Multiscale Modeling And Computer Simulation Of Polyhedral Oligomeric Silsesquioxane Assemblies

Exploring recent developments in the field, Coarse-Graining of Condensed Phase and Biomolecular Systems examines systematic ways of constructing coarse-grained representations for complex systems. It explains how this approach can be used in the simulation and modeling of condensed phase and biomolecular systems. Assembling some of the most influential, world-renowned researchers in the field, this book covers the latest developments in the coarse-grained molecular dynamics simulation and modeling of condensed phase and biomolecular systems. Each chapter focuses on specific examples of evolving coarse-graining methodologies and presents results for a variety of complex systems. The contributors discuss the minimalist, inversion, and multiscale approaches to coarse-graining, along with the emerging challenges of coarse-graining. They also connect atomic-level information with new coarse-grained representations of complex systems, such as lipid bilayers, proteins, peptides, and DNA.

Scientific theories that explain how physical systems behave are described by mathematical models which provide the basis for computer simulations of events that occur in the physical universe. These models, being only mathematical characterizations of actual phenomena, are obviously subject to error because of the inherent limitations of all mathematical abstractions. In this work, new theory and methodologies are developed to quantify such modeling error in a special way that resolves a fundamental and standing issue: multiscale modeling, the development of models of events that transcend many spatial and temporal scales. Specifically, we devise the machinery for a posteriori estimates of relative modeling error between a model of fine scale and another of coarser scale, and we use this methodology as a general approach to multiscale problems. The target application is one of critical importance to nanomanufacturing: imprint lithography of semiconductor devices. The development of numerical methods for multiscale modeling has become one of the most important areas of computational science. Technological developments in the manufacturing of semiconductors hinge upon the ability to understand physical phenomena from the nanoscale to the microscale and beyond. Predictive simulation tools are critical to the advancement of nanomanufacturing semiconductor devices. In principle, they can displace expensive experiments and testing and optimize the design of the manufacturing process. The development of such tools rest on the edge of contemporary methods and high-performance computing capabilities and is a major open problem in computational science. In this dissertation, a molecular model is used to simulate the deformation of polymeric materials used in the fabrication of semiconductor devices. Algorithms are described which lead to a complex molecular model of polymer materials designed to produce an etch barrier, a critical component in imprint lithography approaches to semiconductor manufacturing. Each application of this so-called polymerization process leads to one realization of a lattice-type model of the polymer, a molecular statics model of enormous size and complexity. This is referred to as the base model for analyzing the deformation of the etch barrier, a critical feature of the manufacturing process. To reduce the size and complexity of this model, a sequence of coarser surrogate models is generated. These surrogates are the multiscale models critical to the successful computer simulation of the entire manufacturing process. The surrogate involves a combination of particle models, the molecular model of the polymer, and a coarse-scale model of the polymer as a nonlinear hyperelastic material. Coefficients for the nonlinear elastic continuum model are determined using numerical experiments on representative volume elements of the polymer model. Furthermore, a simple model of initial strain is incorporated in the continuum equations to model the inherit shrinking of the A coupled particle and continuum model is constructed using a special algorithm designed to provide constraints on a region of overlap between the continuum and particle models. This coupled model is based on the so-called Arlequin method that was introduced in the context of coupling two continuum models with differing levels of discretization. It is shown that the Arlequin problem for the particle-tocontinuum model is well posed in a one-dimensional setting involving linear harmonic springs coupled with a linearly elastic continuum. Several numerical examples are presented. Numerical experiments in three dimensions are also discussed in which the polymer model is coupled to a nonlinear elastic continuum. Error estimates in local quantities of interest are constructed in order to estimate the modeling error due to the approximation of the particle model by the coupled multiscale surrogate model. The estimates of the error are computed by solving an auxiliary adjoint, or dual, problem that incorporates as data the quantity of interest or its derivatives. The solution of the adjoint problem indicates how the error in the approximation of the polymer model inferences the error in the quantity of interest. The error in the quantity of interest represents the relative error between the value of the quantity evaluated for the base model, a quantity typically unavailable or intractable, and the value of the quantity of interest provided by the multiscale surrogate model. To estimate the error in the quantity of interest, a theorem is employed that establishes that the error coincides with the value of the residual functional acting on the adjoint solution plus a higher-order remainder. For each surrogate in a sequence of surrogates generated, the residual functional acting on various approximations of the adjoint is computed. These error estimates are used to construct an adaptive algorithm whereby the model is adapted by supplying additional fine-scale data in certain subdomains in order to reduce the error in the quantity of interest. The adaptation algorithm involves partitioning the domain and selecting which subdomains are to use the particle model, the continuum model, and where the two overlap. When the algorithm identifies that a region contributes a relatively large amount to the error in the quantity of interest, it is scheduled for refinement by switching the model for that region to the particle model. Numerical experiments on several configurations representative of nano-features in semiconductor device fabrication demonstrate the effectiveness of the error estimate in controlling the modeling error as well as the ability of the adaptive algorithm to reduce the error in the quantity of interest. There are two major conclusions of this study: 1. an effective and well posed multiscale model that couples particle and continuum models can be constructed as a surrogate to molecular statics models of polymer networks and 2. an error estimate of the modeling error for such systems can be estimated with sufficient accuracy to provide the basis for very effective multiscale modeling procedures. The methodology developed in this study provides a general approach to multiscale modeling. The computational procedures, computer codes, and results could provide a powerful tool in understanding, designing, and optimizing an important class of semiconductormanufacturing processes. The study in this dissertation involves all three components of the CAM graduate program requirements: Area A, Applicable Mathematics; Area B, Numerical Analysis and Scientific Computation; and Area C, Mathematical Modeling and Applications. The multiscale modeling approach developed here is based on the construction of continuum surrogates and coupling them to molecular statics models of polymer as well as a posteriori estimates of error and their adaptive control. A detailed mathematical analysis is provided for the Arlequin method in the context of coupling particle and continuum models for a class of one-dimensional model problems. Algorithms are described and implemented that solve the adaptive, nonlinear problem proposed in the multiscale surrogate problem. Large scale, parallel computations for the base model are also shown. Finally, detailed studies of models relevant to applications to semiconductor manufacturing are presented.

