Self-Organization of n-Alkane Chains in Water: Length Dependent Crossover from Helix and Toroid to Molten Globule

We demonstrate a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures of the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like (circular) for small chains (CnH2n+2; n <= 20) and spherical for very long ones (n = 100), we find the emergence of ordered helical structures at intermediate lengths (n similar to 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier.

Geometrically simple linear weirs using circular quadrants

A detailed theoretical analysis of flow through a quadrant plate weir is made in the light of the generalized theory of proportional weirs, using a numerical optimization procedure. It is shown that the flow through the quadrant plate weir has a linear discharge-head relationship valid for certain ranges of head. It is shown that the weir is associated with a reference plane or datum from which all heads are reckoned.Further, it is shown that the measuring range of the quadrant plate weir can be considerably enhanced by extending the tangents to the quadrants at the terminals of the quadrant plate weir. The importance of this weir (when the datum of the weir lies below its crest) as an outlet weir for grit chambers is highlighted. Experiments show excellent agreement with the theory by giving a constant average coefficient of discharge.

Phase Relations in the System Cu-Gd-O and Gibbs Energy of Formation of CuGd204

The phase relations in the system Cu-Gd-O have been determined at 1273 K by X-ray diffrac- tion, optical microscopy, and electron microprobe analysis of samples equilibrated in quartz ampules and in pure oxygen. Only one ternary compound, CuGd2O4, was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt, Cu2O + CuGd2O4 + Gd2O3 // (Y2O3) ZrO2 // CuO + Cu2O, Pt in the temperature range of 900 to 1350 K. For the formation of CuGd2O4 from its binary component oxides, CuO (s) + Gd2O3 (s) → CuGd2O4 (s) ΔG° = 8230 - 11.2T (±50) J mol-1 Since the formation is endothermic, CuGd2O4 becomes thermodynamically unstable with respect to CuO and Gd2O3 below 735 K. When the oxygen partial pressure over CuGd2O4 is lowered, it decomposes according to the reaction 4CuGd2O4 (s) → 4Gd2O3 (s) + 2Cu2O (s) + O2 (g) for which the equilibrium oxygen potential is given by Δμo 2 = −227,970 + 143.2T (±500) J mol−1 An oxygen potential diagram for the system Cu-Gd-O at 1273 K is presented.

Gibbs energy of formation of orthorhombic CaZrO3

The Gibbs free energy of formation of the orthorhombic form of CaZrO3(o) from monoclinic ZrO2(m) and periclase CaO(p) has been determined as a function of temperature in the range 950-1225 K, using an electrochemical cell incorporating single-crystal CaF2 as the solid electrolyte. The results are corrected for the small solid solubility of CaO in ZrO2. For the reaction, ZrO2(m) + CaO(p) --> CaZrO3(o), DELTAG(phi) = -31590 -13.9T(+/- 180) J mol-1. The ''second-law'' enthalpy of formation of CaZrO3 obtained from the results of this study at a mean temperature of 1090 K is in excellent agreement with the high-temperature solution calorimetric measurements of Muromachi and Navrotsky at 1068 K (J. Solid State Chem., 72 (1988) 244), and the average value of the bomb and acid solution calorimetric studies of Lvova and Feodosev (Zh. Fiz. Khim., 38 (1964) 28), Korneev et al. (Izv. Akad. Nauk SSSR, Neorg. Mater., 7 (1971) 886) and Brown and Bennington (Thermochim. Acta, 106 (1986) 183). The standard entropy of CaZrO3(o) at 298.15 K from the free energy data is 96.4 (+/- 3.5) J K-1 mol-1. The results of this study are discussed in comparison with high-temperture e.m.f. measurements reported in the literature on cubic zirconia solid solutions.

