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Síntese e caracterização de material micro-mesoestruturado a partir de precursores microporosos

Teixeira, André Luiz
Fonte: Universidade de Brasília Publicador: Universidade de Brasília
Tipo: Dissertação
POR
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Dissertação (mestrado)—Universidade de Brasília, Instituto de Química, Programa de Pós-Graduação em Química, 2013.; As peneiras moleculares microporosas por apresentarem boa atividade catalítica em relação ao craqueamento do petróleo, são os mais importantes catalisadores, usados para estes fins. Entretanto o seu uso no craqueamento do petróleo é limitado em relação à difusividade, já que as moléculas de diâmetro cinético maiores, não se difundem no interior dos canais do catalisador, não sendo assim catalisada uma gama muito grande de moléculas. Com o objetivo de ampliar o número de aplicações destes catalisadores, os pesquisadores conseguiram obter peneiras moleculares mesoporosas com os poros maiores que os dos materiais zeolíticos. Devido aos seus mesoporos, estas apresentam uma ótima difusividade em relação às moléculas de diâmetros maiores sendo possível assim, catalisar uma gama maior de moléculas. Entretanto estas estruturas apresentam uma baixa atividade catalítica, o que torna limitado seu uso em reações que precisam de sítios catalíticos. Recentemente, pesquisas realizadas nesta área têm obtido estrutura...

Pyridazine chromium complexes in NaY zeolite

Figueiredo, Hugo; Quintelas, C.; Silva, Bruna Andreia Nogueira Airosa; Tavares, M. T.; Raposo, M. Manuela M.; Fonseca, A. Maurício C.; Neves, Isabel C.
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Conferência ou Objeto de Conferência
Publicado em /04/2007 ENG
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The immobilization of transition metal complexes with redox catalytic activity in solid supports has attracted much interest due to their potential use as hete rogeneous catalysts in mild conditions. One of the most common strategies for the preparation of zeolites with metal transition complexes is the flexible ligand method. The incorporation of the cation requires the exchange with the charge-balancing cation from zeolite framework. Two different procedures for ion exchange are: the traditional ion exchange from aqueous solutions containing the metal and metal biosorption by microorganisms supported on the zeolite. In previous work, we reported the development of a biosorption system for Cr(IV) removal from industrial wastewater, by using bacterial biofilm supported on zeolites. The system has shown ability to remove chromium from aqueous solutions with concentrations ranging 10 – 250 mg/L. The biological activity of the employed bacteria, Arthrobacter viscosus, induces reduction of the Cr (VI) to Cr (III) species. The aim of this work is to evaluate the traditional ion exchange and the biosorption paths for the immobilization of chromium complexes in NaY zeolite. The bio-monomer under investigation, the 3-methoxy-6-chloropyridazine...

Colonization of Aspergillus japonicus on synthetic materials and application to the production of fructooligosaccharides

Mussatto, Solange I.; Aguilar Gonzalez, Cristobal Noé; Rodrigues, L. R.; Teixeira, J. A.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Publicado em /04/2009 ENG
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The ability of Aspergillus japonicus ATCC 20236 to colonize different synthetic materials (polyurethane foam, stainless steel sponge, vegetal fiber, pumice stones, zeolites, and foam glass) and to produce fructooligosaccharides (FOS) from sucrose (165 g/L) is described. Cells were immobilized in situ by absorption, through direct contact with the carrier particles at the beginning of fermentation. Vegetal fiber was the best immobilization carrier as A. japonicus grew well on it (1.25 g/g carrier), producing 116.3 g/L FOS (56.3 g/L 1-kestose, 46.9 g/L 1-nystose, and 13.1 g/L 1-β-fructofuranosyl nystose) with 69% yield (78% based only in the consumed sucrose amount), giving also elevated activity of the β-fructofuranosidase enzyme (42.9 U/mL). In addition, no loss of material integrity, over a 2 day-period, was found. The fungus also immobilized well on stainless steel sponge (1.13 g/g carrier), but in lesser extents on polyurethane foam, zeolites, and pumice stones (0.48, 0.19, and 0.13 g/g carrier, respectively), while on foam glass no cell adhesion was observed. When compared with the FOS and β-fructofuranosidase production by free A. japonicus, the results achieved using cells immobilized on vegetal fiber were closely similar. It was thus concluded that A. japonicus immobilized on vegetal fiber is a potential alternative for high production of FOS at industrial scale.; Fundação para a Ciência e a Tecnologia (FCT)

