Partitioning and adsorption in gas-liquid-solid chromatography: Models of temporal moments for retention and variance

Summary The resolution of gaseous chemical species in gasliquid-solid chromatography is influenced by absorption (partitioning) in the liquid and adsorption at the liquid-solid interface. We consider fundamental mass transfer models with adsorption and partitioning effects for solid chromatographic supports covered with thin films of stationary liquid. The dynamic models, based on mass-balance partial-differential equations, include the significant phenomena: convection, axial dispersion, gas-liquid mass transfer, intraparticle diffusion, and liquid-solid adsorption. Expressions for retention time and band variance (first and second temporal moments) are presented and evaluated for four distinct models: (1) capillary tube with inner surface covered with a uniform-thickness liquid film, (2) column of nonporous spheres covered with a uniform-thickness liquid film, (3) porous spherical particles with intraparticle pores covered with a uniform-thickness liquid film, (4) porous spherical particles with intraparticle pores completely filled with liquid.     

Probing the dependence of long-range, four-atom interactions on intermolecular orientation: 2. Molecular deuterium and iodine monochloride

Laser-induced fluorescence and action spectroscopy experiments have identified multiple conformers of the D2...ICl van der Waals complex for both ortho-D2 (o-D2) and para-D2 (p-D2). As with the analogous H2...ICl van der Waals complexes [Darr, J. P.; Crowther, A. C.; Loomis, R. A.; Ray, S. E.; McCoy, A. B. J. Phys. Chem. A 2007, 111, 13387], the C2v conformer with the deuterium molecule localized at the iodine atom end of the dihalogen is significantly more stable than the asymmetric conformer that has the deuterium positioned orthogonally to the ICl bond axis, D0' = 223.9(2.4) versus 97.3(8)-103.9(3) cm(-1) for p-D2...I(35)Cl(X, v'=0). For both conformers, complexes containing p-D2 are found to be more strongly bound than those with o-D2. The electronically excited D2...ICl(A, v') and D2...ICl(B, v') complexes are found to have equilibrium geometries that are nearly the same as those of the ground-state asymmetric structures. Calculated D2...ICl(B, v'=3) energies and probability amplitudes obtained using a simple scaled He + ICl(B, v'=3) potential provide clues to the nature of the different excited-state levels accessed.     

Why does argon bind to deuterium? Isotope effects and structures of Ar x H5O2(+) complexes

Recently, we reported the spectrum of Ar x D4HO2(+) [McCunn; et, al. J. Phys. Chem. B 2008, 112, 321], and here, we extend that work to include the Ar x H4DO2(+) isotopologue in order to explore why the Ar atom has a much greater propensity for attachment to a dangling OD group than it does for OH, even when many more of the latter binding sites are available. Calculated (MP2/6-311+G(d,p) level of theory/basis) harmonic frequencies reproduce the observed multiplet patterns of OH and OD stretches and confirm the presence of various isomers arising from the different Ar binding sites. The preferential bonding of Ar to OD is traced to changes in the frequencies of the wag and rock modes of the H5O2(+) moiety rather than to shifts in the oscillator that directly binds the Ar atom.     

Spaces of Densely Continuous Forms

The set C(X,Y) of continuous functions from a topological space X into a topological space Y is extended to the set D(X,Y) of densely continuous forms from X to Y, such form being a kind of multifunction from X to Y. The topologies of pointwise convergence, uniform convergence, and uniform convergence on compact sets are defined for D(X,Y), for locally compact spaces X and metric spaces Y having a metric satisfying the Heine–Borel property. Under these assumptions, D(X,Y) with the uniform topology is shown to be completely metrizable. In addition, if X is compact, D(X,Y) is completely metrizable under the topology of uniform convergence on compact sets. For this latter topology, an Ascoli theorem is established giving necessary and sufficient conditions for a subset of D(X,Y) to be compact.     

Continued fractions and fermionic representations for characters of M(p,p′) minimal models

We present fermionic sum representations of the characters _{, s} ^{(p, p)} of the minimal M(p,p) models for all relatively prime integers p>p for some allowed values of r and s. Our starting point is biomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin 1/2 chain of anisotropy –=–cos((p/p)). We use the Takahashi-Suzuki method to express the allowed values of r (and s) in terms of the continued fraction decomposition of {p/p} (and p/p), where {x} stands for the fractional part of x. These values are, in fact, the dimensions of the Hermitian irreducible representations of SU _q- (2) (and SU _q+ (2)) with q–=exp(i{p/p}) (and q+=exp(i(p/p))). We also establish the duality relation M(p,p) M(p–p,p) and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Dedicated to Prof. Vladimir Rittenberg on his 60th birthday