Case 1:05-cv-00737-JJF Document 160-5 Filed 09/03/2008 ... · A wide range of linear (HDPE and LLDPE) and branched (HP- LDPE) polyethylenes ... kglhr per cm, narrow gap extrusion

Case 1:05-cv-00737-JJF Document 160-5 Filed 09/03/2008 Page 1 of 42


Wall Slip in Viscous Fluids and Influence of Materials of Construction

A. V. RAMAMURTHY, Unwn Carbide Corporation, P. 0. Box 670, Bound Brook, New Jersey 08805

Synopsis

The question of slip and the influence of materials of mnstruction on the observed -date irregularities are examined for high viscosity molten polyethylenes. Capillary rheometer studies were conducted for several linear (LLDPE and HDPE) and branched (HP-LDPE) polyethylenes. Viton A, and Barex-210. Exten- sive blown film fabrication studies were wnducted for n a m w MWD UNIPOL process LLDPE resins. The results indicate tha t the assumption of "no-slip a t the rigid boundary" is generally not valid for polyethy1enes above a critical shear stress of approximately 0.1-0.14 MPa, when either surface or gmss irregularities are present in the extrudate. Lass of extrudate gloss a t the critical shear stress defines the on+ of melt fracture. Within the range of variables examined, the critical stress is relatively insensitive to molecular characteristics (molecular weight, MWD, and chain branching), melt temperature, and the detailed design of the capillary, Contrary to capillary rheometer observations, blown film fabrication results for LLDPE indicate that materials of construction for the die land region have a significant influence on melt fracture, and suggest breakdown of adhesion at the polymer/metal interface as a primary cause of slip and melt fracture. The results demonstrate that methods to improve adhesion, by proper choice of materials of construction for the die land region andfor use of adhesion promoters in the resin, virtually eliminate the rate-limiting effects of melt fracture in commercial blown film fabrication The m l t s highlight a deficiency of standard capillary rheometer methods to delineate the influence of materials of construction and/or adhesion promoters on observed melt fracture characteristics with molten polyethylenes.

INTRODUCTION

Extrudate irregularities, commonly referred to as melt fracture, occur a t low deformation rates with some polymers, such as the narrow molecular weight distribution (MWD) linear low-density polyethylenes (LLDPE). With large-scale commercial use and

02986 by The Society of Rheology, Inc. Published by John Wiley & Sons, Inc. Journal of Rheology, 30(2), 337-357 (1986) CCC 0148-6055l86l020337-21$04.00

EXHIBIT PAGE 000978


342 RAMAMURTHY

as linear polymers are concerned. It is almost certain that slip is negligible for branched polymers."

In contrast to studies on gross melt fracture, surface melt fracture has received less attention, although it has been observed, to varying degrees, with a wide range of polymers including HDPE: HP-LDPE,9 and PVC.'O The literature suggests that surface melt fracture is a die exit phenomenon and occurs as a consequence of high local stresses as the viscoelastic melt parts company with the die. That is, surface melt fracture is distinctly different from gross melt fracture which is a die-entry and/or a die-land effect. The possibility of slip in the die land region under surface melt fracture conditions has not been considered.

This paper focuses attention on some results which may be useful in resolving the question of slip in the die land region for polyethylenes in general, and for linear polymers such as HDPE and LLDPE in particular. The influence of materials of construction on the observed extrudate irregularities is examined in both capillary and blown film fabrication situations.

EXPERIMENTAL

A capillary rheometer, built by the R&D team a t Union Car- bide, was used for studies to determine the flow curves and extrudate characteristics of molten polymers. Capillary dies (orifice dimensions: 0,5-2.5 mm diameter, 2-20 UD, and 60-180" included angle) constructed from SAE 4140 steel were employed. Abrupt entry dies (1 mm diameter and 20 UD) of various metals were used to study the influence of materials of construction on extrudate characteristics for LLDPE resins. A stepwise regres- sion was used to fit the steady-state data to a power-law model. Particular attention was paid to determine the conditions for the onset of surface (loss of gloss) and gross melt fracture.

A wide range of linear (HDPE and LLDPE) and branched (HP- LDPE) polyethylenes (see Table I for nominal characteristics) were studied. The characteristics of two other commercial polymers, Barex-210 (a copolymer of acrylonitrile and methylmethac- rylate, supplied by Vistron Corporation) and Viton A (a flu- oroelastomer, supplied by E. I. duPont de Nemours & Co., Inc.), were also examined. A .c

Blown film fabrication studies were conducted with a 50 mm, L .

WALL SLIP IN VISCOUS FLUIDS 34 1

TABLE I Nominal Characteristics of Polyethylenes Studied

MI or range studied Density

T Y pe (dglmin) MFR (kgim') MWiMn

LLDPE" 0.2-20 26 918 3.9 LLDPEb 0.2-2 26 918 3.9 HDPEY," 1 .O 26 950 3.9 HDPE" 1.3 39 950 7.9 HP.LDPE^.~ 2 65 920 14.0 HP-LDPE*.~ 0.1 128 917 11.8

"Capillary studies. * '~ . - bBlown film studies.

24/1 LID extruder fitted with a 75 mm spiral die of standard hard chrome-plated steel construction, and a dual lip air ring for bub- ble cooling. The influence of construction materials for the die land region on melt fracture in the film was studied. For this, a modified mandrel design (Fig. 2) was constructed to allow use of metal inserts. Using standard fabrication procedures, 38 pm films were fabricated. The onset of melt fracture was determined by visual examination of the film. Surface roughness measurements with a Bendix Proficorder (Bendix Corporation, Southfield,

DIE CAP.H IMM M'ETAL INSERTS

Fig. 2, Schematic die land insert design for'screening materials of construction.

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EXHIBIT PAGE 000980


RAMAMURTHY

TABLE 111 Measured Power-Law Constants with Some Die Materials 1 MI LLDPE; 220°C

Ca~i l l a rv : 1 mm x 20 WD

Metal 11 , KI n, K, T, .~ '1.2

Aluminum (6061.'1'6) 0.61 1.47 0.41 3.30 13.7 39.1 Beryllium copper 0.55 1.54 0.42 2.41 10.4 37.7 Carbon steel (SAE 41401 0.64 0.93 0.46 1.95 14.4 43.5 Carbon steel (SAE 43401 0.64 0.93 0.46 1.95 14.4 43.5 CDA 360" 0.62 1.05 0.39 2.96 17.2 41.3 CDA 464" 0.64 0.98 0.44 2.31 15.3 40.7 Bronze (Ampco 45) 0.61 1.20 0.44 2.43 14.6 43.4 Copper 0.61 0.99 0.44 2.09 13.2 41.5 Stainless steel (3041 0.65 1.01 0.46 2.32 15.1 44.1

Subscript 1 refers to smooth and glossy conditions. Subscript 2 refers to conditions above T,,. K is expressed in Pa,sec" x Critical stress values expressed in Pa x 'Copper Development Association designations.

Nominal compositions, %: Cu Zn Pb Sn CDA.360: 61.5 35.5 3.0 - CDA.464: 60.0 39.2 - 0.8

fracture, is less dependent on the materials of construction, which is consistent with the reported observations of Tordella, and Metzger and Hamilton for HDPE. However, as the results to follow indicate, the influence of the materials of construction for the die land region under blown film fabrication conditions is entirely different from that indicated by the capillary rheometer results.

Blown Film Fabrication Studies

Table IV lists observations to illustrate the rate-limiting effects of melt fracture with a 1 mm die gap of conventional chrome- plated steel configuration. For the 1 MI LLDPE, melt fracture in the film occurs at.an uneconomically low rate of extrusion (0.41 kglhr per cm of die circumference). At commercial rates of 1.5-2 kglhr per cm, narrow gap extrusion results in unacceptable prod- ucts, due to severe melt fracture, as indicated by the measured surface roughness. It may be noted that the shearra te for the onset of melt fracture, under film fabrication conditionsyis higher

WALL SLIP IN VISCOUS FLUIDS 349

TABLE IV Effects of Extrusion Rate on Melt Fracture for 1 MI LLDPE-Conventional

Chrome-Plated Steel Surfaces

Equipment: 50 mm, 2411 U D extruder; 75 mm spiral die with hard ch~orne .~ l a t ed 4140 steel surfaces; dual lip a i r ring

Conditions: Die gap, mm Land lengthlgap Die rate, kglhrlcm C, (slit), llsec Melt temp., "C BUR Film thickness, &m

Observations: Melt fracture None Onset' High Severe

Roughness, &m MD 0.05 0.41 0.46 0.51 T D 0.05 0.66 1.07 1.51

MD-Machine direction. TD-Transverse direction. '-Onset determined by visual examination.

(about 100 llsec) than that (about 60 l/sec) predicted from Eq. (1) for capillary dies.

Blown film fabrication experiments were conducted with a modified design of the mandrel extension region (see Fig. 2) to allow use of metal inserts for the die land region. Note that the rest of the die, including the die entry, was constructed from conventional chrome-plated steel. Several metals (ferrous and nonferrous) and coatings were examined for the 1 MI LLDPE under identical extrusion conditions. The die land surfaces were visually examined, before and after extrusion, for any discernible changes in the surface appearance. 'Table V lists qualitative observations with some representative

die land surfaces. These illustraQ, contrary to the capillary rheometer observations, a significant influence of the materials of construction on melt fracture under continuous, film-blowing conditions. At identical fabrication conditions, films with melt fracture may appear qualitatively similar. However, the details of film surface (roughness, ridge amplitude, and ridge separation) are a fbnction of the nature of the d i a a n d surface. For example, films fabricated with titanium nitride coating exhibited the most

EXHIBIT PAGE 000981


. '\

RAMAMURTHY WALL SLIP IN VISCOUS FLUIDS 353

available results (not presented here), indicate that within the range of variables examined, the equilibrium performance of CDA-360 is independent of the gap, land length to gap ratio WH), extrusion rate, and melt temperature for a wide range of resins. The induction time is dependent on the shear rate in the die land region, Higher shear rates generally require shorter induction time. An important point illustrated by Table VI (note the shear rate ranges with 1 and 0.5 mm gaps) is that, for the 1 MI LLDPE, no melt fracture was observed with CDA-360 at shear rates in excess of 20,000 l/sec, which totally contradicts the capillary rheometer observations with CDA-360 (Table 111). Since specific time-dependent interfacial effects are involved, it seems clear that standard capillary rheometer methods are unable to provide useful information for delineating the influence of materials of construction on the extrudate irregularities with molten polymers.

BASIC METHODS FOR ELIMINATION OF MELT FRACTURE

The results of the present studies indicate that the die land region is the primary site of initiation, and slip due to breakdown of adhesion a t the polymertmetal interface is the primary cause of the observed extrudate irregularities with polyethylenes. Thus, methods to improve adhesion a t the interface in the die land region would essentially eliminate the rate-limiting effects of melt fracture in commercial blown film fabrication. The necessary chemical forces for good adhesion can be achieved by either proper choice of the materials of cons t r~c t ion , '~ or use of adhesion promoters in the resin, or,an optimum combination of both.14 The hfluence of the materials of construction for the die land region is clear from the above film fabricati2n studies and will not be discussed further.

Adhesion Promoters

There are several polymers and low molecular weight additives which, although not recognized as su& improve adhesion of melt fracture prone polyethylenes to even conventional chrome-plated die surfaces. Included here are additives, normaIly referred to as

EXHIBIT PAGE 000982


356 RAMAMURTHY

sumption is limited to a certain critical shear stress below which the extrudates are smooth and glossy. T h e assumption is not valid when either surface or gross irregularities a r e present.

2. Loss of extrudate gloss and the initiation of slip in the die land region occur a t a critical shear stress of approximately 0.1- 0.14 MPa, and denotes the condition for onset ofextrudate irregularities.

3. Within the range of variables examined, the critical shear stress is independent of the molecular structure (molecular weight, MWD, and branching), melt temperature, And the de. tailed design of the capillary.

4 . Breakdown of adhesion a t the polymerlrnetal interface in the die land region a t the critical stress appears to be primarily responsible for the initiation of slip and the observed extrudate irregularities.

5. Under continuous blown film fabritation conditions, methods to provide good adhesion a t the polymerlrnetal interface, by proper choice of the materials of construction for the die land region and/or use of adhesion promoters in the resin, essentially eliminate the rate-limiting effects of melt fracture.

6. Standard capillary rheorneter methods a re unable to delineate the influence of materials of construction andlor adhesion promoters on melt fracture behavior of polyethylenes. The in- Ruence of such variables should be determined under a ~ t u a l ~ f a b - rication conditions.

The author wishes to thank Union Carbide Corporation for permission to pub. lish this work. The author is extremely grateful to the meticulous experimental support provided by Messrs. T. Dorrell, B. H. Gumbert, W. D. Kendzulak, and J. 2. Pawlowski, Mr. Pawiowski d e s e ~ e s particular thnnks for all fabrication studies reported here.

Sincere thanks to Professor' A. 8. Jfetzner of the Department of Chemical En- gineering, University of Delaware, for'the niany helpful discussions, constructive criticisms, comments, and suggestions on this work.

References

1. D. E. ,James, Paper presented at the 11th CDC International Business Con- ference. Brussels, Belgium, April 11-16, 1985.

2. J. C. Miller and S. J. Kurtz, Paper presented at the IX International Con. gress on Rheology, October 8, 1984.

3. C. J. S. Petrie and M. M. Denn, MChE J., 22, 209-236 (1976).

I , .

WALL SLIP IN VISCOUS FLUIDS 357 - , . - . I

b S. Middleman, Fundamentals of Polymer Processing, McGraw-Hill, I ~ c , ' 1' -. - . . . . New York 11977), p 475,

5: 5 P Tordella, J. Appl. Polym. Sci., 7, 215-229 (1963). 6. A. P, Metzger and C. W. Hariiilton, SPE. Trans., 4, 107-112 (1964). , ., 7. J. J. Benbow and P. Lamb, S.PB, Trans. (Jan. 1963). 8. J. P. Tordelia, In Rheology, Vol. 5, F. R. Eirich, ed., Academic Press. New

York 11969). 9. P. L. Clegg, In The Rheology of Elastomers, P, Mason and N, Wookey, eda.,

Pergamon Press, New York (1958), p 174. Also see: Trans. J . Plas. Ins:., 28, 245 (1960).

10. C. L. Sieglaff, SPB. Trans., 4, 129 (1964). 11. J. M. Lupton and R. W. Register, Polym. Engr. Sci., 5, 235 (1965). 12. A. B, Metzner, E. L. Carley, and I. K. Park, Mod. Plas., 133 (July 1960). 13, E. B. Bagley, Trans. SOC. Rheol., 5, 355-368 (1961). 14. A. V. Ramarnurthy, U S . Patent 4,552,712 (1985). 15. A. V. Ramamurthy, U S . Patent 4,554,120 (1985). 16. A. V. Ramamurthy, U S . Patent 4,522,776 (1985). 17. S. S. Schwartr and S. H. Goodman, Plastic Maleriais and Processes, Van

Nostrand Reinhold Co., New York (1982). 18. Barex 210 Technical Literature, Vistron Corp., Cleveland, Ohio. 19, P. S. Blatz, U.S. Patent 3,125,547 (1964).

Received September 9, 1985 Accepted November 22, 1985

EXHIBIT PAGE 000983


RHEOME'IRICAL ROWS INVOCVlNG RECTILINEAR SHEAR 91

crjment. Thus, the ROW , dldefincd rhcological

.& indexei' is a useful per , in comparing tes-

1 &e that two materials 1 have viscosity C u m of 1 -4-13- i ile test exactly the samc

;s defined only in terms 1 rimental procedure, the 1 enations made using a \ -",vices. If a quantity of

1 3 melt indexer can be

i j i:terize molten poIymen, r s the Rossi-Peaks flow I s t method D569-59% i ;ic molding compounds."

