Langevin dynamics simulations for the critical adsorption of end-grafted active polymers.

The critical adsorption of end-grafted active polymer chains on an attractive surface is studied using Langevin dynamics simulations. The active polymers are composed of an active Langevin particle located at the head and a sequential passive chain. Results show that the active force exerted by the active head pulls the active polymer away from the surface. Consequently, the adsorption of the active polymer is hindered, and the critical surface attraction strength, , increases proportionally to the square of the active force, Fa2. The increase in depends on the rotation behavior of the active head. Specifically, for the restricted rotating active polymer (RRAP) chain with a longer rotational persistence time as the rotation of the active head is restricted, increases significantly with Fa. On the other hand, for the freely rotating active polymer (FRAP) chain with a shorter rotational persistence time as the rotation of the active head is free, shows a weak dependence on Fa. The results show that the active force has a significantly stronger pulling effect on the RRAP chain than on the FRAP chain. Furthermore, knotted conformations are observed for the adsorbed RRAP chain at large Fa. These knots reduce the adsorption of monomers near the grafted end. In contrast, no knotted conformations are observed for the FRAP chains due to the comparatively weaker pulling effect of the active force.

Adsorption of active polymers on attractive nanoparticles.

The adsorption of active polymers on an attractive nanoparticle (NP) is studied using Langevin dynamics simulations. The active polymers consist of an active Brownian particle (ABP) at the head and a subsequent passive polymer chain. The ABP experiences an active force of magnitude Fa. The interactions between the active polymer and NP are modeled as Lennard-Jones potential with a strength εpn. We find the critical adsorption point εpn* increases with increasing the active force Fa. The increment of εpn*, denoted as Δεpn*, due to Fa can be expressed approximately as Δεpn* ∝ Fa2.5 for the restricted rotating active polymer (RRAP) where the rotation of the head ABP is restricted and Δεpn* ∝ Fa1.7 for the freely rotating active polymer (FRAP) where the ABP rotates freely. Meanwhile, the conformation of the adsorbed polymer, such as adsorbed trains on NP and the tail near the ABP, are also dependent on Fa. When the tail near the ABP is short, the adsorption is significantly affected by the active force. However, when the tail is long, the whole polymer can be viewed as a long tail stretched by the active force and unperturbed adsorption monomers. Simulation results show that the active force has a direct and significant effect on εpn* and the structure of the adsorbed active polymers.

Translocation of two-dimensional active polymers through nanopores using Langevin dynamics simulations.

The translocation of polymers through nanopores is a complex process influenced by various factors. In this study, the translocation behavior of a two-dimensional active polymer chain, comprised of a head active Brownian particle (ABP) and a tail passive polymer chain, through a nanopore is studied using Langevin dynamics simulations. Results show that the effect of the self-propulsion force of the ABP on the translocation differs significantly from the driving force inside the pore for traditional polymer translocations. Specifically, the translocation time τ initially increases with increasing the magnitude fs of the self-propulsion force and then decreases with a further increase in fs. A small fs lowers the potential barrier for the translocation and thus promotes slow translocations, whereas a large fs directly pulls the polymer chain through the nanopore following the scaling relation τ ∝ fs-1. Moreover, two asymptotic scaling relations between τ and polymer length N, τ ∝ Nα, are found, with the exponent α of about 2.5 for small fs or long N and the exponent α of about 1.4 for short active polymers with large fs. We discover that the slow rotation of the ABP accelerates the translocation process.

Langevin Dynamics Study on the Driven Translocation of Polymer Chains with a Hairpin Structure.

The hairpin structure is a common and fundamental secondary structure in macromolecules. In this work, the process of the translocation of a model polymer chain with a hairpin structure is studied using Langevin dynamics simulations. The simulation results show that the dynamics of hairpin polymer translocation through a nanopore are influenced by the hairpin structure. Hairpin polymers can be classified into three categories, namely, linear-like, unsteady hairpin, and steady hairpin, according to the interaction with the stem structure. The translocation behavior of linear-like polymers is similar to that of a linear polymer chain. The time taken for the translocation of unsteady hairpin polymers is longer than that for a linear chain because it takes a long time to unfold the hairpin structure, and this time increases with stem interaction and decreases with the driving force. The translocation of steady hairpin polymers is distinct, especially under a weak driving force; the difficulty of unfolding the hairpin structure leads to a low translocation probability and a short translocation time. The translocation behavior of hairpin polymers can be explained by the theory of the free-energy landscape.

