Phase behavior and orientational ordering in block copolymers doped with anisotropic nanoparticles

A molecular field theory and coarse-grained computer simulations with dissipative particle dynamics have been used to study the spontaneous orientational ordering of anisotropic nanoparticles in the lamellar and hexagonal phases of diblock copolymers and the effect of nanoparticles on the phase behavior of these systems. Both the molecular theory and computer simulations indicate that strongly anisotropic nanoparticles are ordered orientationally mainly in the boundary region between the domains and the nematic order parameter possesses opposite signs in adjacent domains. The orientational order is induced by the boundary and by the interaction between nanoparticles and the monomer units in different domains. In simulations, sufficiently long and strongly selective nanoparticles are ordered also inside the domains. The nematic order parameter and local concentration profiles of nanoparticles have been calculated numerically using the model of a nanoparticle with two interaction centers and also determined using the results of computer simulations. A number of phase diagrams have been obtained which illustrate the effect of nanoparticle selectivity and molar fraction of the stability ranges of various phases. Different morphologies have been identified by analyzing the static structure factor and a phase diagram has been constructed in coordinates' nanoparticle concentration-copolymer composition. Orientational ordering of even a small fraction of nanoparticles may result in a significant increase of the dielectric anisotropy of a polymer nanocomposite, which is important for various applications

Molecular theory of the tilting transition and computer simulations of the tilted lamellar phase of rod-coil diblock copolymers

Symmetric rod-coil diblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter. It has been found that the tilted lamellar phase appears to be the most stable one at strong segregation. The rod-coil copolymer tilt angle and orientational order parameters have been determined as functions of the segregation strength. The density functional theory of rod-coil diblock copolymers has been generalized to the case of the tilted lamellar phase and used to study the stability of the orthogonal lamellar phase with respect to tilt. The orthogonal phase indeed appears to be unstable in the broad region of the parameter space in the case of relatively strong segregation. It has also been shown that the transition into the tilted lamellar phase is determined by a strong coupling between two independent tilt order parameters

Orientational ordering of nanorods of different length in diblock copolymers

Orientational and positional ordering of nanorods in the lamellae phase of diblock copolymers has been investigated using a simple theoretical model and dissipative dynamics simulations. Orientational order parameter and local concentration profiles of nanorods are calculated numerically and extracted from computer simulations data for different values of the nanoparticle length and different number of the interaction sites in the model nanorod. The predictions of the molecular theory are compared with the results of computer simulations. It has been found that the nanorods are orientationally ordered in the boundary region between the domains and the orientational order parameter changes its sign at the domain wall. At the same time there exists some quantitative discrepancy between theory and computer simulations which is partially removed when a similar model of a nanorod is employed both in the molecular theory and in coarse-grained molecular dynamics simulations

Hybrid approach combining dissipative particle dynamics and finite-difference diffusion model: Simulation of reactive polymer coupling and interfacial polymerization

A novel hybrid approach combining dissipative particle dynamics (DPD) and finite difference (FD) solution of partial differential equations is proposed to simulate complex reaction-diffusion phenomena in heterogeneous systems. DPD is used for the detailed molecular modeling of mass transfer, chemical reactions, and phase separation near the liquid/liquid interface, while FD approach is applied to describe the large-scale diffusion of reactants outside the reaction zone. A smooth, self-consistent procedure of matching the solute concentration is performed in the buffer region between the DPD and FD domains. The new model is tested on a simple model system admitting an analytical solution for the diffusion controlled regime and then applied to simulate practically important heterogeneous processes of (i) reactive coupling between immiscible end-functionalized polymers and (ii) interfacial polymerization of two monomers dissolved in immiscible solvents. The results obtained due to extending the space and time scales accessible to modeling provide new insights into the kinetics and mechanism of those processes and demonstrate high robustness and accuracy of the novel technique. © 2013 AIP Publishing LLC

End-coupling reactions in incompatible polymer blends: From droplets to complex micelles through interfacial instability

Simulations by dissipative particle dynamics revealed a possibility to produce micelles of diverse morphologies via irreversible end-coupling reaction in polymer melts containing a particulate phase. It is demonstrated that the reaction at the surface of a polymer A droplet immersed in a melt of polymer B leads to the droplet instability and subsequent micelle formation. Depending on the length ratio of reacting chains and its own size, the droplet is either emulsified into a set of small micelles or converted into a single micelle, which can have rather complex internal structure. A morphology diagram containing structures that are typical for polymer solutions, in particular vesicles, bowls, worms, star-like and crew-cut micelles with multiple internal domains, is first presented for polymer melts. Investigation of the reaction kinetics reveals subsequent linear, saturation, and exponential autoacceleration regimes. By simulations and using simple scaling arguments, it is explained how the barrier properties of a diblock copolymer layer formed at the A/B interface depend on the copolymer composition and droplet curvature. It is found that the scenario of the instability development is much different for flat and spherical A/B interfaces. © 2013 American Chemical Society

Linear interfacial polymerization: Theory and simulations with dissipative particle dynamics

Step-growth alternating interfacial polymerization between two miscible or immiscible monomer melts is investigated theoretically and by dissipative particle dynamics simulations. In both cases the kinetics for an initially bilayer system passes from the reaction to diffusion control. The polymer composed of immiscible monomers precipitates at the interface forming a film of nearly uniform density. It is demonstrated that the reaction proceeds in a narrow zone, which expands much slower than the whole film, so that newly formed polymer is extruded from the reaction zone. This concept of ldquoreactive extrusionrdquo is used to analytically predict the degree of polymerization and distribution of all components (monomers, polymer, and end groups) within the film in close agreement with the simulations. Increasing the comonomer incompatibility leads to thinner and more uniform films with the higher average degree of polymerization. The final product is considerably more polydisperse than expected for the homogeneous step-growth polymerization. The results extend the previous theoretical reports on interfacial polymerization and provide new insights into the internal film structure and polymer characteristics, which are important for membrane preparation, microencapsulation, and 3D printing technologies. A systematic way of mapping the simulation data onto laboratory scales is discussed