The electrodeposition of indium onto vitreous carbon from acidic chloride media

Cyclic voltammetry and potential step techniques have been used to study the electrodeposition of indium metal from 1 mol dm^?3 potassium chloride, pH 2–4.5, onto a vitreous carbon electrode. It is confirmed that the In/In³⁺ couple is fast in chloride media and the nucleation and growth of the indium phase is discussed. It is shown that instantaneous nucleation occurs at an overpotential of only a few mV and that the growth of the nuclei is three dimensional.     

A new algorithm to evaluate bielectronic integrals with 1s Slater‐type orbitals obtained by the integral transforms

This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12|34), with 1s Slater‐type orbitals. It is proved that it is possible to define, out of the expression of (12|34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) = (12|34). Therefore, F(q) may be used to calculate (12|34). It is shown that the evaluation of F(Q) turns out to be simpler than the three‐dimensional integral involved in the calculation of (12|34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10^?3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Multiple solutions of the single-reference coupled-cluster equations. I. H4 model revisited

Single-reference coupled-cluster methods corresponding to various approximate forms of the cluster operator including up to four-electron operators are applied to the simple H 4 model system with the aim of numerically studying the attainability and properties of multiple solutions of the systems of nonlinear equations for the cluster amplitudes. Various solutions have been obtained for the excited states 2¹ A₁ and 5¹ A₁. It is documented that there exist nonphysical nonstandard solutions that yield energies very close to the physical ones. A simple way of selecting the physically meaningful solutions is proposed. It is demonstrated that the attainability of nonstandard solutions describing a state of H4 within the framework of a given SE -CC method strongly depends on the cluster structure of that state. © 1994 John Wiley & Sons, Inc.     

An investigation of the reliability of the Galerkin-Petrov method

It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 2¹ S and 3¹ S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.     

Gold Nanoparticles Formation via Au(III) Complex Ions Reduction with l‐Ascorbic Acid

In this paper, the kinetics and mechanism of gold nanoparticles formation during the redox reaction between [AuCl₄]− complex and l ‐ascorbic acid under different conditions were described. It was also shown that reagent concentration, chloride ions, and pH influence kinetics of nucleation and growth. To establish rate constants of these stages, the model of Finke and Watzky was applied. From Arrhenius and Eyring dependencies, the values of activation energy (22.5 kJ mol⁻¹ for the nucleation step and 30.3 kJ mol⁻¹ for the growth step), entropy (about −228 J K⁻¹ mol⁻¹ for the nucleation step and −128 J K⁻¹ mol⁻¹ for the growth step), and enthalpy (19.8 kJ mol⁻¹ for nucleation and 27.8 kJ mol⁻¹ for particles growth) were determined. It was also shown that the disproporationation reaction had influence on the rate of nanoparticles formation and may have impact on final particles morphology.     

Effect of H<Subscript>2</Subscript>SeO<Subscript>3</Subscript> on the early stages of nucleation and growth during Cu electrocrystallization in acidic medium on glassy carbon electrode

The early stages of Cu electrodeposition onto a GC electrode were investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] was 1.10⁴ to 2.10². The H₂SeO₃ solution in 0.5 M H₂SO₄ was also used. The electrochemical techniques such as cyclic voltammetry and chronoamperometry and structural investigation using ex situ AFM were applied to study the nucleation and growth of Cu onto a GC electrode. Chronoamperometric results were shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model by Scharifker and Hills. The values of number of Cu nuclei N and average nuclei radius r _av were calculated. It was shown that, in the presence of H₂SeO₃ in amounts of 0.001 to 0.005 mM, N increases and r _av decreases. At higher concentrations of the additive, the changes of these parameters with the deposition potential E _dep were shown to be somewhat more complex. The dependences of N and r _av on the concentration of H₂SeO₃ in different regions of Cu overpotentials were also revealed.     

Thermal and dielectric studies of 2,2’-dihydroxybenzophenone

Thermal and dielectric properties of 2,2’-dihydroxybenzophenone were studied in relation with the potential progress of crystal nucleation and growth below the ordinary glass transition temperature, T_gα. Differential scanning calorimetry was carried out in a range 100-350 K. The α glass transition was found to occur at T_gα=239 K. Crystallization and fusion were observed to take place when the sample was cooled down to 103 K, but not observed when cooled to 203 K. Crystal nucleation was interpreted as having happened during annealing for a short time at 103 K which is much below the T_gα. Heat capacities were measured in a range 7-350 K by an intermittent heating method with an adiabatic calorimeter. The temperature, enthalpy and entropy of fusion were determined to be 334.46 K, 20.07 kJ mol^-1 and 60.01 J K^-1mol^-1, respectively. Crystal growth was found to proceed even at 220 K below the T_gα, but no glass transition was detected below 220 K. Dielectric losses were measured in a temperature range of 100-250 K and a frequency range of 30Hz-10 kHz. β-Relaxation process was found dielectrically with the activation energy of 22.6 kJ mol^-1, and the corresponding glass transition was expected to occur at 76.9 K. It is discussed, based on the “structurally ordered clusters aggregation” model for supercooled liquids and glasses, that the β process is potentially attributed to the crystal nucleation progressing at 103 K.     