Height-Switching Dynamics of Mixed Polymer Brushes with Polymers of Different Stiffnesses.

Mixed brushes consisting of flexible and semiflexible polymers of the same chain length exhibit a height-switching phenomenon because of rigidity-dependent critical adsorption [Yang et al. Macromolecules 2020, 53, 7369]. Semiflexible polymers stand higher at weak surface attraction (high temperature), but they close to the attractive surface at strong attraction (low temperature). In this work, the height-switching dynamics of the mixed polymer brushes is studied by Metropolis Monte Carlo simulation. The height-switching time is calculated by a sudden change in the surface attraction. Two surface attraction change modes, i.e., the weak-to-strong mode where the attraction is changed from weak to strong and the strong-to-weak mode where it is changed from strong to weak, are investigated. Simulation results show that the height-switching time is related to the grafting density, the polymer stiffness, and surface attraction change mode. We find that the height-switching time is significantly decreased for the strong-to-weak mode. And our results also show that the height switching in the mixed polymer brushes is reversible.

Simulation study on the effect of polydisperse nanoparticles on polymer diffusion in crowded environments.

The diffusion of polymer chains in a crowded environment with large and small immobile, attractive nanoparticles (NPs) is studied using Langevin dynamics simulations. For orderly distributed NPs on the simple cubic lattice, our results show that the diffusion of polymer chains is dependent on the NP-NP distance or lattice distance d. At low d where NPs are placed closely, subdiffusion occurs at a sufficiently high polydispersity of NPs, PD. Both the apparent diffusion coefficient and subdiffusion exponent of polymer chains decrease with increasing PD, attributed to the adsorption of polymers on NP clusters formed by larger NPs. At large d, normal diffusion is always observed, and the diffusion coefficient increases with increasing PD. The reason is that, at high PD, the difference between single large NP adsorption and double large NP adsorption is reduced, which increases the exchange of a polymer between the two adsorption states. Finally, the impact of size polydispersity of NPs on the diffusion of polymer chains in a crowded environment with randomly distributed NPs is also investigated. The results show that the position disorder of NPs enhances the subdiffusion of the system.

Dynamics of a two-dimensional active polymer chain with a rotation-restricted active head.

The dynamics of a two-dimensional active polymer composed of an active Brownian particle (ABP) at the head and a passive polymer chain is investigated using Langevin dynamics simulation. The ABP experiences a self-propulsion force fs and a resistance torque M as the passive polymer chain is bonded to the edge of the ABP. M restricts the rotation of the ABP, and thus the dynamics of the ABP and that of the whole active polymer are influenced significantly. Due to this restriction, the persistence time τr, which characterizes the random rotation of the ABP, is increased significantly and changes non-monotonically with the rotational friction coefficient ηr. Our simulation results show that the effect of M on the dynamics of the active polymer can be characterized mainly by the change of τr. Moreover, the propulsive diffusion coefficient DP of the whole polymer chain originated from the self-propulsion force can be described by a scaling relation DP ∝ fs2τr/N2ηt2 with ηt the translational friction coefficient and N the polymer length. Our results show that the diffusion is promoted by the resistance torque M and τr is a key factor for the diffusion of active polymers.

A simulation study on the subdiffusion of polymer chains in crowded environments containing nanoparticles.

Polymer chains in crowded environments often show subdiffusive behavior. We adopt molecular dynamics simulations to study the conditions for the subdiffusion of polymer chains in crowded environments containing randomly distributed, immobile, attractive nanoparticles (NPs). The attraction is strong enough to adsorb polymer chains on NPs. The results show that subdiffusion occurs at a low concentration of polymer chains (cp). A transition from subdiffusion to normal diffusion is observed when cp exceeds the transition concentration , which increases with increasing concentration of NPs while decreases with increasing size of NPs. The high concentration and small size of NPs exert a big effect on the subdiffusion of polymer chains. The subdiffusive behavior of polymer chains can be attributed to the strong adsorption of polymer chains on the attractive NPs. For the subdiffusion case, polymer chains are adsorbed strongly on multiple NPs, and they diffuse via the NP-exchange diffusion mechanism. However for the normal diffusion case, polymer chains are either free or weakly adsorbed on one or a few NPs, and they diffuse mainly via the adsorption-and-desorption diffusion mechanism.

