Hydrogen bonded rings,chains and lassos: the case of t-butyl alcohol clusters

Infrared OH stretching spectra of hydrogen bonded 2-methyl-propan-2-01 (t-butyl alcohol) clusters are investigated by ragout-jet FTIR spectroscopy. A spectral difference technique is used to discriminate approximately between neighbouring cluster sizes. Dimers, trimers and cyclic tetramers can be detected along with larger clusters, which exhibit a surprisingly structured vibrational fingerprint. Comparison is made to the spectra of related alcohols and to energetic and harmonic vibrational predictions from electronic structure calculations. The experimentally observed 32% increase in OH stretching wavenumber shift from methanol dimer to t-butyl alcohol dimer is reproduced at the HF/3-21G level (+ 33%). It is also qualitatively correct at the MP2/6-31 +G* level (+ l5%), whereas it has the wrong sign at the B3LYP/6-31+ G* level (5%) and is negligible at the HF/6-31+ G* level, disregarding anharmonic effects. The cyclic tetramer of t-butyl alcohol is found to be particularly stable due to a favourable updown alternation of the bulky t-butyl groups. Beyond the t-butyl alcohol tetramer, lasso structures are found to be energetically competitive with simple ring structures. A many-body decomposition shows that this is due to a reduced cooperativity in the sterically hindered pentamer ring. The resulting thermodynamic and kinetic relevance of cyclic tetramers is discussed.     

OPTIMAL HARVEST FEEDBACK RULE ACCOUNTING FOR THE FISHING‐UP EFFECT AND SIZE‐DEPENDENT PRICING

Abstract Fishing leads to truncation of a population's age and size structure. However, large‐sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size‐related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon–Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon–Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size‐dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies, potentially causing rent dissipation and suboptimal utilization of renewable resources.     

Anion polarizability functions in alkali halide crystals

Anion polarizabilities in alkali halide crystals are analysed as a function of interionic separation R. The anion polarizability is treated as a function of the anion and cation radii, with its partial derivatives approximated by those with respect to R for fixed cation and anion, respectively. With pressure derivatives of the ionic radii deduced from the crystal compressibility, assuming transferability among crystals, the polarizability derivatives with respect to ionic radius yield pressure derivatives of the polarizability that agree with experiment to within a factor of two. These results offer a useful means of predicting the pressure dependence of dielectric data.     

Models of environmental effects on anion polarizability

This paper deals with three different approaches to the representation of environmental effects on anion polarizability in cubic crystals of the stoichiometry MX, where M is an alkali metal and X is a halogen. Ab initio embedded cluster calculations of the variation in anion polarizability with pressure in a fixed crystal type are presented and compared with experiment. The results are then used in a scaled ab initio model used to predict further values for the pressure dependence of the in-crystal anion polarizability. This scaled model is compared with a fully empirical ‘universal’ model due to Batana et al. based on polarizability change with ionic radius [1997, Molec. Phys., 92, 1029]. The assumptions of the two models differ substantially and the central purpose of this paper is to contrast these differences and highlight their consequences for prediction. Although the empirical model typically overestimates the experimental pressure derivatives, and the ab initio calculations somewhat underestimate them, it is shown that the assumption of incompressible cations in the scaled ab initio-derived model has a firmer physical basis than the empirical picture in which all ions are compressible.     

Molecular dynamics study of the mobility in poly(butyl methacrylate) isomers

Molecular mobility is studied in poly(butyl methacrylate) isomers with molecular dynamics simulations in order to understand the role of the side chain steric hindrance on the β and δ relaxation mechanisms. The simulations suggest that in the temperature range studied the δ process is weakly influenced by the α process. Conversely, the β process seems to be significantly changed as compared with the low frequency regime. The results exposed also show evidence that the intramolecular cooperativity is higher in PnBMA than in PtBMA, which, could be related to the distance to the α-β crossover.     

o-Terphenyl: flips of the end rings in the crystal phase

We demonstrate by selective saturation deuteron NMR experiments on a crystal of selectively deuterated o-terphenyl (OTP) that both end rings I and II attached to the central ring undergo thermally activated flip motions. In crystals of OTP, the end rings I and II are not symmetry related, their dynamics can be different and, in fact, is different, although mutual steric hindrance of the rings suggests a strong correlation. We measured the rates k _I and k _II of the flips of both end rings I and II as a function of temperature. We find that, independent of the temperature, k _I exceeds k _II by roughly a factor of 100. This result excludes correlated flips of rings I and II in the sense that a flip of one ring necessarily entails a flip of the other. The activation energies E_aI and E_aII of the two flip processes turn out to be equal (80.5 kJ mol^?1) within experimental errors. This is taken as a hint that the flips are, after all, related to each other. A mechanism is proposed of how this is possible under the constraint k _I » k _II.     

Determining Knotsw and Links by Cyclic Branched Coverings

It is well known that different knots or links in the 3-sphere can have homeomorphic n-fold cyclic branched coverings. We consider the following problem: for which values of nis a knot of link determined by itsn-fold cyclic branched covering? We consider the class of hyperbolic resp.2π/n-hyperbolic links. The isometry or symmetry groups of such links are finite, and their n-fold branched coverings are hyperbolic 3-manifolds. Our main result states that if ndoes not divide the order of the finite symmetry group of such a link, then the link is determined by its n-fold branched covering. In a sense, the result is best possible; the key argument of its proof is algebraic using some basic result about finite p-groups. The main result applies, for example, to the cyclic branched coverings of the 2-bridge links; in particular, it gives a classification of the maximally symmetricD₆-manifolds which are exactly the 3-fold branched coverings of the 2-bridge links.     

Deuterium—carbon multiple-quantum NMR in liquid crystals: polarization transfer and off-magic-angle spinning

The polarization transfer dynamics in a recently introduced deuterium—carbon NMR correlation method is studied, both theoretically and experimentally. The technique, which exploits heteronuclear multiple-quantum coherences, is useful for measuring and assigning ²H quad-rupolar couplings in ordered media. It is also shown that the experiment is suitable for implementation under off-magic-angle spinning conditions. The approach is demonstrated on a perdeuterated liquid crystal.