Improved approximations of the exponential integral in tempering kinetics

The exponential integral in non-isothermal kinetic equations for tempering with linear heating can be represented in the following analytical form $$\int\limits_0^T {e^{ - E/kT'} dT'} = \frac{{kT^2 /E}}{{\sqrt {1 + 4kT/E} }}e^{ - E/kT} ,$$ which is one order inkT/E?1 more accurate than two other representations recently proposed in this journal [1, 2]. A few variants of approximated forms for the exponential integral are compared with regard to the error due to the kind of approximation, which appears when activation energies are evaluated from experimental non-isothermal kinetic curves.     

Electron capture by protons from theK-shell of H and Ar

Whenever a collision takes place between charged particles, the first Born approximation for electron capture from hydrogenlike ions (Z _T ,e) by a bare nucleusZ _P , must be modified in order to account for the long-range Coulomb effects. One of the simplest ways to fulfill this requirement is provided by theT-matrix of the following form: $$T_{if}^{(1)} = \left\langle {\Phi _f exp\left\{ { - i\frac{{Z_T (Z_p - 1)}}{\upsilon } ln (\upsilon R + v \cdot R)} \right\}\left| {\frac{{Z_P }}{R} - \frac{{Z_P }}{{r_P }}} \right| exp\left\{ {i\frac{{Z_P (Z_T - 1)}}{\upsilon } ln (\upsilon R + v \cdot R)} \right\}\Phi _i } \right\rangle $$ where Φ's are the usual unperturbed channel states andZ's are the nuclear charges. In this transition amplitude, both initial and final scattering states satisfy the correct asymptotic boundary conditions in their respective channels. In the present paper, detailed computation of theK-shell cross sections is carried out for charge exchange in H⁺-H and H⁺-Ar collisions. The results are in good agreement with experimental data.     

Effects of washing conditions on the thermal decomposition behaviour of gelled UO3 microspheres

DTA, TG and DTG curves obtained in various atmospheres using different heating rates were used together with X-ray examinations to study the thermal decomposition mechanisms of two types of gelled UO₃ microspheres: ammonia-washed (UN) and hot water-washed (UH) microspheres. The kinetics of the thermal decompositions were studied. The specific reaction rate constantk _r for the decomposition of UO₃ to U₃O₈ could be expressed in terms of the activation energy and the pre-exponential factor by the expressions: $$\begin{gathered} K_r (s^{ - 1} ) = 1.277 \times 10^{18} \exp \frac{{ - 295.4}}{{RT}}for the UN spheres, \hfill \\ K_r (s^{ - 1} ) = 8.406 \times 10^{19} \exp \frac{{ - 263.2}}{{RT}}for the UH spheres. \hfill \\ \end{gathered} $$      

Temperature Dependence of the Parameter of the SIT Model for Activity Coefficients of 1:1 Electrolytes

This work analyzes the temperature dependence of the only fitting parameter of the SIT (Specific Ion Interaction Theory) model for activity coefficients. Relations based on the so-called “primitive” model for the inter-ionic potential suggest that the binary interaction parameter is proportional to the pure water density. In order to check this correlation, activity coefficients and related data are tested for twenty 1:1 electrolytes, where the necessary data are available at temperatures up to at least 523 K. A strong correlation with water density is universally observed at temperatures T > 360 K (or water densities, $ \rho_{1}^{*} $ ρ 1 ? , below 950 kg·m^?3). In accordance with expectations from theoretical considerations, at these temperatures and water densities, the SIT parameter is constant under isochoric conditions (a constant water density), and decreases with decreases of $ \rho_{1}^{*} $ ρ 1 ? . Over the whole temperature range, usually between 273 and 573 K, the temperature and water density dependence of the SIT model interaction parameters, $ \varepsilon_{\gamma } (M,X) $ ε γ ( M , X ) , where M stands for a cation and X for an anion, is well described (including data at pressures up to 100 MPa) by the following expression $ \varepsilon_{\gamma } (M,X) = b_{0} + b_{1} \rho_{1}^{*} + \frac{{b_{2} }}{T - 210} $ ε γ ( M , X ) = b 0 + b 1 ρ 1 ? + b 2 T ? 210 .     

