A chemical test of the principle of critical point universality: the solubility of nickel (II) oxide in isobutyric acid + water near the consolute point

A mixture of isobutyric acid + water has an upper consolute point at 38.8 mass?% isobutyric acid and temperature near 26?°C. Nickel (II) oxide dissolves in this mixture by reacting with the acid to produce water and nickel isobutyrate. The solubility of nickel (II) oxide in isobutyric acid + water has been measured as a function of temperature at compositions, 25, 38.8, and 60 mass?% isobutyric acid. For values of the temperature, T, which were at least 2 K in excess of the liquid-liquid phase transition temperature, the measured values of the solubility, s, lie on a straight line when plotted in van't Hoff form with ln?s versus 1∕T. The slope, (?ln?s∕?(1∕T)), of the line is negative indicating that the dissolution reaction is endothermic. When the temperature was within 2 K of the phase transition temperature, however, (?ln?s∕?(1∕T)) diverged toward negative infinity. The principle of critical point universality predicts that when excess solid nickel (II) oxide is in dissolution equilibrium with liquid isobutyric acid + water, (?ln?s∕?(1∕T)) should diverge upon approaching the consolute point along the critical isopleth at 38.8 mass?% isobutyric acid. As determined by the sign of the enthalpy of solution, the sign of this divergence is expected to be negative. Not only do our experiments confirm these predictions, but they also show that identical behavior can be observed at both 25 and 60 mass?% isobustyric acid, compositions which lie substantially to either side of the critical composition.     

The new insight into dynamic crossover in glass forming liquids from the apparent enthalpy analysis

One of the most intriguing phenomena in glass forming systems is the dynamic crossover (T(B)), occurring well above the glass temperature (T(g)). So far, it was estimated mainly from the linearized derivative analysis of the primary relaxation time τ(T) or viscosity η(T) experimental data, originally proposed by Stickel et al. [J. Chem. Phys. 104, 2043 (1996); J. Chem. Phys. 107, 1086 (1997)]. However, this formal procedure is based on the general validity of the Vogel-Fulcher-Tammann equation, which has been strongly questioned recently [T. Hecksher et al. Nature Phys. 4, 737 (2008); P. Lunkenheimer et al. Phys. Rev. E 81, 051504 (2010); J. C. Martinez-Garcia et al. J. Chem. Phys. 134, 024512 (2011)]. We present a qualitatively new way to identify the dynamic crossover based on the apparent enthalpy space (H(a) (')=dlnτ/d(1/T)) analysis via a new plot lnH(a) (') vs. 1∕T supported by the Savitzky-Golay filtering procedure for getting an insight into the noise-distorted high order derivatives. It is shown that depending on the ratio between the "virtual" fragility in the high temperature dynamic domain (m(high)) and the "real" fragility at T(g) (the low temperature dynamic domain, m = m(low)) glass formers can be splitted into two groups related to f < 1 and f > 1, (f = m(high)∕m(low)). The link of this phenomenon to the ratio between the apparent enthalpy and activation energy as well as the behavior of the configurational entropy is indicated.     

Computer simulation study of thermodynamic scaling of dynamics of 2Ca(NO3)2·3KNO3

Molecular dynamics (MD) simulations of the glass-former 2Ca(NO(3))(2·3KNO(3), CKN, were performed as a function of temperature at pressures 0.1 MPa, 0.5 GPa, 1.0 GPa, and 2.0 GPa. Diffusion coefficient, relaxation time of the intermediate scattering function, and anion reorientational time were obtained as a function of temperature and densitiy ρ. These dynamical properties of CKN scale as ρ(γ)∕T with a common value γ = 1.8 ± 0.1. The scaling parameter γ is consistent with the exponent of the repulsive part of an effective intermolecular potential for the repulsion between the atoms at shortest distance in the equilibrium structure of liquid CKN, Ca(2+), and oxygen atoms of NO(3)(-). Correlation between potential energy and virial is obeyed for the short-range terms of the potential function, but not for the whole potential including coulombic interactions. Decoupling of diffusion coefficient and reorientational relaxation time from relaxation time take place at a given ρ(γ)∕T value, i.e., breakdown of Stokes-Einstein and Debye-Stokes-Einstein equations result from combined thermal and volume effects. The MD results agree with correlations proposed between long-time relaxation and short-time dynamics, lnτ ∝ 1∕, where the mean square displacement concerns a time window of 10.0 ps. It has been found that scales as ρ(γ)∕T above and below the glass transition temperature, so that thermodynamic scaling of liquid dynamics can be thought as a consequence of theories relating short- and long-time dynamics, and the more fundamental scaling concerns short-time dynamical properties.     

