Rate and product studies in the solvolyses of methanesulfonic anhydride and a comparison with methanesulfonyl chloride solvolyses

The specific rates of solvolysis of methanesulfonic anhydride have been measured conductometrically at ?10 °C in 41 solvents. Use of the extended Grunwald–Winstein equation, with the N_T scale of solvent nucleophilicity and the Y_OTs scale of solvent ionizing power, leads to sensitivity to changes in solvent nucleophilicity (? value) of 0.95 and a sensitivity to changes in solvent ionizing power (m value) of 0.61, with a multiple correlation coefficient (R) of 0.973. Product selectivity values (S) in binary hydroxylic solvents favor alcohol attack in EtOH–H₂O (a value of 1.2 in 90% EtOH rising to 4.0 in 40% EtOH) and in MeOH–H₂O (a value of 3.7 in 90% MeOH rising to 6.0 in 50% MeOH). In 2,2,2,‐trifluoroethanol–H₂O, the S values are much lower at about 0.1. Entropy of activation values are appreciably negative. Literature values for the specific rates of solvolysis of methanesulfonyl chloride have been extended to fluoroalcohol‐containing solvents (titrimetric method) and, at 45.0 °C, for an overall 43 solvents values are obtained (using N_T and Y_C1 scales) of 1.20 for ? and of 0.52 for m (R = 0.969). It is proposed that both substrates solvolyze by an S_N2 pathway. Copyright © 2007 John Wiley & Sons, Ltd.     

The SN3–SN2 spectrum. Rate constants and product selectivities for solvolyses of benzenesulfonyl chlorides in aqueous alcohols

Rate constants for a wide range of binary aqueous mixtures and product selectivities (S) in ethanol–water (EW) and methanol–water (MW) mixtures, are reported at 25 °C for solvolyses of benzenesulfonyl chloride and the 4‐chloro‐derivative. S is defined as follows using molar concentrations: S = ([ester product]/[acid product]) × ([water solvent]/[alcohol solvent]). Additional selectivity data are reported for solvolyses of 4‐Z‐substituted sulfonyl chlorides (Z = OMe, Me, H, Cl and NO₂) in 2,2,2‐trifluoroethanol–water. To explain these results and previously published data on kinetic solvent isotope effects (KSIEs) and on other solvolyses of 4‐nitro and 4‐methoxybenzenesulfonyl chloride, a mechanistic spectrum involving a change from third order to second order is proposed. The molecularity of these reactions is discussed, along with new term ‘S_N3–S_N2 spectrum’ and its connection with the better established term ‘S_N2–S_N1 spectrum’. Copyright © 2009 John Wiley & Sons, Ltd.     

Rate and product studies with 2‐adamantyl fluoroformate under solvolytic conditions

The specific rates of solvolysis of 2‐adamantyl fluoroformate have been measured at 25.0 °C in 20 pure and binary solvents. These are well correlated using the extended Grunwald–Winstein equation, with incorporation of the N_T solvent nucleophilicity scale and the Y_Cl solvent ionizing power scale. The sensitivities (l = 2.15 ± 0.17 and m = 0.95 ± 0.07) toward the changes in solvent nucleophilicity and solvent ionizing power, and the k_F/k_Cl values are very similar to those previously observed for solvolyses of n‐octyl fluoroformate, consistent with the addition step of an addition‐elimination pathway being rate‐determining. For aqueous ethanol, measurement of the product ratio allowed selectivity values (S) to be determined. The results are compared with those reported earlier for 2‐adamantyl chloroformate and mechanistic conclusions are drawn. Copyright © 2007 John Wiley & Sons, Ltd.     

Solvolytic reactivity of pyridinium ions

The leaving group abilities of pyridine, 4‐methylpyridine, and 4‐chloropyridine in S_N1 solvolytic reactions have been determined by analyzing the rate constants of X,Y‐substituted benzhydrylpyridinium salts obtained in various solvents. By applying the linear free energy relationship equation, log k = s_f (E_f + N_f), the nucleofuge specific parameters of 4‐substituted pyridine have been extracted. Because of solvation in the reactant ground state, the reactivity (nucleofugality, N_f) of a given pyridine decreases as the polarity of the solvent increases. High slope parameters (s_f > 1) may be due to the spread of the energy levels of the benzhydrylium ion/pyridine pair intermediates in comparison to benzhydrylium ion/chloride pairs (s_f ≈ 1). Because of slow heterolysis step of pyridinium salts in various solvents, some are stable under normal conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

