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Register a new userFluctuations in Symmetric Diblock Copolymers: Testing A Recent Theory
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Composition fluctuations in disordered melts of symmetric diblock copolymers are studied by Monte Carlo simulation over a range of chain lengths and interaction strengths. Results are used to test three theories: (1) the random phase approximation (RPA), (2) the Fredrickson-Helfand (FH) theory, which was designed to describe large fluctuations near an order-disorder transition (ODT), and (3) a more recent renormalized one-loop (ROL) theory, which reduces to FH theory near the ODT, but which is found to be accurate over a much wider range of parameters.
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A renormalized one-loop theory (ROL) is used to calculate corrections to the random phase approximation (RPA) for the structure factor $Sc(q)$ in disordered diblock copolymer melts. Predictions are given for the peak intensity $S(q^{star})$, peak position $q^{star}$, and single-chain statistics for symmetric and asymmetric copolymers as functions of $chi N$, where $chi$ is the Flory-Huggins interaction parameter and $N$ is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity $S(q^{star})$ upon $chi N$ for symmetric diblock copolymers in the limit of strong scattering, or large $chi N$, but yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of $S(q^star)$ and a decrease of $q^{star}$ for large values of $chi N$, relative to the RPA predictions, but an enhancement of $S(q^{star})$ and an increase in $q^{star}$ for small $chi N$ ($chi N < 5$). By separating intra- and inter-molecular contributions to $S^{-1}(q)$, we show that the decrease in $q^{star}$ near the ODT is caused by the $q$ dependence of the intermolecular direct correlation function, and is unrelated to any change in single-chain statistics, but that the increase in $q^{star}$ at small values of $chi N$ is a result of non-Gaussian single-chain statistics.
Solvent vapor annealing (SVA) is known to be a simple, low-cost and highly efficient technique to produce defect-free diblock copolymer (BCP) thin films. Not only can the solvent weaken the BCP segmental interactions, but it can vary the characteristic spacing of the BCP microstructures. We carry out systematic theoretical studies on the effect of adding solvent into lamellar BCP thin films on the defect removal close to the BCP order-disorder transition. We find that the increase of the lamellar spacing, as is induced by addition of solvent, facilitates more efficient removal of defects. The stability of a particular defect in a lamellar BCP thin film is given in terms of two key controllable parameters: the amount of BCP swelling and solvent evaporation rate. Our results highlight the SVA mechanism for obtaining defect-free BCP thin films, as is highly desired in nanolithography and other industrial applications.
The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (DBCPs) is studied using the polymeric self-consistent field theory. The theoretical study predicts that the double-diamond and the plumbers nightmare phases, which are metastable for neat diblock copolymers, could be stabilized in block copolymers with designed dispersity, namely, binary blends composed of a gyroid-forming DBCP and a homopolymer-like DBCP. The spatial distribution of different monomers reveals that these two types of DBCPs are segregated such that the homopolymer-like component is localized at the nodes to relieve the packing frustration. Simultaneously, the presence of a local segregation of the two DBCPs on the AB interface regulates the interfacial curvature. These two mechanisms could act in tandem for homopolymer-like diblock copolymers with proper compositions, resulting in larger stability regions for the novel bicontinuous phases.
The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space.
The phase behaviour of binary blends composed of A$_1$B$_1$ and A$_2$B$_2$ diblock copolymers is systematically studied using the polymeric self-consistent field theory, focusing on the formation and relative stability of various spherical packing phases. The results are summarized in a set of phase diagrams covering a large phase space of the system. Besides the commonly observed body-centered-cubic (BCC) phase, complex spherical packing phases including the Frank-Kasper A15 and $sigma$ and the Laves C14 and C15 phases could be stabilized by the addition of longer A$_2$B$_2$-copolymers to asymmetric A$_1$B$_1$-copolymers. Stabilizing the complex spherical packing phases requires that the added A$_2$B$_2$-copolymers have a longer A-block and an overall chain length at least comparable to the host copolymer chains. A detailed analysis of the block distributions reveals the existence of inter- and intra-domain segregation of different copolymers, which depends sensitively on the copolymer length ratio and composition. The predicted phase behaviours of the A$_1$B$_1$/A$_2$B$_2$ diblock copolymer blends are in good agreement with available experimental and theoretical results. The study demonstrated that binary blends of diblock copolymers provide an efficient route to regulate the emergence and stability of complex spherical packing phases.
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