Interpretation of differences in temperature and pressure dependences of density and concentration fluctuations in amorphous poly(phenylmethyl siloxane)

Differences in the temperature and pressure dependences of the relaxation times of a slow diffusional process and the α structural relaxation pose an interesting problem. This feature, observed by dynamic light scattering in amorphous poly(phenylmethyl siloxane), is related to another basic feature of lack of thermorheological simplicity discovered by Plazek in polystyrene, poly(vinyl acetate), and amorphous polypropylene. A quantitative explanation based on the predictions of a general coupling theory of relaxations has been found. The coupling theory also predicts the Kohlrausch fractional exponential time correlation function exp[?(tτ^*)^1?n] at long times, as observed by photon correlation spectroscopy, and crossover to an exponential time dependence exp–(t/τ₀) at short times, as frequently assumed in Brillouin scattering. An additional relation between τ^* and τ₀ predicted by the theory is confirmed also by the experimental data.     

Slowing down of oxygen migration in the processes of radical oxidation and of phenanthrene phosphorescence quenching in methanol glasses at 90 K

The hydroxymethyl radical oxidation kinetics follows the second-order equation with a time-dependent rate constant, K(t). The annealing effect is described by way of dividing K(t) into two factors, one of them depending on the preliminary annealing time (τ): K(t) = K₁(t + τ)K₂(t). The time dependence of both factors is fairly well approximated by the power functions: K₁(t + τ) ≈ (t + τ)^−0.18 and K₂(t ≈ t^−0.26. The oxygen quenching of phenanthrene phosphorescence follows an exchange mechanism, with the static conditions setting in at 77 K. At 90 K oxygen diffusion adds to the quenching efficiency. The time of oxygen jumps (τ_j) and its time dependence under the matrix annealing at 90 K are determined by comparing the theoretical 1/τ_j dependence of the quenching volume with experiment. The 1/τ_j(τ) is well described by the power function τ^{−0.18 ± 0.02)}. The annealing time functions of the oxidation rate constant and of the inverse jumping time are similar. The oxidation rate constant and the diffusion constant coincide in the order of magnitude. Consequently, the slowing down of oxygen migration contributes essentially to the time dependence of the rate constant.     

Thermal relaxation of poled non-linear optical sidechain polymers: A new,semi-empirical model

Electro-Optic relaxation of a poled, Non-Linear Optical sidechain polymer with T_g 140°C, containing 4-dimethylamino-4′-nitrostilbene (“DANS”) in the sidechains, has been studied at 120°C with and without annealing at the same temperature. The time-dependence of the decaying EO coefficients r(t) shows a strong departure from the classical single-exponential Debye model, especially in the unannealed samples. This departure is attributed to physical ageing, slowing down the orientational relaxation of the sidechains. The Debye model with r(t)-r(0). exp -t/τ] is modified semi-empirically by introducing a time-dependent characteristic Debye relaxation time τ(t). Of several trial expressions, one is selected which fits the relaxation data. This is τ(τ)-τ_i+C.t^b     

On the Evaluation of Boys Functions Using Downward Recursion Relation

A new, simple, and efficient technique is presented for the accurate evaluation of the Boys functions F _m (x) (BFs) with integer and noninteger values of m appearing for the calculation of multicenter multielectron molecular integrals in a mixed Gaussian and plane-wave basis set. The extensive test calculations show that the proposed in this work algorithm is the most efficient in practical computations.     

Evaluation of the Boys Function using Analytical Relations

The analytical relations for Boys function F _m (x) are presented. These relations are useful in the fast and more accurate calculations of multicenter molecular integrals over Gaussian type orbitals (GTOs). The formulas obtained are numerically stable for all values of m and x.     

