Translocation of a looped polymer threading through a nanopore.

Recent experiments reported that the complicated translocation dynamics of a looped DNA chain through a nanopore can be detected by ionic current blockade profiles. Inspired by the experimental results, we systematically study the translocation dynamics of a looped polymer, formed by three building blocks of a loop in the middle and two tails of the same length connected with the loop, by using Langevin dynamics simulations. Based on two entering modes (tail-leading and loop-leading) and three translocation orders (loop-tail-tail, tail-loop-tail, and tail-tail-loop), the translocation of the looped polymer is classified into six translocation pathways, corresponding to different current blockade profiles. The probabilities of the six translocation pathways are dependent on the loop length, polymer length, and pore radius. Moreover, the translocation times of the entire polymer and the loop are investigated. We find that the two translocation times show different dependencies on the translocation pathways and on the lengths of the loop and the entire polymer.

A simulation study on the self-assembly of rod-coil-rod triblock copolymers within nanoslits.

Self-assembly of rod-coil-rod R4C12R4 triblock copolymers within a nanoslit is investigated by using dissipative particle dynamics simulations. Perpendicular lamellae (L⊥) in nonselective or weak selective slits and parallel lamellae (L∥) in coil-selective slits are observed, and both are almost independent of the slit thickness. However, in the rod-selective slits, the assembled structures are strongly dependent on the slit thickness. With an increase in the slit thickness, we sequentially observe hexagonally packed cylinders (HC) of rod blocks perpendicular to surfaces in thin slits, parallel wavy lamellae, orderly packed alternating cylinders in moderate slits, a mixture structure of HC near surfaces and L⊥ in the interior region, and finally L∥ in wide slits. Our simulation results reveal that the rod block and surface properties play an important role in the assembly of confined rod-coil-rod triblock copolymers. Results also illustrate the competition between the slit thickness and the length scale of lamellae in bulk for the confined copolymers in nanoslits.

Study on the polymer diffusion in a media with periodically distributed nano-sized fillers.

The effect of nano-sized fillers on the equilibrium and dynamical properties of a linear polymer is studied by using off-lattice Monte Carlo simulation. Fillers are arranged periodically in the system with period d and Lennard-Jones interaction between polymer and fillers is considered. Results show that the statistical dimension and dynamical diffusion of the polymer are dependent on the polymer-filler interaction strength ɛ(pf) and the relative size between R(G0) and d, here R(G0) is the radius of gyration of polymer in dilute solution. Normal diffusion of polymer is always observed in the regime 2R(G0) > d. And the diffusion coefficient D is scaled with chain length N as D ~ N(-α), where the exponent α increases with ɛ(pf). Whereas in the regime 2R(G0) < d ≪ Nl0 with l0 the mean bond length of polymer, normal diffusion is observed only at ɛ(pf) < 2, but the polymer will be adsorbed on the fillers and cannot diffuse at ɛ(pf) > 2. In addition, we find that there is a critical interaction strength ɛ*(pf) = 2 in our model system.

Separating different polymers using an interacting nanopore: a Monte Carlo study.

Translocation of a multi-polymer system containing two kinds of polymers, polymer A and polymer B, through an interacting nanopore is studied using dynamic Monte Carlo method. Polymer A and polymer B have different polymer-pore interactions. The probability of one kind of polymer first translocating through a nanopore is dependent on the polymer-pore interactions and the magnitude of driving force for monomers inside the nanopore. At weak driving, there are separation regions where one kind of polymer translocates through the pore always before another kind of polymer. A phase diagram containing separation regions and mixed region is presented. At last, the first-in first-out rule for the polymer translocation is investigated.

Polymer translocation through a gradient channel.

