Papers by Glenn Fredrickson
Most ABA triblock copolymer-based physical hydrogels form three-dimensional networks through mice... more Most ABA triblock copolymer-based physical hydrogels form three-dimensional networks through micellar packing, and formation of polymer loops represents a topological defect that diminishes hydrogel elasticity. This effect can be mitigated by maximizing the fraction of elastically effective bridges in the hydrogel network. Herein, we report hydrogels constructed by complexing oppositely charged multiblock copolymers designed with a sequence pattern that maximizes the entropic and enthalpic penalty of micellization. These copolymers self-assemble into branched and bridge-rich network units (netmers), instead of forming sparsely interlinked micelles. We found that the storage modulus of the netmer-based hydrogel was 11.5 times higher than that of the micelle-based hydrogel. Complementary coarse grained molecular dynamics (CGMD) simulations revealed that in the netmer-based hydrogels, the numbers of charge-complexed nodes and mechanically reinforcing bridges increase substantially rela...
Journal of Photopolymer Science and Technology, 2014
arXiv (Cornell University), May 4, 2007
Bulletin of the American Physical Society, Mar 3, 2014
Bulletin of the American Physical Society, Mar 16, 2017
Bulletin of the American Physical Society, Mar 13, 2017
Reduced defectivity in lamellae through combined thermal and solvent annealing CORINNE CARPENTER,... more Reduced defectivity in lamellae through combined thermal and solvent annealing CORINNE CARPENTER, KRIS DELANEY, GLENN FREDRICKSON, Univ of California -Santa Barbara -We present a combination of string calculations and self-consistent field theoretic (SCFT) calculations of a symmetric block copolymer (BCP) in the presence of a small molecule solvent in order to examine its effects on the stability of dislocations and disclinations in confined lamellar systems. The use of string calculations provides information about the relevant energy barriers in the melting pathways of the two relevant defects at a range of solvent concentrations. As the defect is resolvated, we expect its extensive free energy difference from the perfect lamellar structure to increase, leading to a lower concentration of these defects at equilibrium. By combining these defect energies and their solvent conditions, we propose potential experimental annealing conditions for the removal of the two most prominent defects in the confined lamellar system.
Bulletin of the American Physical Society, Mar 18, 2016
Using chemically patterned substrates to suppress thermal placement errors in the directed self-a... more Using chemically patterned substrates to suppress thermal placement errors in the directed self-assembly of block copolymer multicylinder linear arrays CORINNE CARPENTER, KRIS DELANEY, GLENN FREDRICKSON, Univ of California -Santa Barbara -Directed self assembly (DSA) of block copolymers is a promising alternative approach for ˜10nm microelectronics patterning, both for feature-size reduction and rectification. One prototypical application of DSA is the use of vertical interconnect access (VIA) cylinders for fabricating conducting channels between circuit layers. Typically a compromise exists between the fidelity and low defect density obtained by using a small number of cylinders per pre-pattern guide and the objective to further increase feature density. In particular for 1D linear arrays of multiple VIAs in a single prepattern, prior experimental and theoretical work has demonstrated that thermal fluctuations in larger arrays cause cylinder placement to vary widely around the equilibrium positions in a manner analogous to the collective excitations in a simple 1D coupled oscillator model (Landau-Peierls instability). In the present work, we assess the efficacy of using chemically patterned substrates to suppress the thermal placement errors using both a phenomenological oscillator model and full field theoretic simulations.
Bulletin of the American Physical Society, Mar 4, 2014
Computational study of solvated block-copolymer microphases WEI LI, KRIS DELANEY, GLENN FREDRICKS... more Computational study of solvated block-copolymer microphases WEI LI, KRIS DELANEY, GLENN FREDRICKSON, Univ of California -Santa Barbara -Using field-theoretic simulations, we study the equilibrium self-assembly of solvated block copolymer microphases with different chain architectures and block selectivities. Initially within the mean-field approximation (self-consistent field theory), we employ unit-cell calculations to determine the phase diagram by comparing the free energy of candidate phases. We find good agreement with prior computational and experimental reports in the literature. We subsequently move beyond the mean-field approximation using Complex Langevin sampling to investigate the effect of fluctuations on relative phase stabilities.
Bulletin of the American Physical Society, Mar 4, 2014
Nucleation of ordered microphases in fluctuation-induced firstorder phase transitions MICHAEL CAR... more Nucleation of ordered microphases in fluctuation-induced firstorder phase transitions MICHAEL CARILLI, GLENN FREDRICKSON, KRIS DELANEY, University of California Santa Barbara -The Landau-Brazovskii model is a field-based Hamiltonian describing a variety of systems which exhibit ordered microphases defined by characteristic periodicity and symmetries (e.g., lamellar, hexagonal, body-centered cubic). Interestingly, this model can undergo a fluctuation-induced first-order phase transition: for the symmetric model, the disorder-to-lamellar transition is second-order at the mean-field level but takes on first-order character when fluctuations are added. A disordered phase supercooled to within the resulting metastable region will then transition to the stable lamellar phase via nucleation. We demonstrate it is possible to discover the critical nucleus' size and geometry by applying the numerical string method 1 to a renormalized Landau-Brazovskii Hamiltonian which incorporates the effects of fluctuations. We find good agreement with predicted nucleus size and shape obtained by analytic approximation. Hohenberg and Swift 2 predict that for this transition, certain defect structures in the critical nucleus might act to lower the nucleation free energy barrier; we present a search for these structures.
