Process for polymerizing trifunctional long-chain branched olefins

Abstract

This is a process for synthesizing long-chain branched polymers. The process involves the synthesis of one or more C2-C 14 contacting together an alkene monomer, at least one diene, optionally a solvent, and a multi-chain catalyst, optionally in the presence of hydrogen, wherein the multi-chain catalyst comprises a plurality of polymerization sites; and 14 The method includes: producing at least two polymer chains of alkene monomers, each polymer chain polymerizing at one of the polymerization sites; synthesizing a long-chain branched polymer by connecting the two polymer chains with a diene, wherein the joining of the two polymer chains is carried out in a concerted manner during polymerization; producing trifunctional and tetrafunctional long-chain branches from the diene, wherein the long-chain branched polymer has a ratio of trifunctional to tetrafunctional long-chain branches of 0.05:1 to 100:0; and adjusting the ratio of trifunctional and tetrafunctional long-chain branches. The diene has a structure according to formula (I): [Formula 1] JPEG2022528531000098.jpg45170

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 62 / 826,414, filed March 29, 2019, 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 trifunctional long chain branching and processes by which the polymer compositions are synthesized. [Background technology]

[0003] Olefin-based polymers, such as polyethylene, are produced through a variety of 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 long 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 branches primarily affect the mechanical and thermal properties. As the branch length increases, the branches can form lamellar crystals and the mechanical and thermal properties decrease. Small amounts of long chain branching can significantly alter the processing properties of the polymer. Summary of the Invention [Problem to be solved by the invention]

[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.

[0006] Embodiments of the present disclosure include a process for synthesizing long chain branched polymers. In one or more embodiments, the process comprises one or more C2-C 14 The process comprises contacting together an alkene monomer, at least one diene, optionally a solvent, and a multi-chain catalyst, optionally in the presence of hydrogen, the multi-chain catalyst comprising multiple polymerization sites. 14 At least two polymer chains of alkene monomers are produced, and each polymer chain is polymerized at one of the polymerization sites. The long-chain branched polymer is then synthesized by connecting the two polymer chains with a diene. The connection of the two polymer chains is carried out in a concerted manner during polymerization. The trifunctional long-chain branches are produced from the diene, and the long-chain branched polymer has a ratio of trifunctional to tetrafunctional long-chain branches of 0.05:1 to 100:0. The ratio of trifunctional to tetrafunctional long-chain branches is C2-C ... 14 It can be adjusted by varying the feed ratio of alkene monomer to hydrogen.

[0007] In one or more embodiments, the diene has a structure according to formula (I): [ka]

[0008] In formula (I), X is CR2, SiR2, or GeR2, and each R is independently C1-C 12 In some embodiments, X in formula (I) is -C(R)-, where each R is -H or each R is C-C 12 In another embodiment, X in formula (I) is -Si(R)-, where each R is C-C 12 In one or more embodiments, the diene is dimethyldivinylsilane.

[0009] Various embodiments of the process occur in a solution polymerization reactor or a particle-forming polymerization reactor such as a slurry reactor or a gas phase reactor, the molecular or solid supported catalyst is delivered to or generated in the reaction medium, the reactor system is batch, continuous or hybrid such as semi-batch, and the reactor residence time distribution is narrow, such as in non-backmixed reactors, or broad, such as in backmixed reactors and series and recycle reactors. [Brief description of the drawings]

[0010] [Figure 1] FIG. 1 is a graphical representation of polymer molecular weight as the number of branched methines per 1000 carbons. [Figure 2A] FIG. 2A is a plot of molecular weight increase versus diene linkage.

[0011] [Figure 2B] FIG. 2B is a plot of polydispersity versus diene linkages. [Diagram 3] FIG. 3 is a graphical representation of the predicted dependence of molecular weight distribution (MWD) curves on trifunctional diene branching level. [Figure 4] FIG. 4 is a graphical representation of the predicted dependence of relative peak molecular weight (MW) on trifunctional diene branching level. [Diagram 5] FIG. 5 is a graphical representation of a MWD curve illustrating how the point of maximum slope is used to define the high MWD tail area metric. [Figure 6] FIG. 6 is a conventional (RI) GPC of dimethyldivinylsilane samples (Example 1.C and Examples 1.1-1.7) with increasing amounts of diene. [Figure 7] FIG. 7 is a global carbon NMR spectrum of dimethyldivinylsilane branched polyethylene (Example 12.1). [Figure 8] 8 is the Si(Me)2 region of the carbon NMR spectrum of dimethyldivinylsilane branched polyethylene (Example 12.1). Trifunctional LCB carbons = 0.17 Me / 1000C, and tetrafunctional LCB carbons = 0.12 Me / 1000C. [Figure 9] Figure 9 shows the methine region of the carbon NMR spectrum of dimethyldivinylsilane branched polyethylene (Example 12.1). Trifunctional LCB = 0.09 CH / 1000C, tetrafunctional LCB = 0.16 CH / 1000C. [Figure 10] FIG. 10 is the conventional (RI) and absolute (LS) GPC for the linear PE (Example 12.C) and the dimethyldivinylsilane branched PE (Example 12.1). [Figure 11] FIG. 11 is the extensional viscosity fixture (EVF) of dimethyldivinylsilane branched PE (Example 12.1). [Figure 12] FIG. 12 is a melt strength plot of dimethyldivinylsilane branched polyethylene (Example 12.1). [Figure 13] FIG. 13 is the DMS of dimethyldivinylsilane branched polyethylene (Example 12.1) at 190° C. [Figure 14A] FIG. 14A is a graph of absolute molecular weight distributions of comparative conventional branched polymer samples having varying amounts of diene. [Figure 14B] FIG. 14B is a graph of conventional molecular weight distributions of comparative conventional branched polymer samples having varying amounts of diene. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] 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.

[0013] 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.

[0014] "Polyethylene" or "ethylene-based polymer" is intended to mean a polymer containing greater than 50 mole percent 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).

[0015] "Ethylene-diene based polymer" is intended to mean a polymer that contains more than 50 mol% units derived from ethylene monomer and also contains a small amount of a diene component. An ethylene-diene based polymer may optionally contain one or more (C3-C 12 ) α-olefin derived units.

[0016] Embodiments of the present disclosure include a process for synthesizing long chain branched polymers. In one or more embodiments, the process comprises one or more C2-C 14 The process comprises contacting together an alkene monomer, at least one diene, optionally a solvent, and a multi-chain catalyst, optionally in the presence of hydrogen, the multi-chain catalyst comprising multiple polymerization sites. 14 At least two polymer chains of alkene monomers are produced, and each polymer chain is polymerized at one of the polymerization sites. The long-chain branched polymer is then synthesized by connecting the two polymer chains with a diene. The connection of the two polymer chains is carried out in a cooperative manner during polymerization.

[0017] In various embodiments, the long chain branched polymer has a ratio of trifunctional to tetrafunctional long chain branches from 0.05:1 to 100:0.

[0018] In one or more embodiments, the trifunctional long chain branches are produced from dienes and the trifunctional long chain branches occur at a frequency of at least 0.03 per 1000 carbon atoms.

[0019] With respect to "connecting two polymer chains," the term "connect" broadly means that the polymer chains are covalently linked.

[0020] In one or more embodiments, the ratio of trifunctional to tetrafunctional long chain branches is adjusted if the ratio deviates from a target ratio of trifunctional to tetrafunctional long chain branches. 14 Alkene monomer feed, hydrogen feed, C2-C 14 It is adjusted by varying the ratio of alkene monomer feed to hydrogen, the reactor temperature, or a combination thereof.

[0021] In some embodiments, C2-C 14 The feed ratio of alkene monomer feed to hydrogen is 100:0 to 1:100. In one or more embodiments, the feed ratio is 3:1 to 1:1. In various embodiments, the feed ratio is 100:1 to 2:1, 10:2 to 1:2, or 3:1 to 1:5.

[0022] In various embodiments, the diene has a structure according to formula (I): [ka]

[0023] In formula (I), X is CR2, SiR2, or GeR2, and each R is independently C1-C 12 In some embodiments, X in formula (I) is -C(R)-, where each R is -H or each R is C-C 12 In another embodiment, X in formula (I) is -Si(R)-, where each R is C-C 12 In one or more embodiments, the diene is dimethyldivinylsilane.

