Computing the Kekulé structure count for alternant hydrocarbons

A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekulé structure count. A simple method is presented for determining the Kekulé structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekulé structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 × N/2 matrix need be evaluated. The Kekulé structure count correlates with topological indices. The inclusion of the number of cycles improves the fit. When comparing with previous results, the variance decreases 74%. The calculated standard heat of formation correlates with the logarithm of the Kekulé structure count. This heat increments 349 kJ/mol each time the Kekulé structure count increases by one order of magnitude. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

On the deformation mechanisms of oriented PET and PP films under load

Uniaxially orienred semicrystalline poly(ethylene terephthalate) (PET) and poly(propylene) (PP) films were loaded parallel to draw direction at various temperatures. Changes in the submicroscopical structure of the films under load were examined by small and wide-angle x-ray scattering (SAXS; WAXS) and birefringence measurements. WAXS measurements reveal a decrease of the initial high orientation of the chains in the crystallites during deformation. Simultaneously, an increase of the birefringence was detected, indicating an orientation of chains in the amorphous regions. The alteration of the long period reflections in the SAXS patterns give strong evidence that lamellar stacks with different orientation angles according to load direction are present. Depending on the orientation of stacks, the contribution of lamellar separation to sample deformation alters, giving rise to different amounts of density changes in the stacks. Absolute intensity measurements of SAXS using a Kratky apparatus reveal that lamellar separation occurs preferentially below or in the range of the glass-transition temperature at small strain. With increasing strain and temperatures above the glass-transition slip deformation mechanisms become more important. The formation of microvoids was observed at strain near to elongation at break below or in the range of glass-transition temperature.     

Synthesis and characterization of MCM-48 tubular membranes

MCM-48 membranes have been prepared on alumina supports of different pore sizes. A battery of characterization techniques has been used to study the physical properties and the quality of the membranes prepared. The highest quality membranes were prepared on supports with pore size of up to 60 nm. The MCM-48 membranes were tested in the separation of gas phase mixtures and a cyclohexane/O₂ selectivity higher than 270 was obtained. The selective separation of organic compounds from inert components is a result of the cooperative effects of capillary condensation in MCM-48 pores and of the specific interactions of the permeating compounds and the membrane material.     

Determination of various deformation processes in impact-modified PMMA at strain rates up to 105%/min

The deformation processes in impact-modified PMMA, which deforms homogeneously, were determined by means of the stress/strain experiment (, ) with simultaneous lateral strain measurement (_lat) in a wide range of strain rates () up to 10⁵%/min (impact stress). The elastic, plastic cavitation and plastic shear processes were determined as a function of strain. Therefore we calculated the elastic strain ( _el), the elastic volume expansion ( _{vol el}), the cavitation strain ( _cav), which is identical with the plastic volume expansion ( _{vol pl}), the shear strain ( _sh) and the energy densities (W_el, W_cav, W_sh) related to these three processes.For strains of 3 % onward it was found that plastic shear processes and plastic cavitation processes are responsible for a partial loss of elastically stored energy. Both plastic processes turn out to be mostly anelastic deformations, their amount depending strongly on the strain rate. The contributions of the processes to the total deformation of the unmodified PMMA in its strain range are similar to those of the impact-modified PMMA, and the high impact strength is caused by a shift of the catastrophic rupture to very high strains.     

VISCOELASTIC BEHAVIOR OF THE NON-HOOKE DEFORMATION BEFORE YIELDING IN UNIAXIAL DRAWING OF AMORPHOUS POLY(ETHYLENE TEREPHTHALATE)*

Viscoelastic behavior of the non-Hooke deformation of amorphous PET film before yield was investigated in thetemperature region 74--80.5℃ around the glass transition temperature. The film specimen was drawn to yield point followedby unloading to zero stress, then the residual deformation was held constant, while the subsequent evolution of the stress wasrecorded. An induction period was found in the course of stress evolution fol1owed by a stress step-increase. The inductionperiod decreases with increasing drawing temperature with an activation energy of 1.10 MJ/mol·K, which is attributed tothe time needed for the relaxation of rubbery deformation through cooperative internal rotations. At temperatures lower than74℃, there is no stress increase or the induction period becomes too long to be observed. Thus the nature of anelasticity inthe non-Hooke region before yielding is attributed to stress induced rubbery deformation. The experimental results areinterpreted in terms of Perez' rheological model of a series connected Hooke spring and a Voigt element consisting of aparallel connected elastic spring and a dashpot.     