Estimation of the critical rate of temperature rise for thermal explosion of nitrocellulose using non-isothermal DSC

The expressions to calculate the critical rate of temperature rise of thermal explosion $ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $ for energetic materials (EMs) were derived from the Semenov’s thermal explosion theory and autocatalytic reaction rate equation of nth order, C_nB, B_na, first-order, apparent empiric-order, simple first-order, A_u, apparent empiric-order of m = 0, n = 0, p = 1 and m = 0, n = 1, p = 1, using reasonable hypotheses. A method to determine the kinetic parameters in the autocatalytic-decomposing reaction rate equations and the $ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $ in EMs when autocatalytic decomposition converts into thermal explosion from data of DSC curves at different heating rate was presented. Results show that (1) under non-isothermal DSC conditions, the autocatalytic-decomposing reaction of NC (12.97 % N) can be described by the first-order autocatalytic reaction rate equation dα/dt = 10^16.00exp(?174520/RT)(1 ? α) + 10^16.00exp(?163510/RT)α(1 ? α); (2) the value of $ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $ for NC (12.97 % N) when autocatalytic decomposition converts into thermal explosion is 0.354 K s^?1.     

Asymptotics (p\rightarrow \infty ) of L_p-norms of hypergeometric orthogonal polynomials

The determination of the weighted $L_p$ norms of the real orthogonal polynomials of hypergeometric type $\left\{ y_n(x)\right\} $ is not only a very important problem per se in the theory of special functions, but also because of their recent entropic characterization and applications in quantum chemistry, quantum physics and information theory. Indeed, they essentially describe the $p$ th-order Rényi and Tsallis entropies of the numerous quantum systems whose wavefunctions are controlled by these polynomials. Moreover, for different values of $p$ , up to a constant factor, these norms characterize various fundamental and experimentally accessible quantities of many-electron systems. As well, the $L_p$ norms have been used to develop and interpret all energy components in the density-functional theory of the ground-state of atoms and molecules. The asymptotics of these quantities when $n \rightarrow \infty $ and $p>0$ have been recently calculated for Hermite polynomials, although not yet for Laguerre and Jacobi polynomials. Here, we determine the asymptotics ( $p\rightarrow \infty $ , $n$ fixed) of the weighted $L_p$ norms for general orthogonal polynomials in terms of the weight function and the coefficients of the second-order hypergeometric differential equation that they satisfy, and we apply it to the three classical families of real orthogonal polynomials. Moreover we analyse and discuss the monotonicity of this asymptotics, and we carry out a detailed numerical study of it.     

Quasi-Particle Dual Mappings on \widetilde{\mathbb{H}}_v Carrier Spaces for Dynamical Structures of S 2n -Invariant-Based, Integer-Rank Tensorial Sets: A Democratic-Recoupling S 2n -Compatible Overview of v-Auxiliary Labelling in Superboson Algebras of Uniform Multispin NMR Ensembles

The independent cardinalities of invariants (SIs) of the dual group and its (2n)-fold uniform spin ensembles are derived via S _2n -decompositional approaches. The fundamental terms arise from character theory, whereas the (2i < 2n) subsidary statistical subsets arise from arguments based on time-reversal symmetry (TRV) in the context of democratic recoupling – an approach consistent with a projective view and also with the nature of (Weyl) (I ? I)₁???() _i ???(I ? I) _n single pairwise exchange yielding TRV spin symmetry. In contrast to traditional |D ⁰(U)|((?SU(2))⁽²ⁿ⁾) formalisms, democratic sampling and recoupling now play important roles. As derived via superboson algebra, the dual tensorial properties of [A...]_(2n) uniform 2n-fold NMR spin systems are seen also as fundamental in defining aspects of quantum computing via NMR analogues. Representational aspects of (quasiparticle) pattern algebras are given for superbosons over dual projective carrier subspaces of Liouville space. Hence an independent Lie-algebraic proof is derived of the fundamental “sign” structure of superbosons acting on { $\sum_v \oplus_{\tilde\lambda}\widetilde{\mathbb{H}}_v^(\tilde\lambda)|[\tilde\lambda]$ ${\mathcal{S}}_n$ ;vaux. SU(2) × ${\mathcal{S}}_n$ } carrier subspaces. This constitutes a direct extension of earlier work [Physica A 198 (1993) 245]. The explicit SI-based tensorial v-auxiliary labels of the latter are defined via the dual action $\tilde U \times {\mathcal{P}}:\tilde {\mathbb{H}} \to \tilde {\mathbb{H}}\left\{ { \cdot \left| {\tilde U \in SU\left( 2 \right),} \right.{\mathcal{P}}\left( {\tilde \Gamma } \right) \in {\mathcal{S}}_n } \right\}$ for the dual group and [A...] _n (S _n ) identical spin ensembles involving high degeneracies. Motivation for the work arose from certain fundamental quantum questions for dual group actions on multiple invariant-based systems, themselves subject to projective-compatible, S _n democratic recoupling. to graph-based results for such specialised uniform systems. Attention is drawn to various correspondences to geometric, quasiparticle (or superboson) and Lie-algebraic concepts for these systems, as being of topical interest both to quantum physics and to computing.     