A premolded. cylindfical specimen is placed at room temperature in a "charge chamber*' (barrel) a t the bottom of a steam-heated block which also contains a capillary with a diameter of 0.125 inch and a length of 1.5 inches. A piston is immediately raised into position and prcsscs against the polymer, causing i t to flow upward into the capillary. A specified upward driving pressure is supplied by means of weights sus- pended from pulleys. The rate of rise of polymer in the capillary is mon- itored by means of a follower rod which rests on the surface of the melt. The quantity reported is the temperature a t which the flow in the first 2 minutes is 1 inch.

If polymer were preheated and allowed to fill the capillary. the Rassi- Pcakes flow tester could be used as a crude capillary viscorneter. In this case, it would be subject to most of the samc sources of inaccuracy as the melt indexer, although the standard capillary for the Rossi-Peaks test has a much larger L/D. However, when used as specified in ASTM D569-59, device yields a reading which depends not only on an unknown combination of rheological properties. but also on its melting and heat transfer characteristics. It is not intended to measure a mate- rial property, but to simulate, in some sense, the molding process.

A commercial version of the Rassi-Pcaku tester is described in See- tion 9.3.

Maxwell and lung [85] designed a weightdriven capillary rhwmeter for the study of the effect of pressure on melt viscosity. Like the Wes- tover instrument described in the next section, it has barrel sections c.? both sides of the capillary, and both are fitted with pistons. A hydraulic hand pump, acting on the upper piston, supplies the elevated static pre- sure, while the driving pressure is applied to the lower piston by means of dead weight loading. This rheometer is simple, compact and portable.

Weightdriven capillary rheometers are, for practical reasons, limited lo moderate driving pressures and thus to rathcr low shear rates. They therefore supply information only about the lower end of the viscosity curve and are of little value in distinguishing between resins whose viscosity curves are different in shape. This was recognized by Bagley and others working in the CIL laboratories,* and Bagley [53] has described the rheometer they developedas a result. In this device, which has come

'Canadian lndustria Limircd. Montreal.

EXHIBIT PAGE 000984


PO!. stai atir

I I I 1

The len gra

I CQI

1 Ro- as mi ca: Sc "'1 c n no st<

PC

Ct el. PI a1

11 01

u b ti ti fl

EXHIBIT PAGE 000985


flow and also as a quality control tester. A widely used t s t involves the use of the following die geometry and oper-

eter = 0.01925 inch h = 0.1760 inch

urc = 1,500 psia

w rate is determined by weighing the polymer extruded in a fixed f time and, for these particular conditions, the extrusion rate in 0 minutes is called the "CIL flow index." w and Lamb (861 designed a miniature version of the CIL vis- for use with very small samples.

as been reported that it is sometimes difficult to achieve steady in the CIL-type instrument. Schreiber [87] measured the flow rate

"a.

-?:'a a continuous function of time and found that periods of 30 to 60 '9 minutes were often required to achieve a constant flow rate. In some -' cuesclxs, no steady state was obtained even after one hour. Furthermore. E; - Schreiber and Rudin 1841 found that a sudden increase in pressure dur-

ing extrusion actually decreased the flow rate of low density polyethylene. These observations demonstrate that a constant gas pressure does not necessarily lead to a constant flow rate, so that the existence of a steady state must be verified by flow measurements over several time pcriods.

For viscosity measurement at high shear rates, the CIL type viscom- eter has been largely replaced by rheometers with servohydraulic and electromechanical drive systems, in spite of their much greater com- plexity and cost. However, three commercial versions that are still available are described in Chapter 9.

Ramsteiner [88] has developed a pressuredriven capillary device that allows one to monitor with high precision the flow rate as a function of time. Gas pressure in the barrel forces the polymer through the die into an oil bath, which is heated electrically. The volume of oil displaced by the molten extrudate is measured electronically A viewing port in the oil bath allows for observation of the behavior of the extrudate so that this devlce IS useful for the study of so thermal extrudate swell and

cblanc

EXHIBIT PAGE 000986


Correlation af Low Density Polyethylene Rheological- Measurements with

Optical and Processing Properties . .

hi. Si-{IDA, R. N. SHROFF, a t ~ d L. V. CANCIO*

Cheii~plex Coinpany Rolhg Meadows, lNfnofs MXMB

- . Tile processing propertles of low densky polyethylene

tilelts. such PS dmwclown nnd neck-In, and the Rnal product proper+les, such as film hnze nnd gloss, have h e n successfully mrretnted with rheolo [cat functions and the level of long- chuln 1)mnchlng. The r l! eological functions employed are the entmnce pressure drop AP, and the swell ratio S., determined at a speclRed shear stress uslng an otlRce with a length1 diameter (LID) ratlo of zero. The calculation of shear stress requires additional measurements using adie wltli a Rnite WD ''

e.g. 20. The rheologicul functions AP. und S . are governed by the level of high moleculnr we1 ht species andlor the level of long-chain binnching(lCp). ~faetermined at a mndanl shear stress, in order to elimfii>te the effect of viscosity, they are a relutive meanure of e~al t thi t~, Higher AP. and S, indicate a higher level of LCB and corrclnte with poorer optical proper- -

ties awl drawdown in Rlnis.

INTRODUCTION ur previ(ms study (I) involved the sufccssful predic

O t t o n of the processihil:ty of Sigh density polyethylenes Gum capilla flow stcudy-flow viscosity vs shear rute data in the s 7 ear rute runge of appmxl- mntcly 1-600 see". Such duta were curve-fitted to the empirical equution of Su lh (2):

where a6 = 35, a is the attJustubIe pont~neter and tl. Jimiting viscosity at low shear) und r, (muximu~n relnxa- tion tinre) are ohtuined as shin. fuctors in the least squares u~uilysis of the lineur form of Eq 1 through an iterative prmdure using u mniputcr. The limiting vis- rwsity at low shcar, tl,, generully ngrced well with values nrc;~surecl using a Weissenberg rheogoniometer (WRG) for ;I nutnl~cr ofhigh denslty polyethylet~es. Also emerg- ing fronr such a curve fitting procedure is the proc- cssi1)ility pararncter R,, defined by the relation (1):

where C is a11 ;~rbitrerily selected mnst;tnt chosen to yield numerical value for Ro of hhveen 1 and 20.

W u were, however, not su~~essful i n applying Eq 1 to m;my of the low density or the I)riinched p o l y e t l ~ ~ l e ~ ~ c s studied Itere. The reasons are hvorold. First, q, obtained fro111 the curve fitting procedure does not agree with the measured q. fro111 WRC. Second, the viscosity-shear rate data in the -j range of 1-600 sec-' are 11ot nwcssarily different for resins diFfrring greatly in tiwir 1nolccu1;ir weight distribrttio~t (XI WD) or the level - tPc,..~.,~e A&I,V,.. <:I*,,>.~, c ~ ~ r l ~ . c , ,~~i t l t~.~t~. oh t , , a x a t ;

of longchain branching. Specifically, Rn nray not differ rlgnifiantly among various restns even though the hlWD ~i the high molecular weight end wries greatly.

SInce the vkimus response at the higher shear rates docs not re9ect the change in the high MW portion of the MWD curve, we hnve shined our emphasis to the nie;lsr:rements ofelastlcitv in an effort to relute the latter to some of the prncessin&and the product properties of the low densitv wlvethvlenes. The reason is thnt ovticol a. <

and dnwdown propertl& ofbranched polyethylen;s are governed by the presence or lack of high MW species. The elasticity functions of Interest are the entrance pressure drop AP, and swell S , measured usingcapillary rheometer with an orifice huving u lengthldiameter (LID) ratio of zero.

EXPERIMENTAL A numl)er of comlnercially avuilable low density or

branched polyethylene (LDPE) resins. ranging in melt index (MI) from 0.2-13. were used in this study.

The molecular weight distribution was obtained on n - Waters Associates gel permeation chronratograph (GPC) hlotlel 200 with n series arrangement of four col~i~ncls of porosity rating fronl2.5 X loJ h to 5 X lo6 h. 1. 2, 4-tricl1lorol)c117.~11e W;L< used ;L< the solvent at 135°C. The flow rate was 1 nlV~nin, injectio~l tinw \\<IS 2

.~nin, and the snnlple weight WLT 0.5 g (diluted to 200 1111). The longch;~iu 1)~u~ching (LCB) level w v ~ derived using cornbined CPC and intrinsic viscosity nlea- sure~uents in TCB i t 135-3.

Stcatly state Row date in the shwr rate r ; u l ~ c of0.CM-2

POLYMFK FNGiNlFRiNG A N D SCIENCF. N O V F M B f R , 1 9 7 7 , V o l 1 7 , No. I t 769

EXHIBIT PAGE 000987


at 190°C using 2.5 cm diametcr platens. At shear rates for 4-1000 sec-', the thta were ol)tainccl from a gts extrusion rhcmnetcr at 190°C using hvo dies: One wvzs of 0.043 in. cfhmcter ( D ) end h;td a90" cntrmcc angle with an WD of 20. Thc othcr wnc ;tn orifice (WD = 0) with ;I 90" entry nnglc and D = 0.060 in. Both R;tl)inowitsch ;ind etitr~~ncc corrections ( 3 ) were itpplicd in the ttsi~~tl . wvay to clctcrtnine the truc shciv n t e nnd the truc shear stress at the npilhtry \;dl. respcctivcly. A gns cxtntsion~ rhcotnrtcr wits used in prcfercnce to thc Instron rhconictcr inmitsc the entnincc pressurc drop and the swc!l citio tnensc~rc~~ ustttg the orifice lnvolvc pressures as low ILC 5 pst. Ttrc rhcmnetcr wm equtppcd wtth 0-100 psi p u g c with nn nccitrncy of 20.1 percent of full scale. In this rhcomcter. volu~nctdc Row rates Q nncl swell cots were tna~rtrrctl nt preselected prcssrrrcs. yfcl~tng the true shcur strcss sand the truc shear rute 3 from thc rchtions: r = (AP - AP.)/4(L/D)und 3 (32Q/nD3)[(3u + 1)/h 1. wherc tt is thc slope ofuppuretit shoir stress vs :tppitrctit shcnr nttecrtrve. Here, AP is the ~,csst t rc clmp cu~rr~spotrtltttg to ti (lie wlth WD = 20, nnd bP, is the prcwrtrr drop at the sattte shew nttc in the Lit! = 0 oriRcv.

Along with A?,, ~ncctsrtrcd tlirirtly using the orifice, we ulsct nreusurcul S,, tleR~tcul 11s thc rutlo of nn unntt- tiraltd cxtntdate su~uplc cliatnctcr to the orifice diatnc- trr. For the ptqxwe of this artjclc, wc dtd not And I t t~c~xssnry to utt~rctil the nvell cxtnidtttcr; (4, 5).

Pemnt I I I ~ b dcAnnl us thc pcrccntugeof tntnstnlt- tcul light sa~tterrul Iy the Rhtl nrow thun 2.5" from the normul ittcidcnt Iwatn and wvu.. t n c n w d acmrcllng to - ASTht D-1003 rtsing e Cardner pivotable xphzre hnzctticter.

Filtns were t n d c usitrfit~ Itlow Rltrr process itsing 113.5 In. extruder of 24:l U D which wnq equlppcd with ntl 8 . 111. side fcd clie. Thc die gap wu.. sct nt 0.025 in. tiud Rl~n with tton~inttl p\lgC of 0.001 in. wvw pmlun.cI at lm p o ~ ~ t d s prr hr ut a 1)low rtp nttlo of 2:l.

RESULTS AND DISCUSSION Nclt tt&x ( M I ) u t d clctrslty (p) ure the most widely

~tsr t l p;~riit~trtcrs I)!. wliich vurious 1)r:itwhed p)lycthylrttc* rwin gn~tles nrc (lcscrilnd. While MI pm- vitlcs :I relative niritstirc of tnolectthtr wetght und viscosity Irvri. it ignorcs the non-Ncwtoniara nuture of flow end t1oc.s not um)unt for the differences in nrolccrtlor \wight clistril~ntion (M WD) und loug-chnin Iminching. For rsantplr. two resins used in extrusion coating and c:istiug :ipplications have flow curvcs with different low shear viscositirs Iiut the same viscosities at shear cites greater tli;w al)out 2 sec-' (Fig. 1 ) even though the app:~rw~ t nlolecttl;~r weight tlist rilir~tions are widely dif- f.brcnt (Fig. 2). As niay 1)e inferred Iron1 the intercept \ v i t l ~ thr line i n Fig. 1 giving thc v;~lrte of the melt index s1ic:lr strcss, the nwlt indices. n1c;tsured;tt -j> 2, ;ire the s:unc6 (111 = 3.3). In Fig. 2 ant1 other figures showing . \ l l \ 'I) . tlic nornralimtl curve height is plotted ag i r~c t riittion count. which is inversely related to lop-itlt~nic ~nol~-uil:tr \wight. TIir .\f \\ID c u n w are not corrected for lot~~-c.hnin I~r;111chin~ :tnd :Ire sho\vti ;IS r:lts C ~ ~ ~ - I ~ I I I ; I ~ I ~ ~ ~ ; I I ~ > S k)r the. s;tkc of con\wliencc.

ELUTION COUNT

From the data in Figs. 1 and 2, it is noticcd that the great difference in the high MW portion, or the level of LCB, is not reflected in the viscous response at + > 2 sec-I. Thus. R,, for rcsins C and D in Fig. 1 is the sanle. However. a difference in the viscous response at + > 2 we-' tltics exist if there is a significant difference i n the lo\vrr ,\lW cntl of thc CPC distril)ution curvc. For esatnplt-. two LDPE tnoltling resins hive th: same $11 and density but differing level of lower M W

- species (Fik. 3) and show ri sigiific.utt difTcrcncc in Rn (Fig. 4).

For the majority of low dcnsity resins studied here. however. some S t h e processibiiity and product properties arc inRr~cnccd ty the level of LCB or the level of

7 7p POLYMER FNGlNiFRlNG A N D SCIFNCF, NOVfMBER, 1977, V o l 17, N o I 1

EXHIBIT PAGE 000988


. .

Correlation of Low Densily Polyethy lcne Rheolo$cal dfcasurcnrents w fflt Opfical and Processir~fi fropcrti~s

CLUTMN COUNT

FIG. 4. Vl~ccrslty ptottctl n nlnst shear rntc for !too I~rr~t~cl~cd plt,cr/tycttc rrrl~~s. G aadfi~. at W C .

higher hlW species (6). We will not consider here the eRect of a diffcrence in the low molecular weight species on thc rhcvlogicnl functions. It is difficult to make a true distinction behveen LCB and high MW spccics because. i n the free rdical process of LDPE polymcrim tion, one accompanies the other. Therefore. in vicw of the concept of a shear rate-depet~dent relasation spectrum. (7). i t would he rensonnble tn expect that the flow properties of importance for such LDPE rcsins should he those 01,tainecl at low shear rxtes, such as the stcldy- flow viscosity q and the first nor~nal stress diFference (PSI - P,,)--both measured at low shear n tes using the

- '-VRG. The transieilt shear stress and normal strcss tnea- surctncnts i n the WRG would perhaps 11e even more scnsitive th:m the stend\. state tneasttrernents i n detect-

?Pi ' f L L r c F V C l N f r ? ' V , 7 ANQ SClINCF. NOVFMEER. 1 9 7 7 , V o l 17, N o I 1 771

ing such n change in LCB l e ~ l and hencc the resrtItillR change in the product propcrtics atid tllc pnwcssing behavior.

