Physical Chemistry of Foods

instance with respect to the ‘‘surface’’ of a macromolecule. If there is no net
attraction or repulsion between the surface and the solute, the latter stays
away (is sterically excluded) from the surface. This is illustrated in Figure
8.7a. WhenRwis the radius of a water molecule andRsthat of a solute
molecule, a layer of thicknessRwis devoid of water, and one of thicknessRs
devoid of solute. In first approximation, the amount of nonsolvent water
then is given by

wns¼

1

2

ðRSRWÞrA ð 8 : 8 Þ

in kg water per kg polymer, wherer¼mass density of water andAthe
specific surface area (m^2 ?kg^1 ) of the polymer. The factor 1/2 derives from
the concentration profile that develops due to Brownian motion of solute;
the factor depends somewhat on conditions of separation. Figure 8.7b gives
some results for nonsolvent water for various solutes (most of them sugars)
with respect to milk protein. Equation (8.8) is not precisely obeyed, but this
is only to be expected, since it is assumed in the equation that the protein
surface is flat and smooth and that the solute molecules are spherical, and
neither will be the case. The value ofwnscorresponding toRwmay be
considered to be true hydration water, about 0.15 g per g protein in the
present case.
The amount of nonsolvent water for a certain solute in a food can be
considerable, especially if the solute is a large molecule, the concentration of
polymer in the food is large, and the specific surface area of the polymer is
large. Most of the nonsolvent water is, of course, freely exchangeable with
bulk water. Nevertheless, negative adsorption of a solute causesawto be
decreased, since the effective concentration of solute is increased.

Note For a solute that shows positive, i.e., real, adsorption onto a

polymer present, the amount of nonsolvent water may be negative.

In such a caseawis increased.

3. Nonfreezing water. When a food is cooled to slightly below 0 8 C,
   not all water will freeze, owing to the freezing point depression caused by the
   solutes. This is discussed in Section 15.3. But even at a low temperature, say
    308 C, part of the water will not freeze, and this is often considered to be
   bound water. However, at low temperatures, where most of the water is
   frozen and where the viscosity of the remaining solution becomes extremely
   high, diffusivity of water is so small that freezing becomes infinitely slow.
   This is further discussed in Section 16.2. The quantity of nonfreezing water
   can depend on the conditions during freezing.