[0024] In some embodiments, R of formula (I) is C-C 12 When it is alkyl, it is C1-C 12 Alkyl is methyl, ethyl, 1-propyl, 2-propyl, 1-butyl, 2-butyl, 2-methylpropyl, 1,1-dimethylethyl, 1-pentyl, 1-hexyl, 1-heptyl, n-octyl, tert-octyl, nonyl, decyl, undecyl, or dodecyl. 12 The term "alkyl" means a saturated straight or branched chain hydrocarbon radical of 1 to 12 carbon atoms.

[0025] In one or more embodiments, the process of the present disclosure comprises producing a polymerization product of ethylene, at least one diene comonomer, and optionally at least one C-C14 A polymer is produced that includes the comonomer, the polymer including trifunctional long chain branches derived from a diene occurring at a frequency of at least 0.03 per 1000 carbon atoms of the polymer.

[0026] In various embodiments, the polymers produced from the polymerization processes of the present disclosure contain trifunctional long chain branches occurring at a frequency of at least 0.05 per 1000 carbon atoms. In one or more embodiments, the trifunctional long chain branches of the polymer occur at a frequency of at least 0.1 per 1000 carbon atoms. In various embodiments, the trifunctional long chain branches of the polymer occur at a frequency of at least 0.2 per 1000 carbon atoms.

[0027] The process of synthesizing the polymer according to the present disclosure is different from conventional long chain branching or previous "ladder" branching described in Application Nos. PCTUS2019 / 053524, PCTUS2019 / 053527, PCTUS2019 / 053529, and PCTUS2019 / 053537, each of which was filed on September 27, 2019 and is incorporated herein by reference in its entirety. The term "long chain branching" refers to a branch having more than 100 carbon atoms. A "branch" refers to a portion of a polymer that extends from a tertiary carbon atom. When a branch extends from a tertiary carbon atom, there are two other branches, which collectively may be the polymer strand from which the branch extends. In the present disclosure, the branch is defined as a trifunctional long chain branch in that the branch point has three polymer chains emanating from it. Conventionally, long chain branching (LCB) can occur naturally in a polymerization process, as shown in Scheme 1. Naturally occurring LCBs may arise through vinyl termination of polymer chains and reinsertion of polymeric vinyls to create trifunctional long chain branches. Depending on the degree of branching, various methods, such as nuclear magnetic resonance (NMR), may determine LCBs or identify the effect of LCBs in polymers. For example, the effect of LCBs 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 may be attributed to LCBs. In extensional flow, the effect of LCBs is usually identified in the degree of strain hardening or strength of the melt, and the maximum deformation achieved. 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 LCBs, it is difficult to achieve high levels of natural LCBs in polymers. To ensure high conversion, the ethylene concentration in the reactor is low, and therefore a large amount of vinyl-terminated polymers may be reinserted into a second polymer chain. [ka]

[0028] In Scheme 1, "Cat" is the catalyst and "P" is the polymer chain.

[0029] There is minimal long chain branching formed through naturally occurring branching. One way to enhance LCB is to add α,ω-dienes to the polymerization system, whether it is a radical, heterogeneous, or homogeneous process. Generally, dienes are added to the polymer chain in a similar manner to α-olefins, but leave pendant vinyl groups that can be inserted once more into the polymer chain to create LCB, as illustrated in Scheme 2. In general, 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. [ka] In Scheme 2, "Cat" is the catalyst, "P" is the polymer chain, and the diene in this example is 1,5-hexadiene.

[0030] 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 LCB has 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. nis 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.

[0031] 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.

[0032] The term "ladder branched" polymer refers to a polymer formed from a "ladder branching mechanism." As depicted in Scheme 2, the polymer has a tetrafunctional long chain branching structure. In addition, the terms "ladder branched" polymer and "ladder branching mechanism" also refer to polymerization processes that produce trifunctional polymers and trifunctional long chain branching polymers.

[0033] The process of synthesizing tetrafunctional 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. [ka]

[0034] Depending on the catalyst or diene, different intermediates can result from the diene reaction. Previous work has shown the formation of tetrafunctional LCBs by addition of dienes to double-chain catalysts (Scheme 3), but the formation of trifunctional long-chain branches is also possible (Scheme 4). [ka]

[0035] A polymer strand is a linear segment of a polymer, or more specifically a copolymer, optionally joined at its ends 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.

[0036] Without intending to be bound by theory, as explained in this section, the mechanism describes how a dual chain catalyst can produce a unique trifunctional bridged molecular structure when a diene comonomer is polymerized under desired conditions. The term "diene" refers to a monomer or molecule having two alkenes. An illustration of the mechanism is shown in Scheme 5, where the catalytic center produces two polyolefin chains. Scheme 5 shows how a combination of diene bridges and chain transfer can produce a diene "ladder branched" trifunctional polymer structure. The term diene "ladder branched" polymer refers to long chain branches in which short chains or rungs containing 1-12 carbon atoms link two polymer 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 a second polymer chain, thereby forming a bridge or rung. This successive addition of dienes is referred to as "concerted" addition of dienes, and is distinguished 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. [ka]

[0037] As illustrated in Scheme 5, upon introduction of hydrogen gas, trifunctional ladder branching can occur. Introduction of hydrogen gas terminates the polymer chain at one of the polymerization sites of the multi-chain catalyst. Upon termination, the polymer chain is scissioned, thus resulting in a trifunctional polymer. The polymers of the present disclosure contain trifunctional long chain branches arising from the diene of formula (I).

[0038] In one or more embodiments, the ratio of trifunctional to tetrafunctional long chain branches is adjusted to C2-C if the ratio deviates from the target ratio of trifunctional to tetrafunctional long chain branches. 14 The ratio of trifunctional to tetrafunctional branches is adjusted by changing the feed ratio of alkene monomer to hydrogen. In some embodiments, the feed ratio can be changed during the reaction. The ratio of trifunctional to tetrafunctional branches depends on hydrogen. If the concentration of hydrogen increases, the ratio of trifunctional to tetrafunctional branches increases. In addition, when the polymerization process occurs in a solution, the concentration of hydrogen in the solution affects the ratio of trifunctional to tetrafunctional branches. In some embodiments, before starting the polymerization reaction, a certain amount of hydrogen may be introduced into the reactor, and the temperature may be increased or decreased to adjust the ratio of trifunctional or tetrafunctional branches. As the temperature increases, the ratio of hydrogen and C2-C 14 The reactivity of the alkene monomers increases, producing increased amounts of trifunctional long chain branches.

[0039] In one or more embodiments, the ratio of trifunctional to tetrafunctional branches is controlled via adjusting the ethylene / hydrogen ratio in the reactor or other reactor conditions such as temperature. In some embodiments, the ratio of trifunctional to tetrafunctional long chain branches is greater than 0.1:1 to about 100:0.

[0040] 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.

[0041] The combination of multi-chain catalysts and dienes 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, 3) a combination of polymerization environments including multiple reactor zones or zone gradients, or 4) the control and combination of different types of long chain branching, e.g., trifunctional and tetrafunctional long chain branching.

[0042] 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 carbon atom. When 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.

[0043] 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 (a multi-chain catalyst), the close proximity including a distance of less than 8 angstroms (Å), less than 6 Å, or about 5 Å.

[0044] It is well known that modern computational techniques can reproduce known experimental structures with high accuracy as a way to estimate the distance between the chains of the catalyst. The diene structure according to formula (I), where X is -C(R)2-, -Si(R)2-, or -Ge(R)2-, where each R is independently hydrogen or a hydrocarbyl group, allows the size of the diene to be estimated. The end-to-end distance of the diene according to formula (I), where X is -Ge(R)2-, is about 7.5 Å. Thus, the polymerization sites of the multi-chains may be within 8 Å, and in the case of bimetallic catalysts, the two metals may be within 8 Å.

[0045] For heterogeneous systems, the surface concentration of the metal can be estimated, 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 distances, which reflect the distance between polymer chains. For extended surfaces, it is approximately 1 metal / nm 2 This leads to a distance between metal atoms of 10 Å. At 8 Å, there are 1.5 metal atoms / nm 2 A coverage of 100% can be obtained.

