Ordered Toroid Structures of Nanoparticles in Self-attractive Semiflexible Polymer/Nanoparticle Composites

By employing dynamic Monte Carlo simulations, we investigate a coil-to-toroid transition of self-attractive semiflexible polymers and the spatial distributions of nanoparticles in self- attractive semiflexible polymer/nanoparticle composites. The conformation of self-attractive semiflexible polymers depends on bending energy and self-attractive interactions between monomers in polymer chains. A three-stage process of toroid formation for self-attractive semiflexible chains is shown： several isolated toroids, a loose toroid structure, and a compact toroid structure. Utilizing the compact toroid conformations of self-attractive semiflexible chains, we can control effectively the spatial distributions of nanoparticles in self-attractive semiflexible polymer nanocomposites, and an unconventional toroid structure of nanoparti- cles is observed.

Stretching strongly confined semiflexible polymer chain

By the so-called wormlike chain （WLC） model in polymer physics envision- ing an isotropic rod that is continuously flexible, the force-extension relations of semi- flexible polymer chains strongly constrained by various confinements are theoretically investigated, including a slab-like confinement where the polymer chains are sandwiched between two parallel impenetrable walls, and a capped nanochannel confinement with a circular or rectangular cross-section where the chains are bounded in three directions. The Brownian dynamics （BD） simulations based on the generalized bead-rod （GBR） model are performed to verify the theoretical predictions.

Stretching instability of intrinsically curved semiflexible biopolymers:A lattice model approach

We apply a Monte Carlo simulation method to lattice systems to study the effect of an intrinsic curvature on the mechanical property of a semiflexible biopolymer.We find that when the intrinsic curvature is sufficiently large,the extension of a semiflexible biopolymer can undergo a first-order transition at finite temperature.The critical force increases with increasing intrinsic curvature.However,the relationship between the critical force and the bending rigidity is structuredependent.In a triangle lattice system,when the intrinsic curvature is smaller than a critical value,the critical force increases with the increasing bending rigidity first,and then decreases with the increasing bending rigidity.In a square lattice system,however,the critical force always decreases with the increasing bending rigidity.In contrast,when the intrinsic curvature is greater than the critical value,the larger bending rigidity always results in a larger critical force in both lattice systems.

Thermal properties of a two-dimensional intrinsically curved semiflexible biopolymer

We study the behaviors of mean end-to-end distance and specific heat of a two-dimensional intrinsically curved semiflexible biopolymer with a hard-core excluded volume interaction. We find the mean square end-to-end distance R2 N∝ Nβ at large N, with N being the number of monomers. Bothβ and proportional constant are dependent on the reduced bending rigidity κ and intrinsic curvature c. The larger the c, the smaller the proportional constant, and 1.5 ≥β ≥ 1. Up to a moderate κ = κc, or down to a moderate temperature T = Tc, β = 1.5, the same as that of a self-avoiding random walk, and the larger the intrinsic curvature, the smaller the κc. However, at a large κ or a low temperature,β is close to 1, and the conformation of the biopolymer can be more compact than that of a random walk. There is an intermediate regime with 1.5 〉β 〉 1 and the transition fromβ = 1.5 toβ= 1 is smooth. The specific heat of the system increases smoothly with increasing κ or there is no peak in the specific heat. Therefore, a nonvanishing intrinsic curvature seriously affects the thermal properties of a semiflexible biopolymer, but there is no phase transition in the system.

Microphase Separation of Semiflexible Ring Diblock Copolymers

Aiming at the difficult problem of solving the conformation statistics of complex polymers, this study presents a novel and concise conformation statistics theoretical approach based on Monte Carlo and Neural Network method. This method offers a new research idea for investigating the conformation statistics of complex polymers, characterized by its simplicity and practicality. It can be applied to more complex topological structure, more higher degree of freedom polymer systems with higher dimensions, theory research on dynamic self-consistent field theory and polymer field theory, as well as the analysis of scattering experimental data. The conformation statistics of complex polymers determine the structure and response properties of the system. Using the new method proposed in this study, taking the semiflexible ring diblock copolymer as an example, Monte Carlo simulation is used to sample this ring conformation to construct the dataset of polymer. The structure factor describing conformation statistics are expressed as continuous functions of structure parameters by neural network supervised learning. This is the innovation of this work. As an application, the structure factors represented by neural networks were introduced into the random phase approximation theory to study the microphase separation of semiflexible ring diblock copolymers. The influence of the ring's topological properties on the phase transition behavior was pointed out.

