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Structural, elastic, and dynamic properties of swollen polymer networks

  • Sauveur Candau
  • Jacques Bastide
  • Michel Delsanti
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 44)

Abstract

This article reviews some recent developments in the physics of gels, due to both new methods of synthesis and modern techniques for the study of microscopic properties of gels. The review consists of four major sections. In the first section, some of the recent methods of synthesis allowing to prepare labelled networks are described.

The second section is concerned with the structural properties of networks. A critical discussion of both classical and scaling theories in the light of small-angle neutron scattering data is presented. In the their section, scaling relations for the elastic moduli of networks swollen in good solvents are discussed. The fourth section deals with the dynamic properties of swollen networks with special emphasis on inelastic light-scattering experiments.

The conclusion of this review stresses the important progress made in the understanding of the static and dynamic properties of swollen networks and describes possible future developments.

Keywords

Network Chain Vinyl Acetate Elementary Chain Exclude Volume Effect Longitudinal Modulus 
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 and Abbreviations

a3

size of the site; volume of the monomer; volume of the chain link

a1

diluent activity

b

radius of a spherical gel sample

c

polymer concentration expressed in g cm−3

ce

polymer concentration in a network at swelling equilibrium, expressed in g cm−3

c*

cross-over concentration between dilute and semi-dilute regimes

f

functionality of the crosslinks

\(\tilde f\)

effective frictional coefficient per monomer

f

driving force per unit volume

fm

force exerted on a monomer

g

number of links in a blob

g(r)

spatial pair-correlation function between monomers

h

volume fraction of polymer in the reference state

is

photocurrent due to the polarized scattered light

kB

Boltzmann constant

exponent in the scaling form of the elastic free energy

m*

apparent mass of the monomer immersed in a solvent

n

total number of neighbours of a given crosslink

nc

number of statistical units in a Gaussian subchain

p

exponent of the scaling law ξ (Φ)

q

scattering wave vector (transfer momentum)

r

modulus of the vector position

s

shear deformation

sd

sedimentation coefficient

t

time

tp

number of topological neighbours of a given crosslink

u

1/2 − χ

u′

interaction parameter between blobs

u*

effective interaction parameter in a semi-dilute regime

u(r, t)

displacement fluctuation of the polymer network from its equilibrium position at point r and time t

\(\underline {\dot u}\) (r, t)

displacement velocity

\(\dot u_m\)

drift velocity of a monomer

uq(t)

longitudinal component of u(r, t) with wave vector q

\(\dot u_s\)

velocity of the solvent

v1

molecular volume of the solvent

xs, xk

exponents of the scaling laws as a

xD

function of the polymer concentration for sedimentation, permeability, and diffusion coefficients, respectively

A

background of c(t)

A0

numerical constant in the expression of the photocurrent due to the polarized light scattered

B

prefactor in the scaling form of the elastic free energy

c(t)

time autocorrelation function of the photocurrent

D

diffusion coefficient

E

Young modulus

Eθ(t)

scattered electric field at an angle θ

F′el

elastic free energy density (per unit volume of the gel)

F″el

elastic free energy density (per site)

G

total Gibbs energy

G′

Gibbs energy density (per unit volume of the solution)

G″

Gibbs energy density (per site)

G″dil

Gibbs energy density of mixing (per site)

G′(s)

Gibbs energy density (per unit volume) of a gel under shear deformation

I0

incident light intensity

K

compressional modulus

Kel

inverse of the elastic contribution to the compressional modulus arising from permanent linking of the chains

Kgel

compressional modulus of a gel

Kp

permeability coefficient

Ksol

compressional modulus of a solution (at zero frequency)

M

longitudinal modulus

Mn

number average molecular weight

Mw

weight average molecular weight

N

polymerization index

N′

N/g

P

pressure

R

end-to-end distance of a chain

R0

unperturbed end-to-end distance of a chain

Rg

radius of gyration of a chain

Rg0

radius of gyration of a network chain in the reference state

Rg‖

radius of gyration of a network chain parallel to the stretching

Rg⊥

radius of gyration of a network chain perpendicular to the stretching

Rgi

radius of gyration of an elastic chain for unstretched network

〈R2d〉

mean-square end-to-end distance of a network chain in bulk

〈R0s2

mean-square end-to-end distance of a network chain in the reference state

〈Re2

mean-square end-to-end distance of a network chain in the swollen state

RF

end-to-end distance of a single chain in a good solvent

S(q)

scattering function

T

temperature

TR

lifetime of physical entanglements

δ

numerical constant characteristic of chain packing in the swollen network

ε

dielectric constant

ηs

viscosity of solvent

θ

scattering angle

ϰ

correction term in the expression of S(q) for semi-dilute solutions in a good solvent

λ

deformation ratio

λi

wavelength of the light in the scattering medium

μ

shear modulus

μi

chemical potential of the solvent in the solution or in the gel

μ10

chemical potential of the pure solvent

ξ

screening length

π

osmotic pressure

ϱ

number density of monomers

σ

compressional stress

σs

shear stress

τ

characteristic swelling time of the network

ω

circular frequency

Φ

volume fraction of polymer

Φ*

cross-over volume fraction of polymer between dilute and semi-dilute regimes

Φ0

volume fraction of polymer in the reference state

Φc

volume fraction of polymer in the solution prior to crosslinking

Φe

equilibrium volume fraction of polymer in a swollen network

χ

Flory-Huggins interaction parameter

χ0

osmotic compressibility

CGD

classical gradient diffusion

PDMS

polydimethylsiloxane

PS

polystyrene

QELS

quasi-elastic light scattering

SANS

small-angle neutron scattering

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Sauveur Candau
    • 1
  • Jacques Bastide
    • 2
  • Michel Delsanti
    • 3
  1. 1.Laboratoire d'Acoustique MoléculaireUniversité Louis Pasteur, Institut de PhysiqueStrasbourg Cedex
  2. 2.Centre de Recherches sur les MacromoléculesStrasbourg Cedex
  3. 3.C.E.N. Saclay S. DNF-Gif-sur-Yvette Cedex

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