High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

State-to-state dynamics of elementary chemical reactions using Rydberg H-atom translational spectroscopy

In this review, a few examples of state-to-state dynamics studies of both unimolecular and bimolecular reactions using the H-atom Rydberg tagging TOF technique were presented. From the H2O photodissociation at 157 nm, a direction dissociation example is provided, while photodissociation of H2O at 121.6 has provided an excellent dynamical case of complicated, yet direct dissociation process through conical intersections. The studies of the O(D-1) + H-2 --> OH+H reaction has also been reviewed here. A prototype example of state-to-state dynamics of pure insertion chemical reaction is provided. Effect of the reagent rotational excitation and the isotope effect on the dynamics of this reaction have also been investigated. The detailed mechanism for abstraction channel in this reaction has also been closely studied. The experimental investigations of the simplest chemical reaction, the H-3 system, have also been described here. Through extensive collaborations between theory and experiment, the mechanism for forward scattering product at high collision energies for the H+HD reaction was clarified, which is attributed to a slow down mechanism on the top of a quantized barrier transition state. Oscillations in the product quantum state resolved different cross sections have also been observed in the H+D-2 reaction, and were attributed to the interference of adiabatic transition state pathways from detailed theoretical analysis. The results reviewed here clearly show the significant advances we have made in the studies of the state-to-state molecular reaction dynamics.

Study on structure and molecular dynamics of starch/poly(sodium acrylate)grafted superabsorbent by C-13 solid state NMR

The domain-structure of samples containing a series of starch/poly(sodium acrylate)-grafted superabsorbents, pure starch, pure poly(sodium acrylate), and blend of starch/poly(sodium acrylate) has been studied by high-resolution solid-state C-13 NMR spectroscopy at room temperature. The result shows that the crystallinity of starch decreases greatly in the grafted and blended samples.

Spontaneous volume transition of polyampholyte nanocomposite hydrogels based on pure electrostatic interaction

A circular system is employed in this paper to investigate the swelling behaviors of polyampholyte hydrogels; this circular system can effectively eliminate the disturbance of various factors and keep the surrounding environment constant. It is found that there exists a spontaneous volume transition to the collapsed state of polyampholyte hydrogels, which is attributed to the overshooting effect, and the transition can occur repeatedly under certain conditions. C-13 NMR is employed to investigate the swelling behavior of polyampholyte hydrogels.

Synthesis of PtNPs/AQ/Ru(bpy)(3)(2+) colloid and its application as a sensitive solid-state electrochemiluminescence sensor material

The facile synthesis of the novel platinum nanoparticles/Eastman AQ55D/ruthenium(II) tris( bipyridine) (PtNPs/ AQ/Ru(bpy)(3)(2+)) colloidal material for ultrasensitive ECL solid-state sensors was reported for the first time. The cation ion-exchanger AQ was used not only to immobilize ECL active species Ru(bpy)(3)(2+) but also as the dispersant of PtNPs. Colloidal characterization was accomplished by transmission electron microscopy (TEM), X-ray photoelectron spectrum (XPS), and UV-vis spectroscopy. Directly coating the as-prepared colloid on the surface of a glassy carbon electrode produces an electrochemiluminescence (ECL) sensor. The electronic conductivity and electroactivity of PtNPs in composite film made the sensor exhibit faster electron transfer, higher ECL intensity of Ru(bpy)(3)(2+), and a shorter equilibration time than Ru(bpy)(3)(2+) immobilized in pure AQ film. Furthermore, it was demonstrated that the combination of PtNPs and permselective cation exchanger made the sensor exhibite excellent ECL behavior and stability and a very low limit of detection (1 x 10(-15) M) of tripropylamine with application prospects in bioanalysis. This method was very simple, effective, and low cost.

A new preparation of zinc sulfide nanoparticles by solid-state method at low temperature

A novel solid-state method of the preparation of zinc sulfide nanoparticles is reported. By solid-state reaction of zinc acetate and thioacetamide at low temperature, zinc sulfide nanoparticles of different sizes were prepared. The temperature of preparation varied from room temperature to 300 degrees C. The particles were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), differential thermal analysis (DTA), and photoluminescence spectrum. X-ray diffraction patterns revealed that the particles exhibited pure zinc-blende crystal structure and that particle size increased with increasing temperature. The TEM micrograph showed that the mean particle size was about 40 nm for the sample heated at 100 degrees C. A blue shift was observed in the photoluminescence emission spectrum. A possible mechanism of the reaction corresponding to our observation is proposed, (C) 2000 Elsevier Science Ltd. All rights reserved.

