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Molecular mobility, deformation and relaxation processes in polymers

  • Werner Holzmüller
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 26)

Keywords

Glass Transition Temperature Relaxation Process Free Volume Flow Process External Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

Ael or A

Elastic potential caused by an external stress

Adiel

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 (Eor orientation field strength)

E or Em

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

F

Force

G or G′, G″

Shear modules (G′ real, G″ imaginary component) (G0 for purely elastic deformation)

fr

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 (Pdef deformation, Por orientation polarisation)

px

Momentum coordinate

r

Spatial coordinate

r0

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 (Ri inner, Ra outer radius)

S

Entropy

T

Temperature (Tg glass transition temperature)

z

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

z0

Number of flowing units or segments (per unit area)

U

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

v

Velocity

V

Volume

W

Probability (Wp 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

βth

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

νth

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

α

Molecular polarisability

τ

Relaxation time; τstress for stress, τstrain for strain

τfl

Fluctuation time

ω

Angular velocity, frequency

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Werner Holzmüller
    • 1
  1. 1.Sektion PhysikKarl-Marx-UniversitätLeipzigGDR

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