On the Kirkwood-modified Tait equation

The pairwise additive potential energy and molecular distribution functions are obtained for a one-dimensional fluid satisfying a version of the Kirkwood-modified Tait equation of state.This work was supported by the National Science Foundation Grant CHE 7404171A02.     

Improved equation of state for ionic liquids using surface tension

The major objective of this work was the development of a reliable model to describe volumetric properties of ionic liquids (ILs). In this regard, we have applied the Ihm–Song–Mason equation of state (EOS) to some phosphonium- and imidazolium-based ILs. Three temperature-dependent parameters in the equation of state have been scaled based on the surface tension and the liquid density at room temperature. In order to improve the predictive power of the mentioned EOS for ILs, we have proposed using a simple modification. We have taken 1,228 experimental points to show the reliability of the improved EOS. The comparison of predicted densities with literature data over a broad range of temperature, 293–472 K, and pressures up to 200 MPa led to encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.75%.     

A thin-film equation for viscoelastic liquids of Jeffreys type

We derive a novel thin-film equation for linear viscoelastic media describable by generalized Maxwell or Jeffreys models. As a first application of this equation we discuss the shape of a liquid rim near a dewetting front. Although the dynamics of the liquid is equivalent to that of a phenomenological model recently proposed by Herminghaus et al. (S. Herminghaus, R. Seemann, K. Jacobs, Phys. Rev. Lett. 89, 056101 (2002)), the liquid rim profile in our model always shows oscillatory behaviour, contrary to that obtained in the former. This difference in behaviour is attributed to a different treatment of slip in both models.     

On the Kudryashov-Sinelshchikov equation for waves in bubbly liquids

A nonlinear evolution equation for wave propagation in bubbly liquids, taking into account viscosity and heat transfer, has been derived by Kudryashov and Sinelshchikov. In the case of no dissipation the authors have provided analytical solutions representing undistorted waves. These results are cast into a simpler form and studied in more detail. In addition to the wave profiles the corresponding phase curves are presented. Depending on some parameter the solutions represent solitary or periodic waves. Some of the periodic waves exhibit peaks or cusps. From the periodic waves a new type of “meandering” solutions is constructed.     

Thermodynamic properties of some ionic liquids using a simple equation of state

In this work, we have used a simple equation of state (EoS) to predict the density and other thermodynamic properties such as isobaric expansion coefficient, α_P , isothermal compressibility, κ_T, and internal pressure, P_i, for nine ionic liquids including trihexyl (tetradecyl) phosphonium chloride ([(C₆H₁₃)₃P(C₁₄H₂₉)][Cl]), trihexyl (tetradecyl) phosphonium acetate ([(C₆H₁₃)₃P(C₁₄H₂₉)][Ac]), trihexyl (tetradecyl) phosphonium bis {(trifluoromethyl) sulfonyl} amide ([(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂]), 1-butyl-3-methylimidazolium bis {(trifluoromethyl) sulfonyl} amide ([bmim][NTf₂]), 1-hexyl-3-methylimidazolium bis {(trifluoromethyl) sulfonyl} amide ([hmim][NTf₂]), 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF₄]), 1-butyl-3-octylimidazolium tetrafluoroborate ([omim][BF₄]), 1-butyl-3-octylimidazolium hexafluorophosphate ([omim][PF₆]), and 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF₆]) at different temperatures and pressures. A wide comparison with experimental and literature data has been made. The results show that this EoS can be used to reproduce and predict different thermodynamic properties of ionic liquids within experimental errors.     

Calculation of the Green function for the Laplace equation

A modification of the traditional method of calculating the Green function in a layered medium is suggested that allows one to substantially increase its accuracy. In addition, a technique for calculating the Green function that makes it possible to control the accuracy of the calculated potential is offered. This technique is based on the properties of the Bessel and Struve functions. An example of calculation using the suggested technique is illustrated. The results may be extended for a wide class of problems the solution to which requires calculation of the Green function for the Laplace equation in a layered medium.     

