Chapter 19
Thermoreversible Gelation of Syndiotactic Poly(methyl methacrylate) Based Block Copolymers in o-Xylene 1
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J. M. Yu and R. Jerome CERM, University of Liege, B6 Sart-Tilman, 4000 Liege, Belgium
Thermoreversible gelation has been studied in o-xylene for syndiotactic poly(methyl methacrylate) based block copolymers. The dynamic properties of solutions and gels have been analyzed and discussed on the basis of scaling assumptions. At the gel point, where the loss angle tan δ=G"/G' is independent of the probing frequency, the samples obey the typical power law G'(ω)~ G"(ω)~ω . The scaling exponent Δis found in the 0.65-0.75 range, independently of the experimental conditions, the copolymers composition and the nature of the midblock. Modulus-frequency master curves have been built up by using appropriate reaction time dependent renormalisation factors for the individual frequency and modulus data. The scaling of these factors with reaction time has allowed to calculate the static scaling exponents for the increase observed in both modulus and viscosity. c
Δ
The study of polymer gels has stimulated considerable interest from both theoretical and experimental points of view. In the last decade, much attention has been paid to modifications in the structure and viscoelastic properties of systems going through a sol-gel transition. As a rule, gelation may be of physical or chemical origins, depending on the structure of the cross-links. In physical gels, the cross-linking is reversible and the cross-linking sites can be of a large size and of a high functionality. In contrast, chemical gels are permanently cross-linked by covalent bonds and the branching point has a well-defined functionality, i.e. that one of the cross-linker. Chemical gelation has been extensively investigated by sophisticated experiments (7) and accounted for by different theories from the original mean-field theory of Flory (2) to the concept of fractal geometry and the connectivity transition Current address: ICI Polyurethanes, Everslaan 45-B-3078 Everberg, Belgium.
© 1999 American Chemical Society Khan and Harrison; Field Responsive Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
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278 model of percolation (1,3,4). A special attention has been paid to the viscoelastic behavior of near-critical gels (5-14). Analysis of the dynamics near the critical gelation point has led to predictions for the frequency dependence of shear storage and loss moduli (eq.l) ,
,,
G*(©)=G (a))+iG (co)
(1)
where G*(G>), G'(G>) and G"(G>) are the complex, storage and
loss moduli,
respectively, and © the angular frequency. At the gel point, these moduli are predicted (5-7) and observed(5,#,9) to scale with frequency(f) according to eq.2 GW-G'W-CDA
(2)
where ®=2nf, f is the frequency and A is the scaling exponent. As a rule, the loss angle at the gel point (Sc) which is a measure of the phase difference between G' and G" (G7G'=tan 8 ), has an universal value at least at low frequencies^) C
8 =A(7t/2)
(3)
c
Analysis of dynamics at the gel point and theory of viscoelasticity provide a method to determine the static scaling exponents. Indeed, scaling arguments allow to show that the viscoelastic functions, G' and G", at different stages of the network formation, can be superimposed into a master curve, provided that frequency and complex modulus are renormalized by appropriate reaction time (t ) dependent factors. The theory shows that the renormalisation factors for the frequency and the complex modulus are the longest relaxation time (T ) and the steady-state creep r
z
compliance ( J ° ) (15), respectively, which at the gel point scale with e = (I t -tg I )/tg, according to eqs.4 and 5 e
r
J °~e-t
(5)
e
In these expressions, tg is the reaction time at gel point, s and t are the static scaling exponents which describe the divergence of the static viscosity, r|0~ s" , at t
