CHARACTERIZATION OF BRANCHED POLYMERS IN SOLUTION (I)

Transcription

1 CHARACTERIZATION OF BRANCHED POLYMERS IN SOLUTION (I) Overview: General Properties of Macromolecules in Solution Molar Mass Dependencies Molar Mass Distributions Generalized Ratios Albena Lederer Leibniz-Institute of Polymer Research Dresden Member of Gottfried Wilhelm Leibniz Society WGL Hohe Strasse 6, D Dresden, Germany

2 General solution properties of polymers Experimental techniques Global parameters give insight in the topological and not in the internal structure Molar mass M w SLS Radius of gyration R g [<S 2 > z ] 1/2 Second virial coefficient A 2 DLS Translation diffusion coefficient D z Viscometry Instrinsic viscosity [η]

3 General solution properties of polymers Static Light Scattering R θ is normalized scattering intensity Scattering vector Contrast constant (for solution) (in SAXS depends on e - density in SANS depends on scattering lenght) R g [<S 2 > z ] 1/2 average over all possible conformations! z-average over the molar mass!

4 General solution properties of polymers Dynamic Light Scattering Brownian diffusion for flexible chain segments (Gaussian statistics) C depends on the internal flexibility: C = 0 hard spheres C = 0.2 for linear flexible chains 0 < C < 0.2 for branching and cyclisation

5 General solution properties of polymers Dynamic Light Scattering Brownian diffusion compared to common diffusion (Stokes-Einstein) Stokes Einstein Stokes-Einstein R h is the actual sphere radius only for well defined sphere periphery R h average value over all conformations (z-average) R h is the 1 st moment of the size distribution R g is the 2 nd moment of the size distribution

6 General solution properties of polymers Intrinsic Viscosity Staudinger Index Kuhn-Mark-Howink-Sakurada Flory-Fox Φ for linear flexible chains approaches constant for M w > Φ depends on hydrodynamic interaction (interparticle distance, segmental concentration) (branched molecules have higher segmental density, and Φ increases)

7 General solution properties of polymers Intrinsic Viscosity Einstein equivalent sphere radius Φ describes how deeply a particle is drained by the solvent: - deeply drained flexible linear chains - reduces the hydrodynamically effective sphere radius - if shallow drained, R η >>R g

8 General solution properties of polymers Second virial coefficient A 2 A 2 describes interparticle thermodynamic interactions at c 0 Ψ is interpenetration function and describes segment-segment interaction In good solvents Ψ Ψ =const.(linear chains) Ψ increases for branching (higher segment density) 1/3 T Thermodynamically effective equivalent radius

9 General solution properties of polymers Comparison of different sphere radii Φ Ψ = 0,26 Similarities dependence on molar mass, different values for branched and linear polymers Differences depend on properties description: R g describes sphere geometry R T domains of interaction between two macromolecules excluded volume (thermodynamical) R η, R h domains of interaction of macromolecules with solvent molecules (hydrodynamical) (R η = R h + shear gradient field) Ratios - ρ = R g /R h V T = R T /R h A 2 M w /[η]

10 Molar mass dependencies Irregular stars Constant KMHS behavior in θ and in good solvents Flory (1948): polyamides from AB-type polycondensation with non-monodisperse arms behave like linear chains (Mw/Mn ~ 2) Mw/Mn reduces after coupling to f-functional core Flory et al 1948, J.Am. Soc.

11 Molar mass dependencies Regular stars Fetters and Roovers: living anionic polymerisation of styrene, isoprene, butadiene Similar behavior of the global parameters Roovers et al. Macromolecules, 1993 At f>8 constant radius, unperturbed statistics!

12 Molar mass dependencies Regular stars Fetters and Roovers: living anionic polymerisation of styrene, isoprene, butadiene Similar behaviour of the global parameters Depends on hydrodynamic interactions of the monomeric units for branching R g decreases, Φ increases Roovers et al. Macromolecules, 1993 Ψ* = const. for z>0,75: linear chains at DP>100, branched at DP<100. With branching A 2 decreases

13 Molar mass dependencies Randomly branched polymers Polyester R g M wν, ν < 0.5 but Α 2 > 0 pregel Good solvent behaviour postgel linear Burchard, Macromol. Symp. 1994

14 Molar mass dependencies Randomly branched polymers Random branching M w /M n DP w branched linear Weight averages of the molar mass Log R g (z) Broad size distribution Contraction due to branching Log M w Burchard, Macromol. Symp. 1994

15 Fractal dimensions Why a A2 changes from 0,2 for linear to 0,65 for randomly branched polymers? Hard sphere Flat discs Thin rods ν d f Linear chain coils in a good solvent Self-similarity: independent on the length scale, the same d f is obtained (b, l K ). If changes depend on molar mass no self similarity D object with local 1D thread - such disordered objects are fractals!

