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.     

Probing chain ends in adsorbed polymer layers

We study theoretically the pull-out of polymer chains from an adsorbed polymer layer by sticking of the chain ends on an opposing surface using scaling arguments and a mean field theory. When only one chain is pulled out from the layer, we extend previous results obtained for a single adsorbed chain and calculate the force necessary to extract the chain from the layer. We then discuss end adsorption from an adsorbed layer of polymers bearing specific end groups onto a second surface. Two bridging regimes are predicted: a diffuse layer regime at weak separations (or/and weak interaction) and a large separation strong interaction regime where the bridges stretch into a brush like structure. Bridging fractions and force profiles are displayed that could be compared to atomic force microscope or surface force apparatus experiments.     

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.     

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.     

Computer simulation of linkage of two ring chains

We performed off-lattice Monte Carlo simulations of links of two model ring chains with chain length N up to 32,768 in the theta solution or amorphous bulk state by using a random walk model (Model I), and molecular dynamics simulations of two model ring chains in solution with excluded volume interaction (Model II) to investigate topological effects on the geometry of link and ring conformation. In the case of Model I, the mean squared linking number, its distribution, and the size of two chains with fixed linking number are investigated. Our simulation results confirm the previous theoretical prediction that the mean squared linking number decays as pe(-qs(2)) with the distance of centers of chain mass s, where p and q are found to be chain length dependent and q asymptotically approaches to 0.75 as chain length increases. The linking number distribution of two chains has a universal form for long chains, but our simulation results clearly show that the distribution function deviates from the Gaussian distribution, a fact not predicted by any previous theoretical work. A scaling prediction is proposed to predict the link size, and is checked for our simulations for the Model II. The simulation results confirmed the scaling prediction of the blob picture that the link with linking number m occupies a compact volume of m blobs, and the size of the link is asymptotic to R(L) ≈ bN(ν)m(1/3-ν), where N is the chain length, and v is the Flory exponent of polymer in solutions.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

The equilibrium fraction of bridging chains and the swelling behavior of ABA triblock copolymer mesophases

The physical cross-linked network due to B blocks bridging different A domains of a microphase separated melt formed by an ABA copolymer in the strong-segregation limit is examined. The system is considered to consist of swollen elements of the same size, each containing an A domain and a B layer anchored to the A domain as loops or bridges. A lattice model and a generator-matrix method are employed to calculate the equilibrium fraction of the bridging B chains of the ABA mesophase and the equilibrium swelling concentration of the B layer in a selective solvent for the planar, cylindrical and spherical A domain structures. The effects of chain length and of two-dimensional surface density of the AB joints are discussed. The equilibrium fraction of the bridging chains as a function of chain stiffness and the equilibrium swelling concentration as a function of the fraction of bridging chains and of the interaction parameter are calculated. In addition, the segment density distributions of both loop and bridging chains for both the pure ABA and the swollen ABA mesophases are provided.     

Polyelectrolyte brushes

The simple scaling theory of weakly-charged polyelectrolyte brush (the layer of polyelectrolyte chains grafted at one end onto an impermeable surface) immersed into a good solvent has been developed.The asymptotic scaling dependences of the free layer thickness on charge density and solvent strength are obtained. The behavior of polyelectrolyte brush subjected to normal and tangential external forces is considered. New “polyelectrolyte effect” is predicted: shear of a free polyelectrolyte brush leads to a decrease in brush thickness in contrast to the case of a free neutral brush. Such behavior is equivalent to that of a neutral brush subjected to external normal stretching force. This force in the case of polyelectrolyte brush is created by the osmotic pressure of mobile counterions neutralizing grafted chain charges.     

Irreversible adsorption of tethered chains at substrates: Monte Carlo study

The irreversible adsorption of single chains grafted with one end to the surface is studied using scaling arguments and computer simulations. We introduce a two-phase model, in which the chain is described by an adsorbate portion and a corona portion formed by nonadsorbed monomers. The adsorption process can be viewed as consisting of a main stage, during which monomers join by "zipping" (along their order in the chain) the surface, and a late stage, in which the remaining corona collapses on the surface. Based on our model we derive a scaling relation for the time of adsorption t(M) as a function of the number M of adsorbed monomers; t(M) follows a power law, M(alpha), with alpha > 1. We find that alpha is related to the Flory exponent nu by alpha = 1 + nu. Using further scaling arguments we derive relations between the overall time of adsorption, the characteristic time of adsorption (given by the crossover time between the main and the last stage of adsorption), and the chain length. To support our analysis we perform Monte Carlo simulations using the bond fluctuation model. In particular, the sequence of adsorption events is very well reproduced by the simulations, and an analysis of the various density profiles supports our theoretical model. Especially the loop formation during adsorption clearly shows that the growth of the adsorbate is dominated by zipping. The simulations are also in almost quantitative agreement with our theoretical scaling analysis, showing that here the assumption of a linear relation between Monte Carlo steps and time is well obeyed. We conclude by also discussing the geometrical shape of the adsorbate.     

