Molecular Weight & Polymer Solutions

Chemical and BioengineeringKonkuk University

Sep. 19, 20080820

몇몇 천연 고분자 (monodisperse): all polymer molecules  같은 분자량

합성 고분자 (polydisperse): • Polydisperse - a polymer that exists over a wide range of molecular mass

es

•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)

Number average and weight average moleculart weight

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

 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 ,      )

3-1-1. 평균 분자량

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 risemolecular weight increase polymer property increaseThreshold molecular weight: the increase rate slow , differ depend on the p

olymer type(structure) Polyethylene(nonpolar polymer): low attractive force, high thresholdPolyamide (H-bond polymer): high attractive force, low threshold

 The effect of the average molecular weightthe concentration solution viscosityOver the critical molecular weight suddenly riseEntanglement molecular weight: Because of the bridging

phenomenon, the viscosity suddenly rise

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).                  

Polydispersity index (PDI)

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

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

3-1-2. Polymer solution

 C.  Solubility parameter : δ

                                                               

  ψ1, ψ2 = volume fraction

  ΔE1/V1, ΔE2/V2 = cohesive energy densities ( 응집 에너지 밀도 )

  δ1, δ2 = solubility parameter

                              

                                            

                               

                                       

 if          , then          

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)

Group molar attraction constants

 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

E. Hydrodynamic volume of polymer molecules in solution

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.                                    

3-2. Number Average Molecular Weight- Measurement

n / end-group moles per 1 g (n=number of end-group)

3-2-1. End-group Analysis

COOH: 염기로 페놀프탈레인 end point 까지 적정OH: acetylation 후 적정

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

D. Requirement for end group analysis

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 g 이 과량의 acetic anhydride 와 반응 시킨 후 , 반응

혼합물을 0.0102 M KOH 로 적정하니 8.17 ml 의 KOH 가 소모됨 . Polyester 의

수평균 분자량은 ?

(Acid number: mg KOH/g polymer)KOH: 56.1g/mol

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 polymer 의

경우 , 표준 KOH 용액으로 부터 조사된 acid number 가 11 이라면 이때의 DP는 ?

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

(1) Boiling-point elevation (Ebulliometry)                                                 

A2 : second virial coefficient                  : boiling point elevation                  : the latent heats of vaporization

limitation of     : below 30,000

수평균 분자량 측정

 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         

(3) 분리막 삼투압법 (Membrane Osmometry)

According to van't Hoff equation

limitation of     : 50,000~2,000,000

The major error arises from low-MW species diffusing through the membrane.

g h

용매와 용액의 높이차 (cm)

i. Static Osmometer

ii. Dynamic Osmometer

(4) 증기상 삼투압법 (Vapor Pressure Osmometry)

Raoult 의 법칙 : 이상용액에서 각 성분의 분압은 몰분율에 비례

평형상태 : 양쪽 방울 용매 증기압 동일온도 상이 온도차 증기압 강하 정도

Raoult 의 법칙 : 이상용액에서 각 성분의 분압은 몰분율에 비례Raoult’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

The equilibrium state: Solvent pressure of both sides equal, the Temperature differ

Gap of temperature The steam pressure drop

  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

Vapor Pressure Osmometry

Mw 30,000 over: the separation osmotic pressure method Mw 30,000 under: steam osmotic pressure method

The average molecular weight

A. Conventional mass spectrometer for low molecular-weight compound  energy of electron beam : 8 -13 electron volts(eV)

(5) Mass Spectrometry

개개의 고분자 분자를 이온화 응축상에서 기체상으로 변환 TOF (time-of-flight) MS 에서 분자이온질량 측정

The each polymer’s molecular ionization the condensation phase-> gas phase tranformation TOF (time-of-flight) MS: the molecular ion mass measure

  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.

B. Modified mass spectrometer for synthetic polymer

MS Analysis of p-Aminobenzyl Amine Conversion Product

PrnD

CH2

NO2

NH2

CH2NH2

NH2

CH2NH2

NO2

CH2NO2

NH2

2D SDS-PAGE and MALDI-TOF Mass Analysis

Spot expected to be PrnD

MALDI-TOF MS• MS fingerprinting• MS sequencing

Peptides identical to PrnD

pQE 80L-PrnD is expressed in E. coli

1

2

3

1. 1329.656: QPTLVTAER

2. 1710.910: AFYRGWVDRVASER

3. 2021.235: AVVMDRHCSHLGANLAD

MALDI-TOF Mass Analysis

Poly(methyl methacrylate): 수평균 분자량 6,400

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

3-3. Measurement of Weight Average Molecular Weight

3-3-1. Light Scattering

B. Light source  High pressure mercury lamp and laser light

C. Limitation of molecular weight(     ) : 104~107

(a) When the scattering particle was small

(a) When the scattering particle was large

The light scattering of the particle

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 비례침강평형방법 , 침강속도방법

3-3-2. Ultracentrifugation

Sedimentation( 침강 속도 ): proportion of molecular weight침강평형방법 , 침강속도방법

1) 5% polymer solution: too sticky  to flow   low molecular weight solution: easy flow2) Viscosity: resistance of flow        long chain molecule: large friction

3-4. Viscosity: the method of relative molecular weight from the assumption of the molecular

size

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 :

3-4-1. Viscosity & Molecular weight

3-4. 점도법

3-4-2. 점도평균 분자량 :

상대적 분자량

Condition: Unperturbed statea = 0.5

Mark-Houwink-Sakurada (MHS) equation                    

                            (K, a : viscosity-Molecular weight constant)                              

         is closer to      than    

3-5. Measuring Molecular Weight Distribution

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

3-5-1. Fractionation of Molecular weight

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    ,     

3-5-2. Gel Permeation Chromatography(GPC)

Schematic representaion of a GPC systemSchematic diagram of GPC separation