Lattice and Continuum Studies of Fluids and Fluid Mixtures

Dartmouth College, Hanover NH

Investigators

Abstract

0099541 Lipson This grant, jointly funded by the Materials Theory Program in DMR and the Theoretical and Computational Chemistry Program in CHE, is targeted at understanding the correlation between microscopic structure and macroscopic behavior for fluids and their mixtures. The research tools are theoretical, but a major thrust of the research is to make connections and comparisons with experimental data both for small-molecule and polymeric fluids. In addition, a real opportunity afforded by this work is the ability to compare the results for the lattice and continuum models using the same theoretical approach. The behavior of complex fluids has been of high interest in recent years, stimulated by the increasingly sophisticated kinds of measurements accessible to researchers. In addition, the ability to simulate mixtures of dense fluids has expanded dramatically within the last decade. Thus, more data capable of testing statistical mechanical theories are appearing, particularly for complex liquid mixtures. The research here involves the Born-Green-Yvon (BGY) integral equation technique. Using the BGY formalism, descriptions of lattice and continuum systems have been derived, and comparisons between the results using the two have been initiated. The lattice theory yields closed-form expressions for thermodynamic quantities of interest. The advantages of lattice theory include its accessibility to non-theorists, and the ability to test it using lattice simulation results on relatively complex fluids and mixtures, which are more plentiful than continuum simulation data. The continuum theory is capable of tackling more subtle issues involving the interplay between local structure and bulk properties. However, continuum solutions involve numerical methods, and simulation data on mixtures are not yet plentiful. As indicated above, the development of analogous lattice and continuum theories yields the possibility of determining what kinds of equilibrium properties are expected to be sensitive to the imposition of a lattice constraint. In the current grant, the lattice studies will focus on developing an understanding of polymer solutions and blends, building on the demonstrated ability of the lattice BGY theory to describe simple alkane fluids and mixtures and hydrocarbon polymer solutions and blends. This work will involve analysis of data, including (new to this effort) small angle neutron scattering results, in order to obtain the characteristic microscopic parameters. Having determined what minimum data set is required to characterize a system, the goal is to predict less accessible properties, such as the pressure dependence of the coexistence curve. Such information is important, for example in deciding on processing conditions. The BGY theory is also capable of probing the effects of structural and energetic differences on miscibility in an effort to understand at a more sophisticated level the balance between the two. On the continuum side, recent research by this group has shown that the BGY theory is effective in describing such phenomena as chain collapse and the contraction of a hard-sphere chain in a hard-sphere solvent. The research will focus on dense fluids and mixtures which interact via a square-well potential. This potential is of interest because it is simple, yet capable of capturing the essential physics of real fluids. This potential has been used in making the first lattice-continuum comparisons, finding (among other things) that the scaling relationship between chain dimensions and chain length exhibits universal behavior. Future work will test the ability of a square-well fluid to serve as a model for alkanes, allowing a comparison with BGY lattice studies on n-alkanes. This connection between lattice and continuum will enable a 'meta' study on n-alkanes, involving both theories as well as simulation and experimental data. A major question is whether analogous results may be obtained using lattice and continuum BGY theories and, if so, what level of sophistication is required. Another issue is whether it is desirable to leave the theoretical development at different stages in the lattice and continuum, sacrificing subtlety for ease of use on the lattice, and accessibility for the ability to describe more complex systems in the continuum. %%% This grant, jointly funded by the Materials Theory Program in DMR and the Theoretical and Computational Chemistry Program in CHE, is targeted at understanding the correlation between microscopic structure and macroscopic behavior for fluids and their mixtures. The research tools are theoretical, but a major thrust of the research is to make connections and comparisons with experimental data both for small-molecule and polymeric fluids. In addition, a real opportunity afforded by this work is the ability to compare the results for the lattice and continuum models using the same theoretical approach. ***