Direct determination of selenium in urine samples by electrothermal atomic absorption spectrometry using a Zr plus Rh-treated graphite tube and co-injection of Rh as chemical modifier

Different chemical modifiers for use with electrothermal atomic absorption spectrometry (ET AAS) were investigated in relation to determining the selenium in human urine samples. The samples were diluted in a solution containing 1% v/v HNO₃ and 0.02% m/v cetyltrimethylammonium chloride (CTAC). Studying the modifiers showed that the use of either Ru or Ir as the permanent modifier gave low sensitivity to Se and the peak shape was very noisy, while Zr or Rh gave no peak at all. The same occurred when Zr was used in solution. For mixtures of permanent modifiers, Ir plus Rh or Zr plus Rh gave very low sensitivity, Zr plus Rh with co-injection of Ir in solution was also not efficient, Zr plus Rh in solution gave good sensitivity, but the best results were obtained with a mixture of Zr and Rh as the permanent modifier and co-injection of Rh in solution. Using this last modifier, the following dilutions with the HNO₃ and CTAC were studied: 1:1, 1:2, 1:3 and 1:4. The best dilution was 1:1, which promoted good sensitivity and a more defined peak shape and made it possible to correct for the background using a deuterium arc lamp. Under these conditions, a characteristic mass of 26±0.2 pg was obtained for Se in aqueous solution. Six certified urine samples were analyzed using matrix matching calibration and the measured concentrations were in agreement with the certified values, according to a t-test at the 95% confidence level. Recovery tests were carried out and the recoveries were in the range 100–103%, with relative standard deviation better than 9%. The limit of detection (LOD, 3 sd, n=10) was 3.0 μg L⁻¹ in the sample. The treated graphite tube could be used for at least 600 atomization cycles without significant alteration of the analytical signal.     

Uniaxial deformation and orientation of ethylene–tetrafluoroethylene films

This study concerns the thermal and mechanical response of several commercial grades of ethylene – tetrafluoroethylene copolymer films. Differential scanning calorimetry was used to show that, although films have similar degrees of crystallinity and melting temperature, the melting endotherms and crystallisation exotherms differ between materials, suggesting small changes in composition between manufacturers. Films were deformed in tension at a range of temperatures and rates. Selected films were unloaded immediately after stretching, and measurement of the elastic recovery highlighted further differences between materials. Batches of films were pre-drawn uniaxially above the glass transition and immediately quenched. When these materials were subsequently re-drawn below the glass transition temperature, most of them exhibited much improved yield stress, modulus and tensile strength (improving by factors of 5, 5 and 4, respectively at a draw ratio of 3), but a reduced strain to failure. In most of the films, the pre-drawing, as well as the initial orientation of the films, is accounted for by a simple shift in the true strain axis. This is indicative of a material response dominated by entropic network stretch. It also suggests that, in the cases where strain superposition does not work, a different arrangement of crystalline lamellae may be present, limiting the extent to which improved properties can be achieved in some materials.     

Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

On the temperature Dependence of the orientational Order Parameter in the Nematic Phase of Cyanophenyl Behzoates

The orientational order parameters fot two liquid crystal materials, 4-cyanophenyl 4-butylbenzoate and 4-cyanophenyl 4-pentylbenzoate, have been derived by measuring the change in the refractive index as function of temperature. The order parameters are compared with MaierSaupe theory, and the sharpness of the transitions has been shown using the Haller's plot.     

A novel design of membrane mirror with small deformation and imaging performance analysis in infrared system

A method of diminishing the shape error of membrane mirror is proposed in this paper. The inner inflating pressure is considerably decreased by adopting the pre-shaped membrane. Small deformation of the membrane mirror with greatly reduced shape error is sequentially achieved. Primarily a finite element model of the above pre-shaped membrane is built on the basis of its mechanical properties. Then accurate shape data under different pressures can be acquired by iteratively calculating the node displacements of the model. Shape data are applicable to build up deformed reflecting surfaces for the simulative analysis in ZEMAX. Finally, ground-based imaging experiments of 4-bar targets and nature scene are conducted. Experiment results indicate that the MTF of the infrared system can reach to 0.3 at a high spatial resolution of 10l p/mm, and texture details of the nature scene are well-presented. The method can provide theoretical basis and technical support for the applications in lightweight optical components with ultra-large apertures.