Critical behavior of brittle-ductile transition of polymers

We report that the brittle-ductile transition of polymers induced by temperature exhibits critical behavior. When t close to 0, the critical surface to surface interparticle distance (IDc) follows the scaling law: IDc proportional to t(-v) where t = 1 - T/T-BD(m) (T and T-BD(m) are the test temperature and brittle-ductile transition temperature of matrix polymer, respectively) and v = 2/D. It is clear that the scaling exponent v only depends on dimension (D). For 2, 3, and 4 dimension, v = 1, 2/3, and 1/2 respectively. The result indicates that the ID, follows the same scaling law as that of the correlation length (xi), when t approach to zero.

Brittle-ductile transition of polypropylene/ethyllene-propylene-diene monomer blends induced by size, temperature, and time

To study the brittle-ductile transition (BDT) of polypropylene (PP)/ethylene-propylene-diene monomer (EPDM) blends induced by size, temperature, and time, the toughness of the PP/EPDM blends was investigated over wide ranges of EPDM content, temperature, and strain rate. The toughness of the blends was determined from the tensile fracture energy of the side-edge notched samples. The concept of interparticle distance (ID) was introduced into this study to probe the size effect on the BDT of PP/EPDM blends, whereas the effect of time corresponded to that of strain rate. The BDT induced by size, temperature, and time was observed in the fracture energy versus ID, temperature, and strain rate. The critical BDT temperatures for various EPDM contents at different initial strain rates were obtained from these transitions. The critical interparticle distance (IDc) increased nonlinearly with increasing temperature, and when the initial strain rate was lower, the IDc was larger. Moreover, the variation of the reciprocal of the initial strain rate with the reciprocal of temperature followed different straight lines for various EPDM contents. These straight lines were with the same slope.

Transition from crazing to shear deformation in ABS/PVC blends

ABS/PVC blends were prepared over a range of compositions by mixing PVC, SAN, and PB-g-SAN. All samples were designed to have a constant rubber level of 12 wt % and the ratio of total-SAN to PVC in the matrix of the blends varied from 70.5/17.5 to 18/80. Transmission electron microscope and scanning electron microscope have been used to study deformation mechanisms in the ABS/PVC blends. Several different types of microscopic deformation mechanisms, depending on the composition of blends, were observed for the ABS/PVC blends. When the blend is a SAN-rich system, the main deformation mechanisms were crazing of the matrix. When the blend is a PVC-rich system, crazing could no longer be detected, while shear yielding of the matrix and cavitation of the rubber particles were the main mechanisms of deformation. When the composition of blend is in the intermediate state, both crazing and shear yielding of matrix were observed. This suggests that there is a transition of deformation mechanism in ABS/PVC blends with the change in composition, which is from crazing to shear deformation.

Phase transition in polyamide-66/montmorillonite nanocomposites on annealing

The crystalline-phase transition in polyamide-66/montmorillonite nanocomposites before melting was investigated by in situ X-ray diffraction and is reported for the first time in this work. The phase-transition temperature in the nanocomposites was 170 degreesC, 20 degreesC lower than that in polyamide-66. The lower phase-transition temperature of the nanocomposites could be attributed to the gamma-phase-favorable environment caused by silicate layers. Meanwhile, the addition of silicate layers changed the crystal structure of the polyamide-66 matrix and influenced the phase-transition behavior.

