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Knotted polymers have been found in biological systems, such as DNA knotting in phage capsids. Many biochemical reactions involve a close spatial contact between two reactive sites of a biopolymer and are often limited by the diffusive encounter rate of reacting groups. Therefore, the intrachain reaction is significantly regulated by topological constraints due to knotting. We investigated the reversible intrachain reaction of a knotted flexible polymer by Monte Carlo simulation and demonstrated that the intraknot association−dissociation crossover is mainly governed by both the essential crossing number and the topological similarity. Depending on the contour separation between reactive sites, the reaction may display qualitatively different behavior. The knotting (increment of the crossing number) favors the reaction with global contour separation but hinders that with local contour separation. In contrast to the latter case, the topological interactions of the former are clearly classified into differe...

Dynamic light scattering (DLS) along with centrifugation and shaking tests reveal that dissolved gases can significantly affect the aggregation behavior of carbon nanotubes (CNTs) dispersed in water. The CNTs in non-degassed samples form loose, stable networks having the DLS result reminiscent of semidilute polymer solutions, whereas the CNTs in degassed samples aggregate to form Brownian colloids that sediment quickly. Interestingly, the CNTs dispersed in acetone, with or without degassing, also behave like semidilute polymers in DLS experiments. We propose a surface nanobubble-assisted mechanism to explain the observed aggregation behaviors. Our work signifies that dissolved gases may play an important role in determining hydrophobicity and biomolecular functions in aqueous environments.

The deformation of a knotted polymer under a stretching force is studied by modeling the deformed knot as a composite spring system. Our results predict that the elastic modulus of a knotted polymer is larger when compared to an equal-length linear chain. More complex knots are in general stiffer. The increase in stiffness of knots relative to the linear chain is also derived. Monte Carlo simulations are also performed to investigate the stetching of polymer knots. Chain lengths up to N = 82 and prime knots 0 1 , 3 1 , 4 1 , 5 1 , 6 1 and 8 1 are considered. Segregation of the crossings into a small tight region of the knot structure at strong forces is observed. The increase in stiffness predicted by the composite spring model agree well with the simulation data. Our simularion data show that the scaling laws proposed by de Gennes and Pincus for a single linear chain under traction force still hold for the knotted type polymers.

The static properties of a knotted polymer under a stretching force f are studied by Monte Carlo simulations. Chain lengths up to $N=82$ and knot types of ${0}_{1},$ ${3}_{1},$ ${4}_{1},$ ${5}_{1},$ ${6}_{1},$ and ${8}_{1}$ are considered. Our simulation data show that the scaling laws proposed by de Gennes and Pincus for a single linear chain under traction force still hold for the knotted type polymers. That is, the average knot size under a force f scales as $〈{R}_{f}〉\ensuremath{\sim}{R}_{F}^{2}f$ at weak tension forces while for strong forces $〈{R}_{f}〉\ensuremath{\sim}{R}_{F}^{1/\ensuremath{\nu}}{f}^{(1/\ensuremath{\nu})\ensuremath{-}1},$ where ${R}_{F}\ensuremath{\sim}{N}^{\ensuremath{\nu}}{p}^{\ensuremath{-}4/15},$ $\ensuremath{\nu}\ensuremath{\approx}3/5$ is the usual self-avoiding walk exponent and p is a topological invariant representing the aspect ratio (length to diameter) of a knotted polymer at its maximum inflated state. Our results also show that the elastic modulus of a knotted polymer is larger compared to an equal-length linear chain. More complex knots are in general stiffer. A simple composite spring model is employed to derive the increase in stiffness of knots relative to the linear chain, and the results agree well with the simulation data. Segregation of the crossings into a small tight region of the knot structure at strong forces is also observed.

The kinetics of formation and the structure of an adsorbed layer formed by homopolymer chains irreversibly adsorbed onto a flat wall are studied by Monto Carlo simulation using the bond fluctuation model. The rapid initial adsorption is followed by slow kinetics at later times. The surface coverage can be described by an empirical law of stretched exponential approach to the final value. The formation time constant τ can be interpreted by scaling theories of diffusion inside a dense pseudo‐brush. The detailed structure of the layer in a good solvent saturated by the adsorbed chains is also measured. The extension of the layer and the distributions of the loops and tails are also analyzed in light of recent scaling theories.

