Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Polymer translocation through a nanopore induced by adsorption: Monte Carlo simulation of a coarse-grained model

Dynamic Monte Carlo simulation of a bead-spring model of flexible macromolecules threading through a very narrow pore in a very thin rigid membrane are presented, assuming at the cis side of the membrane a purely repulsive monomer-wall interaction, while the trans side is attractive. Two choices of monomer-wall attraction epsilon are considered, one choice is slightly below and the other slightly above the "mushroom to pancake" adsorption threshold epsilon(c) for an infinitely long chain. Studying chain lengths N=32, 64, 128, and 256 and varying the number of monomers N(trans) (time t=0) that have already passed the pore when the simulation started, over a wide range, we find for epsilonepsilon(c) a finite number N(trans)(t=0) suffices that the translocation probability is close to unity. In the case epsilonepsilon(c), we find that the translocation time scales as tau proportional, variant N(1.65+/-0.08). We suggest a tentative scaling explanation for this result. Also the distribution of translocation times is obtained and discussed.     

Structure, dynamics, and phase transitions of tethered membranes: a Monte Carlo simulation study

A coarse-grained model of a self-avoiding tethered membrane with hexagonal coordination, embedded in three-dimensional space, is studied by means of extensive Monte Carlo computer simulations. The simulations are performed at various temperatures for membranes with linear size 5< or =L< or =50. We find that the membrane undergoes several folding transitions from a high-temperature flat phase to multiple-folded structure as the temperature is steadily decreased. Using a suitable order parameter and finite size scaling analysis, these phase transitions are shown to be of first order. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues lambda(max) (2)> or =lambda(med) (2)> or =lambda(min) (2) of the inertia tensor. We present a systematic finite size scaling analysis of the radius of gyration and the eigenvalues of the inertia tensor at different phases of the observed folding transitions. In the high-temperature flat phase, the radius of gyration R(g) grows with the linear size of the membrane L as R(g) proportional to L(nu), where the exponent nu is approximately equal to 1.0. The eigenvalues of the inertia tensor scale as lambda(max) proportional to lambda(med) proportional to L(nu) and lambda(min) proportional to L(nu(min) ), whereby the roughness exponent nu(min) is approximately equal to 0.7. We also find that the time tau(R) of a self-avoiding membrane to diffuse a distance R(g) scales as tau(R) proportional to L(2nu+2), which is in good agreement with the theoretical predictions.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Polymer translocation through a nanopore: a two-dimensional Monte Carlo study

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For LR(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.     

A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time tau as function of the polymer length N: In the general expression tau approximately N(beta)E, the exponent changes from beta=1 for moderately long chains to beta=1+nu or beta=2nu for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.     

Dynamical scaling of single chains on adsorbing substrates: diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.     

Finite-size scaling analysis on the phase transition of a ferromagnetic polymer chain model

The finite-size scaling analysis method is applied to study the phase transition of a self-avoiding walking polymer chain with spatial nearest-neighbor ferromagnetic Ising interaction on the simple cubic lattice. Assuming the scaling M2(T,n) = n(-2beta/nu)[phi0 + phi1n(1/nu)(T-T(c)) + O(n(2/nu)(T-T(c))2)] with the square magnetization M2 as the order parameter and the chain length n as the size, we estimate the second-order phase-transition temperature T(c) = 1.784 J/k(B) and critical exponents 2beta/nu approximately 0.668 and nu approximately 1.0. The self-diffusion constant and the chain dimensions (R2) and (S2) do not obey such a scaling law.     

Scaling and the Smoluchowski equations

The Smoluchowski equations, which describe coalescence growth, take into account combination reactions between a j-mer and a k-mer to form a (j+k)-mer, but not breakup of larger clusters to smaller ones. All combination reactions are assumed to be second order, with rate constants K(jk). The K(jk) are said to scale if K(lambda j,gamma k) = lambda(mu)gamma(nu)K(jk) for j < or = k. It can then be shown that, for large k, the number density or population of k-mers is given by Ak(a)e(-bk), where A is a normalization constant (a function of a, b, and time), a = -(mu+nu), and b(mu+nu-1) depends linearly on time. We prove this in a simple, transparent manner. We also discuss the origin of odd-even population oscillations for small k. A common scaling arises from the ballistic model, which assumes that the velocity of a k-mer is proportional to 1/square root of m(k) (Maxwell distribution), i.e., thermal equilibrium. This does not hold for the nascent distribution of clusters produced from monomers by reactive collisions. By direct calculation, invoking conservation of momentum in collisions, we show that, for this distribution, velocities are proportional to m(k)(-0.577). This leads to mu+nu = 0.090, intermediate between the ballistic (0.167) and diffusive (0.000) results. These results are discussed in light of the existence of systems in the experimental literature which apparently correspond to very negative values of mu+nu.     