A thermodynamic criterion for selection of gas compositions for diamond deposition

Isoactivity lines for carbon with respect to diamond as the standard state have been calculated in the ternary system C-H-O at 1223 K to identify the diamond deposition domain. The gas composition is calculated by suppressing the formation of all condensed forms of carbon using the SOLGASMIX free-energy minimization program. Thirty six gas species were included in the calculation. From the gas composition, isoactivity lines are computed using recent data on the Gibbs energy of diamond. Except for activities less than 0.1, the isoactivity lines are almost linear on the C-H-O ternary diagram. Gas compositions which generate activity of diamond ranging from 1 to 100 at 1223 K fall inside a narrow wedge originating from the point representing CO. This wedge is very similar to the revised lens-shaped diamond growth domain identified by Bachman et al., using inputs from experiment. The small difference between the calculated and observed domains may be attributed to variation in the supersaturation required for diamond deposition with gas composition. The diamond solubility in the gas phase along the isoactivity line for a(di)=100 and P=6.7 kPa exhibits a minimum at 1280 K, which is close to the optimum temperature found experimentally. At higher supersaturations, non-diamond forms of carbon, including amorphous varieties, are expected. The results suggest that thermodynamic calculations can be useful for locating diamond growth domains in more complex CVD systems containing halogens, for which very little experimental data is available.

Determination of the Gibbs energy of diamond using a solid state cell

he chemical potential of carbon in diamond, relative to its value in graphite, has been directly determined using a solid state electrochemical cell incorporating single crystal CaF2 as the solid electrolyte. The cell can be represented as Pt, C(graphite) + CaC2 + CaF2double vertical barCaF2double vertical barCaF2 + CaC2 + C(diamond), Pt The reversible emf of this cell is directly related by the Nernst equation to the Gibbs free energy change for the conversion of diamond to graphite. The difference in the chemical potential of carbon in the two crystal structures varies linearly with temperature in the range 940 to 1260 K ?C(diamond) ? ?C(graphite) = 1100 + 4.64T (±50) J mol?1 On the average, the values given by the equation are 320 J mol?1 less positive than the currently accepted ones based on calorimetric studies. The difference is primarily in the enthalpy term.

Activities and their relation to cation distribution in NiAl2O4 MgAl2O4 spinel solid solutions

The activity of NiAl2O4 in NiAl2O4MgAl2O4 solid solutions has been measured by using a solid oxide galvanic cell of the type, Pt, Ni + NiAl2O4 + Al2O3(α)/CaOZrO2/Ni + NixMg1−xAl2O4 + Al2O3(α). Pt, in the temperature range 750–1150°C. The activities in the spinel solid solutions show negative deviations from Raoult's law. The cation distribution in the solid solutions has been calculated using site preference energies independent of composition for Ni2+, Mg2+, and Al3+ ions obtained from crystal field theory and measured cation disorder in pure NiAl2O4 and MgAl2O4, and assumi g ideal mixing of cations on the tetrahedral and octahedral positions. The calculated values correctly predict the decrease in the fraction, α, of Ni2+ ions on tetrahedral sites for 1>x>0.25, observed by Porta et al. [J. Solid State Chem.11, 135 (1974)] but do not support their tentative evidence for an increase in α for x < 0.25. The measured excess free energy of mixing can be completely accounted for by using either the calculated or the measured cation distributions. This suggests that the Madelung energy is approximately a linear function of composition in the solid solutions. The composition of NiOMgO solid solutions in equilibrium with NiAl2O4MgAl2O4 solid solutions has been calculated from the results and information available in literature.

Gibbs free energies of formation of indium (III) oxide and sulphate

Emf measurements on the galvanic cell Pt, Ta, In + In,O, / Tho,-Y,03 / Cu + C+O, Pt were used to obtain the standard free energy of formation of 1%03fr om 600 to 900°C. Differential thermal analysis was used to detect the decomposition of In2(S0,), under controlled SO2 + O2 + Ar mixtures in thqtemperature range 640-8wC. X-ray diffraction analysis indicated that the decomposition product was 1%03 without an oxywlphate intermediate. The following equations were obtained for the variation of the standard free-energy change(Jlmole) with temperature:

Spinel deoxidation equilibria in the Fe Mn Al O system - experiments and computation

