Outline Brief overview of research approach Estimating effects on tensile stress & strain values Pre-yield Post yield Summary

PREDICTING POLYOLEFIN RESIN TENSILE PROPERTIES USING MICROSTRUCTURE DISTRIBUTIONS Paul J. DesLauriers and Mark J. Lamborn Outline Brief overview of research approach Estimating effects on tensile stress & strain values Pre-yield Post yield Summary

BACKGROUND: PURPOSE OF STUDIES Purpose of work is not directed at replacing current methods of measuring tensile properties Develop/refine molecular simulation tools that reasonably predict PE properties from experimental or digitally generated data Explore and optimize structure/property relationships i.e., Help understand fundamental concepts Estimate product performance limits Help guide catalyst and product design Connect reaction models to resin properties Examine what if structure property scenarios

RESEARCH APPROACH

MICROSTRUCTURES EXAMINED A B Mw ranges (kg/mol) A: 40 to 440 B: 135 to 250 C: 20 to 750 D: 340 to 500 C D

ESTIMATING EFFECTS ON PRE AND POST YIELD STRESS & STRAINS 6

ESTIMATING TENSILE VALUES FROM DENSITY* *Data from: J. Janzen & D. Register; Annual Technical Conference - Society of Plastics Engineers (1996), 54th(Vol. 2), 2190-2194) 60 resins, 16,000 individual test pieces Fitted correlation to Young s Modulus also found (plot not shown) 9

PROPERTIES OF METALLOCENE GENERATED PE HOMOPOLYMERS *Samples compression molded and cooled according to ASTM D4703; Annex A1 C; density measured using gradient column (ASTM D1505)

Density (g/cm 3 ) Dr (cm 3 ) CURRENT METHOD TO ESTIMATE DENSITY FROM MWD AND SCB CONTENT 1.01 0.99 0.97 0.95 1.006 r = 1.075 (0.0241) Log(M) 0.140 0.120 0.100 0.080 1 n C n C SCB PDI C SCB PDI 4 Dr C 2 3 C1 1.25E-02 C2 0.50 C3 7.51E-05 C4 0.62 n 0.32 0.93 0.91 0.89 M p Narrow MW homopolymers Model values 2 3 4 5 6 7 8 Log M 0.920 0.060 0.040 0.020 0.000 Fitted data (R 2 = 0.9935) 0.0 0.1 1.0 10.0 100.0 SCB/PDI n r r Dr H SCB Good fit found for numerous resin types and architectures tested 7

dw/dlog M Estimated r (g/cm 3 ) DENSITY FROM MWD & SCBD Correlations developed from homo & copolymer samples r r H Dr SCB 1/ r (wi / ri ) 0.35 0.3 0.25 0.2 Log M slices 1 r dw dlogm dlogm 1.00 0.98 0.96 0.94 0.92 0.90 0.88 Homopolymers Copolymers Elastomers 1 to 1 line +/- 0.002 g/cm 3 0.15 0.1 SCB/1000TC 0.05 0 2 3 4 5 6 Log M 0.86 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 Measured r (g/cm 3 ) density on a slice by slice basis added up to obtain whole polymer density 8

DENSITY FROM MWD & SCBD Application to digital Schulz Flory Distributions r r H Dr SCB 1/ r (wi / ri ) 1 r dw dlogm dlogm MWDs fixed at 2 Density vs. Mw calibration curve calculated SCBD is assumed to be flat Density change with SCB calculated as before All SFD values are additive

YOUNG S MODULUS FROM DENSITY* E where h E c and c E a 1 1 E 1 a where Poisson' s ratio is 0. 45 2.4 2 h h 4 E E a c 2 3478 MPa; E r r r r a c a a c 62.06 MPa c 1 *General working form of this equation developed by J. Janzen (see Poly. Eng. and Science, 1992, 32, 1242)

