Linearization of second-order reaction data

Reaction data described by the second-order growth function A(t) = A_∞(αt) (1 + αt)^?1, where A_∞ is the ultimate value of the product concentration A(t), can be linearized by plotting a suitable function F(t) against the time (t). The slope of the straight line obtained is (2α), where α is the product of the rate constant (k₂) and the initial concentration of either reactant, with the result that k₂ can be determined without knowledge of A?. Optimal determination of the parameter α requires that data taking be limited to the interval 0 ≤ t ≤ T, where (αT) is approximately 4.0. Numerical data derived from an experiment on the exchange of lead by zinc ions in the enzyme carbonic anhydrase are analyzed to illustrate the method. The effects of small errors in the initial concentrations and of small deviations from second-order kinetics are briefly discussed.     

Very low-pressure pyrolysis. VIII. The decomposition of Di-t-amyl peroxide

The very low-pressure pyrolysis (VLPP) technique has been applied to the pyrolysis of di-t-amyl peroxide (DTAP) over the temperature range 523-633°K. VLPP yields a low-pressure rate constant, k_uni The conversion of k_uni to k_∞ which must be made to calculate the Arrhenius parameters, is accomplished via the RRKM theory. The transition state model used in the RRKM calculations was based on a transition state model which accurately reproduced the VLPP data for di-t-butyl peroxide for which the Arrhenius parameters are well known. For the decomposition of DTAP it was found that log k_∞(300°K) = 15.8 - 36.4/θ, where θ = 2.303RT, in kcal/mole, and the units of k_∞, are sec^?1.     

Time-domain dielectric relaxation of poly(methyl methacrylate) and nitrile rubber

The time-domain dielectric response (after-effect) of poly(methyl methacrylate) (PMMA) and nitrile butadiene rubber (NBR) to a voltage step (100 V) was measured at varying temperatures. From the variation of the sample capacitanceC with time, we determined the ratioF _d/C, withF _d=(dC/dlnt)_max and C denoting the difference between the initial and the extrapolated equilibrium capacitance values. For PMMA around room temperature (RT) this ratio assumed values similar to those reported for mechanical stress relaxation. With NBR, such values were observed only at temperatures significantly below RT. A modified Kohlrausch-Williams-Watts (stretched exponential) function provided a good fit to the measuredC(t) data.     

Induced helical structure of nematics in a magnetic field

Abstract

Nematics MBBA, EBBA, PBBA, BBBA, 5CB, 8OCB and PCH5 doped with chiral 2-(4′-phenylbenzylidene)-p-menthan-3-one are studied. A numerical solution in terms of the Landau-de Gennes theory is obtained to describe the experimental temperature dependence of P/P ₀, where P ₀ corresponds to P in zero magnetic field. The angle of tilt θ from the plane perpendicular to the helical axis is evaluated and the domain wall energy in a constant magnetic field analysed. To take into account the helical structure deformation, the helicoidal order parameter G is defined, so that G = 0 in the N phase and G = 1 with d?/dz = const. and θ = 0 in the N* phase. The relaxation of the helical structure to the equilibrium state (N* → N) is shown to be determined by the domain wall energy with the magnetic field H ≠ 0.     

Thermodynamic properties of normal and deuterated cyclopropenes

The specific heat, entropy, enthalpy, and Gibbs free energy of cyclopropene-d₀, cyclopropene-1-d₁, cyclopropene-3-d₁, cyclopropene-1,2-d₂, cyclopropene-3,3-d₂, cyclopropene-1,3,3-d₃, and cyclopropene-d₄ have been calculated for the temperature range 100–1500 K using the rigid-rotor and harmonic oscillator model. The standard enthalpy and Gibbs free energy of formation of cyclopropene-d₀ have also been evaluated for the same temperature range using the experimental standard enthalpy of formation at 298.15 K.     

Electron transfer reactions between the superoxide ion and quinones

The electron transfer reactions of the superoxide ion with benzoquinone, trimethylbenzoquinone, and menadione in dimethylformamide were studied. A procedure of the determination of the relative rate constants of these reactions was developed; the reaction of O? ₂ with butyl bromide was chosen as a standard one. The relative rate constants measured at 20,°, 35°, and 50°C were slightly dependent on the quinone structure. The relationship between the free energy ΔF*of the electron transfer reactions and the standard free energy ΔF^o was discussed. This relationship is proposed as ΔF* = αΔF^o + β, where the proportionality coefficient α is equal to 0.04–0.11 for exothermal reactions and to 0.90–0.96 for endothermal reactions.     

