We consider the rupture dynamics of a homopolymer chain pulled at one end at a constant loading rate r. Compared to single bond breaking, the existence of the chain introduces two new aspects into rupture dynamics: the non-Markovian aspect in the barrier crossing and the slow-down of the force propagation to the breakable bond. The relative impact of both these processes is investigated, and the second one was found to be the most important at moderate loading rates. The most probable rupture force is found to decrease with the number of bonds as f_{max} const-(ln(N/r))^(2/3) and finally to approach a saturation value independent on N. All our analytical findings are confirmed by extensive numerical simulations.
We consider the rupture dynamics of a homopolymer chain pulled at one end at a constant loading rate. Our model of the breakable polymer is related to the Rouse chain, with the only difference that the interaction between the monomers is described by the Morse potential instead of the harmonic one, and thus allows for mechanical failure. We show that in the experimentally relevant domain of parameters the dependence of the most probable rupture force on the chain length may be non-monotonic, so that the medium-length chains break easier than the short and the long ones. The qualitative theory …
It is shown that the intrinsic stress in solvent cast polymer coatings plays a key role in the nucleation of holes in the film. Nucleation is important because it is meanwhile clear that heterogeneous nucleation is the only relevant rupture mechanism for the technologically relevant thickness regime well above 100 nm. The most striking feature is that in contrast to what has been widely believed, the number density of holes scales not algebraically, but exponentially with the film thickness.
Progressive damage, which eventually leads to failure, is ubiquitous in biological and synthetic polymers. The simplest case to consider is that of elastomeric materials, which can undergo large reversible deformations with negligible rate dependence. In this paper, we develop a theory for modeling progressive damage and rupture of such materials. We extend the phase-field method, which is widely used to describe the damage and fracture of brittle materials, to elastomeric materials undergoing large deformations. A central feature of our theory is the recognition that the free energy of elasto…
We present the first experimental study on the simultaneous capillary instability amongst viscous concentric rings suspended atop an immiscible medium. The rings ruptured upon annealing, with three types of phase correlation between neighboring rings. In the case of weak substrate confinement, the rings ruptured independently when they were sparsely distanced, but via an out-of-phase mode when packed closer. If the substrate confinement was strong, the rings would rupture via an in-phase mode, resulting in radially aligned droplets. The concentric ring geometry caused a competition between the…
To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level to macroscopic quantities that govern damage and failure must be established. Constitutive models based upon statistical mechanics have used variants of the freely jointed chain (FJC) model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to c…
Common experience tells us that a knot significantly weakens the polymer strand in which it is tied, which in turn leads to more facile chain rupture under tensile loading. Using first-principles molecular dynamics calculations we describe the dynamical evolution of the radicals that form after chain rupture of a single knotted alkane molecule in their very early stages of life. They are able to recombine, to form cyclic alkanes and to undergo disproportionation phenomena with nearby chain segments. The breaking of a single knotted polymer chain under mechanical loading is thus predicted to re…
In capillary-driven fluid dynamics, simple departures from equilibrium offer the chance to quantitatively model the resulting relaxations. These dynamics in turn provide insight on both practical and fundamental aspects of thin-film hydrodynamics. In this work, we describe a model trilayer dewetting experiment elucidating the effect of solid, no-slip confining boundaries on the bursting of a liquid film in a viscous environment. This experiment was inspired by an industrial polymer processing technique, multilayer coextrusion, in which thousands of alternating layers are stacked atop one anoth…
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 recom…
The strength of a simple soft bond under constant loading rate is studied theoretically. We find a scaling regime where rebinding is negligible and the rupture force of the bond scales as $const. + (\ln (kv))^{2/3}$, where $kv$ is the loading rate. The scaling regime is smaller for weaker bonds and broader for stronger bonds. For loading rate beyond the upper limit of the scaling regime, bond rupture is deterministic and thermal effects are negligible. For loading rate below the lower limit of the scaling regime, contribution from rebinding becomes important, and there is no simple scaling rel…
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 ov…
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.
Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root or logarithmic.
We calculate the correction-to-scaling exponent $ω_T$ that characterizes the approach to the scaling limit in multicomponent polymer solutions. A direct Monte Carlo determination of $ω_T$ in a system of interacting self-avoiding walks gives $ω_T = 0.415(20)$. A field-theory analysis based on five- and six-loop perturbative series leads to $ω_T = 0.41(4)$. We also verify the renormalization-group predictions for the scaling behavior close to the ideal-mixing point.
