Lattice Model of Equilibrium Polymerization: V. Scattering Properties and the Width of the Critical Regime for Phase Separation
Kyunil Rah, Karl Freed, J Dudowicz, Jack F. Douglas
Dynamic clustering associated with self-assembly in many complex fluids can qualitatively alter the shape of their phase boundaries and produce large changes in the scale of critical fluctuations that are difficult to comprehend within the existing critical phenomena framework for non-associating fluids. In order to elucidate the scattering and critical properties of associating fluids, we consider models of equilibrium polymerization that describe a widely occuring type of associating fluid at equilibrium with a well defined cluster geometry, i.e., linear polymer chains. Specifically, a Flory-Huggins type lattice theory is used, in conjunction with the random phase approximation (RPA), to compute the correlation length amplitude and the Ginzburg number Gi corresponding to the scale of composition fluctuations and a parameter characterizing the temperature range over which Ising critical behavior is exhibited, respectively.Our calculations indicate that upon increasing the interparticle association energy, the polymer chains become increasingly long in the vicinity critical point, leading naturally to a more asymmetric phase boundary. This increase in the average degree of polymerization implies, in turn, a larger and a drastically reduced width of the critical region (as measured by Gi). We thus obtain insight into the common appearance of asymmetric phase boundaries ina wide range of 'complex' fluids and into the observation of apparent mean field critical behavior even rather close to the critical point.
, Freed, K.
, Dudowicz, J.
and Douglas, J.
Lattice Model of Equilibrium Polymerization: V. Scattering Properties and the Width of the Critical Regime for Phase Separation, Journal of Chemical Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=852576
(Accessed June 3, 2023)