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A Brownian Dynamics Algorithm For The Simulation Of Polymers In Confined Media
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Book Synopsis A Brownian Dynamics Algorithm for the Simulation of Polymers in Confined Media by : Grant Ian Nixon
Download or read book A Brownian Dynamics Algorithm for the Simulation of Polymers in Confined Media written by Grant Ian Nixon and published by . This book was released on 1994 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The techniques of electrophoresis have undergone rapid development in recent years. The problem of predicting and explaining results of electrophoretic experiments requires a well designed dynamical model that reproduces the proper dynamics under well-understood conditions.
Book Synopsis Polymer Dynamics in Dilute Media by : Shikha Somani
Download or read book Polymer Dynamics in Dilute Media written by Shikha Somani and published by Stanford University. This book was released on 2011 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymers undergo a sharp coil to stretch conformational transition in extension dominated flows when the strain rate exceeds a critical value. Dramatic change in flow behavior is known to occur at the coil-stretch transition, making it useful for several commercial applications. Despite decades of study, this phenomenon remains surrounded with controversy as the effect of solvent properties and fluid flow elements on this transition is not fully understood. In this work, we present a study of the coil-stretch transition and related hysteresis phenomenon using stochastic computer simulations. We first investigate the effect of solvent quality on the coil-stretch transition using Brownian dynamics simulations. Unlike experiments, which are plagued with problems related to polydispersity of polymers and inaccurate control over flow profiles, simulations offer a powerful platform to systematically study the effect of solvent quality while keeping all other parameters in the system constant. The system consists of a polymer subjected to planar elongational flow in both theta solvents and good solvents. The polymer is represented by a bead-spring chain model undergoing elongational flow. Solvent-mediated effects such as fluctuating hydrodynamic interactions (HI) and excluded volume (EV) are included rigorously. Conformational hysteresis is understood in terms of a 1-D energy landscape theory with an activation energy barrier for transition. At steady state, depending upon the flow rate, the energy landscape can either have one or two energy wells. An energy landscape with one well corresponds to the coiled state at low flow rate and stretched state at high flowrate. The double welled landscape corresponds to the hysteretic regime where both coiled and stretched conformational states coexist across the ensemble population. A key factor in determining the effect of solvent quality is the use of a proper measure of solvent quality. In almost all earlier studies, the effect of molecular weight on solvent quality has been neglected, producing inconsistent results. Here, the solvent quality is quantified carefully such that the effect of molecular weight and temperature is taken into account. Contrary to earlier findings, it is observed that with improvement in solvent quality, the chains unravel faster and the critical strain rate at which the coil to stretch transition takes place decreases. Furthermore, the solvent quality has a profound effect on the scaling of the critical strain rate with molecular weight and on both the transient and steady state properties of the system. Universal functions are shown to exist for the observed dynamic and static properties, which will prove useful in determining the operating parameters for experiments. In particular, the ratio of the two different relaxation times (longest relaxation time and zero shear rate viscosity) is found to be a universal function of solvent quality independent of molecular weight. The relaxation times (both the longest relaxation time and the zero shear rate viscosity) increase while the critical strain rate is found to decrease with solvent quality. Next, the study of conformational hysteresis is extended to more complicated 3-D flows to understand the effect of flow vorticity on this phenomenon. Heretofore, there has been no systematic methodology for studying the dynamical interactions between polymer molecules and elementary flow patterns in three-dimensional flows. Such a framework is essential not just for gaining valuable insights into the physics of complex fluids at a fundamental level, but it is also crucial for various important applications like turbulent drag reduction where the underlying physical mechanisms involve dynamical interactions between polymers and turbulence fine scale flow features. Such a study is presented here to provide a framework to interpret complex fluid phenomenon in terms of elementary flow patterns. We investigate the conformational hysteresis using rigorous Brownian dynamics simulations and specifically explore the effect of flow vorticity on the lifetime and width of the hysteresis window in 3-D flows. A systematic procedure is developed with careful eigenvalue analysis to explore the sole effect of vorticity on polymer dynamics keeping the principal strain rate fixed. It is observed that the hysteresis width shrinks due to increase in flow vorticity irrespective of the flow type (bi-extensional, bi-compressional, spiral-inwards, spiral-outwards etc). This is further traced to the alignment of eigenvectors with the principal eigenvector direction leading to enhanced fluctuations. Vorticity is found to have a significant effect on both the transient and the steady state properties. Understanding the effect of vorticity on polymer conformational hysteresis can further help in understanding the fundamental processes in complex flows.
