Maximal f-Vectors of Minkowski Sums of Large Numbers of Polytopes

It is known that in the Minkowski sum of r polytopes in dimension d, with r<d, the number of vertices of the sum can be as high as the product of the number of vertices in each summand. However, the number of vertices for sums of more polytopes was unknown so far.     

Probing defect species on real surfaces from the analysis of the spectral profile of admolecules

The analysis of changes in the vibrational spectrum of infrared active molecules adsorbed on a ionic surface containing point or extended defects can be an efficient method to determine the nature and density of surface defects. We study the infrared response of ammonia molecules deposited on a ionic surface of MgO containing charge vacancies and dipolar defects in various concentrations and distributions and show significant changes assigned to the defects signature. A Monte Carlo approach is used to randomly deposit the probe molecules on the surface displaying random or regularly arranged defects at low temperature.     

Collision cell pressure effect on CID spectra pattern using triple quadrupole instruments: a RRKM modeling

Control of the ion internal energy in mass spectrometry is needed to establish a workable mass spectral library. The purpose of this study is to understand and to compare the pressure effects on the collision‐induced dissociation (CID) spectrum pattern recorded using triple quadrupole instruments. The monoprotonated Leucine enkephalin [YGGFL, H⁺] was used as a thermometer molecule to calibrate the electrospray ionization (ESI) and the CID internal energies deposited on the molecular species and the time scale of ion decompositions. The survival yield and the ratio of a₄/b₄ fragment ions were mainly monitored. The energy uptake for the ESI source geometry used in our study has no impact on the CID spectrum fingerprint. The collision cell pressure for the [YGGFL, H⁺] has a major influence on the SY curves slope and on the experimental time scale. To demonstrate the pressure effect on internal energy distribution, three models (threshold, thermal and collisional) based on RRKM theory were built using the Masskinetics software. As a result, the limit of each model is discussed, and the investigation demonstrates that the thermal model, using truncated Maxwell‐Boltzmann internal energy distribution, is well‐suited for simulating the experimental data at high pressure widely used in the analytical conditions. Copyright © 2013 John Wiley & Sons, Ltd.     

Liquid crystal side chain polysiloxanes containing various proportions of non-mesogenic units

Abstract

Recent studies have established that side chain polymeric liquid crystals composed of mesogenic and non-mesogenic side groups keep their liquid-crystalline properties even for a low proportion of mesogens. We show that the detailed structures of three kinds of new diluted liquid crystal polysiloxanes depend on the nature of the co-substituent as well as on the proportion of the silicon sites occupied by the mesogenic groups. Mixtures of these systems with low molar mass liquid crystals were also investigated in terms of compatibility and/or stabilization of smectic A phases.