Fractal calibration in size-exclusion chromatography I. An introduction

The elution behaviour of different polymer-solvent systems in three types of organic columns for SEC has been compared and interpreted. The experimental data show that the classical universal calibration is not accomplished. Deviations from a unique curve are observed due to the binary and ternary interactions between the components of the system (solvent, polymer and gel) which results on secondary mechanisms accompanying the main pure or "ideal" SEC separation mechanism. Both, enthalpic and entropic effects are interpreted in terms of the swelling and crosslinking degrees of the gel packings, and are also related with the fractal characteristics of their surfaces, such as the fractal dimension and the available pore size. Moreover, a relationship between the fractal dimension of the pore surface and the chromatographic distribution coefficient is proposed.     

Random replicators with high-order interactions

We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.     

How many Langmuirs are required for monolayer formation?

In the present work, we provide the exact answer to the title question employing a probabilistic approach. The average number of Langmuirs L required for monolayer formation was found to be equal to (1/i), i.e., the armonic series up to the nth term, where n is the number of adsorption sites. This result is particularly useful when a reduced number of adsorption sites is considered, such as adsorption on small terraces of nanoscopic dimensions where the value of n could be in the range of a few thousands sites. In this case, the use of integrated equations derived from the mean-field approach would provide completely misleading results.     

Theoretical study of pattern formation during the catalytic oxidation of CO on Pt{100} at low pressures

Theoretical studies have thus far been unable to model pattern formation during the reaction in this system on physically feasible length and time scales. In this paper, we derive a computational reaction-diffusion model for this system in which most of the input parameters have been determined experimentally. We model the surface on a mesoscopic scale intermediate between the microscopic size of CO islands and the macroscopic length scale of pattern formation. In agreement with experimental investigations [M. Eiswirth et al., Z. Phys. Chem., Neue Folge 144, 59 (1985)], the results from our model divide the CO and O(2) partial pressure parameter space into three regions defined by the level of CO coverage or the presence of sustained oscillations. We see CO fronts moving into oxygen-covered regions, with the 1 x 1 to hex phase change occurring at the leading edge. There are also traveling waves consisting of successive oxygen and CO fronts that move into areas of relatively high CO coverage, and in this case, the phase change is more gradual and of lower amplitude. The propagation speed of these reaction waves is similar to those observed experimentally for CO and oxygen fronts [H. H. Rotermund et al., J. Chem. Phys. 91, 4942 (1989); H. H. Rotermund et al., Nature (London) 343, 355 (1990); J. Lauterbach and H. H. Rotermund, Surf. Sci. 311, 231 (1994)]. In the two-dimensional version of our model, the traveling waves take the form of target patterns emitted from surface inhomogeneities.     

Configurational degeneracy of a set of dipoles in a quasi-two-dimensional system

The purpose of this paper is to provide an exact evaluation of the configurational degeneracy when an arbitrary number (k) of dipoles are placed in a quasi-two-dimensional space (Q2D). This Q2D is made up of three contiguous diagonals 3 × N. Our Q2D space gives to the central sites of the lattice their full coordination number of nearest neighboring compartments. We are going to determine the exact configurational degeneracy W(k, N) when an arbitrary number k of the above mentioned particles are placed in this 3 × NQ2D space. We found that W(k, N) is exactly described by

Unraveling the 13C NMR chemical shifts in single-walled carbon nanotubes: dependence on diameter and electronic structure