A new scaled crossover parametric equation of state for water

In the present work, the asymmetric nature of water coexistence curve has been studied by investigating a new scaled crossover parametric equation of state. To do so, the concept of complete scaling [Fisher and Orkoulas, Phys Rev Lett 696, 85 (2000)] has been applied and the critical amplitudes near and far from the critical point have been derived. Also two mixing parameters $ a_{3} $ and $ b_{2} $ in the definition of scaling fields in terms of physical fields have been obtained for water. We have shown that mixing of the complete scaling theory and parametric equation of state can explain this nature quite carefully.     

Kinetics and mechanism of oxidation of cis-diaquabis(glycinato)chromium(III) by periodate ion in aqueous solutions

The kinetics of oxidation of cis-[Cr^III(gly)₂(H₂O)₂]⁺ (gly = glycinate) by $ {\text{IO}}_{ 4}^{ - } $ has been studied in aqueous solutions. The reaction is first order in the chromium(III) complex concentration. The pseudo-first-order rate constant, k _obs, showed a small change with increasing $ \left[ {{\text{IO}}_{ 4}^{ - } } \right] $ . The pseudo-first-order rate constant, k _obs, increased with increasing pH, indicating that the hydroxo form of the chromium(III) complex is the reactive species. The reaction has been found to obey the following rate law: $ {\text{Rate}} = 2k^{\text{et}} K_{ 3} K_{ 4} \left[ {{\text{Cr}}\left( {\text{III}} \right)} \right]_{t} \left[ {{\text{IO}}_{ 4}^{ - } } \right]/\left\{ {\left[ {{\text{H}}^{ + } } \right] + K_{ 3} + K_{ 3} K_{ 4} \left[ {{\text{IO}}_{ 4}^{ - } } \right]} \right\} $ . Values of the intramolecular electron transfer constant, k ^et, the first deprotonation constant of cis-[Cr^III(gly)₂(H₂O)₂]⁺, K ₃ and the equilibrium formation constant between cis-[Cr^III(gly)₂(H₂O)(OH)] and $ {\text{IO}}_{ 4}^{ - } $ , K ₄, have been determined. An inner-sphere mechanism has been proposed for the oxidation process. The thermodynamic activation parameters of the processes involved are reported.     

Mixed Micellization and Interfacial Properties of Nonionic Surfactants with the Phenothiazine Drug Promazine Hydrochloride at 30 °C

In the present work, the micellization and adsorption behaviors of mixed systems containing an amphiphilic phenothiazine drug, promazine hydrochloride (PMZ) and nonionic surfactants in aqueous media at different mole fractions of nonionic surfactants (?? ₁) were investigated at 30?°C by surface tension measurements. The critical micelle concentrations of the mixtures fall between the values of the individual components, which indicates nonideal mixing. With Tritons the interactions are repulsive at low mole fractions. At high ?? ₁ the mixing becomes almost ideal. On the basis of regular solution theory, the micellar mole fractions of surfactants ( $X_{1}^{m}$ ) and interaction parameter (?? ^m ) were evaluated, while their interfacial mole fractions ( $X_{1}^{\sigma} $ ) and interaction parameters at the interface (?? ^?? ) were calculated using Rosen??s model. The results indicate that the surfactant??s contribution is greater than that of the drug both at the interface and in micelles. The short and rigid hydrophobic structure of the drug resists its participation in micelle formation more than in the monolayer, leading to $X_{1}^{m}<X_{1}^{\sigma}$ . Values of the surface excess (?? _max) and minimum area per head group (A _min) indicate attractive interactions. ?? _max increases and A _min decreases as the surfactant mole fraction increases.     