The translocation of polymer through a channel with a gradient interaction between the polymer and the channel is studied. The interaction is expressed by E = E0 + kx, where E0 is the initial potential energy at the entrance, x is the position of the monomer inside the channel, and k is the energy gradient. The mean first passage time τ is calculated by using Fokker-Planck equation for two cases (1) N > L and (2) N < L under the assumption that the diffusion rate D is a constant, here N is the polymer length and L is the length of channel. Results show that there is a minimum of τ at k = k(c) for both cases, and the value kc is dependent on E0 and driving force f. At large f, the scaling relation τ ∼ N is observed for long polymer chains. But the scaling relation is dependent on the energy gradient k for an unforced driving translocation.

Simulation study on the translocation of a partially charged polymer through a nanopore.

The translocation of a partially charged polymer through a neutral nanopore under external electrical field is studied by using dynamic Monte Carlo method on a simple cubic lattice. One monomer in the polymer is charged and it suffers a driving force when it locates inside the pore. Two time scales, mean first passage time τ(FP) with the first monomer restricted to never draw back into cis side and translocation time τ for polymer continuously threading through nanopore, are calculated. The first passage time τ(FP) decreases with the increase in the driving force f, and the dependence of τ(FP) on the position of charged monomer M is in agreement with the theoretical results using Fokker-Planck equation [A. Mohan, A. B. Kolomeisky, and M. Pasquali, J. Chem. Phys. 128, 125104 (2008)]. But the dependence of τ on M shows a different behavior: It increases with f for M < N/2 with N the polymer length. The novel behavior of τ is explained qualitatively from dynamics of polymer during the translocation process and from the free energy landscape.

Escape of polymer chains from an attractive channel under electrical force.

The escape of polymer chains from an attractive channel under external electrical field is studied using dynamical Monte Carlo method. Though the escaping process is nonequilibrium in nature, results show that the one-dimensional diffusion theoretical model based on the equilibrium assumption can describe the dependence of the average escaping time (τ(0)) on the polymer-channel interaction (ɛ), the electrical field (E), the chain length (n), and the channel length (L), qualitatively. Results indicate that both ɛ and E play very important roles in the escaping dynamics. For small ɛ, the polymer chain moves out of the channel continuously and quickly. While for large ɛ, the polymer chain is difficult to move out of long channels as it is trapped for a long time (τ(trap)) when the end segment is near the critical point x(C). These results are consistent with the theoretical results for the free energy profiles at small ɛ and large ɛ, respectively. The dependence of x(C) and τ(trap) on ɛ and E are discussed, and specific relations are obtained. The configurational properties of polymer chain are also investigated during the escaping process.

Monte Carlo simulation on polymer translocation in crowded environment.

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ~ N(1.25) is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed.

Simulation study on the translocation of diblock copolymer A(n)B(n) through interacting nanopores.

Translocation of diblock copolymer A(n)B(n) through an interacting nanopore is studied using a dynamic Monte Carlo method on a simple three-dimensional cubic lattice. The probabilities and translocation times of two translocation orientations of copolymer, orientation A with block A translocating first and orientation B with block B first, are mainly dependent on the segment-pore interactions ε(A) and ε(B). We find that both the probability and the translocation time are larger for the orientation with stronger attraction. The dynamic behaviors of copolymer translocation at different ε(A) and ε(B) can be explained based on the free energy landscapes of homopolymer at different polymer-pore interaction. The results reveal a complicated free energy landscape for copolymer translocation.

Effect of attractive polymer-pore interactions on translocation dynamics.

The effect of attractive polymer-pore interaction on the translocation of polymer chain through a nanopore under electric field is studied by using dynamical Monte Carlo method. The translocation dynamics is remarkably influenced by the interaction. The translocation time for chain moving through nanopore is strongly dependent on the interaction. It reaches minimum at a moderate interaction which is found to be roughly independent of electric field as well as chain length. At weak interaction region, chain spends long time to overcome the barrier of the pore entrance, i.e., the chain is trapped at the entrance. While at strong interaction region, chain is difficult to leave the nanopore, that is, the chain is trapped at the exit of nanopore. The phenomenon is discussed from the view of free energy landscape.

