**27**: 57-62

https://doi.org/10.1140/epje/i2008-10351-2

## Field-theoretical Renormalization-Group approach to critical dynamics of crosslinked polymer blends

Laboratoire de Physique des Polymères et Phénomènes Critiques, Faculté des Sciences Ben M’sik, B.P. 7955, Casablanca, Morocco

^{*} e-mail: m.benhamou@univh2m.ac.ma

Received:
21
March
2008

Published online:
30
July
2008

We consider a crosslinked polymer blend that may undergo a microphase separation. When the temperature is changed from an initial value towards a final one very close to the spinodal point, the mixture is out equilibrium. The aim is the study of dynamics at a given time *t*, before the system reaches its final equilibrium state. The dynamics is investigated through the structure factor, *S*(*q, t*), which is a function of the wave vector *q*, temperature *T*, time *t*, and reticulation dose *D*. To determine the phase behavior of this dynamic structure factor, we start from a generalized Langevin equation (*model C*) solved by the time composition fluctuation. Beside the standard de Gennes Hamiltonian, this equation incorporates a Gaussian local noise, *ζ*. First, by averaging over *ζ*, we get an effective Hamiltonian. Second, we renormalize this dynamic field theory and write a Renormalization-Group equation for the dynamic structure factor. Third, solving this equation yields the behavior of *S*(*q, t*), in space of relevant parameters. As result, *S*(*q, t*) depends on three kinds of lengths, which are the wavelength *q*
^{−1}, a time length scale *R*(*t*) ∼ *t*
^{1/z
}, and the mesh size *ξ*
^{*}. The scale *R*(*t*) is interpreted as the size of growing microdomains at time *t*. When *R*(*t*) becomes of the order of *ξ*
^{*}, the dynamics is stopped. The final time, *t*
^{*}, then scales as *t*
^{*} ∼ *ξ*
^{*}
^{z}, with the dynamic exponent *z* = 6−*η*. Here, *η* is the usual Ising critical exponent. Since the final size of microdomains *ξ*
^{*} is very small (few nanometers), the dynamics is of short time. Finally, all these results we obtained from renormalization theory are compared to those we stated in some recent work using a scaling argument.

PACS: 64.75.-g Phase equilibria – / 64.60.Ht Dynamic critical phenomena – / 83.80.Tc Polymer blends –

*© Springer, 2008*