Numerical Methods For Polymeric Systems
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Numerical Methods For Polymeric Systems
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Author : Stuart G. Whittington
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Methods For Polymeric Systems written by Stuart G. Whittington and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Polymers occur in many different states and their physical properties are strongly correlated with their conformations. The theoretical investigation of the conformational properties of polymers is a difficult task and numerical methods play an important role in this field. This book contains contributions from a workshop on numerical methods for polymeric systems, held at the IMA in May 1996, which brought together chemists, physicists, mathematicians, computer scientists and statisticians with a common interest in numerical methods. The two major approaches used in the field are molecular dynamics and Monte Carlo methods, and the book includes reviews of both approaches as well as applications to particular polymeric systems. The molecular dynamics approach solves the Newtonian equations of motion of the polymer, giving direct information about the polymer dynamics as well as about static properties. The Monte Carlo approaches discussed in this book all involve sampling along a Markov chain defined on the configuration space of the system. An important feature of the book is the treatment of Monte Carlo methods, including umbrella sampling and multiple Markov chain methods, which are useful for strongly interacting systems such as polymers at low temperatures and in compact phases. The book is of interest to workers in polymer statistical mechanics and also to a wider audience interested in numerical methods and their application in polymeric systems.
Diffusion In Polymer Solvent Systems
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Author : Raymond Franklin Riek
language : en
Publisher:
Release Date : 1967
Diffusion In Polymer Solvent Systems written by Raymond Franklin Riek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Diffusion categories.
Applications Of Numerical Methods In The Solution Of Problems In Statistical Mechanics Of Polymer Systems
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Author : Robert Frank Hoffman
language : en
Publisher:
Release Date : 1967
Applications Of Numerical Methods In The Solution Of Problems In Statistical Mechanics Of Polymer Systems written by Robert Frank Hoffman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Layered Polymeric Systems
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Author : Patrick James Harris
language : en
Publisher:
Release Date : 2015
Layered Polymeric Systems written by Patrick James Harris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Plastics categories.
This dissertation presents novel mechanical designs and advances in both polymer layer multiplication and extensional rheology. In Part I, advances in polymer layer multiplication include the investigation of typical thermoplastic layer multiplication extrusion dies and the redesign of such by means of experimental and computational investigation. Results show a decrease in flow instabilities including viscous encapsulation and elastic instabilities. Similarly, an innovative layer multiplication system for highly filled and elastic rubber compounds is presented. Both of these novel systems for thermoplastic and thermosetting polymer systems are validated and understood by numerical methods using ANSYS Polyflow and CFD-Post. These advances in multilayer coextrusion allow for layering of new families of rheologically complex and as well mismatched materials, thus widening the processing capabilities at the Center for Layered Polymeric Systems. In Part II, advances in extensional rheology include a newly developed extensional rheometer for achieving high Henkystrains. The Meissner Extensional Rheometer Accessory or MERA is limited in strain only by sample rupture. Experimental validation is performed using two materials, a styrene-butadiene rubber (SBR) and a linear polystyrene (PS); the results are compared with those obtained using the well-known SER. Due to its design, it was possible to achieve homogeneous extensional flow up to unprecedented real Hencky strains in excess of 8. The second half of Part II covers a rheological understanding behind the mechanism of sharkskin, a melt fracture instability during extrusion. Solution-styrene-butadiene-styrene blended with various polybutadienes is studied. Experimental extrusion results show a behavior difference depending on the molecular architecture of the latter, polybutadiene. Extensional rheological techniques are used to investigate the behavior. Results show a higher sensitivity to stress relaxation after a step-strain rather than typical stress growth coefficients in extension.
Practical Aspects Of Finite Element Modelling Of Polymer Processing
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Author : Vahid Nassehi
language : en
Publisher: John Wiley & Sons
Release Date : 2002-03-12
Practical Aspects Of Finite Element Modelling Of Polymer Processing written by Vahid Nassehi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-12 with Mathematics categories.
Authored by a respected scientist with a growing international reputation this is a self-contained text that can be used by the beginners and the experts alike, to study the basic aspects of finite element modelling. It provides a sound physical understanding of the basis on which mathematical models of polymer processes are built. * Written from a chemical engineering rather then a mathematical perspective it enables the reader to get up to speed in a relatively short time * Provides the 'parts and tools' required to assemble finite element models, applicable to situations that arise under realistic conditions * Discusses and compares specific finite element schemes that provide the most reliable and robust numerical solution procedures for polymer processing models * Practical examples give a wide ranging view of the application of finite element analysis to industrial problems * Describes non-Newtonian fluid mechanics equations in a self-contained, concise and clear manner * Includes clear and simple readily compiled code to model simple problems that can be extended to solve more complex polymer processing problems This book makes the subject accessible to a wide audience ranging from senior under-graduate to post-graduate engineering students, as well as, researchers and practising engineers involved in polymer industry.
