Water Calorimetry: A Correction to the Heat Defect Calculations

In a recent publication, we used a reaction model (model III) to calculate the heat defect for the irradiation of aqueous solutions with ionizing radiation at 21 °C. Subsequent work has revealed that the literature value used for one of the rate constants in the model was incorrect. A revised model (model IIIR) incorporates the correct rate constant for 21 °C. Versions of models III and IIIR were created for irradiations at 4 °C. For our current water calorimetry protocol, the values of the heat defect for H₂/O₂-water (water saturated with a flow of 43 % H₂ and 57 % O₂, by volume) at 21 °C predicted by model III and model IIIR are similar but the value for 4 °C predicted by III is 30 % smaller than the value predicted by IIIR. Model IIIR predicts that the values of the heat defect at 21 °C and 4 °C lie within the range −0.023±0.002, in agreement with the values obtained from our water calorimetry measurements done using pure water and H₂-saturated water at 21 °C and 4 °C. The yields of hydrogen peroxide in H₂/O₂-water at 21 °C and 4 °C were measured and agree with the predictions of model IIIR. Our water calorimetry measurements made with pure water and H₂-saturated water are now of sufficient quality that they can be used to determine the heat defect for H₂/O₂-water better than can be done by simulations. However, consistency between the three systems continues to be an excellent check on water purity which is crucial, especially for the pure water system.     

Reversibility of Polyester Adsorption on Glass

The adsorption of poly(ethylene o-phthalate) from chloroform solution on glass powder and aluminum oxide was studied. The adsorption of a number of fractions, varying in number average molecular weight from 970 to 6250 showed a decrease in the moles of polymer adsorbed with increase in molecular weight. The results are interpreted to indicate that this polymer molecule lies in a relatively flattened conformation on the glass surface. More polymer was adsorbed on glass powder at 50 °C than at 0 °C. Adsorption on glass powder that had been outgassed to remove adsorbed water was less than on untreated glass. Initial adsorption at one temperature followed by exposure at the other temperature resulted in complete reversibility of sorption on the untreated glass. Decreasing the temperature from 50 to 0 °C resulted in desorption from the outgassed glass, but increasing the temperature did not result in additional adsorption. These differences are ascribed in part to adsorption across an adsorbed water layer on the untreated glass. An explanation for the “one-direction reversibility” observed for the outgassed glass is presented.     

Experimental and Theoretical Study of Kinetics of Bulk Crystallization in Poly(Chlorotrifluoroethylene)

The rate of isothermal bulk crystallization of poly(chlorotrifluoroethylene), T_m=221° C, was measured from 170° to 200° C. The intrinsic bulk crystallization, which accurately followed an n = 2 law, was shown to be a result of the injection of primary nuclei sporadically in time, with one-dimensional growth of centers derived from these nuclei. The crystallites are exceedingly small. The one-dimensional growth process was isolated by nucleating specimens with seed crystals, and its temperature-dependence determined between 191° and 205° C. The seed crystal isotherms followed an n = 1 law. The temperature coefficients of the rate of nucleation and the rate of growth were both strongly negative.A theory of homogeneous nucleation that takes into account the segmental character of the polymer chains is developed in some detail. A cylindrical nucleus is assumed. In the temperature range near the melting point, region A, where the radius and length of the nucleus are unrestricted, the rate of nucleation is shown to be proportional to exp(−α/T³ΔT²). The nucleation rate is proportional to exp (−β/T²ΔT) in region B, which extends from somewhat below the melting point to considerably lower temperatures; the length of the nucleus has a constant value l₀ in this region, but the radius is unrestricted. (In the above expressions, α and β are constants). Finally, at sufficiently low temperatures, region C is entered. Under certain circumstances, the rate of nucleation in region C will be extremely rapid, and correspond to a “nucleative collapse” of the supercooled liquid state. A calculation of the one-dimensional growth rate shows that it is proportional to exp(−γ/T²ΔT) where β=γ.A careful analysis of the experimental data obtained between 170° and 200° C clearly showed that both the rate of nucleation and the rate of growth were proportional to exp(−β/T²ΔT), and not exp(−α/T³ΔT²). The primary nucleation event was thus of type B in this interval. A detailed analysis of the data is given, and surface free energies and the dimensions of the nuclei quoted. Quenching experiments, where the polymer was crystallized well below 170° C, gave a firm indication of the existence of region C.An experimental study was made of the extremely slow crystallization process that prevailed when the degree of crystallinity became high. The onset of this stage of the crystallization was interpreted as being the result of a massive degree of impingement. This interpretation is justified by the calculations of Lauritzen, who has given a theory of impingements that predicts a pseudoequilibrium degree of crystallinity.As indicated above, the growth process originating at homogeneous nuclei is not of a three-dimensional or spherulitic character in the region of study. Such stray spherulites as do appear in this region are shown to originate at heterogeneities. The possibility that the intrinsic growth process may become three-dimensional at crystallization temperatures sufficiently near T_m is discussed.     

