DOI 10.1140/epje/i2010-10643-x Regular Article Eur. Phys. J. E 32, 391–398 (2010) T HE EUROPEAN P HYSICAL JOURNAL E Theory of microphase separation in crosslinked polymer blends immersed in a θ-solvent M. Benhamou a , A. El Fazni, A. Bettachy, and A. Derouiche Laboratoire de Physique des Polym` eres et Ph´ enom` enes Critiques, Facult´ e des Sciences Ben M’sik, P.O. Box 7955, Casablanca, Morocco Received 10 May 2009 and Received in final form 12 June 2010 Published online: 29 August 2010 – c  EDP Sciences / Societ`a Italiana di Fisica / Springer-Verlag 2010 Abstract. The aim of this work is a theoretical study of the effects of the solvent quality on the microphase separation in crosslinked polymer blends, from a static and kinetics point of view. More precisely, we assume that the crosslinked mixture is trapped in a θ-solvent. The static microphase properties are studied through the static structure factor. The latter is computed using an extended blob model, where the crosslinked unlike chains can be viewed as sequences of blobs. We demonstrate that the presence of the θ-solvent simply leads to a multiplicative renormalization of these properties, and the renormalization factors are powers of the overall monomer volume fraction. Second, we investigate the early kinetics of the microphase separation, via the relaxation rate, τ q , which is a function of the wave number q (at fixed temperature and monomer volume fraction). We first show that the kinetics is entirely controlled by local motions of Rouse type, since the slow motions are frozen out by the presence of crosslinks. Using the blob model, we find an explicit form for the growth rate Ω(q)= τ -1 q , which depends, in addition to the wave number q, on the overall monomer volume fraction, Φ. Also, we discuss the effect of initial entanglements that are trapped when the system is crosslinked. In fact, these play the role of true reticulation points, and then, they quantitatively contribute to the microseparation phenomenon. Finally, the results are compared to their homologous relatively to the molten state and to the good solvent case. The main conclusion is that the quality of the solvent induces drastic changes of the microphase properties. 1 Introduction The crosslinked polymer blends (CPBs) constitute new materials that are composed of two chemically incom- patible polymer chains A and B. These chains may be crosslinked in the one-phase region by controlled γ - irradiations. When the system is cooled down, the crosslinked mix- ture has tendency to phase separate. Below some critical temperature, a microphase separation (MPS) takes place. This originates from a competition between the presence of crosslinks and the elasticity of the polymer network that resists to such separation. Then, this MPS is accompanied by the appearance of microdomains alternatively rich in A and B polymers. We recall that the MPS within CPBs has been stud- ied, first, by de Gennes [1], followed by several extended works [2–18]. To elaborate the theory, the author started from the central idea that there exists a strong analogy between the CPB and a dielectric medium, where the monomers of types A and B play the role of charges + and − of this medium, and the displacement vector be- a e-mail: m.benhamou@univh2m.ac.ma tween the mass centres of two adjacent unlike strands is the analog of the polarization. By strands, we mean the sections of chains between consecutive crosslinks. The de Gennes’ theoretical predictions were tested by a small- angle neutron scattering experiment, achieved by Briber and Bauer [19] on PS-PVME mixture. The theory agrees with experiment in all wave vectors range, except in the zero-scattering angle limit. More precisely, the theoretical structure factor vanishes at this limit, while the exper- imental one does not. This discrepancy was solved in a series of published works [4,7,9–11]. In this paper, the main purpose is the study of the ef- fects of the solvent quality on MPS, from a static and kinetics point of view. More precisely, we consider the case of CPBs that are trapped in a θ-solvent. This ex- tends some previous works [13,14] dealt with the study of this separation transition in the presence of a good sol- vent. To do calculations, use is made of an extended blob model [20,21], where a crosslinked polymer chain can be viewed as a sequence having blobs as new units. For the static study, the results show that the θ-solvent effects sim- ply lead to a multiplicative renormalization of microphase properties. The renormalization factors are powers of the total monomer volume fraction Φ, provided that one is