arXiv subjects

V. G. Rostiashvili

Publications and source records attributed to V. G. Rostiashvili.

At least 19 recordsLinked to original sources

arXiv2014

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 DPD-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 $ε_s^A / ε_s^B$ 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 $ε_s^A / ε_s^B < 0.15$. Eventually, performing an atomistic simulation of a (bio)-polymer {\it polyglycine}, we demonstrate that the simulation results, derived from our coarse-grained model, comply favorably with those from the all-atom simulation.

cond-mat.soft↗

arXiv2014

Driven translocation of a polymer: role of pore friction and crowding

Force-driven translocation of a macromolecule through a nanopore is investigated by taking into account the monomer-pore friction as well as the "crowding" of monomers on the {\it trans} - side of the membrane which counterbalance the driving force acting in the pore. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the translocation exponent $α$ in the translocation time - vs. - chain length scaling law, $τ\propto N^α$, becomes smaller when monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings may explain the variety of $α$ values which were found in experiments and computer simulations.

cond-mat.soft↗

arXiv2013

Force spectroscopy of polymer desorption: Theory and Molecular Dynamics simulation

Forced detachment of a single polymer chain, strongly-adsorbed on a solid substrate, is investigated by two complementary methods: a coarse-grained analytical dynamical model, based on the Onsager stochastic equation, and Molecular Dynamics (MD) simulations with Langevin thermostat. The suggested approach makes it possible to go beyond the limitations of the conventional Bell-Evans model. We observe a series of characteristic force spikes when the pulling force is measured against the cantilever displacement during detachment at constant velocity $v_c$ (displacement control mode) and find that the average magnitude of this force increases as $v_c$ grows. The probability distributions of the pulling force and the end-monomer distance from the surface at the moment of final detachment are investigated for different adsorption energy $ε$ and pulling velocity $v_c$. Our extensive MD-simulations validate and support the main theoretical findings. Moreover, the simulation reveals a novel behavior: for a strong-friction and massive cantilever the force spikes pattern is smeared out at large $v_c$. As a challenging task for experimental bio-polymers sequencing in future we suggest the fabrication of stiff, super-light, nanometer-sized AFM probe.

cond-mat.soft↗

arXiv2012

Driven translocation of a polymer: fluctuations at work

The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive Molecular-Dynamics (MD) simulation. The theoretical consideration is based on the so-called velocity Langevin (V-Langevin) equation which determines the progress of the translocation in terms of the number of polymer segments, $s(t)$, that have passed through the pore at time $t$ due to a driving force $f$. The formalism is based only on the assumption that, due to thermal fluctuations, the translocation velocity $v=\dot{s}(t)$ is a Gaussian random process as suggested by our MD data. With this in mind we have derived the corresponding Fokker-Planck equation (FPE) which has a nonlinear drift term and diffusion term with a {\em time-dependent} diffusion coefficient $D(t)$. Our MD simulation reveals that the driven translocation process follows a {\em super}diffusive law with a running diffusion coefficient $D(t) \propto t^γ$ where $γ< 1$. This finding is then used in the numerical solution of the FPE which yields an important result: for comparatively small driving forces fluctuations facilitate the translocation dynamics. As a consequence, the exponent $α$ which describes the scaling of the mean translocation time $<τ>$ with the length $N$ of the polymer, $<τ> \propto N^α$ is found to diminish. Thus, taking thermal fluctuations into account, one can explain the systematic discrepancy between theoretically predicted duration of a driven translocation process, considered usually as a deterministic event, and measurements in computer simulations. In the non-driven case, $f=0$, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).

cond-mat.soft↗

arXiv2012

Polymer Detachment Kinetics from Adsorbing Surface: Theory, Simulation and Similarity to Infiltration into Porous Medium

The force-assisted desorption kinetics of a macromolecule from adhesive surface is studied theoretically, using the notion of tensile (Pincus) blobs, as well as by means of Monte-Carlo (MC) and Molecular Dynamics (MD) simulations. We show that the change of detached monomers with time is governed by a differential equation which is equivalent to the nonlinear porous medium equation (PME), employed widely in transport modeling of hydrogeological systems. Depending on the pulling force and the strength of adsorption, three kinetic regimes can be distinguished: (i) "trumpet" (weak adsorption and small pulling force), (ii) "stem-trumpet" (weak adsorption and moderate force), and (iii) "stem" (strong adsorption and large force). Interestingly, in all regimes the number of desorbed beads $M(t)$, and the height of the first monomer (which experiences a pulling force) $R(t)$ above the surface follow an universal square-root-of-time law. Consequently, the total time of detachment $<τ_d>$, scales with polymer length $N$ as $<τ_d> \propto N^2$. Our main theoretical conclusions are tested and found in agreement with data from extensive MC- and MD-simulations.

