The Physics of Liquid Water 1st Edition by Makoto Yasutomi ISBN 9814877255 978-9814877251

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ISBN 10: 9814877255
ISBN 13: 978-9814877251
Author: Makoto Yasutomi

Unraveling the mystery of the negative thermal expansion of liquid water has been a challenge for scientists for centuries. Various theories have been proposed so far, but none has been able to solve this mystery. Since the thermodynamic properties of matter are determined by the interaction between particles, the mystery can be solved fundamentally if the thermodynamic physical quantities using the laws of thermodynamics and statistical mechanics are determined, the experimental results are reproduced, and the phenomena in relation to the shape of the interaction between particles are elucidated. In this sense, this book has fundamentally unraveled this mystery. In addition, it discusses the mysteries of isothermal compressibility, structural diversity, as well as liquefaction and boiling points of water in relation to the shape of the interaction between particles. It carefully explains the analysis and calculation methods so that they can be easily understood by the readers.

The Physics of Liquid Water 1st Table of contents:

1 Statistical Mechanics and Thermodynamics of Fluids

1.1 Statistical Mechanics

1.2 Thermodynamics

1.2.1 Pressure from Energy Equation

1.2.2 Chemical Potential from Energy Equation

1.2.3 Pressure and Chemical Potential from Compressibility Equation

1.3 Consistency between Energy Equation and Compressibility Equation

2 Strange Temperature Change of Water Density

2.1 Positive Thermal Expansion

2.2 Negative Thermal Expansion

3 Fundamental Clarification of Thermodynamic Phenomena in Water

3.1 Function Form of Interaction between Water Molecules

3.1.1 Water Molecule Shape

3.2 Method by Solving the Basic Equation of Quantum Mechanics

3.3 Method by Using Realistic Water Model

3.4 Simplified Model (Core-Softened Model)

3.5 Method by Self-Consistent Ornstein–Zernike Approximation

3.6 Multi-Yukawa Type Intermolecular Interaction

3.7 Thermodynamic Mechanism of Negative Thermal Expansion

3.7.1 Shape of Intermolecular Interaction That Causes Negative Thermal Expansion

4 Variety of Shapes of Water Molecule Interactions

4.1 Soft-Repulsive Tail Slope and Isothermal Compression Ratio

4.2 Problems with Existing Ideas on Negative Thermal Expansion

5 Ornstein–Zernike Equation

5.1 Hyper-netted Chain Approximation

5.2 Percus–Yevick Approximation

5.3 Mean-Spherical Approximation

5.4 OZ Equations in Baxter Form

5.4.1 Baxter Function Q(r)

5.4.2 Baxter’s First Equation

5.4.3 Baxter’s Second Equation

5.5 Analytical Solution of the Percus–Yevick Equation for Hard Sphere Fluids

5.5.1 Direct Correlation Function

5.5.2 Equation of State Derived from Virial Theorem

5.5.3 Equation of State Derived from Compressibility

5.5.4 Carnahan–Starling’s Empirical Formula

5.6 Self-Consistent OZ Approximation

5.6.1 SCOZA Closure

5.6.2 Laplace Transformation of Baxter-Type OZ Equation

5.6.3 Laplace Transformation of Baxter’s Second Equation

5.6.4 Laplace Transform of Baxter’s First Equation

5.6.5 Analytical Solution of Baxter-Type OZ Equation

5.7 MSA Analytic Display of Diffusion Equation for u

5.7.1 Boundary Conditions

5.7.2 Initial Conditions

5.7.3 The Spinodal Curve

5.8 Numerical Calculation Method of Diffusion (Heat Conduction) Type Equation

5.8.1 In the Case of T ≥ Tc

5.8.1.1 Predictor

5.8.1.2 Corrector

5.8.1.3 Simultaneous linear equations for uj (1 ≤ j ≤ J)

5.8.1.4 Solution method of linear equations Au = r

5.8.1.5 LU decomposition = of matrix A

5.8.1.6 Solution of Au = r

5.8.2 In the Case of T < Tc and 0 < ρ ≤ ρL ≤

5.8.2.1 Predictor

5.8.2.2 Corrector

5.8.2.3 A system of linear equations for uj (1 ≤ j ≤ L)

5.8.2.4 Solutions of Au = r

5.8.3 In the Case of T < Tc and ρR ≤ ρJ

5.8.3.1 Predictor

5.8.3.2 Corrector

5.8.3.3 A system of linear equations for ρR ≤ ρ ≤ ρJ

5.9 Numerical Calculation Method with Two Different Step Sizes of Δ ρa and ρρb

5.10 Method to Mark Density

5.10.1 In the Case of T ≤ Tc

5.10.1.1 Predictor

5.10.1.2 Interpolation of u˜ja+1m

5.10.1.3 Corrector

5.10.1.4 Simultaneous linear equations for uj (1 ≤ j ≤ J)

5.10.1.5 LU decomposition ≤ of matrix A

5.10.1.6 Solutions of Au = r

5.10.2 In the Case of T < Tc

5.10.2.1 Predictor for 1 j ≤ j ≤ L

5.10.2.2 Corrector for 1 ≤ j ≤ L

5.10.2.3 Simultaneous linear equations for uj (1 ≤ j ≤ L)

5.10.2.4 LU decomposition of matrix A

5.10.2.5 Solutions of Au = r

5.10.2.6 Solutions for R ≤ j ≤ J

6 Calculation Procedure of SCOZA

6.1 Method to Determine the Potential Tail

6.2 K(1)(ρ) and z1(ρ)

6.2.1 Calculation of u(ρ, β = 0)

6.2.2 Calculation up to Critical Temperature Tc

6.2.3 Calculation below Critical Temperature

6.2.4 Calculations of Gas Phase Water below the Critical Temperature

6.2.5 Calculations of Liquid Phase Water below the Critical Temperature

7 Pressure and Chemical Potential

7.1 Pressure Derived from Energy Equation

7.2 Pressure Derived from Compressibility Equation

7.3 In the Case of T ≥ Tc

7.3.1 Spinodal Curve

7.3.1.1 Isotherms

7.4 Chemical Potential Derived from the Energy Equation

7.5 Chemical Potential at β = β*

7.6 Chemical Potential Derived from Compressibility Equation

8 Thermodynamic Properties of Subcritical Fluids

8.1 Method to Find Liquefaction Point G and Vaporization Point L

8.2 Absence Temperature Region of Liquefaction Point and Vaporization Point (βc< β < β†)

8.3 Necessity of Two Density Step Sizes

8.4 Comparison of Theory and Experiments

8.4.1 Units of Length σu and Energy εu

8.4.2 Pressure, Temperature, and Density at Critical Point

8.4.3 Comparison of Theoretical and Experimental Vaporization Points

8.5 Simplest and Most Optimum Interactions between Water Molecules

8.6 Concluding Remarks

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Tags: Makoto Yasutomi, The Physics, Liquid Water