Volumetric Properties of the Nucleoside Thymidine in Aqueous Solution at T = 298.15 K and p = (10 to 100) MPa

Sound speeds have been measured for aqueous solutions of the nucleoside thymidine at T = 298.15 K and at the pressures p = (10, 20, 40, 60, 80, and 100) MPa. The partial molar volumes at infinite dilution, $ V_{2}^{\text{o}} $ , the partial molar isentropic compressions at infinite dilution, $ K_{S,2}^{\text{o}} $ , and the partial molar isothermal compressions at infinite dilution, $ K_{T,2}^{\text{o}} $ $ \{ K_{T,2}^{\text{o}} = - (\partial V_{2}^{\text{o}} /\partial p)_{T} \} $ , have been derived from the sound speeds at elevated pressures using methods described in our previous work. The $ V_{2}^{\text{o}} $ and $ K_{T,2}^{\text{o}} $ results were rationalized in terms of the likely interactions between thymidine and the aqueous solvent. The $ V_{2}^{\text{o}} $ results were also compared with those calculated using the revised Helgeson–Kirkham–Flowers (HKF) equation of state.     

Bounds for the Kirchhoff index via majorization techniques

Using a majorization technique that identifies the maximal and minimal vectors of a variety of subsets of ${\mathbb{R}^{n}}$ , we find upper and lower bounds for the Kirchhoff index K(G) of an arbitrary simple connected graph G that improve those existing in the literature. Specifically we show that $$K(G) \geq \frac{n}{d_{1}} \left[ \frac{1}{1+\frac{\sigma}{\sqrt{n-1}}} + \frac{(n-2)^{2}}{n-1-\frac{\sigma}{\sqrt{n-1}}}\right] ,$$ where d ₁ is the largest degree among all vertices in G, $$\sigma ^{2} = \frac{2}{n} \sum_{(i, j) \in E} \frac{1}{d_{i}d_{j}} = \left( \frac{2}{n}\right) R_{-1}(G),$$ and R _?1(G) is the general Randi? index of G for ${\alpha =-1}$ . Also we show that $$K(G) \leq \frac{n}{d_{n}}\left( \frac{n-k-2}{1-\lambda _{2}}+\frac{k}{2}+\frac{1}{\theta}\right) ,$$ where d _n is the smallest degree, ${\lambda _{2}}$ is the second eigenvalue of the transition probability of the random walk on G, $$k = \left \lfloor \frac{\lambda _{2} \left( n-1\right) +1}{\lambda _{2}+1}\right\rfloor {\rm and}\quad\theta = \lambda _{2} \left( n-k-2\right) -k+2.$$      

The role of the heteroatom (X?=?SiIV, PV, and SVI) on the reactivity of {��-[(H2O)RuIII(��-OH)2RuIII(H2O)][X n+W10O36]}(8?n)? with the O2 molecule

The mechanism of reaction of the di-Ru-substituted polyoxometalate, {??-[(H₂O)Ru^III(??-OH)₂Ru^III(H₂O)][X ⁿ⁺W₁₀O₃₆]}^(8?n)?, I_X, with O₂, i.e. I_X?+?O₂????{??-[(^·O)Ru^IV(??-OH)₂Ru^IV(O^·)][X ⁿ⁺W₁₀O₃₆]}^(8?n)??+?2H₂O, (1), was studied at the B3LYP density functional and self-consistent reaction field IEF-PCM (in aqueous solution) levels of theory. The effect of the nature of heteroatom X (where X?=?Si, P and, S) on the calculated energies and mechanism of the reaction (1) was elucidated. It was shown that the nature of X only slightly affects the reactivity of I_X with O₂, which is a 4-electron oxidation process. The overall reaction (1): (a) proceeds with moderate energy barriers for all studied X??s [the calculated rate-determining barriers are X?=?Si (18.7?kcal/mol)?<?S (20.6?kcal/mol)?<?P (27.2?kcal/mol) in water, and X?=?S (18.7?kcal/mol)?<?P (21.4?kcal/mol)?<?Si (23.1?kcal/mol) in the gas phase] and (b) is exothermic [by X?=?Si [28.7 (22.1) kcal/mol]?>?P [21.4 (9.8) kcal/mol]?>?S [12.3 (5.0) kcal/mol]. The resulting $ \left\{ {\gamma - \left[ {\left( {^{ \cdot } {\text{O}}} \right) {\text{Ru}}^{\text{IV}} \left( {\mu - {\text{OH}}} \right)_{2} {\text{Ru}}^{\text{IV}} \left( {{\text{O}}^{ \cdot } } \right)} \right]\left[ {{\text{X}}^{{{\text{n}} + }} {\text{W}}_{10} {\text{O}}_{36} } \right]} \right\}^{{\left( {8 - {\text{n}}} \right) - }} $ , VI_X, complex was found to have two Ru^IV?=?O^· units, rather than Ru^V?=?O units. The ??reverse?? reaction, i.e., water oxidation by VI_X is an endothermic process and unlikely to occur for X?=?Si and P, while it could occur for X?=?S under specific conditions. The lack of reactivity of VI_X biradical toward the water molecule leads to the formation of the stable [{Ru ₄ ^IV O₄(OH)₂(H₂O)₄}[(??-XW₁₀O₃₆]₂}^m? dimer. This conclusion is consistent with our experimental findings; previously we prepared the $ \left[ {\left\{ {{\text{Ru}}_{4}^{\text{IV}} {\text{O}}_{4} ({\text{OH}})_{2} \left( {{\text{H}}_{ 2} {\text{O}}} \right)_{4} } \right\}} \right[\left( {\gamma - {\text{XW}}_{10} {\text{O}}_{36} } \right]_{2} \}^{{{\text{m}} - }} $ dimers for X?=?Si (m?=?10) [Geletii et al. in Angew Chem Int Ed 47:3896?C3899, 2008 and J Am Chem Soc 131:17360?C17370, 2009] and P (m?=?8) [Besson et al. in Chem Comm 46:2784?C2786, 2010] and showed them to be very stable and efficient catalysts for the oxidation of water to O₂.     

