Schulz-Flory Distribution Research Articles

Hydrotalcite supported Co catalysts for CO hydrogenation

It is well known that the catalytic performance of Co catalysts depends on supports and promoters. The focus of this work was to investigate the catalytic activities for CO hydrogenation of Co catalysts supported on the solid base, hydrotalcite (HT), and to probe the role of support in the reaction. A cobalt catalyst containing 10 wt% cobalt supported on HT was prepared using the incipient wetness impregnation method. Pre-calcined HT (CHT), alumina and magnesium oxide were also employed as supports for comparison purposes. Catalysts were characterized by surface area and porosity analysis, XRD, TEM/STEM/EDX, TPR and H 2 chemisorption. The catalytic activity was tested using a fixed-bed reactor at 230 °C, 1.8 atm, and H 2/CO = 2. It was found that the hydrotalcite supported catalyst showed the highest steady-state reaction rates. The activities of Co/HT reduced at different reduction temperatures (from 300 to 600 °C) were also compared. Reduction at 500 °C resulted in the highest activity; however, CH 4 selectivity was also enhanced as the reduction temperature increased. The product distributions for Co/HT obeyed an Anderson–Schulz–Flory distribution. The α values were not impacted by the different reduction temperatures for Co/HT. The characterization and reactivity results suggest that the thermal stability properties of hydrotalcite, BET surface area, particle size of Co, the interaction between Co and the support, and the reducibility of Co were all important in governing the catalytic performance of the Co catalysts for CO hydrogenation. Our study suggests that HT is a promising support for Co for Fischer–Tropsch synthesis because it gives high activity (higher than Co/Al 2O 3) without the need for a reduction promoter.

Depletion interaction between spheres in an ideal equilibrium polymer fluid: Exact asymptotic results

We use a continuum chain model and develop an analytical theory for the interaction between two spheres immersed in a fluid of ideal equilibrium polymers. The theory can be applied to both adsorbing and nonadsorbing spheres. Here we focus on two nonadsorbing spheres and determine the classical depletion interaction between them. Compact, and exact, results are derived for the asymptotic behavior of the depletion interaction, which has a Yukawa form. We show also that in the limit of large spheres (and large surface to surface separation) the Derjaguin approximation is valid. We compare our asymptotic expression with numerical solutions of an ideal equilibrium polymer fluid consisting of discrete chains. Our asymptotic approximation accurately predicts long-range interactions between small spheres. For large spheres it predicts the interaction very well over most of the separation range. We also consider a single sphere immersed in the polymer fluid and show how our results can be generalized to treat polydisperse polymer fluids, where the polydispersity is described by a Schulz-Flory distribution.

Development of Novel Catalysts for Fischer–Tropsch Synthesis: Tuning the Product Selectivity

AbstractFischer–Tropsch synthesis is a heterogeneous catalytic process for the production of clean hydrocarbon fuels or chemicals from synthesis gas (CO+H2), which can be derived from non‐petroleum feedstocks such as natural gas, coal, or biomass. Fischer–Tropsch synthesis has received renewed interests in recent years because of the global demand for a decreased dependence on petroleum for production of fuels and chemicals. The product distributions with conventional Fischer–Tropsch catalysts usually follow the Anderson–Schulz–Flory distribution and are typically unselective with regards to the formation of hydrocarbons from methane to waxes. Selectivity control is one of the key challenges of research into Fischer–Tropsch synthesis. This Review article summarizes the effects of key factors on catalytic properties, particularly the product selectivity, and highlights recent developments of novel Fischer–Tropsch catalysts and new strategies with an aim at controlling the product selectivity.

Efficient solution of the self-consistent field theory for block copolymer fluids displaying Schulz–Flory polydispersity

We develop a new formulation of polymer self-consistent field theory for polydisperse copolymer fluids satisfying the Schulz-Flory distribution. The result we obtain is remarkably simple and quickly solved numerically. The computational effort scales inversely with the width of the Schulz-Flory distribution. This suggests a significant saving in computational effort when compared with existing approximate solutions of the polymer self-consistent field equations for polydispersed systems.

