ROLE OF THE RANGE OF INTERMOLECULAR INTERACTIONS IN FLUIDS (TOWARDS A UNIFIED VIEW OF FLUIDS) Ivo NEZBEDA E. Hala Lab. of Thermodynamics, Acad. Sci., Prague, Czech Rep. and Inst. of Theoret. Physics, Charles University, Prague, Czech Rep. COLLABORATORS: J. Kolafa, M. Lisal, M. Predota, Acad. Sci., Prague A. A. Chialvo, P.T. Cummings, ORNL, Oak Ridge M. Kettler, U of Leipzig, Leipzig

workshop on SHORT RANGE INTERACTIONS IN SOFT CONDENSED MATTER … You are invited to provoke a lively discussion with your ideas. Werner Kunz Excerpts from referee’s reports: …This result may generate some controversy, as it is at odds with the conventional wisdom. …The results are provocative and will likely generate interest and discussion. …This is an interesting study and presents useful results. However, some of their results are rather unusual and defy the conventional wisdom.

QUESTION: What are the main driving forces that determine the observed macroscopic behavior of fluids? WHY? An answer to this question is an indispensable first step towards - more complete understanding of the behavior of fluids - the development of simple theoretically-based models, and hence molecular-based workable expressions for the thermodynamic properties of fluids

HISTORICAL BACKGROUND Accounting for the overall electroneutrality of molecules, physical considerations identify four main types of interactions acting between the molecules of pure fluids: 1. Short-range repulsions that reflect, roughly, the shape and size of molecules (excluded-volume effects); 2. Relatively weak and fast decaying (as 1/R^6 and faster, where R is the intermolecular separation) attractive interactions (called dispersion or van der Waals interactions); 3. Long-range electrostatic interactions (e.g. dipole-dipole) having their origin in the permanent multipoles of molecules; 4. Strong short-range and strongly orientation-dependent attractions identified as hydrogen bonding interactions (H-bonding). It has thus been common to write approximate intermolecular interaction models accordingly,

HISTORICAL BACKGROUND (cont.d) Starting from the above form of u(1,2), it is tempting to express (explain) the properties of a more complex fluid in terms of an excess over a less complex (simpler) fluid, pointing to a perturbation treatment as a suitable tool for both theory and applications. CONSEQUENTLY, the observable differences in the behavior of different substances (classes of fluids) seem thus to reflect differences in the relative strengths of the individual contributions to the total u(1,2), and the properties of fluids belonging to different classes seem to be determined by the different types of predominant interactions. If this is true, problems for theory and applications immediately arise (and they do!).

Accepting the pair potential in this form, one immediately loses the clear (and simple) physical picture of intermolecular interactions. Potentials for different compounds differ only in the geometrical arrangement of the sites and in the strengths of the individual site-site interactions. Nonetheless, there is one general property which might be useful for the characterization of the interactions: their rate of decay with increasing intermolecular separation or, equivalently, the range over which they operate. STATE-OF-THE-ART It is assumes that molecules contain interaction sites which may, but need not necessarily, coincide with the location of the individual atoms. The sites are the seat of two types of interactions: (1) non-electrostatic [short-range repulsions and medium-range attraction] (2) long-range Coulombic charge-charge interaction Effective pair potentials are of the site-site form:

To this end, we may define trial potentials of variable range, ; S=0 for r cc R’’ and examine changes in the structure as the switching range (R’,R’’) varies.

WORKING HYPOTHESIS: Provided that the trial potential u T (1,2) includes the first coordination shell, then the structure of the systems defined by u(1,2) and u T (1,2) is very similar (nearly identical). In other words (and rather provocatively) the hypothesis claims that the long range part of the Coulombic interactions has only marginal effect on the structure of (pure) fluids. OBSERVATIONS: 1. When the potential is switched off at too short separations then too much of the Coulombic interactions is missing  Differences in the structure become even qualitative 2. Close agreement is found for not too large R range  R’’ 

Examination of validity of the hypothesis: Properties examined: - complete sets of the site-site c.f. g ss - dipole-dipole c.f. G k - radial slices through g(1,2) - dielectric constant - thermodynamic properties homogeneous phase liquid in equilibrium with its vapor Compounds considered: carbon dioxide acetone acetonitrile methanol water hydrogen fluoride

Contribution of the electrostatic interactions to the total configurational energy (in dependence on the switching range)

Dielectric constants of the full and short-range models at a number of thermodynamic conditions (ε min, ε max ) … range at the 95% confidence level

SUMMARY OF THE RESULTS: From all the results obtained so far for pure fluids one can unambiguously conclude that the primary driving force determining the structure of pure fluids are short-range interactions (which may be both repulsive and attractive) and that the long-range part of electrostatic interactions plays the role of a mere perturbation only.

POTENTIAL LIMITS: thermodynamic conditions - validity seems to extend to lower densities inhomogeneous fluids - a large body of simulation data available; short-range models follow even such trends as flip over of the water molecules with decreasing curvature of the (hydrophobic) interface kinetic properties - shear viscosity and auto-diffusion coefficients of the full- and short-range models of water perfectly agree TWO QUESTIONS IMMEDIATELY ARISE: (i) what are the limits of the drawn conclusions, and (ii) what are implications of the findings for theory and applications.

POTENTIAL LIMITS: thermodynamic conditions - validity seems to extend to lower densities inhomogeneous fluids - a large body of simulation data available; short-range models follow even such trends as flip over of the water molecules with decreasing curvature of the (hydrophobic) interface kinetic properties - shear viscosity and auto-diffusion coefficients of the full- and short-range models of water perfectly agree

full- and short-range TIP5P-E water at a flat Lennard-Jones 9-3 carbon wall T=298 K, density=1.0 g/cm 3 circles … full model lines … (4,6) short-range model

POTENTIAL LIMITS: thermodynamic conditions - validity seems to extend to lower densities inhomogeneous fluids - a large body of simulation data available; short-range models follow even such trends as flip over of the water molecules with decreasing curvature of the (hydrophobic) interface kinetic properties - shear viscosity and auto-diffusion coefficients of the full- and short-range models of water perfectly agree

OPEN PROBLEM: MIXTURES Due to polarizibility and other possible effects brought about by electrostatic interactions between unlike species, the pair interaction, and hence the local and, particularly, orientational arrangement may be changed. The most difficult mixtures will evidently be solutions of electrolytes. Nonetheless, even in this case there is at least a piece of indirect evidence that the same conclusions may be correct at least for dilute electrolytes

IMPLICATIONS FOR THEORY AND APPLICATIONS Once the long-range part of electrostatic interactions may be ignored at the zeroth level of approximation, then - one can immediately devise a perturbation expansion about a suitably chosen short-range reference. - the way for theoretically-based modeling of complex problems is open For accomplishing the expansion, the so called primitive models (counterparts of hard spheres for non-simple fluids) are employed. A theoretical method has been developed enabling one to derive a primitive model as a direct descendant of a realistic parent model. Primitive models reproduce, even (semi)quantitatively, the structure of the realistic fluids and their main field of applications is thus - in modeling of complex problems, and - in both theoretical and computer simulation studies of details of molecular mechanisms governing the behavior of fluids.

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