Bing Miao

Effects of confinement on the order-disorder transition of diblock copolymer melts

The effects of confinement on the order-disorder transition of diblock copolymer melts are studied theoretically. Confinements are realized by restricting diblock copolymers in finite spaces with different geometries (slabs, cylinders, and spheres). Within the random phase approximation, the correlation functions are calculated using the eigenvalues and eigenfunctions of the Laplacian operator inverted Delta(2) in the appropriate geometries. This leads to a size-dependent scattering function, and the minimum of the inverse scattering function determines the spinodal point of the homogeneous phase. For diblock copolymers confined in a slab or in a cylindrical nanopore, the spinodal point of the homogeneous phase (chiN)(s) is found to be independent of the confinement. On the other hand, for diblock copolymers confined in a spherical nanopore, (chiN)(s) depends on the confinement and it oscillates as a function of the radius of the sphere. Further understanding of the finite-size effects is provided by examining the fluctuation modes using the Landau-Brazovskii model.

Scaling of Polymer Dynamics at an Oil–Water Interface in Regimes Dominated by Viscous Drag and Desorption-Mediated Flights

Polymers are found near surfaces and interfaces in a wide range of chemical and biological systems, and the structure and dynamics of adsorbed polymer chains have been the subject of intense interest for decades. While polymer structure is often inferred from dynamic measurements in bulk solution, this approach has proven difficult to implement at interfaces, and the understanding of interfacial polymer conformation remains elusive. Here we used single-molecule tracking to study the interfacial diffusion of isolated poly(ethylene glycol) molecules at oil-water interfaces. Compared to diffusion in dilute aqueous solution, which exhibited the expected dependence of the diffusion coefficient (D) upon molecular weight (M) of D ∼ M(-1/2) for a Gaussian chain, the behavior at the interface was approximately D ∼ M(-2/3), suggesting a significantly more expanded polymer conformation, despite the fact that the oil was a poor solvent for the polymer. Interestingly, this scaling remained virtually unchanged over a wide range of oil viscosity, despite the fact that at low viscosities the magnitude of the diffusion coefficient was consistent with expectations based on viscous drag (i.e., Stokes-Einstein diffusion), and for high viscosity oil, the interfacial mobility was much faster than expected and consistent with the type of intermittent hopping transport observed at the solid-liquid interface. The dependence on molecular weight, in both regimes, was consistent with results from both self-consistent field theory and previous Monte Carlo simulations, suggesting that an adsorbed polymer chain adopted a partially swollen (loop-train-tail) interfacial conformation.

Fluctuation effects and the stability of the Fddd network phase in diblock copolymer melts.

We examine the effect of composition fluctuations on the stability of the orthorhombic Fddd network phase in the diblock copolymer melt phase diagram within the self-consistent Hartree approximation to the Landau-Brazovskii theory. For weak fluctuations, the Fddd structure is an equilibrium phase; however, stronger fluctuations render this phase metastable. These results suggest a reinterpretation of a recent experiment beyond mean-field theory. Fluctuations may also explain why an equilibrium Fddd phase is not generally observed in analogous self-assembling systems.

Diffusion and Directionality of Charged Nanoparticles on Lipid Bilayer Membrane

Diffusion dynamics of charged nanoparticles on the lipid membrane is of essential importance to cellular functioning. Yet a fundamental insight into electrostatics-mediated diffusion dynamics of charged nanoparticles on the membrane is lacking and remains to be an urgent issue. Here we present the computational investigation to uncover the pivotal role of electrostatics in the diffusion dynamics of charged nanoparticles on the lipid membrane. Our results demonstrate diffusive behaviors and directional transport of a charged nanoparticle, significantly depending on the sign and spatial distribution of charges on its surface. In contrast to the Fickian diffusion of neutral nanoparticles, randomly charged nanoparticles undergo superdiffusive transport with directionality. However, the dynamics of uniformly charged nanoparticles favors Fickian diffusion that is significantly enhanced. Such observations can be explained in term of electrostatics-induced surface reconstruction and fluctuation of lipid membrane. We finally present an analytical model connecting surface reconstruction and local deformation of the membrane. Our findings bear wide implications for the understanding and control of the transport of charged nanoparticles on the cell membrane.

Effects of Embedded Carbon Nanotube on Properties of Biomembrane

We investigated the interaction between embedded nanotube and biomembrane using molecular dynamics (MD) simulations. The effects of embedded nanotube on biomembrane were characterized by investigating the influence on the conformational fluctuation of individual lipid molecules, the organization of membrane molecules, the diffusion behavior of lipid molecules, and the diffusion behavior of penetrants inside biomembrane. The steric interaction with the nanotube leads to an entropy reduction of interfacial membrane molecules, while the long-range electrostatic interaction with the N-DWCNT enhances the conformational fluctuation of lipid molecules. The curvature of embedded nanotube could also influence the flexibility of lipid molecules. When the interaction between nanotube and the membrane molecules is weak, the packing density of the membrane is almost unaffected. On the contrary, when the attraction between nanotube and the membrane molecules significantly increases, the attraction among the membrane molecules decreases effectively, which leads to a relaxation of the organization of membrane. With the increase of the strength of electrostatic interaction between nanotube and small polar molecules, interaction-modified friction increases, which leads to the decrease of the diffusion constant of penetrants inside the biomembrane.

