Simulation and Model Development for the Equation of State of Self-Assembling Nonadditive Hard Chains (original) (raw)
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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.
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.
Polymer, 2004
Chains of the copolymers formed by styrene (S) with two different comonomers, vinylmethylether (VME)and methylmethacrylate (MMA), are studied to see how these two comonomers influence the expansion of the coil and the segregation between blocks (the comonomers differ in that homopolymer PS forms miscible blends with PVME and is incompatible with PMMA). Two comonomer sequences are considered: di-block and alternating. Their chains are simulated by molecular dynamics, at two coil densities: the unperturbed random coil state (attained by use of a cut-off for the non-bonded interactions), and a more dense, collapsed coil state (with no cut-off). Properties analysed are: radius of gyration, scattering form factor, separation between block' centres of mass, and pair distribution function between blocks' monomer units. The alternating copolymers (and the corresponding homopolymers) are divided into two parts and treated as 'block' copolymers, for comparison. The di-block copolymer chains are no more expanded than the corresponding homopolymer chains, and no clear distinction between the VME-S and MMA-S pairs can be established. The analysis of 'copolymer' form factors show a slightly larger global segregation of the MMA-S blocks. On the other hand, the alternating copolymer chains of VME-S and MMA-S can be clearly differentiated. Compared to their corresponding homopolymer chains, the VME-S alternating chain is more contracted, and its two blocks are in closer proximity, while the MMA-S alternating chain is more expanded, and its two blocks are more segregated. Thus, a correlation between the compatibility of the homopolymer pair and the degree of segregation of the alternating copolymer chain has been found. q
Self-Assembly of Block Copolymers: Theoretical Models and Mathematical Challenges
Block copolymers are macromolecules composed of two or more chemically distinct polymer chains linked together by covalent bonds. The thermodynamical incompatiblility between the different sub-chains drives the system to phase separate. However the covalent bonds between the different sub-chains prevent phase separation at a macroscopic length scale. As a result of these two competing trends, block copolymers undergo phase separation at a nanometer length scale, leading to an amazingly rich array of nanostructures. These structures present tremendous potentials for technological application because they allow for the synthesis of materials with tailored mechanical, electrical and chemical properties (see [2, 8, 11]).
Collapse of an AB copolymer single chain with alternating blocks of different stiffness
Russ Chem Bull (2011) 60: 229., 2011
Using the Langevin dynamics, we studied the conformational properties of an AB copolymer single chain built of alternating stiff and flexible blocks having different steady-state affinities to a solvent. Two opposite conditions were simulated, viz., where a solvent is poor for stiff blocks and good for flexible blocks and vice versa. The behavior of the molecules built of equal-length blocks and long stiff blocks linked through short flexible junctions were considered. Upon transition of a chain to the compact state, nanostructures with different morphologies, such as bunches, networks, and others, can form.
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.
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
Entropy-induced microphase separation in hard diblock copolymers
Physical Review E, 2004
Whereas entropy can induce phase behavior that is as rich as seen in energetic systems, microphase separation remains a very rare phenomenon in entropic systems. In this paper, we present a density functional approach to study the possibility of entropy-driven microphase separation in diblock copolymers. Our model system consists of copolymers composed of freely-jointed slender hard rods. The two types of monomeric segments have comparable lengths, but a significantly different diameter, the latter difference providing the driving force for the phase separation. At the same time these systems can also exhibit liquid crystalline phases. We treat this system in the appropriate generalization of the Onsager approximation to chain-like particles. Using a linear stability (bifurcation) analysis, we analytically determine the onset of the microseparated and the nematic phases for long chains. We find that for very long chains the microseparated phase always preempts the nematic. In the limit of infinitely long chains, the correlations within the chain become Gaussian and the approach becomes exact. This allows us to define a Gaussian limit in which the theory strongly simplifies and the competition between microphase separation and liquid crystal formation can be studied essentially analytically. Our main results are phase diagrams as a function of the effective diameter difference, the segment composition and the length ratio of the segments. We also determine the amplitude of the positional order as a function of position along the chain at the onset of the microphase separation instability. Finally, we give suggestions as to how this type of entropy-induced microphase separation could be observed experimentally.