1. Generalization of Einstein’s Theory of Brownian Motion Mahmoud A. Melehy University of Connecticut Storrs, CT 06269-1157

2. Albert Einstein (1879-1955) Nobel Prize 1921

3. Thermal Momentum Significance of Einstein’s Postulate Type: translational, vibrational, and/or rotational H 2, at 300 K, v rms = 1.93 km/s = 6,960 km/hour Conduction electrons in Cu, v rms = 1,570 km/s = 5.65x10 6 km/hour.

4. The Principle of Detailed Balancing

5. The Gibbs Equation and Physical definition of Chemical Potential

6. The Gibbs Equation The Gibbs-Duhem Equation

7. The Gibbs Equation The Gibbs-Duhem Equation

8. Thermodynamic Generalization of The Maxwell-Einstein Diffusion Force

9. The Principle of Detailed Balancing

11. Analogy with Electric Circuits ------ -−-− + ++ + V or L

12. Theory & Experiment for Ge & Si Diodes

13. In Sb and Ga As Diodes

14. Solar Cell Theory & Experiment

15. New Consequences of the First & Second Laws

16. Interfacial Forces, Entropy Change

17. Interfacial Electrification

18. Water Film on Glass

19. Water Film on Corian

20. Surface Charge on Corian

21. Surface Charge on Styrofoam

22. Surface Charge on Mahogany Wood

23. Dipole-Charge Effects on Water-Glass Interfaces

26. Forces Shaping Tornadoes

27. Tornadoes and Lightning

29. Dew Accumulation on Grass

30. Phenomenon of Rising Mist Canadian Niagra Falls

31. Phenomenon of Rising Mist Canadian Niagra Falls

32. Example of Conduction Electrons in Metals and Semiconductors Consistency of Einstein’ Theory of Brownian Motion with: 1. The first and second laws of thermodynamics. 2. The quantum theory.

33. Thermal Momentum and Entropy Uniqueness For any one constituent, the Gibbs-Duhem equation: Quantum mechanics allows to writing: Therefore, (1)

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38. Summary and Conclusion Generalizing thermodynamically Einstein’s theory of Brownian motion has led to an interfacial transport theory, which, in turn led to many consequences, including: Revealing that the first and second laws of thermodynamics require the existence of electric charges on most surfaces, membranes and other interfaces. This nearly universal property of inter- faces makes it possible to readily explain

39. many diverse phenomena, such as: ‘surface’ tension, capillarity, particle adhesion, the separation of charges upon phase change, atmospheric electricity, fog and cloud suspension, and even one mysterious phenomenon that has been observed since ancient times: the generation of static electricity by rubbing two different, insulating surfaces against one another. How much had this particular phenomenon been explained before is described, in the May, 1986 issue of Physics Today, by D. M. Burland, and L. B. Schein, who

40. have stated: "That some materials can acquire an electric charge by contact or rubbing has been known at least since the time of Thales of Miletus, around 600 B.C., and much work has been done on understanding the phenomenology of the effect, particularly in the 18th, and 19th centuries; nevertheless the underlying physics of electrostatic charging of insulators remains unclear.“ Generalizing Einstein’s theory of Brownian motion to interfacial systems has unlocked this ancient mystery, and many other ones too. Thank you.