Density control of ZnO nanowires grown using Au-PMMA nanoparticles and their growth behavior.

Au nanoparticles stabilized by poly(methyl methacrylate) (PMMA) were used as a catalyst to grow vertically aligned ZnO nanowires (NWs). The density of ZnO NWs with very uniform diameter was controlled by changing the concentration of Au-PMMA nanoparticles (NPs). The density was in direct proportion to the concentration of Au-PMMA NPs. Furthermore, the growth process of ZnO NWs using Au-PMMA NPs was systematically investigated through comparison with that using Au thin film as a catalyst. Au-PMMA NPs induced polyhedral-shaped bases of ZnO NWs separated from each other, while Au thin film formed a continuous network of bases of ZnO NWs. This approach provides a facile and cost-effective catalyst density control method, allowing us to grow high-quality vertically aligned ZnO NWs suitable for many viable applications.

Synthetic, structural and mechanistic studies of interactions of carbon, nitrogen, and oxygen nucleophiles with bis-pentamethylcyclopentadienyl zirconium and hafnium derivatives

The reactivity of permethylzirconocene and permethylhafnocene complexes with various nucleophiles has been investigated. Permethylzirconocene reacts with sterically hindered ketenes and allenes to afford metallacycle products. Reaction of these cummulenes with permethylzirconocene hydride complexes affords enolate and σ-allyl species, respectively. Reactions which afford enolate products are nonstereospecific, whereas reactions which afford allyl products initially give a cis-σ-allyl complex which rearranges to its trans isomer. The mechanism of these reactions is proposed to occur either by a Lewis Acid-Lewis Base interaction (ketenes) or by formation of a π-olefin intermediate (allenes).

Permethylzirconocene haloacyl complexes react with strong bases such as lithium diisopropylamide or methylene trimethylphosphorane to afford ketene compounds. Depending on the size of the alkyl ketene substituent, the hydrogenation of these compounds affords enolate-hydride products with varying degrees of stereoselectivity. The larger the substituent, the greater is the selectivity for cis hydrogenation products.

The reaction of permethylzirconocene dihydride and permethylhafnocene dihydride with methylene trimethylphosphorane affords methyl-hydride and dimethyl derivatives. Under appropriate conditions, the metallated-ylide complex 1, (η^5-C_5(CH_3)_5)_2 Zr(H)CH_2PMe_2CH_2, is also obtained and has been structurally characterized by X-ray diffraction techniques. Reaction of 1 with CO affords (η^5-C_5(CH_3)_5)_2 Zr(C,O-η^2 -(PMe_3)HC=CO)H which exists in solution as an equilibrium mixture of isomers. In one isomer (2), the η^2-acyl oxygen atom occupies a lateral equatorial coordination position about zirconium, whereas in the other isomer (3), the η-acyl oxygen atom occupies the central equatorial position. The equilibrium kinetics of the 2→3 isomerization have been studied and the structures of both complexes confirmed by X-ray diffraction methods. These studies suggest a mechanism for CO insertion into metal-carbon bonds of the early transition metals.

Permethylhafnocene dihydride and permethylzirconocene hydride complexes react with diazoalkanes to afford η^2-N, N' -hydrazonido species in which the terminal nitrogen atom of the diazoalkane molecule has inserted into a metal-hydride or metal-carbon bond. The structure of one of these compounds, Cp*_2Zr(NMeNCTol_2)OH, has been determined by X-ray diffraction techniques. Under appropriate conditions, the hydrazonido-hydride complexes react with a second equivalent of diazoalkene to afford η' -N-hydrazonido-η^2-N, N' -hydrazonido species.

Theoretical studies of novel organic systems : biradicals, polyradicals, and conducting polymers

Chapter 1

Cyclobutanediyl has been studied in both its singlet and triplet states by ab initio electronic structure theory. The triplet, which is the ground state of the molecule, exists in both C_(2h) and C_(2v) forms, which interconvert via a C_s transition state. For the singlet, only a C_(2h) form is found. It passes, via a C_s transition state, onto the C_(2v) surface on which bicyclobutane is the only minimum. The ring-flipping (inversion) process in bicyclobutane includes the singlet biradical as an intermediate, and involves a novel, nonleast motion pathway. Semiclassical periodic orbit theory indicates that the various minima on both the singlet and triplet surfaces can interconvert via quantum mechanical tunneling.

