A process for the production of an ionic transition metal catalyst in supported form than is highly productive under gas phase olefin polymerization conditions. In the process a an aluminum alkyl is added to a suitable solvent after which a neutral metallocene compound is added to the solution under stirring in a quantity that provides for a ratio of Al to transition metal of at least 25:1. To this metallocene-aluminum alkyl solution is next added an ionic compound the anionic portion of which is a non-coordinating anion under stirring until all materials are dissolve. The ionic compound is added in a quantity that provides for a ratio of NCA to transition metal of at least 1:1. Next the support particles are added to the solution and thereafter the solution is heated to at least 40xc2x0 C. and held at this elevated temperature for at least 0.5 hour. Thereafter the solvent is removed and the supported catalyst is dried under vacuum.

This invention relates to a method for production of catalyst compositions useful for addition reactions of olefinically unsaturated monomers, e.g., polymerization. The invention is particularly useful in coordination polymerization processes that utilize supported compounds for slurry or gas phase polymerization of olefinically unsaturated monomers, and those processes themselves. The ionic catalyst compositions comprise the final product of the interaction between an aluminum alkyl, a metallocene, an anionic activator, and a support.
Coordination catalyzed polymerization of olefinically unsaturated monomers is well known and has led to the proliferation in modem society of elastomeric and plastic compositions of matter, such as polyethylene, polypropylene, and ethylene propylene rubber. Early pioneers utilized transition metal compounds the ligands of which were non-organic moieties, such as halides, with activators such as aluminum alkyls. Later development extended this work to bulky organo ligand-containing (e.g., eta5-cyclopentadienyl) transition metals (xe2x80x9cmetallocenesxe2x80x9d) with activators such as alumoxanes (a partial hydrolysis product of an aluminum alkyl). More recent developments have shown the-effectiveness of ionic catalysts comprised of metallocene cations activated by non-coordinating anions, see for example EP-A-277,004 and U.S. Pat. No. 5,198,401. These references described protonation of metallocene compounds by anion precursors to form stable xe2x80x9cionicxe2x80x9d catalysts.
Such ionic catalysts have shown to varying degrees significant sensitivity to catalyst poisons present in monomer feed streams, or in recycled fluid streams, in the polymerization process and have posed problems for use with inert oxide supports that typically have either or both of retained moisture or polar hydroxyl groups. Accordingly, processes have been developed to utilize poison scavenging compounds, as for example alkyl aluminums or alumoxanes, for solution polymerization and to remove or neutralize polar groups retained in or on inert oxide supports. For example, see U.S. Pat. No. 5,153,157, describing Group-IIIA metal scavenger compounds, and WO-A-91/09882, WO-A-94/00500 and WO-A-94/03506 describing supporting techniques utilizing similar compounds. U.S. Pat. No. 5,206,197 describes enhanced polymerization of styrene where the ionic catalyst systems include a metal hydrocarbyl, and, which may be supported. All such documents are referred to herein for their description of metallocene compounds, ionic activators, and useful scavenging compounds.
Whereas these ionic catalyst in unsupported form exhibit acceptable levels of productivity, as measured by a part per million (ppm) content of the transitional metal retained as a residue in the polymer product of about 1 to 1.5 ppm, when placed on a support such as silica, for use in a gas phase polymerization procedure, the productivity of these ionic catalyst often drops to an unacceptable, level i.e., the ppm content of transition metal retained as a residue in the polymer product becomes greater than about 1 to 1.5 ppm.
It is desirable to develop a process for producing a supported form of ionic transition metal catalyst that allows it to maintain its high productivity under gas phase polymerization conditions.
This invention comprises a process for the production of an ionic transition metal catalyst in supported form than is highly productive under gas phase polymerization conditions. In the process of the invention an aluminum alkyl is added to a suitable solvent after which a neutral metallocene compound is added to the aluminum alkyl solution under stirring in a quantity that provides for a ratio of Al to transition metal of 2:1 to 200:1, preferably at least 25:1, and more preferably at least 50:1 and stirring is continued until substantially all material is dissolved. To this metallocene-aluminum alkyl solution is next added an ionic compound the anionic portion of which is a non-coordinating anion (NCA) as hereafter defined, under stirring until all materials are substantially dissolved. The ionic compound is preferably added in a quantity that provides for a ratio of NCA to transition metal of at least 1:1. Next the support particles are added to the solution and thereafter the solution is heated to at least 40xc2x0 C., and preferably 90xc2x0 C., and held at this elevated temperature for at least 0.50 hour, and preferably for at least one hour. Thereafter the solvent is removed and the supported catalyst is dried, preferably under vacuum. A supported ionic catalyst produced in this manner is at least about 150% to 350% more productive under gas phase polymerization conditions than an otherwise identical supported metallocene catalyst that is co-catalyzed with methyl alumoxane.
The supported catalyst formed by the process of this invention comprises the product of a sequence of reaction steps wherein first there occurs in a suitable solvent a reaction between a metallocene and an aluminum alkyl to produce a first reaction product that in turn is reacted with an ionic compound that provides a non-coordinating anion (NCA) to the transition metal of the first reaction product after which the resulting transition metal-NCA reaction product is exposed to a support material that is added to the solvent mixture which then elevated in temperature for a period of time before removal of the solvent to recover the catalyst as a free flowing powder.
The Transition Metal Component of the Catalyst
Any catalytically active transition metal compound is suitable in accordance with the invention, including the known transition metal compounds useful in traditional Ziegler-Natta coordination polymerization and, as well, the metallocene compounds similarly known to be useful in coordination polymerization, when such compounds are capable of catalytic activation by an anionic activator. These will typically include transition metal compounds where the metal is in a d0 oxidation state, that is where the metal has its highest oxidation number, and wherein at least one metal ligand can be protonated by the anionic activator, particularly those ligands including hydride, alkyl and silyl. Ligands capable of protonation and transition metal compounds comprising them include those described in the background art, see for example EP-A-277,003, EP-A-277,004 and U.S. Pat. No. 5,198,401. Synthesis of these compounds is well known from the published literature.
Additional metallocene compounds appear in the patent literature, for example EP-A-0 129 368, U.S. Pat. Nos. 4,871,705, 4,937,299, 5,324,800 EP-A-0-418 044, EP-A-0 591 756, WO-A-92/00333 and WO-A-94/01471. Such metallocene compounds can be described for this invention as mono-, bis, or tris-cyclopentadienyl substituted Group 4, 5, 6, 9, or 10 transition metal compounds wherein the cyclopentadienyl substituents themselves may be substituted with one or more groups and may be bridged to each other, or may be bridged through a heteroatom to the transition metal. The size and constituency of the cyclopentadienyl substituents and bridging elements are not critical to the preparation of the ionic catalyst systems of the invention but should normally be selected in the literature described manner to enhance the polymerization activity and polymer characteristics being sought. Preferably the cyclopentadienyl (or substituted cyclopentadienyl, such as indenyl or substituted indenyl) rings, when bridged to each other, will be lower alkyl-substituted (C1 to C6) in the 2 position additionally and comprise alkyl, cycloalkyl, aryl, alkylaryl and or arylalkyl substituents, the latter as either of fused or pendant ring structures including multi-ring structures, for example, those of U.S. Pat. Nos. 5,278,264 and 5,304,614. Such substituents should each have essentially hydrocarbyl characteristics and will typically contain up to 30 carbon atoms but may be hetero-atom containing with not more than 1-3 non-hydrogen/carbon atoms, e.g., N, S, O, P, and Si.
