Tetrafunctional long-chain branched ethylene polymer

Abstract

Ethylene-based polymers are polymers that are produced under defined polymerization reaction conditions by polymerization of ethylene monomer with at least one diene or polyene comonomer and, optionally, at least one C3-C6 copolymer. 14 and a comonomer, and the ethylene-based polymer comprises a reaction product of the polymerization of w / M w0 M w0 is the initial weight average molecular weight of the comparative ethylene-based polymer by gel permeation chromatography. The comparative ethylene-based polymer is a polymer that is produced by polymerization of ethylene monomer and all C3-C6 monomers present in the ethylene-based polymer under defined polymerization reaction conditions. 14 and the comonomer, if present, of the polymerization of at least one polyene comonomer, and the molecular weight tail is determined by the MWD area metric, A TAIL is quantified by A TAIL is less than or equal to 0.04 as determined by gel permeation chromatography using a triple detector. [Selection diagram] None

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 62 / 738,633, filed September 28, 2018, the entire disclosure of which is incorporated herein by reference.

[0002] SUMMARY OF THE DISCLOSURE Embodiments of the present disclosure relate generally to polymer compositions having long chain branching and processes by which the polymer compositions are synthesized. [Background technology]

[0003] Olefin-based polymers, such as polyethylene and polypropylene, are produced through various catalyst systems. The selection of such catalyst system used in the polymerization process of an olefin-based polymer is an important factor that contributes to the characteristics and properties of such an olefin-based polymer.

[0004] Polyethylene and polypropylene are manufactured for a wide variety of products. The polyethylene and polypropylene polymerization process can be varied in several ways to produce a wide variety of resulting polyethylene resins with different physical properties that make the various resins suitable for use in different applications. The amount of short chain branching in a polyolefin affects the physical properties of that polyolefin. The effect of branching on the properties of polyethylene depends on the length and amount of branching. Short branching primarily affects the mechanical and thermal properties. As the short chain branching frequency increases, the polymer is less able to form lamellar crystals and mechanical and thermal properties decrease. Small amounts of long chain branching can significantly alter the processing properties of the polymer.

[0005] To form long chain branches, the vinyl or terminal double bonds of a polymer chain are incorporated into a new polymer chain. Reincorporation of vinyl terminated polymers and introduction of diene comonomers are two mechanisms by which vinyl groups on a polymer strand are incorporated into a second polymer strand. In addition, long chain branching is induced via radicals. In all three mechanisms, it is difficult to control the amount of branching. When using radicals or dienes to initiate long chain branching, too much branching can occur, which can lead to gelling and reactor fouling. The reincorporation mechanism does not produce much branching, and branching can only occur after a polymer strand has been generated, which further limits the amount of branching that can occur. Summary of the Invention

[0006] An embodiment of the present disclosure provides a process for the polymerization of ethylene monomer, at least one diene or polyene comonomer, and optionally at least one C 3 ~C 14 and a comonomer. The ethylene-based polymer has a M of greater than 1.20. w / M w0 M w is the weight average molecular weight of the ethylene-based polymer as determined from a gel permeation chromatography curve of the ethylene-based polymer obtained by refractive index chromatography; M w0 is the initial weight average molecular weight of the comparative ethylene-based polymer by gel permeation chromatography. The comparative ethylene-based polymer is a polymer that is prepared by polymerization of ethylene monomer and all C monomers present in the ethylene-based polymer under the defined polymerization reaction conditions. 3 ~C 14 The reaction product of the polymerization of the comonomer, if present, and at least one polyene comonomer, and the molecular weight tail is determined by the MWD area metric, A TAIL It is quantified by A TAIL is less than 0.04 as determined by gel permeation chromatography using a triple detector.

[0007] In various embodiments, the ethylene-based polymer comprises an elastic modulus, m, at 190° C., less than or equal to 4 seconds / radian, where m is [((tan(δ 0.1 )-tan(δ 100 ))*1000) / (0.1-100))], and tan(δ 0.1 ) is the tangent of the phase angle in 0.1 radians / second, and tan(δ 100 ) is the tangent of the phase angle in 100 radians / second. [Brief description of the drawings]

[0008] [Figure 1] 1 is a graphical representation of polymer molecular weight with increasing number of branched methines per 1000 carbons. [Diagram 2] 1 is a graphical model predicting the dependence of molecular weight distribution (MWD) curves on branching level. [Diagram 3] 1 is a graphical model predicting the dependence of relative peak molecular weight on branching level. [Figure 4] 1 is a graphical representation of predicted molecular weight distribution (MWD) curve dependence on trifunctional diene branching level. [Diagram 5] 1 is a graphical representation of the predicted dependence of relative peak molecular weight (MW) on trifunctional diene branching level. [Figure 6] FIG. 1 is a graphical representation of the model predicted effect of branching on peak molecular weight (Mp) versus branches per polymer molecule for traditional diene branching (solid line) and "ladder branching" (dashed line). [Figure 7] FIG. 1 is a graphical representation of the model predicted effect of branching on weight average molecular weight (Mw) on branches per polymer molecule for traditional diene branching (solid line) and "ladder branching" (dashed line). [Figure 8] 1 is a graphical representation of the model predicted effect of branching on peak weight average molecular weight (Mp) versus branches per linear segment for conventional diene branching (solid line) (vs. Bc) and Mp for "ladder branched" polymers (dashed line) (vs. Rc). [Figure 9]FIG. 1 is a graphical representation of the model predicted effect of branch weight average molecular weight (Mw) on branches per linear segment of conventional diene branching (vs. Bc) (solid line) and "ladder branched" polymer (dashed line) (vs. Rc). [Figure 10] Graphical representation of the MWD slope used to calculate the shape metrics G(79 / 29) and G(96 / 08), where S(X) is the slope at X% of the MWD height. G(A / B)=(S(A)-S(B)) / S(A). [Figure 11] FIG. 1 is a graphical representation of a model predicting molecular weight distribution (MWD) shape metric G(79 / 29) compared to conventional branching and "ladder branching" as a function of branching level as indicated by relative peak MW (Mp / Mpo). [Figure 12] FIG. 1 is a graphical representation of a model predicting the MWD shape metric G(79 / 29) compared to conventional branching and "ladder branching" as a function of branching level as indicated by relative weighted average MW (Mw / Mwo). [Figure 13] FIG. 1 is a graphical representation of a model predicting the MWD shape metric G(98 / 08) compared to conventional and "ladder branching" as a function of branching level as indicated by relative peak MW (Mp / Mpo). [Figure 14] FIG. 1 is a graphical representation of a model predicting the MWD shape metric G(98 / 08) compared to conventional branching and "ladder branching" as a function of branching level as indicated by relative weighted average MW (Mw / Mwo). [Figure 15] 1 is a graphical representation of the MWD curve showing how the point of maximum slope is used to define a high MWD tail area metric. [Figure 16] 1 is a model predicting the MWD area metric, AHIGH, compared to conventional branching and "ladder branching" as a function of branching level as indicated by relative weight average molecular weight (Mp / Mpo). [Figure 17]1 is a model predicting the MWD area metric, AHIGH, compared to conventional branching and "ladder branching" as a function of branching level as indicated by relative peak molecular weight (Mw / Mwo). [Figure 18] Model predicting the MWD area metric, ATAIL, compared to conventional branching and "ladder branching" as a function of branching level as indicated by relative peak molecular weight (Mp / Mpo). [Figure 19] A model predicting the MWD area metric, ATAIL, compared to conventional branching and "ladder branching" as a function of branching level as indicated by relative weight average molecular weight (Mw / Mwo). [Figure 20] 1 is a graph of absolute molecular weight distribution (MWD) curves measured by GPC for Example Series 2.4 as recorded in Table 2. [Figure 21] 1 is a conventional molecular weight distribution curve measured by conventional gel permeation chromatography (GPC). [Figure 22] Absolute molecular weight distribution curve measured by GPC triple light scattering detector (also called absolute GPC). [Figure 23] 1 is a graph of extensional viscosity measured as a function of time in seconds for a "ladder branched" polymer resin. [Figure 24] 1 is a graph of melt strength (cN) as a function of speed (mm / sec) for a "ladder branching" polymer resin. [Diagram 25] 1 is a conventional molecular weight distribution curve measured by GPC of an unbranched ethylene-based polymer and a "ladder-branched" polymer resin. [Figure 26] 1 is an absolute molecular weight distribution curve measured by a GPC triple light scattering detector for an unbranched ethylene-based polymer and a "ladder-branched" polymer resin. [Figure 27] 1 is a graph of extensional viscosity measured as a function of time in seconds for a "ladder branched" polymer resin. [Figure 28]1 is a graph of melt strength (cN) as a function of speed (mm / sec) for a "ladder branching" polymer resin. [Figure 29] Absolute molecular weight distribution curves measured by GPC triple light scattering detector for two comparative examples with no diene and four samples with varying amounts of diene. [Figure 30A] 1 is a graph of absolute molecular weight distributions of comparative conventional branched polymer samples having various amounts of diene. [Figure 30B] 1 is a graph of conventional molecular weight distributions of comparative conventional branched polymer samples having various amounts of diene. [Diagram 31] 1 is a graph of the rheological ratio as a function of average g' for various polymer resins and a "ladder branched" polymer resin. [Diagram 32] 1 is a graph of the rheological ratio as a function of polydispersity index (PDI) for various polymer resins and "ladder branched" polymer resins. [Diagram 33] FIG. 1 is a graph of melt strength (centinewtons, cN) as a function of melt index (Log I2) for polymers produced with single chain and double chain catalysts, with additional lines showing linear polyethylene, tubular low density polyethylene, and autoclave low density polyethylene. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Specific embodiments of the process for synthesizing polymers and the polymers synthesized by the process of the present disclosure are described herein. It should be understood that the process for synthesizing polymers of the present disclosure may be implemented in different forms and should not be construed as being limited to the specific embodiments described in this disclosure. Rather, the embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the subject matter to those skilled in the art.

[0010] definition The term "polymer" refers to a polymeric compound prepared by polymerizing monomers, whether the monomers are the same or different types. Thus, the generic term polymer encompasses the term "homopolymer," which is commonly used to refer to a polymer prepared from only one type of monomer, and "copolymer," which refers to a polymer prepared from two or more different monomers. As used herein, the term "interpolymer" refers to a polymer prepared by polymerization of at least two different types of monomers. Thus, the generic term interpolymer includes copolymers and polymers prepared from three or more different monomers, such as terpolymers.

[0011] "Polyethylene" or "ethylene-based polymer" is intended to mean a polymer containing more than 50% by weight of units derived from ethylene monomer. This includes polyethylene homopolymers or copolymers (meaning units derived from two or more comonomers). Common forms of polyethylene known in the art include low density polyethylene (LDPE), linear low density polyethylene (LLDPE), very low density polyethylene (ULDPE), very low density polyethylene (VLDPE), single-site catalyzed linear low density polyethylene (m-LLDPE) containing both linear and substantially linear low density resins, medium density polyethylene (MDPE), and high density polyethylene (HDPE).

[0012] An embodiment of the present disclosure is 2 Monomer, at least one C 3 ~C 12A process for synthesizing a long-chain branched polymer by adding an α-olefin comonomer, at least one diene, a multi-chain catalyst, and optionally a solvent, where the multi-chain catalyst comprises a molecule having multiple polymerization sites to produce at least two copolymer strands, each copolymer strand copolymerizing at one of the polymerization sites; and synthesizing the long-chain branched polymer by linking the two copolymer strands with a diene, where the linking of the two copolymer strands is performed in concert with the copolymerization.

[0013] The process of synthesizing polymers according to the present disclosure is different from traditional long chain branching. The term "long chain branching" refers to a branch having more than 100 carbon atoms. "Branch" refers to a portion of a polymer that extends from a tertiary or quaternary carbon atom. If a branch extends from a tertiary carbon atom, there are two other branches, which collectively can be the polymer strand from which the branch extends. Traditionally, long chain branching (LCB) can occur naturally in the polymerization process, as shown in Scheme 1. This can occur through vinyl termination of the polymer chain and reinsertion of the polymeric vinyl to form trifunctional long chain branches. Depending on the degree of branching, various methods, such as nuclear magnetic resonance (NMR), can determine LCB or identify the effect of LCB in a polymer. For example, the effect of LCB is observed in shear flow in van Gurp-Palmen analysis, and the increase in shear viscosity at low angular frequencies and the strength of shear thinning behavior can be attributed to LCB. In extensional flow, the effect of LCB is usually identified in the degree of hardening or strength of the melt, and the maximum deformation achieved. Achieving high levels of natural LCB in the polymer is difficult due to the limited concentration of vinyl-terminated polymers (maximum one per polymer chain) and the need to carry out high ethylene conversion to ensure the formation of LCB. To ensure high conversion, the ethylene concentration in the reactor is low, so large amounts of vinyl-terminated polymer can be reinserted into a second polymer chain.

[0014] Scheme 1: Spontaneous long-chain branching: chain transfer events leading to vinyl-terminated polymers [ka] In Scheme 1, "Cat" is the catalyst and "P" is the polymer chain.

[0015] There is minimal long chain branching formed through naturally occurring branching processes. One method to enhance LCB, whether it is a radical, heterogeneous, or homogeneous process, is through the addition of α,ω-dienes to the polymerization system. Generally, dienes are added to the polymer chain in a similar manner as α-olefins, as shown in Scheme 2, but leave pendant vinyl groups that can be inserted once more into the polymer chain to create LCB. Generally, the length of the diene is not important, only that it can link two polymer chains together. In principle, the concentration of the pendant vinyl can be controlled through the amount of diene added to the reactor. Thus, the degree of LCB can be controlled by the concentration of the pendant vinyl.