Book Synopsis Brownian Dynamics Simulations of Macromolecules by :
Download or read book Brownian Dynamics Simulations of Macromolecules written by and published by . This book was released on 2012 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Polymer Dynamics in Confined and Concentrated Media by : Ajey Krishnamurty Dambal
Download or read book Polymer Dynamics in Confined and Concentrated Media written by Ajey Krishnamurty Dambal and published by . This book was released on 2009 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Simulation and Theory of Polymer Dynamics in Sieving Media by : Martin Kenward
Download or read book On the Simulation and Theory of Polymer Dynamics in Sieving Media written by Martin Kenward and published by . This book was released on 2007 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Materials Modeling by : Sidney Yip
Download or read book Handbook of Materials Modeling written by Sidney Yip and published by Springer Science & Business Media. This book was released on 2007-11-17 with total page 2903 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first reference of its kind in the rapidly emerging field of computational approachs to materials research, this is a compendium of perspective-providing and topical articles written to inform students and non-specialists of the current status and capabilities of modelling and simulation. From the standpoint of methodology, the development follows a multiscale approach with emphasis on electronic-structure, atomistic, and mesoscale methods, as well as mathematical analysis and rate processes. Basic models are treated across traditional disciplines, not only in the discussion of methods but also in chapters on crystal defects, microstructure, fluids, polymers and soft matter. Written by authors who are actively participating in the current development, this collection of 150 articles has the breadth and depth to be a major contributor toward defining the field of computational materials. In addition, there are 40 commentaries by highly respected researchers, presenting various views that should interest the future generations of the community. Subject Editors: Martin Bazant, MIT; Bruce Boghosian, Tufts University; Richard Catlow, Royal Institution; Long-Qing Chen, Pennsylvania State University; William Curtin, Brown University; Tomas Diaz de la Rubia, Lawrence Livermore National Laboratory; Nicolas Hadjiconstantinou, MIT; Mark F. Horstemeyer, Mississippi State University; Efthimios Kaxiras, Harvard University; L. Mahadevan, Harvard University; Dimitrios Maroudas, University of Massachusetts; Nicola Marzari, MIT; Horia Metiu, University of California Santa Barbara; Gregory C. Rutledge, MIT; David J. Srolovitz, Princeton University; Bernhardt L. Trout, MIT; Dieter Wolf, Argonne National Laboratory.
Book Synopsis Polymer Dynamics in Dilute Media by : Shikha Somani
Download or read book Polymer Dynamics in Dilute Media written by Shikha Somani and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymers undergo a sharp coil to stretch conformational transition in extension dominated flows when the strain rate exceeds a critical value. Dramatic change in flow behavior is known to occur at the coil-stretch transition, making it useful for several commercial applications. Despite decades of study, this phenomenon remains surrounded with controversy as the effect of solvent properties and fluid flow elements on this transition is not fully understood. In this work, we present a study of the coil-stretch transition and related hysteresis phenomenon using stochastic computer simulations. We first investigate the effect of solvent quality on the coil-stretch transition using Brownian dynamics simulations. Unlike experiments, which are plagued with problems related to polydispersity of polymers and inaccurate control over flow profiles, simulations offer a powerful platform to systematically study the effect of solvent quality while keeping all other parameters in the system constant. The system consists of a polymer subjected to planar elongational flow in both theta solvents and good solvents. The polymer is represented by a bead-spring chain model undergoing elongational flow. Solvent-mediated effects such as fluctuating hydrodynamic interactions (HI) and excluded volume (EV) are included rigorously. Conformational hysteresis is understood in terms of a 1-D energy landscape theory with an activation energy barrier for transition. At steady state, depending upon the flow rate, the energy landscape can either have one or two energy wells. An energy landscape with one well corresponds to the coiled state at low flow rate and stretched state at high flowrate. The double welled landscape corresponds to the hysteretic regime where both coiled and stretched conformational states coexist across the ensemble population. A key factor in determining the effect of solvent quality is the use of a