Retention of ionizable compounds on HPLC. Modelling retention for neutral and ionizable compounds by linear solvation energy relationships

Summary A global LSER model that relates HPLC retention to mobile phase composition and pH is tested for a varied group of solutes, both neutral and ionizable, in a polymeric column and methanol-water mobile phases. It is compared to the local LSER model developed only for a given mobile phase, i.e., a fixed organic modifier content, and to the global LSER model set only for neutral solutes. The global LSER model for neutral and ionizable solutes requires a few supplementary parameters over the other models tested, but it accounts for retention under any experimental conditions for a given column and methanol-water mobile phases, describing properly the interactions established in the HPLC system (hydrophobicity, hydrogen-bond acidity and basicity, dipolarity/polarizability…). This paper is number 13 of a series with the same general title: “Retention of Ionizable Compounds on HPLC” published in various journals.     

The size distribution for theA g RB f−g Model of polymerization

This paper gives the equilibrium distribution of polymer sizes for Flory'sA _g RB _f–g model of polymerization. In this model, the polymers are composed of structural units withg functional groups of the typeA and (f-g) functional groups of the typeB. Reaction is subject to three conditions: (1) Functional groups of the typeA react only with those of typeB, and vice versa. (2) Intramolecular reactions do not occur [and therefore only branched-chain (noncyclic) polymers and formed]. (3) Subject to conditions (1) and (2), all functional groups are equally reactive. The derivation employs Stockmayer's statistical mechanical method (first used on Flory'sRA _f model), coupled with a recursion giving the number of distinct polymers which may be assembled fromk units of theA _g RB _f–g type. We also give distributions for a limiting case of theA _g RB _f–g model, the so-calledA _g RB model. This paper completes the solution of the Smoluchowski coagulation equation (monodisperse case) for the kernelsa _ij =A + B(i +j)+ Cij. The proof will be given in another publication.     

A generalization of the Rouse-Zimm model

The idea of consistently averaging the hydrodynamic interaction and its various consequences for Hookean dumbbells are reviewed. For long chains this idea can be used to generalize the Rouse-Zimm model for polymer solutions. Unlike the usual Rouse-Zimm model, the new model for steady shear flow predicts a nonzero second normal stress coefficient and shear rate dependent material functions. In the limit of long chains, the viscosity and the normal stress coefficients are universal functions of the reduced shear rate.This paper was presented at the Frühjahrstagung des Fachausschusses Polymerphysik der Deutschen Physikalischen Gesellschaft at Kaiserslautern (West Germany), March 12–14, 1986.     

A coupled electron diffraction and rigid unit mode (RUM) study of the crystal chemistry of some zeotypic AlPO4 compounds

Electron diffraction and lattice dynamical calculations are used to investigate the unit cells, space group symmetries and inherent displacive flexibility of the room-temperature average structures of AlPO₄-8, AlPO₄-16 and AlPO₄-tridymite. The zero-frequency rigid unit modes (RUMs) of the idealized high-symmetry polymorphs thereof are also investigated along with their relationship to the lower-temperature polymorphism of these zeotypic aluminophosphates. The clear presence of satellite reflections in addition to the Bragg reflections (G) of the underlying Cmc2₁ parent structure in the case of AlPO₄-8 shows that the true unit cell of the room-temperature polymorph has a doubled c-axis due to a condensed RUM mode. Structured diffuse scattering is also observed which can be related to the thermal excitation of RUM modes. In the case of AlPO₄-tridymite, a complex F1 triclinic polymorph is observed and related to soft RUM modes while, in the case of AlPO₄-16, a soft q=0 RUM mode is shown to be responsible for an observed phase transition in the case of the all SiO₂ analogue of AlPO₄-16. A large number of additional zero-frequency RUM modes also exist in the case of AlPO₄-16.     

Inverse relaxation-model and relation to recovery internal friction

Inverse relaxation is studied for hard elastic polypropylene (HEPP), rubber and non-elastic polypropylene. The results show that contractive stress, stress, and internal friction are three essential factors related to the phenomenon. A three-element model in which each element has a definite meaning is proposed to describe this phenomenon. The results also show that, in the first cyclic deformation, relaxation time increases with the increase of recovery for all the materials, which indicates that recovery viscosity increases with the increase of recovery, but the stress rising amplitude (SRA) of inverse relaxation has a maximum in the recovery range. Analysis indicates that SRA equals recovery internal friction (RIF) for ideal material in which stress is solely a function of strain, independent of paths, and approximately equals RIF for non-ideal material at a given strain. From this principle it is found that the order of the work counteracted by RIF for the four materials is the same as that of their second hysteresis loop, and the RIF of HEPP has a sudden increase at the later recovery range.     

Studies on the properties of ionic liquid EMIInCl4

This paper reports that an ionic liquid (IL) has been prepared by directly mixing InCl₃ and 1-methyl-3-ethylimidazolium chloride (EMIC) with molar ratio 1/1 under dry argon atmosphere. The densities, and surface tension of the pure IL were determined at temperature range of 293.15 to 343.15 ± 0.1 K. The volumetric properties and the properties of surface for ionic liquid based on group III were discussed by Glasser's theory and Yang's interstice model.     

Cellulose: the structure slowly unravels

This article attempts to bring together basic and complex information which has been gathered on cellulose structure, principally that of native cellulose, over the last few decades. Even though advances have been made in the field of crystallography, powder crystallography cannot yield a definitive cellulose structure and single crystal diffraction is not possible due to the lack of suitable crystals. Knowledge obtained on the biosynthesis of native cellulose and on the polymorphy of cellulose and its derivatives help our understanding of ultrastructure. Many inconsistencies between early crystallographic studies of native cellulose have been clarified by the discovery that two polymorphs (α and β) of cellulose I exist. Models of the possible ultrastructural arrangements within native cellulose have been put forward over the decades; with advancement in technology, computer simulations of small and large systems are being created to test the viability of these ultrastructural models. It is hoped that this review will aid in the understanding of the complexity and uncertainties that still exist in this subject. This revised version was published online in August 2006 with corrections to the Cover Date.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Interface motion in a two-dimensional Ising model with a field

We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.     

Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles

We consider the accumulation of immobile particles landing on a one-dimensional lattice and annihilating via the A + B 0 bimolecular reaction. Here we focus on short-range interactions with cutoff. We investigate through computer simulations both the kinetics of the particles' accumulation and also their spatial distribution. The relation between the exponents describing the growth of the particles' concentration and the correlation length of their distribution shows that the kinetics of accumulation is fluctuation-dominated.This work is dedicated to Prof. George H. Weiss.