Adsorption of Semiflexible Polymers in Cylindrical Tubes

Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.

Detachment of semiflexible polymer chains from a substrate: a molecular dynamics investigation

Using Molecular Dynamics simulations, we study the force-induced detachment of a coarse-grained model polymer chain from an adhesive substrate. One of the chain ends is thereby pulled at constant speed off the attractive substrate and the resulting saw-tooth profile of the measured mean force ⟨f⟩ vs height D of the end-segment over the plane is analyzed for a broad variety of parameters. It is shown that the observed characteristic oscillations in the ⟨f⟩-D profile depend on the bending and not on the torsional stiffness of the detached chains. Allowing for the presence of hydrodynamic interactions (HI) in a setup with explicit solvent and dissipative particle dynamics-thermostat, rather than the case of Langevin thermostat, one finds that HI have little effect on the ⟨f⟩-D profile. Also the change of substrate affinity with respect to the solvent from solvophilic to solvophobic is found to play negligible role in the desorption process. In contrast, a changing ratio ε(s)(B)/ε(s)(A) of the binding energies of A- and B-segments in the detachment of an AB-copolymer from adhesive surface strongly changes the ⟨f⟩-D profile whereby the B-spikes vanish when ε(s)(B)/ε(s)(A)<0.15. Eventually, performing an atomistic simulation of (bio)-polymers, we demonstrate that the simulation results, derived from our coarse-grained model, comply favorably with those from the all-atom simulation.

A case of synchronous bleeding from esophageal varices and appendixin a patient with decompensated liver cirrhosis

Lower gastrointestinal bleeding is defined as any bleeding localized distally to Treitz's ligament. The massive bleeding from the appendix is extremely rare and only 21 cases described in the English literature.

CASE PRESENTATION

We present a 61-years-old patient with decompensated liver cirrhosis and bleeding from esophageal varices. He underwent band ligation by Six Shooter (Cook Medical, USA). Due to a massive bleeding from the lower gastrointestinal tract and a rapid decline of hemoglobin level to 3 g/dL, angiography was performed. It revealed a bleeding from distal branches of ileocolic artery, confirmed by the followed computed tomography angiography. The patient underwent appendectomy and was discharged in a good condition on the 6th postoperative day.

CONCLUSION

The synchronous bleeding from upper and lower GIT should be considered, especially in the cases with portal hypertension. The angiography and computed tomography angiography are valuable diagnostic methods, able to localize the bleeding a thus to reduce the morbidity and mortality.

Efficient Separation of Long Polymer Chains by Contour Length and Architecture

On the basis of theoretical considerations and computer experiment, we suggest a new technique for separation of polymer molecules. The method is based on filling an array of nanochannels with macromolecules whereby the subsequent ejection time depends strongly on small differences in the end-to-end distances of elongated configurations inside the nanotubes. In contrast to conventional methods for chromatographic separation, the efficiency of the proposed method increases with growing molecular length of the chains. The method appears promising also for the separation of ring from linear polymer chains.

Structure and dynamics of a polymer melt at an attractive surface

We study the structural and dynamic properties of a polymer melt in the vicinity of an adhesive solid substrate by means of Molecular Dynamics simulation at various degrees of surface adhesion. The properties of the individual polymer chains are examined as a function of the distance to the interface and found to agree favorably with theoretical predictions. Thus, the adsorbed amount at the adhesive surface is found to scale with the macromolecule length as Γ is proportional to √N, regardless of the adsorption strength. For chains within the range of adsorption we analyze in detail the probability size distributions of the various building blocks: loops, tails and trains, and find that loops and tails sizes follow power laws while train lengths decay exponentially thus confirming some recent theoretical results. The chain dynamics as well as the monomer mobility are also investigated and found to depend significantly on the proximity of a given layer to the solid adhesive surface with onset of vitrification for sufficiently strong adsorption.

Thermal decomposition of a honeycomb-network sheet: a molecular dynamics simulation study

The thermal degradation of a graphene-like two-dimensional honeycomb membrane with bonds undergoing temperature-induced scission is studied by means of Molecular Dynamics simulation using Langevin thermostat. We demonstrate that at lower temperature the probability distribution of breaking bonds is highly peaked at the rim of the membrane sheet whereas at higher temperature bonds break at random everywhere in the hexagonal flake. The mean breakage time τ is found to decrease with the total number of network nodes N by a power law τ ∝ N(-0.5) and reveals an Arrhenian dependence on temperature T. Scission times are themselves exponentially distributed. The fragmentation kinetics of the average number of clusters can be described by first-order chemical reactions between network nodes n(i) of different coordination. The distribution of fragments sizes evolves with time elapsed from initially a δ-function through a bimodal one into a single-peaked again at late times. Our simulation results are complemented by a set of 1st-order kinetic differential equations for n(i) which can be solved exactly and compared to data derived from the computer experiment, providing deeper insight into the thermolysis mechanism.

