Exclusion of Spherical Particles from the Nematic Phase of Reversibly Assembled Rod-Like Particles
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EXCLUSION OF SPHERICAL PARTICLES FROM THE NEMATIC PHASE OF REVERSIBLY ASSEMBLED ROD-LIKE PARTICLES Thomas L. Madden and Judith Herzfeld Department of Chemistry, Brandeis University, Waltham, MA 02254-9110 ABSTRACT The open-ended aggregation of amphiphilic molecules in aqueous solution generates a broadly polydisperse population of elongated particles that form a variety of partially ordered phases. Herzfeld and coworkers have shown that the phase behavior of these binary systems is well described by self-consistently combining scaled-particle theory for the effects of excluded volume in fluid dimensions, a simple cell model for the effects of excluded volume in positionally ordered dimensions, a mean-field treatment of soft-interactions, and a phenomenological model of aggregate formation. We have now extended this model to ternary systems. We find that the addition of spherical particles to a solution of rod-forming particles induces a very wide isotropic-nematic coexistence region in which a relatively dilute isotropic solution with little aggregation separates from a rather concentrated nematic solution that almost completely excludes the spherical solutes. The magnitude of this effect depends on the relative diameters of the two solutes. INTRODUCTION The role of excluded volume in the spontaneous ordering of elongated particles is now well understood. In a classic paper, Onsager showed that for sufficiently long rod-like particles the loss of rotational entropy in orientational ordering is exceeded by the gain in translational entropy [1]. Analogously, Taylor et al. have recently shown for monodisperse particles that at sufficiently high concentration the translational entropy lost in positionally ordered dimensions is exceeded by the translational entropy gained in other dimensions [2]. Thus orientational and positional ordering may both be entropically driven. Excluded volume drives similar long-range ordering in solutions of reversibly assembling species. Herzfeld et al. have shown that the experimentally observed phase behavior of these variably polydisperse systems can be described by balancing free energy contributions due to monomer interactions at contacts within the aggregates (driving aggregate growth), the ideal entropy of mixing (tending to broaden aggregate size and orientation distributions), excluded volume (driving orientational and positional ordering), and soft repulsions (opposing alignment). For polyaromatic dyes and drugs that stack to form rod-like aggregates, the theory reproduces the experimentally observed sequences of isotropic, nematic and columnar phases, including the critical point where all three coexist [3, 4, 5]. For rigid surfactants that assemble into plate-like aggregates, the theory reproduces the experimentally observed sequences of isotropic, nematic and lamellar phases, including the critical point where they all coexist [5]. For ordinary surfactants, capable of forming both rod-like and plate-like micelles, the theory reproduces the experimentally observed rearrangement
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