A range of technologies require the directed motion of nanoscale droplets on solid substrates. A way of realizing this effect is durotaxis, whereby a stiffness gradient of a substrate can induce directional motion without requiring an energy source.
Here, we report on the results of extensive molecular dynamics investigations of droplets on a surface with varying stiffness. We find that durotaxis is enhanced by increasing the stiffness gradient and, also, by increased wettability of the substrate, in particular, when droplet size decreases. We anticipate that our study will provide further insights into the mechanisms of nanoscale directional motion.
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 s
aw-tooth profile of the measured mean force $< f >$ vs height $D$ of the end-segment over the plane is analyzed for a broad variety of parameters. It is shown that the observed characteristic oscillations in the $< f >$-$D$ profile depend on the bending and not on the torsional stiffness of the detached chains. Allowing for the presence of hydrodynamic interactions (HI) in a setup with explicit solvent and DPD-thermostat, rather than the case of Langevin thermostat, one finds that HI have little effect on the $< f >$-$D$ profile. Also the change of substrate affinity with respect to the solvent from solvophilic to solvophobic is found to play negligible role in the desorption process. In contrast, a changing ratio $epsilon_s^A / epsilon_s^B$ of the binding energies of $A$- and $B$-segments in the detachment of an $AB$-copolymer from adhesive surface strongly changes the $< f >$-$D$ profile whereby the $B$-spikes vanish when $epsilon_s^A / epsilon_s^B < 0.15$. Eventually, performing an atomistic simulation of a (bio)-polymer {it polyglycine}, we demonstrate that the simulation results, derived from our coarse-grained model, comply favorably with those from the all-atom simulation.
The escape transition of a polymer mushroom (a flexible chain grafted to a flat non-adsorbing substrate surface in a good solvent) occurs when the polymer is compressed by a cylindrical piston of radius $R$, that by far exceeds the chain gyration rad
ius. At this transition, the chain conformation abruptly changes from a two-dimensional self-avoiding walk of blobs (of diameter $H$, the height of the piston above the substrate) to a flower conformation, i.e. stretched almost one-dimensional string of blobs (with end-to-end distance $approx R$) and an escaped part of the chain, the crown, outside the piston. The extension of this problem to the case of star polymers with $f$ arms is considered, assuming that the center of the star is grafted to the substrate. The question is considered whether under compression the arms escape all together, or whether there occurs an arm by arm escape under increasing compression. Both self-consistent field calculations and Molecular Dynamics simulations are found to favor the latter scenario.
The free energy cost of confining a star polymer where $f$ flexible polymer chains containing $N$ monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance $D$ apart is considered, for good solvent conditio
ns. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens-Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent field (SCF) theory yield the correct scaling of the parallel linear dimension of the star with $N$, $f$ and $D$, but cannot be used for estimating the free energy cost reliably. We demonstrate that the same problem occurs already for the confinement of chains in cylindrical tubes. We also briefly discuss the problem of a free or grafted star polymer interacting with a single wall, and show that the dependence of confining force on the functionality of the star is different for a star confined in a nanoslit and a star interacting with a single wall, which is due to the absence of a symmetry plane in the latter case.
A comparative dynamic Monte Carlo simulation study of polydisperse living polymer brushes, created by surface initiated living polymerization, and conventional polymer monodisperse brush, comprising linear polymer chains, grafted to a planar substrat
e under good solvent conditions, is presented. The living brush is created by end-monomer (de)polymerization reaction after placing an array of initiators on a grafting plane in contact with a solution of initially non-bonded segments (monomers). At equilibrium, the monomer density profile phi(z) of the LPB is found to decline as phi(z) ~ z^{-alpha} with the distance from the grafting plane z, while the distribution of chain lengths in the brush scales as c(N) ~ N^{-tau}. The measured values alpha = 0.64 and tau = 1.70 are very close to those, predicted within the framework of the Diffusion-Limited Aggregation theory, alpha = 2/3 and tau = 7/4. At varying mean degree of polymerization (from L = 28 to L = 170) and effective grafting density (from sigma_g = 0.0625 to sigma_g = 1.0), we observe a nearly perfect agreement in the force-distance behavior of the simulated LPB with own experimental data obtained from colloidal probe AFM analysis on PNIPAAm brush and with data obtained by Plunkett et. al., [Langmuir 2006, 22, 4259] from SFA measurements on same polymer.
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 $D(t) propto t^{gamma}$ where $gamma < 1$. 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 $alpha$ which describes the scaling of the mean translocation time $<tau>$ with the length $N$ of the polymer, $<tau> propto N^{alpha}$ 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 non-driven case, $f=0$, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).
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 ch
ange 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 $<tau_d>$, scales with polymer length $N$ as $<tau_d> propto N^2$. Our main theoretical conclusions are tested and found in agreement with data from extensive MC- and MD-simulations.
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 $sigma_g$ of the side chains? How does tension $f$ depend on the length of the side chains $N$, and on the strength of surface adhesion $epsilon_s$? We examine the monomer density distribution profiles across the BB-backbone at different $epsilon_s$ 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 $epsilon_s$, too long side chains mutually block each other and freeze effectively the bottle-brush molecule.
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 invest
igate 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 $<tau>$ of bonds decays with membrane size as $<tau> propto N^{-beta}$ where $beta approx 0.50pm 0.03$ and $N$ denotes the number of atoms in the membrane. The probability distribution of bond scission times $t$ is given by a Poisson function $W(t) propto t^{1/3} exp (-t / <tau>)$. The mean failure time $<tau_r>$ that takes to rip-off the sheet declines with growing size $N$ as a power law $<tau_r> propto N^{-phi(f)}$. We also find $<tau_r> propto exp(Delta U_0/k_BT)$ where the nucleation barrier for crack formation $Delta U_0 propto f^{-2}$, in agreement with Griffiths theory. $<tau_r>$ displays an Arrhenian dependence of $<tau_r>$ on temperature $T$. Our results indicate a rapid increase in crack spreading velocity with growing external tension $f$.
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 f
orce 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 $<tau>$ changes from $<tau> sim N^{2 u}/f^{1/ u}$ to $<tau> sim N^{1+ u}/f$ (for the free-draining case) as the dimensionless force ${widetilde f}_{R} = a N^{ u}f /T$ (where $a$, $N$, $ u$, $f$, $T$ 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 $alpha$ grows with the pulling force ${widetilde f}_{R}$) albeit the observed exponent $alpha$ stays systematically smaller than the theoretically predicted value. This might be associated with fluctuations which are neglected in the quasi-static approximation.
