Thermal conductivity of hydrocarbons in the naphthene group under high pressures

The thermal conductivity of hydrocarbons in the naphthene group has been experimentally determined. An equation is now proposed for calculating the thermal conductivity over the given temperature and pressure ranges.Notation thermal conductivity - ₂₀ and ₃₀ values of the thermal conductivity at 20 and 30°C, respectively - t₀,P₀ thermal conductivity at t₀, p₀ - _t p thermal conductivity at temperature t and under pressure P - change in thermal conductivity - P pressure - P_melt melting pressure - P₀ atmospheric pressure - t₀ 20°C temperature - T, t temperature - T_cr critical temperature - temperature coefficient of thermal conductivity - ₂₀ temperature coefficient of density - density - ₂₀ density at 20°C - _cr critical density - M molar mass - =T/T_cr referred temperature - v specific volume - v₀ specific volume at 20°C - v change in specific volume - _{3 0} a coefficient - B (t) a function of the temperature - S a quadratic functional - W_i, weight of the i-th experimental point - _i error of the i-th experimental value of thermal conductivity - B _{y, =0.6} value of B (t) at T = 0.6T_cr - B = B (t)/B_{, =0.6} referred value of coefficient B (t) Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 491–499, September, 1981.     

Mean polarizabilities and second optical and density virial coefficients of CH3OH and CCl2F2 between 300 and 355 K

Mean dipole polarizabilities ₀(, T) as well as second optical (or refractive index) virial coefficients b _R(, T) and second density virial coefficients B(T) of gaseous CH₃OH and CCl₂F₂ have been determined by precise measurements of the refractive index n(, T, p) [543 nm 633 nm, 300 K T 355 K, p<0.25 bar (CH₃OH) and p<3 bar (CCl₂F₂)]. ₀ critically compared with the few data in literature. The b _R of these gases was measured for the first time with the cyclic-expansion method. The values of ¦B¦ and b _R=3160(25) cm³ · mol^–1 measured for CH₃OH are considerably greater than the values calculated by Buckingham's statistical-mechanical expressions for a Stockmayer interaction potential. This difference is discussed by assuming dimerization via H bonds, with result H ₂ ⁰ –(28 ... 33) kJ · mol^–1 and S ₂ ⁰ –(116 133) J · mol^–1 · K^–1 for the dimerization enthalpy and entropy for standard conditions, respectively. On the other hand, Buckingham's formulae can be used with success to estimate b _R and B of CCl₂F₂.Dedicated to Prof. Dr. F. Kohler on the occasion of his 65th birthday     

Surface tension of liquid4He nearT λ

The surface tension of liquid⁴He in the neighborhood of the transition temperature was measured with very high precision by the surface-wave resonance method. The derivative of the surface tension with respect to temperature decreases by 21.1±0.8 mdyn/cm K as the temperature is increased from T – 20 mK to T + 20 mK. The regular part of the surface tension near T is considered to consist of two parts, a ripplon contribution _R and a bulk contribution _B. In the present analysis, the singular part exists only below T, and is proportional to (T – T)^1.3±0.1. This behavior seems to be related to the Bose-Einstein condensate or the superfluid density.     

The transverse acoustic impedance of He II

The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=/2) of 20.5, 34.1, and 47.8 MHz from 30 mK to the -point T (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1–i)(f _n )^1/2 was used to measure the temperature dependence of the viscosity (T) using tabulated values of the normal fluid density _n (T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the -point,Z(T)/Z(T) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)^–2/3 nm was found, where =(T–T)/T. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as _r =8.5×10^–14 T ^–1/3 exp (8.65/T) sec. Below 1.2 K, _r >1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by f/f=2×10^–7, but the origin of this effect is not yet known.Financial support provided by the SERC, Bedford College, and the Central Research Fund, University of London.     

Effects of the Experimental Geometry on the Vortex Dynamics in High-T c, Superconductors

A brief overview is given on the macroscopic electrodynamics of type-II superconductors with and without vortex pinning, of various shapes and in an applied magnetic field, but also with applied transport current and with finite London penetration depth . The extension to >0 is important at low inductions B to describe the transition to the Meissner state, and for films with thickness not much larger than . The finite width of the surface layer with screening currents and the correct dc and ac responses in various geometries follow from an equation of motion for the current density, with a dependent integral kernel.     