Empirical determination of the harmonic force constants in benzene. 4. The Fermi resonances

In this article, we present a continuation of our work on the refinement of the harmonic force constants Fi,k in benzene (in symmetrized Whiffen's coordinates) and on a growing number of higher order (anharmonic) force constants, Fi,j,k and Fi,j,k,l, that are of importance for the benzene isotopomer invariant potential energy surface. The refined set of harmonic and anharmonic force constants improves the agreement between the experimental levels and those calculated theoretically. The emphasis of the present work is on the analysis of the two notable Fermi resonances in benzene (nu8 +nnu1 <=> (n +1)nu1 + nu6, where n = 0, 1, ... m, and nu20 <=> nu8 + nu19 <=> nu1 + nu6 + nu19). For this purpose, we have further extended our fully dimensional, fully symmetrized, and nonperturbative vibrational procedure to the vibrational structure of the benzene isotopic species with D6h symmetry.     

Phase transitions of a polymer threading a membrane coupled to coil-globule transitions

We theoretically study phase transitions of a polymer threading through a pore imbedded in a membrane. We focus on the coupling between a partition of the polymer segments through the membrane and a coil-globule transition of the single polymer chain. Based on the Flory model for collapse transitions of a polymer chain, we calculate the fraction of polymer segments and the expansion factor of a polymer coil on each side of the membrane. We predict a first-order phase transition of a polymer threading a membrane; polymer segments in one side are discontinuously translocated into the other side, depending on solvent conditions and molecular weight of the polymer. We also discuss the equilibrium conformation of the polymer chain on each side of the membrane.     

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相似文献   

Vacuum ultraviolet-infrared photo-induced Rydberg ionization spectroscopy: C-H stretching frequencies for trans-2-butene and trichloroethene cations

We have demonstrated the two-color vacuum ultraviolet (VUV)-infrared (IR) photoinduced Rydberg ionization (PIRI) experiment. Trichloroethene (ClCH=CCl2) and trans-2-butene (trans-CH3CH=CHCH3) were prepared in Rydberg states in the range of effective principal quantum number n* approximately 7-93 by VUV excitation prior to IR-induced autoionization. The observed VUV-IR-PIRI spectra are found to be independent of n*, suggesting that the electron Rydberg orbital is conserved, i.e., the Rydberg electron is behaving as a spectator during the excitation process. The observed IR active C-H stretching vibrational frequencies nu12+ = 3072+/-5 cm(-1) for ClCH=CCl2+ and nu23+ =2908+/-3 cm(-1), nu25+ =2990+/-10 cm(-1) and nu30+ =3022+/-10 cm(-1) for trans-CH3CH=CHCH3+ are compared with predictions based on ab initio quantum-chemical procedures and density functional calculations.     

Adsorption kinetics of carcinogens to DNA liquid crystalline gel beads

Adsorption behaviors of acridine orange (AO) and biphenyl (BP) to DNA liquid crystalline gel (LCG) beads in aqueous dispersing solution have been studied theoretically and experimentally. A theoretical consideration based on nonequilibrium thermodynamics predicted that the time course of the adsorption process is expressed with a scaled equation, and a scaled number of adsorbed carcinogen molecules ? is expressed with the square root of a scaled immersion time t, ? proportional, variant square root t at early stage, whereas it is expressed with a power law function 1 - ? proportional, variant (te - t)3/2 for ?0 > 1 and an exponential equation ?0 - ? proportional, variant e-t/alpha tau0 for ?0 > 1 at later stages of adsorption. Here, ?0 is the ratio of the initial number of carcinogen molecules in the dispersing solution to the number of the sites of adsorption of carcinogen molecules in the beads, te is the scaled equilibrium time of adsorption, tau0 is a time constant for adsorption, and alpha is a constant. Observed adsorption processes for AO were well expressed by the predicted ones, and the fitting parameters ?0 and tau0 increased with increasing cobalt chloride concentration CCo used for preparation of the beads, and both saturated above CCo > or = 400 mM for the adsorption of AO, whereas the adsorption processes for BP were expressed with the square root function. These results indicate that (1) the adsorption process at early stage is explained by diffusion-limited binding of the carcinogen molecules to DNA beads, and the time range of the early stage depends on the solubility (the solubility of AO in water is high whereas that of BP is low); and (2) the process at later stages depends on the balance of the numbers of adsorption sites and carcinogen molecules.     