The concentration and chemical potential of oxygen in liquid Fe--Mn alloys equilibrated with the spinel solution, (Fe, Mn)Al sub 2+2x O sub 4+3x , and alpha -Al sub 2 O sub 3 have been determined at 1873K as a function of manganese concentration. The composition of the spinel phase has been determined using electron probe microanalysis. The results are compared with data reported in the literature. The deoxidation equilibrium has been computed using data on free energy of solution of oxygen in liquid iron, free energies of formation of hercynite and galaxite, and interaction parameters reported in the literature. The activity--composition relationship in spinel solution was derived from a cation distribution model. The model is in excellent agreement with the experimental data on oxygen concentration and potential and the composition of the spinel phase. 23 ref.--AA

Gibbs’ free energies of formation of Cu2Ln2O5 (Ln = Tb, Dy, Er, Yb) compounds

The standard Gibbs' free energies of formation of compounds of type Cu2L%05 (Ln = Tb,Dy,Er,Yb) were measured using the solid state cell in the temperature range of 970 to 1323 K For formation of Cu2L?O5 compounds from their binary component oxides according to the reaction 2 CUO (s) + L%03 (s) -, Cu,,L%05 (s),the Gibbs' free energy changes can be represented by the following equations:AGO = 13 080 - 13.70 'I" (+80) J mol-' (Ln = Tb)AGq = 11 480 - 13.51 T (260) J mol-I (Ln = Dy)AGO = 10 750 - 13.99 T (260) J mol-I (Ln = Er)AGO = 9 920 - 13.90 T (260) J mol-' (Ln = Yb) Since formation of the compounds is endothermic, the compounds become thermodynamically unstable with respect to their component oxides below 955 K for Cu2Tb205, 850 K for Cu2Dy205, 768 K for Cu2Er205 and 714 K for Cu2Yb2OS When the oxygen partial pressure over Cu2L%05 is lowered, they decompose according to the scheme, 2 CU,L%O, (s) -r 2 L%03 (s) +2 cu20 (s) + 02(g)The equilibrium chemical potentials of oxygen corresponding to the dissociation reactions are computed from the emf data and auxiliary information on Cu20 and CuO. The computed decomposition temperatures at an oxygen partial pressure of 5.0 x ld Pa are compared with those obtained directly from combined thermogravimetric (TGA) and differential thermal analyses (DTA).The free energy, enthalpy and entropy of formation of Cu2Ln205 compounds show systematic variation with the ionic radius of the trivalent lanthanide ion. The trends obtained in this study are compared with information available in the literature. The staZbility of Cu2Ln205 compounds increases with the decrease in ionic radii of the ~ n ion~. +

Phase equilibria in the system NiO-CaO-SiO2 and Gibbs energy of formation of CaNiSi2O6

Phase relations in the pseudoternary system NiO-CaO-SiO2 at 1373 K are established. The coexisting phases are identified by X-ray diffraction and energy-dispersive X-ray analysis of equilibrated samples. There is only one quaternary oxide CaNiSi2O6 with clinopyroxene structure. The Gibbs energy of formation of CaNiSi2O6 is measured using a solid state galvanic cell incorporating stabilized zirconia as the solid electrolyte in the temperature range of 1000 to 1400 K:Pt, Ni + SiO2 + CaSiO3 + CaNiSi2O6 \ (Y2O3)ZrO2 \ Ni + NiO, Pt From the electromotive force (emf) of the cell, the Gibbs energy of formation of CaNiSi2O6 from NiO, SiO2, and CaSiO3 is obtained. To derive the Gibbs energy of formation of the quaternary oxide from component binary oxides, the free energy of formation of CaSiO, is determined separately using a solid state cell based on single crystal CaF2 as the electrolyte: Pt, O-2, CaO + CaF2 \ CaF2 \ CaSiO3 + SiO2 + CaF2, O-2, Pt The results can be expressed by the following equations: NiO (r.s) + CaO (r.s) + 2SiO(2) (qz) --> CaNiSi2O6 (pyr) Delta G degrees = -115,700 + 10.63T (+/-100) J mol(-1) CaO (r.s) + SiO2 (qz) --> CaSiO3 (wol) Delta G degrees = -90,030 -0.61T (+/-60) J mol(-1).

