Physical Chemistry of Foods

ions is governed by two opposing effects. The attractive energy between ions
of opposite charge pulls the counterions to the surface to neutralize the
charge (and in a similar manner, the coions are pushed away from the
surface). This is counteracted by the loss in mixing entropy that it would
cause. The system will strive toward a minimum in free energy, and from
this principle the distribution of the ions can be calculated.
Accordingly, theelectrostatic potential will decrease when going away
from the interface(Fig. 12.2b), according to the Debye–Hu ̈ckel theory
discussed in Section 6.3.2. We recall the equation

c¼c 0 expð
khÞð 6 : 32 Þ

wherec 0 is the surface potential andhthe distance from the surface. The
shielding parameterkdepends primarily on the total ionic strengthIand is
given by

k^2 ¼

2 INAVe^2

e 0 ekBT

ð 12 : 6 Þ

whereeis the charge of the electron,e 0 the permittivity of vacuum, andethe
relative dielectric constant of the medium. For water at room temperature
the equation can be reduced to

1

k

&

0 : 30

ffiffiffi

I

p & 0 : 30 ½ð 1 = 2 ÞSmiz^2 iŠ
^0 :^5 ð 12 :6aÞ

where 1/kis the Debye length or the nominalthickness of the electric double
layer(illustrated in Fig. 12.2b) in nm andIis in moles per liter;mis molar
concentration andz, valence of an ion. Figure 6.8 illustrates the dependence
ofconhand values of 1/kfor various values ofI; it also indicates the
magnitude of the ionic strength in some foods.
The relation between the surface charge density and the magnitude of
the surface potential is far from simple. Consider an adsorption layer of
ionic surfactants. The surface excess may be as high as 5? 10
^6 mol?m
^2 ,
corresponding to 3 molecules per nm^2. Following the discussion in Section
6.3.1, we can conclude that the dissociation of, for instance, carboxyl groups
may be greatly diminished; see especially Figure 6.7a. The pKof these
groups may readily be shifted upwards by two pH units. Sulfate groups have
a much lower pKand will still be dissociated at neutral pH. However, the
concentration of counterions at the charged interface cannot be as high as
would agree with Eq. (6.32). Hence the decrease ofcwithhis different at
very smallhvalues, affecting the value ofc 0. Actually, one has to account
for a layer of about the thickness of a hydrated counterion where these ions