Peter Buhler. NanothermodynamicS

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1 Peter Buhler NanothermodynamicS

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3 Introduction 7 Symbols and definitions 9 1. On the basic concepts of classical thermodynamics Internal energy, heat, and work Internal energy is a property of substance, while heat and work are types of energy transfer Transferring energy from a substance to another one is irreversible The internal energy of substance does not increase owin g to the product PV and in consequence enthalpy (H=U+PV) is not a property of substance Internal energy of substance increases with the growth o f pressure Free energy and entropy of substance Free energy is the level of internal energy and therefor e free enthalpy (GG=H-TSG) is not a property of substance Entropy is a property of substance and not that o f "reversible heat" Entropy of substance has nothing to do with thermodynami c probability Entropy of any substance equals zero at T -4 OK Pressure on each side of the curved surface is identical Interface between two condensed phases is established by the chosen phases Volume of substance is not the pressure derivative o f free energy Free energy and entropy of mixing an ideal binar y solution equal zero Temperature and pressure dependence of thermodynami c properties of substance The first law of thermodynamics at constant pressure an d temperature dependence of internal energy of substance The second law of thermodynamics at constant pressure and temperature dependence of entropy and free energy of substance The third law of thermodynamics at constant pressure The first law of thermodynamics at constant temperature and pressure dependence of the internal energy of substance The second law of thermodynamics at constant temperatur e and pressure dependence of the free energy of substance The third law of thermodynamics at constant temperature 47

4 3. Laws of thermodynamics at isobaric-isothermal increase in the surface area of substance Surface of substance and interfacial area The first law of thermodynamics. Specific surface energy of substance Specific interfacial energy On the defining equation for the specific surface energy of substance in classical thermodynamics Dependence of the surface energy of substance on its surface area The second and third laws of thermodynamics. Specific fre e surface energy of substance Dependence of the free surface energy of substance on its surface area The thermodynamic equation for defining the specifi c surface energy of solid at melting temperature Temperature and pressure dependence of the thermodynamic properties of nanodispersed substance Temperature dependence of the specific surface energy of liquid Temperature dependence of the specific surface energy of solid Temperature dependence of the internal and free energie s of nanodispersed substance Entropy of nanodispersed substance and its temperature dependence Pressure dependence of the internal and free energie s of nanodispersed substance Equilibrium between the phases of nanodispersed substance Phase diagram for macrophases of one substance an d equations for equilibrium lines of two phases Dependence of saturated vapor pressure on the surfac e area for nanodispersed substance Dependence of phase transformation temperature o f nanodispersed substance on the surface area Dependence of temperature and pressure at the first triple poin t on the surface area for nanodispersed substance. The first triple line On the distinction of pressure on each side of the curved surface of substance Thermodynamics of capillary flow of liquid, physical adsorption, and capillary condensation Wetting a solid surface by a liquid. Contact angle Specific interfacial energy and specific energy of wetting Rising and lowering of liquid in a capillary and the capillary energy of wetting 99

5 6.4. Dependence of height of liquid rising and lowering i n capillary on its radius : Capillary free energy of wetting Capillary entropy of wetting Molar area of wetting Energy and free energy of wetting Entropy of wetting Physical adsorption and capillary condensation Experimental data : Internal and free energies of adsorbate and liquid Saturated vapor pressure of adsorbate Thermodynamic characteristics of adsorbate at physical adsorption Thermodynamic characteristics of adsorbate at ga s adsorption by nanoporous solid Thermodynamic properties of binary nanodispersed solutions Thermodynamic properties of binary solution Thermodynamic properties of ideal solution Thermodynamic properties of mixing a solution and its components Thermodynamic properties of binary nanodispersed solution Isotherm of the specific surface energy of ideal binary solution Thermodynamic properties of ideal nanodispersed solution Thermodynamic properties of mixing nanodispersed solution and its components Activity coefficients of the components of nanodispersed solution Pressure of saturated vapor over nanodispersed solution Thermodynamic properties of colloidal dispersed systems Aggregative state and the size of dispersed phase particles Interaction between the dispersed phase and the dispersion medium The interfacial area of dispersed phase/dispersion medium system Surface energy of colloidal dispersed system. Specific interfacial energy Thermodynamic conditions for spontaneous formation o f colloidal dispersed liquid / liquid mixture Equilibrium of chemical reaction involving nanodisperse d substances The law of mass action. The equilibrium constant and th e coefficients µ and y of chemical reaction Reduction of oxide by gas Reactions between the gas phase and condensed substances Decomposition of condensed substance with formation of gas 144

6 9.2. Thermodynamic characteristics of chemical reaction Interrelation between the thermodynamic characteristics of a chemica l reaction, the equilibrium constant, and coefficients µ and y Standard thermodynamic characteristics of a chemical reaction involving nanodispersed substances Equilibrium constant of chemical reaction involvin g nanodispersed substances From the energy of atoms in solid to the energy of atom s in gas Energy of bulk substance From the energy of bulk substance to the energy of nanodispersed substance From the energy of nanodispersed substance to th e energy of aggregates without "bulk" atoms From the energy of aggregates without "bulk" atoms to the energy of atoms in gas From the energy of atoms in gas to the energy of atoms in solid 15 9 Conclusion 16 1 Literature 16 3 Subject index 165