Abstract: An ultra-high molecular weight, ultra-fine particle size polyethylene has a viscosity average molecular weight (Mv) greater than 1×106. The polyethylene is spherical or are sphere-like particles having a mean particle size of 10-100 ?m, having a standard deviation of 2-15 ?m and a bulk density of 0.1-0.3 g/mL. Using the polyethylene as a basic polyethylene, a grafted polyethylene can be obtained by means of a solid-phase grafting method; and a glass fiber-reinforced polyethylene composition comprising the polyethylene and glass fibers, and a sheet or pipe prepared therefrom; a solubilized ultra-high molecular weight, ultra-fine particle size polyethylene; and a fiber and a film prepared from the solubilized ultra-high molecular weight, ultra-fine particle size polyethylene may also be obtained. The method has simple steps, is easy to control, has a relatively low cost and a high repeatability, and can realize industrialisation.

Abstract: The invention relates to a multifilament yarn containing n filaments, wherein the filaments are obtained by spinning an ultra-high molecular weight polyethylene (UHMWPE), said yarn having a tenacity (Ten) as expressed in cN/dtex of Ten(cN/dtex)=f×n?0.05×dpf?0.15, wherein Ten is at least 39 cN/dtex, n is at least 25, f is a factor of at least 58 and dpf is the dtex per filament.

Abstract: The present invention relates to a high-density ethylene-based polymer comprising an ethylene homopolymer or a copolymer of ethylene and at least one comonomer selected from the group consisting of an ?-olefin, a cyclic olefin, and a straight, branched and cyclic diene. According to the present invention, the high-density polyethylene resin has a wide molecular weight distribution and excellent comonomer distribution characteristics, has excellent melt flowability due to a long chain branched structure, and has excellent mechanical characteristics since the comonomer distribution is concentrated in a high-molecular-weight body. The high-density ethylene polymer of the present invention has excellent molding processability during processing such as extrusion, compression, injection and rotational molding by having excellent mechanical characteristics and melt flowability.

Abstract: The present invention relates to a process for operating a polymer powder degasser vessel, and in particular provides a process for operating a polymer powder degasser vessel which vessel comprises a silo comprising a main vertical cylinder and a hopper at the bottom of the cylinder, there being a polymer powder withdrawal pipe connected to the hopper by which polymer powder is withdrawn from the hopper, and wherein the silo contains a polymer powder which occupies less than 45% of the volume of the silo and the polymer powder passes through the polymer powder degasser vessel in a mass flow manner, further wherein at least one of the following is applied: i) polymer powder is withdrawn from the hopper and recirculated to the silo, wherein the recirculation rate of the polymer powder is at least 30 percent per hour of the polymer powder present in the silo, and ii) a purge gas is provided to the silo via the polymer powder withdrawal pipe or via an inlet located on the hopper at a vertical height which is less

Abstract: Biocompatible and implantable in the human body plastic material, for the obtainment of a device that can be implanted in the human body or a spacer device in order to treat a bone or a joint location, including an acrylic resin or polyethylene (PE) or low density polyethylene or high density polyethylene or ultra-high molecular weight polyethylene (UHMWPE) or polypropylene or polyamide or polyetheretherketone (PEEK) or a thermosetting resin or a mixture of the same, wherein the material can be molded and includes at least one pharmaceutical or medical substance; device implantable in the human body or spacer device for treating a bone or a joint location, obtained by the material above and method for manufacturing the material according to the present invention.

Abstract: A polymer composition for producing gel extruded articles is described. The polymer composition contains polyethylene particles combined with a plasticizer. The polyethylene particles are particularly selected so that the particles rapidly form a homogeneous gel-like material when combined with the plasticizer during gel processing. In one embodiment, the polyethylene used to produce the particles has a relatively low bulk density. Alternatively or in addition, the particles can have a carefully controlled particle size distribution. Polymer articles such as fibers and films can be produced having little to no imperfections.

Abstract: The instant invention is a high-density polyethylene composition, method of producing the same, injection molded articles made therefrom, and method of making such articles. The high-density polyethylene composition of the instant invention includes a first component, and a second component. The first component is a high molecular weight ethylene alpha-olefin copolymer having a density in the range of 0.920 to 0.946 g/cm3, and a melt index (I21.6) in the range of 1 to 15 g/10 minutes. The second component is a low molecular weight ethylene polymer having a density in the range of 0.965 to 0.980 g/cm3, and a melt index (I2) in the range of 30 to 1500 g/10 minutes. The high-density polyethylene composition has a melt index (I2) of at least 1, a density in the range of 0.950 to 0.960 g/cm3.