Chapter 2

The dimethylenepolycyclobutadienes (n) are the non-Kekulé analogues of the classical acenes. Application of a variety of theoretical methods reveals several novel features of such structures. Most interesting is the emergence of a parity rule. When n is even, n is predicted to be a singlet, with n disjoint NBMOs. When n is odd, theory predicts a triplet ground state with (n+1) NBMOs that are not fully disjoint.

Chapter 3

Bi(cyclobutadienyl) (2), the cyclobutadiene analogue of biphenyl, and its homologues tri- (3) and tetra(cyclobutadienyl) (4) have been studied using electronic structure theory. Ab initio calculations on 2 reveal that the central bond is a true double bond, and that the structure is best thought of as two allyl radicals plus an ethylene. The singlet and triplet states are essentially degenerate. Trimer 3 is two allyls plus a dimethylenecyclobutanediyl, while 4 is two coplanar bi(cyclobutadienyl) units connected by a single bond. For both 3 and 4, the quintet, triplet, and singlet states are essentially degenerate, indicating that they are tetraradicals. The infinite polymer, polycyclobutadiene, has been studied by HMO, EHCO, and VEH methods. Several geometries based on the structures of 3 and 4 have been studied, and the band structures are quite intriguing. A novel crossing between the valence and conduction bands produces a small band gap and a high density of states at the Fermi level.

Chapter 4

At the level of Hückel theory, polyfulvene has a HOCO-LUCO degeneracy much like that seen in polyacetylene. Higher levels of theory remove the degeneracy, but the band gap (E_g) is predicted to be significantly smaller than analogous structures such as polythiophene and polypyrrole at the fulvenoid geometry. An alternative geometry, which we have termed quinoid, is also conceivable for polyfulvene, and it is predicted to have a much larger E_g. The effects of benzannelation to produce analogues of polyisothianaphthene have been evaluated. We propose a new model for such structures based on conventional orbital mixing arguments. Several of the proposed structures have quite interesting properties, which suggest that they are excellent candidates for conducting polymers.

Chapter 5

Theoretical studies of polydimethylenecyclobutene and polydiisopropylidene- cyclobutene reveal that, because of steric crowding, they cannot achieve a planar, fully conjugated structure in either their undoped or doped states. Rather, the structure consists of essentially orthogonal hexatriene units. Such a structure is incompatible with conventional conduction mechanisms involving polarons and bipolarons.

Zirconocenes as models for homogeneous Ziegler-Natta olefin polymerization catalysts

Using density functional theory, we studied the fundamental steps of olefin polymerization for zwitterionic and cationic Group IV ansa-zirconocenes and a neutral ansa- yttrocene. Complexes [H₂E(C₅H₄)₂ZrMe]ⁿ (n = 0: E = BH₂ (1), BF₂ (2), AlH₂(3); n = +: E = CH₂(4), SiH₂(5)) and H₂Si(C₅H₄)₂YMe were used as computational models. The largest differences among these three classes of compounds were the strength of olefin binding and the stability of the β-agostic alkyl intermediate towards β-hydrogen elimination. We investigated the effect of solvent on the reaction energetics for land 5. We found that in benzene the energetics became very similar except that a higher olefin insertion barrier was calculated for 1. The calculated anion affinity of [CH₃BF₃]^- was weaker towards 1 than 5. The calculated olefin binding depended primarily on the charge of the ansa linker, and the olefin insertion barrier was found to decrease steadily in the following order: [H₂C(C₅H₄)₂ZrMe]⁺ > [F₂B(C₅H₄)₂ZrMe] ≈ [H₂B(C₅H₄)₂ZrMe] > [H₂Si(C₅H₄)₂ZrMe]⁺ > [H₂Al(C₅H₄)₂ZrMe].

