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Nonequilibrium thermodynamics and rheology of viscoelastic polymer media

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Summary

Nonlinear constitutive equations for viscoelastic polymer media have been derived with the help of irreversible thermodynamical methods. These equations contain a small number of constants which have obvious physical meaning. The work is based on the hypothesis that the high-elasticity state characterized by large elastic strains is the local equilibrium thermodynamical state of these media. A theoretical description is given to explain the kinetic transition of fluid polymer media into high-elasticity state at temperatures above the flow temperature.

Zusammenfassung

Mit Hilfe der Methoden der Thermodynamik irreversibler Prozesse werden nichtlineare rheologische Stoffgleichungen für viskoelastische Polymere abgeleitet. Diese Gleichungen enthalten nur wenige Konstanten, die eine klare physikalische Bedeutung haben. Die Untersuchung ist auf die Hypothese gegründet, daß der hochelastische Zustand, der durch große elastische Dehnungen gekennzeichnet ist, der Zustand des lokalen thermodynamischen Gleichgewichts dieser Stoffe ist. Es wird eine theoretische Erklärung des kinetischen Übergangs von flüssigen Polymeren in den hochelastischen Zustand bei Temperaturen oberhalb der Fließtemperatur gegeben.

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Abbreviations

a, ε, h, c :

Eulerian tensors of finite strains

a i , ε i ,h i ,c i :

their principal values

e :

strain rate tensor

ω :

vortex tensor

σ :

stress tensor

a ∇ :

Jaumann tensor derivative of tensora with respect to time

H, H e :

equilibrium thermodynamical flux

I 1,I 2,I 3 :

basis invariants of tensorC

ρ, ρ 0 :

density

T :

temperature

S :

specific entropy

f :

specific free energy

W :

elastic potential

q :

heat flux vector

P s :

production of entropy

D :

dissipation

p :

pressure

v :

speed vector

σ p ,e p :

nonequilibrium tensors of stress and strain respectively

σ e ,H e :

equilibrium tensors of stress and strain respectively

M (k) ijαβ :

kinetic coefficients

x :

heat conductivity tensor

r :

thermal resistance tensor

r ∥,r ⊥ :

its principal values

r 0 :

coefficient of thermal resistance in isotropic case

R 1,R 2 :

constitutive scalars of tensorr

c σ :

heat capacity

A :

thermal equivalent of work

C 1,C 2 :

constitutive scalars of tensore p in Maxwellian case

λ :

scalar coefficient of viscosity

W s :

symmetric elastic potential

µ :

modulus of high-elasticity

M c :

molecular weight of polymer chain between crosslinks

M * :

molecular weight of segment

β :

M */M c

θ 0,θ r :

relaxation and retardation times respectively

s :

θ r /θ 0

η 0 :

maximum Newtonian viscosity

α :

dimensionless parameter of elastic potential

T f ,T g :

flow temperature and glass transition temperature

Δf *,ΔS *,ΔU * :

free energy, entropy and internal energy of activation

R :

gas constant

l, l 0 :

characteristic lengths of segments in the presence and absence of a field respectively

L 0,L 1,⋯,L N :

characteristic sizes of molecular network

θ 0,θ 1,⋯, θ N :

characteristic relaxation times

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Authors and Affiliations

  1. Institute of Mechanical Problems, USSR Academy of Sciences, Leningradskij Prospekt 7, A-40, Moscow, USSR

    A. I. Leonov

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  1. A. I. Leonov
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Leonov, A.I. Nonequilibrium thermodynamics and rheology of viscoelastic polymer media. Rheol Acta 15, 85–98 (1976). https://doi.org/10.1007/BF01517499

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  • DOI: https://doi.org/10.1007/BF01517499

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