The kinetic properties relate to the motion of particles with respect to the dispersion medium. The motion may be thermally induced (Brownian movement, diffusion, osmosis) or gravitationally induced (sedimentation) or applied externally (viscosity). The motion relating to electrical field considered as electro kinetic phenomenon and will be discussed separately.
Brownian Motion
This is the erratic motion of
the particles in colloidal dispersions as can be observed using a
microscope. It is due to bombardment of the particles by moving molecules of
the dispersion medium. The velocity of the particles increases
with decreasing size. Increasing the viscosity
of the dispersion medium e.g. by addition of glycerin, decreases and
finally stops Brownian motion.
Diffusion
This is the movement
of particles from region of higher concentration of solute or disperse
phase to one of lower concentration until the concentration comes to
equilibrium. This movement is due to Brownian motion.
The amount of a substance (δq)
diffusing in time δt across a plane of area S is directly proportional to the
change in concentration δC with distance traveled δx, according to Fick’s first
law.
Δq = -DS δC/ δx δt
Where D is the diffusion
coefficient, which is the amount diffusing per unit time across a unit area
when δC/ δx, concentration gradient =1.
When the material is
allowed to pass through a porous disc, and samples are removed and analyzed
periodically, D can be found. From D, the size of the particle (radius) can be
found using an equation suggested by
Sutherland and Einstein: (Also known as
Stokes- Einstein Equation)
D = kT
6πηr
where k = Boltzman constant, T = absolute
Temperature
η= viscosity of the dispersion medium and r = radius
of the particle
OR D = RT
6πηrN
Where R = Universal Gas constant and N = Avogadro’s
Number.
Osmotic Pressure:
The osmotic pressure of a very diluted solution is
equal to a pressure that a solute would exert if it were a gas occupying the
same volume. Using Van’t Hoff’s Equation,
Π V = nRT
Where Π = Osmotic
pressure, V = volume, n = number of moles,
R =
Universal gas constant and T= absolute temparature.
Π = n RT
V
= c RT (n/V =c)
= Cg
RT Where Cg = grams of solute
per liter of dispersion
M or solution, M = Molecular weight
Rearranging,
Π
= RT
Cg M
By
plotting Π Vs Cg , RT/M = slope
By
plotting Π/Cg Vs Cg, you get a straight
line and the intercept as Cg tends to 0 is RT/M and hence M can be found.
| In practice, the equation is modified to |
Π
= RT (1/M + BCg),
Cg
where B is a constant for any particular
solvent/solute system. The inclusion of BCg is necessary to account for the
effect of shapes of particles, which in the above equation are assumed to be
spherical, but in practice the particles are solvated and may be elliptical,
oblong or linear.
Sedimentation
The velocity of
sedimentation, ν, of spherical particles of radius r and having density δ in a
medium of density δ0 and viscosity η0 can be calculated
from the Stoke’s law:
ν = 2r2 (δ – δ0 )g Where g = acceleration due to gravity
9 η0
Smaller particles (< 5μ
in diameter) are affected by Brownian motion and may not obey Stoke’s law. A
stronger force must be applied to bring about the sedimentation of colloidal
particles. This is accomplished by using ultra centrifuge in which case
g is replaced by the centrifugal force ω2x in which ω = angular
velocity and x is the distance of the
particle from the center of rotation:
ν = 2r2 (δ – δ0 ) ω2x
9
η0
Using Schlieren Photographs to measure the distance
x1-x2 , for a particle falling between times t1
to t2 and by knowing the angular velocy ω, diffusion
coefficient D, it is possible to calculate the molecular weight of a polymer
such as protein, by using the expression
M =
RT s
D(1- υρ0)
Where ν = partial specific volume of the protein and
s = Svedberg sedimentation coefficient s = dx/dt
ω2x
By
integration, ln (x2/x1)
ω2 (t2-t1)
Viscosity:
Viscosity
is resistance to flow of a system under an applied stress. Viscosity data like
those of sedimentation and osmotic pressure can be used to determine molecular
weight and shape of the particles of a given material of a dispersed phase.
If h0
is the viscosity of the dispersion medium, h is the viscosity of
the dispersion and q is the volume fraction of the colloidal particles,
then
h
= h0 (1 + 2.5q )
Relative
viscosity is defined as
hrel
= h/h0 = 1 + 2.5q
Specific
viscosity, hsp
is defined as
hsp = h/h0 - 1 =
2.5q
Since
the volume fraction is directly related to concentration c,
hsp
/c = k
Thus
by plotting hsp /c against c, a straight line is obtained,
with the intercept equal to k, which is a constant known as intrinsic viscosity
[h]
By
using this constant, and applying Mark-Houwink’s equation,
[h] =
kMa
k and a
are constants characteristic of the particular polymer-solvent system
The molecular weight M of a colloid can be found. Molecular weights of dextran, starch and
gelatin have been found using this approach.
The
viscosity of lyophobic dispersions is not much greater than that of a
dispersion medium., while lyophilic dispersions are much more viscous compared
to their respective solvents. Highly concentrated polymers may be jelly-like
solids.
Temperature
also affects the viscosity highly, as T increases h decreases. The shape of
particles of the dispersed phase also affects viscosity. Thus spherocolloids
have low viscosity compared to linear colloids.