The multi-centre integrals of derivative,spherical GTOs

The multi-centre integrals of the orbital system ⁿ Y _lm () exp (–r ²) are evaluated using the Talmi transformation of nuclear shell theory. The integrals are simpler than those of the systems r ²ⁿ Y lm(r) exp (–r ²), x ^l y ^m z ⁿ exp (–r ²), (/x) ^l (/y) ^m (/z) ⁿ exp (–r ²) and the spherical oscillator functions. The integral types investigated are: overlap, electric dipole transition (momentum operator), kinetic energy, three-centre nuclear attraction, four-centre electronic repulsion, three-centre spin-orbit coupling, and magnetic dipole transition (three-centre integrals of the angular momentum operator).     

Interface microstructure and diffusion kinetics in diffusion bonded Mg/Al joint

The interface microstructure, formation of diffusion bonded joint and regulation of atom diffusion were studied by means of scanning electron microscope (SEM), energy dispersion spectroscopy (EDS) and electron probe microanalyser (EPMA). The experimental results indicated that an obvious interfacial transition zone was formed between Mg and Al, and there are three intermetallic layers Mg₁₇Al₁₂, MgAl and Mg₂Al₃ in this zone. Diffusion activation energy of Mg and Al in the above layers was lower than that in the Mg and Al base metals. The thickness (x) of each layer can be expressed as x ² = 4.14exp(−28780/RT)(t−t ₀), x ² = 31.4exp(−25550/RT)(t−t ₀) and x ² = 0.6exp(−22600/RT)(t−t ₀) corresponding to Mg₁₇Al₁₂, MgAl and Mg₂Al₃ with heating temperature (T) and holding time (t).     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

The use of chebyshev polynomials orthogonal on a finite arbitrary system of points for interpolating changes in nematic-isotropic liquid phase transition temperatures in homologous series

Chebyshev polynomials Ψ _q (x) orthogonal on a finite arbitrary system of points x _i (i = 1−N) are used to interpolate changes in nematic-isotropic liquid phase transition temperatures t _c(x) in homologous series of liquid crystals (x = 1/n, where n is the number of the homologue). The expansion of the t _c(x) function into a series in Ψ _q (x) polynomials was found to be very effective. Already at q ≤ 3, this series describes the known types of the t _c(x) dependences with high accuracy and very small root-mean-square deviations for mesogenic molecules of various chemical structures and dimensions. The dependence of the limiting t _l = t _c(0) value on the form of X-shaped molecules and linear dimensions of N-mers with N rigid aromatic fragments linked with each other by flexible spacer chains was studied.

     

Influence of Substance on the Equilibrium Translation Rate for the Isothermal and Isobaric Chemical Reactions of Ideal gases

To increase inert substance i will make the equilibrium translation rate α _j of reactant j decrease if ∑ _i ν _i < 0 or increase if ∑ _i ν _i > 0. When or , to increase non-inert substance i will make α _j increase if i is reactant (i ≠ j) or decrease if i is resultant. When has maximum if i is reactant (i≠ j) or minimum if i is resultant. If i is reactant, (x _r ⁰ is “optimum proportion” of reactant)     

Interstate coupling and dynamics of excited singlet states of isolated diphenylbutadiene

In this paper, we report on absolute fluorescence quantum yields from photoselected vibrational states of jet-cooled 1,4-diphenylbutadiene for excess vibrational energies, E_v = 0−7500 cm⁻¹, above the apparent electronic origin of the S₁(2A_g) state. The pure radiative lifetimes, τ_r, of the strongly scrambled S₂(1B_u)—S₁(2A_g) molecular eigenstates (E_v = 1050−1800 cm⁻¹) show a marked dilution effect, (τ_r/τ_r(S₂) ≈ 40), being practically identical with the τ_r values from the S₁(2A_g) manifold (E_v = 0–900 cm⁻¹), which is affected by near-resonant vibronic coupling to S₂(1B_u) and exhibiting the dynamic manifestations of the intermediate level structure. Isomerization rates in the isolated molecule, which do not exhibit vibrational mode selectivity, were recorded over the energy range 0–6600 cm⁻¹ above the threshold.     