Diffusion activation energy versus the favourable energy in two-order-parameter model:A molecular dynamics study of liquid Al

In the present work, we find that both diffusion activation energy E_a(D) and E_a(S^ex) increase linearly with pressure and have the same slope (0.022±0.001 eV/GPa) for liquid Al. The temperature and pressure dependence of excess entropy is well fitted by the expression -S^ex(T,P)/k_B=a(P)+b(P)T+c(P)exp(E_f/k_BT), which together with the small ratio of E_f/k_BT leads to the relationship of excess entropy to temperature and pressure, i.e. S^ex≈-cE_f/T, where c is about 12 and E_f (=Δ E-PΔV) is the favourable energy. Therefore, there exists a simple relation between E_a(S^ex) and E_f, i.e. E_a(S^ex)≈cE_f.     

On Gell-Mann's λ-matrices,d- andf-tensors,octets, and parametrizations ofS U (3)

The algebra ofS U (3) is developed on the basis of the matrices _i ofGell-Mann, and identities involving the tensorsd _{i j k} andf _{i j k} occurring in their multiplication law are derived. Octets and the tensor analysis of the adjoint groupS U (3)/Z(3) ofS U (3) are discussed. Various explicit parametrizations ofS U (3) are presented as generalizations of familiarS U (2) results.     

Positioning solvolyses within the SN2‐SN1 and SN3‐SN2 spectrum of reaction mechanisms

A simple linear regression (Q equation) is devised to position solvolyses within the established S_N2‐S_N1 spectrum of solvolysis mechanisms. Using 2‐adamantyl tosylate as the S_N1 model and methyl tosylate as the S_N2 model, the equation is applied to solvolyses of ethyl, allyl, secondary alkyl and a range of substituted benzyl and benzoyl tosylates. Using 1‐adamantyl chloride as the S_N1 model and methyl tosylate as the S_N2 model, the equation is applied to solvolyses of substituted benzoyl chlorides in weakly nucleophilic media. In some instances, direct correlations with methyl tosylate were employed. Grunwald–Winstein l values and kinetic solvent isotope effects are also used to locate solvolyses within the spectrum of mechanisms. Product selectivities (S) for solvolyses at 50 °C of p‐nitrobenzyl tosylate in binary mixtures of alcohol–water and of alcohol–ethanol for five alcohols (methanol, ethanol, 1‐propanol and 2‐propanol and t‐butanol) are reported and show the expected order of solvent nucleophilicity (RCH₂OH > R₂CHOH > R₃COH). The data support the original assignments establishing the N_OTs scale of solvent nucleophilicity. Copyright © 2016 John Wiley & Sons, Ltd.     

Single-particle potential in a chiral approach to nuclear matter including short-range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al.Phys. Lett. B 474, 7 (2000)) by calculating the underlying (complex-valued) single-particle potential U(p, k _f) + iW(p, k _f). The potential for a nucleon at the bottom of the Fermi sea, U(0, k _f0) = - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi surface. Also, the imaginary single-particle potential, W(0, k _f0) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear-matter equation of state can be obtained if the short-range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1π-exchange). We also consider the equation of state of pure neutron matter ˉE_n(k _n) and the asymmetry energy A(k _f) in that approach. The downward bending of these quantities above nuclear-matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics. Received: 19 December 2002 / Accepted: 11 February 2003 / Published online: 15 April 2003     

Correlation of the rates of solvolysis of diphenylphosphinyl chloride using an extended form of the Grunwald–Winstein equation

The specific rates of solvolysis of diphenylphosphinyl chloride ( 1 ) have been measured at 25.0 °C in 30 solvents. For six representative solvents, studies were made at several temperatures and activation parameters determined. These were used to calculate a value at 25.0 °C in 100% 2,2,2‐trifluoroethanol (TFE) from values at higher temperatures. The 31 solvents gave a reasonable extended Grunwald–Winstein plot, correlation coefficient (R) of 0.920, which improved to 0.956 when the four TFE–ethanol points were excluded. The sensitivities (l and m) were similar to those obtained for dimethyl phosphorochloridate and phosphorochloridothionate and for N,N,N′,N′‐ tetramethyldiamidophosphorochloridate. As with the three previously studied solvolyses, an S_N2 pathway is proposed for the solvolyses of 1 . Copyright © 2007 John Wiley & Sons, Ltd.     