Abstract: A high-strength conductive polymer composite can be made by mixing a a granular polymer and a conductive material, and processing the mixture using angular extrusion.

Abstract: The present invention provides a method for preparing an oligomer and a catalyst comprising a step of oligomerizing a polymerizable monomer containing an olefin in the presence of a catalyst, which comprises (A) a complex of a diimine compound and at least one metal selected from the group consisting of Group 8 elements, Group 9 elements and Group 10 elements, (B) a mixture of a pyridine diimine compound and an iron salt and/or an iron complex, (C) methylaluminoxane and/or a boron compound, and (D) an organoaluminum compound other than methylaluminoxane and/or an organozinc compound. The components (A), (B), (C) and (D) described above are respectively as defined in the present Description.

Abstract: The present invention provides a microporous membrane having an excellent balance of temperature characteristics, shrinkage characteristics, permeability, and strength, and thereby realizes a separator for a non-aqueous electrolyte secondary battery and a non-aqueous electrolyte secondary battery, having excellent performance and excellent safety. A polyolefin microporous membrane having; a temperature difference not less than 7.2° C. between a shutdown shrinkage temperature and a maximum shrinkage temperature in a TD measured by TMA; a shrinkage rate difference less than 25% between a shutdown shrinkage rate and a maximum shrinkage rate in the TD; a pin puncture strength at a membrane thickness of 16 ?m being not less than 400 gf; and a ratio of pin puncture strength to air permeation resistance at a membrane thickness of 16 ?m being from 2.0 to 4.0 (gf/(sec/100 cc)).

Abstract: An antioxidant combined with UHMWPE prior to subjecting the UHMWPE to crosslinking irradiation. In one exemplary embodiment, the antioxidant is tocopherol. After the antioxidant is combined with the UHMWPE, the resulting blend may be formed into slabs, bar stock, and/or incorporated into a substrate, such as a metal, for example. The resulting product may then be subjected to crosslinking irradiation. In one exemplary embodiment, the UHMWPE blend is preheated prior to subjecting the same to crosslinking irradiation. Once irradiated, the UHMWPE blended product may be machined, packaged, and sterilized in accordance with conventional techniques.

Abstract: A system and method for charging a chromium-based catalyst to a mix vessel; introducing a reducing agent through an entrance arrangement into the mix vessel, and agitating a mixture of the chromium-based catalyst, the reducing agent, and a solvent in the mix vessel to promote contact of the reducing agent with the chromium-based catalyst to give a reduced chromium-based catalyst.

Abstract: Methods of preparing oligomers of an olefin are provided. The methods can include providing a composition that includes an alkylaluminum compound, a chromium compound, and a hydrocarbon solvent. The hydrocarbon solvent can include n-undecane, a C8-C11 alkane compound having one branch, or a mixture thereof. The methods can further include contacting an olefin with the composition to form oligomers of the olefin. The olefin can include ethylene, and the oligomers of the olefin can include 1-hexene.

Abstract: The invention provides a high-strength fabric and a manufacturing method thereof. The manufacturing method includes: connecting at least one group of single yarns according to a certain law to manufacture a fabric body, wherein the high-strength fabric includes at least the fabric body, and each single yarn is manufactured by converging or converging and twisting an ultra-high molecular weight polyethylene thin film or strip. The high-strength fabric has the advantages of good structural integrity, simple manufacturing process, high production efficiency, high strength, high strength utilization ratio, light weight, no pollution and good bulletproof performance.

Abstract: Ultra high molecular weight polyethylene (UHMWPE) polymers that have an average molecular weight of at least 500,000 g/mol and an enthalpy of at least 190 J/g is provided. The UHMWPE polymer may include at least one comonomer. The UHMWPE polymer is used to form a membrane, that, when expanded, has a node and fibril structure. The UHMWPE membrane has an endotherm of about 150° C. associated with the fibrils in the membrane. The membrane has a percent porosity of at least 25%, and in exemplary embodiments, the percent porosity is at least 60%. Additionally, the UHMWPE membrane has a thickness less than 1 mm. An UHMWPE membrane may be formed by lubricating the UHMWPE polymer, subjecting the lubricated polymer to pressure at a temperature below the melting point of the UHMWPE polymer to form a tape, and expanding the tape at a temperature below the melting temperature of the UHMWPE polymer.

