Bending, twisting, and breaking CuCN chains to produce framework materials: the reactions of CuCN with alkali-metal halides

The reactions of the low-temperature polymorph of copper(I) cyanide (LT-CuCN) with concentrated aqueous alkali-metal halide solutions have been investigated. At room temperature, KX (X = Br and I) and CsX (X = Cl, Br, and I) produce the addition products K[Cu-2(CN)(2)Br](H2O)-H-. (I), K-3[Cu-6(CN)(6)I-3](.)2H(2)O (II), Cs[Cu-3(CN)(3)Cl] (III), Cs[Cu-3(CN)(3)Br] (IV), and Cs-2[Cu-4(CN)(4)I-2](H2O)-H-. (V), with 3-D frameworks in which the -(CuCN)- chains present in CuCN persist. No reaction occurs, however, with NaX (X = Cl, Br, I) or KCl. The addition compounds, I-V, reconvert to CuCN when washed. Both low- and high-temperature polymorphs of CuCN (LT- and HT-CuCN) are produced, except in the case of Cs[Cu-3(CN)(3)Cl] (III), which converts only to LT-CuCN. Heating similar AX-CuCN reaction mixtures under hydrothermal conditions at 453 K for 1 day produces single crystals of I-V suitable for structure determination. Under these more forcing conditions, reactions also occur with NaX (X = Cl, Br, I) and KCl. NaBr and KCl cause some conversion of LT-CuCN into HT-CuCN, while NaCl and NaI, respectively, react to form the mixed-valence Cu(I)/Cu(II) compounds [Cu-II(OH2)(4)][Cu-4(I)(CN)(6)], a known phase, and [Cu-II(OH2)(4)][Cu-4(I)(CN)(4)I-2] (VI), a 3-D framework, which contains infinite -(CuCN)- chains. After 3 days of heating under hydrothermal conditions, the reaction between KI and CuCN produces [Cu-II(OH2)(4)][Cu-2(I)(CN)I-2](2) (VII), in which the CuCN chains are broken into single Cu-CN-Cu units, which in turn are linked into chains via iodine atoms and then into layers via long Cu-C and Cu-Cu interactions.

beta-Sheet mediated self-assembly of dipeptides of omega-amino acids and remarkable fibrillation in the solid state

Single crystal X-ray diffraction studies show that the extended structure of dipeptide I Boc-beta-Ala-m-ABA-OMe (m-ABA: meta-aminobenzoic acid) self-assembles in the solid state by intermolecular hydrogen bonding to create an infinite parallel P-sheet structure. In dipeptide II Boc-gamma-Abu-m-ABA-OMe (gamma-Abu: gamma-aminobutyric acid), two such parallel beta-sheets are further cross-linked by intermolecular hydrogen bonding through m-aminobenzoic acid moieties. SEM (scanning electron microscopy) studies reveal that both the peptides I and II form amyloid-like fibrils in the solid state. The fibrils are also found to be stained readily by Congo red, a characteristic feature of the amyloid fiber whose accumulation causes several fatal diseases such as Alzheimer's, prion-protein etc.

A novel cation induced polymeric chain in Na-8[{Cu(gly)(2)}(2)]{H-2(H2W12O42)}] center dot 24H(2)O: hydrothermal synthesis, spectroscopic characterization and X-ray structure analysis

A novel bis(glycinato) copper(II) paradodecatungstate Na-8[{Cu(gly)(2)}(2)]-{H-2(H2W12O42)}] center dot 24H(2)O (1) has been synthesized under hydrothermal conditions. The crystal structure of 1 reveals an infinite one-dimensional chain along the [100] direction and is built from paradodecatungstate (H2W12O42)(10-) clusters joined through [Cu(gly)(2)] moieties. Parallel chains are interlinked by NaO6 octahedra to generate a two-dimensional network.

Novel charge transfer supramolecular assemblies with Keggin anions and 2-amino-5-nitropyridine

Several novel compounds with the non-linear optical chromophore 2-amino-5-nitropyridine (2A5NP) and Keggin polyoxoanions (alpha-isomers), having the general formula (2A5NP)(m)H-n[XM12O40]center dot xH(2)O, M = Mo, W, were synthesised. Compounds were obtained with X = P, n = 3, m = 3 and 4 and X = Si, n = m = 4 ( x = 2 - 6). Thus, for each of the anions [PMo12O40](3-) and [PW12O40](3-) two different compounds were obtained, with the same anion and organic counterpart but with a different stoichiometric ratio. These presented different charge transfer properties and thermal stability. All compounds were characterised by spectroscopic and analytical techniques. The single crystal X-ray diffraction structure of (2A5NP)(4)H-3[PMo12O40]center dot 2.5H(2)O center dot 0.5C(2)H(5)OH showed that the water solvent molecules and the organic chromophores are assembled via infinite one-dimensional chains of hydrogen bonds with formation of open channels, which accommodate [ PMo12O40] 3- and ethanol solvent molecules.