Transformed Dirac equation for the hydrogen atom,comparison with previous approaches in momentum space,and the anomalous Zeeman effect in momentum representation

The solution of a unitarily transformed Dirac equation for the hydrogenic electron in zero magnetic field is investigated here. The momentum‐space representation is adopted as a natural recourse. The spinor part of the transformed wavefunction in momentum space can be easily prescribed for a central potential. Hence, for the Coulomb potential, a pair of equations is obtained for the radial components in momentum space. It is shown that starting from these radial equations, one can recover the equations previously derived by Rubinowicz, Lévy, and Lombardi for the problem of the Dirac hydrogen atom in momentum space. This establishes equivalence among different approaches based on the momentum representation, including the current treatment. The recovery of the equations due to Rubinowicz permits the exact eigenvalues to be written down and exact expressions to be derived for the radial components of the transformed wavefunction in momentum space. A new approach is adopted to carry out a reduction to the nonrelativistic regime and the nonrelativistic limit. At first the transformed momentum‐space equation for the hydrogen atom is rewritten in terms of the hyperspherical coordinates. The zeroth‐order solutions of the new equation are recovered in the limit c → ∞ where c is the speed of light. These are manifestly separable into positive‐ and negative‐energy forms. For positive energy, these solutions have nonvanishing upper components that are two‐component spinors. The latter exactly correspond to the single‐component, nonrelativistic, momentum‐space solutions derived by Fock. It is shown that when the upper component is corrected through first order in v²/c² but the separability is still maintained for the transformed wavefunction, one retrieves the Pauli equation in momentum space. It is also shown that for a hydrogen atom placed in a uniform magnetic field, the nonvanishing momentum‐space matrix elements representing the anomalous Zeeman effect have a simple form, namely, the product of a radial integral and an angular integral. These integrals are equal to the well‐known radial and angular integrals in coordinate representation. The matrix elements can be easily evaluated. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Application of the valence-universal coupled-cluster method based on various model spaces. II. Nonstandard solutions for Be

The impact of the choices of the complete model space (CMS) and of the orbital basis set on the existence, attainability, and properties of the nonstandard solutions of the valence-universal coupled-cluster (VU-CC) methods has been studied for the case of nonlinear equations corresponding to the atomically oriented form of these methods accounting for one- and two-electron excitations (VU-CCSD/R method) and applied to the Be atom. The results for five ¹S states are discussed. In addition to the previously applied CMS defined by the orbital set (2s, 2p) and (2s, 3s), we have employed the CMSs defined by the (2s, 2p, 3s) set. For each of the CMSs several nonstandard solutions are documented. It is found that the energies of the individual states corresponding to standard and nonstandard solutions differ very little. These energies are also almost independent on the choice of CMS. On the other hand, the energies of excited states disclose a strong dependence on the radial structure of the orbital basis set. It is also demonstrated that the magnitudes of the cluster amplitudes representing a set of states depend both on the choice of the CMS and whether they correspond to the standard or nonstandard solutions. © 1996 John Wiley & Sons, Inc.     

Effect of multi-walled carbon nanotubes on crystallization behavior of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

The effect of multi-walled carbon nanotubes on the crystallization behavior of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) has been investigated. The results have shown that carbon nanotubes (CNTs) act as an effective heterogeneous nucleation agent, inducing an increase in crystallinity and crystallite sizes. Comparing with the double melting peaks in pure PHBV, there is only one peak in the melting curves of nanocomposites. The isothermal crystallization kinetics of PHBV and its nanocomposite containing 0.5% CNTs were examined based on Avrami equation, indicating that the crystallization half-time decreases while the overall crystallization rate k increases dramatically with CNTs addition. The spherulitic nucleation and growth kinetics were also discussed grounded on Lauritzen–Hoffman equation. It is found that there is a spherulitic growth rates (G) maximum within selected temperature range in our study. Also, the temperatures corresponding to G maximum shift to a high level with addition of CNTs. The parameters of the equilibrium melting temperature T_m⁰ T_m^0 , the nucleation parameter K _g , the lateral surface free energy σ, the fold surface free energy σ _e , and the work of chain folding q of PHBV and its composite containing 0.5% CNTs were all calculated. The reductions of K _g , σ _e and q values of nanocomposite are in agreement with the fact that the crystallization rate of PHBV increases greatly by addition of CNTs.     

