After an introduction to liquid matter and soft materials, computer numerical simulation methods applied to the physics of liquids and soft matter will be illustrated.

Correlation functions and linear response theory will then be studied with applications to the study of dynamics in the hydrodynamic and visco-elastic limits.

Memory functions will be introduced. The physics of subcooled liquids and the study of the glass transition for soft and liquid materials will be treated.

Curriculum

Mutuazione: 20410585 FISICA DEI LIQUIDI E DELLA MATERIA SOFFICE in Fisica LM-17 GALLO PAOLA

Programme

1 - Review of Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamic functions. Conditions of equilibrium.

Legendre transforms and thermodynamic potentials. Phase stability conditions.

Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations.

2 - Forces between atoms and short-range order.

Characterization of the liquid state of matter. Characterization of soft materials.

Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon.

Radial distribution function and relationship with thermodynamics.

The static structure factor. Measurement of the structure of a liquid with X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.

Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style algorithms.

Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method.

Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials.

4 - Dynamics of liquids and soft matter

Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget.

Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of particles.

Diffusion coefficient. Speed correlation function. Hydrodynamics and collective modes. Scattering Brillouin.

Memory functions.

5 - Metastable states, subcooled liquids and glass transition for liquids and soft materials.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling.

Core Documentation

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.

P. G. Debenedetti, Metastable Liquids, Princeton University Press.

Type of delivery of the course

The exposition part of the theories is done on the board to allow students to understand the necessary analytical developments. In particular, it is shown how from microscopic models it is possible to obtain results to be compared with experiments. The experimental methods are then introduced that allow to observe the properties of the various systems of interest For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation

The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student from among those in the program. This part allows to highlight how well the student knows how to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to present the topic as if it were a seminar, this is useful for his future as a graduate student. The second part of the oral exam consists of a question on another topic in the program. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to outline a topic in an understandable way is also important in the different branches of Physics.Mutuazione: 20410585 FISICA DEI LIQUIDI E DELLA MATERIA SOFFICE in Fisica LM-17 GALLO PAOLA

Programme

1 - Review of Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamic functions. Conditions of equilibrium.

Legendre transforms and thermodynamic potentials. Phase stability conditions.

Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations.

2 - Forces between atoms and short-range order.

Characterization of the liquid state of matter. Characterization of soft materials.

Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon.

Radial distribution function and relationship with thermodynamics.

The static structure factor. Measurement of the structure of a liquid with X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.

Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style algorithms.

Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method.

Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials.

4 - Dynamics of liquids and soft matter

Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget.

Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of particles.

Diffusion coefficient. Speed correlation function. Hydrodynamics and collective modes. Scattering Brillouin.

Memory functions.

5 - Metastable states, subcooled liquids and glass transition for liquids and soft materials.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling.

Core Documentation

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.

P. G. Debenedetti, Metastable Liquids, Princeton University Press.

Type of delivery of the course

The exposition part of the theories is done on the board to allow students to understand the necessary analytical developments. In particular, it is shown how from microscopic models it is possible to obtain results to be compared with experiments. The experimental methods are then introduced that allow to observe the properties of the various systems of interest For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation

The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student from among those in the program. This part allows to highlight how well the student knows how to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to present the topic as if it were a seminar, this is useful for his future as a graduate student. The second part of the oral exam consists of a question on another topic in the program. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to outline a topic in an understandable way is also important in the different branches of Physics.Mutuazione: 20410585 FISICA DEI LIQUIDI E DELLA MATERIA SOFFICE in Fisica LM-17 GALLO PAOLA

Programme

1 - Review of Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamic functions. Conditions of equilibrium.

Legendre transforms and thermodynamic potentials. Phase stability conditions.

Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations.

2 - Forces between atoms and short-range order.

Characterization of the liquid state of matter. Characterization of soft materials.

Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon.

Radial distribution function and relationship with thermodynamics.

The static structure factor. Measurement of the structure of a liquid with X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.

Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style algorithms.

Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method.

Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials.

4 - Dynamics of liquids and soft matter

Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget.

Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of particles.

Diffusion coefficient. Speed correlation function. Hydrodynamics and collective modes. Scattering Brillouin.

Memory functions.

5 - Metastable states, subcooled liquids and glass transition for liquids and soft materials.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling.

Core Documentation

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.

P. G. Debenedetti, Metastable Liquids, Princeton University Press.

Type of delivery of the course

The exposition part of the theories is done on the board to allow students to understand the necessary analytical developments. In particular, it is shown how from microscopic models it is possible to obtain results to be compared with experiments. The experimental methods are then introduced that allow to observe the properties of the various systems of interest For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation

The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student from among those in the program. This part allows to highlight how well the student knows how to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to present the topic as if it were a seminar, this is useful for his future as a graduate student. The second part of the oral exam consists of a question on another topic in the program. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to outline a topic in an understandable way is also important in the different branches of Physics.Mutuazione: 20410585 FISICA DEI LIQUIDI E DELLA MATERIA SOFFICE in Fisica LM-17 GALLO PAOLA

Programme

1 - Review of Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamic functions. Conditions of equilibrium.

Legendre transforms and thermodynamic potentials. Phase stability conditions.

Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations.

2 - Forces between atoms and short-range order.

Characterization of the liquid state of matter. Characterization of soft materials.

Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon.

Radial distribution function and relationship with thermodynamics.

The static structure factor. Measurement of the structure of a liquid with X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.

Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style algorithms.

Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method.

Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials.

4 - Dynamics of liquids and soft matter

Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget.

Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of particles.

Diffusion coefficient. Speed correlation function. Hydrodynamics and collective modes. Scattering Brillouin.

