Showing 1–50 of 79 results for author: Vilgis, T

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

Authors: Johan L. A. Dubbeldam, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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 analysi… ▽ More 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. △ Less

Submitted 3 October, 2014; v1 submitted 1 April, 2014; originally announced April 2014.

Comments: 12 pages

Journal ref: The Journal of Chemical Physics 141, 124112 (2014)

Force spectroscopy of polymer desorption: Theory and Molecular Dynamics simulation

Authors: J. Paturej, J. L. A. Dubbeldam, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

Abstract: 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 obser… ▽ More 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. △ Less

Submitted 14 October, 2013; originally announced October 2013.

Comments: 20 pages, 14 figures, Latex

Journal ref: Soft Matter 10, 2785 (2014)

Driven translocation of a polymer: fluctuations at work

Authors: J. L. A. Dubbeldam, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

Abstract: 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… ▽ More 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). △ Less

Submitted 23 November, 2012; originally announced November 2012.

Comments: 13 pages, 8 figures

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

Authors: J. Paturej, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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… ▽ More 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. △ Less

Submitted 7 March, 2012; originally announced March 2012.

Comments: 26 pages, 9 figures

Journal ref: Macromolecules 45, 4371 (2012)

Tension enhancement in branched macromolecules upon adhesion on a solid substrate

Authors: J. Paturej, L. Kuban, A. Milchev, T. A. Vilgis

Abstract: The effect of self-generated tension in the backbone of a bottle-brush (BB) macromolecule, adsorbed on an attractive surface, is studied by means of Molecular Dynamics simulations of a coarse-grained bead-spring model in the good solvent regime. The BB-molecule is modeled as a backbone chain of $L$ beads, connected by breakable bonds and with side chains, tethered pairwise to each monomer of the b… ▽ More The effect of self-generated tension in the backbone of a bottle-brush (BB) macromolecule, adsorbed on an attractive surface, is studied by means of Molecular Dynamics simulations of a coarse-grained bead-spring model in the good solvent regime. The BB-molecule is modeled as a backbone chain of $L$ beads, connected by breakable bonds and with side chains, tethered pairwise to each monomer of the backbone. Our investigation is focused on several key questions that determine the bond scission mechanism and the ensuing degradation kinetics: how are frequency of bond scission and self-induced tension distributed along the BB-backbone at different grafting density $σ_g$ of the side chains? How does tension $f$ depend on the length of the side chains $N$, and on the strength of surface adhesion $ε_s$? We examine the monomer density distribution profiles across the BB-backbone at different $ε_s$ and relate it to adsorption-induced morphological changes of the macromolecule whereby side chains partially desorb while the remaining chains spread better on the surface. Our simulation data are found to be in qualitative agreement with experimental results and recent theoretical predictions. Yet we demonstrate that the interval of parameter values where these predictions hold is limited in $N$. Thus, at high values of $ε_s$, too long side chains mutually block each other and freeze effectively the bottle-brush molecule. △ Less

Submitted 20 January, 2012; v1 submitted 12 December, 2011; originally announced December 2011.

Comments: 6 pages, 8 figures

Journal ref: EPL 97 (2012) 58003

Force-induced breakdown of flexible polymerized membrane

Authors: J. Paturej, H. Popova, A. Milchev, T. A. Vilgis

Abstract: 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 Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphene-like hexagonal sheet for different pulling force $f$ and… ▽ More 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 Langevin thermostat, we investigate the scission and recombination of bonds, and the formation of cracks in the 2D graphene-like 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 $<τ> \propto N^{-β}$ where $β\approx 0.50\pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W(t) \propto t^{1/3} \exp (-t / <τ>)$. The mean failure time $<τ_r>$ that takes to rip-off the sheet declines with growing size $N$ as a power law $<τ_r> \propto N^{-φ(f)}$. We also find $<τ_r> \propto \exp(ΔU_0/k_BT)$ where the nucleation barrier for crack formation $ΔU_0 \propto f^{-2}$, 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 $f$. △ Less

Submitted 1 February, 2012; v1 submitted 29 November, 2011; originally announced November 2011.

Comments: 12 pages, 10 figures, LaTeX, misprints corrected

Journal ref: Phys. Rev. E 85, 021805 (2012)

Forced translocation of a polymer: dynamical scaling vs. MD-simulation

Authors: J. L. A. Dubbeldam, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

Abstract: 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 c… ▽ More 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. △ Less

Submitted 23 February, 2012; v1 submitted 26 October, 2011; originally announced October 2011.

Comments: 17 pages, 8 figures; figure 5 is new; figures 4 and 6-8 are upgraded

Journal ref: Phys. Rev. E 85, 041801 (2012)

Thermal decomposition of a honeycomb-network sheet - A Molecular Dynamics simulation study

Authors: J. Paturej, H. Popova, A. Milchev, T. A. Vilgis

Abstract: The thermal degradation of a graphene-like two-dimensional triangular membrane with bonds undergoing temperature-induced scission is studied by means of Molecular Dynamics simulation using Langevin thermostat. We demonstrate that the probability distribution of breaking bonds is highly peaked at the rim of the membrane sheet at lower temperature whereas at higher temperature bonds break at random… ▽ More The thermal degradation of a graphene-like two-dimensional triangular membrane with bonds undergoing temperature-induced scission is studied by means of Molecular Dynamics simulation using Langevin thermostat. We demonstrate that the probability distribution of breaking bonds is highly peaked at the rim of the membrane sheet at lower temperature whereas at higher temperature bonds break at random anywhere 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 $τ\propto N^{-0.5}$ 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 a $δ$-function through a bimodal one into a single-peaked again at late times. Our simulation results are complemented by a set of $1^{st}$-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. △ Less

Submitted 12 August, 2012; v1 submitted 21 October, 2011; originally announced October 2011.