Desenvolvimento de compósitos poliméricos baseados em zeólitos

Lopes, Ana Catarina Teixeira Castro
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Dissertação de Mestrado
Publicado em 08/05/2009 POR
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Dissertação de Mestrado em Física (área de especialização em Ensino); A inclusão de nanopartículas em materiais poliméricos tem como objectivo optimizar as propriedades dos materiais para aplicações específicas, despertando actualmente um grande interesse científico e tecnológico. O presente trabalho teve como objectivo a preparação e caracterização de nanocompósitos de poli(fluoreto de vinilideno) (PVDF) com zeólitos do tipo Y, sendo estes preparados sob a forma de filmes finos. Assim, diferentes zeólitos do tipo Y, foram inseridos na matriz polimérica do PVDF, na fase apolar (fase α). Foram estudadas as propriedades eléctricas e mecânicas dos nanocompósitos preparados, considerando os seguintes factores: - desaluminação no zeólito Y; - quantidade do ião sódio presente no zeólito Y; - variação do metal de transição (cobre, níquel e ferro) presente no zeólito Y; - concentração do ião ferro e da sua valência no zeólito Y. Os estudos realizados permitiram verificar que a introdução de nanopartículas de zeólito Y não altera a fase presente no material polimérico nem a sua estrutura esferulítica. Pelo contrário, as suas propriedades eléctricas e mecânicas sofrem alteração, sendo estas dependentes do tipo de nanopartícula inserida no polímero. Para os nanocompósitos contendo NaY verificou-se que a resposta dieléctrica era superior. Após troca iónica com iões ferro...

Effect of the supporting zeolite structure on Cr biosorption : performance of a single-step reactor and of a sequential batch reactor : a comparison study

Figueiredo, Hugo; Silva, Bruna Andreia Nogueira Airosa; Quintelas, C.; Neves, Isabel C.; Tavares, M. T.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Publicado em /09/2010 ENG
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This work presents a study on the applicability of a zeolite-biomass system to the entrapment of metallic ions, starting from Cr(VI) solutions up to 100 mgCr/L, in batch processes. The effect of the zeolitic support on the overall system performance was evaluated comparing two large pore zeolitic structures which differ in chemical composition and ion-exchange capacity: Faujasite (HY and NaY) and Mordenite (HMOR and NaMOR) zeolites. The systems were tested in single-step and in sequential processes. In single-step studies, HY zeolite was found to be the most efficient support when applied to low Cr concentrations (overall Cr removal of 93.4%), whereas for the higher initial Cr concentration, the higher ion-exchange capacity of NaY zeolite was determinant to achieve the highest overall Cr removal of 77.6%. The evolution of Cr(VI) entrapment was strongly dependant on the zeolitic support used in the system. In sequential batch processes, HY zeolite was found to be the most efficient support with a 98.2% overall Cr removal. The reduction of Cr(VI) promoted by the biomass is more suited to the dynamics of the sequential process. NaY zeolite behaved similarly to HMOR and NaMOR zeolites, as these systems removed between 87.3 and 93.4% of the initial Cr.; Fundação para a Ciência e a Tecnologia (FCT)

Development of electroactive polymer nanocomposites with porous structured materials

Lopes, Ana Catarina Teixeira Castro
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Tese de Doutorado
Publicado em 10/09/2013 ENG
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Tese de doutoramento em Ciências (área de especialização em Física); Electroactive polymer composites are interesting materials for advance technological applications due to the possibility to combine the electroactive properties of the polymer matrix with a large variety of fillers that allow tailored responses for specific applications. The best all-around electroactive polymers are poly(vinylidene fluoride) (PVDF) and its copolymers which allied with the properties of porous zeolite materials, with tailored shape, size and Si/Al ratio, among others, leads to the possibility of development of promising PVDF/zeolite composites. In this way, a study of the structural, thermal and electrical properties of PVDF composites prepared with different framework zeolite types (LTL, LTA, FAU and MFI), different polymer solvents (DMF, DMSO, TEP) and different zeolite (NaY) concentrations (4, 16, 24 and 32 wt %) was performed. Further, the dielectric response, electrical conductivity and electric modulus of the composites were investigated as a function of NaYzeolite content. The zeolite influence on the electroactive γ-phase crystallization of PVDF was explored, as well as the effect of clay layered structure (Montmorillonite...