A DFT study of the chain growth probability in Fischer–Tropsch synthesis

The chain growth probability ( α value) is one of the most significant parameters in Fischer–Tropsch (FT) synthesis. To gain insight into the chain growth probability, we systematically studied the hydrogenation and C C coupling reactions with different chain lengths on the stepped Co(0001) surface using density functional theory calculations. Our findings elucidate the relationship between the barriers of these elementary reactions and the chain length. Moreover, we derived a general expression of the chain growth probability and investigated the behavior of the α value observed experimentally. The high methane yield results from the lower chain growth rate for C 1 + C 1 coupling compared with the other coupling reactions. After C 1, the deviation of product distribution in FT synthesis from the Anderson–Schulz–Flory distribution is due to the chain length-dependent paraffin/olefin ratio.

Density-Functional Theory for Polymer Fluids with Molecular Weight Polydispersity

We develop a density-functional theory for polydisperse polymer fluids satisfying the Schulz-Flory distribution. The resulting equations are remarkably simple and quickly solved, the computational effort scaling with the polydispersity index, rather than the average molecular weight. Equilibrium, or "living", polymers enter naturally as very polydisperse samples. We illustrate the importance of polydispersity on colloid stability by investigating interactions between adsorbing and nonadsorbing surfaces. Significant free energy barriers are present in monodisperse samples, but these diminish as the degree of polydispersity increases.

Studies on the reaction mechanism of the Fischer–Tropsch synthesis on iron and cobalt

A new mechanism of the Fischer–Tropsch synthesis is proposed based on the hypothesis that two incompatible mechanisms are involved resting exclusively on methylene and on carbon monoxide insertion, respectively. This hypothesis is reflected by the well known superposition of two Anderson–Schulz–Flory distributions. Experiments with co-feeding of ethene, 1-alkenes and diazomethane as a source of surface methylene and also the carbon number distribution of branched hydrocarbons strongly support the hypothesis of two independent mechanisms and the methylene insertion mechanism of one of them. Co-feeding of alcohols, the dependence of the ratio of the two mechanisms on the pressure of hydrogen and carbon monoxide and the promoter effect of alkali on iron catalysts also prove the hypothesis of the two mechanisms and point to the carbon monoxide insertion mechanism as the second mechanism that is characterized by the higher growth probability of the resulting Anderson–Schulz–Flory distribution. Furthermore new interpretations of the crucial steps of C–C linkage and chain termination are given. The insertion of methylene is interpreted by coupling of an alkylidene and a methylene surface species towards a coordinated olefin with the chance of chain growth termination by 1-alkene desorption. For the carbon monoxide insertion mechanism the termination of chain growth is assumed to occur by the formation of 1-alkenes and of alcohols via an alcoholate intermediate. The new mechanism gives without any exception a sound interpretation of a great variety of experiments and contributes also to the interpretation of the promoter effect of alkali and of the different performance of cobalt and iron catalysts.

Study on products distribution of iron and iron–zeolite catalysts in Fischer–Tropsch synthesis

The dependencies of hydrocarbon product distributions of iron and physical mixture of iron–zeolite catalyzed Fischer–Tropsch synthesis on reaction conditions include: reaction temperature, reaction pressure, H2/CO feed ratios; space velocity and effect of zeolite presence have been investigated. The concept of two superimposed Anderson–Schulz–Flory distributions has been applied for the representation of the product distribution for both iron and iron–zeolite catalysts. Zeolite presence increased secondary reactions that include cracking of heavier products and light olefins oligomerization. Product distribution of iron–zeolite catalyst was comparable with iron catalyst at high space velocity, because the role of the zeolite on overall reaction declined.The results of the product distribution dependency on the reaction conditions over both iron and iron–zeolite catalysts showed that the average number of carbon decreases with H2/CO ratio increasing and the reaction temperature in product.

