Patent Publication Number: US-8987385-B2

Title: Interconnected copolymers of ethylene in combination with one other polyalkene

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of U.S. Provisional Application No. 61/242,137, filed on Sep. 14, 2009, and fully incorporated herein by reference. 
    
    
     BACKGROUND 
     Conventional low density polyethylene (LDPE) has good processability, however when used in film applications, additives, such as polyisobutylene (PIB) are typically required to impart good cling characteristics such as cling strength or improved adhesion to surfaces. However, these additives when blended by standard extrusion or physical blending techniques often must be added at low levels to avoid phase separation and/or migration in or leaching from the film over time. Accordingly, a need exists for LDPE compositions with good processability, which can also be crosslinked if desired, and that can be used to form films with consistent cling behavior. 
     SUMMARY OF THE INVENTION 
     In one embodiment, the invention is a polymer comprising units derived from ethylene and polyalkylene, the polymer having at least 0.15 units of amyl groups per 1000 carbon atoms as determined by  13 C Nuclear Magnetic Resonance (NMR). The polymer comprises a polyalkylene with ethylene-based polymeric branches. The measure of 0.15 amyl groups per 1000 carbon atoms is based on the number of carbon atoms in the ethylene-based polymeric branches exclusive of the carbon atoms that form a part of the polyalkylene. 
     In one embodiment, the invention is a process to form a polymer comprising units derived from ethylene and polyalkylene, the process comprising:
         A. Contacting at least one polyalkylene with ethylene in the presence of a free-radical initiator in a first reactor or a first part of a multi-part reactor; and   B. Reacting the polyalkylene with additional ethylene in the presence of the free-radical initiator to form an ethylene-based polymeric branch bonded to the polyalkylene in at least one other reactor or a later part of the multi-part reactor.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a plot reporting the relationship of peak melting temperature (Tm) and density of commercially available LDPE and two inventive polymers and two comparative polymers. 
         FIG. 2  is a  13 C NMR spectrum of LDPE showing locations of peaks characteristic of different branch types. 
         FIG. 3  is a  13 C NMR spectrum of LDPE showing an example of quantification of C5 branches/1000 carbons. 
         FIG. 4  is a  13 C NMR spectrum of LDPE containing C1 branches. 
         FIG. 5  is a  13 C NMR spectrum of LDPE containing C3 branches. 
         FIG. 6  is a  13 C NMR spectrum of representative inventive polymer showing characteristic peaks of PIB. 
         FIG. 7  is a graph reporting molecular weight distribution of the examples and selective comparative examples. 
         FIG. 8  is a DMS overlay of the two examples and comparative examples. 
         FIG. 9  is a graph reporting the relationship of peak melting temperature Tm and Density of the two inventive examples, commercially available LDPE and comparative polymer. 
         FIG. 10  is a graph reporting the relationship of heat of fusion and density of the two examples, commercially available LDPE and comparative polymers. 
     
    
    
     DETAILED DESCRIPTION 
     Inventive Polymer 
     The term “ethylene-based polymeric branch” refers to a polymeric unit comprising polymerized ethylene and which is bonded to a polyalkylene. In one embodiment the inventive polymer (sometimes referred to as an “ethylenic polymer”) comprises the structural formula of Formula 1. 
                         
In Formula 1 the ethylene-based polymeric branch can be a homopolymer, e.g., LDPE, or an interpolymer, such as an ethylene-propylene copolymer branch. The polymer comprises a polyalkylene unit (here derived from polyisobutylene or PIB) with an ethylene-based polymeric branch covalently attached at a backbone carbon atom. The phrase “unit derived from a polyalkylene” can refer to a oligomeric or polymeric unit of the polyalkylene. The ethylene-based polymeric branch is either formed directly on the polyalkylene, i.e., an ethylene monomer or oligomer attaches at the polyalkylene and is subsequently polymerized or further polymerized with other ethylene monomers (or copolymerized with one or more olefin comonomers) to form the ethylene-based polymeric branch, or an ethylene-based polymer is formed independently and subsequently grafted to the polyalkylene. The polyalkylene can contain one or more ethylene-based polymeric branches, the number of branches on any polyalkylene is a function, at least in part, of the size of the polyalkylene and the conditions under which the ethylene is polymerized or the polyethylene is grafted to the polyalkylene. The ethylene-based polymeric branches can vary in size and structure, but typically and preferably comprise one or more long chain branches (LCB, which are characteristic of high pressure LDPE). If the ethylene-based polymer from which the ethylene-based polymeric branches are derived is made by a high pressure process and/or contains long chain branching, then sometimes this polymer, or branches derived from this polymer, is known as a highly branched ethylene-based polymer.
 
     The covalent bonding of the two constituents—a polyalkylene and a highly branched ethylene-based polymer—results in a polymer with physical properties akin to or better than the polyalkylene component while maintaining processability characteristics akin to the highly branched ethylene-based polymer component. 
     The combination of physical and processing properties for the disclosed polymers of this invention is not observed in mere blends of polyalkylene with highly branched ethylene-based polymers. The unique chemical structure of the disclosed polymers of this invention is advantageous as the polyalkylene and the highly branched ethylene-based polymer substituent are covalently linked. 
     The polymer of this invention may comprise unreacted polyalkylene. The polymer of this invention may also comprise free or unattached ethylene-based polymer that formed or was introduced into the process of making the inventive polymer but did not bond with the polyalkylene. The polyalkylene that is not bonded to an ethylene-based polymer and the ethylene-based polymer that is not bonded to a polyalkylene are usually present at low levels, or can be removed to low levels, through various purification or recovery methods known to those skilled in the art. 
     In one embodiment the polymer comprises units derived from ethylene and polyalkylene, the polymer having at least 0.15, typically at least 0.5 and more typically at least 0.8 units, of amyl groups per 1000 carbon atoms as determined by  13 C Nuclear Magnetic Resonance (NMR). Typically the polymer has one or more of: (1) one, typically at least 1.2 and more typically at least 1.4, units of C6+ branches per 1000 carbon atoms as determined by  13 C NMR, (2) no appreciable methyl branches per 1000 carbon atoms as determined by  13 C NMR; (3) no appreciable propyl branches per 1000 carbon atoms as determined by  13 C NMR, and (4) no greater than 5, typically no greater than 3 and more typically no greater than 2, units of amyl groups per 1000 carbon atoms as determined by  13 C NMR. In one embodiment the polymer, or the ethylene-based polymeric branches of the polymer, has two, three or all four of these properties. 
     In one embodiment the polymer has a density greater than 0.89 or 0.90 or 0.91, and less than 0.93 or 0.925 or 0.92, grams per cubic centimeter (g/cc or g/cm 3 ) as measured by ASTM D 792. In one embodiment the polymer has a density from 0.89 to 0.93, or 0.90 to 0.925 or 0.91 to 0.92, g/cc. 
     In one embodiment the polymer has a melt index from 0.01 to 100, typically from 0.05 to 50 and more typically from 0.1 to 10, grams per 10 minutes (g/10 min) as measured by ASTM 1238-04 (2.16kg/190° C.). 
     In one embodiment less than 70, 60, 50, 40, 30, 20 or 10 weight percent of the polyalkylene used in the process to make the inventive polymer is extractable by solvent extraction from the polymer. 
     In one embodiment, the invention is a composition comprising a polymer comprising units derived from ethylene and polyalkylene, the polymer having at least 0.15 units of amyl groups per 1000 carbon atoms as determined by  13 C NMR. In one embodiment, the invention is an article comprising such a composition, and in one embodiment the invention is an article comprising a component comprising such a composition. In one embodiment the article is a film. 
     In one embodiment the polymer comprises a majority weight percent of polymerized ethylene based on the weight of the polymer. 
     In order to achieve an improvement of physical properties over and above a mere physical blend of at least one polyalkene with a highly branched ethylene-based polymer, it was found that the covalent bonding formed by polymerization of the highly branched ethylene-based polymer in the presence of the polyalkylene results in an ethylenic polymer material with physical properties akin to, or better than, the at least one polyalkene-based polymer component, while maintaining processability characteristics akin to the highly branched ethylene-based polymer component. It is believed that the disclosed ethylenic polymer structure is comprised of highly branched ethylene-based polymer substituents grafted to, or “free-radical polymerization generated ethylene-based long chain polymer branches” originating from a radicalized site on the at least one polyalkene-based polymer. The disclosed composition is an ethylenic polymer comprised of at least one polyalkene-based polymer with long chain branches of highly branched ethylene-based polymer. 
     Polyalkene 
     Suitable polyalkene-based polymers comprise repeating units as illustrated in Formula 2 
                         
in which each R1 and R2 are independently hydrogen or alkyl with the proviso that R1 and R2 cannot simultaneously be hydrogen, and n is an integer typically greater than or equal to 10, more typically greater than or equal to 50, and even more typically equal to or greater than 100. The maximum value of n is a function of cost and practical polymerization considerations. In one embodiment each R1 and R2 is independently hydrogen or a C1-C6 alkyl, preferably a C1-C3 alkyl and even more preferably methyl. The end groups can vary widely, but are typically independently hydrogen or alkyl. The polyalkylenes of this invention specifically exclude homopolymer polyethylene. In one embodiment the polyalkylene is polyisobutylene (PIB). The polyalkylenes of this invention are typically made by cationic polymerization.
 