Grafted polymer layers under variable solvent conditions: A Monte Carlo simulation

Polymer chains anchored with one end at a hard wall under variable solvent conditions are investigated by Monte Carlo simulations using the bond- fluctuation model. Detail information on the structural properties are obtained above, at, and below the Θ-point and discussed in terms of the appropriate theories. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. For the dynamics at the Θ-point, both the relaxation time of the chain configuration and the mean-square time displacement are studied. At temperatures distinctly below the Θ-point, we find that the layer develops considerable lateral inhomogeneity in its density, which has not been predicted by previous theories.     

Conformational statistics of polymer chains in the interphase of semi-crystalline polymers

The microscopic structure of a semi-crystalline polymer interphase has been investigated by off-lattice Monte Carlo techniques for polyethylene-like flexible chains. In this approach, the conformational space consisting of chain populations of loops, bridges and tails is explored by robust cutting and splicing moves in real space. The simulations capture the most probable equilibrium distributions. The populations of loops and tails follow a truncated exponential distribution and the population of bridges shows a maximum as a function of chain length. For simulations of flexible chains, 40–45% of the chains form adjacent entry folds. The effect of molecular weight has been investigated. The bridge population is found to increase from 5 to 10%, for the interphase thicknesses studied, as the molecular weight of material simulated increases from ∼8000 gm/gmol to ∼30 000 gm/gmol. A Gaussian model for the interphase has been developed and compared with simulations of non-interacting phantom chains. The distributions match well at long chain lengths and deviate at short lengths.     

Adsorption of novel thermosensitive graft-copolymers: Core-shell particles prepared by polyelectrolyte multilayer self-assembly

The adsorption properties of thermosensitive graft-copolymers are investigated with the aim of developing self-assembled multilayers from these copolymers. The copolymers consist of a thermoreversible main chain of poly(N-isopropylacrylamid) and a weak polyelectrolyte, poly(2-vinylpyridine), as grafted side chains. Zeta-potential, single particle light scattering and adsorption isotherms monitor the adsorption of the thermoreversible copolymers to precoated colloidal particles. The results show a smaller surface coverage for a larger density of grafted chains. The surface coverage is discussed in terms of surface charge density in the adsorbed monolayer. Taking into account the monolayer adsorption properties, conditions are developed for the multilayer formation from these copolymers. A low pH provides a sufficient charge density of the grafted chains to achieve a surface charge reversal of the colloids upon adsorption. The charge reversal after each adsorbed layer is monitored by zeta-potential and the increase of the thickness is determined by light scattering. Stable and reproducible multilayers are obtained. The results imply that the conformation of the thermosensitive component in multilayers depends strongly on the grafting density, where the polymer with a higher grafting density adsorbs in a flat conformation while that with a lower grafting density adsorbs with more loops.     

Scaling aspects of block co-polymer adsorption on curved surfaces from nonselective solvents

In this paper, we have developed a geometric-based scaling model that describes the adsorption of diblock copolymer chains from good solvents and theta-solvents onto reactive surfaces of varying curvatures. To evaluate the impact of particle size on the adsorption process, we probed the adsorption of poly(styrene-b-methymethacrylate) (PS-PMMA) diblock copolymers from solvents with different degrees of selectivity on aluminum oxide (Al(2)O(3)) surfaces belonging to particles of different sizes. When the adsorbed PMMA layer is dense enough (in the case of a theta-solvent for the PMMA block), our results show good correlation between the theory and experimental results, pointing to the formation of a PMMA adsorption layer and a brushlike PS layer. Conversely, when adsorption occurs from a nonpreferential solvent, particularly on particles with high curvature, the PMMA adsorption layer at the surface becomes less dense and the grafted PS moiety exhibits a transitional morphology consisting of several layers of increasingly sparsely spaced blobs.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

THE ADSORPTION OF LINEAR POLY(N-ISOPROPYLACRYLAMIDE)CHAINS ON SURFACTANT-FREE POLYSTYRENE NANOPARTICLES

The adsorption of linear poly(N-isopropylacrylamide) (PNIPAM) chains on surfactant-freepolystyrene (PS) nanoparticles was used as a model system to study the hydrophobic adsorption of polymeron the surface, because the hydrophobility of PNIPAM can be continuously varied by a small temperaturechange. The adsorption was investigated by a combination of static and dynamic laser light scattering (LLS)measurements, In static LLS, the absolute excess scattered light intensity led to the amount of PNIPAMadsorbed on the surface. In dynamic LLS, the hydrodynamic thickness of the adsorbed PNIPAM layer wasaccurately measured. For a given particle concentration, the adsorption increases as thc PNIPAMconcentration and the incubation temperature increase. The average density of the adsorbed PNIPAM layer isreciprocally proportional to the number of the PNIPAM chains on the surface, revealing a simple scaling ofthe chain density distribution. The adsorption follows the Langmuir's isotherm. The enthalpy changeestimated from the adsorption at 25℃and 30℃is slightly positive, indicating that the adsorption involvesthe coil-to-globule transition of the chains on the surface.     