Thermodynamic and structural aspects of the interaction of l-histidine with urea and dimethylformamide in water

The solubility of l-histidine in water and aqueous solutions of dimethylformamide (DMF) at 25°C was determined. The thermal effects of solution of l-histidine in aqueous solutions of urea and DMF were measured. The standard enthalpies, free energies, and entropies of solution and transfer of the amino acid from water to aqueous solutions of amides were calculated. It was shown that the interaction of l-histidine with urea is attractive, and that with DMF, repulsive, with the change in the free energy determined by the enthalpy term in both cases. The enthalpy-entropy compensation taking place to a certain extent in the interaction of l-histidine and l-phenylalanine with amide was revealed. This effect is the most pronounced in the interaction of predominantly hydrophobic DMF and l-phenylalanine.     

Vapor pressure isotope effects in aqueous systems. VIII. The system dimethyl sulfoxide/H2O/D2O

Vapor pressures for the system I (dimethyl sulfoxide/H₂O=DMSO/H₂O) and isotopic differential pressures I-II (II=DMSO/D₂O) have been measured between 25 and 70°C at DMSO concentrations of 0.05, 0.15, 0.30, 0.45, 0.60, 0.70, 0.80, 0.87, and 0.92 mole fraction. A high-precision differential method was used. The total pressures over the solutions, I, have been fitted to a relation derived from the Duhem-Margules equation, P ^T =P ₁ ^o X₁γ₁+P ₂ ^o X₂γ₂, with γ₁=exp[∑_kα_kX ₂ ^k ] and $$\gamma _2 = exp[\sum \alpha _k X_2^k - \sum (\alpha _k /(k - 1))(kX_2^{k - 1} - 1)].$$ . The α_k are parameters andk is a number ≥2. The α_k were taken as temperature dependent. Four parameters sufficed to fit the data within experimental error. Excess partial molal properties derived from the fits are in quantitative agreement with earlier literature results derived from the directly measured partial pressures, but the present data extend over a wider temperature range. The isotopic differential pressures I-II were similarly fitted to the relation above. The excess free energies and enthalpiesG _I ^E andH _I ^E are large and negative. The isotope effects ΔG _I,II ^E =G _I ^E ?G _II ^E and ΔH _I,II ^E are negative. They are discussed in detail in terms of the theory of isotope effects in condensed phases and demonstrated to be consistent with that theory and with the available spectroscopic data. A small amount of enthalpy data for the solution of DMSO in HOH and DOD is reported.     

Determination of the thermodynamic excess functionsG E,H E,andS E of the liquid ternary system AgCl—LiCl—KCl by means of EMF-measurements

By means of EMF-measurements using the formation cell $$graphite/Ag/AgCl(l,x_{AgCl} ) - LiCl(l,x_{LiCl} ) - KCl x_{KCl} /(Cl_2 )graphite$$ the partial molar excessGibbs energies,G _AgCl ^E , of silver chloride in the ternary system AgCl?LiCl?KCl were determined over the whole concentration range at five temperatures between 973 K and 1,123 K. The experimentally determinedG _AgCl ^E -values were fitted using theRedlich-Kister equation. From theRedlich-Kister parameters and their temperature dependence, obtained by the fitting procedure, the integral and partial molar excessGibbs energies, heats of mixing, and excess entropies were calculated. The fitting process permits also the calculation of the thermodynamic excess function of the binary system lithium chloride—potassium chloride.     