proper measure of solvent quality. In almost all earlier studies, the effect of molecular weight on solvent quality has been neglected, producing inconsistent results. Here, the solvent quality is quantified carefully such that the effect of molecular weight and temperature is taken into account. Contrary to earlier findings, it is observed that with improvement in solvent quality, the chains unravel faster and the critical strain rate at which the coil to stretch transition takes place decreases. Furthermore, the solvent quality has a profound effect on the scaling of the critical strain rate with molecular weight and on both the transient and steady state properties of the system. Universal functions are shown to exist for the observed dynamic and static properties, which will prove useful in determining the operating parameters for experiments. In particular, the ratio of the two different relaxation times (longest relaxation time and zero shear rate viscosity) is found to be a universal function of solvent quality independent of molecular weight. The relaxation times (both the longest relaxation time and the zero shear rate viscosity) increase while the critical strain rate is found to decrease with solvent quality. Next, the study of conformational hysteresis is extended to more complicated 3-D flows to understand the effect of flow vorticity on this phenomenon. Heretofore, there has been no systematic methodology for studying the dynamical interactions between polymer molecules and elementary flow patterns in three-dimensional flows. Such a framework is essential not just for gaining valuable insights into the physics of complex fluids at a fundamental level, but it is also crucial for various important applications like turbulent drag reduction where the underlying physical mechanisms involve dynamical interactions between polymers and turbulence fine scale flow features. Such a study is presented here to provide a framework to interpret complex fluid phenomenon in terms of elementary flow patterns. We investigate the conformational hysteresis using rigorous Brownian dynamics simulations and specifically explore the effect of flow vorticity on the lifetime and width of the hysteresis window in 3-D flows. A systematic procedure is developed with careful eigenvalue analysis to explore the sole effect of vorticity on polymer dynamics keeping the principal strain rate fixed. It is observed that the hysteresis width shrinks due to increase in flow vorticity irrespective of the flow type (bi-extensional, bi-compressional, spiral-inwards, spiral-outwards etc). This is further traced to the alignment of eigenvectors with the principal eigenvector direction leading to enhanced fluctuations. Vorticity is found to have a significant effect on both the transient and the steady state properties. Understanding the effect of vorticity on polymer conformational hysteresis can further help in understanding the fundamental processes in complex flows.
Book Synopsis Brownian Dynamics Simulations of Dilute Polymer Solutions with Complex Hydrodynamics by : Chih-Chen Hsieh
Download or read book Brownian Dynamics Simulations of Dilute Polymer Solutions with Complex Hydrodynamics written by Chih-Chen Hsieh and published by . This book was released on 2005 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unravelling the Dynamics of Semidilute Polymer Solutions Using Brownian Dynamics by : Aashish Jain
Download or read book Unravelling the Dynamics of Semidilute Polymer Solutions Using Brownian Dynamics written by Aashish Jain and published by . This book was released on 2013 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: A polymer solution has three concentration regimes: (i) dilute (ii) semidilute and (iii) concentrated. There are a number of contexts involving polymer solutions, such as in the spinning of nanofi bers or in ink jet printing, where in order to achieve the most optimal outcome the concentration of polymers must be in the semidilute regime. In many biological contexts as well, such as the diffusion of protein and other biomolecules, the essential physics occur in the semidilute regime. Therefore, it is extremely important to understand the behavior of semidilute polymer solutions from the fundamental and also from the technological point of view. A significant amount of research has been carried out in the dilute and concentrated regimes in the past by means of experiments, theories and computer simulations. These two regimes have been explored successfully because the behavior of polymer solutions in the dilute and concentrated regimes can be understood by studying the behavior of single molecules. In the dilute case the motivation for this is obvious, while in the concentrated case, by treating all the molecules that surround a particular molecule as obstacles that constrain its motion, the entire problem is reduced to understanding the motion of a polymer in