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

Force-driven translocation of a macromolecule through a nanopore is investigated systematically by taking into account the monomer-pore friction as well as the "crowding" of monomers on the trans-side of the membrane which counterbalance the driving force acting in the pore. The problem is treated self-consistently, so that the resulting force in the pore and the dynamics on the cis and trans sides mutually influence each other. 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 ∝ N(α), becomes smaller for relatively small chain lengths as the monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings show that the variety of values for α reported in experiments and computer simulations, may be attributed to different pore frictions, whereas crowding effects can generally be neglected.

This chapter deals with the mechanical properties of single polymer chains, aggregates, and supramolecular complexes. The topics discussed cover a broad range from fundamental statistical mechanics of the equilibrium elastic properties of single polymer chains to details of the behavior of binding pockets in biomolecular assemblies as observed by force spectroscopy. The first section treats the equilibrium mechanical properties of single polymer chains in various environments, investigated via extensive simulations employing coarse-grained models that have proven extremely successful in many branches of polymer physics, namely the bond-fluctuation model and the self-avoiding walk model. Apart from the phase behavior and the adsorption properties, the mechanical pulling of a polymer chain from a surface has also been investigated. Molecular dynamics (MD) simulations of spring-bead models and analytical theory are used to describe the stochastic dynamics of the system. After these sections treating fundamental aspects of mechanical adsorption and translocation of polymer chains, we consider the adhesion of specific molecular systems to form networks of hydrogen bonds. In particular, we discuss all-atom force probe MD simulations of calixarene catenane systems, which have recently been synthesized. These simulations have been performed in close collaboration with corresponding experimental investigations utilizing atomic force spectroscopy (AFS) on the same systems, which will be reviewed together with other experimental determinations of the mechanical properties of supramolecular assemblies. Although these investigations can give insight into the reversible dynamics of hydrogen-bond networks, AFS can also be used in order to determine chemical equilibria under the impact of mechanical forces. Corresponding studies of this type are reviewed in the last section.

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 a 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 vc (displacement control mode) and find that the average magnitude of this force increases as vc increases. The probability distributions of the pulling force and the end-monomer distance from the surface at the moment of the final detachment are investigated for different adsorption energies ε and pulling velocities vc. Our extensive MD simulations validate and support the main theoretical findings. Moreover, the simulations reveal a novel behavior: for a strong-friction and massive cantilever the force spike pattern is smeared out at large vc. As a challenging task for experimental bio-polymer sequencing in future we suggest the fabrication of a stiff, super-light, nanometer-sized AFM probe.

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 = 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 time-dependent diffusion coefficient D(t). Our MD simulation reveals that the driven translocation process follows a super diffusive law with a running diffusion coefficient D(t)alpha t(gamma) where < 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 a which describes the scaling of the mean translocation time with the length N of the polymer, alpha N-alpha 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 nondriven case, f = 0, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).

In a series of studies we consider the breakage of a polymer chain of segments, coupled by anharmonic bonds under applied tensional force or subject to rise in temperature. The chain dynamics at the onset of fracture is studied by means of Molecular Dynamics simulation and also using analytic considerations.A deeper insight into the changes in polymer relaxation dynamics when bonding anharmonicity is taken into account, that is, beyond the limits of the conventional Rouse model description, is gained by comparing analytic results from the Gaussian Self-Consistent approach to data derived from Monte Carlo and Molecular Dynamics simulations. Simulation results on polymer chain rupture are confronted with the predictions of Kramers-Langer theory. Two cases are investigated: a) thermally induced fracture of unstrained chain, and b) rupture of a chain under tensile stress. Cases of both underand overdamped dynamics are explored. The recently experimentally observed and intensively studied case of covalent bond scission in “bottle-brush” macromolecules adsorbed on a hard surface is modeled and comprehensively investigated with regard to tension accumulation and breakdown kinetics. Eventually we report on our latest studies of the force-induced rupture and thermal degradation of 2D (graphene-like) networks, focusing on the creation and proliferation of cracks during failure.

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

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 segments of the backbone with grafting density σg. 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. Our simulation results indicate that the mean life time of covalent bonds decreases by more than an order of magnitude upon adsorption even for brush molecules with comparatively short side chains . The distribution of scission probability along the bonds of the backbone is found to change significantly when the length and/or the grafting density of the side chains are varied. The tension, experienced by the covalent bonds is found to grow steadily with increasing σg. The mean life time declines with growing contour length L as , and also with growing side chain length N. The probability distribution of fragment lengths at different times is compatible with experimental observations and reveals a two-stage (initially fast, then slow) process with different rates. The variation of the mean length L(t) of the fragments with elapsed time characterizes the thermal degradation process as a first order reaction.

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 , scales with polymer length N as proportional to N-2. Our main theoretical conclusions are tested and found in agreement with data from extensive MC- and MD-simulations.

We suggest a theoretical description of the force-induced translocation dynamics of a polymer chain through a nanopore. Our consideration is based on the tensile (Pincus) blob picture of a pulled chain and the notion of a propagating front of tensile force along the chain backbone, suggested by Sakaue [Phys. Rev. E 76, 021803 (2007); 81, 041808 (2010); Eur. Phys. J. E 34, 135 (2011)]. The driving force is associated with a chemical potential gradient that acts on each chain segment inside the pore. Depending on its strength, different regimes of polymer motion (named after the typical chain conformation: trumpet, stem-trumpet, etc.) occur. Assuming that the local driving and drag forces are equal (i.e., in a quasistatic approximation), we derive an equation of motion for the tensile front position X(t). We show that the scaling law for the average translocation time changes from similar to N-2 nu/f(1/nu) to similar to N1+nu/f (for the free-draining case) as the dimensionless force (f) over tilde (R) = aN(nu)f/T (where a, N,nu, f, and T are the Kuhn segment length, the chain length, the Flory exponent, the driving force, and the temperature, respectively) increases. These and other predictions are tested by molecular-dynamics simulation. Data from our computer experiment indicate indeed that the translocation scaling exponent a grows with the pulling force (f) over tilde (R), albeit the observed exponent a stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations that are neglected in the quasistatic approximation.

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> ∼ N^2ν/f^1/ν to <τ> ∼ N^1+ν/f (for the free-draining case) as the dimensionless force 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 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.

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

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〉∝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.

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 lifetime 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 lifetime declines with growing contour length L as proportional to L-0.17 and with side-chain length as proportional to 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 indicates the possibility that two different mechanisms may govern the fragmentation process.

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.

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.