Rd. Groot et al., MOLECULAR THEORY OF STRAIN-HARDENING OF A POLYMER GEL - APPLICATION TO GELATIN, The Journal of chemical physics, 104(22), 1996, pp. 9202-9219
The elasticity of gelatin gels at large deformation has been measured
for various experimental conditions. The general pattern is that stres
s increases with strain in a nonlinear way up to the point where the g
el fails. To interpret this nonlinear stress increase, we studied a nu
mber of molecular models by Monte Carlo simulation and by mean-field m
ethods. The effect of finite polymer length is studied via the FENE mo
del (finite extensible nonlinear polymer connections) and via the exac
t statistics of Kramers' model (chains of freely rotating stiff rods)
for a small number of elements per chain. To investigate the effect of
fractal connections, the end-point distribution that comes forward fr
om scaling theory has been generalized to arbitrary fractal dimension.
Finally we studied a heterogeneous network model: connections formed
by rods and coils. We also discuss the consequence of microphase separ
ation. Combining experiment and theory we conclude the following: (i)
The elastically active network connections in gelatin are most certain
ly not Gaussian. (ii) Strain hardening in gelatin can be attributed to
either: (a) finite polymer length(the chain length between connection
points should be some 2.5 times the persistence length), or (b) a fra
ctal structure of the polymer strands (the fractal dimension should be
roughly d(f)=1.3-1.5), or (c) the presence of both stiff rods and fle
xible coils (the length of the rods should be 1.4-4.4 times the radius
of gyration of the coils). (iii) Models b and c describe the experime
ntal data significantly better than model a. From a single parameter (
the fractal dimension) the fractal model correctly describes (1) the n
onlinearity of the stress-strain curve, (2) the scaling of Young's mod
ulus with polymer concentration, (3) the scaling of neutron scattering
intensity with wave number, and (4) it predicts the scaling exponent
of the linear dynamic modulus with frequency in the glassy transition
zone (no experimental data available). The experimental parameters fou
nd for the rod+coils model suggest a Rouse diffusion controlled growth
mechanism for the rods. Although the theory presented here is applied
to gelatin, its formulation is quite general, and its implications ar
e also relevant for other strain hardening polymer gels. (C) 1996 Amer
ican Institute of Physics.