Static and dynamic properties of tethered chains at adsorbing surfaces: a Monte Carlo study

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain's extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength epsilon(c) one has M(c) approximately N(phi), and we find (using the above results) as best candidate phi to equal 0.59. However, slight changes in the estimation of epsilon(c) lead to large deviations in the resulting phi; this might be a possible reason for the difference in the phi values reported in the literature. We also investigate the dynamical scaling behavior at epsilon(c), by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at epsilon(c) the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.     

Dynamical scaling of single chains on adsorbing substrates: diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.     

Concentration and saturation effects of tethered polymer chains on adsorbing surfaces

We consider end-grafted chains at an adsorbing surface under good solvent conditions using Monte Carlo simulations and scaling arguments. Grafting of chains allows us to fix the surface concentration and to study a wide range of surface concentrations from the undersaturated state of the surface up to the brushlike regime. The average extension of single chains in the direction parallel and perpendicular to the surface is analyzed using scaling arguments for the two-dimensional semidilute surface state according to Bouchaud and Daoud [J. Phys. (Paris) 48, 1991 (1987)]. We find good agreement with the scaling predictions for the scaling in the direction parallel to the surface and for surface concentrations much below the saturation concentration (dense packing of adsorption blobs). Increasing the grafting density we study the saturation effects and the oversaturation of the adsorption layer. In order to account for the effect of excluded volume on the adsorption free energy we introduce a new scaling variable related with the saturation concentration of the adsorption layer (saturation scaling). We show that the decrease of the single chain order parameter (the fraction of adsorbed monomers on the surface) with increasing concentration, being constant in the ideal semidilute surface state, is properly described by saturation scaling only. Furthermore, the simulation results for the chains' extension from higher surface concentrations up to the oversaturated state support the new scaling approach. The oversaturated state can be understood using a geometrical model which assumes a brushlike layer on top of a saturated adsorption layer. We provide evidence that adsorbed polymer layers are very sensitive to saturation effects, which start to influence the semidilute surface scaling even much below the saturation threshold.     

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

We investigate the localization of a hydrophobic-polar 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 chi. 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( parallel) 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相似文献   

The critical adsorption point of self-avoiding walks: a finite-size scaling approach

The critical adsorption of self-avoiding polymer chain in a simple cubic lattice onto a flat surface is studied with Monte Carlo simulations. The dependence of number of surface contacts M on chain length N and polymer-surface interaction epsilon is investigated by a finite-size scaling approach. We estimate the critical adsorption point epsilon(c)=0.291+/-0.002 and the exponent phi=0.54+/-0.01. The asymptotic behaviors M proportional variant N for epsilon>epsilon(c) and M proportional variant N(0) for epsilon相似文献   

Random copolymers at a selective interface: saturation effects

Combining scaling arguments and Monte Carlo simulations using the bond fluctuation method we have studied concentration effects for the adsorption of symmetric AB-random copolymers at selective, symmetric interfaces. For the scaling analysis we consider a hierarchy of two length scales given by the excess (adsorption) blobs and by two dimensional thermal blobs in the semidilute surface regime. When both length scales match, a densely packed array of adsorption blobs is formed (saturation). We show that for random copolymer adsorption the interface concentration can be further increased (oversaturation) due to reorganization of excess blobs. Crossing over this threshold results in a qualitative change in the behavior of the adsorption layer which involves a change in the average shape of the adsorbed chains towards a hairpinlike form. We have analyzed the distribution of loops and tails of adsorbed chains in the various concentration regimes as well as the chain order parameter, concentration profiles, and the exchange rate of individual chains. We emphasized the role of saturation scaling which dominates the behavior of static and dynamic quantities at higher surface concentration.     

Monte carlo simulation of polymers in steady potential flows

This work presents a study of the configurational properties of bead-spring chains in steady-state potential flows. These properties are obtained from off-lattice Monte Carlo simulations. The results of our simulations compare favourably with theoretical results for phantom chains. We investigate the effects of excluded volume and hydrodynamic interaction on the configurations of the chains, and compare our results to the predictions of scaling arguments. The scaling law observed here for the latter case deviates from theoretical predictions but is in agreement with findings reported from molecular dynamics simulations.     

