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Published on: August 13, 2019
Three-point susceptibilities chi(n) (k;t) and chi(n)s (k;t): mode-coupling approximation
Grzegorz Szamel1, Elijah Flenner
1Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA.
Summary
This study explores dynamic density correlations in colloidal suspensions. We demonstrate that a specific three-point susceptibility is key to understanding these dynamics and numerically solve its equation of motion.
Area of Science:
- Soft Matter Physics
- Statistical Mechanics
- Colloidal Science
Background:
- A three-point susceptibility, chi{n}(k;t), was recently proposed to be crucial for analyzing dynamic density correlations in colloidal systems.
- This susceptibility relates to the density derivative of the intermediate scattering function.
Purpose of the Study:
- To investigate the equation of motion for chi{n}(k;t) within the framework of mode-coupling theory.
- To numerically solve the derived equations of motion for both chi{n}(k;t) and the density derivative of the self-intermediate scattering function, chi_{n};{s}(k;t).
- To compare the wave vector dependence of these two dynamic quantities.
Main Methods:
- Mode-coupling theory (MCT) was employed to derive the equations of motion.
- Numerical solutions were obtained for the equations governing chi{n}(k;t) and chi_{n};{s}(k;t).
- Analysis focused on the wave vector (k) dependence of the calculated susceptibilities.
Main Results:
- The equation of motion for chi{n}(k;t) was shown to be analogous to the q->0 limit of another three-point susceptibility, chi{q}(k;t).
- Numerical solutions for chi{n}(k;t) and chi_{n};{s}(k;t) were successfully obtained.
- Distinct differences in the wave vector dependence between chi{n}(k;t) and chi_{n};{s}(k;t) were observed.
Conclusions:
- The study confirms the theoretical link between chi{n}(k;t) and established dynamic correlation functions in colloidal suspensions.
- Numerical solutions provide valuable insights into the dynamics described by these susceptibilities.
- The contrasting wave vector dependencies highlight unique aspects of collective versus self-particle dynamics.
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