High resolution solid-state NMR and DSC study of poly(ethylene glycol) silicate hybrid materials via sol-gel process

Hybrid materials incorporating poly(ethylene glycol) (PEG) with tetraethoxysilane (TEOS) via a sol-gel process were studied for a wide range of compositions of PEG by DSC and high resolution solid-state C-13- and Si-29-NMR spectroscopy. The results indicate that the microstructure of the hybrid materials and the crystallization behavior of PEG in hybrids strongly depend on the relative content of PEG. With an increasing content of PEG, the microstructure of hybrid materials changes a lot, from intimate mixing to macrophase separation. It is found that the glass transition temperatures (T-g) (around 373 K) of PEG homogeneously embedded in a silica network are much higher than that (about 223 K) of pure PEG and also much higher in melting temperatures T-m (around 323 K) than PEG crystallites in heterogeneous hybrids. Meanwhile, the lower the PEG content, the more perfect the silica network, and the higher the T-g of PEG embedded in hybrids. An extended-chain structure of PEG was supposed to be responsible for the unusually high T-g of PEG. Homogeneous PEG-TEOS hybrids on a molecular level can be obtained provided that the PEG. content in the hybrids is less than 30% by weight. (C) 1998 John Wiley & Sons, Inc.

CONSTRUCTION OF A TYROSINASE-BASED BIOSENSOR IN PURE ORGANIC-PHASE

A novel immobilization method for construction of a tyrosinase-based biosensor applied in pure organic phase is described. This method gives the enzyme a hydrated shell which allows the enzyme to maintain its biocatalytic activity in a pure organic solvent The enzyme electrode was used to determine several phenols and o-diphenols in pure chloroform and chlorobenzene. The biosensor can be stored in dry state for more than 3 months without any loss of the activity. The kinetic parameters have also been calculated and are presented herein.

STATISTICAL THERMODYNAMICS OF A LATTICE FLUID - PURE POLYMER

A statistical thermodynamics theory of a polydisperse polymer based on a lattice model of a fluid is formulated. The pure polydisperse polymer is completely characterized by three scale factors and the distribution law of the system. The equation of state does not satisfy a simple corresponding state principle, except for the polymer fluid with sufficiently high molecular weight.

CALCULATIONS OF THE EIGENVALUES OF PURE QUADRUPOLE INTERACTION IN MOSSBAUER-EFFECT STUDIES

Two approximate formulae to calculate the eigenvalues of pure quadrupole interaction in Mossbauer effect studies have been proposed and the eigenvalue coefficients in the formulae have been given for various excited states and ground states of the nucleus with different spin. All the eigenvalues of pure quadrupole interaction between both excited state and ground state of nucleus with spin I = 3/2 divided-by 9/2 and the electric-field gradient with different asymmetry parameter (eta = 0 divided-by 1.0) have been calculated by these formulae. The results show that the accuracies in all the calculations are more satisfactory or same in comparison with those obtained by the formula of Shenoy and Dunlap, especially when the asymmetry parameter of electric-field gradient is larger than 0.8 for the nucleus with spin I = 5/2.

Tactile Sensing for Mechatronics: A State of the Art Survey

Lee M.H. and Nicholls H.R., Tactile Sensing for Mechatronics: A State of the Art Survey, Mechatronics, 9, Jan 1999, pp1-31.

Metallic foam processing from the liquid state

Cox, S.J., Bradley, G. and Weaire, D. (2001) Metallic foam processing from the liquid state: the competition between solidification and drainage. Eur. Phys. J. AP 14:87-97. Sponsorship: This research was supported by the Prodex programme of ESA, and is a contribution to ESA contract C14308/AO-075-99. SJC was supported by Enterprise Ireland and a Marie Curie fellowship. GB was supported by the HPC Programme of TCD.

A 3-min all-out test to determine peak oxygen uptake and the maximal steady state

Burnley, M., Doust, J., Vanhatalo, A., A 3-min all-out test to determine peak oxygen uptake and the maximal steady state, Medicine & Science in Sports & Exercise. 38(11):1995-2003, November 2006. RAE2008

Reinventing the Matter of Britain: Undermining the State in Jacobean Masques

Archer, Jayne, Berry, Philippa, 'Reinventing the Matter of Britain: Undermining the State in Jacobean Masques', In: British Identities and English Renaissance Literature, David J. Baker and Willy Maley (eds),(Cambridge: Cambridge University Press), pp.119-134, 2002 RAE2008