Memory functions.

5 - Metastable states, subcooled liquids and glass transition for liquids and soft materials.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling.

Core Documentation

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.

P. G. Debenedetti, Metastable Liquids, Princeton University Press.

Type of delivery of the course

The exposition part of the theories is done on the board to allow students to understand the necessary analytical developments. In particular, it is shown how from microscopic models it is possible to obtain results to be compared with experiments. The experimental methods are then introduced that allow to observe the properties of the various systems of interest For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation

The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student from among those in the program. This part allows to highlight how well the student knows how to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to present the topic as if it were a seminar, this is useful for his future as a graduate student. The second part of the oral exam consists of a question on another topic in the program. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to outline a topic in an understandable way is also important in the different branches of Physics.Mutuazione: 20410585 FISICA DEI LIQUIDI E DELLA MATERIA SOFFICE in Fisica LM-17 GALLO PAOLA

Programme

1 - Review of Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamic functions. Conditions of equilibrium.

Legendre transforms and thermodynamic potentials. Phase stability conditions.

Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations.

2 - Forces between atoms and short-range order.

Characterization of the liquid state of matter. Characterization of soft materials.

Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon.

Radial distribution function and relationship with thermodynamics.

The static structure factor. Measurement of the structure of a liquid with X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.

Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style algorithms.

Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method.

Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials.

4 - Dynamics of liquids and soft matter

Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget.

Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of particles.

Diffusion coefficient. Speed correlation function. Hydrodynamics and collective modes. Scattering Brillouin.

Memory functions.

5 - Metastable states, subcooled liquids and glass transition for liquids and soft materials.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling.

Core Documentation

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.

P. G. Debenedetti, Metastable Liquids, Princeton University Press.

Type of delivery of the course

The exposition part of the theories is done on the board to allow students to understand the necessary analytical developments. In particular, it is shown how from microscopic models it is possible to obtain results to be compared with experiments. The experimental methods are then introduced that allow to observe the properties of the various systems of interest For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation

The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student from among those in the program. This part allows to highlight how well the student knows how to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to present the topic as if it were a seminar, this is useful for his future as a graduate student. The second part of the oral exam consists of a question on another topic in the program. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to outline a topic in an understandable way is also important in the different branches of Physics.Mutuazione: 20410585 FISICA DEI LIQUIDI E DELLA MATERIA SOFFICE in Fisica LM-17 GALLO PAOLA

Programme

1 - Review of Thermodynamics and Statistical Mechanics.Extensive and intensive thermodynamic functions. Conditions of equilibrium.

Legendre transforms and thermodynamic potentials. Phase stability conditions.

Phase transitions and their classification. Van der Waals equation. Review of the theory of statistical ensembles. Fluctuations.

2 - Forces between atoms and short-range order.

Characterization of the liquid state of matter. Characterization of soft materials.

Forces between atoms and effective potentials. Distribution functions in the canon and the grand canon.

Radial distribution function and relationship with thermodynamics.

The static structure factor. Measurement of the structure of a liquid with X-ray and neutron scattering techniques. Structure factors and radial distribution functions of liquid and liquid molecular mixtures. Classic density functional theory. Ornstein-Zernike equation.

Closing relations for the density functional.

3 - Numerical simulation of liquid and soft material

Stochastic and deterministic simulation methods. Molecular Dynamics Method. Verlet-style algorithms.

Molecular dynamics at constant temperature and pressure. The Monte Carlo simulation method.

Monte Carlo simulation in different ensembles. Phase equilibrium simulation methods. Application of Monte Carlo and Molecular Dynamics methods to complex liquids and soft materials.

4 - Dynamics of liquids and soft matter

Time-dependent correlation functions. Inelastic diffusion of neutrons and measurement of the dynamic structure factor. Van Hove correlation functions. Principle of the detailed budget.

Linear response theory. Answer function. Fluctuation-dissipation theorem. Diffusion of particles.

Diffusion coefficient. Speed correlation function. Hydrodynamics and collective modes. Scattering Brillouin.

Memory functions.

5 - Metastable states, subcooled liquids and glass transition for liquids and soft materials.

Stability and metastability. Spinodal curve from the Van der Waals equation. Fluctuations and trends of correlation functions near the critical point. Subcooled liquids and glass transition. Angell diagram. Configurational entropy and Kauzmann temperature. The slow dynamics of subcooled liquids and soft matter and the theory of Mode Coupling.

Core Documentation

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, seconda edizione, Academic Press.N. H. March and M. P. Tosi, Introduction to Liquid State Physics, World Scientific.

P. G. Debenedetti, Metastable Liquids, Princeton University Press.

Type of delivery of the course

The exposition part of the theories is done on the board to allow students to understand the necessary analytical developments. In particular, it is shown how from microscopic models it is possible to obtain results to be compared with experiments. The experimental methods are then introduced that allow to observe the properties of the various systems of interest For this reason, in some phases of the course the lessons on the blackboard are integrated with presentations with projection of experimental results and / or obtained with computer simulation.Type of evaluation

The final exam is in oral form. It consists of two parts. The first is the presentation of a topic chosen by the student from among those in the program. This part allows to highlight how well the student knows how to deepen a theme and go into the details of both the theoretical derivation and phenomenology. The student who is in the last year of the master's degree learns in this way to present the topic as if it were a seminar, this is useful for his future as a graduate student. The second part of the oral exam consists of a question on another topic in the program. In this case the student can answer without going into all the details of the derivation of the results. Knowing how to outline a topic in an understandable way is also important in the different branches of Physics.