Forced-Induced Desorption of a Polymer Chain Adsorbed on an Attractive Surface: Theory and Computer Experiment

Langevin dynamics simulation on optimal conditions for large and stable loops of adsorbed homopolymers on substrates

Adsorption of polymer chains on a solid surface is a universal interfacial behavior. Loops in the adsorbed chains are considered to exert a significant effect on the overall properties of a substrate-supported polymer film via entanglement with non-adsorbed chains in the film. In this work, the size and stability of loops formed by adsorbed homopolymer chains on an attractive substrate were studied by Langevin dynamics simulations. The size of loops decreases while the stability increases with increasing attraction strength of the substrate. In contrast, with an increase in the polymer concentration, the size of loops increases but the stability decreases. However, both the size and stability of loops increase with increasing chain length. Simulation results show that the optimal conditions for forming large and stable loops are long homopolymer chains, substrates with moderate attraction strength, and moderate polymer concentration.

Partition-function-zero analysis of polymer adsorption for a continuum chain model

Polymer chains undergoing adsorption are expected to show universal critical behavior which may be investigated using partition function zeros. The focus of this work is the adsorption transition for a continuum chain, allowing for investigation of a continuous range of the attractive interaction and comparison with recent high-precision lattice model studies. The partition function (Fisher) zeros for a tangent-hard-sphere N-mer chain (monomer diameter σ) tethered to a flat wall with an attractive square-well potential (range λσ, depth ε) have been computed for chains up to N=1280 with 0.01≤λ≤2.0. In the complex-Boltzmann-factor plane these zeros are concentrated in an annular region, centered on the origin and open about the real axis. With increasing N, the leading zeros, w_{1}(N), approach the positive real axis as described by the asymptotic scaling law w_{1}(N)-y_{c}∼N^{-ϕ}, where y_{c}=e^{ε/k_{B}T_{c}} is the critical point and T_{c} is the critical temperature. In this work, we study the polymer adsorption transition by analyzing the trajectory of the leading zeros as they approach y_{c} in the complex plane. We use finite-size scaling (including corrections to scaling) to determine the critical point and the scaling exponent ϕ as well as the approach angle θ_{c}, between the real axis and the leading-zero trajectory. Variation of the interaction range λ moves the critical point, such that T_{c} decreases with λ, while the results for ϕ and θ_{c} are approximately independent of λ. Our values of ϕ=0.479(9) and θ_{c}=56.8(1.4)^{∘} are in agreement with the best lattice model results for polymer adsorption, further demonstrating the universality of these constants across both lattice and continuum models.

Adsorption and Desorption of Polymers on Bioinspired Chemically Structured Substrates

Natural biological surfaces exhibit interesting properties due to their inhomogeneous chemical and physical structure at the micro- and nanoscale. In the case of hair or skin, this also influences how waterborne macromolecules ingredients will adsorb and form cosmetically performing deposits (i.e., shampoos, cleansers, etc.). Here, we study the adsorption of hydrophilic flexible homopolymers on heterogeneous, chemically patterned substrates that represent the surface of the hair by employing coarse-grained molecular dynamics simulations. We develop a method in which the experimental images of the substrate are used to obtain information about the surface properties. We investigate the polymer adsorption as a function of polymer chain length and polymer concentration spanning both dilute and semidilute regimes. Adsorbed structures are quantified in terms of trains, loops, and tails. We show that upon increasing polymer concentration, the length of tails and loops increases at the cost of monomers belonging to trains. Furthermore, using an effective description, we probe the stability of the resulting adsorbed structures under a linear shear flow. Our work is a first step toward developing models of complex macromolecules interacting with realistic biological surfaces, as needed for the development of more ecofriendly industrial products.

