hw6 - in that the order parameter jumps to a non-zero value...

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Department of Chemical Engineering University of California, Santa Barbara ChE 210B Winter 2010 Instructor: Glenn Fredrickson Homework #6 Homework Due: Friday, March 12, 2010 1. The problem of equilibrium phase coexistence between a lamellar mesophase and a liquid phase in symmetric block copolymer melts can be related to a field theory model with the following Landau expansion of the dimensionless free energy density: F [ ψ ] = 2 - ψ 4 + ψ 6 where the ψ 6 term is needed for stability, since the ψ 4 coefficient is negative. The parameter t is the reduced temperature from a reference critical temperature. (a). Analyze this Landau free energy for phase coexistence. Starting from a high temperature liquid ( t ± 0), at what point on cooling (reducing t ) does a lamellar phase with non-zero ψ first form? (Note that this may not coincide with T c .) Show that this model is consistent with a “first-order” phase transition
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Unformatted text preview: in that the order parameter jumps to a non-zero value discontinuously at the phase transition, rather than rising continously from zero on cooling through the transition, as in a second-order phase transition. (b). Add a square-gradient term to the free energy density of this model and build a theory for the interfacial properties of an interface between a lamellar phase and a liquid phase at coexistence (i.e. at the rst-order transition point where the two bulk phases have equal free energy). Find expressions for the interfacial prole (and sketch), the interfacial width, and the interfacial tension. 2. Prepare solutions to the following problems in McQuarries text: 15-11, 15-22, 15-35. G. H. Fredrickson and K. Binder, J. Chem. Phys. 91 , 7265 (1989)....
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This document was uploaded on 05/18/2010.

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