PREDICTED VS. MEASURE YIELD STRAIN VALUES a 27.66; 1.506 c *Error assigned from Table 6, ASTM D-638

DENSITY VS. YIELD STRENGTH VALUES c 1 yield where 1.5x10 b 0.67 c c be 1 a 3 a ; c 2 2 c c 6.1x10 3 10

DENSITY VS. YIELD STRENGTH VALUES yield c c be c 1 a a 2 c c 3 *Error assigned from Table 5, ASTM D-638 10

YIELD STRESS MEASUREMENT; ASTM D-638 Tensile Yield Stress, for Ten Laboratories, Eight Materials* Test Speed Average S r S r S R S R Material in/min MPa MPa % error MPa % error LDPE 20 10.6 1.01 9.49 1.2 11.6 LDPE 20 11.9 1.23 10.34 1.8 15.5 LLDPE 20 12.3 0.95 7.70 1.5 11.9 LLDPE 20 13.0 1.43 11.06 1.9 14.9 LLDPE 20 13.1 1.03 7.85 1.2 9.0 LLDPE 20 20.0 1.07 5.36 1.7 8.5 HDPE 2 24.3 3.39 13.98 9.2 38.0 HDPE 2 28.3 3.79 13.39 7.2 25.4 S r and S R are the within-lab and between-lab standard deviations *Table 5 in ASTM D638; values converted to MPa from psi

TENSILE VALUES FROM ESTIMATED DENSITIES Application to digital Schulz Flory Distributions Tensile values calculated directly from blend density

ESTIMATING STRESS STRAIN VALUES BEYOND YIELD POINT This portion of the stress strain curve governed by molecular architecture and is associated with resin durability E.g., NDR and Strain Hardening Modulus <G p > at 80 o C associated with slow crack growth** Slow Crack Growth Process Natural Draw Ratio Strain Hardening Modulus Break Stress and Strain *ISO 18488 2015 (E) Polyethylene (PE) materials for piping systems-determination of Strain Hardening Modulus in relation to slow crack growth Test method *Picture supplied by Dr. Carlos Dominguez Univ. Rey Juan Carlos, Madrid, ES 11

ESTIMATING STRESS STRAIN VALUES BEYOND YIELD POINT This portion of the stress strain curve governed by molecular architecture and is associated with resin durability E.g., NDR and Strain Hardening Modulus* <G p > associated with slow crack growth Natural Draw Ratio Strain Hardening Modulus Break Stress and Strain *Plot from Sukhadia et. al., Proceeding of Plastics Pipes XV Conference. Vancouver, Canada, Sept. 2010 11

ESTIMATING POST YIELD VALUES Primary Structure Parameter (PSP2)* 1. Density 2. Incorporate the concept of tie molecules a) T m ( o C) from density b) Lamella thickness (GT eq.) c) Probability of tie molecules (P TM ) formation 3. Account for weight fraction effects (both MWD and SCBD) *branch type not taken into account Durability of Resin B ~1000x that of A at the same density (0.950 g/cm 3 ) and MW** ** See Krishnaswamy et al; Macromolecules 2008, 41, 1693 13

CALCULATING PSP2 FOR SFDS PSP2 for SFDs can be calculated using a sigmoidal equation Copolymers r = 0.88 g/cm 3 Homopolymers Where: L = PSP2 max k = PDI constant (equal to 3.8394 for SFD) x = Log Mw x mid pt. = c 1 c 2 (Dr 0.5 Data pts PSP2 values from property model spread sheet for several SFDs Dotted lines PSP2 values from above equation calculated from Log Mw and density values