Metallocene compounds suitable for the preparation of linear polyethylene or ethylene-containing copolymers (where copolymer means comprising at least two different monomers) are essentially any of those known in the art, see again EP-A-277,004, WO-A-92/00333 and U.S. Pat. Nos. 5,198,401, 5,001,205, 5,324,800, 5,308,816, and 5,304,614 for specific listings. Selection of metallocene compounds for use to make isotactic or syndiotactic polypropylene, and their syntheses, are well-known in the art, specific reference may be made to both patent literature and academic, see for example Journal of Organmetallic Chemistry 369, 359-370 (1989). Typically those catalysts are stereorigid asymmetric, chiral or bridged chiral metallocenes. See, For example, U.S. Pat. No. 4,892,851, U.S. Pat. No. 5,017,714, U.S. Pat. No. 5,296,434, U.S. Pat. No. 5,278,264, WO-A-(PCT/US92/10066) WO-A-93/19103, EP-A2-0 577 581, EP-A1-0 578 838, and the academic literature xe2x80x9cThe Influence of Aromatic Substituents on the Polymerization Behavior of Bridged Zirconocene Catalystsxe2x80x9d, Spaleck, W., et al, Organometallics 1994, 13, 954-963, and xe2x80x9cansa-Zirconocene Polymerization Catalysts with Annelated Ring Ligands-Effects on Catalyst Activity and Polymer Chain Lengthsxe2x80x9d, Brinzinger, H., et al, Organometallics 1994, 13, 964-970, and documents referred to therein. Though many above metallocenes are directed to catalyst systems with alumoxane activators, the analogous metallocene compounds will be useful with the activator anions of this invention for active coordination catalyst systems, when at least one of the halogen containing ligands of the metals (where occurring) are replaced with ligands capable of protonation, for example, via an alkylation reaction as described above, and another is a group into which the ethene group xe2x80x94xe2x80x94Cxe2x95x90Cxe2x80x94xe2x80x94 may insert, for example, hydride, alkyl, or even the less effective silyl.
Non-limiting representative metallocene compounds include monocyclopentadieny compounds such as pentamethylcyclopentadienyltitanium isopropoxide, pentamethylcyclopentadienyltribenzyl titanium, dimethyl-silyltetramethylcyclopentadienyl tert-butylamido titanium dichloride, pentamethyl-cyclopentadienyl titanium trimethyl, dimethylsilyltetramethylcyclopentadienyl-tert-butylamido zirconium dimethyl, Dimethylsilyltetramethylcyclopentadienyl-dodecylamido hafnium dihydride, dimethylsilyltetramethylcyclopentadienyl-dodecylamido hafnium dimethyl, unbridged biscyclopentadienyl compounds such as bis(1,3-butyl, methylcyclopentadienyl) zirconium dimethyl, entamethylcyclopentadienylcyclopentadienyl zirconium dimethyl; bridged bis cyclopentadienyl compounds such as imethylsilyl-bis(tetrahydroindenyl) zirconium dichloride; bridged bisindenyl compounds such as dimethylsilylbisindenyl zirconium dichloride, dimethylsilylbisindenyl hafnium dimethyl, dimethylsilylbis(2 methylbenzindenyl) zirconium dichloride, dimethylsilylbis(2-methylbenzindenyl) zirconium dimethyl; ethylene bridged compounds such as ethylenebis(indenyl)zirconium dichloride; and the additional mono-, bis-, and triscyclopentadienyl compounds such as those listed and described in U.S. Pat. No. 5,324,800 and EP-A-0 591 756.
Representative traditional Ziegler-Natta transition metal compounds include tetrabenzyl zirconium, tetra bis(trimethylsiylmethyl) zirconium, oxotris(trimethylsilylmethyl) vanadium, tetrabenzyl hafnium, tetrabenzyl titanium, bis(hexamethyl disilazido)dimethyl titanium, tris(trimethyl silyl methyl) niobium dichloride, tris(trimethylsilylmethyl) tantalum dichloride. The important features of such compositions for coordination polymerization are the ligand capable of abstraction by protonation and that ligand into which the ethene (olefinic) group can be inserted. These features enable the protonation of the transition metal compound and the concomitant formation of the ionic catalyst composition of the invention.
Aluminum Alkyl Compounds
As before noted, to prepare the highly productive ionic catalyst in supported form, the metallocene must first be reacted in solution with an aluminum alkyl. For this purpose the aluminum alkyl may comprise any aluminum alkyl within the following formula:
Al(R)3xe2x88x92xXx
wherein R is an alkyl group or aryl group, X is a halogen atom, alkoxy group, or hydrogen atom, x is a number and is 0 1 or 2. Preferred alkyl aluminum compounds and a mixture thereof or complex thereof have 1 to 18 carbon atoms, preferably 2 to 6 carbon atoms, such as trialkyl aluminum, dialkyl aluminum monohalide, monoalkyl aluminum dihalide, alkyl aluminum sesquihalide, dialkyl aluminum monoalkoxide, and dialkyl aluminum monohydride. Examples of such compounds include trialkyl aluminum such as trimethyl aluminum, triethyl aluminum, tripropyl aluminum, triisobutyl aluminum, and trihexyl aluminum; dialkyl aluminum monohalide such as dimethyl aluminum chloride, diethyl aluminum chloride, diethyl aluminum bromide, diethyl aluminum iodide, and diisobutyl aluminum chloride; monoalkyl aluminum dihalide such as methyl aluminum dichloride, ethyl aluminum dichloride, ethyl aluminum dibromide, ethyl aluminum diiodide, and isobutyl aluminum dichloride; alkyl aluminum sesquihalide such as ethyl aluminum sesquichloride; dialkyl aluminum monoalkoxide such as dimethyl aluminum methoxide, diethyl aluminum ethoxide, diethyl aluminum phenoxide, dipropyl aluminum ethoxide, and diisobutyl aluminum phenoxide; and dialkyl aluminum hydride such as dimethyl aluminum hydride, diethyl aluminum hydride, dipropyl aluminum hydride, and diisobutyl aluminum hydride.
Preferred aluminum alkyls for use within this invention are triethyl aluminum, tripropyl aluminum, and tri isobutyl aluminum.
