SubjectsSubjects(version: 902)
Course, academic year 2021/2022
Introduction to the modern theory of phase transitions - M403019
Title: Úvod do moderní teorie fázových přechodů
Guaranteed by: Department of Physical Chemistry (403)
Actual: from 2020
Semester: winter
Points: winter s.:4
E-Credits: winter s.:4
Examination process: winter s.:
Hours per week, examination: winter s.:3/0 [hours/week]
Capacity: unlimited / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type: Master's (post-Bachelor)
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Malijevský Alexandr doc. Mgr. Ph.D., DSc.
Interchangeability : N403042
Annotation -
Last update: Kubová Petra Ing. (29.01.2018)
In this course the fundamental principles of phase transitions and critical phenomena will be introduced. The lecture includes a brief summary of the most important parts of thermodynamics and statistical mechanics.
Aim of the course -
Last update: Kubová Petra Ing. (29.01.2018)

Students will be able to master the key concepts of phase transitions and critical phenomena.

Literature -
Last update: Kubová Petra Ing. (29.01.2018)

In the form of notes

Learning resources -
Last update: Kubová Petra Ing. (29.01.2018)


Teaching methods -
Last update: Kubová Petra Ing. (29.01.2018)

Lecture or self-study

Syllabus -
Last update: Kubová Petra Ing. (29.01.2018)

1. Fundamentals: Thermodynamic potentials, Legendre transformation, intensive and extensive variables, ensembles, Boltzmann factor, partition function, statistical definition of entropy, intermolecular forces, correlation functions.

2. Consequences of the Second Law: Entropy, the fundamental equations of thermodynamics, Euler's theorem for homogeneous functions, conditions of equilibrium, potential convexity.

3. Theory of Stability: metastable states, spinodal, Hessian, general conditions of stability.

4. Theory of Stability (continued): Examples, stability in different representations, phase diagrams.

5. Van der Waals theory: Classification of phase transitions, critical point, the van der Waals equation of state and its solution.

6. Nucleation: Mechanisms of phase transitions, classical theory of nucleation, heterogeneous nucleation, spinodal decomposition.

7. Phase transitions of the second kind: Ising model, Heisenberg model, percolation, ferromagnetism, the relationship between magnetic and molecular models.

8. Landau theory: order parameters, concept of symmetry, mean-field theory.

9. Critical Phenomena: Perturbation theory, Bogoliubov inequality, upper and lower critical dimensions, critical exponents, scaling relations, universality.

10. Beyond the mean-field theory: Fluctuations and their role in the vicinity of the critical point, renormalization, fixed points, intro to the renormalization group theory.

11. Phase transitions of inhomogeneous systems: Thermodynamic relations, surface contributions, Wenzel and Cassie models, hemiwicking, super-hydrophobic surfaces.

12. Theory of wetting: Contact angle, surface tension, Young's and Laplace equations, partial and complete wetting, first-order and critical wetting, prewetting, short- versus long-ranged forces, binding potential, approximation "sharp-kink", Hamaker constant, long-range critical wetting, wetting on curved surfaces, filling.

13. Phase transitions in nanopores: Effect of limited space on thermodynamics and phase behavior, capillary condensation, layering, the limits of the classical theories, microscopic approach, the influence of intermolecular effects on the phase behavior, adhesion versus cohesion, applications for nanotechnology.

14. Phase transitions of complex systems: Phase transitions of liquid crystals, isotropic, nematic and smectic phases, Onsager theory, colloid-polymer solutions, entropically driven phase transitions, changes in conformations of polymers.

Registration requirements -
Last update: Kubová Petra Ing. (29.01.2018)

Physical chemistry I

Course completion requirements -
Last update: Kubová Petra Ing. (29.01.2018)

Oral exam

Teaching methods
Activity Credits Hours
Účast na přednáškách 2 56
Příprava na zkoušku a její absolvování 2 56
4 / 4 112 / 112