Abstract: Provided is a method of making a polymeric material with a spatially controlled distribution of one or more additives including the steps of blending the one or more additives with a polymeric material, consolidating the polymeric material, heating at least a portion of at least one surface of the consolidated additive-blended polymeric material, and cooling the heated consolidated additive-blended polymeric material, thereby forming a polymeric material with a spatially controlled distribution of additive.

Abstract: Disclosed herein is a polymerization method of propylene, which can prepare a propylene homopolymer with both high fluidity and high rigidity as well as a propylene/?-define copolymer having both high fluidity and a good rigidity-toughness balance by, for example, control of polymerization steps and elevation of polymerization temperature, while the catalyst still maintains a relatively high polymerization activity.

Abstract: This disclosure relates to rotomolded articles, having a wall structure, where the wall structure contains at least one layer containing an ethylene interpolymer product, or a blend containing an ethylene interpolymer product, where the ethylene interpolymer product has: a Dilution Index (Yd) greater than ?1.0; total catalytic metal ?3.0 ppm; ?0.03 terminal vinyl unsaturations per 100 carbon atoms. The ethylene interpolymer products have a melt index from about 0.5 to about 15 dg/minute, a density from about 0.930 to about 0.955 g/cm3, a polydispersity (Mw/Mn) from about 2 to about 6 and a CDBI50 from about 50% to about 98%. Further, the ethylene interpolymer products are a blend of at least two ethylene interpolymers; where one ethylene interpolymer is produced with a single-site catalyst formulation and at least one ethylene interpolymer is produced with a heterogeneous catalyst formulation.

Abstract: The present invention relates to film structure suitable for use in stand up pouches comprising all polyethylene material. The film structure can be a monolayer film or a multilayer film structure having specific requirements for each layer. The combination results in a film structure having adequate stiffness to function as a stand-up pouch while also providing acceptable water vapor transmission rates and good tear resistance. Such films have improved sustainability characteristics as they should permit down-gauging of the films and, can more easily be recycled, at least for the preferred embodiment comprising only polyethylene resins.

Abstract: The present disclosure generally relates to a process for separating polymeric and gaseous components of a reaction mixture obtained by high-pressure polymerization of ethylenically unsaturated monomers in the presence of free-radical polymerization initiators into a gaseous fraction and a liquid fraction in a separation vessel, wherein the filling level of the liquid fraction in the separation vessel is measured by a radiometric level measurement system comprising at least two radioactive sources and at least three radiation detectors, and the filling level is controlled by a product discharge valve which operates based on data coming from the level measurement system.

Abstract: Process for enhancing the separation of monomer components from light components other than monomer by providing a first stream containing monomer and light components other than monomer and passing the first stream to a first separator at a first pressure to separate a gaseous second stream containing at least some of the light components other than monomer and provide a liquid third stream containing monomer. A portion of the third stream and a fourth stream containing monomer and light components other than monomer is passed to a second separator at a second pressure which is lower than the first pressure to separate a gaseous fifth stream containing at least some of the light components other than monomer from the fourth stream and provide a liquid sixth stream containing monomer.

Abstract: A continuous polymerization apparatus uses at least a first reactor and a second reactor (10, 20). Each of the reactors (10, 20) includes at least one supply port (11a, 21a, and 21b), an effluent port (11b, 21d), and a temperature detecting means (T1, T2), each of which detects the temperature in the reactor. The supply port (11a) of the first reactor (10) is connected to supply sources (1, 3) of a raw material monomer and a polymerization initiator, and the effluent port (11b) is connected to the first supply port (21a) of the second reactor (20) through a connection line (15a). The second supply port (21b) of the second reactor (20) is connected to a replenishing line (15b) that supplies a new raw material monomer to the second reactor.

Abstract: Process for maintaining a continuous gas-phase (co-) polymerization of olefins in a large fluidized bed reactor in a homogeneous mode while operating at high space time yield and condensation rate in the presence of a polymerization catalyst.

