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

Transcription

1 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

2 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

3 RESEARCH APPROACH

4 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

5 ESTIMATING EFFECTS ON PRE AND POST YIELD STRESS & STRAINS 6

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

7 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)

8 Density (g/cm 3 ) Dr (cm 3 ) CURRENT METHOD TO ESTIMATE DENSITY FROM MWD AND SCB CONTENT r = (0.0241) Log(M) n C n C SCB PDI C SCB PDI 4 Dr C 2 3 C1 1.25E-02 C C3 7.51E-05 C n M p Narrow MW homopolymers Model values Log M Fitted data (R 2 = ) SCB/PDI n r r Dr H SCB Good fit found for numerous resin types and architectures tested 7

9 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 ) Log M slices 1 r dw dlogm dlogm Homopolymers Copolymers Elastomers 1 to 1 line +/ g/cm SCB/1000TC Log M Measured r (g/cm 3 ) density on a slice by slice basis added up to obtain whole polymer density 8

10 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

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

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

13 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 6.1x

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

15 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 LDPE LLDPE LLDPE LLDPE LLDPE HDPE HDPE 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

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

17 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 (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

18 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

19 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,

20 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 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

21 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

22 dw/d(log M) PSP2 22 RELATIONSHIP BETWEEN NDR AND PSP Bimodal PE blend PSP2 = Presented at Adv. In Polyolefins (2011) Log M Various resins measured 65 resins measured Mw kg/mol PDI 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

23 dw/d(log M) PSP2 RELATIONSHIP BETWEEN NDR AND PSP Bimodal PE blend PSP2 = Butene copolymers Log M No distinction seen between various resins architectures 14

24 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,

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

26 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 (+/ 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

27 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

28 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

29 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 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 Log M

30 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 ) * Density calculated for digital Gaussian MWD peaks, M w = 150,000 g/mol

31 Density(g/cm 3 ) Qualitative effects of MW and Polydispersity Index (PDI) on density Mw PDI Density PDI Log M w * Density calculated for digital Gaussian MWD peaks

32 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-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C MTE-C

33 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, 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 SCB/1000 TC * Units = (g/cm 3 )/(SCB/1000 TC) Dr for 0.1 SCB/1000 TC = 0.049

34 Dr (cm 3 ) Effects of SCB on Density: metallocene catalyzed PE copolymers y = x R² = For the MTE samples, the effects of SCB can adequately be described using a power law relationship SCB/1000 TC

35 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 ZN ZN ZN ZN ZN ZN ZN Dr

36 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 y = x R² = However, for ZN resins, a clear off set from MTE data is observed y = 0.01x R² = These data suggest that MWD must be considered when predicting the effects of SCB on density SCB/1000 TC

37 Dr (cm 3 ) Density changes for PE copolymer samples (SCB on Log scale) 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 Use SCB/(PDI) n to shift curves (to the left) and collapse responses into one curve SCB/1000 TC

38 Dr (cm 3 ) Density changes for PE copolymer samples (SCB on Log scale) MTE samples, PDI ~ 2.5 ZN Samples, PDI ~ 4.7 Cr / AlPO4, PDI ~ SCB/PDI n Using SCB/(PDI) n with n = 0.32 all data collapses onto one curve

39 Dr (cm 3 ) Density changes for PE copolymer samples (SCB on Log scale) Cr catalyzed samples, PDI 10 to 36 Bimodal Samples, PDI 14 to SCB/PDI n shift verified using additional resins with varied architectures

40 Dr (cm 3 ) Estimated density contributions from SCB (Dr) captured in one equation n C n C SCB PDI C SCB PDI 4 Dr C C1 1.25E-02 C C3 7.51E-05 C n 0.32 Fitted data (R 2 = ) 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 SCB/PDI n

41 Estimated r (g/cm 3 ) Measured and estimated densities for PE copolymers g/cm 3 Average variation from ASTM value: / g/cm to 1 line g/cm Measured r (g/cm 3 )

42 Estimated r (g/cm 3 ) Measured and estimated densities for PE resins in general Homopolymers Copolymers Elastomers Density can be estimated for any PE resin from SEC and SCB data (experimental and digital) to 1 line +/ g/cm Measured r (g/cm 3 )

43 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, 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 M-5 MET M-4 MET M-3 MET M-2 MET M-1 MET 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 Log M

44 Dr (cm 3 ) Selected Applications: Use of digital data *Selected data reported by Mirabella and Bafna, J. Poly Sci: Part B: Polymer Physics, 2002, Reported data/digital estimates Predicted values SCB/PDI n Results demonstrate ability of digital methodology to approximate reported data

45 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 w c r c r ra r rc ra c wc r rc * Mirabella (prev. ref.) O Stadler (prev. ref.) Bartczak (Polymer 2005, 46, 8210) Reported Crystallinity*

46 dw/d(log M) PSP2 PSP2 calculations and reported values (DesLauriers & Rohlfing, Macromolecular Symposia Volume 282, Issue 1, pages , August 2009) 46 The quantity (dw/dlog M * P TM *100) vs. Log M summed over the MWD defines the PSP2 value Bimodal PE blend PSP2 = 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, Tie Molecule Probability* P P TM 1 3 L 0 r r Where: exp( b exp( b 1 b r 4b L 0 r r r ) dr ) dr 3 2 2r M exp( b 2 r 2 ) dr

47 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 PDI = 1 O PDI = 2 PDI = 4 PDI = 1.0 PDI = 2.0 PDI = PDI g/cm 3 20 PDI g/cm PDI = ,000 M w (kg/mol) * Density calculated for digital Gaussian MWD peaks, M w = 150,000 g/mol

48 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 Polymer -F* mpe P TM Guassian Guassian *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