     In one embodiment the polyalkylene has a weight average molecular weight from 30,000 to 4.1 million, or 40,000 to 2.5 million, or 45,000 to 1.1 million, or 50,000 to 500,000, as determined by GPC. 
     In one embodiment the polyalkylene has a Brookfield viscosity at 150° C. viscosity from 30,000 to 1 million, or 40,000 to 700,000 cP (mPa·s). 
     In one embodiment the polyalkylene has a molecular weight distribution (Mw/Mn) typically from 2 to 5, more typically from 2.5 to 4. 
     Highly Branched Ethylene-based Polymers 
     Highly branched ethylene-based polymers, such as low density polyethylene (LDPE), can be made using a high-pressure process using free-radical chemistry to polymerize ethylene monomer. Typical polymer density is from 0.91 to 0.94 g/cm 3 . The low density polyethylene may have a melt index (I 2 ) from 0.01 to 150 g/10 minutes. Highly branched ethylene-based polymers such as LDPE may also be referred to as “high pressure ethylene-based polymers”, meaning that the polymer is partly or entirely homopolymerized or copolymerized in autoclave or tubular reactors at pressures above 13,000 psig with the use of free-radical initiators, such as peroxides (see, for example, U.S. Pat. No. 4,599,392 (McKinney, et al.)). The process creates a polymer with significant branches, including long chain branches, out of the monomer/comonomer material. 
     Highly branched ethylene-based polymers are typically homopolymers of ethylene; however, the polymer may comprise units derived from one or more α-olefin copolymers as long as there is at least 50 mole percent polymerized ethylene monomer in the polymer. 
     Comonomers that may be used in forming highly branched ethylene-based polymer include, but are not limited to, α-olefin comonomers, typically having no more than 20 carbon atoms. For example, the α-olefin comonomers, for example, may have 3 to 10 carbon atoms; or in the alternative, the α-olefin comonomers, for example, may have 3 to 8 carbon atoms. Exemplary α-olefin comonomers include, but are not limited to, propylene, 1-butene, 1-pentene, 1-hexene, 1-heptene, 1-octene, 1-nonene, 1-decene, and 4-methyl-1-pentene. In the alternative, exemplary comonomers include, but are not limited to α, β-unsaturated C 3 -C 8 -carboxylic acids, in particular maleic acid, fumaric acid, itaconic acid, acrylic acid, methacrylic acid and crotonic acid derivates of the α,β-unsaturated C 3 -C 8 -carboxylic acids, for example unsaturated C 3 -C 15 -carboxylic acid esters, in particular ester of C 1 -C 6 -alkanols, or anhydrides, in particular methyl methacrylate, ethyl methacrylate, n-butyl methacrylate, tert-butyl methacrylate, methyl acrylate, ethyl acrylate n-butyl acrylate, 2-ethylhexyl acrylate, tert-butyl acrylate, methacrylic anhydride, maleic anhydride, and itaconic anhydride. In another alternative, the exemplary comonomers include, but are not limited to, vinyl carboxylates, for example vinyl acetate. In another alternative, exemplary comonomers include, but are not limited to, n-butyl acrylate, acrylic acid and methacrylic acid. 
     Process 
     The at least one polyalkene may be produced before or separately from the reaction process with the highly branched ethylene-based polymer. In other disclosed processes, the at least one polyalkene may be formed in situ and in the presence of highly branched ethylene-based polymer within a well-stirred reactor such as a tubular reactor or an autoclave reactor. The highly branched ethylene-based polymer is formed in the presence of ethylene. 
     The ethylenic polymer is formed in the presence of ethylene. A general representation of two disclosed means—free radical grafting of highly branched ethylene-based polymer molecules onto at least one radicalized polyalkene-based polymer molecule, and free-radical ethylene polymerization to form a long chain branch from at least one radicalized polyalkene-based polymer site—of forming embodiment ethylenic polymers. Other embodiment processes for formation of the at least one polyalkene, the substituent highly branched ethylene-based polymer, and their combination into the disclosed ethylenic polymer may exist. 
     In one embodiment the highly branched ethylene-based polymer and the at least one polyalkene are prepared externally to the reaction process used to form the embodiment ethylenic polymer, are combined in a common reactor in the presence of ethylene under free-radical polymerization conditions, and the two polymers are subjected to process conditions and reactants to effect the formation of the embodiment ethylenic polymer. 
     In one embodiment the highly branched ethylene-based polymer and the at least one polyalkene are both prepared in different forward parts of the same process and are then combined together in a common downstream part of the process in the presence of ethylene under free-radical polymerization conditions. The at least one polyalkene and the substituent highly branched ethylene-based polymer are made in separate forward reaction areas or zones, such as separate autoclaves or an upstream part of a tubular reactor. The products from these forward reaction areas or zones are then transported to and combined in a downstream reaction area or zone in the presence of ethylene under free-radical polymerization conditions to facilitate the formation of an embodiment ethylenic polymer. In some processes, free radical generating compounds are added to the downstream reaction area or zone to facilitate the reaction. In some other processes, a catalyst is added to facilitate and reactions in the downstream reaction area or zone. In some other processes, additional fresh ethylene is added to the process downstream of the forward reaction areas or zones to facilitate both the formation of and grafting of highly branched ethylene-based polymers to the at least one polyalkene and the reaction of ethylene monomer directly with the at least one polyalkene to form the disclosed ethylenic polymer. In some other processes, at least one of the product streams from the forward reaction areas or zones is treated before reaching the downstream reaction area or zone to neutralize any residue or byproducts that may inhibit the downstream reactions. 
     In one embodiment the process is an in situ process in which the at least one polyalkene is created in a first or forward reaction area or zone, such as a first autoclave or an upstream part of a tubular reactor. The resultant product stream is then transported to a downstream reaction area or zone where the there is a presence of ethylene at free-radical polymerization conditions. These conditions support both the formation of and grafting of highly branched ethylene-based polymer to the at least one polyalkene occurs as well as the reaction of ethylene monomer directly with at least one radicalized site on the at least one polyalkene, thereby forming an embodiment ethylenic polymer. In some embodiment processes, free radical generating compounds are added to the downstream reaction area or zone to facilitate the grafting reaction. In some other embodiment processes, a catalyst is added to facilitate grafting and reactions in the downstream reaction area or zone. In some other embodiment processes, additional fresh ethylene is added to the process downstream of the forward reaction areas or zones to facilitate both the formation and grafting of highly branched ethylene-based polymer to and the reaction of ethylene monomer with the at least one polyalkene to form the disclosed ethylenic polymer. In some embodiment processes, the product stream from the forward reaction area or zone is treated before reaching the downstream reaction area or zone to neutralize any residue or byproducts from the previous reaction that may inhibit the highly branched ethylene-based polymer formation, the grafting of highly branched ethylene-based polymer to the at least one polyalkene, or the reaction of ethylene monomer with the at least one polyalkene to form the disclosed ethylenic polymer. 
     Any suitable method may be used for feeding the at least one polyalkene into a reactor where it may be reacted with a highly branched ethylene-based polymer. For example, in the cases where the at least one polyalkene is produced using a gas phase process, the at least one polyalkene may be dissolved in ethylene at a pressure above the highly branched ethylene-based polymer reactor pressure, at a temperature at least high enough to dissolve the at least one polyalkene and at concentration which does not lead to excessive viscosity before feeding to the highly branched ethylene-based polymer reactor. 
     For producing the highly branched ethylene-based polymer, a high pressure, free-radical initiated polymerization process is typically used. Two different high pressure free-radical initiated polymerization process types are known. In the first type, an agitated autoclave vessel having one or more reaction zones is used. The autoclave reactor normally has several injection points for initiator or monomer feeds, or both. In the second type, a jacketed tube is used as a reactor, which has one or more reaction zones. Suitable, but not limiting, reactor lengths may be from 100 to 3000 meters, preferably from 1000 to 2000 meters. The beginning of a reaction zone for either type of reactor is defined by the side injection of either initiator of the reaction, ethylene, telomer, comonomer(s) as well as any combination thereof A high pressure process can be carried out in autoclave or tubular reactors having at least 2 reaction zones or in a combination of autoclave and tubular reactors, each comprising one or more reaction zones. 
     In one embodiment the catalyst or initiator is injected prior to the reaction zone where free radical polymerization is to be induced. In other embodiment processes, the at least one polyalkene may be fed into the reaction system at the front of the reactor system and not formed within the system itself Termination of catalyst activity may be achieved by a combination of high reactor temperatures for the free radical polymerization portion of the reaction or by feeding initiator into the reactor dissolved in a mixture of a polar solvent such as isopropanol, water, or conventional initiator solvents such as branched or unbranched alkanes. 
     Embodiment processes may include a process recycle loop to improve conversion efficiency. In such embodiment processes, the downstream reaction area or zone may be maintained at a temperature which is lower than that at which the highly branched ethylene-based polymer would phase separate from the at least one polyalkene. It is preferred that the reactor in which the copolymerization takes place be a reactor with a high polymer (“solids”) concentration, such as a loop reactor, to maximize the concentration of polymerizable highly branched ethylene-based polymer in the reactor. In some embodiment processes, the recycle loop may be treated to neutralize residues or byproducts from the previous reaction cycle that may inhibit polymerization of either the at least one polyalkene or the highly branched ethylene-based polymer or inhibit the reaction forming the disclosed ethylenic polymer. In some embodiment processes, fresh monomer is added to this stream. 
     Ethylene used for the production of highly branched ethylene-based polymer may be purified ethylene, which is obtained by removing polar components from a loop recycle stream or by using a reaction system configuration such that only fresh ethylene is used for making the at least one polyalkene-based polymers. Typical purified ethylene is not required to make highly branched ethylene-based polymer. In such cases ethylene from the recycle loop may be used. 
     Embodiment processes may be used for either the homopolymerization of ethylene in the presence of a at least one polyalkene or copolymerization of ethylene with one or more other comonomers in the presence of a at least one polyalkene, provided that these monomers are copolymerizable with ethylene under free-radical conditions in high pressure conditions to form highly branched ethylene-based polymers. 
     Chain transfer agents or telogens (CTA) are typically used to control the melt index in a free-radical polymerization process. Chain transfer involves the termination of growing polymer chains, thus limiting the ultimate molecular weight of the polymer material. Chain transfer agents are typically hydrogen atom donors that will react with a growing polymer chain and stop the polymerization reaction of the chain. For high pressure free radical polymerization, these agents can be of many different types, such as saturated hydrocarbons, unsaturated hydrocarbons, aldehydes, ketones or alcohols. Typical CTAs that can be used include, but are not limited to, propylene, isobutane, n-butane, 1-butene, methyl ethyl ketone, propionaldehyde, ISOPAR (ExxonMobil Chemical Co.), and isopropanol. The amount of CTAs to use in the process is about 0.03 to about 10 weight percent of the total reaction mixture. 
     The melt index (MI or I 2 ) of a polymer, which is inversely related to the molecular weight, is controlled by manipulating the concentration of the chain transfer agent. For free radical polymerization, after the donation of a hydrogen atom, the CTA forms a radical which can react with the monomers, or with an already formed oligomers or polymers, to start a new polymer chain. This means that any functional groups present in the chain transfer agents will be introduced in the polymer chains. A large number of CTAs, for example, propylene and 1-butene which have an olefinically unsaturated bond, may also be incorporated in the polymer chain themselves, via a copolymerization reaction. Polymers produced in the presence of chain transfer agents are modified in a number of physical properties such as processability, optical properties such as haze and clarity, density, stiffness, yield point, film draw and tear strength. 
     Hydrogen has been shown to be a chain transfer agent for high pressure free radical polymerization. Control of the molecular weight made in the reaction zones for disclosed processes may be accomplished by feeding hydrogen to the reaction zones where catalyst or initiator is injected. The final product melt index control would be accomplished by feeding chain transfer agents to the reaction zones where free radical polymerization takes place. Feed of the free radical chain transfer agents could be accomplished by direct injection into the reaction zones or by feeding them to the front of the reactor. If hydrogen is fed to the front of the reactor, it would not be expected to act as a chain transfer agent until entering reaction zones where initiator is injected, at which point the unsaturated chain transfer agents would be expected to interact with growing polymer chains. In some embodiment processes, it may be necessary to remove excess CTA from the recycle stream or limit injection so as to prevent excess buildup of CTA in the front end of the process. 
     The type of free radical initiator used in disclosed processes is not critical. Free radical initiators that are generally used to produce ethylene-based polymers are oxygen, which is usable in tubular reactors in conventional amounts of between 0.0001 and 0.005 wt % drawn to the weight of polymerizable monomer, and peroxides. Preferred initiators are t-butyl peroxy pivalate, di-t-butyl peroxide, t-butyl peroxy acetate and t-butyl peroxy-2-hexanoate or mixtures thereof These organic peroxy initiators are used in conventional amounts of between 0.005 and 0.2 wt % drawn to the weight of polymerizable monomers. 
     The peroxide initiator may be, for example, organic peroxide. Exemplary organic peroxides include, but are not limited to, cyclic peroxides, diacyl peroxides, dialkyl peroxides, hydroperoxides, peroxycarbonates, peroxydicarbonates, peroxyesters, and peroxyketals. 
     Exemplary cyclic peroxides include, but are not limited to, 3,6,9-triethyl-3,6,9-trimethyl-1,4,7-triperoxonane. Such cyclic peroxides, for example, are commercially available under the trademark TRIGONOX 301 (Akzo Nobel; Arnhem, The Netherlands). Exemplary diacyl peroxides include, but are not limited to, di(3,5,5-trimethylhexanoyl) peroxide. Such diacyl peroxides, for example, are commercially available under the trademark TRIGONOX 36 (Akzo Nobel). Exemplary dialkyl peroxides include, but are not limited to, 2,5-dimethyl-2,5-di(tert-butylperoxy)hexane; 2,5-dimethyl-2,5-di(tert-butylperoxy) hexyne-3; di-tert-amyl peroxide; di-tert-butyl peroxide; and tert-butyl cumyl peroxide. Such dialkyl peroxides, for example, are commercially available under the trademarks TRIGONOX 101, TRIGONOX 145, TRIGONOX 201, TRIGONOX B, and TRIGONOX T (Akzo Nobel). Exemplary hydroperoxides include, but are not limited to, tert-Amyl hydroperoxide; and 1,1,3,3-tetramethylbutyl hydroperoxide. Such hydroperoxides, for example, are commercially available under the trademarks TRIGONOX TAHP, and TRIGONOX TMBH (Akzo Nobel). Exemplary peroxycarbonates include, but are not limited to, tert-butylperoxy 2-ethylhexyl carbonate; tert-amylperoxy 2-ethylhexyl carbonate; and tert-butylperoxy isopropyl carbonate. Such peroxycarbonates, for example, are commercially available under the trademarks TRIGONOX 117, TRIGONOX 131, and TRIGONOX BPIC (Akzo Nobel). Exemplary peroxydicarbonates include, but are not limited to, di(2-ethylhexyl) peroxydicarbonates; and di-sec-butyl peroxydicarbonates. Such peroxydicarbonates, for example, are commercially available under the trademark TRIGONOX EHP, and TRIGONOX SBP (Akzo Nobel). Exemplary peroxyesters include, but are not limited to, tert-amyl peroxy -2-ethylhexanoate; tert-amyl peroxyneodecanoate; tert-amyl peroxypivalate; tert-amyl peroxybenzoate; tert-amyl peroxyacetate; 2,5 -dimethyl-2,5-di(2-ethylhexanoylperoxy)hexane; tert-butyl peroxy-2-ethylhexanoate; tert-butyl peroxyneodecanoate; tert-butyl peroxyneoheptanoate; tert-butyl peroxypivalate; tert-butyl peroxydiethylacetate; tert-butyl peroxyisobutyrate; 1,1,3,3-tetramethylbutyl peroxy-2-ethylhexanoate; 1,1,3,3-tetramethylbutyl peroxyneodecanoate; 1,1,3,3-tetramethylbutyl peroxypivalate; tert-butyl peroxy-3,5,5-trimethylhexanoate; cumyl peroxyneodecanoate; tert-butyl peroxybenzoate; and tert-butyl peroxyacetate. Such peroxyesters solvents, for example, are commercially available under the trademarks TRIGONOX 121; TRIGONOX 123; TRIGONOX 125; TRIGONOX 127; TRIGONOX 133; TRIGONOX 141; TRIGONOX 21; TRIGONOX 23; TRIGONOX 257; TRIGONOX 25; TRIGONOX 27; TRIGONOX 41; TRIGONOX 421; TRIGONOX 423; TRIGONOX 425; TRIGONOX 42; TRIGONOX 99; TRIGONOX C; and TRIGONOX F (Akzo Nobel). Exemplary peroxyketals include, but are not limited to, 1,1-di(tert-amylperoxy) cyclohexane; 1,1-di(tert-butylperoxy)cyclohexane; 1,1-di(tert-butylperoxy) -3,3,5-trimethylcyclohexane; and 2,2-di(tert-butylperoxy)butane. Such peroxyketals, for example, are commercially available under the trademarks TRIGONOX 122, TRIGONOX 22, TRIGONOX 29, and TRIGONOX D (Akzo Nobel). The free radical initiator system may, for example, include a mixture or combination of any of the aforementioned peroxide initiators. The peroxide initiator may comprise less than 60 percent by weight the free radical initiator system. 
     The free radical initiator system further includes at least one hydrocarbon solvent. The hydrocarbon solvent may, for example, be a C 5  to C 30  hydrocarbon solvent. Exemplary hydrocarbon solvents include, but are not limited to, mineral solvents, normal paraffinic solvents, isoparaffinic solvents, cyclic solvents, and the like. The hydrocarbon solvents may, for example, be selected from the group consisting of n-octane, iso-octane (2,2,4-trimethylpentane), n-dodecane, iso-dodecane (2,2,4,6,6-pentamethylheptane), and other isoparaffinic solvents. Exemplary hydrocarbon solvents such as isoparaffinic solvents, for example, are commercially available under the trademarks ISOPAR C, ISOPAR E, and ISOPAR H (ExxonMobil Chemical Co.). The hydrocarbon solvent may comprise less than 99 percent by weight of the free radical initiator system. 
     In some embodiment processes, the free radical initiator system may further include a polar co-solvent. The polar co-solvent may be an alcohol co-solvent, for example, a C 1  to C 30  alcohol. Additionally, the alcohol functionality of the alcohol co-solvent may, for example, be mono-functional or multi-functional. Exemplary alcohols as a polar co-solvent include, but are not limited to, isopropanol (2-propanol), allylalcohol (1-pentanol), methanol, ethanol, propanol, butanol, 1,4-butanediol, combinations thereof, mixtures thereof, and the like. The polar co-solvent may comprise less than 40 percent by weight of the free radical initiator system. 
