PHYSICS OF SOFT MATTER

This course is one of the optional educational activities in the Master's degree in Science and Technology of Bio and Nanomaterials, and it describes the basic tools to study colloids, macromolecules and polymers through classical statistical thermodynamics and computer simulations with Monte Carlo and Molecular Dynamics method.
The learning objectives involve developing an understanding of the basic assumptions for soft matter systems, in terms of length and time scales, and how statistical thermodynamics and numerical simulations can help investigating these systems. The course will start from an introduction to classical statistical thermodynamics, and then move the the results obtained for some archetipal systems, such as the depletion interactions and the scaling laws for polymers. Then, the basic theory behind numerical simulations will be presented, and a simple simulation program will be developed during the lectures.

The student's active participation and attendance at classes, together with independent study, will allow to reach the following abilities of learning and comprehension:
A. Know the basis of classical statistical thermodynamics.
B. Know the theory behind numerical simulations.

The expected abilities acquired during the lectures are the following:
A. Be able to reproduce the most important theoretical results of soft matter.
B. Know the structure of a simulation program and interpret the results.

The topics treated in the lectures will use mathematical tools such as many-dimensional integrals, Taylor series and mathematical series in general. Being familiar with these mathematical tools is therefore highly recommended. Moreover, during the lectures there will be many connections with classical thermodynamics, and therefore a good knowledge of the latter is required to follow the lectures.

THERMODYNAMIC ENSEMBLES
1. The concept of ensemble
2. Isolated systems and microcanonical ensembles
3. Connection with thermodynamics in microcanonical ensemble
4. Thermodynamics of the ideal gas with microcanonical ensemble
5. Thermally coupled systems and canonical ensemble
6. Connection with thermodynamics in canonical ensemble
7. Equivalence of canonical and microcanonical ensembles
8. Thermodynamics of the ideal gas with canonical ensemble
9. Systems thermally and chemically coupled and grand-canonical ensemble
10. Equivalence of the grand-canonical ensemble and the canonical ensemble
11. Thermodynamics and equation of state in the grand-canonical ensemble
12. Thermodynamics of the ideal gas with the grand-canonical ensemble

PHASE TRANSITIONS AND CRITICAL PHENOMENA
1. Introduction to critical phenomena
2. Order parameters
3. General phenomenology of the phase transitions
4. Phase coexistence and Gibbs phase rule

REAL GAS AND THEORETICAL TECHNIQUES
1. Elementary derivation of the van der Waals equation
2. Mean field theory of van der Waals equation
3. Pair correlation functions, radial distribution functions and structure factor
4. Relation of thermodynamic functions to g(r)
5. The cluster and virial expansions
6. Thermodynamic perturbation theory

COLLIDAL SYSTEMS AND INTERACTIONS
1. Order of magnitudes
2. Depletion forces and Asakura-Oosawa mechanism
3. Debye-Huckel theory and screening
4. Simple example of solution and order of magnitude

POLYMERS
1. The Freely-Joint-Chain (FJC) model
2. Continuum limit and Gaussian chain
3. Entropy of a Gaussian Chain
4. Structure factor and radius of gyration
5. Exact calculation of the structure factor for Gaussian chains
6. Excluded volume effects and Flory theory
7. Stiffness effects and Worm-like-Chain (WLC) model

NUMERICAL SIMULATIONS:
1. Basic theory behind numerical simulations.
2. Monte Carlo method and Metropolis rule.
3. Molecular Dynamics method.
4. MC-MD equivalence.
5. Connection with experimentally-accessible quantities: g(r)
6. Temporal correlation, relaxation times and interpretation of results.

D. Frenkel, B. Smit, Understanding Molecular Simulation

The knowledge acquired by the students will be verified through a presentation of a theoretical method, or through the development of a working simulation program.

Face-to-face lessons.

English

Accessibility, Disability and Inclusion

Accommodation and support services for students with disabilities and students with specific learning impairments:
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding supportservices and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). In the case of disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

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