We prepared ansa-zirconocene dicarbonyl complexes Me₂ECp₂Zr(CO)₂ (E = Si, C), and t-butyl substituted complexes (t-BuCp)₂Zr(CO)₂, Me₂E(t-BuCp)₂Zr(CO)₂ (E = Si, C), (Me₂Si)₂(t-BuCp)₂Zr(CO)₂ as well as analogous zirconocene complexes. Both the reduction potentials and carbonyl stretching frequencies follow the same order: Me₂SiCp₂ZrCl₂> Me₂CCp₂ZrCl₂> Cp₂ZrCl₂> (Me₂Si)₂Cp₂ZrCl₂. This ordering is a result of both the donating abilities of the cyclopentadienyl substituents and the orientation of the cyclopentadiene rings. Additionally, we prepared a series of analogous cationic zirconocene complexes [LZrOCMe₃][MeB(C₆F₅)₃] (L = CP₂, Me₂SiCp₂, Me₂CCP₂, (Me₂Si)₂Cp₂) and studied the kinetics of anion dissociation. We found that the enthalpy of anion dissociation increased from 10.3 kcal•mol^-1 to 17.6 kcal•mol^-1 as exposure of the zirconium center increased.

We also prepared series of zirconocene complexes bearing 2,2-dimethyl-2-sila-4-pentenyl substituents (and methyl-substituted olefin variants). Methide abstraction with B(C₆F₅) results in reversible coordination of the tethered olefin to the cationic zirconium center. The kinetics of olefin dissociation have been examined using NMR methods, and the effects of ligand variation for unlinked, singly [SiMe₂]-linked and doubly [SiMe₂]-linked bis(cyclopentadienyl) arrangements has been compared (ΔG‡ for olefin dissociation varies from 12.8 to 15.6 kcal•mol^-1). Methide abstraction from 1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(CH₃)-(CH₂CMe₂CH₂CH = CH₂) results in rapid β-allyl elimination with loss of isobutene yielding the allyl cation [{1,2-(SiMe₂)₂(η⁵-C₅H₃)₂Zr(η³-CH₂CH=CH₂)]⁺.

Model studies of Ziegler-Natta olefin polymerization using group 3 and group 4 metallocenes

Evidence for the stereochemical isomerization of a variety of ansa metallocene compounds is presented. For the scandocene allyl derivatives described here, we have established that the process is promoted by a variety of salts in both ether and hydrocarbon solvents and is not accelerated by light. A plausible mechanism based on an earlier proposal by Marks, et al., is offered as an explanation of this process. It involves coordination of anions and/or donor solvents to the metal center with cation assistance to encourage metalcyclopentadienyl bond heterolysis, rotation about the Si-Cp bond of the detached cyclopentadienide and recoordination of the opposite face. Our observations in some cases of thermodynamic racemic:meso ratios under the reaction conditions commonly used for the synthesis of the metallocene chlorides suggests that the interchange is faster than metallation, such that the composition of the reaction mixture is determined by thermodynamic, not kinetic, control in these cases.

Two new ansa-scandocene alkenyl compounds react with olefins resulting in the formation of η³-allyl complexes. Kinetics and labeling experiments indicate a tuck-in intermediate on the reaction pathway; in this intermediate the metal is bound to the carbon adjacent to the silyllinker in the rear of the metallocene wedge. In contrast, reaction of permethylscandocene alkenyl compounds with olefins results, almost exclusively, in vinylic C-H bond activation. It is proposed that relieving transition state steric interactions between the cyclopentadienyl rings and the olefin by either linking the rings together or using a larger lanthanide metal may allow for olefin coordination, stabilizing the transition state for allylic σ-bond metathesis.

A selectively isotopically labeled propylene, CH₂CD(¹³CH₃), was synthesized and its polymerization was carried out at low concentration in toluene solution using isospecific metallocene catalysts. Analysis of the NMR spectra (¹³C, ¹H, and ²H) of the resultant polymers revealed that the production of stereoerrors through chain epimerization proceeds exclusively by the tertiaryalkyl mechanism. Additionally, enantiofacial inversion of the terminally unsaturated polymer chain occurs by a non-dissociative process. The implications of these results on the mechanism of olefin polymerization with these catalysts is discussed.

Strategies for the Stereoselective Synthesis of Carbon Quaternary Centers via Transition Metal-Catalyzed Alkylation of Enolate Compounds

Notwithstanding advances in modern chemical methods, the selective installation of sterically encumbered carbon stereocenters, in particular all-carbon quaternary centers, remains an unsolved problem in organic chemistry. The prevalence of all-carbon quaternary centers in biologically active natural products and pharmaceutical compounds provides a strong impetus to address current limitations in the state of the art of their generation. This thesis presents four related projects, all of which share in the goal of constructing highly-congested carbon centers in a stereoselective manner, and in the use of transition-metal catalyzed alkylation as a means to address that goal.