Co-catalyst Activator Compositions
The supported ionic catalyst composition of the invention can be prepared, for example, by selecting as the Lewis acid which forms the Lewis acid-base complex, one that is capable of serving as a suitable counter anion upon protonation of the transition metal compound with the proton from Lewis acid-base hydroxyl group complex. Activation of the transition metal compound to a catalytic state may be achieved with ionizing compounds which contain an active proton, or some other cation associated with but not coordinated to or only loosely coordinated to the remaining ion of the ionizing compound. Such compounds and the like are described in European publications EP-A-0 570 982, EP-A-0 520 732, EP-A-0 495 375, EP-A-500 944, EP-A-0 277 003 and EP-A-0 277 004, and U.S. Pat. Nos. 5,153,157, 5,198,401, 5,066,741, 5,206,197, 5,241,025, 5,384,299 and 5,502,124 and U.S. patent application Ser. No. 08/285,380, filed Aug. 3, 1994, all of which are herein fully incorporated by reference.
A preferred class of compatible non-coordinating anions (NCA) includes chemically stable, non-nucleophilic substituted anionic complexes having a molecular diameter of about 4 Angstroms or more.
Any metal or metalloid compound capable of forming an anionic complex which is resistant to irreversibly transferring a substituent or fragment to the cation to neutralize the cation to produce a neutral molecule may be used as the NCA. In addition any metal or metalloid capable of forming a coordination complex that is stable in water may also be used or contained in a composition comprising the anion. Suitable metals include, but are not limited to aluminum, gold, platinum, and the like. Suitable metalloids include, but are not limited to, boron, phosphorus, silicon, and the like. Compounds containing anions that comprise coordination complexes containing a single metal or metalloid atom are, of course, well known and many, particularly such compounds containing a single boron atom in the anion portion, are available commercially. In light of this, salts containing anions comprising a coordination complex containing a single boron atom are preferred.
In general, preferred NCAs may be represented by the following general formula:
[(Mxe2x80x2)m+Q1 . . . Qn ]dxe2x80x94
wherein: M is a metal or metalloid; Q1 to Qn are, independently, hydride radicals, dialkylamido radicals, alkoxide and aryloxide radicals, hydrocarbyl and substituted hydrocarbyl radicals, halocarbyl and substituted-halocarbyl radicals and hydrocarbyl and halocarbyl-substituted organometalloid radicals and any one, but not more than one of Ql to Qn may be a halide radical; m is an integer representing the formal valence charge of Mxe2x80x2; n is the total number of ligands Q, and d is an integer greater than or equal to 1.
It is of course understood that the anions described above and below may be counter balanced with a positively charged component that is removed before the anion reacts with the cation.
In a preferred embodiment Mxe2x80x2 is boron, n=4, Q1 and Q2 are the same or different aromatic or substituted-aromatic hydrocarbon radicals containing from about 6 to about 20 carbon atoms and may be linked to each other through a stable bridging group; and Q3 and Q4 are, independently, hydride radicals, hydrocarbyl and substituted-hydrocarbyl radicals, halocarbyl and substituted-halocarbyl radicals, hydrocarbyl- and halocarbyl-substituted organometalloid radicals, disubstituted pnictogen radicals, substituted chalcogen radicals and halide radicals, with the proviso that Q3 and Q4 will not be halide at the same time.
Illustrative, but not limiting, examples of boron components which may be used as NCAs are: tetra-valent boron compounds such as tetra(phenyl)boron, tetra(p-tolyl)boron, tetra(o-tolyl)boron, tetra(pentafluorophenyl)boron, tetra(o,p-dimethylphenyl)boron, tetra(m,m-dimethylphenyl)boron, (p-tri-fluoromethylphenyl)boron and the like.
In a particularly preferred embodiment M=boron, n=4, Q1, Q2 and Q3 are each (C6F5) and Q4 is as defined above. Illustrative but not limiting, examples of these preferred NCAs comprising boron triphenylmethyl salts where Q is a simple hydrocarbyl such as methyl, butyl, cyclohexyl, or phenyl or where Q is a polymeric hydrocarbyl of indefinite chain length such as polystyrene, polyisoprene, or poly-paramethylstyrene. Another preferred class of NCAs is that class comprising those NCA containing a plurality of boron atoms, including boranes and carboranes.
Illustrative, but not limiting, examples of NCAs include carboranes such as dodecaborate, decachlorodecaborate, dodecachlorododecaborate, 1-carbadecaborate, 1-carbadecaborate, 1-trimethylsilyl-1-carbadecaborate; borane and carborane complexes and salts of borane and carborane anions such as decaborane(14), 7,8-dicarbadecaborane(13), 2,7-dicarbaundecaborane (13), undecahydrido-7,8-dimethyl-7,8-dicarbaundecaborane, 6-carbadecaborate(12), 7-carbaundecaborate, 7,8-dicarbaudecaborate; and metallaborane anions such as bis(nonahydrido-1,3-dicarbanonaborato)cobaltate(III), bis(undecahydrido-7,8-dicarbaundecaborato) ferrate(III), bis(undecahydrido-7,8-dicarbaundecaborato) cobaltate(III), bis(undecahydrido-7,8 dicarbaunaborato) nikelate(II), bis(nonahydrido-7,8-dimethyl-7,8-dicarbaundecaborato)-ferrate(III), bis(tribromooctahydrido-7,8-dicarbaundecaborato)-cobaltate(I), bis-(undecahydridodicarbadodecaborato) cobaltate(III) and bis(undecahydrido-7-carbaundecaborato) cobaltate(III).
The NCA compositions most preferred for forming the catalyst system used in this process are those containing a tris-perfluorophenyl boron, tetrapentafluorphenyl boron anion and/or two or more tripentafluorophenyl boron anion groups covalently bond to a central atomic molecular or polymeric complex or particle. A particularly preferred ionic compound utilized to provide the NCA is dimethyl anilinium tetrakis (pentafluorophenyl)borate.
The Support Material
For purposes of this patent specification the terms xe2x80x9ccarrierxe2x80x9d or xe2x80x9csupportxe2x80x9d are used interchangeable and can be any support material, preferably a porous support material, such as for example, talc, inorganic oxides, inorganic chlorides, for example magnesium chloride and resinous support materials such as polystyrene polyolefin or polymeric compounds or any other organic support material and the like that has an average particle size greater than 10 xcexcm.
The preferred support materials are inorganic oxide materials, which include those from the Periodic Table of Elements of Groups 2, 3, 4, 5, 13 or 14 elemental oxides. In a preferred embodiment, the catalyst support materials include silica, alumina, silica-alumina, and mixtures thereof. Other inorganic oxides that may be employed either alone or in combination with the silica, alumina or silica-alumina are magnesia, titania, zirconia, and the like.
It is preferred that the carrier of the catalyst of this invention has a surface area in a range of from about 10 to about 700 m2/g, pore volume in a range of from about 0.1 to about 4.0 cc/g and an average particle size in a range of from about 10 to about 500 xcexcm. More preferably, the surface area is in the range of from about 50 to about 500 m2/g, pore volume is of from about 0.5 to about 3.5 cc/g and average particle size is of from about 20 to about 200 xcexcm. Most preferably the surface area range is from about 100 to about 400 m2/g, pore volume is from about 0.8 to about 3.0 cc/g and average particle size is from about 30 to about 100 xcexcm. The carrier of the invention typically has pore size in the range of from 10 to 1000 xc3x85, preferably 50 to about 500 xc3x85, and most preferably 75 to about 350 xc3x85.
