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Simulations of five different coarse-grained models of symmetric diblock copolymer melts are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy on the invariant degree of polymerization $overline{N}$, and to study universal properties of the order-disorder transition (ODT). The ODT appears to exhibit two regimes: Systems of very long chains ($overline{N} gtrsim 10^{4}$) are well described by the Fredrickson-Helfand theory, which assumes weak segregation near the ODT. Systems of smaller but experimentally relevant values, $overline{N} lesssim 10^4$, undergo a transition between strongly segregated disordered and lamellar phases that, though universal, is not adequately described by any existing theory.
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An extensive study of single block copolymer knots containing two kinds of monomers $A$ and $B$ is presented. The knots are in a solution and their monomers are subjected to short range interactions that can be attractive or repulsive. In view of possible applications in medicine and the construction of intelligent materials, it is shown that several features of copolymer knots can be tuned by changing the monomer configuration. A very fast and abrupt swelling with increasing temperature is obtained in certain multiblock copolymers, while the size and the swelling behavior at high temperatures may be controlled in diblock copolymers. Interesting new effects appear in the thermal diagrams of copolymer knots when their length is increased.
Using dissipative particle dynamics (DPD) simulation method, we study the phase separation dynamics in block copolymer (BCP) melt in $d=3$, subjected to external stimuli such as light. An initial homogeneous BCP melt is rapidly quenched to a temperature $T < T_c$, where $T_c$ is the critical temperature. We then let the system go through alternate light on and off cycles. An on-cycle breaks the stimuli-sensitive bonds connecting both the blocks A and B in BCP melt, and during the off-cycle, broken bonds reconnect. By simulating the effect of light, we isolate scenarios where phase separation begins with the light off (set 1); the cooperative interactions within the system allow it to undergo microphase separation. When the phase separation starts with the light on (set 2), the system undergoes macrophase separation due to the bond breaking. Here, we report the role of alternate cycles on domain morphology by varying bond-breaking probability for both the sets 1 and 2, respectively. We observe that the scaling functions depend upon the conditions mentioned above that change the time scale of the evolving morphologies in various cycles. However, in all the cases, the average domain size respects the power-law growth: $R(t)sim t^{phi}$ at late times, here $phi$ is the dynamic growth exponent. After a short-lived diffusive growth ($phi sim 1/3$) at early times, $phi$ illustrates a crossover from the viscous hydrodynamic ($phi sim 1$) to the inertial hydrodynamic ($phi sim 2/3$) regimes at late times.
The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in these approaches is the mobility function, which describes the effect of chain connectivity on the nonlocal response of monomers to thermodynamic driving fields. In a recent study [Mantha et al, Macromolecules 53, 3409 (2020)], we have developed a method to systematically construct mobility functions from reference fine-grained simulations. Here we focus on melts of linear chains in the Rouse regime and show how the mobility functions can be calculated semi-analytically for multiblock copolymers with arbitrary sequences without resorting to simulations. In this context, an accurate approximate expression for the single-chain dynamic structure factor is derived. Several limiting regimes are discussed. Then we apply the resulting density functional theory to study ordering processes in a two-length scale block copolymer system after instantaneous quenches into the ordered phase. Different dynamical regimes in the ordering process are identified: At early times, the ordering on short scales dominates; at late times, the ordering on larger scales takes over. For large quench depths, the system does not necessarily relax into the true equilibrium state. Our density functional approach could be used for the computer-assisted design of quenching protocols in order to create novel nonequilibrium materials.
Poly(ethylene oxide)-$textit{b}$-poly(butylmethacrylate) (PEO-$textit{b}$-PBMA) copolymers have recently been identified as excellent building blocks for the synthesis of hierarchical nanoporous materials. Nevertheless, while experiments have unveiled their potential to form bicontinuous phases and vesicles, a general picture of their phase and aggregation behavior is still missing. By performing Molecular Dynamics simulations, we here apply our recent coarse-grained model of PEO-$textit{b}$-PBMA to investigate its self-assembly in water and tetrahydrofuran (THF) and unveil the occurrence of a wide spectrum of mesophases. In particular, we find that the morphological phase diagram of this ternary system incorporates bicontinuous and lamellar phases at high copolymer concentrations, and finite-size aggregates, such as dispersed sheets or disk-like aggregates, spherical vesicles and rod-like vesicles, at low copolymer concentrations. The morphology of these mesophases can be controlled by tuning the THF/water relative content, which has a striking effect on the kinetics of self-assembly as well as on the resulting equilibrium structures. Our results disclose the fascinating potential of PEO-$textit{b}$-PBMA copolymers for the templated synthesis of nanostructured materials and offer a guideline to fine-tune their properties by accurately selecting the THF/water ratio.
Experimental data on thin films of cylinder-forming block copolymers (BC) -- free-standing BC membranes as well as supported BC films -- strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns are embedded. We analyze this phenomenon using general symmetry considerations and numerical self-consistent field studies of curved BC films in cylindrical geometry. The stability of the films against curvature-induced dewetting is also analyzed. In good agreement with experiments, we find that the BC cylinders tend to align along the direction of curvature at high curvatures. At low curvatures, we identify a transition from perpendicular to parallel alignment in supported films, which is absent in free standing membranes. Hence both experiments and theory show that curvature can be used to manipulate and align BC patterns.
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