CHAPTER 19: FIGURE 19C.4 PHYSICAL CHEMISTRY: THERMODYNAMICS, STRUCTURE, AND CHANGE 10E | PETER ATKINS | JULIO DE PAULA ©2014 W. H. FREEMAN AND COMPANY PHYSICAL CHEMISTRY: QUANTA, MATTER, AND CHANGE 2E| PETER ATKINS| JULIO DE PAULA | RONALD FRIEDMAN ©2014 W. H. FREEMAN D COMPANY

CHAPTER 19: FIGURE 19C.5 PHYSICAL CHEMISTRY: THERMODYNAMICS, STRUCTURE, AND CHANGE 10E | PETER ATKINS | JULIO DE PAULA ©2014 W. H. FREEMAN AND COMPANY PHYSICAL CHEMISTRY: QUANTA, MATTER, AND CHANGE 2E| PETER ATKINS| JULIO DE PAULA | RONALD FRIEDMAN ©2014 W. H. FREEMAN D COMPANY

Statistical Ideas: One-dimensional Random walk Consider a particle restricted to movement in one direction, starting at x=0 Can take one step of fixed length ℓ at random in positive or negative direction, then another, again at random, etc. Each step takes time . After j steps, it has travelled a path jℓ, but it will not be that distance away from x=0. Probability of finding a particle at distance x after time t: Compare with one-dimensional diffusion:

Connect random walk with the solution of the diffusion equation and get Microscopic interpretation of  and : Diffusion on a microscopic scale can be interpreted as “jumps” of molecules by step size  in time  (e.g. moving through a H-bonding network, or diffusing through a crystal lattice)  connection with “molecular dynamics simulations”

CHAPTER 20: FIGURE 20A.3 PHYSICAL CHEMISTRY: THERMODYNAMICS, STRUCTURE, AND CHANGE 10E | PETER ATKINS | JULIO DE PAULA ©2014 W. H. FREEMAN AND COMPANY PHYSICAL CHEMISTRY: QUANTA, MATTER, AND CHANGE 2E| PETER ATKINS| JULIO DE PAULA | RONALD FRIEDMAN ©2014 W. H. FREEMAN D COMPANY