Examining the effect of chain length polydispersity on the phase behavior of polymer solutions with the statistical associating fluid theory (Wertheim TPT1) using discrete and continuous distributions

Polymers are naturally polydisperse. Polydispersity may have a large effect on the phase behavior of polymer solutions, in particular, on the liquid-liquid phase equilibria. In this paper, we determine the cloud and shadow curves bounded by lower critical solution temperatures for a number of polymer+solvent systems where the polymer is polydisperse in terms of molecular weight (chain length). The moment method [P. Sollich, P. B. Warren, and M. E. Cates, Adv. Chem. Phys. 116, 265 (2001)] is applied with the SAFT approach to determine cloud and shadow curves with continuous Schulz-Flory distributions. It is seen that chain length polydispersity always enhances the extent of liquid-liquid phase equilibria. The predicted cloud curves obtained for continuous distributions are very similar to those obtained for simple ternary mixtures with the same polydispersity index, while the corresponding shadow curves can be very different depending on the composition of the parent distribution. The ternary phase behavior can be used to provide an understanding of the shape of the cloud and shadow curves. Regions of phase equilibria between three liquid phases are found for ternary systems when the chain length distribution is very asymmetrical; such regions are not observed for Schulz-Flory distributions even in the case of a large degree of polydispersity.

Electrochemical synthesis of the σ-aryl complex [NiBr(Mes)(bpy)] and its use as catalyst precursor for the oligomerization of ethylene (Mes = 2,4,6-trimethylphenyl, bpy = 2,2′-bipyridine)

The oxidative addition of mesityl bromide either to electrochemically generated [Ni(bpy)] or to [Ni(COD) 2] (COD = 1,5-cyclooctadiene) in the presence of 2,2′-bipyridine allows the selective, high-yield synthesis of the σ-aryl complex [NiBr(Mes)(bpy)] (Mes = 2,4,6-trimethylphenyl, bpy = 2,2′-bipyridine), which is an efficient catalyst precursor for the oligomerization of ethylene to even-numbered olefins in the C 4–C 26 range with a Schulz–Flory distribution.

Kinetics of CO hydrogenation on modified Cu/ZnO catalyst in a slurry reactor

CO hydrogenation activity and product selectivity of a modified Cu/ZnO catalyst was investigated in a wide range of temperatures, pressures, space velocities, and synthesis gas compositions. Except alcohols, the catalyst produced a significant amount of hydrocarbons and CO 2 . The formation of alcohols and hydrocarbons follows the Anderson–Schulz–Flory distribution. Based on the experimental results obtained in a stirred tank slurry reactor, a mechanistic-kinetic model was developed. The main assumption of the model was that formation of alcohols and hydrocarbons occurred independently on different types of active sites. The model successfully predicts product formation rates within the range of experimental conditions used in this study.

Synthesis of higher alcohols from syngas over Cu-Co 2O 3/ZnO, Al 2O 3 catalyst

Cu-Co 2O 3/ZnO, Al 2O 3 catalysts prepared by co-precipitation were studied by temperature-programmed reduction (TPR) and chemisorption of nitrous oxide (N 2O). Catalytic activity for synthesis of C 1–C 6 alcohols was determined in a fixed bed flow reactor system. Changes in activity and selectivity were obtained with respect to changes of percentage composition of Co-Cu catalyst, temperature (270–355 °C), ratio of H 2/CO (0.5–2), pressure (40–70 atm), feeding flow with GHSV (2260–5060 h −1). In optimum condition, the selectivity for alcohol ( S A) and heavier alcohols ( S C 2 O H + ) were more that 80% and 50%, respectively. The distribution of alcohol products obeys Schulz-Flory distribution. The chain growth probability factor of higher alcohols was independent of conversion.

