Experimental Aspects of Fluid Properties at the Nano/Meso Scale - Fluid Properties at Nano/Meso Scale: A Numerical Treatment - page 173

Therefore plotting K 1 versus q 2 should result in a straight line that passes
through the origin and has a gradient that is equal to the effective diffusion coef-
ficient, D eff ( q ).
Experimental data can now be obtained and treated in the following way:
(a) For given concentrations of the nano-particles and electrolyte strengths the
normalized field autocorrelation function can be measured at different scatter-
ing angles.

(b) Taking the initial portion of the ln G 1 ( curve (at least 15 data points

starting from the minimum time value) a straight line is fitted through the data
(giving a correlation coefficient

τ ) versus τ

0.95) to obtain K 1 , the first cumulant.
(c) A curve of K 1 versus q 2 can now be plotted and a regression line that passes
through the origin can be fitted through the points. The gradient diffusion
coefficient is then determined from the regression curve gradient, which is
equal to D eff ( q ) (Equation (7.19)).

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Figure 7.10 shows how the first cumulant data, K 1 , determined at each scatter-
ing angle may be used to determine the gradient diffusion coefficient for a 10 g/L
dispersion of BSA particles in a 0.01MKCl electrolyte. The gradient of the plot of
K 1 versus q 2 yields the effective diffusion coefficient, D eff ( q ), in Equation (7.19).
Figure 7.10 shows that the data are well represented by a straight line fit through
the origin of the graph. For larger particles this linear dependence on the scatter-
ing angle is unlikely to be present as light scattering may be used to detect the
structure factor of the dispersion [128], thus introducing into the diffusion coeffi-
cient determination, a dependence on the scattering angle, as shown by the data of
Petsev and Denkov [117] for latex particles. However, for smaller particles where
the length scales are often too small to be resolved by light, the linear relation-
ship shown in Figure 7.10 is typical. It is, however, necessary to measure the light
scattering at different scattering angles in order to check that this is the case and
that no dependence on the scattering angle is apparent because if there was a de-
pendence on the scattering angle then the gradient diffusion coefficient would be
obtained via an extrapolation of a curve of D eff versus q to the zero scattering
vector, i.e. D m = D eff (0) [117].

Figure 7.11 shows the overall results for the measured gradient diffusion coef-
ficients for BSA at various ionic strengths and concentrations all at a constant pH.
As with the osmotic pressure, it can be seen that the physicochemical conditions
have a great effect on the gradient diffusion coefficient. Again by modelling the
nano-fluid, predictions of the gradient diffusion coefficient may be obtained.

7.4.3 Gradient Diffusion Coefficient Calculation

The calculation of the gradient diffusion coefficient will be briefly outlined here
as a thorough review of such calculations may be found elsewhere [127]. At finite