Impenetrable Surface Research Articles

Exact results for the adsorption of a semiflexible copolymer chain in three dimensions

Lattice model of directed self-avoiding walk has been solved analytically to investigate adsorption–desorption phase transition behaviour of a semiflexible sequential copolymer chain on a two-dimensional impenetrable surface perpendicular to the preferred direction of the walk of the copolymer chain in three dimensions. The stiffness of the chain has been accounted by introducing an energy barrier for each bend in the walk of the copolymer chain. Exact value of adsorption–desorption transition points have been determined using the generating function method for the cases in which one type of monomer is having interaction with the surface, namely (i) no interaction (ii) attractive interaction and (iii) repulsive interaction. Results obtained in each of the case show that for stiffer copolymer chain adsorption transition occurs at a smaller value of monomer surface attraction than a flexible copolymer chain. These features are similar to that of a semiflexible homopolymer chain adsorption.

Effect of Comonomer Sequence Distribution on the Adsorption of Random Copolymers onto Impenetrable Flat Surfaces

We study the effect of comonomer sequence distributions in random copolymers (RCPs) on RCP adsorption on flat impenetrable surfaces. RCP poly(styrene-co-4-bromostyrene) (PBrxS), where x denotes the mole fraction of 4-bromostryrene (4-BrS), is prepared by bromination of parent homopolystyrene. By varying the solvent quality during the bromination, either “truly random” (good solvent) or “random-blocky” (poor solvent) PBrxS RCPs are prepared. Adsorption studies of PBrxS from various solvents at silica surfaces reveal that the adsorption of PBrxS increases with (1) increasing blockiness of the macromolecule, (2) increasing content of 4-BrS in PBrxS, and (3) decreasing solvent quality. Additionally, the effect of comonomer sequence distribution on RCP adsorption is modeled in detail using a coarse-grained statistical mechanical model and fully atomistic simulations based on configurational-biased grand-canonical Monte Carlo (CB-GCMC) technique. The main result from the simulations can be summarized as follows: (1) Increasing the degree of “blockiness” in comonomer distribution enhances the adsorption of macromolecules dissolved in a good solvent. (2) Near the adsorption transition, the amount of adsorbed segments in “random-blocky” copolymers is larger relative to their regular multiblock counterparts. (3) Lowering the solvent quality facilitates copolymer adsorption. Overall, the findings from computer modeling are found to be in a good agreement with the experimental data.

The structure of polymer chains in confinement. A Monte Carlo study

A coarse-grained model of polymer star chains confined in two parallel impenetrable surfaces, which were attractive for polymer beads was studied. The flexible homopolymer chains were built of united atoms whose positions in space were restricted to vertices of a simple cubic lattice. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between polymer beads--only the excluded volume was present. The influence of the polymer density and the distances between the confining surfaces on the properties of star-branched polymers was studied. It is shown that the chains adsorbed on one surface could change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the density of the system only. The increase of the polymer density diminished the frequency of jumps and caused that chains became only partially adsorbed. The analysis of structural elements of chains showed that the increase of the density of the system leads to increase of the number of bridges connecting the two adsorbing surfaces, thus, the frequency of jumps between them decreases.

Monte Carlo Simulations of Self‐Assembling Copolymer Brushes

AbstractWe studied a simplified model of a polymer brush formed by linear chains, which were restricted to vertices of a simple cubic lattice. The macromolecules consisted of a sequence of two different kinds of united atoms arranged in a specific sequence. The chains were grafted to an impenetrable surface, i.e. they were terminally attached to the surface with one end. The model system was studied at different solvent quality from good to poor solvent. The properties of this model system were determined by means of Monte Carlo simulation using a Metropolis‐like sampling algorithm based on local changes of chain's conformations. The size and the structure of the brush were determined.

Critical behavior of interacting two-polymer system in a fractal solvent: an exactrenormalization group approach

We study the polymer system consisting of two polymer chains situated in a fractalcontainer that belongs to the three-dimensional Sierpinski gasket (3D SG) family offractals. Each 3D SG fractal has four fractal impenetrable 2D surfaces, which are, in fact,2D SG fractals. The two-polymer system is modeled by two interacting self-avoiding walks(SAW), one of them representing a 3D floating polymer, while the other corresponds to achain confined to one of the four 2D SG boundaries (with no monomer in the bulk).We assume that the studied system is immersed in a poor solvent inducing theintra-chain interactions. For the inter-chain interactions we propose two models:in the first model (ASAW) the SAW chains are mutually avoiding, whereas inthe second model (CSAW) chains can cross each other. By applying an exactrenormalization group (RG) method, we establish the relevant phase diagrams forb = 2,3 and 4 members of the 3D SG fractal family for the model with avoiding SAWs, and forb = 2 and 3 fractals for the model with crossing SAWs. Also, at the appropriate transition fixedpoints we calculate the contact critical exponents, associated with the number of contactsbetween monomers of different chains. Throughout this paper we compare results obtainedfor the two models and discuss the impact of the topology of the underlying lattices onemerging phase diagrams.