We discuss the soundness of the scaling functional (SF) approach proposed by Aubouy Guiselin and Raphael (Macromolecules 29, 7261 (1996)) to describe polymeric interfaces. In particular, we demonstrate that this approach is a variational theory. We emphasis the role of SF theory as an important link between ground-state theories suitable to describe adsorbed layers, and "classical" theories for polymer brushes.
The crossover region in the phase diagram of polymer solutions, in the regime above the overlap concentration, is explored by Brownian Dynamics simulations, to map out the universal crossover scaling functions for the gyration radius and the single-chain diffusion constant. Scaling considerations, our simulation results, and recently reported data on the polymer contribution to the viscosity obtained from rheological measurements on DNA systems, support the assumption that there are simple relations between these functions, such that they can be inferred from one another.
We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the results in perspective, we compare with in part rigorous theoretical scaling laws for canonical condensation in a supersaturated gas at fixed temperature, and derive corresponding scaling predictions for an undercooled gas at fixed density. The latter allows one to efficiently employ parallel multicanonical simulations and to reach previously not accessible …
Extensive Monte Carlo data analysis gives clear evidence that collapsed linear polymers in two dimensions fall in the universality class of athermal, dense self-avoiding walks, as conjectured by B.Duplantier [Phys.Rev.Lett. 71, 4274 (1993)]. However, the boundary of the globule has self affine roughness and does not determine the anticipated nonzero topological boundary contribution to entropic exponents. Scaling corrections are due to subleading contributions to the partition function corresponding to polymer configurations with one end located on the globule-solvent interface.
We study the cooperative rupture of multiple adhesion bonds under shared linear loading. Simulations of the appropriate Master equation are compared with numerical integration of a rate equation for the mean number of bonds and its scaling analysis. In general, force-accelerated rupture is rather abrupt. For small clusters and slow loading, large fluctuations occur regarding the timepoint of final rupture, but not the typical shape of the rupture trajectory. For vanishing rebinding, our numerical results confirm three scaling regimes predicted before for cluster lifetime as a function of loadi…
In this paper we show that the virial expansion up to third order for the osmotic pressure of a dilute polymer solution, including first-order perturbative corrections to the virial coefficients, allows for a scaling description of phase-separation data for polymer solutions in reduced variables. This scaling description provides a method to estimate the Theta-temperature, where demixing occurs in the limit of vanishing polymer volume fraction $ϕ$ and infinite chain-length $N$, without explicit assumptions concerning the chain-length dependence of the critical parameters $T_c$ and $ϕ_c$. The s…
Large scale molecular dynamics simulations on graphic processing units (GPUs) are employed to study the scaling behavior of ring polymers with various topological constraints in melts. Typical sizes of rings containing $3_1$, $5_1$ knots and catenanes made up of two unknotted rings scale like $N^{1/3}$ in the limit of large ring sizes $N$. This is consistent with the crumpled globule model and similar findings for unknotted rings. For small ring lengths knots occupy a significant fraction of the ring. The scaling of typical ring sizes for small $N$ thus depends on the particular knot type and …
Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse in computer simulations. Primary focus of these approaches is to understand various dynamic scaling laws related to coarsening and aging during the collapse in space dimension $d=3$, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overvie…
We study the viscoelasticity of surface polymer monolayers by measuring the dynamics of thermal concentration fluctuations with surface light scattering. For various systems of proteins and synthetic polymers we find a semi-dilute regime in which both the elastic and viscous components of the dilational modulus show power law dependencies on the concentration. Surprisingly there is a universal relationship between the exponents for the two components: the viscosity scales with a power double that of the elasticity. These results cannot be explained on the basis of theory developed for bulk sys…
The hydrodynamic radius of a polymer chain, obtained using Brownian dynamics simulations of the continuum Edwards model, is found to obey a crossover in the excluded volume parameter z, which is significantly different from that observed for the radius of gyration. It is shown that this difference arises from contributions due to dynamic correlations to the diffusivity, which are ignored in the commonly used definition of hydrodynamic radius based on the Kirkwood expression. The swelling of the hydrodynamic radius from the theta-state, obtained from simulations, shows remarkable agreement with…
The rupture of a polymer chain maintained at temperature $T$ under fixed tension is prototypical to a wide array of systems failing under constant external strain and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the ta…
We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time $τ\sim N^α$ and the mean-square change of the PT coordinate $<s^2(t)> \sim t^β$. We find $α=1+2ν$ and $β=2/α$ for unbiased PT in 2D and 3D. The relation $αβ=2$ holds for driven PT in 2D, with crossover from $α\approx 2ν$ for short chains to $α\approx 1+ν$ for long chains. This crossover is, however, absent in 3D where $α= 1.42 \pm 0.01$ and $αβ\app…
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 …
We present large statistics simulations of 3-dimensional star polymers with up to $f=80$ arms, and with up to 4000 monomers per arm for small values of $f$. They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor $v<1$. We use this to allow all arms to be attached at the central site, and we use the `magic' value $v=0.6$ to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with re…
We study the elasticity of fibrous materials composed of generalized stiff polymers. It is shown that in contrast to cellular foam-like structures affine strain fields are generically unstable. Instead, a subtle interplay between the architecture of the network and the elastic properties of its building blocks leads to intriguing mechanical properties with intermediate asymptotic scaling regimes. We present exhaustive numerical studies based on a finite element method complemented by scaling arguments.