Unfortunately. such mcasuremcnts are t i~nc mnsum- ing, relatively inaccurate and. therefore. not st~ital,l~ for rapid resin charncterfzntion. The solution to this pro[>- lem emcrged from the following hvo conslderat~o~~: (a) the entrance pressure drop M. 1s reported to I= rclatcd (8) to the first normal stress differcncc nnd other elasticity functions such N the exlb pressure (8) nnd thc die well ratio, and (h) we hnve itscd (10) a technique of mensurfng bP, directly wing nn orifice (die with LID 9

0). thus avoiding time consuming Bugley plots (3). A further advantage from a practical standpoint for using dP, and S, 1s that these functions represent the result of a tensile or elongntional deformation superftnposcd on a shenrdeformation, deformations thnt exist tn all proccss- in& operations (11).

Since we nre itrtcrestcd 111 rchting AP and S. to thc LCE level, nnd they it1 turn mrrclntc wftli tltc optical ttnd the dmwdown propcrtirs of Ltn~ttcl~cd plyet l~) . tc~~cs, we will Ixiefly rcvlcw how thc LC0 levcl, 1t.5 repre- scntfil by the welght averngc rtuml~cr of I~rn~rch poltits

er molecule, n,. is ohtnit~etl. It Is derlvet! fmtn a m - r i n d CPC-lntrlaric vlsmsity data (1'2) a s l ~ g the fol lo~- ing relation:

whcrc ($1 and ($8 arc the Intrinsic viscosities for the liltcar and hmnchcd polpthylcne of thc sntnc molecular welght, and K and a are the constants In tbc Mark Houwink equation. The g factor In Eq (3) Is relatcd to thc nunrlw of hnit\ch points pcr molecules, 11, hy the equation:

where 1, and 1s nre thc modIficd Bessel functio~is' of order 2 and 3, respectively. An iterntive procedure is used by assuming nu Initial vnlue of A (unlinowt~) untll the calculated (& ngrees with the men..ured d u e . Because of the uon-linear dependence of A on the moleculnr weight, the relntion ti, = Mi, docs not hold, although us o first approsinration tl, 5. MI,. The details of this cnlculntion nppenr in nn earlier publicatio~l (12).

An lllustrntion of the influence of n, on AP, nnd S, is shown In Fig. 5 for the hvo resins whose nppnrcnt XIWD trppea& in Fig. 1. h'ote that Imth resins C~IIC! D hwe the same melt in Ffg. 1. Note that both rcsins C and D haw the swlw ~nclt index. I ~ t t resin C, with a high n, 0156. has significantly higher A!',, ~ n t l S , at ;I given shew n t c t11;ul does resin D (F~E. 5). where n,, = 9. \\'bile thc resins C and D are chose11 for illt~str;tti\vr ~IIIJWSC, O ~ T

srltlotn uses in cou~i~~crci;tl pr;tcticc twi \vitlc.ly dissiwi- h r resills for the satne ;~pp\ic;~tion. One is thus in- terested it, detecting sr~~al l rliffcrcGtws it1 the LCR Iwcl fclr resin\ with roughly the san~c SIWD mid X i 1 and relating these differencrs to :.etch protltlct properties as haze and gloss nntl to it prwxssin~ ~ ; I T ; I I I I C ~ C ~ such :LS drx\vdo~vn.

EXHIBIT PAGE 000989


M. Shida. R. N. Shrofj, and L. V. Cancio

l lo \vev~~. thc funct~ans AP. autd S, for u set of rcstns urc8clcpndrnt t1n MI ~sr.rtsrnslty leveleven tfthe MWD or LCR lcvcl is the sum. AP, undS, at ugfvcn ahear rutc uw h~gllcr if the mclt index is lower. This is illurtmted in Fig. 6 fbr thrcu. low density ntslns with anon! o r less st~nllar MWD. In order to climhutc the melt index or the vlsmsity vuriution effcct. the same two functlonr are

used at constant shcar strcxs r instcad of at ~oust l l l t shew rxte f. APe and 7, at a given shear stress reflect tllc elasticity of resins even if the viscosity is differcot.

From the data in Fig. 6 nnd our experience, it is observed that for many brmched p~lyethylenes, I,oth AP, and S. become less sensitive to LCB level or n, as pile goes to higher fo r higher 7. Thorefore, @,and S, at the lowest common r nre used to correlate seven1 resills with-respect to. their optical propcrtbsor dnwclmvll Iehavior. It may be noted that the resins dedglatcd d c s C, D. C and H nncl showit in Flg.9. 2 5 nrc usct[ o~aly to illustmte how n lnrgc difference In LCB level Rffccts thc viscosity nnd the clwticity o i tttc resins tmci hcnce the optical properties. For example. percent ha= for RIm from rcsin type C is 17. whereus It I s 6.0 for resin type D. Ourdircussion helow, on the other hand, will 1 ) ~ cottflncd to reslns whose "gross" I)ehnvfor h the same I N I ~ where finer differences need to I)e dlstinguirhed.

Ham for Clarlty R e h .The rcstnr uscd in a clarity Rlm spplicutlon nll hud u

nominul mclt index of 1.6 and a density of 0.922 glctnJ. The lowest common r for these resins is 2.8 x 10" dynrdctn', which corresponds to data meusurement tn the vicintty of 17 pst for the oriflee.

The general purpose clarity Alm grude resins considered here all have the MWD of the type shown for rcrrfn D In FIg. 1. We will now consider what factors overn the optical properties of the Rlm produced by a

!I- A I ~ W X S S .

Huek an CIcgg (13) have pointed out that If the density of the restn Is hclow 0.925 e;lrmS, extruston defects are the predominant contributor to the total huze of the Alrn. For higher density reslns, c!ystdlization defects cun he uite signiRcant and contribute consider- 1 J l y to the totu huze. Extruston defects in low denstty blown Rlmr are predomtnantly caused by higher melt elt~sttcity and u htgher level of LCB. Therefore, huze hcreuses with increase in elasticity as mcnsured hy hP, (Fig. 7) and S, (Flg. 8) w d an increase in LCB as reflected by an increase in the level of htgh MW species (Fig. 9). It may IK remarked here that the difference in the high MW portion of the GPC curves as seen in Fig. 9 is reproducible hut small, whereas the same three resins show u large difference in the rheological parameters AP, and S, (Figs. 78). It may also be noted that if the internal haze contrihution to the total haze is large, as when the film is thick andlor if the resin density is high, t h e n At', and S. may preferahl~ be correlated with another optical property parameter, gloss, which de- petitls only on the surface irregularity.

7 , Drawdown for Liner Resins Resills for use i l l ;\ li~tcr fil l11 ; ~ ~ ~ l i c ; r t i o r l h:td :I rrornirtal

tnrlt index of 3.0, ;tnd the lowest cotntno~t r for these resins was I. 1 X los dyncs/ctnz, cortcspotdit>g roughly to the datu t~tcti ' ;~t 7 psi it; an orifice.

The liner film resins considered here all have the X I WD of tht- type shown for resin C in Fig. I , although the cntcnt of such a high level of LCR may be reduced Jepcnding on how the resin is manuhctured.

7 7 2 POLYMER ENGINEERING AND SCIENCE. NOVEMBER, 1977, Vol . 1 7 , No. l l

EXHIBIT PAGE 000990


-3

Correlation of Low Dcrrsify Polyc!lrylcnc Rl~cological hfcast~rerrrertts c~itlt Oi~!ical aucl Proccssitrg Prcrl~crffct

I .

I I I 1

8 6 7 8

H A Z E X

Flg. ~ . ~ p p a r r i t &iecutarcoclgkt dktrltutlon jortltc fltrec law det~alty ~~olycthy~cncr dctlgnated 1,2, and3 In Flgr. 7 and 8.

vnluer cctrltl not be relinhly measured I)ecnase of the snggfn of the cxtrudate its it cnlcrgccl fro111 the oriRce. Thew f ore. hP, at mnstant r was u s d ns n mensure of elatticity and LCB level In order to chnrncter!~ dmwdown pcrfonni~~~ee. As cnn be see11 fro111 the cluta in Table I , AP. pt u gfve~r zmrrelntcs well with 1)ehnvior in the Relcl.

CONCLUSIONS AND SIGNIFICANCE

F:tctors vcr). sitnilar to those :tfTectit~g the optical properticmfa filr11 apply to the easc with which LDPE tnelt GUI I)c drown dow11 to give ;I thin fih or coating. E;~sc ofdrawdown depends on 1)oth the viscosity :nd the elasticity of the melt. Accodit~gl~. low XtW (high MI), low elasticity. and ;i low level of long-chain Int t~hi i tg we prefcrrcd. For resins with :I higher h1I. such ;IS those considered hew for lit~c;~r rcsiti applic;ttior~s, the swell

POI YMFR FNGINfEr7Ifi!S AND SCIFIICC, NOVEMBCR. 1977, V o l 17, N o I ? m

We have shown how cnplllary rheometry, using nn orlfice die. Le., a die whose lengthldiameter ratio is zero, yields rheologicnl elasticity functions which relate to the level of longchain b n n c h i ~ ~ g in low density polyethylene. Such functions are the entrance pressure drop AP,, and swell S, at a specified shear stress. The usefulness ofthese functions is illustn~ted by the correla-

Table 1. Drawdown Behavior

bP, at r = 1.1 x 10'

Resin Mt Fleld exparfence dyneslcm'

1 3.3 Good--Customer A 4.5 2 3.3 Good--Customer B 4.9 3 3.0 Good-4hemplex 5.2 4 3.2 Good--Customer C 5.7 5 3.5 Barderfinelbad-Cuslomer C 6.0 6 3.4 Bad--Customer A 6.2 7 2.7 Bad--Customer D 6.9 8 3.1 Bad--Customer C 7.7 9 2.7 Bad--Customer E 7.7

EXHIBIT PAGE 000991


M. Shida. R. N. Shroff, and L. V. Cancio

tion ofchmges in the film optical properties ofaseries of commercial film grade resins with changes in S.. For resins with higher MI, where swell of the extrudates is difficult to measure 1)ecause of sagging. the drawdown

or the alility of the film to be drawn down to thin gauge is successfully correlated with &,.This *

study illustrates the xpplicntion of fundamental rheolog- icd principles to the optimizatioi~ of resin processiIdity and physicxl properties.

REFERENCES 1. hf. Shldanncl L V.Cando.Polym. Eng. Scl.. 11,124 (1971). 2. R. SahIn. j. Ap11l. Polym, Sci., 7, 347 (1863). 3. E. B. Baglcy,]. Appl. Pl~yr.. 28,624 (1957). 4. N. Nakajimu and M. Shlda. l'rottr. Soc. Rhcnl.. 10. 288

Wm.

5. R C. Kowalski."Elutic Bchavior in hfolbn Viscotlnztic Polymeric Materids," Ph.D. dissertation. Pnlytechnic In- rtltute of' Brooklyn (1963).

6. E. J. Knltcnbacher. J. K. Lund. and R. A. ~ l r n d c l s o ~ t , ~ p ~ ] . . 23.55 (Nov. 1967).

7. R. N. ShrofTand M. Shidn.]. Polym. Scl.. C35, 153(1$71). 8. H. L LPNieve and D C. Bogue.]. Appl- Polyni. Scf.. 12,353

(186HI. I' 9. C. D. Han. M. Chorlcr, and W. Fhlllppoff, Trutir. Soc.

Rhcol, 14,393 (1870). 10. R. N. ShmK M. Shldn, and T. M. Krtgar. 34th SPE Antcc,

41 1 (IrGO!. 11. F. N. Cogswcll, poty;. Bng. Sci., 12.64 (1872). 12. J.A.Cote and M. Shldn,j.A!ti;!. Polyrn. Scl.. I4,3083(1970).

13. N. D. Huck and P. t Cleffg. SPE Antrc. Tech. Paltcrr, 1. (1961).

POLYMES ENGfNEERlNG AND SCIENCE, NOVEMBER, 1977, Vo l . 17. No. 1 1

EXHIBIT PAGE 000992


EXHIBIT PAGE 000993


- - RANDALL

I . INTRODUCTION

The use of 13carbon nuclear magnetic resonnnce (NhIR) spectroscopy in the moleculnr charocterfzntion of macromole- cules has advanced o u r knowledge Into s t ructurul areas thut Itave been nenrly Imposslblc to measure by o thc r spectroucopic techniques. Innovative applicntions have led lo determinations of polymer configurntionnl d is t r ibut ions , comonor?er aequencc dis t r ibut ions , nvcrnge sequence l eng ths , structure and dis t r ibu- tion of shor t c h d n brnnches, ond unulyscs of r~onrenctjvc e r ~ d

groupa. As a resul t , t he in~por lnncc of I3C NAlll to thc field of polymer science cunnot be overempl~usizcd. The key to t l ~ c

succesa of I 3 c - ~ h l ~ s tudies 11) de f in l l~~ : I I O I Y I I I ~ V ~ I O I C C U I U I ~ SI I*UC-

t u rc hsa bccn u eitructurul sc t~s i t iv i ty wtdch cttcon~poyscs rllorc than Juat a few funcllonul groups o r ca~*bon citoms. A scnsi. tlvity to polymer repeat unit scquenccs of Iengthu from two to us many as five, s even , und oven nine contiguous repout units [ 1 , 21 hus been obscrvcd. Of cour se , uny s t ructura l t c c l t ~ d ~ l u c O t u t senses u utiique response from us fc~v us two uucccssive rcpcnt units will Icod to u nlcusurentcnt of uvcritge scqucncc Icr~gttis [ 1 , 31 und run nuntbcrs [ 4 1 . In t rdd i t lo~~ to this cxccl- 1c11t s t r u c t u ~ . d scnslt ivlty, t l ~ e t ~ ltus bccn tin cnormous In~provc-

mcnt in tllc qumti tn t ivc sensit ivity of NQIR in receut yctirs. Dclection of long-choln branclting 111 polycthylct~c cun notv bc trtudc ul u level of one p e r ten thouswld c ~ ~ r b o t ~ utoms ( 5 1 , und newer generutiona o l high ficld, h i g l ~ c r sensit ivity Nhlll spcct ro- meters promise to extend this dctectlort limit onother o rdc r of mugnltude.

It would be ins t rucl ivc ut t lds point in l ids d i s c u s s i o ~ ~ to

review some of the ntlributev (hut huvc mudc NhlR s o nmenable to polymer s t r u c t u r d unalyses. For the sake of brevi ty , It will be assumed thnt the render i s busicnlly fumilinr

1 with the phenomenologicnl descriptions of both I I nnd NhlR, ( I t la a primary objcctivc of I ) J s articlc to discuss the frmtc-

work through wNch 1 3 ~ - ~ h l ~ spectral inlormution is t ransfcrrcd to useful polymcr s l ructurnf infonnutlon, conucquently ve ry little time wlll be spent In phenomenological clcacrlptions thul ore not rcqulred for un u t ~ d c r v l r t n d i ~ ~ g of t lds " l v ~ ~ r t ~ f e r

proceaa.") A slgnlficant ndvuntuge of 13c N M R over corrcspond-

ing NhlR sludiea of o the r nuclci i s thnt the nucleus hus u spin of 1 1 2 and occurs at a nutural ubundnncc of npproximntcly 1 % . This latter proper ty prccludcs any oppreciublc complicutiotrs

ETHY LENE-6 ASED POLYMERS --

from I % internuclear interactions and the f o r n ~ c r ensu rcs isu tropic magnetic behavior. T h u s , from o quantum mechnrlicul

s tandpoint , NhlR can be t rea ted i n n similur wuy to 'il NhI11. The curbon NhlR spect ra l response lo polymer s t r u c t ~ ~ r c

is s o sonsit lvc to umoll cllu~rgcs t l ~ u t Idgltcr lavcls of I3C iso- topes would lend to hopelessly complex Nhlll spectrul p u t t c ~ ~ ~ ~ s ,

us cncountercd Nstoricully in co r rc spo l~d ing l ~ ~ - ~ h l l ~ studics ," of I J

vurious hot~~opolymcru untl copolyt~tcry [ 2 1 . Soc~~c isotulric C l u b c l i ~ ~ g I IUS been uscful 111 ccrluiri pulymcrs st t idics I G , 7 1 :

efncietltly to rcnlovc 1111 "c, '11 i ~ ~ t c r ~ t c t i o t r s . ws111ti11,:

spcct ru corttuin only sin&Io litrcs, cuclr of wl~icli ct~tr be rclntctl to u specific cui-bon s l r ~ ~ c t ~ t r i ~ l c t ~ v i ~ ~ o ~ t ~ ~ ~ c ~ r t .