Because of availability, both of silica and silica containing metal oxide based supports, for example, silica-alumina, are preferred. Silica particles, gels and glass beads are most typical.
Forming the Supported Catalyst
In the process of the invention an aluminum alkyl is added to a suitable solvent after which a neutral metallocene compound is added to the solution under stirring in a quantity that preferably provides for a ratio of Al to transition metal of at least 50:1. To this metallocene-aluminum alkyl solution is next added an ionic compound the anionic portion of which is a non-coordinating anion (NCA) under stirring until all materials are dissolve. The ionic compound is added in a quantity that provides for a ratio of NCA to transition metal of at least 1:1. Next the support particles are added to the solution and thereafter the solution is heated to at least 40xc2x0 C. and held at this elevated temperature for at least 0.5 hour. Thereafter the solvent is removed and the supported catalyst is dried under vacuum.
For the purposes of this patent specification and appended claims the term xe2x80x9csolutionxe2x80x9d includes a suspension, a slurry or a mixture. Any compatible solvent or other liquid capable of forming a solution or the like with at least one metallocene catalyst component and/or at least one activator of the invention can be used.
As indicated, the improved catalyst compositions of the present invention will be prepared in a suitable solvent or diluent. Suitable solvents or diluents include any of the solvents known in the prior art to be useful as solvents in the polymerization of olefins, diolefins and acetylenically unsaturated monomers. Non-limiting examples of solvents are those aliphatic, aromatic and saturated hydrocarbons and cyclic hydrocarbons, such as isopentane, heptane, toluene, and the like. Suitable solvents, then, include, but are not necessarily limited to, straight and branched-chain hydrocarbons such as isobutane, butane, pentane, hexane, heptane, octane and the like; cyclic and alicyclic hydrocarbons such as cyclohexane, cycloheptane, methylcyclohexane, methylcycloheptane and the like and aromatic and alkyl-substituted aromatic compounds such as benzene, toluene, xylene and the like. The more preferred solvents are the cyclic aliphatic and aromatic hydrocarbons, the most preferred of which is toluene.
In the first step of the process the aluminum alkyl and metallocene may be brought together in the solvent by any convenient means, meaning that each may be separately dissolved in an alloquate of the solvent then these two solvent portions combined, or one or the other of the components may first be dissolved in the solvent and thereafter the other of the components then added to the solvent. The combination of the metallocene and aluminum alkyl in the solvent may be achieved at ambient temperature or at an elevated temperature not exceeding that of the boiling point of the solvent. The quantity of aluminum alkyl compared to the metallocene should be selected so as to achieve a ratio of aluminum to transition metal of the metallocene in the range of 2:1 to 200:1, preferably at least 25:1, and more preferably at least 50:1, there generally be no further advantage to the use of greater quantities of the aluminum alkyl than that of a 200:1 ratio. The ingredients are preferably kept under stirring for about 15 minutes or until no further color change is observed to occur in the solution.
Next, to the metallocene-aluminum alkyl solution the ionic compound is added under stirring in a quantity that puts its non-coordinating anion moiety in a ratio to the transition metal of the metallocene in the range of 0.9:1 to 2:1, and preferably in the range of 0.9:1 to 1:1.1, most preferably in a range of 1:1 to 1.1:1, and ideally at a ratio of 1:1. This addition of the ionic compound to the solution may be achieved at ambient temperature or at an elevated temperature not exceeding that of the boiling point of the solvent.
Next, to the metallocene-aluminum alkyl-ionic compound solution is added under stirring the support particles in a quantity that will provide the desired loading of transition metal on the support which generally ranges from 0.05 to 0.50 weight per cent of the total dry weight of the catalyst, and is preferably 0.15 to 0.50 weight per cent. Following addition of the support to the solution the temperature of the metallocene-aluminum alkyl-ionic compound-support solution should be elevated to at least 40xc2x0 C., preferably 60xc2x0 C., more preferably 90xc2x0 C., and most preferably to a temperature just below the boiling point of the solvent by a degree or two. The metallocene-aluminum alkyl-ionic compound-support solution is held at this elevated temperature for at least 5 minutes, preferably 15 minutes, more preferably for 30 minutes, and most preferably for 60 minutes. Following this passage of time the solvent may be removed by evaporation or other means to recover a free flowing powder product that is an active catalyst.
Polymerization with the Supported Catalyst
This catalyst of this invention is useful in coordination polymerization of unsaturated monomers conventionally known to be polymerizable under slurry or gas phase coordination polymerization conditions. The supported catalysts of the invention are thus particularly useful in the known operating modes employing fixed-bed, moving-bed, fluid-bed, or slurry processes conducted in single, series or parallel reactors.
Linear polyethylene, including high and ultra-high molecular weight polyethylenes, including both homo- and copolymers with other alpha-olefin monomers, alpha-olefinic and/or non-conjugated diolefins, for example, C3 to C20 olefins/diolefins, are produced by adding ethylene, and optionally the other monomers, to a reaction vessel under low pressure (typically  less than 50 bar), at a typical temperature of 20-250xc2x0 C. with the invention catalyst that has been slurried with a solvent, such as heptane, toluene or mineral oil. Heat of polymerization is typically removed by cooling. In slurry phase polymerization the polymer forms as granules that are usually insoluble in the reaction diluent. Termination of polymerization generally occurs via beta hydride elimination resulting in terminal olefinic unsaturation or by the addition of a chain transfer agent such as hydrogen or aluminum alkyl resulting in chain end saturation. The polymer may be filtered or centrifuged off, washed, and dried, i.e., for slurry reactions. As indicated, chain transfer agents should be avoided if chain end unsaturation is to be retained.
Gas phase polymerization can be conducted, for example, in a continuous fluid bed gas-phase reactor operated at 2000-3000 kPa and 60-160xc2x0 C., using hydrogen as a reaction modifier (100-200 ppm), C4-C8 comonomer feedstream (0.5-1.2 mol %), and C2 feedstream (25-35 mol %). See, U.S. Pat. Nos. 4,543,399, 4,588,790, 5,028,670 and co-pending U.S. application Ser. No. 08/053,067 filed Apr. 26, 1993.
Polypropylene typically can be prepared essentially as described for linear polyethylene above. The reaction diluent is often comprised of liquid propylene monomer in which the supported ionic catalyst is slurried. Other monomers, typically the lower alpha-olefins (e.g., C2 to C10) and/or non-conjugated diolefins, can be introduced into the reaction diluent or solvent when either of polyethylene or polypropylene copolymers are to be prepared. The polymerization reactions for all of linear polyethylene, polypropylene and polyolefin polymers may be conducted in any suitable reactor, for example, in batch, continuous flow, parallel or series reactors.
