Table 2.2. Critical exponents and associated quantities of the dynamic scaling hypothesis; the dynamic exponent is z = 3.05.

The inverse relaxation time Γ, or relaxation rate, is obtained from the linewidth in dynamic light scattering and provides the starting point for the dynamic scaling hypothesis. As with the static scaling hypothesis (Section 2.2.2), Γ is treated as a generalized homogeneous function of the inverse correlation length ξ⁻¹ of critical fluctuations and the wave vector q obtained from the autocorrelation function [26].

Here λ is initially an arbitrary number and z denotes the degree of homogeneity. Choosing λ = q⁻¹ leads to the following scaling relation for the linewidth:

The function Ω(qξ) is called the dynamic scaling function. This presentation is only an outline of the underlying theoretical approach. Dynamic scaling is discussed in greater detail in Chapter 3 in connection with critical ultrasonic absorption.