Effect of head group size, temperature and counterion specificity on cationic micelles

The critical micelle concentration (cmc) and ionisation degree (α), of micelles of cetyltrimethylammonium bromide (CTABr), cetyltrimethylammonium chloride (CTACl), cetyltripropylammonium bromide (CTPABr) and cetyltripropylammonium chloride (CTPACl) have been measured over a narrow temperature range at 2 degree intervals using electrical conductivity. CTPACl and CTPABr are very soluble in water and were measured in the temperature range 275.15-323.15K. The Krafft temperatures for CTABr and for CTACl are 293.15K and 284.15K, respectively and established a lower temperature limit for our studies on these two surfactants. The cmc vs temperature curves have a smooth minimum near room temperature and α linearly increases with temperature. The changes of cmc and α with temperature are smaller than those associated with the modification of head group size or counterion nature. Using these results, basic thermodynamic quantities associated with the phenomena of micellization have been evaluated. Thermodynamic properties of the surfactant solutions were discussed in terms of temperature dependence of the free energy, enthalpy and entropy of micellization. A close similarity between the effects of change in temperature on protein folding and micellization process appears from the data.     

Exploring the free energy surfaces of clusters using reconnaissance metadynamics

A new approach is proposed for exploring the low-energy structures of small to medium-sized aggregates of atoms and molecules. This approach uses the recently proposed reconnaissance metadynamics method [G. A. Tribello, M. Ceriotti, and M. Parrinello. Proc. Natl. Acad. Sci. U.S.A. 107(41), 17509 (2010)] in tandem with collective variables that describe the average structure of the coordination sphere around the atoms/molecules. We demonstrate this method on both Lennard-Jones and water clusters and show how it is able to quickly find the global minimum in the potential energy surface, while exploring the finite temperature free energy surface.     

Quantum mechanical embedding theory based on a unique embedding potential

We remove the nonuniqueness of the embedding potential that exists in most previous quantum mechanical embedding schemes by letting the environment and embedded region share a common embedding (interaction) potential. To efficiently solve for the embedding potential, an optimized effective potential method is derived. This embedding potential, which eschews use of approximate kinetic energy density functionals, is then used to describe the environment while a correlated wavefunction (CW) treatment of the embedded region is employed. We first demonstrate the accuracy of this new embedded CW (ECW) method by calculating the van der Waals binding energy curve between a hydrogen molecule and a hydrogen chain. We then examine the prototypical adsorption of CO on a metal surface, here the Cu(111) surface. In addition to obtaining proper site ordering (top site most stable) and binding energies within this theory, the ECW exhibits dramatic changes in the p-character of the CO 4σ and 5σ orbitals upon adsorption that agree very well with x-ray emission spectra, providing further validation of the theory. Finally, we generalize our embedding theory to spin-polarized quantum systems and discuss the connection between our theory and partition density functional theory.     

Monte Carlo and event-driven dynamics of Brownian particles with orientational degrees of freedom

Recently, a simple scaling argument was introduced that allows us to map, with some precautions, Brownian and Monte Carlo dynamics for spherical particles. Here, we extend the scaling to study systems that have orientational degrees of freedom and carefully asses its validity over a wide region of temperature and density. Our work allows us to devise a Brownian Monte Carlo algorithm that produces, to a good approximation, physically meaningful trajectories with a minimum programming effort, although at the expense of some sampling efficiency.     

The continuous-flow cycloaddition of azomethine ylides to carbon nanotubes

This communication demonstrates a straightforward continuous-flow method for efficient exohedral functionalisation of carbon nanotubes which affords soluble samples in a much shorter time over conventional batch processing.     

On the intensity of linear elastic high order singularities ahead of cracks and re-entrant corners

The paper deals with high order elastic singular terms at cracks and re-entrant corners (sharp V-notches), which are commonly omitted in linear elastic analyses by the argument that the strain energy and displacements in the near-tip region should be bounded. The present analysis proves that these terms are fully included in the elastic part of complete elastic–plastic stress and strain solutions.The intensities of high order singular terms are found to be linked to the linear elastic stress intensity factor and the extension of the plastic zone along the crack bisector line. The smaller the plastic radius, the smaller the intensities of high order singular terms are.A physical justification of the existence of high order singular terms is provided on the basis of the strain energy density distribution detected along the crack bisector line. Finally, the influence of the V-notch opening angle is made explicit, discussing also the relationship between the singularity orders and the solution of a Williams’ type sinusoidal eigen-equation.     

Hysteresis cycles and fatigue criteria using anelastic models based on fractional derivatives

The constitutive equation and the fatigue of anelastic media are described by using fractional order derivatives. The stress–strain relation, based on a generalization of the Kelvin–Voigt model, describes typical hysteresis cycles with the stress increasing as the number of cycles increases, a phenomenon known as cyclic hardening and observed in many materials such as, for instance, steel. Criteria are established to find the number of cycles which may cause fatigue for a strain with a given amplitude and frequency. They are based on the yield and fatigue stresses, on the melting temperature through the dissipated energy, and on the strain energy. In all the cases, it is seen that the number of cycles to failure is inversely proportional to the amplitude and to the frequency of the applied strain. Comparison to experimental data indicates that the model satisfies, at least qualitatively, the behavior of real materials under cyclic loading.     

A preconditioning technique for a class of PDE-constrained optimization problems

We investigate the use of a preconditioning technique for solving linear systems of saddle point type arising from the application of an inexact Gauss?CNewton scheme to PDE-constrained optimization problems with a hyperbolic constraint. The preconditioner is of block triangular form and involves diagonal perturbations of the (approximate) Hessian to insure nonsingularity and an approximate Schur complement. We establish some properties of the preconditioned saddle point systems and we present the results of numerical experiments illustrating the performance of the preconditioner on a model problem motivated by image registration.     

Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity

We consider a two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity. In both the focusing and defocusing case we prove local well-posedness, i.e., existence and uniqueness of the solution for short times, as well as energy and mass conservation. In addition, we prove that this implies global existence in the defocusing case, irrespective of the power of the nonlinearity, while in the focusing case blowing-up solutions may arise.