Page 36 - Introduction to Colloid and Surface Chemistry

Kinetic properties 27
The proportionality factor D is called the diffusion coefficient. It is
not strictly a constant, since it is slightly concentration-dependent.
Equations (2.4) and (2.5) can be derived using equation (2,8), as
follows.

Brownian displacement equation (2.4)

Consider a plane AB (Figure 2.2) passing through a dispersion and
separating regions of concentration Ci and c 2, where c\ > c 2. Let the
average Brownian displacement of a given particle perpendicular to
AB be x in time t. For each particle, this displacement has equal
probability of being 'left to right' or 'right to left'. The net mass of
particles displaced from left to right across unit area of AB in time t
is, therefore given by

—2
m —
2x

„.. „ dc
If x is small,

Therefore,

1 dc_ 2
OT = X (2.10)
2dx

From equation (2.8)

dc (2.11)
m = -D—t
dx

1 1
q 1

x EI x

Figure 2.2