The atomic specificity afforded by nuclear magnetic resonance (NMR) spectroscopy could enable detailed mechanistic information about single-walled carbon nanotube (SWCNT) functionalization as well as the noncovalent molecular interactions that dictate ground-state charge transfer and separation by electronic structure and diameter. However, to date, the polydispersity present in as-synthesized SWCNT populations has obscured the dependence of the SWCNT (13)C chemical shift on intrinsic parameters such as diameter and electronic structure, meaning that no information is gleaned for specific SWCNTs with unique chiral indices. In this article, we utilize a combination of (13)C labeling and density gradient ultracentrifugation (DGU) to produce an array of (13)C-labeled SWCNT populations with varying diameter, electronic structure, and chiral angle. We find that the SWCNT isotropic (13)C chemical shift decreases systematically with increasing diameter for semiconducting SWCNTs, in agreement with recent theoretical predictions that have heretofore gone unaddressed. Furthermore, we find that the (13)C chemical shifts for small diameter metallic and semiconducting SWCNTs differ significantly, and that the full-width of the isotropic peak for metallic SWCNTs is much larger than that of semiconducting nanotubes, irrespective of diameter.     

Maturation of auditory temporal integration and inhibition assessed with event-related potentials (ERPs)

Background

We examined development of auditory temporal integration and inhibition by assessing electrophysiological responses to tone pairs separated by interstimulus intervals (ISIs) of 25, 50, 100, 200, 400, and 800 ms in 28 children aged 7 to 9 years, and 15 adults.

Results

In adults a distinct neural response was elicited to tones presented at ISIs of 25 ms or longer, whereas in children this was only seen in response to tones presented at ISIs above 100 ms. In adults, late N1 amplitude was larger for the second tone of the tone pair when separated by ISIs as short as 100 ms, consistent with the perceptual integration of successive stimuli within the temporal window of integration. In contrast, children showed enhanced negativity only when tone pairs were separated by ISIs of 200 ms. In children, the amplitude of the P1 component was attenuated at ISIs below 200 ms, consistent with a refractory process.

Conclusions

These results indicate that adults integrate sequential auditory information into smaller temporal segments than children. These results suggest that there are marked maturational changes from childhood to adulthood in the perceptual processes underpinning the grouping of incoming auditory sensory information, and that electrophysiological measures provide a sensitive, non-invasive method allowing further examination of these changes.     

Unified analysis of thermodynamic and rheological properties of high polymer solutions. II. Ternary systems

We extend to ternary solutions our previous study of conformational, thermodynamic, and rheological properties of semidilute polymer solutions in good solvent. Osmotic pressure and viscosity measurements were performed in several mixtures of two compatible polymers in a common solvent. Renormalization group results were used to analyze the data, using de Gennes's blobs model to connect dynamic and conformational properties. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1071–1079, 2002     

Front waves in the NO + NH3 reaction on Pt{100}

In the present work, we spatially extended a brand new kinetic mechanism of the NO + NH3 reaction on Pt{100} to simulate the experimentally observed spatiotemporal traveling waves. The kinetic mechanism developed by Irurzun, Mola, and Imbihl (IMI model) improves the former model developed by Lombardo, Fink, and Imbihl (LFI model) by replacing several elementary steps to take into account experimental evidence published since the LFI model appeared. The IMI model achieves a better agreement with the experimentally observed dependence of the oscillation period on temperature. In the present work, the IMI model is extended by considering Fickean diffusion and coupling via the gas phase. Traveling waves propagating across the surface are obtained at realistic values of temperature and partial pressure. A transition from amplitude to phase waves is observed, induced either by temperature or by the gas global coupling strength. The traveling waves simulated in the present work are not associated with fixed defects, in agreement with experimental evidence of spiral centers capable of moving on the surface. Also, the IMI model adequately predicts the presence of macroscopic oscillations in the partial pressures of the reactants coexisting with front wave patterns on the surface.     

Hydrodynamic properties of regular star-branched polymer in dilute solution

We calculate quantities such as g = [η]_b/[η]_l and h = (f_t)_b/(f_t)_t for regular star-branched polymer with and without excluded volume. We have applied a numerical method introduced by Barrett for the linear chain and have solved the integral equations which are conducive to calculate the translational coefficient friction and the intrinsic viscosity in the Kirkwood-Riseman theory. We utilize preaveraging but avoid other approximations. In general, we obtain values which have a better accord with experimental data than traditional Kirkwood-Riseman and Zimm-Kilb formulas. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 563–567, 1997