Harmonic oscillations in a polymerization

A simple radical polymerization is proposed in this paper, with step‐by‐step chain growth (R_i + M → R_i+1), and termination by transfer to a third body (R_i + S → polymer) such as the solvent. It is assumed that, for a certain critical degree of polymerization n, the propagator R_n reacts with substrate H to produce a deactivator (V) of the first propagator (H + R_n → R_n + V; V + R₁ → P₁) R₁. Assuming that monomer, M, and precursor concentrations are constant, and assuming that the deactivator reaches fast a steady state, the resulting kinetic equations are formally linear, but they admit, perturbations r_j(t) of the steady‐state concentrations of the propagators R₁, R₂, …, R_n, which are periodic functions of time. Even more, they can be purely sinusoidal functions (which have been called “harmonic,” in analogy to the solutions of the well‐known classical harmonic oscillator) with phase shift between perturbations r_j(t) = R_j? (R_j)₀ and r_j+1(t) = R_j+1 ? (R_j+1)₀. Based on these periodic solutions and aiming to a model as simple as possible, a theoretical analysis is made, resulting in that the minimum value for n would be n = 3. Of course, these harmonic oscillations “driven by trimer” are equally found in the group of all the remaining propagators with polymerization degree higher than 3 (variable Y = ∑ R_j). © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 507–511, 2009     

A detailed chemical kinetic model for high temperature ethanol oxidation

A detailed chemical kinetic model for ethanol oxidation has been developed and validated against a variety of experimental data sets. Laminar flame speed data (obtained from a constant volume bomb and counterflow twin‐flame), ignition delay data behind a reflected shock wave, and ethanol oxidation product profiles from a jet‐stirred and turbulent flow reactor were used in this computational study. Good agreement was found in modeling of the data sets obtained from the five different experimental systems. The computational results show that high temperature ethanol oxidation exhibits strong sensitivity to the fall‐off kinetics of ethanol decomposition, branching ratio selection for C₂H₅OH + OH ↔ Products, and reactions involving the hydroperoxyl (HO₂) radical. The multichanneled ethanol decomposition process is analyzed by RRKM/Master Equation theory, and the results are compared with those obtained from earlier studies. The ten‐parameter Troe form is used to define the C₂H₅OH(+M) ↔ CH₃ + CH₂OH(+M) rate expression as k^∞ = 5.94E23 T^−1.68 exp(−45880 K/T) (s⁻¹) k^o = 2.88E85 T^−18.9 exp(−55317 K/T) (cm³/mol/sec) F_cent = 0.5 exp(−T/200 K) + 0.5 exp(−T/890 K) + exp(−4600 K/T) and the C₂H₅OH(+M) ↔ C₂H₄ + H₂O(+M) rate expression as k^∞ = 2.79E13 T^0.09 exp(−33284 K/T) (s⁻¹) k^o = 2.57E83 T^−18.85 exp(−43509 K/T) (cm³/mol/sec) F _cent = 0.3 exp(−T/350 K) + 0.7 exp(−T/800 K) + exp(−3800 K/T) with an applied energy transfer per collision value of <ΔE_down> = 500 cm⁻¹. An empirical branching ratio estimation procedure is presented which determines the temperature dependent branching ratios of the three distinct sites of hydrogen abstraction from ethanol. The calculated branching ratios for C₂H₅OH + OH, C₂H₅OH + O, C₂H₅OH + H, and C₂H₅OH + CH₃ are compared to experimental data. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 183–220, 1999     

Coordination formulation of tetrahedrally close packed structures: An addendum to the observations of Yarmolyuk and Kripyakevich

Ya. P. Yarmolyuk and P. I. Kripyakevich (Kristallographiya 19, 539 (1974)) showed that all tetrahedrally close packed (t.c.p.) structures have coordination formulae P_pQ_qR_rX_x → (PX₂)_i(Q₂R₂X₃)_j (R₃X)_k, where P, Q, R, and X represent coordination numbers (CN) 16, 15, 14, and 12 polyhedra respectively: p, q, r, and x indicate the numbers of such polyhedra in the unit cells of t.c.p. structures and i, j, and k are positive integers. We propose and demonstrate a limitation to the above formulation: if i ≥ 1 and k ≥ 1, then j ≥ 1 (or if both p> 0 and r> 0, then q> 0). We give reasons for this and discuss the Aufbauprinzip of t.c.p. structures and the results of C. B. Shoemaker and D. P. Shoemaker (Acta Crystallogr. B 42, 3 (1986)).     

