Triple Point Temperature Research Articles

Effect of Impurities on Water Triple-Point Cells

Water triple-point cells are the basis for the definition of the kelvin and for the realization of the International Temperature Scale of 1990. The temperature differences between the cells are mainly caused by impurities arising in the cell water from the dissolution of the cell envelope (borosilicate glass or quartz). In order to investigate the effects of such impurities on the realized triple-point temperature, water triple-point cells doped with known amounts of Si and Na impurities ( $$0.1\,{\upmu }\hbox {mol}{\cdot }\hbox {mol}^{{-1}}$$ to $$1\,{\upmu }\hbox {mol}{\cdot }\hbox {mol}^{{-1}}$$ of Si and $$0.2\,{\upmu }\hbox {mol}{\cdot }\hbox {mol}^{{-1}}$$ to $$2\,{\upmu }\hbox {mol}{\cdot }\hbox {mol}^{{-1}}$$ of Na) were manufactured at VSL by adding gravimetric mixtures of a Si standard reference material and ultra high-purity water to the cell high-purity water. Water samples were taken from the manufactured cells, partitioned into three samples, and distributed to different laboratories for isotope and impurity analysis (inductively coupled plasma mass spectrometry, ICPMS). The results of two independent ICPMS analyses were compared with impurity calculations based on the gravimetric data of the prepared mixtures and manufactured cells. One undoped cell manufactured by UME and one undoped cell manufactured by VSL were intercompared at both VSL and SMD to demonstrate the equivalence of the manufacturing processes of UME and VSL. The triple-point temperatures realized by the doped cells and the undoped cell manufactured by VSL were measured at SMD. The results showed that, in doped cells, the equilibration time after the last freezing is directly dependent on the impurity concentration, and the temperature depression of doped triple-point-of-water cells is significantly greater than the values predicted by Raoult’s law for an ideal dilute solution.

Effect of the temperature scale on the difference between the triple point temperatures of pure 22Ne and 20Ne

The construction of the ITS-90 gives rise to relatively small temperature differences depending on the specific interpolation equation (temperature range) used. Also the use of different thermometers gives rise to small temperature differences. These and the already published temperature differences between the ITS-90 and thermodynamic temperature lead to an additional small uncertainty in the difference between the triple point temperatures of pure 22Ne and 20Ne. Estimates are given for the various contributions.

Phase equilibrium in argon films stabilized by homogeneous surfaces and thermodynamics of two-stage melting transition

Freezing of gases adsorbed on open surfaces (e.g., graphite) and in narrow pores is a widespread phenomenon which is a subject of a large number of publications. Modeling of the gas/liquid-solid transition is usually accomplished with a molecular simulation technique. However, quantitative analysis of the gas/liquid-solid coexistence and thermodynamic properties of the solid layer still encounters serious difficulties. This is mainly due to the effect of simulation box size on the lattice constant. Since the lattice constant is a function of loading and temperature, once the ordering transition has occurred, the simulation box size must be corrected in the course of simulation according to the Gibbs-Duhem equation. A significant problem is also associated with accurate prediction of the two-dimensional liquid-solid coexistence because of a small difference in densities of coexisting phases. The aim of this study is thermodynamic analysis of the two-dimensional phase coexistence in systems involving crystal-like free of defects layers in narrow slit pores. A special attention was paid to the determination of triple point temperatures. It is shown that intrinsic properties of argon monolayer adsorbed on the graphite surface are similar to those of isolated monolayer accommodated in the slit pore having width of two argon collision diameters. Analysis of the latter system is shown to be clearer and less time-consuming than the former one, which has allowed for explanation of the experimentally observed two-stage melting transition of argon monolayer on graphite without invoking the periodic surface potential modulation and orientational transition.

