1. Thermophysical properties of fluids: From simple models to applications Ivo NEZBEDA E. Hala Lab. of Thermodynamics, Acad. Sci., 165 02 Prague, Czech Rep. Dept. of Physics, J. E. Purkyne University, 900 46 Usti n. Lab., Czech Rep. COLLABORATORS: J. Kolafa M. Lisal M. Predota L. Vlcek SUPPORT: Grant Agency of the Czech Republic Grant Agency of the Academy of Sciences

2. General bla, bla

3. PERTURBATION THEORY – general considerations (1) Given an intermolecular pair potential u, the perturbation expansion method proceeds as follows: u is first decomposed into a reference, u ref, and a perturbation, u pert, part, u = u ref + u pert The decomposition is not unique and is dictated by both physical and mathematical considerations. This is the crucial step of the method that determines convergence (physical considerations) and feasibility (mathematical considerations) of the expansion. (2) The properties of the reference system must be estimated accurately and relatively simply so that the evaluation of the perturbation terms is feasible. (3) Finally, property X of the original system is then estimated as X = X ref +  X where  X denotes the contribution that has its origin in the perturbation potential u pert.

4. STEP 1: Separation of the total u into a reference part and a perturbation part, u = u ref + u pert This problem seems to have been solved during the last decade and the results may be summarized as follows: Regardless of temperature and density, the effect of the long-range forces on the spatial arrangement of the molecules is very small. Specifically: (1) The structure of both polar and associating realistic fluids and their short- range counterparts, described by the set of the site-site correlation functions, is very similar (nearly identical). (2) The thermodynamic properties of realistic fluids are very well estimated by those of suitable short-range models; (3) The long-range forces affect only details of the orientational correlations and hence, to a certain extent, also pressure. However, integral quantities, such as e.g. the dielectric constant, remain unaffected. THE REFERENCE MODEL IS A SHORT-RANGE FLUID, u ref = u short-range model

5. STEP 2: Estimate the properties of the reference accurately (and relatively simply) in a CLOSED form HOW?? HINT: Recall theories of simple fluids: u LJ = u soft spheres + Δ u X LJ = X soft spheres + ΔX X HARD SPHERES + ΔX SOLUTION: Find a simple model (called primitive model) that (i) approximates reasonably well the short-range reference, and (ii) is amenable to theoretical treatment

6. GOAL: Given a short-range REALISTIC (parent) site-site potential model, develop a methodology to construct from ‘FIRST PRINCIPLES’ a simple (primitive model) which reproduces the structural properties of the parent model. IDEA: Use the geometry (arrangement of the interaction sites) of the parent model,, Example: 3-site model of methanol  PROBLEM: PROBLEM: How to set the parameters of interaction and mimic short-range repulsion by a HARD-SPHERE interaction, and short-range attraction by a SQUARE-WELL interaction.

7. Early (intuitive/empirical) attempts Ben-Naim, 19xx; M-B model of water (2D) Dahl, Andersen, 19xx; double SW model of water Bol, 19xx; 4-site model of water Smith, Nezbeda, 198x; 2-site model of associated fluids Nezbeda, et al., 198x, 199x, 199x; models of water, methanol, ammonia Kolafa, Nezbeda, 199x; hard tetrahedron model of water

8. SOLUTION: Use the reference molecular fluid defined by the average site-site Boltzmann factors, and apply then the hybrid Barker-Henderson theory to get effective HARD CORES (diameters d ij ): HOW: ??? FACTS: Because of strong cooperativity, site-site interactions cannot be treated independently. HINT: Recall successful perturbation theories of molecular fluids that use sphericalized effective site-site potentials and which are known to produce quite accurate site-site correlation functions.