ISSN:
1435-1528
Keywords:
Key words Stretched-exponential
;
relaxation
;
retardation
;
creep
;
stress relaxation
;
linear viscoelasticity
;
critical gel
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
,
Physics
Notes:
Abstract The use of the stretched-exponential function to represent both the relaxation function g(t)=(G(t)–G ∞)/(G 0–G ∞) and the retardation function r(t)=(J ∞+t/η–J(t))/(J ∞–J 0) of linear viscoelasticity for a given material is investigated. That is, if g(t) is given by exp(–(t/τ)β), can r(t) be represented as exp(–(t/λ)μ) for a linear viscoelastic fluid or solid? Here J(t) is the creep compliance, G(t) is the shear modulus, η is the viscosity (η–1 is finite for a fluid and zero for a solid), G ∞ is the equilibrium modulus G e for a solid or zero for a fluid, J ∞ is 1/G e for a solid or the steady-state recoverable compliance for a fluid, G 0=1/J 0 is the instantaneous modulus, and t is the time. It is concluded that g(t) and r(t) cannot both exactly by stretched-exponential functions for a given material. Nevertheless, it is found that both g(t) and r(t) can be approximately represented by stretched-exponential functions for the special case of a fluid with exponents β=μ in the range 0.5 to 0.6, with the correspondence being very close with β=μ=0.5 and λ=2τ. Otherwise, the functions g(t) and r(t) differ, with the deviation being marked for solids. The possible application of a stretched-exponential to represent r(t) for a critical gel is discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00366673
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