Simulation study on the critical adsorption and diffusion of polymer chains on heterogeneous surfaces with random adsorption sites.

The critical adsorption and diffusion of a linear polymer chain on a heterogeneous surface with randomly distributed adsorption sites are studied using dynamic Monte Carlo simulations. Results show that the critical fraction of the adsorption sites at which critical adsorption takes place decreases exponentially with the increasing polymer-surface attraction strength and, at the same time, decreases with the increasing intra-polymer attraction strength. For adsorbed polymers with large intra-polymer attraction strength, we also find an adsorption-induced structural transition from a three-dimensional compact globule to a two-dimensional compacted pancake with an increasing fraction of adsorption sites. Anomalous sub-diffusion is observed for the adsorbed polymer diffusion on heterogeneous surfaces, in contrast to the normal diffusion on a homogeneous surface. The polymer on heterogeneous surfaces shows larger fluctuation in the total surface attraction energy and a longer waiting time.

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 effect of nanoparticle size on the glass transition temperature of polymer nanocomposites.

The effect of the size of nanoparticles, σNP, on the glass transition temperature, Tg, of polymer nanocomposites is studied by using molecular dynamics simulations. The variation of Tg with σNP shows two distinct behaviours for polymer nanocomposites at low and high volume fractions of nanoparticles (fNP). At a low fNP, Tg decays almost exponentially with σNP, whereas at a high fNPTg shows a complex behaviour: it initially increases and then decreases with increasing σNP. The decrease in Tg with σNP is due to the significant decrease of adsorbed polymer monomers, while the increase in Tg with σNP is attributed to the slower diffusion of larger nanoparticles. We have also investigated the diffusion and relaxation of polymer chains at a temperature above Tg for both low and high fNPs. The diffusion constant and relaxation time of polymer chains are highly consistent with the behaviour of Tg.

A novel shift in the glass transition temperature of polymer nanocomposites: a molecular dynamics simulation study.

The effect of the loading of nanoparticles on the glass transition temperature, Tg, of polymer nanocomposites is studied by using molecular dynamics simulations. Tg is estimated from the variation of system volume with temperature and the temperature-dependent diffusion of the polymer described by the Vogel-Fulcher-Tammann law. The estimated values of Tg from the two methods are consistent with each other. Results show that Tg can be regulated by changing the volume fraction of nanoparticles, fNP. A novel shift in Tg is observed, that is, Tg increases with fNP at fNP < , while it decreases with increasing fNP at fNP > . The basic mechanism behind the novel shift in Tg is the competition between the attraction of nanoparticles towards polymer chains and the fast diffusion of nanoparticles. The increase in Tg at low fNP is due to the attraction of nanoparticles, whereas the decrease in Tg at high fNP is attributed to the fast diffusion of nanoparticles. The diffusion of the polymer above Tg is also investigated. The diffusion of the polymer decreases with increasing fNP below and increases with fNP above , in agreement with the variation of Tg.

Dynamic behaviors of interfacial water on the self-assembly monolayer (SAM) heterogeneous surface.

Dynamic behaviors of water molecules near the surface with mixed hydrophobic and hydrophilic areas are studied by molecular dynamics simulation. More specifically, the diffusion coefficient and hydrogen bond lifetime of interfacial water on the self-assembly monolayer composed of hydrophobic and hydrophilic groups and their dependence on the mixing ratio are studied. The diffusion dramatically slows down, and the hydrogen bond lifetime considerably increases when a few hydrophilic groups are added to the hydrophobic surface. When the percentage of hydrophilic groups increases to 25%, the behavior of interfacial water is similar to the case of the pure hydrophilic surface. The sensitivity to the hydrophilic group can be attributed to the fact that the grafted hydrophilic groups can not only retard the directly bound water molecules but also affect indirectly bound water by stabilizing hydrogen bonds among interfacial water molecules.