Comments: 21pages, 9 figures, LaTeX, revised version

Journal ref: J. Chem. Phys. 137, 054901 (2012)

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

Authors: K. L. Sebastian, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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 ext… ▽ More 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 $τ\sim n_d^2$. △ Less

Submitted 31 August, 2011; originally announced August 2011.

Comments: 6 pages, 2 figures

Journal ref: Europhysics Letters, 95, 48006 (2011)

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

Authors: J. Paturej, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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 manifesti… ▽ More 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. △ Less

Submitted 26 March, 2011; originally announced March 2011.

Comments: 6 pages, 7 pages

Journal ref: EPL 94 48003 (2011)

Dynamics of two topologically entangled chains

Authors: F. Ferrari, J. Paturej, M. Piatek, T. A. Vilgis

Abstract: Starting from a given topological invariant, we argue that it is possible to construct a topological field theory with a finite number of Feynman diagrams and an amplitude of gauge invariant objects that is a function of that invariant. This is for example the case of the Gauss linking number and of the abelian BF models which has been already successfully applied in the statistical mechanics of p… ▽ More Starting from a given topological invariant, we argue that it is possible to construct a topological field theory with a finite number of Feynman diagrams and an amplitude of gauge invariant objects that is a function of that invariant. This is for example the case of the Gauss linking number and of the abelian BF models which has been already successfully applied in the statistical mechanics of polymers. In this work it is shown that a suitable generalization of the BF model can be applied also to polymer dynamics, where the polymer trajectories are not static, but change their shape during time. △ Less

Submitted 17 March, 2011; originally announced March 2011.

Comments: 8 pages, 1 figure, to appear in Jour. Math. Phys

Journal ref: J.Math.Phys.52:043301,2011

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

Authors: J. Paturej, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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… ▽ More 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. △ Less

Submitted 11 March, 2011; originally announced March 2011.

Comments: 13 pages, 13 figures

Journal ref: J. Chem. Phys. 134 (22) 2011

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

Authors: Andrey Milchev, Jaroslaw Paturej, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments… ▽ More The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time $<τ>$ decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 ÷4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time $<τ>$ declines with growing contour length $L$ as $<τ>\propto L^{-0.17}$, and with side chain length as $<τ>\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction. △ Less

Submitted 3 March, 2011; originally announced March 2011.

Comments: 15 pages, 7 figures

Journal ref: Macromolecules 44 (10) 3981 2011

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

Authors: Johan L. A. Dubbeldam, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

Abstract: 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,… ▽ More 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. △ Less

Submitted 13 December, 2010; v1 submitted 22 July, 2010; originally announced July 2010.

Comments: 11 pages, 7 figures; Accepted for publication in Phys. Rev. E; Replacement of arXiv:1007.3853v1: 1) Added new references 2) Changed title 3) Improved figures

Journal ref: Phys. Rev. E, 83, 011802 (2011)

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

Authors: A. Ghosh, D. I. Dimitrov, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

Abstract: 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… ▽ More 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. △ Less

Submitted 11 February, 2010; originally announced February 2010.

Comments: 25 pages, 13 pictures

Journal ref: J. Chem. Phys. 132, 204902 (2010)

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

Authors: A. Milchev, V. G. Rostiashvili, S. Bhattacharya, T. A. Vilgis

Abstract: 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… ▽ More 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. △ Less

Submitted 13 September, 2009; originally announced September 2009.

Comments: Conference paper for "Recent Development in Computer Simulation Studies in Condensed Matter Physics", 22-nd Annual Workshop, Athens, GA, USA, 19-24 February 2009

Polymer Chain Adsorption on a Solid Surface: Scaling Arguments and Computer Simulations

Authors: A. Milchev, V. Rostiashvili, S. Bhattacharya, T. Vilgis

Abstract: We examine the phase transition of polymer adsorption as well as the underlying kinetics of polymer binding from dilute solutions on a structureless solid surface. The emphasis is put on the properties of regular multiblock copolymers, characterized by block size M and total length N as well as on random copolymers with quenched composition p of sticky and neutral segments. The macromolecules ar… ▽ More We examine the phase transition of polymer adsorption as well as the underlying kinetics of polymer binding from dilute solutions on a structureless solid surface. The emphasis is put on the properties of regular multiblock copolymers, characterized by block size M and total length N as well as on random copolymers with quenched composition p of sticky and neutral segments. The macromolecules are modeled as coarse-grained bead-spring chains subject to a short-ranged surface adhesive potential. Phase diagrams, showing the variation of the critical threshold for single chain adsorption in terms of M and p are derived from scaling considerations in agreement with results from computer experiment. Using both scaling analysis and numerical data from solving a system of coupled Master equations, we demonstrate that the phase behavior at criticality, and the adsorption kinetics may be adequately predicted and understood, in agreement with the results of extensive Monte Carlo simulations. Derived analytic expressions for the mean fraction of adsorbed segments as well as for Probability Distribution Functions of the various structural building blocks (i.e., trains, loops, tails) at time t during the chain attachment process are in good agreement with our numeric experiments and provide insight into the mechanism of polymer adsorption. △ Less

Submitted 2 September, 2009; originally announced September 2009.

Comments: To appear in "Nanophenomena at Surfaces: Fundamentals of Exotic Condensed Matter Properties", Sunny Beach, Bulgaria September 20-26, 2008

Pulling an adsorbed polymer chain off a solid surface

Authors: S. Bhattacharya, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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 adsorptio… ▽ More 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. △ Less

Submitted 13 August, 2009; v1 submitted 7 April, 2009; originally announced April 2009.