Optimal Reactivity and Improved Self-Healing Capability of Structurally Dynamic Polymers Grafted on Janus Nanoparticles Governed by Chain Stiffness and Spatial Organization

Structurally dynamic polymers are recognized as a key potential to revolutionize technologies ranging from design of self-healing materials to numerous biomedical applications. Despite intense research in this area, optimizing reactivity and thereby improving self-healing ability at the most fundamental level pose urgent issue for wider applications of such emerging materials. Here, the authors report the first mechanistic investigation of the fundamental principle for the dependence of reactivity and self-healing capabilities on the properties inherent to dynamic polymers by combining large-scale computer simulation, theoretical analysis, and experimental discussion. The results allow to reveal how chain stiffness and spatial organization regulate reactivity of dynamic polymers grafted on Janus nanoparticles and mechanically mediated reaction in their reverse chemistry, and, particularly, identify that semiflexible dynamic polymers possess the optimal reactivity and self-healing ability. The authors also develop an analytical model of blob theory of polymer chains to complement the simulation results and reveal essential scaling laws for optimal reactivity. The findings offer new insights into the physical mechanism in various systems involving reverse/dynamic chemistry. These studies highlight molecular engineering of polymer architecture and intrinsic property as a versatile strategy in control over the structural responses and functionalities of emerging materials with optimized self-healing capabilities.

The study of the structure factor of a wormlike chain in an orientational external field.

A precise representation of the structure factor of a wormlike chain for the arbitrary chain flexibility in an orientational external field is obtained by virtue of the numerical solution to the modified diffusion equation satisfied by the Greens function. The model is built from a standard wormlike chain formalism in a continuous version which crossovers from the rigid-rod limit to the flexible chain limit and the Maier-Saupe interaction which describes the orientational effects from the nematic field. The behaviors of the structure factor in the distinct wavevector k regimes are numerically investigated as functions of chain flexibility and tilt angle between the directors of the nematic field and k. The radius of gyration extracted from the structure factor in small-k regime is also carefully analysed in both the directions along and perpendicular to the nematic axis. Our calculations exactly recover the prediction of the structure factor undergoing an orientational field in the rigid rod limit.

Conformation-assisted fluctuation of density and kinetics of nucleation in polymer melts

The phase separation kinetics of density and conformation in polymer melts is studied by the linearized time-dependent Ginzburg–Landau equations. In the present model of the free energy density, there are two order parameters which are the density and the conformation. A new nucleation mechanism is proposed, in which the fluctuation in density and the fluctuation in conformation are coupled by the mixed derivative term and the cross gradient term of these two parameters. These terms are important factors for the phase separation kinetics, since the density and the conformation further each other and induce the phase separation both in density and in conformation, which finally induce the nucleation in polymer melts. The structure factors for both density and conformation are calculated. The relevant small x-ray scattering and depolarized light scattering experimental results are compared to test this model.

ON THE STRUCTURE OF STATISTICAL FIELD THEORY OF POLYMERS

We examine several widely used statistical field theoretic methods in theoretical polymer physics. A systematic derivation for the polymer field theoretic model is given within the framework of the effective Landau theory. After constructing the field theoretic model, we perform a perturbative expansion of the model, and then the mean-field approximation and the Gaussian fluctuation approximation are introduced into the treatment of the model in order. We also outline a derivation for the self-consistent Hartree theory in polymer physics within a variational scheme. The applications of these methods are also discussed accordingly.

How Implementation of Entropy in Driving Structural Ordering of Nanoparticles Relates to Assembly Kinetics: Insight through Reaction-Induced Interfacial Assembly of Janus Nanoparticles

The ability to understand and exploit entropic contributions to ordering transition is of essential importance in the design of self-assembling systems with well-controlled structures. However, much less is known about the role of assembly kinetics in entropy-driven phase behaviors. Here, by combining computer simulations and theoretical analysis, we report that the implementation of entropy in driving phase transition significantly depends on the kinetic process in the reaction-induced self-assembly of newly designed nanoparticle systems. In particular, such systems comprise binary Janus nanoparticles at the fluid-fluid interface and undergo phase transition driven by entropy and controlled by the polymerization reaction initiated from the surfaces of just one component of nanoparticles. Our simulations demonstrate that the competition between the reaction rate and the diffusive dynamics of nanoparticles governs the implementation of entropy in driving the phase transition from randomly mixed phase to intercalated phase in these interfacial nanoparticle mixtures, which thereby results in diverse kinetic pathways. At low reaction rates, the transition exhibits abrupt jump in the mixing parameter, in a similar way to first-order, equilibrium phase transition. Increasing the reaction rate diminishes the jumps until the transitions become continuous, behaving as a second-order-like phase transition, where a critical exponent, characterizing the transition, can be identified. We finally develop an analytical model of the blob theory of polymer chains to complement the simulation results and reveal essential scaling laws of the entropy-driven phase behaviors. In effect, our results allow for further opportunities to amplify the entropic contributions to the materials design via kinetic control.