Kim

A single-bond approach to orientation-dependent interactionsand its implications for liquid water: 

A single-bond approach to orientation-dependent interactions and its implications for liquid water Kyungil Kim Physics and Astronomy Northwestern Univ.

Water: 

Water Hydrogen bonded to its 4 nearest neighbors Density maximum at 4℃ Polyamorphism:Supercooled water exhibits 2 amorphous(glassy) forms termed LDA(low density amorphous ice) and HDA(high density amorphous ice). They are separated by a seemingly first-order transition. Liquid water cannot be studied experimentally below its homogeneous nucleation temperature(ca.-42 ℃ at 1 atm), the hypothesis of a liquid-liquid transition has not been unambiguously verified.

supercooled water senarios : 

supercooled water senarios 1. The two-critical-point(TCP) senario attributes the anomalies of supercooled water to the presence of a second critical point, where the first-order phase transition between LDA and HAD terminates. 2. According to singularity free senario(SFS), large increase in the thermodynamic response functions occur in the absence of any assumed low-temp. singularity. SFS is related to the thermodynamic requirement that the increase in isothermal compressibility upon supercooling is inseparable from the existence of a negative-sloped locus of density maxima in the P-T plane.

suggestion: 

suggestion 3. The retracing spinodal hypothesis(experimentally revealed to be false) Can we provide insight into possible global behaviors using an extended van der Waals model that incorporates the effects of hydrogen bonding?

Model formulation: 

Model formulation 1.no other molecular centers in radius of 2.hydrogen bonding shell within 3.favorable orientation 4.hydrogen bond 5.penalty for non-bonding

Statistical Mechanics: 

Statistical Mechanics The canonical partition function Q Helmholtz free energy Thermodynamic(macroscopic) variables thermal expansion coefficient isothermal compressibility molar heat capacity

Formula: 

Formula Bonding energy Potential where Pressure acquired

6 Parameters in P: 

6 Parameters in P Closely packing at infinite pressure determines probability function according to SPT theory with the constraint can be determined by fixing the water density maximum at 4℃ and 1 g/cm^3 (1bar) Fixes the vapor-liquid critical point at 647K

RESULTS: 

RESULTS Two critical-point Singurarity free senario Intersect each other!

Comparison with experimental results: 

Comparison with experimental results Minimum 46℃(1bar)(Exp) 33℃(TCP) 15℃(SFS) Minimum 34℃ (1bar)(Exp) 96℃ (TCP) 127℃ (SFS) Inlets: SFS

Analysis: 

Analysis The grossly simplified orientational entropy relative to real water results in an underestimation of the molar heat capacity in the liquid state. Vapor-liquid critical point: due to the simple treatment of the dispersion term. Each senario can describes the anomalies in supercooled liquid water. The change from liquid-liquid immiscibility to singularity-free behavior seems to be connected to subtle features of hydrogen bonding geometry. The addition of three more rigid bonding arms to the molecule seems to be the most important and challenging modification.

Reference: 

Reference T.M. Truskett, J.of chem. Phys. 111,6(1999). S.Satry, P.G. Debenedetti, etc. Phys. Rev. E 53, 6144(1996) C. Garrod, Statistical Mechanics and Thermodynamics (Oxford, New york, 1995).