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Poly and Polymer Electrolytes for Energy Conversion: Ab Initio, Molecular, and Continuum Models
“Block Copolymers at Surfaces: Patterns, Templates and Electric Fields”
Diblock copolymers (BCP) exhibit a wide variety of spatially modulated phases due to competing molecular and entropic forces. The resulting self-assembly nano-structures and morphologies have many uses and applications. In recent years an intensive effort has been devoted to control ordering of block copolymers close to surfaces and in thin film set-ups as is required by many applications. In this talk I will review our theoretical investigations aimed at understanding the ways to control orientation of anisotropic BCP phases. One line of studies is devoted to use of electric fields in order to orient lamellar and hexagonal phases of BCP. More recently, reported experiments and modeling included doping of BCP by ionic impurities that enhance and complement the dielectric response of BCP to external electric fields. In a separate line of research, we also investigated the effect of patterned surfaces on orientation and ordering of lamellar BCP phases. By using analytical free-energy expansions (Ginzburg-Landau like) as well as numerical solutions of self-consistent field theory, surface characteristics that enable BCP lamellar to orient perpendicular to bounding surfaces are explored. Two types of surfaces are considered: (i) chemical patterns in the form of far-apart stripes that induce in-between ordering of perpendicular BCP lamellar phases; and, (ii) a grooved mold used as in nano-imprint lithography to orient lamellar phases. For both surfaces, we present the conditions to induce perpendicular ordering and orientation within the theoretical framework.
Douwe Jan Bonthuis
“Electro-hydraulic Power Conversion in Water-filled Nanochannels”
We explore mechanisms for flow generation in water-filled nanochannels, employing the coupling between translational and rotational momentum. We discuss two central questions: First, can a dipolar surface ordering give rise to a non-zero zeta-potential? And second, can the dipolar nature of water be exploited to drive a nanoscale electro-osmotic pump? Using a generalized Navier-Stokes equation that includes dipolar polarization and relaxation, we show that static electric fields do not induce flow in ordered dipolar fluids, while rotating electric fields efficiently convert electric into hydraulic power on the nanoscale. We also perform molecular dynamics simulations of water and find that erroneous force truncation can give rise to spurious flow effects for static electric fields.
Joint work with Dominik Horinek, Lyderic Bocquet and Roland R. Netz
"Emergent scaling laws in dielectric materials"
When an alternating potential is placed across a dielectric material the current through the material usually depends upon the frequency of the potential. For low and high frequencies this dependence is dominated by percolation paths through the material and is very sensitive to the material composition. However for intermediate frequencies with more regular conduction paths, it is often possible to observe emergent behaviour which is much less dependent upon the precise form of the material composition. In this behaviour we often see anomolous power laws in which the material admmitance depends on a fractional power of the potential frequency. In this talk we will aim to explain this behaviour by modelling the dielectric as a random binary network. The electrical properties can then be described by certain types of random operator. We will show that the power law and percolation behaviour is then a consequence of certain properties of the spectrum of this operator. We will then show how these results can be generalised to other materials. Chris Budd, N. McCullen and D. Almond, Bath Institute for Complex Systems
“Gels: mechanis and chemistry”
James A. Elliott
“A unified morphological description of Nafion membranes from SAXS and mesoscale simulations”
Over the past three decades, numerous structural models have been proposed for perfluorosulfonic acid ionomers (PFSAs), of which we focus here on Nafion as being the archetype, based on small angle X-ray scattering (SAXS) data. Unfortunately, despite a great deal of effort, the very high degree of disorder in these materials makes it difficult, if not impossible, to deduce their morphology unambiguously from such information alone. On the other hand, over the last decade, it has become possible to carry out very detailed atomistic, even first principles based, simulations and calculations of increasingly larger model systems of PFSAs. However, until very recently, these systems were still too small to describe the main morphological features (e.g. ionic clustering or fluorocarbon crystallites) thought to give rise to the SAXS reflections. Here, we present a combination of a model-independent procedure for obtaining structural information from SAXS patterns based on a Maximum Entropy (MaxEnt) approach coupled with mesoscale simulations of Nafion morphology using Dissipative Particle Dynamics (DPD) parameterized via atomistic calculations and density functional theory. Together, these two methods show that the nanoscale ionic clustering in PFSAs is intimately linked to, but spatially separate from, the larger scale organization of the fluorocarbon backbone. Although we are unable to observe directly crystallization of the backbone in the DPD simulations, the high density regions of fluorocarbon segments correspond exactly to those regions where the density of ionic clusters is lowest, each forming an independent bicontinuous domain. By averaging multiple independent realizations of the DPD morphology, we are able to construct a structural model that agrees well with the MaxEnt reconstructions from SAXS data over an area of several square microns. This lends credence to the mesoscale simulations, and the atomistic calculations which underpin them. For the first time, we are able to demonstrate a unified morphological description of PFSAs based on both statistical (MaxEnt) and thermodynamic (DPD) descriptions, which broadly favours a continuous network of spherical ionic clusters embedded in a matrix of fluorocarbon chains.
