Tilt grain boundaries in a diblock copolymer ordered nanocomposite lamellar phase

Copyright (2010) AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics 133 and may be found at http://dx.doi.org.proxy.lib.uwaterloo.ca/10.1063/1.3498784A hybrid self-consistent field theory/density functional theory method is applied to predict tilt(kink) grain boundary structures between lamellar domains of a symmetric diblock copolymer with added spherical nanoparticles. Structures consistent with experimental observations are found and theoretical evidence is provided in support of a hypothesis regarding the positioning of nanoparticles. Some particle distributions are predicted for situations not yet examined by experiment.Natural Sciences and Engineering Research Council of Canad

Predicting the phases of a two-dimensional hard-rod system with real-space self-consistent field theory

The following article appeared in Physical Review E 74, 041501 and may be found at http://link.aps.org/doi/10.1103/PhysRevE.74.041501 DOI = 10.1103/PhysRevE.74.041501 ©2006 The American Physical SocietyPolymer self-consistent field theory numerical tools are applied to a two-dimensional hard-rod colloidal system. Rods are represented through an interaction site model density functional theory that is derived and expressed from a self-consistent field theory perspective. A weighted density approximation is used within the density functional theory, and the phase space is sampled without bias for any particular morphology. A completely ordered crystal phase is found as well as a liquid crystal state.National Sciences and Engineering Research Council (NSERC) of Canad

Benchmarking a self-consistent field theory for small amphiphilic molecules

DOI: 10.1039/C2SM26352A (Paper) Soft Matter, 2012, 8, 9877-9885 This journal is © The Royal Society of Chemistry 2012A minimalist self-consistent field theory for small amphiphilic molecules is presented. The equations for this model are less involved than those for block copolymers and are easily implemented computationally. A new convergence technique based on a variant of Anderson mixing is also presented which allows the equations to be solved more rapidly than block copolymer self-consistent field theory. The computational speed up and simplicity of equations result from a lack of configurational degrees of freedom in the amphiphilic molecular model. The omission of polymeric flexibility leads to qualitatively different predictions compared to known diblock copolymer behaviour.University of Waterloo International Work Study Progra

Maximal cell density predictions for compressible polymer foams

Published by Elsevier in the journal "Polymer" volume 54, issue 2. doi:10.1016/j.polymer.2012.11.067.Thermodynamic upper bounds for polymer foam cell densities are predicted using compressible selfconsistent field theory. It is found that the incompressible limit always gives the highest, and therefore ultimate, upper bound. Qualitative comparisons between the compressible and incompressible cases agree, indicating that low temperatures and high blowing agent content should be used to achieve high cell densities. The inhomogeneous bubble structure reveals deviations from the expected homogeneous SanchezeLacombe equation of state, consistent with some experimental results. A generalized Sanchez eLacombe equation of state is discussed in the context of its suitability as a simple alternative to the SimhaeSomcynsky equation of state

Towards Maximal Cell Density Predictions for Polymeric Foams

Published by Elsevier in the journal "Polymer" volume 52, issue 24. doi:10.1016/j.polymer.2011.09.046.Self-consistent field theory is used to make direct predictions for the maximum possible cell densities for model polymer foam systems without recourse to classical nucleation theory or activation barrier kinetic arguments. Maximum possible cell density predictions are also made subject to constraining the systems to have maximal possible internal interface and to have well formed bubbles (no deviation from bulk conditions on the interior of the bubble). This last condition is found to be the most restrictive on possible cell densities. Comparison is made with classical nucleation theory and it is found that the surface tension is not an important independent consideration for predicting conditions consistent with high cell density polymeric foams or achieving the smallest possible bubble sizes. Instead, the volume free energy density, often labelled as a pressure difference, is the dominant factor for both cell densities and cell sizes.NSERC Canad

Origins of the failure of classical nucleation theory for nanocellular polymer foams