Theory of helium under heat flow near the λ point. I. Interface of He I and He II

A He I-He II interface is shown to exist under heat flow and is studied near the point. The temperature in the superfluid region is found to be of the form T –T Q^3/4 if dynamic scaling is assumed, where T is the critical temperature andQ is the heat flow. In the normal region the temperature has a finite gradient. Here we are neglecting a small thermal resistance due to vortices in the superfluid region. In a finite system with size much greater than the correlation length a first-order phase transition occurs as an inverted bifurcation as the temperature at the cooler boundary is lowered slightly below T. Namely, the system will jump from the disordered state to a state in which the two phases are separated by an interface. The theory can be constructed analogously to the theory of superconductors in a magnetic field.     

Estimation of the Mean Thermal Conductivity of Anisotropic Materials

An estimation method of the plane directional thermal conductivity of fibrous insulations using the cyclic heat method and the transient hot-wire method is proposed. By assuming that the thermal conductivity _h of anisotropic materials measured by the transient hot-wire method is equivalent to that of the isotropic materials which have the same bulk density and specific heat c as the anisotropic materials, the thermal conductivity _h is shown to be equal to , which is a geometrical mean of the thermal conductivities in the direction of the plane _x and the thickness _y of the anisotropic materials. For an alumina silica blanket (=125 kg·m^–3), the thermal conductivities _h , _x , and _y were measured in the temperature range between –140 and 300°C using the transient hot-wire method for _h and the cyclic heat method for _x and _y . In the same way, the thermal conductivities _h , _x , and _y of a rock wool (=121 kg·m^–3) insulation were also measured in the temperature range, 100 to 600°C. From a comparison of the measured results with the estimated values of _x , it is confirmed that the proposed method can estimate the measured values reasonably well.     

Superfluid density near the lambda point of4He under pressure

The superfluid density in ⁴ He was determined near T from the second-sound velocity as a function of T–T and pressure. The critical exponent of the superfluid density was found to depend, even slightly, on the pressure. Furthermore, the fundamental length ₀ in the coherence length = ₀ [1–(T/T)]^–' seemed to be proportional to the mean interatomic distance. The implications of the results are also discussed.This work was partly supported by The Ito Science Foundation and by The Nishina Memorial Foundation.     

The behavior of the4He viscosity near the superfluid transition

Measurements of the shear viscosity at saturated vapor pressure through the lambda transition indicate a singular behavior of the form |1 – (/)|=A ^x , (where =|1–(T/T )|, with equal values for the critical exponent on both sides of the transition.Work sponsored by Consiglio Nazionale delle Ricerche, Rome (Italy).     

Thermal conductivity and heat capacity of solid silver bromide (AgBr) under pressure

The thermal conductivity, , and the heat capacity per unit volume, c _p , have been measured for solid silver bromide (AgBr) using the transient hot-wire method. Measurements were made at temperatures in the range 100–400 K and at pressures up to 2 GPa. c _p was found to be independent of temperature and pressure over these ranges. of AgBr was found to be similar to that of AgCl, which was measured previously. For AgBr, only acoustic phonons needed to be taken into account up to 340 K, but optic phonons probably carried some heat at higher temperatures. The Leibfried-Schlömann (LS) formula could describe the ratio (AgCl)/(AgBr), but not the ratio (1 GPa)/(0) for either substance. An empirical modification of the LS formula could describe the latter ratios but not the former. Further theoretical developments are required for understanding of (P) for even such relatively simple substances as AgCl and AgBr.     

Antiplane strain problem of diamond inclusion

In this paper, the singular stress fields created by an antiplane deformation at an inclusion corner are studied. It is shown that these singular stress fields can be separated into two independent types: a symmetric type with the stress singularity of 1/ ^1–1 and a skew-symmetric type with the stress singularity of 1/ ^1–2. These two types of the singular stress field can not occur simultaneously at the corner. If G ₂<G ₁, there exists only the singularity of the skew-symmetric type, and if G ₂>G ₁, there exists only the singularity of the symmetric type. A general expression of stress fields in the vicinity of the corner is presented. In the expression the singular stress fields for the symmetric type and the skew-symmetric type are defined in terms of the constants K _III, ₁ and K _III, ₂, respectively. K _III, ₂ and K _III, ₂ have to be determined from the complete boundary conditions of the given problem. For the problem of an infinite plate containing a diamond inclusion and subjected to a uniform longitudinal shear stress at infinity, the values of K _III, ₁ and K _III, ₂ are obtained by body force method. In the body force method, the investigated stresses are simulated by the superposition of the fundamental stress fields due to point forces. In order to obtain accurate solutions, the basic density functions of the distributed point forces are used, so that the stress singularities at the corner tip can be simulated by the point forces.     