James A. Elliott†, Dongsheng Wu‡, Stephen J. Paddison‡, Robert B. Moore§
†Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, CB2 3QZ.
‡Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996.
§Macromolecules and Interfaces Institute, Department of Chemistry, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.
Carlos J. Garcia-Cervera (talk)
“A Linear Scaling Subspace Iteration Algorithm with Optimally Localized Non-Orthogonal Wave Functions for Kohn-Sham Density Functional Theory”
We present a new linear scaling method for electronic structure computations in the context of Kohn-Sham density functional theory (DFT). The method is based on a subspace iteration, and takes advantage of the non-orthogonal formulation of the Kohn-Sham functional, and the improved localization properties of non-orthogonal wave functions. We demonstrate the efficiency of the algorithm for practical applications by performing fully three-dimensional computations of the electronic density of alkane chains.
Carlos J. Garcia-Cervera --> Informal tutorial
“Numerical advances in Self-Consistent Field Theory simulations, and applications to block copolymer lithography”
I will discuss some recent developments in the numerical simulation of self-consistent field theory (SCFT) for block copolymers. I will focus on the following applications:
* SCFT simulations of block copolymers laterally confined in a
square well: Here we explore the conditions for which
self-assembly in laterally confined thin block copolymer films
results in tetragonal square arrays of standing up cylinders. More
specifically, we study the equilibrium phase behavior of thin
films composed of a blend of AB block copolymer and A homopolymer
laterally confined in square wells. By using suitable homopolymer
additives and appropriately sized wells, we observed square
lattices of upright B cylinders that are not stable in pure AB
block copolymer systems. Considering the potential application of
such films in block copolymer lithography, we also conducted
numerical SCFT simulations of the role of line edge roughness at
the periphery of the square well on feature defect populations.
Our results indicate that the tetragonal ordering observed under
square confinement is robust to a wide range of boundary
* SCFT simulations of block copolymers on the surface of a sphere:
In this model, we assume that the composition of the thin block
copolymer film is independent of the radial direction. Using this
approach we were able to study the phase separation process, and
specifically the formation of defects in the lamellar and
cylindrical phases, and its dependence on the radius of the
sphere. If time permits, I will discuss recent work on polymer
“Investigating Polyelectrolyte Multilayers (PEMs) via Simulations”
Polyelectrolyte multilayers (PEMs) are composed of alternating layers of oppositely charged polyelectrolytes (PEs), which are generally built up based on the Layer-by-Layer technique [1, 2]. PEMs have stimulated great interests from both academic researchers and industries due to their potential applications, such as membrane, encapsulation, and matrix materials for enzymes and proteins in sensor applications. Nevertheless, despite the large amount of experimental works, theoretical and computational studies are relatively scarce (for a review see Refs. [3, 4]). Our goal is to understand the interphase and interface structures and interactions via simulation methods. We try to combine coarse- grained (CG) and all-atom (AA) molecular dynamics (MD) simulations to construct a viable model for PEMs. The CG-MD method is very efficient in dealing with the systems in larger time and length scale, and AA-MD approach is necessary to understand the details, e.g., the conformation of adsorbed PE chains, the influence of the aqueous solvent at a higher resolution. We find that the first layers, in particular the second layer, is very important in PEM buildup. Our AA-MD simulations reproduce the experimental dielectric constant and diffusion of waters in the central (interphase) region of PSS/PDADMA PEMs. On the other hand, the PSS adsorption has been investigated in AA-MD to understand the interfacial behavior close to the adsorbing substrate. We find both the surface charges and surface hydrophilic groups promote the adsorption of PSSs.