     The polar co-solvent may be an aldehyde. Aldehydes are generally known to a person of skill in the art; for example, propionaldehyde may be used as a polar co-solvent. However, the reactivity potential of aldehydes as chain transfer agents should be taken into account when using such aldehydes as polar co-solvents. Such reactivity potentials are generally known to a person of skill in the art. 
     The polar co-solvent may be a ketone. Ketones are generally known to a person of skill in the art; for example, acetone may be used as polar co-solvents. However, the reactivity potential of ketones as chain transfer agents should be taken into account when using such ketones as polar co-solvents. Such reactivity potentials are generally known to a person of skill in the art. 
     In some embodiment processes, the free radical initiator system may further comprise a chain transfer agent as a solvent or as a blend for simultaneous injection. As previously discussed, chain, transfer agents are generally known to a person of skill in the art, and they include, but are not limited to, propane, isobutane, acetone, propylene, isopropanol, butene-1, propionaldehyde, and methyl ethyl ketone. In other disclosed processes, chain transfer agent may be charged into the reactor via a separate inlet port from the initiator system. In another embodiment process, a chain transfer agent may be blended with ethylene, pressurized, and then injected into the reactor in its own injection system. 
     In some embodiment processes, a peroxide initiator may initially be dissolved or diluted in a hydrocarbon solvent, and then a polar co-solvent added to the peroxide initiator/hydrocarbon solvent mixture prior to metering the free radical initiator system into the polymerization reactor. In another embodiment process, a peroxide initiator may be dissolved in the hydrocarbon solvent in the presence of a polar co-solvent. 
     In some embodiment processes, the free-radical initiator used in the process may initiate the graft site on the at least one polyalkene by extracting the extractable hydrogen from the at least one polyalkene. Example free-radical initiators include those free radical initiators previously discussed, such as peroxides and azo compounds. In some other embodiment processes, ionizing radiation may also be used to free the extractable hydrogen and create the radicalized site on the at least one polyalkene. Organic initiators are preferred means of extracting the extractable hydrogen, such as using dicumyl peroxide, di-tert-butyl peroxide, t-butyl perbenzoate, benzoyl peroxide, cumene hydroperoxide, t-butyl peroctoate, methyl ethyl ketone peroxide, 2,5-dimethyl-2,5-di(tert-butyl peroxy) hexane, lauryl peroxide, and tert-butyl peracetate, t-butyl α-cumyl peroxide, di-t-butyl peroxide, di-t-amyl peroxide, t-amyl peroxybenzoate, 1,1-bis(t-butylperoxy) -3,3,5-trimethylcyclohexane, α,α′-bis(t-butylperoxy)-1,3-diisopropylbenzene, α,α′-bis(t-butylperoxy) -1,4-diisopropyl-benzene, 2,5-bis(t-butylperoxy)-2,5-dimethylhexane, and 2,5-bis(t-butylperoxy)-2,5-dimethyl-3-hexyne. A preferred azo compound is azobisisobutyl nitrite. 
     In some embodiment processes, processing aids, such as plasticizers, can also be included in the embodiment ethylenic polymer product. These aids include, but are not limited to, the phthalates, such as dioctyl phthalate and diisobutyl phthalate, natural oils such as lanolin, and paraffin, naphthenic and aromatic oils obtained from petroleum refining, and liquid resins from rosin or petroleum feedstocks. Exemplary classes of oils useful as processing aids include white mineral oil such as KAYDOL oil (Chemtura Corp.; Middlebury, Conn.) and SHELLFLEX 371 naphthenic oil (Shell Lubricants; Houston, Tex.). Another suitable oil is TUFFLO oil (Lyondell Lubricants; Houston, Tex). 
     In some embodiment processes, embodiment ethylenic polymers are treated with one or more stabilizers, for example, antioxidants, such as IRGANOX 1010 and IRGAFOS 168 (Ciba Specialty Chemicals; Glattbrugg, Switzerland). In general, polymers are treated with one or more stabilizers before an extrusion or other melt processes. In other embodiment processes, other polymeric additives include, but are not limited to, ultraviolet light absorbers, antistatic agents, pigments, dyes, nucleating agents, fillers, slip agents, fire retardants, plasticizers, processing aids, lubricants, stabilizers, smoke inhibitors, viscosity control agents and anti-blocking agents. The embodiment ethylenic polymer composition may, for example, comprise less than 10 percent by the combined weight of one or more additives, based on the weight of the embodiment ethylenic polymer. 
     The embodiment ethylenic polymer may further be compounded. In some embodiment ethylenic polymer compositions, one or more antioxidants may further be compounded into the polymer and the compounded polymer pelletized. The compounded ethylenic polymer may contain any amount of one or more antioxidants. For example, the compounded ethylenic polymer may comprise from 200 to 600 parts of one or more phenolic antioxidants per one million parts of the polymer. In addition, the compounded ethylenic polymer may comprise from 800 to 1200 parts of a phosphite-based antioxidant per one million parts of polymer. The compounded disclosed ethylenic polymer may further comprise from 300 to 1250 parts of calcium stearate per one million parts of polymer. 
     Uses 
     The embodiment ethylenic polymer may be employed in a variety of conventional thermoplastic fabrication processes to produce useful articles, including objects comprising at least one film layer, such as a monolayer film, or at least one layer in a multilayer film prepared by cast, blown, calendered, or extrusion coating processes; molded articles, such as blow molded, injection molded, or rotomolded articles; extrusions; fibers; and woven or non-woven fabrics. Thermoplastic compositions comprising the embodiment ethylenic polymer include blends with other natural or synthetic materials, polymers, additives, reinforcing agents, ignition resistant additives, antioxidants, stabilizers, colorants, extenders, crosslinkers, blowing agents, and plasticizers. 
     The embodiment ethylenic polymer may be used in producing fibers for other applications. Fibers that may be prepared from the embodiment ethylenic polymer or blends thereof include staple fibers, tow, multi-component, sheath/core, twisted, and monofilament. Suitable fiber forming processes include spin bonded, melt blown techniques, as disclosed in U.S. Pat. No. 4,340,563 (Appel, et al.), U.S. Pat. No. 4,663,220 (Wisneski, et al.), U.S. Pat. No. 4,668,566 (Nohr, et al.), and U.S. Pat. No. 4,322,027 (Reba), gel spun fibers as disclosed in U.S. Pat. No. 4,413,110 (Kavesh, et al.), woven and nonwoven fabrics, as disclosed in U.S. Pat. No. 3,485,706 (May), or structures made from such fibers, including blends with other fibers, such as polyester, nylon or cotton, thermoformed articles, extruded shapes, including profile extrusions and co-extrusions, calendared articles, and drawn, twisted, or crimped yarns or fibers. 
     The embodiment ethylenic polymer may be used in a variety of films, including but not limited to clarity shrink films, collation shrink films, cast stretch films, silage films, stretch hood, sealants, and diaper backsheets. 
     The embodiment ethylenic polymer is also useful in other direct end-use applications. The embodiment ethylenic polymer is useful for wire and cable coating operations, in sheet extrusion for vacuum forming operations, and forming molded articles, including the use of injection molding, blow molding process, or rotomolding processes. Compositions comprising the embodiment ethylenic polymer can also be formed into fabricated articles using conventional polyolefin processing techniques. 
     Other suitable applications for the embodiment ethylenic polymer include elastic films and fibers; soft touch goods, such as tooth brush handles and appliance handles; gaskets and profiles; adhesives (including hot melt adhesives and pressure sensitive adhesives); footwear (including shoe soles and shoe liners); auto interior parts and profiles; foam goods (both open and closed cell); impact modifiers for other thermoplastic polymers such as high density polyethylene, isotactic polypropylene, or other olefin polymers; coated fabrics; hoses; tubing; weather stripping; cap liners; flooring; and viscosity index modifiers, also known as pour point modifiers, for lubricants. 
     Further treatment of the embodiment ethylenic polymer may be performed to apply the embodiment ethylenic polymer for other end uses. For example, dispersions (both aqueous and non-aqueous) can also be formed using the present polymers or formulations comprising the same. Frothed foams comprising the embodiment ethylenic polymer can also be formed, as disclosed in PCT Publication No. 2005/021622 (Strandeburg, et al.). The embodiment ethylenic polymer may also be crosslinked by any known means, such as the use of peroxide, electron beam, silane, azide, or other cross-linking technique. The embodiment ethylenic polymer can also be chemically modified, such as by grafting (for example by use of maleic anhydride (MAH), silanes, or other grafting agent), halogenation, amination, sulfonation, or other chemical modification. 
     Additives and adjuvants may be added to the embodiment ethylenic polymer post-formation. Suitable additives include fillers, such as organic or inorganic particles, including clays, talc, titanium dioxide, zeolites, powdered metals, organic or inorganic fibers, including carbon fibers, silicon nitride fibers, steel wire or mesh, and nylon or polyester cording, nano-sized particles, clays, and so forth; tackifiers, oil extenders, including paraffinic or napthelenic oils; and other natural and synthetic polymers, including other polymers that are or can be made according to the embodiment methods. 
     Blends and mixtures of the embodiment ethylenic polymer with other polyolefins may be performed. Suitable polymers for blending with the embodiment ethylenic polymer include thermoplastic and non-thermoplastic polymers including natural and synthetic polymers. Exemplary polymers for blending include polypropylene, (both impact modifying polypropylene, isotactic polypropylene, atactic polypropylene, and random ethylene/propylene copolymers), various types of polyethylene, including high pressure, free-radical LDPE, Ziegler-Natta LLDPE, metallocene PE, including multiple reactor PE (“in reactor” blends of Ziegler-Natta PE and metallocene PE, such as products disclosed in U.S. Pat. No. 6,545,088 (Kolthammer, et al.); U.S. Pat. No. 6,538,070 (Cardwell, et al.); U.S. Pat. No. 6,566,446 (Parikh, et al.); U.S. Pat. No. 5,844,045 (Kolthammer, et al.); U.S. Pat. No. 5,869,575 (Kolthammer, et al.); and U.S. Pat. No. 6,448,341 (Kolthammer, et al.)), ethylene-vinyl acetate (EVA), ethylene/vinyl alcohol copolymers, polystyrene, impact modified polystyrene, ABS, styrene/butadiene block copolymers and hydrogenated derivatives thereof (SBS and SEBS), and thermoplastic polyurethanes. Homogeneous polymers such as olefin plastomers and elastomers, ethylene and propylene-based copolymers (for example, polymers available under the trade designation VERSIFY™ Plastomers &amp; Elastomers (The Dow Chemical Company) and VISTAMAXX™ (ExxonMobil Chemical Co.)) can also be useful as components in blends comprising the embodiment ethylenic polymer. 
     Blends and mixtures of the embodiment ethylenic polymer may include thermoplastic polyolefin blends (TPO), thermoplastic elastomer blends (TPE), thermoplastic vulcanizates (TPV) and styrenic polymer blends. TPE and TPV blends may be prepared by combining embodiment ethylenic polymers, including functionalized or unsaturated derivatives thereof, with an optional rubber, including conventional block copolymers, especially an SBS block copolymer, and optionally a crosslinking or vulcanizing agent. TPO blends are generally prepared by blending the embodiment polymers with a polyolefin, and optionally a crosslinking or vulcanizing agent. The foregoing blends may be used in forming a molded object, and optionally crosslinking the resulting molded article. A similar procedure using different components has been previously disclosed in U.S. Pat. No. 6,797,779 (Ajbani, et al.). 
     Definitions 
     Any reference to the Periodic Table of Elements is that as published by CRC Press, Inc., 1990-1991. Reference to a group of elements in this table is by the new notation for numbering groups. Unless stated to the contrary, implicit from the context, or customary in the art, all parts and percents are based on weight and all test methods are current as of the filing date of this disclosure. For purposes of United States patent practice, the contents of any referenced patent, patent application or publication are incorporated by reference in their entirety (or its equivalent US version is so incorporated by reference) especially with respect to the disclosure of definitions (to the extent not inconsistent with any definitions specifically provided in this disclosure) and general knowledge in the art. 
     The numerical ranges in this disclosure are approximate, and thus may include values outside of the range unless otherwise indicated. Numerical ranges include all values from and including the lower and the upper values, in increments of one unit, provided that there is a separation of at least two units between any lower value and any higher value. As an example, if a compositional, physical or other property, such as, for example, molecular weight, viscosity, melt index, etc., is from 100 to 1,000, it is intended that all individual values, such as 100, 101, 102, etc., and sub ranges, such as 100 to 144, 155 to 170, 197 to 200, etc., are expressly enumerated. For ranges containing values which are less than one or containing fractional numbers greater than one (e.g., 1.1, 1.5, etc.), one unit is considered to be 0.0001, 0.001, 0.01 or 0.1, as appropriate. For ranges containing single digit numbers less than ten (e.g., 1 to 5), one unit is typically considered to be 0.1. These are only examples of what is specifically intended, and all possible combinations of numerical values between the lowest value and the highest value enumerated, are to be considered to be expressly stated in this disclosure. Numerical ranges are provided within this disclosure for, among other things, density, melt index, molecular weight, reagent amounts and process conditions. 
     The term “composition,” as here used means a combination of two or more materials. With the respective to the inventive polymer, a composition is the inventive polymer in combination with at least one other material, e.g., an additive, filler, another polymer, catalyst, etc. In the context of this invention, the inventive polymer is not a composition because of the presence of unreacted polyalkylene and/or ethylene-based polymer since the association of these materials with a polymer as described by formula 1 is part of the definition of the inventive polymer. 
     The terms “blend” or “polymer blend,” as used, mean an intimate physical mixture (that is, without reaction) of two or more polymers. A blend may or may not be miscible (not phase separated at molecular level). A blend may or may not be phase separated. A blend may or may not contain one or more domain configurations, as determined from transmission electron spectroscopy, light scattering, x-ray scattering, and other methods known in the art. The blend may be effected by physically mixing the two or more polymers on the macro level (for example, melt blending resins or compounding) or the micro level (for example, simultaneous forming within the same reactor). 
     The term “polymer” refers to a compound prepared by polymerizing monomers, whether of the same or a different type. The generic term polymer thus embraces the term homopolymer (which refers to polymers prepared from only one type of monomer with the understanding that trace amounts of impurities can be incorporated into the polymer structure), and the term “interpolymer” as defined infra. 
     The term “interpolymer” refers to polymers prepared by the polymerization of at least two different types of monomers. The generic term interpolymer includes copolymers (which refers to polymers prepared from two different monomers), and polymers prepared from more than two different types of monomers. 
     The term “ethylene-based polymer” refers to a polymer that comprises a majority amount of polymerized ethylene based on the weight of the polymer and, optionally, may comprise at least one comonomer. 
     The term “ethylene-based interpolymer” refers to an interpolymer that comprises a majority amount of polymerized ethylene based on the weight of the interpolymer, and comprises at least one comonomer. 
     The term “no appreciable” as used in the context of reporting alkyl branches in a  13 C NMR analysis means that at a given signal to noise ratio, the branch was not detectable. 
     The term “multi-part reactor” as used herein refers to a reactor with multiple reaction zones wherein a reaction zone typically includes a feed port and/or one or more physical barriers. 
     Additional Embodiments of the Invention 
     In one embodiment of the invention, a polymer comprises units derived from ethylene and polyalkylene, the polymer having at least 0.15, or at least 0.5, or at least 0.8, units of amyl groups per 1000 carbon atoms as determined by  13 C Nuclear Magnetic Resonance (NMR). 
     In one embodiment the inventive polymer comprises a portion of the ethylene bonded to one or more carbon atoms. 
     In one embodiment the inventive polymer comprises at least one ethylene-based polymeric branch bonded to the polyalkylene at a backbone carbon atom. 
     In one embodiment the ethylene-based polymeric branch bonded to the polyalkylene at a backbone carbon atom of the inventive polymer contains long chain branching. 
     In one embodiment the inventive polymer of any of the preceding embodiments comprises at least 1, or at least 1.2, or at least 1.4, units of C6+branches as determined by  13 C NMR. 
     In one embodiment the inventive polymer of any of the preceding embodiments comprises no greater than 5, or no greater than 3 or no greater than 2, units of amyl groups per 1000 carbon atoms as determined by  13 C NMR. 
     In one embodiment the inventive polymer of any of the preceding embodiments has a density of less than 0.93 or less than 0.92 g/cm 3 . 
     In one embodiment the inventive polymer of any of the preceding embodiments has a density of less than 0.92 or less than 0.915 g/cm 3 . 
     In one embodiment the inventive polymer of any of the preceding embodiments has a melt index (I 2 ) of less than 15, or less than 10, or less than 6, g/10 min. In one embodiment the inventive polymer of any of the preceding embodiments has a melt index (I 2 ) of greater than 0.1, or greater than 0.5, g/10 min. 
     In one embodiment the inventive polymer of any of the preceding embodiments has a melt flow ratio (I 1 O 2 ) of least 5, or of at least 8, or of at least 10. 
     In one embodiment the inventive polymer of any of the preceding embodiments has an I 10 /I 2  of less than 30, less than 25, less than 20. 
     In one embodiment the inventive polymer of any of the preceding embodiments has an I 2  of less than 10, less than 8 or less than 6, and an I 10 /I 2  of greater than 5, greater than 8 or greater than 10. 
     In one embodiment the inventive polymer has a molecular weight distribution (MWD) from 5 to 20, or from 10 to 15. 
     In one embodiment the inventive polymer comprises from I to 30 or from 4-20 weight percent polyalkylene based on the weight of the polymer. 
     In one embodiment the invention is a composition comprising the inventive polymer of any of the preceding polymer embodiments. 
     In one embodiment the composition of the preceding embodiment comprises one or more additives. 
     In one embodiment the invention is an article comprising a composition of any of the preceding composition embodiments. 
     In one embodiment the invention is an article comprising at least one component formed from a composition of any of the composition embodiments. 
     In one embodiment the article of any of the preceding article embodiments is in the form of a film. 
     In one embodiment the invention is a process to form a polymer comprising units derived from ethylene and polyalkylene, the process comprising:
         A. Contacting at least one polyalkylene with ethylene in the presence of a free-radical initiator in a first reactor or a first part of a multi-part reactor; and   B. Reacting the polyalkylene with additional ethylene in the presence of the free-radical initiator to form an ethylene-based polymeric branch bonded to the polyalkylene in at least one other reactor or a later part of the multi-part reactor.       