Ethylene-alpha olefin(-diolefin) elastomers of high molecular weight and low crystallinity can be prepared utilizing the catalysts of the invention by introducing ethylene gas into a slurry utilizing the alpha olefin or mixture thereof with other monomers, polymerizable and not, as a polymerization diluent in which the invention catalyst is suspended. Typical ethylene pressures will be between 10 and 1000 psig (69-6895 kPa) and the polymerization diluent temperature will typically be between xe2x88x9210-100xc2x0 C. The process can be carried out in a stirred tank reactor, or more than one operated in series or parallel. Deashing can be accomplished in accordance with conventional knowledge in the art, or if to be avoided a process using one or more fixed bed or packed column reactors (see below) may be used. See the general disclosure of U.S. Pat. No. 5,001,205 for general process conditions and selection of preferred transition metal compounds.
Pre-polymerization of the supported catalyst of the invention may also be used for further control of polymer particle morphology in typical slurry or gas phase reaction processes in accordance with conventional teachings. For example such can be accomplished by pre-polymerizing a C2 to C6 alpha olefin for a limited time, for example, ethylene is contacted with the supported catalyst at a temperature of xe2x88x9215 to 30xc2x0 C. and ethylene pressure of up to about 250 psig (1724 kPa) for 75 min. to obtain a polymeric coating on the support of polyethylene of 30,000-150,000 molecular weight. The pre-polymerized catalyst is then available for use in the polymerization processes referred to above. In a similar manner, the activated catalyst on a support coated with a previously polymerized thermoplastic polymer can be utilized in these polymerization processes.
Additionally it is preferred to avoid the effect of polymerization poisons that may be introduced via feedstreams, solvents or diluents, by removing or neutralizing the poisons. For example, monomer feed streams or the reaction diluent may be pre-treated, or treated in situ during the polymerization reaction, with a suitable scavenging agent. Typically such will be an organometallic compound employed in processes such as those using the Group-13 organometallic compounds of U.S. Pat. No. 5,153,157 and WO-A-91/09882 and WO-A-94/03506, noted above, and that of WO-A-93/14132. Preferably the amount of scavenging agent is minimized, or avoided altogether, during polymerization reactions when it is desired to retain terminal unsaturation since they tend to act as chain transfer agents resulting in terminal saturation.
Other olefinically unsaturated monomers besides those specifically described above may be polymerized using the catalyst according to the invention either by coordination or carbocationic polymerization, for example, styrene, alkyl-substituted styrene, ethylidene norbornene, norbornadiene, dicylopentadiene, cyclopentene, norbornene and other alpha olefinic unsaturated and strained geometry cyclic olefins, isobutylene, isoprene, butadiene, vinyl ethers, vinyl carbazoles, etc. Additionally because of the ability of the catalytically active transition metal based catalysts of the invention to incorporate higher alpha-olefin monomers, alpha-olefinic macromonomers of up to 100 mer units, or more, may also be incorporated by copolymerization. The resulting polymers may be homopolymers or copolymers of more than one monomer, and may be of any of the recognized tacticity forms depending upon the selection of metallocene cation precursor and monomer in accordance with conventional knowledge in the art. See for example: U.S. Pat. Nos. 5,066,741 and 5,206,197, which address the preparation of syndiotactic vinyl aromatic polymers with single eta5 -cyclopentadienyl metallocene compounds activated by non-coordinating, compatible anions; U.S. Pat. Nos. 5,278,265, and 5,304,523 addressing preparation of isotactic and syndiotactic polypropylene under low temperature conditions using stereorigid metallocenes with non-coordinating anions; and, U.S. Pat. No. 5,324,801 addressing preparation of cyclic olefin-containing copolymers using specific metallocene compounds as catalysts, each of which can be activated in accordance with this invention.
The alpha-olefin based polymers produced with invention catalyst system have utility according to molecular weight, level of comonomer incorporation, where included, and polydispersity (xe2x80x9cMWDxe2x80x9d), etc. for their conventional and known uses. Thus films, fibers, and moldable thermoplastics by any of the known means of melt processing and subsequent extrusion, and/or, thermoforming are typical applications. In such, inclusion of additives such as processing aids, stabilizers, pigments, fillers as conventionally known can be utilized. High density polyethylene and isotactic polypropylene films, including those that are oriented in one or both axes and those modified with other components such as hydrocarbon tackifier resins are specific examples.
Further, inclusion of other thermoplastic components both in greater and lower amounts will be useful as known for various polymer blends and compositions. Thus the use of elastomeric polyolefins of the invention for impact modification of polar engineering resins or in co-vulcanizable elastomer blends (typically when containing diolefin comonomer and/or further derivatized as by free-radical grafting of polar monomers) is suitable. For a preferred derivatization process see WO-A-93/12148 and equivalent U.S. Pat. No. 5,424,367.

Method for producing highly productive supported ionic catalyst for gas phase polymerization


A structure including a pair of helically wound interlocking forms located on a cylindrical closure for an open headed medical implant and in a receiver between arms of the implant respectively. The interlocking forms each include overlapping gripping elements that engage mating elements during assembly to prevent radial splaying of arms of the implant.

The present invention is directed to a structure for use in interlocking together two elements and, in particular, to a structure for joining together parts of a medical implant. The structure includes a first interlocking form on a closure and a mating second interlocking form on a receiver. The closure is operably rotated into the receiver. The first and second interlocking forms are both helically wound so that the first interlocking form advances relative to the second interlocking form, when the closure with the first interlocking form is inserted in the receiver and rotated. At least one of the first or second interlocking forms includes a projection that overlaps and radially locks with the other interlocking form when the two forms are mated.
Medical implants present a number of problems to both surgeons installing implants and to engineers designing them. It is always desirable to have an implant that is strong and unlikely to fail or break during usage. It is also desirable for the implant to be as small and lightweight as possible so that it is less intrusive on the patient. These are normally conflicting goals, and often difficult to resolve.
One particular type of implant presents special problems. In particular, spinal bone screws, hooks, etc. are used in many types of back surgery for repair of injury, disease or congenital defect. For example, spinal bone screws of this type are designed to have one end that inserts threadably into a vertebra and a head at an opposite end thereof. The head is designed to receive a rod or rodlike member in a channel in the head which rod is then both captured in the channel and locked in the head to prevent relative movement between the various elements subsequent to installation.
There are two different major types of bone screws and similar devices which are classified as closed headed and open headed. While the closed headed devices are highly effective at capturing and securing a rod, since the rod is threaded through an opening in the head, it is very difficult during surgery to thread the rod through the heads. This is because there are many heads and the rod is curved or the heads do not align. Consequently, the more screw heads that the rod must pass through, the more difficult it is to thread the rod into them.
The second type of head is an open head wherein a channel is formed in the head and the rod is simply laid in an open channel. The channel is then closed with a closure member. The open headed bone screws and related devices are much easier to use and in some situations must be used instead of the closed headed devices.