cond-mat.soft↗

arXiv2012

Forced translocation of a polymer: dynamical scaling vs. MD-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 propagating front of tensile force along the chain backbone, suggested recently by T. Sakaue. 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 quasi-static 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 $<τ> \sim N^{2ν}/f^{1/ν}$ to $<τ> \sim N^{1+ν}/f$ (for the free-draining case) as the dimensionless force ${\widetilde f}_{R} = a N^νf /T$ (where $a$, $N$, $ν$, $f$, $T$ 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 (MD) simulation. Data from our computer experiment indicates indeed that the translocation scaling exponent $α$ grows with the pulling force ${\widetilde f}_{R}$) albeit the observed exponent $α$ stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations which are neglected in the quasi-static approximation.

cond-mat.soft↗

arXiv2011

Dynamics of pulled desorption with effects of excluded volume interaction: The p-Laplacian diffusion equation and its exact solution

We analyze the dynamics of desorption of a polymer molecule which is pulled at one of its ends with force $f$, trying to desorb it. We assume a monomer to desorb when the pulling force on it exceeds a critical value $f_{c}$. We formulate an equation for the average position of the $n^{th}$ monomer, which takes into account excluded volume interaction through the blob-picture of a polymer under external constraints. The approach leads to a diffusion equation with a $p$-Laplacian for the propagation of the stretching along the chain. This has to be solved subject to a moving boundary condition. Interestingly, within this approach, the problem can be solved exactly in the trumpet, stem-flower and stem regimes. In the trumpet regime, we get $τ=τ_{0}n_d^{2}$ where $n_d$ is the number of monomers that have desorbed at the time $τ$. $τ_{0}$ is known only numerically, but for $f$ close to $f_{c}$, it is found to be $τ_{0}\sim f_c/(f^{2/3}-f_{c}^{2/3})$. If one used simple Rouse dynamics, this result changes to {\normalsize $τ\sim f_c n_d^2/(f-f_{c})$.} In the other regimes too, one can find exact solution, and interestingly, in all regimes $τ\sim n_d^2$.

cond-mat.soft↗

arXiv2011

Polymer chain scission at constant tension - an example of force-induced collective behaviour

The breakage of a polymer chain of segments, coupled by anharmonic bonds with applied constant external tensile force is studied by means of Molecular Dynamics simulation. We show that the mean life time of the chain becomes progressively independent of the number of bonds as the pulling force grows. The latter affects also the rupture rates of individual bonds along the polymer backbone manifesting the essential role of inertial effects in the fragmentation process. The role of local defects, temperature and friction in the scission kinetics is also examined.

cond-mat.soft↗

arXiv2011

Thermal Degradation of Unstrained Single Polymer Chain: Non-linear Effects at Work

We examine the thermally-induced fracture of an unstrained polymer chain of discrete segments coupled by an anharmonic potential by means of Molecular Dynamics simulation with a Langevin thermostat. Cases of both under- and over-damped dynamics are investigated, and a comparison with recent studies of bond scission in model polymers with harmonic interactions is performed. We find that the polymer degradation changes qualitatively between the inertial regime and that of heavily damped dynamics. The role of bond healing (recombination) is also studied and probability distributions for the recombination times and overstretched bond lengths are obtained. Our extensive simulations reveal many properties of the scission dynamics in agreement with the notion of random breakdown of independent bonds, e.g., the mean time of chain rupture, $<τ>$ follows an Arrhenian behavior with temperature $T$, and depends on the number of bonds $N$ in the polymer as $<τ> \propto N^{-1}$. In contrast, the rupture rates of the individual bonds along the polymer backbone indicate clearly the presence of self-induced inhomogeneity resulting from the interplay of thermal noise and nonlinearity. Eventually we examine the fragmentation kinetics during thermolysis. We demonstrate that both the probability distribution function of fragment sizes as well as the mean length of fragments at subsequent times $t$ characterize degradation as predominantly a first order reaction.

cond-mat.soft↗

arXiv2010

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

We suggest a governing equation which 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 sub-diffusive increase of the distribution variance $Δ(t)$ with elapsed time, $Δ(t) \propto t^α$. The latter quantity measures the mean-squared number $s$ of polymer segments which 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 - 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 in ref.\cite{Kantor_3}, that the exponent $α$ changes from $0.91$ to $0.55$, to $0.91$, for short, intermediate and long time regimes, respectively.

cond-mat.soft↗

arXiv2010

Thermal Breakage and Self-Healing of a Polymer Chain under Tensile Stress

We consider the thermal breakage of a tethered polymer chain of discrete segments coupled by Morse potentials under constant tensile stress. The chain dynamics at the onset of fracture is studied analytically by Kramers-Langer multidimensional theory and by extensive Molecular Dynamics simulations in 1D- and 3D-space. Comparison with simulation data in one- and three dimensions demonstrates that the Kramers-Langer theory provides good qualitative description of the process of bond-scission as caused by a {\em collective} unstable mode. We derive distributions of the probability for scission over the successive bonds along the chain which reveal the influence of chain ends on rupture in good agreement with theory. The breakage time distribution of an individual bond is found to follow an exponential law as predicted by theory. Special attention is focused on the recombination (self-healing) of broken bonds. Theoretically derived expressions for the recombination time and distance distributions comply with MD observations and indicate that the energy barrier position crossing is not a good criterion for true rupture. It is shown that the fraction of self-healing bonds increases with rising temperature and friction.