Stereo‐dynamics of the F + HCl → HF + Cl reaction

We present a quasi‐classical trajectory (QCT) study on product polarization for the reaction F(²P) + HCl(v = 0, j = 0) → HF + Cl(²P) on a recently computed 1² A′ ground‐state surface reported by Deskevich et al. J Chem Phys, 2006, 124, 224303. Four polarization dependent generalized differential cross‐sections (2π/σ)(dσ₀₀/dω_t), (2π/σ)(dσ₂₀/dω_t), (2π/σ)(dσ₂₂₊/dω_t), and (2π/σ)(dσ_21?/dω_t) were calculated in the center‐of‐mass frame at four different collision energies. The obtained P(θ_r), P(?_r), and P(θ_r, ?_r), which denote respectively the distribution of angles between k and j′, the distribution of dihedral angle denoting k‐k′‐j′ correlation and the angular distribution of product rotational vectors in the form of polar plots, indicate that the degree of rotational alignment of the product HF molecule is strong and the degree of the rotational alignment decreases as collision energy increases. The product rotational angular momentum vector j′ is not only aligned, but also oriented along the y‐axis, and the molecular rotation of the product prefers an in‐plane reaction mechanism rather than the out‐of‐plane mechanism. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ions in Aqueous Acetic Acid Mixtures: Solvent Reorganization around Protons and Gibbs Energies of Transfer from Water

The photo-absorbing, basic sensor, 4-nitroaniline, has been used to determine theequilibrium constant for solvent reorganization around the proton in mixtures ofvarying composition of water with acetic acid. In all the mixtures used, theself-ionization of the acetic acid was suppressed. In contrast to mixtures of waterwith the related ethanol or acetone, this equilibrium is shifted more toward thewater-solvated species as the mole fraction x ₂ of the cosolvent increases. TheGibbs energy of transfer of protons from water into the mixture G ^o _t (H⁺) can bederived with the aid of this equilibrium constant for the solvent reorganization.Using G ^o _t (H⁺), G ^o _t (i) for i denoting anions and other cations can be evaluated.In comparison the G ^o _t (i) for cations have lower negative values than when eitherethanol or acetone is added to water. Correspondingly, for halide anions, thepositive G ^o _t (i) with added acetic acid are rather less than is found with eitherethanol or acetone added. The influence on the ion-solvent interaction of bothelectron withdrawing hydroxy and carbonyl groups in acetic acid may beresponsible for this. Although G ^o _t (i) for C10^– ₄ and Re0^– ₄ are also positive, both picrateions and OH^– give negative values with acetic acid added to water. With picrateions, the hydrophobic effect of the carbon ring produces stabilization in themixture relative to water. With OH^–, complete conversion to acetate anionsoccurs. As is found with other cosolvents, the contribution of the charge onacetate anion to G ^o _t (CH₃COO^–) is found to increase as x ₂ rises. The aciddissociation constant K _a for acetic acid is found to decrease slowly as x ₂ rises to0.5, followed by a rapid decrease for x ₂ greater than 0.7 where dimerization ofacetic acid occurs.     

