RF/Microwave Interaction Mechanisms in Biological Materials - RF/Microwave Interaction with Biological Tissues - page 86

circuit with capacitance e 1 and conductance s 1 ; (3) a capacitance e • in par-

allel both with a series circuit with capacitance e 1 and conductance s 1 and

with a conductance s 0 ; (4) a capacitance e • in parallel with two series cir-

cuits with capacitance e 1 and conductance s 1 and capacitance e 2 and con-

ductance s 2 . A general assumption is that the values of conductivity do

not contribute significantly to e≤ ( w ). Observe that a steady conductivity

distorts the permittivity plot.

2.2. The representation of complex dielectric data is convenient where the
conductivity does not contribute significantly to

). Where the con-
ductivity is appreciable, Grant uses the complex conductivity, plotting its
imaginary part versus its real part [5]. Draw Grant's diagrams for the four
cases described in problem 2.1 and compare with the corresponding
Cole-Cole diagrams. Observe that the presence of

e≤ ( w

e • distorts the con-

ductivity plot.

2.3. In a system of several phases the extensive parameters of the entire
system are the sums of the extensive parameters of the separate phases.
In one phase, however, one cannot measure extensive parameters for each
of the chemical constituents present. (Dissolution of sugar in coffee does
not increase the volume of the sweetened coffee by an amount equal to
the volume of the dissolved sugar.) In the absence of field- and stress-
dependent terms, show that one has for the system of several phases

ÂÂ Â Â

dU = T dS - p dV + m D m

a a i a i a

a a a i

The variable m i a is the total number of “molecules” of chemical con-

stituent i in phase a and D m i a the change in this number. The parameter

m
i

. It has
the dimensions of energy per molecule and is the energy that must be
given to one molecule of i to move it into a particular phase

is known as the chemical potential for constituent i in phase a

a

. This equa-
tion permits description of an open system , for one can add molecules
from an external supply as well as exchange them between phases. Sub-
stitute in the above equation the definition of G [Eqn. (2.9)], again in the
absence of fields and stresses, and obtain the expression for dG , similar
to that shown for dU .

a