A quasi analytical method for the calculation of virial coefficients for realistic intermolecular potentials

The difficulties of accurately representing the Ursell function, f, for molecules interacting with a Lennard-Jones potential by a hard sphere core and a truncated exponential series are discussed. The range of R for which a hard sphere approximates f with negligible error is established and the range of arguments in f is determined. The accuracy with which the exponential series, S_k , truncated after k terms, represents the function is established for several ranges of arguments. It is shown that it is possible to represent f accurately by a hard sphere core and S ₄ or S ₆ for all values of R except over a short range of R.

Values of B and C, accurate to within a few per cent, can be obtained analytically through approximating f by S ₄ or S ₆ and a hard core whose diameter is determined by the range of arguments for which the series is valid. More accurate values of B and C required additional approximations for f. Two of these, the repulsive square well and the Barker-Henderson radius, give accurate values of B and C at all temperatures that were examined.     

A DFT study of transition structures and reactivity in solvolyses of tert‐butyl chloride,cumyl chlorides,and benzyl chlorides

DFT computations were performed on the S_N1 and S_N2 solvolyses of substituted cumyl chlorides and benzyl chlorides in ethanol and water, by increasing stepwise the C? Cl distance and by optimization. The total energy increases with the increase in the Cl? C distance in S_N1 reactions, while free energy of activation pass through maximum. To validate the results, the calculated free energies of activation were compared with data obtained by kinetic measurements. The structural parameters of the transition states were correlated with the Hammett substituent constants and compared with the data of hydrolyses of tert‐butyl chloride and methyl chloride, which proceed with known mechanisms. Conclusions on the mechanisms of the reactions were driven from the effect of substituents on free energies of activation. Cumyl chlorides substituted with electron‐donating (e‐d) groups solvolyze with S_N1 mechanism, while the reactions of substrates that bear electron‐withdrawing groups proceed with weak nucleophilic assistance of the solvent. Benzyl chlorides hydrolyze through an S_N2 pathway except those derivatives that have strongly e‐d groups, where the reaction has S_N1 character, but a weak nucleophilic assistance of the water should also be taken into consideration. Copyright © 2007 John Wiley & Sons, Ltd.     

The statistics of Curie-Weiss models

LetS _n denote the random total magnetization of ann-site Curie-Weiss model, a collection ofn (spin) random variables with an equal interaction of strength 1/n between each pair of spins. The asymptotic behavior for largen of the probability distribution ofS _n is analyzed and related to the well-known (mean-field) thermodynamic properties of these models. One particular result is that at a type-k critical point (S _n-nm)/n^1–1/2k has a limiting distribution with density proportional to exp[-_s ^2k/(2k)!], wherem is the mean magnetization per site and A is a positive critical parameter with a universal upper bound. Another result describes the asymptotic behavior relevant to metastability.Research supported in part by National Science Foundation Grants MPS 76-06644 (to RSE) and MPS 74-04870 A01 (to CMN).     

Nanocomposites with fumed silica/poly(vinyl pyrrolidone) prepared at a low content of solvents

Highly disperse nanocomposites with fumed silica/poly(vinyl pyrrolidone) (PVP) prepared using different methods were studied by infrared spectroscopy, adsorption, and quantum chemistry methods. Low amounts of water or ethanol (30 wt.% with respect to the silica content) promote appropriate distribution of PVP on silica particles. The use of ethanol leads to a smaller loss of the specific surface area (S_BET) than in the case of water used as a solvent. On PVP distribution on a silica surface, treatment of the system in a pseudo-liquid state reactor (PLSR) provides slightly better results (a lower loss in S_BET) in comparison with mechanochemical activation (MCA) in a ball mill at the PVP monolayer coverage. An increase in the activation time to 6-9 h leads to an increase in the |ΔS_BET/S_BET| value to 0.29-0.35 for both treatment methods.     