[0016] Scheme 2: Long-chain branching via diene incorporation [ka] In Scheme 2, "Cat" is the catalyst, "P" is the polymer chain, and the diene in this example is 1,5-hexadiene.

[0017] Conventional processes incorporating dienes into polymer synthesis systems suffer from the fundamental flaw of gel formation or reactor fouling. Kinetic modeling, which will be discussed in a later section, can provide good predictive results that allow for a better understanding of gel formation. For example, longer polymer chains have more inserted olefins, and therefore more inserted dienes, and therefore more pendant vinyls, meaning that the longer polymer chains are more likely to reinsert into the catalyst to form LCBs. Thus, the longer polymer chains preferentially reinsert to form tetrafunctional branches, which are even larger polymer molecules, resulting in gel problems. As shown in Scheme 2, the tetrafunctional LCBs have a short segment (the number of carbons between the two double bonds of the diene) that bridges the two long chains on either side of the short segment. The weight average molecular weight (M) as a function of branching is shown in Fig. 2. w ) and number average molecular weight (M n A simulation of M ) is shown in FIG. 1 for polyethylene in a constant pressure semi-batch reactor. n is M w As goes to infinity, there is only a slight increase. w When the number increases to more than 200,000 grams per mole (g / mol), there is polymer gel, gelation, or reactor fouling.

[0018] The term "gel" or "gelation" refers to a solid composed of at least two components, the first being a three-dimensional cross-linked polymer, and the second being a medium in which the polymer is not completely soluble. If the polymer gels and does not completely dissolve, the reactor may become fouled with the polymer gel.

[0019] The term "ladder branched" polymer refers to a tetrafunctional long chain branched polymer as disclosed in this application, and the term "ladder branching mechanism" refers to how the "ladder branched" polymer is formed.

[0020] In one or more embodiments of the present disclosure, the process of synthesizing long-chain branched polymers achieves long-chain branching and avoids gel formation or reactor fouling. Without intending to be bound by theory, it is believed that reactor fouling is avoided by reacting two alkenes of a diene in a concerted manner across two proximal polymer chains. For example, as shown in Scheme 3, one alkene of a diene reacts before the second alkene, which reacts before too many ethylene molecules are added to the polymer strand, thereby removing the second alkene from proximity to the reaction site. The reaction of the first alkene of a diene to one polymer and the second alkene of a diene to the adjacent polymer chain before too many ethylene monomers are inserted is referred to as concerted addition of a diene to the proximal polymer chain.

[0021] Scheme 3: Description of the incorporation of dienes in a concerted manner, also referred to as the "ladder branching" mechanism (P is the polymer chain). [ka]

[0022] A polymer strand is a linear segment of a polymer, or more specifically a copolymer, optionally joined at an end(s) by a branched junction. For example, as shown in Scheme 1, a tetrafunctional branched junction joins the ends of four polymer strands, as opposed to a trifunctional branched junction, which joins the ends of three polymer strands.

[0023] The combination of multi-chain catalyst and diene affects the amount and type of branching. Embodiments of the present disclosure relate to controlling polymer properties, such as 1) the use of multiple diene species, 2) the use of multiple multi-chain catalyst species, or 3) a combination of polymerization environments including multiple reactor zones or zone gradients.

[0024] Nevertheless, conventional branching may be possible by using multiple catalysts, including single chain catalysts. The use of multiple diene species also includes those dienes that do not create branches or tend to result in "conventional" LCB. The process of synthesizing polymers according to the present disclosure is different from conventional long chain branching. The term "long chain branch" refers to a branch having more than 100 carbon atoms. The term "branch" refers to a portion of a polymer that extends from a tertiary or quaternary carbon atom. If a branch extends from a tertiary carbon atom, there are two other branches, which collectively may be the polymer chain from which the branch extends. Long chain branching (LCB) may occur naturally in the polymerization process, as shown in Scheme 1. It may occur through the termination of the polymer chain and the reinsertion of the polymeric vinyl to create trifunctional long chain branches.

[0025] In one or more embodiments, the process for polymerizing long-chain branched polymers includes a catalyst having at least two active sites in close proximity (multi-chain catalyst). To bring the two active sites into close proximity, the two active sites can be less than 18.5 angstroms (Å) apart. In some embodiments, the two active sites include a distance of 2.5 angstroms (Å) to 18.5 Å, 9 Å to 14 Å, or about 11 Å. In various embodiments, the process for polymerizing long-chain branched polymers includes a multi-chain catalyst. In one or more embodiments, the multi-chain catalyst can include at least one metal center, where the two active sites are on the same metal center. In some embodiments, the multi-chain catalyst can include a metal-ligand complex, where the two active sites (two polymer chains) are on the same metal center.

[0026] According to the X-ray crystal structure (ADBond, Chem. Comm. 2002, 1664), 1,9-decadiene has a terminal carbon-to-carbon distance of 10.8 Å. Although there is data that 1,9-decadiene forms rungs between two polymer chains via a "ladder branching" mechanism, it may be considered that α,ω-dienes with more than 10 carbon atoms may also form rungs via the "ladder branching" mechanism. Without wishing to be bound by theory, the question of whether α,ω-dienes with more than 10 carbon atoms can form rungs may be determined by the distance between the two polymer chains. For example, if the two polymer chains are present on different metal atoms of the catalyst (e.g., bimetallic, heterogeneous), the α,ω-dienes may contain additional methylene units (same C-C bond length and angle) that extend this structure to 1,15-hexadecadiene. Without wishing to be bound by theory, it is presumed that this 16 carbon analogue still has the potential to form rungs via a "ladder branching" mechanism. In this manner, the dienes 1,11-dodecadiene (terminal carbon distance of 13.3 Å), 1,13-tetradecadiene (terminal carbon distance of 15.9 Å), 1,15-hexadecadiene (terminal carbon distance of 18.5 Å) may be considered. In some embodiments, when the double-chain catalyst in the "ladder branching" mechanism is a bimetallic catalyst, the diene is 18.5 Å or less.

[0027] Modern computational techniques are known to be able to reproduce known experimental crystal structures with high accuracy as a way to estimate the interchain distance of the catalyst. For heterogeneous systems, one can estimate the surface concentration of the metal, which is often expressed as metal atoms per nanometer squared (M / nm 2 ) This surface coverage, if uniformly distributed, provides an estimate of the accessible metal on the surface, which can be converted to M-M distance, which reflects the distance between polymer chains. For extended surfaces, it is 1 metal / nm 2 yields a distance of 10 Å between metal atoms, which is well within the desired cutoff. At 18.5 Å, 0.3 metal / nm 2 The coverage at may be determined.

[0028] Examples of catalysts having at least two active sites in close proximity include, but are not limited to, bimetallic transition metal catalysts, heterogeneous catalysts, dianionic activators having two associated active catalysts, linked transition metal catalysts having two or more growing polymer chains, Group IV olefin polymerization catalysts containing a monoanionic group, a bidentate monoanionic group, a tridentate monoanionic group, or a monodentate, bidentate, or tridentate monoanionic group with an external donor.

[0029] The catalysts in Table 1 are exemplary embodiments of the aforementioned classes of catalysts and the specific catalysts contemplated. The examples in Table 1 are not intended to be limiting; rather, they are merely illustrative and specific examples of the aforementioned classes of catalysts. [Table 1]

[0030] Without wishing to be bound by theory, the mechanism as described in this section describes how a dual chain catalyst can create a unique cross-linked molecular structure when a diene comonomer is polymerized under the desired conditions. The term "diene" refers to a monomer or molecule having two alkenes. An illustration of the kinetics is shown in Scheme 4, where the catalyst center produces two polyolefin chains. Scheme 4 shows how a diene "ladder branched" polymer structure can be created by a combination of diene cross-linking and chain transfer. The term diene "ladder branched" polymer refers to a long chain branch where a short chain or rung containing 1-12 carbon atoms links two long chains together. As shown, a metal-ligand catalyst with at least two polymer chain sites grows two separate polymer chains. It is believed that one alkene of the diene is incorporated into one of the sites of the catalyst and, due to the proximity of the propagation sites, the second alkene of the diene is then rapidly incorporated into the second polymer chain, thereby forming a bridge or rung. This successive addition of dienes is referred to as "concerted" addition of dienes to distinguish them from catalysts that do not have two proximal chains, where the addition of dienes results in the concentration of vinyl-containing polymer that reacts later in the reactor. The term "rung" refers to the diene once it has been incorporated into two separate polymer strands, thereby linking the strands together. The first and second polymer strands continue to grow until the polymer is transferred to another catalyst, the polymer is released from the catalyst, the catalyst dies, or another diene is added.

[0031] kinetics Scheme 4. Illustration of "ladder branching" kinetics with resulting molecular structures. Metal-ligand catalysts are LM + are jointly represented by [ka]

[0032] Without wishing to be bound by theory, it is believed that the molecular weight distributions associated with these proposed kinetics are essentially stable at high branching levels when diene crosslinking reactions are the only source of branching. Molecular weight distribution (MWD) is defined as the weight average molecular weight divided by the number average molecular weight (M w / M n The inherent stability of MWD is dependent on the weight average molecular weight (M w ) increases moderately even at high branching levels, which means that M w and M. w / M n However, this is in contrast to conventional diene comonomer branching technology, which becomes infinite at moderate tetrafunctional branching levels.

[0033] A mathematical model is derived for the purpose of demonstrating how a process for synthesizing polyethylene creates long-chain branched polymers with diene "ladder branching" molecular architecture. The mathematical model is also used to establish the metrics and scope of the claims. The mathematical model of the branching structure as described in this disclosure can be derived from a kinetic description of the proposed branching mechanism. The model is based on several assumptions to promote mathematical simplicity, but these assumptions are not intended to limit the scope of this disclosure. The assumptions follow common industrial applications of non-living addition of copolymers, as well as additional assumptions specific to the hypothesized diene branching mechanism. The general assumptions made include: (1) propagation is much faster than chain transfer, and therefore the average chain length is much longer than that of one monomer; (2) only a single pure catalytic species is active; (3) the catalytic center creates many chains during its lifetime, and therefore the lifetime of a chain is a small fraction of the reaction or residence time; and (4) copolymerization can be approximated by a homopolymerization model when the drift in composition is negligible.

[0034] Kinetics of the diene "ladder branching" theory. In addition to the four commonly made assumptions, there are four assumptions based on the kinetics of the diene "ladder branching" theory. The first assumption is that the catalytic center simultaneously generates two kinetic chains with identical kinetics and statistics. Second, rungs are formed when a diene bridges two polymer chains that increase in length. Third, a branch point is formed whenever two unbridged chains are bridged by a diene. Finally, diene reactions that do not form bridges are ignored, since the MWD is unaffected.

[0035] The kinetic description of the proposed diene "ladder branching" mechanism requires the development of a nomenclature that describes how each reaction affects molecular structure. Some nomenclature elements below represent small molecules (M, A, D), while others represent large molecular structures (P n,m ,S n ,D n Kinetics describes how the named elements interact to form a molecular structure.

[0036] Kinetic nomenclature M: monomer or comonomer, A: chain transfer agent species, D: diene branch species, n, m: index reflecting the number of monomer repeat units of the subspecies, P n,m Catalyst having two non-crosslinked growing polymers with monomer repeat units of n and m, D n : a dead polymer molecule having n monomer repeat units, S n : a catalyst that produces crosslinked polymer molecules with n monomer repeat units; Kc: a kinetic chain is defined as a linear segment created by chain transfer; Rg: a rung is defined as a bridge between chain segments; Br: a branch is created when two previously unbridged molecules are bridged.

[0037] The branching kinetic equations are set forth below using the nomenclature and assumptions introduced above. A brief description of each reaction is provided. Anyone skilled in the art of polymerization kinetics should be able to understand the kinetic schemes and reaction rate laws. [Table 2]

[0038] The result of propagation is an incremental increase in chain size by one repeat unit. Propagation is described separately for each of the two molecules that increase in length from the catalytic center. For example, P n,m The first index is for the left strand on the catalyst, and the second index is for the right strand on the catalyst. n If growth is modeled for an increase in β-directed γ, then a factor of 2 appears in the rate because there are two strand positions, left and right, at each center that are equally available for reaction.

[0039] Chain transfer, like propagation, is described separately for the left and right positions of the catalyst. n,m ) chain transfer occurs through the dead polymer molecule (D n Or D m ) and empty positions (P 0,m or P n,0 ) is generated. n ) participates in chain transfer, the non-bridging species ( n,0 or P 0,n ) is produced and no dead polymer is produced because all n repeat units are still attached to the catalyst. 0,m and P n,0 ) are hypothesized to reinitiate very rapidly and participate in propagation. Because each diene has two polymerizable groups and each catalytic center has two positions (left and right) for diene incorporation, the reaction rate expression for the diene crosslinking includes a factor of 4.

[0040] Diene bridges are non-bridged (P n,m Only when the ) species reacts productively with a diene does it result in the formation of a tetrafunctional branch (br). A tetrafunctional branch refers to a short segment from which four polymer chains can emanate, two on each side of the short segment. With dienes, a tetrafunctional branch is the expected type of LCB. Lang has also shown that crosslinking (S n ) or non-crosslinked (P n,m) molecule is generated when any catalytic center productively incorporates a diene (rg). Diene reactions that do not result in crosslinking, such as in-chain cyclization and pendant vinyl formation, are ignored and considered nonproductive in these kinetics.