Bulletin of the American Physical Society, Mar 6, 2015
Bulletin of the American Physical Society, Mar 19, 2009
We investigate the phase diagram of oppositely charged polymers in a good solvent using a field-t... more We investigate the phase diagram of oppositely charged polymers in a good solvent using a field-theoretic model. Mean-field solutions fail to predict the experimentally observed macroscopic phase separation into a solvent-rich phase and a dense liquid aggregate of polymers -a "complex coacervate." We therefore study the model within a one-loop approximation, which accounts for Gaussian fluctuations in electrostatic and chemical potentials. Our particular focus is the effect of molecular weight, ionic strength, and charge asymmetry on the phase envelope. A set of dimensionless parameters is identified that dictate the size and shape of the two-phase region. Our results should be helpful in guiding experimental studies of coacervation.
Bulletin of the American Physical Society, Mar 6, 2007
The American Physical Society Field Theory of Polyelectrolyte Complexation YURI POPOV, GLENN FRED... more The American Physical Society Field Theory of Polyelectrolyte Complexation YURI POPOV, GLENN FREDRICKSON, University of California, Santa Barbara -We study polyanion-polycation solutions using a field-theoretic approach formulated in terms of auxiliary fields (conjugate to mass and charge densities). Within this framework, we derive exact Hamiltonians for a wide variety of systems: with implicit or explicit solvents, for symmetric or asymmetric polyions, with or without salt. By systematic expansion, we analytically obtain one-loop fluctuation corrections to the mean-field results for these systems in arbitrary dimensions. As an example, we study the symmetric salt-free polyanion-polycation mixture in implicit solvent. We demonstrate that this basic system and its phase diagram are described by three universal reduced variables. We obtain simple analytical expressions for thermodynamic quantities and structure factors, including two correlation lengths -Edwards's length and a polymer electrostatic length. We also conduct scaling analysis in dilute and semi-dilute regimes and show that the concentration of pair formation is exponentially small in polymer length.
Bulletin of the American Physical Society, Mar 13, 2017
I was privileged to have a seventeen year friendship and scientific collaboration with Edward J. ... more I was privileged to have a seventeen year friendship and scientific collaboration with Edward J. Kramer that produced 55 papers and countless student and postdoc co-advisements. This talk will discuss our last project together; an ongoing research program to achieve thermoplastic polymer materials that are uniquely hard, tough, and elastic, with moduli greater than 100 MPa and elastic recovery greater than 0.9 at strains of 1 or more. The targeted materials are based on an A(BA')n mikto-arm block copolymer architecture, and alloys of these molecules with A homopolymer. The molecular design of the miktopolymer was optimized using self-consistent field theory and the materials realized in a polystyrene (A)-polyisoprene (B) system. TEM, SAXS, and tensile mechanical tests were used to validate the designs and probe microstructure/mechanics relationships. An unexpected discovery was the emergence of a new structured disordered phase -the bricks and mortar phase -in which the A domains remain discrete at up to a volume fraction of 0.7. Field-theoretic simulations have been used to understand the origins of this new fluctuation-stabilized equilibrium phase, which has no precedent in the polymer physics literature.
Bulletin of the American Physical Society, Mar 20, 2013
Successful development of lithium polymer batteries has been limited by low ionic conductivities ... more Successful development of lithium polymer batteries has been limited by low ionic conductivities in the polymer electrolyte, especially at low temperatures. In order to generate strategies for improvement of ionic conductivity, we have developed highlycontrolled syntheses for a number of well-defined poly(glycidyl ether)s, PGEs, to serve as low temperature polymer electrolytes. The properties of PGEs can be tuned through structure control and functionalization, making them model systems for understanding ion transport and elucidating structure-property relationships. In this work we will discuss the synthesis and characterization of a family of PGEs that exhibit systematic differences in glass transition temperature (Tg), viscosity, oxygen-content, dielectric constant, and ionic conductivity.
Bulletin of the American Physical Society, Mar 2, 2015
Accelerating the search for globally stable block polymer microphases using genetic algorithms 1 ... more Accelerating the search for globally stable block polymer microphases using genetic algorithms 1 CAROL TSAI, KRIS DELANEY, GLENN FREDRICKSON, UC Santa Barbara -The diverse array of block copolymer (BCP) applications is possible because in the melt state, various morphologies that are periodic structures on the nanoscale emerge depending on the particular composition and architecture of the BCPs used. However, knowing which compositional parameters to use to obtain materials with desired properties is a Herculean task: there is an enormous parameter space to search. Furthermore, the problem is exacerbated by the fact that even at a fixed set of compositional parameters, it is difficult to determine the globally stable morphology and low-lying metastable states that will emerge, as complications arise from a rough free-energy landscape: a self-consistent field search may become trapped in high-energy metastable states, resulting in long and computationally expensive searches. We show that genetic algorithms, which are a biologically-inspired global search heuristic, may be a promising way to ameliorate this problem when used in conjunction with local optimizations performed by SCFT.
