1 2.Properties of Colloidal Dispersion Colloidal size : particle with linear dimension between 10-7 cm (10 AO) and 10-4 cm (1  ) nm particle weight/ particle size etc. Shapes of Colloids : linear, linear, spherical, rod, cylinder spiral sheet Shape & Size Determination

2 Molar Mass ( for polydispersed systems) Number averaged Weight averaged Viscosity averaged Surface averaged Volume averaged Second moment Third moment Radius of gyration Number averaged Molar Mass n

3 2.1 Colligative Propery In solution Vapor pressure lowering  P = ik p m Boiling point elevation  T b = ik b m Freezing point depression  T f = ik f m Osmotic pressure  = imRT (m = molality, i = van’t Hoff factor) In colloidal dispersion  Osmotic pressure

4 Osmosis Osmosis  the net movement of water across a partially permeableartially permeable membranemembrane from a region of high solvent potential to an area of low solvent potential, up a solute concentration gradient

5 Osmotic pressure  the hydrostatic pressure produced by a solution in a spacehydrostaticpressure divided by a semipermeable membrane due to a differential insemipermeable membrane the concentrations of solute For colloidal dispersion The osmotic pressure π can be calculated using the Macmillan & Mayer formula π = 1 [1 + Bc + B’c 2 + …] cRT M M M 2  =  gh

6 Molar Mass Determination Dilute dispersion h = RT [1 + Bc ] c  gM M Where c = g dm -3 or g/100 cm -3 M = M n = number-averaged molar mass B = constants depend on medium Intercept = RT  g n Slope = intercept x B/M n h (cm g -1 L) c c (g L -1 )

7 Estimating the molar volume From the Macmillan & Mayer formula : B = ½N A Vp where B = Virial coefficient N A = Avogadro # V p = 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 Osmotic pressure on blood cells Donnan Equlibrium : activities product of ions inside = outside

9 Reverse Osmosis  a separation process that uses pressure to force a solventsolvent through a membrane that retains the solute on one side and allowsmembranesolute the pure solvent to pass to the other sidesolvent 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.Wiener process  The mathematical model of Brownian motion has several real-world applications. An often quoted example is stock market fluctuations.stock market = 2Dt D = diffusion coefficient Brownian Motion

2.2 Kinetic property : DiffusionDiffusion the random walk of an ensemble of particles from regions of high concentration to regions of lower concentration

Einstein Relation (kinetic theory) where D = Diffusion constant,Diffusion constant μ = mobility of the particles mobility k B = Boltzmann's constant,Boltzmann's constant and T = absolute temperature.absolute temperature The mobility μ is the ratio of the particle's terminal drift velocity to an applied force, μ = v d / F.

For spherical particles of radius r, the mobility μ is the inverse of the frictional coefficient f, therefore Stokes law givesStokes law f = 6  r where η is the viscosity of the medium.viscosity Thus the Einstein relation becomes This equation is also known as the Stokes-Einstein Relation. Diffusion of particles

2.2 Kinetic property : ViscosityViscosity a measure of the resistance of a fluid to deform under shear stressresistancefluid shear stress where: is the frictional force, r is the Stokes radius of the particle,Stokes radius η is the fluid viscosity, and is the particle's velocity.

 = -  PR 4 t 8VL R P L  =  t  o  o t o  = viscosity of dispersion  o = 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 nitrogenliquid 77K0.158 acetone0.306 methanol0.544 benzene0.604 ethanol1.074 mercury1.526 nitrobenzene1.863 propanol1.945 sulfuric acid24.2 olive oil81 glycerol934 castor oil985  [c P] honey2,000–10,000 molasses5,000–10,000 molten glass10,000–1,000,000 chocolate syrup 10,000–25,000 chocolate chocolate * 45,000–130,000 ketchup ketchup * 50,000–100,000 peanut butter~250,000 shortening shortening * ~250,000   Intermolecular forces

Einstein Theory  =  o (1+2.5  )  = volume fraction of solvent replaced by solute molecule  = N A cV h MV where c = g cm -3 v h =hydrodynamic volume of solute  -1 =  sp = 2.5 ,  sp : specific viscosity  o

Einstein Theory  =  o (1+2.5  )  = N A cV h MV  -1 =  sp = 2.5 ,  sp : specific viscosity  o [  ] = lim  sp = 2.5 , [  ] : intrinsic viscosity c c [  ] = K(M v ) a Mark-Houwink equation K - types of dispersion a – shape & geometry of molecule

Assignment -2a At 25 o C D of Glucose = 6.81x m  s -1  of water = 8.937x10 3 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 o C, calculate its molecular mass c/g cm  /10 -4 kg m -1 s 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