'I'lris p w t of llrc d i s c u u s i o ~ ~ lct~tls u s to t l ~ c scct)~rcl ttt~~jtit'

u d v u n t u ~ c of ~ h l l i ol. p o l y t ~ ~ c r s , which is tllc wide t.til~gc

covcrcd by 13c chcn~icul shi f ts . Lsp rcs scd in ppttr, tlrc cI\uwicit\ shift i s ficld i t ~ d c p n d c r i l U I I ~ i s tlclitwd by tltc f rcquc~tcy t l i l '

3~ N M R covers u c i t c~ i t i c i~~ s l ~ i f t t4uttgc 01. t,vct. Z O O 1 r l u i i . w I I ~ C I I

is 20 tinit!s thut usually c ~ i c o u r ~ t c r c d in ' 1 1 N X I I ( . In polyiiler

spectl'u, this churuclcrist ic lcuds to wcll- d c t i ~ ~ c t ~ t e d r c s l ~ u t ~ s c s from the s t ruc tu ra l building uni ts nroMng up u polyn~cr n~olcculc.

The internul stnndnrd most often uscd in h igh - t cmpcru tu~~c Nhlll s tudies of polymcrs in solution is Ircxun~cttryldisiloxcll,c (I lhIUS) . Tctrumethylsilunc (ThlS) i s still Ilrc Nhlit chct~~iciii shifl s l u t ~ d u r d of choice but i t s low boili l~g poi111 1'rcclucr1lly precludes I t s use In Nhlll s tudics or polyntcrs. I t is p r c f c r ~ ~ l ) l c lo rcpor t all polymer chcmlcul s N f t s wittr r c s l~cc l to tctriiittcll\yl- sllune (ThlS) by correcting thc IlhlDS chccnicul shirts to 11 ThlS t u n t r d . l ' lw cl~cmicttl sliifl cllffcrcttcc 1)c:ttvcctt 'I'hlS I I I I ~

IihlDS i s u ~ ~ p r o x l n ~ u t c l y 2. 0 pprn, but tltc precisc t l i f l o ~ ~ t c c should be established i ~ t d c ~ ~ c n d e ~ ~ t l y on c w l ~ slroctromctcr.

Thc finul uttrfbr~tcu con t r ibu t i r~g to tllc success of I 3 C N R I I ( polyntor s t r u e t u r d unulyscs urc u rcsull of s i g t u l ' i ~ ~ t ~ ~ l I I I ~ V I I I ~ C E S

EXHIBIT PAGE 000994


. . .------ K a h u x ~ L

In instrument techt~oloyy. OperuUon irt the Fouricr trunsform mode [ 8 j has made Ngh senslllvltles possible and permits a trade-off between high sensitivity and resolution ( 8 ) whenever

desirable. Sometimes the low nutural abundance of the '=c isotope Is enally glossed over Irr vlcw of tlrc cuvc with which

' % - N ~ I R spectra are obtllincd on tho comnrcrclul NAlH Instru- rncntatlon uvallable today. Broad-band decoupUrtg ( 9 1 not

otriy removes ull '11 spin-spirt couplitty rvitlt 1 3 ~ ~itrclei but ulso results In the creutlot~ of tltc nuclcur Overltc~user effect (NOE) , a phenomenon that occurs only during broud- bar~d dccouplirlg und leuds to enhunccmcnts I I I resonuncc in te~~s l t l eu i~~dcpendently of the populution of contrlbutfny nuelel. The ~irugttituda of thc ttucleur Overhuuser effect ~ I I I I be vurfublc und Is rclutcd to thc spcclnc tnccl~ur~lsms tltrou,.$~ ivl~lch ttuclcu~~ s ~ i ~ t s relux ufter cxcitcmcnl by u rudlofrcqucrtcy licld. For- tunutcly for most polymers, the nuclc~tr Ovurlrurtscr cffcct is nwrc un ussct lhun u Ilublllty becuusc of tlrc restricted mobility o f polymers 191 , whlch feuds to thc dipole-dipole rclnxntion rnccltunism us the principul, i f not tttc o ~ t l y , n~ndc of nuclcnr reluxulion. Tltc rtuclcur Ovcrlruuscr cffcct opcrutcs cxcluslvcly through the dipole- dipole rclaxutlon mccltc~rtism, corisequently most polymers exhiblt the muximum NOE cffcct of 3.0 191 und desirable quantltutivc annlyscs go unimpeded, I f there Is nny question of differences antong NOE's it1 polynrcr NSlll spcctru , guted dewupling experiments cart be perfomcd to ensure equul NOE's throughout the N h l R spectrum 181. These fuctors, to- gether with a patient eccumulatlo~~ of duta tltrouglt time uverug- ing, have led to quantitative mensurements of cot~centrotion levels of one carbon type per 10,000 totul curbon i~tomu, u s mcnlioned earUer, I t i s this combinutiort of good spcctrul sctt- sitlvlty to low conccntratlori levels In conju~rcllott with exccllcttt

structural senaltlvitles that hus mude Nhllt so v~tluublc In polymer characterization.

Wth the advantages of 13c NhlR now briefly reviewed, I t Is uppropriute ut this polnt to dlscuvs polyntcr strtictutSc In ternts of II frurnework cotrrputiblc wlth lltc informutio~r rctrlcvcd Iwnr

1 3 c - ~ h l R snalyaes. "Polymer atructure" can evoke u diffcrcnt response, depending upon the purtlculur arcu of I r~tcrcst , fmm varfoue polymer adentlsts. It can cncmtpus morpho- loglenl s t ructures , properties, rnolcculur weights, und even flow propertfeu of polymer melts. Polymer atruclurc In this discusslon will refer to the actual molecular chain s t ructure. that i s , the identlty of the repeat unit and Its chirullty, sc- quertce atruclurcs and their dlslributlocts. tlrc identity of crtd

ETHYLENE-BASED POLYMERS 2 1

gmups lncludir~g nunlbers urid types per ntolecule, t l ~ c d c ~ r c c of polyrnerizotion, and the identillcution of both short- and- long-chdn branching. For homopolymers, the interest in polymcr molecular s t ructure Is Umited to the d o p e e of poly- mcrizutlun, cliirnlity u ~ t d vurlutlorl 111 n~odcs of rnonoinct* itddi lions, tho idctrtity of en11 groups, ctttd extent of long-clrilit~ branching, Copolymer structurnl unulyses olconrpuss all of the fuctors cncountercd in unalyses of t~omo~)olynters but w i l l \ udditlo~rul ~oiepUcutiotts urising rront vtii4ous possible scqrtct~cc distribt~tlons. llotnopolyn~cru with one petldirnt group per repent unit cun often bc trcntcd u s copolynters becwse of cltiriil dlffcret~ccs tltul ntuy nrlsu ivitllj~t I ' C O C U ~ unit sequences. Rlittltc- ntutlcully , scqucttcc dl~tr ibut iotrs nrc trctrtcd i l l the slutre w u y wltc thc~~ they urisc frottt cltirul diffcrwriccs 01% d i l f e ~ ~ c ~ w c s i l l

rcpcut unit structur'es cro~ltcd by trsiltg dil'lc~~crtt conro11~t1ct~s driring ~~oly~rrcrizutiott. Ucctrusu ~rolyrncr ct>irulity is inhcrettlly I~rcludcd lo A ,1J copolyntcr* tlcuc~.iptiot~s u t l t l I t t r s I ICCI I well coverccl itrdcl,crtdc~~tly pr~cviorrsly [ 2 , 31 , tltc dcvc l~q~r~tc~t t ul' structrtr-it1 co~tcepts u~rd e l tu~~~rc te t~ iz~ i l lo~ t ~ ~ u r u n c t c r s i t 1 tlrc U I I -

contl~rg discussior~ will bc ii~nilcd to A , U tylrcs of colwlyntct*r. y h ~ ' ~ttr~ll~cnrirti~ul trcuttrtcrtt i s , t l r c ~ ~ d u r c , qtlitc gettct~ul but w i l l bc u p ~ ~ l i c d axclusivcly 16 ctlrylwrc-bnsed polymers, t l ru l i s , low-dctrsity polpctl~ylcr~a, tineur low-derislty polyethylcws, ottd etltylcnu- vltryl ucctutc copolyr~~e!'~, w hlch tire ulso prodwxcl f r e t rwlicdly 111 u I ~ i g l ~ - ~ ~ r c s u u t ~ c proccss.

Prlor to tlic udvctit of 13c Nhlli, knowledge of rcpcut unIl s t ructure und tho rclutivc A , B cottceritrcrtlons for copolytncrs w u s usuufly ull :hut could bc detcrwined front u nticrontolccului~ structural vicwpoit~t. Eridgl'oup co~~cc~t t r r t t io~ ts could be I I I C I I -

surcd for rnutty step- pwvtl t polyn~crs if tlrc ~)olyrito* cltrti~t cndcd it1 u tu~~ctiortul croup thut W I I S nctlvc c l ~ c ~ ~ ~ i c u l l y , but uliphulic crtd groups frola clruln-growth ~)oly~ttcrs ust~nlly wetrt unct~ut~uctcrircct. Ilcpent urrit structirrcs of both c I ~ ~ u t ~ - g r ~ o \ ~ t l ~ and s tep-growtl~ polynters ivcr-c ul'tcn dcterniittcd by citltcr

1 lnT~.orcd or I I N h I R . Tho n~issittg ingrt!dict~l ill ntosl col)olyniur I I I I ~ ~ Y S C ? I wi t s tlte C O I I C C I I ~ I ~ ~ I ~ ~ O I I of ~r t~ l lke cot i t ipt t ) \ t~ ))~titls 01' polyntcr9 r.cl)ctrt urlits. t I i i1 t Is, tltc All lllr\ tlicld ctritcctttrntic~t~ Any poly~~rcr cliuin, wltcthcr+ u lttut~ol~olynrcr or co~~oly~i tc r , cu~t bc visudlzcd u s bcl~rg derived front ttrty one 01. i t l l of llte t11rcc c ~ c l ~ s l v e types of dlods, tltut i s , A h , A U + U h , 01' UU, li1101~I- edge of tlrc three diud conccnt ro t io~~s , w l ~ c t l ~ c r ubsolutc or rclutivc, feuds to tllc h ,U ntotc Cructiotw, uvcrnge S C I I I I C I I C ~

lengths for both h and D, und t l ~ c "rutt ~runtber," wlkicll i s thc riuotl~cr of il.utrs collcctivcly of botlt units per 100 cor~tiguous rcpuut u ~ t l t s , us tlcll~tcd by Il~~rworrd n ~ r t l ilitcltcy L 4 1 . 'l'lrc

EXHIBIT PAGE 000995


I " " - RANDALL

relotlon6ihlps among "n-eds." thut i s , dinds, t r iuds , te t ruds , e t c . , end the various resulting derived s t ructura l parnmcters cnn best be understood by examining n model A,B copolymer c h i n where the sequence arrungcments ond l~umber o r r u n s , c l c . . cun bc eneily vlcwcd and counted.

The following A ,B copolymer chain ltns u typicul random copolymer sequence distribution. The ends ure tied togethcr for two reuaons: f lrsl , to up1rfoximutc n iotig clltifn, end sccond, to remove nny discrepuncles In the vurious n - s d dls t r i - bullone created by cnd groups . The i~dvu~t tuj ic or dcplctlr~l: such o copolymcr clluln ie tltut uny dorived ulgebruic s t r u c t u r t ~ l rclutlonshlps con be tested directly.

A "vurt Lu dcf i~ie t l us url u ~ J ~ t t c r ~ - u p ~ c d seclucrlcc ol' like rcl~crtt utlils U I I ~ vurics f r o m unlty to 01c longest scquenco the chuln rviU Illlow. In tho ubove n~odol clttdn, the length of euch "A" run Is giveii directly ubove euch conllguous "A" scqucnce wlulc the length of eoch "D" r u n i s givcn directly below cuch c o ~ ~ l i g u o u s "B" sequence. The "A" and "U" s c q u u ~ ~ c e diutribu- tions con be broken down ns follows:

Run length N um be r Number (1) Scq ucnce (Al) Scqucnce (Bi)

1 DAB 2 AB A 5

2 BAAB 2 ARBA 1 3 BAAAU I AIIUUA 2

4 BAAAAB 2 ABBUBA 0

5 BAAAAAB 1 AUBUUDA 0 6t B f A f 6+B 0 A(U)6+A o

A 2 = WUAAU scquenccs , c tc .

ETHYLENE-BASED POLYMERS ' 2 0 7 - and the corresponding definition goes for the "B" sequences.

The number of "A" sequences ond the number of "B" s e a quences In the above model chnill ore , therefore , g i v e ~ t by

Wllenevcr the onds of the c l t ~ l i ~ t ore coi~nectcd cor~ceptunlly, tlic numbcr of "A" s c t ~ u c r ~ c c s will ulwuys ctluul tho nunlbcrq of "U" scclucnccs, wldclt Ilcrcuftcr w i l l bc cttllcd tllc "scqucitcc ntl lnbc~*." In procUcc, Eq. (3 ) wilt bc vulld for copolyn~crs l ~ ~ r v i ~ l g Id611 degrees of ullcr~lutions bctweerl A 111td U ~ c q u c ~ r c c s o r n rttndoi~r distribuliort of "A" v c r s u s "B" c h d n ends . Othcrrvise tltc " A " scqucnce number cull d i f fcr from tlrc "U" S C ~ ~ U C I I C ~ ~ttttnl~ei' b y 21 , d q ~ c ~ t d i t t g U ~ I I w h c t l ~ e r ~ tlw c111ti11 t c ~ w l ~ ~ t ~ t c s t111it111i!ly i lk

"A" units o r "U" u~rl tu . Thlv dil'fcrcritx bccorncs i tnpol~tt~nl only whett tlw number of A,U ullcrrlutions i s low. Fut. rrrnclo~~l und ultcrnuting ~wpolynw~.n, t l ~ u " A " t r t t t l "11" scqticncc I I I I I I I ~ C W

will bc 1110 fiwl~c. Cotraldcrt~lio~t h t ~ s to Itc givcll for block co- polynlcrs huving o111y u fcw blocks p e r chuin. Fur I I I I A U A triblock copolymcr, the "A" scc~uctrcc riumbcv Is 2 rv11iIc t11c "U" sequence numbcr i s 1. If tltc codu of tltis Iriblock copolymer ore connected conccptunlly, both scqueltce numbers bccomc tirtity.