Surface free energy of the crystal-liquid interface on the metastable extension of the melting curve

The surface free energy γ, excess surface energy e, and excess surface stress τ at the crystal-liquid interface of a Lennard-Jones system have been determined by molecular dynamics simulation. The calculations have been performed for temperatures both above and below the triple-point temperature for the region where each of the coexisting phases is metastable and is at a negative pressure. The asymptotic behavior of γ, e, and τ has been analyzed near the endpoint of the melting curve, which is a point of the contact of the metastable extension of the melting curve and the spinodal of the stretched liquid [V.G. Baidakov and S.P. Protsenko, Phys. Rev. Lett. 95, 015701 (2005)]. It has been found that γ, e, and τ at this point are finite and the excess surface entropy is zero.

Recommended sublimation pressure and enthalpy of benzene

Recommended vapor pressures of solid benzene (CAS Registry Number: 71-43-2) which are consistent with thermodynamically related crystalline and ideal-gas heat capacities as well as with properties of the liquid phase at the triple point temperature (vapor pressure, enthalpy of vaporization) were established. The recommended data were developed by a multi-property simultaneous correlation of vapor pressures and related thermal data. Vapor pressures measured in this work using the static method in the temperature range from 233K to 260K, covering pressure range from 99Pa to 1230Pa, were included in the simultaneous correlation. The enthalpy of sublimation was established with uncertainty significantly lower than the previously recommended values.

Phase-field crystal model with a vapor phase

Phase-field crystal (PFC) models are able to resolve atomic length scale features of materials during temporal evolution over diffusive time scales. Traditional PFC models contain solid and liquid phases, however many important materials processing phenomena involve a vapor phase as well. In this work, we add a vapor phase to an existing PFC model and show realistic interfacial phenomena near the triple point temperature. For example, the PFC model exhibits density oscillations at liquid-vapor interfaces that compare favorably to data available for interfaces in metallic systems from both experiment and molecular-dynamics simulations. We also quantify the anisotropic solid-vapor surface energy for a two-dimensional PFC hexagonal crystal and find well-defined step energies from measurements on the faceted interfaces. Additionally, the strain field beneath a stepped interface is characterized and shown to qualitatively reproduce predictions from continuum models, simulations, and experimental data. Finally, we examine the dynamic case of step-flow growth of a crystal into a supersaturated vapor phase. The ability to model such a wide range of surface and bulk defects makes this PFC model a useful tool to study processing techniques such as chemical vapor deposition or vapor-liquid-solid growth of nanowires.

Pore structure development of polyacrylonitrile nascent fibers in water stretching process

The effects of stretching temperature and ratio on the pore structure of wet-spun polyacrylonitrile nascent fibers was investigated by thermoporometry (TPM), a calorimetric technique based on lowering liquid triple point temperature inside the pores. The patterns of molecular chain movement were characterized by the tensile recovery. The fibers’ glass-transition temperature determined by the variation of elongation at break at different temperatures was about 75°C. The pore size distribution (PSD) and pore volume which was determined by the TPM decreased with the stretching temperature and ratio increasing. The reason for the variation of pore structure was the pore collapse, which was characterized by the movement of molecular chains. The stretching temperature and ratio were the two key parameters to induce the molecular chains or microfibrils to move easily. This study also shows that TPM can be used to analyze closed pores of wet-spun nascent fibers inaccessible by other standard porosimetry methods.

Correlation for the Viscosity of Normal Hydrogen Obtained from Symbolic Regression

We report the results of a symbolic-regression methodology to obtain both the functional form and the coefficients for a wide-ranging correlation for the viscosity of normal hydrogen. The correlation covers the temperature range from the triple-point temperature to 1000 K and pressures up to 200 MPa and extrapolates in a physically reasonable manner to 2000 K. The estimated uncertainty is 4 % for the saturated liquid from the triple point to 31 K, with larger deviations as the critical region is approached. The estimated uncertainty is 4 % for the supercritical fluid phase at pressures to 200 MPa. For the limited range of 200 K to 400 K at pressures up to 0.1 MPa, the uncertainty is 0.1 %.