CALCULATING PSP2 FOR SFDS Digital bimodal blends obtained from DoE (40 samples) of reactor condition and kinetic models Sigmodal PSP2 values for SFDs are additive and compare well to values obtained from property models

dw/d(log M) PSP2 22 RELATIONSHIP BETWEEN NDR AND PSP2 0.6 0.5 Bimodal PE blend PSP2 = 10.4 14 12 Presented at Adv. In Polyolefins (2011) 0.4 0.3 0.2 10 8 6 4 0.1 2 0 0 2 3 4 5 6 7 8 Log M Various resins measured 65 resins measured Mw 80-550 kg/mol 2.1 50 PDI 0.916-0.965 g/cm3 monomodal and bimodal samples Similar correlations found in other SCG resin and pipe tests: PENT, SP-NCTL.,ESCR, Notched pipe test, ductile to brittle transition in pressure pipe testing 14

dw/d(log M) PSP2 RELATIONSHIP BETWEEN NDR AND PSP2 23 0.6 0.5 0.4 0.3 0.2 0.1 Bimodal PE blend PSP2 = 10.4 14 12 10 8 6 4 2 1-Butene copolymers 0 2 3 4 5 6 7 8 0 Log M No distinction seen between various resins architectures 14

ESTIMATING STRESS STRAIN VALUES BEYOND YIELD POINT This portion of the stress strain curve governed by molecular architecture and is associated with resin durability E.g., NDR and Strain Hardening Modulus <G p > at 80 o C associated with slow crack growth Natural Draw Ratio Strain Hardening Modulus Break Stress and Strain Re-plot of data reported by Kurelec et. al., Polymer 2005, 46, 6369 11

ESTIMATING STRESS STRAIN VALUES BEYOND NDR Effects of short chain branch type clearly seen *Measurements made by University of Rey Juan Carlos (Madrid, Spain)

SUMMARY MWD and SCBD data for polyolefin resins that can used for further resin property assessments By using density correlations for MW and SCB effects, density values for any MWD and SCBD can be estimated (+/- 0.002 g/cm 3 ) Micro-deformations such as tensile elastic modulus, yield stress and yield strain can be estimated from density and hence MWD and SCBD data Macro-deformation such as tensile NDR and Strain Hardening Modulus <Gp> are dependent on placement of SCB in the MWD and can be estimated using PSP2 values Future work will focus on estimating other portions of the stress strain curve (e.g., draw and break stress/strain values) as well as looking at the effects of SCB length and LCB content on both NDR and <Gp> These methods are powerful tools for product design concepts when coupled with other statistical tools, kinetic models and experimental blend studies 18

ACKNOWLEDGMENTS Mr. Alan Miller Mr. Nathan Cole Dr. Dave Rohlfing (digitizing Janzen & Register figures) Advances in Polyolefins 2015 Organizers Chevron Phillips Chemical Company, LP 19

EXTRA SLIDES FROM APO 2009 & 2011 APO2009 Estimating Polyethylene Densities from Molecular Weight and Short Chain Branching Distributions Paul J. DesLauriers* and David C. Rohlfing APO2011 Unraveling Convoluted Structural Effects on Slow Crack Grow (SCG) Resistance using the Primary Structure Parameter (PSP2) Paul J. DesLauriers

dw/dlog M Molecular weight contributions to density: MWD integral approach Estimate density across MWD by optimizing the values of a and b 1/ r (wi / ri) 1 r dw dlogm dlogm Use squares of the residual (SQR) between know and calculated densities for each sample 0.35 0.3 where : r a blogm Log M slices Use excel solver to minimize SQR sum and get best fit for a and b Do this simultaneously for all 11 MTE homopolymer samples 0.25 0.2 0.15 0.1 0.05 0 2 3 4 5 6 Log M

Qualitative effects of MW and Polydispersity Index (PDI) on density At a set Mw, increasing the PDI leads to an increase in density Since PDI = M w /M n. Nominal PDI Estimated Homopolymer Density (g/cm 3 ) 2 0.951 3 0.953 5 0.955 8 0.957 12 0.959 16 0.960 20 0.961 * Density calculated for digital Gaussian MWD peaks, M w = 150,000 g/mol