[0046] 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, ligated 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.

[0047] 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]

[0048] Without intending to be bound by theory, as explained in this section, the mechanism describes how a dual chain catalyst can produce a unique trifunctional bridged molecular structure when a diene comonomer is polymerized under desired conditions. The term "diene" refers to a monomer or molecule having two alkenes. An illustration of the mechanism is shown in Scheme 5, in which a catalytic center produces two polyolefin chains. Scheme 5 shows how a combination of diene bridges and chain transfer can produce a diene "ladder branched" trifunctional polymer structure. The term diene "ladder branched" polymer refers to long chain branches in which a short chain or rung links two polymer 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.

[0049] In the above embodiments, the polymer of the present disclosure is an ethylene-based copolymer comprising at least 50 mol% ethylene. In the present disclosure, "ethylene-based polymer" refers to a homopolymer of ethylene and / or an interpolymer (including copolymer) of ethylene and optionally one or more comonomers such as α-olefins, and may comprise at least 50 mol% (mol%) of monomer units derived from ethylene. All individual values ​​and subranges encompassed by "from at least 50 mol%" are disclosed herein as separate embodiments, for example, an ethylene-based polymer, a homopolymer and / or interpolymer (including copolymer) of ethylene, and optionally one or more comonomers such as α-olefins, may comprise at least 60 mol% of monomer units derived from ethylene, at least 70 mol% of monomer units derived from ethylene, at least 80 mol% of monomer units derived from ethylene, 50 to 100 mol% of monomer units derived from ethylene, or 80 to 100 mol% of monomer units derived from ethylene.

[0050] kinetics A mathematical model has previously been derived for tetrafunctional "ladder branching" long chain branching and is described in Applications PCTUS2019 / 053524, PCTUS2019 / 053527, PCTUS2019 / 053529, and PCTUS2019 / 053537, each filed on September 27, 2019. Here, the model is derived for trifunctional "ladder branching" long chain branching. 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. Common 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) a catalytic center makes 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 if the drift in composition is negligible.

[0051] Kinetics for the trifunctional "ladder branch" theory of dienes. Model derivation. The first step in deriving a model of a system is to describe the kinetics in symbolic form and show the effect of each reaction on the molecular attributes of interest. It is standard practice to use indices to indicate the number of repeat units associated with a growing (living) or dead polymer chain. Furthermore, it is recognized that the molecular structure of an addition copolymer can be accurately described by homopolymer kinetics and models when the rate constants of the homopolymers are considered as the rate constants of the effective complex copolymerization (Tobita and Hamielec, Polymer 1991, 32(14), 2641).

[0052] P n,mThe kinetics of a simple addition polymerization with a dual-site catalyst, where the active catalytic center grows two polymer molecules, is described below, with the molecule on the left having n repeat units and the molecule on the right having m repeat units. Previous work has investigated the formation of tetrafunctional branches from diene bridges across two growing polymer molecules. In the kinetics below, we consider diene bridges where trifunctional (b3) branches or difunctional linkages (b2) are assumed to be created from diene bridging across two growing molecules. Diene reactions such as cyclization or single insertion are considered to be non-productive and are ignored in the kinetics scheme.

[0053] Kinetics of diene trifunctional and difunctional ladder branching theory. [Table 2]

[0054] The kinetics are described for each of two polymer molecules growing on the catalyst, identified as left and right. The outcome of the growth is the left side (P n+1,m ) or right side (P n,m+1 ) is an incremental increase in molecular size by one repeat unit. Chain transfer reactions involve cleaving a chain from the catalyst and transferring it to the left (D n ) or right side (D m ) to produce dead polymer molecules. Additional simple chain transfer type reactions such as hydrogenation or beta hydride elimination do not add complexity to the model.

[0055] Diene crosslinking reaction k d is written for each catalyst side, and each ratio uses a factor of 2 for the two reactive groups on the diene (D). g is written once on both (2) sides, and the diene (D) uses a factor of 4 in its ratio because it has two reactive sites. Thus, the diene consumption kinetics has a rate constant defined on a group-wise basis rather than a molecular basis.

[0056] It is standard practice to assume that reinitiation of polymer chains occurs very rapidly and relatively infrequently relative to propagation. By assuming instantaneous reinitiation, the species P n,0 , P 0,m , and P 0,0 are essentially excluded from consideration in the polymer population.

[0057] Population balances and rates. A kinetic scheme can be a set of balanced equations that describe how each reaction affects the molecular structure. In describing these balances, it is convenient to use a shorthand notation to represent the rate of each reaction. These rates are defined as follows: Ω=k tra A+k trh H2+k b Only by expanding the definition of the transfer terms such as trh ) and beta hydride desorption (k b ) can be included.

[0058] Defined kinetic rate group: Ω=k tra A Ψ=k d D П=k g D Φ=k p M

[0059] Growing polymer (P n,m ) molecule and dead polymer molecule (D n Discrete population balances for δ are written below for molecular sizes n > 1 and m > 1 using the kinetics groups defined above. These balances can be modified to include additional convective terms, which define the rate of change of molecular population vs. size, and are the balances that apply to a particular reactor environment or type. k The term is used in these discrete balances to specify that the term is included only when K=0.

[0060]

number

number

number

[0061] Other important population balances are on the left (L n ) and right side (R n ) growing polymer subpopulation distribution, and the convolution distribution (V n ) can be derived from above. Due to the symmetry imposed in defining the kinetic scheme, the left and right side distributions of growing polymer subspecies are equal.

[0062]

number

number

[0063] ξ as the total active catalyst concentration 0,0 Using

[0064] During the ceremony,

number

[0065] The first step to a usable model is to determine the proportion of related polymer subspecies (RP n,m ,RL n ,RV n The key to this is to implement a "steady-state assumption" on the distribution of growing polymer species by setting θ to zero. This is a very common assumption in additive polymerization modeling when the lifetime of the growing chains is a small fraction of the time period of interest. In most non-living commercial polymerizations of this type, the reactor residence times are at least several minutes, whereas the chain lifetimes are typically much shorter than a second.

[0066] Method of moments for prediction of MWD mean 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.

[0067] Living Polymer Moment:

number

[0068] Bulk Polymer MWD Moment:

number

[0069] Considering that the rate of change of the rib species was assumed to be zero, the rate of change of the bulk moment is easily derived from the population balance of the dead polymer.

[0070]

number

[0071] It is expected that any skilled polymer reaction engineer can derive a moment model from a series of population balances for the rates of change of the major bulk polymer moments (λ0, λ1, λ2) shown below, after imposing the assumption that the kinetic chains are long, hence Φ>>Ω, Φ>>Ψ, Φ>>П, and removing negligible terms.

[0072]

number

[0073] Evaluation of the rate of change of these bulk moments requires a large number of living polymer subspecies moments. These live polymer moments are algebraic quantities due to the "steady state assumption" and are given below. If higher bulk moments, such as λ3, are predicted, additional live moments are required.

[0074]

number

[0075] Evaluation of moment rates After algebraic simplification, the instantaneous number and weight average chain length (DP n , D.P. w ) is shown 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).

[0076]

number

number

[0077] Branch Metric The expression of this model is the diene-free average linear kinetic chain length DP, which is equal to Φ / Ω. no The model is further simplified by some substitutions such as . The model also includes the fraction of diene junctions that are difunctional, F b This can be further simplified by expressing it in terms of a dimensionless instantaneous branching metric such as b While one might expect that F is approximately constant, it certainly varies with catalyst choice and probably with reaction conditions, so F as a metric bThe use of is reasonable.

number

[0078] An additional metric is needed to describe the relative level of branching, and two options are presented. One preferred option is the ratio of diene junctions to the original polymer molecule, R c The solution is to use R. c One advantage of R is that it is simply a scaling of diene junctions and is expected to increase linearly with diene. kc A disadvantage of is that the original kinetic chain length or concentration is generally only directly available when a series of data involving zero diene branching levels is measured.

number

[0079] Metric R n is the branch metric R kc is an alternative to R n is the ratio of diene junctions to polymer molecules. n The use of R is exploited by the measurability of chain length or concentration through GPC measurement of number average molecular weight. However, bifunctional junctions affect the number of polymer molecules, so R n is not simply proportional to the diene. b =0), the two metrics R kc and R n are identical.

number

[0080] Average chain lengths and molecular weights are reported below in terms of polydispersity, with the diene-free polydispersity index being 2 due to the assumed simplicity and ideality of the kinetics.

