One-dimensional rigorous hole theory of fluids: Internally constrained ensembles

A hole in a fluid is specified in a well-defined manner. The concentration of holes is a thermodynamic property of the fluid and we derive this concentration in three different ensembles for a one-dimensional fluid of hard rods. The thermodynamics of these rigorously defined holes is developed, and the properties of holes are explored. The ensemble in which the concentration of holes is maintained fixed exhibits dramatic properties. Finally, pair correlation functions for hard rods in the various ensembles are computed. Contrary to a frequently made assumption, the equilibrium number of holes is found to never be proportional to the probability of finding a single hole in the fluid. Constraining the concentration of holes as well as the density leads to dramatic structural effects prominently displayed by the pair correlation function. The ensemble in which the concentration of holes is fixed is an example of an internally constrained metastable system.     

Synthesis,Structure, and Optical Properties of Terminally Sulfur‐Functionalized Core‐Substituted Naphthalene‐Bisimide Dyes

The synthesis, characterization, and optical properties of a series of new 2,6‐disubstituted naphthalene‐bisimide dyes as molecular rods comprising terminal AcS groups is reported. The first series of dyes ( 1 – 3 ), comprising phenylhetero (Ph‐X) core substituents, cover a broad range of the VIS spectrum, ranging from yellow ( 2 ) over red ( 3 ) to blue ( 1 ). The second series of dyes contains benzylhetero (Bn‐X) core substituents ( 4 – 7 ). For the same heteroatom connecting the substituent to the naphthalene core, both series were found to display comparable colors. For the second series, the colors were blue ( 4 ), red ( 5 ), and violet ( 6, 7 ). The Ph‐X‐substituted dyes 1 – 3 are nonfluorescent, in contrast to the Bn‐X‐substituted compounds 4 – 7 . This rich variety of optical features that can be adjusted by rather small alterations of the core substituents makes these structurally very comparable molecular rods ideal candidates for optically triggered molecular‐transport investigations. Also, thanks to the terminal AcS groups, these compounds can be placed between nobel‐metal electrodes for optically triggered transport experiments.     

Solvatochromism and prototropism of diaminodiphenyl sulphones and 2-aminodiphenyl sulphone: a comparative study by electronic spectra

A comparative study of absorption and fluorescence maxima of 4,4′-diaminodiphenyl sulphone (4DADPS), 3,3′-diaminodiphenyl sulphone (3DADPS) and 2-aminodiphenyl sulphone (2ADPS) in different solvents reveals that (i) solvatochromic shifts are found to be mainly due to interaction of solvents with amino group, (ii) in any one solvent the net solvatochromic shifts of two amino groups are less than that of one amino group, (iii) fluorescence shift from cyclohexane to water is a maximum for 4DADPS and a minimum for 2ADPS and (iv) 4DADPS and 3DADPS possess more twisted intramolecular charge transfer character than 2ADPS. The excited-state acidity constants, determined by fluorimetric titration and Förster cycle methods, have been reported and discussed.     

Twisted amides: X-ray crystallographic and theoretical study of two acylated glycolurils with aromatic substituents

X-ray crystallography and theoretical analysis were applied to explore the molecular basis for the efficient and selective Claisen-like condensations of diacylglycolurils. The crystal structures of 1-acetyl-6-benzoyl-3,4,7,8-tetramethylglycoluril (4b), and of 1-(3′-oxo-3′-phenylpropionyl)-3,4,7,8-tetramethylglycoluril (5b), the product of base-promoted intramolecular condensation of 4b, were obtained by X-ray diffraction. The acetyl (Ac) group in 4b is essentially coplanar with the attached tetrahydroimidazolone ring of the glycoluril core (τ=7°), while the benzoyl (Bz) group is twisted by τ=45° relative to a plane through the ring to which it is bonded. Product 5b contains a flat amide (τ=7°). Ab initio energy optimizations of the experimental structures for 4b and 5b give optimized geometries which are not dramatically altered, suggesting that crystal packing effects are small. An atoms-in-molecules study of the delocalization of the Fermi hole reveals that electrons in the Bz C=O group of 4b are delocalized into the phenyl ring as well as into the urea moiety of the glycoluril core. This effect stabilizes the Bz over the Ac carbonyl group, and accounts for selective twisting of the Bz group. The Laplacian of the electron density reveals a non-bonded valence shell charge concentration at O of the Ac group, corresponding to a lone-pair region, aligned with a charge depletion in the valence shell of the Bz C=O carbon [(C15–O16C18)=113°]. The angle of approach [(O16C18=O19)] is 100°, equal to the angle for ideal nucleophilic attack on a carbonyl group. Oxygen atom O16 is thus poised to attack C18; only the O16C18 distance (3.248 Å) seems to prevent reaction. These results suggest that the same distance restraint may prevent O-acylation in the enolate intermediate 6b derived from4b. By contrast, the transition state for C-acylation, leading from 6b towards product 5b requires a different geometry, which may explain the observed selectivity for C-acylation in this enolate. The results show that, as 4b is converted to 5b, amide torsional strain is relieved, which may account for the high reactivity of 4b and the efficiency and irreversibility of this condensation process. This study provides a starting point for quantitative correlation of substrate structure in diacylglycolurils with kinetic data for the rearrangement reaction.     