An X-ray crystallographic study of the inclusion properties of additionally dimethylated members of the 2′-hydroxy-2,2,4-trimethylflavan host series

Consideration of the shape and hydrogen bonding pattern of anentire guest unit, in the known 2:1:2 complex of 2′-hydroxy-2,4,4,7,4′-pentamethylflavan (1) with 1,4-dioxan and water, has indicated a structurally compatible guest,trans-1,4-bis(hydroxymethyl)cyclohexane (3b) which is selectively clathrated from a mixture with itscis isomer (3a). The new complex is triclinic, space group,P \(\bar 1\) , witha=8.137(1),b=9.106(1),c=14.552(2) Å, α=93.56(1), β=94.08(1), γ=98.62(1)°, and two host and one guest molecule in the unit cell. A novel hydrogen bonded host-guest arrangement has also been found for host (1), involving ethanol and piperazine [triclinic, space groupP \(\bar 1\) , witha=8.438(1),b=10.252(1),c=14.052(1) Å, α=71.28(1), β=89.72(1), γ=83.88(1)δ]; while for the 1:1 ether adduct of (1) the triclinic unit cell, space groupP \(\bar 1\) , is approximately doubled in volume [a=8.309(2),b=10.546(3),c=26.664(6) Å, α=102.10(2), β=100.48(2), γ=81.04(2)°], there now being two crystallographically independent host-guest units involving ?OH·OEt₂ hydrogen bonds of length 2.71(1) Å and 2.77(1)Å. In the 2:1 complex of the isomeric host 2′-hydroxy-2,4,4,6,5′-pentamethylfavan (2) withN, N′-dimethylpiperazine (5) [triclinic space groupP \(\bar 1\) , witha=7.411(1),b=10.143(3),c=15.109(3)Å, α=98.73(2), β=88.30(1), γ=109.72(2)°] the centrosymmetric chair-shaped guest molecule is clamped by two axially oriented ?OH...N hydrogen bonds of length 2.759(3)Å.     

Kinetics investigation on the combustion of waste capsicum stalks in Western China using thermogravimetric analysis

The combustion kinetics of waste capsicum stalk (WCS) in Western China is investigated through thermogravimetric analysis compared with sawdust and coal, and co-combustion of WCS with coal is also investigated. Results show that the ignition characteristics of WCS is better than that of sawdust and coal, and the activation energy E of WCS-volatile combustion and WCS-char combustion are 78.55?kJ?mol^?1 and 44.59?kJ?mol^?1. However, integrating the characteristics of ignition and burnout, the combustion characteristic factor (S _N) of WCS is lower than that of sawdust. With the increasing in the heating rate, the ignition of WCS is delayed. Oxygen concentration $ C_{{{\text{O}}_{2} }} $ affects E and k ₀ of volatile combustion largely under rich-oxygen condition, when $ C_{{{\text{O}}_{2} }} $ increases from 0.2 to 0.8, E has increased threefold and k ₀ also intensively increases from 10⁶ to 10¹³?C10²². Oppositely, effect of $ C_{{{\text{O}}_{2} }} $ on the E and k ₀ of char combustion is little, and there is an exponential relationship $ S_{\text{N}} = 7. 1 2 8 \times 10^{ - 9} \times { \exp }(C_{{{\text{O}}_{2} }} /0. 3 6 8) - 6. 1 2 6 \times 10^{ - 9} $ between S _N and $ C_{{{\text{O}}_{2} }} $ . For the tests of co-combustion, all the experimental and weighted-average curves coincide well, and there is no remarkable synergistic effect. With the increase of mixing ratio that WCS added, E and k ₀ of volatile combustion increase, but correspondingly E and k ₀ of char combustion decrease.     

Effect of the long-range potential on ion mobility measurements

The temperature dependence of ion mobilities in helium was studied by using the ion chromatography method to investigate the effect of long-range terms in the ion-buffer gas interaction. Experimental cross sections thus determined increased significantly as the temperature was lowered from 300 to 80 K for all ions investigated, which were fullerene C ₆₀ ⁺ , cationized PEG polymers, cationized crown ethers, and protonated and sodiated oligoglycines. The temperature dependence of the collision cross sections was successfully modeled by employing simple atom-atom interaction potentials including a repulsive R ^?12 term and the attractive long-range R ^?6 and R ^?4 terms, R being the distance between the colliding particles.