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Relationship of Rheological Behavior and Molecular Architecture for LDPE Designed for Extrusion Coating

Bert Nijhof Technical Paper-7603

Paper 7603 - Bert Nijhof

Introduction

• LDPE produced commercially for first time in 1939
• Process

– Radical polymerization (initiated by oxygen/peroxides) – Conditions: 1000–3000 bar / 80–300 oC – 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, Me (entanglement molecular weight)

• Transition in rheology behavior at Me.

Paper 7603 - Bert Nijhof

Macromolecules

• Long flexible chain of N repeating monomer units of

molecular weight m0

– Ethylene (C2H4) polyethylene H-(C2H4)N-H

• Real polymers are mixtures of chains with different

weight M. Distribution of M, with moments, Mn , Mw etc.. m N M ⋅ =

∑

⋅ =

M k M k

M n M

M nM

∆H

Paper 7603 - Bert Nijhof

Macromolecules

• Molecule with molecular weight M is ‘coil’ in 3D space.
• Characterized by a radius of gyration (Rg)
• 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>Me (Mark-Houwink)

D g

M R

1

∝

D - fractal dimension

ρs – molecular density single coil in solvent/melt

( )

1 3 ) 3 ( − − − −

∝ ∝

D D g s

M R ρ

• r

8 . 6 4 . 3 −

∝ ∝

s

M ρ η

Zero shear viscosity

Paper 7603 - Bert Nijhof

MWD plot (example)

0.2 0.4 0.6 0.8 1 2 3 4 5 6 7

Molecular Weight, log(M) (dwt/dlogM)

Autoclave Tubular Autoclave Tubular

Mn (M1) 11182 13313 Mw (M2) 119477 100138 Mz (M3) 510364 360125 D (M2/M1) 10.68 7.52

Paper 7603 - Bert Nijhof

Effect of branching

y = 0.5784x - 1.5811 R2 = 0.9991 1 1.2 1.4 1.6 1.8 2 2.2 3 4 5 6 7

Molecular weight, log(M) Radiius of Gyration, log(Rg)

Tubular Autoclave Linear (HDPE) model Linear (model)

D= 1.7

Conformation plot obtained from Gel Permeation Chromatography (GPC) with Multiple Angle Laser Light Scattering (MALLS) detector (GPC-MALLS).

Paper 7603 - Bert Nijhof

LDPE melt viscosity

3.0 3.5 4.0 4.5 5.0 4.75 4.95 5.15

Molecular weight, log(Mw) [g.mol-1] Zero shear viscosity, log( η0) [Pa.s]

Tubular Autoclave Linear (Linear MH)

Plot obtained from Oscillatory shear rheometry (OSR) Temperature 170 oC

Paper 7603 - Bert Nijhof

Effects of branching

• Branching reduces swell of polymer

– For same M lower Rg 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=Mξ

Exponent D DL (M<Mξ) DH (M>Mξ) Autoclave (1.7-2) 3 Tubular (1.7-2.5) Various

Paper 7603 - Bert Nijhof

Density plot (example)

y = 126x-1.27 y = 69x-1.00 0.1 1 10 10 100

Radius of gyration (Rg) density (ρs)

HDPE ref Autoclave Tubular LLDPE

ξ1 ξ2 ρ1 ρ2

ξ − Correlation length

Density plot obtained from GPC-MALLS

Paper 7603 - Bert Nijhof

Summary

– Transition marks change from SCB => LCB – Critical molecular weight Mξ related to entanglement molecular weight, Me – 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

Paper 7603 - Bert Nijhof

Critical conditions

SCB LCB ⇔

1< exponent < 1.3 (Graessley)

y = 2799.6x -1.1363 R2 = 0.678 200 400 600 800 1000 1200 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Critical density, ρξ Critical molecular weight, M

ξ

Plot obtained from GPC-MALLS

Paper 7603 - Bert Nijhof

Autoclave products

1 10 10 100

Rg Density, ρs

ξ 2ξ

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ ∝

− β α

ξ ρ

g g s

R F R

α

ρ

−

∝

g s

R

ξ <

g

R ξ >

g

R

β

ξ ρ ∝

s

Rheology of autoclave products depends on:ξ (or Mξ / ρξ) and (depending

• n conditions and sample set) on one or more of the moments Mk.

Paper 7603 - Bert Nijhof

Melt Index 1

• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 1.2 5.40 5.60 5.80 6.00 6.20

Cross-over Molecular weight, log(Mξ) [g.mol-1] Melt index, log( I2) [dg.min-1]

Tubular Autoclave Mixture

Paper 7603 - Bert Nijhof

Melt Index 2

• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 1.2 4.50 5.00 5.50

Weight average molecular weight, log(Mw) [g.mol-1] Melt index, log( I2) [dg.min-1]

Tubular Autoclave Mixture

Paper 7603 - Bert Nijhof

Application example: Neck-in

y = 0.9975x R2 = 0.9893 50 100 150 200 250 300 50 100 150 200 250 300

Neck-in observed [mm] Neck-in predicted [mm]

320/100 320/300 290/100 290/300 all Linear (all)

β α ξ z

M M a in Neck ⋅ ⋅ = −

MODEL Stdev NI Mz/Mξ 4.1 Mw/Mξ 7.8 Mz 6.9 Mw 12.7

Measured on Pilot Coater at different Temperature(oC) /Linespeed(m/min) and 12 g/m2