[0081]

number

number

number

[0082] F b , R kc , R n Some simple conclusions can be made from the above model when it is expressed as a function of physically significant parameters such as the weight average chain length (DP w ) or molecular weight (M w ) indicates that the incorporation of a diene can only increase the maximum by a factor of 2. Any bifunctional linkage can be n or M n It is predicted to reduce DP w or M w Starting with a zero diene polydispersity of 2, the polydispersity at high trifunctional branching levels (Z p ) is at most 4 and is moderated by the occurrence of any bifunctional linkage.

[0083] Figure 2 shows the relationship between the diene-grafted functionality (F) and the molecular weight and polydispersity of the polymer. b The model demonstrates the effect of a pure trifunctional diene bridge having a limited two-fold potential effect on molecular weight and polydispersity, and the incremental effect is R kc It is clear that the F b If a moderate level of difunctional diene conjugation, such as =5% or 10%, is expected, the experimental data suggest that the diene level and M w It is possible that the authors may not even demonstrate a positive correlation between

[0084] Complete MWD curve model Sometimes it is possible to solve the population balance of the molecular weight distribution curve. An explicit algebraic solution is usually only available if there are no spatial or temporal variations in the reaction rate, as is assumed in this case. Of particular interest is the polymer distribution function D, which was previously used to express a model equation for the moments of the bulk MWD. n Similarly, the instantaneous bulk polymer chain length distribution, X n can be expressed as follows:

[0085] Instantaneous bulk chain length distribution:

number

[0086] Since we are assuming a long chain, the distribution of all species (X n , D n , L n , V n It is possible to treat the population balance of a steady-state polymer species as if it were a continuous function rather than a discrete function. The population balance of a steady-state polymer species can be closely approximated by a differential equation in a continuous variable n when the difference terms are replaced by their derivatives. For example, L n The steady-state population balance with respect to is the difference term L, which is replaced by its derivative as shown below: n -L n-1 Contains:

number

[0087] Similar substitutions result in the following set of ordinary differential equations (ODEs), which can be integrated to yield the chain length distributions for the various predefined rib subspecies distributions L(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.

[0088]

number

number

[0089] Analytical solutions exist for the continuous distribution functions L(n) and V(n), which can be used to express the function for the continuous bulk polymer chain length distribution (X(n)).

[0090]

number

[0091] The solution for X(n) is a bit more complicated, but can be easily expressed as:

number

[0092] The terms have the following assignments:

number

number

number

number

[0093] An alternative assignment for the X(n) function terms is the branching metric (F b , R kc , R n ) The following terms for X(n) can be expressed using F b and R kc is written as a function of the substitution R kc =R n / (1-F b R n ) to obtain R n can be converted to use

[0094] α=1+R kc +1 / 2F b R kc

[0095]

number

number

number

[0096] The integral of X(n) can be used to represent the number and weight average chain length as well as the polydispersity.

number

number

[0097] As expected, integration of the distribution equation X(n) gives results that are in exact agreement with the instantaneous moment model previously expressed for the average degree of polymerization and average molecular weight. The X(n) distribution model does not provide additional or contradictory predictions of the MWD average and polydispersity. However, this complete chain length distribution model can be used to gain an understanding of how nuances in the MWD are affected by diene addition. In particular, the model can predict the modality, steepness, and tailing of the MWD as a function of diene incorporation level and mode of incorporation.

[0098] The limiting case of the MWD model There are two limiting cases for the chain length distribution model. In the trivial case, Fb = 1, and occurs when the polymer is perfectly linear and has the most probable MWD. ​​The resulting average chain length of the most probable MWD decreases with the diene bridge level, which is b = 1, so it is completely bifunctional.

[0099] A more interesting and limiting case is the bifunctional linkage (F b = 0), and the branch metric R kc and R n are identical. Because each diene linkage is a trifunctional branch point, a unique nomenclature can be used for the branched polymer.

[0100] F b If =0, B n = branch points per polymer molecule = R kc =R n

[0101] F b If =0, B c = Branch points per linear chain segment = (1 + B n ) / B n

[0102] This pure trifunctional branch chain length distribution is shown below against B n and B. c As shown in the figure.

[0103] F b If =0,

number

[0104] F b If =0,

number

[0105] The above distribution function is F b= 0, which can be integrated to give an MWD average of 0.05, which is shown below. The number average molecular weight of this trifunctional branched system does not change with increasing diene incorporation because the branching reaction does not change the number of polymer molecules in the system.

number

number

number

[0106] 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.

[0107] The chain length distribution function can again be used to generate predicted MWD curves. c Or B n ) is a series of simulated SEC curves varying. The independent variables in FIG. 3 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. 3 is the known "most likely" MWD and is predicted for linear addition copolymerizations carried out under ideal homogeneous conditions. FIG. 4 is a plot of relative peak MW versus trifunctional diene branching, showing that the MWD peak is greater than 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.

[0108] 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.

[0109] 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

[0110] b) the traditional diene semi-batch branching model, Cozewith-1979 (C. Cozewith, W.W. Graessley, G. Ver Strate, Chem. Eng. Sci. 1979, 34, 245), and d) the polymer batch coupling model, Cozewith-1979, Flory-1953 (P.J.Flory, Principles of Polymer Chemistry, Cornell University Press, 1953), Tobita-1995 (H.Tobita, J.Polym.Sci.B 1995, 33, 1191):

number

number

[0111] c) Polymer CSTR coupling model:

number

[0112] Characterization of trifunctional 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 strain hardening 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.

[0113] To distinguish between trifunctional and tetrafunctional long chain branches, NMR analysis is best. Some dienes allow for diagnostic measures of trifunctional and tetrafunctional long chain branches. The mechanism in Scheme 6 illustrates the difference in the formation of trifunctional and tetrafunctional long chain branches. In this case, the ratio of branches can be controlled by the ratio of ethylene to hydrogen in the reactor. In this particular example, dimethyldivinylsilane has a diagnostic methyl group on the silicon atom, which can be used to determine trifunctional or tetrafunctional long chain branching (see Scheme 6 and Figures 7-9). The carbon on the silicon of the tetrafunctional branched polymer is shifted upfield relative to the carbon on the silicon of the trifunctional branched polymer (see Figure 8). The example shows that control of the ratio of trifunctional to tetrafunctional long chain branches is possible. [ka]

[0114] In addition to hydrogenolysis, termination events such as β-hydride elimination can also lead to trifunctional long chain branches. If β-hydride elimination is the key mechanism, unsaturation must be present, for example as shown as the vinylene group in Scheme 7. Temperature effects can often be used to control intramolecular (β-hydride) versus bimolecular processes (growth of ethylene). [ka]

[0115] Conventional processes incorporating dienes into polymer synthesis systems suffer from the fundamental drawback of gel formation or reactor fouling at high branching levels. The kinetic modeling 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 branching 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 w When 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 ).

[0116] 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.

[0117] Means to account for the high molecular weight tailing effect when dienes are added to the polymerization have been previously disclosed and are described in Applications PCTUS2019 / 053524, PCTUS2019 / 053527, PCTUS2019 / 053529, and PCTUS2019 / 053537, each filed on September 27, 2019. Tetrafunctional "ladder branch" polymers do not exhibit this tailing effect. A series of metrics that quantify the amount of high MW polymer, namely G(79 / 29), G(96 / 08), A(100 / 100), B(100 / 100), C(100 / 100), D(100 / 100), E(100 / 100), F(100 / 100), G ... HIGH , and A TAIL has been previously disclosed (see FIG. 5). The term "high MW tailing" or "high molecular weight tail" refers to the high molecular weight fraction as shown by conventional and absolute GPC. Depending on the catalyst and diene pairing and the experimental conditions, it can be expected that the "ladder branching" 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".