Uranium-Platinum System

The phase diagram of the uranium-platinum system was constructed from data obtained by thermal analysis, metallographic examination, and X-ray diffraction. The system is characterized by four intermetallic compounds: UPt, formed peritectoidally at 961° C; UPt₂, formed peritectically at 1,370° C; UPt₃, melting congruently at 1,700° C; and UPt₅, formed peritectically at 1,460° C. One eutectic occurs at 1,005° C and 12 a/o platinum, and a second at 1,345° C and 87.5 a/o platinum. The maximum solubilities are 4.5 a/o uranium in platinum and 5 a/o platinum in gamma-uranium. Platinum lowers the gamma-beta uranium transformation to 705° C and the beta-alpha transformation to 589° C.     

Phase Equilibrium Relations in the Sc2O3-Ga2O3 System

The phase equilibrium diagram was determined for the Sc₂O₃-Ga₂O₃ system. A quenching furnace, wound with 60 percent Pt—40 percent Rh wire, was employed for experiments conducted at temperatures up to 1,800 °C. An induction furnace, having an iridium crucible susceptor, was used to obtain higher temperatures. Temperatures in the quenching furnace were measured with both an optical pyrometer and a 95 percent Pt—5 percent Rh versus 80 percent Pt—20 percent Rh thermocouple. The melting point of Ga₂O₃ was determined as 1,795 ±15 °C. Experiments at temperatures as high as 2,405 °C failed to melt Sc₂O₃. Two intermediate binary phases, a compound believed to be 6Sc₂O₃·5Ga₂O₃ and a solid solution occur in the system. The solid solution phase appears as a single phase in the region roughly defined by the compositional limits of 55 to 73 mole percent Ga₂O₃ at the solidus. The 6:5 compound, stable only at high temperatures, melts incongruently at 1,770 ±15 °C and decomposes below 1,700 ±15 °C. The compound appears to have orthorhombic symmetry with a=13.85 A, b= 9.80 A, and c=9.58 A. The indicated uncertainties in the melting points are a conservative estimate of the overall inaccuracies.     

Cryoprotection–lyophilization and physical stabilization of rifampicin-loaded flower-like polymeric micelles

Rifampicin-loaded poly(ε-caprolactone)–b-poly(ethylene glycol)–poly(ε-caprolactone) flower-like polymeric micelles display low aqueous physical stability over time and undergo substantial secondary aggregation. To improve their physical stability, the lyoprotection–lyophilization process was thoroughly characterized. The preliminary cryoprotectant performance of mono- and disaccharides (e.g. maltose, glucose), hydroxypropyl-β-cyclodextrin (HPβCD) and poly(ethylene glycol) (PEG) of different molecular weights was assessed in freeze–thawing assays at −20°C, −80°C and −196°C. The size and size distribution of the micelles at the different stages were measured by dynamic light scattering (DLS). A cryoprotectant factor (f_c) was determined by taking the ratio between the size immediately after the addition of the cryoprotectant and the size after the preliminary freeze–thawing assay. The benefit of a synergistic cryoprotection by means of saccharide/PEG mixtures was also assessed. Glucose (1 : 20), maltose (1 : 20), HPβCD (1 : 5) and glucose or maltose mixtures with PEG3350 (1 : 20) (copolymer:cryoprotectant weight ratio) were the most effective systems to protect 1 per cent micellar systems. Conversely, only HPβCD (1 : 5) cryoprotected more concentrated drug-loaded micelles (4% and 6%). Then, those micelle/cryoprotectant systems that displayed f_c values smaller than 2 were freeze-dried. The morphology of freeze-dried powders was characterized by scanning electron microscopy and atomic force microscopy and the residual water content analysed by the Karl Fisher method. The HPβCD-added lyophilisates were brittle porous cakes (residual water was between 0.8% and 3%), easily redispersable in water to form transparent systems with a minimal increase in the micellar size, as determined by DLS.     