Synthesis and thermal analysis of linear triblock copolymers based on methacrylate ester

Two linear triblock copolymers poly(t-butyl methacrylate-b-2-hydroxyl ethyl methacrylate-b-N,N-dimethylaminoethyl methacrylate) (PtBMA₉₇-b-PHEMA₁₈-b-PDMAEMA₉₈) and poly(t-butyl methacrylate-b-glycidyl methacrylate-b-styrene) (PtBMA₁₃₇-b-PGMA₂₃-b-PSt₁₅₆) were controlled synthesized with living RAFT polymerization technique under the chain transfer of cumyl dithiobenzoate. The results of FT-IR spectra illustrate that the characteristic groups of copolymer fit well with the result of ¹H-NMR, which successfully determines the corresponding molecular structure of triblock copolymers. The thermal stability of PtBMA-b-PGMA-b-PSt and PtBMA-b-PHEMA-b-PDMAEMA was also complementarily explained by the activation energy of thermal decomposition from Friedman differential method and Ozawa–Flynn–Wall integral method. The results show that the degradation energy of the former copolymer was much higher than that of the latter copolymer, because the aromatic groups were introduced into the polymer segments of the former copolymer during the RAFT polymerization process, and the other reason is the oxirane rings are typically reactive which they occurred intermolecular crosslinking reaction during the thermal decomposition.     

Gravimetric determination of the diffusion characteristics of polymers using small specimens

An investigation has been undertaken of the factors controlling the rate of ingress of water into relatively small epoxy specimens. The application of a three-dimensional diffusion model, fully acknowledging that the specimen geometry controls the rate of ingress, has successfully resolved the problems of determining the diffusion characteristics—the diffusion coefficient D and the uptake M_∞ corresponding to saturation—and making theoretical predictions of the uptake M_t by small specimens. On the theoretical front, simulations have been carried out to demonstrate that (1) theoretical predictions require two equations to be used to obtain correct relative uptake M_t/M_∞ values for short and long exposure times; (2) a cube of the side h is saturated faster than an infinite slab of the thickness h, and (3) determination of the D value by applying the model derived for an infinite slab to specimens of finite dimensions results in an apparent value that may grossly exceed the true diffusion coefficient. On the experimental front, suggestions are made regarding (4) elimination of a systematic error that might be introduced by single weighing of a specimen prior exposure, (5) determination of the product M_∞ D^1/2 from the gravimetry data for short exposure times, and (6) splitting this product into absolute values D and M_∞ by means of a minimization procedure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42:2122–2128, 2004     

A principle to correlate extreme values of excess thermodynamic functions with partial molar quantities

Excess thermodynamic properties are widely used quantitatively for fluids. It was found that at constant temperature and pressure a molar excess quantity of a mutually miscible binary mixture at the extreme points equals the excess partial molar quantities of the two components, i.e.F ^E ₁=F ^E ₂=F ^E _m, forming a triple cross point. The relationship is hold for properties such as enthalpy, entropy, Gibbs free energy, and volume, and is applicable for excess functions with multi extreme points. Solutions at extreme points can be referred to as special mixtures. Particularly for a special mixture of Gibbs free energy, activity coefficients of the two components are identical.     

Effect of Thallium Ions on Anodic Dissolution of Gold in Alkali–Cyanide Electrolytes at Potentials More Positive Than the NHE Potential

The gold dissolution rate iin solutions containing 0.1 M KOH, 0.1 M KCN, and 2.5 × 10^–7to 1.5 × 10^–5M TlNO₃is studied as a function of potential Eof the electrode whose surface is renewed prior to each experiment, the TlNO₃concentration c, and the time tof the electrode contact with solution. At cexceeding 0.5 × 10^–5M and t 0, the rate is 1.5–2 times that at c= 0. Initial portions of ivs. tcurves in the absence and presence of TlNO₃coincide only at cbelow 10^–6M. Potentiostatic and potentiodynamic measurements show that, at positive E, only small coverages of the electrode surface with thallium are obtained, which make no impact on iat E< 0 and heavily increase it at 0 < E< 0.3 V. The discovered effects are attributed to the formation, during the adsorption of oxidized thallium forms, of dipoles comprising thallium adions and gold atoms. Presumably, the dipoles face the gold with their negative ends and make the potential of zero free charge more negative.     