Comments: 17 pages, 9 pictures

Journal ref: Eur. Phys. J. E 29, 285-297 (2009)

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

Authors: S. Bhattacharya, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

Abstract: 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 a… ▽ More 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. △ Less

Submitted 31 March, 2009; originally announced March 2009.

Comments: 24 pages, 14 figures

Journal ref: Macromolecules 42, 2236-2250 (2009)

Dynamics of a three-dimensional inextensible chain

Authors: Franco Ferrari, Jaroslaw Paturej, Thomas A. Vilgis

Abstract: In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to the $z-$axis is studied using a path integral approach. It is shown that it is possible to reduce this problem to a two-dimensional case, in a way which is sim… ▽ More In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to the $z-$axis is studied using a path integral approach. It is shown that it is possible to reduce this problem to a two-dimensional case, in a way which is similar to the reduction of the statistical mechanics of a directed polymer to the random walk of a two-dimensional particle. △ Less

Submitted 22 May, 2009; v1 submitted 12 January, 2009; originally announced January 2009.

Comments: 15 pages, 3 figures, LaTeX, version accepted for publication

Journal ref: Acta Phys. Pol. B 40 5, 1369 (2009)

Polymer desorption under pulling: a novel dichotomic phase transition

Authors: S. Bhattacharya, V. G. Rostiashvili, A. Milchev, T. A. Vilgis

Abstract: 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 detachme… ▽ More 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. △ Less

Submitted 26 November, 2008; originally announced November 2008.

Comments: 10 pages, 4 figures

Journal ref: Phys. Rev. E 79, 030802(R) (2009)

The probability distribution of the average relative distance between two points in a dynamical chain

Authors: Franco Ferrari, Jaroslaw Paturej, Thomas A. Vilgis, Tomasz Wydro

Abstract: Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a given interval of time is computed. The physical meaning of the obtained result is investigated in the limiting case of a stiff chain. Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a given interval of time is computed. The physical meaning of the obtained result is investigated in the limiting case of a stiff chain. △ Less

Submitted 12 September, 2008; originally announced September 2008.

Comments: 9 pages, latex + revtex4, no figures

Dynamics of a stretched nonlinear polymer chain

Authors: M. Febbo, A. Milchev, V. Rostiashvili, T. A. Vilgis, D. Dimitrov

Abstract: We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modelled as a string of beads, connected by anharmonic springs, subject to a tensile force applied at the end monomer of the chain while the other end is fixed at the origin of coordinates. The impact of bond non-linearity… ▽ More We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modelled as a string of beads, connected by anharmonic springs, subject to a tensile force applied at the end monomer of the chain while the other end is fixed at the origin of coordinates. The impact of bond non-linearity on the relaxation dynamics of the polymer at different degrees of stretching is treated analytically within the Gaussian self-consistent approach (GSC) and then compared to simulation results derived from two different methods: Monte-Carlo (MC) and Molecular Dynamics (MD). At low and medium degrees of chain elongation we find good agreement between GSC predictions and the Monte-Carlo simulations. However, for strongly stretched chains the MD method, which takes into account inertial effects, reveals two important aspects of the nonlinear interaction between monomers: (i) a coupling and energy transfer between the damped, oscillatory normal modes of the chain, and (ii) the appearance of non-vanishing contributions of a continuum of frequencies around the characteristic modes in the power spectrum of the normal mode correlation functions. △ Less

Submitted 6 August, 2008; originally announced August 2008.

Comments: 17 pages, 9 figures

Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain

Authors: Franco Ferrari, Jaroslaw Paturej, T. A. Vilgis

Abstract: Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publicati… ▽ More Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant. △ Less

Submitted 25 October, 2008; v1 submitted 25 July, 2008; originally announced July 2008.

Comments: 21 pages, Latex + revtex 4, the text of the manuscript has been largely revised, misprints have been corrected and new references have been added

Adsorption Kinetics of a Single Polymer on a Solid Plane

Authors: S. Bhattacharya, A. Milchev, V. G. Rostiashvili, A. Y. Grosberg, T. A. Vilgis

Abstract: 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… ▽ More 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. △ Less

Submitted 27 June, 2008; v1 submitted 18 March, 2008; originally announced March 2008.

Comments: 14 pages, 8 figures; typos were corrected

Journal ref: Phys. Rev. E 77, 061603 (2008)

Description of the dynamics of a random chain with rigid constraints in the path integral framework

Authors: Franco Ferrari, Jaroslaw Paturej, Thomas A. Vilgis

Abstract: In this work we discuss the dynamics of a three dimensional chain which is described by generalized nonlinear sigma model The formula of the probability distribution of two topologically entangled chain is provided. The interesting case of a chain which can form only discrete angles with respect to the $z-$axis is also presented. In this work we discuss the dynamics of a three dimensional chain which is described by generalized nonlinear sigma model The formula of the probability distribution of two topologically entangled chain is provided. The interesting case of a chain which can form only discrete angles with respect to the $z-$axis is also presented. △ Less

Submitted 11 December, 2007; originally announced December 2007.

Comments: 4 pages. To appear in the proceedings of `Path Integrals - New Trends and Perspectives`, 23-28 September 2007, Dresden, Germany

Adsorption of Multi-block and Random Copolymer on a Solid Surface: Critical Behavior and Phase Diagram

Authors: Swati Bhattacharya, Hsiao-Ping Hsu, Andrey Milchev, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: The adsorption of a single multi-block $AB$-copolymer on a solid planar substrate is investigated by means of computer simulations and scaling analysis. It is shown that the problem can be mapped onto an effective homopolymer adsorption problem. In particular we discuss how the critical adsorption energy and the fraction of adsorbed monomers depend on the block length $M$ of sticking monomers… ▽ More The adsorption of a single multi-block $AB$-copolymer on a solid planar substrate is investigated by means of computer simulations and scaling analysis. It is shown that the problem can be mapped onto an effective homopolymer adsorption problem. In particular we discuss how the critical adsorption energy and the fraction of adsorbed monomers depend on the block length $M$ of sticking monomers $A$, and on the total length $N$ of the polymer chains. Also the adsorption of the random copolymers is considered and found to be well described within the framework of the annealed approximation. For a better test of our theoretical prediction, two different Monte Carlo (MC) simulation methods were employed: a) off-lattice dynamic bead-spring model, based on the standard Metropolis algorithm (MA), and b) coarse-grained lattice model using the Pruned-enriched Rosenbluth method (PERM) which enables tests for very long chains. The findings of both methods are fully consistent and in good agreement with theoretical predictions. △ Less

Submitted 23 November, 2007; originally announced November 2007.