Density(g/cm 3 ) Qualitative effects of MW and Polydispersity Index (PDI) on density Mw PDI Density 500 2 0.9388 500 5 0.9429 500 20 0.9494 350 2 0.9423 350 5 0.9465 350 20 0.9529 0.99 0.98 0.97 PDI 20 5 2 150 2 0.9508 150 5 0.955 150 20 0.9614 50 2 0.9617 50 5 0.9659 50 20 0.9723 0.96 0.95 0.94 25 2 0.9686 25 5 0.9728 25 20 0.9793 0.93 4 4.5 5 5.5 6 Log M w * Density calculated for digital Gaussian MWD peaks

Effects of SCB on Density: metallocene catalyzed PE copolymers Sample Mw (kg/mol) PDI SCB/1000 TC Calculated Homopolymer r (g/cm 3 ) Measured Copolymer r (g/cm 3 ) Dr MTE-C1 182 2.42 0.1 0.951 0.947 0.005 MTE-C2 139 2.5 1.2 0.956 0.942 0.014 MTE-C3 159 2.34 2.3 0.953 0.937 0.016 MTE-C4 142 3.13 3.5 0.955 0.933 0.022 MTE-C5 129 2.3 3.7 0.956 0.933 0.023 MTE-C6 134 2.72 3.7 0.955 0.936 0.019 MTE-C7 111 2.75 6.8 0.957 0.931 0.027 MTE-C8 204 2.25 9.3 0.950 0.917 0.033 MTE-C9 187 2.11 10.7 0.951 0.916 0.035 MTE-C10 120 2.2 12.4 0.956 0.916 0.040 MTE-C11 180 2.33 12.9 0.951 0.913 0.038 MTE-C12 117 2.5 13.6 0.956 0.918 0.038 MTE-C13 95 3.5 32 0.960 0.902 0.058 MTE-C14 102 3.52 36.3 0.959 0.897 0.062 MTE-C15 147 2.63 49.5 0.954 0.880 0.074

Dr /SCB 1000 TC Effects of SCB on Density: metallocene catalyzed PE copolymers From the literature Similar non-linear plots reported for variation in lamella thickness with SCB e.g., J. R. Isasi et. al; Polymer 2000, 41, 8813 0.014 0.012 0.010 0.008 SCB contribution to density change is nonlinear, greatest change takes place below 15 SCB/1000 TC Crystal thickening unaffected after ~ 10 SCB/1000 TC e.g., F. M. Mirabella; Journal of Polymer Science, Part B: Polymer Physics 2000, 41, 235 Most SCB lengths give similar effects e.g., F. J. Stadler et. al; e-polymers 2009, no. 041 0.006 0.004 0.002 0.000 0.0 20.0 40.0 60.0 SCB/1000 TC * Units = (g/cm 3 )/(SCB/1000 TC) Dr for 0.1 SCB/1000 TC = 0.049

Dr (cm 3 ) Effects of SCB on Density: metallocene catalyzed PE copolymers 0.09 0.08 0.07 y = 0.0124x 0.4393 R² = 0.9909 0.06 0.05 0.04 0.03 0.02 For the MTE samples, the effects of SCB can adequately be described using a power law relationship 0.01 0 0 20 40 60 80 SCB/1000 TC

Effects of SCB on Density: Ziegler-Natta catalyzed PE copolymers Sample M w (kg/mol) PDI SCB/1000 TC (NMR) Calculated Homopolymer r (g/cm 3 ) Measured Copolymer r (g/cm 3 ) ZN-1 133 5 1.5 0.958 0.947 0.012 ZN-2 439 4.4 3.75 0.946 0.929 0.017 ZN-3 138 5.0 7.1 0.958 0.936 0.023 ZN-4 144 4.9 7.3 0.958 0.935 0.023 ZN-5 130 4.9 12.6 0.959 0.926 0.032 ZN-6 135 4.0 12.6 0.958 0.927 0.031 ZN-7 131 4.0 13.9 0.959 0.924 0.035 ZN-8 115 4.0 23.9 0.960 0.915 0.046 Dr