Effect of molecular weight on the growth rates of low melting spherulites of trans-1,4-polyisoprene

Growth rates of G of low-melting spherulites in fractions of trans-1,4-polyisoprene have been measured. The data were analyzed by use of an equation, ln G = ln G₀ ? ΔF^*/RT_c, valid at temperatures close to the equilibrium melting point. Plots of ln G against a function of the critical free energy of nucleation ΔF^* result in a family of straight lines having a common intercept, ln G₀, which is independent of molecular weight. The slope of these lines is a measure of the interfacial free energy of the crystallites and increases with the molecular weight, reflecting increasing irregularity in the structure of the semicrystalline mass. Comparison of growth rates of low-melting and high-melting trans-1,4-polyisoprene indicates that G₀ does not, to a first approximation, depend on the nature of the crystals growing from the melt. The temperature at which spherulites of the two crystalline forms grow at equal rates has been calculated.     

Ion Selective Electrode Determination of Free Versus Total Fluoride Ion in Simple and Fluoroligand Coordinated Hexafluoropnictate (PnF<Subscript>6</Subscript><Superscript>−</Superscript>, Pn = P,As, Sb,Bi) Salts

Interpretation of the results of determinations of free fluoride (F_f⁻) and total fluoride (F_t⁻) obtained with fluoride ISE while conducting elemental chemical analysis of bulk material of newly synthesized inorganic fluoride compounds is of crucial importance for the purpose of determination of purity and stoichiometry of these compounds. Knowledge of the properties and behavior of these compounds in aqueous media is therefore essential. Observations are presented on the determinations of the amounts of F_t⁻ and F_f⁻ in fluorinated compounds, in the particular hexafluoropnictate salts (PnF₆⁻, Pn = P, As, Sb, Bi) as found in aqueous media and in some compounds with XeF₂, AsF₃ ligands. A critical look at the determined amounts of F_f⁻, F_t⁻and calculated amounts of bound fluoride (F_b⁻) is provided.     

Stress-optical behavior of poly(cis/trans-1, 4-cyclohexane dimethanol-alt-formaldehyde) (PCDO) networks

Two samples of poly(cis/trans-1,4-cyclohexane dimethanol-alt-formaldehyde), having fractions of trans configuration of cyclohexylene rings F_t = 0.1 and 0.7, were synthesized by polycondensation of the appropriate mixtures of glycols with paraformaldehyde. These two samples were crosslinked by a chemical reaction using 2,4-bis(p-isocyanatebenzyl) phenylisocyanate as the crosslinking agent. The stress-optical behavior of the resulting networks was studied at several temperatures in the range 10–80°C. The values of the optical configuration parameter Δα were 9.9 and 7.2 in units of 10^?24 cm³ for F_t = 0.7 and 0.1, respectively. The temperature coefficient of this quantity was roughly zero. Theoretical analysis, performed using the rotational isomeric state model, proved that the only parameters that have an appreciable effect on the calculated values of Δα are those concerning the cyclohexane ring (i.e., F_t and the optical parameter Γ_CC = Δα_CC ? 2Δα_CH). Conformational energies, geometrical parameters, and contributions to the optical anisotropies from the oxymethylene oxide have no noticeable effect on the value of Δα calculated for the polymer. In fact, values of Δα calculated for the polymer at F_t = 0 and 1 are very close to those obtained, respectively, for cis and trans cyclohexane dimethylene. The theoretical values of Δα are roughly one order of magnitude lower than the experimental results; however, the theory reproduces satisfactorily both the variation of Δα with F_t and its temperature coefficient.     

Kinetics and mechanism of gold dissolution in thiourea solutions: Effect of sulfide ions

Chronoamperograms for gold in solutions containing 0.1 M thiourea, 0.5 M H₂SO₄, and catalytically active sulfide ions at the concentration c ₁ from 1 × 10^?5 to 4 × 10^?5 M are obtained at different potentials with the aid of an automated setup intended for renewing the electrode surface directly in the solution by cutting off a thin surface layer of the metal. It is shown that the results of measurements of the current practically coincide at a constant value of the product c ₁ t, where t is the time period elapsed after the renewal of the electrode surface. Such a coincidence testifies to a diffusion nature of processes that hamper accumulation of sulfide ions at the gold surface. This fact permitted the use of a procedure developed previously for the calculation of polarization curves at constant values of surface coverage θ by catalytically active ions. At θ = const, the voltammetric curves for gold in sulfide-containing thiourea solutions are shown to correspond to the Tafel equation. With the surface coverage increasing, the effective values of the exchange current i ₀, transfer coefficient α, and anodic reaction order with respect to thiourea P _a increase from the values i }~ 10^?5 A cm^?2, α }~ 0.12, and P _a = 0.2, which are characteristic of pure solutions, to 2 × 10^?4 A cm^?2, α }~ 0.5, and P _a = 1.1 (at θ }~ 0.5). An interpretation to the established regularities is given.     