A perturbed hard-sphere equation of state extended to imidazolium-based ionic liquids

A perturbed hard-sphere equation of state (EOS) has been previously employed to predict pressure–volume–temperature properties of some ionic liquids (ILs) with phosphonium-, pyridinium-, and pyrrolidinium cations. In this work, we have extended the considered EOS to another class of ILs in compressed states. This class consists of 14 imidazolium-based ILs. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 0.1 to 200 MPa. From 1,122 data points examined for the aforementioned ILs, the total average absolute deviation was found to be 1.05%.     

Calculation of the thermodynamic properties of electrolyte solutions using a modified Poisson-Boltzmann equation

Further results are presented of the numerical study made by Burley, Huston and Outwaite on a modified Poisson-Boltzmann equation in electrolyte solution theory. Activity and osmotic coefficients are calculated for 1 : 1 and 2 : 2 electrolytes using the Güntelberg charging process and comparisons made with the Poisson-Boltzmann coefficients. The consistency of the activity coefficients is checked by considering the Debye charging process and the second-moment condition of Stillinger and Lovett. Comparisons are also made with the Monte Carlo studies of Card and Valleau. Our results indicate that the long-range effects predicted by the modified Poisson-Boltzmann equation are considerably more accurate than those of the Poisson-Boltzmann equation.     

A perturbed hard-sphere equation of state for phosphonium-, pyridinium-, and pyrrolidinium-based ionic liquids

In this work, a perturbed hard-sphere equation of state has been employed to predict the pressure–volume–temperature properties of some phosphonium-, pyridinium-, and pyrrolidinium-based ionic liquids in compressed states. Two temperature-dependent parameters that appeared in the equation of state have been determined using the critical properties of abovementioned ionic liquids as the scaling constant, i.e., knowing only two available scaling constants is sufficient to utilize the proposed equation of state to this class of fluids. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 1 to 65 MPa. From 550 data points examined for the aforementioned ionic liquids, the total average absolute deviation, AAD was found to be 1.12%.     

Thermodynamic properties of the mixtures of some ionic liquids with alcohols using a simple equation of state

In the present work, we have used a simple equation of state called the GMA EoS to calculate the density of three ionic liquid mixtures including 1-butyl-3-methylimidazolum hexafluorophosphate, [BMIM] [PF₆] + methanol, 1-butyl-3-methylimidazolum tetrafluoroborate, [BMIM] [BF₄] + methanol, and [BMIM] [BF₄] + ethanol at different temperatures, pressures, and compositions. The isothermal compressibility, excess molar volumes, and excess Gibbs molar energy of these mixtures have been computed using this equation of state. The values of statistical parameters show that the GMA EoS can predict these thermodynamic properties very well within the experimental errors. The results show that isothermal compressibility of ionic liquids is lower than alcohols and the effect of temperature and pressure on the isothermal compressibility of ionic liquids is lower than alcohols. The excess molar volumes and excess molar Gibbs energy for these ionic liquid mixtures with alcohols are all negative at various temperatures and pressures over the whole composition range. The results have been interpreted in terms of intermolecular interactions and structural factors of the ionic liquids and alcohols.     

Calculation of the kaon B parameter using strictly local sum rules

The kaon B-parameter is computed in the framework of strictly local QCD sum rules for a threepoint function involving pseudoscalar currents. As an application of these sum rules we derive a low energy formula for the B-parameter. We show that strictly local QCD sum rules yield more reliable results than other QCD sum rules, since they need less phenomenological information and do not suffer from stability problems. Our result for the B-parameter isB=0.74±0.17.     

A novel approach for solving the Fisher equation using Exp-function method

In this Letter, Exp-function method is employed to obtain traveling wave solutions of the Fisher equation. It is shown that, on this example, the Exp-function method is easy to implement and concise method for nonlinear evolution equations in mathematical physics.     

Calculation of the frequency response in step-index plastic optical fibers using the time-dependent power flow equation

The time-dependent power flow equation, which is reduced to its time-independent counterpart is employed to calculate frequency response and bandwidth in addition to mode coupling and mode-dependent attenuation in a step-index plastic optical fiber. The frequency response is specified as a function of distance from the input fiber end. This is compared to reported measurements. Mode-dependent attenuation and mode dispersion and coupling are known to be strong in plastic optical fibers, leading to major implications for their frequency response in data transmission systems.     

