The objectives of this work are to discuss multiscale models that are used to characterize the constitutive relations of the granular composite materials with dual functions. This is accomplished by the use of ab initio methods to obtain the constitutive relations of the structural energetic materials without conducting tests. First, it is necessary to study the quantum many body problem to quantitatively determine the internal energy of the material when subjected to different strain conditions. It is impossible to obtain an exact solution to the quantum many body problem that is modeled by the Schrödinger's equations with the current technology. It is possible to solve these equations approximately by the density functional theory which yields only energies at absolute 0ºK. Thus it becomes necessary to add both the lattice thermal contributions and electron thermal contribution. Then, resulting energy is used to bridge to the continuum level and obtain the constitutive equations. This is the procedure that is used in this work. The issues of the constitutive equations form the focus of this thesis. More specifically, the scope of the thesis is further restricted to analyze the constitutive equations of specific mixtures of nickel, aluminum with PTFE or Teflon as the binder. It is to be noted that the equations of state forms only a part of the complete constitutive relationships. This thesis presents solutions to the following problems: (1) Determination of the thermodynamically complete equation of state of the binder and the energetic material PTFE or Teflon, from ab initio methods based on the density functional theory. (2) Determination of the equations of state of the granular composite or the mixture of nickel, aluminum and PTFE from ab initio methods. (3) Determination of the complete constitutive equation of aluminum, from ab initio methods, under conditions of finite deformations, with principle of objectivity, material symmetry conditions and polyconvexity of the strain energy. All results are compared to test results whenever they are available.

This thesis is concerned with the mathematical modelling of elastic-plastic deformation in regimes of stress far exceeding the yield stress. Such scenarios are typically encountered in violent impact testing, where millimetre-thick samples of metal are subjected to pressures on the order of the bulk modulus of the material. We begin with an overview of violent impact testing, with particular attention paid to a specific class of experiments known as isentropic compression experiments (ICEs), which will provide motivation for the mathematical modelling and analysis in subsequent chapters. In chapter 2, by appealing to sound notions from rational mechanics and thermodynamics, we construct a mathematical model which aims to encapsulate the essential phenomena involved in violent elastic-plastic deformation. This is followed in chapter 3 with a numerical analysis of the mathematical model in uniaxial strain, which is the geometry relevant ICEs. In chapters 4 and 5, we corroborate the observations made in chapter 3 via a systematic mathematical analysis. In particular, our focus will be on the elastic and plastic waves that can propagate through finite metal samples during isentropic compression. Finally, in chapter 6, we explore the applicability of our model to other geometries, specifically the radially axisymmetric expansion of a circular cavity embedded in an infinite elastic-plastic medium. We conclude with a summary of our findings and suggest some avenues for future investigation.

Les travaux de cette thèse portent sur le développement de système microfluidiques génériques pour la mesure de propriétés thermodynamiques de solutions de proteines. Un procédé simple de fabrication de puces microfluidiques résistantes à la pression ainsi qu'à la majorité des solvants organiques a été développé. En outre, les propriétés de surface des microcanaux peuvent être ajustées afin de générer des émulsions eau dans huile ou huile dans l'eau. L'étude des interactions proteines-proteines en solution a été réalisée en couplant ces dispositifs expérimentaux à la diffusion de rayonnement X aux petits angles. Avec seulement quelque milligramme de produit, les données expérimentales obtenues ont permis de calculer le second coefficient du Viriel, grandeur thermodynamique permettant de quantifier les interactions entre protéines. Une nouvelle approche expérimentale a également été développée afin de déterminer l'équation d'état du lysozyme, équation reliant la pression osmotique à la fraction volumique. Ce système microfluidique est basé sur le transfert de matière entre d'une phase dispersée vers une phase continue. Dans une certaine gamme d'activité de l'eau, l'équation d'état obtenu est en bon accord avec les données de la littérature. Afin de relier la dynamique du transfert aux propriétés thermodynamique du système une première approche de modélisation est proposée. Cette approche a pour but de déterminer l'équation d'état de la protéine avec une seule goutte. / This thesis is focused on the development of more efficient protocols and systems, by means of generic microfluidic platforms for measuring thermodynamic properties of protein solutions. A simple method for manufacturing pressure-resistant microfluidic structures with high chemical resistance has been developed. In addition, the surface properties of the fabrication materials can be adjusted to generate hydrophilic and hydrophobic surfaces allowing to generate aqueous and non-aqueous emulsions. On a first approach, the study of protein-protein interactions in solution was successfully performed using just a few milligrams of product by coupling a microfluidic platform, developed ad-hoc for this application, to small angle X-ray scattering. The obtained experimental data were used to calculate the second virial coefficient, thermodynamic parameter which quantifies protein interactions. A second and new experimental approach has also been developed to determine protein equations of state (EOS), which relate protein osmotic pressure to its volume fraction in solution. This novel methodology is based on the study of the mass transfer between a dispersed and a continuous phase, which are generated and controlled by means of a microfluidic setup. For a given range of water activity, the resulting EOS was found to be in good agreement with data reported in the literature. To link the mass transfer dynamics to the thermodynamic properties of the system a first modeling approach was proposed. This approach aims to determine the EOS of the protein using a single droplet.