Dr (cm 3 ) Effects of SCB on Density: Ziegler-Natta catalyzed PE copolymers As in MTE samples, ZN catalyzed PEs show a nonlinear density change with SCB well described by a power law 0.09 0.08 0.07 0.06 0.05 y = 0.0124x 0.4393 R² = 0.9909 However, for ZN resins, a clear off set from MTE data is observed 0.04 0.03 0.02 y = 0.01x 0.4574 R² = 0.9754 These data suggest that MWD must be considered when predicting the effects of SCB on density 0.01 0 0 20 40 60 80 SCB/1000 TC

Dr (cm 3 ) Density changes for PE copolymer samples (SCB on Log scale) 0.09 0.08 0.07 0.06 MTE samples, PDI ~ 2.5 ZN Samples, PDI ~ 4.7 Cr / AlPO 4 samples, PDI ~ 60 (four samples) Effects of MWD on needed SCB are complex 0.05 0.04 0.03 0.02 0.01 Use SCB/(PDI) n to shift curves (to the left) and collapse responses into one curve 0 0.1 1 10 100 SCB/1000 TC

Dr (cm 3 ) Density changes for PE copolymer samples (SCB on Log scale) 0.080 0.070 0.060 MTE samples, PDI ~ 2.5 ZN Samples, PDI ~ 4.7 Cr / AlPO4, PDI ~ 60 0.050 0.040 0.030 0.020 0.010 0.000 0.0 0.1 1.0 10.0 100.0 SCB/PDI n Using SCB/(PDI) n with n = 0.32 all data collapses onto one curve

Dr (cm 3 ) Density changes for PE copolymer samples (SCB on Log scale) 0.080 0.070 0.060 0.050 0.040 Cr catalyzed samples, PDI 10 to 36 Bimodal Samples, PDI 14 to 25 0.030 0.020 0.010 0.000 0.0 0.1 1.0 10.0 100.0 SCB/PDI n shift verified using additional resins with varied architectures

Dr (cm 3 ) Estimated density contributions from SCB (Dr) captured in one equation 0.140 1 n C n C SCB PDI C SCB PDI 4 Dr C 2 3 0.120 0.100 C1 1.25E-02 C2 0.50 C3 7.51E-05 C4 0.62 n 0.32 Fitted data (R 2 = 0.9935) 0.080 0.060 0.040 0.020 Good fit found for various resins and architectures tested Equation valid down 0.1 SCB/1000 TC Dr vs. SCB/PDI curve can also be generated 0.000 0.0 0.1 1.0 10.0 100.0 SCB/PDI n

Estimated r (g/cm 3 ) Measured and estimated densities for PE copolymers 0.96 0.95 + 0.003 g/cm 3 Average variation from ASTM value: 0.94 +/- 0.002 g/cm 3 0.93 0.92 1 to 1 line 0.91 0.90-0.003 g/cm 3 0.90 0.92 0.94 0.96 Measured r (g/cm 3 )

Estimated r (g/cm 3 ) Measured and estimated densities for PE resins in general 1.00 0.98 0.96 0.94 0.92 Homopolymers Copolymers Elastomers Density can be estimated for any PE resin from SEC and SCB data (experimental and digital) 0.90 0.88 1 to 1 line +/- 0.002 g/cm 3 0.86 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 Measured r (g/cm 3 )

