The free energy of expansion and contraction: treatment of arbitrary systems using the Jarzynski equality

Thermodynamic integration, free energy perturbation, and slow change techniques have long been utilised in the calculation of free energy differences between two states of a system that has undergone some transformation. With the introduction of the Jarzynski equality and the Crooks relation, new approaches are possible. This paper investigates an important phenomenon - systems undergoing a change in volume/density - and derives both the Jarzynski equality and Crooks relation of such systems using a statistical mechanical approach. These results apply to systems with arbitrary particle interactions and densities. The application of this approach to the expansion/compression of particles confined within a vessel with a piston and within a periodic system is considered.     

Ambient temperature zincation of N-Boc pyrrolidine and its solvent dependency

Sodium TMP-zincate, [(TMEDA)Na(TMP)((t)Bu)Zn((t)Bu)], can deproto-zincate N-Boc pyrrolidine at ambient temperature in hexane solution, whereas in toluene the captured α-carbanion of the heterocycle attacks the solvent setting off a cascade of reactions that ultimately produce a pyrrolidine-substituted enolate.     

Selective formation of a polar incomplete coordination cage induced by remote ligand substituents

Instead of highly symmetrical T-symmetry cages common in self-assembly, the p-NMe(2)-substituted triphosphine CH(3)C{CH(2)P(4-C(6)H(4)NMe(2))(3) gives open, polar C(3) symmetry cages [Ag(6)(triphos)(4)X(3)](3+) which lack one of the expected face-capping anions; despite its subtlety this difference occurs selectively in solution and two examples have been crystallographically characterised.     

Ln(III)(2)Mn(III)(2) heterobimetallic "butterfly" complexes displaying antiferromagnetic coupling (Ln = Eu, Gd, Tb, Er)

The isostructural heterometallic complexes [Ln(III)(2)Mn(III)(2)O(2)(ccnm)(6)(dcnm)(2)(H(2)O)(2)] (Ln = Eu (1Eu), Gd (1Gd), Tb (1Tb), Er (1Er); ccnm = carbamoylcyanonitrosomethanide; dcnm = dicyanonitrosomethanide) have been synthesised and structurally characterised. The in situ transition metal promoted nucleophilic addition of water to dcnm, forming the derivative ligand ccnm, plays an essential role in cluster formation. The central [Ln(III)(2)Mn(III)(2)(O)(2)] moiety has a "butterfly" topology. The coordinated aqua ligands and the NH(2) group of the ccnm ligands facilitate the formation of a range of hydrogen bonds with the lattice solvent and neighbouring clusters. Magnetic measurements generally reveal weak intracluster antiferromagnetic coupling, except for the large J(MnMn) value in 1Gd. There is some evidence for single molecule magnetic (SMM) behaviour in 1Er. Comparisons of the magnetic properties are made with other recently reported butterfly-type {Ln(III)(x)M(III)(4-x) (d-block)} clusters, x = 1, 2; M = Mn, Fe.     

Engineering of an active animal fatty acid synthase dimer with only one competent subunit

Animal fatty acid synthases are large polypeptides containing seven functional domains that are active only in the dimeric form. Inactivity of the monomeric form has long been attributed to the obligatory participation of domains from both subunits in catalysis of substrate loading and condensation reactions. However, we have engineered a fatty acid synthase containing one wild-type subunit and one subunit compromised by mutations in all seven functional domains that is active in fatty acid synthesis. This finding indicates that a single subunit, in the context of a dimer, is able to catalyze the entire biosynthetic pathway and suggests that, in the natural complex, each of the two subunits forms a scaffold that optimizes the conformation of the companion subunit.     

Multifractal models via products of geometric OU-processes: Review and applications

This paper reviews a class of multifractal models obtained via products of exponential Ornstein–Uhlenbeck processes driven by Lévy motion. Given a self-decomposable distribution, conditions for constructing multifractal scenarios and general formulas for their Renyi functions are provided. Together with several examples, a model with multifractal activity time is discussed and an application to exchange data is presented.     

Desorption of polymers: role of the stagnant layer

The desorption of polymers is studied theoretically and with Monte Carlo simulations. Two regimes can be distinguished: in one regime the detachment of the polymer from the surface is the slowest process, and in the other it is the diffusion of the polymer away from the surface. In both regimes the desorption rate depends on the thickness H of the stagnant layer, i.e. the layer in which the polymer movement is dominated by diffusion. In the diffusion-limited regime the desorption rate scales as H ^{? 2}, as expected for diffusive processes. In the detachment-limited regime the desorption rate scales as H ^{? 1}. The importance of the thickness of the stagnant layer in the detachment-limited regime is due to the fact that the polymer, after it has detached, will most likely readsorb soon after: the probability that the polymer does not readsorb, but crosses the stagnant layer, is inversely proportional to the thickness of the stagnant layer.     

MISUNDERSTANDING MODELLING IN MECHANICS: A REVIEW OF THE A-LEVEL TEXTBOOK LITERATURE

All A-level boards have included a modelling approach in the syllabus of their respective mechanics modules and the plethora of textbooks during the past decade is structured according to this approach. This review will attempt to show that these books have confused modelling that is specific to mechanics with mathematical modelling in general. To place the recent textbooks in perspective, this review outlines the logical structure of mechanics, how this relates to the specificity of modelling in mechanics, the philosophical assumptions underlying the traditional textbook, how these assumptions have influenced the modern textbook and how history has been rewritten to justify these assumptions. The conclusion drawn is that the modular scheme has made this confusion unsustainable.