Effects of changes in temperature on Zika dynamics and control

When a rare pathogen emerges to cause a pandemic, it is critical to understand its dynamics and the impact of mitigation measures. We use experimental data to parametrize a temperature-dependent model of Zika virus (ZIKV) transmission dynamics and analyse the effects of temperature variability and control-related parameters on the basic reproduction number (R₀) and the final epidemic size of ZIKV. Sensitivity analyses show that these two metrics are largely driven by different parameters, with the exception of temperature, which is the dominant driver of epidemic dynamics in the models. Our R₀ estimate has a single optimum temperature (≈30°C), comparable to other published results (≈29°C). However, the final epidemic size is maximized across a wider temperature range, from 24 to 36°C. The models indicate that ZIKV is highly sensitive to seasonal temperature variation. For example, although the model predicts that ZIKV transmission cannot occur at a constant temperature below 23°C (≈ average annual temperature of Rio de Janeiro, Brazil), the model predicts substantial epidemics for areas with a mean temperature of 20°C if there is seasonal variation of 10°C (≈ average annual temperature of Tampa, Florida). This suggests that the geographical range of ZIKV is wider than indicated from static R₀ models, underscoring the importance of climate dynamics and variation in the context of broader climate change on emerging infectious diseases.     

Polymorphism of Bismuth Sesquioxide. I. Pure Bi2O3

Stability relationships of the four polymorphs of bismuth oxide have been determined by means of DTA and high-temperature x-ray studies. The stable low-temperature monoclinic form transforms to the stable cubic form at 730 ±5 °C, which then melts at 825 ± 5 °C. By controlled cooling, the metastable tetragonal phase and/or the metastable body-centered cubic (b.c.c.) phase appear at about 645 °C. Whereas b.c.c. can be preserved to room temperature, tetragonal will transform to monoclinic between 550 and 500 °C. Tetragonal Bi₂O₃, however, is easily prepared by decomposing bismutite (Bi₂O₃·CO₂) at 400 °C for several hours. The greatest transition expansion occurs at the monoclinic to cubic inversion, and cubic Bi₂O₃ shows the greatest coefficient of volume expansion. With exposure to air, Bi₂O₃ carbonates and partially transforms to bismutite and an unknown phase.     

Phase Equilibria in Systems Involving the Rare Earth Oxides. Part III. The Eu2O3?In2O3 System

The equilibrium phase diagram was determined for the Eu₂O₃−In₂O₃ system. An induction furnace, having an iridium crucible as the heating element (susceptor), was used to establish the solidus and liquidus curves. The 1:1 composition melts congruently at 1745 ± 10 °C. Melting point relations suggest that the 1:1 composition is a compound with solid solution extending both to 31 mole percent In₂O₃ and 71 mole percent In₂O₃. The compound is pseudohexagonal with a_H = 3.69 A and c_H = 12.38 A. Isostructural phases also occur in the 1:1 mixtures of both Gd₂O₃ and Dy₂O₃ with In₂O₃. The melting points of Eu₂O₃ and In₂O₃ were determined to be 2,240 ± 10 °C and 1910 ± 10 °C respectively. A eutectic occurs in the Eu₂O₃−In₂O₃ system at 1,730 °C and about 73 mole percent In₂O₃. The indicated uncertainties in the melting points are conservative estimates of the overall inaccuracies of temperature measurement.     

Systems Silver Iodide-Sodium Iodide and Silver Iodide-Potassium Iodide

The phase relations for the systems AgI-NaI and AgI-KI have been determined for the temperature range from room temperature to 685° C, using differential thermal analysis techniques. The AgI-NaI system has a eutectic at 50 mole percent NaI and 384° C. The AgI-KI system has eutectics at 20.8 and 28.5 mole percent KI and 254° C and 244° C, respectively. A compound of formula KAg₃I₄ is formed with a congruent melting point of 268° C.     

Treasure of the Past VI: Standard Potential of the Silver-Silver-Chloride Electrode from 0° to 95° C and the Thermodynamic Properties of Dilute Hydrochloric Acid Solutions

From electromotive-force measurements of the cell without liquid junction: Pt;  H₂,  HCl (m),  AgCl;  Agthrough the range 0° to 95° C, calculations have been made of (1) the standard potential of the silver–silver-chloride electrode, (2) the activity coefficient of hydrochloric acid in aqueous solutions from m (molality) =0 to m=0.1 and from 0° to 90° C, (3) the relative partial molal heat content of hydrochloric acid, and (4) the relative partial molal heat capacity of hydrochloric acid.The extrapolations were made by the method of least squares with the aid of punch-card techniques. Data from at least 24 cells were analyzed at each temperature, and 81 cells were studied at 25° C. The value of the standard potential was found to be 0.22234 absolute volt at 25° C, and the standard deviation was 0.02 millivolt at 0° C, 0.01 millivolt at 25° C, and 0.09 millivolt at 95° C. The results from 0° to 60° C are compared with earlier determinations of the standard potential and other quantities derived from the electromotive force.     

