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Predictions of nucleation theory applied to ehrenfest thermodynamic transitions: II. The effects of pressure and stress
Author(s) -
Campbell K. W.,
Barker R. E.
Publication year - 1985
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760251709
Subject(s) - thermodynamics , compressibility , supercooling , nucleation , order (exchange) , phase transition , materials science , energy (signal processing) , hydrostatic pressure , bulk modulus , thermal expansion , degree (music) , classical nucleation theory , heat capacity , function (biology) , physics , quantum mechanics , finance , acoustics , economics , evolutionary biology , biology
This paper is a sequel to an earlier one on the applicability of classical nucleation theory to second‐order transitions in the Ehrenfest sense (1). In each case the approach was to obtain the critical size r c and energy barrier Δ G c for the growth of a nucleus of β‐phase in an α‐phase matrix by a Maclaurin series expansion of the free‐energy‐density g = ( G β − G α )/ v β as a function of θ (in BC‐I) and of Δ P and Δσ in this paper where θ = ( T − T t ) is the degree of undercooling and Δ P and Δσ are analogous terms for the hydrostatic pressure shift and tensile stress shift away from the equilibrium transition. The expansion coefficients were determined by the use of thermodynamic relationships. For second‐order transitions, r c = 4γ v β T t /Δ C p θ 2 , r c = 4γ/Δβ(Δ p ) 2 , and r c = 4γ/ Y α Y β (Δσ) 2 , respectively, for the three cases. The terms Δ C p , Δβ, and Δ Y denote the differences in heat capacity, compressibility, and Young's modulus, e.g., Δ Y = Y β − Y α . The interfacial energy γ αβ is denoted by γ. The activation energy barriers for the cases developed in this paper were Δ G c = (16π/3)γ 3 /(Δβ) 2 (Δ p ) 4 and Δ G c = (64π/3)γ 3 Y α 2 Y β 2 /(Δ Y ) 2 (Δσ) 4 . More complicated expressions are given in the paper for the r c and Δ G c for first‐order transitions. In the long run, these expressions may prove more useful than the ones for second‐order because of the modifications expressions for the kinetics of transformations.