A simple method based on UV/ozone treatment is proposed to control the surface energy of dense grafted silane layers for orientating block copolymer mesophases. Our method allows one to tune the surface energy down to a fraction of a mN/m. We show that related to the surface, perpendicular orientation of a lamellar phase of a PS-PMMA diblock copolymer (neutral surface) is obtained for a critical surface energy of 23.9-25.7 mN/m. Perpendicular cylinders are obtained for 24.6 mN/m and parallel cylinders for 26.8 mN/m.
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 "plumber's 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 …
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 $σ$ and the Laves C14 and C15 phases could be stabilized by the addition of longer A$_2$B$_2$-copolymers to asymmet…
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.
We numerically investigate local defectiveness control of self-assembled diblock copolymer patterns through appropriate substrate design. We use a nonlocal Cahn-Hilliard (CH) equation for the phase separation dynamics of diblock copolymers. We discretize the nonlocal CH equation by an unconditionally stable finite difference scheme on a tapered trench design and, in particular, we use Dirichlet, Neumann, and periodic boundary conditions. The value at the Dirichlet boundary comes from an energy-minimizing equilibrium lamellar profile. We solve the resulting discrete equations using a Gauss-Seid…
Phase behavior of diblock copolymer/homopolymer blends (AB/C) is investigated theoretically. The study focuses on a special case where all three binary pairs, A/B, B/C and C/A, are miscible. Despite the miscibility of the binary pairs, a closed-loop immiscible region exists in the AB/C blends when the A/C and B/C pair interactions are sufficiently different. Inside the closed-loop, the system undergoes microphase separation, exhibiting different ordered structures. This phenomenon is enhanced when the homopolymer (C) interacts more strongly to one of the blocks (A or B).
A technique is presented which maps the parameters of a bead spring model, using the Flory Huggins theory, to a specific experimental system. By keeping only necessary details, for the description of these systems, the mapping procedure turns into an estimation of a few characteristic parameters. An asset of this technique is that it is simple to apply and captures the behavior of block copolymer phase separation. In our study this mapping technique is utilized in conjunction with a Monte Carlo (MC) algorithm to perform simulations on block copolymer systems. The microphase separation is inves…
The order-disorder transition of a sphere-forming block copolymer thin film was numerically studied through a Cahn-Hilliard model. Simulations show that the fundamental mechanisms of pattern formation are spinodal decomposition and nucleation and growth. The range of validity of each relaxation process is controlled by the spinodal and order-disorder temperatures. The initial stages of spinodal decomposition are well-approximated by a linear analysis of the evolution equation of the system. In the metastable region, the critical size for nucleation diverges upon approaching the order-disorder …
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 $χN$, where $χ$ 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^…
In this work we investigated the phase behavior of melts of block-copolymers with one charged block by means of dissipative particle dynamics with explicit electrostatic interactions. We assumed that all the Flory-Huggins \c{hi} parameters were equal to 0 and showed that the charge correlation attraction solely can cause microphase separation with long-range order; a phase diagram was constructed by varying the volume fraction of the uncharged block and the electrostatic interaction parameter λ. The obtained phase diagram was compared to the phase diagram of corresponding neutral diblock-copol…
The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer composition but also on the size, shape, and surface properties of the colloids. The dynamics of this kind of systems using a hybrid mesoscopic approach has been studied in this work. A continuum description for the polymer is used, while colloids are individually resolved. The method allows for a variable preference of the colloids, which can have different sizes,…
Using fast off-lattice Monte Carlo simulations with experimentally accessible fluctuations, we report the first systematic study unambiguously quantifying the shift of the order-disorder transition (ODT) $χ^*$ of symmetric diblock copolymers from the mean-field prediction $χ^*_{\rm MF}$. Our simulations are performed in a canonical ensemble with variable box lengths to eliminate the restriction of periodic boundary conditions on the lamellar period. Exactly the same model system (Hamiltonian) is used in both our simulations and mean-field theory; the ODT shift is therefore due to the fluctuati…
We consider conformations and intra-molecular conformational transitions in amphiphilic starlike polymers formed by diblock copolymer arms with inner hydrophobic and outer polyelectrolyte blocks. A combination of an analytical mean-field theory with the assumption-free numerical self-consistent field (SCF) modeling approach is applied. It is demonstrated that unimolecular micelles with collapsed hydrophobic cores and swollen polyelectrolyte coronae are formed in dilute aqueous solutions at high ionic strength or/and low degree of ionization of the outer hydrophilic block. An intra-molecular co…