Vibrational relaxation in liquids

A new theory is presented for vibrational energy relaxation in a liquid. It is shown that a vibrationally excited probe molecule relaxes through interaction with the density fluctuations in the surrounding solvent fluid. This interaction occurs through a potential V(k), which is expressed in terms of the intermolecular force between the excited probe molecule and the surrounding fluid molecules. By assuming spherically symmetric solvent particles the T ₁ energy relaxation time for direct V-T processes is related to the translational dynamic structure factor for the fluid S(k, ω_v), evaluated at the vibrational resonance frequency. It is shown that this is described by gas-like particle motions on a very short distance scale corresponding to k vectors lying well beyond the first or second peaks of the fluid structure factor S(k). Such motions can be pictured as high-frequency, short-distance distortions of the local equilibrium configuration of the solvent particles around the probe. T ₁ ^-1 is found to be proportional to ρ_e T ^1/2 ω_v ^-3. The V-V energy exchange relaxation time is also calculated. This is found to be proportional to S(k, ω′) evaluated at a frequency ω′, corresponding to the vibrational energy missmatch. An energy gap law for the V-V process is derived.     

Solvent network at the transition state in the solvolysis of hindered sulfonyl compounds

Alcoholysis rates of unhindered benzenesulfonyl chlorides (X‐ArSO₂Cl, X = H‐; 4‐Br‐; 4‐Me‐) are similar in methanol; the same behavior is also observed in ethanol, whereas the reactivity order in iso‐propanol is 4 Me‐ < H‐ < 4‐Br‐. On the other hand, alcoholysis of sterically hindered arenesulfonyl chlorides (X‐ArSO₂Cl) (X = 2,4,6‐Me₃‐3‐NO₂‐; 2,6‐Me₂‐4‐tBu‐; 2,4,6‐Me₃‐; 2,3,5,6‐Me₄‐; 2,4,6‐iPr₃‐; 2,4‐Me₂‐; 2,4,6‐(OMe)₃‐) in all studied alcohols show a significant increase in reactivity, the so‐called positive steric effect. Most of the substrates showed a reaction order b ~ 2 with respect to the nucleophile in methanol and ethanol, and b ~ 3 in iso‐propanol. The correlation between reactivity and the Kirkwood function (1/ξ) gives negative sensitivity (U) for all systems. All substrates showed high sensitivity to media nucleophilicity that depends on Σσ_X. Obtained results suggest the alcoholysis of benzenesulfonyl chlorides proceeds through S_N2 mechanism where the transition state (TS) involves the participation of 2–3 alcohol molecules; such a TS can be cyclic, in the case of unbranched alcohols, or linear, for alcohols with bulkier hydrocarbon groups like iso‐propanol. To include the number of alcohol molecules playing such a role in the TS, the following terminology is proposed: cS_N2s_n for S_N2 reactions involving n solvent molecules in a cyclic (c) TS, where “s” stands for the solvent and “n” is either the closest integer or half‐integer to the reaction order relative to the solvent or, in computational studies, the proposed number of solvent molecules taking part in the TS, whereas S_N2s_n is proposed when the TS is not cyclic. Copyright © 2016 John Wiley & Sons, Ltd.     

U-perturbation treatment of heavy fermion systems

Heavy fermion systems are described by the periodic Anderson Model (PAM), i.e. a lattice of localized, highly correlatedf-electron states hybridized with the delocalized states of a conduction band. We treat the PAM within the second orderU perturbation theory around the non-magnetic Hartree-Fock solution (U on site Coulomb correlation between thef-electrons). This treatment has the advantage that Fermi liquid relations (Luttinger theorem) are automatically fulfilled. Thef-electron selfenergy and spectral function are calculated for different temperatures, and, for the symmetric PAM, we obtain single-particle peaks near toE _f andE _f +U and in addition many-particle (Kondo) resonance peaks near to the chemical potential (E _f baref-electron energy). The resonance peaks are strongly temperature dependent and vanish on a characteristic temperature scaleT _K. For the symmetric PAM and a constant on-site hybridization the Fermi energy falls into a hybridization gap. A second, smaller characteristic temperature scaleT _coh (coherence temperature), on which the hybridization gap vanishes, is observed within this approach. For the non-symmetric PAM (i.e.E _f andE _f +U not symmetric around the chemical potential) we obtain a similar behaviour, but the single-particle peaks are no longer at the correct positionsE _f andE _f +U. The proper behaviour for the symmetric PAM but less satisfactory behaviour for the non-symmetric PAM can be understood from the fact that only for the symmetric PAM the exactly solvable limit of a vanishing hybridization is reproduced within this approach.     

