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PubMed2006

Shape evolution of Cu2O nanostructures via kinetic and thermodynamic controlled growth.

We report the shape evolution process of Cu(2)O nanocrystals upon slow oxidation of Cu under ambient conditions, yielding novel hexagonal and triangular platelike morphologies. The shape of the obtained nanocrystals evolves from hexagonal to triangular to octahedral; the growth patterns are governed by kinetically and thermodynamically controlled growth. Preferential adsorption of I(-) on {111} planes of Cu(2)O nanoparticles induced the selective crystal growth of metastable platelike structures with {111} faces as the basal planes. On aging, the growth process appeared to shift into the thermodynamic regime and the thermodynamically stable octahedral shape is obtained. The possible growth mechanisms were investigated by varying the synthetic conditions. The band gap of Cu(2)O nanooctahedrons was determined by the classical Tauc approach to be 2.24 eV, which is blue shifted with respect to the bulk Cu(2)O value (2.17 eV). Results suggest that the slow oxidation process and use of crystallographic selective surfactants are essential for the appearance of anisotropic metastable shapes. In general, surface energy control by surfactant molecules might provide a convenient channel for tailoring nanocrystal shapes of metal oxides.

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PubMed2006

Theoretical study on silver- and gold-loaded zeolite catalysts: thermodynamics and IR spectroscopy.

Density functional calculations have been carried out to determine geometries, adsorption energies and vibrational frequencies of NO, N(2)O, CO, O(2), and H(2)O, on a model for Ag(I) and Au(I) ion-exchanged ZSM-5 catalysts. Using statistical mechanics, the DeltaH and DeltaG values were calculated in order to evaluate the stability of the adsorbates on Ag(I) and Au(I) sites. The calculated vibrational frequencies are in reasonable agreement with the reported experimental values. The analysis of the results shows that at 475 degrees C the adsorption of two NO molecules and the direct N(2)O decomposition on AgZSM-5 are thermodynamically unfavorable. The adsorption of one NO molecule presents a small positive DeltaG value. On the contrary, in the case of AuZSM-5, the adsorption of one NO molecule and the direct N(2)O decomposition to produce N(2) are thermodynamically favorable. For both models, the N(2)O decomposition by AgO and AuO species is thermodynamically very favorable. The analysis of the interaction with H(2)O shows that water displaces the adsorbed NO on AgZSM-5 but not on AuZSM-5 which indicates that the AuZSM-5 catalyst is less sensitive to deactivation by H(2)O than the AgZSM-5 catalyst.

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PubMed2005

Thermodynamic properties of the unique self-assembly of {Mo72Fe30} inorganic macro-ions in salt-free and salt-containing aqueous solutions.

Static and dynamic laser light scattering techniques are used to monitor the slow self-assembly of 2.5-nm-diameter, hollow spherical, fully hydrophilic heteropolyoxometalate {Mo72Fe30} macro-ions into single-layer vesicle-like "blackberries" (averaging approximately 50-60 nm in diameter) in dilute salt-free and salt-containing aqueous solutions, to obtain the thermodynamic properties of the unique self-assembly. A very high activation energy is observed during the transition from the single ion (general solute state) to blackberries (so-called "second solute state"), which might be responsible for the interestingly slow self-assembly process in dilute solutions. The thermodynamic parameters of the blackberry formation can be affected by adding simple electrolytes into the solution, because the electrostatic interactions are responsible for the unique self-assembly, and the effects of various anions and cations (in the low salt concentration regimes) are discussed. Multivalent anions make the single {Mo72Fe30} macro-ions more stable and make the blackberry formation more difficult. Small cations carrying more charges tend to accelerate the self-assembly process. This is the first study on the thermodynamic properties of the novel self-assembly in dilute solutions and the equilibrium and transition between the two solute states of macro-ions in solution.

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PubMed2004

Thermodynamics of micellization and adsorption of three alkyltrimethylammonium bromides using isothermal titration calorimetry.

