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Structural, elastic, and dynamic properties of swollen polymer networks

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Polymer Networks

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

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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

f m :

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

ℓ:

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

〈R 20s 〉:

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

〈R 2e 〉:

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

η s :

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

λ i :

wavelength of the light in the scattering medium

μ:

shear modulus

μ i :

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

μ 10 :

chemical potential of the pure solvent

ξ:

screening length

π:

osmotic pressure

ϱ:

number density of monomers

σ:

compressional stress

σ s :

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

Φ 0 :

volume fraction of polymer in the reference state

Φ c :

volume fraction of polymer in the solution prior to crosslinking

Φ e :

equilibrium volume fraction of polymer in a swollen network

χ:

Flory-Huggins interaction parameter

χ 0 :

osmotic compressibility

CGD:

classical gradient diffusion

PDMS:

polydimethylsiloxane

PS:

polystyrene

QELS:

quasi-elastic light scattering

SANS:

small-angle neutron scattering

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Authors and Affiliations

  1. Laboratoire d'Acoustique Moléculaire, Université Louis Pasteur, Institut de Physique, 4, rue Blaise Pascal, F-67070, Strasbourg Cedex

    Sauveur Candau

  2. Centre de Recherches sur les Macromolécules, 6, rue Boussingault, F-67083, Strasbourg Cedex

    Jacques Bastide

  3. C.E.N. Saclay S. DN, 91191, F-Gif-sur-Yvette Cedex

    Michel Delsanti

Authors
  1. Sauveur Candau
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  2. Jacques Bastide
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  3. Michel Delsanti
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Editor information

Karel Dušek

Additional information

We dedicate this review to Prof. Manfred Gordon on the occasion of his 65th birthday.

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Candau, S., Bastide, J., Delsanti, M. (1982). Structural, elastic, and dynamic properties of swollen polymer networks. In: Dušek, K. (eds) Polymer Networks. Advances in Polymer Science, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11471-8_2

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