Diffusivity and glass transition of polymer chains in polymer nanocomposites.

The diffusivity and glass transition of polymer chains in polymer nanocomposites are studied by using dynamic Monte Carlo simulation. Nanoparticles are modeled as immobile and distributed in a cubic lattice in the system. The diffusion coefficient D of polymer chains is reduced, while the glass transition temperature Tg is increased by nanoparticles. Our results show that the effect of nanoparticles can be summarized as D = D0[1 - exp(-α·ID/2Rg)] and Tg = Tg,0[1 - exp(-α·ID/2Rg)]-1, with D0 and Tg,0 being the diffusion coefficient and the glass transition temperature in the absence of nanoparticles, Rg the radius of gyration of polymer chains, and ID the surface spacing between nearest-neighbor nanoparticles. The parameter α that governs the dynamics of polymer chains decreases with increasing nanoparticles' size or decreasing the temperature. Our results also show that smaller nanoparticles exert a stronger influence on the polymer dynamics at the same concentration of nanoparticles, whereas larger nanoparticles show a stronger effect at the same ID.

Trapped and non-trapped polymer translocations through a spherical pore.

The polymer translocation through a spherical pore is studied using the Langevin dynamics simulation. The translocation events are classified into two types: one is the trapped translocation in which the entire polymer is trapped in the pore and the other is the non-trapped translocation where the pore cannot hold the whole polymer. We find that the trapped translocation is favored at large spheres and small external voltages. However, the monomer-pore attraction would lead to the non-monotonic behavior of the trapped translocation possibility out of all translocation events. Moreover, both the trapped and non-trapped translocation times are dependent on the polymer length, pore size, external voltage, and the monomer-pore attraction. There exist two pathways for the polymer in the trapped translocation: an actively trapped pathway for the polymer trapped in the pore before the head monomer arrives at the pore exit, and a passively trapped pathway for the polymer trapped in the pore while the head monomer is struggling to move out of the pore. The studies of trapped pathways can provide a deep understanding of the polymer translocation behavior.

Simulation study on the migration of diblock copolymers in periodically patterned slits.

The forced migration of diblock copolymers (ANABNB) in periodically patterned slits was investigated by using Langevin dynamics simulation. The lower surface of the slit consists of stripe α and stripe ß distributed in alternating sequence, while the upper one is formed only by stripe ß. The interaction between block A and stripe α is strongly attractive, while all other interactions are purely repulsive. Simulation results show that the migration of the diblock copolymer is remarkably dependent on the driving force and there is a transition region at moderate driving force. The transition driving force ft, where the transition region occurs, decreases monotonously with increasing length of block B (NB) but is independent of the polymer length and the periodic length of the slit, which is interpreted from the free energy landscape of diblock copolymer migration. The results also show that periodic slits could be used to separate diblock polymers with different NB by tuning the external driving force.

Static and dynamic properties of a semiflexible polymer in a crowded environment with randomly distributed immobile nanoparticles.

Molecular dynamic simulations are performed for semiflexible polymers in a crowded environment with randomly distributed immobile nanoparticles (NPs). Herein, the effects of chain stiffness (kθ), polymer-NP interaction (εPN), and concentration of NPs (CNP) on the static and dynamic properties of the polymers have been studied. The mean square radius of gyration RG2 can be increased, decreased, or unchanged depending on these three variables. For a fully flexible polymer (kθ = 0), RG2 changes non-monotonously with εPN and CNP. However, for a semiflexible polymer (kθ = 10 with its persistence length larger than the inter-particle distance of the NPs), RG2 decreases monotonously or remains unchanged with an increase in εPN or CNP; this indicates the softening of polymer by the NPs. Moreover, the translational diffusion and rotation of the polymer are retarded by the NPs. Subdiffusion is observed for both the fully flexible polymer and semiflexible polymer at a sufficiently large εPN. The effect of NPs on the translational diffusion is more obvious for the fully flexible polymer because more monomers are in contact with the NPs in the fully flexible polymer. In contrast, the effect of NPs on rotation is more obvious for the semiflexible polymer because it is in contact with more NPs. Furthermore, the rotational relaxation time τR of the semiflexible polymer increases faster with an increase in εPN or CNP than that of the fully flexible polymer.

