Calculations and Simulations

1997 ◽  
Author(s):  
Burak Erman ◽  
James E. Mark
Keyword(s):  
Gaussian Approximation ◽  
Rubber Elasticity ◽  
Chain Model ◽  
Chain Molecules ◽  
Rotational Isomeric State ◽  
End To End ◽  
State Models ◽  
Areas Of Interest ◽  
Segmental Orientation

The classical theories of rubber elasticity are based on the Gaussian chain model. The only molecular parameter that enters these theories is the mean-square end-to-end separation of the chains constituting the network. However, there are various areas of interest that require characterization of molecular quantities beyond the Gaussian description. Examples are segmental orientation, birefringence, rotational isomerization, and finite extensibility, and we will address these properties in the following chapters. One often needs a more realistic distribution function for the end-to-end vector, as well as for averages of the products of several vectorial quantities, as will be evident in these chapters. The foundations for such characterizations, and several examples of their applications, are given in this chapter. Several aspects of rubber elasticity (such as the dependence of the elastic free energy on network topology, number of effective junctions, and contributions from entanglements) are successfully explained by theories based on the freely jointed chain and the Gaussian approximation. Details of the real chemical structure are not required at the length scales describing these phenomena. On the other hand, studies of birefringence, thermoelasticity, rotational isomerization upon stretching, strain dichroism, local segmental orientation and mobility, and characterization of networks with short chains require the use of more realistic network chain models. In this section, properties of rotational isomeric state models for the chains are discussed. The notation is based largely on the Flory book, Statistical Mechanics of Chain Molecules. More recent information is readily found in the literature. Due to the simplicity of its structure, a polyethylene-like chain serves as a convenient model for discussing the statistical properties of real chains. This simplicity can be seen in figure 8.1, which shows the planar form of a small portion of a polyethylene chain. Bond lengths and bond angles may be regarded as fixed in the study of rubber elasticity because their rapid fluctuations are usually in the range of only ±0.05 A and ±5°, respectively. The chain changes its configuration only through torsional rotations about the backbone bonds, shown, for example, by the angle for the ith bond in figure 8.1.

Implicit Side-Chain Model and Experimental Characterization of Bottlebrush Block Copolymer Solution Assembly

2021 ◽  
Author(s):  
Tianyuan Pan ◽  
Bijal B. Patel ◽  
Dylan J. Walsh ◽  
Sarit Dutta ◽  
Damien Guironnet ◽  
...  
Keyword(s):  
Block Copolymer ◽  
Side Chain ◽  
Chain Model ◽  
Experimental Characterization ◽  
Copolymer Solution

scholarly journals On the Integrability of a Tritrophic Food Chain Model

2010 ◽  
Vol 10 (2) ◽  
Author(s):  
Jaume Llibre ◽  
Clàudia Valls
Keyword(s):  
Food Chain ◽  
Formal Series ◽  
Complete Characterization ◽  
First Integrals ◽  
Chain Model ◽  
Darboux Polynomials ◽  
Analytic First Integrals ◽  
Exponential Factors ◽  
Food Chain Model

AbstractIn this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.

Dipole moments and conformation energies for substituted ethanes

1982 ◽  
Vol 60 (16) ◽  
pp. 2049-2056 ◽  
Author(s):  
Victor M. S. Gil ◽  
António J. C. Varandas
Keyword(s):  
Simple Model ◽  
Potential Energy ◽  
Dipole Moments ◽  
Model Potential ◽  
Energy Functions ◽  
Electric Dipole Moments ◽  
Potential Energy Functions ◽  
Rotational Isomeric State ◽  
State Models ◽  
The Continuum

By using simple model potential energy functions for internal rotation of ethane derivatives (CH2X–CH2X and CHX2–CHX2), a comparison was made between the continuum and the rotational isomeric state models for obtaining conformation information (especially energy differences for the staggered conformers) from electric dipole moments. It is found that the results obtained by the two procedures may be appreciably different, depending on the features of the conformational energy function and on the temperature considered.