Comments: 27 pages, 12 figures

Journal ref: Macromolecules 41, 2920-2930 (2008)

A path integral approach to the dynamics of a random chain with rigid constraints

Authors: Franco Ferrari, Jaroslaw Paturej, Thomas A. Vilgis

Abstract: In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimen… ▽ More In this work the dynamics of a freely jointed random chain which fluctuates at constant temperature in some viscous medium is studied. The chain is regarded as a system of small particles which perform a brownian motion and are subjected to rigid constraints which forbid the breaking of the chain. For simplicity, all interactions among the particles have been switched off and the number of dimensions has been limited to two. The problem of describing the fluctuations of the chain in the limit in which it becomes a continuous system is solved using a path integral approach, in which the constraints are imposed with the insertion in the path integral of suitable Dirac delta functions. It is shown that the probability distribution of the possible conformations in which the fluctuating chain can be found during its evolution in time coincides with the partition function of a field theory which is a generalization of the nonlinear sigma model in two dimensions. Both the probability distribution and the generating functional of the correlation functions of the positions of the beads are computed explicitly in a semiclassical approximation for a ring-shaped chain. △ Less

Submitted 27 February, 2008; v1 submitted 29 May, 2007; originally announced May 2007.

Comments: 36 pages, 2 figures, LaTeX + REVTeX4 + graphicx, minor changes in the text, reference added

Journal ref: Phys. Rev. E 77, 021802 (2008)

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

Authors: J. L. A. Dubbeldam, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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… ▽ More 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. △ Less

Submitted 5 June, 2007; v1 submitted 20 February, 2007; originally announced February 2007.

Comments: 6 pages, 4 figures, accepted to Europhys. Lett; some references were supplemented; typos were corrected

Journal ref: Europhys. Lett. 79, 18002 (2007)

Polymer translocation through a nanopore - a showcase of anomalous diffusion

Authors: J. L. A. Dubbeldam, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: 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 governe… ▽ More 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 $0 <s < N$ 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 $<s^2(t)> - < s(t)>^2$ 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. △ Less

Submitted 26 June, 2007; v1 submitted 26 January, 2007; originally announced January 2007.

Comments: 5 pages, 3 figures, accepted for publication in Phys. Rev. E

Journal ref: Phys. Rev. E 76, 010801(R) (2007)

Globular Structures of a Helix-Coil Copolymer: Self-Consistent Treatment

Authors: Christian Nowak, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: A self-consistent field theory was developed in the grand-canonical ensemble formulation to study transitions in a helix-coil multiblock globule. Helical and coil parts are treated as stiff rods and self-avoiding walks of variable lengths correspondingly. The resulting field-theory takes, in addition to the conventional Zimm-Bragg (B.H. Zimm, I.K. Bragg, J. Chem. Phys. 31, 526 (1959)) parameters… ▽ More A self-consistent field theory was developed in the grand-canonical ensemble formulation to study transitions in a helix-coil multiblock globule. Helical and coil parts are treated as stiff rods and self-avoiding walks of variable lengths correspondingly. The resulting field-theory takes, in addition to the conventional Zimm-Bragg (B.H. Zimm, I.K. Bragg, J. Chem. Phys. 31, 526 (1959)) parameters, also three-dimensional interaction terms into account. The appropriate differential equations which determine the self-consistent fields were solved numerically with finite element method. Three different phase states are found: open chain, amorphous globule and nematic liquid-crystalline (LC) globule. The LC-globule formation is driven by the interplay between the hydrophobic helical segments attraction and the anisotropic globule surface energy of an entropic nature. The full phase diagram of the helix-coil copolymer was calculated and thoroughly discussed. The suggested theory shows a clear interplay between secondary and tertiary structures in globular homopolypeptides. △ Less

Submitted 29 January, 2007; v1 submitted 28 December, 2006; originally announced December 2006.

Comments: 26 pages, 30 figures, corrected some typos

Journal ref: J. Chem. Phys. 126, 034902 (2007)

Field - Driven Translocation of Regular Block Copolymers through a Selective Liquid - Liquid Interface

Authors: A. Corsi, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: We propose a simple scaling theory describing the variation of the mean first passage time (MFPT) $τ(N,M)$ of a regular block copolymer of chain length $N$ and block size $M$ which is dragged through a selective liquid-liquid interface by an external field $B$. The theory predicts a non-Arrhenian $τ$ vs. $B$ relationship which depends strongly on the size of the blocks, $M$, and rather weakly on… ▽ More We propose a simple scaling theory describing the variation of the mean first passage time (MFPT) $τ(N,M)$ of a regular block copolymer of chain length $N$ and block size $M$ which is dragged through a selective liquid-liquid interface by an external field $B$. The theory predicts a non-Arrhenian $τ$ vs. $B$ relationship which depends strongly on the size of the blocks, $M$, and rather weakly on the total polymer length, $N$. The overall behavior is strongly influenced by the degree of selectivity between the two solvents $χ$. The variation of $τ(N,M)$ with $N$ and $M$ in the regimes of weak and strong selectivity of the interface is also studied by means of computer simulations using a dynamic Monte Carlo coarse-grained model. Good qualitative agreement with theoretical predictions is found. The MFPT distribution is found to be well described by a $Γ$ - distribution. Transition dynamics of ring- and telechelic polymers is also examined and compared to that of the linear chains. The strong sensitivity of the ``capture'' time $τ(N,M)$ with respect to block length $M$ suggests a possible application as a new type of chromatography designed to separate and purify complex mixtures with different block sizes of the individual macromolecules. △ Less

Submitted 16 October, 2006; originally announced October 2006.

