9. Nichtlineare Polymere: Verzweigungen und Vernetzungen

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Steffen Kranz
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1 9. ichtlineare Polymere: Verzweigungen und Vernetzungen

2 Branching architectures Topologies linear hyperbranched polymers stars dendrimers short chain branching (SCB) comb polymers (e.g. long chain branching, LCB) networks e.g., microgels

3 Branched vs. Linear Properties linear polymers branched polymers cristallinity molar mass distribution viscosity amorphous coils or ordered chains does not change with the molar mass (free radical polymerisation or linear polycondensation) high viscosity low crystallization increases with molar mass low viscosity functionallity lower with the molar mass higher with the molar mass

4 Branched architectures Synthetic ways vs. MMD Free radical polymerisation and polycondensation high molar mass distributions (MMD,M w / M n ) long and short chain branching in polyolefins (electron beam irradiation, chain-walking, metalocen catalysis);graft copolymers (star, comb) (if controlled lower MMD) M w / M n M w ( for linear polymers M w / M n = acc. Schulz-Flory Distribution) Living polymerisation low molar mass distributions Stars, comb polymers (for linear even M w / M n 1 + M 0 / M n ) ne-pot polycondensation high MMD hyperbranched polymers (AB or A +B 3 ) with M w / M n M w 1/ Multistepp polycondensation no MMD dendrimers with M w / M n = 1

5 Branched architectures Characterization methods In solution Light Scattering (R g, R h, A,M w ), Size Exclusion Chromatography (M w, M n ), Viscosity ([h]) Informations about: Contraction factors: g = R g, branched / R g, linear (linear and branched polymers of g = [h] branched / [h] linear the same chemical character) Controlled by molecular architecture, excluded volume, intermolecular hydrodynamic interactions Molar mass dependencies, i.e. Conformation, Shape, Scaling parameters In Bulk rheological characterization scillatory Shear Flow, Uniaxial Elongation Flow Information about entangled dynamics and melt flow. Identification of branches is very sensitive but only qualitative. Spectroscopy MR, FTIR Information about branching frequency in SCB polymers and degree of branching in hyperbranched polymers. Simulation umerical simulations: Monte Carlo, Molecular dynamics, Brownian dynamics Information about equilibrium and dynamic behaviour and rheological and hydrodynamical properties of simple polymer systems.

6 Branching topology Regularly branched star polymers f = functionality of the core = branching parameter f=3 f=4 linear chain with m units f=6 - Global parameters of non linear polymer - Internal structure can be easilly characterized by spectroscopy (comprable to linear structures)

7 Branching topology Regular comb polymers m f = number of side chains n short side chains (like substituted linear chain) short backbone (like star polymer)

8 Branching topology Dendrimers f = functionality of the branching unit g1 g g 3 g 4 g 1 g

9 Branching degree Long chain branching Branching ratio Radius Method or Viscosity Method (contraction factor) R g, branched g Rg, linear atthesamem g' [ h] [ h] branched linear atthesamem 1.0 where 0 g 1 Influence of b on g Branching ratio Mass Method M g M linear branched ( a1) b at the samev g = (M linear /M branched ) (a+1)/b a = 0,7, b= 0,5 a = 0,7, b= 1 a = 0,7, b= 1, where b is a drainage parameter with values between M linear /M branched 0,5 and 1,5

10 Branching degree Long chain branching Determination of g for randomly branched polymers (Zimm and Stockmayer, 1949) Trifunctional branching Polydisperse g 3 1/ 1/ 1/ 6 1 B ( B) B ln 1 1/ 1/ B B ( B) B Monodisperse g 3 1 B 7 1/ 4B 9 1/ Tetrafunctional branching Polydisperse g 4 ln(1 B B) Branching per molecule, B Monodisperse g 4 1 B 6 1/ 4B 3 1/

11 Branching degree Branching per molecule, B Long chain branching Influence of B on g branching ratio, g 1,0 0,8 0,6 0,4 0, 4-functional polydisperse 4-functional monodisperse 3-functional monodisperse 3-functional polydisperse Long chain branching per 1000 repeat units M 1000B 0 M repeat unit molar mass 0,0 0,01 0, branching per molecule B molar mass of a branched polymer

$degree of branching via 1 H-MR: T+L DB Fréchet = DB Frey = T+L+D Aryl -H 1D T D L 1L 1T D D+L DB Fréchet suitable for higher molar masses DB Frey also for oligomers 1 H MR signals fraction DB Fréchet$

12 Degree of branching For AB polycondensation D=dendritic units, two B functionalities reacted L=linear units, one B functionality reacted T=terminal units, no B functionality reacted Determination of degree of branching via 1 H-MR: T+L DB Fréchet = DB Frey = T+L+D Aryl -H 1D T D L 1L 1T D D+L DB Fréchet suitable for higher molar masses DB Frey also for oligomers 1 H MR signals fraction DB Fréchet DB Frey H F6 0,54 0,45 F9 0,54 0,47 F11 0,55 0,51 F13 0,56 0,5 F15 0,56 0,5 H H H H H H H H H H H Hyperbranched polymers H H H H H H H H H D H H H H H H L H H H H H H H = n,hb H H H T H H H hyperbranched poly(etheramide) -H DLT ( ppm ) F6 0,56 0,48 F9 0,57 0,50 F11 0,57 0,53 F13 0,56 0,53 F15 0,56 0,54 FB Branching fraction D D L 1 DB

Polymernetzwerke kovalente Vernetzung interpenetrierendes etzwerk physikalische Vernetzung Spezifische Eigenschaften - Elastizität -

13 Polymernetzwerke kovalente Vernetzung interpenetrierendes etzwerk physikalische Vernetzung Spezifische Eigenschaften - Elastizität - Unlöslichkeit - Kein Schmelzen Spezifische Parameter - f Funktionalität n Vernetzungsdichte - M c Molmasse der etzketten - Q Quellungsgard

Polymernetzwerke Quellung Flory-Huggins Quellung wird beschrieben durch die Flory-Rehnert Gleichung

(Rubber-Elasticity- Theory, RET) s Spannung, Deformationsverhältnis (x def /x o ; x o undeformierte

14 Polymernetzwerke Quellung Flory-Huggins Quellung wird beschrieben durch die Flory-Rehnert Gleichung höhere Entropie durch LM Aufnahme (Flory- Huggins-Theorie) & niedirgere Entropie durch die Deformation (Rubber-Elasticity- Theory, RET) s Spannung, Deformationsverhältnis (x def /x o ; x o undeformierte Dimension in x- Richtung); h Memory Term (h 1 trockene Vernetzung); A Mikrostruktur, A 1 affine Deform, A (1/f) freifluktuierendes etzwerk. B = Volumenfaktor (affin: B = /f; freie Fluktuation: B = 0) V A molares Volumen LM; j = 1/Q RET s AhRT( ) Messung von Q durch M c : Q~ M c 3/5 gutes LM (Q > 5) Q~ M c 3/8 schlechtes LM (Q < 5)

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