Interactive script for molecular simulations / Interaktivní skript pro molekulové simulace
Presentation about how to present science
Physics I - exercises (MC260P34)
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Physical Chemistry of Polymers (MC260P130)
Course materials have been moved to moodle.
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In case of problems please contact me by e-mail.
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Physical Chemistry IV: Statistical Thermodynamics (MC260P105)
Lecture notes from the year 2016/2017 (will be updated after each lecture)
- Introdution + Canonical ensemble
- Other ensembles and fluctuations
- Ideal gas + Bose-Einstein and Fermi-Dirac statistics
- Diatomic ideal gas -- vibrations and rotations
- From quantum to classical mechanics and polyatomic ideal gas
- Chemical equilibrium. Virial expansion. Theorem of corresponding states
- Pair correlation function. Simulation methods
- Integral equations and perturbation theories of liquids
- Solutions of strong electrolytes
- Lecture 11 Ising model and phase transitions
To get a clue of what comes in the next lectures, check lecture notes from previous years.
Please note that each year the lectures are updated, so the old ones are not identical to the present.
Some useful information regarding the exam
- Each student is given three topics from the following categories:
Oral examination follows after 30 min of preparation time.
The student is expected to discuss the given topics in his/her own words (+notes) within the scope
of the lecture.
The use of any supporting material is allowed during the
preparation, including paper, electronic, or internet resources.
Only handwritten notes can be used during the subsequent examination.
If the there are more students, I prefer to examine them simultaneously.
Individual projects have to be submitted before the beginning of the oral exam.
If submitted later, they cannot be considered for the final grade.
Depending on its quality, an individual project can help improve the student's score from the oral exam by up to one grade.
If the score from the oral exam is 4 (fail), the individual project will be considered
in the subsequent attempt(s) in the examination.
- Fundamental concepts, ensembles, most probable distribution,
partition function, thermodynamic functions from the partition
function ... (Lectures 1 and 2).
- One topic selected by the student.
- One topic selected by the lecturer, complementary to 2.
Suggestions for individual projects (Exercises in Statistical Thermodynamics)
- Whatever project you choose, consult it with the lecturer before you start working on it.
- Find >3 significant mistakes in the lecture slides.
Significant mistakes change the meaning of the text or a result. Misprints in equations are always significant mistakes. A mistake which is repeated throughout a derivation counts as one.
- Work out one or several problems from the textbook (at the end of each chapter).
- Work through some of the derivations which were omitted in the lecture.
- Compute vibrational and rotational partition functions for selected molecules and a series of temperatures.
Test the applicability of various approximations (direct summation, high T, Padé approximant)
- Show how occupation of different states differs between Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann statistics. Examine cases at high and low temperatures.
- Try to reproduce the curves from Fig.6-9 in the textbook (fraction of ortho and para hydrogen at low temperatures).
- Compute (numerically) the second virial coefficient of some realistic potentials as a function of temperture (Fig.12-5 in the textbook).
- Implement a numerical solution of some of the integral equations for a realistic potential.
- Derive expression for thermodynamic functions from the two forms of the Percus-Yevick equation of states for hard spheres.
- Generalize the virial expansion to a two-component mixture.
- Calculate the temperature-dependence of the Joule-Thompson coefficient for the square-well fluid. Discuss the role of
excluded volume and attractive interactions. Show that it obeys the theorem of corresponding states.
- Calculate the temperature-dependence of equilibrium constants of gas-phase reactions discussed in the textbook.
- Generalize some of the equations of the liquid state theory to two-component mixtures.
- Write a simple MC or MD simulation program and verivy its function by simulation of a well known system.
- Use a simulation program for the Ising model (will be provided by the lecturer) to study magnetization and energy as a function of temperature and system size.
- Feel free to suggest any other topic which you find interesting.
Useful online resources
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