The dynamics of a single homopolymer chain strongly adsorbed on a flat surface is investigated by Monte Carlo simulation using the bond-fluctuation model. Previously observed anomalous glassy dynamics at low temperatures [Phys. Rev. E 49, 5420 (1994)] is revisited in detail. We also study the dynamics of a polymer chain confined in a narrow slit of width of a monomer and a modified bond-fluctuation model in three dimensions to include more relevant bond vectors. We show that the previously observed glassy dynamics is due to an artifact of the bond-fluctuation model in three dimensions in that it does not cross-over to the two dimensional bond-fluctuation model with the correct Rouse dynamics. With the proper inclusion of the extra bond vectors P(2,2,0) and P(3,2,0), no glassy behavior appears for the strongly adsorbed chain.

Monodispersed polymer chains under good solvent condition adsorbed on a short‐range attractive impenetrable wall (xy‐plane) is investigated by dynamic Monte Carlo simulation using the bond‐fluctuation model. Chain conformation, segment orientation, fraction of segment adsorbed, surface coverage, chain dimensions and volume fraction profiles are measured for systems with a different number of chains over a wide range of temperatures. An adsorbed layer begins to form at the same adsorption transition temperature Ta of a single chain. However, the second‐order phase transition at Ta in the single chain adsorption is suppressed in the multi‐chain system as is indicated in the disappearance of the peak at Ta in the specific heat. Volume fraction profiles near the adsorption regimes are found to be in agreement with previous theoretical results. For the dynamics, the time auto‐correlation function, relaxation time, and mean square displacements are measured. The auto‐correlation function can be described by a s...

Polymer chains anchored with one end at a hard wall are investigated by Monte Carlo simulations using the bond-fluctuation model. We present results for several different interesting situations: (1) grafted layers in the good and poorer solvent conditions, (2) grafted layers under the effect of shear solvent flow, (3) the formation/desorption kinetics of the grafted layers, and (4) the behavior of a layer of binary mixture of incompatible grafted chains.

Grafted polymer layer composed of a binary mixture of incompatible chains under good solvent condition is simulated using the bond‐fluctuation model. The equilibrium structures of the partially phase separated states are investigated as a function of the incompatibility and relative fraction by monitoring the monomer distribution functions and the chain linear dimensions. For the case of symmetric binary mixtures, we observe the chains of the same type cluster together laterally forming the ‘‘ripple state’’ while the layer state is never observed. For asymmetric mixtures, layer structures with the minority chains staying further away from the grafting plane are observed which is in contrary to previous theoretical predictions. The heights of both the minority and majority chains in the layer state are shown to be proportional to their chain lengths.

Linear chain surfactants in a densely packed arrangement (such as alkane chains in lipid monolayers in the “uniform tilt” structures) are described by a crude coarse-grained model where the endgroups grafted on the interface form a regular lattice and the chains are described by the bond fluctuation model with chains containing N = 4 effective monomers only. Square-well interactions between the monomers are studied for both the attractive and repulsive case for three choices of the interaction range. None of these models exhibits a structure with uniform tilt. For attractive interactions the last bond has a strong tendency to fold back thus leading to a very high density close to the interface. Only when an intrachain-potential favoring stiff chain configurations also is included one can obtain configurations with uniform tilt order. Although related models (with much longer chain lengths and lower grafting densities) are very useful for the study of polymer brushes, the present case of very short chains in a high-density state clearly is plagued by various lattice artefacts and it is concluded that for modelling linear chain surfactants one should use an off-lattice model even on a coarse-grained level.