[0041] The creation of a model from the kinetics requires that a series of population balances be derived for each type of polymer species involved. These population balances are derived as a function of chain length (n, m) and represent the dynamic rates of change of the various polymer subspecies. The population balances are expressed as P n,m , S n The symbols D,,, and Dn are given below assuming the mass action rate law, representing the molar concentrations of the subspecies for n ≥ 1 and m ≥ 1. The kinetic model can be extended to other chain transfer reactions, e.g., the definition of the transfer period, Ω = k tra A+k trh H 2 +k b By simply expanding trh ) and beta hydride removal (k b ) may be used.

number

number

[0042] Other important population balances are found in equations (1)-(8), e.g., the left side (L n ) and right side (R n ) etc. Due to the symmetry imposed in defining the kinetic scheme, the distributions of growing polymer subspecies on the left and right sides are equal.

number

[0043] The rates of formation of molecular attributes such as chains (kc), branches (br), and rungs (rg) are expressed below using the mass action rate law derived from the kinetics scheme. A shorthand notation is used to express the rate of formation of the catalyst and non-bridging molecules (ξ 0,0 ), as well as the concentration of catalyst and crosslinked polymer molecules (μ 0 ) is used to define the concentration of the catalyst. Therefore, the total catalyst concentration is 0,0 +μ 0 It is.

number

[0044] The first step in rendering a usable model is to determine the ratios of the relevant polymer subspecies (

number

number

[0045] The "steady state assumption" allows for simple branching metrics (B c , B n , R c ) relationship. In this particular case, the instantaneous characteristics are convenient and relevant as they apply to a variety of reactors, such as steady-state, well-mixed reactors, or batch reactors with negligible temperature or composition drift. The instantaneous bifurcation metrics (B c , Bn , R c ) is equivalent to the cumulative average value in the absence of spatial or temporal variations in the chain transfer (Ω) and diene bridge rate (Ψ) parameters. Instantaneous 4-functional branches per kinetic chain,

number

number

number

[0046] Moments of MWD mean forecast Models describing the moments of chain length distribution of polymer species can often be derived from population balances obtained from kinetic schemes. Moment-based models are useful for predicting molecular weight averages and polydispersity indices, but generally do not account for smaller nuances in MWD such as bimodality, peak MW, and tailing. The method of moments involves the definition of chain length distribution moments for various polymer subspecies, such as: Bulk polymer moments (λ i ) reflects bulk polymer properties, and the solution of the bulk moment model generally requires the solution of the various living polymer moments. Living Polymer MWD Moment:

number

number

[0047] Any experienced polymer reaction engineer will understand the derivation of the moment models (Equations (20) and (21)) from a series of population balances. The main bulk polymer moments (λ 0 ,λ 1 ,λ 2 ) is given below with the removal of terms that are long kinetic chains and therefore negligible after imposing the assumption that Φ>>Ω.

number

[0048] The evaluation of the rate of change of these bulk moments requires the moment of a large number of living polymer subspecies. These live polymer moments are algebraic quantities due to the "steady state assumption" and are given below: λ 3 If higher bulk moments, such as 0.25 mm or 0.5 mm, are predicted, then additional live moments are required.

number

[0049] After algebraic simplification of the moment ratios, the instantaneous number-average and weight-average chain lengths (DPn, DPw) are provided below. Of course, the average molecular weight (M n , M w ) is equal to the average chain length multiplied by the apparent monomer repeat unit weight (g / mol).

number

[0050] The model expression is the average linear kinetic chain length DP no This is further simplified by some substitutions, such as making Φ / Ω equal. The model also has an instantaneous branching metric B c , B n , and R c The model can be expressed as a function of the number of diene "ladder branches" (B c) and branches per polymer molecule (B n ) is described below. In this system, the branches per polymer molecule are equal to the rungs per kinetic chain (B n =R c ) has been shown previously.

number

[0051] Number-average and weight-average molecular weight (M n , M w ) is M no and M. wo After defining the number-average and weight-average linear kinetic chain weights as c ) or branches per polymer molecule (B n ) can also be predicted as a function of

number

[0052] An unexpected prediction arising from the moment model (Eqs. (20) and (21)) is that at high diene branching levels, the maximum polydispersity is approximately 4. Of course, this prediction is for an ideal copolymerization and a single symmetric catalyst system; non-ideal ones can increase the polydispersity.

[0053] Complete MWD curve model Sometimes it is possible to solve the population balance of a molecular weight distribution curve. An explicit algebraic solution is usually only available if there is no spatial or temporal variation in the reaction rate, as is assumed in this case. The solution begins with the definition of yet another distribution volume Vn, which is derived from Pn,m. The population balance of Vn is derived by summing the population balances of Pn,m, with simplifications due to symmetry.

number

[0054] Due to the long chain assumption, it is possible to treat all subspecies distributions as if they were continuous functions rather than discrete. The population balance of a discrete steady-state polymer species can be approximated by a differential equation in a continuous variable n, where the difference terms are replaced by their derivatives. For example, the steady-state population balance of Sn contains the difference term Sn-Sn-1, which is replaced by its derivative as shown in equation (31).

number

[0055] Similar substitutions result in the following set of ordinary differential equations (ODEs), which can be integrated to obtain the chain length distributions for the various defined live subspecies distributions L(n), S(n), and V(n). The model is summarized below as an initial value problem, where the chain length distribution function is assumed to start at n=0. The n=0 lower limit on the distribution function is chosen solely for mathematical simplicity and ultimately does not significantly affect the predictions of the model when high molecular weight polymers are formed.

number

[0056] The instantaneous dead polymer chain length distribution is calculated by the ratio of species (

number

number

[0057] Complete MWD curve solution The distribution function for increasing polymer chain length can be solved either numerically or analytically by one familiar with the integration of ordinary differential equations. The analytical solution, although algebraically complex, is given here because it is in perfect agreement with the moment model (Equations (20) and (21)) while also predicting nuances in the MWD such as multimodality and tailing of peak positions.

[0058] A software package known as Mathematica™ was used to develop analytical solutions to a system of ordinary differential equations describing the growing polymer distribution functions L(n), S(n), and V(n). The analytical solution for L(n) was used to describe the instantaneous dead polymer distribution X(n) by normalizing L(n) by its integral.

number

[0059] An explicit analytical solution for X(n) can be obtained using Mathematica™. The analytical solution for X(n) is given by n and D.P. no The solution is given below as a function of R c =B n =B c / (1-B c )(36) via R c Or B n may be resumed with respect to

[0060] The chain length distribution function X(n) is evaluated from the definition of RootSum given by Mathematica™ as follows: 1 , x 2 , and x 3 Two of the three roots of the polynomial are in B n is complex over the range of possible values ​​of 0=1+B n +(3+5B n +2B n 2)x+3(1+B n )x 2 +x 3 (37)

[0061] root x 1 , x 2 , and x 3 is used in the instantaneous dead chain length distribution function X(n).

number

[0062] Various moments of X(n) are evaluated to determine the instantaneous number-average and weight-average chain lengths (DP n , D.P. w ), or molecular weight (M n , M w ) is obtained. The average chain length and weight obtained from the continuous distribution X(N) are equal to the moment model predictions given earlier for the long chain polymerization and discrete distributions, B c and B. n where R c =B n It is.

number

[0063] Those skilled in the art of polymer reaction engineering are familiar with the use of predicted bulk polymer MWD models to generate simulated size exclusion chromatography (SEC) curves. Such simulations are useful for relating how kinetics and recipes are expected to affect SEC measurements. The primary calibration result of an SEC measurement is a table or plot of dw / dLog(M) versus Log(M), where M is the molecular weight or size of the species, and dw / dLog(M) indicates the relative amount of polymer corresponding to M. The SEC results are expressed as n 2 It can be simulated by a table or plot of X(n) versus Log(M), where n 2 X(n) is expected to be proportional to dw / dLog(M).

[0064] Figure 2 shows the diene "ladder branch" (B c , B n , R c 2 shows a series of simulated SEC curves with varying levels of linear molecular weight (MWD) and chain length (C). The independent variables in FIG. 2 are scaled by linear molecular weight or chain length so that the plot is universal and independent of starting molecular weight. The zero branching case in FIG. 2 is the known "most probable" MWD (P. J. Flory, J. Am. Chem. Soc. 1936, 58, 1877), which is the MWD expected for a linear addition copolymerization carried out under ideal homogeneous conditions.

[0065] A more detailed analysis of the peak MW values ​​was carried out using a larger series of branching levels applied to the MWD model. Figure 3 shows a general plot of the relative peak MW as a function branching level. Figure 3 shows the peak MW insensitive low branching region (0 <R c <0.15), as well as in the higher branching regimes (R c ≧0.15), where the peak MW increases steadily with branching level.

[0066] Alternative trifunctional diene "ladder branching" mechanisms and models If the dual catalyst incorporates dienes under the desired conditions, there is an alternative mechanism that may explain the observed branching and MWD trends. n It is often observed that increases with the addition of diene, but for some catalyst-diene combinations, M w On the other hand, elevated diene levels were not associated with any measurable M n Little or no increase in M n One explanation for this is that the elimination of a single beta hydride (or chain transfer to hydrogen) may tend to occur immediately after the diene is inserted into both growing chains. This scenario would lead to the creation of a trifunctional branch by diene insertion, which in its pure form would not be a bridging growing species (S n ) is excluded from the kinetics.

[0067] The kinetic scheme is modified to account for this alternative mechanism by replacing "diene bridge" with the following reaction: [Table 3]

[0068] Any polymer reaction engineer familiar with the art of modeling and kinetics can re-derive these alternative kinetic moment and MWD function models using the same set of assumptions as before. The resulting instantaneous dead chain length distribution function, X(n), is given below for this trifunctional branching mechanism:

number

[0069] In equation (41), B c is defined as the branching point per kinetic chain, and DP no is defined as the average linear chain length without dienes. The kinetic scheme assumes that the linear (kinetic) chain length actually decreases with diene incorporation due to diene induced removal of beta hydrides. Therefore, a good surrogate for branching is B n which is defined as the number average number of branch points per polymer molecule, where B c =B n / (1+B n ) The function X(n) can be easily expressed as B n will be rewritten with respect to.

[0070] By integrating X(n), we obtain the instantaneous number-average and weight-average chain lengths (DP n , D.P. w ) or molecular weight (M n , M w ) results. The average chain length and weight obtained from the continuous distribution X(n) are equal to the moment model predictions when long chain polymerization is assumed. By integrating X(n), the DP n and M. n However, the branch level (B c Or Bn ) is confirmed to be constant over n. If the diene is assumed to create trifunctional branches, the integral of X(n) also shows how the polydispersity is expected to change with branching level.

number

number

[0071] Polydispersity (M w / M n The above relationship between ) and trifunctional branching level shows no instability or divergence at any branching level. Most surprising is that at higher branching levels, the polydispersity is predicted to plateau at 4. Of course, this prediction is for an ideal copolymerization and symmetric catalyst system; non-ideal ones would be expected to increase the polydispersity.

[0072] The chain length distribution function can again be used to generate predicted MWD curves. c Or B n )). The independent variables in FIG. 4 are scaled by linear molecular weight or chain length so that the plot is universal and independent of starting molecular weight. The zero branching case in FIG. 4 is the known "most likely" MWD and would be expected for a linear addition copolymerization carried out under ideal homogeneous conditions. FIG. 5 is a plot of the relative peak MW of trifunctional diene branches, with the MWD peak at 0.2 n <0.9 or 0.17 c It demonstrates the greatest sensitivity to branching levels with mid-branching levels in the approximate range of <0.5.

[0073] Traditional branching model ​​The purpose of this section is to compare various conventional diene branching and random polymer couplings with the "ladder branching" model. This comparison demonstrates the inherent instability of conventional diene branching and random polymer couplings as opposed to "ladder branching." The molecular structures resulting from diene "ladder branching" are different from (a) the conventional diene continuous stirred tank reactor (CSTR) branching model, (b) the conventional diene semi-batch branching model, (c) the polymer-CSTR coupling model, and (d) the polymer-batch coupling model.

[0074] a) Traditional diene CSTR branching model, Ver Strate-1980 (G. Ver Strate, C. Cozewith, W.W. Graessley, J. App. Polym. Sci. 1980, 25, 59), Guzman-2010 (J.D. Guzman, D.J. Arriola, T. Karjala, J. Gaubert, B.W.S. Kolthammer, AIChE 2010, 56, 1325):

number

number

number

[0075] Characterization of tetrafunctional long-chain branched polyolefins Depending on the degree of branching, various methods, such as nuclear magnetic resonance (NMR), can determine LCB or identify the effect of LCB in a polymer. For example, the effect of LCB is observed in shear flow in van Gurp-Palmen analysis, and the increase in shear viscosity at low angular frequencies and the strength of shear thinning behavior can be attributed to LCB. In extensional flow, the effect of LCB is usually identified in the degree of stiffening or strength of the melt and the maximum deformation achieved. Other plots, such as Mark-Houwink plots, extended molecular weight distribution (MWD), and g' vis Plots such as these provide additional information regarding LCBs. Due to the limited concentration of vinyl-terminated polymers (maximum one per polymer chain) and the need to run high conversions to ensure the formation of LCBs, it is difficult to achieve high levels of native LCBs in the polymer. To ensure high conversions, the ethylene concentration in the reactor is low, so large amounts of vinyl-terminated polymers can be reinserted into a second polymer chain.

