HADROIVC JOURNALYOLUME 36, NUMBER 2, APRrL 2013

GENO-BRAGG'S LAW AND GENO-EINSTEIN'S GENERAL RELATIVITY THEORYFOR QUASICRYSTAL STRUCTURES, 149Alexander O.E. Animalu

Department of Physics and AstronomyUniversity of Nigeria, NsukkaandEnugu State, Nigeria & International Centre for Basic Research20 Limpopo Street, FHA, Maitama, Abuja, Nigeria

DYNAMIC ISO-TOPIC LIFTING WITH APPLICATION TO FIBONACCI'SSEQUENCE AND MANDELBROT'S SET,167

Nathan O. SchmidtDepartment of Mathematics, Boise State University1910 University DriveBoise,ID 83725 USA

ACTIVE SITES, COMPLEXITY STRUCTURES AND HYPERSTRUCTURES INCATALYSTS,177

M. PiumettiDepartment of Applied Science and TechnologyPolitecnico di Torino, 10129 Torino,ItalyN. LygerosLGPC (UMR 5285),Universitd de LYon696 16, Villeurbanne, France

DARK ENERGY,INERTIA AND MACH'S PRINCTPLE,I9TC. SivaramIndian Institute of AstrophysicsBangalore - 560 034,IndiaKenath ArunChrist Junior CollegeBangalore - 560 029,lndia

MAGNETIC EFFECT OF NON-COMMUTATIYITY, 205B.G. SidharthG.P. Birla Observatory & Astronomical Research CentreB.M. Birla Science CentreAdarsh Nagar, Hyderbad - 500 063 IndiaC.V. AdityaUniversity of Stuttgart, Germany

MADELBROT ISO-SETS: ISO-UNIT IMPACT ASSESSMENT, 21IReza KatebiDepartment of Physics, California State UniversityFullerton,800 North State College BoulevardFullerton, CA 92831 USANathan SchmidtDepartment of Mathematics, Boise State University1910 University DriveBoise,ID 83725 USA

ISO-GALOIS FIELDS,225Arun S. MuktibodhDepartment of MathematicsMohota College of ScienceNagpur-44Q009 India

ON THE MASS-ENERGY RELATIONSHIP E=mc2,237John Shim

FERMIODYNAMICS THROUGH GENBRALIZED ELE CTRODYNAMIC S, 243Sushama V. VaidyaPhysics Department S.B. College of ScienceAurangabad - 431001, IndiaM.T. TeliPhysics DepartmentDr. Babasaheb AmbedkarAurangabad - 431004, India (Retd.)

HADRONIC JOURNAL 36, r77 -195 (2013)

ACTIVE SITES, COMPLEXITY STRUCTURES ANDHYPERSTRUCTURES IN CATALYSTS

M. PiumettiDepartment of Applied Science and Technology

Politecnico di Torino, 10129 Torino,Italymarco.piumetti @polito.it

N. LygerosLGPC (UMR 5285), Universit6 de Lyon

69616, Villeurbanne, Francenlygeros@gmail.com

Received October 20, 2Ol3

AbstractThis paper locuses on the problem of active sites in heterogeneous catalysisthrough a review based on three examples fiom the literature, namely metalnanoparticles, zeolites and transition metal oxides (redox MvK-typemechanism). Self-organizing phenomena in catalysis may reflect variouscomplexity structures, including the self-repair and reorganization of activesites, the mutual interactions between neighbouring sites, the mass transferlimitations (i.e. shape selective control), the dynamic active networks of"sites-joined", and so on. These phenomena may give rise to non-lineardynamics in catalytic processes. The latter typically result in a non-linearcombination of distinct complexity structures and hence catalyticbehaviours may appear with multicomponent systems, as zeolites and mixedoxides. Thus, the algebraic hyperstructures are introduced as a rnodel todescribe the cornplexity of catalysis. The solid catalyst acts as ahyperoperator computing a non-linear combination of cornplexity structures,narnely multivalued operation (o). This hyperoperation is r.veak associativesince the complexity structures (sets) contain the n-polytopes as commonelements. As a result, the complexity structures in catalysis belong to Hv-structures, the iargest class of hyperstructures u4rich satisfy the weakproperties.

Keylvords: Catalytically active sites; self-organizing phenomena;complexity structures; hyperstructures; Hv-structures.

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Copyright A 2C1'3 by Hadronic Press,Inc., Palm Harbor, FL 34684, USA