Monte Carlo simulation on the dynamics of a semi-flexible polymer in the presence of nanoparticles.

The dynamics of a semi-flexible polymer chain in the presence of periodically distributed nanoparticles is simulated by using off-lattice Monte Carlo simulations. For repulsive or weak attractive nanoparticles, the dynamics are slowed down monotonically by increasing the chain stiffness kθ or decreasing the inter-particle distance d. For strong attractive nanoparticles, however, the dynamics show nonmonotonic behaviors with kθ and d. An interesting result is that a stiff polymer may move faster than a flexible one. The underlying mechanism is that the nanoparticle's attraction is weakened by the chain stiffness. The nonmonotonic behavior of the polymer's dynamics with kθ is explained by the competition between the weakening effect of the chain stiffness on the nanoparticle's attraction and the intrinsic effect of chain stiffness which reduces the dynamics of the polymer. In addition, the nonmonotonic behavior of the polymer's dynamics with d is explained by the competition between the nanoparticle-exchange motion of the polymer dominated at small d and the desorption-and-adsorption motion at large d. The excluded volume effect of the nanoparticles plays a more important role for stiffer polymers as the attraction of the nanoparticles is weakened by the chain stiffness.

Theoretical study on the polymer translocation into an attractive sphere.

We report a non-sampling model, combining the blob method with the standard lattice-based approximation, to calculate the free energy for the polymer translocation into an attractive sphere (i.e., spherical confined trans side) through a small pore. The translocation time is then calculated by the Fokker-Planck equation based on the free energy profile. There is a competition between the confinement effect of the sphere and the polymer-sphere attraction. The translocation time is increased due to the confinement effect of the sphere, whereas it is reduced by the polymer-sphere attraction. The two effects offset each other at a special polymer-sphere attraction which is dependent on the sphere size, the polymer length, and the driving force. Moreover, the entire translocation process can be divided into an uncrowded stage where the polymer does not experience the confinement effect of the sphere and a crowded stage where the polymer is confined by the sphere. At the critical sphere radius, the durations of the two (uncrowded and crowded) stages are the same. The critical sphere radius R* has a scaling relation with the polymer length N as R* ∼ Nß. The calculation results show that the current model can effectively treat the translocation of a three-dimensional self-avoiding polymer into the spherical confined trans side.

Spontaneous protein desorption from self-assembled monolayer (SAM)-coated gold nanoparticles.

When nanoparticles enter blood or other biological fluids, they tend to contact with a variety of proteins which may hamper their application and even bring adverse impacts. Such nonspecific protein binding is usually weak and proteins reach dynamic equilibrium between adsorption and desorption. Studies on the spontaneous desorption of weakly bound proteins should not only be helpful to enrich our understanding about such nonspecific interactions but also shed light on the strategy to avoid nonspecific binding of proteins. Here, we use molecular dynamics simulations to investigate the interactions of human serum albumin with the self-assembled monolayer (SAM)-coated gold(111) surface, a typical facet of various gold nanoparticles. The response of the protein interfacial behavior to solution pH, especially the spontaneous desorption, is studied. When the solution pH is relatively low, the protein can adsorb to the SAM surface. Such adhesion is attributed to several salt bridges between acidic residues and SAM's protonated groups, and there are water molecules distributed under the adsorbed protein, i.e. interlayer water. Interestingly, the increase of the solution pH reduces the binding affinity of the protein, which engenders the lateral diffusion of the protein and the increase of interlayer water. When the solution pH is further increased, the enhanced lateral diffusion of the protein and the growth of interlayer water disrupt the formation of salt bridges between the protein and the SAM, and the protein progressively dissociates from the SAM. The spontaneous desorption process of the protein and the corresponding mechanisms illustrated in this work may be helpful to develop an antifouling surface and enhance the biosafety of nanomaterials.