Kinetic Properties

1
Kinetic Properties (see Chapter 2 in Shaw, pp.
21-45)

• Sedimentation and Creaming Stokes Law
• Brownian Motion and Diffusion
• Osmotic Pressure
• Next lecture
• Experimental Methods
• Centrifugal Sedimentation (Chapter 2)
• Light Scattering (Chapter 3)

2
Gravitation and Sedimentation Stokes Law
r2gtr1 sedimentation r2ltr1 creaming
Fb
Fv
r1
g
r2

Fg

• Independent of shape
• No solvation (which
• changes the density)

Now we need to find an expression for f...
3
Stokes Law

• Assumptions
• Spherical particles, (no solvation)
• Particle size much larger than size of
• particles making up the medium
• (i.e.much larger than solvent molecules)
• Infinitely dilute solution
• Particles travelling slowly (no turbulence)

4
Effects of Non-Sphericity Solvation
Solvation

• absorbs solvent
• m increases
• measured f increases

• absorbs solvent
• Rs increases
• measured f increases

dry
Non-sphericity
ideal particle of radius Rs

• sphere excluded by
• tumbling ellipsoid of
• same volume is larger
• Rs increases
• measured f increases

5
Consider quantitatively
The actual measured friction factor The ideal
friction factor unsolvated sphere given by
Stokes law as Minimum possible value of
f friction factor for spherical particle having
same volume as solvated one of mass m Ratio
measuring increase due to asymmetry Ratio
measuring increase due to solvation
6
mass of bound solvent
Analyses also exist for the asymmetry contribution
but are complex.
Sedimentation allows for unambiguous
particle mass determination, and upper limits on
size and shape.
7
Furthermore, if intrinsic viscosity measurements
are also performed we can determine
unambiguously particle hydration and axis ratio
8
Brownian Motion and Diffusion

• All suspended particles have kinetic
• energy 1/2mv2 3/2kT.
• Smaller the particle, the faster is moves.
• Moving particles trace out a complex and
• random path in solution as they hit other
• particles or walls--Brownian motion
• (Robert Brown, 1828).

Average distance travelled by a particle
9
Diffusion - tendency for particles to move from
regions of high concentration to regions of low
concentration. DS gt 0, second law of
thermodymanics
Two laws govern diffusion
Ficks first law Ficks second law
A
dm
c
x
From these laws, we may derive (text) Einsteins
law of diffusion (pp.27-29)
10

• No assumptions!
• Any particle shape or size.
• D and f determined
• experimentally

Stokes-Einstein equation

• Assumes spheres
• No solvation
• Original use
• --finding Avogadros
• number!

Note the two are complementary measurement of
diffusion coefficient gives a friction factor
with NO assumptions can determine particle
masses
11
Competition between sedimentation and diffusion
Note tables 2.1 and 2.2 in the text
Spheres of r2 2.0 g/cm3 in water at 20oC
At particle sizes ca. 10-7 m radius (0.1 mm) the
sedimentation is perturbed to a significant step
by Brownian motion i.e particles of this size
dont sediment.
12
Experimental Methods
Diffusion Constants Free boundary method
x
0
c dc/dx

• Must thermostat (no convection effects)
• Must remove any mechanical vibration

13
Porous Plug Method