MOLAR MASS of POLYMERS

Transcription

1 MOLR MSS of POLYMERS Recogize the ifluece of molar mass (molecular weight) o polymer properties. Uderstad the relatioship betwee molecular weight ad degree of polymerizatio. Uderstad the sigificace of umber-average (M ) ad weight-average (M w ) molecular weights. Uderstad the ature of polydispersity. Recogize that the molecular weight of a polymer iflueces its physical properties. X: Degree of Polymerizatio The molecular weight (M) of a homopolymer is the sum of the masses of the repeat uits (M 0 ) i the polymer chai: M = XM 0 where X is the degree of polymerizatio, the umber of repeat uits i the chai. The molecular weight of a copolymer is based o a weighted average of the masses of all repeat uits (M i0, M j0 M k0, etc.) i the polymer chai: M 0 copoly = χ i M i0 + χ j M j0 + χ k M k0 + where χ i, χ j, χ k, etc. are the mole fractios of the repeat uits. Mol Wgt 2-1

2 Polymer Size ad Shape Most polymers are polydisperse they cotai more tha oe chai legth. The average distributio of chai masses ca be described i more tha oe way: M, the umber-average molecular weight M w, the weight-average molecular weight M z, the z-average molecular weight M v, the viscosity-average molecular weight M z M w M v > M Each value is determied by a aspect of polymer structure. Mass Distributio i Low-MW Polystyree = 110 = 120 Sigal Itesity = 100 H H C C H = 130 = M dapted from K. Rollis et al., 1990 Rapid Commu. Mass Spectrom., 4, Mol Wgt 2-2

3 M : Number-verage Mol. Wgt. The umber-average molecular weight (molar mass) of a polymer cotaiig N i molecules of mass M i is the arithmetic mea of the molar mass distributio: M = ΣN i M determies the polymer s colligative properties ad tesile stregth (= C 1 C 2 /M ). M may be determied directly by ed-group aalysis, osmometry, ebullioscopy (bp elevatio), ad cryoscopy (fp depressio). M w : Weight-verage Mol. Wgt. The weight-average molecular weight (molar mass) is the sum of the products of the molar mass of each fractio multiplied by its weight fractio (w i ). I terms of w i or umbers of molecules, M w is M w = Σw i M i 2 M w = M w accouts for the distributio of molar mass i the polymer. M w may be determied directly by light scatterig. Mol Wgt 2-3

4 Molecular Weight Distributio The molecular weight distributio, or polydispersity idex, is the ratio of the weight-average molecular weight to the umber-average molecular weight: M w PDI = M The polydispersity idex of a moodisperse polymer is The polydispersity idex icreases as the polymer distributio broades. Example You have a polymer sample that cotais the followig molecules: M, Da* N 1,000, , , , ,000 2 Total: 23 *Da = dalto, g/mol What are M, M w, ad the polydispersity idex? Mol Wgt 2-4

5 M = ΣN i 10,000,000 Da M = 23 M = 435,000 Da M w = Σw i M i N i M i w i = M w = 609,500 Da M, Da N N M, Da w w M, Da 1,000, ,000, , , ,500, , , ,000, , , , ,000 50, , Totals: 23 10,000, ,500 2 M w = M w PDI = M Da 2 M w = Da M w = 609,500 Da 609,500 Da PDI = 435,000 Da PDI = 1.40 M, Da N 1,000, , , , ,000 2 Totals: 23 N M, Da 2,000,000 3,500,000 4,000, , ,000 10,000,000 N M 2, Da Mol Wgt 2-5

6 M z : Z-verage Mol. Wgt. The z-average molecular weight (molar mass) is 3 M z = 2 M z is especially sesitive to the presece of high-mw chais. M z may be determied directly by sedimetatio equilibrium (ultracetrifugatio) ad light scatterig. M v : Viscosity-verage Mol. Wgt. The viscosity-average molecular weight (molar mass) is : (1+a) 1/a M v = where the expoet a (0.5 a 2.0) is determied by the polymer, solvet, ad temperature. For typical polymers, M w > M v > M. M w = M v whe a = 1. M v may be determied idirectly by dilute solutio viscometry. Mol Wgt 2-6

7 M = 195,322 M w = 220,715 M z = 259,299 PDI = 1.13 RI M = 181,986 M w = 260,091 M z = 417,392 PDI = log M Experimetal Methods Method Static light scatterig Dilute solutio viscometry Small agle X-ray scatterig Membrae osmometry Ebullioscopy, cryoscopy Ed group aalysis (titratio) Vapor phase osmometry Sedimetatio equilibrium Mass spectrometry Dyamic light scatterig Type* R M i w v w Rage, g/mol > 100 > 200 > 500 Size-exclusio chromatography R,w,z > 1,000 E R w,z,w,z z > 5,000 < 20,000 < 40,000 < 50,000 < 1,000,000 < 1,500,000 < 10,000,000 * = mass calculatio requires o assumptios about polymer structure, E = mass calculatio requires iformatio about polymer structure, R = mass calculatio requires iformatio about polymer structure ad polymer-solvet iteractios. dapted from H.-G. Elias, Itroductio to Polymer Sciece, 2 d Ed, 1997, p 31 Mol Wgt 2-7

8 Mass Distributio i a Step-Growth Polymer M w = 11,980 (115) M = 11,980 (114) PDI = 1.01 M z = 12,060 (116) Polystyree Oligomer Sigal Itesity H C H C H M dapted from K. Rollis et al., 1990 Rapid Commu. Mass Spectrom., 4, Mass Distributio i a Chai-Growth Polymer O O O O ( CH 2 ) 4 O C ( CH 2 ) 4 C O ( CH 2 ) 4 O C ( CH 2 ) 8 C O m Copolyester Sigal Itesity M = 3,940 PDI = 1.10 M w = 4,320 M z = 4, M dapted from M.S. Motaudo et al, 1998 Rapid Commu. Mass Spectrom., 12, Mol Wgt 2-8

9 Impact of MW o Physical Properties M : Brittleess (resi versus elastomer), stressstrai properties M w : Tesile stregth, hardess M z : Flex life, stiffess, melt viscosity M v : Solutio viscosity, extrudablility, moldig properties Mol Wgt 2-9