# Browsing by Subject "Self-Consistent Field Theory"

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Item Data for "Stability of the Double Gyroid Phase in Bottlebrush Diblock Copolymer Melts"(2021-10-04) Park, So Jung; Cheong, Guo Kang; Bates, Frank S; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin D; Dorfman Research GroupShow more This data set contains the input and output data files used for the self-consistent field theory simulations in "Stability of the double gyroid phase in bottlebrush diblock copolymer melts" by Park et al. Self-consistent field theory was used to study the self-assembly of bottlebrush block copolymers, focusing on the effect of the bottlebrush architecture on the stability of the double gyroid phase.Show more Item Data for Alternating Gyroid in Block Polymer Blends(2022-04-27) Park, Sojung; Bates, Frank S; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin D; Dorfman Research Group - University of Minnesota Department of Chemical Engineering and Materials ScienceShow more This data set contains the input and output files from the PSCF C++ program used for the self-consistent field theory (SCFT) simulation in "Alternating gyroid in block polymer blends" by Park et al. (doi/10.1021/acsmacrolett.2c00115). Self-consistent field theory was used to investigate the stability of alternating gyroid phase in the ternary AB/BC/ABC block polymer mixture. With this dataset, users should be able to regenerate all the calculations that appeared in the paper, using the open-source C++ SCFT program.Show more Item Data for Alternating Gyroid Stabilized by Surfactant-like Triblock Terpolymers in IS/SO/ISO Ternary Blends(2023-03-22) Chen, Pengyu; Bates, Frank S; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin, D; Dorfman Research Group - University of Minnesota Department of Chemical Engineering and Materials ScienceShow more This dataset contains the self-consistent field theory (SCFT) simulation results in the associated paper (https://doi.org/10.1021/acs.macromol.2c02485)Show more Item Data for Single Gyroid in H-shaped Block Copolymers(2023-10-05) Park, Sojung; Bates, Frank S; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin D; Dorfman Research Group - University of Minnesota Department of Chemical Engineering and Materials ScienceShow more This data set contains the input and output files from the PSCF C++ program used for the self-consistent field theory (SCFT) simulation in "Single Gyroid in H-shaped Block Copolymers." Self-consistent field theory was used to investigate the equilibrium phase behavior of H-shaped block copolymers. With this dataset, users should be able to regenerate all the calculations that appeared in the paper, using the open-source C++ SCFT program available on GitHub (https://github.com/dmorse/pscfpp).Show more Item Data from Complex Phase Behavior in Binary Blends of AB Diblock Copolymer and ABC Triblock Terpolymer(2023-02-08) Park, Sojung; Bates, Frank S; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin D; Dorfman Research Group - University of Minnesota Department of Chemical Engineering and Materials ScienceShow more This data set contains the input and output files from the PSCF C++ program used for the self-consistent field theory (SCFT) simulation in "Complex Phase Behavior in Binary Blends of AB Diblock Copolymer and ABC Triblock Terpolymer." Self-consistent field theory was used to investigate the phase behavior in the binary AB/ABC block polymer blends. With this dataset, users should be able to regenerate all the calculations that appeared in the paper, using the open-source C++ SCFT program available on GitHub (https://github.com/dmorse/pscfpp).Show more Item Data from: Thermal Processing of Diblock Copolymer Melts Mimics Metallurgy(2017-05-22) Kim, Kyungtae; Schulze, Morgan W; Arora, Akash; Lewis III, Ronald M; Hillmyer, Marc A; Dorfman, Kevin D; Bates, Frank S; dorfman@umn.edu; Dorfman, Kevin DShow more Small-angle x-ray scattering experiments conducted with compositionally asymmetric low molar mass poly(isoprene)-b-poly(lactide) diblock copolymers reveal an extraordinary thermal history dependence. The development of distinct periodic crystalline or aperiodic quasicrystalline states depends on how specimens are cooled from the disordered state to temperatures below the order-disorder transition temperature. Whereas direct cooling leads to the formation of documented morphologies, rapidly quenched samples that are then heated from low temperature form the hexagonal C14 and cubic C15 Laves phases commonly found in metal alloys. Self-consistent mean-field theory calculations show that these, and other associated Frank-Kasper phases, have nearly degenerate free energies, suggesting that processing history drives the material into long-lived metastable states defined by self-assembled particles with discrete populations of volumes and polyhedral shapes.Show more Item Data supporting Laves Phase Field in a Diblock Copolymer Alloy(2022-04-06) Magruder, Benjamin R; Park, So Jung; Collanton, Ryan P; Bates, Frank S; Dorfman, Kevin D; dorfman@umn.edu; Dorfman, Kevin D; Dorfman Research Group - University of Minnesota Department of Chemical Engineering and Materials