Structure and Dynamics of Confined Polymer Melts from Attractive Interaction to Repulsive Interaction Between Polymer and Smooth Wall

We studied the static and dynamic properties of unentangled polymer chains which have a variable strength of interaction with the confining smooth walls by means of the lattice Monte Carlo simulation based on the bond-fluctuation model, that is, investigated the wall-polymer interactions which systematically vary from attraction to repulsion. A critical value of attractive potential(ε_wc) is found to be -0.6k_BT, and only below it can the adsorption layer of monomers be formed near the wall. At the critical point of attraction ε_wc, attractive interaction counterba- lances the wall-polymer excluded volume effect, which minimizes the confinement effects on both chain dimension and mobility. Influences on both chain dimension and mobility increase with the increasing of either attraction or repulsion imposed by the walls. Despite of the nature and strength of the wall-polymer interaction, with the decrease of film thickness, configurations more parallelly aligned and flattened are adopted by confined chains, and a systematic trend of deceleration is found. Variations of chain dynamics with both film thickness and wall-polymer interaction can be well explained by the corresponding changes in the confinement of the nearest-neighboring particles that surround the chains. Besides, the thickness of the interfacial layer inside polymer films, where chains adopt a flattened “pancake” shape, is about two times the bulk radius of gyration and independent of the wall-polymer interaction.     

Scaling of mesoscale simulations of polymer melts with the bare friction coefficient

Both the Rouse and reptation model predict that the dynamics of a polymer melt scale inversely proportional with the Langevin friction coefficient xi. Mesoscale Brownian dynamics simulations of polyethylene validate these scaling predictions, providing the reptational friction xi(R)=xi+xi(C) is used, where xi(C) reflects the fundamental difference between a deterministic and a stochastic propagator even in the limit of xi to zero. The simulations have been performed with Langevin background friction and with pairwise friction, as in dissipative particle dynamics. Both simulation methods lead to equal scaling behavior with xi(C) having almost the same value in both cases. The scaling is tested for the diffusion g(t), the shear relaxation modulus G(t), and the Rouse mode autocorrelations of melts of C(120)H(242), C(400)H(802), and C(1000)H(2002). The derived dynamical scaling procedure is very useful to reduce run-time in mesoscale computer simulations, especially if pairwise friction is applied.     

Lattice Monte Carlo simulation of polymer adsorption at an interface, 1. Monodisperse polymer

Adsorption of a monodisperse polymer at a solid-liquid interface is comprehensively studied by Monte Carlo simulation. The distributions of total segment density and different adsorption configurations including trains, loops and tails are obtained. Effects of reduced exchange interaction energies $ \tilde \varepsilon $, bulk concentrations ϕ^*, reduced adsorption energies $ \tilde \varepsilon_a $ and chain lengths r on those distributions are studied. Comparisons with predictions of the Scheutjens-Fleer (SF) theory are also provided. Generally, the chain molecules are more easily adsorbed at an interface in non-solvents than in good solvents. Longer chains are more likely to be adsorbed than shorter ones. The reduced adsorption energy and the bulk concentration have shown strong effects on the segment-density distributions. In addition, the thickness of the adsorption layer is mainly determined by the extension of tails into the bulk solution, which are in turn determined by the chain length. The trains, loops and tails are overwhelmingly short. On the other hand, the amounts of trains and loops are usually much greater than that of tails. Though not perfect, satisfactory agreement is found in comparison with the theoretical predictions of the SF theory.     

Computer simulations of thin polymer layers

Molecular dynamics calculations are used to explore the structure of dense monolayers of long-chain molecules supported on a planar surface. As a model we consider ensembles of flexible chains consisting of N segments (N=32, 64 and 128) in a box with lateral (x, y) periodicity conditions. The effect of surface coverage on the conformational properties of chains is studied. At high coverages, the results of the simulations show that each chain is strongly stretched along the normal to the surface and the mean layer thickness is linear in N. The segment density distribution along the normal is found to be an universal function A^2/3 f (zA^1/3 N), where A is the surface area per chain. The high-coverage distribution has a well defined broad plateau, in agreement with the so-called blob model. In contrast to the predictions of this model, however, we observe that the chains are strongly stretched at all space scales. Differences between the results of simulations and those predicted by the mean-field theory are also discussed.