Entropy change on the cooling and heating paths between liquid and glass and the residual entropy

We analyze the C(p)-T data for the glassy state of eight materials of varied molecular interactions and structures to investigate how the use of the C(p)d ln T integral in the time-dependent (nonreversible) thermodynamic path between a liquid and glass affects our estimates of the entropy. Since the change in entropy on such a path cannot be determined, we estimate the upper and lower values of the change, Δσ, from the C(p)d ln T integral. For the same rates of cooling and heating and without annealing, Δσ on the cooling path is negligibly different from that on the heating path. The difference is ～1∕60th-1∕25th of the lowest known value of the residual entropy and even less than the configurational entropy of the supercooled liquid at its kinetic freezing temperature. Thus use of the C(p)d ln T integral in the nonreversible path does not introduce significant errors in estimating the residual entropy. Dynamic C(p) data cannot be used to infer that configurational entropy decreases on glass formation. Time dependence of the C(p)-T path has little consequence for reality of the residual entropy.     

Theoretical study of isomerization and decomposition of propenal

We investigated the dynamics of isomerization and multi-channel dissociation of propenal (CH(2)CHCHO), methyl ketene (CH(3)CHCO), hydroxyl propadiene (CH(2)CH(2)CHOH), and hydroxyl cyclopropene (cyclic-C(3)H(3)-OH) in the ground potential-energy surface using quantum-chemical calculations. Optimized structures and vibrational frequencies of molecular species were computed with method B3LYP∕6-311G(d,p). Total energies of molecules at optimized structures were computed at the CCSD(T)∕6-311+G(3df,2p) level of theory. We established the potential-energy surface for decomposition to CH(2)CHCO + H, CH(2)CH + HCO, CH(2)CH(2)∕CH(3)CH + CO, CHCH∕CH(2)C + H(2)CO, CHCCHO∕CH(2)CCO + H(2), CHCH + CO + H(2), CH(3) + HCCO, CH(2)CCH + OH, and CH(2)CC∕cyclic-C(3)H(2) + H(2)O. Microcanonical rate coefficients of various reactions of trans-propenal with internal energies 148 and 182 kcal mol(-1) were calculated using Rice-Ramsperger-Kassel-Marcus and Variational transition state theories. Product branching ratios were derivable using numerical integration of kinetic master equations and the steady-state approximation. The concerted three-body dissociation of trans-propenal to fragments C(2)H(2) + CO + H(2) is the prevailing channel in present calculations. In contrast, C(3)H(3)O + H, C(2)H(3) + HCO and C(2)H(4) + CO were identified as major channels in the photolysis of trans-propenal. The discrepancy between calculations and experiments in product branching ratios indicates that the three major photodissociation channels occur mainly on an excited potential-energy surface whereas the other channels occur mainly on the ground potential-energy surface. This work provides profound insight in the mechanisms of isomerization and multichannel dissociation of the system C(3)H(4)O.     