Liquid-vapor phase diagram and surface properties in oppositely charged colloids represented by a mixture of attractive and repulsive Yukawa potentials

The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.

Liquid-vapor equilibrium and interfacial properties of square wells in two dimensions

Liquid-vapor coexistence and interfacial properties of square wells in two dimensions are calculated. Orthobaric densities, vapor pressures, surface tensions, and interfacial thicknesses are reported. Results are presented for a series of potential widths λ* = 1.4, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5, where λ* is given in units of the hard core diameter σ. Critical and triple points are explored. No critical point was found for λ* < 1.4. Corresponding states principle analysis is performed for the whole series. For λ* = 1.4 and 1.5 evidence is presented that at an intermediate temperature between the critical and the triple point temperatures the liquid branch becomes an amorphous solid. This point is recognized in Armas-Pérez et al. [unpublished] as a hexatic phase transition. It is located at reduced temperatures T* = 0.47 and 0.35 for λ* = 1.4 and 1.5, respectively. Properties such as the surface tension, vapor pressure, and interfacial thickness do not present any discontinuity at these points. This amorphous solid branch does not follow the corresponding state principle, which is only applied to liquids and gases.

Experimental verification of ideality of 22Ne in 20Ne mixtures at the triple point by means of certified artificial mixtures

The paper reports the results of an experimental verification of the assumption of ideality for mixtures of 22Ne in 20Ne by means of binary mixtures, artificially-produced and certified by weighing and whose full isotopic compositions were then measured at KRISS using a mass-spectrometer calibrated with these mixtures. Thermal measurements on the mixtures were performed at INRIM. The assessment of the validity of the ideality condition was critical to the conclusion of a comprehensive study on the effect of neon isotopic composition on the values of its triple point temperature. At KRISS three mixtures were prepared with 22Ne amount concentrations 22x=62088(20)·10−6, 91678(22)·10−6 and 166025(26)·10−6 in 20Ne, respectively, the intermediate one being very close to the range of ‘natural’ compositions. The thermal measurements were performed in the same INRIM experimental apparatus of previous published studies, with an expanded uncertainty (k=2) of ≈30μK for a single sample and ≈50μK for the comparison of sample pairs, using the same model of cryogenic metal sealed cell for each sample. The results, corrected for the measured, low, content of 21Ne and of relevant chemical impurities (H2 and N2) showed an agreement with a theoretical model for the binary mixture assuming ideal behaviour within 10μK, with a standard uncertainty of uc=50μK. These results allowed to construct a ternary-mixture model for the actual neon isotopic composition, including 21Ne, where the IUPAC recommended composition was used as the reference composition, and whose characteristics are discussed in the paper. This also allowed reassigning the Ttp,90 values to all samples.

Traceability of temperature measurements in Estonia

This paper presents an overview of the establishment of the national measurement standard for temperature at METROSERT - the national metrology institute in Estonia. The temperature scale and traceability arrangements are realized in the temperature range from - 40 °C to + 300 °C by means of a group of calibrated standard platinum resistance thermometers and water triple point cells. The linkage of the realized water triple point temperature to the international key comparison value with the expanded uncertainty of 187 µK (coverage factor k = 2) is demonstrated. The established laboratory is capable of providing calibration services to customers by comparison calibration with the expanded uncertainty (k = 2) values of 5 mK in the range from - 40 °C to + 200 °C and 12 mK in the range from + 200 °C to + 300 °C.

Why don't clumps of cirrus dust gravitationally collapse?