[0076] Conventional processes incorporating dienes into polymer synthesis systems suffer from the fundamental drawback of gel formation or reactor fouling at high branching levels. Kinetic modeling, as discussed in the previous section, can provide good predictive results that allow for a better understanding of gel formation. For example, longer polymer chains have proportionally more pendant vinyls, and polymer chains containing more pendant vinyls are more likely to reinsert into the catalyst to form LCBs. Thus, larger polymer chains preferentially reinsert to form even larger polymer molecules, tetrafunctional branches, and gel problems or instability results when the LCB level reaches a threshold. Conventional weight average molecular weight (M) as a function of tetrafunctional branches w ) and number average molecular weight (M n A simulation of M is shown in FIG. 1 for an ethylene-based polymer in a constant pressure semi-batch reactor. n is M w As goes to infinity, there is only a slight increase. In this example, M wWhen the number of glycerols per mole increases to more than 200,000 grams per mole (g / mol), the molecular weight distribution (MWD) of the polymer becomes unstable and gel formation begins. The MWD is the weight average molecular weight M w The number average molecular weight M n is defined as dividing by (M w / M n ).

[0077] For the purposes of this disclosure, polymer gels are narrowly defined as polymer fractions that are phase separated due to their high branching levels and / or high molecular weight. Polymer gels can be observed in solution or in the melt and tend to interfere with properties such as optical clarity and film and fiber performance. Polyethylene interpolymer gels can be measured by the degree of insolubility of the polymer in hot xylene. Gel content often correlates with, and is therefore estimated from, the recovery percentage of GPC polymers. When polymer gels form, they can accumulate in the reactor and cause fouling.

[0078] Figures 7 and 8 show the differences in MWD curves expected from conventionally branched and "ladder branched" polymers. A set of metrics describing MWD properties was developed from the study of MWD data and comparison with MWD models. Each of the MWD describing metrics presented herein is independent of the average MW and focuses on the high MW portion of the MWD. ​​The MWD metrics are derived from the scaled MWD curve (dW / dlogM), where the main or highest peak of the MWD is defined as having a value of unity. If two or more peaks have the same height, the highest MW peak is the main peak. The independent variable in the MWD curve is Log(M), which is the logarithm of M to the base 10. The M metrics are defined and can be converted to branches per molecule or segment using Figures 6, 7, 8, and 9. w / M wo and M. p / M po Those skilled in the art of GPC data interpretation will understand these metrics and be able to calculate them from GPC data.

[0079] A family of GPC shape metrics, G(A / B), is calculated from the slopes at defined points on the right side of the MWD curve, where S(A) and S(B) are the first occurrences of these slopes to the right of the main peak at A% and B% of the height of the main peak. Points A and B are selected as pairs with approximately the same slopes when the MWD is "most likely". A description of these points and their slopes is shown in the graph of FIG. 10, with respect to the most likely MWD. ​​These slope pairs S(A) and S(B) are used together to calculate a function G(A / B), similar to a second derivative, which is shown to be a useful metric for distinguishing "ladder branching" MWDs from conventional or randomly branched MWDs. The values ​​of G(79 / 29) and G(96 / 08) describe the change in slope of the right side (RHS) of the MWD, defined below from the high MW slope. G(79 / 29)=(S(79)-S(29)) / S(79) (48) G(96 / 08)=(S(96)-S(8)) / S(96) (49)

[0080] The shape metrics G(79 / 29) and G(96 / 08) were tested on the MWD models for tetrafunctional "ladder branching" and conventional diene branching, and the results are plotted in Figures 11, 12, 13, and 14. These figures show that conventional branching yields G(79 / 29) and G(96 / 08) values ​​that steadily increase as the MW responds to branching. However, when applied to "ladder branching," these shape metrics tend to be more sensitive to the low levels of branching (low M w / M wo ) and then approaches zero at mid- to high-level branching. This is not surprising, since the high-MW portion of the "ladder branching" MWD is similar to the most likely MWD.

[0081] Figures 11, 12, 13, and 14 show similar responses of the G(79 / 29) and G(96 / 08) metrics to branching, although the G(96 / 08) metric is expected to be more sensitive to the high MW tailing resulting from conventional diene branching. The term "high MW tailing" or "high molecular weight tail" refers to the high molecular weight fraction as indicated by conventional and absolute GPC. Depending on the catalyst and diene pairing and the experimental conditions, it can be expected that the "ladder branched" system will have some conventional branching, which will result in the shape metric values ​​above being higher than would be expected for pure "ladder branching".

[0082] MWD Area Metrics Visual inspection of the "ladder branching" MWD indicates that there is a characteristic lack of the high MW tails typically seen in branched polymers. Figures 16 and 17 demonstrate how the model predicts the lack of tailing for "ladder branching" polymers. The "ladder branching" MWD data shows a characteristic lack of tails in many of the experiments, but also indicates that tails can form depending on the polymerization conditions and diene / catalyst pairing.

[0083] Polydispersity index (M w / M n , M z / M w ) are known metrics of tailing, but are not preferred due to their sensitivity to low MWD artifacts. Therefore, a more focused version of the polydispersity index is used to develop standards where integration is performed only in the high MW portion of the MWD. w / M n and M. z / M w The metric successfully distinguishes diene "ladder branches" from conventional branches and is highly sensitive to high MW baseline selection and baseline noise.

[0084] The area under the MWD curve is the MWD dispersibility index (M w / M n , M z / M wIt is relatively insensitive to baseline problems compared to the higher moments required to calculate the MWD. ​​It was therefore decided to develop a metric that involves an unweighted integration of the MWD. ​​These MWD area metrics, A HIGH and A TAIL is calculated from the area of ​​the GPC curve for a region defined to the right of the MWD curve. The MWD area metric (A HIGH and A TAIL ) is derived from the scaled MWD curve (dW / logM), and the major or highest peak of the MWD is defined as having a value of unity. When two or more peaks have the same height, the highest MW peak is the major peak. The independent variable in the MWD curve is Log(M), which is the logarithm of M to the base 10. Both of the MWD area metrics depend on the point of maximum slope of the high MW portion of the MWD. ​​The quantities and limits required to evaluate the area metrics are listed below and demonstrated in Figure 15 for the most likely MWDs. S max = the first case of maximum downward slope on the RHS (higher MW side) of the main peak (absolute value of slope) of the scaled MWD H smax = Scaled MWD height at the point of maximum gradient pt1=S max LogM value of pt2=S max LogM value where the tangent crosses the x-axis

[0085] The MWD area metric is defined below, where A HIGH is simply the area of ​​the MWD region after the point of maximum gradient. The second area metric, A TAIL is the small high MW area shown in Figure 15, and A HIGH It is evaluated by subtracting the area of ​​the triangle from

number

[0086] A is the area metric HIGH and A TAIL was tested on the MWD model for "ladder branching" and traditional diene branching, and the results are plotted in Figures 16, 17, 18, and 19. The plots are HIGH Or A TAIL We show that the high MW area, defined by A, increases dramatically as the conventional branching level increases. However, the “ladder branching” model does not provide a high MW area metric (A HIGH Or A TAIL ) is predicted to be largely unaffected by the "ladder branch" level. HIGH and A TAIL The values ​​of A are about 0.07 and 0.015, respectively. The exemplary MWD data shows that the diene-free linear polymers exhibit a large A due to the non-ideal aspects of the polymerization. HIGH and A TAIL The exemplary data also show a variety of highly branched "ladder branched" polymers that are essentially free of high MW tails beyond those expected from the most probable MWD. ​​The high MW area metric is also diagnostic of the slight level of high MW tail formation that "ladder branched" polymers may exhibit when accompanied by some degree of conventional branching. Metric A TAIL A HIGH It is less affected by linear MWD non-ideality than HIGH and A TAIL The metrics equally indicate high MW tail formation.

[0087] Tetrafunctional long chain branched polyolefin Polymers produced from "ladder branches," as depicted in Scheme 4, are included in the present disclosure.

[0088] In embodiments, the ethylene-based polymers of the present disclosure have a melt viscosity ratio or rheology ratio (V 0.1 / V 100 ), where V 0.1is the viscosity of the ethylene-based polymer at 190°C and an angular frequency of 0.1 rad / sec, and V 100 is the viscosity of the ethylene-based polymer at 190° C. and an angular frequency of 100 rad / sec. In one or more embodiments, the melt viscosity ratio is at least 14, at least 20, at least 25, or at least 30. In some embodiments, the melt viscosity ratio is greater than 50, at least 60, or greater than 100. In some embodiments, the melt viscosity ratio is from 14 to 200.

[0089] "Rheology ratio" and "melt viscosity ratio" are V at 190°C 0.1 / V 100 where V 0.1 is the viscosity of the ethylene-based polymer at 190°C and an angular frequency of 0.1 rad / sec, and V 100 is the viscosity of the ethylene-based polymer at 190° C. and an angular frequency of 100 rad / sec.

[0090] In one or more embodiments, the ethylene-based polymers of the present disclosure have an average g' of less than 0.86, where the average g' is the intrinsic viscosity ratio as determined by gel permeation chromatography using a triple detector. In some embodiments, the ethylene-based polymers of the present disclosure have an average g' of 0.64 to 0.86. All individual values ​​and subranges encompassed by "0.64 to 0.86" are disclosed herein as separate embodiments, for example, the average g' of the ethylene-based polymers can be in the range of 0.64 to 0.75, 0.68 to 0.79, or 0.65 to 0.83. In one or more embodiments, the average g' is 0.65 to 0.84, 0.66 to 0.82, or 0.66 to 0.80.

[0091] In some embodiments, the ethylene-based polymers have a G(79 / 29) value of 0.035 or less, as determined from a gel permeation chromatography curve having the peak height, a slope M79 at 79% of the peak height, and a slope M29 at 29% of the peak height, where the G(79 / 29) value is equal to (M79-M29) / M79. All individual values ​​and subranges encompassed by "0.035 or less" are disclosed herein as separate embodiments, for example, "0.035 or less" includes from greater than 0.0 to 0.035, from 0.010 to 0.034, including negative values. In one or more embodiments, the ethylene-based polymers of the present disclosure can have a G(79 / 29) value of 0.030 or less, as determined from a gel permeation chromatography curve.

[0092] In one or more embodiments, the melt viscosity ratio of the ethylene-based polymers of the present disclosure may be greater than 10 times the elastic modulus, and the melt viscosity ratio (V 0.1 / V 100 ) is the viscosity V of ethylene-based polymers at 190°C and an angular frequency of 0.1 rad / sec. 0.1 , and the viscosity V of ethylene-based polymers at 190°C and an angular frequency of 100 rad / s 100 The elastic modulus m is determined by [((tan(δ 0.1 )-tan(δ 100 ))*1000) / (0.1-100))], where tan(δ 0.1 ) is the tangent of the phase angle in 0.1 radians / second, and tan(δ 100 ) is the tangent of the phase angle in 100 radians / second.

[0093] In one or more embodiments, the ethylene-based polymer can have an elastic modulus, m, at 190° C., less than or equal to 8 seconds / radian, where m is [((tan(δ 0.1 )-tan(δ 100 ))*1000) / (0.1-100)). In other embodiments, the ethylene-based polymer may have an elastic modulus, m, at 190° C. that is less than or equal to 4 seconds / radian.

[0094] In various embodiments, the melt strength of the ethylene-based polymers of the present disclosure may be greater than 6 cN (Rheotens apparatus, 190° C., 2.4 mm / sec 2 , 120mm from die exit to wheel center, 38.2 seconds -1 extrusion speed, capillary die length 30 mm, diameter 2 mm, and entrance angle 180°). In some embodiments, the melt strength of the ethylene-based polymer can be greater than 10 cN.

[0095] In an embodiment, the ethylene-based polymer has an MWD area metric A TAIL and a molecular weight tail quantified by A TAIL is less than or equal to 0.04. All individual values ​​and subranges encompassed by "less than or equal to 0.04" are disclosed herein as separate embodiments. For example, in some embodiments, the A of the ethylene-based polymers of the present disclosure TAIL is greater than 0 and less than or equal to 0.03 as determined by gel permeation chromatography using a triple detector.

[0096] In an embodiment, the M of the ethylene-based polymer w may be less than or equal to 800,000 daltons as determined by gel permeation chromatography using a triple detector. In one or more embodiments, the M w can be up to 400,000 daltons.

[0097] In various embodiments, the ethylene-based polymer has a M p / M p0 where M p is the peak molecular weight of the ethylene-based polymer as determined by conventional gel permeation chromatography, and M p0 is the initial peak molecular weight of the ethylene-based polymer without the polyene comonomer.

[0098] In an embodiment, the ethylene-based polymer has a M w / M w0 where M wis the weight average molecular weight of the ethylene-based polymer as determined from the GPC curve of the ethylene-based polymer obtained by gel permeation chromatography. w0 is the initial weight average molecular weight of the comparative ethylene-based polymer by gel permeation chromatography. The comparative ethylene-based polymer is a polymer that is prepared by polymerization of ethylene monomer and all C monomers present in the ethylene-based polymer under the defined polymerization reaction conditions. 3 ~C 14 It is the reaction product, free of at least one polyene comonomer, of the polymerization of with a comonomer, if present.