Heavy atomic nuclei are thought to have proton and neutron radial distributions which have different extents. This difference is usually quantified in terms of a neutron skin (rnp), defined as the difference between the root mean square radii of the neutron and proton radial distributions (rnp = rn - rp). The nature, or even existence, of the neutron skin is currently not well established for many nuclei. Different nuclear theories give different predictions for the neutron skin thickness ranging for a typical heavy nucleus from 0.05 to 0.35 fm. Accurate measurement of the properties of the neutron skin would be a powerful constraint to differentiate between models of nuclear structure, improving our knowledge of the basic Equation Of State (EOS) for neutron rich matter. Particularly, the rate at which the neutron skin thickness changes across an isotopic chain of nuclei gives a tight constraint on the EOS and is also amenable to experimental determination with small systematic error. Improving our knowledge of the EOS for neutron rich matter is a crucial step towards gaining a deeper understanding of nuclear structure and nuclear matter in general. These results will also impact our knowledge of compact astrophysical objects such as neutron stars. This thesis describes the first measurement of neutron skin thicknesses along an isotopic chain using an electromagnetic probe. The neutron skin is measured through the study of the coherent photoproduction of neutral π mesons emitted from nuclei. This experiment was carried out in the A2 hall of the MAMI facility in Mainz, Germany in October 2012. The incident photon beam comprised of energy tagged photons in the range of Eγ=150-800 MeV with an intensity of 10⁸ photons per second. Experimental data was obtained for three different tin targets, 116Sn, 120Sn and 124Sn. The products from the resulting photoreactions were measured in the Crystal Ball detector and in the TAPS calorimeter systems, with track and particle identification information for charged particles provided by a multi wire proportional chamber (MWPC) and a particle identification detector (PID). The experiment provides the first information on the evolution of the neutron skin thickness along an isotopic chain using an electromagnetic probe. The results are compared with a range of theoretical models and previous data from strongly interacting probes. The new data will provide an important new experimental constraint on the basic properties of the EOS in atomic nuclei.

Made available in DSpace on 2014-06-11T19:24:06Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-11Bitstream added on 2014-06-13T20:11:56Z : No. of bitstreams: 1 medeiros_lg_me_ift.pdf: 943733 bytes, checksum: 8f5f1180edcd48023b600dfce45adc22 (MD5) / Sabemos, do modelo padrão da cosmologia, que quatro equações regem a dinâmica do universo. As duas primeiras são as equações de Friedmann, a terceira é a equação de conservação do tensor energia momento e a última é uma equação de estado. Através desta equação de estado podemos definir 3 períodos bastante distintos na evolução de nosso universo: era da matéria; era da radiação; era inflacionária . Por outro lado, baseado na termodinâmica, é razoável supor que a equação de estado do universo primordial seja bastante complexa, principalmente devido ao fenômeno de produção de pares. Nesta dissertação, propomos algumas equações de estado p(kT) para o universo primordial, baseado em um gás de fótons mais um gás de nucleons provenientes da radiação. Utilizando o método de Mayer de expansão de clusters, estes nucleons são tratados estatisticamente como partículas clássicas que interagem através de potenciais nucleares fenomenológicos. A principal característica destas equações de estado é que, devido à forte atração da interação nuclear, conforme a energia kT aumenta a pressão torna-se negativa. Portanto, as equações de estado p(kT) são capazes de ligar de forma natural as relações da era da radiação, da era inflacionária, possibilitando assim um mecanismo físico de geração de inflação no universo primordial. / We knows, from the standard model of cosmology, that four equations determine the dynamics of the universe. The first two are the Friedmann's equations, the third one is the equation of the conservation of the energy-momentum tensor and the last one is a equation of state. Through this equation of state we can define 3 much distinct periods in the evolution of the universe: matter era; radiation era; inflationary era. Nevertheless, based on thermodynamics, it's reasonable to suppose that the equation of state of the early universe is very complex, mainly due to the pair production phenomenon. In this dissertation we propose some equations of state p(KT) for the early universe, based in a gas of fotons plus a gas of radiation-belonging nucleons. Using the Mayer's method of cluster expansion, these nucleons are treated statisticaly as classical particles that interact through phenomenological nuclear potentials. The main characteristic of these equations of state is that, due to the strong attraction of the nuclear interaction, as the energy kT grows the pressure become negative. Thus, the equations of state p(kT) are able to link naturally the equation of the radiation era and of the inflationary era, enabling in this way a physical mechanism that produces inflation in the early universe.