     In one process embodiment the ethylene-based polymeric branch is formed by the ethylene monomer bonding with the polyalkylene to form an ethylene-polyalkylene moiety, and the resulting moiety polymerizing with at least additional ethylene monomer to form the ethylene-based polymeric branch. 
     In one process embodiment the ethylene-based polymeric branch is formed independently of the polyalkylene and is then grafted to the polyalkylene. 
     In one embodiment the invention is a polymer made by any of the processes embodiments. 
     In one embodiment the inventive polymer comprises less than 70, 60, 50, 40, 30, 20 or 10, weight percent of polyalkylene that is extractable by solvent extraction. 
     In one embodiment the inventive composition comprises less than 70, 60, 50, 40, 30, 20 or 10, weight percent of polyalkylene that is extractable by solvent extraction. 
     In one embodiment the inventive polymer has a melt point Tm of less than 105° C. and a density of less than 0.915 g/cc. 
     In one embodiment the inventive polymer has a heat of fusion of less than 130 J/g and a density of less than 0.915 g/cc. 
     In one embodiment the inventive polymer has a viscosity ratio (V0.1/V100) of at least 15, preferably of at least 17. 
     In one embodiment the inventive polymer has a viscosity ratio (V0.1/V100) less than 30, or less than 25. 
     EXPERIMENTAL 
     Reference Resins 
     Thirty commercially available LDPE resins (designated “Commercially Available Resins” or “CAR”) are tested for density, melt index (I 2 ), heat of fusion, peak melting temperature, g′, gpcBR, and LCBf using the Density, Melt Index, DSC Crystallinity, Gel Permeation Chromatography, g′ by 3D-GPC, and gpcBR Branching Index by 3D-GPC methods, all described infra. The Commercially Available Resins have the properties listed in Table 1. 
                     TABLE 1                  CAR Properties                                                 Melt                       Commercially       Index   Heat of   Peak       Available   Density   (I 2 )   Fusion   T m     gpcBR       Resins   (g/cm 3 )   (g/10 min)   (J/g)   (° C.)   Whole   LCBf                                                 CAR1   0.920   0.15   147.2   110.9   1.26   2.05       CAR2   0.922   2.5   151.1   111.4   0.89   2.03       CAR3   0.919   0.39   146.8   110.4   1.19   2.39       CAR4   0.922   0.80   155.0   112.5   0.78   1.99       CAR5   0.916   28   139.3   106.6   1.27   3.59       CAR6   0.917   6.4   141.5   107.8   1.48   3.24       CAR7   0.924   1.8   155.1   112.2   0.77   1.84       CAR8   0.926   5.6   157.9   113.4   0.57   1.64       CAR9   0.923   0.26   151.4   110.3   1.13   2.06       CAR10   0.924   0.22   151.2   111.4   1.03   1.96       CAR11   0.924   0.81   154.1   112.3   0.95   2.48       CAR12   0.926   5.9   158.0   113.1   0.70   1.90       CAR13   0.924   2.0   155.2   111.8   0.84   2.03       CAR14   0.923   4.1   157.3   111.6   1.26   2.32       CAR15   0.922   33   153.5   111.8   0.46   1.95       CAR16   0.922   4.1   151.0   109.3   1.89   2.61       CAR17   0.918   0.46   141.2   107.4   3.09   3.33       CAR18   0.921   2.1   145.9   110.2   0.85   2.11       CAR19   0.918   8.2   143.2   106.4   2.27   3.20       CAR20   0.922   0.67   148.7   110.4   0.68   1.59       CAR21   0.924   0.79   154.2   111.8   0.74   1.96       CAR22   0.922   0.25   150.0   110.5   0.92   1.92       CAR23   0.924   3.4   153.6   111.3   0.65   1.94       CAR24   0.921   4.6   148.2   106.9   1.49   2.54       CAR25   0.923   20   150.9   108.9   NM   2.21       CAR26   0.925   1.8   157.5   112.4   0.82   1.86       CAR27   0.923   0.81   153.7   111.5   0.87   1.94       CAR28   0.919   6.8   145.1   105.7   1.72   2.75       CAR29   0.931   3.6   167.3   115.6   NM   NM       CAR30   0.931   2.3   169.3   115.8   NM   NM               “NM” means not measured.            
Test Methods
 