Adsorption of semiflexible block copolymers on homogeneous surfaces

We present the results of extensive numerical off-lattice Monte Carlo simulations of semiflexible block-copolymer chains adsorbed onto flat homogeneous surfaces. We have compared the behavior of several chain structures, such as homopolymers, diblocks, (A(alpha)B(alpha)) block copolymers, and random heteropolymers. In all the cases studied, we have found the adsorption process to be favored with an increase of the chain rigidity. Particularly, the adsorption of diblock structures becomes a two-step process characterized by two different adsorbing temperatures that depend on the chain stiffness kappa, the chain length N, and the adsorbing energies epsilon(A) and epsilon(B). This twofold adsorbing process changes to a single one for copolymers of reduced block size alpha. Each block of the stiff copolymer chain is found to satisfy the classical scaling laws for flexible chains, however, we found the scaling exponent phi to depend on the chain stiffness. The measurement of the radius of gyration exhibits a typical behavior of a polymer chain composed of Nl(p) blobs whose persistence length follows l(p) approximately (kappa/k(B)T)(0.5) for large stiff chains.     

Calcium mediated polyelectrolyte adsorption on like-charged surfaces

Monte Carlo simulations within the primitive model of calcium-mediated adsorption of linear and comb polyelectrolytes onto like-charged surfaces are described, focusing on the effect of calcium and polyion concentrations as well as on the ion pairing between polymers and calcium ions. We use a combination of Monte Carlo simulations and experimental data from titration and calcium binding to quantify the ion pairing. The polymer adsorption is shown to occur as a result of surface overcharging by Ca(2+) and ion pairing between charged monomers and Ca(2+). In agreement with experimental observations, the simulations predict that the polymer adsorption isotherm goes through a maximum as the calcium or the polymer concentration is increased. The non-Langmuir isotherms are rationalized in terms of charge-charge correlations.     

Folding probabilities: a novel approach to folding transitions and the two-dimensional Ising-model

The theoretical concept of folding probability, p(fold), has proven to be a useful means to characterize the kinetics of protein folding. Here, we illustrate the practical importance of p(fold) and demonstrate how it can be determined theoretically. We derive a general analytical expression for p(fold) and show how it can be estimated from simulations for systems where the transition rates between the relevant microstates are not known. By analyzing the Ising model we are able to determine the scaling behavior of the numerical error in the p(fold) estimate as function of the number of analyzed Monte Carlo runs. We apply our method to a simple, newly developed protein folding model for the formation of alpha helices. It is demonstrated that our technique highly parallelizes the calculation of p(fold) and that it is orders of magnitude more efficient than conventional approaches.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Critical polymer-polymer phase separation in ternary solutions

We study polymer-polymer phase separation in a common good solvent by means of Monte Carlo simulations of the bond-fluctuation model. Below a critical, chain-length-dependent concentration, no phase separation occurs. For higher concentrations, the critical demixing temperature scales nonlinearly with the total monomer concentration, with a power law relatively close to a renormalization-group prediction based on "blob" scaling arguments. We point out that earlier simulations and experiments have tested this power-law dependence at concentrations outside the validity regime of the scaling arguments. The critical amplitudes of the order parameter and the zero-angle scattering intensity also exhibit chain-length dependences that differ from the conventional predictions but are in excellent agreement with the renormalization-group results. In addition, we characterize the variation of the average coil shape upon phase separation.     

Surface order-disorder phase transitions and percolation

In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in the presence of repulsive interactions have been considered. Namely, monomers on honeycomb, square, and triangular lattices, and dimers (particles occupying two adjacent adsorption sites) on square substrates. By using Monte Carlo simulation and finite-size scaling analysis, we obtain the percolation threshold theta(c) of the adlayer, which presents an interesting dependence with w/k(B)T (w, k(B), and T being the lateral interaction energy, the Boltzmann constant, and the temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a nonpercolating region is determined.     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Effects of lateral diffusion on the dynamics of desorption

The adsorbate dynamics during simultaneous action of desorption and lateral adsorbate diffusion is studied in a simple lattice-gas model by kinetic Monte Carlo simulations. It is found that the action of the coverage-conserving diffusion process during the course of the desorption has two distinct, competing effects: a general acceleration of the desorption process, and a coarsening of the adsorbate configuration through Ostwald ripening. The balance between these two effects is governed by the structure of the adsorbate layer at the beginning of the desorption process.     