N,N,N-Tridentate iron(II) and vanadium(III) complexesPart II: Catalytic behavior for the oligomerization and polymerization of ethene and characterization of the resulting products

Abstract A series of N , N , N -tridentate vanadium(III) complexes were tested after activation with methyl aluminoxane (MAO) for ethene oligomerization and polymerization. Variations in the catalyst structure as well as the influence of physical parameters were investigated and the properties of the obtained oligomeric products were determined. Methods of altering the Schulz–Flory distribution of the oligomeric products were investigated. The product properties of the polymers and oligomers obtained with the vanadium(III) complexes and the structurally identical iron(II) complexes were compared. Depending on their substitution pattern, the N , N , N -tridentate vanadium(III) catalysts exhibit high productivities and selectivities towards α-olefin oligomerization products under mild conditions when activated with MAO whereas the corresponding iron complexes produce higher molecular weight materials. The synthesis of these new vanadium(III)- and iron(II)-diiminepyridyl complexes was reported earlier.

Kinetics of CO hydrogenation on modified Cu/ZnO catalyst in a slurry reactor

CO hydrogenation activity and product selectivity of a modified Cu/ZnO catalyst was investigated in a wide range of temperatures, pressures, space velocities, and synthesis gas compositions. Except alcohols, the catalyst produced a significant amount of hydrocarbons and CO 2. The formation of alcohols and hydrocarbons follows the Anderson–Schulz–Flory distribution. Based on the experimental results obtained in a stirred tank slurry reactor, a mechanistic-kinetic model was developed. The main assumption of the model was that formation of alcohols and hydrocarbons occurred independently on different types of active sites. The model successfully predicts product formation rates within the range of experimental conditions used in this study.

Halogen-Substituted 2,6-Bis(imino)pyridyl Iron and Cobalt Complexes: Highly Active Catalysts for Polymerization and Oligomerization of Ethylene

A series of halogen-substituted 2,6-bis(imino)pyridyl ligands and their iron and cobalt complexes [｛2,6-(2,6-X1X2C6H3NdCCH3)2C5H3N＝MCl2] (X1 ＝ X2 ) Br, M ＝ Fe (1), Co (2); X1＝ X2 ＝ Cl, M ＝ Fe (3), Co (4); X1 ＝ Cl, X2 ＝ H, M ＝ Fe (5), Co (6); X1 ＝ Br, X2 ＝ H, M ＝ Fe(7), Co (8); X1＝ I, X2 ＝ H, M ) Fe (9), Co (10)) and [M｛2,6-(2,6-X1X2C6H3NdCCH3)2C5H3N?2｝]2+- [MCl4]2- (X1 ) F, X2 ) H, M ) Fe (11)) have been synthesized. The molecular structures of complexes 1, 8, 9, 10, and 11 were determined by X-ray diffraction. Crystallographic analyses indicate that 1, 8, 9, and 10 are five-coordinate complexes, while 11 is an ion-pair complex with one six-coordinate iron center and one four-coordinate iron center. These metal coordinative complexes, activated by modified methylaluminoxane (MMAO), lead to highly active ethylene polymerization and/or oligomerization catalysts. The catalyst productivity and product properties crucially depended on the metal center and the halogen substituents on the aryl rings. The catalyst productivities are in the range of (0-73.0) _ 106 g/mol of catah. The species 11, having ion-pair structure, is inactive. In particular, the product molar masses were changed from high molar mass (Mw of 377 000) to low molar mass oligomers by varying the halogen substituents. NMR and thermal analyses reveal the polymer is highly linear. The oligomer products follow a Schulz-Flory distribution with high selectivity for linear R-olefins. The effects of reaction condition on the polymerization and oligomerization have also been studied.

Comments about the causes of deviations from the Anderson–Schulz–Flory distribution of the Fischer–Tropsch reaction products

The purpose of this communication is to challenge the “evidence” for higher olefin incorporation into the Fischer–Tropsch (FT) products in secondary reactions and dispute the claims that these postulated reactions are responsible for the “positive deviations” from the Anderson–Schulz–Flory (ASF) distributions. Furthermore, arguments and information are presented to show that multiplicity of the chain growth probability is the only reasonable cause of the reported “positive deviations” in the C 6+ product range.