While the open headed devices are often necessary and often preferred for usage, there is a significant problem associated with them. In particular, the open headed devices conventionally have two upstanding arms that are on opposite sides of a channel that receives the rod member. The top of the channel is closed by a closure member after the rod member is placed in the channel. The closure can be of a slide in type, but such are not easy to use. Threaded nuts are sometimes used that go around the outside of the arms. Such nuts prevent splaying of the arms, but nuts substantially increase the size and profile of the implant which is not desirable. Many open headed implants are closed by plugs that screw into threads between the arms, because such have a low profile. However, threaded plugs have encountered problems also in that they produce radially outward forces that lead to splaying of the arms or at least do not prevent splaying that in turn loosens the implant. In particular, in order to lock the rod member in place, a significant force must be exerted on the relatively small plug or screw. The forces are required to provide enough torque to insure that the rod member is clamped or locked in place relative to the bone screw, so that the rod does not move axially or rotationally therein. This typically requires torques on the order of 100 inch-pounds.
Because open headed implants such as bone screws, hooks and the like are relatively small, the arms that extend upwardly at the head can be easily bent by radially outward directed forces due to the application of substantial forces required to lock the rod member. Historically, early closures were simple plugs that were threaded with V-shaped threads and which screwed into mating threads on the inside of each of the arms. But, as noted above, conventionally V-shaped threaded plugs tend to splay or push the arms radially outward upon the application of a significant amount of torque, which ends up bending the arms sufficiently to allow the threads to loosen or disengage and the closure to fail. To counter this, various engineering techniques were applied to allow the head to resist the spreading force. For example, the arms were significantly strengthened by increasing the width of the arms by many times. This had the unfortunate effect of substantially increasing the weight and the profile of the implant, which was undesirable.
Many prior art devices have also attempted to provide outside rings or some other type of structure that goes about the outside of the arms to better hold the arms in place while the center plug is installed and thereafter. This additional structure may cause the locking strength of the plug against the rod to be reduced which is undesirable, especially when the additional structure is partly located beneath the plug. Also, the additional elements are unfavorable from a point of view of implants, since it is typically desirable to maintain the number of parts associated with the implants at a minimum and, as noted above, the profile as minimal as possible.
Other designers have attempted to resolve the splaying problem by providing a closure with a pair of opposed radially extending wedges or flanges that have mating structure in the arms of the implant. Such devices serve as a closure and do somewhat resist splaying of the arms, but are often very difficult to use. In particular, the rods normally have some curvature as the rods are bent to follow the curvature of the spine and normally bow relative to the bottom of the bone screw channel that receives such a rod. The rod thus fills much of the channel and must be xe2x80x9cunbentxe2x80x9d to rest on the bottom of the channel and be held securely in place. Therefore, the rod is preferably compressed by the plug and unbent by advancement of the plug into the channel in order to assume that the plug will securely hold the rod and that the rod and plug will not loosen when post assembly forces are placed on the rod. Because it takes substantial force to unbend the rod, it is difficult to both place the plug fully in the channel and rotate it for locking while also trying to line up the wedges with the mating structure. It is much easier to align the plug mating structure with the mating structure of the arms at the top of the arms and then rotate the plug so as to screw the plug into a plug receiver to advance the plug toward the rod. In this way the plug starts applying significant force against the rod only after parts of the mating structure have at least partly joined at which time torque can be applied without having to worry about alignment. It is noted that where wedges are used, the cross section of the structure changes therealong so that the device xe2x80x9clocks upxe2x80x9d and cannot turn further after only a small amount of turning, normally ninety degrees.
Consequently, a lightweight and low profile closure plug was desired that resists splaying or spreading of the arms while not requiring significant increases in the size of the screw or plug heads and not requiring additional elements that encircle the arms to hold the arms in place.
It is noted that the tendency of the open headed bone screw to splay is a result of the geometry or contour of the threads typically employed in such devices. In the past, most bone screw head receptacles and screw plugs have employed V-shaped threads. V-threads have leading and trailing sides oriented at angles to the screw axis. Thus, torque on the plug is translated to the bone screw head at least partially in an axial direction, tending to push or splay the arms of the bone screw head outward in a radial direction. This in turn spreads the internally threaded receptacle away from the thread axis so as to loosen the plug in the receptacle.
The radial expansion problem of V-threads has been recognized in various types of threaded joints. To overcome this problem, so-called xe2x80x9cbuttressxe2x80x9d threadforms were developed. In a buttress thread, the trailing or thrust surface is oriented perpendicular to the thread axis, while the leading or clearance surface remains angled. This theoretically results in a neutral radial reaction of a threaded receptacle to torque on the threaded member received.
Development of threadforms proceeded from buttress threadforms which in theory have a neutral radial effect on the screw receptacle to reverse angled threadforms which theoretically positively draw the threads of the receptacle radially inward toward the thread axis when the plug is torqued. In a reverse angle threadform, the trailing side of the external thread is angled toward the thread axis instead of away from the thread axis, as in conventional V-threads. While buttress and reverse threadforms reduce the tendency to splay, the arms can still be bent outward by forces acting on the implant and the threads can be bent by forces exerted during installation. Therefore, while certain threadforms may not exert radial forces during installation, at most such threadforms provide an interference or frictional fit and do not positively lock the arms in place relative to the closure plug.
Finally, it is noted that plugs of this type that use threadforms are often cross threaded. That is, as the surgeon tries to start the threaded plug into the threaded receiver, the thread on the plug is inadvertently started in the wrong turn or pass of the thread on the receiver. This problem especially occurs because the parts are very small and hard to handle. When cross threading occurs, the plug will often screw part way in the receiver and then xe2x80x9clock upxe2x80x9d so that the surgeon is led to believe that the plug is properly set. However, the rod is not tight and the implant fails to function properly. Therefore, it is also desirable to have a closure that resists crossthreading in the receiver.
A non threaded guide and advancement structure is provided for securing a set screw, plug or closure in a receiver. Preferably the receiver is a rod receiving channel in an open headed bone screw, hook or other medical implant wherein the channel has an open top and is located between two spaced arms of the implant.
The guide and advancement structure has a first part or interlocking form located on the closure and a second part or interlocking form that is located on the interior of the receiving channel.
Both parts of the guide and advancement structure are spirally or more preferably helically wound and extend about the closure and receiving channel for at least one complete 360xc2x0 pass or turn. Preferably, both parts include multiple turns such as 2 to 4 complete 360xc2x0 rotations about the helixes formed by the parts. The helixes formed by the parts are coaxial with the closure when the closure is fully received in or being rotated into the receiving channel between the arms.
One major distinguishing feature of the guide and advancement structure is that each of the parts include elements that mechanically interlock with the opposite part as the closure is rotated and thereby advanced into the receiving channel toward the bottom of the channel and into engagement with a rod received in the channel.