DOI: 10.1039/C1SM05575E (Paper) Soft Matter, 2011, 7, 7351-7358 This journal is © The Royal Society of Chemistry 2011Relative nucleation rates for fluid bubbles of nanometre dimensions in polymer matrices are calculated using both classical nucleation theory and self-consistent field theory. An identical model is used for both calculations showing that classical nucleation theory predictions are off by many orders of magnitude. The main cause of the failure of classical nucleation theory can be traced to its representation of a bubble surface as a flat interface. For nanoscopic bubbles, the curvature of the bubble surface is comparable to the size of the polymer molecules. Polymers on the outside of a curved bubble surface can explore more conformations than can polymers next to a flat interface. This reduces the free energy of the curved interface which leads to a significantly smaller barrier energy to nucleation and thus a much higher nucleation rate. Also, there is a reduction of unfavorable energetic contacts between polymer and fluid molecules in the vicinity of a curved interface. Polymers on the outside of a curved interface are less likely to find a portion of themselves in the interior of the unfavorable fluid bubble. A secondary cause of the failure of classical nucleation theory is due to the collapse of the bulk region inside the bubble. As the radius of a bubble is reduced, eventually the diffuse walls collide causing increased mixing of polymer and fluid molecules everywhere. This causes a reduction of internal energy associated with the interface, leading to smaller nucleation barrier energies and, again, a reduced barrier energy to nucleation.NSERC Canada, Strategic Projects Grant and Discovery Grant

An alternative derivation of orbital-free density functional theory

The following article appeared in (Thompson, R. B. (2019). An alternative derivation of orbital-free density functional theory. The Journal of Chemical Physics, 150(20), 204109. https://doi.org/10.1063/1.5096405) and may be found at https://doi.org/10.1063/1.5096405. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is constructed directly from a Hamiltonian so that the results are, in principle, valid at finite temperatures. The main governing equations are found to be a set of modified diffusion equations, and the set of self-consistent equations are essentially identical to those of a ring polymer system. The equations are shown to be equivalent to Kohn-Sham density functional theory and to reduce to classical density functional theory, each under appropriate conditions. The obtained noninteracting kinetic energy functional is, in principle, exact but suffers from the usual orbital-free approximation of the Pauli exclusion principle in addition to the exchange-correlation approximation. The equations are solved using the spectral method of polymer self-consistent field theory, which allows the set of modified diffusion equations to be evaluated for the same computational cost as solving a single diffusion equation. A simple exchange-correlation functional is chosen, together with a shell-structure-based Pauli potential, in order to compare the ensemble average electron densities of several isolated atom systems to known literature results. The agreement is excellent, justifying the alternative formalism and numerical method. Some speculation is provided on considering the timelike parameter in the diffusion equations, which is related to temperature, as having dimensional significance, and thus picturing pointlike quantum particles instead as nonlocal, polymerlike, threads in a higher dimensional thermal-space. A consideration of the double-slit experiment from this point of view is speculated to provide results equivalent to the Copenhagen interpretation. Thus, the present formalism may be considered as a type of “pilot-wave,” realist, perspective on density functional theory.Natural Sciences and Engineering Research Council of Canad

Polymeric Foaming Predictions from the Sanchez-Lacombe Equation of State: Application to Polypropylene-Carbon Dioxide Mixtures

