260089 VU Modelling of acid-base equilibria in polymeric and colloidal systems (2024S)

The aim of the course is to introduce the students to various modeling and simulation methods for simulating acid-base reactions in solutions of polymers and colloids. It includes a set of hands-on sessions, in which the students have the opportunity to apply the theoretical knowledge from the lectures to real simulation problems.

The lectures cover the following topics:
- Review of the basics of molecular simulations - Molecular Dynamics and Monte Carlo
- Statistical mechanics of simple fluids - overview of concepts required to complete the first hands-on task: ideal gas equation of state, corrections for non-ideality, virial expansion, pair correlation function, phase diagram of a Lennard-Jones fluid, theorem of corresponding states and reduced units
- Statistical analysis of correlated time series - estimation of statistical error of the simulation results, determining the optimum sampling rate and length of the simulation run

- Review of basic Chemical Thermodynamics, focusing on theoretical description of chemical reaction equilibria,
- Overview of statistical ensembles for simulating chemical reactions and their typical use cases: grand canonical ensemble, Reaction Ensemble, constant-pH ensemble, Grand-reaction ensemble

- Acid-base equilibria and pH
- Properties of dilute electrolyte solutions - primitive model of electrolytes, Debye-Hückel theory, Poisson-Boltzmann equation, electrostatic contribution to excess chemical potential, effect of ionic strength on the acid-base equilibrium of simple acids and bases, effect of ionic strength on the acid-base equilibrium of simple acids and bases, activity coefficients, effect of ionic strength on the acid-base equilibrium of simple acids and bases
- Overview of simulation algorithms for charged systems - Ewald summation, etc.
- Acid-base properties of polyelectrolytes and charged colloids

The hands-on sessions include
1. Simulation of a lennard-jones fluid - a toy problem to familiarize the students with basic simulation workflow, data analysis including error estimation, p(V) isotherm, interpretation of the results and comparison with theory - ideal gas and Van der Waals at various densities and temperatures;
2. RxMC simulation of a reactive mixture of gases - effect of intermolecular interactions on equilibrium composition, estimation of activity coefficients from simulation and from the second virial coefficient.
3. Grand-canonical simulation of a salt solution - in this problem the students learn how to compute the chemical potentials and activity coefficients in electrolyte solutions, comparison of computed activity coefficients with DH theory
4. Constant-pH simulation - acid-base properties + theory - monomeric acid in salt solution, oligomeric acid or base, represented as a charged rod or a flexible polymer

The hands-on sessions are based on scripts written in python3. To successfully complete the tasks, some experience in programming and python is necessary.

Specific Recommended starting knowledge (prerequisites):
- Knowledge of Physics and Mathematics corresponding to the standard Bachelor courses
- Basics of Statistical Mechanics (Thermodynamics) and molecular simulations (Molecular Dynamics and Monte Carlo)
- Basics of Chemistry, pH, acids and bases
- Basics of programming (experience in python is advantageous but not required)