2008 Sep. 19, 2008 Molecular Weight & Polymer Solutions Chemical and Bioengineering Konkuk University Number average and weight a verage moleculart weight (monodisperse):monodisperse): all polymer molecules (monodisperse):polydisperse):
Polydisperse - a polymer that exists over a wide range o f molecular masses Characteristic of man-made polymers. ; poor mechanical property ; too tough to process ; 105~106 for vinyl polymer 15,000~20,000 for polar functional group containing polymer (polyamide) (Methods to determine molecular weight)
a. Absolute method : mass spectrometry, colligative property end group analysis, light scattering, ultracentrifugation b. Relative method : solution viscosity c. Fractionation method : GPC Polymer mass 3-1-1. A. number average molecular weight ( ) (monodisperse):colligative property and end group anaylsis)
B. weight average molecular weight ( ) (monodisperse):light scattering) C. z average molecular weight ( ) (monodisperse):ultracentrifugation) D. general equation of average molecular weight : (monodisperse): a=0 , E.
> > a=1 , a=2 , ) 3-1-2. Property of weight and polymer Molecular
molecular weight determines the property: the attractive force between molec ular change identity chemical structure : chain length, surface, attractive force rise molecular weight increase polymer property increase Threshold molecular weight: the increase rate slow , differ depend on the p olymer type(structure) Polyethylene(nonpolar polymer): low attractive force, high threshold Polyamide (H-bond polymer): high attractive force, low threshold The effect of the average molecular weight the concentration solution viscosity Over the critical molecular weight suddenly rise Entanglement molecular weight: Because of the bridging
phenomenon, the viscosity suddenly rise olydispersity index (PDI) Measure of the distribution of molecular mass in a given polymer sample. The PDI calculated is the weight average molecular weight divided by the number average molecular weight. The PDI has a value always greater than 1, But as the polymer chains approach uniform chain length, the PDI approaches unity (1). D. Polydispersity index : width of distribution polydispersity index (PI) =
/ 1 E. Example of molecular weight calculation a. 9 moles, molecular weight ( 5 moles, molecular weight ( ) = 30,000 ) = 50,000 b. 9 grams, molecular weight ( 5 grams, molecular weight (
) = 30,000 ) = 50,000 3-1-2. Polymer solution A. Two-step process of polymer dissolution first step : the solvent diffuses into polymer masses to make a swollen polymer gel second step : swollen polymer gel breaks up to solution B. Thermodynamics of solubility : Gibb's free energy relationship G < 0 : spontaneously dissolve G < 0 : spontaneously dissolve T and G < 0 : spontaneously dissolve S are always positive for dissolving process Conditions to be negative G < 0 : spontaneously dissolve G,
G < 0 : spontaneously dissolve H must be negative or smaller than TG < 0 : spontaneously dissolve S C. Solubility parameter : 1, 2 = volume fraction G < 0 : spontaneously dissolve E1/V1, G < 0 : spontaneously dissolve E2/V2 = cohesive energy densities ( ) 1, 2 = solubility parameter if , then D. Small's and Hoy's G parameter a. Small(monodisperse):designated G derived from Heat of vaporization)
(d: density, M: molecular weight of unit) ex) polystyrene : b. Hoy(monodisperse):designated G based on vapor pressure measurement) ex) polystyrene : Group molar attraction constants E. Hydrodynamic volume of polymer molecules in solution a. polymer-polymer interaction b. solvent-solvent interaction c. polymer-solvent interaction d. polymer structure (branched or not)
e. brownian motion r = end-to-end distance s = radius of gyration Figure. Coil molecular shape 3-2. Number Average Weight- Measurement Molecular
3-2-1. End-group Analysis A. Molecular weight limitation up to 50,000 B. End-group must have detectable species a. vinyl polymer : -CH=CH2 b. ester polymer : -COOH, -OH c. amide and urethane polymer : -NH2, -NCO d. radioactive isotopes or UV, IR, NMR detectable functional group e. MW of linear polymer C. n / end-group moles per 1 g (n=number of end-group) COOH: end point OH: acetylation
D. Requirement for end group analysis 1. The method cannot be applied to branched polymers 2. In a linear polymer there are twice as many end of the chain and groups as poly mer molecules 3. If having different end group, the number of detected end group is average MW 4. End group analysis could be applied for polymerization mechanism identified E. High solution viscosity, low solubility, steric hindrance : Mn = 5,000 ~ 10,000 Ex. A 0.5 g sample of an unsaturated polyester resin was reacted with exces s acetic anhydride. Titration of the reaction mixture with 0.0102 M KOH requir ed 8.17 ml to reach the end point. What is the number average molecular wei ght?