The author has the right to post and update the article on a free-access e-print server using files prepared and formatted by the author. Any such posting made or updated after acceptance of the article for publication by APS should include a link to the online APS journal article abstract. In all cases, the appropriate bibliographic citation (von Konigslow, K., Park, C. B., & Thompson, R. B. (2017). Polymeric Foaming Predictions from the Sanchez-Lacombe Equation of State: Application to Polypropylene-Carbon Dioxide Mixtures. Physical Review Applied, 8(4), 044009. https://doi.org/10.1103/PhysRevApplied.8.044009) and notice of the APS copyright must be included.A simple off-lattice method of deriving the Sanchez-Lacombe equation of state is presented. The Sanchez-Lacombe equation of state for mixtures is shown to be thermodynamically inconsistent for all mixing rules in such a way that fugacity coefficients, until now thought to correct for mixing inconsistencies, cannot make the theory consistent. The theory is consistent, however, for constant hole volumes and it is shown, for a sample mixture of polypropylene and carbon dioxide, that excellent agreement with experimental solubility results is achieved without changing the mixture parameters with temperature or pressure. To this end, pure-component Sanchez-Lacombe characteristic parameters for both branched and linear polypropylene are also provided. The agreement between theory and experiment for solubility using a constant hole volume for carbon dioxide mixtures with both branched and linear polypropylene is much better than for typical mixing rules for the Sanchez-Lacombe equation of state. Fair agreement with experimental swelling-ratio data at saturation is also achieved with no further free parameters, making this equation of state a good choice for predictions related to polymeric foaming. A consideration of the hole volume is given in terms of correlations, and evidence to support this perspective is presented in terms of the characteristic parameters regressed from different architectures of pure polypropylene. It is shown that only a single pure-polypropylene characteristic parameter is needed to characterize mixtures with carbon dioxide, and that an estimate of this parameter can be extracted from mixture solubility data. This example demonstrates the feasibility of applying the Sanchez-Lacombe equation of state to mixtures in which one of the pure components has not been independently characterized.Natural Sciences and Engineering Research Council of Canada (NSERC) || Consortium for Cellular and Microcellular Plastics (CCMCP)

Atomic shell structure from an orbital-free-related density-functional-theory Pauli potential

The author has the right to post and update the article on a free-access e-print server using files prepared and formatted by the author. Any such posting made or updated after acceptance of the article for publication by APS should include a link to the online APS journal article abstract. In all cases, the appropriate bibliographic citation and notice of the APS copyright must be included.Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modeled as Gaussian threads with ring-polymer architecture in a four-dimensional thermal space, and a Pauli potential is postulated based on classical excluded volume implemented in the thermal space using Edwards–Flory-Huggins interactions in a mean-field approximation. Other approximations include a Fermi-Amaldi correction for electron-electron self-interactions, a spherical averaging approximation to reduce the dimensionality of the problem, and the neglect of correlations. Polymer scaling theory is used to show that the excluded volume form of Pauli potential reduces to the known Thomas-Fermi energy density in the uniform limit. Self-consistent equations are solved using a bilinear Fourier expansion, with radial basis functions, for the first 18 elements of the periodic table. Radial electron densities show correct shell structure, and the errors on the total binding energies compared to known binding energies are less than 9% for the lightest elements and drop to 3% or less for atoms heavier than nitrogen. More generally, it is suggested that only two postulates are needed within classical statistical mechanics to achieve equivalency of predictions with static, nonrelativistic quantum mechanics: First, quantum particles are modeled as Gaussian threads in four-dimensional thermal space and, second, pairs of threads (allowing for spin) are subject to classical excluded volume in the thermal space. It is shown that these two postulates in thermal space become the same as the Heisenberg uncertainty principle and the Pauli exclusion principle in three-dimensional space.Natural Sciences and Engineering Research Council of Canada (NSERC

Intrinsic and extrinsic factors drive ontogeny of early-life at-sea behaviour in a marine top predator

Young animals must learn to forage effectively to survive the transition from parental provisioning to independent feeding. Rapid development of successful foraging strategies is particularly important for capital breeders that do not receive parental guidance after weaning. The intrinsic and extrinsic drivers of variation in ontogeny of foraging are poorly understood for many species. Grey seals (Halichoerus grypus) are typical capital breeders; pups are abandoned on the natal site after a brief suckling phase, and must develop foraging skills without external input. We collected location and dive data from recently-weaned grey seal pups from two regions of the United Kingdom (the North Sea and the Celtic and Irish Seas) using animal-borne telemetry devices during their first months of independence at sea. Dive duration, depth, bottom time, and benthic diving increased over the first 40 days. The shape and magnitude of changes differed between regions. Females consistently had longer bottom times, and in the Celtic and Irish Seas they used shallower water than males. Regional sex differences suggest that extrinsic factors, such as water depth, contribute to behavioural sexual segregation. We recommend that conservation strategies consider movements of young naïve animals in addition to those of adults to account for developmental behavioural changes