TItu totttl c~u~nbet . of " A " Iwlwttt trrrlls r r ~ t t l tlw loti11 t~uinl)cl' ol' "U" velreul tt~tilu colt be tlcli~rctl I'r'o~rr tltc ~ I I I O V ~ SCOII ( : I IL '~ dis t r ibut io t~s u s bolluws:

EXHIBIT PAGE 000996


H T O l = LID i ( 5 1

The average " A " and "U" scqucncc I c n ~ t l t s urc hdvctt, rcsl)cctively, by tho nutnbcr of "A" rcpcut utlils tlividcd by thc sequcnce number and thc number of "U" rcpcttt units divided by the sequence number:

"A" uvcrugc scclucncc I c t t~ t I t - ; . IA . l i . , \ . I t (6)

: 2 2 1 8 = 2 . 7 5

und

"11" Average sequcnce length = i : i B . l i B . t t

Finnlly, the run number ( 4 1 , which Is thc totul tlumbcr of " A " plus "£3" sequertccs p e r 100 uiiits, i s hdvctt by

The " run number" ie not a s useful a s the "sequence number." but does give the overage number of times the rcpcut units

ETHY LENE-BASED POLYMERS ' 209

switch from A to B and back to A per 100 repent units. Thc "sequence number" expressed p e r 100 uni ts wilt always be onc- half the r u n rumber , whlch i s 22.85 in the above example. hloro wlll be given tutor regtwding the rclatlvc volue of run nuntbcru vu r sus ~ c c l u c ~ t c c r lun tbc~ ,~ . I:or llle tltnc I x i n g , I t is In~portunt to s c c how s c c ~ u c t ~ c c distrlbtrtlotls cut1 be uliliscLL to gcncrulc much-nccdcd s t ructurnl i t~fom~ut iot t .

Thc cibovc unulysls dcpcrlilcd upon obscrvttlioits of cot~tplctc "A" uttd "U" scquence dlstribtrtiotls ove r sequctices of t i l l 1)os- slblc "A" and "U" Icngths. Such s t r t tc turr~l infortntttiot~ is gcnerully not uvullublo. It i s possiblc front Nhlll to obt tur~ t t

conipietc A .U sequcnce diutributiotl within u finite sc t luct~cc Icngth. This lutter distrlbutiotl rcprcset l t s thc totttl tturnber of wtrys h und I3 coil be contblt~cd rvitlur~ tt spccil ic give11 sc- qucrtcc Icitgth. The tlct rcsul t Is IUI h ,U clit~d, t r iud, o r higher o r d e r 11-ud distt ibutiott . A s it lutatls o u t , this Ittttcr distribution cart leud to the sumo s t ruc tu ru l i t~fotntuliot~ 41s tlie forntcr distrlbutiott without ktlowli~g tllc l o t g t l ~ o f thc lotlgest "A" o r " U " scqucttcc. In udditiott, sinlilttr s t r~tc l t l r t t l i~tl'oritt~t tiott cutt I J ~ obtdttc!d i't'otit ~ t ~ k y y i t l ) l c t e "it titl" clisttlbuliott bccllus&! 11142 V U V ~ O U S i t d/11t'ib~(iOt18 I t l W I ' C ' ~ I I ~ C ~ ~ I I I ' o u ~ : ~ I S l l

cullcd "r tcccssu~~y rc lu t io t~s ld l )~" 1 3 ) . 'L'l~c cl~nruclcrizutiott o f tlrc prcvious ntodel cl~ultt will trow be rciwntctf, but tltis tltlte nwro rcutisticully itt tcr'tttu of clutttttitutivc It~fol-tttutiott t l ~ o t i s nvailublc cxpcrinrctltully f~un t NRlIl. 'I'hc model clluitt is rq)e~ttcCJ bclow with diuds of rcj)cttt uttits ldcrtliiicd. Ertch rcpcrtt uttlt i s pa r t of two diuds by bcing tllc c t ~ d unit uf it prcviotts clit~d and the bebdntting unit of the next dirtd. Thc A A utld B U diads are idcntlficd above the c h d t ~ wldlc thc A D ttnd B A d i tds are idenlificd below tho clruin:

EXHIBIT PAGE 000997


TABLE 1

The Necessary Relationships among Helntive Concentrntions of All Possible Sequence Combinations fmrn Monads to Pentads

hlonnd- Diud I :

Diad-Triad

AA = AAA + 112fBAA+AAB) (BA+AB) = BAB + l /Z(BAA+AAB) + ABA + 1 /2 (ABB+BBA)

= 2BAB + (BAA+AAB) = 2ABA + ( A B B + B B X ) B B = B B B + l /Z(ABB+BBA)

Triad- Tetrad

AAA = AAAA + 1 /Z(BAAA+AAAB) BAA+AAB = BAAB + l /f(BA.PA+AAAB ) + 1 /2(AABA+ABAA) + 1 /Z(BBAA+AABB)

= ZBAAB + (BAAA+AAAB) = (AABA+ABAA) + (BBAA+AABB) BAB = I /2(BABA+ABAB) + 1 /2 (BABB+BBAB) ABA = 1 IZ(BABA+ABAB ) + 1 /2(ABAA+AABA )

ABB+BBA = ABBA + l IZ(ABBB+BBBA) + 1/2(BBAB+fjABB) + 1 /2 (AABB+BBAA) = 2ABBA + (ABBB+BBBA) = (BBAB+BABB) + (AABB+BBAA)

B B B = B B B B + l /Z(ABBB+BBBA) - (continued )

11.

EXHIBIT PAGE 000998


TABLE 1 ( c o n t i n u e d )

Tetrnd-Pentad

AAAA = AAAAA + 1 /Z(BAAAA+AXAAB) BAAA+AAAB = BAAAB + ~IZ(BAAAA+AAAAB) + lIZ(BBAAA+AAABB + 1/2(ABAAA+AAABA)

BAAB = 1 IZ(BAABA+ABAAB + l IZ(BAABB+BBAAB )

ABBA = 1 /Z(ABBAB+UABBA) + 1 /Z(ABBAA+AAUUA) BBBA+ABBB = ABBBA + l IZ(BBBBA+ABBBB) + 1 IZ(BUBAB+BABBU) + 1 II(BUBAA+AABBB)

BBBB = UBBBB + l IZ(BBBBA+ABBBB)

EXHIBIT PAGE 000999


48 * RANDALL

orrlrlyses involving triad and lughcr o r d e r n-ud distributions bccause the sequence number can be determined independently frcm A-centered and B-centered n-ad distributions. ThIs result i s on important verification of thc reliability of the NhlR dulu expcrfmcntully us will bc sccn Itttcr in dlveussions of ut~ulyscs of lincur low-density polyethylcncs. Alll~ouglr it muy u l f irst appeur pedantic, a revicw will be givcn of the triud distribution to demonstrntc this very point.

A triud distribution is cusicr to develop conccptuully bc- cuuse euch repeut unit is the center unit of u unique triud. '1'110 A-ccntercd und U-centcrcd t r iads ore Identiflcd bclow for tlrc sume niodel c h d n uscd in tlbc previous u~itlurictic dcvelop- orcnls utilizing, initially, lllc complete scclucncc distributiorr und , secondly , thc diud distribution.

A B A BAA

AAB ADB

BBA BAA

AAA : AAB :

ABA i BAB

ABB EBB

eris A 8 A

AAB A A A

AAA BAA

: ABA : AAB i BAA

BBA BBtt

ABB BBA A A B - ~

BAA AAA AAA : AAA

AAA : AAA AAB: BAA

ABA

The triade total s e follows:

AAA = 8 U U U = 2

AAB+BAA = 12 ABUtUUA = 6

BAD = 2 ABA = 5

The triuds ure grouped by likc ccn tc r s bccuusc thc conrplctc s e t s of A-centcrcd t r iads and B-centered t r i ads r e p r e s e n t , respectively, all of t he possible ar rangements for the neighboring units of the "A" and "B" repeat units. Conscquently, the totul ttumbcr of "A" utllts ant1 ttlc totul truorbct- of " U " units urc b4vcn by

A = ):iAi = AAh t (UAAtAAU) + UAU : 22 ( 1 5)

nnd

'I'l~c s c q u c ~ ~ c c rttnnbcrs a re liltcrvisc givcrr by

Equutioti (171 is cusy to visuulizc conccptu~tlly bccnusc UAU gives the conccntrutforr for thc s c q ~ ~ c n c c Icrlgl11 of onc wiulc 1/2(BAAtAAU) givcv tlbc collcelivc concoblrutio~r ol' ull of tlic remuirlfng sequences becuuse c ~ r c h scqucnce of two nnd I O I I ~ C I . bcglns with UAA nntl cnds with AAU, 'Tlw nrrttlo(.;ut~s silr~~itioci produces 1:q. ( 1 8 ) . As wus tIw cnsc ftrr tlrc dit~cl clislribuliori, It was possiblc to determine tlic t o l d nuniber of scquenccs 1)ci' chaln o r for any spedf i ed number of rcpcat units without knowing tlrc Icngtlr of the longest scquencc in tho clrnin, Tlic triud distribution i s mom valuablo expcrinicntully tlinn u diutl distributio~b bccausc t l ~ c s c q w n c c nun~l~c: ' curl Ibc t l c t c~wi~rcd indcitcndcntly fmcn t t ~ c A-ccnlcrcd c ~ t ~ c l 1)-ccntcrctl l t lnds IS

atiowt~ ubovc by Eqs. (17) c ~ ~ r c l ( 18 ) . 111 l o l c ~ + (liuc~rssiorrs i r lv~~lv

ing cxpcr~inic~rl~tl ttiud dibt r ibut iw~v 11~0111 1 3 ~ - ~ h l l l duttr of vni iou.~ copolymers, this rclutionstJp will be uscd to clicck thc r3cli~tbility of tho N h l N duta.

EXHIBIT PAGE 001000


EXHIBIT PAGE 001001


. ." - RANDALL

posnlble sequence lengths , as shown in the first model analysis. What Is more Important fs to ob!aln an accurate resul t , which can be done If the most reliable n-ad dlstrfbution avrdlable i s selected for analysis. The necessary relationships a re an In- dispensable Ingredient for r e d u d n g NhlR Information , rcspon- slve to sequence lengths from two to a s many as seven o r nine contiguous uni ts , to a complcte ael ovc r 11 spcclfic n-ad Icngth.

In the enaulng discus don^, acqucncc unulyses of the following s p e d f l c ethylene-based polymers will be given: e thylcnel propylene copolymers; the throe most lmportunt commerJul litrcur low- dcnslt y polycthylcncs (cthylcrte- 1- butcne , ethylcnc- 1 -hexene , and ethylene- 1-octene copolymcrs); h igh-pressure , low-density polyethylenes; and ethylenelvlnyl ucctate copolymers, which a re also produced in a h igh.prcssurc process. Long- chuln branclltng will bc discussed riot only in the polymcrv produced in the h igh -p res su re processes but also a s an unplanned s t ructurul moieties in h igh-densi ty , linear polycthylenes. Dis- cussions of expcrimcntul Nhlit conditions, usslgnntcnts, nrld equipment will be introduced in thc following scctlon. At this poirtt , i t is Imporla~tt to emphusizc how Irlforctttrtior~ ie obtcrit~ctl u ~ ~ d thcn procecd to dutu m~~rvpu la t io r~s lutcr tvitt~out pli~ciltl; . -

I J too grent an emphasis on C Nhlll l'mn~ u pitc11ot11~11olo~1~1ri vicwpolnt. Any o the r required prcrccpdsitcu will be I n t w d u c ~ d simply ~d bricfly a s needed throughout the discusslons,

I I . EXPERIMENTAL

Pl~enomenologicrtl dcscripllons of both convontionnl continuous wuve and Fourier t rmsfo rm nuclear magnetic resonance techniques have been well describcd previously ( 8 , 101 and rvill not bc repeated in this art icle, Thc re a r c , howover, some prcrc- qulslles for procUcal considerations worthy of fu r the r discussion when investigating mncromolccules. Thcsc urc NAIU acquisition condluons, experimental ef f ic iency, d y n m i c range, and opU- mlzed snmple aolutlon conccntrotlons und t cn~pcru tu rcs with respect to experimcntd running conditions. Curbon-13 Nhllt data a re efflclently collected In the Ume domdn tmd thcn mutltc- rnuticolly separated Into I t s frequency domuln tiwough Fouricr trunefomotlon a f t c r data acquisltlon Is cotnplclc. The cltoiccs for date acqulaition conditions ore c r l t i cd if un efficient nnd quuntitatively reliable experiment Is to be pcrformcd.

In 8 typical NhlR exper lmer~t , in the time dcindn the snmple la exdtc t l by a long scr ics of s t r o n g , scluure-wave radiofrequency pulscs of ve ry short duration. If pmper ly

ki O Y LENE-BASEU POLYMERS I 219:

choscn with respect to both f requency a r ~ d duration, euch pulse will "t ipo the local nuclear moments b y a predetermi~lcd angle, usually 90°, a f t e r which the local nlornents will r c t u r n to their previous s t a l e pr ior to c x c l t n t i o ~ ~ by 81 i ~ r o c c s s dcscribcd a s free i r~ducl lon dccuy (FID). T h e sprrcings bctwcen Ihc r f pulscs should bc such Lltnt thc usscn~bly of t~uclctrr spinv cr111 r c tu rn to cc lu i l lb~~ iu~~ t bcforc titc rloxl p t l s c is rrpplicd. 1:rce induction decay cull bc obscrvcd l ~ y ~)lucinl: n rcccivcil coil 111

n dircctlorl or t i logond to the upplicd rl' pulsc , I I Ihc rf pulsc frcqucncy trttd nuc lc t~ r spln preccssion~rl frcquctlcy pcrfcctly coincide, rcsonuncc is uchicvecl ttnd 11 putSe expor lc~~t i t t l will 11c observed for tlw FID [ a ) . Notvnnily, a more contplcx I:ID pa t t e rn a ~ ~ u l o g o u s to "ringing" 11% the contlrruous wuvc exl)clSi- rncllt is obscrvcd bccousc the uppllcd rf pttlsc is ~ ~ c c c s s ~ t ~ i l y o f f - r c so iu~~rcc for nwst orgruilc ~ ~ ~ o i c t i e s , wI1ic11 typIc11I1y cxltil~i l

s p c c t r d I l~ t e s vrlthi~t a 200 p p n ~ runge front 1111 i11te1+11uI tetril- mettrylsilonc (ThlS) stertdard. 'rimc crwstai%ts for 1:lD urc dclcr~nirlcd ido~tg two axes 111 t l t c , r o t ~ r t i ~ l g ~ I ' I I I I I C [ 81. thc I'icld uxis o r "z" d i r c c t i o ~ ~ urld tllc o ~ ~ t l ) o g o ~ ~ u l ay plutic. 'Slie fur~r~ct .

i s cttllccl l u ~ r ~ t u d l ~ t u l rcluxulion, ucid the tili,c c o ~ , s t u t ~ t fur dccuy is tltc s l ) i~r . lu l l icc r~v l t rx~~ t io t~ tiictc, T I . Uccily ill tlw

As thc nuwcs fos thcsc dccuy c o ~ t s t r t ~ ~ t s ilrll)ly, d i f f~ rc111 mcchurilsrns urc rcvponsiblu for t%ttclcrrr r c l n x n t i o ~ ~ i11 tltc tritris ve r sc ond l o f l b ~ t ~ d l n ~ l dlrcctlotis. Spill-lritticc rctnxotiolt dc - pcnds up011 thc s t r eng th of coupling bctwccn tllc n t~clcur spill system uud the "lutticc" to which It belongs, und is govct+~\cd by locul, fluctuittirtg mugneUc ficlds with conlponcnts o r t l ~ o - gonul to the main field direction. Spin-spin rclaxution l ln~cs may contain a contribution from field inhomogeneity and dcpe t~d upon locul molcculiw motions wit11 components 111 1111 threc dircc- Uons, i n general, low- f requency processcs o r ~tiolcculnr motions will only uffect T 2 wNle high-frcqucncy ptsocesscu w i l l

uffcct both T, and T2. Thc tipl)ropriutc tlmc spncir~g bclwccn

pulses 111 u lo11g truin of pulscs durit tg N h l H t1t1l11 ~~cquisit iori depends up011 T 1 [ 81. For polynlcrs, 7' will typici~lly vury

2 1

bctwcctt 1 0 - ' U I I ~ 10 s . '1'0 ctisurc 991 rc lnx~r t in~l , t ~ ~ c p u ~ s c spac i~ rg s l~ou ld bc 5 T1 for thc longest ubscrvctl '1'1 1 1 1 ) .