polyester 0.5 g acetic anhydride , 0.0102 M K OH 8.17 ml KOH . Polyester ? Ex. What is the DP of a sample of polyester prepared from 4-hydroxybenzoic aci d if the acid number, determined with standard KOH solution, is 11.2? (monodisperse):CH4O2) , carboxyl polymer , KOH acid number 11 DP ? (Acid number: mg KOH/g polymer) KOH: 56.1g/mol 3-2-2. The measure of colligative property (colligative property) Colligative properties are properties of solutions that depend on the
number of particles in a given volume of solvent and not on the mass o f the particles. the freezing point depression, the boiling point elevation, the st eam pressure depression, the osmotic pressure The mole number of polymer average molecular weight This equation show that the concentration equation of solvent was t he chemcal potential difference between the solution of solvent and pure solvent (monodisperse):1) Boiling-point elevation (monodisperse):Ebulliometry) A2 : second virial coefficient
: boiling point elevation : the latent heats of vaporization C : the concentration in grams per cubic centimeter R : gas constant limitation of : below 30,000 (monodisperse):2) Freezing-point depression (monodisperse):Cryoscopy) : freezing-point depression, T : freezing point : the latent heats of fusion (monodisperse):3) (monodisperse):Membrane Osmometry)
According to van't Hoff equation (monodisperse):cm) g h limitation of : 50,000~2,000,000 The major error arises from low-MW species diffusing through the membrane. i. Static Osmometer ii. Dynamic Osmometer
(monodisperse):4) (monodisperse):Vapor Pressure Osmometry) Raoult : The equilibrium state: Solvent pressure of both sides equal, the Temperature differ Gap of temperature The steam pressure drop :
Raoult : Raoults law: the vapor press ure of an ideal solution is dep endent on the vapor pressure of each chemical component and the mole fraction of the c omponent present in the solu tion Vapor Pressure Osmometry The measuring vapor pressure difference of solvent and solution drops.
: the heat of vaporization per gram of solvent m : molality limitation of : below 30,000 Calibration curve is needed to obtain MW of polymer sample Standard material : Benzil Mw 30,000 over: the separation osmotic pressure method Mw 30,000 under: steam osmotic pressure method The average
molecular weight (monodisperse):5) Mass Spectrometry A. Conventional mass spectrometer for low molecular-weight compound energy of electron beam : 8 -13 electron volts(eV) The each polymers molecu lar ionization the condensation phase -> gas phase tranformation TOF (time-of-flight) MS: t he molecular ion mass mea sure
TOF (time-of-flight) MS B. Modified mass spectrometer for synthetic polymer a. matrix-assisted laser desorption ionization mass spectrometry (MALDI-MS) b. matrix-assisted laser desorption ionization time-of-flight (MALDI-TOF) c. soft ionization sampling: polymers are imbedded by UV laser absorbable organic compound containing Na and K. d.
, are calculated by using mass spectra. e. The price of this mass is much more than conventional mass. f. Up to = 400,000 for monodisperse polymers. MS Analysis of p-Aminobenzyl Amine Conversion Product CH2 NH2
NO2 CH2NH2 NH2 PrnD CH2NH2 CH2NO2 NO2
NH2 2D SDS-PAGE and MALDI-TOF Mass Analysis Peptides identical to PrnD MALDI-TOF MS Spot expected to be PrnD MS fingerprinting MS sequencing 1. 1329.656: QPTLVTAER
2. 1710.910: AFYRGWVDRVASER 3. 2021.235: AVVMDRHCSHLGANLAD 2 1 3 pQE 80L-PrnD is expressed in E. coli MALDI-TOF Mass Analysis
Poly(monodisperse):methyl methacrylate): 6,400 3-3. Measurement of Weight Average Molecular Weight 3-3-1. Light Scattering A. The intensity of scattered light or turbidity() is dependon following factors) is depend on following factors a. size, b. concentration, c. polarizability, d. refractive index, e. angle f. solvent and solute interaction g. wavelength of the incident light : concentration : refractive index of the solvent : wavelength of the incident light
: Avogadro's number : specific refractive increment : function of the angle, Zimm plot(after Bruno Zimm): double extrapolation of conc. and angle to zero B. Light source High pressure mercury lamp and laser light C. Limitation of molecular weight( ) : 104~107 The light scattering of the particle (a) When the scattering particle was small
(a) When the scattering particle was large 3-3-2. Ultracentrifugation A. This technique is used a. for protein ( ) rather than synthetic polymers b. for determination of synthetic polymers B. Principles: under the centrifugal field, size of molecules are distributed perpendicularly axis of rotation Distribution process: sedimentation : ,
Sedimentation( ): proportion of molecular weight , 3-4. Viscosity: the method of relative molecular weight from the assumption of the molecular size 1) 5% polymer solution: too sticky to flow low molecular weight solution: easy flow 2) Viscosity: resistance of flow long chain molecule: large friction 3-4-1. Viscosity & Molecular weight IUPAC suggested the terminology of solution viscosities as following.
Relative viscosity : : solution viscosity : solvent viscosity : flow time of solution : flow time of solvent Specific viscosity : Reduced viscosity : Inherent viscosity : Intrinsic viscosity : 3-4. 3-4-2. :
Mark-Houwink-Sakurada (monodisperse):MHS) equation (monodisperse):K, a : viscosity-Molecular weight constant) Condition: Unperturbed state a = 0.5 is closer to than 3-5. Measuring Molecular Weight Distribution 3-5-1. Fractionation of Molecular weight Fractional Solution Soxhlet-type extraction by using mixed solvent Reverse GPC: from low MW fraction to high MW fraction
Inert beads are coated by polymer sample Fractional Precipitation Dilute polymer solution is precipitated by variable non-solvent mixture Precipitate is decanted or filtered Reverse fractional solution: from high MW fraction to low MW fraction Thin-layer Chromatography (monodisperse):TLC) Alumina- or silica gel coated plate Low cost and simplicity Preliminary screening or monitoring polymerization processes 3-5-2. Gel Permeation Chromatography(monodisperse):GPC) A. GPC or SEC (monodisperse):size exclusion chromatography) a. GPC method is a modified column chromatography b. Packing material: Poly(monodisperse):styrene-co-divinylbezene), glass or silica bead
swollen and porous surface c. Detector: RI, UV, IR detector, light scattering detector d. Pumping and fraction collector system for elution e. By using standard (monodisperse):monodisperse polystyrene), we can obtain , Schematic diagram of GPC separation Schematic representaion of a GPC system
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