Self-Consistent Field Modeling of Pulling a Test-Chain away from or Pushing It into a Polymer Adsorption Layer

We consider single chain force measurements to unravel characteristics of polymers at interfaces and to determine parameters that control adsorption or probe layer characteristics that are difficult to access otherwise. The idea is to have at the tip of an atomic force microscope (AFM), a probe chain and measure its behaviour near interfaces by pushing it to, or pulling it away from it. The self-consistent field modeling of this reveals that in the pulling mode—i.e., when the chain has an affinity for the surface—a typically inhomogeneous flower-like conformation forms with an adsorbed ’pancake’ and a stretched stem (tether) from the surface to the tip of the AFM. When about half the segments is in the tether it snaps loose in a first-order like fashion. The critical distance of the end-point from the surface and the critical force are experimentally accessible. Details of this transition depend on the surrounding of the test chain. Inversely, and this opens up many possibilities, the test chain reports about its surroundings. Our focus is on the classical case of homopolymers at interfaces. Pulling experiments may reveal the adsorption strength, the (average) chain length and/or the polymer concentration of the freely dispersed/adsorbed polymers. When the test-chain is non-adsorbing we envision that pushing this test-chain into the adsorption layer reports about various layer characteristics such as the layer thickness and (local) density. Moreover, when the test-chain has a length longer than the entanglement length, we can imagine that non-trivial dynamical properties of loops and tails may be scrutinised.

Effect of Uniformly Applied Force and Molecular Characteristics of a Polymer Chain on Its Adhesion to Graphene Substrates

The force-induced desorption of a polymer chain from a graphene substrate is studied with molecular dynamics (MD). A critical force needs to be exceeded before detachment of the polymer from the substrate. It is found that for a chain to exhibit good adhesive properties the chain configuration should consist of fibrils-elongated, aligned sections of polymers and cavities which dissipate the applied energy. A fibrillation index is defined to quantify the quality of fibrils. We focus on the molecular properties of the polymer chain, which can lead to large amounts of fibrillation, and find that both strong attraction between the polymer and substrate and good solvency conditions are important conditions for this. We also vary the stiffness of the chain and find that for less stiff chains a plateau in the stress-strain curve gives rise to good adhesion however for very stiff chains there is limited elongation of the chain but the chain can still exhibit good fibrillation by a lamella-like rearrangement. Finally, it is found that the detachment time, t, of a polymer from the adsorbed substrate is inversely proportional to force, F (i.e., t ∝ F(-γ)), where exponent γ depends on the solvent quality, polymer-substrate attraction, and chain stiffness.

Adsorption-induced changes of the structure of the tethered chain layers in a simple fluid

We use density functional theory to study the influence of fluid adsorption on the structure of grafted chain layer. The chains are modeled as freely jointed spheres. The chain segments and spherical molecules of the fluid interact via the Lennard-Jones potential. The fluid molecules are attracted by the substrate. We calculate the excess adsorption isotherms, the average height of tethered chains, and the force acting on selected segments of the chains. The parameters that were varied include the length of grafted chains, the grafting density, the parameters characterizing fluid-chain and fluid-surface interactions, the bulk fluid density, and temperature. We show that depending on the density of the bulk fluid the height of the bonded layer increases, remains constant, or decreases with increasing temperature.

Force spectroscopy of polymer desorption: theory and molecular dynamics simulations

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.

Stretching tethered polymer chains: density functional approach

We propose application of density functional theory to calculate the force acting on a selected segment of a tethered polymer chain that leads to stretching the chain. The density functional allows one to determine the effects due to the presence of other chains and solvent molecules. For high and moderate solvent densities the plot of the force versus the distance of the segment from the surface exhibits oscillatory behavior that has not been predicted by other approaches.

Brownian dynamics simulation of peeling a strongly-adsorbed polymer molecule from a frictionless substrate

We used brownian dynamics to study the peeling of a polymer molecule, represented by a freely jointed chain, from a frictionless surface in an implicit solvent with parameters representative of single-stranded DNA adsorbed on graphite. For slow peeling rates, simulations match the predictions of an equilibrium statistical thermodynamic model. We show that deviations from equilibrium peeling forces are dominated by a combination of Stokes (viscous) drag forces acting on the desorbed section of the chain and a finite rate of hopping over a desorption barrier. Characteristic velocities separating equilibrium and nonequilibrium regimes are many orders of magnitude higher than values accessible in force spectroscopy experiments. Finite probe stiffness resulted in disappearance of force spikes due to desorption of individual links predicted by the statistical thermodynamic model under displacement control. Probe fluctuations also masked sharp transitions in peeling force between blocks of distinct sequences, indicating limitation in the ability of single-molecule force spectroscopy to distinguish small differences in homologous molecular structures.