Baofu Qiao, Juan J. Cerda` and Christian Holm (Institut für Computerphysik, Universität Stuttgart)
"Organic Materials for Molecular Electronics: Scale Bridging Simulation Approach"
Despite the long history of organic electronics, there has been only very little understanding how the chemistry of a particular compound relates to the properties of the final device. The main difficulty is that processes at all length scales equally contribute to the final efficiency. In solar cells, for example, the global morphology (micro- and nanometers) assists percolation of charges to the electrodes; the local molecular arrangement (on the Angstrom and nm scale) facilitates charge hopping, increasing the charge mobility. Finally, the electronic structure is tuned to achieve efficient photon harvesting, as well as creation, diffusion and dissociation of excitons. Theory and simulation on different length scales can help to understand these fundamental processes by linking self-organizing, structural, and electronic properties together.
“Energetic Variational Approaches in Modeling the Ionic Fluids”
In this talk, we study several multi-scale, multi-physics models for the ionic fluids. Depending on the specific physical situations, the models involves the macroscopic continuum descriptions (fluids, elasticity, diffusion etc), electrostatic Poisson equation, microscopic (atomic) modeling, as well as the cross-scale couplings, such as the kinematic transport and the induced (macro)stresses. We will present an unified energetic variational framework which can be used to derive the self consistent coupled system. I will focus on the analysis and numerical issues arising from the models.
James K. McCusker
“The Science of Solar Energy Conversion: Fundamental Issues and Global Applications”
“Modeling of carbon nanostructures for capacitive energy storage”
During this talk, I will discuss the use of atomistic modeling for understanding capacitive electrical energy storage (i.e. not involving chemical reaction) in carbon nanostructures. Supercapacitors based on nanoporous carbon materials, commonly called electric double-layer capacitors (EDLCs), are emerging as a novel type of energy-storage device with the potential to substitute batteries in applications that require high power densities. The EDLC model has been used to characterize the energy storage of supercapacitors for decades. I will point to the shortcomings of this model and show how it can be modified to account for recent experimental observations. In particular, I will present a heuristic model that improves the EDLC model by explicitly including pore curvature and nano-confinement. The new model allows the properties of a supercapacitor to be correlated with pore size, specific surface area, Debye length, electrolyte concentration, dielectric constant, and solute ion size, and lead to a optimization pathway of carbon supercapacitors properties through experiments. I will also present our recent results on the dynamics of ion adsorption and desorption and its effect on capacitor performance.
“Structure formation in multicomponent polymer materials: soft, coarse-grained models”
We investigate the ability of soft, coarse-grained models to describe the kinetics of structure formation in dense multi-component polymer melt. The softness of the interactions on the mesoscopic scale allows the coarse-grained segments to overlap and the high segmental density is crucial for describing experimentally relevant values of the invariant degree of polymerization. We will discuss the following topics:
a) calculation of free energies of self-assembled structure
b) influence of the single chain dynamics on the kinetics of structure formation
c) relation between particle-based models and a continuum description in terms of a Ginzburg-Landau free-energy functional
Joint work with Kostas Ch. Daoulas
“Split charge equilibration: A charge transfer method for electrolytes and other non-metallic materials”
“On a mathematical model for contemplative amoeboid locomotion”
It has been reported that even single-celled organisms appear to be "indecisive" or
"contemplative" when confronted with an obstacle. During migration in a narrow lane, the amoeboid organism Physarum plasmodium, upon encountering the chemical repellent quinine, stops for a period of time (typically several hours, but the duration differs for each plasmodium) and then suddenly begins to move again. When movement resumes, three distinct behaviors are observed (continuing forward, turning back, and migrating in both directions). Here, we report a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. The model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of
pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). This is a joint work
with Kei-Ichi Ueda, Seiji Takagi, and Toshiyuki Nakagaki.
