Relationship of Rheological Behavior and Molecular Architecture for LDPE Designed for Extrusion Coating. Bert Nijhof Technical Paper-7603
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1 Relationship of Rheological Behavior and Molecular Architecture for LDPE Designed for Extrusion Coating Bert Nijhof Technical Paper-7603
2 Introduction LDPE produced commercially for first time in 1939 Process Radical polymerization (initiated by oxygen/peroxides) Conditions: bar / o C Autoclave or Tubular process (or combination) Product Branched with varying branch length: Copolymerization with e.g. propylene (short) Intra molecular H transfer (short) Inter molecular H transfer (short - long) Long chain branches (LCB) dominate flow of the LDPE melt Transition from short to long chain branch at a critical molecular weight, M e (entanglement molecular weight) Transition in rheology behavior at M e.
3 Macromolecules Long flexible chain of N repeating monomer units of molecular weight m 0 H Ethylene (C 2 H 4 ) polyethylene H-(C 2 H 4 )N-H M = N m 0 Real polymers are mixtures of chains with different weight M. Distribution of M, with moments, M n, M w etc.. n M M k = n M M M k M
4 Macromolecules Molecule with molecular weight M is coil in 3D space. Characterized by a radius of gyration (R g ) 1 R g M D - fractal dimension ρ s molecular density single coil in solvent/melt D For linear polymers independent of M or polymer type D=1.7 in good solvent (Flory) D=2 in the melt (ideal chain) Density determines overlap between molecules in the melt. Melt viscosity for M>M e (Mark-Houwink) or ρ R s M ( 3 D 1) ( 3 D) g Zero shear viscosity η 0 M 3.4 ρ 6.8 s
5 MWD plot (example) Autoclave Tubular 1 (dwt/dlogm) Autoclave Tubular Mn (M 1 ) Mw (M 2 ) Mz (M 3 ) D (M 2 /M 1 ) Molecular Weight, log(m)
6 Effect of branching 2.2 Radiius of Gyration, log(r g ) Tubular Autoclave Linear (HDPE) model Linear (model) D=1.7 y = x R 2 = Molecular weight, log(m) Conformation plot obtained from Gel Permeation Chromatography (GPC) with Multiple Angle Laser Light Scattering (MALLS) detector (GPC-MALLS).
7 LDPE melt viscosity Zero shear viscosity, log( η0) [Pa.s] Tubular Autoclave Linear (Linear MH) Molecular weight, log(m w ) [g.mol -1 ] Plot obtained from Oscillatory shear rheometry (OSR) Temperature 170 o C
8 Effects of branching Branching reduces swell of polymer For same M lower R g i.e. denser molecule Less overlap for same M, viscosity decreases. Mark Houwink no longer valid, especially for autoclave products. Transition observed in exponent D at a critical molecular weight M=M ξ Exponent D D L (M<M ξ ) D H (M>M ξ ) Autoclave (1.7-2) 3 Tubular ( ) Various
9 Density plot (example) 10 ρ 1 y = 69x ρ 2 density (ρs) HDPE ref Autoclave Tubular LLDPE y = 126x ξ 1 ξ 2 Radius of gyration (R g ) Density plot obtained from GPC-MALLS ξ Correlation length
10 Summary Transition marks change from SCB => LCB Critical molecular weight M ξ related to entanglement molecular weight, M e Intra molecular entanglements affect swell behavior Autoclave products (CSTR): single variable scaling (ξ) Tubular products (PFR with axial dispersion): multivariable scaling (cascade of CSTR s) or Approximate scaling
11 Critical conditions Critical molecular weight, Mξ y = x R 2 = < exponent <1.3 (Graessley) LCB SCB Critical density, ρ ξ Plot obtained from GPC-MALLS
12 Autoclave products 10 ρ s R F ξ α g R g β 2ξ Density, ρs R g < ξ R g > ξ ρ s R α g ξ R g β ρ s ξ Rheology of autoclave products depends on:ξ (or M ξ / ρ ξ ) and (depending on conditions and sample set) on one or more of the moments M k.
13 Melt Index Melt index, log( I 2 ) [dg.min -1 ] Tubular Autoclave Mixture Cross-over Molecular weight, log(m ξ ) [g.mol -1 ]
14 Melt Index Melt index, log( I 2 ) [dg.min -1 ] Tubular Autoclave Mixture Weight average molecular weight, log(m w ) [g.mol -1 ]
15 Application example: Neck-in 300 Neck-in predicted [mm] / / / /300 all Linear (all) Neck 0 in = a M α ξ M β z y = x R 2 = MODEL Stdev NI M z /M ξ 4.1 M w /M ξ 7.8 M z 6.9 M w Neck-in observed [mm] Measured on Pilot Coater at different Temperature( o C) /Linespeed(m/min) and 12 g/m 2
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