Forced translocation of a polymer: Dynamical scaling versus molecular dynamics simulation

We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of a propagating front of tensile force along the chain backbone, suggested by Sakaue [Phys. Rev. E 76, 021803 (2007); Phys. Rev. E 81, 041808 (2010); Eur. Phys. J. E 34, 135 (2011)]. The driving force is associated with a chemical potential gradient that acts on each chain segment inside the pore. Depending on its strength, different regimes of polymer motion (named after the typical chain conformation: trumpet, stem-trumpet, etc.) occur. Assuming that the local driving and drag forces are equal (i.e., in a quasistatic approximation), we derive an equation of motion for the tensile front position X(t). We show that the scaling law for the average translocation time 〈τ〉 changes from <τ> ∼ N2ν/f1/ν to <τ> ∼ N^1+ν/f (for the free-draining case) as the dimensionless force f[over ̃]R=aNνf/T (where a, N, ν, f, and T are the Kuhn segment length, the chain length, the Flory exponent, the driving force, and the temperature, respectively) increases. These and other predictions are tested by molecular-dynamics simulation. Data from our computer experiment indicate indeed that the translocation scaling exponent α grows with the pulling force f[over ̃]R, albeit the observed exponent α stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations that are neglected in the quasistatic approximation.

Force-induced breakdown of flexible polymerized membrane

We consider the fracture of a free-standing two-dimensional (2D) elastic-brittle network to be used as protective coating subject to constant tensile stress applied on its rim. Using a molecular-dynamics simulation with a Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphenelike hexagonal sheet for different pulling force f and temperature T. We find that bond rupture occurs almost always at the sheet periphery, and the first mean breakage time <τ> of bonds decays with membrane size as <τ> ∝N(-β), where β≈0.50±0.03 and N denotes the number of atoms in the membrane. The probability distribution of bond scission times t is given by a Poisson function W(t)∝t(1/3)exp(-t/<τ>). The mean failure time <τ(r)> necessary to rip off the sheet declines with growing size N as a power law <τ(r)>∝N(-φ(f)). We also find <τ(r)>∝exp(ΔU(0)/k(B)T), where the nucleation barrier for crack formation ΔU(0)∝f(-2), in agreement with Griffith's theory. <τ(r)> displays an Arrhenian dependence of <τ(r)> on temperature T. Our results indicate a rapid increase in crack spreading velocity with growing external tension f.

Fractional Brownian motion approach to polymer translocation: the governing equation of motion

We suggest a governing equation that describes the process of polymer-chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time t after the process has begun, and (ii) a subdiffusive increase of the distribution variance Δ(t) with elapsed time Δ(t)∝t(α). The latter quantity measures the mean-squared number s of polymer segments that have passed through the pore Δ(t)=([s(t)-s(t=0)](2)), and is known to grow with an anomalous diffusion exponent α<1. Our main assumption [i.e., a Gaussian distribution of the translocation velocity v(t)] and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation, which we performed in 3D. We also numerically confirm the predictions made recently that the exponent α changes from 0.91 to 0.55 to 0.91 for short-, intermediate-, and long-time regimes, respectively.

Polymer brushes with nanoinclusions under shear: A molecular dynamics investigation

We use molecular dynamics simulations with a dissipative particle dynamics thermostat to study the behavior of nanosized inclusions (colloids) in a polymer brush under shear whereby the solvent is explicitly included in the simulation. The brush is described by a bead-spring model for flexible polymer chains, grafted on a solid substrate, while the polymer-soluble nanoparticles in the solution are taken as soft spheres whose diameter is about three times larger than that of the chain segments and the solvent. We find that the brush number density profile, as well as the density profiles of the nanoinclusions and the solvent, remains insensitive to strong shear although the grafted chains tilt in direction of the flow. The thickness of the penetration layer of nanoinclusions, as well as their average concentration in the brush, stays largely unaffected even at the strongest shear. Our result manifests the remarkable robustness of polymer brushes with embedded nanoparticles under high shear which could be of importance for technological applications.