A Brownian dynamics algorithm is used to describe the static behaviour of associative polymer solutions. Predictions for the fractions of stickers bound by intra-chain and inter-chain association, as a function of system parameters, such as the number of stickers, the number of monomers between stickers, the solvent quality, and concentration are obtained. A systematic comparison with the scaling relations predicted by the mean-field theory of Dobrynin (Macromolecules, 37, 3881, 2004) is carried out. Different regimes of scaling behaviour are identified depending on the monomer concentration, …
We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of star polymers were obtained as well as provide some examples of the phenomena governed by these exponents. In particular we treat the interaction between star polymers in a good solvent, the Brownian motion near absorbing polymers, and diffusion-controlled reactions involving polymers.
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to 2-loo…
A scaling relation for the disjoining pressure of strongly confined polymer fluids is proposed for the first time, which yields directly the scaling exponent, nu, of the radius of gyration for polymers. To test the proposed scaling relation we performed extensive particle based, coarse grained computer simulations of polymers confined under theta solvent conditions and found that the value of nu agrees with the expected value for strictly two dimensional chains, nu = 4/7, which points towards the essential correctness of our scaling relation. New approaches are suggested for experimental tests…
We extend existing renormalization group calculations for the exponents describing scaling of star polymers and polymer networks constituted by chains of different species (the so-called copolymer star exponents). Our four loop results find application in the description of various phenomena involving self-avoiding and random walks that interact.
The breakdown of dynamical scaling for a dilute polymer solution in 2D has been suggested by Shannon and Choy [Phys. Rev. Lett. {\bf 79}, 1455 (1997)]. However, we show here both numerically and analytically that dynamical scaling holds when the finite-size dependence of the relevant dynamical quantities is properly taken into account. We carry out large-scale simulations in 2D for a polymer chain in a good solvent with full hydrodynamic interactions to verify dynamical scaling. This is achieved by novel mesoscopic simulation techniques.
The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been calculated recently. The walks can be considered to model the polymer-induced steric stabilisation and sensitised floculation of colloidal dispersions. The large width asymptotics led to a phase diagram different to that of a polymer attached to, and attracted to, a single wall. The question that arises is: can one interpolate between the single wall and two wall cases? In this paper we calculate the exact scaling functions for th…
We expand the blob theory for freely-jointed chains and perform molecular dynamics simulations to study the behavior of polymers confined in cylindrical channels. From weak to strong confinement, five scaling regimes, de Gennes, extended de Gennes, transition, backfolding, and Odijk regimes, are distinguished for neutral polymers.The size scalings in each regime are derived as a function of the channel width. The scaling exponents $-1$ and $-1/3$ are obtained for the transition and backfolding regimes, respectively, which result from the reduction of the excluded volume of the segments by rest…
The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density σ, assuming good solvent conditions. A phenomenological scaling theory, describing the variation of the linear dimensions of the chains with σ, is developed and tested by Molecular Dynamics simulations of a bead-spring model.