ACS symposium

The SCF potential surface of the ground state for NO₂ was calculated by using program JAMOL 3. The McLean–Loew–Berkowitz CGTO 's were used as basis functions. One of the two N? O distance R is fixed to 2.25 a.u. and the other one r and the ONO angle θ are varied from 2.25 to 5.0 a.u. and from 0° to 180°, respectively. The potential surface has the minimum around r = 2.50 a.u. and θ = 120°, where the energy is found to be ?203.954 a.u.     

Unperturbed chain dimensions of isotactic polypropylene in theta solvents

The unperturbed mean-square end-to-end distance 〈R₀²〉 and its temperature variation d In 〈R₀²〉/dT for isotactic polypropylene have been estimated from intrinsic viscosity data in three theta solvents, i.e., diphenyl, diphenyl ether, and dibenzyl ether, measured at their θ temperatures as determined by precipitation temperature measurements. The characteristic ratios, 〈R₀²〉/nl², where n is the number of bonds of length l in the main chain, evaluated by assuming Φ = 2.87 × 10²¹, are 5.80 in diphenyl (at θ = 125.1°C.), 5.41 in diphenyl ether (at θ = 142.8°C.), and 4.56 in dibenzyl ether (at θ = 183.2°C.). These values lead to the temperature coefficient d In 〈R₀²〉/dT = ?4.09 × 10^?3 deg.^?1 Results are compared with the data previously reported on polyethylene.     

Species formed in the potentiometric titration of fluoride with thorium or lanthanum nitrate and functions suitable for the evaluation of the equivalence points

Calculations by means of SILLÉN's HALTAFALL program have been performed on experimental curves by LINGANE for the potentiometric titration of fluoride with thorium and lanthanum in different media. After adjusting the stability constants for some of the main species formed during the titration a good fit was obtained between the experimental data and the calculated titration curves. In the cases where the solution was buffered with acetate it was necessary to consider the formation of mixed fluoride-acetate complexes. Suitable functions for the evaluation of the equivalence point could be derived from the calculations. If the functions: F₁=(v₀+v)[F^-] and F₃=(v₀+v)[F^-]^-3 are used before and after the equivalence point, respectively, it ought to be possible to determine fluoride very accurately by titration with lanthanum nitrate in an unbuffered solution. A value proportional to [F^-] is obtained from 10 exp (—EF/RT In 10), the Nernst e.m.f. equation.     

Diffusion of Organic Vapors in Materials for Gas Sensing Application

Mass-variation measurements were carried out on carbon black (CB)-poly(vinyl chloride) (PVC) composite film with 40% by weight of di(2-ethylhexyl)-phthalate (DOP), cast on resonant piezo-layer (RPL) elements of lead zirconat titanate (PZT). Even if anomalous diffusion is predicted by fitting the data with M_t/M_∞=kt^α, the fractional uptake M_t/M_∞ is linear with the square root of the time up to M_t/M_∞=0.6, suggesting Fickian behavour. The anomalous values of α are probably due to experimental time lag. A dependence of the diffusion on the morphology of the material and the penetrant shape and flexibility has been found.     

Possible smectic A ordering in a droplet of 4-n-octyloxybenzoic acid liquid crystal

Abstract

Our microtextural as well as depolarized light scattering analyses of 4-n-octyloxybenzoic acid liquid crystal droplets provide evidence for a possible smectic A ordering induced by the free surface. This appears near the bulk smectic C-nematic transition at T _SCN. A simple mean field analysis, based on a Landau-de Gennes-Benguigui free energy functional with an additional surface parameter K _s, allows, in principle, the possibility for a smectic A surface phase at temperatures slightly above T _SCN.     

Some remarks on the perturbation and variation–perturbation calculations of the free energy for quantum systems

A generalization of the Gibbs–Bogoliubov inequality F ? F₀ + 〈H ? H₀〉₀ for the free energy F is studied which leads to a variation principle for this quantity that may be of importance in certain computational applications to quantum systems. This approach is coupled with a study of the perturbation expansion of the free energy for a canonical ensemble with H = H₀ + λV in the general case when H₀ and V do not commute. The second- and high-order derivatives of the free energy with respect to the perturbation parameter λ are calculated. From the second-order term is finally obtained a second-order correction to the previous variational minimum for the free energy.