[0099] Each M w0 and M. p0 is the metric for a polymer resin with no diene added to the reactor during polymerization, as previously discussed. Each subsequent addition of diene increases the metric M w or M p The amount of diene incorporated into the reactor is small compared to the other reactants in the reactor, and therefore the addition of the diene does not affect the total amount of comonomer, ethylene, and solvent in the reactor.

[0100] In various embodiments, the ethylene-based polymer has a gpcBR branching index from 0.1 to 3.0. All individual values ​​and subranges encompassed by "0.10 to 3.00" are disclosed herein as separate embodiments, for example, the ethylene-based polymer can include a gpcBR branching index from 0.10 to 2.00, 0.10 to 1.00, 0.15 to 0.65, 0.20 to 0.75, or 0.10 to 0.95.

[0101] The long chain branching polymerization process described in the preceding section is utilized for the polymerization of olefins, primarily ethylene and propylene. In some embodiments, only a single type of olefin or α-olefin is present in the polymerization scheme, essentially creating a homopolymer with a small amount of incorporated diene comonomer. However, additional α-olefins may be incorporated into the polymerization procedure. The additional α-olefin comonomer typically has 20 or fewer carbon atoms. For example, the α-olefin comonomer may have 3 to 10 carbon atoms, or 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, 4-methyl-1-pentene, and ethylidene norbornene. For example, the one or more α-olefin comonomers may be selected from the group consisting of propylene, 1-butene, 1-hexene, and 1-octene, or alternatively from the group consisting of 1-hexene and 1-octene.

[0102] Long chain branched polymers, e.g., homopolymers and / or interpolymers (including copolymers) of ethylene and, optionally, a comonomer such as one or more α-olefins, can contain at least 50 weight percent of units derived from ethylene. All individual values ​​and subranges encompassed by "from at least 50 weight percent" are disclosed herein as separate embodiments, e.g., ethylene-based polymers, homopolymers and / or interpolymers (including copolymers) of ethylene and, optionally, a comonomer such as one or more α-olefins, can contain at least 60 weight percent of units derived from ethylene, at least 70 weight percent of units derived from ethylene, at least 80 weight percent of units derived from ethylene, or from 50 to 100 weight percent of units derived from ethylene, or from 80 to 100 weight percent of units derived from ethylene.

[0103] In some embodiments of the ethylene-based polymer, the ethylene-based polymer comprises an additional α-olefin. The amount of the additional α-olefin in the ethylene-based polymer is less than or equal to 50 mole percent (mol %), in other embodiments the amount of the additional α-olefin comprises at least 0.01 mol % to 25 mol %, and in further embodiments the amount of the additional α-olefin comprises at least 0.1 mol % to 10 mol %. In some embodiments, the additional α-olefin is 1-octene.

[0104] In some embodiments, the long chain branched polymer may comprise at least 50 mole percent of units derived from ethylene. All individual values ​​and subranges from at least 90 mole percent are included herein and disclosed herein as separate embodiments. For example, the ethylene-based polymer may comprise at least 93 mole percent units derived from ethylene, at least 96 mole percent units derived from ethylene, at least 97 mole percent units derived from ethylene, or alternatively, 90-100 mole percent units derived from ethylene, 90-99.5 mole percent units derived from ethylene, or 97-99.5 mole percent units derived from ethylene.

[0105] In some embodiments of the long chain branched polymer, the amount of additional α-olefin is less than 50%, other embodiments include at least 1 mole percent (mol %) to 20 mol %, and in further embodiments the amount of additional α-olefin includes at least 5 mol % to 10 mol %. In some embodiments, the additional α-olefin is 1-octene.

[0106] Any conventional polymerization process may be used to produce the long-chain branched polymers, including, but not limited to, solution polymerization processes, gas phase polymerization processes, slurry phase polymerization processes, and any combination thereof, using one or more conventional reactors, such as loop reactors, isothermal reactors, fluidized bed gas phase reactors, stirred tank reactors, batch reactors, etc., in parallel, in series, or in any combination thereof.

[0107] In one embodiment, the ethylene-based polymer can be produced by solution polymerization in a dual reactor system, e.g., a single loop reactor system, where ethylene and optionally one or more α-olefins are polymerized in the presence of the catalyst system described herein and optionally one or more cocatalysts. In another embodiment, the ethylene-based polymer can be produced by solution polymerization in a dual reactor system, e.g., a dual loop reactor system, where ethylene and optionally one or more α-olefins are polymerized in the presence of the catalyst system described herein and optionally one or more other catalysts. The catalyst system described herein can be used in the first reactor or the second reactor, optionally in combination with one or more other catalysts. In one embodiment, the ethylene-based polymer can be produced by solution polymerization in a dual reactor system, e.g., a dual loop reactor system, where ethylene and optionally one or more α-olefins are polymerized in both reactors in the presence of the catalyst system described herein.

[0108] In another embodiment, the long-chain branched polymers can be produced by solution polymerization in a single reactor system, such as a single loop reactor system, where ethylene and, optionally, one or more α-olefins are polymerized in the presence of a catalyst system as described in this disclosure, and, optionally, one or more cocatalysts as described in the preceding section. In some embodiments, the long-chain branching polymerization process to produce the long-chain branched polymers comprises polymerizing ethylene and at least one additional α-olefin in the presence of a catalyst system.

[0109] The long-chain branched polymer may further include one or more additives. Such additives include, but are not limited to, antistatic agents, color enhancers, dyes, lubricants, pigments, primary antioxidants, secondary antioxidants, processing aids, UV stabilizers, and combinations thereof. The ethylene-based polymer may contain any amount of additives. The ethylene-based polymer may compromise from about 0 to about 10 percent by weight of such additives, based on the weight of the ethylene-based polymer and the one or more additives. The ethylene-based polymer may further include a filler, which may include, but is not limited to, organic or inorganic fillers. The long-chain branched polymer may comprise, for example, calcium carbonate, talc, or Mg(OH), based on the total weight of the ethylene-based polymer and all additives or fillers. 2 The ethylene-based polymer may contain from about 0 to about 20 weight percent of a filler such as, for example, ethylene-based copolymers, ethylene-based terpolymers, etc. The ethylene-based polymer may be further compounded with one or more polymers to form a blend.

[0110] In some embodiments, a long chain polymerization process for producing a long chain branched polymer may include polymerizing ethylene and at least one additional α-olefin in the presence of a catalyst having two polymer formation sites. The long chain branched polymer obtained from such a catalyst having two polymer formation sites may have a molecular weight of, for example, 0.850 g / cm. 3 ~0.960g / cm 3 , 0.880g / cm 3 ~0.920g / cm 3 , 0.880g / cm 3 ~0.910g / cm 3 , or 0.880 g / cm 3 ~0.900g / cm 3 The composition may have a density in accordance with ASTM D792, which is incorporated herein by reference in its entirety.

[0111] In another embodiment, the long chain branched polymer obtained from the long chain polymerization process has a melt flow ratio (I 10 / I 2 ), where the melt index I 2is measured at 190° C. under a load of 2.16 kg in accordance with ASTM D1238, which is incorporated herein by reference in its entirety, and the melt index I 10 is measured according to ASTM D1238 at 190° C. and under a load of 10 kg. In another embodiment, the melt flow ratio (I 10 / I 2 ) is 5-50, in others the melt flow ratio is 5-25, and in others the melt flow ratio is 5-9.

[0112] In some embodiments, the long chain branched polymer obtained from the long chain polymerization process may have a molecular weight distribution (MWD) of 1 to 20, where MWD is the molecular weight distribution of M w / M n is defined as M w is the weight average molecular weight, M n is the number average molecular weight. In another embodiment, the polymer resulting from the catalyst system has an MWD of 1 to 10. Another embodiment includes an MWD of 1 to 3, and another embodiment includes an MWD of 1.5 to 2.5.

[0113] Parallel Polymerization Reactor (PPR) An example of a small scale solution polymerization is carried out in a 15 mL vial using a total liquid volume of 5 mL, a constant ethylene pressure of 150 psig, and a polymerization temperature of 120° C. The 5 mL liquid volume consists of 0.84 mL of comonomer mixture containing 500 nmoles of MMAO-3A, ​​catalyst and activator solutions in toluene, and enough Isopar-E added to achieve a liquid volume of 5 mL. Hydrogen (H 2 ) for any given diene, the experiment will be 2 To perform the load test, place an empty reaction vial under 20 ± 3 psig H 2, at 80 °C, were added to the reaction mixture by simultaneous prepressurization. All liquid volumes were dispensed at room temperature and added volumetrically in relation to the 5 mL total volume. The catalyst was added last to the reaction mixture as a 5 mM solution in toluene, which was activated separately with 1.5 equivalents of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate). The comonomer solution consisted primarily of 1-octene, and small (0-6%) volume fractions of diene species. Polymerizations were carried out for no more than approximately 30 min and quenched by CO addition followed by vial depressurization.

[0114] Gel Permeation Chromatography (GPC) (conventional GPC) The chromatographic system consisted of a PolymerChar GPC-IR (Valencia, Spain) high temperature GPC chromatograph equipped with an internal IR5 infrared detector (IR5), and a 4-capillary viscometer (DV) coupled to a Precision Detectors (now Agilent Technologies) 2-angle laser light scattering (LS) detector model 2040. For all absolute light scattering measurements, a 15 degree angle is used for the measurements. The autosampler oven compartment was set to 160 degrees Celsius and the column compartment was set to 150 degrees Celsius. The columns used were four Agilent "Mixed A" 30 cm, 20 micron linear mixed bed columns. The chromatographic solvent used was 1,2,4-trichlorobenzene containing 200 ppm of butylated hydroxytoluene (BHT). The solvent source was nitrogen injected. The injection volume used was 200 microliters and the flow rate was 1.0 milliliters / min.

[0115] Calibration of the GPC column set was performed with at least 20 narrow molecular weight distribution polystyrene standards with molecular weights ranging from 580 to 8.4 million, arranged in six "cocktail" mixtures with at least 10 intervals between each individual molecular weight. Standards were purchased from Agilent Technologies. Polystyrene standards were prepared at 0.025 grams in 50 milliliters of solvent for molecular weights equal to or greater than 1 million, and 0.05 grams in 50 milliliters of solvent for molecular weights less than 1 million. The polystyrene standards were dissolved at 80 degrees Celsius for 30 minutes with gentle agitation. The peak molecular weight of the polystyrene standards was calculated using Equation 52 (described in Williams and Ward, J. Polym. Sci., Polym. Let., 6, 621 (1968)): M ポリエチレン =A×(M ポリスチレン ) B (52) was used to convert to polyethylene molecular weight. where M is the molecular weight, A has a value of 0.4315, and B is equal to 1.0.

[0116] A polynomial between the third and fifth order was used to fit each polyethylene equivalent calibration point. A small adjustment (approximately 0.415 to 0.44) was made to A to correct for column resolution and band broadening effects so that the NIST standard NBS 1475 was obtained at 52000 Mw.

[0117] Total plate counts of the GPC column set were performed using eicosane (prepared at 0.04 g in 50 milliliters of TCB and dissolved for 20 minutes with gentle agitation). Plate counts (Equation 53) and symmetry (Equation 54) were measured with a 200 microliter injection according to the following equations:

number

number

[0118] Samples were prepared semi-automatically using the PolymerChar "Instrument Control" software to target sample weights of 2 mg / ml and add solvent (containing 200 ppm BHT) via the PolymerChar high temperature autosampler to septa-capped vials that had been pre-sparged with nitrogen. Samples were dissolved at 160 degrees Celsius with "slow" shaking for 2 hours.

[0119] M n(GPC) , M w(GPC) , and M. z(GPC) The calculation was based on GPC results using the internal IR5 detector (measurement channel) of a PolymerChar GPC-IR chromatograph according to Equations 55-57 using PolymerChar GPCOne™ software, baseline-subtracted IR chromatograms at each equally spaced data collection point (i), and the polyethylene equivalent molecular weights obtained from a narrow standard calibration curve for point (i).

number

[0120] To monitor deviations over time, a flow marker (decane) was introduced into each sample via a micropump controlled by the PolymerChar GPC-IR system. This flow marker (FM) was used to linearly calibrate the pump flow rate (Flow (apparent)) of each sample by aligning the respective decane peak in the sample (RV (FM sample)) with the decane peak in the narrow standard calibration (RV (FM calibrated)). Any change in time of the decane marker peak is thus assumed to be related to a linear shift in flow rate (Flow (effective)). To facilitate the highest accuracy of the RV measurement of the flow marker peak, a least squares fitting routine is used to fit the peaks of the flow marker concentration chromatogram to a quadratic equation. The first derivative of the quadratic equation is then used to determine the true peak position. After calibrating the system based on the flow marker peaks, the effective flow rate (relative to the narrow standard calibration) is calculated as in Equation 58. Processing of the flow marker peaks was done via PolymerChar GPCOne™ software. An acceptable flow correction should be that the effective flow rate is within + / - 2% of the apparent flow rate. Flow (effective) = Flow (apparent) * (RV(FM calibrated) / RV(FM sample)) (58)

[0121] Triple detector GPC (TDGPC) (absolute GPC) The chromatographic system, analytical conditions, column set, column calibration and calculation and distribution of conventional molecular weight moments were performed according to the methods described in Gel Permeation Chromatography (GPC).

[0122] With regard to the determination of the viscometer and light scattering detector offsets from the IR5 detector, a systematic approach for the determination of multi-detector offsets was performed in a manner consistent with that published by Balke, Mourey et al. (Mourey and Balke, Chromatography Polym. Chpt 12, (1992)) (Balke, Thitiratsakul, Lew, Cheung, Mourey, Chromatography Polym. Chpt 13, (1992)) using PolymerChar GPCOne™ software to measure the offsets of broad homopolymer polyethylene standards (M w / M n >3) to the narrow standard column calibration results from the narrow standard calibration curve.