dw/d(log M) SCB/1000TC Selected Applications: Use of digital data *Selected data reported by Mirabella and Bafna, J. Poly Sci: Part B: Polymer Physics, 2002, 40 1637 Sample Catalyst type SCB/1000 Mw (kg/mol) PDI Total Carbons Calculated Measured Homopolymer Copolymer r (g/cm 3 ) r (g/cm 3 ) Dr (g/cm 3 ) M-6 MET 108 2.2 18.5 0.958 0.910 0.048 M-5 MET 75 2.5 25.3 0.962 0.905 0.057 M-4 MET 81 2.2 30.7 0.961 0.900 0.061 M-3 MET 98 2.1 43.9 0.958 0.888 0.070 M-2 MET 137 2.4 51.4 0.956 0.880 0.076 M-1 MET 63 2.3 84.6 0.963 0.865 0.098 1.0 25 1. For MTE samples M1 to M6, assumed Gaussian MWD, use reported MW/MWD 2. Assumed a flat SCBD, Use reported SCB level for the 1-butene copolymers 3. Use reported density and calculate density difference 0.8 0.6 0.4 0.2 0.0 2 3 4 5 6 7 8 20 15 10 5 0 Log M

Dr (cm 3 ) Selected Applications: Use of digital data *Selected data reported by Mirabella and Bafna, J. Poly Sci: Part B: Polymer Physics, 2002, 40 1637 0.140 0.120 Reported data/digital estimates Predicted values 0.100 0.080 0.060 0.040 0.020 0.000 10 100 SCB/PDI n Results demonstrate ability of digital methodology to approximate reported data

Estimated Crystallinity Estimated crystallinity from digital data Mono-modal MTE samples MW/MWD, SCB given C4,C6,C8,C12 & homopolymers Density, DSC, SAXS & WAXS measurements 1 0.9 0.8 0.7 0.6 0.5 + 0.5-0.5 w c r c r ra r rc ra c wc r rc 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 * Mirabella (prev. ref.) O Stadler (prev. ref.) Bartczak (Polymer 2005, 46, 8210) Reported Crystallinity*

dw/d(log M) PSP2 PSP2 calculations and reported values (DesLauriers & Rohlfing, Macromolecular Symposia Volume 282, Issue 1, pages 136 149, August 2009) 46 The quantity (dw/dlog M * P TM *100) vs. Log M summed over the MWD defines the PSP2 value 0.6 0.5 0.4 0.3 0.2 0.1 0 Bimodal PE blend PSP2 = 10.4 2 3 4 5 6 7 8 Log M Wt. frac. PSP2 Cumulative PSP2 *R. M. Patel, K. Sehanobish,P. Jain, S. P. Chum, G. W. Knight, J. Appl. Poly. Sci. 1996, 60, 749. 14 12 10 8 6 4 2 0 Tie Molecule Probability* P P TM 1 3 L 0 r r Where: 1 3 2 2 exp( b exp( b 1 b r 4b 2 2 3 2 2 L 0 r r r 2 2 2 ) dr ) dr 3 2 2r M 0.159 14 exp( b 2 r 2 ) dr

PSP2 General effects of MWD on SCG resistance 47 Increasing polydispersity (i.e., Mw/Mn) at a set Mw deceases PSP2 values for homopolymer like structures 35 30 25 20 PDI = 1 O PDI = 2 PDI = 4 PDI = 1.0 PDI = 2.0 PDI = 4.0 2 PDI 0.951 g/cm 3 20 PDI 0.961 g/cm 3 15 10 5 0 PDI = 50 0 200 400 600 800 1,000 M w (kg/mol) * Density calculated for digital Gaussian MWD peaks, M w = 150,000 g/mol

ESTIMATING EFFECTS OF STRUCTURE VIA DIGITAL DATA AND LITERATURE STUDIES* Reference Catalyst Type Mw (kg/mol) PDI SCB /1000 TC Density (g/cm 3 ) Polymer -A* Cr 223 13.2 6.8 0.934 0.13 Polymer -F* mpe 118 6.3 11.5 0.924 0.14 P TM Guassian 1 223 13.2 6.8 0.934 0.12 Guassian 2 118 6.3 11.5 0.924 0.12 *Janimak & Stevens J. Material Sci., 2001, 36, 1879 Exercise demonstrates applicability of method and usefulness in addressing what if structure /performance scenarios using digital data 15