Statistical Mechanics of Soft Core Fluid Mixtures Andrew John Archer

223 Pages·2012·3.48 MB·English

Statistical Mechanics of
Soft Core Fluid Mixtures
Andrew John Archer
H. H. Wills Physics Laboratory
University of Bristol
A thesis submitted to the University of Bristol in
accordance with the requirements of the degree of
Ph.D. in the Faculty of Science
August 2003

Abstract
In this thesis we investigate the statistical mechanics of binary mixtures of soft-core (cid:176)uids.
The soft-core pair potentials between the (cid:176)uid particles are those obtained by considering
the efiective potential between polymers in solution. The efiective pair potential between
the centers of mass of polymers is well approximated by a repulsive Gaussian potential.
A binary mixture of Gaussian particles can phase separate, and we calculate the phase
diagrams for various size ratios of the two species. Using a simple mean fleld density
functional theory (DFT) , which generates the random phase approximation for the bulk
pair direct correlation functions, we calculate the surface tension and density proflles for
the free interface between the demixed (cid:176)uid phases. We flnd that the asymptotic decay of
the interfacial proflles into bulk can be oscillatory on both sides of the interface. We also
calculate density proflles for the binary Gaussian core model (GCM) adsorbed at a planar
wall and flnd a wetting transition from partial to complete wetting for certain purely
repulsive wall potentials. By applying a general DFT approach for calculating the force
between two big particles immersed in a solvent of smaller ones we calculate the solvent
mediated (SM) potential between two big Gaussian core particles in the phase separating
binary mixture of smaller GCM particles. We show that the theory for calculating the SM
potential captures efiects of thick adsorbed fllms surrounding the big solute particles and
we flnd extremely attractive, long ranged SM potentials between the big particles whose
range is determined by the fllm thickness. In the region of the solvent critical point we
alsoflndextremelyattractiveSMpotentialswhoserangeisnowsetbythebulkcorrelation
length in the binary solvent.
In addition to the GCM, we also consider the efiective potential between the central
monomers on each polymer chain; this potential features a weak (logarithmic) divergence
as the particle separation r 0. A binary mixture of these particles can also phase
!
separate and displays many features in common with the binary GCM.

To my family:
Sarah, Mum, Dad and Alice.

Acknowledgments
First,andforemost,Iwouldliketothankmysupervisor,BobEvans,forallhissupport,
encouragement and patience, as well as his wisdom in suggesting the topics in this thesis
for me to study. When I started out, I had a suspicion that doing physics could be fun.
Working with Bob has proved to me that my inkling was right: physics is a lot of fun and
to a great extent this has been due to Bob’s enthusiasm.
There are also others I would like to thank: Joe Brader, who answered many of my
questionsatthebeginningandhelpedmetogetstarted. ChristosLikosandRolandRoth:
great scientists, good collaborators; they are both people I admire and like a lot.
IwouldalsoliketoacknowledgetheBristoltheorygroup, forprovidingagoodworking
atmosphere and for being a friendly group. I mention especially the other PhD students
{ my friends and peers: Joe, Ben, Mark, Jorge, Dan, Denzil, Danny, David, Jamie, Maria
and Emma.
Last, but not least, I mention my family: Sarah, my wife, for all her love and support,
and my parents for the same. When, as an 18 year old, I asked my parents what I should
study at university, they encouraged me to do whatever I enjoyed. I have been grateful
for that advice many times.

Authors Declaration
I declare that the work in this thesis was carried out in accordance with the regulations of
the University of Bristol. The work is original except where indicated by special reference
in the text and no part of the thesis has been submitted for any other degree. Any
views expressed in the thesis are those of the author and in no way represent those of
the University of Bristol. The thesis has not been presented to any other University for
examination either in the United Kingdom or overseas.