For some polymer systems this could lcud to un i~,ordinute m o u n t of limo for data uccwnulullot~, u11t1 tllcrc trrc tinlcs when a dcdslort must be mudc os to wlrctlrer tlm i~tl 'urn~t~liorl acquired should only be uscd for tlirulitotivc pur1,oscs.

EXHIBIT PAGE 001002


Quuntitativc meusurernents requlro e i ther , complete reltlxution o r identical amounts of partial relaxation to obtnin rellable rasul ts . In the development of quantitative procedures , i t i s usually prudent to select those resonances for ~ I i l y s i S where relaxollon r eqdremen t s huvo been stringently met.

Conr;lderuble polymer spln-lalt lce reluxution time dutu a rc uvailable In the Iiterulure. A typicul rungc of molccular mobilltics is represented by polycthylcne I l l ] , polypropylcnc 112, 131, and polystyrctic 18, 1 4 ) . Tlte obsc~:vcd T ' s cult bc

I convcnicnlly und directly rclntctl to the cxtcnt local, f l t ictut~l- Ing segmental motions contribute to the rclaxution proccss. For example, slower ra tes of rcloxation o r longcr "lime constunts" ore observed for carbons close to the cnds of shor t sidc-chrlin branches o r at t l ~ e e n d s of the polymer c l~uln . Shor tcr T, ' s

ure observed for intcrior curbons in lortg, recurr ing tncthylcr~e scqucnces o r acljucenl to u brunch 1 11 1 . In ethylene- 1- Itcxcnc copolymers, for example, thc recurr ing methylole curbons from long, uninterrupted ethylene scquerices cxhiblt u T I of

branches uniformly exhibit T 's of opproxh~~utely 1 s 111 I . In I low-denslly polyctl tylcl~es, prepared in Idglb-prcssuru prsoccsscs, thc ovcrnli chuirt s t r u c t u r c I I U S 'cl.cutcd c u ~ ~ s l t l c r t ~ b l y niorc locttl scgtnctrtul notions tl tu~t fou~td 111 tltc Itighcr d o ~ s l l y c t l ~ y l c ~ t c ~ . I -hcxcne copolyntor dcscribcd ubove. The ntcthyl carbons from the butyl branch in this case display a T I of 7.1 s [ 11 1 .

Very shor t T ' s a r e observed for polymors with consideruble 1

side-chaln s ter ic Nndrance. Both the buckbonc and s i d o - c h l n curboris In polyutyrcne exhibit e x t ~ ~ e n ~ e l y short T 's of npproxi-

1 mately 0.1 to 0.2 a at 40- 44°C 1 9, 141. The longest observed T in polystyrene occurs for the r ing quaternary carbons , 1 wNch have no directly bonded protons to contribute to the relaxation process 191. Fortui~utc ly , there i s enough infonrtu- lion presently in tho l i teruturc lo muke uomc well-aducctlcd guensca us lo the propcr pulse s p u d n g 111 ttw long trrdn of . ..

i J puloes required to grencrutc C-NhlR polynrcr spccl ra f run~ t l ~ c Fourior trunaform type of Nhllt e x p c r i m e ~ ~ l .

Although of equal importunce. the.-e has been up to now leas attention paid to the mcasurement of spin- spin reluxution times o r T 's in NhlR soluUon s tudies of polymers. Line widths 2

13 u i C-Nh1R polyrncr s p x t r t ~ vury s t ro r~g iy with both cuncc~~l ru t ion

ETHY LENE-t3AStD POLYIUEKS ' 2 1 1

uild tenlperuture [ I S ] . Also, l i ~ ~ e widths urc 1101 tieccsstitnily unilorm s o the use of peuk heights in quu~t t i tu t lvc nwusurc- mcnts con yield misleading resul ts . A cootpo~ison of pcuk Iicight to pouk arc0 mcusuiwnetits i s given in 'ruble 2 for tlw e n d g ~ o u p rcsotlui~ccs fro111 NBS 1475 polyct llylcllc, wiuclt is known lo Ituvc u tiuntbcr-uvcruge ~~rolcculur weight o~'ou~tcl l8,000. At tc~~tpcl.uturcu closc to 125°C 0114 nl co !~cc l t t~~u t iu~ i s under 15'6 by rvcigltt , line roidtlrs of less 1Itii11 1 Ilerlz nt t r ~ t c ! .

hulf t l ~ c ~ w u k Iicigltt cun bc o l r t ~ ~ i t ~ e t l witlt I I I I c q ~ t i ~ ~ ~ i z c i i ~ u t i j : t ~ i ~ t i ( '

field. In wollcrr polyctrcrs uv swollc~t gels w lww tltc I ) I I I ~ I I I I ~ I ~ co11ec111:'utions upprouch 50'1 o r bc t t c r b y wcigltt, littc widll~b ut onc-hul l height nluy cxcccd 10 Ilcrlz.

hlost irtvcstigulors cissu~uc tli~rt tltc sc\ntl~lc col t t l i t io~~s i t , lltc typicul NhlR cxpcrinlent usctl for polymers Ictttl to :I co~ l t l i t i i~~ i k ~ ~ o r v n us "cxlrcmc I ~ ~ I I ' ~ ' O \ V ~ I I K ' [ IG, 171, wl t t -~x T I is tltc S I I I I I ~

- - - - - -

Curbon Peuk height (ntnt) Norwafized 1)cuk circa

1s

'Is

33

A i A +

'*(I"

A l (culcululed)

d l (observed) , - - - . . . . . . . . ,.

0.91

0. 88

I .0.1

902. .I

0. Jti

17,800

18,300

EXHIBIT PAGE 001003


A11 - RANDALL

There L conaidcrablo evidence In the literature to suggest that these conditions a r e met In ,&lute solutions and a t tempers- tures in s range of 100-150°C. It has been reported that even molten polyethylene exhibits a full NOE, wNch sugges t s a condillon of "extreme narrowing " [ 171. Nuclear Overhauser ef fects occur only du r ing proton-carbon hcteronuclear spin de- coupUng, which removes all proton spin coupling in teract io~ls

. . 13 with C nuclei du r ing datu ucquisition. Under guch drcunl-

s t ances , energy t ronsfcr C U I I occur 1rot11 t l ~ c proton to the

curbon nucleur spin syiitem end crcute cntrunccd resonuncc inlenslt les by s factor of 3 for full NOE's. Thc NOE reprcsents .

1 J a bonus when C-NhIR cxpcrimcnts orc pcrformcd lo dctcct s l ructurul moictics 111 s rungc of onc to tcn pcr 10,000 curbon

uloms. Full NOEts e r e typicully obscrvcd in polymcr 1 3 ~ - ~ h l i ' l spcclro 6s a consequcnco of 11 rcloxution proccss totolly datl i- nutcd by the dipolc-dipole mcchonism [ 191.

Another conslderstion equcilly importont to molcculor dynamics for a properly dcnigncd FT-NhIR cxper in~cnl f o ~ polymors iu dynumic rungo, Outing u t ra ln of rf pulses, cctcl~ FIU is rccordcd and s torcd uritl~meticully ut a prcsct computer memory location. Signul- to- noise a v e r u ~ d n g occurs becousc , * the weuk " c - N ~ I H signole continuc to d v c it posltivo resporlsc wtulc lhc noise s igr~uls odd in u rundon1 mutmcr. The nnc~l signul-to-noiec lmprovcrncnt is cquul to the squurc root of t l ~ c nwnber of sccumuloted FID1s. At tho outset of data accumulo- l ion , the spectrometer g d n sc t t i ng should bo such that the FlD just Blls thc rcceivcr. The s t m n ~ c s t tlnto domuin s ign~t l should not be clipped. The rccciver u~lulog- to- dih4tol convcr- sion, ADC, should be in a runge of 13-15 bits including s ign. Each odditiond ADC bit doubles the sizc of tho FED thot con be digitized; however, this requirement i s not so s t r ingent s s the wordsize in memory where the FID's ore stored arithmetically. For exnmple, I f one has only u 16-bit word und wis l~es to uvcrilt;c FID's where the signals in tho tlme domnin Iluvc o 1000 to I peak height ratio, 10 bi ts of thot word arc requlrcd to record the f i rs t FID If the weakest signal requires only one bit of storage. Aftcr the odditionul nccumulution of only 31 FID's, the computer word is completely flllcd nnd from thot point on the dots In memory will be truncated to nccnnmodole f u r t h e r storage of FID'e. hloet systems s N f t one bi t , which i s equiva- lent to dividing the da te by a fuctor of 2 , nftcr the wordsize

is Illled. Even if the receiver cupobilily wore lo5 to 1 , tho dntu could not be recorded with sufficient precision to ensu re a

ETHYLENE-RASED POLYMERS ' 223

correct obiiervetion. This problcm Is ensily solvcd by uving double precision arithmetic du r ing ds tn acquisition. U ~ l d c r

such circumstances, 221 FIDts con bc recorded In II 100011 experiment beforc the wordsizc Is cxlrirustcd. Tho nccd to

satisfy dynumic runge requirements for nt leust u 1000 to 1 signal rotlo occurs frequently in FT-NhIR s tud ic s of polymers. Typical commercitd polycthylenes, for example, hove numbcr- nvcrogc mo\cculur weights bctwccn 10,000 ~ i n d 20,000, corresponding to nrolcculor curbon nuwburs b c t w c c ~ ~ 700 rind 1500. 11 crld corbon rcsoncinces o r brirnchitrg ill n rtcllgc' ol' one pc r polyn~er molecule urc to be reliably obsc rvcd , the PT-NAlR cxpcrimcnt must meet the proper d y n m l c rilr1h.c r c - quircmcnts. Fini~liy, 1I1c crfect of c l~o icc ol' s o l v c ~ ~ t o t ~ tlytrttt~tie rung" r cqu i ronrc~~ t s slrould 1101 Oc ovcrlookctl. I:rcclucritly t l ~ c

s t rong 1 3 ~ - ~ ~ l l i s igr~uls of i l s owu. I t i s ~ w s s i b l c for tlrc mcmory ttvuilublc for tinrc uvcrugl~lg to bccomc cxlren~cly llmitcd if tlot~littg poi~, t t~ r~ i t l~ t t~c t i c cttnnot bc trscd c l t r~ i~ rg dttlo uvcrugict~;.

It hus ulso bcen rccog~rizcd thut thc c~t tu i~rn~cnt of l 3 ~ - ~ h l l ( si,cctrir wit11 Idgh dynamic rungc rcq\~ircnrcrrts also recjuircs un u ~ ~ p r q t 1 4 u t c handling of t l ~ c B o u ~ l c r t r ~ t ~ ~ s f o r n ~ crr lcul~~l ior~, I lour~d.off crl.ors cun s c ~ i o u s l y disttrrt spcct ru wlrcn ~tctrk i l l -

t u ~ ~ s i t y rullos III% 1000 to I o r Iriglrcr. Tlris { I I ~ O I I I ~ I I I 1111s

been diver ted by usillg floirtiny ltoint t r~i l lu~ic l ic dilI'il1g I:orrl~ier* trunsform calculations 120). \$ith co~is idcruble ultcntion 1)rtid to both i l~s t rurnc~l tn l und nli~tl~cn~ulicrrl distortions possible i l l

I:T-Nhllt cxpcrliactrts, excclleirt r c su l t s en11 l ~ c utttdt~ccl ir\ tltiinr titutivc s tudies of polyn~cru. T h e fu tu rc looks cvcn bi*igl~tcr~ with wcil-desigtred probcs ( 21 1 und ftrster. more cflicic~it nnt l l s r g c r , yct cost ef'fectlve conrpt~ter systems.

A final, and perhups the nlost important , considerittiotr in

plunning 1Ilgl1-quulity polyrtrcr 3 ~ - N h l R cxl)c141rlc1rts i s stunl~lc prc~,urution. Ifiyll- qunlity slrcctru wilh nrrvrow l i ~ ~ c widths necessary for quuntitntive tncnsuren~crlts con bc cosily ulld routinely obtained. 111 thc in teres t of efficiency, polytncrs rrrc somclin~cs cxuminctl in YT NRlll cxporitner~ts ns swollct~ gels 01'

111 the moltcn s lu tc . The rcsuiting spcct rn cxlJbit vcry 1)tutrd t i~ t c widltis, son~ctinrcs c x c c c d i ~ ~ g 10 llz 111 t l ~ c otic- l ~ c t l f 1)cclk height for 50 hlllz spect rn obtulncd ut 125OC, whc11 l l ~ c soltrlio~r conccntrolions trrc 500 o r grcotcr weight perccnt polynlcr. An

cxurnplc of how tlic upl~tr rc l~t r c s o l t ~ l i o ~ ~ cun \)c c o n ~ i d c ~ l l \ J l y rcduced by cor~ccntrution fov u polyctlrylcnc is S ~ I U W I I i t 1 'l'u11Ic 3. Second, I f thc polymcr spcctrunr i s doitiinoted b y u s i ~ r g l c ,

EXHIBIT PAGE 001004


EXHIBIT PAGE 001005


ethylene-- 1-butene, ethylene-1-hexenc, and ctlrylcne-1-octenc copolymers wlU be discussed in detail. , The nomenclature employed will be "E" for ethylene, "P" for propylene, "ti" for 1.hexene. and "0" for 1-octene In descriptions of sequence distributions. A more specific nomenclnture Is required as op- posed to the general A,U nomenclature to both dlfferentlatc utrd mmpore homologous sequences nmong the various copolyntcrs.

