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Molecular Weight & Polymer Solutions

20. 08. Sep. 19, 2008. Molecular Weight & Polymer Solutions. Chemical and Bioengineering Konkuk University. Number average and weight average moleculart weight. 몇몇 천연 고분자 (monodisperse): all polymer molecules   같은 분자량 합성 고분자 (polydisperse):

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Molecular Weight & Polymer Solutions

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  1. 20 08 Sep. 19, 2008 Molecular Weight & Polymer Solutions Chemical and Bioengineering Konkuk University

  2. Number average and weight average moleculart weight • 몇몇 천연 고분자 (monodisperse): • all polymer molecules  같은 분자량 • 합성 고분자 (polydisperse): • Polydisperse - a polymer that exists over a wide range of molecular masses • Characteristic of man-made polymers. • 고분자의 기계적 성질에 대한 분자량의 영향 •     매우 작은 분자량 ; poor mechanical property • 매우 큰 분자량 ; too tough to process • 최적 분자량; 105~106 for vinyl polymer • 15,000~20,000 for polar functional group containing polymer (polyamide)

  3. 분자량 결정(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

  4. 3-1-1. 평균 분자량  A. number average molecular weight (    )  B. weight average molecular weight (     )  C. z average molecular weight (    )  D. general equation of average molecular weight : E.     >       >     (colligative property and  end group anaylsis) (light scattering) (ultracentrifugation) ( a=0 ,         a=1 ,          a=2 ,      )

  5. 3-1-2. Property of Molecular weight and polymer • molecular weight determines the property: the attractive force between molecular 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 polymer type(structure) • Polyethylene(nonpolar polymer): low attractive force, high threshold • Polyamide (H-bond polymer): high attractive force, low threshold

  6.  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

  7. Polydispersity 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).

  8. D. Polydispersity index :  width of distribution  polydispersity index (PI) =      /     ≥ 1 E. Example of molecular weight calculation  a. 9 moles, molecular weight (     ) = 30,000     5 moles, molecular weight (     ) = 50,000 b. 9 grams, molecular weight (   ) = 30,000     5 grams, molecular weight (     ) = 50,000

  9. 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   ΔG < 0 : spontaneously dissolve   T and ΔS are always positive for dissolving process   Conditions to be negative ΔG,   ΔH must be negative or smaller than TΔS

  10.  C.  Solubility parameter : δ   ψ1, ψ2 = volume fraction   ΔE1/V1, ΔE2/V2 = cohesive energy densities (응집 에너지 밀도)   δ1,δ2 = solubility parameter  if          , then          

  11. D. Small's and Hoy's G parameter a. Small(designated G derived from Heat of vaporization)   ex) polystyrene :                                       b. Hoy(designated G based on vapor pressure measurement) ex) polystyrene :                                                    (d: density, M:  molecular weight of unit)

  12. Group molar attraction constants

  13. 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  Figure. Coil molecular shape r = end-to-end distance s = radius of gyration

  14. 3-2. Number Average Molecular Weight- Measurement 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: 염기로 페놀프탈레인 end point 까지 적정 OH: acetylation 후 적정

  15. 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 polymer 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

  16. Ex. A 0.5 g sample of an unsaturated polyester resin was reacted with excess acetic anhydride. Titration of the reaction mixture with 0.0102 M KOH required 8.17 ml to reach the end point. What is the number average molecular weight? 불포화 polyester 0.5 g이 과량의 acetic anhydride와 반응 시킨 후, 반응 혼합물을 0.0102 M KOH로 적정하니 8.17 ml의 KOH가 소모됨. Polyester의 수평균 분자량은? Ex. What is the DP of a sample of polyester prepared from 4-hydroxybenzoic acid if the acid number, determined with standard KOH solution, is 11.2? 기본 단위가 (CH4O2)이고, 하나의 carboxyl 그룹을 말단기로 갖는 polymer의 경우, 표준 KOH 용액으로 부터 조사된 acid number가 11이라면 이때의 DP는? (Acid number: mg KOH/g polymer) KOH: 56.1g/mol