Mechanochemically synthesized CsH2PO4–H3PW12O40 composites as proton-conducting electrolytes for fuel cell systems in a dry atmosphere

Cesium dihydrogen phosphate (CsH₂PO₄, CDP) and dodecaphosphotungstic acid (H₃PW₁₂O₄₀·nH₂O, WPA·nH₂O) were mechanochemically milled to synthesize CDP–WPA composites. The ionic conductivities of these composites were measured by an ac impedance method under anhydrous conditions. Despite the synthesis temperatures being much lower than the dehydration and phase-transition temperatures of CDP under anhydrous conditions, the ionic conductivities of the studied composites increased significantly. The highest ionic conductivity of 6.58×10⁻⁴ Scm⁻¹ was achieved for the 95CDP·5WPA composite electrolyte at 170 °C under anhydrous conditions. The ionic conduction was probably induced in the percolated interfacial phase between CDP and WPA. The phenomenon of high ionic conduction differs for the CDP–WPA composite and pure CDP or pure WPA under anhydrous conditions. The newly developed hydrogen interaction between CDP and WPA supports anhydrous proton conduction in the composites.     

Novel temperature-responsive polymer brushes with carbohydrate residues facilitate selective adhesion and collection of hepatocytes

Temperature-responsive glycopolymer brushes were designed to investigate the effects of grafting architectures of the copolymers on the selective adhesion and collection of hypatocytes. Homo, random and block sequences of N-isopropylacrylamide and 2-lactobionamidoethyl methacrylate were grafted on glass substrates via surface-initiated atom transfer radical polymerization. The galactose/lactose-specific lectin RCA₁₂₀ and HepG2 cells were used to test for specific recognition of the polymer brushes containing galactose residues over the lower critical solution temperatures (LCSTs). RCA₁₂₀ showed a specific binding to the brush surfaces at 37 °C. These brush surfaces also facilitated the adhesion of HepG2 cells at 37 °C under nonserum conditions, whereas no adhesion was observed for NIH-3T3 fibroblasts. When the temperature was decreased to 25 °C, almost all the HepG2 cells detached from the block copolymer brush, whereas the random copolymer brush did not release the cells. The difference in releasing kinetics of cells from the surfaces with different grafting architectures can be explained by the correlated effects of significant changes in LCST, mobility, hydrophilicity and mechanical properties of the grafted polymer chains. These findings are important for designing ‘on–off’ cell capture/release substrates for various biomedical applications such as selective cell separation.     

Preparation of Fluoro- and Bromofluoroaryl Compounds by Copyrolysis of Bromofluoroalkanes

Pyrolysis of tribromofluoromethane yields chiefly hexafluorobenzene. Copyrolysis of this material with several bromine-containing compounds was studied at 540 °C and under several atmospheres’ pressure of nitrogen gas. The addition of bromine or dibromodifluoromethane has very little effect on the pyrolysis products of tribromofluoromethane. Copyrolysis with carbon tetrabromide or bromoform yields increased amounts of bromopentafluorobenzene and dibromotetrafluorobenzene at the expense of hexafluorobenzene. The addition of relatively small amounts of 1,1,1-tribromo-2,2,2-trifluoroethane gives a significant yield of octafluorotoluene.     

Heats of Solution,Transition, and Formation of Three Crystalline Forms of Metaboric Acid

The three crystalline forms of metaboric acid HBO₂ were prepared, purified, and analyzed. Heats of solution in water or of reaction with sodium hydroxide solution were compared with those of orthoboric acid H₃BO₃(c). The best values for the heats of transition at 25 °C are: (c,I) to (c,II), 2.33±0.23 kcal/mole; (c,II) to (c,III), 1.30±0.05 kcal/mole; (c,I) to (c,III), 3.63±0.24 kcal/mole. The following heats of formation at 25 °C were derived: −192.77 ± 0.35 kcal/mole for the cubic HBO₂(c,I), −190.43 ±0.34 kcal/mole for the monoclinic HBO₂ (c,II), and −189.13 ± 0.34 kcal/mole for the orthorhombic HBO₂(c,III).     