Dielectric spectroscopy study on ionic liquid microemulsion composed of water, TX-100, and BmimPF6

We report here a broadband dielectric spectroscopy study on an ionic liquid microemulsion (ILM) composed of water, Triton X-100 (TX-100), and 1-butyl-3-methylimidazolium hexafluorophosphate (bmimPF(6)). It is found that the phase behavior of this ILM can be easily identified by its dielectric response. The dielectric behavior of the ILM in the GHz range is consistent with that of TX-100∕water mixtures with comparable water-to-TX-100 weight ratio. It consists of the relaxations due to ethylene oxide (EO) unit relaxation, hydration water dynamics, and∕or free water dynamics. The water content dependence of the EO unit relaxation suggests that this relaxation involves dynamics of hydration water molecules. In the IL-in-water microemulsion phase, it is found that bmimPF(6) molecules are preferentially dissolved in water when their concentration in water is lower than the solubility. An additional dielectric relaxation that is absent in the TX-100∕water mixtures is observed in the frequency range of 10(7)-10(8) Hz for this ILM. This low-frequency relaxation is found closely related to the bmimPF(6) molecule and could be attributed to the hopping of its cations∕anions between the anionic∕cationic sites.     

Thermal diffusion behavior of nonionic surfactants in water

We studied the thermal diffusion behavior of hexaethylene glycol monododecyl ether (C12E6) in water by means of thermal diffusion forced Rayleigh scattering (TDFRS) and determined Soret coefficients, thermal diffusion coefficients, and diffusion constants at different temperatures and concentrations. At low surfactant concentrations, the measured Soret coefficient is positive, which implies that surfactant micelles move toward the cold region in a temperature gradient. For C12E6/water at a high surfactant concentration of w1 = 90 wt % and a temperature of T = 25 degrees C, however, a negative Soret coefficient S(T) was observed. Because the concentration part of the TDFRS diffraction signal for binary systems is expected to consist of a single mode, we were surprised to find a second, slow mode for C12E6/water system in a certain temperature and concentration range. To clarify the origin of this second mode, we investigated also, tetraethylene glycol monohexyl ether (C6E4), tetraethylene glycol monooctyl ether (C8E4), pentaethylene glycol monododecyl ether (C12E5), and octaethylene glycol monohexadecyl ether (C16E8) and compared the results with the previous results for octaethylene glycol monodecyl ether (C10E8). Except for C6E4 and C10E8, a second slow mode was observed in all systems usually for state points close to the phase boundary. The diffusion coefficient and Soret coefficient derived from the fast mode can be identified as the typical mutual diffusion and Soret coefficients of the micellar solutions and compare well with the independently determined diffusion coefficients in a dynamic light scattering experiment. Experiments with added salt show that the slow mode is suppressed by the addition of w(NaCl) = 0.02 mol/L sodium chloride. This suggests that the slow mode is related to the small amount of absorbing ionic dye, less than 10(-5) by weight, which is added in TDFRS experiments to create a temperature grating. The origin of the slow mode of the TDFRS signal will be tentatively interpreted in terms of a ternary mixture of neutral micelles, dye-charged micelles, and water.     

The influence of secondary interactions during the formation of polyelectrolyte multilayers: layer thickness, bound water and layer interpenetration

With X-ray and neutron reflectivity, the structure and composition of polyelectrolyte multilayers from poly(allyl amine) (PAH) and poly(styrene sulfonate) (PSS) are studied as function of preparation conditions (salt concentration and solution temperature, T). The onset of a temperature effect occurs at 0.05 M NaCl (Debye length approximately 1 nm). At 1 M salt, the film thickness increases by a factor of 3 on heating the deposition solution from 5 to 60 degrees C. The PAH/PSS bilayer thickness is independent of the kind of salt (NaCl or KCl), yet its composition is different (more bound water for NaCl). At low T, the internal roughness is 33% of the bilayer thickness; it increases to 60% at high T. The roughening is accompanied by a total loss of bound water. At which temperature the roughening starts is a function of the kind of salt (50 degrees C for NaCl and 35 degrees C for KCl). The strong temperature dependence and the eventual loss of bound water molecules may be attributed to the hydrophobic force; however, there is an isotope effect, since the loss of bound water is less pronounced in the deuterated layers.     