Comments: 20 pages, 10 figures

Journal ref: Macromolecules 39, 7115 - 7124 (2006)

A path integral approach to the dynamics of random chains

Authors: Franco Ferrari, Jaroslaw Paturej, Thomas A. Vilgis

Abstract: In this work the dynamics of a freely jointed random chain with small masses attached to the joints is studied from a microscopic point of view. The chain is treated using a stringy approach, in which a statistical sum is performed over all two dimensional trajectories spanned by the chain during its fluctuations. In the limit in which the chain becomes a continuous curve, the probability functi… ▽ More In this work the dynamics of a freely jointed random chain with small masses attached to the joints is studied from a microscopic point of view. The chain is treated using a stringy approach, in which a statistical sum is performed over all two dimensional trajectories spanned by the chain during its fluctuations. In the limit in which the chain becomes a continuous curve, the probability function for such a system coincides with the partition function of a generalized nonlinear sigma model. The cases of open or closed chains in two and three dimensions are discussed. In three dimensions it is possible also to introduce some rigidity at the joints, allowing the segments of the chain to take only particular angles with respect to a given direction. △ Less

Submitted 29 July, 2006; originally announced July 2006.

Comments: 23 pages, 4 figures, LaTeX + RevTeX 4

Journal ref: Phys.Rev.E77:021802,2008

Kinetics of copolymer localization at a selective liquid-liquid interface

Authors: A. Corsi, A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: The localization kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface is studied in the limit of strong segregation between hydrophobic and polar segments in the chain. We propose a simple analytic theory based on scaling arguments which describes the relaxation of the initial coil into a flat-shaped layer for the cases of both Rouse… ▽ More The localization kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface is studied in the limit of strong segregation between hydrophobic and polar segments in the chain. We propose a simple analytic theory based on scaling arguments which describes the relaxation of the initial coil into a flat-shaped layer for the cases of both Rouse and Zimm dynamics. For Rouse dynamics the characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with block length $M$ and chain length $N$ as $τ_{\perp} \propto M^{1+2ν}$ (here $ν\approx 0.6$ is the Flory exponent) and as $τ_{\parallel} \propto N^2$, although initially the characteristic coil flattening time is predicted to scale with block size as $\propto M$. Since typically $N\gg M$ for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface, in contrast to the case of Zimm dynamics where the two components relax with comparable rate, and proceed considerably slower than in the Rouse case. We also demonstrate that, in the case of Rouse dynamics, these scaling predictions agree well with the results of Monte Carlo simulations of the localization dynamics. A comparison to the localization dynamics of {\em random} copolymers is also carried out. △ Less

Submitted 13 March, 2006; originally announced March 2006.

Comments: 11 pages, 15 figures

Journal ref: Macromolecules, 39, 1234-1244 (2006)

Aggregates of rod-coil diblock copolymers adsorbed at a surface

Authors: C. Nowak, T. A. Vilgis

Abstract: The behaviour of rod-coil diblock copolymers close to a surface is discussed by using extended scaling methods. The copolymers are immersed in selective solvent such that the rods are likely to aggregate to gain energy. The rods are assumed to align only parallel to each other, such that they gain a maximum energy by forming liquid crystalline structures. If an aggregate of these copolymers adso… ▽ More The behaviour of rod-coil diblock copolymers close to a surface is discussed by using extended scaling methods. The copolymers are immersed in selective solvent such that the rods are likely to aggregate to gain energy. The rods are assumed to align only parallel to each other, such that they gain a maximum energy by forming liquid crystalline structures. If an aggregate of these copolymers adsorbs with the rods parallel to the surface the rods shift with respect to each other to allow for the chains to gain entropy. It is shown that this shift decays with increasing distance from the surface. The profile of this decay away from the surface is calculated by minimisation of the total free energy of the system. The stability of such an adsorbed aggregate and other possible configurations are discussed as well. △ Less

Submitted 3 January, 2006; originally announced January 2006.

Comments: 10 pages, 11 figures

Entropically driven transition to a liquid-crystalline polymer globule

Authors: Christian Nowak, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: A self-consistent-field theory (SCFT) in the grand canonical ensemble formulation is used to study transitions in a helix-coil multiblock copolymer globule. The helices are modeled as stiff rods. In addition to the established coil-globule transition we show for the first time that, even without explicit rod-rod alignment interaction, the system undergoes a transition to a nematic liquid-crystal… ▽ More A self-consistent-field theory (SCFT) in the grand canonical ensemble formulation is used to study transitions in a helix-coil multiblock copolymer globule. The helices are modeled as stiff rods. In addition to the established coil-globule transition we show for the first time that, even without explicit rod-rod alignment interaction, the system undergoes a transition to a nematic liquid-crystalline (LC) globular state. The LC-globule formation is driven by the hydrophobic helical segment attraction and the anisotropy of the globule surface energy. The full phase diagram of the copolymer was calculated. It discriminates between an open chain, amorphous globule and LC-globule. This model provides a relatively simple example of the interplay between secondary and tertiary structures in homopolypeptides. Moreover, it gives a simple explanation for the formation of helix bundles in certain globular proteins. △ Less

Submitted 26 August, 2005; v1 submitted 4 July, 2005; originally announced July 2005.