Preparation and luminescence properties of hybrid materials containing europium(III) complexes covalently bonded to a silica matrix

A new kind of luminescent organic-inorganic hybrid material (denoted Hybrid I) consisting of europium 1,10-phenanthroline complexes covalently attached to a silica-based network was prepared by a sol-gel process. 1,10-Phenanthroline grafted to 3-(triethoxysilyl)propyl isocyanate was used as one of the precursors for the preparation of an organic-inorganic hybrid materials. For comparison purposes, the hybrid material (denoted Hybrid II) in which phenanthroline was not grafted onto the silica backbone of the frameworks was also prepared. Elemental analysis; NMR, FT-IR, UV/vis absorption, and luminescence spectroscopies, and luminescence decay analysis were used to characterize the obtained hybrid materials. It is shown that the homogeneity of Hybrid I is superior to that of Hybrid II, and a higher concentration europium can be incorporated into Hybrid I than Hybrid II. Excitation at the ligand absorption wavelength (283 nm) resulted in the strong emission of the Eu3+ D-5(0)-F-7(J) (J = 0-4) transition lines as a result of the efficient energy transfer from the ligands to the EU3+ in Hybrid I. The number of water molecules coordinated to the europium ion was estimated, and the structure of the as-synthesized Hybrid I was predicted on the basis of the experimental results.

Study of electron transfer across the liquid/ice-like matrix interface by scanning electrochemical microscopy

In this work, we report the findings of a study on scanning electrochemical microscopy (SECM) to investigate the interfacial electron-transfer (ET) reaction between the 7,7,8,8-tetracyanoquinodimethane radical anion (TCNQ(.-)) in 1,2-dichloroethane and ferricyanide in an ice-like matrix (a mixture of insulting ice and conductive liquid) under low temperatures. Experimental results indicate that the formed liquid/ice-like matrix interface is superficially similar in electrochemical characteristics to a liquid/liquid interface at temperatures above -20 degreesC. Furthermore, imaging data show that the surface of the ice-like matrix is microscopically flat and physically stable and can be applied as either a conductive or an insulting substrate for SECM studies. Perchlorate ion was selected as the common ion in both phases, the concentrations of which controlled the interfacial potential difference. The effect of perchlorate concentration in the DCE phase on interfacial reactions has been studied in detail. The apparent heterogeneous rate constants for TCNQ(.-) oxidation by Fe(CN)(6)(3-) in another phase under different temperatures have been calculated by a best-fit analysis, where the experimental approach curves are compared with the theoretically derived relationships. Reaction rate data obey Butler-Volmer formulation before and after the freezing point, which is similar to most other known cases of ET reactions at liquid/liquid interfaces. However, there is a sharp change observed for heterogeneous rate constants around the freezing point of the aqueous phase, which reflects the phase transition. At temperatures below -20 degreesC, surface-confined voltammograms for the reduction of ferricyanide were obtained, and the ice-like matrix became an insulating one, which indicates that the aqueous phase is really a frozen phase.

Observation of inverted phases in poly(styrene-b-butadiene-b-styrene) triblock copolymer by solvent-induced order-disorder phase transition

We report observation of inverted phases consisting of spheres and/or cylinders of the majority fraction block in a poly(styrene-b-butadiene-b-styrene) (SBS) triblock copolymer by solvent-induced order-disorder phase transition (ODT). The SBS sample has a molecular weight of 140K Da and a polystyrene (PS) weight fraction of 30%. Tapping mode atomic force microscopy (AFM) and transmission electron microscopy (TEM) were utilized to study the copolymer microstructure of a set of solution-cast SBS films dried with different solvent evaporation rates, R. The control with different R leads to kinetic frozen-in of microstructures corresponding to a different combination parameter chi (eff)Z of the drying films (where chi (eff) is the effective interaction parameter of the polymer solution in the cast film and Z the number of "blobs" of size equal to the correlation length one block copolymer chain contains), for which faster evaporation rates result in microstructures of smaller chi (eff)Z. As R was decreased from rapid evaporations (similar to0.1 mL/h), the microstructure evolved from a totally disordered one sequentially to inverted phases consisting of spheres and then cylinders of polybutadiene (PB) in a PS matrix and finally reached the equilibrium phase, namely cylinders of PS in a PB matrix. We interpret the formation of inverted phases as due to the increased relative importance of entropy as chi (eff)Z is decreased, which may dominate the energy penalty for having a bigger interfacial area between the immiscible blocks in the inverted phases.