[0118] A HIGH Or A TAIL The value defined by increases dramatically as the conventional branching level increases. However, the "ladder branching" model (tetrafunctional or trifunctional) does not provide a high MW area metric (A HIGH Or A TAIL ) is largely unaffected by the "ladder branch" level. HIGH and A TAIL The values ​​of A and B are approximately 0.07 and 0.015, respectively. The exemplary MWD data shows that the diene-free linear polymers have low A due to non-ideal aspects of the polymerization. HIGH and A TAIL The exemplary data also show that a variety of highly branched "ladder-branched" polymers 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 AHIGH It is less affected by linear MWD non-idealities than HIGH Metric and A TAIL The metrics equally indicate high MW tail formation.

[0119] Trifunctional long chain branched polyolefin Polymers produced from "ladder branches," as depicted in Scheme 4, are included in the present disclosure.

[0120] In some embodiments, the polymers of the present disclosure have a level of trifunctional long chain branching greater than 0.1 per 1000 carbon atoms. In some embodiments, the polymers of the present disclosure have a level of trifunctional long chain branching greater than 0.2 per 1000 carbon atoms, greater than 0.3 per 1000 carbon atoms, greater than 0.4 per 1000 carbon atoms, or greater than 0.5 per 1000 carbon atoms.

[0121] In embodiments, the ethylene-based polymers of the present disclosure have a melt viscosity ratio or rheology ratio (V 0.1 / V 100 ), including V 0.1 is the viscosity of the ethylene-based polymer at 190 °C at an angular frequency of 0.1 rad / s, and V 100 is the viscosity of the ethylene-based polymer at 190° C. at 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.

[0122] "Rheology ratio" and "melt viscosity ratio" are V at 190°C. 0.1 / V 100 is defined by V 0.1 is the viscosity of the ethylene-based polymer at 190 °C at an angular frequency of 0.1 rad / s, and V 100 is the viscosity of the ethylene-based polymer at 190° C. at an angular frequency of 100 rad / sec.

[0123] 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 0.55 to 0.86. All individual values ​​and subranges within "0.55 to 0.86" are disclosed herein as separate embodiments, and for example, the average g' of the ethylene-based polymers can range from 0.64 to 0.75, 0.58 to 0.79, or 0.65 to 0.83. In one or more embodiments, the average g' is 0.55 to 0.84, 0.59 to 0.82, or 0.66 to 0.80.

[0124] 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.

[0125] 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.

[0126] In one or more embodiments, the polymers of the present disclosure have a weight average molecular weight (M) of 800,000 Daltons or less, as determined by gel permeation chromatography using a triple detector. wIn various embodiments, the polymer may have a weight average molecular weight (M) of 400,000 daltons or less, 200,000 daltons or less, or 150,000 daltons or less, as determined by gel permeation chromatography using a triple detector. w ).

[0127] In one or more embodiments, the polymers of the present disclosure have an M of 6 or less as determined by gel permeation chromatography using a triple detector. w / M n (weight average molecular weight / number average molecular weight). In various embodiments, the polymers may have an M of less than 5, or less than 4, as determined by gel permeation chromatography using a triple detector. w / M n In some embodiments, the MWD of the long chain branched polymer is from 1 to 3, while other embodiments include an MWD of from 1.5 to 2.5.

[0128] 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.

[0129] 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.

[0130] 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-l-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.

[0131] 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.

[0132] 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.

[0133] 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.

[0134] 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.

[0135] 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.

[0136] 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 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.

[0137] 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.

[0138] 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 contain from about 0 to about 20 percent by weight of a filler, such as, for example, calcium carbonate, talc, or Mg(OH)2, based on the total weight of the ethylene-based polymer and all additives or fillers. The ethylene-based polymer may be further compounded with one or more polymers to form a blend.

[0139] In some embodiments, a long chain polymerization process for producing a long chain branched polymer may comprise polymerizing ethylene and at least one additional α-olefin in the presence of a catalyst having two polymer forming sites. The long chain branched polymer obtained from such a catalyst system having two polymer forming sites has a molecular weight of, for example, 0.850 g / cm according to ASTM D792, which is incorporated herein by reference in its entirety. 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 density of the sintered body may be 0.01 to 0.01.

[0140] In another embodiment, the long chain branched polymer obtained from the long chain polymerization process has a melt flow ratio (I 10 / I2), where I2 is measured according to ASTM D1238 under 190° C. and a load of 2.16 kg (herein incorporated by reference in its entirety), and I 10 is measured according to ASTM D1238 at 190° C. and a load of 10 kg. In another embodiment, the melt flow ratio (I 10 In some, the melt flow ratio is 5-25, and in others, the melt flow ratio is 5-9.

[0141] 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 at 160 degrees Celsius and the column compartment was set at 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 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.

[0142] 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 8,400,000, arranged in six "cocktail" mixtures with at least 10 intervals between each molecular weight. Standards were purchased from Agilent Technologies. Polystyrene standards were prepared at 0.025 grams in 50 milliliters of solvent for molecular weights of 1,000,000 and above, and 0.05 grams in 50 milliliters of solvent for molecular weights below 1,000,000. The polystyrene standards were dissolved at 80 degrees Celsius for 30 minutes with gentle agitation. The polystyrene standard peak molecular weights were converted to polyethylene molecular weights using Equation 48 (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 (48) where M is the molecular weight, A has a value of 0.4315, and B is equal to 1.0.

[0143] A polynomial between third and fifth order was used to fit each polyethylene equivalent calibration point, with A adjusted slightly (approximately 0.415 to 0.44) to correct for column resolution and band broadening effects, such as the NIST standard NBS1475 obtained at 52,000 Mw.

[0144] 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 49) and symmetry (Equation 50) were measured with a 200 microliter injection according to the following equations:

number

number

[0145] Samples were prepared in a semi-automated fashion using the PolymerChar "Instrument Control" software: 2 mg / ml sample target weight was used to add solvent (containing 200 ppm BHT) via the PolymerChar high temperature autosampler to a septa-capped vial that had been pre-sparged with nitrogen. Samples were dissolved at 160 degrees Celsius with "slow" shaking for 2 hours.

[0146] M n(GPC) , M w(GPC) , and M. z(GPC) The calculations were based on GPC results obtained using the internal IR5 detector (measurement channel) of a PolymerChar GPC-IR chromatograph according to Equations 51-53 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) from Equation 1.

number

number

number

[0147] 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 RV matching 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 7. Processing of the flow marker peaks was performed by PolymerChar GPCOne™ software. An acceptable flow correction is that the effective flow rate should be within + / - 2% of the apparent flow rate. Flow (effective) = Flow (apparent) * (RV(FM calibrated) / RV(FM sample)) (54)

[0148] 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).

[0149] 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.

[0150] 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).

[0151] 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 55-56 as follows:

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[0152] Dynamic Mechanical Spectroscopy (or Small Angle Oscillatory Shear) The complex viscosity (η*), elastic modulus (G', G"), tangent delta, and phase angle (δ) are obtained by dynamic oscillatory frequency sweep testing in the frequency range of 0.1-100 rad / s at 190 °C. The level of strain is set within the linear viscoelastic region identified by strain sweep testing at 100 rad / s at 190 °C. The tests are performed using stainless steel parallel plates of 25 mm diameter on a strain-controlled rheometer ARES-G2 from TA Instruments. Prior to the actual test, the samples with a thickness of 3.3 mm are drawn 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 soak at 190 °C for 2.5 minutes, the samples are drawn to a gap of 2 mm and the excess material is trimmed. The method incorporates an additional delay of 5 minutes to allow the system to reach temperature equilibrium. The tests are performed under a nitrogen atmosphere.

[0153] 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 (57) and (58).

number

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[0154] 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 light scattering detector signal to concentration detector signal required in traditional g' determination. Sample intrinsic viscosity was also obtained independently using TDGPC using Eq. (59). The area calculation in this case provides greater accuracy since it is less sensitive to detector noise and fluctuations caused by TDGPC settings to the baseline and integration limits as the overall sample area. More importantly, the peak area calculation was not affected by detector volume offsets. Similarly, highly accurate sample intrinsic viscosity (IV) was obtained by the area method in Eq. (59).

number

[0155] In equation (59), 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.

