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# 409 Class Note for MATSE 443 at PSU

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This 12 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15

LIQUIDS 4 I0 875 4 7 r995 scatterers per unit volume mgmsi Polarizability Geometry of Characteristics of observation the incident beam TO A FIRST APPROXIMATION a 317 HENCE PURE LIQUIDS SHOULD NOT SCATTER LIGHT FLUCTUATIONS Pure liquids density Solutions concentration K1coszec 1 0 12FZC R MW e E A Inc1 ent eam 39 But a polymer is too large to Be considered a single oscillatoI V V V A B ie a point source of radiation Must consider interference effects ZIMM PLOT K 1 cosze c L 39 2 Q Re MWl21 2c l S 81112 Experimentally measured parameters n 739 Weight Average a 3 l 2quot 39III 39 MolecularWeight 9 0 hue I 7 39 6 I 3quot 39 quot Fquot Klcoszec nquot I quotr 39l i 1quot 47 1 Virial Expansion Dependence upon angle of observation THE VISCOSITY OF POLYMER SOLUTIONS Measure the time taken to flow between fixed marks in a capillary tube under the draining effect of gravity The volume rate of flow 0 is then related to the viscosity by Poiseuille39s equation where P is the pressure difference maintaining the flow r and l are the radius and length of the Capillary and n is the viscosity of the liquid Relative Viscosity Defined as the viscosity of a polymer solution divided by that of the pure solvent and for dilute solutions where t is the time taken for a volume V of solution no subscript or solvent subscript o to flow between the marks I u I L6 I I I I Relatlve Vlsc03ty as a Function of Concentration 39 39 14 39 39 A power series similar to that used in the treatment of HM 39 39 osmotic pressure and light scattering data 39 is commonly used to fit relative Viscosity data 1392 11m lo 1H nckc 2 10 Both 1 and k are constants 39 I I I 39 lled the intrinsic viscosit 0 1 2 3 4 5 n ls ca y Concentration g 100 cc Plot of 11m versus c for PMMA in chloroform Plotted from the data of G V Schultz and F Blaschke If Viscosity measurements are confined to dilute solution so that we can neglect terms in a and higher 11 1 nn n0 n1kc The Specific Viscosity isde nedas nsp nrell Note also that as c goes to zero infinite dilution then the intercept on the yaXis of a plot of aspC against c is the intrinsic Viscosity n MEASURING THE INTRINSIC VISCOSITY In practice we use two semiempirical equations suggested by Huggins and Kraemer Tlsp v 2 c n1 k n c E c 11 TI 1 2 in n ku n c 8 o n s V V 3 to V lnnrel I ll c 0 0 hnml I I ll c 0 Concentration c gdl 025 Schematic diagram illustrating the effect of strong intermolecular interactions Concentration c g d1 025 Schematic diagram illustrating the graphical determination of the intrinsic viscosity THE MARKHOUWINKSAKURADA EQUATION The RelaTionship BeTween InTrinsic ViscosiTy and Molecular WeighT If The log of The inTrinsic viscosiTies of a range of sample is ploTTed againsT The log of Their molecular weighTs Then linear ploTs are obTained ThaT obey equaTion SchemaTic diagram of The DeTerminaTion of The MarkHouwinkSakurada consTanTs K and quotaquot V Monodisperse standards Ternp 10g Solvmt 3 PS 3 PMMA slope a 2 2 A Intercept log K Log 11 10 M 1 1 o 0 4 5 e 7 4 5 e 7 NoTe ThaT K and IIaII are noT universal consTanTs Log Molecular Weight buT vary wiTh The naTure of The polymer PloTs of The log h versus log M for PS and PMMA The solvenT and The TemperaTure ReploTTed from The daTa of Z Grubisic P Rempp and H Ben THE VISCOSITY AVERAGE MOLECULAR WEIGHT For Osmotic Pressure and Light Scattering we saw that there is a clear relationship between experimental measurement and the number and weight molecular weight average respectively Viscosity measurements are related to molecular weight by a semiempirical relationship and a new average the Viscosity Average for polydisperse polymer samples is defined In very dilute solutions nsp nsp TISP a a p 1 Now C 1KM 1 Hence nspK ZMici And 11 C If i By substitution and rearranging we obtain Note that the Viscosity Molecular Weight is Not an Absolute Measure as it is a function of the solvent through the MarkHouwink parameter quotaquot SIZE EXCLUSION OR GEL PERMEATION CHROMATOGRAPHY Schematic diagram depicting the separation of Schematic diagram of an SEC instrument molecules of differem size by SEC Small Lar e Solvent Reserv01r Permeating Exc uded Molecules Molecules D Injection Port Void Volume O Mixing Valve SEC Columns Bulk Pump Detectors Movement of Solvent For a given volume of solvent flow molecules of different size travel different pathlengths within the columnThe smaller ones travel greater distances than the larger molecules due to permeation into the molecular mazeHence the large molecules are eluted first from the column followed by smaller and smaller molecules THE CALCULATION OF MOLECULAR WEIGHT BY SEC The Simplest Case where Monodispersed Standards of the Polymer are Availab Intensity L og Molecular Weight Polydisperse V Permeation l Total Selective Permeation l Elution Volume Schematic diagram depicting the calibration of an SEC instrument Area normalized Elution Volum e V Log Molecular Weight M HOW DOES SEC SEPARATE MOLECULES Benoit and his coworkers recognized that SEC separates not on the basis of molecular weight but rather on the basis of hydrodynamic volume of the polymer molecule in solution Same solvent Same temperature Calibration Curves for Linear PolyB Star shaped PolyA gt Linear PolyA gt Elution Volume a If we model The properTies of The polymer c in Terms of an equivalenT hydrodynamic sphere Then The inTrinsic viscosiTy n is relaTed To The hydrodynamic volumth via The equaTion39 25 A V n T A is Avogadro39s number and M is The molecular weighT The Universal CalibraTion Curve 10 IDDDIOIOE BenoiT and his coworkers recognized ThaT The producT of inTrinsic viscosiTy and molecular weighT was direchy proporTional To hydrodynamic volume linear polystyrene linear PMIVIA linear PVC polystyrene combs polystyrene stars PSPMlA graft copolymers comb PSPMMA heterograft copolymers Polyphenyl siloxane ladder polymers PSPMMA statistical copolymers 18 20 22 24 26 28 30 Elution Volume A universal calibraTion ploT of log 11M vs eluTion volume for various polymers Redrawn from The daTa of Z Grubisic P Rempp and H BenoiT

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