Conformational Behavior of Single Circular Semiflexible Polyelectrolyte in the Presence of Multivalent Counterions

Langevin dynamics simulations are employed to explore the effects of chain stiffness and electrostatic interaction(EI) on the conformational behavior of a circular semiflexible polyelectrolyte(CSPE) in presence of trivalent counterions.We investigate the effect of bending energy b and the dimensionless Bjerrum length A on the conformational behavior of the CSPE with a fixed chain length.The competition among the EIs,chain stiffness and entropy of the system leads to rich conformations for the CSPE.As the b is less than or equal to 50,The shape of the CSPE changes from a oblate ring to a rod at small A,then to a toroid at intermediate A,and finally to a globule at very large A.However,the globular conformation is not observed for large b.In addition,we find that the number of torus ring increases with A increase,while decreases with b increase.This study should be helpful in gaining insight into the conformational behaviour of charged biopolymer.

Ejection Dynamics of Semiflexible Polymers out of a Nanochannel

Using theoretical analysis and three-dimensional Langevin dynamics simulations, we investigate the influence of chain rigidity on the ejection dynamics of polymers from a nanochannel. We find that there exist two distinct dynamical regimes divided by a critical chain length for both flexible and semiflexible chains. At the short chain regime, semiflexible chains eject faster than flexible chains of the same chain length due to the longer occupying length. In contrast, at the long chain regime, semiflexible chains eject slower than flexible ones as the effective entropic driving force decreases. Based on these results, we propose that the nanochannels could be used to separate flexible and semiflexible chains effectively.

Ordered quasi-two-dimensional structure of nanoparticles in semiflexible ring polymer brushes under compression

Molecular dynamics simulations of a coarse-grained bead-spring model of ring polymer brushes un- der compression are presented. Flexible polymer brushes are always disordered during compression, whereas semiflexible polymer brushes tend to be ordered under sufficiently strong compression. Fur- ther, the polymer monomer density of the semiflexible polymer brush is very high near the brush surface, inducing a peak value of the free energy near the surface. Therefore~ when nanoparticles are compressed in semifiexible ring polymer brushes, they tend to exhibit a closely packed single-layer structure between the brush surface and the impenetrable wall, and a quasi-two-dimensional ordered structure near the brush surface is formed under strong compression. These findings provide a new approach to designing responsive applications.

A Hybrid Immersed Boundary/Coarse-Graining Method for Modeling Inextensible Semi-Flexible Filaments in Thermally Fluctuating Fluids Dedicated to Professor Karl Stark Pister for his 95th birthday

A new and computationally efficient version of the immersed boundary method,which is combined with the coarse-graining method,is introduced for modeling inextensible filaments immersed in low-Reynolds number flows.This is used to represent actin biopolymers,which are constituent elements of the cytoskeleton,a complex network-like structure that plays a fundamental role in shape morphology.An extension of the traditional immersed boundary method to include a stochastic stress tensor is also proposed in order to model the thermal fluctuations in the fluid at smaller scales.By way of validation,the response of a single,massless,inextensible semiflexible filament immersed in a thermally fluctuating fluid is obtained using the suggested numerical scheme and the resulting time-averaged contraction of the filament is compared to the theoretical value obtained from the worm-like chain model.

Particle Distribution Informed by Chain Rigidity in Diblock Copolymer Melts: The Effect of Entropy

We study the effect of chain rigidity on tailoring the nanoparticle locations for neutral and selective particles embedded in the lamellar morphology formed by semiflexible diblock copolymer chains using self-consistent field calculations. The nanoparticles are modeled through a cavity function, and the semiflexible chains are represented by the continuous Kratsky-Porod chain model. In general situation, the nanoparticles prefer to stay at the interface in order to reduce the interface areas and thus the system free energy. However, the particle distribution at the domain center is subtle, and the underlying physics is intrinsically different depending on the polymer flexibility. In the case of flexible chains, the entropy just contributes a constant shift to the free energy when the nanoparticles move around the domain center indicating that the local metastable state if appears at the domain center is wholly attributed to the local minimum in the enthalpy. If the polymers are rigid, the variation of the particle distribution at the domain center has a close relation with the polymer rigidity and nanoparticle size. In the case of strongly rigid polymers with small nanoparticles, a nearly uniform particle distribution at the domain center is observed, while in other cases, a local enhancement of particle distribution there is found. In contrast to the case of flexible chains, further analysis reveals the crucial role of entropy in controlling the shape of particle distributions at the phase domain. Specifically, the local metastable state appears in the domain center is determined by the large entropy there which arises from the weak coupling of bond orientations that allows the polymer chains to be relatively relaxed. When the particle becomes selective, its distribution in the phase domain exhibits a shift almost uniformly rather than changes its profile, and the underlying physics still holds. In all, our study establishes a strong coupling between the chain rigidity and effect of entropy.