CHINESE JOURNAL OF PHYSICS VOL. 51, NO. 4 August 2013 Colloidal Aggregation in Critical Crosslinked Polymer Blends M. Benhamou, 1,2, ∗ F. Elhajjaji, 1 K. Elhasnaoui, 1 and A. Derouiche 1 1 Polymer Physics and Critical Phenomena Laboratory Sciences Faculty Ben M’sik, P. O. Box 7955, Casablanca, Morocco 2 Moulay Ismail University, Morocco (Received August 9, 2011; Revised July 23, 2012) We consider a low-density assembly of small colloidal particles that are immersed in a critical crosslinked polymer blend made of two polymers of different chemical nature. We assume that, near the spinodal temperature at which the mixture exhibits a microphase separation, the particles preferentially adsorb one of the two polymers. The consequence is that the beads aggregate in the non-preferred phase. The aim is an extensive study of the thermodynamical properties of the colloidal aggregation under a change of a suitable parameter such as temperature. This phase transition drives the colloids from a dispersed phase (gas) to a dense one (liquid). To this end, we elaborate a new field theory that allows the determination of the effective free energy of the mobile colloids as a functional of their density. From this effective free energy, we draw the phase diagram in the particle volume fraction-temperature plane, and investigate all the critical properties of the colloidal flocculation from both a static and dynamical point of view. Finally, the discussion is extended to impregnated crosslinked polymer blends in solution. DOI: 10.6122/CJP.51.700 PACS numbers: 61.25.hp, 82.70.-y, 05.70.Fh I. INTRODUCTION The aggregation phenomenon within the traditional colloidal solutions are due to the van der Waals attractive forces, which generally originate from the fact that the particles possess a dipolar moment [1]. The same phenomenon may be produced within so-called critical systems with immersed colloidal particles, such as a fluid near the liquid-gas critical point, a mixture of simple liquids (or polymers) near the consolute point, liquid 4 He near the λ-transition, or liquid-crystals. For these systems, the critical fluctuations of the order parameter generate long-range attractive forces between colloids, termed critical Casimir forces [2]. The word Casimir is attributed to the well-known Casimir effect [3], according to which two perfectly conducting parallel metals attract each other, due to the vacuum quantum fluctuations. The latter play the role of the critical fluctuations for physical systems exhibiting a critical point. The physics of the colloidal aggregation in critical two-component liquid mixtures is a very exciting and rich problem, and has received a great deal of attention from both the theoretical and experimental points of view. Theoretically, the critical Casimir effect has been studied by several methods, such as conformal invariance in dimension 2 [4–8], * Electronic address: benhamou.mabrouk@gmail.com http://PSROC.phys.ntu.edu.tw/cjp 700 c ⃝ 2013 THE PHYSICAL SOCIETY OF THE REPUBLIC OF CHINA