Abstract: An ethylene-based polymer, which is a low density polyethylene (LDPE), obtained by free radical polymerization of ethylene, and wherein the LDPE has a GPC parameter “LSP” less than 1.60. An ethylene-based polymer that comprises the following features: a) at least 0.1 amyl groups per 1000 total carbon atoms; b) a melt index of 0.01 to 0.3; c) a z-average molecular weight of Mz (conv.) of greater than 350,000 g/mol and less than 425,000 g/mol; d) a gpcBR value from 1.50 to 2.05, and e) a MWD(conv) [Mw(conv)/Mn(conv)] from 6 to 9. An ethylene-based polymer that comprises the following features: a) at least 0.1 amyl groups per 1000 total carbon atoms; b) a melt viscosity ratio (V0.1/V100), at 190° C., greater than, or equal to, 58; c) a melt viscosity at 0.1 rad/s, 190° C., greater than, or equal to, 40,000 Pa·s, and d) a gpcBR value from 1.50 to 2.25.

Abstract: The present invention relates to a non-cryogenic process for the large scale synthesis of disentangled ultra high molecular weight polyethylene (DUHMWPE) polymers. The process comprises of the following steps: a. mixing FI catalyst of formula I with a hydrocarbon solvent containing poly-methyl aluminoxane (P-MAO) co-catalyst in a vessel under stirring before polymerization or directly in the polymerization vessel at a temperature ranging between 25° C. and 29° C. under a dry Nitrogen atmosphere; and lower concentration of co-catalyst resulting in the associated benefits as described earlier in the claims and descriptions. b. pressurizing ethylene in the polymerization vessel and polymerizing ethylene in a solution or a suspension, continuously or batch wise, in one or more stages at a temperature is in the range of 30° C. to 50° C.

Abstract: Plastic optical fibers or plastic optical fiber cores with good high temperature resistance to optical attenuation loss are prepared from a cyclic block copolymer characterized by a: A. Weight ratio of hydrogenated conjugated diene polymer block to hydrogenated vinyl aromatic polymer block of 35:65 to 10:90; B. Number average molecular weight (Mn) of from 40,000 to 150,000, grams per mole (g/mol); and C. Hydrogenation level such that each hydrogenated vinyl aromatic polymer block and each hydrogenated conjugated diene polymer block has a hydrogenation level of at least 95 percent.

Abstract: A first embodiment which is a bimodal polymer having a weight fraction of a lower molecular weight (LMW) component ranging from about 0.25 to about 0.45, a weight fraction of a higher molecular weight (HMW) component ranging from about 0.55 to about 0.75 and a density of from about 0.931 g/cc to about 0.955 g/cc which when tested in accordance with ASTM D1003 using a 1 mil test specimen displays a haze characterized by equation: % Haze=2145?2216*FractionLMW?181*a molecular weight distribution of the LMW component (MWDLMW)?932*a molecular weight distribution of the HMW component (MWDHMW)+27*(FractionLMW*MWDLMW)+1019*(FractionLMW*MWDHMW)+73*(MWDLMW*MWDHMW) wherein fraction refers to the weight fraction of the component in the polymer as a whole.

Abstract: A gas-phase polyolefin reactor system for rapidly transitioning from one polyolefin product to another is disclosed. The reactor system comprises a control valve, a high-flow valve, a polyolefin reactor, a flow meter, a totalizer and an empirical model. During a transition, the empirical model predicts a required amount based upon an initial concentration and a selected ending concentration, the flow meter measures a flow rate, the totalizer determines a totalized amount when the flow rate of the first stream reaches the required amount based upon the measured flow rate and outputs the totalized amount to the empirical model, and the empirical model compares the required amount to the totalized amount and determines a transition endpoint. A method of rapidly transitioning the reactor system from one polyolefin product to another is also disclosed.

Abstract: The invention provides a process to form an ethylene-based polymer, said process comprising polymerizing ethylene in presence of at least the following: A) a free-radical agent; B) an alkylated phenol selected from Formula (I), wherein R1, R2, R3, R4 and R5 are each, independently, hydrogen or an alkyl; and C) a “metal alkyl-containing compound” selected from the group consisting of the following: i) at least one “Group II metal alkyl-containing compound,” ii) at least one “Group III metal alkyl-containing compound,” and iii) a combination of i) and ii).