Efficiency of heating methods for polymer fibers with formation of adhesion compounds

Efficiency of contact and contactless methods of heating of a fiber polymer material upon formation of adhesion compounds between its layers is analyzed. The advisability of contact heating in the preliminary stage and contactless heating in the final stage of formation of compounds is shown.Notation e spectral density of radiation - T temperature - a spectral absorption coefficient - radiation density within the spectral region ₂–₁, and 0–, respectively - wavelength - _max wavelength of the maximum of black-body radiation - E _0– total density of black-body radiation - the Boltzmann constant - E _ef effective radiation density - E radiation density absorbed by the material - X dimensionless coordinate - r radius of the filament of the lamp - h distance from the lamp to the surface of the material - S area - P power absorbed by the portion of the material - T _m temperature of the onset of variations in the appearance, shrinking, and melting of the material - Q heat - T ₀ initial temperature of heating - c specific heat capacity of the polymer - m mass of the material being heated - time of heating toT _m - y coordinate - R thickness - T _s stabilized temperature - Fo Fourier number - thermal conductivity of the material Institute of Mechanics of Metal-Polymer Systems, Academy of Sciences of Belarus, Gomel', Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, May–June, 1995.     

Effect of phosphorus additions on the spacing between primary silicon particles in a Bridgman solidified hypereutectic Al-Si alloy

The effect of 100 ppm addition of phosphorus on primary silicon particle number density per unit area N _A and corresponding interparticle spacing is reported for a Bridgman solidified Al-20 wt%Si base alloy. The phosphorus (added as Al-Fe-P base or Al-Cu-P alloys) results in a factor of 3 increase in N _A and a factor of 2 reduction in for the range of conditions studied. In its absence the results conform to = 256 ± 24 m (K/s)_1/3 where is cooling rate during solidification in good agreement with earlier data. When published data on the effect of 0.02 to 0.2 wt%P are included the combined results are well represented by = 250 – 215 (wt%P)^0.17 ( in m, in K/s).     

Effect of sample density on magnetic penetration depth in YBaCuO ceramic superconductors

We have measured magnetic penetration depth(0) of high-T _c YBCO samples of different density by the cavity resonant frequency shift method at 10, 16.65, and 22.3 GHz microwave frequencies. The value of(0) at 10 GHz is found to decrease from 5850 Å to 2550 Å as the density of the sample increases from 4.4 to 5.3 g/cm³. The results of the frequency response of the penetration depth show a fairly constant value of(0) for all the three samples in the frequency range 10–22.3 GHz. The wide variation observed in the value of(0) for different density samples has been explained in terms of varying Josephson coupling strength in these ceramics.     

Longitudinal critical current in type II superconductors. I. Helical vortex instability in the bulk

The vortex lattice in type II superconductors is unstable against the growth of helical perturbations if the current along the vortices exceeds a critical value. The longitudinal critical current, the pitch, and the spatially varying amplitude of the elliptically polarized helices are calculated from the London theory at the onset of instability in planar current distributions far from the surface. For weak pinning (_L² c ₆₆) the wavelength and width of the mode extend over the entire specimen, and the critical current is 2H(c ₆₆/c ₁₁)^1/4. For moderate pinning (c _{66 L}² c ₁₁) the wavelength and width are close to Campbell's pinning length (c ₁₁/_L)^1/2, and the critical current times its mean density is 2H ²(_L/c ₁₁)^1/2. For strong pinning (_L² c ₁₁) helical instability occurs at pin-free vortex sections, the helix wavelength is 2.2d, and the critical current density is 0.47Hd/² (H, d, c ₁₁ and c ₆₆), and _L are the magnetic field, spacing, elastic moduli, and pinning parameter of the vortex lattice, and is the magnetic penetration depth).     