The first research described is an extension of allylic alkylation methodology previously developed in the Stoltz group to small, strained rings. This research constitutes the first transition metal-catalyzed enantioselective α-alkylation of cyclobutanones. Under Pd-catalysis, this chemistry affords all–carbon α-quaternary cyclobutanones in good to excellent yields and enantioselectivities.

Next is described our development of a (trimethylsilyl)ethyl β-ketoester class of enolate precursors, and their application in palladium–catalyzed asymmetric allylic alkylation to yield a variety of α-quaternary ketones and lactams. Independent coupling partner synthesis engenders enhanced allyl substrate scope relative to allyl β-ketoester substrates; highly functionalized α-quaternary ketones generated by the union of our fluoride-triggered β-ketoesters and sensitive allylic alkylation coupling partners serve to demonstrate the utility of this method for complex fragment coupling.

Lastly, our development of an Ir-catalyzed asymmetric allylic alkylation of cyclic β-ketoesters to afford highly congested, vicinal stereocenters comprised of tertiary and all-carbon quaternary centers with outstanding regio-, diastereo-, and enantiocontrol is detailed. Implementation of a subsequent Pd-catalyzed alkylation affords dialkylated products with pinpoint stereochemical control of both chiral centers. The chemistry is then extended to include acyclic β-ketoesters and similar levels of selective and functional group tolerance are observed. Critical to the successful development of this method was the employment of iridium catalysis in concert with N-aryl-phosphoramidite ligands.

Preparação e caracterização de microesferas poliméricas à base de metacrilato de glicidila e divinilbenzeno com propriedades magnéticas

Nesta Dissertação, foram sintetizadas microesferas poliméricas com propriedades magnéticas à base de metacrilato de glicidila e divinilbenzeno pela técnica de polimerização em suspensão. O material utilizado para conferir as propriedades magnéticas ao copolímero foi magnetita sintetizada no laboratório. Foram estudados os efeitos da modificação da magnetita com ácido oleico, da velocidade de agitação, do teor de agente reticulante, do teor de material magnético adicionado e do teor de agente de suspensão sobre as características das partículas poliméricas obtidas. As microesferas foram caracterizadas quanto ao seu aspecto morfológico, à estabilidade térmica, à incorporação de material magnético e quanto às suas propriedades magnéticas. A quantidade de partículas de ferro incorporadas foi afetada pela velocidade de agitação durante a síntese, pelo teor de material magnético adicionado, pela fase de dispersão do material magnético e pelo teor de monômeros no copolímero. A estabilidade térmica dos copolímeros foi afetada, principalmente, pelo teor de material magnético incorporado e pelo teor de monômeros, levando em consideração resinas com a mesma quantidade de material magnético adicionado. A magnetização de saturação para as microesferas foi afetada pelo teor de material magnético incorporado. A modificação da superfície da magnetita com ácido oleico foi considerada importante para a incorporação do material magnético na matriz do copolímero.Partículas poliméricas magnéticas com comportamento superparamagnéticos foram obtidas com morfologia esférica e magnetização de saturação de 7,11 (emu/g), utilizando razão molar de monômeros de 50/50 %, 1 % de PVA, 20 % de magnetita modificada com ácido oleico adicionada à fase orgânica e velocidade de agitação mecânica de 500 rpm

Síntese e caracterização de copolímeros à base de poli(metacrilato de metila) e divinilbenzeno com propriedades magnéticas

