RF/Microwave Interaction Mechanisms in Biological Materials - RF/Microwave Interaction with Biological Tissues - page 83

another, or chemical reactions may take place to minimize the free energy G .
At equilibrium (constant temperature and pressure), passage of one molecule
from one phase to another, or of an atom from one chemical compound to
another, should not further lower the value of G . Thus, if one molecule of a
specific constituent goes from one phase to another, the increase of G in this
second phase must exactly equal the decrease of G in the first phase. The chem-
ical potential at equilibrium is therefore the same in all phases for each
constituent.
An important principle that can be inferred from energy functions is the
so-termed Gibbs phase rule , which states the number of degrees of freedom
(variables) available in a system. Description of the thermodynamic state of
a system of P phases ( 1, 2,

..., C ) includes the pressure and temperature of the system and the compo-
sition of each phase. The latter requires in general C

a = 1,2,..., P ) and C chemical constituents ( i =

- 1 variables; one needs

specify only the fraction of C 1 constituents, the final one being given auto-

matically. In P phases, allowing the possibility that each phase contains at least
a small quantity of each constituent, one requires P ( C

-

1) composition meas-
ures with temperature and pressure, the total number of variables is PC

-

- P

+ 2 . All are not independent, however: There are constraints relating the chem-

ical potentials . These are chemical potentials for each constituent in each
phase; they have the dimensions of energy per molecule and are the energy
that must be given to one molecule of a specific constituent to move it into a
particular phase. There are C ( P

1) of these constraints. As an example, three
phases have two such constraint relations for each constituent. Each constraint
reduces the number of independent system variables required by one .The
total number of independent variables required to describe the system is
therefore

-

( )+- ( ) =-+=

PC - 1 2 CP - 1 C P 2 degrees of freedom (2.17)

This is the Gibbs phase rule. It helps to explain phase diagrams , but this is
essentially related to metal mixtures.

REFERENCES

[1] J. P. Reilly, Electrical Stimulation and Electropathology , New York: Cambridge
University Press, 1992.
[2] J. P. Reilly, L. A. Geddes, C. Polk, “Bioelectricity,” in R. C. Dorff (Ed.), The Elec-
trical Engineering Handbook , Boca Raton, FL: CRC Press, 1993.
[3] J.-M. Guérit, Les Potentiels Évoqués , 2nd ed., Paris: Masson, 1993.
[4] A. L. Hodgkin, A. F. Huxley, “A quantitative description of membrane current and
its application to conduction and excitation in nerve,” J. Physiol. , Vol. 117, pp.
500-544, 1952.