Magnetic soy protein isolate–bovine serum albumin nanoparticles preparation as a carrier for inulinase immobilisation

Magnetic nanoparticles (NPs) were functionalised with soy protein isolate (SPI) and bovine serum albumin (BSA) for inulinase immobilisation. The results revealed the nanomagnetite size of about 50 nm with a polydispersity index (PDI) of 0.242. The average size of the SPI NPs prepared by using acetone was 80–90 nm (PDI, 0.277), and SPI–BSA NPs was 80–90 nm (PDI, 0.233), and their zeta potential was around −34 mV. The mean diameter of fabricated Fe₃ O₄ @SPI–BSA NPs was <120 nm (PDI, 0.187). Inulinase was covalently immobilised successfully through glutaraldehyde on Fe₃ O₄ @SPI–BSA NPs with 80% enzyme loading. Fourier transform infrared spectra, field emission scanning electron microscopy, and transmission electron microscopy images provided sufficient proof for enzyme immobilisation on the NPs. The immobilised inulinase showed maximal activity at 45°C, which was 5°C higher than the optimum temperature of the free enzyme. Also, the optimum pH of the immobilised enzyme was shifted from 6 to 5.5. Thermal stability of the enzyme was considerably increased to about 43% at 75°C, and K _m value was reduced to 25.4% after immobilisation. The half‐life of the enzyme increased about 5.13‐fold at 75°C as compared with the free form. Immobilised inulinase retained over 80% of its activity after ten cycles.Inspec keywords: magnetic particles, nanoparticles, proteins, molecular biophysics, nanofabrication, enzymes, Fourier transform spectra, infrared spectra, scanning electron microscopy, field emission ion microscopy, transmission electron microscopy, pH, biochemistry, nanobiotechnology, biomagnetism, electrokinetic effects, iron compoundsOther keywords: magnetic nanoparticles, soy protein isolate, bovine serum albumin, inulinase immobilisation, nanomagnetite, polydispersity index, SPI‐BSA NP, zeta potential, inulinase, glutaraldehyde, enzyme loading, Fourier transform infrared spectra, field emission scanning electron microscopy, transmission electron microscopy images, enzyme immobilisation, pH, size 80 nm to 90 nm, temperature 45 degC, temperature 75 degC, Fe₃ O₄      