Boltzmann bias grand canonical Monte Carlo

We derive an efficient method for the insertion of structured particles in grand canonical Monte Carlo simulations of adsorption in very confining geometries. We extend this method to path integral simulations and use it to calculate the isotherm of adsorption of hydrogen isotopes in narrow carbon nanotubes (two-dimensional confinement) and slit pores (one-dimensional confinement) at the temperatures of 20 and 77 K, discussing its efficiency by comparison to the standard path integral grand canonical Monte Carlo algorithm. We use this algorithm to perform multicomponent simulations in order to calculate the hydrogen isotope selectivity for adsorption in narrow carbon nanotubes and slit pores at finite pressures. The algorithm described here can be applied to the study of adsorption of real oligomers and polymers in narrow pores and channels.     

Quantum Drude oscillator model for describing the interaction of excess electrons with water clusters: an application to (H2O)13(-)

Cluster anions for which the excess electron occupies an extended nonvalence orbital can be described by use of a model Hamiltonian employing quantum Drude oscillators to represent the polarizable charge distributions of the monomers. In this work, a Drude model for water cluster anions is described and used to investigate the (H2O)13(-) cluster. Several low-energy isomers are characterized, and the finite-temperature properties of the cluster are investigated by means of parallel tempering Monte Carlo simulations. Two structural motifs, one with double-acceptor water monomers and the other with four-membered rings of double-acceptor single-donor monomers with four free OH groups pointed in the same direction, are found to lead to large (approximately > eV) electron binding energies. The distributions of the computed vertical detachment energies qualitatively reproduce the experimentally measured photoelectron spectrum, and our simulations indicate that both of the main peaks in the measured spectrum derive from several isomers.     

Polymers confined between two parallel plane walls

Single three-dimensional polymers confined to a slab, i.e., to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by N-step walks on a simple cubic lattice confined to the region 1< or = z < or = D. The simulations cover both regions DRF (where RF approximately Nnu is the Flory radius, with nu approximately 0.587), as well as the cross-over region in between. Chain lengths are up to N=80 000, slab widths up to D=120. In order to test the analysis program and to check for finite size corrections, we actually studied three different models: (a) ordinary random walks (mimicking Theta polymers); (b) self-avoiding walks; and (c) Domb-Joyce walks with the self-repulsion tuned to the point where finite size corrections for free (unrestricted) chains are minimal. For the simulations we employ the pruned-enriched-Rosenbluth method with Markovian anticipation. In addition to the partition sum (which gives us a direct estimate of the forces exerted onto the walls), we measure the density profiles of monomers and of end points transverse to the slab, and the radial extent of the chain parallel to the walls. All scaling laws and some of the universal amplitude ratios are compared to theoretical predictions.     

Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

Computer simulation of the adsorption of light gases in covalent organic frameworks

Grand canonical Monte Carlo simulations of argon, hydrogen, and methane adsorption in four covalent organic frameworks are presented. Argon adsorption isotherms from computer simulations overestimate the amount adsorbed by 25% upon saturation, with respect to the available experiments at T = 87 K. Hydrogen adsorption isotherms show that these materials might attain a 30% increase for the uptake when compared with analogous simulations performed for metal organic frameworks at T = 77 K and T = 298 K. Methane adsorption isotherms give a strong indication that at least one material in this class, COF-102, could meet or exceed the Department of Energy's target of 180 cm3 (STP)/cm3 for P = 35 bar and room temperature. The origin of this large affinity for methane is investigated by analyzing the structure of the potential energy surface of interaction between the adsorbate and the adsorbent.