We consider the Herschel–Planck infrared observations of presumed condensations of interstellar material at a measured temperature of approximately 14 K (Juvela et al 2012 Astron. Astrophys.541 A12), the triple point temperature of hydrogen. The standard picture is challenged that the material is cirrus-like clouds of ceramic dust responsible for Halo extinction of cosmological sources (Finkbeiner, Davis and Schlegel 1999 Astrophys. J.524 867). Why would such dust clouds not collapse gravitationally to a point on a gravitational free-fall time scale of 108 years? Why do the particles not collide and stick together, as is fundamental to the theory of planet formation (Blum 2004 PASP Conf. Ser.309 369; Blum and Wurm 2008 Annu. Rev. Astron. Astrophys.46 21) in pre-solar accretion discs? Evidence from 3.3 μm and UIB emissions as well as extended red emission data point to the dominance of polycyclic aromatic hydrocarbon (PAH)-type macromolecules for cirrus dust, but such fractal dust will not spin in the manner of rigid grains (Draine and Lazarian 1998 Astrophys. J.494 L19). IRAS dust clouds examined by Herschel–Planck are easily understood as dark matter proto-globular-star-cluster clumps of primordial gas planets, as predicted by (Gibson 1996 Appl. Mech. Rev.49 299–315) and observed by (Schild 1996 Astrophys. J.464 125).

Impact of the Spacer on the Condensing Effect of Fluorinated Chains Investigated by Grazing Incidence X-ray Diffraction on Ultrathin Langmuir Monolayers

Langmuir monolayers of double perfluoroalkyl(alkyl) chain amphiphiles fitted with a monomorpholinophosphate polar head, [C(n)F(2n+1)(CH(2))(m)O](2)P(O)[N(CH(2)CH(2))(2)O] (di(FnHm)MP with n = 6, 8, or 9; and m = 1 or 2), were investigated by surface pressure (π)/molecular area (A(0)) compression isotherms for temperatures ranging from 15 to 50 °C, and by grazing-incidence X-ray diffraction (GIXD) at 25 °C. Ultrathin monolayers were obtained for these short surfactants. Though the hydrocarbon spacer is short, it has a remarkable impact on the monolayer's organization. At 25 °C, whereas di(F8H2)MP monolayer presents a liquid expanded (LE)/liquid condensed (LC) transition, simply replacing one CH(2) by a CF(2) in the latter compound's structure at constant chain length, i.e. shortening the spacer from 2 to 1 CH(2) (as in di(F9H1)MP), suppresses the LE phase. At 25°, GIXD established that for both di(F8H2)MP and di(F9H1)MP, the chains form an hexagonal lattice in the LC phase. The collective tilt of the two compounds is close to zero. The lattice of the dense phase can be compressed, as assessed by the continuous linear decrease of the d spacing with increasing pressure. This indicates that the azimuthal distribution of the molecular tilts is progressively reduced upon compression. The d value for di(F9H1)MP is significantly lower than that of di(F8H2)MP, providing evidence for strong condensing effect of the fluorinated chains. Molecular areas were determined directly from the compression curves and also from the X-ray data, the latter allowing reconstruction of the compression isotherms. The calculated lattice compressibilities are ~30% and 50% of the macroscopic compressibilities for di(F9H1)MP and di(F8H2)MP, respectively. Comparison with the experimentally determined isotherms shows that the monolayer of di(F9H1)MP is more stable than that of di(F8H2)MP. The enthalpies and entropies determined for di(F9H1)MP and di(F8H2)MP, derived from the Clausius-Clapeyron equation, confirm that the observed transitions are both of the LE/LC type, although the triple point temperatures are strikingly different (27 °C vs -18 °C); this large difference further illustrates the stabilizing effect of the fluorinated chains. Disorder is hindered by the fluorinated chains and facilitated by a hydrocarbon spacer when larger than 1 CH(2).

Measurements for the Future—A Complete SI From Physical Constants

Basing the SI units entirely on the values of fundamental physical constants involves extremely difficult metrology. It is desirable that the reproducibilities of a newly defined kilogram and of a thermodynamic temperature scale are at least equal to those of the present artifact kilogram and the water triple-point temperature. This paper discusses the benefits of an updated SI, the principal difficulties in attaining it, and why the effort expended is justified.

