Kinetic rate laws as derived from order parameter theory II: Interpretation of experimental data by laplace-transformation, the relaxation spectrum, and kinetic gradient coupling between two order parameters
✍ Scribed by E. Salje; B. Wrack
- Publisher
- Springer-Verlag
- Year
- 1988
- Tongue
- English
- Weight
- 566 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0342-1791
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✦ Synopsis
A unifying theory of kinetic rate laws, based on order parameter theory, is presented. The time evolution of the average order parameter is described by
where t is the time, x is the effective inverse susceptibility, and L indicates the Laplace transformation. The probability function P(x) can be determined from experimental data by inverse Laplace transformation. Five models are presented:
(a) Polynomial distributions of P(x) lead to Taylor expansions of (Q) as
t t 2 "'" (b) Gaussian distributions (e.g. due to defects) lead to a rate law 1r~2 / /T\ (Q):e-Xo ' e ~ erfc[V2t )
where Xo is the most probable inverse time constant, F is the Gaussian line width and erfc is the complement error integral.
(c) Maxwell distributions of P are equivalent to the rate law (QSoce-k . (d) Pseudo spin glasses possess a logarithmic rate law (Q)ocln t.
(e) Power laws with P(x)=x ~' lead to a rate law:
The power spectra of Q are shown for Gaussian distributions and pseudo spin glasses. The mechanism of kinetic gradient coupling between two order parameters is evaluated.