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Flow and electric birefringence in rigid-chain polymer solutions

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Polymer Products

Part of the book series: Advances in Polymer Science ((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.

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Abbreviations

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

Δn ν :

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

ℰ:

electric field affecting the particle (molecule)

F:

coefficient depending on the asymmetry of a worm-like chain

G:

coefficient

K:

Kerr's constant

K η , 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

α1−α2:

optical anisotropy of a segment

β :

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

β M :

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

η 0 :

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

μ 0 :

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

μ s :

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

τ d :

time of deformation of the macromolecule

τ 0 :

time of reorientation of the macromolecule as a whole

Δτ=g(n−η 0):

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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  1. Institute of Macromolecular Compounds, USSR Academy of Science, 199004, Leningrad, USSR

    Victor N. Tsvetkov & Larisa N. Andreeva

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  1. Victor N. Tsvetkov
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Tsvetkov, V.N., Andreeva, L.N. (1981). Flow and electric birefringence in rigid-chain polymer solutions. In: Polymer Products. Advances in Polymer Science, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10218-3_3

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