Matrix Representation of Polymer Chain Size Distributions, 2

Analysis of the mass balance equations that describe a reaction system may be useful to provide information about its dynamics, such as the restricted set of compositions that can be achieved from a given set of initial compositions and the effect of feeding reactants to the reaction environment along the reaction course. Since these results may be important for the formulation of reaction policies, this work presents the properties of a matrix polymerization model previously developed and extended to describe transient conditions. This model is based on the definitions of two matrices: the consumption matrix ( A − Kt ), which contains information about chemical transformations among the many active polymer species in the system, and the propagation matrix Kp , which contains information about chain growth. It is shown that the set of mass balance equations that describes the dynamics of active chemical species in polymerization reactions has a stable and unique solution, which is bounded if feed rates are also bounded. It is also shown that the set of compositions that may be reached through manipulation of the feed rates is restricted and may not include all possible chemical compositions. Finally, it is shown that the obtained molecular weight distributions are special multiple time convolutions of the initiation rates.

     

Synthesis and crystallization kinetics of the novel ion exchanger Na<Subscript>4</Subscript>Ti<Subscript>4</Subscript>Si<Subscript>3</Subscript>O<Subscript>10</Subscript> for cesium removal

Thermodynamics and crystallization kinetics of the hydrothermal synthesis of Na₄Ti₄Si₃O₁₀ (NaTS) were systemically studied by both experiments and model simulation. Experimental results showed that the curve of crystallinity with time was a characteristic signmoid in the shape that indicated the crystallization of Na₄Ti₄Si₃O₁₀ was a typical spontaneous nucleation process on the laboratory scale. Crystallization of NaTS belongs to the liquid-liquid transformation mechanism and the reaction is endothermic (ΔH = 15.3 kJ/mol). A mathematic model of crystallization kinetics was developed to simulate the synthesis of NaTS. Runge-Kutta and simplex methods were adopted to solve the partial differential equations. Model results fitted well with the experimental data and showed that the synthesis process belongs to spontaneous nucleation and crystal growth. Moreover, the very small crystal growth constant (5.6·10⁻⁷) and gel dissolution constant (7.0·10⁻⁷) indicate they are the rate-limiting steps of the whole synthesis process.     

Extension of the Adaptive Huber Method for Solving Integral Equations Occurring in Electroanalysis,onto Kernel Function Representing Fractional Diffusion

Electroanalytical transient experiments performed under conditions of anomalous diffusion have recently attracted some attention. In order to enable automatic simulation of such experiments in the framework of the formalism of integral equations, the adaptive Huber method, recently elaborated by the present author, is extended onto integral transformation kernel function K(t,τ)=(t?τ)^α/2?1 (where 0<α≤1), representing fractional diffusion. The extended method is tested on a model integral equation describing cyclic voltammetry for a reversible charge transfer reaction. The performance of the method is found similar to the case of ordinary diffusion.     

Dependence of the frequency factor on the temperature: a new integral method of nonisothermal kinetic analysis

A new integral method of nonisothermal kinetic analysis has been developed with the dependence of the frequency factor on the temperature (A = A ₀ T ^m ). The new integral method is obtained from the newly proposed approximation for the general temperature integral, which is more accurate than the other existed approximations. For applications, nonisothermal thermoanalytical data obtained by theoretical simulation have been processed. The results have shown that the newly proposed integral method is an ideal solution for the evaluation of kinetic parameters from nonisothermal thermoanalytical data with the frequency factor dependent the temperature.     

氧化锌纳米线自组装定向生长动力学研究

研究了以极性高分子(如聚丙烯酰胺)长分子链作为自组装网络, 利用高分子软模板控制ZnO纳米点成核和ZnO纳米线定向生长, 从而使ZnO纳米线在半导体硅衬底上自组装生长的过程; 采用差示扫描量热法(DSC)测试了高分子络合-烧结法制备ZnO纳米线的结晶曲线, 对其结晶动力学进行了研究, 推导出结晶动力学方程为: 1－X_t＝exp(－7.475×10^－2t^1.9); 并利用热重(TG)测试结果, 通过热分解反应, 导出了反应动力学方程: dα/dT＝(3.76×10²³/Φ)e^－21340.8/T(1－α) ^2.8, 从而得到了化学反应速度随时间、浓度和温度变化的关系, 并用结果解释了实验现象.     