CD-ROM contains conference manuscripts.

This book presents contributions on the current problems in a number of topical areas of nonlinear dynamics and physics, written by experts from Russia, Ukraine, Israel, Germany, Poland, Italy, the Netherlands, the USA, and France. The book is dedicated to Professor Leonid I. Manevitch, an outstanding scholar in the fields of Mechanics of Solids, Nonlinear Dynamics, and Polymer Physics, on the occasion of his 80th birthday.

Clay–Polymer Nanocomposites is a complete summary of the existing knowledge on this topic, from the basic concepts of synthesis and design to their applications in timely topics such as high-performance composites, environment, and energy issues. This book covers many aspects of synthesis such as in- situ polymerization within the interlamellar spacing of the clays or by reaction of pristine or pre-modified clays with reactive polymers and prepolymers. Indeed, nanocomposites can be prepared at industrial scale by melt mixing. Regardless the synthesis method, much is said in this book about the importance of theclay pre-modification step, which is demonstrated to be effective, on many occasions, in obtaining exfoliated nanocomposites. Clay–Polymer Nanocomposites reports the background to numerous characterization methods including solid state NMR, neutron scattering, diffraction and vibrational techniques as well as surface analytical methods, namely XPS, inverse gas chromatography and nitrogen adsorption to probe surface composition, wetting and textural/structural properties. Although not described in dedicated chapters, numerous X-ray diffraction patterns of clay–polymer nanocomposites and reference materials are displayed to account for the effects of intercalation and exfoliations of layered aluminosilicates. Finally, multiscale molecular simulation protocols are presenting for predicting morphologies and properties of nanostructured polymer systems with industrial relevance. As far as applications are concerned, Clay–Polymer Nanocomposites examines structural composites such as clay–epoxy and clay–biopolymers, the use of clay–polymer nanocomposites as reactive nanocomposite fillers, catalytic clay-(conductive) polymers and similar nanocomposites for the uptake of hazardous compounds or for controlled drug release, antibacterial applications, energy storage, and more. The most comprehensive coverage of the state of the art in clay–polymer nanocomposites, from synthesis and design to opportunities and applications Covers the various methods of characterization of clay–polymer nanocomposites - including spectroscopy, thermal analyses, and X-ray diffraction Includes a discussion of a range of application areas, including biomedicine, energy storage, biofouling resistance, and more

Long-Term Durability of Polymeric Matrix Composites presents a comprehensive knowledge-set of matrix, fiber and interphase behavior under long-term aging conditions, theoretical modeling and experimental methods. This book covers long-term constituent behavior, predictive methodologies, experimental validation and design practice. Readers will also find a discussion of various applications, including aging air craft structures, aging civil infrastructure, in addition to engines and high temperature applications.

Superlubricity is defined as a sliding regime in which friction or resistance to sliding vanishes. It has been shown that energy can be conserved by further reducing/removing friction in moving mechanical systems and this book includes contributions from world-renowned scientists who address some of the most fundamental research issues in overcoming friction. Superlubricity reviews the latest methods and materials in this area of research that are aimed at removing friction in nano-to-micro scale machines and large scale engineering components. Insight is also given into the atomic-scale origins of friction in general and superlubricity while other chapters focus on experimental and practical aspects or impacts of superlubricity that will be very useful for broader industrial community. * Reviews the latest fundamental research in superlubricity today* Presents 'state-of-the-art' methods, materials, and experimental techniques* Latest developments in tribomaterials, coatings, and lubricants providing superlubricity