In controst to s tep- growl h polymers w hcrc fu~tctlonnl gioupti o r hctero utoms allow tlrc individu~il repcut units to bc idcntified. the monomer Identity la "lost" in c l i d n - b ~ o w t l r polymers such as a poly( 1-olcfiit) o r un etlrylci~c- I-olefin copolymer. For example, a "poly(ethylene)" Is uctuully n long choin of methylene sequences , a n d , in "poly(propylene)," lrcud- to-tnil ve r sus tail- to- hcnd repcat unit sequences cnnnot bc diatlnpulol~cd when t h e w a rc no repcut urllt l~rvcrs lons . In ethylene-I-olcfirr copolymers whcrc 1-olc l i i~ iirvcrslon ctrlr occur , the scqucncc dcticriptions mrty lrot bc unlquc. For exnmplc, In ethylene-propylene copofymers, u I' sequcncc connot be dlstingulshcd from u P E P scquc i~cc [ 2 2 - 251, tlrtit i s ,

Since the above molecular s t ruc tu res w e the some end it i s only the sequence descriptions that dlffer. it nkust be oointed

out that 13c-t4~n resononccs from polymcrs urisc from carbon o t m e In specific s t ruc tu ra l environments, and it Is up to tlic polymer chemist to tranelutc a curboil rcsonnncc idenU5cetlon to nn identlflcstlon of the p r e d s e sequence In which I1 resldes. A carbon ntom nomenclature Is needed, therefore , In adaitlon to o sequence tdentlfication. Out of necessity, n iromencleture system lnltleted by Randall 1261 and niccly expundcd by Curman [ 2 2 ] has slowly evolved ove r thc years , hlethylenc curbons located d o n g the backbone of an ethylene- 1-olefin copolymer chaln ere Identified by a pai r of Creek lc t tera , Indi- cntlng the locations of the neercst methlne corbor~s 111 e l ther diroctlon. The Crcek lc t tcr u Indicntea thul a mcthlne curbon Is bonded to a methylene carbon of Intereat. Two Creek le t ters , aa, Indlcate that the Identified methylene carbon Is sandwiched between two methine carbons. A 0 indlcatea that a methine carbon 1s two carbons removed from the cerbon of

k 1 HY LENE-BASED POLYMERS 2 2 7

In t e re s t , and s o forth. Slnce neighboring curbon coirtributiol1s to chemical sh i f t s seldom exceed fou r carbons removed, a methine cerbon four o r more carbons from the methylcne curboil

of in teres t Is indlcuted by n 5 ' . Tlrc followitlg s t ructurul b e -

qucnces give churuclerist ic inclhylcnc rcsonitnccs in 1 3 C - ~ h l l i spcct rn of cthylcne-1-olcfiir copolymcrs:

ah+ Y Y ah*

CH 'CH' I 0 6 I R R

EXHIBIT PAGE 001006


2 2 8 - - R A N D A L L

hlethine and s ide -chdn carbons from shorl-chafn brunches a re identifled a s the center unit of e i ther a t r iad , pentad, etc. sequence, whichever Is appropriate. (Note that methine and s i d e - c h d n carbona wiU be scnsit lve to odd mcmbcrcd n-ad sc - qucnces only.) As u f u r t h e r illustration, the three types of mcthine carbons e re ldentllied for an cthyletlc-propylene copolymer below:

The methine carbons and methyl brclnches, ul)ovc, w e itlcrt- tified according to the scqucnce in whlch they ure locltted. I t Is nlso necessury to Identlfy the localion of each carbon Ir t tllc vurlous types of brnnches. Carbons in side-chtdn t~rr~rtcltes are idcnllficd by iBn where "i" d c s i ~ n u t c s tltc positiort in t l ~ c

branch s tar t ing with the methyl carbon us "1." The subscript "n" is used to designate the length of the branch, as Illus- trolcd here:

E T H Y L E N E - B A S E D POLYhlEMS 2 2 9 -

us cull be found it1 un c t h y l c n c - I - b l ~ t c r ~ c C O P O I Y I I I ~ I . ~011t~tjc1ittg both isolntcd urid blockctl I - b n t c n c scrlucttccs.

I'olycthylcnc ctldgroitl) rcsututnccs cnny bc t).l)icc~lly t~bsu t~vcd ul'lcr only 11 fcrv hours rut~ttir tg tllnc t l~c~rrks to ( I t ( ! n c w c ~ ~ ~ c r t c t ~ i ~ l i t~tts o f l:t~~tr~i~!r* t r i ~ r ~ s f t ~ r ~ r ~ Nhllt s~~( : c ! lvo~~~~! tcvs . As st~\tt!tl \ktx! viously, II dcltx!tlt~r~ 11f stt~ttt!ttrv~il t!tttili~!s 111 1i:vcIs 01' 1 /lllOll und 1/10,000 1trt11 lowc!i' ttr'c poss i t~lc . As show^^ 111 'l'11l)lc 2 , 1111! sctluruti~tl ottll:roul~ c c ~ r l ~ c ~ t ~ s it1 ~wlyi!t l~)flcttc rlrc tl~!sil:tl~~lc(l 41s I s , 2s. I I I I ~ 3s utuvtirtg wit11 l l ~ c tncthyl c t ~ d gtsoul) C I I ~ * ~ ) O I I

u s " I ." '1'11~ cilrl)i~tr itllylii: to 11 tct~tultlnl vittyl }:rottl' i s ctt!sii$- onlcd 11s " i t . "

IV. ASSIGNhfENTS

Assignn~crtts ure tho key to u succcssFul copolyr~tcr qrlitt~ti- tativc utlulysiu, but tltcre Is not ulrvuys ogrccrnetll I U I I O I I ~

vurious workers u s lo which uss ignn~cnls nrc cot'rcct. Rlodcl copolymers offe!. tho best approach but urc tot nlwl~ys nvriii- able. Off-resonunce decoupling cun bc uscd to distittguistt curbons by the nuntbcr of directly bonilcd protot \s , but it docs not u lwuy~ lcud to uttot~~rivocctl c l~oiccs . 'I'l~c tt~cthocls CIS cl~oicc

, ., 1 .J

for idctt t ifyi~tg curbort types i t t C-NRIIt sl)ccl~' i l nr'c 11ic vot*iuus sophlsticutcd pulsc sctlucrrccu, urlricli con be uscd i t , ccknt[klcx polyrncr systcms with fur lcss tm~bigttity thrtn c~~cuut t lc t 'cd wit11 off-rcsottuttcc dccoupl i t~g. Al'T [ 27) ur t t l IN1:I''l' ( 28, 231 , whlch stctrtd for "Attactrcd Prototi Tcst" uttd " l ~ ~ s c n s i t i v e Nttclci Enhenccmenl by Polarlzatlon T r a n ~ f e r , ' ~ rcspcctivcly, involvc the usc of omplltudc moduletions Inlrnduccd illto noisc-dccor~l)lctl

EXHIBIT PAGE 001007


230 -- RANDALL

1 3 C - ~ t t l ~ spect ra by heteronuclear J couplings. In the APT t e s t , methyl and methine cnrbon resonances wf l l have an oppo- si te sfgn to methytene and quaternary cnrbon resonances. The

identlflcallon i s unambiguous. When proton-coupled 1 3 ~ - ~ b l ~ apcctrn a r e investigated by thc INEPT method. tlrc usual i n - tensity ratios for muJtlplcts no longer upply. l 'hc methitto carbons respond with a - 1: 1 i~ t t cns i ty rtttio, n~ctltylenc cc~r l~oi is give a -1 :0:1 rutio, and mcthyl curbons givc u -1:-1:1:1 rutio 1301.

'I'hc gcnerutlon of i 3 ~ - ~ h l l l s u b s l ~ c c l r u , wlticl~ ttrc tiortctl by cnrbon resonunce n~ultiplicity, hos bcen best optimized thrnugh the development of thc DEPT (DIstorUoi~lcss Enltr~~rcc- men1 by Polarizution Trans fc r ) t cc l~n iquc 1 3 1 , 321. i t ntiiy be bcnefldul to diacusa the DEPT tcchrtiquc I I I sotttcwltut nwrc deltdl than APT and INEPT bccuusc it is bccot~ring U C C C ~ I C ~ ;IS

the s ta te-of- the-ar t technique. "DEPT" ulso hus tltc udditiutt~il

and vuiuable benefit of yielding sensit ivity cnhunecd 1 3 ~ - ~ \ ; . \ 1 1 1 spectra. The baslc DEPT pulse sequence is dvcr l bclow 131 1:

- *!th nolie decoupllng

-.*lo noise decoupltng

YO' 180'

The DEPT technique also utllizcs phnse ntodulutior~ introduccd

by 1 3 ~ - 1 t i scalar coupling and refocusing pulses similar to the A P T and INEPT methods. After an appropriate delay to crt- s u r e the proton spin s t a t e s hnvc reached ccjujlibrium, the

'11 tlpins urc pulacd 90°. A deltry of i / ( W ) in i r~l roduccd

(where J ia thc correct 1 3 ~ - i 1 1 scaiur coupling constunt) to 1 pennlt phase modulation. The l l sp ins a rc then rcfocuscd

wlth a 180a pulae wttile Ihc I3c spins a r c pulsed 90° for the first time. A second delay of 11121) i s introduccd for both

spin ayatems, a f t c r which thc I3C spins urc rcfocuscd "6th u

180° pulae while thc '11 system is simultuncously pulticd ut un

ETHYLENE- BASED POLYhlEKS 1 231

snglc C . If Ihc 0 pulsc Is phusc sltiftcd with respccl to tltc ,f irst 90° pulse, t runsfer of polurizatlon Is ocldcvcd fl0ola t lie

' t t to tho 1 3 ~ splns . A mnxirnunr enhancement occurs for tltc ntcthine curbons ut tJ = 90°, tire cucthylcnc cnrbons ~ t t 4S0, t t l \ c l

the mctltyi curbtms ut 3S0. ,411 udvontct~:c of tlic 1)IiI)'l' tcclr ttiquc over A P T t t ~ ~ d INEPT is tltut both IIic cottplctl I I I I ~

chcn~lcul sliift ussigtt t t te~~ts ill 1 3 ~ - ~ l \ l l l s p ~ c t r ~ t of 1~0th or-gl t~~ic cotnpounds und ntctcron~olcculcs. A Ikurttbcr of tttotiiliculio~ts u r t t l

lmproveniunts were la ter introduced 134- 36) ; Iiorvevcr, i t tvris

Totielii [ 371 who dcmonstrutcd that tltc number of crnpiticul pur iwctcrs I W I U ~ I W ~ by Grrtiit t ~ n d I ' i t t t I ttt~d ot11crs [3Gj wcr5c t i i ~ ~ ~ l ) l y o muttlfcstution of diffct90rci!s titrtott~: I I I I I I ~ O I I ~ ~ ~ I 1 r ) ~ i t l

intorucliutis. A ootrsldca'uliott of ~ ~ ~ l ~ i t i o ~ r ~ t l S I I I I ~ S itttd tlte I I I I I I I ~ I ~ ' ~ ~

of tttrcc-bo~lcl t in tcruct io~ts clc~irirt ly ttccuur~t SOY inttlty of t l ~ e

EXHIBIT PAGE 001008


k:IG. 2. A "DEPT" curbon- 13 Nhlil spcclrt tn~ of tin LDI'E u l 50. 3 M11z ut I 2S0C In t c t r ~ ~ c l ~ l t r ~ ~ o c l l ~ ~ t ~ ~ o ~ d,,,

model compounds [ 40- 4 2 1 . A single pnrunlctcr ol. -. 5. 3 i)pnl tiucccssfully ucco~c~rtctl fu r t he obst!rvctl c x p c ~ i c n c ~ ~ t u l chcnricul tihift differences. Tho Grunt und Puul pnramctcrs huve built in the y .inteructlons through the utlmhcr of direct puramctcrs ( u through c ) end ltlc subsequent "corrcctivc tcrms." I f one rcalizcs that the Crnnt und Puul q ) p r o u c t ~ is strictly cmpiricnl und an oversirnplificution, It cnrl still be uscfully u()plled In N R I f < s tudies of mocromolccules. The ToncllI mcthod does rcquirc computer fucilitics to gcncrote the requlrcd Informa- lion for assignment purposes whltc the Grunt and Puul method c u n bc performed with n pockct culculotor. A brief overvicw of t l t t ! Grunt end Puul mcthod, thcrcforo, would be usclu!.

Curbon-13 NhlR chemicnl ~ h i f t s con bc culculolctl bused on Ihc pruximlly and nunlbcr of m u r r t c i g l ~ l ~ o ~ l n g crtrl~r~rt trtomtr In lcrme of parwnctcrs derivotl front thc cl~cmicul s l ~ i f t behovior observcd for an extensive sc t of both linertr nnd brrit~ched olkuncs 1331. The rcfcrcncc poi111 is ntcll~urrc IIINI C O ~ I ~ C C ~ ~ O I I B

a r c mude to tho melhu~re chcn~ictll shift uccording tu the numbcr ortd geometry of neighboring cu rbo t~ uttms, The contribution

€THY LENE-BASED POLYMERS 2 3 3

of dlrcctly bolrdcd curbon utorns to tho tt~ctltunc cl~c~t~icctl shll t Is " h , " the contribution from carbotrs two bonds ren~ovcd is " b ," the contribution from curbons th lvc bonds rcmovcd is , I . . 11 the conlrlbution from carbons f o ~ t r I,onds rcmovcd is " c * ," und, finully, t l ~ c contribution f ron~ curbonv five lmnds rcn~ovcd 1% " c . " " C ~ r r ~ c t i v c ternls" ure ulso inclutlcd to acco~ in t for stct4c: o r ~ c o ~ n c t r i c n l d i f lcrcnccs . 111 Ilie c:orrcctive t c ~ w s . quttlc!ri.rtrvy , tt:rtinry, sc:ct)~tdury, ~ t t ~ t l I I ~ ~ I I I I I I ~ ) ' ~ : ~ I I - ~ I I I I I S itrt: clcsigr~utcd ns d o , xu, 2". unt1 I " , r e s ~ ) ~ ! ~ t i v t : I y . l ~ i . ! s e r i ~ ~ t i v ~ ~ l y , thc curbon of in l c~ ' c s t i s plrtccrl f irst 111 t l ~ c co r~wcl ivc tt!rtt~ utrd Illc cct~~tributitkg c o r b o ~ t t s listctl sccontl i ~ t ~ > ~ r i ' c ~ ~ t l ~ t ! s c s . The culcitl~ttcd c11c111it:uI s l ~ i f t for t11c tt~t!tIti~tc t!r1r11t111 i t t 1111:

c x t w l ~ l c bt!luir is:

EXHIBIT PAGE 001009


2 3 4 RANDALL

TABLE 4

T h e G r a n t and Paul Parameters for Alkanes Which A r c &lost Of ten Applled In

A n a l y s e s of 1 3 ~ - ~ h l l t S p c c t r u of hlucromolcculas

6 = 9.09 ppm 3O(2“) = - 3.65 ppm

.----...- - U ~ ~ t l ~ r c s p c c t to ThlS.

