1

2.P roperties of C olloidal Dispersion

Colloidal sizeColloidal size :: • particle with linear dimension between

10-7 cm (10 AO) and 10-4 cm (1 )1 - 1000 nm

• particle weight/ particle size etc.

Shapes of Colloids :Shapes of Colloids :linear, linear, spherical, rod, cylinder spiral sheet

Shape & Size Determination

2

MMolar olar MMass ass ( for polydispersed systems)( for polydispersed systems)• Number averaged • Weight averaged • Viscosity averaged • Surface averaged• Volume averaged• Second moment • Third moment• Radius of gyration

i in

i iMi

nM

Number averagedMolar Mass

n

3

2.1 Colligative Propery

In solution• Vapor pressure lowering P = ikpm

• Boiling point elevation Tb = ikbm

• Freezing point depression Tf = ikfm

• Osmotic pressure = imRT(m = molality, i = van’t Hoff factor)

In colloidal dispersion Osmotic pressure

4

OOsmosis smosis the net movement of water across a partially permeable membrane from a region of high solvent potential to an area of

low solvent potential, up a solute concentration gradient

5

OOsmotic pressure smotic pressure the hydrostatic pressure produced by a solution in a space

divided by a semipermeable membrane due to a differential in the concentrations of solute

For colloidal dispersionFor colloidal dispersion The osmotic pressure π can

be calculated using the Macmillan & Mayer formula

π = 1 [1 + Bc + B’c2 + …] cRT M M M2

= gh

6

MMolar olar MMass Determination ass Determination Dilute dispersion

h = RT [1 + Bc ]

c gM MWhere c = g dm-3 or g/100 cm-3

M = Mn = number-averaged molar mass

B = constants depend on medium

Intercept = RT g n M

Slope = intercept x B/Mn

h (cm g-1L)c

c (g L-1)

7

Estimating the molar volume

From the Macmillan & Mayer formula :

B = ½NAVp

whereB = Virial coefficientNA = Avogadro #Vp = excluded volume, the volume into which the center

of a molecule can not penetrate which is approximately equals to 8 times of the molar volume

Example/exercise : Atkins

8

OOsmotic smotic ppressure on ressure on bloodblood ccellsells

Donnan Equlibrium : activities product of ions inside = outside

9

RReverseeverse O Osmosissmosis

a separation process that uses pressure to force a solvent through a membrane that retains the solute on one side and allows

the pure solvent to pass to the other side

Look for its application : drinking and waste water purifications, aquarium keeping, hydrogen production, car washing, food industry etc.

Pressure

2.2 Kinetic property :

either the random movement of particles

suspended in a fluid or the mathematical model used to

describe such random movements, often called a

Wiener process.

The mathematical model of Brownian motion has several

real-world applications . An often quoted example is

stock market fluctuations .

x2= 2Dt

D = diffusion coefficient

Brownian Motion

2.2 Kinetic property : Diffusion

the random walk of an ensemble of particl es from regions of high concentration to re

gions of lower concentration

E instein R elation (kinetic theory)

where           D = Diffusion constant,

μ = mobility of the particleskB = Boltzmann's constant ,

and T = absolute temperature.

The mobility μ is the ratio of the particle's termin al drift velocity to an applied force, μ = vd / F.

For spherical particles of radius r, the mobility μ is the inverse of the frictional coefficient f, therefore Stokes law gives

f = 6r

where η is the viscosity of the medium .Thus the Einstein relation becomes

         

This equation is also known as the - Stokes EinsteinRelation.

Diffusion of particles

2.2 Kinetic property : Viscosity

a measure of the resistance of a fluid to

deform under shear stress

     where:   is the frictional force, r is the Stokes radius of the particle,

η is the fluid viscosity, and   is the particle's velocity .

= - PR4t 8VL

R P

L

= to oto

= viscosity of dispersiono = viscosity of medium

Unit:Poise (P) 1 P = 1 dyne s-1 cm-2 = 0.1 N s m-2

Viscosity Measurement

Viscometer

[c P]

liquid nitrogen 77@ K

0.158

acetone 0.306

methanol 0.544

benzene 0.604

ethanol 1.074

mercury 1.526

nitrobenzene 1.863

propanol 1.945

sulfuric acid 24.2

olive oil 81

glycerol 934

castor oil 985

[c P]

honey 2,000–10,000

molasses 5,000–10,000

molten glass 10,000–1,000,000

chocolate syrup

10,000–25,000

chocolate* 45,000–130,000

ketchup* 50,000–100,000

peanut butter ~250,000

shortening* ~250,000

Intermolecular forces

E instein Theory = o (1+2.5)

= volume fraction of solvent replaced by solute molecule

= NAcVh

MV

where c = g cm-3

vh=hydrodynamic volume of solute

-1 = sp = 2.5 , sp : specific viscosity o

E instein Theory = o (1+2.5)

= NAcVh

MV

-1 = sp = 2.5 , sp : specific viscosity o

[] = lim sp = 2.5 , [] : intrinsic viscosity c c

[] = K(Mv)aMark-Houwink equation

K - types of dispersiona – shape & geometry of molecule

Assignment -2a

At 25 oC

D of Glucose = 6.81x10-10 m s-1

of water = 8.937x103 P

of Glucose = 1.55 g cm-3 Use the Stokes law to calculate the

molecular mass of glucose, suppose that glucose molecule has a spherical shape with radius r

5 points

(3-5 students per group)

Assignment -2b

Use the data below for Polystyrene in Toluene at 25 oC, calculate its molecular mass

c/ g cm-3 0 2.0 4.0 6.0 8.0 10.0/10-4 kg m-1s-1 5.58 6.15 6.74 7.35 7.98

8.64

Given : K and a in the Mark-Houwink equation equal 3.80x10-5 dm-3/g and 0.63, respectively

(5 points)Due Date : 21 Aug 2009