Dynamics of branched chain solutions in adsorbing slit. A Monte Carlo study

A coarse-grained model of branched polymers confined in a slit formed by two parallel impenetrable surfaces that were attractive for polymer segments was developed and studied. The model chains were regular stars consisting of f = 3 branches of equal length. The positions of chains were restricted to vertices of a simple cubic lattice. The chains were at good solvent conditions—the excluded volume was the only interaction between the segments of the chain. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on chain’s local changes of conformation. The dependence of chain mobility on the width of the slit and the polymer concentration was studied. The conditions at which the strongly adsorbed chains could swap between both confining surfaces were studied. The mechanism of the chain motion was also discussed.

Structure of polymer films in adsorbing slit: A computer simulation study

The introduction of confinement has an impact on most properties of polymer chains. A coarse-grained model of branched polymers confined in a slit formed by two parallel impenetrable surfaces which were attractive for polymer segments was developed and studied. The model chains were regular stars consisted of three branches of equal length. The positions of chains were restricted to vertices of a simple cubic lattice. The chains were at good solvent conditions and, therefore, the excluded volume was the only interaction between the segments of the chain. The properties of the model systems were determined by means of dynamic Monte Carlo simulations with a sampling algorithm based on chain's local changes of conformation. The dependence of polymer density in the slit on a structure of the macromolecular film was studied. An interesting mechanism of the chain motion – jumps between surfaces – was also shown.

Thermodynamics and kinetics of competing aggregation processes in a simple model system

A simple model system has been used to develop thermodynamics and kinetics for bulk and surface aggregation processes capable of competing with each other. The processes are the stepwise aggregation of monomers in a fluid medium and on an impenetrable solid surface bounding the fluid medium, besides the adsorption and desorption of the same species at the solid-fluid interface. Emphasis is on aggregation processes in the high friction limit. The theoretical model is used to compare the kinetics and thermodynamics of the processes and to infer the conditions in which one process dominates another, in the high friction limit, such as in a liquid. The motivation of this study is obtaining insight into competition between aggregation in solution and on an adjoining surface, such as a cell membrane.

Computer simulation of grafted polymer chains

A model of a film formed by polymer chains was used for theoretical considerations. The linear block heteropolymer chains were constructed on a cubic lattice. The lower fragment of chain was athermal while the upper one was interacting. Chains were terminally attached (grafted) to an impenetrable surface. The computer simulation of the system was performed by means of a Monte Carlo Metropolis-like sampling algorithm basing on the micromodifications of local conformation. The size of the brush components and the structure of the polymer film were investigated and discussed for different chain lengths and for good and bad solvent conditions.

Properties of polymer chains in confinement. Monte Carlo simulations

The main goal of this study was to investigate the dynamic properties of polymer chains located in a slit. The idealized models of polymers were built of united atoms (segments) restricted to vertices of a simple cubic lattice. The macromolecules were linear, cyclic and star-branched with f=3 and f=4 arms. The chains were at good solvent conditions and the only interaction between the segments was the excluded volume. The polymers were located in a slit formed by a pair of two parallel and impenetrable surfaces which were attractive for polymer segments. The properties of the model chains were determined by means of dynamic Monte Carlo method using a sampling algorithm based on chain’s local changes of conformation. It was shown, for all polymer architectures under consideration, that at a certain temperature and for a certain size of the slit the chains were adsorbed at one of the confining surfaces and after a certain period of time they detached from this surface and approached the opposite one. The conditions necessary for these jumps were determined. The influence of the internal chain architecture on the frequency of jumps was shown and discussed.

Flow of polymer chains in thin confined layers. A computer Monte Carlo study

The aim of the study was the investigation of the polymer molecules located between two parallel and impenetrable surfaces which were attractive for polymer segments. The positions chains were restricted to knots of a simple cubic lattice. The chains were at good solvent conditions – the excluded volume was the only interactions between the segments of the chain. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on chain’s local changes of conformation. The differences and similarities in the structure for different adsorption regimes and the size of the slit were shown and discussed. The dependence of chain mobility expressed by mean-square displacement on the width of the slit and the temperature was studied.