Comments: 5 pages, 5 figures, submitted to Europhys. Lett

Journal ref: Europhys. Lett. 74, 76-82 (2006)

Copolymer adsorption kinetics at a selective liquid-liquid interface: Scaling theory and computer experiment

Authors: Andrea Corsi, Andrey Milchev, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: We consider the adsorption kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling considerations which describes the relaxation of the initial coil into a flat-shaped layer. The characteristic times for attaining equilibrium values of the gyration… ▽ More We consider the adsorption kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling considerations which describes the relaxation of the initial coil into a flat-shaped layer. The characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with chain length $N$ and block length $M$ as $τ_{\perp} \propto M^{1+2ν}$ (here $ν\approx 0.6$ is the Flory exponent) and as $τ_{\parallel} \propto N^2$, although initially the rate of coil flattening is expected to decrease with block size as $\propto M^{-1}$. Since typically $N\gg M$ for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface. We also demonstrate that these scaling predictions agree well with the results of extensive Monte Carlo simulations of the localization dynamics. △ Less

Submitted 26 August, 2005; v1 submitted 3 April, 2005; originally announced April 2005.

Comments: 4 pages, 4 figures, submited to Europhys. Lett

Journal ref: Europhys. Lett. 73, 204-210 (2006)

Self-consistent variational theory for globules

Authors: Arti Dua, Thomas A. Vilgis

Abstract: A self-consistent variational theory for globules based on the uniform expansion method is presented. This method, first introduced by Edwards and Singh to estimate the size of a self-avoiding chain, is restricted to a good solvent regime, where two-body repulsion leads to chain swelling. We extend the variational method to a poor solvent regime where the balance between the two-body attractive… ▽ More A self-consistent variational theory for globules based on the uniform expansion method is presented. This method, first introduced by Edwards and Singh to estimate the size of a self-avoiding chain, is restricted to a good solvent regime, where two-body repulsion leads to chain swelling. We extend the variational method to a poor solvent regime where the balance between the two-body attractive and the three-body repulsive interactions leads to contraction of the chain to form a globule. By employing the Ginzburg criterion, we recover the correct scaling for the $θ$-temperature. The introduction of the three-body interaction term in the variational scheme recovers the correct scaling for the two important length scales in the globule - its overall size $R$, and the thermal blob size $ξ_{T}$. Since these two length scales follow very different statistics - Gaussian on length scales $ξ_{T}$, and space filling on length scale $R$ - our approach extends the validity of the uniform expansion method to non-uniform contraction rendering it applicable to polymeric systems with attractive interactions. We present one such application by studying the Rayleigh instability of polyelectrolyte globules in poor solvents. At a critical fraction of charged monomers, $f_c$, along the chain backbone, we observe a clear indication of a first-order transition from a globular state at small $f$, to a stretched state at large $f$; in the intermediate regime the bistable equilibrium between these two states shows the existence of a pearl-necklace structure. △ Less

Submitted 17 March, 2005; originally announced March 2005.

Comments: 7 pages, 1 figure

Directed Polymers with Constrained Winding Angle

Authors: Franco Ferrari, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: In this article we study from a non-perturbative point of view the entanglement of two directed polymers subjected to repulsive interactions given by a Dirac $δ-$function potential. An exact formula of the so-called second moment of the winding angle is derived. This result is used to provide a thorough analysis of entanglement phenomena in the classical system of two polymers subjected to repul… ▽ More In this article we study from a non-perturbative point of view the entanglement of two directed polymers subjected to repulsive interactions given by a Dirac $δ-$function potential. An exact formula of the so-called second moment of the winding angle is derived. This result is used to provide a thorough analysis of entanglement phenomena in the classical system of two polymers subjected to repulsive interactions and related problems. No approximation is made in treating the constraint on the winding angle and the repulsive forces. In particular, we investigate how repulsive forces influence the entanglement degree of the two-polymer system. In the limit of ideal polymers, in which the interactions are switched off, we show that our results are in agreement with those of previous works. △ Less

Submitted 8 March, 2005; v1 submitted 16 December, 2004; originally announced December 2004.

Comments: 34 pages, LaTeX + RevTeX 4, minor typos corrected, 2 figures added, a major revision of Section V

Journal ref: Phys.Rev. E71 (2005) 061802

Localization of a multiblock copolymer at a selective interface: Scaling predictions and Monte Carlo verification

Authors: Andrea Corsi, Andrey Milchev, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: We investigate the localization of a hydrophobic - polar (HP) - regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length $M$ on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copo… ▽ More We investigate the localization of a hydrophobic - polar (HP) - regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length $M$ on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter χ. The scaling relations differ for the case of weak and strong localization. In the strong localization limit a scaling relation for the lateral diffusion coefficient D is also derived. We implement a dynamic off-lattice Monte - Carlo model to verify these scaling predictions. For chain lengths in a wide range (32 < N < 512) we find good agreement with the scaling predictions. △ Less

Submitted 16 November, 2004; originally announced November 2004.

Comments: 19 pages, 9 figures, submitted to J. Chem. Phys

Journal ref: J. Chem. Phys. 122, 094907 (2005)

Constrained dynamics of a polymer ring enclosing a constant area

Authors: Arti Dua, Thomas A. Vilgis

Abstract: The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the Lagrange multiplier function which is time dependent. The time dependence of the Lagrange multiplier is evaluated in a closed form both at short and long times.… ▽ More The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the Lagrange multiplier function which is time dependent. The time dependence of the Lagrange multiplier is evaluated in a closed form both at short and long times. At long times, the time dependence is weak, and is mainly governed by the inverse of the first mode of the area. The presence of the constraint changes the nature of the relaxation of the internal modes. The time correlation of the position vectors of the ring is found to be dominated by the first Rouse mode which does not relax even at very long times. The mean square displacement of the radius vector is found to be diffusive, which is associated with the rotational diffusion of the ring. △ Less

Submitted 8 September, 2004; originally announced September 2004.