Orientador: Ruben Aldrovandi / Banca: Sandro Silva e Costa / Banca: Diógenes Galetti / Resumo: Sabemos, do modelo padrão da cosmologia, que quatro equações regem a dinâmica do universo. As duas primeiras são as equações de Friedmann, a terceira é a equação de conservação do tensor energia momento e a última é uma equação de estado. Através desta equação de estado podemos definir 3 períodos bastante distintos na evolução de nosso universo: era da matéria; era da radiação; era inflacionária . Por outro lado, baseado na termodinâmica, é razoável supor que a equação de estado do universo primordial seja bastante complexa, principalmente devido ao fenômeno de produção de pares. Nesta dissertação, propomos algumas equações de estado p(kT) para o universo primordial, baseado em um gás de fótons mais um gás de nucleons provenientes da radiação. Utilizando o método de Mayer de expansão de clusters, estes nucleons são tratados estatisticamente como partículas clássicas que interagem através de potenciais nucleares fenomenológicos. A principal característica destas equações de estado é que, devido à forte atração da interação nuclear, conforme a energia kT aumenta a pressão torna-se negativa. Portanto, as equações de estado p(kT) são capazes de ligar de forma natural as relações da era da radiação, da era inflacionária, possibilitando assim um mecanismo físico de geração de inflação no universo primordial. / Abstract: We knows, from the standard model of cosmology, that four equations determine the dynamics of the universe. The first two are the Friedmann's equations, the third one is the equation of the conservation of the energy-momentum tensor and the last one is a equation of state. Through this equation of state we can define 3 much distinct periods in the evolution of the universe: matter era; radiation era; inflationary era. Nevertheless, based on thermodynamics, it's reasonable to suppose that the equation of state of the early universe is very complex, mainly due to the pair production phenomenon. In this dissertation we propose some equations of state p(KT) for the early universe, based in a gas of fotons plus a gas of radiation-belonging nucleons. Using the Mayer's method of cluster expansion, these nucleons are treated statisticaly as classical particles that interact through phenomenological nuclear potentials. The main characteristic of these equations of state is that, due to the strong attraction of the nuclear interaction, as the energy kT grows the pressure become negative. Thus, the equations of state p(kT) are able to link naturally the equation of the radiation era and of the inflationary era, enabling in this way a physical mechanism that produces inflation in the early universe. / Mestre

O plasma de quarks e glúons é um assunto que vem sendo muito estudado nos últimos anos, devido ao advento dos colisores de partículas modernos e os avanços nas pesquisas relacionadas a estrelas compactas. Assim, nesta tese tivemos como objetivo principal o estudo deste plasma. Para isto, aprimoramos uma equação de estado desenvolvida pelo nosso grupo, na qual foi adicionada a interação com um campo magnético constante. De posse desta nova equação de estado, que é formulada a partir da técnica de aproximação de campo médio, fizemos diversas aplicações. Em particular, no estudo de propagação de ondas lineares e não lineares, com o objetivo de verificar se a causalidade e estabilidade são respeitadas. Resolvemos a equação de Tolman-Oppenheimer-Volkoff para obter o diagrama massa-raio para uma estrela de quarks compacta. Estudamos como é a evolução temporal do Universo primordial resolvendo as equações de Friedmann e a evolução temporal de bolhas do plasma de quarks e glúons no gãs de hádrons (e também de bolhas de gás de hádrons no plasma de quarks e glúons) utilizando a equação de Rayleigh-Plesset relativística. / The quark gluon plama is a subject that has been actively studied in recent years, due to the advent of modern particle colliders and advances in research related to compact stars. Thus, in this thesis we had as main goal the study of this plasma. For this, we improved an equation of state developed by our group, where an interaction with a constant magnetic field was added. With this new equation of state, which is formulated from the mean field approximation technique, we made several applications. As in the study of propagation of linear and non-linear waves, with the goal of verifying whether the causality and stability are respected. We solved the Tolman-Oppenheimer-Volkoff equation to obtain the mass-radius diagram for a compact quark star. We study how the temporal evolution of the primordial Universe by solving Friedmanns equations and the temporal evolution of bubbles of quark gluon plasma in a hadrons gas (and also of bubbles of hadrons gas in a quark gluon plasma) using the relativistic Rayleigh-Plesset equation.

