Transition Metal Complexes with Pyrazole-based Ligands. Part 12. Characterisation and thermal decomposition of CuCl2 complexes with di- and trisubstituted pyrazoles

The synthesis of copper(II) chloride complexes with 3,5-dimethylpyrazole, 1-carboxamidine-3,5-dimethylpyrazole, 5-amino-4-carboxamide-1-phenylpyrazole and 4-acetyl-3-amino-5-methylpyrazole is described. The compounds are characterized by elemental analysis, FT-IR spectroscopy, thermal methods, magnetic moment and molar conductivity measurements. Thermal decomposition of the dichloro-(3,5-dimethylpyrazole)-copper(II) complex results in an unstable intermediate with a stochiometric composition. The decomposition of the other compounds is continuous. This revised version was published online in August 2006 with corrections to the Cover Date.     

Novel recognition mechanisms in biological adhesion

Molecular recognition is generally thought of in terms of bond formation between unique sites on host and complementary guest molecules, but recent studies have revealed new complexities in biological recognition at cell. Adhesion between cell surfaces similarly involves specific interactions between analogous ligands and receptors. Recent force measurements, however, suggest that cell adhesion proteins may bind via multiple interaction sites that can form in a sequential manner. Other studies further show that in some instances, the principal recognition event may not be receptor–ligand docking, but the assembly of a complex pattern of many receptors and ligands.     

High‐throughput characterization of pattern formation in symmetric diblock copolymer films

Surface‐pattern formation in thin block copolymer films was investigated by utilizing a high‐throughput methodology to validate the combinatorial measurement approach and to demonstrate the value of the combinatorial method for scientific investigation. We constructed measurement libraries from images of subregions of block copolymer films having gradients in film thickness and a range of molecular mass, M. A single gradient film covers a wide range of film morphologies and contains information equivalent to a large number of measurements of films having a fixed thickness, h. Notably, the scale of the surface patterns is generally much larger than the molecular dimensions so that the interpretation of the patterns is more subtle than ordering in bulk block copolymer materials, and there is no predictive theory of this type of surface‐pattern formation. We observed a succession of surface patterns that repeat across the film with increasing h [extended smooth regions, regions containing circular islands, labyrinthine (“spinodal”) patterns, holes, and smooth regions again]. The extended smooth regions and the labyrinthine patterns appear to be novel features revealed by our combinatorial study, and these patterns occurred as bands of h that were quantized by integral multiples of the bulk lamellar period, L_o. The magnitude of the height gradient influenced the width of the bands, and the smooth regions occupied an increasing fraction of the film‐surface area with an increasing film gradient. The average size of the spinodal patterns, λ, was found to scale as λ ～ L or λ ～ M^?1.65 and reached a limiting size at long annealing times. The hole and island features had a size comparable to λ, and their size likewise decreased with increasing M. The smooth regions were attributed to an increase in the surface‐chain density in the outer brushlike block copolymer layer with increasing h, and the scaling of λ with M was interpreted in terms of the increasing surface elasticity with M. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2141–2158, 2001     

Effect of the comonomer content on the mechanical parameters and microhardness values in poly(ethylene‐co‐1‐octadecene) synthesized by a metallocene catalyst

Stress–strain and microhardness measurements were carried out on a series of copolymers of ethylene and 1‐octadecene with different comonomer contents in the corresponding homopolymer of ethylene, synthesized with a metallocene catalyst. The different mechanical properties, deduced from the stress–strain curves (Young's modulus, yield stress, deformation at break, and energy to break) are interpreted in terms of the crystallinity and molecular weight of the samples because these two characteristics show considerable variations with the comonomer content. The microhardness values are explained in terms of these properties, and they are also correlated with Young's moduli and yield stresses deduced from the stress–strain curves. Linear relations are found between microhardness and yield stress and between the logarithm of the microhardness and the logarithm of the elastic modulus. The properties deduced from these lines are compared with literature values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 277–285, 2001     

On the determination of dynamic surface tensions by means of a modified bubble pressure method

A method for the determination of the dynamic surface tension of surfactant solutions is presented which allows to cover adsorption times down to 10 seconds. This method is based on the determination of the pressure inside two communicating bubbles. There is no deformation of the solution/air interface during the experimental procedure. Hence, in evaluating the kinetic data no surface area enlargement has to be taken into account. An automatically operating procedure should allow to cover adsorption times down to approximately one second and should improve the measuring accuracy substantially. Experimental investigations with aqueous n-decanoic acid solutions using the method proposed provided evidence that decanoic acid is adsorbed by a diffusioncontrolled mechanism.     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.     

Simulated annealing with noisy or imprecise energy measurements

The annealing algorithm (Ref. 1) is modified to allow for noisy or imprecise measurements of the energy cost function. This is important when the energy cannot be measured exactly or when it is computationally expensive to do so. Under suitable conditions on the noise/imprecision, it is shown that the modified algorithm exhibits the same convergence in probability to the globally minimum energy states as the annealing algorithm (Ref. 2). Since the annealing algorithm will typically enter and exit the minimum energy states infinitely often with probability one, the minimum energy state visited by the annealing algorithm is usually tracked. The effect of using noisy or imprecise energy measurements on tracking the minimum energy state visited by the modified algorithms is examined.The research reported here has been supported under Contracts AFOSR-85-0227, DAAG-29-84-K-0005, and DAAL-03-86-K-0171 and a Purdue Research Initiation Grant.     

Phase and Interfacial Tension Behavior of Certain Model Gas Condensates: Measurements and Modeling

This contribution reports on the phase and interfacial tension behavior of some model high-temperature–high-pressure gas condensates. On the one hand these types of gas condensate are becoming a subject of major interest for the oil industry, while on the other their phase and interfacial tension behavior have not been very well studied. For two different model gas condensates, both composed of the three n-alkanes, methane, butane, and decane, experimental results on their fluid phase behavior have been obtained in the temperature region 270 < T (K) < 490 and up to pressures as high as 24 MPa. Also, critical points of the two mixtures have been determined experimentally. Both mixtures show an extended retrograde region. Using the Peng–Robinson equation of state, the phase behavior of the two mixtures was modeled. In addition, the interfacial tension behavior of the model gas condensates was modeled. For that purpose, the Cahn–Hilliard theory was applied in combination with the Peng–Robinson equation of state. Satisfactory results were obtained.     

THREE-DIMENSIONAL NUMERICAL LOCALIZATION OF IMPERFECTIONS BASED ON A LIMIT MODEL IN ELECTRIC FIELD AND A LIMIT PERTURBATION MODEL

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes： the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.     

NUMERICAL LOCALIZATION OF ELECTROMAGNETIC IMPERFECTIONS FROM A PERTURBATION FORMULA IN THREE DIMENSIONS

This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.