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[0156] 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 values ​​of are 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 ​​have been determined using the procedure discussed.

[0157] 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.

[0158] 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 calculated as 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.

[0159] NMR analysis Sample preparation: The raw polymer samples contained solvent and catalyst residues that had to be removed prior to NMR measurements of unsaturation and branching. The polymer was first dissolved in tetrachloroethane (TCE) at 120-125 °C, then precipitated using 3-propanol (IPA) and cooled to room temperature. The polymer was isolated by centrifugation. This process of washing the polymer was repeated at least three times. The resulting polymer was then dried in a vacuum oven at 50 °C.

[0160] Approximately 70 mg of the washed and dried polymer was placed in a 10 mm NMR tube with 2.8 ml of TCE. The sample was purged by bubbling house nitrogen through the sample for 15 minutes. The purged sample was then placed in an aluminum heating block at 125°C.

[0161] For bifurcation analysis, a single pulse of the sample 13 C NMR spectra were acquired at 120 °C using a 600 MHz Bruker Avance III HD spectrometer equipped with a 10 mm 13C / 1H DUL CryoProbe, collecting 1400–5000 scans with 90 pulses and a total relaxation delay of 10 s (AQ+D1).

[0162] A single pulse of the sample for quantification of tetrafunctional and trifunctional long chain branches in polymers made using dimethyldivinylsilane as the diene 13 C NMR spectra were acquired at 120 °C using a 600 MHz Bruker Avance III HD spectrometer equipped with a 10 mm C / H DUL CryoProbe to collect 960-5000 scans with 90 pulses and a total relaxation delay of 12 seconds (AQ+D1). Alternatively, QA-RINEPT spectra (J. Hou, Y. He, X. Qiu, Macromolecules, 2017, 50, 2407-2414) were acquired using a 7 second relaxation delay. The parameters QA-RINEPT were chosen to match the methyl to total carbon ratio for QA-RINEPT and the single pulse data.

[0163] Methods for data processing and assignment. All NMR data were processed using Mnova using a linewidth of 0.5 Hz for proton spectra and 3 Hz for carbon spectra. Proton data were referenced to the TCE solvent resonance at 5.99 ppm. Carbon spectra were referenced to the main CH2 of the polymer at 29.99 ppm.

[0164] Virtual assignments for the trifunctional LCB (-3.36 ppm) and tetrafunctional LCB silylmethyl (-4.06 ppm) were obtained using an ACD C NMR predictor and were found to be in close agreement with the observed resonances. These assignments were confirmed using quantitative relationships between the branched methine resonances (tetrafunctional at 24.9 ppm, trifunctional at 25.7 ppm) and the resonance to the CH2 carbon alpha to the Y-branched silicon (~15.3 ppm).

[0165] 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 and the second containing Q5. Ethylene is passed through A204 alumina and 4

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[0166] 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 with a micromotion flow meter. In some experiments, standard conditions at 150°C are 13g ethylene, 15g 1-octene, and 240 psi hydrogen in 585g IsoparE, and standard conditions at 150°C are 15g ethylene, 45g 1-octene, and 200 psi hydrogen in 555g IsoparE.

[0167] 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.

[0168] Example from a batch reactor [ka]

[0169] Batch Reactor Example 1 In Table 2, the polymer properties of the comparative linear polymer sample (1.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 150° C., 585 g of ISOPAR-E™, 15 g of octene, and 240 psi of hydrogen pressure (ΔH2). 14 g of ethylene was charged and the pressure was maintained in the presence of 0.3 micromoles of catalyst 1, 0.36 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 3] [Table 4]

[0170] Table 2 collects data on the comparative example, 1.C, and other diene examples, 1.1-1.7. The NMR data demonstrates both tri- and tetra-functional LCBs, and increasing levels of LCBs with increasing diene.

[0171] FIG. 6 illustrates conventional molecular weight distributions of examples using different amounts of diene.

[0172] Batch Reactor Example 2 In Table 3, the polymer properties of the comparative linear polymer sample (2.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 150° C., 585 g of ISOPAR-E™, 15 g of octene, and 240 psi of hydrogen pressure (ΔH2). 15 g of ethylene was charged and pressure was maintained in the presence of 0.3 micromoles of catalyst 1, 0.36 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 5] [Table 6]

[0173] Table 3 collects data for Comparative Example 2.C and Diene Example 2.1. The NMR data demonstrates both tri- (0.15 LCB / 1000C) and tetra- (0.10 LCB / 1000C) functionality in a ratio of 1.4:1 (3:4 LCB).

[0174] Dynamic mechanical spectra of branched Example 2.1 were measured and the results are recorded in Table 3. The viscosity at 0.1 rad / sec was determined to be 609,361 Pa s, the viscosity at 100 rad / sec was measured to be 2,453 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0175] Batch Reactor Example 3 In Table 4, the polymer properties of the comparative linear polymer sample (3.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 140° C., 585 g ISOPAR-E™, 15 g octene, and 240 psi hydrogen pressure (ΔH2). 10 g ethylene was charged and pressure was maintained in the presence of 0.3 micromoles of catalyst 1, 0.36 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 7] [Table 8]

[0176] Table 4 collects data for Comparative Example 3.C and Diene Example 1.1. The NMR data demonstrates both tri- (0.23 LCB / 1000C) and tetra- (0.13 LCB / 1000C) functionality in a ratio of 1.8:1 (3:4 LCB).

[0177] Dynamic mechanical spectra of branched Example 3.1 were measured and the results are recorded in Table 4. The viscosity at 0.1 rad / sec was determined to be 515,022 Pa s, the viscosity at 100 rad / sec was measured to be 2,140 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0178] Batch Reactor Example 4 In Table 5, the polymer properties of the comparative linear polymer sample (4.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 150° C., 585 g of ISOPAR-E™, 15 g of octene, and 160 psi of hydrogen pressure (ΔH2). 15 g of ethylene was charged and the pressure was maintained in the presence of 0.4 micromoles of catalyst 1, 0.48 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 9] [Table 10]

[0179] Table 5 collects data for Comparative Example 4.C and Diene Example 4.1. The NMR data demonstrates both tri- (0.31 LCB / 1000C) and tetra- (0.30 LCB / 1000C) functionality in a ratio of 1.03:1 (3:4 LCB).

[0180] Dynamic mechanical spectra of branched Example 4.1 were measured and the results are recorded in Table 5. The viscosity at 0.1 rad / sec was determined to be 867,379 Pa s, the viscosity at 100 rad / sec was measured to be 2,818 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0181] Batch Reactor Example 5 In Table 6, the polymer properties of the comparative linear polymer sample (5.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 160° C., 585 g of ISOPAR-E™, 15 g of octene, and 80 psi of hydrogen pressure (ΔH2). 15 g of ethylene was charged and pressure was maintained in the presence of 0.4 micromoles of catalyst 1, 0.48 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 11] [Table 12]

[0182] Table 6 collects data for Comparative Example 5.C and Diene Example 5.1. The NMR data demonstrates both tri- (0.25 LCB / 1000C) and tetra- (0.30 LCB / 1000C) functionality in a ratio of 0.8:1 (3:4 LCB).

[0183] Dynamic mechanical spectra of branched Example 5.1 were measured and the results are recorded in Table 6. The viscosity at 0.1 rad / sec was determined to be 813,746 Pa s, the viscosity at 100 rad / sec was measured to be 2,742 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0184] Batch Reactor Example 6 In Table 7, the polymerization reaction for Example 6.1 occurred at a temperature of 150° C., 585 g ISOPAR-E™, 15 g octene, and 240 psi hydrogen pressure (ΔH2). 13 g ethylene was charged and pressure was maintained in the presence of 0.3 micromoles of catalyst 1, 0.36 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. In Table 7, the polymerization reaction for Example 6.2 occurred at a temperature of 160° C., 600 g ISOPAR-E™, no octene, and 240 psi hydrogen pressure (ΔH2). 13 g of ethylene was charged and pressure was maintained in the presence of 0.4 micromoles of catalyst 1, 0.48 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Dienedimethyldivinylsilane was added as indicated in the table. In Table 7, the polymerization reaction for Example 6.3 occurred at a temperature of 160° C., 600 g of ISOPAR-E™, no octene, and a hydrogen pressure (ΔH2) of 240 psi. 13 g of ethylene was charged and pressure was maintained in the presence of 0.4 micromoles of catalyst 2, 0.48 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Dienedimethyldivinylsilane was added as indicated in the table. [Table 13] [Table 14]

[0185] Table 7 collects data for diene examples 6.1, 6.2, and 6.3. Examples 6.2 and 6.3 show that different catalysts can form different amounts of trifunctional LCBs and different ratios of trifunctional LCBs:tetrafunctional LCBs. For examples under the same conditions, catalyst 1 (example 6.2) and catalyst 2 (example 6.3) had trifunctional LCB levels of 0.26 LCB / 1000C and 0.07 LCB / 1000C, and trifunctional:tetrafunctional LCB ratios of 2.2:1 and 0.4:1, respectively. The amount of trifunctional LCBs and the ratio of trifunctional:tetrafunctional LCBs are highly dependent on the catalyst.