Method for wettability characterization based on contact line pinning

We demonstrate an efficient and reliable method for wettability characterization by determining the contact angle theta which a liquid-vapor interface makes with a solid wall. The purpose is to overcome the difficulties, related to the curvature of the liquid-vapor interface, which make measurements of theta rather uncertain, especially on the micro- and nanoscale. The method employs a specially designed slitlike channel in contact with a reservoir whereby the wettability of one of the slit walls is to be examined whereas the other (auxiliary) wall is separated by half into a lyophilic and a lyophobic part so as to pin the incoming fluid and fix the one end of the liquid-vapor interface. In the present work, the physical background of the method is elucidated theoretically while the method's applicability is demonstrated by molecular-dynamics simulation of a typical Lennard-Jones fluid, in contact with an atomistic wall. The wettability of the latter, as described by the corresponding contact angle theta, is accurately determined by variation of the liquid-wall interaction in a very broad interval.

Capillary filling in microchannels with wall corrugations: a comparative study of the Concus-Finn criterion by continuum, kinetic, and atomistic approaches

We study the impact of wall corrugations in microchannels on the process of capillary filling by means of three broadly used methods: computational fluid dynamics (CFD), lattice Boltzmann equations (LBE), and molecular dynamics (MD). The numerical results of these approaches are compared and tested against the Concus-Finn (CF) criterion, which predicts pinning of the contact line at rectangular ridges perpendicular to flow for contact angles of theta > 45 degrees . Whereas for theta = 30, 40 (no flow), and 60 degrees (flow) all methods are found to produce data consistent with the CF criterion, at theta = 50 degrees the numerical experiments provide different results. Whereas the pinning of the liquid front is observed both in the LB and CFD simulations, MD simulations show that molecular fluctuations allow front propagation even above the critical value predicted by the deterministic CF criterion, thereby introducing a sensitivity to the obstacle height.

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (N) of the average translocation time <tau>, the average velocity of the center of mass <vCM>, and the effective radius of gyration <Rg> during the translocation process defined as <tau> approximately Nalpha, <vCM> approximately N(-delta), and Rg approximately Nnu respectively, and the exponent of the translocation coordinate (s-coordinate) as a function of the translocation time <s2(t)> approximately tbeta. We find alpha = 1.36 +/- 0.01, beta = 1.60+/- 0.01 for <s2(t)> approximately taubeta and beta = 1.44 +/- 0.02 for <Deltas2(t)> approximately taubeta, delta = 0.81 +/- 0.04, and nu congruent with nu = 0.59 +/- 0.01, where nu is the equilibrium Flory exponent in 3D. Therefore, we find that <tau> approximately N1.36 is consistent with the estimate of <tau> approximately <Rg>/<vCM>. However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent alpha = 1.36 +/- 0.01 < 1 + nu. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the "cis" and "trans" parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.

Pulling an adsorbed polymer chain off a solid surface

The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain-ends is investigated. We perform our study in the "fixed height" statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain-end is kept fixed at height h over the solid plane at different adsorption strength [Formula: see text]. The phase diagram in the h-[Formula: see text] plane is calculated both analytically and by Monte Carlo simulations. We demonstrate that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than f is used as an independent control parameter.

Polymer translocation through a nanopore: a showcase of anomalous diffusion

We investigate the translocation dynamics of a polymer chain threaded through a membrane nanopore by a chemical potential gradient that acts on the chain segments inside the pore. By means of diverse methods (scaling theory, fractional calculus, and Monte Carlo and molecular dynamics simulations), we demonstrate that the relevant dynamic variable, the transported number of polymer segments, s(t), displays an anomalous diffusive behavior, both with and without an external driving force being present. We show that in the absence of drag force the time tau, needed for a macromolecule of length N to thread from the cis into the trans side of a cell membrane, scales as tauN(2/alpha) with the chain length. The anomalous dynamics of the translocation process is governed by a universal exponent alpha= 2/(2nu + 2 - gamma(1)), which contains the basic universal exponents of polymer physics, nu (the Flory exponent) and gamma(1) (the surface entropic exponent). A closed analytic expression for the probability to find s translocated segments at time t in terms of chain length N and applied drag force f is derived from the fractional Fokker-Planck equation, and shown to provide analytic results for the time variation of the statistical moments <s(t)> and <s(2) (t)>. It turns out that the average translocation time scales as tau proportional, f(-1)N(2/alpha-1). These results are tested and found to be in perfect agreement with extensive Monte Carlo and molecular dynamics computer simulations.