Each part of the guide and advancement structure preferably has a generally constant and uniform cross section, when viewed in any cross sectional plane fully passing through the axis of rotation of the closure during insertion, with such uniform cross section extending along substantially the entire length of the interlocking form. It is noted that at opposite ends of each interlocking form, the form must be feathered or the like and so the cross section does change some at such locations, while retaining part of the overall shape. In particular, the outer surfaces of each interlocking form remain sufficiently uniform to allow interlocking forms to be rotated together and slide tangentially with respect to each other through one or more complete turns of the closure relative to the receiving channel. Each part may be continuous from near a bottom of the closure or receiving channel to the top thereof respectively. In certain circumstances one or both parts may be partly discontinuous, while retaining an overall helical configuration with a generally uniform cross sectional shape. When the interlocking form has multiple sections due to being discontinuous, each of the sections has a substantially uniform cross section along substantially the entire length thereof.
In order to provide an interlocking structure, the parts of the structure include helical wound projections or interlocking forms that extend radially outward from the closure and radially inward from the receiving channel. The interlocking forms may be of many different shapes when viewed in crossection with respect to a plane passing through the axis of rotation of the plug during insertion. In general, the interlocking forms increase in axial aligned width or have a depression at a location spaced radially outward from where the interlocking form attaches to a respective closure or receiving channel, either upward (that is, parallel to the axis of rotation of the closure in the direction from which the closure comes or initially starts) or downward or in both directions. This produces a first mating element that is in the form of a protrusion, bump, ridge, elevation or depression on the interlocking form that has a gripping or overlapping portion. The opposite interlocking form has a second mating element with a gripping or overlapping portion that generally surrounds or passes around at least part of the first mating element in such a way that the two are radially mechanically locked together when the closure is advanced into the receiving channel.
Therefore, in accordance with the invention a mating and advancement structure is provided for joining two devices, that are preferably medical implants and especially are an open headed implant that includes a rod receiving channel and a closure for closing the receiving channel after the rod is received therein. The mating and advancement structure includes a pair of mateable and helical wound interlocking forms with a first interlocking form located on an outer surface of the closure and a second interlocking form located on an inner surface of the receiving channel or receiver. The first and second interlocking forms are startable so as to mate and thereafter rotatable relative to each other about a common axis so as to provide for advancement of the closure into the receiver during assembly when the closure interlocking form is rotated into the receiver interlocking form. The first and second interlocking forms have a helical wound projection that extends radially from the closure and the receiver respectively. Each interlocking form projection has a base that is attached to the closure or receiver respectively and preferably includes multiple turns that may each be continuous or partially discontinuous with constant or uniform cross-sectional shape. The interlocking forms have substantial axial width near an outer end thereof that prevents or resists misalignment of the interlocking form during initial engagement and rotation thereof.
After assembly, in some embodiments each turn of each projection generally snugly engages turns of the other projection on either side thereof. In other embodiments there must be sufficient tolerances for the parts to slide tangentially, so that when thrust surfaces of the interlocking forms are very close during tightening, some gap occurs on the leading side of the closure interlocking form. In such a case the portions of the interlocking forms on the thrust side thereof lock together and prevent radial splaying. Located radially spaced from where the base of each projection is attached to either the closure or receiver respectively, is an axially extending (that is extending in the direction of the axis of rotation of the plug or vertically) extension or depression. The opposite or mating interlocking form has elements that wrap around or into such extensions or depressions of the other interlocking form. That is, the forms axially interdigitate with each other and block radial movement or expansion. In this way and in combination with the interlocking forms preferably being snug relative to each other with sufficient clearance to allow rotation, the interlocking forms, once assembled or mated lock to prevent radially slipping or sliding relative to each other, even if the base of one or both is bent relative to the device upon which it is mounted. It is possible that the cross section of the projection (in a plane that passes through the plug axis of rotation of the plug) of each section of each turn or pass of the interlocking form be the same, although this is not required in all embodiments. For example, part of the interlocking form may be missing in the region between opposed arms when assembly is complete as this area is not required to hold the arms together.
Preferably the present invention provides such an interlocking form for use in a medical implant closure which resists splaying tendencies of arms of a receiver. In one embodiment the interlocking form of the present invention provides a compound or xe2x80x9cnon-linearxe2x80x9d surface on a trailing face, thrust face or flank of the interlocking form.
The interlocking form located on the closure in one embodiment is helically wound about a cylindrical outer surface of the closure and has an inner radius or root, and an outer radius or crest that remain constant over substantially the entire length of the interlocking form. The receiver has a mating or similar shaped interlocking form wound about the interior thereof. In this embodiment the interlocking form has leading or clearance surfaces and trailing or thrust surfaces, referenced to the direction of axial movement of the form when rotated into one another.
The structure also includes an internal helical wound interlocking form located on an internal surface of a receiver member and having an outer root and an inner crest. The internal interlocking form has thrust surfaces which are oriented in such a direction so as to be engaged by the thrust surfaces of the external interlocking form of a member engaged therewith.
In the interlocking forms of this series of embodiments, the thrust surfaces are xe2x80x9cnon-linearxe2x80x9d or compound. That is, the thrust surfaces have a non-linear appearance when represented in cross section. The purpose for the non-linear or compound surface is to provide a portion of the thrust surface which is oriented in such a direction as to resist a tendency of the receiver to expand when tightening torque is applied to rotate the interlocking forms into a mating relationship. As applied to a closure for an open headed bone implant screw, the non-linear or compound surfaces of the interlocking forms resist splaying tendencies of the arms of the head. The objective of the interlocking form is not necessarily to generate a radially inwardly directed force on the receptacle in tightening the fastener (although this may occur in some embodiments), but importantly to resist and prevent outward forces generated by engagement of the closure with the closure receptacle or by other forces applied to the components joined by the closure and closure receptacle. It is noted that the present invention requires that only a portion of the thrust surfaces of a closure be so configured as to face toward the closure axis and only a portion of thrust surfaces of a closure receptacle face away from the axis.
While the axial extension or depression in one series is located on the thrust or trailing surface, it is also possible for such to be located on the opposite or leading surface or both.
In this series of embodiments, a section of the interlocking form at the crest, that is located radially outward of the root, is enlarged in cross sectional area to create a gripping, locking or stopping surface that resists slippage or sliding in a radial direction relative to an opposed interlocking form. In a complementary manner, a section of the interlocking form between the root and the crest and that is radially spaced from the root is enlarged in cross sectional area to create a gripping, locking or stopping surface that engages a like surface of the opposite interlocking form. The enlarged sections of the inner and outer interlocking forms are created, in practice, by cutting, molding, machining or the like grooves or channels or the like into a radially inward portion of the thrust surface of the external interlocking form and mating grooves or channels into a radially outward portion of the thrust surface of the internal interlocking form. Such grooves or channels may be formed by specially shaped taps and dies, cutting elements or by other suitable manufacturing processes and technologies, including molding.