[0123] Absolute molecular weight data are obtained using PolymerChar GPCOne™ software in a manner consistent with that published by Zimm (Zimm, BH, J. Chem. Phys., 16, 1099 (1948)) and Kratochvil (Kratochvil, P., Classical Light Scattering from Polymer Solutions, Elsevier, Oxford, NY (1987)). The overall injection concentration used in determining the molecular weight is obtained from the mass detector area and mass detector constant derived from a suitable linear polyethylene homopolymer or one of the polyethylene standards of known weight average molecular weight. The calculated molecular weight (using GPCOne™) is obtained using the light scattering constant and the refractive index concentration coefficient, dn / dc, of 0.104 derived from one or more of the polyethylene standards described below. In general, the mass detector response (IR5) and light scattering constant (determined using GPCOne™) can be determined from a linear standard having a molecular weight greater than about 50,000 g / mole. Viscometer calibration (determined using GPCOne™) can be accomplished using methods described by the manufacturer, or alternatively, using published values ​​of suitable linear standards, such as Standard Reference Material (SRM) 1475a (available from the National Institute of Standards and Technology (NIST)). A viscometer constant (obtained using GPCOne™) is calculated that relates the specific viscosity area (DV) and injected mass for the calibration standard to its intrinsic viscosity. The chromatographic concentration is assumed to be low enough to preclude addressing the second viral coefficient effect (concentration effect on molecular weight).

[0124] Absolute weight average molecular weight (M w(Abs) ) is obtained by dividing (using GPCOne™) the area integrated chromatogram of the light scattering (LS) (factored by the light scattering constant) by the mass constant and the mass recovered from the mass detector (IR5) area. The molecular weight and intrinsic viscosity responses are linearly extrapolated (using GPCOne™) at the chromatographic ends where the signal to noise is low. The other respective moments, Mn(Abs) and M. z(Abs) is calculated according to equations 59-60 as follows:

number

[0125] g' ave value g' is defined as the viscosity of the branched polymer divided by the viscosity of a linear polymer of the same MW.

number

[0126] g' ave Or average g' is the weighted average value of g' (BH Zimm, WH Stockmayer, J. Chem. Phys. 1949, 17, 1301).

[0127] Dynamic Mechanical Spectroscopy (or Small Angle Oscillatory Shear) The complex viscosity (η*), elastic modulus (G', G''), tan delta, and phase angle (δ) are obtained by dynamic oscillatory frequency sweep testing at 190 °C in the frequency range of 0.1-100 rad / s. The level of strain is set within the linear viscoelastic regime identified by strain sweep testing at 100 rad / s and 190 °C. The tests are carried out on stainless steel parallel plates of 25 mm diameter on a strain-controlled rheometer ARES-G2 by TA Instruments. Before the actual test, the samples are drawn to a thickness of 3.3 mm and then trimmed in two steps. In the first step, the samples are melted for 2.5 minutes, drawn to a gap of 3 mm, and trimmed. After a further 2.5 minutes of soaking time at 190 °C, the samples are drawn to a gap of 2 mm and the excess material is trimmed. The method incorporates an additional 5 minutes delay to allow the system to reach temperature equilibrium. The tests are carried out under a nitrogen atmosphere.

[0128] gpcBR branching index by triple detector GPC (TDGPC) The gpcBR branching index was determined by first calibrating the light scattering, viscosity, and concentration detectors as described above. The baseline was then subtracted from the light scattering, viscometer, and concentration chromatograms. An integration window was 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 were then used to establish the Mark-Houwink constants for polyethylene and polystyrene. Once the constants were obtained, the two values ​​were used to construct two linear reference conventional calibrations for polyethylene molecular weight and polyethylene intrinsic viscosity as a function of elution volume, as shown in Equations (62) and (63).

number

[0129] The gpcBR branching index is a robust method for characterizing long chain branching, as described in Yau, Wallace W., “Examples of Using 3D-GPC-TREF for Poly-olefin Characterization,” Macromol. Symp., 2007, 257, 29-45. This index avoids the traditionally used “slice-by-slice” TDGPC calculations in determining g′ values ​​and calculating branching frequency in favor of the entire polymer detector area. From the TDGPC data, the peak area method was used to obtain the sample bulk absolute weight average molecular weight (M w, absolute) can be obtained. This method avoids the "slice-by-slice" ratio of the light scattering detector signal to the concentration detector signal, as required in conventional g' determinations. TDGPC also independently obtained the intrinsic viscosity of the sample using Eq. (64). The area calculation in this case provides greater accuracy, since as the overall sample area is much less sensitive to detector noise and fluctuations caused by the TDGPC settings to the baseline and integration limits. More importantly, the peak area calculation was not affected by detector volume offsets. Similarly, the high-precision sample intrinsic viscosity (IV) was obtained by the area method in Eq. (64).

number

[0130] In equation (64), DPi represents the differential pressure signal monitored directly from the online viscometer. To determine the gpcBR branching index, the light scattering elution area of ​​the sample polymer was used to determine the molecular weight of the sample. The viscosity detector elution area of ​​the sample polymer was used to determine the intrinsic viscosity (IV or [η]) of the sample. First, the molecular weight and intrinsic viscosity of a linear polyethylene standard sample, such as SRM1475a or equivalent, were determined using conventional calibration ("cc") for both molecular weight and intrinsic viscosity as a function of elution volume.

number

number

[0131] All statistics with "cc or conventional" subscripts are determined using their respective elution volumes, corresponding conventional calibrations as described above, and concentrations (Ci). Values ​​without subscripts are measurements based on mass detectors, LALLS, and viscometer areas. PE The value of is iteratively adjusted until the linear reference sample has a gpcBR measurement of zero. For example, in this particular case, the final values ​​of α and log K for determining the gpcBR are 0.725 and -3.355, respectively, for polyethylene, and 0.722 and -3.993, respectively, for polystyrene. Once the K and α values ​​are determined using the procedure discussed.

[0132] Previously, the procedure was repeated using a branched sample. The branched sample was analyzed using the final Mark-Houck constant as the best "cc" calibration value.

[0133] The interpretation of gpcBR is straightforward. For linear polymers, the values ​​measured by LS and viscometer are close to the traditional calibration standards, so gpcBR is close to zero. For branched polymers, the measured polymer molecular weight is the calculated M w,cc higher than the calculated IV ccis higher than the measured polymer IV, so that gpcBR becomes greater than zero, especially at high levels of long chain branching. In fact, the gpcBR value represents the fractional IV change due to the molecular size shrinkage effect as a result of polymer branching. A gpcBR value of 0.5 or 2.0 means a molecular size shrinkage effect of IV at a level of 50% and 200%, respectively, for an equivalent weight of linear polymer molecules. In these particular examples, the advantage of using gpcBR compared to traditional "g' index" and branching frequency calculations is due to the higher accuracy of gpcBR. All parameters used in gpcBR index determination are obtained with good accuracy and are not adversely affected by the low TDGPC detector response at high molecular weights from the concentration detector. Errors in the alignment of the detector volume also do not affect the accuracy of the gpcBR index determination.

[0134] Batch Reactor Polymerization Procedure The batch reactor polymerization reaction is carried out in a 2L Parr™ batch reactor. The reactor is heated by an electric heating mantle and cooled by an internal serpentine cooling coil containing cooling water. Both the reactor and the heating / cooling system are controlled and monitored by the Camile™ TG process computer. The bottom of the reactor is fitted with a dump valve that transfers the reactor contents to a stainless steel dump pot. The dump pot is pre-filled with catalyst deactivation solution (typically 5 mL of an Irgafos / Irganox / toluene mixture). Both the pot and the tank are purged with nitrogen and the dump pot is vented to a 30 gallon blowdown tank. All solvents used for polymerization or catalyst make-up are passed through a solvent purification column to remove any impurities that may affect the polymerization. 1-Octene and IsoparE are passed through two columns, the first containing A2 alumina, the second containing Q5. Ethylene is passed through A204 alumina and

number

number

[0135] The reactor is first charged from a shot tank which may contain IsoparE solvent and / or 1-octene depending on the reactor load. The shot tank is filled to the load set point using a lab scale attached to the shot tank. After the liquid feed is added, the reactor is heated to the polymerization temperature set point. If ethylene is used, it is added to the reactor at the reaction temperature to maintain the reaction pressure set point. The amount of ethylene added is monitored by a Micro Motion flow meter. In some experiments, the standard conditions at 150°C are 13g ethylene, 15g 1-octene, 240 psi hydrogen in 585g IsoparE and the standard conditions at 150°C are 15g ethylene, 45g 1-octene, 200 psi hydrogen in 555g IsoparE.

[0136] The procatalyst and activator are mixed with an appropriate amount of purified toluene to obtain a solution of the desired molar concentration. The procatalyst and activator are handled in an inert glove box, drawn into a syringe, and pressure transferred into the catalyst shot tank. The syringe is rinsed three times with 5 mL of toluene. Immediately after the catalyst is added, a run timer is started. If ethylene is used, it is added by Camille to maintain the reaction pressure set point in the reactor. The polymerization reaction is run for 10 minutes, then the agitator is stopped and the bottom dump valve is opened to transfer the reactor contents to a dump pot. The dump pot contents are poured into a tray and placed in a lab hood where the solvent is allowed to evaporate overnight. The tray containing the remaining polymer is transferred to a vacuum oven and heated to 140° C. under vacuum to remove any remaining solvent. After the tray is cooled to ambient temperature, the polymer yield is measured to measure efficiency and subjected to polymer testing. EXAMPLES

[0137] Tetrafunctional branching in the presence of various multichain catalysts and various dienes The results of the small scale polymerizations are summarized in Tables 3-7 (the experiments are carried out in a parallel polymerization reactor, PPR). The polymer results recorded in Tables 3-7 were produced by polymerizing ethylene, octene, and diene species in the presence of a multi-chain catalyst and a single chain catalyst control. The polymer results in each table in Tables 3-7 were the products of various catalysts and diene species. The results in Table 3 are based on the polymer products of 3-methyl-1,4-pentadiene, ethylene, and octene in the presence of Comparative Catalyst C1 ("Comparative Catalyst C1"), Catalyst 1 ("Catalyst 1"), and Catalyst 2 ("Catalyst 2"). The results in Table 4 are based on the polymer products of 1,4-pentadiene, ethylene, and octene in the presence of Catalyst 2, and Catalyst 4 ("Catalyst 4"). The results in Table 5 are based on the polymer products of 1,5-hexadiene, ethylene, and octene in the presence of Comparative Catalyst C1, Catalyst 3 ("Catalyst 3"), Catalyst 5 ("Catalyst 5"), and Catalyst 6 ("Catalyst 6"). The results in Table 6 are based on the polymer products of 1,7-octadiene, ethylene, and octene in the presence of Comparative Catalyst C1, Catalyst 6, Catalyst 2, and Catalyst 4. The results in Table 7 are based on the polymer products of 1,9-decadiene, ethylene, and octene in the presence of Catalyst 3, Catalyst 5, Catalyst 6, and Catalyst 2. (Figueroa,R.;Froese,RD;He,Y.;Klosin,J.;Theriault,CN;Abboud,KAOrganometallics 2011,30,1695-1709,Froese,RD;Jazdzewski,BA;Klosin,J.;Kuhlman,RL;Theriault,CN;Welsh,DM;Abboud,KAOrganometallics 2011,30,251-262) [ka]

[0138] The short chain catalyst in Series 3.C (Comparative Catalyst C1) incorporated increased amounts of α-olefins as indicated by more than double the octene levels in the polymer when compared to the other catalysts. When using the short chain catalyst in Series 3.C (Comparative Catalyst C1), the various levels of diene added did not significantly affect the polymer MWD. ​​However, by adding diene to the double chain catalysts in Tables 3-7, the diene levels were increased, resulting in higher M w Value and M p Values ​​were obtained and in many cases there was no evidence of high molecular weight tail formation.

[0139] In each example, the amount of diene that was incorporated into the reactor was small compared to the other reactants in the reactor, and therefore the addition of the diene did not affect the amount of comonomer, ethylene, and solvent added to the reactor. Example 1 - Tetrafunctional branching using 3-methyl-1,4-pentadiene [Table 4] Example 2 - Tetrafunctional branching using 1,4-pentadiene [Table 5] [Table 6]

[0140] Figure 20 shows that the peak weight average molecular weight shifts as the amount of diene increases. In Figure 20, the P2.4.1-P2.4.4 series, as recorded in Table 4, are plotted as dWdLogM as a function of LogM, which is a GPC plot. As the volume percent of diene increases, the peak of the GPC plot shifts to the right. Example 3 - Tetrafunctional branching using 1,5-hexadiene [Table 7] Example 4 - Tetrafunctional branching using 1,7-octadiene [Table 8] Example 5 - Tetrafunctional branching using 1,9-decadiene [Table 9]

[0141] Example of branching from a batch reactor The molecular weight distribution (MWD) curves and DSC of the two branched examples were investigated and compared to the linear sample.