Stephen J. Paddison
"Connecting the structure and transport properties of polymer electrolyte membranes
through modeling and experiments"
Proton exchange membranes (PEMs) are the electrolyte in current state-of-the-art fuel cells and function as not only the separator of the electrodes and reactant gases (H2 and O2) but importantly as the internal ion conductor . Efficient operation of these energy conversion devices in diverse applications (vehicular, portable, and stationary) places demands on the PEM which include: longtime thermal and chemical stability (including resistance to oxidation and degradation by reactive species) at temperatures as high as 120°C, and high proton conductivity (≈ 10-1 Scm-1) under low humidity conditions (25-50% relative humidity). Although a large number of strategies  have been devised in the pursuit to design membrane materials that meet these requirements current PEM fuel cells still utilize perfluorosulfonic acid (PFSA) ionomers such as Nafion®. Recently, proton conduction in these polymeric materials has been developed within a framework consisting of: complexity, connectivity, and cooperativity . Experiments and modeling have shown that the transport of water and hydrated protons within PFSAs is dependent upon: the characteristic dimensions of the phase-separated hydrated polymer morphology (typically on the order of only a few nanometers); acidity, density, and distribution of the sulfonic acid groups; and the external conditions including humidity, temperature, and pressure. A complete understanding of how all these factors may be used in a synergetic fashion in the engineering of novel high performance materials remains forth-coming . This talk will describe our ongoing efforts in securing a fundamental molecular-level understanding how the degree of hydration of PFSA ionomers determines morphology, state of absorbed water, and proton transport [5-10]. We will outline a multi-scale modeling effort employing a diverse suite of methodologies and that is closely coupled and, where possible, validated to characterization experiments.
 K. D. Kreuer, S. J. Paddison, E. Spohr, and M. Schuster, Chem. Rev. 2004, 104, 4637.
 M. A. Hickner, Mater. Today 2010, 13, 34.
 Device and Materials Modeling in PEM Fuel Cells; Paddison, S. J., Promislow, K. S., Eds.; Springer-Verlag Berlin: Berlin, 2008, 113, pp. 1-588.
 J. A. Elliott and S. J. Paddison, Phys. Chem. Chem. Phys. 2007, 9, 2602.
 S. J. Paddison and J. A. Elliott, Phys. Chem. Chem. Phys. 2006, 8, 2193.
 D.-S. Wu, S. J. Paddison, and J. A. Elliott, Energy Environ. Sci. 2008, 1, 284.
 D.-S. Wu, S. J. Paddison, and J. A. Elliott, Macromolecules 2009, 42, 3358.
 R. L. Hayes, S. J. Paddison, and M. E. Tuckerman, J. Phys. Chem. B 2009, 113, 16574.
 C. Wang and S. J. Paddison, Phys. Chem. Chem. Phys. 2010, 12, 970.
 B. F. Habenicht, S. J. Paddison, and M. E. Tuckerman, J. Mater. Chem. 2010, 20, 6342.
“Moving interfaces and elliptic systems”
Mathematical models of material phenomena often involve complex moving interfaces, with velocities determined by elliptic systems which connect the material physics to interface geometry. Such interfaces are evolved by a semi-Lagrangian contouring (SLC)
algorithm which treats the velocity as a black box, and separates model-dependent physics from interface motion. SLC converts stiff moving interfaces to an implicit grid-free contouring problem, and computes highly accurate solutions with merging, anisotropy, faceting, curvature, dynamic topology and nonlocal interactions.
The interface velocity is computed by locally-corrected spectral (LCS) methods which convert arbitrary elliptic problems to first-order overdetermined systems, mollify a periodic fundamental solution for convergence, and correct via Ewald summation.
Local linear algebra and distribution theory yield a simple boundary integral equation. With a new geometric nonuniform fast Fourier transform, LCS methods provide efficient accurate solutions to elliptic systems in complex domains.
