where C is the specific heat of the colloid, φ is the concentration
of Fe per ml of solution, ρ is the density of the colloid
and T/t represents the heating rate. Equation (12) does
not take into account the heat capacity of the sample holder.
The heating of the sample holder will use a significant
proportion of the power generated. Hence, it is crucial that all
measurements are made using identical conditions in the same
volume of sample. However, this also suggests that it might
not be possible to compare measurements made in different
measurement systems.
All samples studied in this work were supplied by Liquids
Research Ltd [12]. The particles were prepared by the coprecipitation
method [13], with controlled growth conditions
giving a narrow size distribution. The particles are nominally
Fe3O4 but the exact composition will lie between Fe3O4 and
Fe2O3. The samples were dispersed in two solvents with
different viscosities to study the effect of the viscosity of the
suspension on the heating properties of the samples and did
not have identical surfactant coatings. The solvents used were
the isoparaffin oils Isopar M and Isopar V [14], which have
viscosities of 3.0 cP and 10.8 cP, respectively. The samples
were also dispersed in awax to eliminate heating effects arising
from Brownian relaxation of the particles and viscous heating.
The critical diameter above which hysteresis heating will occur
is independent of the colloid environment. The matrix used
will only affect Brownian and viscous heating effects. For
in vivo applications the viscosity is likely to be significantly
greater than in a colloid, for example the viscosity of blood
is 10 cP, and hence dynamic effects will be suppressed if not
eliminated.
The physical median particle size (Dm) for each sample
was measured by TEM using a 200 keV JEOL 2011 TEM.
Samples were prepared by placing one drop of a dilute
suspension of the particles in hexane on a carbon coated grid
and allowing the solvent to evaporate. Over 500 particles were
measured using a Zeiss particle size analyser to ensure good
statistics. This technique uses an equivalent area process to
obtain the particle diameter. The data were fitted to a lognormal
distribution.