     Density 
     Samples that are measured for density are prepared according to ASTM D 1928. Samples are pressed at 374° F. (190° C.) and 30,000 psi for 3 minutes, and then at 70° F. (21° C.) and 30,000 psi for 1 minute. Density measurements are made within one hour of sample pressing using ASTM D792, Method B. 
     Melt Index 
     Melt index, or I 2 , is measured in accordance by ASTM D 1238, Condition 190° C./2.16 kg, and is reported in grams eluted per 10 minutes. I 10  is measured in accordance with ASTM D 1238, Condition 190° C./10 kg, and is reported in grams eluted per 10 minutes. 
     Viscosity Determination for Polyalkylene 
     Melt viscosity is determined using a Brookfield Laboratories (Middleboro, Mass.) DVII+ Viscometer and disposable aluminum sample chambers. The spindle used is a SC4-25 hot-melt spindle suitable for measuring viscosities from about 480,000 to about 950,000 centipoises. Other spindles may be used to obtain viscosities if the viscosity of the polymer is out of this range or in order to obtain the recommended torque ranges as described in this procedure. The sample is poured into the sample chamber, inserted into a Brookfield Thermosel, and locked into place. The sample chamber has a notch on the bottom that fits the bottom of the Brookfield Thermosel to ensure that the chamber is not allowed to turn when the spindle is inserted and spinning. The sample is heated to the required temperature (150° C.), until the melted sample is about 1 inch (approximately 8 grams of resin) below the top of the sample chamber. The viscometer apparatus is lowered and the spindle submerged into the sample chamber. Lowering is continued until brackets on the viscometer align on the Thermosel. The viscometer is turned on, and set to operate at a shear rate which leads to a torque reading from about 30 to about 60 percent. Readings are taken every minute for about 15 minutes or until the values stabilize, at which point, a final reading is recorded. 
     Differential Scanning Calorimetry (DSC) 
     Differential Scanning calorimetry (DSC) can be used to measure the crystallinity of a sample at a given temperature for a wide range of temperatures. For the Examples, a TA model Q1000 DSC (TA Instruments; New Castle, Del.) equipped with an RCS (Refrigerated Cooling System) cooling accessory and an auto-sampler module is used to perform the tests. During testing, a nitrogen purge gas flow of 50 ml/min is used. Resins are compression-molded into 3 mm thick by 1 inch circular plaques at 350° F. for 5 minutes under 1500 psi pressure in air. The sample is then taken out of the press and placed on a counter top to cool to room temperature (˜25° C.). A 3-10 mg sample of the cooled material is cut into a 6 mm diameter disk, weighed, placed in a light aluminum pan (ca 50 mg), and crimped shut. The sample is then tested for its thermal behavior. 
     The thermal behavior of the sample is determined by changing the sample temperature upwards and downwards to create a response versus temperature profile. The sample is first rapidly heated to 180° C. and held at an isothermal state for 3 minutes in order to remove any previous thermal history. Next, the sample is then cooled to −40° C. at a 10° C./min cooling rate and held at −40° C. for 3 minutes. The sample is then heated to 150° C. at a 10° C./min heating rate. The cooling and second heating curves are recorded. The values determined are peak melting temperature (T m ), peak crystallization temperature (T c ), heat of fusion (H f ) (in J/g), and the calculated percent crystallinity for polyethylene samples using Equation 1:
 