ScienceShow more We have used self-consistent field theory to predict a phase field in a blend of micelle-forming AB and B'C diblock polymers with different lengths and incompatible core blocks. The resulting paper was published in Macromolecules (doi.org/10.1021/acs.macromol.2c00346). The data were generated using the Fortran version of the open-source software PSCF (https://pscf.cems.umn.edu/). All input and output files from PSCF used to generate the data in the paper are included in this dataset, as well as the code used to process the data and generate the figures.Show more Item Interfaces and Fluctuations in Diblock Copolymer Melts and Ternary Mixtures with Homopolymers(2020-10) Yadav, MridulShow more Self-consistent field theory (SCFT) is a powerful tool for study of equilibrium phase behavior of block copolymer melts and mixtures. However, it fails to take into account the effect of fluctuations. This leads to some incorrect predictions for the phase behavior including the nature and location of order-disorder tran- sitions, associated phenomemon and phases. SCFT solutions are also limited by finite amount of computer resources available for numerical calculations. This is especially true of highly swollen self-assembled structures with large characteris- tic length scales. Accurate thermodynamic description of the interfaces in these swollen structures is sufficient to describe the phase behavior in this limit. Here we present our studies of the phase behavior of and interfaces in block copolymer melts and mixtures where we incorporate fluctuation effects and study highly swollen phases. The different approaches we take are, in a large part, guided by the limitations of SCFT.We present the first theoretical study into the role of conformational asym- metry in ternary mixtures of AB diblock copolymers, A homopolymers and B homopolymers which are high molecular counterparts of oil-water-surfactant mixtures. We show that the sign of the spontaneous curvature of an asym- metric diblock copolymer monolayer in these ternary mixtures is controlled by competition between swelling and stretching of copolymer brushes. We explore the phase behavior in highly swollen limit using the analytical Helfrich theory of bending elasticity for diblock copolymer monolayers. Further, we present a generalized version of the Helfrich theory that eliminates arbritrary choices in controlling variables needed to stabilize interfaces and presents a simplified description of these monolayers as a pseudo-one component system. We demon- strate the utility of our generalized theory by presenting an accurate thermody- namic description of a metastable phase in the highly swollen limit. Fluctuation effects are considered in the latter part of this thesis. In neat melts of volumetrically symmetric diblock copolymers, we view the strongly correlated disordered phase, near the order-disorder transition to the ordered lamellar phase, as an ensemble of multiple network topologies. We claim that the entropy associated with this ensemble is a constant per junction of the network. We present a free energy model of the disordered phase as the free energy per junction of a surrogate ordered network phase stabilized by this constant junction entropy. We test this claim and the predictions from this model by comparing to results from molecular simulations. We then extend this model to the ternary mixtures. We incorporate the effect of interfacial fluctuations in these mixtures through their effect on the renormalization of rigidities in the disordered phase and an undulation pressure in the lamellar phase. Using these models we predict phase behavior that is consistent with reported behavior in experiments and simulations.Show more Item Self-assembly of Block Polymers: Self-Consistent Field Theory and Monte-Carlo Simulations(2018-05) Arora, AkashShow more Block polymers are a class of soft materials that self-assemble at mesoscopic length scales to form a wide variety of ordered structures. The resulting nanostructures have been instrumental in the development of several advanced technologies such as separation membranes and photonic crystals. This thesis focuses on three diverse problems that use self-consistent field theory (SCFT) and Monte Carlo simulations to study the fundamental phase behavior of block polymers. In recent years, several experimental studies have witnessed the formation of complex low-symmetry structures, commonly referred to as Frank–Kasper phases, contain- ing particles of disparate sizes arranged in multiple coordination environments. The first problem of this thesis focuses on examining the stability of various Frank–Kasper phases in AB diblock copolymers. Using SCFT, we computed the free energies of a host of Frank–Kasper phases and observed that the associated free energies differ only marginally (10−3kBT), leading to a rugged free energy surface with many local minima that may be accessible via different nucleation pathways. We have highlighted the significance of these theoretical predictions in the context of two new Frank–Kasper phases discovered experimentally in poly(isoprene)-b-poly(lactide) diblock copolymers. During the course of this project, we