The escape transition of a polymer: a unique case of non-equivalence between statistical ensembles

A flexible polymer chain under good solvent conditions, end-grafted on a flat repulsive substrate surface and compressed by a piston of circular cross-section with radius L may undergo the so-called "escape transition" when the height of the piston D above the substrate and the chain length N are in a suitable range. In this transition, the chain conformation changes from a quasi-two-dimensional self-avoiding walk of "blobs" of diameter D to an inhomogeneous "flower" state, consisting of a "stem" (stretched string of blobs extending from the grafting site to the piston border) and a "crown" outside of the confining piston. The theory of this transition is developed using a Landau free-energy approach, based on a suitably defined (global) order parameter and taking also effects due to the finite chain length N into account. The parameters of the theory are determined in terms of known properties of limiting cases (unconfined mushroom, chain confined between infinite parallel walls). Due to the non-existence of a local order parameter density, the transition has very unconventional properties (negative compressibility in equilibrium, non-equivalence between statistical ensembles in the thermodynamic limit, etc.). The reasons for this very unusual behavior are discussed in detail. Using Molecular Dynamics (MD) simulation for a simple bead-spring model, with N in the range 50<or=N<or=300, a comprehensive study of both static and dynamic properties of the polymer chain was performed. Even though for the considered rather short chains the escape transition is still strongly rounded, the order parameter distribution does reveal the emerging transition clearly. Time autocorrelation functions of the order parameter and first passage times and their distribution indicate clearly the strong slowing down associated with the chain escape. The theory developed here is in good agreement with all these simulation results.

Comment on 'Anomalous dynamics of unbiased polymer translocation through a narrow pore' and other recent papers by D Panja, G Barkema and R Ball

In a recent publication of Panja et al (2007 J. Phys.: Condens. Matter 19 432202) they suggested a new interpretation of the translocation problem of polymer chain threading through a narrow pore. Here we point out some contradictions and inconsistencies in this treatment which question the plausibility of the obtained results.

Polymer desorption under pulling: a dichotomic phase transition

The structural properties and phase behavior of a self-avoiding polymer chain on an adhesive substrate, subject to pulling at the chain end, are described by means of a grand canonical ensemble approach. We derive analytical expressions for the probability distributions of the basic structural units of an adsorbed polymer, such as loops, trains, and tails, in terms of the adhesive potential and applied pulling force f . In contrast to conventional, f=0 , polymer adsorption, the chain detachment transition under pulling turns out to be of first (rather than second) order, albeit it is dichotomic, i.e., no coexistence of different phase states exists. Also, the hitherto controversial value of the critical adsorption exponent varphi is found to depend essentially on the degree of interaction between different loops so that 0.34< or =varphi< or =0.59 . The theoretical predictions are verified by means of extensive Monte Carlo simulations.

Adsorption kinetics of a single polymer on a solid plane

We study analytically and by means of an off-lattice bead-spring dynamic Monte Carlo simulation model the adsorption kinetics of a single macromolecule on a structureless flat substrate in the regime of strong physisorption. The underlying notion of a "stem-flower" polymer conformation, and the related mechanism of "zipping" during the adsorption process are shown to lead to a Fokker-Planck equation with reflecting boundary conditions for the time-dependent probability distribution function (PDF) of the number of adsorbed monomers. The theoretical treatment predicts that the mean fraction of adsorbed segments grows with time as a power law with a power of (1+nu)-1, where nu approximately 3/5 is the Flory exponent. The instantaneous distribution of train lengths is predicted to follow an exponential relationship. The corresponding PDFs for loops and tails are also derived. The complete solution for the time-dependent PDF of the number of adsorbed monomers is obtained numerically from the set of discrete coupled differential equations and shown to be in perfect agreement with the Monte Carlo simulation results. In addition to homopolymer adsorption, we also study regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.