Polymer chains anchored with one end at a hard wall under variable solvent conditions are investigated by Monte Carlo simulations using the bond- fluctuation model. Detail information on the structural properties are obtained above, at, and below the Θ-point and discussed in terms of the appropriate theories. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. For the dynamics at the Θ-point, both the relaxation time of the chain configuration and the mean-square time displacement are studied. At temperatures distinctly below the Θ-point, we find that the layer develops considerable lateral inhomogeneity in its density, which has not been predicted by previous theories.

By introducing a head‐group energy of adsorption with the grafting surface, we simulate the grafted polymer layer including chain exchange with the bulk solution using the bond‐fluctuation model. The kinetics of adsorption is relatively rapid in short times and becomes much slower in later time as the layer is formed. The self‐adjusted surface coverage is measured for different values of chain lengths and head‐group energies. We also found that the polymer chains in a grafted layer are replaced by introducing shorter chains of identical head groups, which is also observed in recent experiments.

A model with solution viscoelasticity is proposed to explain the ratchetlike stretching of DNA by a symmetric ac electric field in polymer solutions. In this model, DNA is stretched by the interaction between the fluid elasticity and the oscillatory flow induced by DNA. Predictions of the model are confirmed by DNA stretching experiments performed in various polymer solutions and the corresponding rheological measurements of the solutions. In particular, experiments have verified that a net migration of stretched DNA in polymer solutions can be induced by a zero-mean asymmetric ac electric field. This last finding cannot be explained by other existing models.

Using the bond-fluctuation model, Monte Carlo simulations are performed for polymer brushes composed of chains of two different chain lengths under good solvent condition. Profiles of monomer density and free end density, chain linear dimensions, and average monomer position along a chain are studied. Quantities measured in the simulations are derived from the analytic self-consistent field (SCF) theory and compared with the simulation data. The structural properties can be quite accurately described by the theory only when both the long and short chains are stretched

The bond fluctuation model of polymer chains on lattices is used to study layers of polymers anchored with one end at a hard wall, assuming good solvent conditions and repulsive interactions between the monomers and the wall. Chain lengths from N=10 to N=80 and grafting densities σ from 0.025 to 0.20 are considered, both for the ‘‘quenched’’ case, where the anchor points are kept fixed at randomly chosen surface sites, and the ‘‘annealed’’ case, where lateral diffusion of the anchored ends at the wall is considered. Profiles of monomer density and free end density, chain linear dimensions parallel and perpendicular to the wall, as well as corresponding mean square displacements of inner and end monomers are studied and discussed in the light of current theoretical predictions, and it is shown that most of these properties can be understood in terms of appropriate scaling concepts. Both the relaxation of the total chain configurations and the time dependence of monomer mean square displacements are studied...

The behavior of a strongly charged polymer adsorbed on an oppositely charged surface of low-dielectric constant is formulated by the functional integral method. By separating the translational, conformational, and fluctuational degrees of freedom, the scaling behaviors for both the height of the polymer and the thickness of the diffusion layer are determined. Unlike the results predicted by scaling theory, we identified the continuous crossover from the weak compression to the compression regime. All teh analytical results are found to be consistent with Monte-Carlo simulations. Finally, an alternative (operational) definition of a charged polymer adsorption is proposed., Comment: 4 pages, 3 figures

Turbulent drag reduction induced by � -DNA is studied. The double-stranded DNA is found to be a good drag reducer when compared with the other normal linear polymers. However, this drag reducing power disappears when the DNA denatures to form two single-strand molecules. Mechanical degradation of DNA is also different from that of the normal linear-chain polymers: DNA is always cut in half by the turbulence. Our results suggest that the mechanism for turbulent degradation of DNA is different from that of the normal flexible long-chain polymers. microscales of the turbulent flow. Since the length of the polymers traditionally used in DR studies are much smaller than the microscales of the turbulence, the inter- actions between the polymer and the flow might be quite different. Second, a large change in molecular properties of DNA can be induced by a change in pH or temperature. At the appropriate pH or temperature, a DNA molecule will change from its double-stranded (ds) natural state to its denatured state of two single-strand (ss) molecules. This configurational change might help to probe the details of the DR phenomenon. Hand and Williams (8) reported in a brief note that the natural state of DNA is preferable to the denatured state for maximum drag reduction in an experiment using calf- thymus DNA with pH control. But no explanation was given. In our experiments, we find that the same phenom- ena can be observed in our system, and this change in DR behavior of the DNA can be attributed to the change in mechanical properties of the two different states of DNA. It is found that the drag reducing power of the molecule is controlled mainly by the stiffness of the molecule. Dif- ferent from other linear polymers, our MMD results in- dicate that dsDNA molecules are always cut exactly in half by the turbulence even when the microscale of the turbu- lence is smaller than the size of the DNA. This simple degradation suggests that the dynamics of degradation of dsDNA is different from those of normal linear chain polymers. It is possible that the difference is due to the long persistence length of the double helix. Furthermore, the simple degradation and monodispersity of DNA allow the construction of a simple degradation model. From this model, various physical parameters not easily accessible or reported before can be estimated.