% Crystallinity=(( H   f )/(292 J/g))×100   (Eq. 1).
 
     The heat of fusion (H f ) and the peak melting temperature are reported from the second heat curve. Peak crystallization temperature is determined from the cooling curve. 
     Gel Permeation Chromatography (GPC) 
     The GPC system consists of a Waters (Milford, Mass.) 150° C. high temperature chromatograph (other suitable high temperatures GPC instruments include Polymer Laboratories (Shropshire, UK) Model 210 and Model 220) equipped with an on-board differential refractometer (RI). Additional detectors can include an IR4 infra-red detector from Polymer ChAR (Valencia, Spain), Precision Detectors (Amherst, Mass.) 2-angle laser light scattering detector Model 2040, and a Viscotek (Houston, Tex.) 150R 4-capillary solution viscometer. A GPC with the last two independent detectors and at least one of the first detectors is sometimes referred to as “3D-GPC”, while the term “GPC” alone generally refers to conventional GPC. Depending on the sample, either the 15-degree angle or the 90-degree angle of the light scattering detector is used for calculation purposes. Data collection is performed using Viscotek TriSEC software, Version 3, and a 4-channel Viscotek Data Manager DM400. The system is also equipped with an on-line solvent degassing device from Polymer Laboratories (Shropshire, UK). Suitable high temperature GPC columns can be used such as four 30 cm long Shodex HT803 13 micron columns or four 30 cm Polymer Labs columns of 20-micron mixed-pore-size packing (MixA LS, Polymer Labs). The sample carousel compartment is operated at 140° C. and the column compartment is operated at 150° C. The samples are prepared at a concentration of 0.1 grams of polymer in 50 milliliters of solvent. The chromatographic solvent and the sample preparation solvent contain 200 ppm of butylated hydroxytoluene (BHT). Both solvents are sparged with nitrogen. The polyethylene samples are gently stirred at 160° C. for four hours. The injection volume is 200 microliters. The flow rate through the GPC is set at 1 ml/minute. 
     The GPC column set is calibrated before running the Examples by running twenty-one narrow molecular weight distribution polystyrene standards. The molecular weight (MW) of the standards ranges from 580 to 8,400,000 grams per mole, and the standards are contained in 6 “cocktail” mixtures. Each standard mixture has at least a decade of separation between individual molecular weights. The standard mixtures are purchased from Polymer Laboratories (Shropshire, UK). The polystyrene standards are prepared at 0.025 g in 50 mL of solvent for molecular weights equal to or greater than 1,000,000 grams per mole and 0.05 g in 50 ml of solvent for molecular weights less than 1,000,000 grams per mole. The polystyrene standards were dissolved at 80° C. with gentle agitation for 30 minutes. The narrow standards mixtures are run first and in order of decreasing highest molecular weight component to minimize degradation. The polystyrene standard peak molecular weights are converted to polyethylene molecular weight using Equation 2 (as described in Williams and Ward,  J. Polym. Sci. , Polym. Let., 6, 621 (1968)):
 
 M   polyethylene   =A ×( M   polystyrene ) R    (Eq. 2),
 
where M is the molecular weight of polyethylene or polystyrene (as marked), A has a value of 0.43, and B is equal to 1.0. Use of this polyethylene calibration to obtain molecular weight distributions and related statistics is defined as the method of Williams and Ward. Other values of A and B in Equation 3 may result from different choices of the Mark-Houwink K and a (sometimes referred to as α) values for polystyrene and polyethylene and are referred to generally as a conventionally calibrated 3D-GPC.
 
     With 3D-GPC absolute weight average molecular weight (“M w,Abs ”) and intrinsic viscosity are also obtained independently from suitable narrow polyethylene standards using the same conditions mentioned previously. These narrow linear polyethylene standards may be obtained from Polymer Laboratories (Shropshire, UK; Part No.&#39;s PL2650-0101 and PL2650-0102). 
     The systematic approach for the determination of multi-detector offsets is performed in a manner consistent with that published by Balke, Mourey, et al. (Mourey and Balke,  Chromatography Polym. , Chapter 12, (1992)) (Balke, Thitiratsakul, Lew, Cheung, Mourey,  Chromatography Polym. , Chapter 13, (1992)), optimizing triple detector log (M W  and intrinsic viscosity) results from Dow 1683 broad polystyrene (American Polymer Standards Corp.; Mentor, Ohio) or its equivalent to the narrow standard column calibration results from the narrow polystyrene standards calibration curve. The molecular weight data, accounting for detector volume off-set determination, are obtained in a manner consistent with that published by Zimm (Zimm, B. H.,  J. Chem. Phys.,  16, 1099 (1948)) and Kratochvil (Kratochvil, P.,  Classical Light Scattering from Polymer Solutions , Elsevier, Oxford, N.Y. (1987)). The overall injected concentration used in the determination of the molecular weight is obtained from the mass detector area and the mass detector constant derived from a suitable linear polyethylene homopolymer, or one of the polyethylene standards. The calculated molecular weights are obtained using a light scattering constant derived from one or more of the polyethylene standards mentioned and a refractive index concentration coefficient, do/dc, of 0.104. Generally, the mass detector response and the light scattering constant should be determined from a linear standard with a molecular weight in excess of about 50,000 daltons. The viscometer calibration can be accomplished using the methods described by the manufacturer or alternatively by using the published values of suitable linear standards such as Standard Reference Materials (SRM)  1475   a ,  1482   a ,  1483 , or  1484   a . The chromatographic concentrations are assumed low enough to eliminate addressing 2 nd  viral coefficient effects (concentration effects on molecular weight). 
     gpcBR Branching Index by 3D-GPC 
     In the 3D-GPC configuration the polyethylene and polystyrene standards can be used to measure the Mark-Houwink constants, K and α, independently for each of the two polymer types, polystyrene and polyethylene. These can be used to refine the Williams and Ward polyethylene equivalent molecular weights in application of the following methods. 
     The gpcBR branching index is determined by first calibrating the light scattering, viscosity, and concentration detectors as described previously. Baselines are then subtracted from the light scattering, viscometer, and concentration chromatograms. Integration windows are then set to ensure integration of all of the low molecular weight retention volume range in the light scattering and viscometer chromatograms that indicate the presence of detectable polymer from the refractive index chromatogram. Linear polyethylene standards are then used to establish polyethylene and polystyrene Mark-Houwink constants as described previously. Upon obtaining the constants, the two values are used to construct two linear reference conventional calibrations (“cc”) for polyethylene molecular weight and polyethylene intrinsic viscosity as a function of elution volume, as shown in Equations 3 and 4: 
     
       
         
           
             
               
                 
                   
                     
                       M 
                       PE 
                     
                     = 
                     
                       
                         
                           ( 
                           
                             
                               K 
                               PS 
                             
                             
                               K 
                               PE 
                             
                           
                           ) 
                         
                         
                           
                             1 
                             / 
                             
                               α 
                               PE 
                             
                           
                           + 
                           1 
                         
                       
                       · 
                       
                         M 
                         PS 
                         
                           
                             α 
                             PS 
                           
                           + 
                           
                             1 
                             / 
                             
                               α 
                               PE 
                             
                           
                           + 
                           1 
                         
                       
                     
                   
                   , 
                   and 
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       [ 
                       η 
                       ] 
                     
                     PE 
                   
                   = 
                   
                     
                       K 
                       PS 
                     
                     · 
                     
                       
                         M 
                         PS 
                         
                           α 
                           + 
                           1 
                         
                       
                       / 
                       
                         
                           M 
                           PE 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     The gpcBR branching index is a robust method for the characterization of long chain branching. Yau, Wallace W., “Examples of Using 3D-GPC—TREF for Polyolefin Characterization”,  Macromol. Symp.,  2007, 257, 29-45. The index avoids the slice-by-slice 3D-GPC calculations traditionally used in the determination of g′ values and branching frequency calculations in favor of whole polymer detector areas and area dot products. From 3D-GPC data, one can obtain the sample bulk M W  by the light scattering (LS) detector using the peak area method. The method avoids the slice-by-slice ratio of light scattering detector signal over the concentration detector signal as required in the g′ determination. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           M 
                           W 
                         
                         = 
                         
                           
                             ∑ 
                             i 
                           
                           ⁢ 
                           
                             
                               w 
                               i 
                             
                             ⁢ 
                             
                               M 
                               i 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ∑ 
                             i 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   C 
                                   i 
                                 
                                 
                                   
                                     ∑ 
                                     i 
                                   
                                   ⁢ 
                                   
                                     C 
                                     i 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               M 
                               i 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               ∑ 
                               i 
                             
                             ⁢ 
                             
                               
                                 C 
                                 i 
                               
                               ⁢ 
                               
                                 M 
                                 i 
                               
                             
                           
                           
                             
                               ∑ 
                               i 
                             
                             ⁢ 
                             
                               C 
                               i 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               ∑ 
                               i 
                             
                             ⁢ 
                             
                               LS 
                               i 
                             
                           
                           
                             
                               ∑ 
                               i 
                             
                             ⁢ 
                             
                               C 
                               i 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               LS 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               Area 
                             
                             
                               Conc 
                               . 
                               
                                   
                               
                               ⁢ 
                               Area 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
     The area calculation in Equation 5 offers more precision because as an overall sample area it is much less sensitive to variation caused by detector noise and GPC settings on baseline and integration limits. More importantly, the peak area calculation is not affected by the detector volume offsets. Similarly, the high-precision sample intrinsic viscosity (IV) is obtained by the area method shown in Equation 6: 
                         IV   =     [   η   ]                 =       ∑   i     ⁢       w   i     ⁢     IV   i                     =       ∑   i     ⁢       (       C   i         ∑   i     ⁢     C   i         )     ⁢     IV   i                     =         ∑   i     ⁢       C   i     ⁢     IV   i             ∑   i     ⁢     C   i                     =         ∑   i     ⁢     DP   i           ∑   i     ⁢     C   i                       =       DP   ⁢           ⁢   Area       Conc   .           ⁢   Area         ,                 (     Eq   .           ⁢   6     )               
where DP i  stands for the differential pressure signal monitored directly from the online viscometer.
 
     To determine the gpcBR branching index, the light scattering elution area for the sample polymer is used to determine the molecular weight of the sample. The viscosity detector elution area for the sample polymer is used to determine the intrinsic viscosity (IV or [η]) of the sample. 
     Initially, the molecular weight and intrinsic viscosity for a linear polyethylene standard sample, such as SRM 1475   a  or an equivalent, are determined using the conventional calibrations for both molecular weight and intrinsic viscosity as a function of elution volume, per Equations 7 and 8: 
                       Mw   CC     =         ∑   i     ⁢       (       C   i         ∑   i     ⁢     C   i         )     ⁢     M   i         =       ∑   i     ⁢       w   i     ⁢     M   i             ,   and           (     Eq   .           ⁢   7     )                   [   η   ]     CC     =         ∑   i     ⁢       (       C   i         ∑   i     ⁢     C   i         )     ⁢     IV   i         =       ∑   i     ⁢       w   i     ⁢       IV   i     .                   (     Eq   .           ⁢   8     )               
Equation 9 is used to determine the gpcBR branching index:
 
                     gpcBR   =     [         (         [   η   ]     CC       [   η   ]       )     ·       (       M   W       M     W   ,   CC         )       α   PE         -   1     ]       ,           (     Eq   .           ⁢   9     )               
where [η] is the measured intrinsic viscosity, [η] cc  is the intrinsic viscosity from the conventional calibration, M w  is the measured weight average molecular weight, and W w,cc  is the weight average molecular weight of the conventional calibration. The Mw by light scattering (LS) using Equation (5) is commonly referred to as the absolute Mw; while the Mw,cc from Equation (7) using conventional GPC molecular weight calibration curve is often referred to as polymer chain Mw. All statistical values with the “cc” subscript are determined using their respective elution volumes, the corresponding conventional calibration as previously described, and the concentration (C i ) derived from the mass detector response. The non-subscripted values are measured values based on the mass detector, LALLS, and viscometer areas. The value of K PE  is adjusted iteratively until the linear reference sample has a gpcBR measured value of zero. For example, the final values for α and Log K for the determination of gpcBR in this particular case are 0.725 and −3.355, respectively, for polyethylene, and 0.722 and −3.993 for polystyrene, respectively.
 