Module Correspondences for Twisted Group Algebras

Abstract

Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K ^α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K ^α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K ^α G-modules and the set of irreducible K ^α C _G (A)-modules.     

New lower bounds on 2-spontaneous emission error designs

The combinatorial object named $t$-spontaneous emission error design ($t$-SEED) was proposed by Beth et al. in 2003 in order to correct errors caused by quantum jumps. The newly rising category of $t$-SEEDs has been studied extensively in recent years. Especially, the maximal possible dimensions for 2-SEEDs with block size 3 were determined completely; lower bounds on 2-SEEDs were established by applying affine groups. In this paper we utilize the action of twisted affine groups on finite fields and obtain new lower bounds on the dimensions of 2-$(q^2,k;m)$ SEEDs, some of which outperform the known ones.     

Inducing a high twisted conformation in the polyimide structure by bulky donor moieties for the development of non-volatile memory

Two polyimides, PI(DAT-6FDA) and PI(DAPT-6FDA), from N-(2,4-diaminophenyl)-N,N-diphenylamine (DAT) or N-(4-(2′,4′-diaminophenoxy)phenyl-N,N-diphenylamine (DAPT) and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6FDA) were prepared to clarify the structural effect on the resulting memory properties. The memory device based on PI(DAT-6FDA) showed an unstable volatile behavior, while the device based on PI(DAPT-6FDA) with a more bulky donor (D) unit exhibited a stable non-volatile FLASH type memory characteristic with a long retention time over 10⁴ s. The theoretical simulation based on the density functional theory (DFT) suggested that the greater distinct charge separation between the ground and charge transfer (CT) states led to a highly stable memory behavior. Also, it was clarified that PI(DAPT-6FDA) had a highly twisted conformation compared to PI(DAT-6FDA) in the ground state, and a more twisted dihedral angle between the D and acceptor (A) units was induced in the CT state, which led to the non-volatile memory characteristic.     

Synthesis and Spectroscopic Characterization of Fluorophore‐Labeled Oligospiroketal Rods

Fluorescence probes consisting of well‐established fluorophores in combination with rigid molecular rods based on spirane‐type structures were investigated with respect to their fluorescence properties under different solvent conditions. The attachment of the dyes was accomplished by 1,3‐dipolar cycloaddition between alkynes and azides (‘click’ reaction) and is a prime example for a novel class of sensor constructs. Especially, the attachment of two (different) fluorophores on opposite sides of the molecular rods paves the way to new sensor systems with less bulky (compared to the conventional DNA‐ or protein‐based concepts), nevertheless rigid spacer constructs, e.g., for FRET‐based sensing applications. A detailed photophysical characterization was performed in MeOH (and in basic H₂O/MeOH mixtures) for i) rod constructs containing carboxyfluorescein, ii) rod constructs containing carboxyrhodamine, iii) rod constructs containing both carboxyfluorescein and carboxyrhodamine, and iv) rod constructs containing both pyrene and perylene parts. For each dye (pair), two rod lengths with different numbers of spirane units were synthesized and investigated. The rod constructs were characterized in ensemble as well as single‐molecule fluorescence experiments with respect to i) specific rod? dye and ii) dye? dye interactions. In addition to MeOH and MeOH/NaOH, the rod constructs were also investigated in micellar systems, which were chosen as a simplified model for membranes.     

Recent advances in surface x-ray diffraction and the potential for determining structure-sensitivity relations in single-crystal electrocatalysis

Determining how electrode structure governs the performance of an electrocatalyst requires techniques capable of probing structure at the atomic scale, often in situ and operando. In recent years, there have been numerous advances in the main experimental techniques for determining the structure of the electrochemical interface. In situ/operando synchrotron surface x-ray diffraction measurements are key to investigate the atomic structure of the electrode surfaces as well as understand the structure-reactivity relations in electrocatalysis. Here we discuss some recent improvements that have taken place in surface x-ray diffraction and how we expect them to lead to an enhanced understanding of electrocatalysis.