Relaxation spectra of concentrated polystyrene solutions

The relaxation modulus G(t) and the stress decay after cessation of steady shear flow were measured on concentrated solutions of polystyrenes in diethyl phthalate. Ranges of concentration c and molecular weight M of the polymer were from 0.112 to 0.329 g/ml and from 1.23 × 10⁶ to 7.62 × 10⁶, respectively. The relaxation spectrum H(τ) as calculated from G(t) for the solution of very high M was found to be composed of two parts. One, at relatively short times, was a broad distribution (plateau zone) with height proportional to c². The second, at the long-time end, was very sensitive to concentration and gave rise to a maximum in H(τ) for very high concentrations. The behavior of H(τ) at long times was examined quantitatively by evaluating the longest relaxation time τ₁⁰ and the corresponding relaxation strength G₁⁰ from G(t) and from the stress decay function, on the assumption of a discrete distribution of relaxation times at long times. The longest relaxation time was approximately proportional to M^3.5, even at relatively low concentrations where the zero-shear viscosity was not proportional to M^3.5. The strengths of relaxation modes with the longest few relaxation times are proportional to the third power of concentration.     

Multicenter integrals over polarization potential operators

Analytic expressions for multicenter integrals over the general one‐particle operator x^n′y^l′z^m′| r |^−k(1−exp(−αr²))ⁿ(n′, m′, l′, n≥0, k>2, α>0), employing Cartesian Gaussians, are presented. While until now only P. Schwerdtfeger and H. Silberbach (Phys Rev A 1988, 37, 2834) have succeeded in finding such expressions, using a Laplace transform, we shall show that one can also get them according to the method of L. E. McMurchie and E. R. Davidson (J Comp Phys 1978, 26, 218; J Comp Phys 1981, 44, 289). ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 403–416, 1999     

Exchange energy for two closed shells generated by a bare Coulomb potential energy −<Emphasis Type="Italic">Ze</Emphasis><Superscript>2</Superscript>/<Emphasis Type="Italic">r</Emphasis> in the limit of large <Emphasis Type="Italic">Z</Emphasis>, in two dimensions

Two-dimensional (2D) inhomogeneous electron assemblies are becoming increasingly important in Condensed Matter and associated technologies. Here, therefore, we contribute to the Density Functional Theory of such 2D electronic systems by calculating, analytically, (i) the idempotent Dirac density matrix γ(r, r′) generated by two closed shells for the bare Coulomb potential −Ze ²/r and (ii) the exchange energy density e_x(r){\varepsilon_x({\bf r})} . Some progress is also possible concerning the exchange potential V _x (r), one non-local approximation being the Slater potential 2e_x(r)/n(r){2\varepsilon_x(r)/n(r)} , with n(r) the ground state electron density. However, to complete the theory of V _x (r), the functional derivative of the single-particle kinetic energy per unit area δt(s)/δn(r) is still required.     

Particle behaviour in shear and electric fields

Summary The interactions between two equal rigid conducting spheres in a Newtonian dielectric liquid in combined shear and electric fields are analyzed. The forces and torques, the translational and rotational velocities, and the resulting trajectories of the spheres are calculated for various ratios of the electric field strength to shear rate.The conditions under which the spheres can capture one another are deduced from which capture cross-sections, capture frequencies, and capture efficiencies are calculated, leading to a second order rate equation for capture at low particle concentrations.It is demonstrated that on capture the spheres should come into physical contact in a finite time. However, it is conjectured from previous experiments that dielectric breakdown is apt to occur in the interparticle gap because of the high electric field intensification; when this occurs, complications may be expected which are different in static and alternating electric fields.Closely related to the two sphere problem is the interaction of a rigid conducting sphere with a rigid conducting plane wall; this is discussed in the Addendum.

