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Transcript
```Kinetic/Optical
Properties of
Colloids
PhD Halina Falfushynska
Motion
• Thermal motion
– Brownian Motion on the microscopic scale
– Diffusion and translation on the macroscopic scale
• Techniques for measuring colloidal sizes
– Sedimentation (under gravitational or applied
field)
– Colligative Properties
– Scattering techniques
Robert Brown
(1827)
vsed 
Brownian motion
Peclet
Mainz-02-11-04

George Gabriel Stokes
(1851)
mg
Albert Einstein
(1905)
D
Pe 


diffusion
D
kBT
kT

3
Sedimentation Potential
Sedimentation Of A Single
Particle Generates a Potential
Stokes Law
Stokes' law, for the frictional force – also called drag
force – exerted on spherical objects with very small
Reynolds numbers (e.g., very small particles) in a
continuous viscous fluid.
Fd  6Rv s
Fd is the frictional force – known as Stokes' drag
– acting on the interface between the fluid and the
particle (in N),
•μ is the dynamic viscosity (N s/m2),
•R is the radius of the spherical object (in m), and
•vs is the particle's settling velocity (in m/s).
Calculate the fall or settling velocity (Vt) for the
given details through Stoke's Law formula.
• Acceleration of Gravity (g) = 25 m/s2
Particle Diameter (d) = 15 m
Density of Medium (ρm) = 5 kg/m4
Particle Density (ρp) = 10 kg/m3
Viscosity of Medium (μ) = 20 kg/m-s
Vt = gd2 (ρp - ρm)/18μ
Problem
• Find the largest possible diameter for water
drops falling in air with a velocity where
Stoke’s law can be used In the calculation.
Giver: density of air 1.2 kg/m3, μ – 1.8×10-5
kg/(m×s)
Vt = gd2 (ρp - ρm)/18μ
A terminal velocity is reached
dx
mg 1     f
dt
Where m – mass of particle
 - specific volume of colloidal
particle
- solvent density
f – particle frictional factor
Stokes Law
• In the limit of
– Slow particle motion
– Dilute colloidal suspensions
– Solvent is considered as a continuum of viscosity 
dx 2 R g  2  1 

dt
9
2
dx 2 R g  p   f 

dt
9
2
The Frictional Factor
• The frictional factor in a given medium is
obtained from Stokes Law
f  6R
 – solvent viscosity
f, is a measure of the resistance to movement
of a molecule; this resistance is a function of
both the size and the shape of the molecule
The Frictional Factor
• D – diffusion coefficient
• S – sedimentation coefficient
Frictional Factors
• Frictional factors depend on the particle
shape
• f increases as
– Particle asymmetry increases
– Degree of interaction with solvent
increases
• Define the frictional ratio, f/fo.
– Ratio of the f value of the particle to that of
an unsolvated sphere.
Poiseuille's Law Calculation
• In the case of smooth flow (laminar flow), the
volume flowrate is given by the pressure
difference divided by the viscous resistance.
This resistance depends linearly upon the
viscosity and the length, but the fourth power
dependence upon the radius is dramatically
different.
Sedimentation of colloids
buoyant mass
F   Vsed  mg
kT
Fg
  6 R ( Stokes)
mg
Vsed 
6 R
R
2
The bigger the particles the
faster they sediment
F
F
15
Sedimentation
• Under gravity
– Balance method – cumulative mass of settling
particles is obtained as a function of time
– Practical lower limit is about 1 micron
• Under centrifugal force
– High Field – up to 4 x 105g is applied.
– Displacement of boundary is monitored with time
• Under low field
– Measure concentration profile in the tube as a
function of position.
Erythrocyte sedimentation rate
Erythrocyte sedimentation rate
• Sedimentation rate or is the rate at which red blood
cells sediment in a period of one hour.
• To perform the test, anticoagulated blood is placed
in an upright tube, known as a Westergren tube.
The rate at which the red blood cells fall is
measured and reported in mm/h.
• The ESR is governed by the balance between prosedimentation factors, mainly fibrinogen, and those
factors resisting sedimentation, namely the
negative charge of the erythrocytes (zeta potential).
• When an inflammatory process is present, the
high proportion of fibrinogen in the blood causes
red blood cells to stick to each other. The red cells
form stacks called 'rouleaux,' which settle faster.
Rouleaux formation can also occur in association
with some lymphoproliferative disorders in which
one or more immunoglobulin are secreted in high
amounts.
• The ESR is increased by any cause or focus of
inflammation. The ESR is increased in pregnancy,
inflammation, anemia or rheumatoid arthritis, and
decreased in sickle cell anemia and congestive
heart failure. The basal ESR is slightly higher in
Diffusion
• Diffusion is one of several transport
phenomena that occur in nature. A distinguishing
feature of diffusion is that it results in mixing or
mass transport without requiring bulk motion.
• There are two ways to introduce the notion
of diffusion: either a phenomenological approach
starting with Fick’s laws and their mathematical
consequences, or a physical and atomistic one, by
considering the random walk of the diffusing
particles
Fick’s Laws of Diffusion
• The diffusion flux is proportional to
the minus gradient of concentrations. It
goes from regions of higher concentration
to regions of lower concentration.
c
J  D
z
Diffusion
• From the atomistic point of view, diffusion
is considered as a result of the random
walk of the diffusing particles.
In molecular diffusion, the moving
molecules are self-propelled by thermal
energy. Random walk of small particles in
suspension in a fluid was discovered in
1827 by Robert Brown.
Diffusion and Frictional Factors
• The diffusion coefficient of a suspended
particle is related to f via the Einstein Equation
Df  k BT
For spherical particles
k BT
D
6R
where D is the diffusion constant;
μ is the mobility";
T is the absolute temperature
kB is Boltzmann's constant;
1.3806503 × 10-23 m2 kg s-2K-1
Diffusion of ions through a membrane
the flux is equal to mobility×concentration×force per
gram ion. This is the so-called Teorell formula.
The force under isothermal conditions consists of two
parts:
1.Diffusion force caused by concentration gradient:
2.Electrostatic force caused by electric potential gradient:
Here R is the gas constant, T is the absolute temperature, n is the
concentration, the equilibrium concentration is marked by a
superscript "eq", q is the charge and φ is the electric potential.
Measurement of Diffusion Coefficients
• Free boundary methods
– a boundary between two solutions of
different concentrations is formed in a
cylindrical cell
– Determine the evolution of the concentration
distribution with time.
Measurement of Diffusion Coefficients
• Taylor Dispersion methods
• NMR Techniques
– Pulsed gradient spin echo experiments (PGSE)
– Diffusion oriented spectroscopy (DOSY)
Intensity of transmitted radiation related to solution turbidity ()
It

e
Io
Nobel Prize for
Chemistry for his work
on the heterogeneous
nature of colloidal
solutions.
Light Scattering and Colloidal Sizes
• Size and shapes of colloidal systems can be
obtained from scattering measurements
– Absolute
– No perturbations of system
– Polydispersed systems
– Fast
Molar Masses from Scattering
• Obtain the Rayleigh ratio at 90
16

R 90
3
1
Kc

M R 90
2 no  dn 
K 

4 
N A o  dc 
2
2
2
The distilled solution of
absent, solve by water in
different ratio
Crab nebulosity
Opal
Tooth opalescence
Light for the dental technician is essential, especially when it comes to
aesthetics. In a healthy tooth light effects manifest themselves from
inside. Separate layers of tissues react for the light at different angles.
Interestingly, the structure of dentin and enamel differently behave to
the light. Especially noticeable light blue opalescent glow enamel
```
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