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Flux
of neutral molecules – Theory
Basic Theory Chemicals in solution move under the
influence of chemical forces of diffusion directed towards lower
concentration regions. Neutral molecules, with valence z = 0, do
not have electric forces that are experienced by ions. Otherwise, the
assumptions and general conditions are the same as for ions. See the
review (Newman, 2001). The following treatment is also given in Pang et al (2006). µ = µ_{0}
+ RT ln(gc).
[Equ 1] The molecular flux J (mol m^{2}
s^{1}) into the tissue is given by Newman (2001, Equ 2):  J
= c u (dµ/dx).
[Equ 2] The concentration is c (mol m^{3}),
g is the activity coefficient,
u is the mobility (m s^{1} per N mol^{1}) and x
is distance (m) from the tissue. Mathematically (dµ/dx)
= (dµ/dc)(dc/dx), J
= u R T (dc/dx).
[Equ 3] This equation is known as Fick’s
Law of diffusion, J = D (dc/dx), where the
diffusion coefficient D = u R T. Thus for uncharged
molecules, unlike the situation for ions, the treatment based on
electrochemical potential is identical to diffusion theory based on Fick’s
Law. Calibration of electrodes Electrodes used to measure the
concentration of neutral molecules require calibration to obtain a graph
of output voltage ~ concentration. If this graph is linear, as is the case
for Clarktype oxygen electrodes for example ( e.g Armstrong et al.
2000), the equation is:  V
= V_{0} + a
c.
[Equ 4] The intercept is V_{0}
and the slope of the graph is a. Thus, (dV/dc) = a,
or dc = dV/a,
so the flux Equ 3 becomes:  J
= u R T (dV/dx)/a.
[Equ 5] This is the equation used in the MIFE
software to calculate flux of oxygen or other uncharged molecules. The
intercept and slope of the calibration graph are recorded and
are transferred by the calibration average file to MIFEFLUX for analysis.
For each manipulator cycle, MIFEFLUX uses Equ 4 to calculate the local
concentration (mean for the two positions). Equ 5 is used to calculate the
flux, using the measured dV and dx values, with the known
parameters. Geometrical considerations When the diffusion is not from a source
having a flat surface, for a cylindrical root or spherical protoplast with
radius r for example, Equ 5 must be modified. By doing the
appropriate integration, it can be shown that the dx in Equ 5 must
be replaced as described by Newman (2001, Equs 8 & 9):  for a sphere:
dx = r^{2}[1/(r + x) – 1/(r
+ x + dx)]; for a cylinder:
dx = r ln[(r + x + dx)/(r
+ x)]. These are used in the MIFEFLUX analytical
software.

Maintained by Ian Newman. Date . © University of Tasmania.