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Statistical Mechanics of Soft Core Fluid Mixtures Andrew - Bris.ac.uk PDF

223 Pages·2012·3.48 MB·English
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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.

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Abstract. In this thesis we investigate the statistical mechanics of binary mixtures of soft-core fluids. The soft-core pair potentials between the fluid particles are
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