Nico van der Vegt
"Systematic coarse-graining of molecular models: simple-yet-specific models for polymers and polyelectrolytes"
I will discuss methods for systematic coarse-graining of molecular models. The obtained coarse-grained models are particularly useful in hierarchical simulations in which we can readily switch from a detailed-atomistic description to a coarse-grained description, and back. Systematic coarse-graining involves integration over molecular degrees of freedom. Depending on the "lost degrees of freedom", state-dependent coarse-grained potentials are obtained, which in general limit the applicability of the model in a fairly narrow window of temperatures and densities. I will present coarse-grained models which we have recently developed for polymers, aqueous electrolytes, and aqueous solutions of hydrophobic solutes. Based on these examples, I will illustrate some aspects of representability and (thermodynamic) transferability of the models.
Dimitri D. Vvedensky
"Coarse-Grained Theory of Surface Nanostructure Formation"
This talk will present the development of a stochastic continuum theory of the formation of surface nanostructures. The first step of the methodology is the systematic transformation of a lattice model for a particular system into a stochastic continuum equation of motion. With these regularized equations as initial conditions, differential renormalization group (RG) equations are formulated for the changes in the model coefficients under coarse graining. The solutions of the RG equations yield trajectories that describe the original model over a hierarchy of scales, ranging from transient regimes, which are of primary experimental interest, prior to the crossover to the asymptotically stable fixed point. Thus, our method yields sequences of continuum equations that describe atomistic growth models over expanding length and time scales, but retain a direct connection to the underlying atomistic transition rules.
“Multiscale modelling of excitonic solar cells”
In excitonic solar cells, excitons (bound electron-hole pairs) are generated upon light absorption, and if not created directly at the heterointerface as in dye-sensitized solar cells, they must diffuse to it in order to photogenerate charge carriers. The distinguishing characteristic of excitonic solar cells is that charge carriers are generated and simultaneously separated across a heterointerface. Most organic-based solar cells, including dye-sensitized solar cells, fall into this category.
The properties of these cells are extremely sensitive to the morphology, for example in organic blend cells the chain packing and phase segregation of the materials making up the active layer. To progress the design of efficient devices requires device simulators with solid physical models, high accuracy and predictive capabilities.
In this talk I will describe Monte Carlo simulation models I havedeveloped that show how the morphology influences device performance through integration of all the processes occurring in the device. I will provide results from my group on organic blend and dye-sensitized solar cells that compare well with experimental data. I will also discuss how to link this work with continuum models of device simulation.
David Qiang Wang
“Numerical Modeling of Polyelectrolyte Adsorption and Layer-by-Layer Assembly”
Through alternating exposure of a charged substrate to solutions of polyanions and polycations, hundreds of thin adsorbed layers of polyions (polyelectrolyte multilayers, or PEM) can be readily built-up on the substrate. Particularly attractive for its exceptional simplicity and versatility, this layer-by-layer (LbL) assembly technique has been used to produce multi-component polymeric films and microcapsules with interesting and unusual properties. It can be applied to solvent accessible surfaces of almost any kind and any shape, is very robust, and has broad processing window. This technique therefore has great potential for many applications, including surface modification, sensors, enzyme immobilization, drug delivery, nano-reactors, etc.
In great contrast to thousands of experimental papers on LbL assembly, however, very few theoretical or simulation studies have been reported. The lack of understanding on the formation mechanism, internal structure, and molecular properties of PEM has hindered further development and application of this very promising technique. In this talk, I will present our recent work towards understanding and predicting PEM structure and properties. Using a continuum self-consistent field theory, we first studied the adsorption of flexible polyelectrolytes on flat surfaces, and found strong charge inversion by relatively long polyelectrolytes adsorbed on oppositely charged, attractive surfaces in poor solvent at high salt concentrations, which can be understood from the adsorption behavior of neutral (uncharged) polymers in a good solvent. We then modeled the sequential process of LbL assembly of flexible polyelectrolytes on flat surfaces as a series of kinetically trapped states. Up to 60 depositions of oppositely charged polyelectrolytes (1 and 2) are performed, each followed by a washing step. We have systematically examined the effects of substrate charge density, degrees of ionization of 1 and 2, bulk salt concentrations, solvent qualities for 1 and 2, and their incompatibility on the internal structure and charge compensation of PEM formed by either strongly or weakly dissociating polyelectrolytes. Our results agree with most experimental findings.
Department of Chemical and Biological Engineering, Colorado State University
1370 Campus Delivery, Fort Collins, CO 80523-1370, U.S.A.