Syntheses and crystal structures of two new coordination polymers of Cd(II) using organic spacer and inorganic-bridging ligands

Two new cadmium (II) complexes [Cd(hmt)(dca)(2)] (n) (1) and [Cd-3(hmt)(2)(SeCN)(6)(H2O)(2)] (n) (2) (hmt=hexamethylenetetramine, dca=dicyanamide) have been synthesized and characterized by X-ray single-crystal analysis. The complex 1 is a 2D rectangular grid of octahedral cadmium (II) with CdN6 chromophore where cadmium centers are doubly bridged by dicyanamide and hmt along a-axis, which are interlinked by dicyanamide running along c-axis. Whereas, complex 2 is a 1D chain of octahedral cadmium (II) with a three-leg ladder topology running along a-axis. The Cd(II) centers are doubly bridged through SeCN (infinite rail) along a-axis and singly bridged by hmt (two-step rung) along c-axis, having cadmium centers with CdSe2N3O and CdSe2N4 chromophores. The adjacent chains through H-bonding between coordinated water and hmt, and (SeSe)-Se-... interaction are extended to 2D supramolecular architecture.

The threading of [(CuCN)(2)(mu-4,4 '-bpy)] sheets by CuCN chains

Yellow (CuCN)(2)[(CuCN)(2)(mu-4,4'-bpy)], formed in the hydrothermal reaction of CuCN with 4,4'-bipyridine at 453 K, contains two types of infinite CuCN chains. One set of CuCN chains is linked by 4,4'-bpy ligands to form almost flat sheets of composition [(CuCN)(2)(mu-4,4'-bpy)]. Holes in these sheets are aligned to allow pairs of approximately linear, infinite -(CuCN)- chains to thread through them. The closest interatomic approach between copper atoms in the threading chains and host sheets (similar to2.74 Angstrom) does not appear to represent a significant covalent bond as it leads to only a small distortion of the -(CuCN)- chains from linearity The relationship of this material to the previously determined structures of the host [(CuCN)(2)(mu-4,4'-bpy)] sheets and (CuCN)(3)[(CuCN)(2)(mu-4,4'-bPY)](2), in which these sheets are threaded by single -(CuCN)- chains, is discussed.

Structure of AuCN determined from total neutron diffraction

The structure of gold cyanide, AuCN, has been determined at 10 and 300 K using total neutron diffraction. The structure consists of infinite -Au-(CN)-Au-(CN)-Au-(CN)- linear chains, hexagonally packed, with the gold atoms in sheets. The Au-C and Au-N bond lengths are found to be identical, with d(Au-C/N) = 1.9703(5) Angstrom at 300 K. This work supersedes a previous study, by others, which used Rietveld analysis of neutron Bragg diffraction in isolation, and found these bonds to have significantly different lengths (Deltad = 0.24 Angstrom) at 300 K. The total correlation function, T(r), at 10 and 300 K, has been modeled using information derived from total diffraction. The broadening of inter- and intrachain correlations differs markedly due to random displacements of the chains in the direction of the chain axes. This is a consequence of the relatively weak bonding between the chains. An explanation for the negative thermal expansion in the c-direction, which occurs between 10 and 300 K, is presented.

Methylammonium antimony sulfide

Bis(methylammonium) octaantimony(III) dodecasulfide persulfide, (CH3NH3)(2)[Sb8S12(S-2)], contains pairs of [Sb4S7](2-) chains joined through an unusual persulfide bond to create infinite double [Sb8S14](2-) chains. The double chains are interlocked by longer Sb center dot center dot center dot S interactions to form sheets approximately parallel to the (101) crystallographic plane. Methylammonium cations, formed by decomposition of 2-methylpropane-1,2-diamine during the synthesis, are located in large (Sb8S10) hetero-ring apertures created within the double chains.

Modelling oil absorption during post-frying cooling - I: model development

Several studies have highlighted the importance of the cooling period in oil absorption in deep-fat fried products. Specifically, it has been established that the largest proportion of oil which ends up into the food, is sucked into the porous crust region after the fried product is removed from the oil bath, stressing the importance of this time interval. The main objective of this paper was to develop a predictive mechanistic model that can be used to understand the principles behind post-frying cooling oil absorption kinetics, which can also help identifying the key parameters that affect the final oil intake by the fried product. The model was developed for two different geometries, an infinite slab and an infinite cylinder, and was divided into two main sub-models, one describing the immersion frying period itself and the other describing the post-frying cooling period. The immersion frying period was described by a transient moving-front model that considered the movement of the crust/core interface, whereas post-frying cooling oil absorption was considered to be a pressure driven flow mediated by capillary forces. A key element in the model was the hypothesis that oil suction would only begin once a positive pressure driving force had developed. The mechanistic model was based on measurable physical and thermal properties, and process parameters with no need of empirical data fitting, and can be used to study oil absorption in any deep-fat fried product that satisfies the assumptions made.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Perspex machine IX: transreal analysis

We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

Examining random number generators used in stochastic iteration algorithms

This paper investigates random number generators in stochastic iteration algorithms that require infinite uniform sequences. We take a simple model of the general transport equation and solve it with the application of a linear congruential generator, the Mersenne twister, the mother-of-all generators, and a true random number generator based on quantum effects. With this simple model we show that for reasonably contractive operators the theoretically not infinite-uniform sequences perform also well. Finally, we demonstrate the power of stochastic iteration for the solution of the light transport problem.

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.

On the spectra of certain integro-differential-delay problems with applications in neurodynamics

We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.