Molecular dynamics simulations of capillary rise experiments in nanotubes coated with polymer brushes

The capillary filling of a nanotube coated with a polymer brush is studied by molecular dynamics simulations of a coarse-grained model, assuming various conditions for the fluid-wall and fluid-brush interactions. Whereas the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers that form the brush coating are described by a standard bead-spring model. Our experiments reveal that capillary filling is observed even for walls that would not be wetted by the fluid, provided the polymer brush coating itself wets. Generally, it is found that the capillary rise always proceeds through a t1/2 law with time t while the underlying molecular mechanism differs for wettable and nonwettable walls. For wettable walls, fluid imbibition is compatible with the Lucas-Washburn mechanism whereby the total influx of matter drops steadily with growing chain length N and the meniscus speed goes through a minimum at intermediate chain lengths. Moreover, because of flow, the polymer brush reorganizes its structure by forming a dense plug of chain segments under the meniscus that follows the meniscus in its motion. When the tube wall does not wet, one observes no meniscus formation for short chains although the fluid seeps through the wet brush. For a brush coating with longer chains, axial segregation between the brush segments and the fluid occurs by a kind of diffusive spreading, reminiscent of invasion percolation transport in a random medium, leading to the formation of a moving meniscus. For even longer chains that reach the tube axis, the rise of a meniscus with vanishing curvature-like imbibition in a porous medium is observed to take place.

Polymer brushes in solvents of variable quality: Molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.

Capillary rise in nanopores: molecular dynamics evidence for the Lucas-Washburn equation

When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by molecular dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a (time)1/2 law. For the polymer melt, however, we find that the capillary flow exhibits a slip length delta, comparable in size with the nanotube radius R. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification of the Lucas-Washburn law which takes explicitly into account the slip length delta. We also demonstrate that the velocity field of the rising fluid close to the interface is not a simple diffusive spreading.

Polymer brushes in cylindrical pores: simulation versus scaling theory

The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density sigma, assuming good solvent conditions. A phenomenological scaling theory, describing the variation of the linear dimensions of the chains with sigma, is developed and tested by molecular dynamics simulations of a bead-spring model. Different regimes are identified, depending on the ratio of D to the size of a free polymer N(3/5). For D>N(3/5) a crossover occurs for sigma=sigma*=N(-6/5) from the "mushroom" behavior (R(gx)=R(gy)=R(gz)=N(35)) to the behavior of a flat brush (R(gz)=sigma(1/3)N,R(gx)=R(gy)=sigma(-1/12)N(1/2)), until at sigma**=(D/N)3 a crossover to a compressed state of the brush, [R(gz)=D,R(gx)=R(gy)=(N(3)D/4sigma)(1/8)<D], occurs. Here coordinates are chosen so that the y axis is parallel to the tube axis, and the z direction normal to the wall of the pore at the grafting site. For D<N(3/5), the coil structure in the dilute regime is a cigar of length R(gy)=ND(-2/3) along the tube axis. At sigma*=(ND(1/3))(-1) the structure crosses over to "compressed cigars," of size R(gy)=(sigmaD)(-1). While for ultrathin cylinders (D<N(1/4)) this regime extends up to the regime where the pore is filled densely (sigma=D/N), for N(1/4)<D<N(1/2) a further crossover occurs at sigma***=D(-9/7)N(-3/7) to a semidilute regime where R(gy)=(N(3)D/4sigma)(1/8) still exceeds D. For moderately wide tubes (N(1/2)<D<N(3/5)) a further crossover occurs at sigma****=N(3)D(-7), where all chain linear dimensions are equal, to the regime of compressed brush. These predictions are compared to the computer simulations. From the latter, extensive results on monomer density and free chain end distributions are also obtained, and a discussion of pertinent theories is given. In particular, it is shown that for large D the brush height is an increasing function of D(-1).

Polymer translocation through a nanopore: a showcase of anomalous diffusion

The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one-dimensional anomalous diffusion process in terms of the reaction coordinate s (i.e., the translocated number of segments at time t ) and shown to be governed by a universal exponent alpha=2(2nu+2-gamma(1), where nu is the Flory exponent and gamma(1) is the surface exponent. Remarkably, it turns out that the value of alpha is nearly the same in two and three dimensions. The process is described by a fractional diffusion equation which is solved exactly in the interval 0<s<N with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments <s(t) and <s2(t)-<s(t)>2, which provide a full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.

Polymer chains in a soft nanotube: A Monte Carlo Study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D<<Rg. The observed scaling of static conformational properties with chain length N and tube diameter D follows the predictions of scaling theory and displays no significant difference between soft and rigid tubes. The Brownian dynamics of the polymer diffusion in a rigid tube is found to slow down in a tube with soft walls by an amount which depends on the Rg/D ratio albeit the relaxation time tau(parallel) for diffusive motion along the tube still scales as tau(parallel) proportional, N3.