The dynamics of microphase separation and the orientation of lamellae in diblock copolymers is investigated in terms of a mean-field model. The formation of lamellar structures and their stable states are explored and it is shown that lamellae are stable not only for the period of the structure corresponding to the minimum of the free energy. The range of wavelengths of stable lamellae is determined by a functional approach, introduced with this work, which is in agreement with the results of a linear stability analysis. The effects of the interaction of block copolymers with confining plane b…
Monte Carlo simulation on the crystallization of double crystalline diblock copolymer unravels an intrinsic relationship between block asymmetry and crystallization behaviour. We model crystalline A-B diblock copolymer, wherein the melting temperature of A-block is higher than that of the B-block. We explore the composition dependent crystallization behaviour by varying the relative block length with weak and strong segregation strength between the blocks. In weak segregation limit, we observe that with increasing the composition of B-block, its crystallization temperature increases accompanyi…
The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussia…
A general theory has been developed for a polydisperse semi-flexible multi-block copolymer melt. Using the Bawendi-Freed approach to model semi-flexible chains an expression for the Landau free energy is derived in the weak segregation regime which includes the density and orientation order-parameters. The orientation order-parameter is described in the smectic phase and in more complicated structures such as the hexagonal phase. The Landau free energy contains contributions of two kinds of interactions. The first kind is the Flory- Huggins interaction which describes the incompatibility of ch…
Recent experiments have highlighted the intrinsic magnetic anisotropy in coil-coil diblock copolymers, specifically in poly(styrene-b-4-vinylpyridine) (PS-b-P4VP), that enables magnetic field alignment at field strengths of a few tesla. We consider here the alignment response of two low molecular weight (MW) lamallae-forming PS-b-P4VP systems. Cooling across the disorder-order transition temperature ($\mathrm{T_{odt}}$) results in strong alignment for the higher MW sample (5.5K), whereas little alignment is discernible for the lower MW system (3.6K). This disparity under otherwise identical co…
Diblock copolymers by virtue of the chemical dissimilarity between the constituting blocks exhibit microphase separation in the melt state. The phase separated melt can successfully be exploited to control the morphology of the final semi crystalline materials by allowing an extended thermal annealing. Thermal annealing accelerates coalescence of microdomains, yielding a phase separated melt that would exhibit a distinctly different crystallization behaviour than microphase separated melt without annealing. In this paper, we report simulation results on the crystallization behavior of A-B dibl…
Coarse-grained theories of dense polymer liquids such as block copolymer melts predict a universal dependence of equilibrium properties on a few dimensionless parameters. For symmetric diblock copolymer melts, such theories predict a universal dependence on only chi N and Nbar, where chi is an effective interaction parameter, N is a degree of polymerization, and Nbar is a measure of overlap. We test whether simulation results for the structure factor S(q) obtained from several different simulation models are consistent with this two-parameter scaling hypothesis. We compare results from three m…
A generalized self-consistent field approach for polymer networks with fixed topology is developed. It is shown that the theory reproduces the localization of crosslinks which is characteristic for gels. The theory is then used to study the order-disorder transition in regular networks of endlinked diblock copolymers. Compared to diblock copolymer melts, the transition is shifted towards lower values of the incompatibility parameter $χ$ (the Flory- Huggins parameter). Moreover, the transition becomes strongly first order already at the mean-field level. If stress is applied, the transition is …
Brownian Dynamics simulations are carried out to understand the effect of temperature and dielectric constant of the medium on microphase separation of charged-neutral diblock copolymer systems. For different dielectric media, we focus on the effect of temperature on the morphology and dynamics of model charged diblock copolymers. In this study we examine in detail a system of partially charged block copolymer consisting of 75% neutral blocks and 25% of charged blocks with 50% degree of ionization. Our investigations show that due to the presence of strong electrostatic interactions between th…
Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent CS2, the concentration of the polymer CP, and the polymer-solvent interactions εij (i = A, B; j = S1, S2). Morphology diagrams are constructed as functions of CP, CS2, and/or εAS2. The copolymer morphological sequence from dissolved -> sphere -> rod-> ring/cage-> vesicle is obtained upon increasing CS2 a…