Zonal PANS: evaluation of different treatments of the RANS–LES interface

The partially Reynolds-averaged Navier–Stokes (PANS) model can be used to simulate turbulent flows either as RANS, large eddy simulation (LES) or DNS. Its main parameter is f_k whose physical meaning is the ratio of the modelled to the total turbulent kinetic energy. In RANS f_k = 1, in DNS f_k = 0 and in LES f_k takes values between 0 and 1. Three different ways of prescribing f_k are evaluated for decaying grid turbulence and fully developed channel flow: f_k = 0.4, f_k = k^3/2 _tot/? and, from its definition, f_k = k/k_tot where k_tot is the sum of the modelled, k, and resolved, k_res, turbulent kinetic energy. It is found that the f_k = 0.4 gives the best results. In Girimaji and Wallin, a method was proposed to include the effect of the gradient of f_k. This approach is used at RANS– LES interface in the present study. Four different interface models are evaluated in fully developed channel flow and embedded LES of channel flow: in both cases, PANS is used as a zonal model with f_k = 1 in the unsteady RANS (URANS) region and f_k = 0.4 in the LES region. In fully developed channel flow, the RANS– LES interface is parallel to the wall (horizontal) and in embedded LES, it is parallel to the inlet (vertical). The importance of the location of the horizontal interface in fully developed channel flow is also investigated. It is found that the location – and the choice of the treatment at the interface – may be critical at low Reynolds number or if the interface is placed too close to the wall. The reason is that the modelled turbulent shear stress at the interface is large and hence the relative strength of the resolved turbulence is small. In RANS, the turbulent viscosity – and consequently also the modelled Reynolds shear stress – is only weakly dependent on Reynolds number. It is found in the present work that it also applies in the URANS region.     

Effect of aggregation on the radiative (T1 → S0) and nonradiative (T1⇝S0 and S1⇝T1) transitions in xanthene dyes

The measurement of triplet decay time (τ_p) and the relative yields of phosphorescence to fluorescence (φ_p/φ_f) have been made in solutions of xanthene dyes. The value of φ_p/φ_f increases while that of τ_p decreases as the concentration of the solution is increased. The rate constants k_p, k_qp and k_is have been estimated. It is found that the values of k_qp and k_is increase while that of k_p remains substantially constant for the entire range of concentration. The deuterium solvent effect is observed in τ_p and φ_p.     

Correlations in pp-collisions and two-component models

Some general consequences of charge conservation inclusive sum rules for the correlation integralsf _kandf _0k are given. It is also pointed out that the energy dependence off _korf _0k is 〈n〉 ^k fork≤7 for pp-collisions and that the data suggest all thef _k andf _0k ’s are non-zero. Further, two-component models for the charge multiplicity distribution consistent with charge conservation, are considered and compared with the data for pp-collisions.     

Chiral approach to nuclear matter: role of two-pion exchange with virtual delta-isobar excitation

We extend a recent three-loop calculation of nuclear matter by including the effects from two-pion exchange with single and double virtual Δ(1232)-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, , ρ₀=0.16 fm⁻³, can be well reproduced by adjusting the strength of a two-body term linear in density (and tuning an emerging three-body term quadratic in density). The nuclear matter compressibility comes out as K=304 MeV. The real single-particle potential U(p,k_f0) is substantially improved by the inclusion of the chiral πNΔ-dynamics: it grows now monotonically with the nucleon momentum p. The effective nucleon mass at the Fermi surface takes on a realistic value of M^*(k_f0)=0.88M. As a consequence of these features, the critical temperature of the liquid-gas phase transition gets lowered to the value T_c15 MeV. In this work we continue the complex-valued single-particle potential U(p,k_f)+iW(p,k_f) into the region above the Fermi surface p>k_f. The effects of 2π-exchange with virtual Δ-excitation on the nuclear energy density functional are also investigated. The effective nucleon mass associated with the kinetic energy density is . Furthermore, we find that the isospin properties of nuclear matter get significantly improved by including the chiral πNΔ-dynamics. Instead of bending downward above ρ₀ as in previous calculations, the energy per particle of pure neutron matter and the asymmetry energy A(k_f) now grow monotonically with density. In the density regime ρ=2ρ_n<0.2 fm⁻³ relevant for conventional nuclear physics our results agree well with sophisticated many-body calculations and (semi)-empirical values.