Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up ...approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processesevaporation, solvent–nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrestthat dictates the complex structure of the membrane on different scales.
Patterning strategies based on directed self-assembly (DSA) of block copolymers, as one of the most appealing next-generation lithography techniques, have attracted abiding interest. DSA aims at ...fabricating defect-free geometrically simple patterns on large scales or irregular device-oriented structures. Successful application of DSA requires to control and optimize multiple process parameters related to the bulk morphology of the block copolymer, its interaction with the chemical or topographical guiding pattern, and the kinetics of structure formation. Most studies have focused on validating DSA patterning techniques using PS-b-PMMA block copolymers as a prototypical material. As the development of DSA techniques advances, recent efforts have been devoted to extending the materials selection in order to fabricate more complex geometric patterns or patterns with smaller characteristic dimensions. How to select appropriate polymer materials in a vast parameter space is a critical but also challenging step. In this review, we discuss recent progress in the research of DSA of block copolymers focusing on three aspects: (i) screening the block copolymer materials, (ii) controlling the film properties, and (iii) tailoring the phase separation kinetics.
Using self-consistent field theory (SCFT) and Monte-Carlo simulations, we study the structure and dynamics of loops and bridges in the lamellar phase of symmetric ABA triblock copolymers at χN = 80. ...The bridge fraction, νB, linearly correlates with the average variance, X 1 2 = ⟨X̂ 1i 2⟩, of the first Rouse mode. Using SCFT with constraint X 1 2, we calculate the free-energy landscape, F(L,X 1 2), and observe a nonmonotonic variation of the optimal lamellar spacing, L*, with X 1 2. SCFT also provides information about the distribution, P(X̂ 1i ), of Rouse modes of individual chains. In the lamellar phase, P exhibits two pronounced peaks, corresponding to the single-chain loop and bridge states. This suggests that the system can be conceived as a mixture of noninteracting loops and bridges with a two-state Markov dynamics, yielding a dynamic equation for the relaxation of the nonconserved, collective order parameter, X 1 2. These findings are corroborated by multichain simulations of a soft, coarse-grained model. We observe an extremely long relaxation time, 4 × 105 τR, compared to the Rouse time, τR, in the disordered state. This timescale is the inverse of the conversion rates from loops to bridges and vice versa, which we obtain by single-chain simulations in conjunction with forward-flux sampling. These results suggest that the multichain simulations can be significantly accelerated by the heterogeneous multiscale method (HMM).
Block copolymer membranes offer a bottom-up approach to form isoporous membranes that are useful for ultrafiltration of functional macromolecules, colloids, and water purification. The fabrication of ...isoporous block copolymer membranes from a mixed film of an asymmetric block copolymer and two solvents involves two stages: First, the volatile solvent evaporates, creating a polymer skin, in which the block copolymer self-assembles into a top layer, comprised of perpendicularly oriented cylinders, via evaporation-induced self-assembly (EISA). This top layer imparts selectivity onto the membrane. Subsequently, the film is brought into contact with a nonsolvent, and the exchange between the remaining nonvolatile solvent and nonsolvent through the self-assembled top layer results in nonsolvent-induced phase separation (NIPS). Thereby, a macroporous support for the functional top layer that imparts mechanical stability onto the system without significantly affecting permeability is fabricated. We use a single, particle-based simulation technique to investigate the sequence of both processes, EISA and NIPS. The simulations identify a process window, which allows for the successful in silico fabrication of integral-asymmetric, isoporous diblock copolymer membranes, and provide direct insights into the spatiotemporal structure formation and arrest. The role of the different thermodynamic (e.g., solvent selectivity for the block copolymer components) and kinetic (e.g., plasticizing effect of the solvent) characteristics is discussed.