Studies of the thermodynamic properties of micellization, as well as the enthalpy change of adsorption (displacement), were conducted using isothermal titration calorimetry (ITC). The cationic surfactants, dodecyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, and hexadecyltrimethylammonium bromide or cetyltrimethylammonium bromide were used. Adsorption studies were performed utilizing HiSil 233 precipitated silica as the substrate. The thermodynamics of micellization were studied at 28, 30, and 35 degrees C using ITC. DeltaHdil was calculated and graphed versus concentration in order to determine DeltaHmic and critical micelle concentration. From these data, DeltaGmic and DeltaSmic were also determined and found to be in agreement with values previously determined using traditional temperature-variation methods. The thermodynamics of adsorption were also determined at the above temperatures using ITC. Using the results, the heat of displacement, Qdisp, and enthalpy of displacement, DeltaHdisp, were calculated. A plot of DeltaHdisp as a function of concentration was generated and used to interpret the mechanism of adsorption in the four regions of a typical cationic surfactant adsorption isotherm.

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PubMed2006

Molecular-thermodynamic theory of micellization of pH-sensitive surfactants.

A predictive, molecular-thermodynamic theory is developed to model the micellization of pH-sensitive surfactants. The theory combines a molecular-thermodynamic description of micellization in binary surfactant mixtures with the protonation equilibrium of the surfactant monomers. The thermodynamic component of the theory models the pH-mediated equilibrium between micelles, surfactant monomers, and counterions. These counterions may originate from the surfactant or from added salt, acid, or base. The molecular component of the theory models the various contributions to the free energy of micellization, which corresponds to the free-energy change associated with forming a mixed micelle from the protonated and deprotonated forms of the surfactant and from the bound counterions. The free energy of micellization includes hydrophobic, interfacial, packing, steric, electrostatic, and entropic contributions, which are all calculated molecularly. The theory also requires knowledge of the surfactant molecular structure and the solution conditions, including the temperature and the amount of any added salt, acid, or base. To account for the pH sensitivity of the surfactant, the theory requires knowledge of the surfactant monomer equilibrium deprotonation constant (pK1), which may be obtained from experimental titration data obtained below the critical micelle concentration (cmc). The theory can be utilized to predict the equilibrium micelle and solution properties, including the cmc, the micelle composition, the micelle shape and aggregation number, the solution pH, and the micelle deprotonation equilibrium constant (pKm). Theoretical predictions of the cmc, the micelle aggregation number, and the pKm compare favorably with the available experimental data for alkyldimethylamine oxide surfactants. This class of pH-sensitive surfactants exhibits a form of self-synergy, which has previously been attributed to hydrogen-bond formation at the micelle interface. Instead, we show that much of the observed synergy is related to the electrostatic contribution to the free energy of micellization. Although we do not explicitly include hydrogen bonding in the molecular model of micellization, we briefly discuss how it may be incorporated and its anticipated effect on the predicted micellization behavior.

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PubMed2002

Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment.

Edwards has proposed a thermodynamic description of dense, slowly flowing granular matter, in which the grains (the 'atoms' of the system) interact with inelastic forces and enduring contacts. In Edwards' ensemble-one of the very few generalizations of standard statistical mechanics-thermodynamic quantities are computed as flat averages over configurations in which the grains are static or jammed, leading to a natural definition of configurational temperature. But the approach is not justified from first principles and hence, in the absence of explicit tests of its validity, has not been widely accepted. Here we report a numerical experiment involving a realistic model of slowly sheared granular matter; our results strongly support the thermodynamic description. Considering particles of different sizes in a slowly sheared dense granular system, we extract an effective temperature from a relation connecting their diffusivity and mobility. We then perform an explicit computation to show that the effective temperature measured from this relation coincides with the Edwards configurational temperature. Our approach, which is specifically conceived to be reproducible in the laboratory, may thus render the Edwards temperature accessible to experiments.

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PubMed2005

Hexafluoroantimony(V) salts of the cationic Ti(IV) fluoride non metallocene complexes [TiF3(MeCN)3]+ and [TiF2L]2+ (L = 15-Crown-5 and 18-Crown-6). Preparation, characterization and thermodynamic stability.