Orientador: Martín Aznar, Rubens Maciel Filho / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química / Made available in DSpace on 2018-08-17T00:28:23Z (GMT). No. of bitstreams: 1 AlvarezAlvarez_VictorHugo_D.pdf: 123512819 bytes, checksum: ab445a730c3a4943154e0b3ab2a37b10 (MD5) Previous issue date: 2018-08-16T21:28:09Z / Resumo: Os líquidos iônicos são uma interessante alternativa para aperfeiçoar processos com objetivos econômicos e ecológicos. Esta pesquisa tem como objetivo estudar propriedades físico-químicas de líquidos iônicos, próticos e apróticos, puros ou em misturas binárias com ésteres e aldeídos, tais como densidade, velocidade do som, viscosidade aparente, índice de refração e temperatura de decomposição térmica. Além disso, é estudado o comportamento termodinâmico de algumas aplicações dos líquidos iônicos, como equilíbrio líquido-vapor, absorção de gases e equilíbrio líquido-líquido. Inicialmente, foram sintetizados onze líquidos iônicos próticos usando moléculas de hidroxiaminas no cátion e moléculas de ácido orgânico com cadeias alquílicas de diferentes tamanhos no ânion. As propriedades físico-químicas dos líquidos iônicos, no estado puro e em misturas, indicam a formação de agregados nos líquidos iônicos próticos com mais de dois carbonos no ânion, e que o líquido iônico prótico contendo o ânion formiato é instável, formando um éster com o passar do tempo. Nos líquidos iônicos puros, a densidade diminui com o crescer da temperatura ou a cadeia alquílica do ânion; além disso, a viscosidade diminui com o crescer da temperatura, mas aumenta com o crescer da cadeia alquílica do ânion. Nos resultados das misturas binárias de líquidos iônicos com aldeídos ou ésteres, mostra-se que os líquidos iônicos baseados no cátion amônio são parcialmente insolúveis em aldeídos, ocorrendo o contrário para o líquido iônico baseado no cátion imidazólio, embora sejam insolúveis em ésteres. No equilíbrio líquido-vapor a baixas pressões de sistemas binários, observa-se o aumento da temperatura de ebulição do aldeído ou éster influenciado pela concentração do líquido iônico, e a mudança do ponto azeotrópico na mistura etanol-água. No equilíbrio líquido-vapor a altas pressões, o CO2 é mais absorvido nos líquidos iônicos próticos do que nos líquidos iônicos apróticos, especialmente naqueles que contêm o ânion acetato, mostrando quimisorção nesse grupo funcional. No equilíbrio líquido-líquido do sistema ternário líquido iônico + dibenzotiofeno + n-dodecano, observa-se que os líquidos iônicos baseados no cátion amônio conseguem extrair dibenzotiofeno do n-dodecano, tanto quanto um líquido iônico baseado no cátion imidazólio de estrutura mais complexa. Nos estudos de absorção desde uma corrente de CO2 em dois líquidos iônicos próticos a pressão ambiente, a temperatura e o fluxo de gás foram as variáveis limitantes da absorção. Os dados do equilíbrio líquido-vapor e densidade das misturas binárias foram correlacionados através da equação de estado de Peng-Robinson acoplada com a regra de mistura Wong-Sandler/GE. Para o cálculo de GE, foram implementados os modelos termodinâmicos de NRTL, UNIQUAC e COSMO-SAC. Para o equilíbrio líquido-vapor, os desvios na predição foram menores que 2,5% e na correlação menores que 1,5%. Para a densidade da solução, os desvios na predição foram menores que 2,7%. Assim, os líquidos iônicos e as aplicações estudadas demonstram que estes novos compostos podem ser usados para produzir novos processos e os modelos termodinâmicos disponíveis na literatura podem representar esses processos com precisão / Abstract: The ionic liquids are an interesting alternative to improve processes with ecological and economic goals. This research aims to study the physicochemical properties of aprotic and aprotic ionic liquids, pure or in binary mixtures with esters and aldehydes, such as density, sound velocity, viscosity, refractive index and thermal decomposition temperature. Furthermore, it is analized the thermodynamic behavior of some applications of ionic liquids as vapor-liquid equilibrium, gas absorption, and liquid-liquid equilibrium. Initially, eleven protic ionic liquids were synthesized using hydroxylethylamine molecules in the cation and organic acid molecules with alkyl chains of different sizes in the anion. The physicochemical properties in pure and in mixtures of ionic liquids indicate the formation of agregates with more than two carbons in the anion. The protic ionic liquid containing