A polymer chain under good solvent condition near a short-range attractive impenetrable wall (xy plane) is investigated by dynamic Monte Carlo simulation using the bond-fluctuation model. For the statics, the adsorption transition is clearly observed and the adsorption transition temperature, ${\mathit{T}}_{\mathit{a}}$ for this model is determined. Chain conformation, segment orientation, fraction of segment adsorbed, chain dimensions, and layer thickness as a function of temperature and distance away from the wall are studied and discussed. Our results for the scaling behavior of the radii of gyration and fraction of segment adsorbed confirm previous analytical theories and static simulation results. We also obtain an estimate for the critical exponent which is consistent with previous static simulations of self-avoiding walks. Furthermore, our data on specific heat show another peak, apart from the one at ${\mathit{T}}_{\mathit{a}}$, at a temperature ${\mathit{T}}_{2}$ distinctively below ${\mathit{T}}_{\mathit{a}}$, suggesting a second transition. As for the dynamics, both the time autocorrelation function and the time dependence of the mean square displacement of the center of mass of the chain are studied. We find that the time autocorrelation function in the adsorbed state can be fitted to a stretched exponential form and the relaxation time starts to diverge for temperatures below ${\mathit{T}}_{2}$. The diffusion coefficients for motions parallel (${\mathit{D}}_{\mathit{z}}$) and perpendicular (${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$) to the z axis are also extracted. ${\mathit{D}}_{\mathit{z}}$ shows a sharp drop as the temperature is lowered below the adsorption transition temperature while ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$ remains constant until around ${\mathit{T}}_{2}$ at which it decreases abruptly. Furthermore we also observe that the lateral diffusion (${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$) crosses over from a Rouse behavior (${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\sim}${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$) to a ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\sim}${\mathit{N}}^{\mathrm{\ensuremath{-}}2}$ behavior for temperatures below ${\mathit{T}}_{2}$. These results are discussed in terms of the appropriate scaling theories.

Turbulent drag reduction efficiencies (%DR) of aqueous poly (ethylene oxide) solutions at various distances τ≡(Tθ−T)/Tθ away from the theta temperature (Tθ) are studied. It is found that only the long-time behavior of %DR of the system is sensitive to τ in that %DR decays faster for systems closer to the theta-point. Usually, this faster decay is attributed to the faster mechanical molecular degradation (MMD) of polymers in bad solvents produced by turbulence. However, temperature quenches experiments close to Tθ show that the apparent faster decrease in %DR for polymers closer to Tθ is not due to MMD but rather because of the shrinking of the polymer after they have been injected into the turbulent flow. The relative insensitivity of the initial maximum %DR can be understood if Tθ is considered as a function of the flow.

The bond-fluctuation model of polymer chains has been used to study layers of end-grafted polymers anchoring at repulsive walls for a broad range of chain length, grafting densities and solvent quality. The dynamics of monomers and associated relaxation times are investigated and interpreted by phenomenological theories and scaling arguments. The case is also considered where a chain is cut off from its anchor point and the chain is subsequently expelled from the brush. Both the velocity with which the chain leaves the brush and the associated conformational changes (chain contraction etc.) are analysed and interpreted in terms of recent theoretical concepts.