The “1958 He4 Scale of Temperatures”: Part 1. Introduction

The generally used practical scale of temperatures between 1° and 5.2° K is the He⁴ vapor pressure scale based on an accepted vapor pressure equation or table. In Sèvres (near Paris), October 1958, the International Committee on Weights and Measures recommended for international use the “1958 He⁴ Scale” based on a vapor pressure table arrived at through international cooperation and agreement. This table resulted from a consideration of all reliable He⁴ vapor pressure data obtained using gas thermometers, and paramagnetic susceptibility and carbon resistor thermometers. The theoretical vapor pressure equation from statistical thermodynamics was used with thermodynamic data on liquid He⁴ and the vapor equation of state to insure satisfactory agreement of the vapor pressure table with reliable thermodynamic data.The International Committee on Weights and Measures at a meeting in Sèvres (near Paris), France, September 29 to October 3, 1958, approved the “1958 He⁴ Vapor Pressure Scale of Temperatures” as an international standard for thermometry from 1° to 5.2° K. This was the culmination of several years of intensive research and cooperation on the helium vapor pressure scale at the Kamerlingh Onnes Laboratory in Leiden, Holland, and the U.S. Naval Research Laboratory in Washington.The vapor pressure of liquid He⁴ has for a long time been used as a standard for thermometry between 1° and 5.2° K. The first measurements of thermodynamic temperatures in the liquid He⁴ range were made with constant volume gas thermometers filled with He⁴. Simultaneous measurements of the vapor pressure of liquid helium in temperature equilibrium with the gas thermometer established a vapor pressure-temperature relation which then was used as the basis for determining thermodynamic temperatures from vapor pressure measurements. With these vapor pressure-gas thermometer measurements there were measurements of He⁴ vapor pressures made simultaneously with measurements of the He⁴ isotherms from which temperatures were obtained by extrapolating the isotherms to zero density (N/V→0) in accordance with the virial equation of state: pV/N = RT[1 + B(N/V) + C(N/V)² + …](1)After the latent and specific heats of liquid He⁴ had been measured, the experimental vapor pressure-temperature relation was improved through the use of the theoretical vapor pressure (P) equation: lnP=i0−L0RT+52lnT−1RT∫0TSldT+1RT∫0PVldP+ϵ(2)where i₀ ≡ ln (2πm)^3/2k^5/2/h³(3)and ? ≡ ln (PV/NRT)?2B (N/V)?(3/2) C (N/V)²(4)L₀ is the heat of vaporization of liquid He⁴ at 0° K, S_l and V_l are the molar entropy and volume of liquid He⁴, m is the mass of a He⁴ atom, B and C are the virial coefficients in eq (1), and the other symbols have their usual meaning. Both theoretically calculated and directly measured vapor pressures were considered in arriving at the 1958 He⁴ Temperature Scale.Equation (2) presupposes that the thermodynamic properties entering the equation have been measured on the thermodynamic scale, otherwise the use of this equation for the calculation of P is not valid. In practice, however, these properties are measured on an empirical scale that only approximates the thermodynamic scale. In general this empirical scale has been a He⁴ vapor pressure scale based on gas thermometer measurements.As T is lowered, the fourth, fifth, and sixth terms in eq (2) become smaller and less important relative to the first three terms. At 1.5° K, the inclusion or exclusion of the sum of the fourth, fifth, and sixth terms in eq (2) affects the temperature calculated from a given value of P by only 0.0005 deg. It may be said then, that below 1.5° K, the vapor pressure of He⁴ is in effect really determined, within the present accuracy of the vapor pressure measurement, by a single empirical constant, the heat of vaporization of liquid He⁴ at 0° K. At present, L_o for He⁴ is normally calculated from vapor pressure data obtained with a gas thermometer. The magnitude of the last three terms in eq (2) increases rather rapidly with rising T, and above the λ-point (2.172° K) the accuracy of the evaluation of these terms is a very important consideration.In Amsterdam in 1948, on the occasion of a General Assembly of the International Union of Physics, a small group of low temperature physicists, meeting informally, agreed to use and recommend for temperature measurements between 1° and 5.2° K, a table of vapor pressures of He⁴, then in use in Leiden, which came to be known as the “1948 Scale” [1].⁵ This scale has sometimes been referred to as the “1949” Scale. From 1° to 1.6°K, the “1948 Scale” was based on vapor pressures calculated by Bleaney and Simon [2] using eq (2). From 1.6° to 5.2° K, the scale was based on measured vapor pressures and temperatures determined with gas thermometers. From 1.6° to 4.2° K, it was based primarily on the vapor pressure measurements of Schmidt and Keesom [3].Even in 1948, when the “1948 Scale” was agreed to, there was evidence in the measurements and calculations of Kistemaker [4] that the “1948 Scale” deviated significantly from the thermodynamic scale. However, it was thought at the time that, on general principles, indicated changes in an existing scale should be made only after these changes had been confirmed. With improvements in the precision and accuracy of physical measurements at low temperatures, irregularities appeared in the temperature variation of physical properties between 1° and 5° K that were in the main reproducible in different substances and properties and were, therefore, attributable to errors in the “1948 Scale” [5]. Stimulated by these results which corroborated Kistemaker’s work, the investigations of the He⁴ vapor pressure scale were undertaken that culminated in the “1958 He⁴ Scale.”Paramagnetic susceptibility and carbon resistor thermometers were later employed in investigations of the He⁴ vapor pressure-temperature relation [6]. These thermometers were used for the interpolation of temperatures between calibration points (temperatures) using an assumed relation connecting temperature and paramagnetic susceptibility or carbon resistance for the calculation of the temperatures. For suitably chosen paramagnetic salts, the Curie-Weiss Law was assumed to hold: χ=CT+Δ(5)where χ is the magnetic susceptibility and C and Δ are empirical constants. Measurements at two temperatures would suffice to determine these two empirical constants if the measurement were really of χ or a quantity directly proportional to χ. However, a calibration of the paramagnetic thermometer at a third calibration