-178-I IntroductionThe active sites represent the "heaft" of a catalyst and hence it is notsulprising that a large number of theoretical studies and experiments in thefield of heterogeneous, homogeneous and enzymatic catalysis focus on thecharacterisation of active centres present on the catalyst surface.In recent years, considerable progress has been made in the characterizationof catalytic reactions at solid surfaces. Indeed, thanks to the developnient ofin-situ spectroscopies and to advanced scanning probe techniques, it hasbeen possible to study active sites under lvorking conditions and toinvestigate the elementary processes underlying a reaction on an atomicscale []. As a result, many investigations have confirmed that active sitesare dynamic entities that can continuously change their physico-chemicalproperlies depending on the reaction conditions 11,2]. Dynamic STManalysis also revealed that active centers may include l11ore than one singlesite to form "reactive networks" [3-5].A o'real" catalyst surface is structurally and compositionally complex andrnultifunctional interiace, exposing various adsorption/reaction sites. Thus,the surlace properties have their relevant consequences on the chemicalreactivity [6,8]. Moreover, there is an important aspect contributing to thegap betrveen surface science and catalysis, that is related to the reactionmechanism and can be denoted as "chernical complexity". Catalyticreactions may involve mixtures of several reactants and/or intricate reactionnetworks with multiple steps and pathways 19,10]. Typically, the morecomplex the reaction mechanism, the slower the turnover rate as theelementary reaction steps involve more complex molecular rearrangements111]. The catalyst has to regenerate itself through the desorption of productsand the self-repair ofactive sites after each catalytic cycle.During a reaction, the catalyst surface typically receives a mix of fluctuatingmolecules (i.e. reactants, products, poisons, etc.) and hence many activecentres (or regions) on the surlace may interact rvith each other throughmass/heat transpofi phenomena and surface strain [2,7]. This suggests thatsolid catalysts operate through sophisticated self-organizing phenomena, inwhich both structural parameters and kinetic eft-ects play a role [6].Tlre concept of "self-organization" indicates the order formation in boththerrnodynarnically closed and open chemical systerns [2]. Closed systemstend to reach the equilibrium conditions by reducing their fiee energy,

-t79-although kinetic constrains may limit the attainment of equilibrium. On thecontrary, open systems far from the equilibrium (i.e. reactions at steady-state flor.v conditions) exhibit the interaction between chemical kinetics andtransport phenomena. Moreover, there is an unexpected relation between thechemical kinetics and the space-time structures of reaction systems. Thesesystems belong to the class of irreversible processes creating entropy andmay be described through kinetic equations r,vith broken time symmetryinstead of canonical equations 112].Non-equilibrium systems were first studied by L Prigogine [13]rvho denotedthern as "dissipative structures" and were later incorporated in theframeu,ork of synergetics by H. Haken [14]. Specifically, Prigogine showedthe complexity of tirne in non-equilibrium systerns, through the concepts ofsymmetry breaking, irreversibility and time's arrow. Consequently, catalyticreactions cannot be reduced to classical dynamics or quantum mechanics indeterministic, time-reversible descriptions [12], However, it is irnpossible toknou, exactly the spatio-temporal self-organizing phenomena occuning insystems far from equilibriurn due to fundamental lirnitations having theirorigins in the matheuratical structures I8] Noteworthy, the causalitycondition on a space-time appears inaccessible by strictly deterrninisticprocesses and the coraplexity of time is still greater than one can imagine ina linear fiamervork.Such effects have been experiniented r.vith CO oxidation over Pt singlecrystal surfaces by G. Ertl 12,8,16].Indeed, under cerlain external conditions(i.e. pc,_, and ternperature) the Pt surface can altemate betrveen tr,vo states,shorving regular oscillations in reaction rates. Holvever, at high CO pressurevalues (pco> 5'10-5 rnbar) a ne\\/ irregular behaviour o..u.r, giving rise tochaotic phenomena.Self-organization phenomena appear in different regions of the solid surfaceand the interactions ivhich determine the values of relevant kinetic constantsand transporl coefficients mainly depend on short-range forces [8,15].In open systems r,vhere different entities, such as atoms, molecules, defects,and so on are able to motr/e and interact with each other, phenomenologicalrate equations of the concentrations of the reactant species are usuallyderived from material, energy or momenturn balance equations, Ieading toreaction-diflusion dynarnics. Consequently, the resulting spatio-temporalconcentration patterns are no longer goven-red by atomic dimensions but

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through the so-called diffusion length. Thus, the temporal evolution of theresulting concentration patterns in open systems far from the equilibriumcan be described through a set of non-linear partial differential equations,combining the chemical kinetics tvith the diffusion processes ol theadsorbed species, as follows:

v2

rvhere ,ri ore the state variables (i.e. surt-ace concentrations) of the reactingchemicals, Fi dre the non-linear operators expressing the chernical kinetics,Diare the diffusion coefficients andpr are a set of parameters [16].In fair agreement lvith our previous studies [17,18], in the present work weinvestigate the complexity of active sites in heterogeneous catalysis througha revieu, based on three examples from the literature, namely metalnanoparlicles, zeolites and transition metal oxides acting via redox MvK-type mechanism. Moreover, the hyperstructures are proposed as a model todescribe the complexity of catalysis. Introduced in 1990, the Hv-structuresproved to have a lot of applications in several applied sciences, such aslinguistics, biology, chemistry, physics, and so on 120].Algebraic hyperstructures are a natural extension of classical algebraicstructures: in an algebraic structure, the cornposition of two elements is anelement, rvhile in an algebraic hypestructure, the cornposition of twoelernents (i.e. reactant molecules) is a set (i.e. the reaction products) L19,2A1.Thus, it lvill be proved that various complexity structures in catalysis belongto the Hv-structures, the largest class of hyperstructures r,vhich satisfy ther.veak properties I I 9].

2 Metal clusters and nanoparticlesThe chemical reactivity of nanostructured systems is often related to the sizeand shape of the metal particles ( : structure-sensitive reactions), as rvell asto the nature of the support materials 121-241. On the contrary, in structure-insensitive reactions all the surface sites exhibit comparable reactivity onseveral planes of a single crystal. For instance, hydrogenation reactions areusually structure-insensitive since they can occur in many differentarrangements of surface atoms. This is rnainly due to the fact that