The cationic titanium fluoride containing complexes [fac-TiF3(MeCN)3][SbF6].MeCN (1), [trans-TiF2(15-Crown-5)][SbF6]2(2) and [trans-TiF2(18-Crown-6)][SbF6]2(2), were prepared by the reaction of TiF4, the molecular ligand and SbF5 in MeCN. Complexes 1-3 were characterized by X-ray single crystal analysis, elemental analysis, IR, NMR and mass spectroscopy. Titanium tetrafluoride reacts with the SbF5 in SO2 with the formation of fac-[TiF3(SO2)3]+, detected by 19F NMR. Application of the volume-based approach to thermodynamics (VBT) offers a means, for the first time, of exploring the energetics surrounding these materials and in the thermodynamic section a discussion of this new approach is provided. It emerges that the basis of the thermodynamic driving force of formation of [TiF3L3][SbF6](s) salts, that enforces the unfavourable [DeltaH degrees =+ 237 (+/-20) kJ mol(-1)] fluoride ion transfer from the Lewis acid TiF4(s) to SbF5(l) to give the hypothetical [TiF3]+[SbF6]-(s), is the higher Ti-L (L = ligand) bond energy in the cationic complexes [TiF3L3]+ as compared to that in the molecular adducts TiF4L2(s) and SbF5L(s) so giving rise to larger enthalpies of complexation of [TiF3]+(g) by 3L(g) compared to those for complexation of TiF4(g) by 2L(g) and SbF5(g) by 1L(g). Formation of the trans-[TiF2(15-Crown-5)]2+ and trans-[TiF2(18-Crown-6)]2+ is accounted for the stabilization of [TiF2]2+ cation by the five donor acceptor Ti-O contacts and the accompanying positive charge delocalization. Cationic titanium(IV) complexes fac-[TiF3MeCN)3-nLn]+(n= 0-3) and cis-[TiF318-Crown-6)]+, trans-[TiF2(Crown)]2+(Crown = 15-Crown-5 and 18-Crown-6) were obtained in MeCN solution by the reaction of fac-[TiF3(MeCN)3]+ and L = Et2, THF, H2 or crown ethers. Complexes fac-[TiF3(MeCN)3-nLn][SbF6] L = Et2, THF, H2O, crown ethers are unstable in MeCN solution and slowly decompose giving molecular complexes cis-TiF4L2, cis-TiF4(Crown), SbF5L, titanium oxofluoride and alkoxide complexes. The structure of the fac-[TiF3(MeCN)3]+ is similar to the fac-[TiCl3(MeCN)3]+ and the complexes trans-[TiF2L]2+ L = 15-Crown-5, 18-Crown-6 have very similar geometries to that of trans-[TiCl2(15-Crown-5)]+ showing that the essential features of coordination are the same for the cationic titanium chloride and fluoride complexes with MeCN and 15-Crown-5, 18-Crown-6.

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PubMed2001

Thermodynamics of computing: Entropy of nonergodic systems.

Landauer discussed the minimum energy necessary for computation and stated that erasure of information is accompanied with kT ln 2/ bit of heat generation. We reconsider this problem on the basis of Clausius's equation defining the thermodynamic entropy. We show that the erasing process, involving a transition from a nonergodic to an ergodic state, is irreversible and accompanied with k ln 2/bit of entropy generation, while the heat generation occurs in a writing process. The inverse of the erasing process corresponds to spontaneous symmetry breaking from an ergodic to a nonergodic state, which induces a decrease(!) in thermodynamic entropy. Our theory is examined by a simulation of a binary device described by a Langevin equation. We argue that the so-called residual entropy of symmetry broken states, such as in ice, is not a thermodynamic quantity, even if it might be called "information entropy." (c) 2001 American Institute of Physics.

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PubMed2004

Thermodynamics of soft anisotropic interfaces.

The Gibbs-Duhem equation for interfaces between nematic liquid crystals and isotropic fluids is formulated and shown to be a generic equation for soft anisotropic surfaces. The one-to-one correspondence between the nematic and crystalline surface Gibbs-Duhem equations is established. Consistency between the surface Gibbs-Duhem equation and the classical equations of interfacial nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic surface Gibbs-Duhem equation reveals the presence of couplings between shape, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for morphactancy, that is, adsorption-induced interfacial shape selection. The specific roles of gradient bulk Frank elasticity, interfacial tension, and anchoring energy are elucidated by analyzing particular paths in the thermodynamic-geometric phase space.

