A methodology to define the Cubic Equation of State of a simple fluid

A method to define the Cubic Equation of State (CES) of a simple substance is presented in this work. CES is constructed with only three parameters of the fluid, namely, the critical compressibility Z_c≡P_cv_c/RT_c, the acentric factor ω ≡ − log  (P^(sat)/P_c) − 1 (where P^(sat) is the saturated vapor pressure), and the saturated vapor volume v^(sat) at the temperature T^(sat)/T_c = 0.7 (where T_c is the critical temperature, v_c is the critical volume, and P_c is the critical pressure). The resulting CES is unique for each substance and, in general, it is different from other known CES in the literature.     

An improved model of the fringing fields of a quadrupole mass filter

The fringing field region of a quadrupole mass filter is modelled using an iterative finite difference technique to solve Laplace's equation for the electrostatic potential. The results are used to formulate an expression f(z) such that the electrostatic potential of the fringing field, F(x, y, z, t) may be written in the form F(x, y, z, t) = f(z) φ(x, y, t), where φ(x, y, t) is the hyperbolic field of the quadrupole. The function f(z) is expressed in the form f(z) = 1 - exp {- az - bz²}), where a and b are constants and z is in units of r_O, where 2r_O is the spacing of the quadrupole rods. The effect of the distance from the quandrupole rods to the end plate of the quadrupole mass filter, d on f(z) is investigated and the results presented show that for d < 0.125 r_O the function f(z) does not alter significantly.     

Synthesis of (1R,cis,αS)-cypermethrine via lipase catalyzed kinetic resolution of racemic m-phenoxybenzaldehyde cyanohydrin acetate

A technical scale preparation of optically active (1R,cis,αS)-cypermethrine 4 from racemic m-phenoxybenzaldehyde cyanohydrin acetate (RS)-1 and (1R,cis)-3-(2,2-dichlorovinyl)-2,2-dimethylcyclopropanecarboxylic acid chloride (1R,cis)-3 is described. Key steps of the new procedure are a lipase catalyzed enantioselective transesterification of (RS)-1 with n-butanol and direct acylation of the mixture of (R)-1 and (S)-cyanohydrin (S)-2 with (1R,cis)-3 to give enantiomerically pure (1R,cis,αS)-4. The unchanged (R)-1 is removed from (1R,cis,αS)-4 by distillation, and is racemized with triethylamine to give (RS)-1 which is returned to the process. The total yield of (1R,cis,αS)-4 referred to (RS)-1 is 80%.     

A simple sum rule in raman theory

It is shown that in the limit of large detuning energy and in the absence of coordinate dependence of the transition moment, the resonance Raman amplitude for a 0 → n transition on a harmonic potential surface is proportional to (δ²_? + δ²₊)^?1 × ?^∞_?∞ exp (?q²) · [?ⁿΔV(q)/?q¹¹] dq< where ΔV(q) is the difference between the arbitrary excited-state surface and the initial harmonic potential. The resonant and non-resonant detuning energies are given by δ_? = E ? hv and δ₊ = E + hv, where v is the incident laser frequency and E is the minimum separation between the potential surfaces.     

A different approach to X-ray stress analysis

A different approach to X-ray stress analysis has been developed. At the outset, it must be noted that the material to be analyzed is assumed homogeneous and isotropic. If a sphere with radius r within a specimen is subjected to a state of stress, the sphere is deformed into an ellipsoid. The semi-axes of the ellipsoid have the values of (r + ε_x), (r + ε_y), and (r + ε_z), which are replaced by d_x, d_y, and d_z, or for the cubic case, a_x, a_y, and a_z. In this technique, at a particular ϕ angle (see Fig. 1), the two-theta position of a high angle (hkl) peak is determined at ψ angles of 0, 15, 30, and 45°. These measurements are repeated for 3 to 6 ϕ angles in steps of 30°. The d_ϕψ or a_ϕψ values are then determined from the peak positions. The data is then fitted to the general quadratic equation for an ellipsoid by the method of least squares. From the coefficients of the quadratic equation, the angle between the laboratory and the specimen coordinates (direction of the principle stress) can be determined. Applying the general rotation of axes equations to the quadratic, the equation of the ellipse in the x–y plane is determined. The a_x, a_y, and a_z values for the principal axes of the lattice parameter ellipsoid are then evaluated. It is then possible to determine the unstressed a₀ value from Hooke's Law using a_x, a_y, and a_z. The magnitude of the principal strains/stresses is then determined.     

Rectangular source integral and recurrence relations

In this paper Hubbell's rectangular source integral H′(a,b), which is a double integral, is expressed as a series of many converging single integrals I_n (a,b). Recurrence relations relate these integrals. Once one integral I₁ is computed, recurrence relations are used to compute other integrals. I₁(a,b) can be computed analytically. H′(a,b) is approximated by considering the first seven terms in the series and the results are found to give good results for various values of a and b. Results are presented for the values of a and b (0.1 to 20 and to 2), respectively. The rate of convergence depends on the values of a and b.     

