Liquid Chromatographic Resolution of Racemic α-Hydroxycarboxylic Acids on Ligand Exchange Chiral Stationary Phases

Two ligand exchange chiral stationary phases (CSPs) based on (S)-leucinol derivative, sodium N-((S)-1-hydroxymethyl-3-methylbutyl)-N-undecylaminoacetate, and (R)-phenylglycinol derivative, sodium N-((R)-2-hydroxy-1-phenylethyl)-N-undecylaminoacetate, covalently bonded to silica gel have been successfully applied in the resolution of nine -hydroxycarboxylic acids. The latter was more effective than the former, the separation factors () being 1.05 to 2.12 while the resolution factors (R_S) varying from 0.18 to 5.29 on the latter. The chromatographic resolution behaviors were dependent on the type and the content of organic modifier and the content of CuSO₄ in aqueous mobile phase and the column temperature. A possible chiral recognition mechanism was also proposed based on the chromatographic resolution behaviors.     

Ion Association in Lanthanide Chloride Solutions

A better understanding of the solution chemistry of the lanthanide (Ln) salts in water would have wide ranging implications in materials processing, waste management, element tracing, medicine and many more fields. This is particularly true for minerals processing, given governmental concerns about lanthanide security of supply and the drive to identify environmentally sustainable processing routes. Despite much effort, even in simple systems, the mechanisms and thermodynamics of Ln^III association with small anions remain unclear. In the present study, molecular dynamics (MD), using a newly developed force field, provide new insights into LnCl₃(aq) solutions. The force field accurately reproduces the structure and dynamics of Nd³⁺, Gd³⁺ and Er³⁺ in water when compared to calculations using density functional theory (DFT). Adaptive-bias MD simulations show that the mechanisms for ion pairing change from dissociative to associative exchange depending upon cation size. Thermodynamics of association reveal that whereas ion pairing is favourable, the equilibrium distribution of species at low concentration is dominated by weakly bound solvent-shared and solvent-separated ion pairs, rather than contact ion pairs, reconciling a number of contrasting observations of Ln^III–Cl association in the literature. In addition, we show that the thermodynamic stabilities of a range of inner sphere and outer sphere coordination complexes are comparable and that the kinetics of anion binding to cations may control solution speciation distributions beyond ion pairs. The techniques adopted in this work provide a framework with which to investigate more complex solution chemistries of cations in water.     

Evaporation of the liquid stationary phase in gas chromatography

Summary The theory of the evaporation of the liquid stationary phase is elaborated and experimentally verified. On the basis of this theory the role played by the losses in the amount of liquid phase present is quantitatively determined. General techniques are examined which minimize the losses; these techniques are based on saturating the incoming carrier gas with liquid phase vapours and raising the pressure of the carrier gas in the column, e.g. by connecting a capillary to the column outlet in order to offer resistance to the gas flow. The application of these techniques ensures stable performance of the gas chromatographic columns using a volatile liquid phase.     

The effect of the structure of bonded cyanoalkyl stationary phases on their selectivity in the liquid chromatographic separation of polynuclear aromatic hydrocarbons

Summary The paper discusses the effect of the length and structure of the hydrocarbon chain connecting the nitrile group to the silica gel surface on the chromatographic properties of cyanoalkyl phases.When using non-polar and polar mobile phases, the selectivity of the cyanodecyl phases toward PAHs is higher than of the cyanopropyl phase and of hydroxylated silica gel.Polar additives to the mobile phase drastically decrease the retention on silica gel and on the cyanopropyl phase while affect the properties of cyanodecyl phases only to a considerably less degree. Newly synthesized phases with different structures of the hydrocarbon chain are compared with the commerical cyano-and ODS-phases. The retention mechanism on the cyanoalkyl phases is discussed.     

Comparison of enantiomer separation on two chiral stationary phases derived from (+)-18-crown-6-2,3,11,12-tetracarboxylic acid of the same chiral selector

Liquid chromatographic comparisons for enantiomer resolution of α-amino acids and chiral primary amino compounds were made using chiral stationary phases (CSPs) prepared by covalently bonding (+)-(18-crown-6)-2,3,11,12-tetracarboxylic acid (18-C-6-TA) of the same chiral selector. The resolution of all α-amino acids on CSP 1 developed in our group was found to be better than that on CSP 2 reported by Machida et al. All α-amino acids examined in this study were well enantioseparated on CSP 1 (α=1.22–2.47), while four analytes were not resolved or all the other analytes were poorly resolved on CSP 2 than on CSP 1. However, in resolving the primary amino compounds without a carbonyl group, CSP 1 was comparable with CSP 2. Although (+)-18-C-6-TA of the same chiral selector was used to prepare CSP 1 and CSP 2, this study showed that different connecting methods for the CSPs might influence their ability to resolve the analytes depending on their structures related to the chiral recognition mechanism.     

Analysis of critical points on the potential energy surface

A simple classification scheme is proposed for critical points, based only on rankr and signatures of the (n,n)-matrixG of harmonic force constants. The determination ofr ands, e.g. by the well-known factorizationG=L ^T gL (L: triangular matrix,g: diagonal matrix), has several theoretical as well as practical (computational) advantages over the inspection of eigenvalues ofG, so far used in quantum chemistry. The eigenvalues are sufficient butnot necessary for a classification whereas rank and signature are the only necessary and sufficient prerequisites for solving the task. For the purpose of presenting a working example, by calculating only a 2×2 torque constant matrix, it is shown that the coplanar ethylbenzene is unstable in the CNDO/2 picture.     

Optimal convergence properties of kernel density estimators without differentiability conditions

Let X ₁, X ₂, ..., X _n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-<x<, with h=h _n (h _n O and nh _n , as n) the bandwidth and K a kernel function of order r. Optimal rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of finite differences.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta Central Research Fund.     

Proof of some conjectures on the mean-value of Titchmarsh series — III

With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σ _n ^∞ =1a_n λ _n ^−s be a generalized Dirichlet series with 1 =λ ₁ <λ ₂ < …,λ _n≤Dn, andλ _n+1 -λ _n ≥D ^{− 1} λ _n+1 ^{− a} where α>0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for . These results will be applied in other papers to appear later.     

Light traffic for workload in queues

General exact light traffic limit theorems are given for the distribution of steadystate workloadV, in open queueing networks having as input a general stationary ergodic marked point process {(t _n ,K _n )n0 (where t_n denotes the arrival time and K_n the routing and service times of the nth customer). No independence assumptions of any kind are required of the input. As the light traffic regime, it is only required that the Palm distribution for the exogenous interarrival time converges weakly to infinity (while the service mechanism is not allowed to change much). As is already known in the context of a single-server queue, work is much easier to deal with mathematically in light traffic than is customer delayD, and consequently, our results are far more general than existing results forD. We obtain analogous results for multi-channel and infinite-channel queues. In the context of open queueing networks, we handle both the total workload in the network as well as the workload at isolated nodes.Research supported in part by the Japan Society for the Promotion of Science during the author's fellowship in Tokyo, and by NSF Grant DDM 895 7825.