Bioinspired Shear-Flow-Driven Layer-by-Layer in Situ Self-Assembly.

Layer-by-layer (LbL) assembly is widely applied as a coating technique for the nanoscale control of architecture and related properties. However, its translational applications are limited by the time-consuming and laborious nature of the process. Inspired by the blood-clotting process, herein, we develop a shear-flow-driven LbL (SF-LbL) self-assembly approach that accelerates the adsorption rate of macromolecules by mechanically configuring the polymer chain via a coil-stretch transition, which effectively simplifies and speeds the diffusion-controlled assembly process. The structural characteristics and surface homogeneity of the SF-LbL films are improved, and diverse three-dimensional structures can be achieved. Functional SF-LbL-assembled surfaces for corneal modification are successfully fabricated, and the surface of wounded rat corneas and skin can be directly decorated in situ with SF-LbL nanofilms due to the advantages of this approach. Furthermore, in situ SF-LbL self-assembly has promise as a simple approach for the wound dressing for interventional therapeutics in the clinic, as illustrated by the successful in situ fabrication of drug-free layers consisting of chitosan and heparin on the dorsal skin of diabetic mice to rescue defective wound healing. This bioinspired self-assembly approach is expected to provide a robust and versatile platform with which to explore the surface engineering of nanofilms in science, engineering, and medicine.

Dynamic Monte Carlo study on the probability distribution functions of tail-like polymer chain.

The configurational properties of tail-like polymer chains with one end attached to a flat surface are studied by using dynamic Monte Carlo technique. We find that the probability distribution of the free end in z direction P(R(z)) and the density profile rho(z) can be scaled approximately by a factor beta to be a length independent function for both random walking (RW) and self-avoiding walking (SAW) tail-like chains, where the factor beta is related to the mean square end-to-end distance . The scaled P(R(z)) of the SAW chain roughly overlaps that of the RW chain, but the scaled rho(z) of the SAW chain locates at smaller betaz than that of the RW chain.

Translocation of polymers into crowded media with dynamic attractive nanoparticles.

The translocation of polymers through a small pore into crowded media with dynamic attractive nanoparticles is simulated. Results show that the nanoparticles at the trans side can affect the translocation by influencing the free-energy landscape and the diffusion of polymers. Thus the translocation time τ is dependent on the polymer-nanoparticle attraction strength ɛ and the mobility of nanoparticles V. We observe a power-law relation of τ with V, but the exponent is dependent on ɛ and nanoparticle concentration. In addition, we find that the effect of attractive dynamic nanoparticles on the dynamics of polymers is dependent on the time scale. At a short time scale, subnormal diffusion is observed at strong attraction and the diffusion is slowed down by the dynamic nanoparticles. However, the diffusion of polymers is normal at a long time scale and the diffusion constant increases with the increase in V.

Langevin dynamics simulation on the translocation of polymer through α-hemolysin pore.

The forced translocation of a polymer through an α-hemolysin pore under an electrical field is studied using a Langevin dynamics simulation. The α-hemolysin pore is modelled as a connection of a spherical vestibule and a cylindrical ß-barrel and polymer-pore attraction is taken into account. The results show that polymer-pore attraction can help the polymer enter the vestibule and the ß-barrel as well; however, a strong attraction will slow down the translocation of the polymer through the ß-barrel. The mean translocation time for the polymer to thread through the ß-barrel increases linearly with the polymer length. By comparing our results with that of a simple pore without a vestibule, we find that the vestibule helps the polymer enter and thread through the ß-barrel. Moreover, we find that it is easier for the polymer to thread through the ß-barrel if the polymer is located closer to the surface of the vestibule. Some simulation results are explained qualitatively by theoretically analyzing the free-energy landscape of polymer translocation.

Critical adsorption of a flexible polymer confined between two parallel interacting surfaces.