Brittle-tough transition in elastomer toughening thermoplastics: effects of the elastomer stiffness

The effect of the elastomer stiffness on brittle-tough transition in elastomer toughening thermoplastics was quantitatively studied. A correlation between brittle-tough transition temperature and the elastomer stiffness was obtained. The calculation from this correlation showed that the brittle-tough transition temperature (T-bt) Of elastomer toughening thermoplastics slowly increased up to one tenth of the modulus of matrix, thereafter it increased rapidly with increasing the modulus of elastomer. The results indicated that the modulus of the elastomer must be one-tenth or less of that of the matrix in order to be effective at low temperature. (C) 2001 Elsevier Science Ltd. All rights reserved.

Crystallization of micelles and matrix in dilute diblock copolymer/homopolymer solutions

The crystallization, morphology, and crystalline structure of dilute solid solutions of tetrahydrofuran-methyl methacrylate diblock copolymer (PTHF-b-PMMA) in poly(ethylene oxide) (PEO) and PTHF have been studied with differential scanning calorimetry (DSC), X-ray, and optical microscopy. This study provides a new insight into the crystallization behavior of block copolymers. For the dilute PTHF-b-PMMA/PEO system containing only 2 to 7 wt % of PTHF content, crystallization of the PTHF micellar core was detected both on cooling and on heating. Compared the crystallization of the PTHF in the dilute solutions with that in the pure copolymer, it was found that the crystallizability of the PTHF micellar core in the solution is much greater than that of the dispersed PTHF microdomain in the pure copolymer. The stronger crystallizability in the solution was presumably due to a softened PMMA corona formed in the solution of the copolymer with PEG. However, the "soft" micelles formed in the solution (meaning that the glass transition temperatures (T-g) of the micelle is lower than the T-m of the matrix phase) showed almost no effects on the spherulitic morphology of the PEO component, compared with that of the pure PEO sample. In contrast, significant effects of the micelles with a "hard" PMMA core (meaning that the T-g of the core is higher than the T-m of the PTHF homopolymer) on the nucleation, crystalline structure, and spherulitic morphology were observed for the dilute PTHF-b-PMMA/PTHF system. (C) 1998 John Wiley & Sons, Inc.

基于MRF模型的油气储层属性随机建模方法研究

Stochastic reservoir modeling is a technique used in reservoir describing. Through this technique, multiple data sources with different scales can be integrated into the reservoir model and its uncertainty can be conveyed to researchers and supervisors. Stochastic reservoir modeling, for its digital models, its changeable scales, its honoring known information and data and its conveying uncertainty in models, provides a mathematical framework or platform for researchers to integrate multiple data sources and information with different scales into their prediction models. As a fresher method, stochastic reservoir modeling is on the upswing. Based on related works, this paper, starting with Markov property in reservoir, illustrates how to constitute spatial models for catalogued variables and continuum variables by use of Markov random fields. In order to explore reservoir properties, researchers should study the properties of rocks embedded in reservoirs. Apart from methods used in laboratories, geophysical means and subsequent interpretations may be the main sources for information and data used in petroleum exploration and exploitation. How to build a model for flow simulations based on incomplete information is to predict the spatial distributions of different reservoir variables. Considering data source, digital extent and methods, reservoir modeling can be catalogued into four sorts: reservoir sedimentology based method, reservoir seismic prediction, kriging and stochastic reservoir modeling. The application of Markov chain models in the analogue of sedimentary strata is introduced in the third of the paper. The concept of Markov chain model, N-step transition probability matrix, stationary distribution, the estimation of transition probability matrix, the testing of Markov property, 2 means for organizing sections-method based on equal intervals and based on rock facies, embedded Markov matrix, semi-Markov chain model, hidden Markov chain model, etc, are presented in this part. Based on 1-D Markov chain model, conditional 1-D Markov chain model is discussed in the fourth part. By extending 1-D Markov chain model to 2-D, 3-D situations, conditional 2-D, 3-D Markov chain models are presented. This part also discusses the estimation of vertical transition probability, lateral transition probability and the initialization of the top boundary. Corresponding digital models are used to specify, or testify related discussions. The fifth part, based on the fourth part and the application of MRF in image analysis, discusses MRF based method to simulate the spatial distribution of catalogued reservoir variables. In the part, the probability of a special catalogued variable mass, the definition of energy function for catalogued variable mass as a Markov random field, Strauss model, estimation of components in energy function are presented. Corresponding digital models are used to specify, or testify, related discussions. As for the simulation of the spatial distribution of continuum reservoir variables, the sixth part mainly explores 2 methods. The first is pure GMRF based method. Related contents include GMRF model and its neighborhood, parameters estimation, and MCMC iteration method. A digital example illustrates the corresponding method. The second is two-stage models method. Based on the results of catalogued variables distribution simulation, this method, taking GMRF as the prior distribution for continuum variables, taking the relationship between catalogued variables such as rock facies, continuum variables such as porosity, permeability, fluid saturation, can bring a series of stochastic images for the spatial distribution of continuum variables. Integrating multiple data sources into the reservoir model is one of the merits of stochastic reservoir modeling. After discussing how to model spatial distributions of catalogued reservoir variables, continuum reservoir variables, the paper explores how to combine conceptual depositional models, well logs, cores, seismic attributes production history.