Novel environmental catalysts prepared with residual metals on bioactive nanomaterials

Tavares, M. T.; Neves, Isabel C.; Quintelas, C.; Currás, M.
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Conferência ou Objeto de Conferência
Publicado em /05/2009 ENG
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Volatile organic compounds (VOCs), which are emitted from many industrial processes and transport activities, constitute an important concern for the scientific community due to their role in atmospheric pollution and subsequent impact on human health. Among the various methods that can be applied to efficiently control VOCs emissions, catalytic oxidation over solid catalysts seems to be the most efficient and cost-effective technology. Catalysts used for the treatment of gas streams contaminated with VOCs are mostly based on noble metals. Using low cost transition metals such as chromium to replace the noble metal in the catalysts is quite desirable in terms of economical and practical consideration. The catalytic oxidation of 1,2-dichlorobenzene was investigated over NaY and NaX zeolites, loaded with chromium through the action of a robust biosorption system consisting of a bacterial biofilm supported on the zeolites. The results of biosorption showed that the maximum metal removal efficiency was 20%, in both systems based on NaYor NaX, starting from solutions with chromium(VI) concentrations ranging from 50 to 250 mgCr/L [1]. The bacterial biofilm, Arthrobacter viscosus, supported on the zeolite reduces Cr(VI) to Cr(III). The Cr(III) is retained in the zeolite by ion exchange. The new catalysts were characterized by spectroscopic methods (FTIR and ICP-AES)...

Biosorption system produced from biofilms supported on Faujasite (FAU) zeolite, process for obtaining it and its usage for removal of hexavalent chromium (Cr(VI))

Tavares, M. T.; Neves, Isabel C.
Fonte: Universidade do Minho Publicador: Universidade do Minho
Tipo: Patente
Publicado em 23/04/2008 ENG
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The present invention refers to a biosorption system composed of a bacterial biofilm supported in synthetic zeolites, for usage in various types of industry for the removal of hexavalent chromium, through the retention of metal ions in the biofilm, in solutions with concentrations between 50 and 250 mgCr/L, process for obtaining it and respective usages. This process consists in obtaining a bacterial biofilm of Arthrobacter viscosus, supported on a faujasite (FAU) zeolite. The biofilm promotes the reduction of Cr (VI) to Cr (III) and, subsequently, Cr (III) is fixed in the zeolite by ion exchange. Several characterization procedures, like spectroscopic techniques (FTIR and ICP-AES), surface analysis (XRD and SEM) and thermal analysis (TGA) reveal that the biosorption process does not modify the morphology or the structure of the FAU zeolite. The biosorption system, and respective fixation process of hexavalent chromium in faujasite (FAU) zeolites, may be applicable to the treatment of industrial, mining or agriculture wastewater, for hexavalent chromium removal.

Conversão de xilanas-a-furfural na presença de sólidos ácidos mesoporosos

Dias, Ana Sofia Vagueiro de Sousa
Fonte: Universidade de Aveiro Publicador: Universidade de Aveiro
Tipo: Tese de Doutorado
POR
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O objectivo deste trabalho era encontrar catalisadores ácidos mesoporosos para a conversão das xilanas em furfural, que pudessem substituir o ácido sulfúrico usado no processo industrial. Esta conversão ocorre, em meio ácido, por hidrólise da xilana em xilose que, por sua vez, dá origem ao furfural por desidratação e ciclização. O desempenho destes catalisadores foi estudado na reacção da xilose, o passo limitante, em dimetilsulfóxido ou num sistema bifásico (água/solvente orgânico). Nos Capítulos 2 a 4, descreve-se a actividade catalítica dos heteropoliácidos (HPAs) do tipo Keggin em fase homogénea e heterogénea. O ácido dodetungstofosfórico (PW) foi o HPA mais interessante. O PW foi suportado em sílicas mesoporosas, obtendo-se materiais mais activos do que o PW livre e equiparáveis ao ácido sulfúrico. A lixiviação de PW durante a reacção resultou na perda de actividade nas reutilizações. A actividade de sais de césio de PW livres ou suportados em sílicas mesoporosas foi também estudada na reacção da xilose, não se tendo observado vantagens significativas destes materiais relativamente aos correspondentes de PW. No Capítulo 5 descreve-se a preparação e caracterização de sílicas mesoporosas e um material híbrido contendo grupos ácidos organo-sulfónicos imobilizados. O desempenho catalítico destes materiais foi superior ao obtido com zéolitos comerciais...