have also made a few advancements in the numerical framework of SCFT. Specifically, we have developed a physically informed and robust approach that uses information from experiments to create guess structures of the ordered phases that are required to perform the SCFT calculations. Additionally, we have developed an improved version of the Anderson-mixing iteration algorithm that increases the computational efficiency by at least 5-10 times compared to the previous version. The second problem focuses on studying the phase behavior of three different multiblock polymers, ABC triblocks, ABCA tetrablocks, and ABAC tetrablocks. In each of the cases, we have performed extensive SCFT calculations and compared the resulting predictions with experimental results to further the understanding of experimentally observed morphologies. While investigating the phase behavior of multiblock polymers, we observed that an accurate temperature-dependence of all the involved Flory–Huggins χ parameters is crucial for making any reliable predictions using SCFT. In this context, we have studied the sensitivity of the phase behavior of a specific ABAC-type multiblock, poly(styrene)-b-poly(isoprene)-b-poly(styrene)-b-poly(ethylene oxide) tetrablock terpolymer, towards the set of required χ parameters (χIS,χSO,χIO). In the third problem, we have studied the order–disorder transition of short lamellae- forming diblock copolymers using Monte Carlo simulations. We have developed a systematic approach to accurately estimate the domain spacing of the lamellar structure, and thereby remove the incommensurability and finite-size effects in lattice simulations. This enabled us to precisely determine the order–disorder transition value for short symmetric diblock copolymers.Show more Item Structure and Dynamics of Micelle-Forming Asymmetric Diblock Copolymer Chains(2021-09) Chawla, AnshulShow more Experiments on micelle-forming asymmetric diblock copolymer melts have shown the existence of a liquid-like state of micelles at temperatures greater than the order-disorder transition temperature (ODT).These micelles have been hypothesized to appear at an even greater temperature called the critical micelle temperature (CMT). The regime between the CMT and ODT, called the disordered micellar regime, has been known to affect the formation of many exotic phases like the Frank-Kasper and the Laves phases due to its slow dynamics. Self-Consistent Field Theory (SCFT), one of the most commonly employed theoretical tools, only predicts the appearance of micelles in stationary and periodic configurations, and hence is incapable of capturing the disordered micellar regime. Some previous theoretical studies do provide predictions of the structural properties of the disordered micelles, however, these studies used SCFT predictions of free energies of isolated micelles to approximate the free energy of disordered micelles. We have used coarse-grained classical molecular dynamics to simulate melts of asymmetric diblock copolymer chains having a minority block volume fraction, $f = 0.125$.At high $\chi N$, where $\chi$ is the Flory-Huggins interaction parameter and $N$ is the degree of polymerization, SCFT predicts the formation of ordered micellar phases for this volume fraction. Our simulations show the existence of a disordered micellar regime for $\chi N$ above the $\cNso$, where $\cNso$ is the value of $\chi N$ corresponding to the ODT predicted from SCFT. We study melts having two significantly different invariant degree of polymerization, $\overline {N} = 960$ and $3820$, that span the disordered homogenous phase, disordered micellar regime, and the ordered body-centered cubic (BCC) phase. The first part of this thesis pertains to analyzing the evolution of the structure of these melts as a function of $\chi N$.By using a cluster identification algorithm, we show that micelle-like clusters appear at a CMT with the appearance being much more sudden for the higher $\overline {N}$ simulations. Moreover, micelles appear when $\chi N$ is near $\cNso$. We also show that the signature of the presence of disordered micelles in scattering experiments (SAXS and SANS) arises at a somewhat higher $\chi N$ as compared to $\cNso$. Comparisons of the free energy derivative, peak wavenumber, micelle aggregation number and the free chain fraction obtained from simulations with these quantities calculated from SCFT show close agreement, thus emphasizing similarities in the structure of the disordered micelles and the ordered micelles predicted by SCFT at the same $\chi N$. Analysis of the shape of the identified clusters also reveal a rapid formation/breaking of bridges between micelles present in both disordered and ordered phases. The latter part of this thesis considers the dynamics of these melts, namely single chain diffusion and structural relaxation.Signatures of the sudden appearance of micelles at the CMT is also reflected in the analysis of the dynamic properties as a sudden slowdown in the molecular relaxation and an even more significant slow down in the structural relaxation. We measure the rate at which polymers are expelled from micelles, and relate this to the polymer diffusivity.Show more