Vesicles on substrates play a fundamental role in many biological processes, ranging from neurotransmitter release at the synapse on small scales to the nutrient intake of trees by large vesicles. ...For these processes, the adsorption or desorption of vesicles to biological substrates is crucial. Consequently, it is important to understand the factors determining whether and for how long a vesicle adsorbs to a substrate and what shape it will adopt. Here, we systematically study the adsorption of a vesicle to planar substrates with short- and long-range interactions, with and without buoyancy. We assume an axially symmetric system throughout our simulations. Previous studies often considered a contact potential of zero range and neutral buoyancy. The interaction range alters the location and order of the adsorption transition and is particularly important for small vesicles, e.g., in the synapse. Whereas even small density differences between the inside and the outside of the vesicle give rise to strong buoyancy effects for large vesicles, e.g., giant unilamellar vesicles, as buoyancy effects scale with the fourth power of the vesicle size. We find that (i) an attractive membrane-substrate potential with nonzero spatial extension leads to a pinned state, where the vesicle benefits from the attractive membrane-substrate interaction without significant deformation. The adsorption transition is of first order and occurs when the substrate switches from repulsive to attractive. (ii) Buoyancy shifts the transversality condition, which relates the maximal curvature in the contact zone to the adhesion strength and bending rigidity, up/downward, depending on the direction of the buoyancy force. The magnitude of the shift is influenced by the range of the potential. For upward buoyancy, adsorbed vesicles are at most metastable. We determine the stability limit and the desorption mechanisms and compile the thermodynamic data into an adsorption diagram. Our findings reveal that buoyancy, as well as spatially extended interactions, are essential when quantitatively comparing experiments to theory.
The thermodynamics of dislocations in thin films of lamella-forming diblock copolymers and their climb and glide motions are investigated using single-chain-in-mean-field (SCMF) simulations and ...self-consistent field theory (SCFT) in conjunction with the string method. The glide motion of a defect perpendicular to the stripe pattern is characterized by large free energy barriers. The barriers not only stem from altering the domain topology; an additional barrier arises from a small-amplitude but long-range domain displacement. In contrast, the climb motion along the stripes does not involve a free energy barrier in accord with the continuous translational invariance along the stripe. Thus, the perpendicular distance (“impact parameter”) between a pair of defects is approximately conserved. Dislocation pairs with opposite Burgers vectors attract each other and move toward each other (“collide”) via climb motion. We find that the forces between apposing defects significantly depend on system size, and the Peach–Koehler force in smectic structures only becomes accurate for extremely large system sizes. Moreover, we observe in SCMF simulations that the defect annihilation time qualitatively and nonmonotonously depends on the defects’ perpendicular distance and rationalize this finding by the collective kinetics along the minimum free energy path (MFEP) and the single-chain dynamics in an inhomogeneous environment.
Using computer simulations and phenomenological considerations, we study the interplay between elasticity and microphase separation in quasi-two-dimensional phantom networks, obtained by ...cross-linking AB diblock copolymers at their ends. In the limit of weak stretching, where the average distance, l u , of A cross-links (or the mesh-cell size of the regular network) in the disordered phase is much smaller than the lamellar spacing, L*, of the diblock copolymer melt, network elasticity plays only a minor role. Upon increasing the stretching, we find that the incompatibility χN db, at which the order–disorder transition occurs, decreases, and it becomes vanishingly small for l u ≫ L* and large networks. At intermediate stretching, we observe a multigrain state, where the lamellae tilt with respect to the network orientation.
On short length and time scales, the collective kinetics of relaxation or structure formation in multicomponent polymer melts, such as homopolymer blends and copolymers, is influenced by the ...subdiffusive single-chain dynamics. We compare the predictions of the dynamic random-phase approximation (D-RPA) and dynamic self-consistent field theory (D-SCFT) to that of particle-based simulation, focusing on the decay of a density fluctuation in the disordered phase, the spinodal phase separation after a quench from the disordered phase, and the response of the disordered phase to an external field. D-SCFT with a wavevector-dependent Onsager coefficient qualitatively fails to predict the time evolution on time scales shorter than the Rouse relaxation time of the underlying polymers, whereas D-RPA successfully captures the collective behavior observed in particle-based simulation. Extensions of D-SCFT, employing a time-dependent Onsager coefficient that is derived from D-RPA and that accounts for the subdiffusive single-chain dynamics on short time scales, are discussed.
Conditions of rapid processing often drive polymers to adopt nonequilibrium molecular conformations, which, in turn, can give rise to structural, dynamical, and mechanical properties that are ...significantly different from those in thermodynamic equilibrium. However, despite the possibility to control the desired nonequilibrium properties of polymers, a rigorous microscopic understanding of the processing–property relations is currently lacking. In an attempt to stimulate progress along this topical direction, we focus here on three prototypical and apparently different cases: spin-coated polymer films, rapidly drawn polymer fibers, and sheared polymer melts. Inspired by the presence of common observations in the chosen cases, we search for order parameters as, for example, topological correlations and heterogeneities, which may allow characterizing the processing-induced behavior of polymers. We highlight that such approaches, necessitating concerted efforts from theory, simulations, and experiments, can provide a profound understanding leading to predictable and tunable properties of polymers.
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