temperature is necessary because the arbitrariness in the size and arrangement of the paramagnetic salt samples and the induction coils that surround the salt sample for the susceptibility measurement make the measurement a linear function of χ. Interpolation equations for carbon resistor thermometers are not as simple as eq (5) and do not have a theoretical basis. Hence, vapor pressure data obtained with carbon resistor thermometers are of more limited usefulness for the determination of the He⁴ vapor pressure-temperature relation. Clement used carbon thermometer data to examine the derivative d (ln P)/d (1/T), [7].Important use has been made of He⁴ vapor pressure measurements made with magnetic susceptibility and carbon resistor thermometers in arriving at the “1958 He⁴ Scale.” These vapor pressure measurements were considered along with those made with gas thermometers and vapor pressures calculated using eq (2). Temperature measurements with magnetic and carbon resistor thermometers are much simpler to make than measurements with gas thermometers, and hence vapor pressure data obtained with magnetic and carbon resistor thermometers are more numerous. Also, the measurements made with these secondary thermometers are more precise (to be distinguished from accurate) which makes them especially useful for interpolation between the gas thermometer data.There are, accordingly, three practical methods for determining the He⁴ vapor pressure-temperature relation: (1) By use of the direct vapor pressure measurements made with gas thermometers, (2) through the use of eq (2) with some vapor pressure-gas thermometer data, and (3) through the use of vapor pressure measurements with secondary thermometers which have been calibrated using some gas thermometer data. If all the pertinent experimental data were accurate and all temperatures were on the thermodynamic scale, these three methods would yield results in good agreement with each other, and any one might be relied upon for the construction of the He⁴ vapor pressure-temperature table defining the scale. Because of experimental errors, however, the vapor pressures obtained by the different methods differ when carried to the limit of the sensitivity of the measurements. For He⁴ between 1° and 4.5° K, different choices of the methods and different selections of the experimental data used, weighting factors and corrections to the published data yield scales all within about 4 millidegrees of each other. The primary evidence for this is that 4 millidegrees is the maximum difference between the L55 Scale [8] obtained by method (2) and the 55E Scale [9] obtained by method (3). This then is a measure of the range (total spread) of uncertainty at present in the He⁴ vapor pressure scale of temperatures between 1° and 4.5° K.All published He⁴ vapor pressure measurements, and thermodynamic data needed for eq (2) were independently studied and correlated by H. Van Dijk and M. Durieux at the Kamerlingh Onnes Laboratory in Leiden [8] and by J. R. Clement and J. K. Logan at the U.S. Naval Research Laboratory in Washington [9]. As far as possible, the experimental data of the original investigators were recalculated on the basis of later knowledge of the temperature scale, fundamental constants, and the properties of He⁴. In some cases, limitations were imposed on these recalculations by the incomplete reporting of the experimental data by the original investigator.After working independently, van Dijk and Clement cooperated to compromise their differences. They met first in Leiden, August 1955 and later in Washington, summer of 1957. From January 22 to March 14, 1958, Logan worked at Leiden, and later represented Clement at a conference in Leiden, June 1958, at which agreement was reached on the “1958 He⁴ Scale.” This cooperation was an important factor in the improvement of the scale.Where the differences between the values obtained by handling the experimental data differently are largest (4 millidegrees), the “1958 Scale” falls between the extremes. At other places it is close to the mean of these values and at no place does it deviate by more than 2 millidegrees from the mean. The estimated uncertainty of the “1958 He⁴ Scale” is accordingly ±2 millidegrees between 1° and 4.5° K. At higher temperatures, the estimated uncertainty is larger.Now that the International Committee on Weights and Measures has recommended the “1958 He⁴ Scale” as an international standard it is presumed that henceforth the International Committee on Weights and Measures will take the initiative in improving the scale when changes are needed. Before the International Committee on Weights and Measures assumed responsibility for the He⁴ vapor pressure scale, the Commission on Very Low Temperature Physics in the International Union of Pure and Applied Physics concerned itself with the scale. This began with the informal meeting in Amsterdam in 1948 that resulted in the “1948 Scale.” At the Low Temperature Conferences sponsored by the Commission on Very Low Temperature Physics of the International Union of Physics at Paris in 1955, and at Madison, Wisconsin, in 1957, sessions were held at which the He⁴ vapor pressure scale of temperatures was discussed.The National Bureau of Standards sponsored meetings, for discussion of the helium vapor pressure scale of temperatures, held at the NBS during the spring meetings of the American Physical Society in Washington, 1955 and 1957. Also, the NBS encouraged cooperation in reaching national and international agreement on the scale. It initiated or promoted the meetings for discussion of the differences between the L55 and 55E Scales proposed respectively by Van Dijk and Durieux, and by Clement. These were the meetings held August 26 and 27, 1955 in Leiden (before the Low Temperature Conference in Paris) [10], July 30, 31, and August 1, 1957 in Washington (before the Low Temperature Conference in Madison) [11], and June 13, 14, and 16, 1958 in Leiden (before the meeting of the Advisory Committee on Thermometry of the International Committee on Weights and Measures in Sèvres) [12]. Also, the National Bureau of Standards promoted the arrangement which sent Dr. Logan of the U.S. Naval Research Laboratory to work in the Kamerlingh Onnes Laboratory from January 22, to March 14, 1958.The Scale agreed upon at Leiden, June 13 to 16, 1958 was presented to the Advisory Committee on Thermometry of the International Committee on Weights and Measures at its meeting in Sèvres, June 20 and 21, 1958. The recommendation of the Advisory Committee to the International Committee was as follows [12]:

• “Le Comité Consultatif de Thermométrie,
• “avant reconnu la nécessité d’établir dans le domaine des très basses températures une échelle de température unique,
• “ayant constaté l’accord général des spécialistes dans ce domaine de la physique,
• “recommande pour l’usage général l’ “Echelle ⁴He 1958,” basée sur la tension de vapeur de l’hélium, comme définie par la table annexée.
• “Les valeur des températures dans cette échelle sont désignées par le symbole T₅₈.”

The table of He⁴ vapor pressures that was sent to the International Committee with this recommendation was the table distributed at the Kamerlingh Onnes Conference on Low Temperature Physics at Leiden, June 23 to 28, 1958. It was published in the Proceedings of the Kamerlingh Onnes Conference [13].On the recommendation of its Advisory Committee on Thermometry, the International Committee on Weights and Measures approved the “1958 He⁴ Scale of Temperatures” at its meeting at Sèvres, September 29 to October 3, 1958.The table adopted by the International Committee on Weights and Measures was a table of vapor pressures at hundredth degree intervals. This table was expanded by Clement and Logan making table I of this paper with millidegree entries. Table I was inverted to give tables II and III which express T as a function of vapor pressures. Auxiliary tables were added including a table of the differences between the 1958 Scale and other earlier used scales. Linear interpolation is valid for all tables except at the lower temperature end of table IV.The assistance at Leiden of H. ter Harmsel and C. van Rijn, students of Dr. H. van Dijk at the Kamerlingh Onnes Laboratory, with the computations for the defining and auxiliary tables is gratefully acknowledged.Various members of the Cryogenics Branch of the Naval Research Laboratory at Washington assisted with numerous calculations which contributed toward the development of the present scale. This assistance, especially that of Dr. R. T. Swim, is gratefully acknowledged.     

Thermodynamic Properties of Some Methylphosphonyl Dihalides From 15 to 335 °K

Measurements of the heat capacity of methylphosphonyl difluoride (CH₃POF₂), methyl phosphonyl dichloride (CH₃POCl₂), and methylphosphonyl chlorofluoride (CH₃POClF) were made from about 15 to 335 °K by means of an adiabatic calorimeter. These highly reactive and toxic substances were purified in a completely closed glass apparatus by combining slow crystallization and fractional melting procedures. The purities determined by the freezing-curve method are shown to be generally in agreement with those values obtained by the calorimetric method. From the results of the heat measurements, the triple-point temperature, heat of fusion, and their corresponding estimated uncertainties were found to be, respectively, 236.34±0.05 °K and 11,878±12 J/mole for CH₃POF₂, 306.14± 0.02 °K and 18,076±15 J/mole for CH₃POCl₂, and 250.70± 0.20 °K and 11,853±30 J/mole for CH₃POClF. Triple-point temperatures obtained by the freezing-curve method are in agreement with the above values. A table of smoothed values of heat capacity, enthalpy, enthalpy function, entropy, Gibbs free energy, and Gibbs free energy function from 0 to 335 °K was obtained from the data. The entropy and its corresponding estimated uncertainty for CH3POF2, CH3POCl2, and CH3POClF in their respective condensed phase at 298.15 °K and saturation pressure was found to be 208.3± 0.3, 164.8± 0.3, and 216.4± 0.4 J/deg mole, respectively. The entropies in the gaseous state at 298.15 °K and 1 atm pressure were found to be 312.7±3, 339.7±3, and 335.0±3 J/deg mole, respectively.     

Infrared Spectrum of the v2+ v6 Band of C13C12H6

The infrared spectrum of the v₂+v₆ band of C¹³C¹²H₆ has been analyzed and a value of B₀= 0.64865 ±0.00005 cm⁻¹ determined. When this value is combined with that found in recent work on isotopically normal ethane, a “r_s” value of 1.527±0.004 A for the carboncarbon bond distance is obtained. (Uncertainties are probable errors.)     

Thermal Degradation of Polymers at High Temperatures

Work on thermal degradation of polymers has previously been carried out at temperatures up to about 500° C. In the present work the range has been extended to 850° C. Polystyrene was pyrolyzed in a vacuum and also in helium at atmospheric pressure at 362° and at 850° C. Analysis of the volatile products indicates that higher temperatures and higher pressures cause a greater fragmentation of the volatile products. Samples of poly (vinylidene fluoride), polyacrylonitrile, and polytrivinylbenzene, were pyrolyzed in a vacuum at temperatures from 350° to 800° C. The more volatile products were analyzed qualitatively and quantitatively in a mass spectrometer. The less volatile products were tested for their average molecular weight by a microcryoscopic method.Rates of thermal degradation were also determined for the last three polymers. The activation energies in the temperature range 218° to 440° C were found to be 48, 31, and 73 kcal/mole, respectively, for poly(vinylidene fluoride), polyacrylonitrile, and polytrivinylbenzene.