Estabilização de solo contaminado com zinco usando zeólitas sintetizadas a partir de cinzas de carvão

Fungaro,Denise Alves; Flues,Marlene Sotto-Mayor; Celebroni,Amanda Paccini
Fonte: Sociedade Brasileira de Química Publicador: Sociedade Brasileira de Química
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2004 PT
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The effect of synthetic zeolites on stabilizing Zn-contaminated soil using 0.01 mol L-1 CaCl2 leaching solution in batch experiments was investigated. The zeolites were synthesized from coal ash by hydrothermal treatment with alkaline solution. The additive enhanced the sorption capacity of the soil and reduced leaching. Zinc leaching was reduced by more than 80% using a minimum of 10% additive. The higher cation exchange capacity of the zeolite/soil mixtures and higher pH were responsible for stabilizing Zn in soil. The poly(2-aminobenzenesulfonic acid)-coated mercury thin-film electrode was used for the determination of zinc.

Materiais magnéticos baseados em diferentes zeólitas para remoção de metais em água

Pergher,Sibele B. C.; Oliveira,Luiz C. A.; Smaniotto,Alessandra; Petkowicz,Diego I.
Fonte: Sociedade Brasileira de Química Publicador: Sociedade Brasileira de Química
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/10/2005 PT
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In this work the adsorption features of zeolites (NaY, Beta, Mordenite and ZSM-5) have been combined with the magnetic properties of iron oxides in a composite to produce a magnetic adsorbent. These magnetic composites can be used as adsorbents for contaminants in water and subsequently removed from the medium by a simple magnetic process. The magnetic zeolites were characterized by XRD, magnetization measurements, chemical analyses, N2 adsorption isotherms and Mössbauer spectroscopy. These magnetic adsorbents show remarkable adsorption capacity for metal ion contaminants in water.

Isobutane/2-butene alkylation with zeolite Y without BrÆnsted acidity

Rosenbach Jr,Nilton; Mota,Claudio J. A.
Fonte: Sociedade Brasileira de Química Publicador: Sociedade Brasileira de Química
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/08/2005 EN
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Alkylation of isobutane with 2-butene was performed on metal-exchanged Y zeolites, using an alkylchloride as carbocation initiator. The results indicated that, compared with a protonic zeolite, the deactivation was significantly slower and the production of trimethylpentanes was higher on the metal-exchanged zeolites. The metal cations act as Lewis acids, interacting with the chloride initiating the carbocationic reactions. The results also support the view that protonic sites on the catalyst favor adsorption of the olefin, thus increasing oligomerization rate.

Oxidative dehydration of glycerol to acrylic acid over vanadium-impregnated zeolite beta

Pestana,Carolina F. M.; Guerra,Antônio C. O.; Ferreira,Glaucio B.; Turci,Cássia C.; Mota,Claudio J. A.
Fonte: Sociedade Brasileira de Química Publicador: Sociedade Brasileira de Química
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2013 EN
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The oxidative dehydration of glycerol to acrylic acid was studied over vanadium-impregnated zeolite Beta. Catalysts were prepared by wet impregnation of ammonium metavanadate over ammonium-exchanged zeolite Beta, followed by air calcination at 823 K. Impregnation reduced the specific surface area, but did not significantly affected the acidity (Brønsted and Lewis) of the zeolites. The catalytic evaluation was carried out in a fixed bed flow reactor using air as the carrier and injecting glycerol by means of a syringe pump. Acrolein was the main product, with acetaldehyde and hydroxy-acetone (acetol) being also formed. Acrylic acid was formed with approximately 25% selectivity at 548 K over the impregnated zeolites. The result can be explained by XPS (X-ray photoelectron spectroscopy) measurements, which indicated a good dispersion of the vanadium inside the pores.