Cooperative polymer dynamics under nanoscopic pore confinements probed by field-cycling NMR relaxometry

Reptational dynamics of bulk polymer chains on a time scale between the Rouse mode relaxation time and the so-called disengagement time is not compatible with the basic thermodynamic law of fluctuations of the number of segments in a given volume. On the other hand, experimental field-cycling NMR relaxometry data of perfluoropolyether melts confined in Vycor, a porous silica glass of nominal pore dimension of 4 nm, closely display the predicted signatures for the molecular weight and frequency dependences of the spin-lattice relaxation time in this particular limit, namely T1 proportional M-1/2nu1/2. It is shown that this contradiction is an apparent one. In this paper a formalism is developed suggesting cooperative chain dynamics under nanoscopic pore confinements. The result is a cooperative reptational displacement phenomenon reducing the root-mean-squared displacement rate correspondingly but showing the same characteristic dependences as the ordinary reptation model. The tube diameter effective for cooperative reptation is estimated on this basis for the sample system under consideration and is found to be of the same order of magnitude as the nominal pore diameter of Vycor.     

Nucleation and size distribution of nucleus during induction period of polyethylene crystallization

The crystallization process from supercooled melt results in the formation of nanosize nuclei in the earlier stage (induction period) through subsequent attachment or detachment of repeating unit to nuclei. The size distribution of nucleus f(N(j),t) in the induction period of nucleation process from the melts has not been experimentally confirmed yet by direct observation. The reason is that the number density of nuclei nu is too small to be detected experimentally. In our previous work, we showed the direct evidence of nucleation experimentally by means of small angle x-ray scattering (SAXS) technique. Further we have succeeded to observe the nucleation and f(N(j),t) of polymer crystallization from the melts by SAXS using synchrotron radiation. We increased nu by adding a nucleating agent to a polymer (polyethylene). The time evolution of f(N(j),t) was observed for the first time.     

Environmentally induced quantum dynamical phase transition in the spin swapping operation

Quantum information processing relies on coherent quantum dynamics for a precise control of its basic operations. A swapping gate in a two-spin system exchanges the degenerate states |(up arrow, down arrow)> and |(down arrow, up arrow)>. In NMR, this is achieved turning on and off the spin-spin interaction b=DeltaE that splits the energy levels and induces an oscillation with a natural frequency DeltaE/Planck's. Interaction of strength Planck's/tau(SE), with an environment of neighboring spins, degrades this oscillation within a decoherence time scale tau(phi). While the experimental frequency omega and decoherence time tau(phi) were expected to be roughly proportional to b/Planck's and tau(SE), respectively, we present here experiments that show drastic deviations in both omega and tau(phi). By solving the many spin dynamics, we prove that the swapping regime is restricted to DeltaEtau(SE) similar or greater than Planck's. Beyond a critical interaction with the environment the swapping freezes and the decoherence rate drops as 1/tau(phi) proportional to (b/Planck's)2tau(SE). The transition between quantum dynamical phases occurs when omega proportional to sqrt (b/Planck's)2-(k/tau(SE)2 becomes imaginary, resembling an overdamped classical oscillator. Here, 0< or =k2< or =1 depends only on the anisotropy of the system-environment interaction, being 0 for isotropic and 1 for XY interactions. This critical onset of a phase dominated by the quantum Zeno effect opens up new opportunities for controlling quantum dynamics.     