Comments: 6 pages

Semiflexible polymers in a random environment

Authors: Arti Dua, Thomas A. Vilgis

Abstract: We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to… ▽ More We present using simple scaling arguments and one step replica symmetry breaking a theory for the localization of semiflexible polymers in a quenched random environment. In contrast to completely flexible polymers, localization of semiflexible polymers depends not only on the details of the disorder but also on the ease with which polymers can bend. The interplay of these two effects can lead to the delocalization of a localized polymer with an increase in either the disorder density or the stiffness. Our theory provides a general criterion for the delocalization of polymers with varying degrees of flexibility and allows us to propose a phase diagram for the highly folded (localized) states of semiflexible polymers as a function of the disorder strength and chain rigidity. △ Less

Submitted 24 May, 2004; originally announced May 2004.

Comments: 10 pages, 3 figures, Revtex4

Localization and freezing of a Gaussian chain in a quenched random potential

Authors: Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: The Gaussian chain in a quenched random potential (which is characterized by the disorder strength $Δ$) is investigated in the $d$ - dimensional space by the replicated variational method. The general expression for the free energy within so called one - step - replica symmetry breaking (1 - RSB) scenario has been systematically derived. We have shown that the replica symmetrical (RS) limit of t… ▽ More The Gaussian chain in a quenched random potential (which is characterized by the disorder strength $Δ$) is investigated in the $d$ - dimensional space by the replicated variational method. The general expression for the free energy within so called one - step - replica symmetry breaking (1 - RSB) scenario has been systematically derived. We have shown that the replica symmetrical (RS) limit of this expression can describe the chain center of mass localization and collapse. The critical disorder when the chain becomes localized scales as $Δ_c \simeq b^d N^{-2 + d/2}$ (where $b$ is the length of the Kuhn segment length and $N$ is the chain length) whereas the chain gyration radius $R_{\rm g} \simeq b (b^d/Δ)^{1/(4 - d)}$. The freezing of the internal degrees of freedom follows to the 1-RSB - scenario and is characterized by the beads localization length $\bar{{\cal D}^2}$. It was demonstrated that the solution for $\bar{{\cal D}^2}$ appears as a metastable state at $Δ= Δ_A$ and behaves similarly to the corresponding frozen states in heteropolymers or in $p$ - spin random spherical model. △ Less

Submitted 17 December, 2003; originally announced December 2003.

Comments: 18 pages, 6 figures, submitted to J. Chem. Phys

Journal ref: J. Chem. Phys. 120, 7194-7205 (2004)

Dynamics of a polymer in a quenched random medium: A Monte Carlo investigation

Authors: A. Milchev, V. G. Rostiashvili, T. A. Vilgis

Abstract: We use an off - lattice bead - spring model of a self - avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte - Carlo (MC) simulation. The chain center of mass mean-squared displacement as a function of time reveals two crossovers which depend both on chain length $N$ and on the degree of Gaussian disorder $Δ$. The first one from no… ▽ More We use an off - lattice bead - spring model of a self - avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte - Carlo (MC) simulation. The chain center of mass mean-squared displacement as a function of time reveals two crossovers which depend both on chain length $N$ and on the degree of Gaussian disorder $Δ$. The first one from normal to anomalous diffusion regime is found at short time $τ_1$ and observed to vanish rapidly as $τ_1 \propto Δ^{- 11}$ with growing disorder. The second crossover back to normal diffusion, $τ_2$, scales as $τ_2 \propto N^{2ν+ 1} f(N^{2-3ν}Δ)$ with $f$ being some scaling function. The diffusion coefficient $D_N$ depends strongly on disorder and drops dramatically at a {\em critical dispersion} $Δ_{c} \propto N^{-2 + 3ν}$ of the disorder potential so that for $Δ> Δ_c$ the chain center of mass is practically frozen.The time-dependent Rouse modes correlation function $C_{p}(t)$ reveals a characteristic plateau at $Δ> Δ_c$ which is the hallmark of a non - ergodic regime. These findings agree well with our recent theoretical predictions. △ Less

Submitted 16 December, 2003; originally announced December 2003.

Comments: 7 pages, 6 figures, submitted to Europhys. Letters

Journal ref: Europhys. Lett. 68, 384-390 (2004)

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

Authors: Gabriele Migliorini, Vakhtang G. Rostiashvili, Thomas A. Vilgis

Abstract: The Langevin dynamics of a self - interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one - loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dyna… ▽ More The Langevin dynamics of a self - interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one - loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, $(Δ/b^d) N^{2 - νd} \ge 1$, where $Δ$ is a disorder strength, $b$ is a Kuhnian segment length, $N$ is a chain length and $ν$ is the Flory exponent. We have derived the general equation for the non - ergodicity function $f(p)$ which characterizes the amplitude of frozen Rouse modes with an index $p = 2πj/N$. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength $Δ_c \sim N^{-γ}$ where the exponent $γ\approx 0.25$ and does not depend from the solvent quality. △ Less

Submitted 19 December, 2002; originally announced December 2002.