A SATURATED LIQUID DENSITY CORRELATION FOR PURE REFRIGERANTS AND OTHER SUBSTANCES

A modification is proposed of the Chouaieb–Ghazouani–Bellagi (CGB) correlation for the saturated liquid density. After we examined the values of the critical exponent, which is a nonlinear parameter for the CGB correlation, we assumed that the exponent deviates by a small amount from the theoretical value of 0.325. Then, a Taylor-series expansion was conducted for the CGB correlation in order to develop a new correlation with two linear adjustable parameters. Data on the saturated liquid density for 70 pure fluids including 43 refrigerants from the NIST Chemistry WebBook in the whole vapor-liquid saturation range were fitted to the new and existing correlations. The results show that the new correlation yields better performance for substances of which reduced triple point temperature is higher than 0.4. Excellent performance (i.e., AAD &lt; 0.1%) can be achieved with the modified CGB for 14 fluids but only for four fluids with the modified Guggenheim model.

On liquid phases in cometary nuclei

In this paper we review the relevant literature and investigate conditions likely to lead to melting of H2O ice, methanol (CH3OH) ice, ethane (C2H6) ice and other volatile ices in cometary nuclei. On the basis of a heat balance model which takes account of volatiles loss, we predict the formation of occasional aqueous and hydrocarbon liquid phases in subsurface regions at heliocentric distances, rh of 1–3AU, and 5–12AU, respectively. Low triple-point temperatures and low vapour pressures of C2H6, C3H8, and some higher-order alkanes and alkenes, favour liquid phase formation in cometary bodies at high rh. Microporosity and the formation of a stabilization crust occluding the escape of volatiles facilitate liquid-phase formation. Characteristics of the near-surface which favour subsurface melting include; low effective surface emissivity (at low rh), high amorphous carbon content, average pore sizes of ∼10μm or less, presence of solutes (e.g. CH3OH), mixtures of C2–C6 hydrocarbons (for melting at high rh), diurnal thermal cycling, and slow rotation rate. Applying the principles of soil mechanics, capillary forces are shown to initiate pre-melting phenomena and subsequent melting, which is expected to impart considerable strength of ∼104Pa in partially saturated layers, reducing porosity and permeability, enhancing thermal conductivity and heat transfer. Diurnal thermal cycling is expected to have a marked effect on the composition and distribution of H2O ice in the near-surface leading to frost heave-type phenomena even where little if any true melting occurs. Where melting does take place, capillary suction in the wetted zone has the potential to enhance heat transfer via capillary wetting in a low-gravity environment, and to modify surface topography creating relatively smooth flat-bottomed features, which have a tendency to be located within small depressions. An important aspect of the “wetted layer” model is the prediction that diurnal melt–freeze cycles alter the mixing ratio vs. depth of solutes present, or of other miscible components, largely through a process of fractional crystallization, but also potentially involving frost heave. Wetted layers are potentially durable and can involve significant mass transport of volatile materials in the near-surface, increasing in extent over many rotations of the nucleus prior to and just after perihelion passage, and causing stratification and trapping of the lowest-melting mixtures at depths of several metres. A possible mechanism for cometary outbursts is proposed involving a heat pulse reaching the liquid phase in the deepest wetted zone, leading to supersaturation and triggering the sudden release under pressure of dissolved gases, in particular CO2, CO, CH4 or N2, contained beneath a consolidated near-surface layer. This study indicates that liquid water can persist for long periods of time in the near-surface of some intermediate-sized bodies (102–103km radius) within protoplanetary discs.