  17. 3-2-2. The measure of colligative property • 용액의 총괄적 성질 (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 of the particles. • the freezing point depression, the boiling point elevation, the steam pressure depression, the osmotic pressure •  The mole number of polymer  average molecular weight This equation show that the concentration equation of solvent was the chemcal potential difference between the solution of solvent and pure solvent

  18. 수평균 분자량 측정 (1) Boiling-point elevation (Ebulliometry) A2 : second virial coefficient                  : boiling point elevation                  : the latent heats of vaporization limitation of     : below 30,000  C :  the concentration in grams per cubic centimeter  R :  gas constant (2) Freezing-point depression (Cryoscopy) : freezing-point depression,              T : freezing point               : the latent heats of fusion

  19. (3) 분리막 삼투압법 (Membrane Osmometry) According to van't Hoff equation 용매와 용액의 높이차 (cm) p = r gh 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

  20. (4) 증기상 삼투압법 (Vapor Pressure Osmometry) • Raoult의 법칙: 이상용액에서 각 성분의 분압은 몰분율에 비례 The equilibrium state: Solvent pressure of both sides equal, the Temperature differ  Gap of temperature  The steam pressure drop 평형상태: 양쪽 방울 용매 증기압 동일 온도 상이  온도차  증기압 강하 정도 • Raoult의 법칙: 이상용액에서 각 성분의 분압은 몰분율에 비례 • Raoult’s law: the vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in the solution

  21. Vapor Pressure Osmometry   The measuring vapor pressure difference of solvent and solution drops.                        λ : 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

  22. (5) Mass Spectrometry A. Conventional mass spectrometer for low molecular-weight compound   energy of electron beam : 8 -13 electron volts(eV) • The each polymer’s molecular ionization • the condensation phase-> gas phase tranformation • TOF (time-of-flight)MS: the molecular ion mass measure • 개개의 고분자 분자를 이온화 • 응축상에서 기체상으로 변환 • TOF (time-of-flight)MS에서 분자이온질량 측정

  23. 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.

  24. MS Analysis of p-Aminobenzyl Amine Conversion Product PrnD

  25. 2D SDS-PAGE and MALDI-TOF Mass Analysis Peptides identical to PrnD • MALDI-TOF MS • MS fingerprinting • MS sequencing 1.1329.656: QPTLVTAER 2.1710.910: AFYRGWVDRVASER 3.2021.235: AVVMDRHCSHLGANLAD Spot expected to be PrnD 2 3 1 • pQE 80L-PrnD is expressed in E. coli

  26. MALDI-TOF Mass Analysis Poly(methyl methacrylate): 수평균 분자량 6,400

  27. 3-3. Measurement of Weight Average Molecular Weight 3-3-1. Light Scattering A. The intensity of scattered light or turbidity(τ) 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        λ : wavelength of the incident light          : Avogadro's number            : specific refractive increment            : function of the angle,θ 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

  28. The light scattering of the particle • When the scattering particle was small • When the scattering particle was large

  29. 3-3-2. Ultracentrifugation A. This technique is used  a. for protein (생체 고분자) rather than synthetic polymers  b. for determination of synthetic polymer’s B. Principles: under the centrifugal field, size of molecules are  distributed perpendicularly axis of rotation  Distribution process: sedimentation 침강 속도: 분자량에 비례 침강평형방법, 침강속도방법 Sedimentation(침강 속도): proportion of molecular weight 침강평형방법, 침강속도방법

  30. 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

  31. 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 :                                         Intrinsic viscosity :  Reduced viscosity : Inherent viscosity :

  32. 3-4. 점도법 3-4-2. 점도평균 분자량: 상대적 분자량 Mark-Houwink-Sakurada (MHS) equation                             (K, a : viscosity-Molecular weight constant)          is closer to      than     • Condition: Unperturbed state a = 0.5

  33. 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 (TLC) •  Alumina- or silica gel coated plate •  Low cost and simplicity •  Preliminary screening or monitoring polymerization processes

  34. 3-5-2. Gel Permeation Chromatography(GPC) A. GPC or SEC (size exclusion chromatography)  a. GPC method is a modified column chromatography  b. Packing material: Poly(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 polystyrene), we can obtain    ,     

  35. Schematic diagram of GPC separation Schematic representaion of a GPC system

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