     Once the K and αvalues have been determined, the procedure is repeated using the branched samples. The branched samples are analyzed using the final Mark-Houwink constants as the best “cc” calibration values and applying Equations 5-9. 
     The interpretation of gpcBR is straight forward. For linear polymers, gpcBR calculated from Equation 9 will be close to zero since the values measured by LS and viscometry will be close to the conventional calibration standard. For branched polymers, gpcBR will be higher than zero, especially with high levels of LCB, because the measured polymer M w  will be higher than the calculated M w,cc , and the calculated IV cc  will be higher than the measured polymer IV. In fact, the gpcBR value represents the fractional IV change due the molecular size contraction effect as the result of polymer branching. A gpcBR value of 0.5 or 2.0 would mean a molecular size contraction effect of IV at the level of 50% and 200%, respectively, versus a linear polymer molecule of equivalent weight. 
     For these particular Examples, the advantage of using gpcBR in comparison to the g′ index and branching frequency calculations is due to the higher precision of gpcBR. All of the parameters used in the gpcBR index determination are obtained with good precision and are not detrimentally affected by the low 3D-GPC detector response at high molecular weight from the concentration detector. Errors in detector volume alignment also do not affect the precision of the gpcBR index determination. In other particular cases, other methods for determining M w  moments may be preferable to the aforementioned technique. 
     Nuclear Magnetic Resonance ( 13 C NMR) 
     The samples are prepared by adding approximately 2.7 g of a 50/50 mixture of tetrachloroethane-d2/orthodichlorobenzene containing 0.025 M Cr(AcAc) 3  (tris(acetylacetonato)-chromium(III)) to 0.25 g sample in a NORELL 1001-7 10 mm NMR tube. The samples are dissolved and homogenized by heating the tube and its contents to 150° C. using a heating block and heat gun. Each sample is visually inspected to ensure homogeneity. 
     The data are collected using a BRUKER 400 MHz spectrometer equipped with a BRUKER DUAL DUL high-temperature CRYOPROBE. The data are acquired using 320 transients per data file, a 6 second pulse repetition delay, 90 degree flip angles, and inverse gated decoupling with a sample temperature of 120° C. All measurements are made on non-spinning samples in locked mode. Samples are allowed to thermally equilibrate for 7 minutes prior to data acquisition. The  13 C NMR chemical shifts are internally referenced to the EEE triad at 30.0 ppm. 
     Identification and Quantification of Various Branch Types in LDPE 
       FIG. 2  shows the  13 C NMR spectrum of an LDPE (Sample C-3 below), and indicates characteristic peaks resulting from various branch lengths. Only the most important identifying peaks are labeled. Assignments for the remaining peaks are given in Table 2. C53 refers to the third carbon in a 5-carbon branch with the methyl counted as carbon 1. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Characteristic Chemical Shifts for Branches of 1 to 6 or More Carbons as Observed in 
               
               
                 Polyethylene 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Br 
                   
                   
                   
                 Bx1 
                   
                   
                   
                   
                   
               
               
                 Length 
                 Methines 
                 Alphas 
                 Betas 
                 (Methyl) 
                 Bx2 
                 Bx3 
                 Bx4 
                 Bx5 
                 Bx6 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 33.3± 
                 37.6± 
                 27.5± 
                 20.0± 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 2 
                 39.8± 
                 34.1± 
                 27.3* 
                 11.1± 
                 26.8± 
                 — 
                 — 
                 — 
                 — 
               
               
                 3 
                 37.9± 
                 34.6* 
                 27.3* 
                 14.7± 
                 20.3± 
                 37.0± 
                 — 
                 — 
                 — 
               
               
                 4 
                 38.2* 
                 34.6* 
                 27.3* 
                 14.1* 
                 23.4± 
                 29.6 
                 34.2 
                 — 
                 — 
               
               
                 5 
                 38.2* 
                 34.6* 
                 27.3* 
                 14.1* 
                 22.9* 
                 32.7± 
                 26.9 
                 34.6* 
                 — 
               
               
                 6 or more 
                 38.2* 
                 34.6* 
                 27.3* 
                 14.1* 
                 22.9* 
                 32.2* 
                 30.4{circumflex over ( )} 
                 27.3* 
                 34.6* 
               
               
                 PE Chain 
                 — 
                 — 
                 — 
                 14.1* 
                 22.9* 
                 32.3* 
                 29.6{circumflex over ( )} 
                 — 
                 — 
               
               
                 Ends 
               
               
                   
               
               
                 ±values are unique peaks that can be used for ID and/or quantification. 
               
               
                 *values indicate that the shift overlaps with other branching. 
               
               
                 {circumflex over ( )}values indicate that the shift was not resolved/overlap with large 30 ppm peak. 
               
            
           
         
       
     
     Determination of C5 (Amyl) Branching 
     C5 (amyl) branches are determined by the peak at 32.7 ppm. The number of C5 branches per 1000 total carbons is determined by setting the integral of the full LDPE spectrum, about 40 to 5 ppm, to a value of 1000, and integrating the 32.7 ppm peak. The 32.7 ppm peak integral is then a direct measure of the number of C5 branches per 1000 carbons. The example in  FIG. 3  contains 1.67 C5 branches/1000C. 
     Determination of C1 (Methyl) Branches 
     C1 branches result in peaks at about 20, 33.3, 37.6, and 27.5 ppm.  FIG. 4  shows a  13 C NMR spectrum of which was produced using propylene as the chain transfer agent (CTA), and therefore exhibits a significant level of C1 (methyl) branches. This is because propylene acts both as a CTA and as a comonomer, and introduces C1 branches as would be observed in an ethylene-propylene LLDPE. 
     Determination of C3 (Propyl) Branches 
     C3 branches result in peaks at 37.9, 37.0, 20.3 and 14.7 ppm (and others that would be obscured in a LDPE spectrum).  FIG. 5  shows a  13 C NMR spectrum of a HDPE made with pentene comonomer, and therefore containing C3 branches. This particular sample also contains a very low level of C2 branching from butene. 
     Determination of C6+ Branches 
     C6 and longer branching (C6+) are determined algebraically in LDPE spectra. This is due to overlap in peaks from C4, C5, and C6+ branches. C4 and C5 can be determined independently, and their sum is subtracted from peaks containing contributions of two or more of these. C6+ branches are determined by a direct measure of C6+ branches in LDPE, where the long branches are not distinguished from “chain ends”. The 32.2 ppm peak, representing the 3 rd  carbon from the end of all chains or branches of 6 or more carbons, is used for C6+ determination. 
     Extraction of Polyalkylene 
     To a 100 mL jar is added 2.0 g of LDPE-grafted polyisobutylene (PIB) weighed to the nearest 0.0001 gm. To this solid is added 50+/−1 g of HPLC grade tetrahydrofuran, and the mixture is shaken for 4 hours. The mixture is filtered through a #41 ashless filter paper into a tared 2 oz jar. The solvent is evaporated to dryness under a stream of nitrogen overnight. The undissolved solids are also dried overnight under a stream of nitrogen. The residue from the tetrahydrofuran solution is weighed as is the dried undissolved solids. The percentage of extracted material is determined by the following formula:
 
((residue mass/(residue mass+undissolved solids mass))*100.
 
     Dynamic Mechanical Spectroscopy (DMS) 
     Resin is compression-molded into a 3 mm thick×1 inch circular plaque at 350° F. (177° C.) for 5 minutes under 1500 psi pressure in air. The sample is then taken out of the press and placed on the counter to cool. 
     Melt rheology, constant temperature frequency sweeps, are performed using a TA Instruments “Advanced Rheometric Expansion System (ARES),” equipped with 25 mm parallel plates, under a nitrogen purge. The sample is placed on the plate and allowed to melt for five minutes at 190° C. The plates are then closed to 2 mm, the sample trimmed, and then the test is started. The method has an additional five minute delay built in, to allow for temperature equilibrium. The experiments are performed at 190° C. over a frequency range of 0.1 to 100 rad/s. The strain amplitude is constant at 10%. The stress response is analyzed in terms of amplitude and phase, from which the storage modulus (G′), loss modulus (G″), dynamic viscosity η*, and tan (δ) are calculated. 
     Sample (Inventive Polymer) Preparation 
     PIB (OPPANOL B 15 SFN available from BASF) is added to the reactor. After closing the 100 ml high-pressure stainless steel batch reactor, the agitator is turned on at 1000 rpm (revolutions per minute). The reactor is deoxygenated by pulling vacuum on the system and pressurizing with nitrogen. This is repeated three times. The reactor is then pressurized with ethylene up to 2000 bar while at ambient temperatures and then vented off. This is repeated three times. On the final ethylene vent of the reactor, the pressure is dropped only to a pressure of about 100 bars, where the reactor heating cycle is initiated. Upon achieving an internal temperature of about 225° C., the reactor is then pressurized with ethylene up to starting pressure (see Table 3A). The ethylene/PIB mixture is stirred and held at 225° C. for at least 30 minutes. Ethylene is then used to sweep 1.32 ml of a mixture of 0.2395 mmol/ml propionaldehyde as chain transfer agent, 0.00599 mmol/ml di-tert-butyl peroxide and 0.00239 mmol/ml tert-butyl peroxy 2-ethylhexanoate as initiators in n-heptane into the reactor. An increase in pressure in conjunction with the addition of initiator causes the ethylene monomers to free-radical polymerize. The polymerization leads to a temperature increase. After allowing the reactor to continue to mix for 15 minutes and cooling down to 225° C. a second injection of 1.32 ml of a mixture of 0.00599 mmol/ml di-tert-butyl peroxide and 0.00239 mmol/ml tert-butyl peroxy 2-ethylhexanoate in n-heptane is swept with ethylene into the reactor. An increase in pressure in conjunction with the addition of initiator causes the ethylene monomers to free-radical polymerize. The second polymerization leads to a temperature increase. A third initiator injection is done at the same feed conditions as the second one. The formed polymer is purged with ethylene out of the reactor at 1600 bars for 5 minutes. With this procedure two samples are made. The process conditions are given in Tables 3A-3B, 
     
       
         
           
               
             
               
                 TABLE 3A 
               
             
            
               
                   
               
               
                 Polymerization Conditions for the First Initiator Injection of PIB 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Sample 
                 m(PIB) 
                 p start,1   
                 p max,1   
                 T start,1   
                 T max,1   
               
               
                   
                 — 
                 g 
                 bar 
                 bar 
                 ° C. 
                 ° C. 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 PIB-1 
                 2.31 
                 1350 
                 1720 
                 225 
                 290 
               
               
                   
                 PIB-2 
                 6.20 
                 1420 
                 1750 
                 225 
                 290 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3B 
               
             
            
               
                   
               
               
                 Polymerization Conditions for the Second Initiator Injection of PIB 
               
            
           
           
               
               
               
               
               
            
               
                 Sample 
                 p start,2   
                 p max,2   
                 T start,2   
                 T max,2   
               
               
                 — 
                 bar 
                 bar 
                 ° C. 
                 ° C. 
               