the formate anion is unstable, forming an ester over time. In pure ionic liquids, the density decreases with increasing temperature or alkyl chain of the anion, the viscosity decreases with increasing temperature, but increases with increasing alkyl chain anion. In the results of binary mixtures of ionic liquids with aldehydes and esters, it is shown that ionic liquids based on ammonium cation are partly insoluble in aldehydes ans soluble in esteres, but for the ionic liquid based on imidazolium was the opposite. In the vapor-liquid equilibrium at low pressures of binary systems, there is a increase of the boiling point of the aldehyde or ester influenced by the concentration of ionic liquid. It changes the azeotropic point of ethanol-water mixture. In the vapor and liquid at high pressures, more CO2 is absorbed in the protic ionic liquids than in aprotic ionic liquids. This is especially shown in those containing acetate anion, indicating quimisorption with this functional group. In liquid-liquid equilibrium of ternary system ionic liquid + dibenzothiophene + n-dodecane, it is observed that the ionic liquids based on ammonium cation can be extracted dibenzothiophene from n-dodecane. Both as an ionic liquid based on imidazolium cation of more complex structure. In studies of absorption from a CO2 flow in two protic ionic liquids at ambient pressure, the variables limiting the absorption were the temperature and flow rate. Data from the vapor-liquid equilibrium and density of binary mixtures were correlated using the equation of state of Peng-Robinson with the mixing rule of Wong-Sandler/GE. For the calculation of GE, it was implemented thermodynamic models as NRTL, UNIQUAC and COSMO-SAC. For the vapor-liquid equilibrium, the deviations in the prediction and correlation were lower than 2.5% and 1.5%, respectively. For the mixture density, the deviations in the prediction were lower than 2.7%. Therefore, the ionic liquids an the applications studied demonstrate that these new compounds are reliable to yield new processes and the current thermodynamic models can represent these processes with accuracy / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

Orientador: Liliane Lona / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-09T09:29:23Z (GMT). No. of bitstreams: 1 Pereira_YuriGuerrieri_M.pdf: 1827964 bytes, checksum: 8c6635139bee2d39bd01aba8b6a2c335 (MD5) Previous issue date: 2007 / Resumo: Os sistemas poliméricos, sejam eles reacionais ou não-reacionais, são em geral bastante complexos, devido à própria estrutura das cadeias das suas moléculas e pela existência de diversas interações entre elas. No que se refere à termodinâmica de sistemas poliméricos, este é um aspecto fundamental em muitos processos de polimerização, uma vez que têm impacto direto nas características dos materiais formados. Neste sentido, este trabalho tem como objetivo investigar o comportamento de sistemas poliméricos em duas plantas industriais de produção de polietileno, denominadas aqui como Planta PEBD, onde é produzido polietileno de baixa densidade (PEBD), e Planta PEL, onde são produzidos polietileno linear de baixa densidade (PELBD) e polietileno alta densidade (PEAD). Na Planta PEBD foi estudado o equilíbrio líquido-líquido a alta pressão, presente no reator, e o equilíbrio líquido-vapor presente no separador de baixa pressão (flash). Para este estudo foram utilizadas 8 resinas produzidas comercialmente. Na Planta PEL foi estudado o equilíbrio líquido-vapor presente no separador de pressão intermediaria (flash). Para este estudo foram utilizadas 25 resinas produzidas comercialmente. De um modo geral foram feitas as modelagens de sistemas binários e multicomponentes constituídos por: etileno, etano, propeno, propano, 1-buteno, cicloexano, 1-octeno e polímero. Os dados experimentais utilizados foram gerados a partir de medições disponíveis e balanços de massa e energia em ambas as plantas industriais. Para a modelagem dos equilíbrios de fases investigados neste trabalho foi utilizada a equação de estado PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory, Teoria Estatística de Fluidos Associativos com Cadeia Perturbada), que tem apresentado desempenho superior ao das suas antecessoras. Após a implementação computacional, o modelo foi validado para ambas as plantas industriais. Os resultados mostram que, para alguns sistemas, os parâmetros binários encontrados na literatura são suficientes para uma boa modelagem; para