Thermodynamic Properties of Dimethyl Carbonate

A thermodynamic property formulation for dimethyl carbonate has been developed with the use of available experimental thermodynamic property data. The equation of state was developed with multiproperty fitting methods involving pressure-density-temperature (pρT), heat capacity, vapor pressure, and saturated-liquid density data. The equation of state conforms to the Maxwell criterion for two-phase liquid-vapor equilibrium states, and is valid for temperatures from the triple-point temperature (277.06 ± 0.63) K to 600 K, for pressures up to 60 MPa, and for densities up to 12.12 mol dm−3. The extrapolation behavior of the equation of state at low and high temperatures and pressures is reasonable. The uncertainties (k = 2, indicating a 95% confidence level) of the equation of state in density are 0.05% for saturated-liquid states below 350 K, rising to 0.1% in the single phase between 278 K and 400 K at pressures up to 60 MPa. Due to the lack of reliable data outside this region, the estimated uncertainties increase to 0.5% to 1% in the vapor and critical regions. The uncertainties in vapor pressure are 0.6% from 310 K to 400 K, and increase to 1% at higher temperatures and to 2% at lower temperatures due to a lack of experimental data. The uncertainty in isobaric heat capacity and speed of sound in the liquid phase at saturation or atmospheric pressure is 0.5% from 280 K to 335 K. The uncertainties are higher for all properties in the critical region. Detailed comparisons between experimental and calculated data, and an analysis of the equation, have been performed.

Adapting the International System of Units to the twenty-first century

We review the proposal of the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM), currently being considered by the General Conference on Weights and Measures (Conférences Générales des Poids et Mesures, CGPM), to revise the International System of Units (Le Système International d'Unitès, SI). The proposal includes new definitions for four of the seven base units of the SI, and a new form of words to present the definitions of all the units. The objective of the proposed changes is to adopt definitions referenced to constants of nature, taken in the widest sense, so that the definitions may be based on what are believed to be true invariants. In particular, whereas in the current SI the kilogram, ampere, kelvin and mole are linked to exact numerical values of the mass of the international prototype of the kilogram, the magnetic constant (permeability of vacuum), the triple-point temperature of water and the molar mass of carbon-12, respectively, in the new SI these units are linked to exact numerical values of the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant, respectively. The new wording used expresses the definitions in a simple and unambiguous manner without the need for the distinction between base and derived units. The importance of relations among the fundamental constants to the definitions, and the importance of establishing a mise en pratique for the realization of each definition, are also discussed.

Phase equilibria and the thermodynamic properties of methyl and ethyl esters of carboxylic acids. 1. Methyl n-butanoate and ethyl propanoate

The heat capacity of methyl n-butanoate in crystalline and liquid states was measured by vacuum adiabatic calorimetry over the temperature range from (8 to 372) K. The triple point temperature, the enthalpy and entropy of fusion, and the purity of the sample were determined. The saturated vapour pressure and the boiling temperatures were determined by comparative ebulliometry in the “atmospheric” pressure range 10.8 ⩽ ( p/kPa) ⩽ 99.6. The normal boiling temperature, T n.b, and the enthalpy of vaporization at T = 298.15 K and T n.b were derived. The thermodynamic functions (absolute entropy and changes of the enthalpy, and Gibbs free energy) were derived for the solid and liquid states in the temperature range studied and for the ideal gas state at T = 298.15 K. The ideal gas heat capacities and the absolute entropies of methyl n-butanoate (MeBu) and ethyl propanoate (EtPr) were calculated by statistical thermodynamics on the basis of the molecular constants determined by the use of density functional theory on the B3LYP level. The experimental vapour pressure of MeBu and EtPr [1] of moderate temperature intervals, Δ exp T = (59/65) K, were extended to the entire range of the liquids, Δ liq T = (364.7/345.7) K by the methods of the corresponding states law and simultaneous treatment of the pT-parameters and low-temperature heat capacities of the ideal gas and liquid, respectively. An additive contribution of the carbonyl group CO–(C, O) connected with C and O atoms was determined for calculation of the absolute molar entropies at T = 298.15 K, S m 0 ( g ) ( 298 K ) , by additive Benson’s scheme.