a tube. This approximation, however, is not valid in the semidilute regime, which lies between the dilute and concentrated regimes, because of all the many-body interactions, that arise in this regime. The main focus of this thesis is to develop an optimized Brownian dynamics (BD) simulation algorithm for semidilute polymer solutions at and far from equilibrium, that is capable of accounting for the many-body interactions. The goal is to use this algorithm to predict various physical properties for a range of concentrations and temperatures and to interpret the results in terms of the blob scaling theory. The development of a BD simulation algorithm for multi-chain systems requires the consideration of a large system of polymer chains coupled to one another through excluded volume interactions (which are short-range in space) and hydrodynamic interactions (which are long-range in space). In the presence of periodic boundary conditions, long-ranged hydrodynamic interactions are frequently summed with the Ewald summation technique (Beenakker, 1986; Stoltz et al., 2006). By performing detailed simulations that shed light on the influence of several tuning parameters involved both in the Ewald summation method, and in the efficient treatment of Brownian forces, we describe the development of a BD algorithm in this thesis, in which the computational cost scales as O(N^{1.8}), where N is the number of monomers in the simulation box. It is also shown that Beenakker's original implementation of the Ewald sum, which is only valid for systems without bead overlap, can be modified so that _ solutions can be simulated by switching off excluded volume interactions. Comparison of the predictions by the BD algorithm of the gyration radius, the end-to-end vector, and the self-diffusion coefficient with the hybrid lattice Boltzmann-Molecular dynamics (LB-MD) method (Ahlrichs and Dunweg, 1999) shows excellent agreement between the two methods. This study has been published in the paper Jain et al. (2012). The behavior of semidilute polymer solutions at equilibrium varies significantly with concentration and solvent quality. These effects are reflected in the concentration driven crossover from the dilute to the concentrated regime, and in the solvent quality driven crossover from theta solvents to good solvents in the phase diagram of polymer solutions. This double crossover region for concentration above the overlap concentration, is explored by Brownian dynamics simulations to map out the universal crossover scaling functions for the gyration radius and the single-chain diffusion constant. Scaling considerations (Rubinstein and Colby, 2003), our simulation results, and recently reported experimental data (Pan, Nguyen, Sunthar, Sridhar & Prakash, Pan et al.) on the polymer contribution to the zero-shear rate viscosity obtained from rheological measurements on DNA systems support the assumption that there are simple relations between these functions, such that they can be inferred from one another. This study has been published in the paper Jain et al. (2012). Unlike the simulation of equilibrium systems where periodic boundary conditions (PBCs) are used in an orthogonal cell to get rid of wall effects, for the simulation of far from equilibrium systems, appropriate PBCs need to be used such that they are compatible with any particular imposed flow. One should also be able to carry out the simulation for an arbitrary amount of time. Commonly, the Lees Edwards PBC (Lees and Edwards, 1972) is used for planar shear flow and the Kraynik-Reinelt PBC (Kraynik and Reinelt, 1992) is used for planar elongational flow. These PBCs have been used and tested in molecular dynamics simulations (Bhupathiraju et al., 1996; Todd and Daivis, 1998) and multi-chain BD simulations (Stoltz et al., 2006). In this thesis PBCs that can handle a planar mixed flow (which is a linear combination of planar elongational flow and planar shear flow) (Hunt et al., 2010) is implemented in a multi-chain BD simulation algorithm for semidilute polymer solutions. Preliminary results on the validation of the planar mixed flow algorithm are presented. References: 1. Beenakker, C. W. J., 1986: Ewald sum of the Rotne-Prager tensor. J.Chem.Phys., 85, 1581-1582. 2. Stoltz, C., J. J. de Pablo, and M. D. Graham, 2006: Concentration dependence of shear and extensional rheology of polymer simulations: Brownian dynamics simulations. J.Rheol., 502, 137. 3. Ahlrichs, P. and B. Dunweg, 1999: Simulation of a single polymer chain in solution by combining Lattice Boltzmann and molecular dynamics. J.Chem.Phys., 111, 8225. 4. Jain, A., P. Sunthar, B. Dunweg, and J. R. Prakash, 2012: Optimization of a Brownian-dynamics algorithm for semidilute polymer solutions. Phys. Rev. E, 85, 066703. 5. Rubinstein, M. and R. H. Colby, 2003: Polymer Physics. Oxford University Press 6. Pan, S., D. A. Nguyen, P. Sunthar, T. Sridhar, and J. R. Prakash Universal solvent quality crossover of the zero shear rate viscosity of semidilute DNA solutions. 