16 Fractal dimensions Molar mass dependence of A 2 Why a A2 changes from 0,2 for linear to 0,65 for randomly branched polymers? d f v -a A2 a η Freely swollen Poorly swollen If we have a polydisperse ensamble, ensamble fractal dimension τ = 2,2 to 2,5 or if M z is known direct determination of d f is possible.

17 Molar mass distributions Schulz-Zimm Distribution for linear chains Distribution of f chains coupled to each other independent on the way of coupling f=1 most probable distribution f>>1 Poisson distribution

18 Molar mass distributions Strong increase of polydispersity indices (x w /x n and x z /x w ) This distribution follows w(x) x 1-τ with τ=2.5 at the gel point: This is fulfilled if: -intermolecular reactions are excluded -excluded volumes are neglected -all functional groups have the same probability of reaction Stockmayer Distribution for randomly branched polymers Special case hyperbranched polymers AB x monomers -A can react only with B -the reaction is not clearly random

19 SEC-RI-MALLS-VISC c j (v e ) RI or UV detector c j M j (v e ) LS detector (θ = 0) R gj (v e ) c j [η] j (v e ) LS detector (θ dependent) VISC detector Quantities measured at the j-slice of the elution volume v e

20 SEC-RI-MALLS-VISC Molar mass dependence on R g or Practically monodisperse slices For self-similar molecules give us possibility to directly determine d f without using of d f,e Problem: different R g at large molar masses: -limited separation capability of the column or -different fractal behaviour for large particles (aggregates or non similar clusters)

21 SEC-RI-MALLS-VISC KMHS relationship fractionated non-fractionated Burchard, Acta Polym. 1997

22 SEC-RI-MALLS-VISC Zimm, Stockmayer calculation of branching quantitatively: Contraction factors Stockmayer, Fixman f - functionality of the branching units DP=x=(m.B), B is number of branches per molecule m is average number monomer units containing one branching point for stars monodisperse arms polydisperse arms

23 SEC-RI-MALLS-VISC Contraction factors Dependence between g and g from Flory-Fox-Eq. (Zimm and Stockmayer) if Φ * = 1, but for branched chains Φ factor can be different For star polymers (Zimm and Kilb) if calculated (Kurata et al.) for b=0.6 empirically

24 SEC-RI-MALLS-VISC Contraction factors Burchard, Adv. Polym. Sci. 143, 1998

25 SEC-RI-MALLS-VISC Comb macromolecules Calculation of contraction factor by using the behaviour of the non-attached side chains as a linear reference Burchard, Adv. Polym. Sci. 143, 1998

26 Generalized ratios R g / R h Possibility to detect branching without using of linear reference: since SLS and DLS are done simultaneously (e.g. for the same molecule) ρ linear = 1,504 in θ-solvent (Kirkwood-Riseman) ρ depends directly on the segment density C depends on internal flexibility C = 0 inflexible hard sphere C = 0.2 flexible chain Burchard, Adv. Polym. Sci. 143, 1998

27 Generalized ratios Comparison between ρ and C Burchard, Adv. Polym. Sci. 143, 1998

28 Generalized ratios A 2 M w / [η] - Compares volumes and not radii - Shows the change of the coil interpenetration function Φ relative to the draining function Ψ - V Α2η, linear = 1.07 V Α2η, sphere = 1.6 Galisnky, Burchard, Macromolecules 1996 Burchard, Adv. Polym. Sci 143, 1998

29 Generalized ratios A 2 M w / [η] random and hyperbranched polymers star polymers - Compares volumes and not radii - Shows the change of the coil interpenetration function Φ relative to the draining function Ψ -V Α2η, linear = 1.07 V Α2η, sphere = 1.6 -With branching Ψ increases (interpenetration inhibited) faster than Φ and V Α2η, increases Galisnky, Burchard, Macromolecules 1996 Burchard, Adv. Polym. Sci 143, 1998

30 Generalized ratios R T / R h - only some single experiments on this ratio - R T / R h was verified for star polymers with f = 32, 64 and 128 arms R T / R h = 1,18 for short arms 1,06 for long arms 1,0 for unreacted (linear) arms Weissmüller, PhD Thesis 1996