Loss of entanglement density during crazing

The formation of fibril surface area during craze growth requires a loss of entangled strand density in the fibrils themselves. To demonstrate the decrease in entangled chain density, thin films of polystyrene are bonded to soft copper grids and strained in tension. This procedure produces crazed specimens in which the craze fibrils can be characterized by a well-defined draw ratio, ₀. The films are then exposed to electron irradiation. This produces chemical crosslinks between the molecules, thus forming a crosslinked network. Subsequent heating of the film aboveT _g results in the entanglement network trying to retract to=1. The crosslink network, however, tries to maintain the. of the craze fibrils at ₀. The craze fibrils thus retract to Ferry's state of ease, _S, where the tension of the entanglement network is balanced by the compression of the crosslink network. Measurements of _s in crazes crosslinked and then healed confirm that a 25 to 50% loss of entanglement density in craze fibrils occurs, in agreement with theoretical predictions.     

Normal-State Optical Response Functions of MgB2 Superconductor

The reflectivity of superconducting MgB₂ (T _c = 39 K) has been measured on a randomly oriented thin film at room temperature over a wide-range of frequencies, 20 < 100000 cm^–1. The conductivity shows highly metallic behavior but cannot be explained with a simple Drude model alone. The electronic contribution is analyzed by a generalized Drude model. The scattering rate 1/() and the mass renormalization ratio m*()/m = 1 + () exhibit clear frequency dependence. The electron–phonon coupling strength is estimated to be 1.5 ± 0.5 while the plasma frequency _p is 2.4 eV.     

Triple Approach to Determination of the c-Axis Penetration Depth in BSCCO Crystals

The c-axis penetration depth _c in Bi₂Sr₂CaCu₂O₈₊ (BSCCO) single crystals as a function of temperature has been determined using three high-frequency techniques, namely (1) measurements of the ac-susceptibility at a frequency of 100 kHz for different sample alignments with respect to the ac magnetic field; (2) measurements of the surface impedance in both superconducting and normal states of BSCCO crystals at 9.4 GHz; (3) measurements of the surface barrier field H_J(T) 1/_c(T) at which Josephson vortices penetrate into the sample. Careful analysis of these measurements, including both numerical solution of the electrodynamic problem of the magnetic field distribution in an anisotropic plate at an arbitrary temperature and influence of defects in the sample has allowed us to estimate _c(0) 50 m in BSCCO crystals overdoped with oxygen (T_c 84 K) and _c(0) 150 m at the optimal doping level (T_c 90 K). The results obtained by different techniques are in reasonable agreement.     

4He very nearT λ heated from above

We discuss the feasibility and likely results of measurements of the thermal conductivity (Q,t) of⁴He very nearT T (Q = 0) as a function of the heat currentQ and the reduced temperature t [T —T]/T by heating a sample from above and cooling it from below. Although the expansion coefficient is negative, the experiment should be possible without inducing convection in the HeI layer provided the sample length does not significantly exceed one cm. Fort 10^–7(Q 0.2 erg/s cm²), a state of self-organized criticality can be attained. For these conditions, the thermal gradient cancels the gradient inT induced by gravity, thus permitting measurements extremely close to the transition even in an Earthbound laboratory. However, the data will be only for a unique path in the Q—t plane. For 0.2 Q 0.5 erg/s cm² (10^–7t 10^–8) they will be in the range of linear response and give (0,t); for Q between about 0.5 and 10 erg/s cm² and over a temperature range of about 20 nK, the experimental path samples the regime where the conductivity is expected to be influenced by nonlinear finite-current effects. The small currents and narrow temperature range of the experiment imply that ultra-high resolution thermometry as well as very careful control of stray heat currents will be required. ForQ 10 erg/s cm² and up to very largeQ, the method can be used to determine the onset temperatureT _c (Q) of thermal resistance.     

A linear differential equation with a time-periodic damping coefficient: stability diagram and an application

In this paper the second-order differential equation with time-dependent damping coefficientx + cos (2t) x + x = 0,will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of -periodic solutions occurs for 4n ² where n is integer. This implies that the instability area which is emanating from =4n ² in the – stability diagram disappears. In applications, this equation can be considered as a model equation for the study of rain-wind-induced vibrations of a special oscillator.on leave as a PhD reseacher at Delft University of Technology, The Netherlands