Part III: Polymer Characterization - Chapter 6: Characterization of Molecular Weight - Chapter 7: Polymer Solubility and Solution - Chapter 8: Phase Transition in Polymer

Chapter 6: Characterization of Molecular Weight Average molecular weight – : number-average molecular weight – : weight- average molecular weight –x n : no. avg. degree of polymerization –x w : wt. avg. degree of polymerization –M o : Mw of monomer (or repeating unit) –PI, MWD: polydispersity index =

M w, M n calculations M n = first moment =  C(M)M dM  C(M) dM M w = 2 nd moment =  C(M)M 2 dM  C(M)M dM

Definition of M w, M n In integral form In discrete summation form

Ex1. Measurements on two monodisperse fractions of a linear polymer, A and B, yield molecular weights of and , respectively. Mixture 1 is prepared from one part by weight of A and two parts by weight of B. Mixture 2 contains two parts by weight of A and one of B. Determine the weight- and number-average molecular weights of mixtures 1 and 2

Solution. For mixture 1 For mixture 2

Ex2. Two polydisperse samples are mixed in equal weights. Sample A has M n = and M w = Sample B has M n = and M w = What are M n and M w of the mixture ? Solution. First, let’s derive general expressions for calculating the averages of mixtures: Where the subscript i refers to various polydisperse components of the mixture.Now, for a given component,

Where ( ) is the weight fraction of component i in the mixture. In this case, Let W A =1 g and W B = 1 g. Then Note that even though the polydispersity index of each component of the mixture is 2.0, the PI of the mixture is greater, 2.25.

Determination of average molecular weight 2 catagories (a) Absolute methods: (b) Relative methods: -Measured quantities are theoretically related to MW -Measured quantities are related to MW -but need calibration with one of the absolute methods Ex. Endgroup analysis (Mn) Colligative property measurement (Mn) Light scattering (Mw) Ultracentrifuge (Mw) Ex. Solution viscosity (Mv) Size-Exclusion Chromatography (MWD)

(a) Absolute methods: -Measured quantities are theoretically related to MW A1. Endgroup analysis (Mn) A2. Colligative property measurement (Mn) A3. Light scattering (Mw) A.4 Ultracentrifuge (Mw)

(b) Relative methods: -Measured quantities are related to MW -but need calibration with one of the absolute methods Ex.1 Solution viscosity (M v ) Ex.2 Size-Exclusion Chromatography (MWD)

Solution viscosity (M v ) Vis=a+bt t = travel time a,b = constants

 r = relative viscosity  SP =  -  S =  - 1 =  r – 1  S  S Solution viscosity  =  (  S, T, polymer conc., no. of entanglements, M ) - measure using Ostwald type Viscometer Ublelohde type Definition :  = solution viscosity  s = solvent viscosity Specific viscosity  SP

Get quantitative MW show effect of [  ] = lim (  /  S ) – 1 ขึ้นกับ coil dimension Single polymer c  0 C coil to viscosity = lim  red c  0 Reduced viscosity (normalized for conc.) C  red =  SP = (  /  S ) – 1 get rid of entanglement effect by reducing viscosity to zero conc. Intrinsic viscosity [  ]  M W of polymer in sol n  polymer – solvent system fix solvent, temp.  temp.

Huggin’s equation for  r < 2 or (  solution < 2  solvent )  red = = [  ] + k′[  ] 2 c (Huggin’s equation) where k′ is ~ 0.4 ( for a variety of polymer – solvent system) Advantage if [  ] is known  can obtain relationship of  red and conc. Equivalent form of Huggin’s equation  inh = = [  ] + k” [  ] 2 c where  inh = inherent viscosity k” = k’ – 0.5

Ref: S.L. Rosen,JohnWiley & Sons 1993 Vis conc

(alternative definition of intrinsic viscosity) [  ] = Relationship of [  ] vs. M [for monodisperse sample of a certain MW] เรียกว่า Mark-Houwink-Sakurada (MHS) relation [  ] x = K(M x ) a (0.5<a<1) K, a  Look up inpolymer handbook at a specific temp. โดย 0.5 < a < 1, M n << M v < M w

Ref: S.L. Rosen,JohnWiley & Sons 1993 [  ] x = K(M x ) a

Ex. M v (viscosity average molecular weight) Example 1: PMMA, calculate M v for mixture 1 and 2 in acetone at 30 o C and compare with M n and M w (From experiment: a = 0.72) Mixture 1: Mixture 2:

Ex1. Measurements on two monodisperse fractions of a linear polymer, A and B, yield molecular weights of and , respectively. Mixture 1 is prepared from one part by weight of A and two parts by weight of B. Mixture 2 contains two parts by weight of A and one of B. Example 1: PMMA, calculate Mv for mixture 1 and 2 in acetone at 30 oC and compare with Mn and Mw (From experiment: a = 0.72)

Solution viscosity terminology Ref: S.L. Rosen,JohnWiley & Sons 1993

Size-Exclusion Chromatography (MWD) (or Gel Permeation Chomatography (GPC)) - หา Molecular weight + MWD รวดเร็ว “gel” – a cross linked polymer that is swollen by solvent Porous particle (gel) Last but Not Least!

Unimodal = 1 peak Bimodal =2 peak

big molecule smallest come out last “column” large molecules come out first small molecule large moleculessmall molecules come out firstcome out last (go through interstices of the substrate pores) Most common detector : differential refractometer (measure refractive index difference)

Ref: S.L. Rosen,JohnWiley & Sons 1993