particle polarization. The proposed theory explains the recent experimental findings and presents the alternative to mean spherical approximation which predicts the nonlinear I–V characteristics of dilute colloidal polyelectrolytes due to entropy changes.

Some Explicit Results for the Mean Spherical Approximation for Mixtures of Yukawa Fluids

2008 ◽  
Vol 73 (3) ◽  
pp. 424-438 ◽  
Author(s):  
Douglas J. Henderson ◽  
Osvaldo H. Scalise
Keyword(s):  
Integral Equation ◽  
Spherical Approximation ◽  
Mean Spherical Approximation ◽  
Inverse Temperature ◽  
Temperature Expansion ◽  
Yukawa Fluid ◽  
The Mean ◽  
Full Solution ◽  
Insight Into ◽  
Reasonable Model

The mean spherical approximation (MSA) is of interest because it produces an integral equation that yields useful analytical results for a number of fluids. One such case is the Yukawa fluid, which is a reasonable model for a simple fluid. The original MSA solution for this fluid, due to Waisman, is analytic but not explicit. Ginoza has simplified this solution. However, Ginoza's result is not quite explicit. Some years ago, Henderson, Blum, and Noworyta obtained explicit results for the thermodynamic functions of a single-component Yukawa fluid that have proven useful. They expanded Ginoza's result in an inverse-temperature expansion. Even when this expansion is truncated at fifth, or even lower, order, this expansion is nearly as accurate as the full solution and provides insight into the form of the higher-order coefficients in this expansion. In this paper Ginoza's implicit result for the case of a rather special mixture of Yukawa fluids is considered. Explicit results are obtained, again using an inverse-temperature expansion. Numerical results are given for the coefficients in this expansion. Some thoughts concerning the generalization of these results to a general mixture of Yukawa fluids are presented.

scholarly journals Modeling and theoretical description of magnetic hybrid materials—bridging from meso- to macro-scales

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Andreas M. Menzel ◽  
Hartmut Löwen
Keyword(s):  
Colloidal Particles ◽  
Colloidal Particle ◽  
Theoretical Description ◽  
Point Of View ◽  
Material Behavior ◽  
Theoretical Point ◽  
Mechanical Stiffness ◽  
Theoretical Approaches ◽  
Theoretical Predictions ◽  
Particle Level

Abstract Magnetic gels and elastomers consist of magnetic or magnetizable colloidal particles embedded in an elastic polymeric matrix. Outstanding properties of these materials comprise reversible changes in their mechanical stiffness or magnetostrictive distortions under the influence of external magnetic fields. To understand such types of overall material behavior from a theoretical point of view, it is essential to characterize the substances starting from the discrete colloidal particle level. It turns out that the macroscopic material response depends sensitively on the mesoscopic particle arrangement. We have utilized and developed several theoretical approaches to this end, allowing us both to reproduce experimental observations and to make theoretical predictions. Our hope is that both these paths help to further stimulate the interest in these fascinating materials.

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