Shape resonances as poles of the semiclassical Green's function obtained from path-integral theory: application to the autodissociation of the He2++ 1sigma(g)+ state

It is known that one-dimensional potentials, V(R), with a local minimum and a finite barrier towards tunneling to a free particle continuum, can support a finite number of shape resonance states. Recently, we reported a formal derivation of the semiclassical Green's function, G(SC)(E), for such V(R), with one and two local minima, which was carried out in the framework of the theory of path integrals [Th. G. Douvropoulos and C. A. Nicolaides, J. Phys. B 35, 4453 (2002); J. Chem. Phys. 119, 8235 (2003)]. The complex poles of G(SC)(E) represent the energies and the tunneling rates of the unstable states of V(R). By analyzing the structure of G(SC)(E), here it is shown how one can compute the energy, E(nu), and the radiation-less width, gamma(nu), of each resonance state beyond the Wentzel-Kramers-Brillouin approximation. In addition, the energy shift, delta(nu), due to the interaction with the continuum, is given explicitly and computed numerically. The dependence of the accuracy of the semiclassical calculation of E(nu) and of gamma(nu) on the distance from the top of the barrier is demonstrated explicitly. As an application to a real system, we computed the vibrational energies, E(nu), and the lifetimes, tau(nu), of the 4He2++, nu = 0, 1, 2, 3, 4, and 4He3He++ nu = 0, 1, 2, 3, 1sigma(g)+ states, which autodissociate to the He(+)+He+ continuum. We employed the V(R) that was computed by Wolniewicz [J. Phys. B 32, 2257 (1999)], which was reported as being accurate, over a large range of values of R, to a fraction of cm(-1). For example, for J = 0, the results for the lowest and highest vibrational levels for the 4He2+ 1sigma(g)+ state are nu = 0 level, E0 = 10,309 cm(-1) below the barrier top, tau0 = 6400 s; nu = 4 level, E4 = 96.6 cm(-1) below the barrier top, tau4 = 31 x 10(-11) s. A brief presentation is also given of the quantal methods (and their results) that were applied previously for these shape resonances, such as the amplitude, the exterior complex scaling, and the lifetime matrix methods.     

Effect of interaction shape on the condensed toroid of the semiflexible chain

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviors of the mean toroidal and cross sectional radii, rc and rcross, as functions of the contour length L: (rc,rcross) approximately Lnu(Nc), with nu=(1/5,2/5) for the van der Waals-type, nu=(-1/3,2/3) for the Coulomb-type, and nu=(-1,1) for the delta-function-type attractions in the asymptotic limit. For the toroids with finite winding number Nc=100-400, we find nu approximately 0 for the Yukawa interaction with screening parameter kappa=0.5-1.0 and nu=0.1-0.13 for the van der Waals-type interactions. These findings could provide a possible explanation for the experimentally well known observation nu approximately 0 of the condensed DNA toroids. Conformational transitions are also discussed.     

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles

Femtosecond/picosecond time-resolved fluorescence study of hydrophilic polymer fine particles (polyacrylamide, PAAm) was reported. Ultrafast fluorescence dynamics of polymer/water solution was monitored using a fluorescent probe molecule (C153). In the femtosecond time-resolved fluorescence measurement at 480 nm, slowly decay components having lifetimes of tau(1) approximately 53 ps and tau(2) approximately 5 ns were observed in addition to rapid fluorescence decay. Picosecond time-resolved fluorescence spectra of C153/PAAm/H2O solution were also measured. In the time-resolved fluorescence spectra of C153/PAAm/H2O, a peak shift from 490 to 515 nm was measured, which can be assigned to the solvation dynamics of polymer fine particles. The fluorescence peak shift was related to the solvation response function and two time constants were determined (tau(3) approximately 50 ps and tau(4) approximately 467 ps). Therefore, the tau(1) component observed in the femtosecond time-resolved fluorescence measurement was assigned to the solvation dynamics that was observed only in the presence of polymer fine particles. Rotational diffusion measurements were also carried out on the basis of the picosecond time-resolved fluorescence spectra. In the C153/PAAm/H2O solution, anisotropy decay having two different time constants was also derived (tau(6) approximately 76 ps and tau(7) approximately 676 ps), indicating the presence of two different microscopic molecular environments around the polymer surface. Using the Stokes-Einstein-Debye (SED) equation, microscopic viscosity around the polymer surface was evaluated. For the area that gave a rotational diffusion time of tau(6) approximately 76 ps, the calculated viscosity is approximately 1.1 cP and for tau(7) approximately 676 ps, it is approximately 10 cP. The calculated viscosity values clearly revealed that there are two different molecular environments around the polyacrylamide fine particles.