The Equilibrium Theory Of Inhomogeneous Polymers
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Author : Glenn Fredrickson
language : en
Publisher: OUP Oxford
Release Date : 2005-12-01
The Equilibrium Theory Of Inhomogeneous Polymers written by Glenn Fredrickson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-01 with Technology & Engineering categories.
The Equilibrium Theory of Inhomogeneous Polymers provides an introduction to the field-theoretic methods and computer simulation techniques that are used in the design of structured polymeric fluids. By such methods, the principles that dictate equilibrium self-assembly in systems ranging from block and graft copolymers, to polyelectrolytes, liquid crystalline polymers, and polymer nanocomposites can be established. Building on an introductory discussion of single-polymer statistical mechanics, the book provides a detailed treatment of analytical and numerical techniques for addressing the conformational properties of polymers subjected to spatially-varying potential fields. This problem is shown to be central to the field-theoretic description of interacting polymeric fluids, and models for a number of important polymer systems are elaborated. Chapter 5 serves to unify and expound the topic of self-consistent field theory, which is a collection of analytical and numerical techniques for obtaining solutions of polymer field theory models in the mean-field approximation. The concluding Chapter 6 provides a discussion of analytical methods for going beyond the mean-field approximation and an introduction to the exciting new field of field-theoretic polymer simulations - the direct numerical simulation of polymer field theory models. No other book brings together in such a detailed and instructive fashion the theoretical and numerical tools for investigating the equilibrium structure and thermodynamics of meso-structured polymer formulations, including those relevant to soft material nanotechnologies, personal care products, and multiphase plastic materials.
Numerical Solution Of The Polymer System By Front Tracking
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Author : V. Haugse
language : en
Publisher:
Release Date : 1999
Numerical Solution Of The Polymer System By Front Tracking written by V. Haugse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics
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Author : John Timothy Cummings
language : en
Publisher:
Release Date : 2017
Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics written by John Timothy Cummings and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Energy dissipation categories.
We consider in this dissertation the mathematical modeling and simulation of a general diffuse interface mixture model based on the principles of energy dissipation. The model developed allows for a thermodynamically consistent description of systems with an arbitrary number of different components, each of which having perhaps differing densities. We also provide a mathematical description of processes which may allow components to source or sink into other components in a mass conserving, energy dissipating way, with the motivation of applying this model to phase transformation. Also included in the modeling is a unique set of thermodynamically consistent boundary conditions which allows flow across the boundary of a select number of components. The result of this modeling is a unique Cahn-Hilliard, Allen-Cahn-like system of equations. For numerical solution of this model, we use cell-centered finite difference methods for discretization and Full Approximation Storage (FAS) multigrid methods to solve the resulting system of equations via use of the BSAM (Block- Structured Adaptive Multigrid) libraries. Upon development of the mathematical model, we consider two applications. The primary application of this mathematical modeling is the time evolution of a quaternary mixture consisting of a volatile solvent in the liquid phase, solvent in the vapor phase, and two polymers. This modeling is motivated by the need to better understand the active layer in Organic Photovoltaics (OPVs). In this mixture, the volatile solvent is evaporating into the its vapor phase, and upon fully evaporating the polymer mixture which results is the active layer of the OPV device. Simulations are provided which demonstrate the solvent evaporation phenomenon and the resulting microstructure of the active layer. As a future application, we consider a mixture of a charged polymer and its counterion. We provide a description of the system based on the dissipation of the electrochemical free energy which allows for the permittivity to be dependent on the volume fractions. Simulations are provided which vary the gradient energies and polymer chain length and demonstrate the different steady-state microstructures which can result.
Analysis And Implementation Of Numerical Methods For Simulating Dilute Polymeric Fluids
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Author : David Knezevic
language : en
Publisher:
Release Date : 2008
Analysis And Implementation Of Numerical Methods For Simulating Dilute Polymeric Fluids written by David Knezevic and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Differential equations, Partial categories.
Random Polymer Models
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Author : Giambattista Giacomin
language : en
Publisher: Imperial College Press
Release Date : 2007
Random Polymer Models written by Giambattista Giacomin and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.
This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials. This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models.
