James W. Schmidt

Universal amplitude ratios and the interfacial tension near consolute points of binary liquid mixtures

The densities of the coexisting phases and the capillary length have been measured to obtain the interfacial tension (σ) near the consolute temperatures Tc of the three binary liquid mixtures: triethylamine+water, triethylamine+heavy water, and methanol+cyclohexane. Our data are combined with data from the literature to test predictions for three temperature‐independent ‘‘universal’’ ratios: U+1=σ(ξ+)2/(kBTc) and Y(±)=σ(αt2C±s/kB) −2/3/(kBT0). [Here ξ+ is the correlation length, C±s is the singular part of the heat capacity per unit volume, α=0.11 is the exponent characterizing the specific heat divergence, and t≡(T−Tc)/Tc]. Near Tc, the new experimental values of Y(+) range from 5.5–5.8 in agreement with the value 5.6 obtained by Moldover [Phys. Rev. 31, 1022 (1985)] in a review of earlier experiments. However, the experimental values of Y(+) are inconsistent with either the value Y(+)=4.4±0.4 obtained from a recent simulation of the simple‐cubic Ising model or the value Y(+)=2.6–3.0 obtained from a one‐...

Partially halogenated hydrocarbons CHFClCF3, CF3CH3, CF3CHFCHF2, CF3CH2CF3, CHF2CF2CH2F, CF3CH2CHF2, CF3OCHF2: critical temperature, refractive indices, surface tension and estimates of liquid, vapor and critical densities

Abstract For seven partially halogenated hydrocarbons, designated by the refrigeration industry as the refrigerants R124, R143a, R236ea, R236fa, R235ca, R245fa, and E125, we determined the critical temperatures Tc (ITS-90), the capillary rise, and the refractive indices of the liquid and vapor phases in the temperature range from 20°C to their critical points. Independently measured liquid densities at lower temperatures, when combined with our refractive indices, produce estimates of the vapor and liquid densities at higher temperatures up to the critical point. The densities combined with the capillary rise data give the surface tensions, σ, up to the critical points. The surface tensions of the seven refrigerants in this study together with nine others measured previously can be represented by the scaled equation σ = 2.51 (1 + 0.609ω) k b T c ( N a V c ) 2 3 t 1.26 (1 + 0.348t 1 2 −0.487t) where t ≡ (T c −T) T c is the reduced temperature, and kb, a, Vc, and ω are the Boltzmann and Avagadro constants, the critical volume, and the acentric factor, respectively. This equation yields values for σ within 5% of the measured values for all 16 candidate replacement refrigerants.

First-order wetting transition at a liquid-vapor interface

In certain binary solutions the lower of the two liquid phases forms a layer which intrudes between the upper liquid phase and the vapor. We find that such intruding layers form above binary solutions of a fluorocarbon (C7F14) and an alcohol (i‐C3H7OH). As the temperature of C7F14–i‐C3H7OH solutions is increased, the intruding layer abruptly appears at a characteristic wetting temperature TW=311 K. This temperature is well below the consolute temperature (363 K). At temperatures slightly above Tw the intruding layer’s thickness (measured by ellipsometry) is several hundred angstroms and its variation with temperature is extremely weak. Below Tw, the layer’s thickness may be zero and is no greater than 20 A when a naive slab model is used to interpret the data. Below Tw, three‐phase contact can occur between the vapor and both the upper and the lower liquid phases. Our measurements show that one of the angles (θ) which characterizes this three‐phase contact has a very simple temperature dependence: cos θ=1...

Dielectric Permittivity of Eight Gases Measured with Cross Capacitors

A four-ring, toroidal cross capacitor was used to measure accurately the relative dielectric permittivity ε(p,T) of He, Ar, N2, O2, CH4, C2H6, C3H8, and CO2. (ε is often called the “dielectric constant.”) The data are in the range from 0 to 50°C and, in many cases, extend up to 7 MPa. The accurate measurement of ε(p,T) required a good understanding of the deformation of the gas-filled capacitors with applied pressure. This understanding was tested in two ways. First, the experimental values of ε(p,T) for helium were compared with theoretical values. The average difference was within the noise, 〈εexpt−εtheory〉=(−0.05±0.21)×10−6, demonstrating that the four-ring cross capacitor deformed as predicted. Second, ε(p,T) of argon was measured simultaneously on three isotherms using two capacitors: the four-ring capacitor, and a 16-rod cross capacitor made using different materials and a different geometry. The results for the two capacitors are completely consistent, within the specifications of the capacitance bridge. There was a small inconsistency that was equivalent to 1×10−6 of the measured capacitances, or, for argon, 3×10−5Aε, where Aε is the zero-density limit of the molar polarizability ℘≡(ε−1)/[(ε+2)ρ].

Quasi-spherical cavity resonators for metrology based on the relative dielectric permittivity of gases

We evaluate a quasi-spherical, copper, microwave cavity resonator for accurately measuring the relative dielectric permittivity er(p,T) of helium and argon. In a simple, crude approximation the cavity’s shape is a triaxial ellipsoid with axes of length a,1.001a and 1.005a, with a=5 cm. The unequal axes of the quasi-sphere separated each of the triply degenerate microwave resonance frequencies of a sphere (f11TM,f12TM,…,f11TE,f12TE,…) into three nonoverlapping, easily measured, frequencies. The frequency splittings are consistent with the cavity’s shape, as determined from dimensional measurements. We deduced er(p,T) of helium and of argon at 289 K and up to 7 MPa from the resonance frequencies flnσ, the resonance half-widths glnσ, and the compressibility of copper. Simultaneous measurements of er(p,T) with the quasi-spherical resonator and a cross capacitor agreed within 1×10−6 for helium, and for argon they differed by an average of only 1.4×10−6. This small difference is within the stated uncertainty of...

