Dynamic heterogeneity, spatially distributed stretched-exponential patterns, and transient dispersions in solvation dynamics

Ranko Richert, Manfred Richert

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

In the context of determining the extent of dynamical heterogeneity of relaxation processes, it has proven useful to represent the ensemble-averaged autocorrelation function φ(t) in the general form φ(t) =f g(τ)Χ(t/τ)d τ, instead of focusing on the usual special case in which the basis functions Χ(t/τ) are exponentials. In practice, φ(t) is often fit by a stretched exponential, φ(t) = exp[-(t/τ)β. Here we analyze the properties of the probability density g(τ) for the case in which φ(t) is a superposition of stretched exponentials, and is itself a stretched exponential, with a stretching exponent greater than or equal to those of the basis functions, Χ(t/τ). Various degrees of nonexponentiality intrinsic in each basis function translate into different values for the time-dependent variance σ2(t) of the stochastic quantity Χ(t/τ), in which τ is considered to be a spatially varying characteristic time scale. We state a simple but exact solution for σ2(t), and assess its relation to experimental data on the inhomogeneous optical linewidth σinh(t), measured in the course of solvation processes in a supercooled liquid.

Original languageEnglish (US)
Pages (from-to)779-784
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume58
Issue number1
StatePublished - 1998
Externally publishedYes

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solvation
Basis Functions
Supercooled Liquid
Linewidth
Autocorrelation Function
Probability Density
autocorrelation
Superposition
Time Scales
Ensemble
Exact Solution
Exponent
Experimental Data
exponents
liquids

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

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abstract = "In the context of determining the extent of dynamical heterogeneity of relaxation processes, it has proven useful to represent the ensemble-averaged autocorrelation function φ(t) in the general form φ(t) =f g(τ)Χ(t/τ)d τ, instead of focusing on the usual special case in which the basis functions Χ(t/τ) are exponentials. In practice, φ(t) is often fit by a stretched exponential, φ(t) = exp[-(t/τ)β. Here we analyze the properties of the probability density g(τ) for the case in which φ(t) is a superposition of stretched exponentials, and is itself a stretched exponential, with a stretching exponent greater than or equal to those of the basis functions, Χ(t/τ). Various degrees of nonexponentiality intrinsic in each basis function translate into different values for the time-dependent variance σ2(t) of the stochastic quantity Χ(t/τ), in which τ is considered to be a spatially varying characteristic time scale. We state a simple but exact solution for σ2(t), and assess its relation to experimental data on the inhomogeneous optical linewidth σinh(t), measured in the course of solvation processes in a supercooled liquid.",
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