Theoretical Modeling of the Surface-Guided Self-Assembly of Functional Molecules

Directing the self-assembly of organic building blocks with 2D templates has been a promising method to create molecular superstructures having unique physicochemical properties. In this work the on-surface self-assembly of simple ditopic functional molecules confined inside periodic nanotemplates was modeled by means of the lattice Monte Carlo simulation method. Two types of confinement, that is honeycomb porous networks and parallel grooves of controlled diameter and width were used in the calculations. Additionally, the effect of (pro)chirality of the adsorbing molecules on the outcome of the templated self-assembly was examined. To that end, enantiopure and racemic assemblies were studied and the resulting structures were identified and classified. The obtained findings demonstrated that suitable tuning of the structural parameters of the templates enables directing the self-assembly towards linear and cyclic aggregates with controlled size. Moreover, chiral resolution of the molecular conformers using honeycomb networks with adjusted pore size was found possible. Our theoretical predictions can be helpful in designing structured surfaces to direct self-assembly and polymerization of organic functional building blocks.     

Neon‐Bearing Ammonium Metal Formates: Formation and Behaviour under Pressure

The incorporation of noble gas atoms, in particular neon, into the pores of network structures is very challenging due to the weak interactions they experience with the network solid. Using high‐pressure single‐crystal X‐ray diffraction, we demonstrate that neon atoms enter into the extended network of ammonium metal formates, thus forming compounds Ne_x[NH₄][M(HCOO)₃]. This phenomenon modifies the compressional and structural behaviours of the ammonium metal formates under pressure. The neon atoms can be clearly localised within the centre of [M(HCOO)₃]₅ cages and the total saturation of this site is achieved after ～1.5 GPa. We find that by using argon as the pressure‐transmitting medium, the inclusion inside [NH₄][M(HCOO)₃] is inhibited due to the larger size of the argon. This study illustrates the size selectivity of [NH₄][M(HCOO)₃] compounds between neon and argon insertion under pressure, and the effect of inclusion on the high‐pressure behaviour of neon‐bearing ammonium metal formates.     

On the Adams–Riemann–Roch theorem in positive characteristic

Let p > 0 be a prime number. We give a short proof of the Adams–Riemann–Roch theorem for the p-th Adams operation, when the involved schemes live in characteristic p. We also answer a question of B. Köck.     

Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x ²ⁿ + y ²ⁿ , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.     

W-shaped mesogens and variations of their molecular structure

New bent-core liquid crystalline dimers with W-shaped molecular geometry have been prepared and studied. We have modified the dimer shape by variation of the connecting part between two bent-core units and changing the terminal chains (perfluoroalkyl, siloxanealkyl). Additionally, we have altered the inner bend angle value (120°, 60° and 148°) by utilization of different aromatic units. Mesomorphic properties of new dimers were established based on the texture observation in the polarizing microscope and DSC measurements. Moreover, x-ray structural analysis has been performed for selected dimers to confirm phase identification. For most of the studied dimers, nematic or columnar phases have been detected, for several compounds appearing in a nematic-columnar phase sequence on cooling from the isotropic phase. The studied dimers showed richer polymorphism than their monomeric counterparts.     

Vortex locking in direct numerical simulations of quantum turbulence

Direct numerical simulations are used to examine the locking of quantized superfluid vortices and normal fluid vorticity in evolving turbulent flows. The superfluid is driven by the normal fluid, which undergoes either a decaying Taylor-Green flow or a linearly forced homogeneous isotropic turbulent flow, although the back reaction of the superfluid on the normal fluid flow is omitted. Using correlation functions and wavelet transforms, we present numerical and visual evidence for vortex locking on length scales above the intervortex spacing.     

Computational studies of aliphatic amine basicity

Computational studies have been used to examine the structural and energetic effects of adding small numbers of water molecules to ammonia, methylamine, dimethylamine, and trimethylamine, and their respective ammoniums ions using the effective fragment potential method. Distinct structural effects with only a few fragment water molecules are revealed. The complexity of structures increases with the number of water fragments with the water fragments forming complex networks. Structural and energetic effects are used to probe the so-called anomalous basicity effect of ammonia and the methylamines on going from the gas phase to aqueous solution.     

Compact two-photon fluorescence microscope based on a single-mode fiber coupler

We present a two-photon fluorescence microscope based on a three-port single-mode optical fiber coupler. It is found that the coupler behaves as a low-pass filter that can deliver an ultrashort-pulsed laser beam of as much as 150 mW of power in the wavelength range from 770 to 870 nm as well as collect a two-photon fluorescence signal in the visible range. As a result of using the fiber coupler, the new two-photon imaging system exhibts a number of advantages, including a compact arrangement, freedom from vibration from lasers and electronic devices, self-alignment, reduction of multiple scattering, and an enhanced optical sectioning effect. The effectiveness of the new instrument is demonstrated with a set of three-dimensional images of biological samples. This instrument may make two-photon fluorescence endoscopy possible for in vivo medical applications.