A search for the prewetting line

This paper describes efforts to locate the prewetting line in a binary liquid system (isopropanol–perfluoromethylcyclohexane) at the vapor–liquid interface. We placed tight upper bounds on the temperature separation (0.2 K) between the prewetting line and the line of bulk liquid phase separation. We did not detect the prewetting line in systems at equilibrium. Experimental signatures indicative of the prewetting line occurred only in nonequilibrium situations. Several theories predict that the adsorption of one of the components (the fluorocarbon, in this case) at the liquid–vapor interface should increase abruptly, at a temperature sightly above the temperature at which the mixture separates into two liquid phases. A regular solution calculation indicates that this prewetting line should have been easily detectable with the instruments used in this experiment. Significant features of the experiment are: (1) low‐gradient thermostatting, (2) in situ stirring, (3) precision ellipsometry from the vapor–liqui...

The Raman spectrum of solid carbon dioxide at high pressure

Raman spectra of carbon dioxide were measured as functions of molar volume and temperature in the region 0 to 200 cm−1. In crystals constrained to remain at constant volume, the frequencies of the Raman active libron modes were found to shift much less with temperature than expected by comparison with solid nitrogen. In fact, when the slight expansion of the alloy steel cell is taken into account the frequency vs temperature plots show a slight positive temperature dependence as opposed to the fairly large negative shift observed in the nitrogen case. From these measurements, the value of the mode Gruneisen parameters (defined by γj=−d lnωj/d lnV) were determined to be 2.3±0.2, almost 3 times that predicted by the quadrupole–quadrupole model but in fairly good agreement with recent calculations by Gibbons and Klein, and Kobashi and Kihara. These are based on models which include short ranged intermolecular repulsive forces. Linewidths were measured and indicate that in carbon dioxide four phonon processes...

Virial equation of state of helium, xenon, and helium-xenon mixtures from speed-of-sound and burnettPρT measurements

The virial equation of state was determined for helium, xenon, and helium-xenon mixtures for the pressure and temperature ranges 0.5 to 5 MPa and 210 to 400 K. Two independent experimental techniques were employed: BurnettPρT measurements and speed-of-sound measurements. The temperature-dependent second and third density virial coefficients for pure xenon and the second and third interaction density virial coefficients for helium-xenon mixtures were determined. The present density virial equations of state for xenon and helium-xenon mixtures reproduce the speed-of-sound data within 0.01% and thePρT data within 0.02% of the pressures. All the results for helium are consistent, within experimental errors, with recent ab initio calculations, confirming the accuracy of the experimental techniques.

The liquid–vapor interface of a binary liquid mixture near the consolute point

The liquid–vapor interface above mixtures of isopropanol (i‐C3H7OH) and perfluoromethylcyclohexane (C7F14) has been studied in the vicinity of the consolute point (Tc=363 K). As three‐phase coexistence is approached, the excess fluorocarbon adsorbed at this interface increases; the adsorption is expected to diverge at Tc for a mixture of the critical composition. A simple model of the interface which incorporates the adsorption anomaly is compared with our ellipticity measurements. Both the model and our data yield ellipticities which have a finite maximum at 0.1 K above Tc. (In general, the ellipticity is not a monotonic function of the adsorption.) The calculation of the ellipticity uses an exact numerical integration of Maxwell’s equations for a model dielectric constant vs height profile. The model dielectric constant profile for the critical composition is consistent with a short‐ranged density vs height profile between the vapor and the liquid mixture as well as a much longer ranged composition vs h...

Primary pressure standards based on dimensionally characterized piston/cylinder assemblies

NIST has characterized two large diameter (35.8 mm) piston/cylinder assemblies as primary pressure standards in the range 0.05 MPa to 1.0 MPa with uncertainties approaching the best mercury manometers. The realizations of the artefacts as primary standards are based on the dimensional characterization of the piston and cylinder, and models of the normal and shear forces on the base and flanks of the piston. We have studied two piston/cylinder assemblies, known at the National Institute of Standards and Technology (NIST) as PG 38 and PG 39, using these methods. The piston and cylinder of both assemblies were accurately dimensioned by Physikalisch Technische Bundesanstalt (PTB). All artefacts appeared to be round within ±30 nm and straight within ±100 nm over a substantial fraction of their heights. PG 39 was dimensioned a second time by PTB, three years after the initial measurement, and showed no significant change in dimensions or effective area. Comparisons of the effective area of PG 38 and PG 39 from dimensional measurements, against those obtained with calibration against the NIST ultrasonic interferometer manometer (UIM), are in agreement within the combined standard (k = 1) uncertainty of the dimensional measurements and the UIM. A cross-float comparison of PG 38 versus PG 39 also agreed with the dimensional characterization within their combined standard uncertainties and with the UIM calibrations. The expanded (k = 2) relative uncertainty of the effective area is about 6.0 × 10−6 for both assemblies.