1 Hydrophobic hydration at the level of primitive models Milan Predota, Ivo Nezbeda, and Peter T. Cummings Department of Chemical Engineering, University of Tennessee Chemical Sciences Division, Oak Ridge National Laboratory Institute of Chemical Process Fundamentals, Academy of Science, Czech Republic

2 Outline Primitive models of water Simulation of hydrophobic hydration Structure of solvation shell Orientational arrangement of water molecules around the solute Hydrogen bonding Dependence on the solute diameter Chemical potential of the solute

3 Play the same role for associative fluids as the hard sphere system for simple fuids Capture the most important interactions, predict structure Direct link between the observed properties and interaction potential Unambiguous interpretation of simulation results Short ranged, simple Easy to simulate Amenable to theoretical approach Perturbation theories - TPT, SAFT Reference system for the parent realistic point-charge model Very good structure, thermodynamics incomplete Primitive models of water

4 Repulsions - hard core and like sites Hard sphere potential Hydrogen bonding - attraction between unlike sites Square well potential Interaction potential

5 4-site EPM4 model - geometry of TIP4P model - tetrahedral angle  HOH=109° - |OH|=0.5, |OM|= inverse temperature  =6 - packing fraction  =  N/6V= site EPM5 model - geometry of ST2 and TIP5P model - tetrahedral angles, |OH|= |OM|= symmetry of negative (M) and positive (H) sites -  =5,  =0.3 Primitive models of water

6 Comparison of EPM with experiment O-O pair correlation function

7 Hydrophobic hydration Changes that take place in bulk water when a single non-polar molecule is brought into it Hard sphere solute of diameters d = 0-1.6, 2, 3, 4, 5, and  = hard wall Only solute - oxygen (hard core) repulsion  hydrophobic hydration Small solutes - virtual insertion, simulation of pure homogenous water, N=1024 Intermediate and large solutes - simulation of N water molecules + 1 solute Hard wall - 2D periodic system confined between two parallel walls  pure nonhomogeneous water

8 Orientational ordering in the solvation shell Solutes up to d=2  the same shape, more pronounced for larger solutes Larger solutes  reorientation

9 Preferred configurations, EPM4 Innermost shell poor bonding Outer shell  =0°  =55°  120°  =70°, 180°  50°  0°, 100° Small and medium size solutes Large solutes  =0°  =55°

10 Angular distribution in the solvation shell at the hard wall, EPM4 Weak hydrogen bonding in the layer closest to the solute, sacrificing bond by pushing the hydrogen to the solute Strong bonding in the subshell of the first solvation shell furthest from the solute

11 Orientational ordering in the solvation shell Monotonous dependence of distribution of  =  SOH on diameter d Symmetry of H- and M sites  symmetric distribution of  Flat distribution of , two preferred orientations

12 Preferred configurations, EPM5  = 0°, 180°  = 55°, 125°  = 90°  = 55°, 125°  = 55°, 125°  =70°, 180° More favorable for large solutes Two preferred orientations for all solute sizes

13 Solvation shell of EPM4 at a hard wall

14 Solvation shell of EPM5 at a hard wall

15 Number of hydrogen bonds per molecule Bonding in the vicinity of the solute reduced for large solutes up to 24 % for EPM4 and 8% for EPM5 Small enhancement of bonding around the second maximum of CF

16 Distribution of number of bonds in the first solvation shell The most probable number of bonds of EPM4 is 3, as opposed to 4 for EPM5, significant number of 1-bonded EPM4 molecules Much larger decrease of 4-bonded molecules in the vicinity of a wall for EPM4

17 Thermodynamic properties EPM4EPM4 EPM5EPM5

18 Comparison with realistic models Small solutes General agreement Small decrease of hydrogen bonding in the solvation shell Strengthened orientational alignment to preserve bonding Water molecules straddle the solute Large solutes and hydrophobic wall Lack of data Model dependent behavior - different potentials Experimental support for behavior consistent with EPM4 Surface vibrational spectroscopy Du, Q., Freysz, E., and Shen, Y.R., 1994, Science 264, % of nonbonded OH groups at interface

19 Hydrophobic hydration of inert gases and methane a Guillot, B., Guissani, Y., and Bratos, S., 1991, J. Chem. Phys. 95, 3643

20 Excess chemical potential of solute Rigorous link between the derivative of chemical potential and contact density Exact limiting behavior Cubic polynomial for d- dependence of excess chemical potential

21 Temperature dependence of the Henry’s law constant Methane Hard sphere of relative diameter d = 1.35 Chemical potential Cubic polynomial Equation of state Reference system for EPM pseudo-hard body Wertheim’s perturbation theory No adjustable parameter Nezbeda, I., 2000, Fluid Phase. Equil., 170, 13

22 Conclusions Studied hydrophobic hydration of extended primitive models of water over the whole range of solute diameters, including flat surface Solute sizes up to d = 2-3 Behavior of both models is qualitatively the same and in agreement with realistic models Larger solutes Entropic effects dominate the energy effects in the interfacial layer of EPM4  reorientation, lack of bonding Strong bonding of EPM5 preserved in the solvation shell for all solutes Detailed study of hydrophobic hydration of realistic models needed More support for behavior consistent with EPM4

23 Acknowledgement Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, DOE Grant Agency of the Academy of Sciences of the Czech Republic