The interlocking forms of the present invention may be implemented in a variety of configurations of non-linear, compound, or complex trailing and/or leading surfaces. The nomenclature used to describe variations in the interlocking forms of the present invention is especially referenced to the external interlocking forms located on a closure, with complementary or similar shapes applied to the internal interlocking forms on a receiver. In an axial shoulder interlocking form of the present invention, a somewhat squared gripping shoulder is formed on an outer periphery of the external interlocking forms and an inner gripping surface on the internal interlocking forms. The axial shoulder interlocking form results in complementary cylindrical surfaces on the external and internal interlocking forms which mutually engage when the fastener or closure is rotated into a closure receptacle.
In an axial extending bead interlocking form, the external interlocking form is provided with a rounded peripheral bead or lateral lip which projects in an axial direction along the interlocking form crest and a complementary rounded concave channel in the internal interlocking form. The reverse occurs with the internal interlocking form.
In a radial bead interlocking form, a rounded bead enlargement is formed on the radially outward periphery at the crest of the external interlocking form, while the internal interlocking form is formed in a complementary manner to receive the radial bead interlocking form.
A scalloped or scooped interlocking form is, in effect, a reciprocal of the axial bead interlocking form and has a rounded channel or groove located along the thrust surface of the external interlocking form, with a complementary rounded convex bead shape formed associated with the internal interlocking form.
A variation of the axial bead interlocking form is a medial bead embodiment. In the medial bead interlocking form, a bead projects from a base thrust surface of an external interlocking form in an axial direction at a location medially between the root and crest of the interlocking form. In a complementary medial bead internal interlocking form, an axial groove is formed in a base thrust surface between the root and crest. In a medial groove interlocking form, an axial groove is formed in a base thrust surface of the external interlocking form medially between the root and crest, while the internal interlocking form has an axial bead located medially between the root and crest.
Variations in the above described interlocking forms are envisioned with respect to relative extensions or enlargements and depressions or depth of grooves of the various interlocking forms. In some variations, the opposite interlocking forms have the same but reversed and inverted cross section, whereas in others the cross section of the paired interlocking forms is different. It is noted that many other configurations of interlocking forms with non-linear, compound or complex thrust surfaces are envisioned, which would be encompassed by the present invention.
The interlocking forms of the present invention find particularly advantageous application in various types of bone implant devices, although the inventive interlocking forms are not limited to such use. The interlocking forms also have advantages in reducing misalignment problems of cross-interlocking and misinterlocking of interlocking forms when the opposed interlocking forms are joined and rotated which is commonly encountered in such devices when threads of various types are used.
Therefore, objects of the present invention include: providing an improved closure for an open headed lightweight and low profile medical implant wherein the implant has a pair of spaced arms and the closure closes between the arms; providing such a closure which includes a pair of opposed interlocking forms and which resists tendencies of the arms to splay or separate during insertion of the closure, to thereby reduce the likelihood of failure of the implant and closure system during use; providing such a closure which can be installed at comparatively high torques to thereby secure the closure in the receiver channel and in certain embodiments to also lock a rod member in the open head of the implant where the closure engages and is urged against the rod by rotation in a receiver channel of the remainder of the implant; providing an interlocking form for such a closure which resists tendencies of parts of the channel receiver to expand radially outward in response to high torque applied to the closure; providing such an interlocking form in which the respective thrust surfaces of mating internal and external interlocking forms are xe2x80x9cnon-linearxe2x80x9d, compound, or complex to provide only a portion of each trailing or leading surface which is oriented in such a direction as to resist the splaying or expanding tendencies of parts of the receiving channel; providing such an interlocking form wherein the interlocking form has a base that is secured to a member and the interlocking form extends radially outward from the base with an axial extension starting at or radially spaced from the base and further wherein the interlocking form has an extension or depression that extends in an axial direction relative to an axis of rotation of the interlocking form and which mates with the opposite interlocking form so as to grip or hold such extension or depression and yet further wherein opposed interlocking forms are rotatable relative to each other during assembly, but are preferably sufficiently snug or located sufficiently near to one another to prevent one interlocking member to slide radially past another when torque is applied thereto or when forces act on the implant; providing embodiments of such an interlocking form having an enlarged radial cross section wherein the enlargement is spaced radially outward of a root of the external interlocking form and a complementary enlarged cross section spaced radially inward of a root of the internal interlocking form; providing embodiments of such an interlocking form having a first groove or channel formed in a surface inward of a periphery of an external interlocking form and a complementary second groove or channel formed in a surface inward of a periphery of an internal interlocking form so that the paired interlocking forms overlap and radially lock together upon assembly; providing embodiments of such an interlocking form in which the enlarged peripheries and grooves of the external and internal interlocking form have or form angularly defined or axially extending shoulders; providing embodiments of such an interlocking form in which the enlarged peripheries of the external and internal interlocking form have or form arcuately defined or rounded shoulders; providing such interlocking forms having a generally uniform cross section along a substantial length thereof; providing such interlocking forms that rotate relative to each other at least one full turn upon assembly; providing such interlocking forms which reduce the likelihood of cross-interlocking or misinterlocking problems of members during initial joining; providing such interlocking forms which can be formed relatively economically using appropriate metal forming technologies; and providing interlocking forms, particularly for implant and bone fixation hardware, which are economical to manufacture, which are secure and efficient in use, and which are particularly well adapted for their intended usage.
Other objects and advantages of this invention will become apparent from the following description taken in conjunction with the accompanying drawings wherein are set forth, by way of illustration and example, certain embodiments of this invention.
The drawings constitute a part of this specification and include exemplary embodiments of the present invention and illustrate various objects and features thereof.

Helical interlocking mating guide and advancement structure


An apparatus for determining probability of error in identifying evidence includes a computer. The apparatus includes a non-transitory memory in communication with the computer in which is stored a software program, and prior and posterior probability distributions from a plurality of independent tests conducted on an item of evidence. For each test, the computer forms a factor distribution from the test's probability distributions using the software program stored in the non-transitory memory of the computer. The computer convolves the independent factor distributions to form a joint factor distribution using the software program. The computer calculates a tail probability from the joint factor distribution using the software program to determine a probability of error in identifying the evidence. The computer stores the probability of error in the non-transitory memory. A method. A computer program.

Statistical computing can provide an accurate match statistic for forensic identification. The resulting likelihood ratio (LR) quantifies the probative force of evidence, capturing in a single number the strength of match. But the LR may be difficult to explain to a non-statistician. Nor does the LR convey the chance of error, often a juror's foremost concern.
Error can be expressed as a false match probability (FMP). With biological evidence, a false match occurs when someone's DNA is not present, but has a match statistic at least as large as the reported LR. FMP is the chance of this misidentification occurring.
This invention shows how to rapidly and accurately calculate the FMP. The approach permits FMP evaluation on very large sets, and provides sharper error estimates than the guaranteed 1/LR upper bound. Mathematical theory is presented, along with a DNA case example of sexual assault and database search. By reporting exact error rates on specific evidence data, FMP assists investigators, scientists, lawyers, jurors and judges in their forensic decision-making.

Method, apparatus and computer software program for determining probability of error in identifying evidence