outros, quando os parâmetros de interação binária são ajustados na equação, o modelo apresenta-se capaz de representar melhor os dados experimentais / Abstract: Polymeric systems, with or without chemical reactions, are in general much complex due to molecules structure and due to the existence of many interactions between them. Thermodynamics of polymeric systems, and more specifically phase equilibria, is a fundamental aspect in many polymerization processes, since they influence directly in the characteristics of the material produced. In this way, the objective of this work is to investigate the behavior of polymeric systems in two industrial plants of polyethylene production, called here as PEBD Plant, where low density polyethylene (LDPE) is produced, and PEL Plant, where linear low density polyethylene (LLDPE) and high density polyethylene (HDPE) are produced. In PEBD Plant liquid-liquid equilibria in the reactor unit and vapor-liquid equilibria in the low pressure separator (flash) were studied. For this study 8 resins produced commercially were used. In PEL Plant vapor-liquid equilibria present in the intermediate pressure separator (flash) was studied. For this study 25 resins produced commercially were used. In a general way binary and multicomponent systems were modeled, with the following components: ethylene, ethane, propylene, propane, 1butene, ciclohexane, 1-octene and polymer. The experimental data used has been generated through a few measurements at disposal and though mass and energy balance calculations in both industrial plants. In modeling phases equilibria investigated in this work, PC-SAFT (Perturbed-Chain Statistical Associating Fluid Theory) equation of state was used, since it has presented superior performance when compared with its predecessors. After the computational implementation, the model was validated for both industrial plants. The results show that, for some systems, the binary parameters found in literature had been good enough for modeling purposes. In others systems, when binary interaction parameters were adjusted in the equation, the model had presented a better capability in representing the experimental data / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

Garnets are major silicates from the upper mantle to the transition zone. Elastic properties of garnets are essential to interpret the variation of seismic velocities at different depths and construct a model of the Earth’s composition. Due to the chemical flexibility at octahedron sites of the crystal structures, garnets usually exist with multiple components and have many composition variations. Pyrope is an important member in the garnet group. Fe2+-Mg2+ substitution in pyrope is one of the common solid solutions. We have synthesized and measured three synthetic solid solutions samples (Py83Alm17, Py54Alm46 and Py30Alm70). Equations of state yielded their isothermal bulk moduli K0 to be 172(4)GPa, 174(2)GPa, and 183(2)GPa, respectively, which confirmed that almandine content (Fe2+ substitution) increased the bulk modulus of the garnet. A relation between the bulk modulus and the almandine mole fraction (n) was derived to be K0 = 170 + 15 n, showing it is a nearly ideal mixing model. Another factor that also significantly influences the elasticity of pyrope is water. Water is transported to the deep Earth by subduction slabs and mainly exists in nominally anhydrous minerals (NAM) as hydroxyl (OH-). Its content in minerals varies as depth increases. We therefore investigated pressure influence on water solubility in pyrope. A suite of pyrope single crystals was synthesized in a water-saturated environment at 6, 7, 9 and 12GPa and water was characterized by FTIR. IR spectra showed a typical peak at 3630 cm-1. At 9 and 12GPa, new peaks at 3572 cm-1 and 3504 cm-1 appeared and indicated that a new substitution mechanism, other than hydrogarnet substitution SiO4=(OH)4, was adopted in the pyrope crystal structure. Water solubility in pyrope reached 0.2wt% at 7GPa. From 4-7GPa, water solubility increased. At 9GPa, water content dropped to 0.07wt% and increased to 0.3wt% at 12GPa, where a cubic to tetragonal phase transition was observed. Water showed a weakening effect on the bulk moduli of hydrous pyrope. Their bulk moduli were 166GPa, 173GPa and 161GPa with water contents of 0.07wt%, 0.1wt% and 0.2wt%, respectively. An approximate linear relationship was proposed about the bulk modulus as a function of water content.