Abstract: Disclosed herein are catalyst compositions containing boron bridged, cyclopentadienyl-indenyl metallocene compounds with an alkenyl substituent. These catalyst compositions can be used for the polymerization of olefins. For example, ethylene homopolymers produced using these catalyst compositions can be characterized by a density less than 0.97 g/cm3 and a melt index greater than 50 g/10 min.

Abstract: Spray-dried catalyst compositions comprising a transition metal complex and polymerization processes employing the same are disclosed herein. An embodiment provides a spray-dried catalyst composition comprising a transition metal catalyst component represented by the following formula: (I) and polymerization process employing the same.

Abstract: A film comprising a polymer blend of: (a) 0.15 to 0.8 wt % of an LDPE having an MI of 0.1 to 0.6 dg/min; and (b) 99.2 to 99.85 wt % of an LLDPE produced with a single-site catalyst comprising a metallocene and having a haze (HZlldpe), dart impact (DIlldpe), MD-Tear (MDTlldpe), and a slice long chain branching index of at least 0.90 for any portion of the composition having a molecular weight of 100,000 or above, wherein the film has a haze (HZblend), a dart impact (DIblend), and an MD-Tear (MDTblend), and HZblend=a*HZlldpe, where a is 0.20 to 0.70; DIblend=b*DIlldpe, where b is 0.9 to 1.3; and MDTblend=c*MDTlldpe, where c is 0.8 to 1.1.

Abstract: A polymer having a long chain branching content peaking at greater than about 20 long chain branches per million carbon atoms, and a polydispersity index of greater than about 10 wherein the long chain branching decreases to approximately zero at the higher molecular weight portion of the molecular weight distribution. A polymer having a long chain branching content peaking at greater than about 8 long chain branches per million carbon atoms, a polydispersity index of greater than about 20 wherein the long chain branching decreases to approximately zero at the higher molecular weight portion of the molecular weight distribution. A polymer having a long chain branching content peaking at greater than about 1 long chain branches per chain, and a polydispersity index of greater than about 10 wherein the long chain branching decreases to approximately zero at the higher molecular weight portion of the molecular weight distribution.

Abstract: Provided is a method of fabricating a thermal conductive polymer, including: a) fabricating a gel filament by primarily elongating a solution filament formed by spinning a mixed solution containing an ultra high molecular weight polyolefin (UHMWPO) resin and a first solvent, followed by cooling; b) secondarily elongating the gel filament; c) fabricating a dry filament by removing the solvent from the gel filament, followed by tertiary elongation; and d) converting the dry filament into the gel filament by adding the first solvent to the dry filament; e) removing the first solvent from the converted gel filament; and f) quaternarily elongating the gel filament from which the first solvent is removed.

Abstract: The invention relates to a process for the production of polyethylene by gas phase polymerisation of ethylene in the presence of a supported chromium oxide based catalyst which is modified with an amino alcohol wherein the molar ratio of amino alcohol:chromium ranges between 0.5:1 and 1:1, wherein the support is silica having a surface area (SA) between 250 m2/g and 400 m2/g and a pore volume (PV) between 1.1 cm3/g and less than 2.0 cm3/g and wherein the amount of chromium in the supported catalyst is at least 0.1% by weight and less than 0.5% by weight.

Abstract: The invention relates to processes for converting a mixture of hydrocarbon and sulfur-containing molecules such as mercaptan into products comprising acetylene, ethylene, and hydrogen sulfide, to processes utilizing the acetylene and ethylene resulting from the conversion, and to equipment useful for such processes.

Abstract: The invention provides a solution polymerization process comprising: A) polymerizing one or more monomers in the presence of a solvent that comprises a heavy hydrocarbon solvent and a light hydrocarbon solvent, to form a polymer solution; B) transferring the polymer solution to a Liquid-Liquid Separator, without adding heat to the solution, and wherein the pressure of the polymer solution is actively reduced in a controlled manner prior to, or within, the Liquid-Liquid Separator, to induce at least two liquid phases, a polymer-rich phase and a solvent-rich phase, and wherein the concentration of polymer in the polymer-rich phase is higher than that in the polymer solution transferred to the Liquid-Liquid Separator; and C) removing the solvent-rich phase.