2011arXiv1112.3720P. 7. Jain, A., B. Dunweg, and J. R. Prakash, 2012: Dynamic crossover scaling in polymer solutions. Phys. Rev. Lett., 109, 088302. 8. Lees, A. W. and S. F. Edwards, 1972: The computer studies of transport processes under extreme conditions. J. Phys. C: Solid State Phys., 5, 1921-1929. 9. Kraynik, A. M. and D. A. Reinelt, 1992: Extensional motions of spatially periodic lattices. Int. J. Multiphase Flow, 18, 1045. 10. Bhupathiraju, R., P. T. Cummings, and H. D. Cochran, 1996: An efficient parallel algorithm for non-equilibrium molecular dynamics simulations of very large systems in planar Couette flow. Mol.Phys., 88(6), 1665-1670. 11.Todd, B. D. and P. J. Daivis, 1998: Non-equilibrium molecular dynamics simulations of planar elongational flow with spatially and temporally periodic boundary conditions. Phys. Rev. Lett., 81, 1118. 12. Hunt, T. A., S. Bernardi, and B. D. Todd, 2010: A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow. J.Chem.Phys., 133(15), 154116.
Book Synopsis Structure and Dynamics of Confined Polymers by : John J. Kasianowicz
Download or read book Structure and Dynamics of Confined Polymers written by John J. Kasianowicz and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymers are essential to biology because they can have enough stable degrees of freedom to store the molecular code of heredity and to express the sequences needed to manufacture new molecules. Through these they perform or control virtually every function in life. Although some biopolymers are created and spend their entire career in the relatively large free space inside cells or organelles, many biopolymers must migrate through a narrow passageway to get to their targeted destination. This suggests the questions: How does confining a polymer affect its behavior and function? What does that tell us about the interactions between the monomers that comprise the polymer and the molecules that confine it? Can we design and build devices that mimic the functions of these nanoscale systems? The NATO Advanced Research Workshop brought together for four days in Bikal, Hungary over forty experts in experimental and theoretical biophysics, molecular biology, biophysical chemistry, and biochemistry interested in these questions. Their papers collected in this book provide insight on biological processes involving confinement and form a basis for new biotechnological applications using polymers. In his paper Edmund DiMarzio asks: What is so special about polymers? Why are polymers so prevalent in living things? The chemist says the reason is that a protein made of N amino acids can have any of 20 different kinds at each position along the chain, resulting in 20 N different polymers, and that the complexity of life lies in this variety.
Book Synopsis Investigating Polymer Physics with Single Molecule Experiment and Brownian Dynamics Simulation by : Charles Martin Schroeder
Download or read book Investigating Polymer Physics with Single Molecule Experiment and Brownian Dynamics Simulation written by Charles Martin Schroeder and published by . This book was released on 2004 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Masters Abstracts International by :
Download or read book Masters Abstracts International written by and published by . This book was released on 1996 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Brownian Dynamics Simulations of Flowing Isolated Polymer Molecules in Solution Near Surfaces by : Manish Chopra
Download or read book Brownian Dynamics Simulations of Flowing Isolated Polymer Molecules in Solution Near Surfaces written by Manish Chopra and published by . This book was released on 2001 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Brownian Dynamics Simulation of Linear and Star Polymers by : Martin Bishop
Download or read book Brownian Dynamics Simulation of Linear and Star Polymers written by Martin Bishop and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Brownian Dynamics Simulations of Star-branched Polymers in Dilute Solution Under Flow by : Yongmin Lee
Download or read book Brownian Dynamics Simulations of Star-branched Polymers in Dilute Solution Under Flow written by Yongmin Lee and published by . This book was released on 2008 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Brownian Dynamics Simulation for the Study of Polymeric Liquids by : Seong Jae Lee
Download or read book Brownian Dynamics Simulation for the Study of Polymeric Liquids written by Seong Jae Lee and published by . This book was released on 1992 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Simulation Methods for Polymers by : Michael Kotelyanskii
Download or read book Simulation Methods for Polymers written by Michael Kotelyanskii and published by CRC Press. This book was released on 2004-03-01 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
