Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids (original) (raw)
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Coarse-graining diblock copolymer solutions: a macromolecular version of the Widom–Rowlinson model
Molecular Physics, 2005
We propose a systematic coarse-grained representation of block copolymers, whereby each block is reduced to a single "soft blob" and effective intra-as well as intermolecular interactions act between centres of mass of the blocks. The coarse-graining approach is applied to simple athermal lattice models of symmetric AB diblock copolymers, in particular to a Widom-Rowlinson-like model where blocks of the same species behave as ideal polymers (i.e. freely interpenetrate), while blocks of opposite species are mutually avoiding walks. This incompatibility drives microphase separation for copolymer solutions in the semi-dilute regime. An appropriate, consistent inversion procedure is used to extract effective inter-and intramolecular potentials from Monte Carlo results for the pair distribution functions of the block centres of mass in the infinite dilution limit. PACS numbers: 61.25.Hq,61.20.Gy,05.20Jj
Interfacial Fluctuations of Block Copolymers: A Coarse-Grain Molecular Dynamics Simulation Study
The Journal of Physical Chemistry B, 2007
The Flory-Huggins parameter χ which governs the phase behavior of a block copolymer is a measure of the relative energies (divided by k B T) of contacts between like (e.g. EO:EO or EE:EE) and unlike (EO:EE or vice versa) monomers. It was initially developed in the context of simple models of solutions, where it can be used to model the mixing thermodynamics of a binary solution (see Reference 31). Small values of χ correspond to highly miscible solutions, while large χ values indicate that the two liquids have a strong propensity to phase separate. When a binary (A+B) liquid phase separates into an A-rich and a B-rich phase in contact with one another, there is still some mole fraction of liquid A in the B-rich phase and vice versa. The combination of χ and the mixing entropy can be used to determine the mole fraction of EO in the EO-rich phase as (equation 4 and Reference 31). χ= (ln [(1-ϕ EO)/ϕ EO ])/(1-2ϕ EO) (MS Equation 4) The true effective χ of a block copolymer system includes contributions from chain properties such as excluded volume, chain stretching, and chain end effects. To a first approximation, however, we can estimate χ for the block copolymer from the χ value for the
Thermodynamic Behavior of Particle/Diblock Copolymer Mixtures: Simulation and Theory
Macromolecules, 2000
We investigate the influence of hard nanoparticles on the phase behavior of diblock copolymers. Using Monte Carlo simulations, we obtain phase diagrams as a function of the nanoparticle size and concentration. When the size of the nanoparticles becomes comparable to the radius of gyration of the minority (A) block, we observe the formation of new superstructures, where the particles selfassemble inside the copolymer micelles. We develop a theoretical model, based on the strong segregation limit approximation, and show that these self-assembled structures can be either stable or metastable, depending on the particle size and volume fraction. The formation of such phases is due to the interplay between the particle-particle excluded-volume interactions, preferential particle/block-A interactions, and the enthalpic and stretching interactions within the diblock.
A theoretical and simulation study of the self-assembly of a binary blend of diblock copolymers
The Journal of Chemical Physics, 2012
Pure diblock copolymer melts exhibit a narrow range of conditions at which bicontinuous and cocontinuous phases are stable; such conditions and the morphology of such phases can be tuned by the use of additives. In this work, we have studied a bidisperse system of diblock copolymers using theory and simulation. In particular, we elucidated how a short, lamellar-forming diblock copolymer modifies the phase behavior of a longer, cylinder-forming diblock copolymer. In a narrow range of intermediate compositions, self-consistent field theory predicts the formation of a gyroid phase although particle-based simulations show that three phases compete: the gyroid phase, a disordered cocontinuous phase, and the cylinder phase, all having free energies within error bars of each other. Former experimental studies of a similar system have yielded an unidentified, partially irregular bicontinuous phase, and our simulations suggest that at such conditions the formation of a partially transformed network phase is indeed plausible. Close examination of the spatial distribution of chains reveals that packing frustration (manifested by chain stretching and low density spots) occurs in the majority-block domains of the three competing phases simulated. In all cases, a double interface around the minority-block domains is also detected with the outer one formed by the short chains, and the inner one formed by the longer chains.
Coarsening and self-organization in dilute diblock copolymer melts and mixtures
Physica D: Nonlinear Phenomena, 2009
This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns. We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto (Calc. Var. and PDE, Vol. 13 (2001)). A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.
Computer simulation of aqueous block copolymer assemblies: Length scales and methods
Journal of Polymer Science Part B-polymer Physics, 2006
received his M.Sc. and Ph.D. degrees from the University of Toronto for his work on the statistical mechanics of mixed quantum-classical systems under the supervision of Raymond E. Kapral. He then moved on to join the group of Michael L. Klein at the University of Pennsylvania as a postdoctoral research associate to work on coarse-grain models of membranes. His current research interests are on the solubilization of carbon nanotubes by cyclic peptides and on a detailed molecular understanding of colloidal stability.
Macromolecules, 2020
We extend our recent coarse-grained model describing semicrystalline homopolymers to simulate the morphology and phase transitions of thermoplastic elastomers made of segmented (hard/soft) block copolymers. The generic model is adapted to match the physical characteristics of the two chemical units involved in the copolymer chains by using classic scaling rules. We investigate the crystallization kinetics of the hard segments as well as their phase separation from the soft units in either triblock or pentablock copolymers. We identify the soft segment molecular weight as a key parameter resulting in the following observations when decreasing the temperature from a homogeneous state. On the one hand, the phase separation preceding the crystallization process in triblock copolymers results in a constant temperature of crystallization when varying the soft segment length. On the other hand, the limited phase separation achieved in pentablock copolymers constrains them to crystallize at progressively lower temperatures while increasing the soft segment length. Finally, increasing the soft segment molecular weight was found to lead to a higher relative crystallinity which can be interestingly related to a rise of the loop segment's content.
Simulation of Diblock Copolymer Self-Assembly, Using a Coarse-Grain Model
The Journal of Physical Chemistry B, 2004
A coarse-grain model for amphiphilic diblock copolymers is developed by fitting the required parameters to properties taken from all-atom molecular dynamics simulations and experimental data. Computations with the present coarse-grain model yield spontaneous self-assembly of a random system into membrane bilayers when the amphiphilic diblock copolymers have a lipid-like hydrophilic/hydrophobic ratio. The model semiquantitatively reproduces a number of experimental results that were not explicitly used in the parametrization. In particular, diblock polymers with the appropriate ratio of hydrophobic-hydrophilic segment lengths self-assemble into membranes whose hydrophobic thickness (determined from mass density profiles) and scaling with molecular weight are found to be in good agreement with the experiment.