Atomistically Informed Continuum Model of Polymer-Based Nanocomposites

2002 ◽  
Vol 740 ◽  
Author(s):  
Catalin R. Picu ◽  
Alireza Sarvestani ◽  
Murat S. Ozmusul
Keyword(s):  
Discrete Models ◽  
Homogenization Theory ◽  
Total Density ◽  
Shape Variation ◽  
Filler Size ◽  
Chain Conformations ◽  
Energetic Interactions ◽  
Composite Moduli ◽  
Curved Interface ◽  
The Continuum

ABSTRACTA model polymeric material filled with spherical nanoparticles is considered in this work. Monte Carlo simulations are performed to determine the polymer chain conformations in the vicinity of the curved interface with the filler. Several discrete models of increasing complexity are considered: the athermal system with excluded volume interactions only, the system in which entropic and energetic interactions take place while the filler is a purely repulsive sphere, and the system in which both filler-polymer and polymer-polymer energetic interactions are accounted for. The total density, chain end density, chain segment preferential orientation and chain size and shape variation with the distance from the filler wall are determined. The structure is graded, with the thickness of the transition region being dependent on the property and scale considered. Hence, the polymer in the vicinity of the filler is represented in the continuum sense by a material with graded properties whose elasticity is determined based on the local structure. Homogenization theory is the used to obtain the overall composite moduli. The filler size effect on the composite elasticity is evaluated.

THE MORPHOLOGY AND EVOLUTION OF THE SURFACE IN EPITAXIAL AND THIN FILM GROWTH: A CONTINUUM MODEL WITH SURFACE DIFFUSION

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 753-766 ◽  
Author(s):  
FEREYDOON FAMILY ◽  
JACQUES G. AMAR
Keyword(s):  
Thin Film ◽  
Surface Diffusion ◽  
Film Growth ◽  
Vertical Jump ◽  
Thin Film Growth ◽  
Discrete Models ◽  
Dynamic Scaling ◽  
Diffusion Operator ◽  
Continuum Equation ◽  
The Continuum

A number of discrete models as well as continuum equations have been proposed for describing epitaxial and thin film growth. We have shown that there exists a macroscopic groove instability in many of these models. This unphysical feature in the continuum equations arises from the truncation or linearization of the diffusion operator along the surface. A similar artifact occurs in the discrete models, because in these models adatoms only diffuse horizontally and must take an unphysical vertical jump at step edges. We have proposed and studied a continuum equation for epitaxial and thin-film growth in which the full diffusion along the surface is taken into account. The results of the solutions of this continuum equation, for the growth and the morphology of the surface, are in excellent agreement with recent low temperature molecular-beam epitaxy and ion-sputtering experiments. In particular, we find that at late times dynamic scaling breaks down and the surface is no longer a self-affine fractal. The surface develops a characteristic morphology whose dependence on deposition rate and surface diffusion is similar to that found in experiments.

Sinhala diglossia: Discrete or continuous variation?

1997 ◽  
Vol 26 (2) ◽  
pp. 269-296 ◽  
Author(s):  
John C. Paolillo
Keyword(s):  
Sri Lanka ◽  
South Asia ◽  
Continuum Model ◽  
Distinct Type ◽  
Continuous Variation ◽  
Discrete Models ◽  
Continuum Models ◽  
Naturally Occurring ◽  
The Continuum

ABSTRACTSociolinguists disagree on how to characterize diglossia with respect to the structural relatedness of the H(igh) and L(ow) varieties: Ferguson 1959, 1991 holds that H and L should be distinct but related varieties of language, while others maintain that a continuum model is more appropriate. Both discrete models (Gair 1968, 1992) and continuum models (De Silva 1974, 1979) have been proposed for Sinhala, as spoken in Sri Lanka. In this article, I employ a computer-generated multidimensional graph of relations between varieties of Sinhala to show that the distribution of H and L grammatical features in a sample of naturally occurring texts supports the discrete H and L model more than the continuum model. A rigorous characterization of diglossia as a distinct type of language situation is proposed, based on the notion “functional diasystem.” (Diglossia, Sinhala, Sri Lanka, diasystem, hybridization, continuum, South Asia, standardization)

Filler Size Effect on the Structure of Polymer-Filler Interface in Polymer-Based Nanocomposites: Entropic and Energetic Effects

2002 ◽  
Vol 733 ◽  
Author(s):  
R.C. Picu ◽  
M.S. Ozmusul
Keyword(s):  
Chain Length ◽  
Configurational Entropy ◽  
Polymer Structure ◽  
Lattice Monte Carlo ◽  
Filler Size ◽  
Polymer Filler ◽  
Segregation Effect ◽  
Degree Of Orientation ◽  
Energetic Interactions ◽  
Energetic Systems

AbstractA study of the polymer structure in the vicinity of an interface with a rigid, curved wall is presented. The study is performed by means of lattice Monte Carlo simulations in melts of low and high density. Both purely entropic and energetic systems are considered. The configurational entropy of the chains as well as the cohesive interactions in the bulk polymer lead to the formation of a low-density layer in the close neighborhood of the wall. This layer is about one monomer thick in the purely entropic case, and has a thickness of about three radii of gyration in presence of energetic interactions. Increasing the wall curvature leads to an increase in density in the depleted layer, the effect being more pronounced in the energetic system. Chain end segregation at the wall is observed in all cases. This effect increases with increasing chain length and decreases with increasing wall curvature. The bonds are preferentially oriented in the direction tangential to the wall. The degree of orientation decreases with increasing wall curvature and is independent of chain length. Finally, the evolution of the density, of the segregation effect and of the bond preferential orientation with temperature is investigated. The density at the wall decreases with decreasing temperature in the melt state, while the segregation becomes more pronounced. The volume of polymer in which the structure is affected by the presence of the wall increases with decreasing temperature.