Scaling of the hysteresis in the glass transition of glycerol with the temperature scanning rate

By measuring the dependences of the temperature-dependent primary ("alpha") dielectric relaxation time behavior on the temperature scanning rate for the glass-forming glycerol, we study the scaling of hysteresis at the glass transition in glycerol. Based on the Vogel-Fulcher-Tammann (VFT) expression and the Angell's fragility concept, notable correlations of the systematic kinetic fragility, and of the hysteresis effect in the vitrification∕fusion "alpha"-relaxation process of glycerol, with the temperature scanning rate, were reasonably analyzed and discussed. It was observed that the kinetic fragility m and the apparent glass-transition temperature hysteresis width ΔT(g)(a), respectively, scaled the temperature scanning rate q as m ≈ α(m)q(-γ) and ΔT(g)(a) ≈ A(0) + αq(β), at which the exponents, γ and β, were suggested to be characteristic of the resistance to the structure change or fragility change of the system during the glass transition. The observed scaling laws are quite similar to the scaling power law for the thermal hysteresis in the first-order phase transition (FOPT) of solids, providing a significant insight into the hysteresis effect in the glass transition of the glass-forming liquids.     

Temperature dependence of dimerization and dewetting of large-scale hydrophobes: a molecular dynamics study

We studied by molecular dynamics simulations the temperature dependence of hydrophobic association and drying transition of large-scale solutes. Similar to the behavior of small solutes, we found the association process to be characterized by a large negative heat capacity change. The origin of this large change in heat capacity is the high fragility of hydrogen bonds between water molecules at the interface with hydrophobic solutes; an increase in temperature breaks more hydrogen bonds at the interface than in the bulk. With increasing temperature, both entropy and enthalpy changes for association strongly decrease, while the change in free energy weakly varies, exhibiting a small minimum at high temperatures. At around T=Ts=360 K, the change in entropy is zero, a behavior similar to the solvation of small nonpolar solutes. Unexpectedly, we find that at Ts, there is still a substantial orientational ordering of the interfacial water molecules relative to the bulk. Nevertheless, at this point, the change in entropy vanishes due to a compensating contribution of translational entropy. Thus, at Ts, there is rotational order and translational disorder of the interfacial water relative to bulk water. In addition, we studied the temperature dependence of the drying-wetting transition. By calculating the contact angle of water on the hydrophobic surface at different temperatures, we compared the critical distance observed in the simulations with the critical distance predicted by macroscopic theory. Although the deviations of the predicted from the observed values are very small (8-23%), there seems to be an increase in the deviations with an increase in temperature. We suggest that these deviations emerge due to increased fluctuations, characterizing finite systems, as the temperature increases.     

Landau theory description of observed isotropic to anisotropic phase transition in mixed clay gels

A characteristic new cooperative dehydration transition, in 1:1 Laponite-MMT cogel, was observed at T(c) ≈ 60 °C, a temperature at which the storage modulus (G(')) and depolarization ratio (D(p)) showed sharp increase, and the isotropic cogel turned into an anisotropic one. The dehydration dynamics could be described through power-law relations: G(') ～ (T(c)-T)(-γ) and D(p) ～ (T(c)-T)(-β) with γ ≈ β = 0.40 ± 0.05. The x-ray diffraction data revealed that the crystallite size decreased from 17 nm (at 20 °C) to 10 nm (at 80 °C) implying loss of free and inter-planar water. When this cogel was spontaneously cooled below T(c), it exhibited much larger storage modulii values which implied the existence of several metastable states in this system. This phase transition could be modeled through Landau theory, where the depolarization ratio was used as experimental order parameter (ψ). This parameter was found to scale with temperature, as ψ ～ (T(c)-T)(-α), with power-law exponent α = 0.40 ± 0.05; interestingly, we found α ≈ β ≈ γ.     