Adsorption of a single polymer chain on a surface: effects of the potential range

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value U(c) corresponding to the adsorption transition scales as W(-1/ν), where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory U(c)≈(π(2)/24)(W+1/2)(-2) and in the best-fit equation for the MC simulation data U(c)=0.585(W+1/2)(-5/3). Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NU(c),U/U(c)). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value <R(g[perpendicular])(2)>/<R(g[parallel])(2)>=0.320±0.003 only at N~5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent φ(eff)(N). Strong corrections to scaling of order N(-0.5) are observed, and the extrapolated value φ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of φ(eff)(N) were identified as the asymptotic value for the crossover exponent.

Structure and dynamics of a polymer melt at an attractive surface

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 is proportional to √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.

Stretching semiflexible polymer chains: evidence for the importance of excluded volume effects from Monte Carlo simulation

Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice (d = 3 dimensions) and square lattice (d = 2 dimensions), varying chain stiffness by an energy penalty ε(b) for chain bending. In the absence of excluded volume interactions, the persistence length l(p) of the polymers would then simply be l(p) = l(b)(2d - 2)(-1)q(b) (-1) with q(b) = exp(-ε(b)/k(B)T), the bond length l(b) being the lattice spacing, and k(B)T is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both q(b) and the chain length N are varied over a wide range (0.005 ≤ q(b) ≤ 1, N ≤ 50,000), and also a stretching force f is applied to one chain end (fixing the other end at the origin). In the absence of this force, in d = 2 a single crossover from rod-like behavior (for contour lengths less than l(p)) to swollen coils occurs, invalidating the Kratky-Porod model, while in d = 3 a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in d = 2, while theories based on the Kratky-Porod model are found to work in d = 3 for stiff chains in an intermediate regime of chain extensions. While for q(b) ≪ 1 in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g., bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.

Mechanical desorption of a single chain: unusual aspects of phase coexistence at a first-order transition

The phase transition occurring when a single polymer chain adsorbed at a planar solid surface is mechanically desorbed is analyzed in two statistical ensembles. In the force ensemble, a constant force applied to the nongrafted end of the chain (that is grafted at its other end) is used as a given external control variable. In the z-ensemble, the displacement z of this nongrafted end from the surface is taken as the externally controlled variable. Basic thermodynamic parameters, such as the adsorption energy, exhibit a very different behavior as a function of these control parameters. In the thermodynamic limit of infinite chain length the desorption transition with the force as a control parameter clearly is discontinuous, while in the z-ensemble continuous variations are found. However, one should not be misled by a too-naive application of the Ehrenfest criterion to consider the transition as a continuous transition: rather, one traverses a two-phase coexistence region, where part of the chain is still adsorbed and the other part desorbed and stretched. Similarities with and differences from two-phase coexistence at vapor-liquid transitions are pointed out. The rounding of the singularities due to finite chain length is illustrated by exact calculations for the nonreversal random walk model on the simple cubic lattice. A new concept of local order parameter profiles for the description of the mechanical desorption of adsorbed polymers is suggested. This concept give evidence for both the existence of two-phase coexistence within single polymer chains for this transition and the anomalous character of this two-phase coexistence. Consequences for the proper interpretation of experiments performed in different ensembles are briefly mentioned.

Pulling an adsorbed polymer chain off a solid surface

The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain-ends is investigated. We perform our study in the "fixed height" statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain-end is kept fixed at height h over the solid plane at different adsorption strength [Formula: see text]. The phase diagram in the h-[Formula: see text] 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.

Polymer desorption under pulling: a dichotomic phase transition

The structural properties and phase behavior of a self-avoiding polymer chain on an adhesive substrate, subject to pulling at the chain end, are described by means of a grand canonical ensemble approach. We derive 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 applied pulling force f . In contrast to conventional, f=0 , polymer adsorption, the chain detachment transition under pulling turns out to be of first (rather than second) order, albeit it is dichotomic, i.e., no coexistence of different phase states exists. Also, the hitherto controversial value of the critical adsorption exponent varphi is found to depend essentially on the degree of interaction between different loops so that 0.34< or =varphi< or =0.59 . The theoretical predictions are verified by means of extensive Monte Carlo simulations.