9 research outputs found
Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute
We derive an expression for the chemical potential of an associating solute
in a solvent relative to the value in a reference fluid using the quasichemical
organization of the potential distribution theorem. The fraction of times the
solute is not associated with the solvent, the monomer fraction, is expressed
in terms of (a) the statistics of occupancy of the solvent around the solute in
the reference fluid and (b) the Widom factors that arise because of turning on
solute-solvent association. Assuming pair-additivity, we expand the Widom
factor into a product of Mayer f-functions and the resulting expression is
rearranged to reveal a form of the monomer fraction that is analogous to that
used within the statistical associating fluid theory (SAFT). The present
formulation avoids all graph-theoretic arguments and provides a fresh, more
intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body
effects are transparently incorporated into the very foundations of the theory.
We illustrate the generality of the present approach by considering examples of
multiple solvent association to a colloid solute with bonding domains that
range from a small patch on the sphere, a Janus particle, and a solute whose
entire surface is available for association
Mini-grand canonical ensemble: chemical potential in the solvation shell
Quantifying the statistics of occupancy of solvent molecules in the vicinity
of solutes is central to our understanding of solvation phenomena. Number
fluctuations in small `solvation shells' around solutes cannot be described
within the macroscopic grand canonical framework using a single chemical
potential that represents the solvent `bath'. In this communication, we
hypothesize that molecular-sized observation volumes such as solvation shells
are best described by coupling the solvation shell with a mixture of particle
baths each with its own chemical potential. We confirm our hypotheses by
studying the enhanced fluctuations in the occupancy statistics of hard sphere
solvent particles around a distinguished hard sphere solute particle.
Connections with established theories of solvation are also discussed
Structure and thermodynamics of a mixture of patchy and spherical colloids: a multi-body association theory with complete reference fluid information
A mixture of solvent particles with short-range, directional interactions and
solute particles with short-range, isotropic interactions that can bond
multiple times is of fundamental interest in understanding liquids and
colloidal mixtures. Because of multi-body correlations predicting the structure
and thermodynamics of such systems remains a challenge. Earlier Marshall and
Chapman developed a theory wherein association effects due to interactions
multiply the partition function for clustering of particles in a reference
hard-sphere system. The multi-body effects are incorporated in the clustering
process, which in their work was obtained in the absence of the bulk medium.
The bulk solvent effects were then modeled approximately within a second order
perturbation approach. However, their approach is inadequate at high densities
and for large association strengths. Based on the idea that the clustering of
solvent in a defined coordination volume around the solute is related to
occupancy statistics in that defined coordination volume, we develop an
approach to incorporate the complete information about hard-sphere clustering
in a bulk solvent at the density of interest. The occupancy probabilities are
obtained from enhanced sampling simulations but we also develop a concise
parametric form to model these probabilities using the quasichemical theory of
solutions. We show that incorporating the complete reference information
results in an approach that can predict the bonding state and thermodynamics of
the colloidal solute for a wide range of system conditions.Comment: arXiv admin note: text overlap with arXiv:1601.0438