[0186] Examples 6.1 and 6.2 show polymerizations carried out under comparable conditions with the important difference that Example 6.1 contains octene while Example 6.2 does not contain octene. The amount of trifunctional LCB and the ratio of trifunctional:tetrafunctional LCB are very similar in the two runs.

[0187] The dynamic mechanical spectrum of Example 6.1 was measured and the results are recorded in Table 7. The viscosity at 0.1 rad / sec was determined to be 306,441 Pa s, the viscosity at 100 rad / sec was measured to be 1,754 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0188] Batch Reactor Example 7 In Table 8, the polymer properties of the comparative linear polymer sample (7.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 160° C., with 580 g of ISOPAR-E™, 20 g of octene, and no hydrogen. 11 g of ethylene was charged and pressure was maintained in the presence of 0.7 micromoles of catalyst 1, 0.84 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Dienedimethyldivinylsilane was added as indicated in the table. [Table 15] [Table 16]

[0189] Table 8 collects data for Comparative Example 7.C and Diene Example 7.1. NMR data demonstrated that there was no trifunctionality in this example in the absence of hydrogen. Tetrafunctional LCB was present (0.14LCB / 1000C) and the trifunctional:tetrafunctional ratio is zero.

[0190] The dynamic mechanical spectrum of Example 7.1 was measured and the results are recorded in Table 8. The viscosity at 0.1 rad / sec was determined to be 475,848 Pa s, the viscosity at 100 rad / sec was measured to be 1,982 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0191] Batch Reactor Example 8 In Table 9, the polymer properties of the comparative linear polymer sample (8.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 160° C., 580 g ISOPAR-E™, 20 g octene, and 28 psi hydrogen pressure (ΔH2). 13 g ethylene was charged and pressure was maintained in the presence of 0.7 micromoles of catalyst 1, 0.84 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 17] [Table 18]

[0192] Table 9 collects data for Comparative Example 8.C and Diene Example 8.1. The NMR data demonstrates both tri- (0.09 LCB / 1000C) and tetra- (0.11 LCB / 1000C) functionality in a ratio of 0.8:1 (3:4 LCB).

[0193] The dynamic mechanical spectrum of Example 8.1 was measured and the results are recorded in Table 9. The viscosity at 0.1 rad / sec was determined to be 721,022 Pa s, the viscosity at 100 rad / sec was measured to be 2,297 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0194] Batch Reactor Example 9 In Table 10, the polymer properties of the comparative linear polymer sample (9.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 160° C., 580 g of ISOPAR-E™, 20 g of octene, and 46 psi of hydrogen pressure (ΔH2). 13 g of ethylene was charged and the pressure was maintained in the presence of 0.7 micromoles of catalyst 1, 0.84 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 19] [Table 20]

[0195] Table 10 collects data for Comparative Example 9.C and Diene Example 9.1. The NMR data demonstrates both tri- (0.09 LCB / 1000C) and tetra- (0.10 LCB / 1000C) functionality in a ratio of 0.9:1 (3:4 LCB).

[0196] The dynamic mechanical spectrum of Example 9.1 was measured and the results are recorded in Table 10. The viscosity at 0.1 rad / sec was determined to be 697,565 Pa s, the viscosity at 100 rad / sec was measured to be 2,782 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0197] Batch Reactor Example 10 In Table 11, the polymer properties of the comparative linear polymer sample (10.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 160° C., 575 g of ISOPAR-E™, 25 g of octene, and 83 psi of hydrogen pressure (ΔH2). 14 g of ethylene was charged and the pressure was maintained in the presence of 0.6 micromoles of catalyst 1, 0.72 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 21] [Table 22]

[0198] Table 11 collects data for Comparative Example 10.C and Diene Example 10.1. The NMR data demonstrates both tri- (0.07 LCB / 1000C) and tetra- (0.10 LCB / 1000C) functionality in a ratio of 0.7:1 (3:4 LCB).

[0199] The dynamic mechanical spectrum of Example 10.1 was measured and the results are recorded in Table 11. The viscosity at 0.1 rad / sec was determined to be 240,894 Pa s, the viscosity at 100 rad / sec was measured to be 1,642 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0200] Batch Reactor Example 11 In Table 12, the polymer properties of the comparative linear polymer sample (11.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 150° C., 575 g of ISOPAR-E™, 25 g of octene, and 160 psi of hydrogen pressure (ΔH2). 14 g of ethylene was charged and the pressure was maintained in the presence of 0.4 micromoles of catalyst 1, 0.48 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 23] [Table 24]

[0201] Table 12 collects data for Comparative Example 11.C and Diene Example 11.1. The NMR data demonstrates both tri- (0.09 LCB / 1000C) and tetra- (0.06 LCB / 1000C) functionality in a ratio of 1.5:1 (3:4 LCB).

[0202] The dynamic mechanical spectrum of Example 11.1 was measured and the results are recorded in Table 12. The viscosity at 0.1 rad / sec was determined to be 203,979 Pa s, the viscosity at 100 rad / sec was measured to be 1,523 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided.

[0203] The measured melt strength of the polymer of Example 11.1 was 18 cN at an extensibility of 32 mm / sec.

[0204] Batch Reactor Example 12 In Table 13, the polymer properties of the comparative linear polymer sample (12.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 150° C., 570 g of ISOPAR-E™, 30 g of octene, and 240 psi of hydrogen pressure (ΔH2). 20 g of ethylene was charged and the pressure was maintained in the presence of 0.3 micromoles of catalyst 1, 0.36 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 25] [Table 26]

[0205] Table 13 collects data for Comparative Example 12.C and Diene Example 12.1. The NMR data demonstrates both tri- (0.08 LCB / 1000C) and tetra- (0.06 LCB / 1000C) functionality in a ratio of 1.3:1 (3:4 LCB) (see Figures 7-9).

[0206] The conventional absolute molecular weights of Example 12.C and Example 12.1 are plotted in FIG.

[0207] The extensional viscosity fixture (EVF) for Example 12.1 is shown in FIG.

[0208] The measured melt strength of the polymer of Example 12.1 was 19 cN at an extensibility of 32 mm / sec (see Figure 12).

[0209] The dynamic mechanical spectrum of Example 12.1 was measured and the results are recorded in Table 13. The viscosity at 0.1 rad / sec was determined to be 395,948 Pa s, the viscosity at 100 rad / sec was measured to be 2,075 Pa s, and the rheological ratio (V 0.1 / V 100 ) was provided (see FIG. 13).

[0210] Batch Reactor Example 13 In Table 14, the polymer properties of the comparative linear polymer sample (13.C) are compared to the branched polymer from the batch reactor. The polymerization reaction took place at a temperature of 150° C., 585 g of ISOPAR-E™, 15 g of octene, and 240 psi of hydrogen pressure (ΔH2). 11 g of ethylene was charged and the pressure was maintained in the presence of 0.4 micromoles of catalyst 1, 0.48 micromoles of cocatalyst A (methyldi(tetradecyl)ammonium tetrakis(pentafluorophenyl)borate), and 10 micromoles of MMAO-3A. ​​Diene dimethyldivinylsilane was added as indicated in the table. [Table 27] [Table 28]

[0211] Table 14 collects data for Comparative Example 13.C and Diene Example 13.1. The NMR data demonstrates both tri- (0.12 LCB / 1000C) and tetra- (0.07 LCB / 1000C) functionality in a ratio of 1.7:1 (3:4 LCB).

