Diffusion of Caffeine in Different Aqueous Media at Physiological Temperature - Caffeine: Chemistry, Analysis, Function and Effects - page 92

counter-current coupled transport of solute i from regions of lower to higher
concentration of solute k.
This phenomenon is an irreversible process. In fact, the gradient of chemical
potential in the real solution is treated as the true virtual force producing
diffusion. However, in most cases, that force can be quantified by the gradient
of the concentration at constant temperature. Thus, we may consider the
following approaches to describe the isothermal diffusion: the thermodynamics
of irreversible processes and Ficks laws (Robinson and Stokes 1959).

d n 0 t 2 n g | 9

6.2.2 Taylor Dispersion Technique
In the Taylor dispersion technique, a small amount of a given solution is
injected into a laminar carrier stream of solvent, or of solution at a different
concentration, to flow throughout a long capillary tube (Barthel et al 1996;
Callendar and Leaist 2006; Tyrrell and Harris 1984). The length of the Teflon 1
dispersion tube used in the present study was measured directly by stretching
the tube in a large hall and using two high quality theodolites and appropriate
mirrors to accurately focus on the tube ends. This technique gave a tube length
of 3.2799 (¡0.0001) 6 10 4 mm, in agreement with less-precise control
measurements using a good-quality measuring tape. The radius of the tube,
0.5570 (¡ 0.00003) mm, was calculated from the tube volume obtained by
accurately weighing (resolution 0.1 mg) the tube when empty and when filled
with distilled water of known density.
In a pattern run, a sample of 0.063 mL of the solution under study (c j ¡ Dc)
is injected into the laminar carrier stream (c j ) through a 6-port Teflon 1 valve
(Rheodyne, model 5020). The flow rate is kept constant (0.17 mL min 21 ) with
the assistance of a metering pump (Gilson model Minipuls 3) which allows
retention times of about 1.1 6 10 4 s. Both the dispersion tube and the injection
valve are placed into an air thermostat bath to keep the temperature constant
at 303.15 K (¡ 0.01 K).
The dispersion of the injected samples is monitored by using a differential
refractometer (Waters model 2410) at the outlet of the dispersion tube. Voltage
values as a function of the elapsed time, V(t), are measured at accurate 5 s
intervals by using a digital voltmeter (Agilent 34401 A) provided with an IEEE
interface. Binary diffusion coefficients are calculated from the dispersion
equation,

Þ 1 = 2 exp ½ 12Dtt ð 2 = r 2 t V ðÞ ~V 0 zV 1 tzV max t R = t ð ð 5 Þ

being the additional fitting parameters: t R , the mean sample retention time;
V max , the peak height; V 0 , the baseline voltage; and V 1 , the baseline slope.
Extensions of the Taylor technique have been used to determine ternary
mutual diffusion coefficients (D ik ) for multicomponent solutions. These D ik
coefficients, defined by eqn (3) and eqn (4), are evaluated from the fitting of
two or more replicate pairs of peaks for each carrier-stream, to the ternary