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PubMed2004

Nonequilibrium thermodynamic description of the three-phase contact line.

In order to give a solid foundation of the description of the motion of the three-phase contact line, we develop the nonequilibrium thermodynamic description of the contact line. It is postulated that during its motion the contact line is featured as a separate thermodynamic system. Conservation laws are given for the excess densities of the components, the momentum and the energy along the line. The Gibbs law is formulated for the contact line and using this law the excess entropy production density along the line is constructed. This identifies the conjugate thermodynamic forces and fluxes for the contact line. Linear laws relating these quantities can then be given. The special case considered by Shikmurzaev, who gave the first satisfactory description of the motion of the contact line, is considered in more detail. A new boundary condition is found, which was not used by Shikhmurzaev. The need for such an additional boundary condition for this case was discussed in recent work by Billingham.

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PubMed2004

Bridging continuum and statistical thermodynamics via equations of state and the density of states.

The connection between molecular force fields and equations of state (EoS) is typically established at the level of predicted quantities, e.g., by comparing simulation data and EoS data. In this paper we show how an EoS can be used to extract the density of states (Omega) of a system thus establishing a deeper connection between EoSs and statistical thermodynamics. We also show how such an EoS Omega can be used to aid molecular simulation methods designed to map out Omega (like the multicanonical approach). Central to the implementation of these ideas is the fact that the configurational Omega is related to thermodynamic properties accessible by an EoS via Boltzmann's equation. Sample calculations are presented for the Omega relevant to isothermal-isobaric and grand canonical ensemble simulations using the hard-sphere system and the Lennard-Jones system as model fluids, and the Carnahan-Starling EoS and a cubic EoS, respectively, as thermodynamic models.

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PubMed2005

Density functional approach to thermodynamics of self-assembly.

A local density functional approximation for predicting the surface crystallization of a thermodynamically small system under gravity is described and tested. Using the model of the classical soft-sphere fluid, the state parameters for such systems are identified. A generalized phase diagram based upon the scaling variables is obtained; systems with the same reduced-state parameters exhibit identical profiles of thermodynamic properties such as density, pressure, and intrinsic chemical potential, measured in the direction of the applied field. The point-thermodynamic approximation of Rowlinson and the local density approximation of the density functional formalism are found to be remarkably accurate. A configurational temperature is defined and shown to agree with the corresponding kinetic temperature for inhomogeneous systems at equilibrium. The structural profiles at the crystal-fluid interface are indicative of a mesolayer of lower density crystal, not seen in the field-free isobaric crystal-liquid interface.

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PubMed2006

Grain-boundary free energy via thermodynamic integration.

In a previous publication by Lusk and Beale [Phys. Rev. E 69, 026117 (2004)], fluctuating cell (FC) theory was used to estimate the free energy of symmetric tilt grain boundaries in an assembly of nearly hard disks. The FC method is much faster than the more traditional thermodynamic integration, but the accuracy of the algorithm has not been assessed in association with persistent defect structures. This motivated the present work wherein the FC free energies are compared directly with the data obtained via thermodynamic integration from an Einstein crystal to an assembly of hard disks. This comparison is made over the range of possible misorientations for symmetric tilt boundaries and indicates that the FC method gives quantitatively accurate estimates for grain-boundary free energy. We also demsonstrate that the FC approximation is quantitatively accurate at determining the free-energy contribution of each particle whether in the bulk or the grain boundary. The FC calculation is about two orders of magnitude faster than a full thermodynamic integration. This approach may offer a numerically efficient means of estimating the free energy of persistent defect structures to greater accuracy than is afforded by the quasiharmonic and local harmonic approximations.

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PubMed2006

Direct calculation of solid-vapor coexistence points by thermodynamic integration: application to single component and binary systems.

