Resolution optimisation in micellar electrokinetic chromatography using empirical models

Theoretical and empirical models can be used to model the migration or separation characteristics in micellar electrokinetic chromatography in order to optimise the resolution. In this paper only empirical models were used, because it is easier and more straightforward to obtain these models. Several empirical approaches for the optimisation of the resolution were compared in order to determine which response should be modelled preferably. The use of models of the effective mobility in combination with average plate numbers proved to be the most suitable approach to optimisation of the resolution, because the relative prediction errors of the models of the effective mobility were a factor of 2-4 smaller than the relative prediction errors of the models of the apparent mobility. Moreover for the least separated peak pair the resolutions based on the models of the apparent and effective mobility showed relative prediction errors that were approximately a factor of 2 smaller than the relative prediction errors of the resolutions based on the models of the resolution and separation factor. The predictions of the separation factor based on the different models generally showed lower prediction errors than the predictions of the corresponding resolutions. Although the relative prediction errors were large, particularly for closely migrating compounds, the empirical approach will probably lead to the optimum separation buffer composition.     

Capillary electrochromatography of basic compounds using octadecyl-silica stationary phases with an amine-containing mobile phase

The capillary electrochromatographic (CEC) analysis of basic compounds on octadecyl-silica stationary phases (Hypersil ODS and Spherisorb ODS I) was studied. A basic drug (fluvoxamine) and one of its possible impurities were used as test compounds. With an eluent of acetonitrile-phosphate buffer (pH 7.0), the compounds could be baseline-separated; however, broad and tailing peaks were obtained. To minimise detrimental interactions with residual silanol groups, the pH of the mobile phase was lowered to 2.5, but the plate numbers were still quite low (<2.6x10(4) plates/m). Addition of a masking agent (hexylamine or triethylamine) to the mobile phase resulted in much better peak efficiencies (ca. 1x10(5) plates/m). Therefore, the influence of the amine concentration and pH of the mobile phase on the CEC performance (peak width, peak tailing, electroosmotic flow, selectivity) was investigated in detail. Highest efficiencies (2.8x10(5) plates/m) could be obtained with the Spherisorb column, while the Hypersil column offered a better selectivity. Furthermore, the results show that the residual silanol groups are (at least partly) responsible for the separation of the basic compounds and that the amount of injected sample has an unusually large effect on the peak efficiency. The usefulness of the system for impurity profiling was demonstrated with a mixture containing fluvoxamine and its stereoisomer (a possible impurity) at the 0.1% level. The general effectiveness of amine additives in CEC was illustrated by the separation of a mixture of five structurally different basic drugs yielding plate numbers in the 1x10(5)-3x10(5) plates/m range. Comparison with capillary electrophoretic analysis revealed a unique selectivity of the CEC system which is based on both electrophoretic mobility and chromatographic partitioning.     

The discrete Gaussian chain with 1/r n interactions: Exact results

We show that the discrete Gaussian chain with interactionV(r) = 1/(r ²–1/4) is self-dual. At the dual temperaturek _B T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent. We also consider interactionsV(r)–1/r ⁿ and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark.     

Universal fluctuations in the support of the random walk

A random walk starts from the origin of ad-dimensional lattice. The occupation numbern(x,t) equals unity if aftert steps site x has been visited by the walk, and zero otherwise. We study translationally invariant sumsM(t) of observables defined locally on the field of occupation numbers. Examples are the numberS(t) of visited sites, the areaE(t) of the (appropriately defined) surface of the set of visited sites, and, in dimension d=3, the Euler index of this surface. Ind≤ 3, theaverages - M(t) all increase linearly witht ast ® ∞. We show that in d=3, to leading order in an asymptotic expansion int, thedeviations from average ΔM(t) = M(t) -M(t) are, up to a normalization, allidentical to a single “universal” random variable. This result resembles an earlier one in dimensiond=2; we show that this universality breaks down ford>3.     

Kinetics of clusters in a binary linear system

We consider the stochastically time-dependent behaviour of a binary linear chain of N units at temperature T and in an external field H. The kinetics is described in terms of clusters (sequences) of specified numbers of units in the same state. A coarse-grained master equation for the cluster densities on the chain is derived by an approximation due to Felderhof. We calculate the relaxation time of fluctuations, and the zero-field frequency-dependent susceptibility, of the fraction of units in a given state. Our results are compared to the phenomenological theory of irreversible thermodynamics.     

Universal attractor and inertial sets for the phase field model

We consider the phase field equations in dimensions 1, 2 and 3. We show that it is well-posed when assuming that the initial data is square integrable and prove the existence of a universal attractor and of inertial sets.     

Random Line Tessellations of the Plane: Statistical Properties of Many-Sided Cells

We consider a family of random line tessellations of the Euclidean plane introduced in a more formal context by Hug and Schneider (Geom. Funct. Anal. 17:156, 2007) and described by a parameter α≥1. For α=1 the zero-cell (that is, the cell containing the origin) coincides with the Crofton cell of a Poisson line tessellation, and for α=2 it coincides with the typical Poisson-Voronoi cell. Let p _n (α) be the probability for the zero-cell to have n sides. We construct the asymptotic expansion of log p _n (α) up to terms that vanish as n→∞. Our methods are nonrigorous but of the kind commonly accepted in theoretical physics as leading to exact results. In the large-n limit the cell is shown to become circular. The circle is centered at the origin when α>1, but gets delocalized for the Crofton cell, α=1, which is a singular point of the parameter range. The large-n expansion of log p _n (1) is therefore different from that of the general case and we show how to carry it out. As a corollary we obtain the analogous expansion for the typical n-sided cell of a Poisson line tessellation.     

Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion

In this paper, we prove the existence and uniqueness of the entropy solution for a first-order stochastic conservation law with a multiplicative source term involving a $Q$-Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure-valued weak entropy solution, which coincides with the unique weak entropy solution of the problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we prove the existence and the uniqueness of the strong solution of an associated stochastic nonlinear parabolic problem by means of an implicit time discretization scheme; we also prove its convergence to a measure-valued entropy solution of the stochastic conservation law, which proves the existence of the measure-valued entropy solution.