Comments: 17 pages, 6 figures, submitted to EPJB (condensed matter)

Journal ref: Eur. Phys. J. B 33, 61-73 (2003)

Collapse or Swelling Dynamics of Homopolymer Rings: Self-consistent Hartree approach

Authors: V. G. Rostiashvili, N. -K. Lee, T. A. Vilgis

Abstract: We investigate by the use of the Martin - Siggia - Rose generating functional technique and the self - consistent Hartree approximation, the dynamics of the ring homopolymer collapse (swelling) following an instantaneous change into a poor (good) solvent conditions.The equation of motion for the time dependent monomer - to - monomer correlation function is systematically derived. It is argued th… ▽ More We investigate by the use of the Martin - Siggia - Rose generating functional technique and the self - consistent Hartree approximation, the dynamics of the ring homopolymer collapse (swelling) following an instantaneous change into a poor (good) solvent conditions.The equation of motion for the time dependent monomer - to - monomer correlation function is systematically derived. It is argued that for describing of the coarse - graining process (which neglects the capillary instability and the coalescence of ``pearls'') the Rouse mode representation is very helpful, so that the resulting equations of motion can be simply solved numerically. In the case of the collapse this solution is analyzed in the framework of the hierarchically crumpled fractal picture, with crumples of successively growing scale along the chain. The presented numerical results are in line with the corresponding simple scaling argumentation which in particular shows that the characteristic collapse time of a segment of length $g$ scales as $t^* \sim ζ_0 g/τ$ (where $ζ_0$ is a bare friction coefficient and $τ$ is a depth of quench). In contrast to the collapse the globule swelling can be seen (in the case that topological effects are neglected) as a homogeneous expansion of the globule interior. The swelling of each Rouse mode as well as gyration radius $R_g$ is discussed. △ Less

Submitted 28 June, 2002; originally announced June 2002.

Comments: 20 pages, 7 figures, submitted to Phys. Rev. E

Journal ref: J. Chem. Phys. 118, 973-951 (2003)

Single Chain Force Spectroscopy: Sequence Dependence

Authors: Namkyung Lee, Thomas A. Vilgis

Abstract: We study the elastic properties of a single A/B copolymer chain with a specific sequence. We predict a rich structure in the force extension relations which can be addressed to the sequence. The variational method is introduced to probe local minima on the path of stretching and releasing. At given force, we find multiple configurations which are separated by energy barriers. A collapsed globula… ▽ More We study the elastic properties of a single A/B copolymer chain with a specific sequence. We predict a rich structure in the force extension relations which can be addressed to the sequence. The variational method is introduced to probe local minima on the path of stretching and releasing. At given force, we find multiple configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which unravel cooperatively. Upon stretching, unfolding path shows stepwise pattern corresponding to the unfolding of each domain. While releasing, several cores can be created simultaneously in the middle of the chain resulting in a different path of collapse. △ Less

Submitted 29 October, 2001; originally announced October 2001.

Comments: 6 pages 3 figures

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

Authors: Gabriele Migliorini, Vakhtang Rostiashvili, Namkyung Lee, Thomas A. Vilgis

Abstract: We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied minimizing the free energy $F_N$, depending on $N(N-1)/2$ trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length… ▽ More We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied minimizing the free energy $F_N$, depending on $N(N-1)/2$ trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length $2^4<N<2^{16}$ and for an open chain of length $2^4<N<2^9$ in poor and theta solvent conditions, including a Coulomb repulsion between the monomers. In theta solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer--monomer correlation function, reminiscence of necklace formation in poor solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented. △ Less

Submitted 18 June, 2001; originally announced June 2001.

Comments: submitted to EPJE (soft matter)

Self- generated disorder and structural glass formation in homopolymer globules

Authors: V. G. Rostiashvili, G. Migliorini, T. A. Vilgis

Abstract: We have investigated the interrelation between the spin glasses and the structural glasses. Spin glasses in this case are random magnets without reflection symmetry (e.g. $p$ - spin interaction spin glasses and Potts glasses) which contain quenched disorder, whereas the structural glasses are here exemplified by the homopolymeric globule, which can be viewed as a liquid of connected molecules on… ▽ More We have investigated the interrelation between the spin glasses and the structural glasses. Spin glasses in this case are random magnets without reflection symmetry (e.g. $p$ - spin interaction spin glasses and Potts glasses) which contain quenched disorder, whereas the structural glasses are here exemplified by the homopolymeric globule, which can be viewed as a liquid of connected molecules on nano scales. It is argued that the homopolymeric globule problem can be mapped onto a disorder field theoretical model whose effective Hamiltonian resembles the corresponding one for the spin glass model. In this sense the disorder in the globule is self - generated (in contrast to spin glasses) and can be related with competitive interactions (virial coefficients of different signs) and the chain connectivity. The work is aimed at giving a quantitative description of this analogy. We have investigated the phase diagram of the homopolymeric globule where the transition line from the liquid to glassy globule is treated in terms of the replica symmetry breaking paradigm. The configurational entropy temperature dependence is also discussed. △ Less

Submitted 31 May, 2001; originally announced May 2001.

Comments: 22 pages, 4 figures, submitted to Phys. Rev. E

Journal ref: Phys.Rev. E 64, 051112 (2001)

Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations

Authors: G. Migliorini, V. G. Rostiashvili, T. A. Vilgis

Abstract: A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length $N$. We… ▽ More A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length $N$. We find $R \simeq N^ν(\log N)^γ$ where $ν= \frac{3}{λ+2}$ and $λ$ is the exponent which characterize the long-range interaction $U \propto 1/r^λ$. The exponent $γ$ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings, by a direct numerical minimization of the variational energy for chains of increasing size $2^4<N<2^{15}$. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length $2^4<N<2^{10}$. The non universal behavior of the exponent $ γ$ previously derived within the variational method, is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in $d=3$ dimension. Particular attention is devoted to the homopolymer chain problem, when short range contact interactions are present. △ Less

Submitted 7 February, 2001; originally announced February 2001.

Comments: to appear in European Phys. Journal E (soft matter)

Journal ref: Eur. Phys. J. E 4, 475-487 (2001)