Nesta dissertação, foram sintetizados copolímeros à base de poli(metacrilato de metila) (PMMA), divinilbenzeno (DVB) com propriedades magnéticas pela técnica de polimerização em suspensão. O material utilizado para conferir propriedade magnética foi o ferro. Foi estudada a influência das variáveis reacionais para a formação de microesferas (ordem de adição das fases orgânica e aquosa e a dispersão do ferro antes e após a pré-polimerização), o efeito da concentração de ferro adicionado na polimerização, a influência da razão molar MMA/DVB na formação do copolímero, o efeito do tipo de agente de suspensão e a velocidade de agitação para a síntese dos copolímeros. Os copolímeros foram caracterizados quanto à morfologia, estabilidade térmica, teor de ferro incorporado, distribuição de tamanho de partículas, propriedades magnéticas, área superficial, volume e tamanho de poros. As análises de propriedades magnéticas mostraram que os materiais obtidos não apresentaram ciclos de histerese, estando assim próximos de um material com propriedades superparamagnéticas, com magnetização de saturação entre 8,0 e 13,0 emu/g. Os copolímeros sintetizados com velocidade de agitação 500 RPM, temperaturade 90 C, tempo de polimerização de 24h, monômeros MMA/DVB 50/50 (% molar); razão volumétrica fase orgânica/fase aquosa 1/3, diluente heptano, grau de diluição 100% apresentaram melhor controle morfológico, melhor magnetização de saturação, tamanho de partículas menores e maior tamanho de poros

Derivatização de polimetacrilatos comerciais: preparação e caracterização de novos suportes químicos e bioquímicos oriundos da alilamina

Esta dissertação avaliou a reação de amidação de poli(metacrilato de metila) (PMMA) comercial de massa molecular de 90000 g/mol (determinado por viscosimetria) com alilamina. A reação foi estudada a temperatura ambiente e sob refluxo. A reação apresentou baixos índices de conversão, 0,5 %, tanto após 24 dias, a temperatura ambiente, quanto sob refluxo por 2 horas. Experimentos executados sob refluxo por períodos maiores apresentaram diminuição no índice de conversão. Todos os experimentos foram acompanhados pela análise elementar e FT-IR e RMN-1H. O material derivatizado foi epoxidado pelo tratamento com ácido m-cloro-perbenzóico (AMCPB) seguido de tratamento com ácido periódico gerado in situ (NaIO4/HCl). Todos os produtos preparados foram submetidos à análise térmica apresentando, em sua maioria, um aumento na Tg relativa ao PMMA

Miscibility and Hydrogen Bonding in Blends of Poly(4-vinylphenol)/Poly(vinyl methyl ketone)

The miscibility and phase behavior of poly(4-vinylphenol) (PVPh) with poly(vinyl methyl ketone) (PVMK) was investigated by differential scanning calorimetry (DSC), Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). It was shown that all blends of PVPh/PVMK are totally miscible. A DSC study showed the apparition of a single glass transition (T-g) over their entire composition range. When the amount of PVPh exceeds 50% in blends, the obtained T(g)s are found to be significantly higher than those observed for each individual component of the mixture, indicating that these blends are capable of forming interpolymer complexes. FTIR analysis revealed the existence of preferential specific interactions via hydrogen bonding between the hydroxyl and carbonyl groups, which intensified when the amount of PVPh was increased in blends. Furthermore, the quantitative FTIR study carried out for PVPh/PVMK blends was also performed for the vinylphenol (VPh) and vinyl methyl ketone (VMK) functional groups. These results were also established by scanning electron microscopy study (SEM).

Efeito do fator cavitário na resistência adesiva à dentina de um sistema restaurador à base de silorano

O objetivo deste estudo foi avaliar o efeito do fator C na resistência adesiva à dentina humana de um compósito à base de silorano, comparando-o com um compósito à base de metacrilato. Foram utilizados 40 molares humanos hígidos. Em metade da amostra foi realizado um preparo do tipo Classe I, com dimensões de 4x4 mm e 2 mm de profundidade, enquanto na outra metade foi realizado um preparo virtual (flat) com auxílio de uma matriz de teflon branco, com as mesmas dimensões da cavidade (4x4x2 mm), apoiada na superfície de dentina exposta. Cada grupo foi divido em dois, de acordo com o sistema restaurador: Sistema Adesivo P90 e resina Filtek P90; Adper Scotchbond Multiuso e resina Filtek Z350 XT (3M ESPE). Após a aplicação do sistema adesivo segundo as especificações do fabricante, as cavidades (real e virtual) foram preenchidas com as resinas (Z350 XT e P90) em dois incrementos. Foi realizada a fotoativação de cada incremento durante 25s. Após uma semana, as coroas foram seccionadas, obtendo-se espécimes constituídos de resina/dente na forma de um paralelepípedo (palitos). Estes palitos foram utilizados para o teste de microtração (Emic), onde a resistência adesiva na unidade MPa foi calculada. Os resultados foram avaliados estatisticamente pelo teste de análise de variância ANOVA One-Way (p = 0,05), e pelo teste de múltiplas comparações Student Newman Keuls. Foi observada uma diferença estatística entre a resina P90 (flat= 16,137,7 MPa e Cavidade= 16,759,0 MPa) e a Z350 XT (flat= 25,8211,6 MPa e Cavidade=24,4713,5 MPa), independentemente do tipo de cavidade restaurada. E não foi possível observar diferença estatística entre os tipos de cavidades (real ou virtual) restauradas com a mesma resina. Através dos testes realizados, foi possível concluir que: o fator C não afetou a resistência adesiva dos dois sistemas restauradores utilizados, e o tipo de sistema restaurador afeta a resistência adesiva, sendo que o sistema à base de silorano apresenta resultados inferiores ao de metacrilato.

