Electrical and Dielectric Behaviour at the Critical Point of Binary Liquids: Acetonitrile + Cyclohexane

The electrical capacitance and resistance of the binary liquid mixture cyclohexane + acetonitrile are measured in the one phase and two phase regions at spot frequencies between 5 kHz and 100 kHz. This sample has a very low gravity affected (∼0.6 mK) region. In one phase region the capacitance data show a sharp, ∼0.7% increase above background within 0.5 degrees of Tc whereas the resistance has a smooth increase of ∼1.5% above background in a (T−Tc) range of 4 degrees. Two phase values of capacitance and resistance from the coexisting phases are used to determine the critical parameters Tc (critical temperature), Rc (resistance at Tc) and Cc (capacitance at Tc). A precise knowledge of these parameters reduces the uncertainty on the critical exponent 0 for C and R. The one phase capacitance data fit to an (1 - α) exponent in a limited temperature range of 0.2 degrees. Resistance data strongly support an (1 - α) exponent over the entire 5 degree range.

Critical-point Properties of Liquids and the Born-Green Theory

Recent work of Jones et al. giving the long-range behaviour of the pair correlation function is used to confirm that the critical ratio Pc/nckBTc = 1/2 in the Born-Green theory. This deviates from experimental results on simple insulating liquids by more than the predictions of the van der Waals equation of state. A brief discussion of conditions for thermodynamic consistency, which the Born-Green theory violates, is then given. Finally, the approach of the Ornstein-Zernike correlation function to its critical point behaviour is discussed within the Born-Green theory.

Critical point phenomena in the electrical resistivity of binary liquid systems: Cs2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS2 + CH3CN and CS2 + CH3NO2 with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT c follows the relationR=R c−A(T−T c) b withb=0·6±0·1. BelowT c the conductivities of the two phases obey a relation σ2−σ1=B(T c−T)β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.

Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

The critical behavior of osmotic susceptibility in an aqueous electrolyte mixture 1-propanol (1P)+water (W)+potassium chloride is reported. This mixture exhibits re-entrant phase transitions and has a nearly parabolic critical line with its apex representing a double critical point (DCP). The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths (by varying t) in the one-phase region. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the TL far away from the DCP, the effective susceptibility exponent γeff as a function of t displays a nonmonotonic crossover from its single limit three-dimensional (3D)-Ising value ( ∼ 1.24) toward its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value toward its nearly doubled mean-field value with increase in t. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend toward shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover to the mean-field limit extends well beyond t>10−2 for the TL’s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques. As far as the critical behavior in complex or associating mixtures with special critical points (like the DCP) is concerned, our results indicate that the influence of the DCP on the critical behavior must be taken into account not only on the renormalization of the critical exponent but also on the range of the Ising regime, which can shrink with decrease in the influence of the DCP and with the extent of structuring in the system. The utility of the field variable tUL in analyzing re-entrant phase transitions is demonstrated. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value toward a value slightly lower than its nonasymptotic mean-field value of 1. This behavior in the nonasymptotic, high tUL region is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values, as foreseen earlier in micellar systems.

Methyl ethyl ketone plus water plus secondary butyl alcohol: A potential system for the exploration of a quadruple critical point

We report preliminary experiments on the ternary-liquid mixture, methyl ethyl ketone (MEK)+water (W)+secondary butyl alcohol (sBA)-a promising system for the realization of the quadruple critical point (QCP). The unusual tunnel-shaped phase diagram shown by this system is characterized and visualized by us in the form of a prismatic phase diagram. Light-scattering experiments reveal that (MEK+W+sBA) shows near three-dimensional-Ising type of critical behavior near the lower critical solution temperatures, with the susceptibility exponent (gamma) in the range of 1.217 <=gamma <= 1.246. The correlation length amplitudes (xi(o)) and the critical exponent (nu) of the correlation length (xi) are in the ranges of 3.536 <=xi(o)<= 4.611 A and 0.619 <=nu <= 0.633, respectively. An analysis in terms of the effective susceptibility exponent (gamma(eff)) shows that the critical behavior is of the Ising type for MEK concentrations in the ranges of 0.1000 <= X <= 0.1250 and X >= 0.3000. But, for the intermediate range of 0.1750 <= X < 0.3000, the system shows a tendency towards mean-field type of critical behavior. The advantages of the system (MEK+W+sBA) over the system (3-methylpyridine+water+heavy water+potassium Iodide) for the realization of a QCP are outlined.

Investigations of the Nature of Critical Line Very Close to a Double Critical Point

The curvature of the line of critical points in a reentrant ternary mixture is determined by approaching the double critical point (DCP) extremely closely. The results establish the continuous and quadratic nature of this line. Out study encompasses as small a loop size (ΔT) as 663 mK. The DCP is realized when ΔT becomes zero.

Behaviour of the curve of critical exponents near and away from a double critical point

To investigate the nature of the curve of critical exponents (as a function of the distance from a double critical point), we have combined our measurements of the osmotic compressibility with all published data for quasibinary liquid mixtures. This curve has a parabolic shape. An explanation of this result is advanced in terms of the geometry of the coexistence dome, which is contained in a triangular prism.