Influence of Temperature and Time of Seed Aging on the Properties of Beta Zeolite/MCM-41 Materials

Saulo T. F.,Grecco; Ernesto A.,Urquieta-González; Patrício,Reyes; Marcelo,Oportus; Maria do Carmo,Rangel
Fonte: Sociedade Brasileira de Química Publicador: Sociedade Brasileira de Química
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/2014 EN
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The diffusion restrictions of the reactants caused by the micropores limit the use of zeolites for processing heavy molecules. This demands the development of materials that combine the properties of zeolites and mesoporous materials. With this goal in mind, the influence of temperature and time of seed aging on the properties of beta zeolite/MCM-41 materials obtained by mesostructuration/ crystallization was studied in this work. It was noted that the most suitable conditions to obtain the crystalline microporous phase of beta zeolite and the MCM-41 mesoporous phase was 140 °C, during 24 h of seed aging. At the other temperatures (60 and 90 °C) poor crystallized solids and a lamellar phase of MCM-50 were produced. On the other hand, increasing time of aging seeds bigger crystals of crystalline beta zeolite and less organized mesoporous phases were obtained at 140 °C.

KINETIC AND THERMODYNAMIC STUDY ON ADSORPTION BY STARCHY MATERIALS IN THE ETHANOL-WATER SYSTEM

Fonte: Brazilian Society of Chemical Engineering Publicador: Brazilian Society of Chemical Engineering
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/09/1997 EN
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Improving adsorptive processes demands a constant search for new adsorbents. In the specific case of ethanol-water separation, A zeolites are successfully being used. The use of nonconventional adsorbents to substitute zeolites, mainly starchy adsorbents in virtue of their known chemical affinity water, has recently been proposed. In this work a thermodynamic and kinetic study has been undertaken on the liquid phase adsorption of water from an ethanol-water mixture using manioc starch pellets as the adsorbent. The fundamental thermodynamic data were obtained by means of the static method, using a thermostated bath at four different temperatures (25, 40, 50 and 60° C), and could be correlated by means of a semi-empirical isotherm. The kinetic data, in turn, were obtained in a finite circulating liquid bath cell, enabling the construction of uptake rate curves, whereby the influence of temperature, interstitial velocity and adsorbent mean particle size on the adsorption rate was analyzed. The effective internal diffusivities at the experimental temperatures were estimated by a pore diffusion model and the results obtained were compared with those for commercial 3A zeolite

Biochemical evolution III: Polymerization on organophilic silica-rich surfaces, crystal–chemical modeling, formation of first cells, and geological clues

Smith, Joseph V.; Arnold, Frederick P.; Parsons, Ian; Lee, Martin R.
Fonte: The National Academy of Sciences Publicador: The National Academy of Sciences
Tipo: Artigo de Revista Científica
Publicado em 30/03/1999 EN
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Catalysis at organophilic silica-rich surfaces of zeolites and feldspars might generate replicating biopolymers from simple chemicals supplied by meteorites, volcanic gases, and other geological sources. Crystal–chemical modeling yielded packings for amino acids neatly encapsulated in 10-ring channels of the molecular sieve silicalite-ZSM-5-(mutinaite). Calculation of binding and activation energies for catalytic assembly into polymers is progressing for a chemical composition with one catalytic Al–OH site per 25 neutral Si tetrahedral sites. Internal channel intersections and external terminations provide special stereochemical features suitable for complex organic species. Polymer migration along nano/micrometer channels of ancient weathered feldspars, plus exploitation of phosphorus and various transition metals in entrapped apatite and other microminerals, might have generated complexes of replicating catalytic biomolecules, leading to primitive cellular organisms. The first cell wall might have been an internal mineral surface, from which the cell developed a protective biological cap emerging into a nutrient-rich “soup.” Ultimately, the biological cap might have expanded into a complete cell wall, allowing mobility and colonization of energy-rich challenging environments. Electron microscopy of honeycomb channels inside weathered feldspars of the Shap granite (northwest England) has revealed modern bacteria...