Solute-solute and solute-solvent interactions in transition metal alloys: Pt-Ti system

An isothermal section of the phase diagram for (silver + rhodium + oxygen) at T = 1173 K has been established by equilibration of samples representing twelve different compositions, and phase identification after quenching by optical and scanning electron microscopy (s.e.m.), X-ray diffraction (x.r.d.), and energy dispersive analysis of X-rays (e.d.x.), Only one ternary oxide, AgRhO2, was found to be stable and a three phase region involving Ag, AgRhO2 and Rh2O3 was identified. The thermodynamic properties of AgRhO2 were measured using a galvanic cell in the temperature range 980 K to 1320 K. Yttria-stabilized zirconia was used as the solid electrolyte and pure oxygen gas at a pressure of 0.1 MPa was used as the reference electrode. The Gibbs free energy of formation of the ternary oxide from the elements, ΔfGo (AgRhO2), can be represented by two linear equations that join at the melting temperature of silver. In the temperature range 980 K to 1235 K, ΔfGo(AgRhO2)/(J . mol-1) = -249080 + 179.08 T/K (±120). Above the melting temperature of silver, in the temperature range 1235 K to 1320 K, ΔfGo(AgRhO2)/(J . mol-1) = -260400 + 188.24 T/K (±95). The thermodynamic properties of AgRhO2 at T = 298.15 K were evaluated from the high temperature data. The chemical potential diagram for (silver + rhodium + oxygen) at T = 1200 K was also computed on the basis of the results of this study.

Size-dependent free flexural vibration behavior of functionally graded nanoplates

In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length. (c) 2012 Elsevier B.V. All rights reserved.

System Ho-Rh-O: Phase Equilibria, Chemical Potentials and Gibbs Energy of Formation of HoRhO3

The thermodynamic properties of the HoRhO3 were determined in the temperature range from 900 to 1300 K by using a solid-state electrochemical cell incorporating calcia-stabilized zirconia as the electrolyte. The standard Gibbs free energy of formation of orthorhombic perovskite HoRhO3, from Ho2O3 with C-rare earth structure and Rh2O3 with orthorhombic structure, can be expressed by the equation; Delta G(f)degrees((ox)) (+/- 78)/(J/mol) = -50535 + 3.85(T/K) Using the thermodynamic data of HoRhO3 and auxiliary data for binary oxides from the literature, the phase relations in the Ho-Rh-O system were computed at 1273 K. Thermodynamic data for intermetallic phases in the binary Ho-Rh were estimated from experimental enthalpy of formation for three compositions from the literature and Miedema's model, consistent with the phase diagram. The oxygen potential-composition diagram and three-dimensional chemical potential diagram at 1273 K, and temperature-composition diagrams at constant oxygen partial pressures were computed for the system Ho-Rh-O. The decomposition temperature of HoRhO3 is 1717(+/- 2) K in pure O-2 and 1610(+/- 2) K in air at a total pressure p(o) = 0.1 MPa.

Solid-solid collapse transition in a two dimensional model molecular system

Solid-solid collapse transition in open framework structures is ubiquitous in nature. The real difficulty in understanding detailed microscopic aspects of such transitions in molecular systems arises from the interplay between different energy and length scales involved in molecular systems, often mediated through a solvent. In this work we employ Monte-Carlo simulation to study the collapse transition in a model molecular system interacting via both isotropic as well as anisotropic interactions having different length and energy scales. The model we use is known as Mercedes-Benz (MB), which, for a specific set of parameters, sustains two solid phases: honeycomb and oblique. In order to study the temperature induced collapse transition, we start with a metastable honeycomb solid and induce transition by increasing temperature. High density oblique solid so formed has two characteristic length scales corresponding to isotropic and anisotropic parts of interaction potential. Contrary to the common belief and classical nucleation theory, interestingly, we find linear strip-like nucleating clusters having significantly different order and average coordination number than the bulk stable phase. In the early stage of growth, the cluster grows as a linear strip, followed by branched and ring-like strips. The geometry of growing cluster is a consequence of the delicate balance between two types of interactions, which enables the dominance of stabilizing energy over destabilizing surface energy. The nucleus of stable oblique phase is wetted by intermediate order particles, which minimizes the surface free energy. In the case of pressure induced transition at low temperature the collapsed state is a disordered solid. The disordered solid phase has diverse local quasi-stable structures along with oblique-solid like domains. (C) 2013 AIP Publishing LLC.