We present a new thermodynamic integration method that directly connects the vapor and solid phases by a reversible path. The thermodynamic integration in the isothermal-isobaric ensemble yields the Gibbs free energy difference between the two phases, from which the sublimation temperature can be easily calculated. The method extends to the binary mixture without any modification to the integration path simply by employing the isothermal-isobaric semigrand ensemble. The thermodynamic integration, in this case, yields the chemical potential difference between the solid and vapor phases for one of the components, from which the binary sublimation temperature can be calculated. The coexistence temperatures predicted by our method agree well with those in the literature for single component and binary Lennard-Jones systems.

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PubMed2006

Exploring the effect of anharmonicity of molecular vibrations on thermodynamic properties.

Thermodynamic properties of selected small and medium size molecules were calculated using harmonic and anharmonic vibrational frequencies. Harmonic vibrational frequencies were obtained by normal mode analysis, whereas anharmonic ones were calculated using the vibrational self-consistent field (VSCF) method. The calculated and available experimental thermodynamic data for zero point energy, enthalpy, entropy, and heat capacity are compared. It is found that the anharmonicity and coupling of molecular vibrations can play a significant role in predicting accurate thermodynamic quantities. Limitations of the current VSCF method for low frequency modes have been partially removed by following normal mode displacements in internal, rather than Cartesian, coordinates.

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PubMed1985

Nonlinear natural engine: Model for thermodynamic processes in mesoscale systems.

To develop intuition on the possible application of concepts from thermodynamic heat engines to mesoscale systems, we have constructed and studied a model thermoacoustic heat engine. The model consists of a chain of coupled nonlinear acoustic vibrators in which the primary thermodynamic medium is argon gas, the secondary thermodynamic medium is constituted by solids bounding the gas, and frequencies are ca. 3 x 10(2) Hz. The nonlinear elements are the necks, made flexible by means of an oil-loaded DuPont Kapton film, of Helmholtz resonators. When the primary medium is driven uniformly by an acoustic driver at a frequency somewhat below the low-amplitude resonant frequency and at a high enough driving amplitude, stationary localized or solitary states appear irreversibly on the chain. These are characterized by a higher vibrational amplitude than that in surrounding vibrators, where the amplitude can decrease; by the appearance of deep subharmonics of the drive frequency, corresponding to driven low-frequency vibrations of the Kapton film-oil systems; and by the pumping of heat toward the localized states. Possible implications of these results for mesoscale systems consisting of chains of molecular vibrators are then discussed.

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PubMed1999

Thermodynamics of a nonionic sponge phase.

Different suggestions for the mechanism governing the narrow stability of the L(3) (sponge) phase have led to a series of debates in recent years. There have been several models developed to describe such a mechanism via thermodynamics. To date, experimental data are insufficient to test present theories. In this study, we revisit the sponge phase with two series of thermodynamic data performed on the well-characterized C(12)E(5)-n-decane-H(2)O system. These thermodynamic data sets stem from phase equilibrium and static light scattering experiments designed to link system-specific parameters such as the temperature dependence of the spontaneous curvature H(o) and the two bending moduli kappa and (-)kappa, which have only been loosely connected in earlier experiments. The use of a well-characterized system is important in that it allows usage of molecular descriptors from earlier studies to reduce fit parameters. Another advantage for using this system is that its phase behavior is analogous to a two-component system which, from an experimental standpoint, is more practical to perform accurate measurements and, from a theoretical standpoint, more simple to model. In the present investigation, we use these tools to quantitatively test parameters obtained by different experimental techniques and assumptions inherited in theoretical models designed to interpret them.

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PubMed1999

Linear response theory for thermodynamic properties.

A fluctuation-dissipation theorem, connecting all thermodynamic response functions to equilibrium fluctuations in the microcanonical ensemble, is derived from classical mechanics. This particular problem is not included in the usual linear response scheme, since the relevant perturbations cannot be stated as additional terms in the Hamiltonian. In experiments where the only control parameter is the heat flow, dissipation is present in terms of an entropy flow from the system to the surroundings. As an example, the full frequency-dependent thermodynamic response matrix is extracted from simulations of a supercooled binary Lennard-Jones fluid. This fluid shows rather high relaxation strength of all response functions, except of the adiabatic compressibility. The low frequency limit of all thermodynamic susceptibilities increases as temperature is decreased along an isocore.

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