Process of sedimentation with mechanism of action and mathematical derivations, different methods for separation of macromolecules by sedimentation, viscometry vs sedimentation

2. CONTENTS
 INTRODUCTION
 Macromolecules
 Characterization of macromolecules
 Various methods for determining molecular weight.
 Sedimentation or ultracentrifugation
 DISCUSSION
 Sedimentation basics
 Basic principle
 Mechanism of action
 Two methods of sedimentation
o Sedimentation velocity method
o Sedimentation equilibrium method
 CONCLUSION
 Sedimentation vs viscometry

4. MACROMOLECULES
• Giant molecules.
• Large number of atoms are linked by covalent
bonds.
• Term “macromolecules” was introduced by
German Chemist Herman Staudinger and
further significant contributions were made by
P.J.Flory.
• Examples of macromolecules are proteins,
starch etc.

5. CHARACTERIZATION OF
MACROMOLECULES
• As these are made up of very minute atoms or
molecules, so characterization of macromolecules is
very difficult or rather impossible directly.
• No doubt, they form true solution, but large sized
particles start settling down due to gravity, though very
slowly.
• By using appropriate variant of technique, the
molecular weight, density, shape etc. of
macromolecule can be detected.
• For determining molecular mass, the various methods
are:

6. Osmotic pressure change.
Sedimentation or
Ultracentrifugation.
Viscometry.
Light scattering method.

7. SEDIMENTATION OR
ULTRACENTRIFUGATION
• Macromolecules are almost insensitive to gravitational
settling.
• So gravitational settling will be useless for separation
or characterisation of macromolecules.
• By increasing gravitational potential energy by high
speed rotation, characterization will be possible and
the particles in solution sediment faster. i.e.
Ultracentrifugation.
• Gravitational force + Centrifugal force.
• Applications range from collection and separation of
cells, organelles, and molecules to study of molecular
weight of macromolecules.

8. DISCUSSION

9. • Sedimentation is tendency for particles in suspension
to settle out of the fluid in which they are entrained
and come to rest against a barrier.
• Due to motion of particles through the fluid in
response to forces acting on them.
• Even a small molecules supply a sufficiently strong
force to produce significant sedimentation.
• It is different from settling, as settling is falling of
suspended particles through the liquid but
sedimentation is termination of settling process.
• Svedberg and Nicols employed centrifuge first time.
SEDIMENTATION BASICS

10. BASIC PRINCIPLE
An object moving in a circle
at a steady angular velocity
will experience a force,
directed outwards.

12. MECHANISM OF ACTION
Particles are made to move by centrifugal force
and distribution in concentration of particles
along the length of centrifuge tube is determined
at one or more times. A measurement made
while the molecules are moving along the
centrifugal axis called sedimentation velocity
determination and the result is a sedimentation
coefficient, that will give information about
molecular weight and shape of particle. Also at
sedimentation equilibrium density and
composition can also be determined.

14. TWO METHODS

15. SEDIMENTATION VELOCITY METHOD
Principle– Rate of sedimentation depends upon the
size of particles.
Mathematical derivation
For any sedimenting particle, 2 forces act on it—
i. Gravitational force, downwards = 4 [(d-d’)gr3]/3
ii. Oppositional frictional force = 6rv
where r=radius, d=density & v= velocity of
sedimentation of particle, d’=density of solvent,
g=acceleration due to gravity, =coefficient of
viscosity of medium.

16. SEDIMENTATION VELOCITY METHOD
Equating both forces , we get
V=[2r2g(d-d’)]/9 ..........(1)
If the level at a distance x from top travels dx distance in
time interval dt, then velocity of sedimentation =
dx/dt=V
dx= {[2r2g(d-d’)]/9} dt
Integrating both sides within proper limits, i.e.
L.H.S from x2 to x1 and R.H.S from t2 to t1 , we get

17. SEDIMENTATION VELOCITY METHOD
 dx ={[2r2g(d-d’)]/9 }  dt
x2 - x1 =[2r2g(d-d’)(t2 - t1)] /9 .........(2)
Thus by knowing value of d and d’ and by
measuring the distances x1 and x2 at two
different times t1 and t2, r (radius) can be
determined.
Then we have mass of particle, m=(4r3d)/3

18. SEDIMENTATION VELOCITY METHOD
And molecular mass of macromolecule =No m
where No is Avogadro number.
This formula was not applicable unless
suspended particles are large. So , Svedberg,
who invented centrifuge overcome the
problem by replacing g with acceleration due
to centrifugal field given by , a= 2 x

19. SEDIMENTATION VELOCITY METHOD
Hence ,
dx= {[2r2(d-d’)2 x] /9} dt
 dx/x= {[2r2(d-d’)2 ] /9} dt
Integrating as before within same limits, we get
Ln(x2 /x1) = [2r2(d-d’)2(t2 - t1)] /9
Using this equation molecular mass can be
determined as before.

20. SEDIMENTATION EQUILIBRIUM METHOD
Principle– When the solution is whirled for
sufficiently long time in an ultracentrifuge, a
stage is reached when the concentrations at
different levels of solution become constant,
known as “ sedimentation equilibrium.“
Mathematical derivation
At sedimentation equilibrium,
Rate of sedimentation=Rate of back diffusion

21. SEDIMENTATION EQUILIBRIUM
METHOD
If C1 and C2 are the concentrations at the two
levels at distances x1 and x2 respectively, then
Ln(C2/C1)={M2(d-d’)(x22 -x12)}/2RTd
Where M=molecular weight of macromolecule, R=
gas constant , T= absolute temperature.
Thus by determining C1 & C2 at two levels x2 & x1
in the settling cell at sedimentation equilibrium,
M can be easily calculated.

23. SEDIMENTATION VS VISCOMETRY
By Sedimentation– sedimentation average
molecular weight equivalent to mass average
molecular weight.
By Viscometry– viscosity average molecular
weight equivalent to number average
molecular weight.

24. THANK YOU