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Molecular mobility, deformation and relaxation processes in polymers

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Book cover Polymer Chemistry

Part of the book series: Advances in Polymer Science ((POLYMER,volume 26))

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Abbreviations

Ael or A:

Elastic potential caused by an external stress

A diel :

Electric potential caused by an external electric field

A, B, C1, C2, C3, C4:

Constants

a:

Characteristic quasiviscosity in the WLF equation

c:

Concentration

D:

Diffusion constant

E:

Electric field strength (E or orientation field strength)

E or Em:

Young modules (E m extended to molecular dimension in our quasicubic model)

F:

Force

G or G′, G″:

Shear modules (G′ real, G″ imaginary component) (G 0 for purely elastic deformation)

f r :

Reducing factor

h:

Planck constant (h=6,62 10−34 Joule sec)

I:

Diffusion current

K:

Modules of compressibility

k:

Boltzmann constant (k=1,380 10−23 Joule/oK)

L:

Length of a capillary

L:

Laplace transformation

M:

Torque

m, n:

Constants characterizing the amorphous state

m:

Mass of a flowing unit

n:

Number of coupled processes, characterizing a network N≈1/n

p:

Pressure

P:

Electric polarisation (P def deformation, P or orientation polarisation)

px :

Momentum coordinate

r:

Spatial coordinate

r 0 :

Radius of a flowing unit, distance between the maximum and the saddle point in the Lennard-Jones potential

R:

Radius of a capillary or cylinder (R i inner, R a outer radius)

S:

Entropy

T:

Temperature (T g glass transition temperature)

z:

Number of molecular dislocations in the direction of an external stress per unit area

z 0 :

Number of flowing units or segments (per unit area)

U:

Potential energy (U i, Uk potential energy at a minimum of an energy hyperplane, U ov energy needed to overcome an energy barrier in special cases, ΔU activation energy)

v:

Velocity

V:

Volume

W:

Probability (W p probability for molecular dislocation processes)

y, z:

Spatial coordinates

α:

Partion of flowing units participating in molecular fluctuation processes (molecules have more than one possible conformation)

α, β, γ, δ, ϕ, ψ, θ:

Special angles

β th :

Linear thermal expansion coefficient

γ:

Shear rate

ε:

Elongation Λ=1+ε=1+Δ1/1

ε:

Dielectric constant (ε0 = 8,854 10−12 As/Vm)

Δ, δ:

Differences

χ:

Quantity describing an amorphous state

η:

Viscosity

μ:

Dipole moment

ν th :

Average frequency for thermal vibrations, ν th=kT/h≈1013

α:

Molecular polarisability

τ:

Relaxation time; τstress for stress, τstrain for strain

τ fl :

Fluctuation time

ω:

Angular velocity, frequency

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  1. Sektion Physik, Karl-Marx-Universität, 7010, Leipzig, GDR

    Werner Holzmüller

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Holzmüller, W. (1978). Molecular mobility, deformation and relaxation processes in polymers. In: Polymer Chemistry. Advances in Polymer Science, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022820

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  • DOI: https://doi.org/10.1007/BFb0022820

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  • Print ISBN: 978-3-540-08677-2

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