The influence of various reaction parameters on the performance of (α‐diimine)nickel(II) catalysts in ethylene oligomerization reactions

AbstractModified (α‐diimine)nickel(II) catalysts are suitable for ethylene oligomerization reactions. Due to the mechanism (“chain running”), the formation of double‐bond isomers and branched olefins can be observed. The obtained oligomer mixtures show a Schulz–Flory distribution. Increasing ethylene pressure favors the selectivity of α‐olefin formation. The same effect can be observed when Lewis bases like thiophene or furane are added to the oligomerization reaction mixture. These results can be related to an interaction of the additives with the catalytic active species during the oligomerization process. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1356–1361, 2003

Phosphinooxazolines as assembling ligands in heterometallic complexes

It is shown that phosphinooxazolines such as (2-oxazoline-2-ylmethyl)diphenylphosphine 1 can be used as P,N assembling ligands for the synthesis of heterometallic complexes. These were obtained in a stepwise manner from the iron carbonyl complexes containing one, [Fe(CO)4(PCH2-oxazoline-P)] 2, or two, trans-[Fe(CO)3(PCH2-oxazoline-P)2] 6, P-bound phosphinooxazoline ligands. These metalloligands were then reacted with metal complexes. With 2, complete ligand transfer from Fe to the second metal (Pd) was sometimes observed. The metal–metal bonded complex [(OC)4Fe(μ-PCH2-oxazoline-P,N)PdCl2] 3 was of limited stability, whereas the trinuclear complex trans-[{(OC)4Fe(μ-PCH2-oxazoline-P,N)}2CoCl2] 4, in which 2 functions as a N-donor metalloligand toward the tetrahedral Co(II) centre, was stable and could be fully characterised by X-ray diffraction. This complex catalyses the oligomerization of ethylene to give linear α-olefins in the range C4–C26, with a maximum of the Schulz-Flory distribution around C6. The complex [{(OC)4Fe(μ-PCH2-oxazoline-P,N)}2HgI2] 5 was also prepared from 6. With the metalloligand 6, the Fe→Pd and Fe→Co metal–metal bonded compounds trans-[(OC)3Fe(μ-PCH2-oxazoline-P,N)2Pd(NCMe)](BF4)28 and trans-[(OC)3Fe(μ-PCH2-oxazoline-P,N)2CoCl2] 9 were obtained.

Schulz–Flory oligomerisation of ethylene by the binuclear nickel(ii) complex Ni2Cl4[cis,trans,cis-1,2,3,4-tetrakis-(diphenylphosphino)cyclobutane

The binuclear nickel(II) complex Ni2Cl4(cyclo-tetraphos) (cyclo-tetraphos = cis,trans,cis-1,2,3,4-tetrakis-(diphenylphosphino)cyclobutane) forms, upon activation with MAO, an effective and robust catalyst for the oligomerisation of ethylene to Schulz–Flory distributions of C4–C14 olefins with a mechanism where both chain transfer and chain propagation are first order in ethylene.

A comparative study of the properties of different distribution curves

The maximum, points of inflection and the derived peak width are enumerated for a Poisson, a Gauss and a Schulz-Flory distribution. Starting with a (not necessarily normalized) number distribution the respective molar mass and hyper distributions are derived and the extrema and the peak width are determined as well. It turned out, that Poisson and (narrow, D < 1.1) Gauss distribution can be characterized by the fact that the peak width is an invariant quantity with respect to the number, molar mass and hyper distribution, whereas the peak width changes considerably for a Schulz-Flory distribution. In order to demonstrate the theoretical results commercial polymer standards (prepared by anionic polymerization) were measured by size exclusion chromatography and the constancy of the peak width is demonstrated but the peak widths exceeded by far the theoretically expected values. The influence of axial broadening in size exclusion chromatography is discussed in this context and a simple correction procedure is presented for an ideal Poisson distribution. On the other hand, polymers prepared by stationary radical polymerization displayed a very marked deviation from an invariant peak width, as derived theoretically. It is demonstrated that the location of the peak maximum in the molar mass and the hyper distribution is identical with M n and M w , respectively.