Critical adsorption of a lattice self-avoiding bond fluctuation polymer chain confined between two parallel impenetrable surfaces is studied using the Monte Carlo method. The dependence of the mean contact number on the temperature T and on the chain length N is simulated for a polymer-surface interaction E=-1. A critical adsorption of the polymer is found at T(c)=1.65 for large surface separation distance D>N(ν)b, whereas no critical adsorption is observed for small distance D

Influence of polymer-pore interaction on the translocation of a polymer through a nanopore.

The translocation of a bond fluctuation polymer through an interacting nanopore is studied using dynamic Monte Carlo simulation. A driving force F is applied only for monomers inside the pore. The influence of polymer-pore interaction on the scaling relation τ~N(α) is studied for both unbiased and biased translocations, with τ the translocation time and N the polymer length. Results show that the exponent α is dependent on the polymer-pore interaction. For a noninteracting pore, we find α=2.48 for unbiased translocation and α=1.35 for strong biased translocation; for strong attraction, we find α=2.35 for unbiased translocation and α=1.22 for strong biased translocation. The unbiased translocation corresponds to the low-NF regime whereas the strong biased translocation corresponds to the high-NF regime.

Effects of an attractive wall on the translocation of polymer under driving.

The effects of an attractive wall at the trans side on the translocation of an eight-site bond-fluctuation model (BFM) polymer through a pore in a membrane under driving are simulated by the dynamic Monte Carlo method. The attractive wall shows two contrary effects: its excluded volume effect reduces configuration entropy and thus hinders the translocation of the polymer, while its attraction decreases the energy and thus accelerates the translocation. At a critical polymer-wall interaction ε* ≈- 1, we find that the two effects compensate each other and the translocation time τ is roughly independent of the separation distance between the wall and the pore. The value ε* ≈- 1 is roughly equal to the critical adsorption point for the BFM polymer. Moreover, the value of the critical attraction is roughly independent of chain length N and chemical potential difference Δµ. At last, a scaling relation τ âˆ¼ N(α) is observed for polymer translocation at a high value of NΔµ. Though the translocation time is highly dependent on the polymer-wall interaction and pore-wall separation distance, the exponent α is always about 1.30 ± 0.05 so long as NΔµ is large enough.

Translocation properties of copolymer (A(n)B(m))(l) through an interacting pore.

The translocation of a copolymer (A(n)B(m))(l) through an interacting pore was investigated by Monte Carlo simulation on a three-dimensional cubic lattice. Interactions between monomer A and pore ɛ(A) and between monomer B and pore ɛ(B) were considered. The difference between two translocation orientations, orientation A with monomer A entering the pore first and orientation B with monomer B first, was studied. Both the orientation probability and translocation time are dependent on monomer-pore interactions, block length, and fractions of monomers. The separation of different copolymers using translocation was also discussed. The results were explained qualitatively from the view of the free energy landscape of the copolymer translocation.

The critical adsorption point of self-avoiding walks: a finite-size scaling approach.

The critical adsorption of self-avoiding polymer chain in a simple cubic lattice onto a flat surface is studied with Monte Carlo simulations. The dependence of number of surface contacts M on chain length N and polymer-surface interaction epsilon is investigated by a finite-size scaling approach. We estimate the critical adsorption point epsilon(c)=0.291+/-0.002 and the exponent phi=0.54+/-0.01. The asymptotic behaviors M proportional variant N for epsilon>>epsilon(c) and M proportional variant N(0) for epsilon<

Simulation study on the translocation of polymer chains through nanopores.

The translocation of polymer chains through nanopores is simulated by dynamical Monte Carlo method. The free energy landscape for the translocation of polymer is calculated by scanning method. The dependence of the free energy barrier Fb and the chemical difference Deltamu on the concentration of chains can explain the behavior of polymer translocation at low and high concentration limits. The relationship between Deltamu and the escaping time tau(2) is in good agreement with the theoretical conclusions obtained by Muthukumar [J. Chem. Phys. 111, 10371 (1999)]. Our simulation results show that the relaxation time is mainly dominated by Fb, while the escaping time is mainly dominated by Deltamu.