Vertical excitation as a transient phenomenon

For a particular model with two electronic states, each with two vibrations, the dipole correlation function governing electronic absorption is e ^?iωOt cosγt with spectrum ω ₀±γ. The function starts as e ^?iωOt (γ?ω ₀), with Fourier transform peaking around ω ₀ instead of ω ₀±γ, and this is associated with vertical excitation. After a time t～2/γ the spectrum goes over into the normal one. As a generalization, a procedure is outlined for characterizing the state reached first after interaction with light is initiated. Finally it is suggested that one can understand aspects of internal conversion by analogy with the case of vertical excitation.     

Volumetric properties of aqueous solutions of amino acids from the singular to critical temperature

The partial volume -V ₂ ⁰ of amino acids in aqueous solution is assumed to be zero for T = 227 K (singular temperature) and T= T _c (critical temperature). The literature data for -V ₂ ⁰(T) of ten amino acids at 278–328 K are reproduced by the two-parameter equation with a standard deviation of 0.06–0.16 cm³/mol. Only for asparagine and tryptophan the standard deviation exceeds 0.3 cm³/mol. In the case of glycine and alanine, the relation -V ₂ ⁰(T) in the high temperature range is obtained. -V ₂ ⁰ is divided into contributions (?-H ₂ ⁰/?p) _T and —T·(?-S ₂ ⁰/?p) _T . Their dependence on the temperature and amino acid nature is discussed. Positive values of ?-C ₂ ⁰/?p) _T characterize amino acids as water structure breakers; however, the differentiation of compounds by this feature is not successful. The behavior of amino acids in aqueous solutions is compared with the behavior of urea.     

Structural stability and energetics of C,Si, and Ge microclusters: empirical many-body potential energy function calculation

The structural stability and energetics of carbon, silicon, and germanium microclusters containing 3?7 atoms have been investigated by using a recently developed empirical many-body potential energy function (PEF), which comprises two- and three-body atomic interactions. The PEF satisfies both bulk cohesive energy per atom and bulk stability exactly. It has been found that the most stable C_3?4 microclusters are linear withD _∞h symmetry but C_5?7 microclusters are planar withD _nh symmetry. Silicon and germanium microclusters show similar structural stability. TheX _n (X=Si, Ge;n=3?7) microclusters are found to be most stable in the following forms:X ₃ is triangular withD _3h symmetry,X ₄ is tetragonal withT _d symmetry,X ₅ is square pyramidal withD _4h symmetry,X ₆ is bipyramidal square withO _h symmetry, and finallyX ₇ is square pyramidal having two atoms underneath withD _2h symmetry.     

A model for transitional plane Couette flow

A simplified model of plane Couette flow is derived by means of a cross-stream (y) Galerkin expansion in terms of trigonometric functions appropriate for idealized stress-free boundary conditions at the plates. A set of partial differential equations is obtained, governing the in-plane (x–z) space-dependence of a velocity field taken in the form: u=U₀(x,z,t)+[1+U₁(x,z,t)]sin(πy/2), v=V₁(x,z,t)cos(πy/2), w=W₀(x,z,t)+W₁(x,z,t)sin(πy/2). Beyond Lorenz-like Waleffe's modeling (Waleffe 1997), this Swift–Hohenberg type of approach is expected to give an access to the microscopic mechanism of spatiotemporal intermittency typical of the transition to turbulence in plane Couette flow (Pomeau 1986, Bergé et al. 1998).     

Structures isomorphes MeX2O4—Evolution structurale entre 2 K et 300 K de l'antimonite FeSb2O4: Elasticité et ordre magnétique anisotropes

Neutron diffraction has been used to study the whole structural evolution of the antimony oxide FeSb₂O₄, from 2 to 300 K. The antiferromagnetic order has been investigated: at 2 K the magnetic moment is M = 3.8 μ_B. An extrapolated Néel temperature T_N = 45 ± 6 K is observed. The function M(T) below T_N is similar to that found in the isomorphous NiSb₂O₄. Magnetostrictive effects are observed. Above 70 K, the thermal expansion tensor is anisotropic with α_a ? α_c. Using the anisotropic temperature factors B_a (Ų), B_c (Ų) at 2 and 300 K, anisotropic Debye temperatures are calculated. Then, using simple approximations, mean force constants F_a, F_c are calculated; they allow to evaluate the anisotropic compressibility coefficients χ_a ～ 0.857 × 10^?11Pa^?1, χ_c ～ 0.467 × 10^?11Pa^?1; the value of the Grüneisen constant is $\text{γ}\text{= 0.33}$.     