               
                   
               
               
                 PIB-1 
                 1350 
                 1700 
                 225 
                 285 
               
               
                 PIB-2 
                 1420 
                 1720 
                 225 
                 285 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3C 
               
             
            
               
                   
               
               
                 Polymerization Conditions for the Third Initiator Injection of PIB 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                   
                 m(PIB-graft- 
                   
                   
               
               
                 Sample 
                 p start,3   
                 p max,3   
                 T start,3   
                 T max,3   
                 p end   
                 PE) 
                 ethylene- 
                 %-PIB in 
               
               
                 — 
                 bar 
                 bar 
                 ° C. 
                 ° C. 
                 bar 
                 g 
                 conversion 
                 end-product 
               
               
                   
               
               
                 PIB-1 
                 1350 
                 1700 
                 225 
                 285 
                 1350 
                 25.63 
                 49.0% 
                 9.01 
               
               
                 PIB-2 
                 1420 
                 1720 
                 225 
                 285 
                 1420 
                 29.67 
                 49.4% 
                 20.9 
               
               
                   
               
            
           
         
       
     
     PIB Grafting 
     PIB is observed in the  13 C NMR spectrum of  FIG. 6  Weight percent PIB is calculated from the sum of the PIB integrals divided by the total spectrum integral (representing all carbons in the spectrum). The isobutylene and ethylene formula weights do not need to be accounted for in this calculation because in PIB and LDPE all carbons, on average, have two protons. 
     Sample PIB-2, contains 16.0±0.5 wt % PIB. The same result (16.0 wt % PIB) is obtained with both NMR acquisitions done on this sample, using two different instruments. Sample PIB-1 contains 4.8±0.3 wt % PIB. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 PIB Grafting Results 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Total 
                   
                   
               
               
                   
                   
                 wt % 
                 wt % Free 
               
               
                   
                   
                 PIB 
                 PIB 
                 wt/wt ratio 
               
               
                   
                 Sample 
                 (NMR) 
                 (Extractable) i   
                 PIB/LDPE 
               
               
                   
                   
               
               
                   
                 1 (PIB-1) 
                 4.8 
                 2.9 
                 0.05 
               
               
                   
                 2 (PIB-2) 
                 16.0 
                 5.2 
                 0.19 
               
               
                   
                   
               
            
           
         
       
     
     Melt Index, Melt Index Ratio I 10 /I 2 , and Density 
     Table 5A shows the measured melt index (I 2 ), melt index ratio (I 10 /I 2 ), and density of two inventive polymers as compared to two commercial LDPE of comparable melt index. 
     
       
         
           
               
             
               
                 TABLE 5A 
               
             
            
               
                   
               
               
                 Properties of PE-graft-PIB Polymers and Comparative LDPE Polymers 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 MI (I 2 ) 
                   
                 Density 
               
               
                   
                 Example 
                 (g/10 min) 
                 I 10 /I 2   
                 (g/cc) 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 1 
                 2.54 
                 13.2 
                 0.912 
               
               
                   
                 2 
                 5.84 
                 11.3 
                 0.914 
               
               
                   
                 C-1 
                 2.54 
                 13.9 
                 0.923 
               
               
                   
                 C-2 
                 5.42 
                 10.3 
                 0.918 
               
               
                   
                   
               
            
           
         
       
     
     Table 5B reports the melt index (for reference) and the molecular weight properties of the Examples and Comparative Examples. The molecular weight distributions are plotted in  FIG. 7 . Both examples have very broad molecular weight distribution. At equivalent melt index, the Examples have broader molecular weight distributions (M w /M n ), relatively high z-average molecular weights (M z ), and high levels of long chain branching as indicated by LCB f  and gpcBR. As shown in  FIG. 7 , the Examples also show a shoulder on the molecular weight distribution which may be attributable to the bonding of the PIB to the PE creating a higher molecular weight fraction. 
     
       
         
           
               
             
               
                 TABLE 5B 
               
             
            
               
                   
               
               
                 Properties of PE-graft-PIB Polymers and Comparative LDPE Polymers 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 MI (I 2 ) 
                   
                   
                   
                   
                   
                   
               
               
                 Exam- 
                 (g/10 
                 M w   
                 M n   
                 M w / 
                 M z   
                   
                   
               
               
                 ple 
                 min) 
                 (g/mol) 
                 (g/mol) 
                 M n   
                 (g/mol) 
                 LCB f   
                 gpcBR 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 1 
                 2.54 
                 159,560 
                 11,840 
                 13.48 
                 502,500 
                 3.76 
                 3.00 
               
               
                 2 
                 5.84 
                 124,520 
                 10,810 
                 11.52 
                 409,300 
                 3.25 
                 2.56 
               
               
                 C-1 
                 2.54 
                 72,930 
                 11,030 
                 6.61 
                 253,700 
                 2.38 
                 1.61 
               
               
                 C-2 
                 5.42 
                 145,940 
                 14,300 
                 10.21 
                 615,900 
                 2.80 
                 3.35 
               
               
                   
               
            
           
         
       
     
     Table 5C reports the melt index and density (for reference) and the DSC properties of the Examples and Comparative Examples. 
     
       
         
           
               
             
               
                 TABLE 5C 
               
             
            
               
                   
               
               
                 Properties of PE-graft-PIB Polymers and 
               
               
                 Comparative LDPE Polymers 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Heat 
                   
                   
               
               
                   
                   
                   
                   
                 of 
               
               
                   
                 MI (I 2 ) 
                 Density 
                 T m   
                 Fusion 
                 % 
                 T c   
               
               
                 Example 
                 (g/10 min) 
                 (g/cc) 
                 (° C.) 
                 (J/g) 
                 Cryst. 
                 (° C.) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 1 
                 2.54 
                 0.912 
                 103.4 
                 127.1 
                 43.5 
                 91.5 
               
               
                 2 
                 5.84 
                 0.914 
                 104.0 
                 105.8 
                 36.2 
                 91.8 
               
               
                 C-1 
                 2.54 
                 0.923 
                 112.1 
                 151.4 
                 51.8 
                 100.2 
               
               
                 C-2 
                 5.42 
                 0.918 
                 107.5 
                 127.6 
                 43.7 
                 96.3 
               
               
                   
               
            
           
         
       
     
     Melting point vs. density is shown in  FIG. 9 , and heat of fusion vs. density is shown in  FIG. 10 . 
     Short Chain Branching 
     All values are in branches per 1000 total carbons. Branching values for the grafted sample are calculated based on total observed carbons, including those of the grafted polymer (PIB) and based on the LDPE carbons only. No C3 (propyl) branches are observed in the sample. 
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Short Chain Branching of Samples and Comparative Samples 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                   
                 C5 
                   
               
               
                   
                 Sample 
                 C1 
                 (amyl) 
                 LCB (C6+) 
               
               
                   
                   
               
               
                   
                 2 (PIB-02) 
                 0 
                 2.69 +/− 0.27 
                 4.32 
               
               
                   
                   
               
            
           
         
       
     
     Table 7 shows the frequency and viscosity data as measured by dynamic mechanical spectroscopy of the Inventive Examples and Comparative Examples. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 DMS Melt Rheology Data of PE-graft-PIB Polymers and 
               
               
                 Comparative Examples 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Viscosity 
                 Viscosity 
                 Viscosity in 
                 Viscosity in 
               
               
                   
                 in Pa-s 
                 in Pa-s 
                 Pa-s 
                 Pa-s 
               
               
                   
                 Example 
                 Example 
                 Comparative 
                 Comparative 
               
               
                 Frequency (rad/s) 
                 1 
                 2 
                 Example 1 
                 Example 2 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0.100 
                 5,554 
                 3,937 
                 5,414 
                 3,298 
               
               
                 0.158 
                 4,939 
                 3,509 
                 5,164 
                 3,129 
               
               
                 0.251 
                 4,335 
                 3,075 
                 4,840 
                 2,883 
               
               
                 0.398 
                 3,741 
                 2,638 
                 4,444 
                 2,599 
               
               
                 0.631 
                 3,184 
                 2,234 
                 4,005 
                 2,300 
               
               
                 1.000 
                 2,675 
                 1,870 
                 3,542 
                 2,007 
               
               
                 1.585 
                 2,223 
                 1,552 
                 3,078 
                 1,728 
               
               
                 2.512 
                 1,827 
                 1,277 
                 2,632 
                 1,471 
               
               
                 3.981 
                 1,486 
                 1,044 
                 2,214 
                 1,238 
               
               
                 6.310 
                 1,199 
                 848 
                 1,834 
                 1,031 
               
               
                 10.000 
                 960 
                 685 
                 1,501 
                 851 
               
               
                 15.849 
                 762 
                 550 
                 1,214 
                 696 
               
               
                 25.119 
                 600 
                 439 
                 969 
                 564 
               
               
                 39.811 
                 472 
                 348 
                 766 
                 454 
               
               
                 63.096 
                 367 
                 276 
                 600 
                 361 
               
               
                 100.000 
                 283 
                 216 
                 466 
                 284 
               
               
                 Viscosity at 
                 5,554 
                 3,937 
                 5,414 
                 3,298 
               
               
                 0.1 rad/s (Pa-s) 
               
               
                 Viscosity at 
                 283 
                 216 
                 466 
                 284 
               
               
                 100 rad/s (Pa-s) 
               
               
                 Viscosity Ratio 
                 19.60 
                 18.19 
                 11.61 
                 11.60 
               
               
                 (V 0.1/V100) 
               
               
                   
               
            
           
         
       
     
     The inventive polymers exhibit better viscosity ratios than the comparative polymers, and this is indicative of better processability. The data is graphically illustrated in  FIG. 8 . 
     Although the invention has been described with certain detail through the preceding description of the preferred embodiments, this detail is for the primary purpose of illustration. Many variations and modifications can be made by one skilled in the art without departing from the spirit and scope of the invention as described in the following claims.