92168.pdf

Kinetic properties 25

position along a given axis after a time t is given by Einstein's

equation:

JT = (2Dtf (2.4)

where D is the diffusion coefficient (see page 26-7).
The theory of random motion helps towards understanding the
behaviour of linear high polymers in solution. The various segments
of a flexible linear polymer molecule are subjected to independent
thermal agitation, and so the molecule as a whole will take up a
continually changing and somewhat random configuration (see page
8). The average distance between the ends of a completely flexible
and random chain made up of n segments each of length / is equal to
/(/i)w (cf. Einstein's equation above). This average end-to-end
distance becomes l(2ri)^ if an angle of 109° 28' (the tetrahedral angle)
between adjacent segments is specified.
The diffusion coefficient of a suspended material is related to the
frictional coefficient of the particles by Einstein's law of diffusion:

Df = kT (2,5)

Therefore, for spherical particles,

D^

kT

=

RT (2-6)

6irpa 6irpaNA

where NA is Avogadro's constant, and

\V4

RTt

(2.1)

Perrin (1908) studied the Brownian displacement (and sedimenta-
tion equilibrium under gravity; see page 35) for fractionated mastic
and gamboge suspensions of known particle size, and calculated
values for Avogadro's constant varying between 5.5 x 1023 mol"^1
and 8 x 1023 mol"^1. Subsequent experiments of this nature have