Packing in honeycomb networks

Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. If H is the complete graph K ₂, the maximum H-packing problem becomes the familiar maximum matching problem. In this paper we give algorithms to find a perfect packing of HC(n) with P ₆ and K _1,3 when n is even and thus determines their packing numbers. Further we also study the packing of HC(n) with 1, 3-dimethyl cyclohexane.     

A comparative study of thermophysical and spectroscopic properties in mixtures of isomeric butanediol and N,N-dimethylformamide

The thermodynamic parameters viz. excess molar volume V^E and ultrasonic speed u, transport parameter viscosity η, and spectroscopic parameters viz. IR, ¹H, ¹³C NMR have been measured for the mixtures of isomeric butanediol (1,2-, 1,3-, 1,4- and 2,3-butanediol) and N,N-dimethylformamide over the whole composition range at 308.15 K. The partial molar quantities $Q_i^{\mathrm{E}}$, isentropic compressibility $K_{\mathrm{S}}^{\mathrm{E}}$, deviation in ultrasonic velocity u^D, viscosity deviation Δη, deviation in Gibbs energies of activation for viscous flow g(x), and excess NMR chemical shift δ^E have also been estimated and analyzed. Results show that the interaction between unlike molecules takes place through hydroxyl groups of isomeric butanediol and >CO group of N,N-dimethylformamide. Excellent correlation between thermodynamic and spectroscopic measurements is observed.     

An efficient method for the calculation of generalized overlap amplitudes for core photoelectron shake-up spectra

Using a Gelfand-Tsetlin N-electron basis and a graphical unitary group approach, an efficient method is derived for the calculation of generalized overlap amplitudes of the formX⁽ⁿ⁾_p = < Ψ⁽ⁿ⁾)(N-1) ¦ψa_p¦ψ⁽⁰⁾ (N) >, whereψ⁽ⁿ⁾(N-1) and ψ⁽⁰⁾(N) denote complete active space wavefunctions and p is a core orbital index. Using this method the computational effort to obtain Xⁿ_p is negligible compared to the wavefunction optimization.     

Theory of dynamic light scattering by polymers and gels

It is shown under very general conditions that the intermediate scattering function for the generalized Rouse—Zimm model always takes the simple form G(K, t) α exp[?K²(k_BT/f)t], when the scattering vector K becomes sufficiently large. (Here k_B is Boltzmann's constant, T is the absolute temperature and f is the individual bead friction factor.) A microscopic formulation for the bulk modulus and friction factor density of a gel network is incorporated into the viscoelastic continuum model of Tanaka et al. The resulting expression for the apparent long-wavelength diffusion coefficient of the gel is D_G = (k_BT/f)2(1 - 2/Φ), where Φ is the network functionality.     

478—Theory of Brdička current and the dependence of the current on cobalt ion concentration

An equation of Brdi?ka current and its experimental verification are presented, in which Brdi?ka current is expressed by a function of the surface concentration of protein, the bulk concentration of cobalt ion and two parameters, n_ck_c and k_f/k_d, characterizing the protein-zero-valent cobalt complex which is to catalize the hydrogen evolution, where n_c is the total number of sites on which the complex can be formed in a protein molecule, and k_c and k_d are the (average) constants representing the intrinsic catalytic activity and the lifetime respectively, of the complex.     

Distribution of reaction products (theory). XI. H + F2

The availability for the first time of detailed rate constants k(V′, R′, T′) (where V′, R′ and T′ are product vibrational, rotational and translational excitation) for the highly exothermic reaction H + F₂ → HF(V′, R′) + F has prompted the 3D classical-trajectory study reported here. The potential-energy surface is found to be predominantly repulsive ($\text{A}$_⊥ ≈ 42%, R_⊥ ≈ 58%) corresponding to the rather low fractional conversion of reaction energy into vibration ((f′V) = 0.58 from experiment, and 0.56 from theory). In the homologous series of reactions H + X₂ (X  F, Cl, Br, I) the percentage of repulsive energy-release decreases for X  Cl, Br, I, but increases from X  F to Cl. It is shown that this cannot be due to charge in mass-combination, but can plausibly be explained by the anomolously short range of interaction between the separating X atoms in the case X  F. It is predicted that the more-forward scattered HF will be more rotationally excited. The form of the cross section function S_r(T) (where T is reagent translation) is analysed. In accordance with the expectation for a strongly exothermic reaction, it is found that S_r(T) rises more steeply than S_r(V) (where V is reagent vibrational energy). The effect on the product energy distribution conforms qualitatively to the “adiabatic” behaviour noted in previous work: ΔT → ΔT′ + ΔR′; ΔV → ΔV′. The explanation is to be found in reaction through more-compressed or more-extended intermediate configurations than are characteristic of room temperature reaction. We note the existence of an amplification effect: (ΔT′ + ΔR′)/ΔT ≈ 2, and ΔV′/ΔV ≈ 2.