End-to-end latency characterization of task communication models for automotive systems

2020 ◽  
Vol 56 (3) ◽  
pp. 315-347 ◽  
Author(s):  
Jorge Martinez ◽  
Ignacio Sañudo ◽  
Marko Bertogna
Keyword(s):  
Automotive Systems ◽  
Communication Models ◽  
End To End

Utilising 4PL solutions to drive efficiency on major capital projects

2015 ◽  
Vol 55 (2) ◽  
pp. 461
Author(s):  
Bill Antonace
Keyword(s):  
Supply Chain ◽  
Chain Model ◽  
Capital Projects ◽  
The Past ◽  
Supply Chain Model ◽  
The Status ◽  
Fourth Party Logistics ◽  
End To End ◽  
Major Project

The Australian resources sector is demanding solutions that will help deliver projects more cost efficiently and with better productivity. This is seeing a shift towards specialist contractors overseeing non-core functions for operators in the sector, reducing their management overheads and allowing for a greater focus on core operations. As a result, there has been an emergence of fourth-party logistics (4PL) and supply chain solutions that centrally manage the complexities of logistics and the supply chain on behalf of the client. Operators have struggled in the past to gain accurate and timely reports on the status of material orders. A 4PL and supply chain model leverages synergies that simplify processes and drive better commercial outcomes. An experienced and reliable 4PL provider will bring value and a re-engineered approach to a major project, as it identifies appropriate suppliers, sources technically acceptable materials, services at the best price, monitors and expedites orders to completion, and designs and plans the delivery, distribution, storage, collection and final removal of materials, waste scraps and surplus. By integrating logistics into the entire end-to-end solution, companies can overcome the supply chain and logistics challenges that often hamper projects, leading to cost and schedule over-runs. This extended abstract will analyse the development and implementation of a 4PL solution, referencing lessons of and experiences from, some of the world’s largest resource projects.

scholarly journals Absorption and Remission Characterization of Pure, Dielectric (Nano-)Powders Using Diffuse Reflectance Spectroscopy: An End-To-End Instruction

2019 ◽  
Vol 9 (22) ◽  
pp. 4933 ◽  
Author(s):  
Sergej Bock ◽  
Christian Kijatkin ◽  
Dirk Berben ◽  
Mirco Imlau
Keyword(s):  
Diffuse Reflectance ◽  
Diffuse Reflectance Spectroscopy ◽  
Mie Scattering ◽  
Reflectance Spectroscopy ◽  
Visible Spectral Range ◽  
Host Matrix ◽  
Material Sciences ◽  
End To End

This paper addresses the challenging task of optical characterization of pure, dielectric (nano-)powders with the aim to provide an end-to-end instruction from appropriate sample preparation up to the determination of material remission and absorption spectra. We succeeded in establishing an innovative preparation procedure to reproducibly obtain powder pellet samples with an ideal Lambertian scattering behavior. As a result, a procedure based on diffuse reflectance spectroscopy was developed that allows for (i) performing reproducible and artifact-free, high-quality measurements as well as (ii) a thorough optical analysis using Monte Carlo and Mie scattering simulations yielding the absorption spectrum in the visible spectral range. The procedure is valid for the particular case of powders that can be compressed into thick, non-translucent pellets and neither requires embedding of the dielectric (nano-)powders within an appropriate host matrix for measurements nor the use of integrating spheres. The reduced spectroscopic procedure minimizes the large number of sources for errors, enables an in-depth understanding of non-avoidable artifacts and is of particular advantage in the field of material sciences, i.e., for getting first insights to the optical features of a newly synthesized, pure dielectric powder, but also as an inline inspection tool for massively parallelised material characterization.

The statistics of stiff chain molecules I. The particle scattering factor

1970 ◽  
Vol 316 (1525) ◽  
pp. 185-199 ◽  
Keyword(s):  
Distribution Functions ◽  
Chain Model ◽  
Particle Scattering ◽  
Hindered Rotation ◽  
Chain Molecules ◽  
Chain Stiffness ◽  
Angle Scattering ◽  
Analytic Expressions ◽  
Scattering Factor ◽  
The Difference

Analytic expressions for the particle scattering factor of stiff chains have been derived, both for the wormlike and a discrete chain model with an axial symmetric potential of hindered rotation. The angular distribution functions agree well with the results of Monte Carlo calculations by Heine, Kratky & Roeppert (1962), if the chains are longer than five persistence lengths. The particle scattering factor of short chains can be well represented by the simple Guinier approximation. A transition point from the behaviour of a coil to that of the rod-like short chain sections has been determined by graphical extrapolation and appears at X a = 2.87 ± 0.05. The difference between the wormlike and the discrete chain models turned out to be smaller than 14% even for an alkane type chain with free rotation of the chain elements and decreases with increasing chain stiffness. The influence of the cross-section has been taken into account by representing the chain by a pearl necklace. Comparison with X -ray small angle scattering measurements of a cellulosetricarbanilate reveals close similarities between calculated and experimental curves.

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