[0212] The dynamic mechanical spectrum of Example 13.1 was measured and the results are recorded in Table 14. The viscosity at 0.1 rad / sec was determined to be 53,390 Pa s, the viscosity at 100 rad / sec was measured to be 887 Pa s, and the rheology ratio (V 0.1 / V 100 ) was provided.

[0213] The measured melt strength of the polymer of Example 13.1 was 10 cN at an extensibility of 65 mm / sec.

[0214] Examples 7 (Table 8) through 13 (Table 14) show that for a given catalyst and comparable conditions, the ratio of tri- to tetra-functional LCBs can be controlled by the ratio of hydrogen to ethylene in the reactor, supporting the mechanism in Scheme 6.

[0215] Examples 7 (Table 8) to 13 (Table 14) show that as the ratio of trifunctional to tetrafunctional LCB increases, M w / M w0 It was shown that M w is the weight average molecular weight of the diene branched sample, and M w0 is the weight average molecular weight of the unbranched comparative sample. When a higher proportion of trifunctional branches is included, M w The increase in β-aminobutyric acid (β-aminobutyric acid) is reduced, supporting the trifunctional kinetic model herein and the previously derived tetrafunctional model described in Application Nos. PCTUS2019 / 053524, PCTUS2019 / 053527, PCTUS2019 / 053529, and PCTUS2019 / 053537, each filed on September 27, 2019.

[0216] 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-2010 was described in detail in 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. The Guzman-2010 data was collected at steady state while the CSTR was operated at a pressure of 525 psig, a temperature of 155° C., and over a range of diene feed concentrations. The various steady-state polymer samples collected by Guzman-2010 did not contain 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.

[0217] In Guzman-2010, a selected series of data was compiled for 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.

[0218] According to the data from Guzman-2010, I2 and I 10It was demonstrated how changing the level of conventional diene branching affects properties such as average molecular weight and polydispersity as well as viscosity, as reflected by the . The effect of conventional diene branching on molecular weight was shown for both absolute and conventional MWD measurement techniques. Absolute MWD measurements are the preferred method for branched polymers, but are not always available. Therefore, Guzman-2010 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.

[0219] Although not reported in Guzman-2010, MWD curves were found and plotted in Figures 14A and 14B for absolute and conventional GPC measurement techniques, respectively. The MWD curve data in Figure 14 shows the expected high M from conventional diene branching. w The lack of significant movement of the peak MW with increasing diene branching is also evident from the MWD curves, demonstrating that tail formation has occurred.

[0220] The molecular weight distribution data in Figures 14A and 14B were reduced to a simple metric that describes the evolution of the position and shape of the MWD curve as more diene monomer is fed to the CSTR. The data showed MWD metrics for both absolute and conventional MWD measurements of Guzman-2010 polymer samples. The absolute MWD measurement data showed up to an 87% increase in molecular weight when the 1,9-decadiene feed amount ranged from 0 to 923 ppm. M 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 (Guzman-2010) and are a function of diene feed level and M w As increases, G 79 / 29 and A TAILThe shape factor is not consistent with a "ladder branched" polymer since the values ​​for both are increased.

[0221] It will be apparent to those skilled in the art that various modifications can be made to the described embodiments without departing from the spirit and scope of the claimed subject matter. Thus, it is intended that this specification cover modifications and variations of the described embodiments provided such modifications and variations come within the scope of the appended claims and their equivalents.

Claims

1. 1. A process for synthesizing a long chain branched polymer, comprising: One or more C ２ -C １４ Contacting together an alkene monomer, at least one diene, optionally a solvent, and a multi-chain catalyst in the presence of hydrogen, wherein the multi-chain catalyst is not a bimetallic catalyst and comprises at least two polymerization sites less than 8 angstroms (Å) apart, and the diene has the formula (I): 【Chemistry 1】 wherein X is -C(R) ２ -, -Si(R) ２ - or -Ge(R) ２ -, each R is independently C １ -C １２ contacting, Said C ２ -C １４ producing at least two polymer chains of an alkene monomer, each polymer chain polymerizing at one of said polymerization sites; synthesizing the long chain branched polymer by connecting the two polymer chains with the diene, wherein the connecting of the two polymer chains is performed in a concerted manner during polymerization, and the long chain branched polymer has a ratio of trifunctional to tetrafunctional long chain branches of 0.05:1 to 100:0; If the ratio deviates from the target ratio of trifunctional to tetrafunctional long chain branches, the C ２ -C １４ and adjusting said ratio of trifunctional to tetrafunctional long chain branches by varying the feed ratio of alkene monomer to hydrogen.

2. X in formula (I) is -C(R) ２ - and each R is -H.

3. X in formula (I) is -C(R) ２ -, each R is C １ -C １２ 2. The process of claim 1 , wherein the alkyl group is an alkyl group.

4. In formula (I), X is -Si(R) ２ -, each R is C １ -C １２ 2. The process of claim 1 , wherein the alkyl group is an alkyl group.

5. 5. The process of claim 4, wherein the diene is dimethyldivinylsilane.

6. The process of any one of claims 1 to 5, wherein the long chain branched polymer is an ethylene-based copolymer comprising at least 50 mol % ethylene.

7. The multi-chain catalyst has a density of 1.5 metal atoms per square nanometer (metal / nm ２ 7. The process of claim 1, wherein the catalyst is a heterogeneous catalyst having a surface concentration of metal atoms of at least 10000000000.

8. 8. The process of any one of claims 1 to 7, wherein the multi-chain catalyst comprises a monoanionic ligand and an IUPAC Group IV metal selected from the group consisting of titanium, hafnium, or zirconium.

9. The process of any one of claims 1 to 8, wherein the trifunctional long chain branches occur at a frequency of at least 0.05 per 1000 carbon atoms.

10. 10. The process of any one of claims 1 to 9, wherein the trifunctional long chain branches occur at a frequency of at least 0.1 per 1000 carbon atoms.

11. The process of any one of claims 1 to 10, wherein the trifunctional long chain branches occur at a frequency of at least 0.2 per 1000 carbon atoms.

12. The process of any one of claims 1 to 11, wherein the ratio of trifunctional to tetrafunctional long chain branches is greater than 0.1:

1.

13. Controlling the ratio of trifunctional and tetrafunctional long chain branches is ２ 13. The process of any one of claims 1 to 12, comprising increasing the amount of trifunctional long chain branching.

14. Controlling the ratio of trifunctional and tetrafunctional long chain branches is ２ -C １４ 14. The process of claims 1-13 comprising adjusting the feed ratio of alkene monomer to hydrogen to greater than 999:1 to provide less than 0.001:1 tri- to tetra-functional long chain branches.

15. Controlling the ratio of trifunctional and tetrafunctional long chain branches is ２ -C １４ 14. The process of claims 1-13, comprising adjusting the feed ratio of alkene monomer to hydrogen to less than 25:1 to provide greater than 0.5:1 tri- to tetra-functional long chain branches.

16. Controlling the ratio of trifunctional and tetrafunctional long chain branches is ２ -C １４ 14. The process of claims 1-13, comprising adjusting the feed ratio of alkene monomer to hydrogen to less than 50:50 to provide greater than 1:1 tri- to tetra-functional long chain branches.

17. The long chain branched polymer has a weight average molecular weight (M) of less than 150,000 Daltons as determined by gel permeation chromatography using a triple detector. ｗ 17. The process according to any one of claims 1 to 16, comprising:

18. 18. The process of any one of claims 1 to 17, wherein the polymerization occurs in a solution polymerization reactor, a slurry reactor, a gas phase reactor, a batch reactor, a continuous reactor, a hybrid reactor, a non-backmixed reactor, a backmixed reactor, a series reactor, or a recycle reactor.

19. The long chain branched polymer has a weight average molecular weight (M) divided by the number average molecular weight of less than 4, as determined by gel permeation chromatography using a triple detector. ｗ / M ｎ The process of any one of claims 1 to 18, wherein the copolymer has a molecular weight distribution (MWD) defined by:

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