[0142] Batch Reactor Example 1 In Tables 8-12, the polymer properties of a comparative linear polymer sample (1C) are compared to the branched polymer from a batch reactor. The polymerization reaction was carried out at a temperature of 150° C., 555 g of ISOPAR-E™, and 200 psi of hydrogen pressure (ΔH 2 The ethylene pressure was kept constant at 150 psi in the presence of 0.3 μmol of catalyst 8, 0.36 μmol of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 μmol of MMAO-3A. [Table 10] [Table 11]

[0143] Figure 21 shows conventional molecular weight distribution curves of polymers in series 8.C (linear) and 8.1 (branched) as determined by GPC. The shape of the curve for the branched polymer, series 8.1, is altered compared to the linear polymer. In addition, the peak of the molecular weight curve is shifted to the right.

[0144] FIG. 22 is the absolute molecular weight distribution curves of polymers in series 8.C (linear) and 8.1 (branched) as determined by GPC.

[0145] FIG. 23 shows the extensional viscosity fixture for the branched sample, series 8.1. [Table 12]

[0146] Dynamic mechanical spectra of branched Example 8.1 were measured and the results are recorded in Table 9. The viscosity at 0.1 rad / sec was calculated to be 27,457 Pa s, the viscosity at 100 rad / sec was measured to be 974 Pa s, and the rheological ratio (V 0.1 / V 100 ) resulted.

[0147] The elastic modulus m is [((tan(δ 0.1 )-tan(δ 100 ))*1000) / (0.1-100)). tan(δ 0.1 ) is the tangent of the phase angle in 0.1 radians / second, and tan(δ 100 ) is the tangent of the phase angle at 100 radians / second. 0.1 ) is 1.6, and tan(δ 100 ) is 0.8, which results in an elastic modulus of 7.9 at 190°C. [Table 13]

[0148] The dynamic mechanical spectrum of Comparative Example 8.C was measured and the results are recorded in Table 10. The shear viscosity at 0.1 rad / sec was calculated to be 892 Pa s and the shear viscosity at 100 rad / sec was measured to be 526 Pa s, giving a rheological ratio (V 0.1 / V 100 ) was obtained. The tan(δ 0.1 ) is 53.3, and tan(δ 100 ) is 2.0, which results in an elastic modulus of 513.4 at 190°C.

[0149] The rheology ratio of the linear comparative polymer resin was very low (1.7) when compared to that of the branched Example, Series 8.1. The increased rheology ratio and low elastic modulus of Branched Example 1, Series 8.1 indicate non-linear polymer behavior. Strong shear thinning and elastic behavior are often indicative of entangled long chain branched polymers.

[0150] FIG. 24 is the melt strength obtained with the Rheotens apparatus of branching example 1, series 8.1.

[0151] Branching Example 2 In Table 11, a branched polyethylene was synthesized where the diene was 1,9-decadiene. The branched polymer was prepared at a temperature of 150° C., 555 g of IsoparE, and 200 psi of hydrogen pressure (ΔH 2 The ethylene pressure was kept constant at 150 psi in the presence of 0.3 μmol of catalyst 7, 0.36 μmol of cocatalyst A, and 10 μmol of MMAO-3A. [Table 14]

[0152] Figure 25 is a conventional molecular weight distribution curve of the polymers of branched Example 2 in series 11.C (linear) and 11.1 (branched) as determined by GPC. Figure 26 is an absolute molecular weight distribution curve of the polymers in series 11.C (linear) and 11.1 (branched) as determined by a light scattering triple photodetector. The shape of the curve for the branched polymer, series 11.1, is altered compared to the linear polymer.

[0153] FIG. 27 is the extensional viscosity obtained with the extensional viscosity fixture of branched Example 2 in Series 11.1. [Table 15]

[0154] Dynamic mechanical spectra of the comparative example were measured and the results are recorded in Table 12. The shear viscosity at 0.1 rad / sec was calculated to be 17,643 Pa s, and the shear viscosity at 100 rad / sec was measured to be 857 Pa s, giving a rheological ratio (V 0.1 / V 100 ) for the branched polymers in Example 2, Series 11.1. 0.1 ) is 2.0, and tan(δ 100 ) is 1.0, which results in an elastic modulus of 10.4 at 190°C.

[0155] FIG. 28 is the melt strength obtained with the Rheotens apparatus of branching example 2, series 11.1.

[0156] Branching studies under various conditions The tetrafunctional "ladder branching" was studied under a variety of conditions, including increasing ethylene pressure, increasing octene monomer, increasing starting molecular weight, decreasing starting molecular weight, various dienes, increasing or decreasing amounts of diene, and various multi-chain catalysts.

[0157] Example 1: Various dienes and amounts of dienes The examples in Tables 13-22 were prepared under identical conditions and polymerized in the presence of Catalyst 7 at a temperature of 150 degrees. Conditions included: 585g IsoparE, 15g 1-octene, 240 psi hydrogen pressure, 150 psi ethylene pressure, 0.3 μmoles Catalyst 7, 0.36 μmoles Cocatalyst A, and 10 μmoles MMAO-3A. [Table 16] [Table 17]

[0158] The results in Table 13 showed that when dienes were present in the polymerization reaction, the molecular weight increased without a high molecular weight tail. Example 2: Conditions for obtaining high molecular weight [Table 18]

[0159] These polymerization conditions were utilized to produce high molecular weight polymers, resulting in tetrafunctional "ladder branches" that arose when dienes were incorporated into the polymerization reaction. The polymerization reaction yielded polymer resins with high molecular weight and tetrafunctional "ladder branches." Example 3: Conditions for obtaining branched homopolymers [Table 19]

[0160] Incorporating a diene into the polymerization reaction used to make the homopolymer (with a small amount of diene) resulted in an increase in molecular weight (tetrafunctional "ladder branching"). The data recorded in Table 15 showed that the ethylene-only resin examples had increased molecular weights when two different dienes were incorporated into the polymerization reaction. [Table 20]

[0161] The results in Table 16 show that branching occurs with different catalysts and at different densities. The resins in Table 16 demonstrated branching with catalyst 8 and sufficient octene to 7 mole % in the polymer. [Table 21]

[0162] Based on the results in Table 17, the molecular weight was increased by the addition of dienes that exhibited tetrafunctional "ladder branching." These examples had higher linear molecular weights. In Examples 5.1 and 5.2, Catalyst 8 produced polymer resins with higher molecular weights when decadiene or pentadiene was present in the polymerization reaction. [Table 22]

[0163] The results in Table 18 showed that molecular weight increases (tetrafunctional "ladder branching") occurred when different α-olefin comonomers were used. The polymer resins in Table 18 were produced with two different catalysts and two different loadings of hexene. [Table 23]

[0164] Based on the results in Table 19, molecular weight increase with dienes (4-functional "ladder branching") occurred at various levels of octane. The examples in Table 19 showed that 4-functional "ladder branching" occurred even at 7 mole % octene in the polymer. [Table 24]

[0165] As evidenced in Table 20, tetrafunctional "ladder branches" occurred at various levels of octene and higher starting molecular weights. Examples 8.1 and 8.2 were prepared using 7 mol % octene and a starting M of approximately 83,000 g / mol. w It has been shown that polymer resins having both decadiene and pentadiene branching are obtained. [Table 25]

[0166] The results in Table 21 showed that there was a much lower density (higher levels of octene in the polymer) and an increase in molecular weight (tetrafunctional "ladder branching") at a lower starting molecular weight. In Example 9.1, the polymer resin had more than 9 mole % octene and a starting M of about 43,000 g / mol. w When dienes were incorporated into the polymerization reaction, the molecular weight increased ("ladder branching" occurred). [Table 26]

[0167] The results in Table 22 show an increase in molecular weight using dienes with different levels of incorporated octene (tetrafunctional "ladder branching") at lower starting molecular weights. In Example 22.1, the starting molecular weight of the polymer resin was about 51,000 g / mole, but when dienes were incorporated into the polymerization reaction, the molecular weight increased to 70,000 g / mole (tetrafunctional "ladder branching" occurred). [Table 27]

[0168] According to the data in Tables 23 and 24, when the ethylene pressure and the amount of octene in the reactor were increased, the molecular weight increased (4-functional "ladder branching" occurred). [Table 28] Example 4: Catalyst 7 for catalyzing decadiene homopolymer [Table 29] [Table 30]

[0169] The results are summarized in Table 25 and show that when octene is not present in the reactor, tetrafunctional "ladder branching" occurs. The molecular weight of each sample in Table 25 increased as the amount of decadiene in the polymerization reaction increased. [Table 31]

[0170] Example 26.C.1 is the result of a polymerization reaction containing 0.2 octene. FIG. 29 is a graph of Log(MW) for Examples 26.C.1, 26.C.2, and 26.1-26.4. Increasing the amount of decadiene shifts the molecular weight peak to the right. Tables 27-32 summarize the dynamic mechanical spectroscopy results for Examples 26.C.1, 26.C.2, and 26.1-26.4. The results in each of Tables 27-32 show that increasing the amount of tetrafunctional "ladder branch" decreases the elastic modulus, m. In addition, the results in each of Tables 27-32 show that increasing the amount of tetrafunctional "ladder branch" decreases the rheology ratio.

[0171] FIG. 29 is a conventional molecular weight distribution curve for series 26.C.1, 26.C.2, and 26.1-26.4. [Table 32]

[0172] Dynamic mechanical spectra of the comparative example were measured and the results are recorded in Table 27. The shear viscosity at 0.1 rad / sec was calculated to be 762 Pa s and the shear viscosity at 100 rad / sec was measured to be 552 Pa s, giving a rheological ratio (V 0.1 / V 100 The tan (δ) of the branched polymer in Example 26.C.1 was 0.1 ) is 192.8, and tan(δ 100 ) is 2.8, which results in an elastic modulus of 1901.6 at 190°C. [Table 33]

[0173] The dynamic mechanical spectrum of the comparative example, Example 26.C.1, was measured and the results are recorded in Table 28. The shear viscosity at 0.1 rad / sec was calculated to be 662 Pa s, the shear viscosity at 100 rad / sec was measured to be 501 Pa s, and the rheological ratio (V 0.1 / V 100 The tan(δ) of the linear polymer of Example 26.C.1 was0.1 ) is 401.3, and tan(δ 100 ) is 3.1, which results in an elastic modulus of 3986.2 at 190°C. [Table 34]

[0174] The dynamic mechanical spectrum of Example 26.1 was measured and the results are recorded in Table 29. The shear viscosity at 0.1 rad / sec was calculated to be 7,410 Pa s, and the shear viscosity at 100 rad / sec was measured to be 883 Pa s, giving a rheological ratio (V 0.1 / V 100 The tan (δ) of the branched polymer in Example 13.1 was 0.1 ) is 4.3, and tan(δ 100 ) is 1.3, which results in an elastic modulus of 29.8 at 190°C. [Table 35]

[0175] The dynamic mechanical spectrum of Example 26.2 was measured and the results are recorded in Table 30. The shear viscosity at 0.1 rad / sec was calculated to be 56,549 Pa s, the shear viscosity at 100 rad / sec was measured to be 1,236 Pa s, and the rheological ratio (V 0.1 / V 100 The tan (δ) of the branched polymer in Example 26.2 was 0.1 ) is 1.2, and tan(δ 100 ) is 0.8, which results in an elastic modulus of 4.2 at 190°C. [Table 36]

[0176] The dynamic mechanical spectrum of Example 26.3 was measured and the results are recorded in Table 31. The shear viscosity at 0.1 rad / sec was calculated to be 56,549 Pa s, the shear viscosity at 100 rad / sec was measured to be 1,236 Pa s, and the rheological ratio (V 0.1 / V 100 The tan (δ) of the branched polymer in Example 26.3 was 0.1 ) is 1.2, and tan(δ 100 ) is 0.8, which results in an elastic modulus of 1.5 at 190°C. [Table 37]

[0177] The dynamic mechanical spectrum of Example 26.4 was measured and the results are recorded in Table 32. The shear viscosity at 0.1 rad / sec was calculated to be 909,000 Pa s, the shear viscosity at 100 rad / sec was measured to be 3,054 Pa s, and the rheological ratio (V 0.1 / V 100 The tan (δ) of the branched polymer in Example 26.4 was 0.1 ) is 0.3, and tan(δ 100 ) is 0.3, which results in an elastic modulus of 0.4 at 190°C.

[0178] Guzman-2010 demonstrated and analyzed the MWD and physical properties resulting from conventional diene branching in a steady-state CSTR. A constrained geometry catalyst (CGC) was used to copolymerize ethylene, 1-octene, and 1,9-decadiene in a very well-mixed one-gallon reactor system. The specific CGC catalyst used by Guzman was described in detail by U.S. Pat. No. 5,965,756 (Structure IX), and U.S. Pat. No. 7,553,917 (Example 3). The Guzman-2010 catalyst was designed to grow single chains from the catalyst center. Guzman's data was collected at steady state while the CSTR was operated over a range of diene feed concentrations at a pressure of 525 psig and a temperature of 155° C. The various steady-state polymer samples collected by Guzman contained no measurable levels of gel or insoluble material. However, at the highest level of diene feed, some internal reactor fouling was observed, and higher levels of diene feed were expected to result in gel formation or reactor MWD instability.