Reduction of nitrogen compounds in oceanic basement and its implications for HCN formation and abiotic organic synthesis

Holm, Nils G; Neubeck, Anna
Fonte: BioMed Central Publicador: BioMed Central
Tipo: Artigo de Revista Científica
Publicado em 22/10/2009 EN
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Hydrogen cyanide is an excellent organic reagent and is central to most of the reaction pathways leading to abiotic formation of simple organic compounds containing nitrogen, such as amino acids, purines and pyrimidines. Reduced carbon and nitrogen precursor compounds for the synthesis of HCN may be formed under off-axis hydrothermal conditions in oceanic lithosphere in the presence of native Fe and Ni and are adsorbed on authigenic layer silicates and zeolites. The native metals as well as the molecular hydrogen reducing CO2 to CO/CH4 and NO3-/NO2- to NH3/NH4+ are a result of serpentinization of mafic rocks. Oceanic plates are conveyor belts of reduced carbon and nitrogen compounds from the off-axis hydrothermal environments to the subduction zones, where compaction, dehydration, desiccation and diagenetic reactions affect the organic precursors. CO/CH4 and NH3/NH4+ in fluids distilled out of layer silicates and zeolites in the subducting plate at an early stage of subduction will react upon heating and form HCN, which is then available for further organic reactions to, for instance, carbohydrates, nucleosides or even nucleotides, under alkaline conditions in hydrated mantle rocks of the overriding plate. Convergent margins in the initial phase of subduction must...

Extra-large pore zeolite (ITQ-40) with the lowest framework density containing double four- and double three-rings

Corma, A.; Díaz-Cabañas, M. J.; Jiang, J.; Afeworki, M.; Dorset, D. L.; Soled, S. L.; Strohmaier, K. G.
Fonte: National Academy of Sciences Publicador: National Academy of Sciences
Tipo: Artigo de Revista Científica
EN
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The first zeolite structure (ITQ-40) that contains double four (D4) and double three (D3) member ring secondary building units has been synthesized by introducing Ge and NH4F and working in concentrated synthesis gels. It is the first time that D3-Rs have been observed in a zeolite structure. As was previously analyzed [Brunner GO, Meier, WM (1989) Nature 337:146–147], such a structure has a very low framework density (10.1 T/1,000 Å3). Indeed, ITQ-40 has the lowest framework density ever achieved in oxygen-containing zeolites. Furthermore, it contains large pore openings, i.e., 15-member rings parallel to the [001] hexagonal axis and 16-member ring channels perpendicular to this axis. The results presented here push ahead the possibilities of zeolites for uses in electronics, control delivery of drugs and chemicals, as well as for catalysis.

Synthesis of an extra-large molecular sieve using proton sponges as organic structure-directing agents

Martínez-Franco, Raquel; Moliner, Manuel; Yun, Yifeng; Sun, Junliang; Wan, Wei; Zou, Xiaodong; Corma, Avelino
Fonte: National Academy of Sciences Publicador: National Academy of Sciences
Tipo: Artigo de Revista Científica
EN
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The synthesis of crystalline microporous materials containing large pores is in high demand by industry, especially for the use of these materials as catalysts in chemical processes involving bulky molecules. An extra-large–pore silicoaluminophosphate with 16-ring openings, ITQ-51, has been synthesized by the use of bulky aromatic proton sponges as organic structure-directing agents. Proton sponges show exceptional properties for directing extra-large zeolites because of their unusually high basicity combined with their large size and rigidity. This extra-large–pore material is stable after calcination, being one of the very few examples of hydrothermally stable molecular sieves containing extra-large pores. The structure of ITQ-51 was solved from submicrometer-sized crystals using the rotation electron diffraction method. Finally, several hypothetical zeolites related to ITQ-51 have been proposed.

Polynomials for crystal frameworks and the rigid unit mode spectrum

Power, S. C.
Fonte: The Royal Society Publishing Publicador: The Royal Society Publishing
Tipo: Artigo de Revista Científica
Publicado em 13/02/2014 EN
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To each discrete translationally periodic bar-joint framework in , we associate a matrix-valued function defined on the d-torus. The rigid unit mode (RUM) spectrum of is defined in terms of the multi-phases of phase-periodic infinitesimal flexes and is shown to correspond to the singular points of the function and also to the set of wavevectors of harmonic excitations which have vanishing energy in the long wavelength limit. To a crystal framework in Maxwell counting equilibrium, which corresponds to being square, the determinant of gives rise to a unique multi-variable polynomial . For ideal zeolites, the algebraic variety of zeros of on the d-torus coincides with the RUM spectrum. The matrix function is related to other aspects of idealized framework rigidity and flexibility, and in particular leads to an explicit formula for the number of supercell-periodic floppy modes. In the case of certain zeolite frameworks in dimensions two and three, direct proofs are given to show the maximal floppy mode property (order N). In particular, this is the case for the cubic symmetry sodalite framework and some other idealized zeolites.