(570f) The Cluster Fluid Phase of Systems With Competing Short and Long-Ranged Interactions | AIChE

(570f) The Cluster Fluid Phase of Systems With Competing Short and Long-Ranged Interactions

Authors 

Lue, L. - Presenter, University of Strathclyde
Sweatman, M. B., University of Edinburgh



We investigate the behavior of low density systems of spherical
particles that interact with a short-ranged attractive and long-ranged
repulsive (SALR) force.  Using a multi-scale statistical thermodynamic
model that goes beyond the mean-field level, we find that this system
can form a uniform fluid of well defined clusters of particles, which
are large, but finite in size.  The clusters form within a narrow
range of model parameters, and the transition from a uniform
unaggregated fluid to a uniform dispersion of clusters (a cluster
fluid) occurs at a critical cluster concentration, or CCC, in analogy
to the critical micelle concentration in aqueous surfactant solutions.
Within this model, the clusters are described as liquid droplets
dispersed within a vapor of unaggregated particles.  Minimizing the
Helmholtz free energy functional yields the equilibrium cluster size
and density, as well as the liquid and vapor densities for a given
bulk density.  The CCC is less than the bulk binodal vapor density,
which is metastable.  A formula for the average cluster size is
determined, which essentially minimizes the cluster self-energy; this
might find use in estimating effective solute-solute interactions from
experimental cluster size data.  We also find that the cluster size
distribution is relatively narrow for the SALR system investigated
here.  As the strength of attractive interactions is increased, we
find the cluster size increases until it diverges, although in
experiments macroscopic crystals might be formed before this limit is
reached.  At bulk densities higher than the CCC, the cluster density
increases, yet the cluster size remains nearly constant, and we
predict the location of a phase transition to a non-uniform, ordered
dispersion (a cluster solid) based on the packing fraction of
clusters.  The CCC increases with decreasing strength of attractive
interactions, and we find a new first-order phase transition, a
cluster vapor to cluster liquid transition, within a very narrow range
of model parameters. We suggest the theoretical framework developed
here could be applied to many physical systems of interest that
exhibit strong effective attractive interactions competing with
screened Coulomb interactions, such as colloid-polymer mixtures, many
kinds of biomolecular dispersion, and perhaps even simple liquid
mixtures that exhibit hydrogen bonding and de-protonation.  The
theoretical framework outlined here for the disordered cluster phase
can be extended to ordered phases, and more complex cluster-forming
systems, such as micellar solutions.

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