Characterization of 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Emim][Tf2N])∕TX-100∕cyclohexane ternary microemulsion: investigation of photoinduced electron transfer in this RTIL containing microemulsion

In this study we have characterized a ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethyl- sulfonyl)imide containing ternary nonaqueous microemulsion ([Emim][Tf(2)N]∕∕TX-100∕cyclo- hexane). The phase behavior and dynamic light scattering study show that the [Emim][Tf(2)N]∕TX-100∕cyclohexane three component system can form microemulsion with [Emim][Tf(2)N] as polar core at suitable condition. We have investigated photoinduced electron transfer (PET) using dimethyl aniline as electron donor and several Coumarin dyes as electron acceptor molecules at two different R values (R = [ionic liquid]∕[surfactant]) to observe how the dynamics of the PET rate is affected in this type of confined microenvironment compared to that of the PET dynamics in neat ionic liquid and other pure solvent media. The plot of observed k(q) values with the free energy change (ΔG(0)) for electron transfer reaction shows an apparent inversion in the observed rate as predicted by the Marcus theory.     

The fragile-to-strong dynamic crossover transition in confined water: nuclear magnetic resonance results

By means of a nuclear magnetic resonance experiment, we give evidence of the existence of a fragile-to-strong dynamic crossover transition (FST) in confined water at a temperature T(L)=223+/-2 K. We have studied the dynamics of water contained in 1D cylindrical nanoporous matrices (MCM-41-S) in the temperature range 190-280 K, where experiments on bulk water were so far hampered by crystallization. The FST is clearly inferred from the T dependence of the inverse of the self-diffusion coefficient of water (1D) as a crossover point from a non-Arrhenius to an Arrhenius behavior. The combination of the measured self-diffusion coefficient D and the average translational relaxation time tau(T), as measured by neutron scattering, shows the predicted breakdown of Stokes-Einstein relation in deeply supercooled water.     

Towards an understanding of the heat capacity of liquids. A simple two-state model for molecular association

A model for the temperature dependence of the isobaric heat capacity of associated pure liquids C(p,m)(o)(T) is proposed. Taking the ideal gas as a reference state, the residual heat capacity is divided into nonspecific C(p) (res,ns) and associational C(p) (res,ass) contributions. Statistical mechanics is used to obtain C(p)(res,ass) by means of a two-state model. All the experimentally observed C(p,m)(o)(T) types of curves in the literature are qualitatively described from the combination of the ideal gas heat capacity C(p)(id)(T) and C(p)(res,ass)(T). The existence of C(p,m)(o)(T) curves with a maximum is predicted and experimentally observed, for the first time, through the measurement of C(p,m)(o)(T) for highly sterically hindered alcohols. A detailed quantitative analysis of C(p,m)(o)(T) for several series of substances (n-alkanes, linear and branched alcohols, and thiols) is made. All the basic features of C(p,m)(o)(T) at atmospheric and high pressures are successfully described, the model parameters being physically meaningful. In particular, the molecular association energies and the C(p)(res,ns) values from the proposed model are found to be in agreement with those obtained through quantum mechanical ab initio calculations and the Flory model, respectively. It is concluded that C(p,m)(o)(T) is governed by the association energy between molecules, their self-association capability and molecular size.     

Translational diffusion in sucrose benzoate near the glass transition: probe size dependence in the breakdown of the Stokes-Einstein equation