[0179] In Table 33, selected series of data from Guzman are summarized for otherwise fixed reactor conditions across a spectrum of diene feed levels. Ethylene and 1-octene feed concentrations were set at 13.8 wt% and 3.6 wt%, respectively, throughout the series. The catalyst feed rate was continuously adjusted to maintain a constant ethylene conversion of 79% throughout the series, resulting in a fixed polymer production rate of 2.2 kg / hr. Polymer density, a measure of copolymer composition, was constant at approximately 0.922 g / cc. [Table 38]

[0180] The data in Table 33 is 2 and I 10This study demonstrated how changing the level of conventional diene branching, as reflected by the MWD, affects properties such as average molecular weight, and polydispersity, as well as viscosity. The effect of conventional diene branching on molecular weight is shown in Table 33 for both absolute and conventional MWD measurement techniques. Absolute MWD measurements are the preferred method for branched polymers, but are not always available. Therefore, Table 33 also contains molecular weights measured by the conventional technique using a refractive index detector. The results in Table 33 show that, for both measurement techniques, increasing diene feed from zero to 923 ppm significantly increases the weight average molecular weight (M w ) is substantially increased.

[0181] Although not reported in Guzman, the MWD curves associated with Table 33 were found and plotted in Figures 30A and 30B for absolute and conventional GPC measurement techniques, respectively. The MWD curve data in Figures 30A and 30B are consistent with the expected high M from conventional diene branching. w It was demonstrated that tail formation occurred. The lack of significant movement of the peak MW with increasing diene branching is also evident from the MWD curves.

[0182] The molecular weight distribution data in Figures 30A and 30B have been reduced to simple metrics that describe the evolution of the position and shape of the MWD curve as more diene monomer is fed to the CSTR. The data in Table 34 show these MWD metrics for both absolute and conventional MWD measurements of Guzman's polymer samples. The absolute MWD measurement data in Table 34 showed that as the 1,9-decadiene feed ranged from 0 to 923 ppm, the molecular weight increased by up to 87%. p The peak molecular weight change, as indicated by M, does not change significantly by either means of molecular weight measurement, which is inconsistent with the results for "ladder-branched" polymers. The shape factors are summarized in Table 34 and are a function of diene feed level and M w As increases, G 79 / 29 and A TAIL This is inconsistent with a "ladder branched" polymer, since both values ​​of [Table 39]

[0183] Some important parameters for the commercial resins are summarized in Table 35. Some of the basic parameters of the materials were made in solution, gas phase, and in a high pressure reactor. [Table 40]

[0184] The data summarized in Table 35 are plotted in the graphs of Figures 31 and 32. The data show differences in the "ladder-branched" polymers compared to LDPE, LLDPE, ULDPE, and ethylene resins containing diene monomers. In Figures 31 and 32, the "ladder-branched" polymers of the present disclosure (Ladder-PE in the graph legend) are clustered together, thus indicating that the "ladder-branched" polymers have unique polymer properties compared to other ethylene-based resins. As shown in the graph of Figure 31, the "ladder-branched" polymers have a rheology ratio of at least 10 and an average g' of less than 0.86. In Figure 31, the plotted LDPE resins have an average g' of less than 0.65, and the prior art ethylene-diene resins (listed as Prior Art ET-Diene in the legend) do not cluster together.

[0185] In Figure 33, melt strength (centinewtons, cN) is plotted against melt index (Log I 2 ) was measured as a function of . The polymers produced from the dual chain catalyst were compared to the polymers produced from the single chain catalyst, as indicated by the triangles and circles, and to literature-based curves for autoclave LDPE, tubular LDPE, and linear polyethylene. The melt strengths of the polymers produced from the dual chain catalyst were lower than those of the autoclave LDPE, tubular LDPE, and single chain catalyst, but significantly higher than the linear polyethylene. This indicates that the polymers produced from the dual chain catalyst have intertwined long chain branches.

[0186]

[0187] The described implementations may be modified without departing from the spirit and scope of the claimed subject matter. It will be apparent to those skilled in the art that various modifications can be made to the form. This specification expressly states that such modifications and variations are to be understood as including, but not limited to, the appended claims and their equivalents. It is intended to cover modifications and variations of the described embodiments to the extent that they come within the scope of equivalents. It is intended that: The present application also relates to the following aspects: (1) An ethylene-based polymer comprising the reaction product of the polymerization of ethylene monomer, at least one diene or polyene comonomer, and optionally at least one C3 to C14 comonomer, under defined polymerization reaction conditions, Mw / Mw0 greater than 1.20, where Mw is the weight average molecular weight of the ethylene-based polymer as determined from a gel permeation chromatography curve of the ethylene-based polymer obtained by refractive index chromatography, and Mw0 is the initial weight average molecular weight of a comparison ethylene-based polymer by gel permeation chromatography, wherein the comparison ethylene-based polymer is the at least one polyene comonomer-free reaction product of the polymerization of ethylene monomer and all C3-C14 comonomers, if present, present in the ethylene-based polymer, under the polymerization reaction conditions defined above; and a high molecular weight tail, as quantified by an MWD area metric, ATAIL, where the ATAIL is less than or equal to 0.04 as determined by gel permeation chromatography using a triple detector. (2) An ethylene-based polymer, an elastic modulus m at 190° C. of less than or equal to 4 seconds / radian, where m is [((tan(δ0.1)-tan(δ100))*1000) / (0.1-100))], where tan(δ0.1) is the tangent of the phase angle at 0.1 radians / second and tan(δ100) is the tangent of the phase angle at 100 radians / second; An ethylene-based polymer having an average g' from 0.64 to 0.86, said average g' being an intrinsic viscosity ratio as determined by gel permeation chromatography using a triple detector. (3) The ethylene-based polymer of (2), wherein the high molecular weight tail is quantified by an MWD area metric, ATAIL, where the ATAIL is 0.04 or less as determined by gel permeation chromatography using a triple detector. (4) The ethylene-based polymer according to any one of (1) to (3), wherein the ethylene-based polymer has Mp / Mp0 greater than 1.20, where Mp is the peak molecular weight of the ethylene-based polymer as determined by refractive index gel permeation chromatography, and Mp0 is the initial peak molecular weight of the ethylene-based polymer without any polyene comonomer. (5) The ethylene-based polymer according to any one of (1) to (4), having a melt viscosity ratio (V0.1 / V100) at 190°C of at least 10, V0.1 being the viscosity of the ethylene-based polymer at 190°C and a shear rate of 0.1 radian / second, and V100 being the viscosity of the ethylene-based polymer at 190°C and a shear rate of 100 radian / second. (6) The ethylene-based polymer according to any one of (1) to (5), having a melt viscosity ratio (V0.1 / V100) at 190°C of at least 25, V0.1 being the viscosity of the ethylene-based polymer at 190°C and a shear rate of 0.1 rad / sec, and V100 being the viscosity of the ethylene-based polymer at 190°C and a shear rate of 100 rad / sec. (7) The ethylene-based polymer according to any one of (1) to (6), wherein the elastic modulus m at 190°C is 1 second / radian or less, m is [((tan(δ0.1)-tan(δ100))*1000) / (0.1-100))], tan(δ0.1) is the tangent of the phase angle at 0.1 radian / second, and tan(δ100) is the tangent of the phase angle at 100 radian / second. (8) The ethylene-based polymer of any of (1) to (7), wherein the ethylene-based polymer has a G(79 / 29) value of 0.04 or less, as determined from a gel permeation chromatography curve using a triple detector having a peak height, a slope M79 at 79% of the peak height, and a slope M29 at 29% of the peak height, wherein the G(79 / 29) value is equal to (M79-M29) / M79. (9) The ethylene-based polymer of any one of (1) to (8), wherein the ethylene-based polymer has a high molecular weight tail, as quantified by an MWD area metric, ATAIL, where ATAIL is 0.03 or less, as determined by gel permeation chromatography using a triple detector. (10) The ethylene-based polymer according to any one of (1) to (9), having a melt strength of greater than 6 cN (Rheotens apparatus, 190° C., 2.4 mm / sec, 120 mm from die exit to center of wheel, extrusion speed of 38.2 sec, capillary die with length of 30 mm, diameter of 2 mm, and inlet angle of 180°). (11) The ethylene-based polymer according to any one of (1) to (10), wherein the melt viscosity ratio (V0.1 / V100) is more than 10 times the elastic modulus (m), and the melt viscosity ratio (V0.1 / V100) is determined by a viscosity V0.1 of the ethylene-based polymer at 190° C. and a shear rate of 0.1 radians / second, and a viscosity V100 of the ethylene-based polymer at 190° C. and a shear rate of 100 radians / second, and the elastic modulus m is [((tan(δ0.1)-tan(δ100))*1000) / (0.1-100))], wherein tan(δ0.1) is the tangent of the phase angle at 0.1 radians / second, and tan(δ100) is the tangent of the phase angle at 100 radians / second. (12) The ethylene-based polymer according to any one of (1) to (11), wherein the melt viscosity ratio (V0.1 / V100) is greater than 50, and the elastic modulus (m) is less than 8 seconds / radian, the melt viscosity ratio (V0.1 / V100) being determined by a viscosity V0.1 of the ethylene-based polymer at 190° C. and a shear rate of 0.1 radian / second, and a viscosity V100 of the ethylene-based polymer at 190° C. and a shear rate of 100 radian / second, the elastic modulus m being [((tan(δ0.1)-tan(δ100))*1000) / (0.1-100))], wherein tan(δ0.1) is the tangent of the phase angle at 0.1 radian / second, and tan(δ100) is the tangent of the phase angle at 100 radian / second. (13) The ethylene-based polymer according to any one of (1) to (12) above, which contains units derived from ethylene, a diene, and one or more C3 to C12 α-olefins. (14) The ethylene-based polymer according to (13) above, wherein the diene is linear. (15) The ethylene-based polymer of (13), wherein the diene is selected from 2-methyl-1,4-pentadiene, 3-methyl-1,4-pentadiene, 1,3-divinylcyclopentane, 2-methyl-1,5-hexadiene, 1,4-pentadiene, 1,5-hexadiene, 1,7-octadiene, 1,8-nonadiene, 1,9-decadiene, 1,11-dodecadiene, and 1,15-hexadecadiene.

Claims

1. Ethylene monomer and at least one diene comonomer, and optionally at least one C ３ ~C １４ and a comonomer, Mw / Mw greater than 1.20 ０ Mw is the weight average molecular weight of the ethylene-based polymer as determined from a gel permeation chromatography curve of the ethylene-based polymer obtained by refractive index chromatography; Mw ０ is the initial weight average molecular weight of a comparative ethylene-based polymer by gel permeation chromatography, the comparative ethylene-based polymer being a mixture of ethylene monomer and any C monomers present in the ethylene-based polymer. ３ ~C １４ and, if present, a comonomer, the reaction product of said polymerization of said at least one diene comonomer, said reaction product having a Mw / Mw of greater than 1.20, ０ and, MWD area metric, A ＴＡＩＬ A high molecular weight tail, quantified by A ＴＡＩＬ is 0.04 or less, as determined by gel permeation chromatography using a triple detector.

2. The ethylene-based polymer has a Mp / Mp ratio greater than 1.

20. ０ 2. The diene ladder branched ethylene-based polymer of claim 1, wherein Mp is the peak molecular weight of the ethylene-based polymer as determined from refractive index gel permeation chromatography and Mp0 is the initial peak molecular weight of the ethylene-based polymer without polyene comonomer.

3. Melt viscosity ratio at 190°C (V ０．１ / V １００ ) is at least 10, and V ０．１ is the viscosity of the ethylene-based polymer at 190° C. and a shear rate of 0.1 rad / sec; V １００ 3. The diene ladder branched ethylene-based polymer of claim 1 or 2, wherein:

4. Melt viscosity ratio at 190°C (V ０．１ / V １００ ) is at least 25; V ０．１ is the viscosity of the ethylene-based polymer at 190° C. and a shear rate of 0.1 rad / sec; V １００ The diene ladder branched ethylene-based polymer of any one of claims 1 to 3, wherein V is the viscosity of the ethylene-based polymer at 190°C and a shear rate of 100 rad / sec.

5. 5. The diene ladder branched ethylene-based polymer of any one of claims 1 to 4, wherein the ethylene-based polymer has a G(79 / 29) value less than or equal to 0.04 as determined from a triple detector gel permeation chromatography curve having a peak height, a slope M79 at 79% of the peak height, and a slope M29 at 29% of the peak height, wherein the G(79 / 29) value is equal to (M79-M29) / M79.

6. The ethylene-based polymer has a MWD area metric, A ＴＡＩＬ and has a high molecular weight tail quantified by A ＴＡＩＬ 6. The ethylene-based polymer of any one of claims 1 - 5, wherein m is less than or equal to 0.03 as determined by gel permeation chromatography using a triple detector.

7. Melt strength >6 cN (Rheotens apparatus, 190° C., 2.4 mm / sec2, 120 mm from die exit to center of wheel, 38.2 sec －１ 7. The ethylene-based polymer of any one of claims 1 to 6, wherein the extrusion speed is 0.05 s, capillary die having a length of 30 mm, a diameter of 2 mm, and an entrance angle of 180°.

8. The ethylene-based polymer comprises ethylene, a diene, and one or more C ３ ~C １２ The ethylene-based polymer of any one of claims 1 to 7, which comprises units derived from an α-olefin.

9. 9. The ethylene-based polymer of claim 8, wherein the diene is linear.

10. 9. The ethylene-based polymer of claim 8, wherein the diene is selected from 2-methyl-1,4-pentadiene, 3-methyl-1,4-pentadiene, 1,3-divinylcyclopentane, 2-methyl-1,5-hexadiene, 1,4-pentadiene, 1,5-hexadiene, 1,7-octadiene, 1,8-nonadiene, 1,9-decadiene, 1,11-dodecadiene, and 1,15-hexadecadiene.

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