Report

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 h pV = n R T n = g/M c = g/V 1 p = c R T ( A2c ...) M Semipermeable membrane: stops polymers, passes solvent. 3 Osmosis Eventually the pressure difference between the arms stops osmosis. 4 5 However A is now increasedby greaterpressure p *A ( p) A ( x A , p ) accountfor thepresenceof solute A ( x A , p ) *A ( p ) RT ln x A take theeffectof pressureintoaccount p *A ( p ) *A ( p) V dp m p where Vmis themolar volume of pure solventA combiningequations,we have p RT ln x A V dp m p Dilute solutions: ln x A replacedby ln(1 x A ) xB andVm is constant RTxB Vm 6 RTxB pVm nB When thesoluteis dilute, xB . Because n AVm V , nA totalvolumeof thesolvent,theequationsimplifiesto p [ B]RT Van’t Hoff Eq. nB where[ B] is themolarconcent ration of thesolute V 7 8 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 25oC. 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: Π= [B] RT {1 + B [B] + ...} where B is the empirically determined osmotic virial coefficient 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) 1.00 0.28 2.00 0.71 4.00 2.01 7.00 9.00 5.10 8.00 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 h RT Bc RT RTB c 1 2 c gM M gM gM Plot h/ c vs. c to find M, expecting a straight line with intercept RT/ ρgM at c = 0. Data set: c(g L-1) 1.00 2.00 4.00 7.00 9.00 h/c(cm g-1 L) 0.28 0.36 0.53 0.729 0.889 12 The data give an intercept of 0.21. 13 The data give an intercept of 0.21 cm g-1 L, which is equal to RT/ ρgM Thus: RT 1 M g 0.21cm g1 L 8.314JK 1 1 m ol (298K ) 1 3 2 (980kgm ) (9.81m s ) 2.1103 m 4 kg 1 1 1.2 10 kgm ol 2 where we have used 1 kg m2 s-2=1J 14 15 16 (A) Ubbelohde, and (B) Cannon-Fenske. 17 IUPAC suggested the terminology of solution viscosities as following. • Relative viscosity : rel = o = t to : 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 0 t t0 sp rel 1 0 t0 sp rel 1 red c c inh ln red c lim c 0 sp c liminh c 0 19 kM a log log k a log M v K and a are Viscosity- MolecularWieght Constant Mw > Mv > Mn ? Derive The MHS equation (use Phys. Chem references 20 Representative Viscosity-Molecular Weight Constants Polymer Solvent 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-costyrene) 30-70 mol% 71-29 mol% Poly(ethylene terephthalate) Nylon 66 Molecular Weight Range 10-4 8-42e 4-137e 3-61f 3-100e K 103 Cyclohexane Cyclihexane Benzene Decalin Temperature, oC 35 d 50 25 135 Benzyl alcohol Cyclohexanone 155.4d 20 4-35e 7-13f 156 13.7 0.50 1.0 Toluene Toluene DMFg DMF 30 30 25 25 5-50f 5-16f 5-27e 3-100f 30.5 29.4 16.6 39.2 0.725 0.753 0.81 0.75 1-Chlorobutane 1-Chlorobutane M-Cresol M-Cresol 30 30 25 25 5-55e 4.18-81e 0.04-1.2f 1.4-5f 80 26.9 9.52 67.7 17.6 24.9 0.77 240 a 0.50 0.599 0.74 0.67 0.67 0.63 0.95 0.61 cAtactic defined temperature. eWeight average. fNumber average. gN,N-dimethylformamide. d 21 22 ? 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 25 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 28 •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 Mn , Mw . 30 Schematic representation of a gel permeation chromatograph. 31 c log10M c DRI Ve c degas pump injector log10M 32 PS standard samples Mw Vendor Specified 3105 6207 10300 43900 102000 212000 170000 422000 929000 1600000 1971000 2145000 Mw/Mn 1.14 1.03 1.03 1.01 1.02 1.01 1.01 1.02 1.01 1.16 1.03 1.1 33 34 Detector response Typical gel permeation chromatogram. Dotted lines represent volume “counts.” Baseline Elution volume (Vr) (counts) 35 Typical semilogarithmic calibration plot of molecular weight versus retention volume. Molecular weight (M) 106 105 104 103 Retention volume (Vr) (counts) 36 37 109 Polystyrene (linear) Polystyrene (comb) Polystyrene (star) Heterograft copolyner Poly (methyl methacrylate) Poly (vinyl chloride) 107 108 Log([η]M) Universal calibration for gel permeation chromatography. THF, tetrahydrofuran. Styrene-methyl methacrylate graft copolymer 106 Poly (phenyl siloxane) (ladder) Polybutadiene 105 18 20 22 24 26 28 Elution volume ,5 ml counts, THF solvent 30 38 Universal calibration method [η]1M1 = [η]2M2 1 logM2 = ( 1 + a 2 KK 12 )log( ) + ( 11 ++ aa1 )logM1 2 39 []AMA = []SMS= f (Ve) [] = KM a Mark-Houwink Relation K A M Aa A 1 K S M SaS 1 K S M SaS 1 MA KA Universal Calibration A = analyte; S = standard 1 a A 1 Combine to get these two equations, useful only if universal calibration works! 40 41