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Thermo-elasticity of networks

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Abstract

Molecular networks may be considered as elastic fluids the conformational abilities of which are adequately characterized with the aid of the model of a van der Waals conformational gas with weak interactions. The internal properties are submitted to the conditions of internal equilibrium, thus, having their changes uniquely related to the global transformations of the network upon deformation. These global properties are at least determining the limits of stability which are expressed in the van der Waals approach by formulating of a reduced equation of state of real networks. It will be discussed on hand of thermo-elastic measurements and its quantitative description what is in need for a full and self-containing phenomenological description of molecular networks.

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Abbreviations

U :

internal energy

T :

absolute temperature

S :

entropy

V :

volume

G :

free enthalpy

F :

free energy

W :

work

Q rev :

heat reversibly transferred

P :

pressure

L :

actual length

L 0 :

length in the unstrained state

L max :

maximum length

λ :

relative elongation

λ m :

maximum relative elongation

ɛ :

strain

f :

force

f u :

energy component of the force

f s :

entropy component of the force

f b :

enthalpy component of the force

K :

modulus

¯G, ¯G 0 :

shear moduli

N :

number of chains in the network

k :

Boltzmanns number

β :

linear thermal expansion coefficient

χ :

isothermal compressibility

〈r 2〉/〈r 20 〉:

memory term

η :

Q/W

D:

λ-λ −2

D m :

λ m- λ −2m

B :

D m/(Dm-D)

n st :

number of Kuhn-segments

M st :

molecular-weigth of the Kuhn segment

ϱ :

density

R :

gas constant

λ m, a:

van der Waals parameters

ΔU :

activation energy

n(T,λ):

number of activated “rotators”

γ :

potential energy parameter

T r :

freezing temperature

T c, Dc, f′c :

critical parameters

f′, d, t :

reduced variables

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Author notes

  1. H. -G. Kilian

    Present address: Abt. Experimentelle Physik, Universität Ulm, Ulm/Donau

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    1. H. -G. Kilian
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    Vorgetragen auf der Frühjahrstagung des Fachausschusses „Polymerphysik“ der Deutschen Physikalischen Gesellschaft, Regenburg 15.–17. März 1982

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    Kilian, H.G. Thermo-elasticity of networks. Colloid & Polymer Sci 260, 895–910 (1982). https://doi.org/10.1007/BF01413126

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