T h e mcthlne curborr chcinicul s h i f t s u r c 111 t l ~ c right o r d c r bill ou l o f plucc will^ r c s p c c t to I h c rcr~rru~~irt( ; c l ~ c t ~ ~ l c i i l s h l f t s :

T h e culculuted chcmical s h l f t s f o r t h o four m c t h y i curbon s c - q u c n c e s f d l c o r r e c t l y 111 t h c o b s e r v e d o r d c r :

What la not cor rec t f o r t h e culculutcd v e r s u s o b s c r v e d m e t h y - lcne c a r b o n chemlcal s h i f t s Is t h c dclfncutions bctween tllc two

t y p e s of a6' s e q u e n c e s , t h e two t y p e s of i35* s e q u e n c e s , a n d t h e t h r e e t y p e s of 0 0 s e q u e n c e s . While t h e methine chemical s h i f t s e r e not oniy incorrectly p r e d i c t c d a s to w h c r e t h e y should a p p e a r rc la t lve t o t h e remai ldng n~et l ly lcnc chemlcnl s h i f t s , t h e calculated v a l u c s d i f f e r b y more thutr u ppm from t h e o b s e r v e d va lues . T h e r c s s o n s for t h e s c d l f fc rcnces probnbly a r i s e f i r s t from t h e posslbi l l ty thut t h c "cor rec l lve terms" for ulknncn cunnot b c i n d i s c r i ~ ~ ~ l i ~ u t c l y upplied to ~ w l y i l ~ c r n 1331 lrr~d

C a r b o n - 13 NhlR Chemical S h i f t s with Respec t t o a11 I n t e r n a l Tetrninethylsi lane S t a n d a r d Calculated wi th tho

G r a n t a n d Paul P a r u m e t e r * ~ for t h o E t l ~ y l c n e - P v o p y l c n c Copolymur Scquenccv 1.istcd In T t ~ b l e 6

O b s e r v e d Calcu la ted chemlcul chcmlcul Curbon

s h i f t s s h i f t s nssigtunents -- 46.52 44.29 , 1 3 6

46.06 43. 98 $1 LL

45.77 43.67 4 4 k

37.111 37.39 s I

37.89 37.08 ' 1 I

37.51 36.77 , ' A I

37.46 37.08 . t ;

33.22 31.66 s R l c t l ~ i ~ ~ c

30.95 29.17 Rlctl~lttc

30.77 30.49 I 'I

30. 36 30.18 I J +

29.98 29. 87 J + J +

28. 91 26.68 Alu l l~ i~ ic +

27.43 27.38 6 A +

27.28 27.49 ti J

24.85 24.89 6 6

24.71 25.00 O d

24.56 25.11 n ii

21.83 20 .80 hlcllryl

21.61 20.39 Rlcthyl

20. 92 2 0 . 1 9 hlctltyl

19. 97 19.66 Rlcl l~yl

EXHIBIT PAGE 001010


.II~J ~ct;~tttn,t!r~lin.t n tq~ts t t? t ls !pu~ rtu nctioanq sntt n l l l~! t t t fnnl s!l\.I. .pa~n.ttl.tolu! .(l!"tn ptut A l r ln t tos~to~ n l l n l ) aq tro),lo ttnn Xntll

' nn~ t~~ .? i t n t l i l n n[qnp!ttt.lq n ltn nyn l sntu!)alttos s to ld IIIyN I~~l tOlSU~W!P . o ~ r l I(.~IIOI~~~Y [ k g 'c'; 1 sctn!~ttctt.ro~tco;r .tnloXlodos Jo s a p n l s

Ittttn!sttntci!p.onr) II! uanq snq l l l q ~ 1nun!sunttt!p-obil JO sosc\ 31t!lso,mltt! 1sntu ntlt j n DUO . I Z S ) ( ~ ~ 0 3 ) Ldonso.t~aoils

pa)nlaJ.Ior, ~nuo!suaw!p-o~t t .rttalsnttowot[ pun Ador,so~lsads ]II~N paAlosa3 - r pico!sttaw!p - 0 ~ r 1 Aq paw.xl,fuos a ~ a ~ t stuaw

II~!SS,II t toload nrl j , ' 17,s 1 oitAn,l prtit t lnn.ln Aq poclsl lqnd ttonq stit( s.tott~,(~otl.rn~ p o ~ t -on 811~ttfrtlrro;, artalAtlln 111 snnwt r l~os .rotu trtrottt j o ~ ) ~ I ~ ~ I I I I . ~ ! ~ s I I .tcy Adoasn.rlnotls ~ [ [ U N pUo!SU~Ut!P-OMl JO nsn s g ] JO a ~ d t m x a lual(aaxa t t y - o . t l ~ a d s pal~[aa.roa 11 -3

I C I

EXHIBIT PAGE 001011


4 b N W ~ P . . . - S - - N N N

EXHIBIT PAGE 001012


I'I'PEPtPEPPP, PPEPP, PPPEtEPPP, PPEPtI'EPp, PPEtEPI', und PEP. The observed chemical sh l f t s and assignments for this 9911 propylene-ethylene copolymer a r e given In Table 7. The assignment for (I.(, PPEPP (mmm), Is cleurly estubllshed by

this model syetem. T h e 1 3 c - ~ h l ~ spectrutn of th is 9911 c thy - Ier~e-propylene copolymer ul 50.3 hlllz u l ~ d 125°C i s rcproduccd in Flg. 4 .

h second uscful modcl copolynier i s u 9911 c t t~y lcnc -p ropy - lcnc copolymer. Only ncqucnccs Involving isolt~lcd propylctlc units will be present wlth tho following secluerlccs urllqucly observable: PEEEtEEEP, EPEEtEEPE, PEEtEEP, und EPE. An

oppor tuni ty is now ufforded to ussign uncc~tdvocttlly the .I:'

El8LE+EEPE tiequcnce us showi~ ill Tublc 8. Tllc f 3 ~ - ~ ~ l l l spcctrum o f thls model copolyml. ut 50. 3 hlllz wid 125OC Is rc1)roduced In Fig. 5. tYeuk r c s o n u ~ ~ c c s urc obscrvcd for * I

U I I ~ fib s c c l u e ~ ~ c c s , Indicuting t l ~ u t a l t e r r~u t ing EI'CPE scqucrlecs ure also p re scn t . Even weukcr rcsonunccs lndicatc tho prcsencc of u sn~ull m o u n t of blocked p ro l~y lcnc S ~ ~ I I C I I C L ' S .

A th i rd copolymer nys1e111 useful for conflr111111l: trssignil~ci~ts is t he ultcrnallng ct hylenc- propylcnc copolymcl. ~ ~ t u d u c c d by . Ilydroycnulion o f cis-polyisoprcnc.

?'hc chen~icul s tuf ts for the u l tc~wut iny c lhylcnc-propyle t~c co-

polymer are given in Table 9, nnd the 1 3 ~ - ~ h 1 1 1 spcctrum ut 50. 3 blllz and 125OC is reproduced in Fig. 6. There Is o common EPE methine resonance In the spect ru of tltc i t l ternutl t~g copolymer m d tho 9911 cthylcno bopolyn~cr tl~rrt crtn s c rvc ns t t

chcmicill sh i f t refcrencc polnt for thcse two modcl uystcms. To create f u r t h e r etandurdlzation of chcnllcul s ldf ts umong t hcue various mwtcl copolyn~crn, u stuull tm~oul~t of 11olyct hylcnc stundurd (NBS 1475) wun uddcd to c r ca l c u r o f c ~ w c c chctnlcul s t f f t at 29.98 ppm. T h e polyettryleno rcfcrcncc was uddcd to the 9911 propylene-ethylcne copolymer nnd the ulternatlng copolymer s o that the data 11, each of t he tubles would huvc a common chemical sh i f t basis,

The sequences obscrvublc 111 thc 1 3 ~ - ~ i \ l ~ spcctrum of the tllternating copolymer a r e EPEPEPE, EPEPC, nnd Et'E. Tlus

EYWY LENE-BASED POLYMERS ' TABLE 7

Carbon-13 NBlR Chemical Shift Assignments at 50. 3 RIilz for a Propylene-Ethylene Copolynier Containing Only Onc hlolc Pcrccnt E t l~y ienc and Principally lsotuctic Prol )y lc i~c Scc i&~c t~ccs .

'I'hc Suinplc \$us Prcpnrcd 111 10% by Weight in 1 , 2 ,4 - '~ r i ch lo robc i~zcnc ttnd tllc Spect1'~111 0 t ) t d n c t l 111 125 .! lo(:

wit11 Respect to an I n t c l w ~ ~ l l ' c t r iu i~et l iy ls i lu~~e S t u t ~ d t ~ r d -- - - -. - - - . . . - .

Clrclr~icul shift Cur l )o t~ Scquc r~cc ~ J ~ C I I , TBIS ussi g l~ rne t~ t u s s ig r~ i t~c l~ t -

46.52 .I 11 I'PI'I' ( ~ I I I I I I I )

46.06 .L J l'l1l'EtEl'I'l) ( I ~ I I U )

'LO, 92 hlctltyl t ~ l l l ~ E l ' r l ~ l : i ~ l ~ I ~ ( I I I I I I I I I ) -.-.-.-.-...-*-..-pep . . - - . - . .- . .-

ThUltC 8

Curbon-13 NhlR Chemlcul Sluft A s s i ~ n m c n t s ut 50. 3 hlllz for t l r l

Ethylcnc-Propylene C o [ ~ o l y t ~ ~ e r Contninlng 011ly 011c hlolc I'crcent I'rogylcnc. T h e Sluir~lta Wus IJrcpnretl ctt 10% by Wcigl~t

in 1 ,2 ,4- T r i c l ~ l o r o b c n z c ~ ~ c und thc Spectrui~r Obttuncd 111 125 i I°C wllh Respect to nn In ternal Te t rme thy l s i l une S lond~u-d

EXHIBIT PAGE 001013


P P P L , ? T P O P

.L

FIG. 4 . 50 .3 hlllz curbon-13 NhlR spcctrum of un 1 / 0 9 el hylcnc-propylcne copolymcr at 1 ZS°C in 1,2,4- trichlorobenzcnc,

Curbon-13 NhlR Chcmlcal Shifl Assignmcnls at 5 0 . 3 hlHz for un A1 ternaling Ethylene- Propylcnc Copolymer P rc l~a red by

llydragenotion of cis-Polyiaoprcnc. The Sample Wus Prepurcd et 10% by Weight in 1,2,4-Trfchlorobcnzcne

nnd the Spectrum Obtained at 125 i 1°C with Respecl to an lnternnl Tetrmethyls i lane Standard

Chemical shlft Carbon ppm, TMS assignment Sequence easignment

3 7 .9 5 r a Y EPEPEPE 37.89 rn a Y EPEPEPE

33.24 MctNnc &llE

0 0

hlcttiyl

hlcthyl

hlcthyl

EIIEPE

EPEPEPE

EPEPEPE

EPEPEPE

ETHYLENE-BASED POLYMERS ' 243

01'

EPEE

rcfcrcncc copolytncr ulso l m m i t t e d t l ~ c cltc~~iiciti sltifl ~ l l l ' f e r e ~ ~ ~ c s for nieso md rnceniic PEP methyl groul,s ond EI'EPEPE 4 x y c i ~ ~ l ) o ~ i s to be established. Tlie 0 . 0 6 ppni a) ruccmic ve r sus mcso chemical shlfl difference is in agreement with the observolions rcported by Zctla e l ul . 1601, T h e effect of c l ~ i t d i t y otr methyl group resonutices frwni propylcnc rcpcut units locut~.d on e i ther s idc of u bridgirtg cthylenc unit i s qui tc sntull ~LS

prcdicted by Torielti 1371. This is at1 important cunsiclcrutio~~ when essigtdng chlrul d i f f c rc~ iccs for I'I'EPI' sccjucnces. Cotl- sidering the thrcc cru'bor~ y cffect in gouchc rlr~rrngcnlcritu u t l l i zh~g u rotulioriol i so~~ ic r i c s t ~ ~ t c ~~ to t l c l , 'l'ottclli ( t~~cd ic l cd lhut thc downlicltl ar f curbon rcsotluttcc tvould bclotig to tltc ruceniic isomcr 1 3 7 1 . The wc t l~y l rcsonunccs i t 1 1:il:. li show 11

1: 2: 1 split t ing potterrb wlllr u ~ e p u r u t i o n of 0. 03- 0.04 piun. l'onelll assigncd tlicsc mctliyl chcmlcul s ld f t s to IIIII) , nlr+L'nt. und r r front low to high fields, rcspcctivcly [ 3 7 J . N o o t l ~ c r spl i t t ings rcl~rted to chirul cliflcrcnccs were observed illtrolli: Ihc rct~~uitking r c s ~ ~ r r ~ ~ ~ l c e s .

EXHIBIT PAGE 001014


A 'I '+ -- RANDALL-

FIG. 6. 50. 3 hlllz curbon- 13 N h l l l s p x t r u m of rl hydro- gcnutcd poly-cis- 1 ,4-Isoprcnc. The sumplc, which is un 111- turnutiny ettrylene-propylenc copolymer, wus run ut 12S°C in 1 , 2 , 4 - trichlorobenzene.

I t was possible to obtain a fourth model copolymer by re- moving the room temperature xylene-soluble atsctic polypropy- lene from the principally Isotactic 9911 propylene-ethylene copolymer. The extrncted copolymer contdned lsoluted ethylene unJls a s a major constituent, but n few elhylcne dimers, t r imers , posslbly tetrnmers and alternating sequences ore present us in-

dicated by the data in Table 10 nnd the 50. 3 hlilz 1 3 ~ - ~ h l l l spectrum In Fig. 7 . At least three new a y types of resonances are clearly visible. Tonelll (38) hog established lhut the PI'EPP chirai effects on the center propylcne unit8 rcsult f rm, the closest propylene repeal unlt and not from the nelghboring propylene unlt across the ethylene bridge a s shown below:

ETlhl f L E N E - B A S E D POLYMERS . 3 4 9 -

Curbon-13 NhlR Chcmicnl Shift Assignntents nt 50. 3 Rtllz Pol' rul

Etliyletlc-Propyletle Copolymer ColltnItdng Approxitnutely Oile hlole Pcrccnt Ethylene und Plil idpnlly Atnctic Pl'opylcl~o Scquct~ccs . I1cuk l lc ights At8c Givot in Rlillituctcrs. The

Sumplc Wos I'reporcd u t 10% by Kciylit i n 1,2.4-Trictilorobu11xct1u mid tllc Spcctrwn Obtuiticd at 125 1? 1°C with Ilcs[)cct

to un Intcrnul Tctromctliylsllune Stundord

EXHIBIT PAGE 001015


I N

x n C: x 8 U-U $1 iJ

U 0 I I f U-U $1 k 0 Y x I U-U

:, I ; . N *I W m u

0 I I I U-U g} 'i n I x I u-U

(? I I Vi- I U-U

EXHIBIT PAGE 001016


given in Table 1. The rieccssnry relationsf~ips will nllow specific resonances to be combined, thus nllowing mow accurate spcctrnl integrations ove r well-resolved r e d o n s . Ambiguities ussocinted with resonance overlup and unccrtufntics In assignmcnls con thereforc be uvoidcd. This i>roccdtirc elm best I JC u r~ t l c r s lwd t h r o u ~ h the fotlorvinl: c~uuntittrllvc dclcrnr l~i r r t io~~ of Ilrc completr? triud sequence distribution in c t l~y lcnc -p ropy lc r~c copolymers.

The initial s tcp in o quilnlilutive t r c i ~ t ~ ~ ~ c ~ i t is lo divide lhc s1)ectrum Into spcctrul regions , A through "X," !I:; dictutcd by ovci~lop und neccssury rclulionshi~) consi t lcr t~t io~is . Such rc~$oris urc described below accordi~rg to ratige in ppm U I I ~ c o n t r i b t ~ t l t ~ g n-ud sequences. The tolul resononce orcu for ec~ch r e d o n is designated as T X , where " X " is A , R , C , ntc. The: final s t cp

is to reduce the vurious n-i~cl ~nclucrrcc di1111 for cite11 r e ~ $ ~ i to u coinbinution of uppro[~riute t ~ l ~ t c l s .

Equutions ( 2 9 ) and (30) follow from the neccssury relationships bclwccn t e t r ads , diuds und diuds , t r iuds , rcspcr:tivcly. Tlic

' fuctor k la the Nhlll proporlionullty conut11111 rclnting tho ob . scrvcd resonance intensities to tllc number of contributing molcculur species. It cun bc Itrtcr removed tlirouglr normotiet~+ tion once a complclc se t of n -ads i s obtoinctl o r by obtuinfng llic k value for onc curbon utorn pe r polymer rnolccule, which Icc~ds directly lo t l ~ c number. or corrlril~utirrl: n - t ~ d s (Icr uvcrltgc polymer chain. Endgroup rcsonunces from liwenr chuins, os in the cuse for high-denslty polyethylene, urc useful for estriblisl~- irrg the value of k for n tiinglc cr~rbon utom (rcr c h ~ u n . i:Iinii~iti- tiuu of k by normulizollon lcuds to the triud dislribution pe r uveruge polymer chain. A distinct odvnntugc of NAII t quu~i t i lo- tive unnlyses over o the r spectroscopic methods Is Itrut the rcsolborrce irltensities ore directly proportior~ul to tlic number of contributing species, and this proportionolity constant rci~tuins the snme throughout uny ~+vctr spcctrtiril.

ETHYLENE-BASED POLYhlERS 249

The following spcciul t~clutiotttilti~) i s ulso rcquirccl to clcli~lc the "D" urcu 111 tcrnts of tr iuds:

EXHIBIT PAGE 001017


Documents

Case 1:05-cv-00737-JJF Document 160-5 Filed 09/03/2008 ... · A wide range of linear (HDPE and LLDPE) and branched (HP- LDPE) polyethylenes ... kglhr per cm, narrow gap extrusion