Introduction to Interfacial Transport
A Generalization of Einstein's Theory of Brownian Motion with Interdisciplinary Applications
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... A significant development occurred in thermodynamics also in the early twentieth century. Specifically, in his theory of Brownian motion, Einstein (1905b) introduced into thermodynamics the time rate of change of momentum, associated with the thermal motion of the particles. The objective was to study the diffusion of particles suspended in a liquid, but excluding the liquid surface. Toward that goal, Einstein derived an expression for the diffusion force, per mole, from which widely used results follow: the diffusion-mobility/viscosity relations. Einstein’s diffusion force is consistent with Maxwell’s diffusion force (1860), expressed for a unit mass of a gas diffusing in another.
What is particularly significant about Einstein’s theory of Brownian motion?
Above absolute zero, molecules, conduction electrons, ions, and other microscopic particles in any phase of matter have random thermal motion, which may be translational, rotational, and/or vibrational. Regardless of its type, this motion is highly significant. For example, in an ideal H2 gas in equilibrium, at 300 K, the root mean square of the particle translational velocity, vrms, is about 1.93 km/s = 6.96 x 103 km/h. Even more significant is the value of vrms for conduction electrons in copper. In a wide range around room temperature, that electron gas has vrms ? 1.22 x 103 km/s = 4.38 x 106 km/h. But the gases mentioned above, and all other particles in a thermodynamic system have finite masses. Therefore, thermal motion inevitably endows each particle with two equally important physical quantities: kinetic energy, and momentum; indeed neither of the two quantities is dispensable.
... ... A possible approach to tackle that problem seemed then to first generalize Einstein’s theory of Brownian motion to interfacial systems, then to apply the resulting theory to those devices. Such a procedure might lead to the unification of the theory of electrical conduction in the said devices and the elimination of the need of using hypotheses ad hoc. Furthermore, the resulting generalized theory might even lead to new, unforeseen fundamental consequences.
Both Maxwell (1860) and Einstein (1905b) had formulated the diffusion force fD on a mechanical basis. The first step needed then was to generalize thermodynamically the Maxwell-Einstein diffusion force fD. Subsequently, an important question had to be answered: how does fD interact generally, in an interfacial system, with electric fields and particle fluxes so that as the state of equilibrium is attained, the principle of detailed balancing is unconditionally satisfied?
After pieces of the jigsaw puzzle were put together, a general thermodynamic theory emerged, which is a statistical field theory that has new, fundamental properties and leads to numerous consequences (Melehy 1968, 1970a, 1970b, 1973, 1997, van Heerden 1976). The first of its applications led to the development of a voltage-current relation relevant to semiconductor diodes and solar cells. The theory has accurately been corroborated by all the experimental data reported for the said devices by about twenty five authors, over a period exceeding a quarter century. The studies have included some 60 experimental V-I characteristics. In some experiments the currents were varied over ranges exceeding ten orders of magnitude. The reported experiments were done in the temperature range 4.2-800 K.
The results just described have provided the first definitive evidence of the importance of generalizing, to interfacial systems, Einstein’s incorporation into thermodynamics of the particle thermal momentum rate of change.
The present thermodynamic theory (Melehy 1988, 1991, 1998b, 2003, 2006) has further revealed that the first and second laws of thermodynamics collectively require electric charges to reside at almost all surfaces, membranes, phase boundaries, and other interfaces. Values of those charges can, in principle, be calculated in terms of the geometric, physical, and thermodynamic parameters. Although all the thermodynamic parameters of interest for holes and/or conduction electrons in metals and semiconductors that are consistent with the uniqueness of entropy have been calculated (Melehy 2001b), assuming standard bands, those parameters pertaining to numerous other systems of interest are yet to be calculated.
This nearly universal property of interfacial electrification, consequential to the first and second laws and revealed by the thermodynamic generalization of Einstein’s theory of Brownian motion, confirms Newton’s speculation that the forces of capillarity, cohesion, and attraction between small particles are electric in nature. On that important, historic fact, Heilbron (1999, 239) wrote: “... One draft of Newton’s Principia that survived asserts that ‘attraction’ between particles, the force of cohesion and capillarity, is ‘of the electric kind.’ ....”
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About the Book
Highlights of this book were selected for inclusion in the
program of the 2005, Paris, “Albert Einstein Century International
Conference.” The Conference Proceedings was published by the American Institute of Physics, Vol. 861, pp. 524-531.
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Second Edition: In
1905, Albert Einstein’s theory of Brownian motion made a monumental
contribution to thermodynamics. Specifically, the theory accounted for
the rate of change of the particle momentum associated with thermal
motion to study the diffusion of suspended particles in liquids. In this
book, the author shows that Einstein’s procedure is
justified, not only for this particular problem, but for thermodynamic
systems generally, including those containing surfaces, membranes,
junctions phase boundaries and other interfaces
The resulting,
new thermodynamic theory has unified the theory of semiconductor diodes
and solar cells. Theoretical results have accurately corroborated
experimental data reported by more than 25 authors over a period
exceeding a quarter century. The new general theory has revealed that to simultaneously satisfy the first and second laws of thermodynamics, electric charges have to reside at most interfaces. This
novel result is the first thermodynamic confirmation of Newton’s
speculation that capillarity and other interfacial phenomena involve
electric forces. Interfacial electrification has explained numerous
phenomena of interdisciplinary interest such as: surface tension,
capillarity, drop coalescence, adhesion of light particles to surfaces,
the separation of charges upon phase change, fog and cloud suspension,
the origin of atmospheric electricity, and the generation of static
electricity, to mention a few examples.
The book provides ideas
and results that will stimulate theoretical and applied research in a
variety of disciplines. The topic coverage is balanced for
both researchers, who will find case studies with fundamental
importance, and students, who will be introduced to the generalization
of Einstein’s theory of Brownian motion and its numerous, interdisciplinary applications.
About the Author
B.S.,E.E., U of Cairo, Egypt M.S., E.E., Ohio State U, Columbus M.S., Math U of Illinois, Urbana Ph.D., E. E., U of Illinois, Urbana Dr. Melehy was on the faculty of the Department of Electrical and Computer Engineering, University of Connecticut for over three decades. He taught a number of graduate and undergraduate courses including: circuit theory, electromagnetism, semiconductor device physics, statistical physics, and interfacial transport. His research has concentrated on generalizing Einstein's theory of Brownian motion and applying the results to a variety of interfacial phenomena and systems. This work was published earlier in one book and parts of two other books, and in over 80 journal and conference articles including the Proceedings of the 1969, Pittsburgh “International Symposium on Thermodynamics,” and the Proceedings of the 2005, Paris “Albert Einstein Century International Conference.” In 2007, Dr. Melehy received the Distinguished Faculty Service Award from the University of Connecticut School of Engineering. In 1960, Dr. Melehy served as a consultant to Shockley transistor, Mountain View, California, where he worked, and published two papers, one of which was coauthored by Dr. William Shockley, inventor of the junction transistor and co-recipient of the 1956 Nobel Prize in Physics.