The translational diffusion coefficient D(trans) for rubrene, 9,10-bis(phenylethynyl)anthracene (BPEA), and tetracene in the fragile molecular glass-former sucrose benzoate (SB) (Tg=337 K) was studied as a function of temperature from Tg+3 K to Tg+71 K by use of the holographic fluorescence recovery after photobleaching technique. The values of D(trans) vary by five to six orders of magnitude in this temperature range. Contrary to the predictions of the Stokes-Einstein equation, the temperature dependence of probe diffusion in SB over the temperature range of the measurements is weaker than that of T/eta, where eta is the shear viscosity. In going from the crossover temperature Tx approximately 1.2Tg to Tg, D(trans)eta/T increases by factors of 2.4+/-0.2 decades for rubrene, 3.4+/-0.2 decades for BPEA, and 3.8+/-0.4 decades for tetracene. The decoupling between probe diffusion in SB and viscosity is characterized by the scaling law D(trans) approximately T/eta(xi), with xi=0.621 for tetracene, 0.654 for BPEA, and 0.722 for rubrene. Data for probe diffusion in SB are combined with data from the literature for probe diffusion in ortho-terphenyl and alphaalphabeta-tris(naphthyl)benzene in a plot of enhancement versus the relative probe size parameter rho(m)=(m(p)m(h))(1/3), where m(p) and m(h) are, respectively, the molecular weights of the probe and host solvent. The plot clearly shows a sharp increase in enhancement of translational diffusion at rho(m) approximately 1. By applying temperature shifts, D(trans) for probe diffusion in SB and the dielectric relaxation time tau(D) can be superimposed on a single master curve based on the Williams-Landel-Ferry equation. This suggests that the dynamics of probe diffusion in SB is described by the scaling relationship D(trans) approximately 1/tau(D)(T+DeltaT), where tau(D)(T+DeltaT) is the temperature-shifted dielectric relaxation time. The results from this study are discussed within the context of dynamic heterogeneity in glass-forming liquids.     

Enhanced small-angle scattering connected to the Widom line in simulations of supercooled water

We present extensive simulations on the TIP4P∕2005 water model showing significantly enhanced small-angle scattering (SAS) in the supercooled regime. The SAS is related to the presence of a Widom line (T(W)) characterized by maxima in thermodynamic response functions and Ornstein-Zernike correlation length. Recent experimental small-angle x-ray scattering data [Huang et al., J. Chem. Phys. 133, 134504 (2010)] are excellently reproduced, albeit with an increasing temperature offset at lower temperatures. Assuming the same origin of the SAS in experiment and model this suggests the existence of a Widom line also in real supercooled water. Simulations performed at 1000 bar show an increased abruptness of a crossover from dominating high-density (HDL) to dominating low-density (LDL) liquid and strongly enhanced SAS associated with crossing T(W), consistent with a recent determination of the critical pressure of TIP4P∕2005 at 1350 bar. Furthermore, good agreement with experimental isothermal compressibilities at 1000, 1500, and 2000 bar shows that the high pressure supercooled thermodynamic behavior of water is well described by TIP4P∕2005. Analysis of the tetrahedrality parameter Q reveals that the HDL-LDL structural transition is very sharp at 1000 bar, and that structural fluctuations become strongly coupled to density fluctuations upon approaching T(W). Furthermore, the tetrahedrality distribution becomes bimodal at ambient temperatures, an observation that possibly provides a link between HDL-LDL fluctuations and the structural bimodality in liquid water indicated by x-ray spectroscopic techniques. Computed x-ray absorption spectra are indeed found to show sensitivity to the tetrahedrality parameter.     

Micellization and solubilization of a model hydrophobic drug nimesulide in aqueous salt solutions of Tetronic T904

The micellar and phase behavior of an ethylene oxide-propylene oxide branched octablock copolymer Tetronic T 904 (hereafter written as T904) in water and NaCl solutions was examined. The copolymer shows a cloud point (CP) ranging from 74-65°C in the concentration range of 1-10% and forms aggregates (micelles) with a hydrodynamic diameter around 10-12nm in the temperature range 30-40°C. Stable, bluish solutions containing aggregates of variable size (several hundred nm in some cases) were observed even at temperatures much less than the critical micellization temperature (CMT=30°C for a 2% solution in water). The CP and the CMT markedly decrease in the presence of NaCl due to the dehydration of the polyethylene oxide shell. The size of the micelles in water or salt solutions increases at temperatures close to the CP as inferred from viscosity measurments. A model drug compound (nimesulide, NIM) was solubilized in T904 micelles which showed a remarkable increase in solubilization at higher temperature; however, a decrease in solubilization was observed in salt solutions. The thermodynamic parameters for solubilization were obtained, and the location of NIM in the copolymer micelles was investigated by UV-Visible spectroscopy.     

