1. CHAPTER 19: FIGURE 19C.4
PHYSICAL CHEMISTRY: THERMODYNAMICS, STRUCTURE, AND CHANGE 10E | PETER ATKINS | JULIO DE PAULA
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2. CHAPTER 19: FIGURE 19C.5
PHYSICAL CHEMISTRY: THERMODYNAMICS, STRUCTURE, AND CHANGE 10E | PETER ATKINS | JULIO DE PAULA
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3. 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:

4. 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”

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