scholarly journals A Contrast on Conductor Galloping Amplitude Calculated by Three Mathematical Models with Different DOFs

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Liu ◽  
KuanJun Zhu ◽  
XiaoQin Sun ◽  
Bing Huo ◽  
XiJun Liu
Keyword(s):  
Mathematical Models ◽  
Transmission Lines ◽  
Damping Ratio ◽  
Influence Factors ◽  
Discrete Models ◽  
Flow Density ◽  
Torsional Angle ◽  
Initial Tension ◽  
The Difference ◽  
The Continuum

It is pivotal to find an effective mathematical model revealing the galloping mechanism. And it is important to compare the difference between the existing mathematical models on the conductor galloping. In this paper, the continuum cable model for transmission lines was proposed using the Hamilton principle. Discrete models of one DOF, two DOFs, and three DOFs were derived from the continuum model by using the Garlekin method. And the three models were compared by analyzing the galloping vertical amplitude and torsional angle with different influence factors. The influence factors include wind velocity, flow density, span length, damping ratio, and initial tension. The three-DOF model is more accurate at calculating the galloping characteristics than the other two models, but the one-DOF and two-DOF models can also present the trend of galloping amplitude change from the point view of qualitative analysis. And the change of the galloping amplitude relative to the main factors was also obtained, which is very essential to the antigalloping design applied in the actual engineering.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

Observations of the continuum near the galactic centre

1967 ◽  
Vol 31 ◽  
pp. 405
Author(s):  
F. J. Kerr
Keyword(s):  
Galactic Centre ◽  
The Past ◽  
Centre Region ◽  
The Continuum

A continuum survey of the galactic-centre region has been carried out at Parkes at 20 cm wavelength over the areal11= 355° to 5°,b11= -3° to +3° (Kerr and Sinclair 1966, 1967). This is a larger region than has been covered in such surveys in the past. The observations were done as declination scans.

Removing Substrate Background in TEM Microanalysis

1974 ◽  
Vol 32 ◽  
pp. 568-569
Author(s):  
John C. Russ ◽  
Nicholas C. Barbi
Keyword(s):  
Electrical Conductivity ◽  
Rapid Growth ◽  
Organic Film ◽  
Absolute Concentration ◽  
Background Signal ◽  
X Ray ◽  
Elemental Concentrations ◽  
Transmission Electron ◽  
Electron Microscopes ◽  
The Continuum

The rapid growth of interest in attaching energy-dispersive x-ray analysis systems to transmission electron microscopes has centered largely on microanalysis of biological specimens. These are frequently either embedded in plastic or supported by an organic film, which is of great importance as regards stability under the beam since it provides thermal and electrical conductivity from the specimen to the grid.Unfortunately, the supporting medium also produces continuum x-radiation or Bremsstrahlung, which is added to the x-ray spectrum from the sample. It is not difficult to separate the characteristic peaks from the elements in the specimen from the total continuum background, but sometimes it is also necessary to separate the continuum due to the sample from that due to the support. For instance, it is possible to compute relative elemental concentrations in the sample, without standards, based on the relative net characteristic elemental intensities without regard to background; but to calculate absolute concentration, it is necessary to use the background signal itself as a measure of the total excited specimen mass.

EELS white line intensities calculated for the 3d and 4d metals

1989 ◽  
Vol 47 ◽  
pp. 388-389
Author(s):  
C. C. Ahn ◽  
D. H. Pearson ◽  
P. Rez ◽  
B. Fultz
Keyword(s):  
Experimental Data ◽  
Line Intensity ◽  
Transition Probabilities ◽  
Initial Increase ◽  
White Line ◽  
Hartree Fock ◽  
Line Intensities ◽  
Integrated Intensity ◽  
X Ray Absorption ◽  
The Continuum

Previous experimental measurements of the total white line intensities from L2,3 energy loss spectra of 3d transition metals reported a linear dependence of the white line intensity on 3d occupancy. These results are inconsistent, however, with behavior inferred from relativistic one electron Dirac-Fock calculations, which show an initial increase followed by a decrease of total white line intensity across the 3d series. This inconsistency with experimental data is especially puzzling in light of work by Thole, et al., which successfully calculates x-ray absorption spectra of the lanthanide M4,5 white lines by employing a less rigorous Hartree-Fock calculation with relativistic corrections based on the work of Cowan. When restricted to transitions allowed by dipole selection rules, the calculated spectra of the lanthanide M4,5 white lines show a decreasing intensity as a function of Z that was consistent with the available experimental data.Here we report the results of Dirac-Fock calculations of the L2,3 white lines of the 3d and 4d elements, and compare the results to the experimental work of Pearson et al. In a previous study, similar calculations helped to account for the non-statistical behavior of L3/L2 ratios of the 3d metals. We assumed that all metals had a single 4s electron. Because these calculations provide absolute transition probabilities, to compare the calculated white line intensities to the experimental data, we normalized the calculated intensities to the intensity of the continuum above the L3 edges. The continuum intensity was obtained by Hartree-Slater calculations, and the normalization factor for the white line intensities was the integrated intensity in an energy window of fixed width and position above the L3 edge of each element.

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