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Flow and electric birefringence in rigid-chain polymer solutions

  • Victor N. Tsvetkov
  • Larisa N. Andreeva
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 39)

Abstract

Results of the investigations of flow and electric birefringence in solutions of some rigid-chain polymers — cellulose derivatives, ladder polymers, aliphatic and aromatic polyamides etc. — are reported and discussed. In their dynamooptical and electrooptical properties, these polymers exhibit some specific features as compared with flexible-chain polymers. Flow birefringence and electric birefringence are efficient methods for studying the structural and conformational characteristics of the macromolecules of rigid-chain polymers.

Keywords

Optical Anisotropy Kuhn Segment Flow Birefringence Kerr Constant Electric Birefringence 
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

a

persistent length

a−a=Δa

difference between the main polarizabilities of the monomer unit

b

parameter of the shape asymmetry of the molecule

b

effective chain anisotropy in a system of axes of the first element

c

solution concentration

d

hydrodynamic diameter of the chain

f

translatory friction coefficient of the molecule

g

velocity gradient

h

end-to-end distance of the chain

〈h2

mean-(overall conformations) square end-to-end distance of the chain

k

Boltzmann's constant

n

refractice index of the solution

[n]

characteristic value of FB

Δn

excess birefringence of the solution

Δnν

EB of solution at field frequency ν

Δn0

EB in a steady field

dn/dc

refractive index increment in a polymer-solvent system

Δn/Δτ

shear optical coefficient

p

axial ratio of the ellipsoid

p(x)

shape asymmetry of a worm-like chain

[s]

sedimentation coefficient

\(\bar v\)

partial specific volume of the polymer

x=L/a

relative length of the molecular chain

A

length of the statistical Kuhn segment

Af

length of the statistical Kuhn segment on the assumption of free rotation about valence bonds

A0

hydrodynamic parameter

B

optical coefficient

C

coefficient

D

translational diffusion coefficient

Dr

rotatory diffusion coefficient

E

electric field strength

electric field affecting the particle (molecule)

F

coefficient depending on the asymmetry of a worm-like chain

G

coefficient

K

Kerr's constant

Kη, KD

coefficients in Mark-Kuhn's equations

L

contour length of the chain

M

molecular weight of the macromolecule

Mn, Mw

number average and weight average molecular weight of the macromolecule

M0

molecular weight of a monomer unit

MS

molecular weight of a segment

N

number of segments in a chain

NA

Avogadro's number

P

function of hydrodynamic interactions in translatory frictions

R

gas constant

〈R2

mean-square radius of gyration

S

number of monomer units in a statistical Kuhn segment

Sf

number of monomer units in a statistical Kuhn segment assuming free rotation about valence bonds

T

absolute temperature

W

rotatory friction coefficient of the macromolecule

Z

relative content of a component in the copolymer

α, β

exponents in Mark-Kuhn's equations

α

orientation angle of flow birefringence

α1α2

optical anisotropy of a segment

β

optical anisotropy of the unit length of a worm-like chain

βM

optical anisotropy of a chain per unit of its molecular weight

γ1, γ2, γ3

main optical polarizabilities of the macromolecule

dielectric permittivity of a solution

0

excess value of dielectric permittivity of a solution in a steady electric field (at ν→0)

excess value of dielectric permittivity of the solution at field frequency ν→∞

Δ/Δc

dielectric increment

ζ

mean effective friction coefficient of a bead

ζ

parameter in the Langevin function

η

viscosity of solution

η0

viscosity of solvent

[η]

intrinsic viscosity

ϑ

angle formed by the dipole moment of a monomer unit with the chain direction

λ

projection of the monomer unit on the chain direction

μ

dipole moment of the chain

μ0

dipole moment of a polar group (monomer unit)

μ0∥, μ0⊥

parallel and perpendicular components of the dipole moment of the monomer unit with respect to the chain direction

μs

dipole moment of a segment

μs∥, μs⊥

parallel (longitudinal) and perpendicular (normal) components of the dipole moment of a segment

ν

electric field frequency

ρ

solvent density

τd

time of deformation of the macromolecule

τ0

time of reorientation of the macromolecule as a whole

Δτ=g(n−η0)

effective shear stress in solution

[χ/g]

characteristic orientation angle

ω

frequency of the sinusoidal electric field (in radians)

Φ

function of hydrodynamic interactions in viscosity phenomenon

ϑ

angle formed by the dipole moment of the molecule and the axis of its optical polarizability

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Victor N. Tsvetkov
    • 1
  • Larisa N. Andreeva
    • 1
  1. 1.Institute of Macromolecular CompoundsUSSR Academy of ScienceLeningradUSSR

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