Chem 444 (Physical Chemistry II), Spring 2020

Statistical Mechanics and Molecular Thermodynamics for Chemistry Undergraduates

Course Webpage: http://nanogold.org/statmech

Lectures: MWF, 10–10.50 am, Noyes 163 during Jan 22–Mar 13, Zoom during Mar 23–May 6

Course Objectives:

- To encourage thinking of chemical and physical processes in the language of microscopic states, stochastics, correlations, dynamics, and fluctuations (achieved through lectures and notes).

- To apply the machinery of statistical mechanics to common problems in physical chemistry, solid-state physics, and materials science (examples in problem sets).

- To appreciate the utility of this problem-solving ability to cutting edge problems of current interest (achieved through individual literature project).

Instructor: Prashant K. Jain, Associate Professor of Chemistry

Contact Info: Office: CLSL A224, Email: jain@illinois.edu, Tel: (217) 333-3417, Web: http://nanogold.org

Office hours: For discussion of lectures, notes, problem sets, and exams: Wed 11 am–noon and Fri 2–3.30 pm in CLSL A224 during Jan 22–Mar13 and Zoom during Mar 23–May6

No lectures: Mar 14–22 (Spring break)

Teaching Assistant: Jaeyoung Heo, 5th year PhD student in Prof. Jain’s lab (Email: heo8@illinois.edu, Office: A206 CLSL). Homework problem sets, solutions, and exams will be composed by Prof. Jain. All homeworks and exams will be graded by Jaeyoung in consultation with Prof. Jain.

Syllabus (Advanced topics, i.e., Chapters 5–7 will not be covered and are listed only for ambitious students)

1) The language of probabilities and microstates

2) Thermodynamic quantities, free energies, equilibrium and stability

3) The method of ensembles and partition functions

4) Ideal non-interacting systems: Quantum and classical statistics of indistinguishable particles: bosons and fermions, application to electrons in metals, phonons in crystals, photons, monoatomic and diatomic gases

5) Non-ideality: Introduction to inter-molecular forces

6) Theory of liquids and the Monte-Carlo method

7) Introduction to chemical kinetics and non-equilibrium statistical mechanics: fluctuations, time-correlations, ergodicity, transition states.

Exams and Grading:

Problem sets (10%): Four sets over semester; posted via Compass; During Jan 22–Mar 13, submit answers in paper form in lecture on due date indicated. During Mar 23–May 6 submit answers in scanned or typewritten form through Compass. Submissions late by one day or less will be graded but only 50% of the points earned will be awarded.

Mid-term Exam 1 (20%): Feb 24 in class. You may bring a calculator and one sheet of paper with concepts, equations, formulae, constants.

Mid-term Exam 2 (20%): Apr 13 from 10–11 am. Exam will be posted on Compass at 9.55 am and will be due at 11 am (no late submissions). Midterm is open book, but no collaboration is allowed as per the honor code. You may use a calculator. You may submit answers on scanned sheets of paper or in typewritten format. Prof. Jain will be available to answer questions via a Zoom lecture session.

Literature Project (20%): Form a group (3–4 students) prior to mid-Apr, chose a topic by the end of Apr, group work via online collaboration tools, and group presentations via Zoom on May 4 and 6. Presentation time: 20 minutes + 5 minutes Q&A time for each group. It is preferable if all group members take turns presenting sub-sections of the topic.

Final Exam: (30%): May 12, 7–10 pm. Exam will be posted on Compass at 6.55 pm and will be due at 10 pm (no late submissions). The final exam is open book, but no collaboration is allowed as per the honor code. You may use a calculator. You may submit answers on scanned sheets of paper or in typewritten format. Prof. Jain will be available to address doubts about anything on the exam via email. A final exam review will be conducted by Prof. Jain in the form of office hours.

Text and Materials

-No required textbook.

-All course notes are provided on Compass in two formats: handwritten (.pdf) and typewritten (.docx). Handwritten course notes can also be downloaded from: https://www.nanogold.org/notes-and-materials

-Recommended texts (not required at all if you attend the lectures): Statistical Thermodynamics by McQuarrie; Atkins' Physical Chemistry: Quanta, Matter, and Change; Introduction to Modern Statistical Mechanics by David Chandler.

-Useful resource: https://www.coursera.org/course/thermodynamics

Sample topics for literature project

-Thermodynamics of life (see What is Life? Book by Schrodinger; you may borrow the book from Prof. Jain)

-Molecular economics and analogies with molecular thermodynamics.

-Thermodynamics of the Ising spin model

-Entropy and free energy in photosynthesis

-Supercooled water (recall demonstration video from lectures).

-Unreasonable effectiveness of mathematics in thermodynamics: see Wigner’s paper: https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160130102.

Sample papers/papers chosen by former students

-Reversible unfolding of single RNA molecules by mechanical force, Science, 292, 733 (2001)

-Probing the catalytic activity and heterogeneity of Au-nanoparticles at the single-molecule level, PCCP, 11, 2767 (2009)

-BEC of photon gas, Nature, 468, 545 (2010)

-Life as a manifestation of thermodynamics and the second law of thermodynamics, Mathematical and Computer Modelling, 19, 25 (1994)

-Casimir force and vacuum fluctuations, Nature, 246, 396 (1973)