Bulletin of the American Physical Society, Mar 6, 2007
Bulletin of the American Physical Society, Mar 22, 2005
Grafting reactions between end-functional polymers at polymer interfaces E.J. KRAMER, B.J. KIM, K... more Grafting reactions between end-functional polymers at polymer interfaces E.J. KRAMER, B.J. KIM, K. KATSOV, G.H. FREDRICKSON, UCSB, H. KANG, K. CHAR, Seoul National University -Reactions to produce graft copolymers at polymer interfaces during extruder mixing are important for controlling dispersed phase size by retarding droplet coalescence and reducing interfacial tension while providing interface reinforcement. We investigate such reactions at various temperatures in a model bilayer film system consisting of amine endfunctional deuterated polystyrene (dPS-NH 2 ) in PS and anhydride end-functional poly(2-vinylpyridine) (P2VP-anh) in P2VP as a function of molecular weight M and initial volume fraction ϕ 0 of the end functional chains. After various times of reaction the interfacial excess z* of block copolymer formed at the interface is determined by detecting the 2 H -ion using dynamic SIMS depth profiling. At low ϕ 0 (∼ 0.01) of dPS-NH 2 and P2VP-anh, such that the normalized interface excess z*/R g < 1 and the blocks are unstretched, the forward reaction rate constant k + decreases as M -0.68 in rough agreement with theoretical predictions (k + ∼ M -0.55 ) for this regime. The rate constant is thermally activated with an activation enthalpy 165 kJ/mol that is independent of M.
Journal of Photopolymer Science and Technology, 2015
We use three-dimensional self-consistent field theory (SCFT) to study the self-assembly of cylind... more We use three-dimensional self-consistent field theory (SCFT) to study the self-assembly of cylinder forming diblock copolymers confined in elongated templates. This situation arises in contact holes where the goal is to produce a contact hole with reduced dimensions as well as with narrowed pitch of the center-to-center distance of cylinders. In this study, we focus on systems where two minor-block cylinders form in inside of the elongated templates. A defective bridge structure is extensively studied in this work and we evaluate the defect in various wall affinities such as "all PMMA-attractive templates", "all neutral templates" and "PMMA-attractive sidewall with the neutral substrate". According to our SCFT simulations, the defect formation energy of the bridge is typically above 20 kT, or fewer than 2 defects per billion in the "all neutral" template and "PMMA-attractive sidewall with the neutral substrate", while the defect preferably forms in the "all PMMA attractive" template.
Bulletin of the American Physical Society, 2016
Multi-fluid models of polymeric liquids DOUGLAS TREE, GLENN FREDRICKSON, Univ of California -Sant... more Multi-fluid models of polymeric liquids DOUGLAS TREE, GLENN FREDRICKSON, Univ of California -Santa Barbara -Industrial processes for producing polymer-based materials often operate away from equilibrium, making the final microstructure -and thus the properties of the material -dependent on processing history. Current simulation methods struggle to accurately describe such processes. Traditional fluid dynamics is able to capture transport behavior, but lacks the complex phase behavior characteristic of many polymeric liquids. Coarsegrained particle models can handle the complexity, but are constrained by time and length scales. Consequently, we explore an alternative field-theoretic framework based on the "two-fluid" model originally proposed by Brochard and de Gennes. To demonstrate feasibility, we derive a model and develop an efficient numerical method for a ternary polymer solution. Subsequently, we use this model and method to examine the physics of the immersion precipitation process, used industrially to produce polymer membranes.
The American Physical Society Field Theory of Polyelectrolyte Complexation YURI POPOV, GLENN FRED... more The American Physical Society Field Theory of Polyelectrolyte Complexation YURI POPOV, GLENN FREDRICKSON, University of California, Santa Barbara -We study polyanion-polycation solutions using a field-theoretic approach formulated in terms of auxiliary fields (conjugate to mass and charge densities). Within this framework, we derive exact Hamiltonians for a wide variety of systems: with implicit or explicit solvents, for symmetric or asymmetric polyions, with or without salt. By systematic expansion, we analytically obtain one-loop fluctuation corrections to the mean-field results for these systems in arbitrary dimensions. As an example, we study the symmetric salt-free polyanion-polycation mixture in implicit solvent. We demonstrate that this basic system and its phase diagram are described by three universal reduced variables. We obtain simple analytical expressions for thermodynamic quantities and structure factors, including two correlation lengths -Edwards's length and a polymer electrostatic length. We also conduct scaling analysis in dilute and semi-dilute regimes and show that the concentration of pair formation is exponentially small in polymer length.
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Papers by Glenn Fredrickson