Correlation of volumetric properties of binary mixtures of some ionic liquids with alcohols using equation of state

In our previous paper, we extended the Tao and Mason equation of state (TM EOS) to pure ionic liquids. Here we apply TM EOS based on statistical?Cmechanical perturbation theory to binary mixtures of ionic liquids. Three temperature-dependent quantities are needed to use the equation of state: the second virial coefficient, B ₂, effective van der Waals co-volume, b, and a scaling factor, ??. The second virial coefficients are calculated from a correlation that uses the normal boiling temperature and normal boiling density. ?? and b can also be calculated from the second virial coefficient by scaling. In this procedure, the number of input parameters, for calculation of B ₂, ??, and b reduced from 5 (i.e., critical temperature, critical pressure, acetric factor, Boyle temperature T _B, and the Boyle volume ?? _B) to 2 (i.e., T _bp and ?? _bp). At close inspection of the deviations given in this work, the TM EOS predicts the densities with a mean AAD of 1.69%. The density of selected system obtained from the TM EOS has been compared with those calculated from perturbed-hard-sphere equation of state. Our results are in favor of the preference of the TM EOS over another equation of state. The overall average absolute deviation for 428 data points that calculated by perturbed-hard-sphere equation of state is 2.60%.     

A new symmetrized solution for phase retrieval using the transport of intensity equation

We propose a novel symmetrization method for solving the transport of intensity equation (TIE) using fast Fourier transforms for situations where the input images may or may not exhibit spatial periodicity. The method is derived from the analysis of intensity conservation law and the internal symmetry of the TIE, and is illustrated for both a computational and an experimental data set.     

A study of the secular equation for rayleigh waves using the root locus method

In a recent note Rahman and Barber [Trans. ASME 62 (1995) 250] proposed an exact expression for the roots of the secular equation for the Rayleigh waves in an isotropic half-space. Using the root locus method, we describe in a very simpler manner the evolution of the roots versus the Poisson's ratio and we derive easily the critical value for which the nature of the roots changes.     

氢、碳氢燃料对向扩散火焰

对氢、正烷烃碳氢燃料与氧的对向扩散火焰,其中正烷烃包含了在工业用燃料中广泛应用的C_nH_2n+2正烷烃CH₄～C1₆H₃₄,对这些燃料的火焰结构进行了分析和比较,系统地分析了压力和拉伸率对火焰行为和热释放率等的影响,其中包含了2115个组分8157个可逆反应．研究结果表明,所有燃料的火焰厚度和热释放率与压力和拉伸率的乘积的平方根成线性关系．在相同工况下,氢的火焰厚度总是大于所有的碳氢燃料,而CH₄～C1₆H₃₄所有的碳氢燃料在相同工况下总是具有几乎相同的燃烧温度分布、燃烧产物分布、火焰厚度和热释放率,该结果表明由这些碳氢燃料组成的混合燃料具有同样的火焰特性.     

A short review on stable metal nanoparticles using ionic liquids,supported ionic liquids,and poly(ionic liquids)

Metal nanoparticles (NPs) are a subject of global interest in research community due to their diverse applications in various fields of science. The stabilization of these metal NPs is of great concern in order to avoid their agglomerization during their applications. There is a huge pool of cations and anions available for the selection of ionic liquids (ILs) as stabilizers for the synthesis of metal NPs. ILs are known for their tunable nature allowing the fine tuning of NPs size and solubility by varying the substitutions on the heteroatom as well as the counter anions. However, there has been a debate over the stability of metal NPs stabilized by ILs over a long period of time and also upon their recycling and reuse in organocatalytic reactions. ILs covalently attached to solid supports (SILLPs) have given a new dimension for the stabilization of metal NPs as well as their separation, recovery, and reuse in organocatalytic reactions. Poly(ILs) (PILs) or polyelectrolytes have created a significant revolution in the polymer science owing to their characteristic properties of polymers as well as ILs. This dual behavior of PILs has facilitated the stabilization of PIL-stabilized metal NPs over a long period of time with negligible or no change in particle size, stability, and size distribution upon recycling in catalysis. This review provides an insight into the different types of imidazolium-based ILs, supported ILs, and PILs used so far for the stabilization of metal NPs and their applications as a function of their cations and counter anions.