There are many times in nature when a solvent will pass spontaneously through a semipermeable membrane, which is a membrane permeable to solvent, but not solute. The osmotic pressure, П, is the pressure that must be applied to stop the influx of solvent. 1

Examples: (a) Transport of fluids through living cell membranes, (b) Basis of osmometry, determination of molecular mass by measurement of osmotic pressure. 2

Semipermeable membrane: stops polymers, passes solvent. h  V = n R T n = g/M c = g/V  = c R T 3

Osmosis Eventually the pressure difference between the arms stops osmosis. 4

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Van’t Hoff Eq. 7

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A solution of polystyrene in benzene contains 10 g/L. The equilibrium height of the column of solution (density 0.88 g cm -3 ) in the osmometer corrected for capillary rise is 11.6 cm at 25 o C. What is the molar mass of polystyrene, assuming the solution is ideal. The osmotic pressure of an aqueous solution at 300 K is 120 kPa. Calculate the freezing point of the solution. 9

Osmotic pressure is easily measured, and is quite large. Osmometry can be applied for the determination of molecular weights of large molecules (proteins, synthetic polymers), which dissolve to produce less than ideal solutions. The Van’t Hoff equation can be rewritten in the virial form: where B is the empirically determined osmotic virial coefficient Π= [B] RT {1 + B [B] +...} 10

Consider poly (vinyl chloride) PVC, in cyclohexanone at 298 K Pressures are expressed in terms of heights of solution, ρ=0.980 g cm -3 in balance with the osmotic pressure c (g L -1 ) h (cm) Use Π = [B] RT {1 + B [B] + …} with [B] = c/M, where c is the mass concentration and M is the molar mass. The osmotic pressure is related to the hydrostatic pressure by Π = ρgh, where g = 9.81 m s -2. Then: 11

Plot h/ c vs. c to find M, expecting a straight line with intercept RT/ ρ gM at c = 0. Data set: c(g L -1 ) h/c(cm g -1 L)

The data give an intercept of

The data give an intercept of 0.21 cm g -1 L, which is equal to RT/ ρ gM Thus: where we have used 1 kg m 2 s -2 =1J 14

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 (A) Ubbelohde, and  (B) Cannon-Fenske. 17

 IUPAC suggested the terminology of solution viscosities as following. Relative viscosity :  rel = oo  = toto t  : solution viscosity  o : solvent viscosity t : flow time of solution t o : flow time of solvent 18

Specific Viscosity Reduced Viscosity Inherent Viscosity Intrinsic Viscosity 19

M w > M v > M n B. Mark-Houwink-Sakurada Equation B. Mark-Houwink-Sakurada Equation ? Derive The MHS equation (use Phys. Chem references 20

Representative Viscosity-Molecular Weight Constants Polymer Polystyrene (atactic) c Polyethylene (low pressure) Poly(vinyl chloride) Polybutadiene 98% cis-1,4, 2% 1,2 97% trans-1,4, 3% 1,2 Polyacrylonitrile Poly(methyl methacrylate-co- styrene) mol% mol% Poly(ethylene terephthalate) Nylon 66 Solvent Cyclohexane Cyclihexane Benzene Decalin Benzyl alcohol Cyclohexanone Toluene DMF g DMF 1-Chlorobutane M-Cresol Temperature, o C 35 d d Molecular Weight Range  e e 3-61 f e 4-35 e 7-13 f 5-50 f 5-16 f 5-27 e f 5-55 e e f f K  a c Atactic defined d  temperature. e Weight average. f Number average. g N,N-dimethylformamide. 21

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? Prepare a report with the definitions for: 1) Dynamic Viscosity; 2) Shear Viscosity; 3) Bulk Viscosity and 4) Extensional Viscosity. 23

Viscosity; is Thickness: “Thin” like water, “Thick” like honey 24

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After a hurricane, many trees fall over and bend into a river. Also, a cow and a dog fall into a flooded river. Which one reaches the ocean first, cow or dog? Moo! Woof! 26

Solvent flow carries molecules from left to right; big ones come out first while small ones get caught in the pores. It is thought that particle volume controls the order of elution. But what about shape ? 27

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The following plot of relative amount of the large solute (blue) and of the smaller solute (red) goes with the animation. Larger solutes elute EARLIER, smaller solutes LATER, from a size exclusion column. 29

Molecular Weight Distribution Gel Permeation Chromatography (GPC) a. GPC or SEC (size exclusion chromatography) b. GPC method is modified column chromatography. c. Packing material: Poly(styrene-co-divinylbezene), glass or silica bead swollen and porous surface. d. Detector : RI, UV, IR detector, light scattering detector e. Pumping and fraction collector system for elution. f. By using standard (monodisperse polystyrene), we can obtain M n, M w. 30

Schematic representation of a gel permeation chromatograph. 31

degas pump injector DRI VeVe log 10 M c c c 32

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Typical gel permeation chromatogram. Dotted lines represent volume “counts.” Elution volume (V r ) (counts) Baseline Detector response 35

Typical semilogarithmic calibration plot of molecular weight versus retention volume. Retention volume (V r ) (counts) Molecular weight ( M ) 36

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Universal calibration for gel permeation chromatography. THF, tetrahydrofuran. Log([ η ]M)     Polystyrene (linear) Polystyrene (comb) Polystyrene (star) Heterograft copolyner Poly (methyl methacrylate) Poly (vinyl chloride) Styrene-methyl methacrylate graft copolymer Poly (phenyl siloxane) (ladder) Polybutadiene                  Elution volume,5 ml counts, THF solvent 38

Universal calibration method [ η ] 1 M 1 = [ η ] 2 M 2 logM 2 = ( 1 + a 2 1 ) log ( K 2 K 1 ) + ( 1 + a a 1 ) logM 1 39

[  ] = KM a [  ] A  M A = [  ] S  M S = f (V e ) Mark-Houwink Relation Universal Calibration A = analyte; S = standard Combine to get these two equations, useful only if universal calibration works! 40

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