Modificação química de amostras de poli(metacrilato de metila) comerciais com aminas funcionalizadas assistidas por micro-ondas

Este trabalho avaliou a reação de amidação sob catálise de DBU/NaCN de amostras comerciais de poli(metacrilato de metila), (PMMA), massa molar 60.000 u.m.a. com as aminas, alilamina, 2-morfolilaminoetano, 1-(3-aminopropil)-imidazol e N,N-dimetil-trimetilenodiamina com ativação por reator de micro-ondas. O estudo com alilamina e 2-morfolilaminoetano se mostrou eficaz, apresentando percentuais de derivatização significativos (27% e 37% , respectivamente). A quantidade de material polimérico obtido na purificação foi de cerca de 36 % para as duas aminas. O estudo evidenciou a importância dos catalisadores DBU/NaCN, pois sem eles a reação não ocorre e quando utilizados isoladamente, o grau de incorporação é muito menor. Já o estudo com as aminas 1-(3-aminopropil)-imidazol e N,N-dimetil-trimetilenodiamina mostrou-se ineficaz devido à dificuldade de purificação dos produtos. Tentativas de purificação por precipitação com metanol e soluções hidrometanólicas de diferentes concentrações mostraram-se ineficazes. Os novos PMMA modificados foram caracterizados por FT-IR, RMN-1H e análise elementar. Foram observadas alterações na taticidade do PMMA em reações ativadas por micro-ondas

Efficient Synthesis of Single-Chain Polymer Nanoparticles via Amide Formation

Single-chain technology (SCT) allows the transformation of individual polymer chains to folded/collapsed unimolecular soft nanoparticles. In this work we contribute to the enlargement of the SCT toolbox by demonstrating the efficient synthesis of single-chain polymer nanoparticles (SCNPs) via intrachain amide formation. In particular, we exploit cross-linking between active methylene groups and isocyanate moieties as powerful "click" chemistry driving force for SCNP construction. By employing poly(methyl methacrylate)- (PMMA-) based copolymers bearing beta-ketoester units distributed randomly along the copolymer chains and bifunctional isocyanate cross-linkers, SCNPs were successfully synthesized at r.t. under appropriate reaction conditions. Characterization of the resulting SCNPs was carried out by means of a combination of techniques including size exclusion chromatography (SEC), infrared (IR) spectroscopy, proton nuclear magnetic resonance (H-1 NMR) spectroscopy, dynamic light scattering (DLS), and elemental analysis (EA).

Two new compounds and anti-HIV active constituents from Illicium verum

Two new compounds named illiverin A (1) and tashironin A (8) were, isolated from the roots of Illicium verum, together with seven known compounds: 4-allyl-2-(3-methylbut-2-enyl)-1,6-methylenedioxybenzene-3-ol (2), illicinole (3), 3-hydroxy-4,5-methylenedi

Fabrication of metallic air bridges using multiple-dose electron beam lithography

The techniques of fabricating metallic air bridges using different resists in a one-step electron beam lithography are presented. The exposure process employed a single-layer polymethyl methacrylate (PMMA) or photoresists with either different doses in the span and feet areas or with varying acceleration voltage of the electron beam. The process using photoresists with different doses has produced air bridges more stable than what the PMMA method using various acceleration voltages would achieve. Using this method, air bridges up to 12 mu m long have been fabricated. The length and height of these metallic air bridges vary with the photoresist thickness. (c) 2006 American Institute of Physics.