Learning Fine Motion by Markov Mixtures of Experts

Compliant control is a standard method for performing fine manipulation tasks, like grasping and assembly, but it requires estimation of the state of contact between the robot arm and the objects involved. Here we present a method to learn a model of the movement from measured data. The method requires little or no prior knowledge and the resulting model explicitly estimates the state of contact. The current state of contact is viewed as the hidden state variable of a discrete HMM. The control dependent transition probabilities between states are modeled as parametrized functions of the measurement We show that their parameters can be estimated from measurements concurrently with the estimation of the parameters of the movement in each state of contact. The learning algorithm is a variant of the EM procedure. The E step is computed exactly; solving the M step exactly would require solving a set of coupled nonlinear algebraic equations in the parameters. Instead, gradient ascent is used to produce an increase in likelihood.

Stochastic comparability and dual q-functions

In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller–Reuter–Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density q-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller–Reuter–Riley transition function is also given.

Uniqueness and extinction properties of generalised Markov branching processes

This paper focuses on the basic problems regarding uniqueness and extinction properties for generalised Markov branching processes. The uniqueness criterion is firstly established and a differential–integral equation satisfied by the transition functions of such processes is derived. The extinction probability is then obtained. A closed form is presented for both the mean extinction time and the conditional mean extinction time. It turns out that these important quantities are closely related to the elementary gamma function.

The near-edge structure in energy-loss spectroscopy: many-electron and magnetic effects in transition metal nitrides and carbides

We investigate the ability of the local density approximation (LDA) in density functional theory to predict the near-edge structure in electron energy-loss spectroscopy in the dipole approximation. We include screening of the core hole within the LDA using Slater's transition state theory. We find that anion K-edge threshold energies are systematically overestimated by 4.22 +/- 0.44 eV in twelve transition metal carbides and nitrides in the rock-salt (B1) structure. When we apply this 'universal' many-electron correction to energy-loss spectra calculated within the transition state approximation to LDA, we find quantitative agreement with experiment to within one or two eV for TiC, TiN and VN. We compare our calculations to a simpler approach using a projected Mulliken density which honours the dipole selection rule, in place of the dipole matrix element itself. We find remarkably close agreement between these two approaches. Finally, we show an anomaly in the near-edge structure in CrN to be due to magnetic structure. In particular, we find that the N K edge in fact probes the magnetic moments and alignments of ther sublattice.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.