Assemblies of functional small-sized molecules having 4-amino-2,2,6,6-tetramethylpiperidine-1-oxyl responsive to heat and pH in water and their water proton relaxivities

1,3,5-Triureabenzene derivatives carrying alkyl (C(n)) and poly(ethylene glycol) (Eg(m)) chains C(n)Eg(3) (1, 2, and 3, n = 6, 7, and 8, respectively) and C(n)N(X)Eg(m) (4 and 5, X = M (methyl), n = 6 and 8, respectively, m = 3; 6 and 7, X = T (2,2,6,6-tetramethylpiperidine-1-oxyl, TEMPO), n = 6, m = 3 and 6, respectively) were prepared. All compounds in aqueous solutions exhibited the lower critical solution temperature (LCST) phenomena unique for small-sized molecules and formed self-assemblies above the transition temperature, T(t), of the LCST. Only compound 3 formed a hydrogel with a minimum gelation concentration of 0.5 mM (0.05 wt %). In 1.0 mM aqueous solution, the T(t) values were determined to be in the range of 12-40 °C. In addition, the T(t) values for 4-7 containing tertiary amine also responded to the solution pH with high sensitivity. The LCST behaviors for all compounds were reversible in the cycles of warming and cooling. The water proton relaxivities, r(1), for 6 and 7 carrying TEMPO were altered below and above T(t) and were largely reduced by the formation of self-assemblies above T(t). Compound 6 showed r(1) values at 25 °C of 0.92 and 0.23 mM(-1) s(-1) at pH 7.0 and 6.0, respectively. In transmission electron microscopy (TEM) images, globular particles with polydispersity were observed, and their average hydrodynamic diameters (D(H)) were determined to be in the range of 2400-730 nm by dynamic light scattering. In the TEM and scanning electron microscopy images of a xerogel sample of 3, bundles of fibers with a diameter of ca. 10 nm and a network structure, respectively, were observed.     

A molecular dynamics study of the thermodynamic properties of calcium apatites. 1. Hexagonal phases

Structural and thermodynamic properties of crystal hexagonal calcium apatites, Ca10(PO4)6(X)2 (X = OH, F, Cl, Br), were investigated using an all-atom Born-Huggins-Mayer potential by a molecular dynamics technique. The accuracy of the model at room temperature and atmospheric pressure was checked against crystal structural data, with maximum deviations of ca. 4% for the haloapatites and 8% for hydroxyapatite. The standard molar lattice enthalpy, delta(lat)H298(o), of the apatites was calculated and compared with previously published experimental results, the agreement being better than 2%. The molar heat capacity at constant pressure, C(p,m), in the range 298-1298 K, was estimated from the plot of the molar enthalpy of the crystal as a function of temperature, H(m) = (H(m,298) - 298C(p,m)) + C(p,m)T, yielding C(p,m) = 694 +/- 68 J x mol(-1) x K(-1), C(p,m) = 646 +/- 26 J x mol(-1) x K(-1), C(p,m) = 530 +/- 34 J x mol(-1) x K(-1), and C(p,m) = 811 +/- 42 J x mol(-1) x K(-1) for hydroxy-, fluor-, chlor-, and bromapatite, respectively. High-pressure simulation runs, in the range 0.5-75 kbar, were performed in order to estimate the isothermal compressibility coefficient, kappaT, of those compounds. The deformation of the compressed solids is always elastically anisotropic, with BrAp exhibiting a markedly different behavior from those displayed by HOAp and ClAp. High-pressure p-V data were fitted to the Parsafar-Mason equation of state with an accuracy better than 1%.