We propose a scaling description of phase separation of polymer solutions. The scaling incorporates three universal limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the "ideal-gas" limit for the pure-solvent phase, and the tricritical limit for the polymer-rich phase asymptotically close to the theta point. We have also developed a phenomenological crossover theory based on the near-tricritical-point Landau expansion renormalized by fluctuations. This theory validates the proposed scaled representation of experimental data and crossover to tricr…
The stress response of polymer double networks depends not only on the properties of the constituent networks, but also on the interactions arising between them. Here we demonstrate, via coarse-grained simulations, that both their global stress response and their microscopic fracture mechanics are governed by load sharing through these inter-network interactions. By comparing our results with affine predictions, where stress redistribution is by definition homogeneous, we show that stress redistribution is highly inhomogeneous. In particular, the affine prediction overestimates the fraction of…
A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice models are studied, one by Monte Carlo methods, the other by Molecular Dynamics, using a fast implementation on graphics processing units (GPUs). It is shown that the monomer density profiles $ρ(z)$ in the $z$-direction perpendicular to the surface for rings and linear chains are practically identical, $ρ_R(2 N_L, z)=ρ_L(N_L, z)$. The same applies to the pr…
Single domain proteins are thought to be tightly packed. The introduction of voids by mutations is often regarded as destabilizing. In this study we show that packing density for single domain proteins decreases with chain length. We find that the radius of gyration provides poor description of protein packing but the alpha contact number we introduce here characterize proteins well. We further demonstrate that protein-like scaling relationship between packing density and chain length is observed in off-lattice self-avoiding walks. A key problem in studying compact chain polymer is the attriti…
We show that the density and temperature dependences of the $α$-relaxation time of several glassforming polymers can be described through a single scaling variable $X=e(ρ)/T$, where $e(ρ)$ is well fitted by a power law $ρ^x$, $x$ being a species-specific parameter. This implies that ``fragility'' is an intrinsic, density-independent property of a glassformer characterizing its super-Arrhenius slowing down of relaxations, and it leads us to propose a modification of the celebrated Angell plot.
DNA translocation through nanopores is one of the most promising strategies for the next-generation sequencing technologies. Most part of experimental and numerical works has focused on polymer translocation biased by electrophoresis, where a pulling force acts on the polymer within the nanopore. An alternative strategy however is emerging, which uses optical or magnetic tweezers. In this case, the pulling force is exerted directly at one end of the polymer, which strongly modifies the translocation process. In this paper, we report numerical simulations of both linear and structured (mimickin…
We perform molecular-dynamics simulations for polymer melts of the coarse-grained polyvinyl alcohol model that crystallizes upon slow cooling. To establish the properties of its high temperature liquid state as a reference point, we characterize in detail the structural features of equilibrated polymer melts with chain lengths $5\le N \le 1000$ at a temperature slightly above their crystallization temperature. We find that the conformations of sufficiently long polymers with $N >50$ obey essentially the Flory's ideality hypothesis. The chain length dependence of the end-to-end distance and the…
From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander - de Gennes theory of polymer brushes successfully describes the intermembrane distance vs. applied osmotic stress data of Kenworthy et al. for PEG-grafted multilamellar liposomes [Biophys. J. (1995) 68:1921]. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equ…
The literature on self- and tracer- diffusion of polymers in solution, and on tracer diffusion of probe polymers through solutions of matrix polymers, is reviewed. I show via systematic reanalysis that the entirety of the published literature has its concentration c and matrix M and probe P molecular weight dependences described by a single functional form, namely the stretched exponential in c, P, and M. Correlations of the scaling prefactor and exponents with polymer molecular weight, concentration, and size are examined. Scaling parameters for the diffusion of star polymers do not differ su…
We present a theoretical argument to derive a scaling law between the mean translocation time $τ$ and the chain length $N$ for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions, which appear as a correction term to asymptotic scaling and are responsible for the dominant finite size effects in the process. By eliminating the correction-to-scaling term we introduce a rescaled translocation time and show, by employing both the Brownian Dynamics Tension Propagation theory [Ikonen {\it et al.}, Phys. Rev. E {\bf 85}, 051803 (2012)] and molecu…
We performed a series of simulations for a linear polymer chain in a solvent using dissipative particle dynamics to check the scaling relations for the end-to-end distance, radius of gyration and hydrodynamic radius in three dimensions. The polymer chains of up to 80 beads in explicit solvent of various quality are studied. To extract the scaling exponent ν, the data are analyzed using linear fits, correction-to-scaling forms and analytical fits to the histograms of radius of gyration distribution. For certain combinations of the polymer characteristics and solvent quality, the correction-to-s…
