Physical Chemistry of Foods

Accuracy. Several kinds of uncertainty can arise.Systematic errors
can readily occur for indirect methods. The signal measured can depend on
other factors besides particle size. The relation between the magnitude of the
signal and the particle size may not be known with sufficient accuracy; often
a linear relation is assumed, but this is not always true. A fairly general
problem is that the method underestimates or even does not notice the
smallest particles. This means that the average size is overestimated,
especially averages involvingS 0 , such asd 10 andd 30 ; an estimate ofd 32 may
then be far closer to reality, since the smallest particles contribute fairly little
to total surface area and even less to total volume.
Even for direct methods, such problems may exist. Several microscopic
methods see in fact cross sections or thin slices of the material. Assuming the
particles to be spherical, a number of circles is seen, and the problem is to
convert their diameter distribution into that of the original spheres; this is
known as the ‘‘tomato salad problem.’’ Good solutions exist for spheres, but
for anisometric particles the problem is far more difficult, especially if the
system as a whole is anisotropic. This is treated in texts on stereology. The
particles in a dispersion are often allowed to sediment before viewing them;
the supporting plane then is commonly the plane of greatest stability, which
means that it is the plane for which the distance to the center of mass of the
particle is minimal. Consequently, averagedpis always larger than average
dsfor anisometric particles. (Can you explain this?) Furthermore, it may be
difficult to distinguish between separate particles being close to each other
and aggregates of particles, or even some irregularly shaped particles.
Conversion of the raw data to a size distribution especially poses
problems for indirect methods. For instance, in scattering methods a range
of data (a spectrum) has to be determined to allow the derivation of
anything else than an average size, be it a range of wavelengths or a range of
scattering angles. If the particle size distribution is known (together with
some other characteristics like particle shape and refractive index), it is
relatively easy to calculate a spectrum. But the inverse problem, calculating
the distribution from a spectrum, is far more difficult, especially because the
amount of information and its accuracy are limited. The algorithms
involved always involve rounding off and even shortcuts, and may lead to
considerable error.
Finally, thereproducibilityshould be taken into account. The sample
taken should be representative, and this is often difficult for powders, which
are prone to segregation between large and small particles. In dispersions,
segregation due to sedimentation or combined aggregation and sedimenta-
tion may occur. Sizing will also give rise to random errors, especially when
the particles are anisometric. The greatest uncertainty is generally due to
random errors in counting or, more precisely, in establishing the number of