Electrochemical formation of a low-dimensional phase on the boundary between the LaF<Subscript>3</Subscript>:Eu<Superscript>2+</Superscript> single crystal and the metal

The kinetics of the formation of a new phase at the interface between the LaF₃:Eu²⁺ single crystal and the (Sn, Bi, or Sb) metallic electrodes was studied using potentiostatic transient measurements and voltammetry with a linear variation of voltage. A comparison of the theoretical and experimental reduced transients that define two-dimensional instantaneous nucleation on a plot of I/I _m vs. t/t _m and three-dimensional growth of the instantaneous and progressive types of nucleation on a plot of I ²/I _m² vs. t/t _m showed that the model was not fully consistent with the experiment. The dependence of the stationary current logI _A(max) of the potentiostatic transients on 1/η during the formation of the intermediate phase on the boundaries of LaF₃:Eu²⁺|Sn and LaF₃:Eu²⁺|Bi was found to be linear, which corresponds to two-dimensional nucleation and growth of the new phase.     

Model-fitting and model-free analysis of thermal decomposition of palladium acetylacetonate [Pd(acac)2]

The non-isothermal decomposition process of the powder sample of palladium acetylacetonate [Pd(acac)₂] was investigated by thermogravimetric (TG) and the X-ray diffraction (XRD) techniques. Model-free isoconversional method of Tang, applied to the investigated decomposition process, yield practically constant apparent activation energy in the range of 0.05≤α≤0.95. It was established, that the Coats-Redfern (CR) method gives several statistically equivalent reaction models, but only for the phase-boundary reaction models (R2 and R3), the calculated value of the apparent activation energy (E) is nearest to the values of E obtained by the Tang’s and Kissinger’s methods. The apparent activation energy value obtained by the IKP method (132.4 kJ mol⁻¹) displays a good agreement with the value of E obtained using the model-free analysis (130.3 kJ mol⁻¹). The artificial isokinetic relationship (aIKR) was used for the numerical reconstruction of the experimental integral model function, g(α). It was established that the numerically reconstructed experimental function follows R3 reaction model in the range of α, taken from model-free analysis. Generally, decomposition process of Pd(acac)₂ starts with initial nucleation which was characterized by rapid onset of an acceleratory reaction without presence of induction period.     

Electrochemical nucleation of lead and copper on indium-tin oxide electrodes

The nucleation process of Pb and Cu onto indium-tin oxide electrodes was studied by single potentiostatic steps using 0.1×10^–4 mol L^–1 Cu(NO₃)₂ and 2×10^–2 mol L^–1 Pb(NO₃)₂ solutions in aqueous 1.0 mol L^–1 NaNO₃. The current, I_max, and the time, t_max, corresponding to the maximum, were evaluated by 3D nucleation with a diffusion-controlled growth model for instantaneous and progressive nucleation. The non-dimensional plots of (I/I_max)² vs. t/t_max showed that Cu and Pb nucleation closely followed the response predicted for instantaneous nucleation. Other parameters, such as I vs. t^1/2 and I²_maxt_max, as well as nuclei micrographs, were analyzed, corroborating the results obtained.     

Crystallization of polydioxolan. III. Microscopy and dilatometric analysis of the crystallization kinetics

Crystallization kinetics has been studied for a polydioxolan (PDOL) sample, over a wide temperature range, by dilatometry and microscopy. The dilatometry results can be analyzed using the Avrami equation. At temperatures higher than 22°C, the crystallization data must be analyzed in two steps: the first part of the curve corresponds to PDOL with a very disordered morphology (Phase I) while the second part of the crystallization curve is related to a spherulitic morphology (Phase II). The passage from the low to the high crystallization temperature region is associated with a change in the Avrami exponent from 3 to 4. The crystal surface free-energy product σσ_e was found to be 18 × 10² erg²/cm⁴, very close to that of polyoxymethylene. The crystallization kinetics was studied by microscopy over the temperature range?18 to 35°C. Growth and nucleation rates were recorded. Two phases are found only at temperatures higher than 22°C. The appearance of Phase II is related to a decrease in the growth rate of the sample. From the growth rates, the crystal surface free-energy product σσ_e was found equal to 17 × 10² erg²/cm⁴. The detailed analysis of the crystallization of the two phases reveals a complicated process which can be divided into four different steps: (a) growth of a disordered phase, Phase I; (b) nucleation of a higher birefringence structure; (c) propagation of a high birefringence phase; and (d) spherulitic growth, Phase II. The analysis of PDOL crystallization strongly suggests the presence of a hedrite → oval → spherulite transition: the hedrite formation corresponds to step (a), the oval formation to steps (b) and (c), and the spherulite formation to step (d).