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Zusammenfassung Die Wechselwirkungen in gleichzeitig angelegten Scherströmungen und elektrischen Feldern zwischen zwei kleinen, gleiche, festen, leitenden, und in einer Newtonschen Flussigkeit schwebenden Kugeln sind untersucht werden. Die Krafte und Drehmomente, die Translations- und Rotationsgeschwindigkeiten, und die resultierenden Trajektionen der Kugeln werden für verschiedene Verhaltnisse der elektrischen Feldstärke und Schergeschwindigkeit berechnet. Entwickelt werden die Kugelanlagerungsbedingungen, wovon sich die Anlagerungsquerschnitte, die Anlagerungsgeschwindigkeiten, und die Anlagerungseffektivwerte ableiten lassen; dies führt zu einer Anlagerungsgleichung zweiter Ordnung bei geringer Teilchenkonzentration. Es wird gezeigt, daß die Kugeln sich physisch berühren sollten nach Ablauf einer bestimmten (endlichen) Anlagerungszeit. Jedoch, wie es sich aus vorhergehenden Experimenten ergab, dielektrischer Kurzschluß erfolgt im Kugelzwischenraum auf Grund der hohen elektrischen Feldverstarkung; folgendermaBen konnen Komplikationen erwartet werden, die sich für statische Felder und Wechselfelder verschieden ausarten mussen. Die Wechselwirkung zwischen einer kleinen, festen, leitenden Kugel und einer festen, leitenden, flachen Wand ist ein Sonderfall des Zwei-Kugel-Problems; dies wird im Addendum beschrieben.

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Nomenclature a, b ^*,c, d, e, f ^*,g, b hydrodynamic force and torque coefficients - a ^* b sinb - b sphere radius - B, C; B₀, C₀; C^E trajectory constants whenf=0 (B0,C0); when 0<f< and 2 (B ₀ 0,C ₀ 0) ; whenf= and 2. - C^* orbit constant of a touching doublet - e _i particle fixed unit vectors,i=1, 2, 3, (fig. 1) - E;E ₀ local electric field strength; uniform field applied to the particle-free medium. Normal type designates scalar quantities - E ₃ ^* E _DB E/E ₀; dielectric breakdown strength of medium - f electrohydrodynamic parameter defined in [28] - f _c;f _c ^E collision frequency per unit volume; capture frequency per unit volume - f _i ^E ;f _i ^r ;f _i ^S ;f _i ^t force coefficients of a sphere near a wall due toE ₀; to rotation; to shear; to translation - f(), h() trajectory functions for f=0 defined in [1] and [2] - F _i;F _i ⁰ electric force coefficients (i =1 to 10) defined in [12] and [13] when spheres have potential Vj; when Vj=0. - F ^E ,F ^r ,F ^S ,F ^t forces acting on a sphere near a plane wall - F _i ^E (j) electric force component alongx _i ^' on spherej =1, 2. - g _i ^r ,g _i ^S ,g _i ^t torque coefficients on a sphere near wall - G shear rate - k capture rate constant defined in [44] - K dielectric constant of medium - n integer (n 0) - n ₀;n ₂ number concentration ofsuspension of single spheres; of captured doublets - P _ij coefficients of electric induction - P(r _p ) orientation function of a rigid conducting prolate spheroid - q ₂,q ₃ defined in [66] - Q _j ;Q _j ^* net charges on spherej = 1, 2; charges induced on spherej =1, 2 if as earthed - r;r _p centre-to-centre distance between spheres; axis ratio of spheroid - S _m () functions defined in [48]m = 1,2 - S _ij pure shear (deformation) tensor components - T period of rotation of doublet about ₁ axis whenf < 1 - T ^E ;T ^E ;T ^*E contact time of two spheres; a sphere and a wall; = (2₀ KE ₀ ² / 3)T ^E - T ^r ,T ^S ,T ^t torques on a sphere near a wall - u undistrurbed flow velocity - U;U(j) particle velocity of sphere near wall; of spherej - V _j electric potential of spherej - w _j ;W ₁ ^* dimensionless electric potential of spherej; of sphere 1 whenQ ₁ =0 - x _i ;x _i ;x ₃ ^* space-fixed coordinates defined in figure 1; particle-fixed coordinates alonge 1; = (2₀ KE ₀ ² /3G) ₃ - cos²₂ - Y _n ;Z _n functions defined in [17d]; in [17e] Script symbols A(),B(),L(),D(),E() functions defined in [23] - (F); (F ^(E ); (F ^(s ) general force-torque vector; in an electric field; in shear - L _i () velocity coefficients of two spheres in an electric field,i=1 to 4