cond-mat.soft↗

arXiv2009

Polymer desorption under pulling: first order phase transition without phase coexistence

We show that when a self-avoiding polymer chain is pulled off a sticky surface by force applied to the end segment, it undergoes a first-order thermodynamic phase transition albeit without phase coexistence. This unusual feature is demonstrated analytically by means of a Grand Canonical Ensemble (GCE) description of adsorbed macromolecules as well as by Monte Carlo simulations of an off-lattice bead-spring model of a polymer chain. Theoretical treatment and computer experiment can be carried out both in the constant-force f statistical ensemble and in the constant-height h ensemble. We find that the force-assisted desorption undergoes a first-order dichotomic phase transition whereby phase coexistence between adsorbed and desorbed states does not exist. In the f-ensemble the order parameter (the fraction of chain contacts with the surface) is characterized by huge fluctuations when the pulling force attains a critical value f_D. In the h-ensemble, in contrast, fluctuations are always finite at the critical height h_D. The derived 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 f or h, provide a full description of the polymer structure and behavior upon force-assisted detachment. In addition, one finds that the hitherto controversial value of the universal critical adsorption exponent ϕdepends essentially on the extent of interaction between the loops adsorbed chain so that ϕmay vary within the limits 0.39 < ϕ< 0.59.

cond-mat.soft↗

arXiv2009

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 $ε$. The phase diagram in the $h - ε$ 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.

cond-mat.soft↗

arXiv2009

Forced-induced desorption of a polymer chain adsorbed on an attractive surface - Theory and Computer Experiment

We consider the properties of a self-avoiding polymer chain, adsorbed on a solid attractive substrate which is attached with one end to a pulling force. The conformational properties of such chain and its phase behavior are treated within a Grand Canonical Ensemble (GCE) approach. We derive theoretical expressions for the mean size of loops, trains, and tails of an adsorbed chain under pulling as well as values for the universal exponents which describe their probability distribution functions. A central result of the theoretical analysis is the derivation of an expression for the crossover exponent $ϕ$, characterizing polymer adsorption at criticality, $ϕ= α-1$, which relates the precise value of $ϕ$ to the exponent $α$, describing polymer loop statistics. We demonstrate that $1-γ_{11} < α< 1 + ν$, depending on the possibility of a single loop to interact with neighboring loops in the adsorbed polymer. The universal surface loop exponent $γ_{11} \approx -0.39$ and the Flory exponent $ν\approx 0.59$. We present the adsorption-desorption phase diagram of a polymer chain under pulling and demonstrate that the relevant phase transformation becomes first order whereas in the absence of external force it is known to be a continuous one. The nature of this transformation turns to be dichotomic, i.e., coexistence of different phase states is not possible. These novel theoretical predictions are verified by means of extensive Monte Carlo simulations.

cond-mat.soft↗

arXiv2008

Polymer desorption under pulling: a novel dichotomic phase transition

We show that the structural properties and phase behavior of a self-avoiding polymer chain on adhesive substrate, subject to pulling at the chain end, can be obtained by means of a Grand Canonical Ensemble (GCE) approach. We derive analytical expressions for the mean length of the basic structural units of adsorbed polymer, such as loops and tails, in terms of the adhesive potential and detachment force, and determine values of the universal exponents which govern their probability distributions. Most notably, the hitherto controversial value of the critical adsorption exponent $ϕ$ is found to depend essentially on the interaction between different loops. The chain detachment transition turns out to be of the first order, albeit dichotomic, i.e., no coexistence of different phase states exists. These novel theoretical predictions and the suggested phase diagram of the adsorption-desorption transformation under external pulling force are verified by means of extensive Monte Carlo simulations.

cond-mat.soft↗

arXiv2008

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 $(1+ν)^{-1}$ where $ν\approx 3/5$ 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 study also regular multiblock copolymers and random copolymers, and demonstrate that their adsorption kinetics may be considered within the same theoretical model.

cond-mat.soft↗

arXiv2007

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 {\em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $α= 2/(2ν+2-γ_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {\em fractional} diffusion equation which is solved exactly in the interval $0 $, and $ - < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.

cond-mat.soft↗

arXiv2007

Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion

We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {\em anomalous} diffusive behavior even in the {\em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $α= 2/(2ν+2 - γ_1)$, where $ν$ is the Flory exponent and $γ_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {\em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $τ\propto f^{-1}N^{\frac{2}α -1}$. Also the corresponding time dependent statistical moments, $< s(t) > \propto t^α$ and $< s(t)^2 > \propto t^{2α}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $α$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.

cond-mat.stat-mech↗