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22.52

Quantum Theory of Materials Characterization

3-0-9 units · Graduate

Holistic theoretical foundation of characterization techniques with photons, electrons, and neutron probes in various spaces. Techniques for assessing real space, reciprocal space, energy space, and time space utilizing microscopy, diffraction, spectroscopy, and time-domain methods. Elucidation of microscopic interaction mechanisms of materials. Practical assessment of what each characterization measures, methods for linking experimental features to microscopic materials information, state of the art methods for combining information, and machine learning aids. Students taking graduate version complete additional assignments.

Spring 2004 · Statistical Thermodynamics of Complex Liquids

Topics

  • The Structure Factor
  • Coherent and Incoherent Scattering
  • Density Auto-correlation Function: G(r)
  • Time-dependent Extension: G(r, t)
  • Dynamic Structure Factor: S(Q, ω)
  • Relation Between the Dynamic Structure Factor and Inelastic Scattering
  • Small Angle Scattering of Neutrons
  • Light and X-Ray Scattering–Static and Dynamic
  • Debye Theory of Scattering from Two-Component Porous Media
  • Models for Debye Correlation Function for the Bulk Contrast Case
  • Debye Correlation Function for the Interface Contrast Case
  • Asymptotic Model Applicable to Analysis of Large Q Data
  • Canonical Ensemble
  • Chemical Potential and the Grand Canonical Ensemble
  • Thermodynamic Definition of Static Pair Correlation Function
  • Energy Equation of States
  • Virial Equation of States
  • Virial Expansion
  • Potential of Mean Force
  • PY Solution for Hard Spheres
  • Thermodynamic Perturbation Theory
  • HNC Approximation
  • One-Component Macroion Theory (OCM)
  • Generalized One-Component Macroion Theory (GOCM)
  • Hard Spheres and Sticky Hard Spheres
  • Hard Sphere and Sticky Hard Sphere Systems
  • Debye-Hückel Approximation
  • The Mean Spherical Approximation
  • Ion Condensation of Planar Surfaces
  • Ion Condensation on Cylindrical Polyelectrolytes
  • Ion Distribution around Spherical Charged Particle

Readings

  • Chen, S. H. “Small Angle Neutron Scattering Studies of the Structure and Interaction in Micellar and Microemulsion Systems_._” Ann. Rev. Phys. Chem . 37 (1986): 351-399.
    Listed reading
  • ———. “Structure of Liquids.” Chapter 2 in Physical Chemistry-An Advanced Treatise – Liquid State _._ Vol. 8 Part A. Edited by Eyring, Henderson, and Jost. San Diego: Academic Press, 1971, pp. 85-155. ASIN: B000DT8NES.
    Listed reading
  • Chen, S. H. “Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution.” NATO ASI 369 (1992): 659-689.
    Listed reading
  • Hansen, J-P., and Ian R. McDonald. Theory of Simple Liquids. 2nd ed. San Diego: Academic Press, 1990. ISBN: 9780123238528.
    Listed reading
  • Egelstaff, P. A. An Introduction to the Liquid State . 2nd ed. New York: Oxford University Press, 1994. ISBN: 9780198517504.
    Listed reading
  • Friedman, H. L. A Course in Statistical Mechanics. New York: Prentice Hall, 1985. ISBN: 9780131845657.
    Listed reading
  • Baxster, R. J. “Distribution Functions.” Chapter 4 in Physical Chemistry-An Advanced Treatise – Liquid State . Vol. 8 Part A. Edited by Eyring, Henderson and Jost. San Diego: Academic Press, 1971, pp. 267-333. ASIN: B000DT8NES.
    Listed reading

Prerequisites & course information

Subject meets with 22.052 Prereq: 8.511 or permission of instructor Acad Year 2027-2028: G (Fall) Acad Year 2028-2029: Not offered 3-0-9 units

Sources