Abstract: A unimodal polymer having a melt index of from about 0.5 g/10 min to about 4 g/10 min, a density of equal to or greater than about 0.945 g/cc which when formed into a film displays a moisture vapor transmission rate of less than about 0.55 g-mil/100 in2 in 24 hours as determined in accordance with ASTM F 1249. A unimodal polymer having a melt index of from about 0.5 g/10 min to about 4 g/10 min, a density of equal to or greater than about 0.945 g/cc which when formed into a film displays a moisture vapor transmission rate of less than about 0.44 g-mil/100 in2 in 24 hours as determined in accordance with ASTM F 1249.

Abstract: A method for controlling the temperature in a polymerization reactor equipped with a cycle gas line for withdrawing reactor gas from the reactor, leading the reactor gas through a heat-exchanger, which is cooled by a cooling medium, which is conveyed in a cooling system through the heat-exchanger, and feeding the reactor gas back to the reactor by adjusting the temperature of the cooling medium entering the heat exchanger, wherein the temperature of the cooling medium entering the heat exchanger is controlled by adjusting the flow rate of the cooling medium in a part of the cooling system by a flow control system comprising two continuously operating flow control devices of different size, which are connected in parallel, a process for polymerizing olefins and a process for controlling the flow rate of a fluid medium.

Abstract: A blow molding ethylene resin composition satisfies the following requirements [a], [b], [c] and [d] at the same time: [a] the melt flow rate (MFR) at a temperature of 190° C. under a load of 21.6 kg is in the range of 1.0 to 15 g/10 min; [b] the density is in the range of 955 to 970 kg/m3; [c] the number of methyl branches per 1000 carbon atoms is less than 0.1 according to 13C-NMR; [d] the tensile impact strength measured at ?40° C. in accordance with JIS K 7160 is not less than 270 kJ/m2.

Abstract: Solution casting a nanostructure. Preparing a template by ablating nanoholes in a substrate using single-femtosecond laser machining. Replicating the nanoholes by applying a solution of a polymer and a solvent into the template. After the solvent has substantially dissipated, removing the replica from the substrate.

Abstract: In a process for producing an elongated polyethylene component, such as a fiber or membrane, polyethylene powder having a molecular weight of at least 3×105 g/mol as determined by ASTM 4020 is dissolved in a solvent to produce an extrudable solution. The solution is then extruded through a die to form an elongated component and at least part of said solvent is removed from the elongated component. The polyethylene powder used in the process is produced by polymerizing ethylene in the presence of a catalyst composition comprising a Group 4 metal complex of a phenolate ether ligand.

Abstract: The present invention relates to methods of processing lignocellulosic material to obtain hemicellulose sugars, cellulose sugars, lignin, cellulose and other high-value products. Also provided are hemicellulose sugars, cellulose sugars, lignin, cellulose, and other high-value products.

Abstract: A polyethylene article comprises crystalline polyethylene in an orthorhombic unit cell. The b-axes of the crystalline polyethylene are substantially aligned with the machine direction of the article. In particular, the Herman's index of the b-axes in the machine direction is greater than zero and greater than the Herman's indices of the b-axes in both the transverse and normal directions. The unique physical attributes exhibited by a polyethylene article having this new morphology are also described.

Abstract: The present invention relates to novel metallocene catalysts of formula I, which is defined herein. The present invention also provides processes for making these catalysts and their use in olefin polymerisation reactions.

Abstract: A novel UHMW polyethylene material, which is displaying excellent abrasion resistance amongst other properties, is devised.

Abstract: The present disclosure relates to a polyethylene resin composition contains an ethylene homopolymer.

Abstract: A novel PE material is devised showing excellent mechanical/optical properties and process ability, e.g. for film extrusion. The polyethylene of the invention is produced in one single e.g. gas phase reactor.

Abstract: Provided are a hybrid supported metallocene catalyst, a method for preparing the same, and a process for preparing an olefin polymer using the same, and more particular, a hybrid supported metallocene catalyst characterized in that two kinds of metallocene compounds containing a new cyclopenta[b]fluorenyl transition metal compound are supported on an inorganic or organic porous carrier surface-treated with an ionic compound and a co-catalyst, a method for preparing the same, and a process for preparing an olefin polymer using the hybrid supported metallocene catalyst.

Abstract: An ethylene polymer having (i) a density defined by equation (1) ?>a?b Log M??(1) where ? is a density of the polymer in g/cc, log M is a log weight average molecular weight of the polymer, a is about 1.0407, and b is about 0.0145; and (ii) a polydispersity index of greater than about 5.