Subquadratic quantum number dependence and other anomalies of vibrational dephasing in liquid nitrogen: Molecular dynamics simulation study from the triple point to the critical point and beyond

Vibrational phase relaxation near gas-liquid and liquid-solid phase coexistence has been studied by molecular dynamics simulations of N-N stretch in N-2. Experimentally observed pronounced insensitivity of phase relaxation from the triple point to beyond the boiling point is found to originate from a competition between density relaxation and resonant-energy transfer terms. The sharp rise in relaxation rate near the critical point (CP) can be attributed at least partly to the sharp, rise in vibration-rotation coupling contribution. Substantial subquadratic quantum number dependence of overtone dephasing rate is found near the CP and in supercritical fluids. [S0031-9007 (99)09318-7].

Temperature dependent vibrational lifetimes in supercritical fluids near the critical point

Vibrational relaxation measurements on the CO asymmetric stretching mode (similar to 1980 cm(-1)) of tungsten hexacarbonyl (W(CO)(6)) as a function of temperature at constant density in several supercritical solvents in the vicinity of the critical point are presented. In supercritical ethane, at the critical density, there is a region above the critical temperature (Tc) in which the lifetime increases with increasing temperature. When the temperature is raised sufficiently (similar to T-c + 70 degrees C), the lifetime decreases with further increase in temperature. A recent hydrodynamic/thermodynamic theory of vibrational relaxation in supercritical fluids reproduces this behavior semiquantitatively. The temperature dependent data for fixed densities somewhat above and below the critical density is in better agreement with the theory. In fluoroform solvent at the critical density, the vibrational lifetime also initially increases with increasing temperature. However, in supercritical CO2 at the critical density, the temperature dependent vibrational lifetime decreases approximately linearly with temperature beginning almost immediately above T-c. The theory does not reproduce this behavior. A comparison between the absolute lifetimes in the three solvents and the temperature trends is made.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Critical Reappraisal Of Plasticity Index Of Soils

A fundamental approach, based on Gouy-Chapman theory of double layer, has been provided to micromechanistically interpret the plasticity index of soils and their relationship with liquid limit. The relationships between plasticity index and liquid limit, developed earlier, through statistical approaches and critical state concepts, have been reexamined. The statistical analysis of extensive published data has resulted in the relationship, IP = 0.74 (wL - 8). On comparison with other relationships in vogue the proposed equation has been found to give better agreement. From the reappraisal of critical state approaches consistent with the micromechanistic interpretation, the possible range of parameters have been computed and compared with those obtained by statistical means to enhance the credibility of the proposed relationship.

Critical-Behavior Of The Diameters Of Liquid-Liquid Coexistence Curves

We have analyzed the diameters of the liquid–liquid coexistence curves of several binary liquid mixtures in search of the critical anomaly predicted by current theories. We find that while the data are consistent with the predicted functional form, the evidence for such an anomaly is not compelling.

Unsteady compressible second-order boundary layers at the stagnation point of two-dimensional and axisymmetric bodies

The unsteady laminar compressible boundary-layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer has been studied for all second-order boundary layer effects when the basic potential flow admits selfsimilarity. The solutions for the governing equations are obtained by using an implicit finite-difference scheme. Computations have been carried out for different values of the parameters characterizing the unsteadiness in the free stream velocity, wall temperature, mass transfer rate and variable gas properties. The results are found to be strongly affected by the unsteadiness in the free stream velocity. For large injection rates the second-orderboundary layer effects may prevail over the first-order boundary layer, but reverse is true for suction. The wall temperature and the variation of the density-viscosity product across the boundary layer appreciably change the skin-friction and heat-transfer rates due to second-order boundary-layer effects.

Critical Evaluation of Determining Swelling Pressure by Swell-Load Method and Constant Volume Method

For any construction activity in expansive soils, determination of swelling pressure/heave is an essential step. Though many attempts have been made to develop laboratory procedures by using the laboratory one-dimensional oedometer to determine swelling pressure of expansive soils, they are reported to yield varying results. The main reason for these variations could be heterogeneous moisture distribution of the sample over its thickness. To overcome this variation the experimental procedure should be such that the soil gets fully saturated. Attempts were made to introduce vertical sand drains in addition to the top and bottom drains. In this study five and nine vertical sand drains were introduced to experimentally find out the variations in the swell and swelling pressure. The variations in the moisture content at middle, top, and bottom of the sample in the oedometer test are also reported. It is found that swell-load method is better as compared to zero-swell method. Further, five number of vertical sand drains are found to be sufficient to obtain uniform moisture content distribution.

A parallel wilf algorithm for complex zeros of a polynomial

A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n 3 p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors are available, it can be realized in parallel with complexityO(n 2 p); also it can be implemented using exact arithmetic. A combined Wilf-Hansen algorithm is suggested for reduction in complexity.