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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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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