Properties of polymers adsorbed on solid surfaces

Simulations of idealized models of heteropolymer/polypeptide chains were carried out by means of the Monte Carlo method. The idealized model chains were constructed of united atoms and were confined to a (3 1 0) hybrid lattice. Each chain consisted of two kinds of segments: hydrophobic and hydrophilic. The segments interacted with a long-distance contact potential and short-distance repulsion that mimic the main types of molecular interactions in polymer chains. The local propensities for forming secondary structures were also incorporated into the model. The chain were placed near an impenetrable and attractive surface. The properties of the system were determined using the replica exchange Monte Carlo algorithm. The influence of the temperature and the force field on the properties of the model system were studied.

Hard-surface effects in polymer self-consistent field calculations

We have investigated several effects due to the confinement of polymer melts by impenetrable (hard) surfaces in the self-consistent field calculations. To adequately represent such confinement, the total (normalized) polymer segmental density (volume fraction) is usually constrained to an imposed profile that continuously decreases from 1 in the interior of confined melts to 0 at the surfaces over a short distance. The choice of this profile strongly influences the numerical performance of the self-consistent field calculations. In addition, for diblock copolymers A-B the hard-surface confinement has both energetic and entropic effects: On one hand, the decrease of polymer density from 1 reduces A-B repulsion and favors morphologies with more A-B interfaces near the surfaces. On the other hand, the enrichment of chain ends and depletion of middle segments near the surfaces favor parallel morphologies where chains orient mainly perpendicular to the surfaces. These two effects are comparable in magnitude, and for asymmetric diblock copolymers result in an entropic preference of a neutral surface for the shorter block as proposed previously [Q. Wang et al., Macromolecules 34, 3458 (2001)]. The hard-surface effects are weak in practice and thus manifested only when the surfaces are nearly neutral.

Computer simulations of polymers in a confined environment

A coarse-grained model of star-branched polymers confined in a slit formed bytwo parallel impenetrable surfaces, which were attractive for polymer segments,was developed and studied. The model chains were regular stars consisting off = 3 branches of equal length. The flexible chains were constructed of united atoms (segments)and were restricted to vertices of a simple cubic lattice. Good solvent conditions weremodelled and, thus, the macromolecules interacted only with the excluded volume.The properties of the model chains were determined by means of Monte Carlosimulations with a sampling algorithm based on the local changes of conformationof the chains. It appeared that the strongly adsorbed chains located in slits ofappropriate width could swap between both confining surfaces. The influenceof the chain length, width of the slit and the temperature on the frequency ofsuch jumps was studied. The mechanism of the chain motion is also discussed.

MONTE CARLO STUDY ON THE ENTROPY OF TAIL-LIKE POLYMER CHAIN WITH ONE END ATTACHED TO FLAT SURFACE

Dynamic Monte Carlo simulations are performed for lattice self-avoiding tail-like polymer chains with one end attached to a non-interacting and impenetrable flat surface. The configurational entropy STL of the tail-like chain is determined by the scanning method. The entropy STL is smaller than that of the free chain without surface SF. The entropy drop ΔS=SF-STL increases linearly with ln n for short chains and increases linearly with n for long chains. However, the average entropy drop per bead ΔS/n decreases with n, indicating that the average effect of the surface on one chain bead decreases with the increase in chain length.

On the dynamics of grafted branched polymers—a Monte Carlo simulation study

A simplified model of grafted branched polymers was designed and investigated. The model consisted of star-branched chains constructed on a simple cubic lattice. The star polymers were built of three arms of equal lengths. The chains were attached to an impenetrable flat surface with one arm’s end. The arm attached to the surface (a stem) was built of segments different from those in two remaining arms (branches). During the Monte Carlo simulation of the system, the conformation of each chain was modified according to the metropolis sampling algorithm with local changes of chain conformations. The simulations were performed for different chain lengths and the temperature of the system (solvent conditions). The structure of a polymer film formed on the grafting surfaces depended strongly on the temperature and the low temperature films consisted of two separate layers with the insoluble layer located near the grafting surface. The short-time relaxation of the branches and stems of chains was also investigated. The analysis of the dynamics of the model system shows the influence of the structure of the system on relaxation times of various parameters.

Computer Simulation Study of Polymer Dynamics in Adsorbing Slit

In this study, we investigated the properties of star-branched polymers confined to a slit. The polymer models used were rather idealized: they consisted of identical united atoms (segments) whose positions were restricted to vertices of a simple cubic lattice. The polymers were put into a slit formed by a pair of parallel and impenetrable surfaces. The system was at good solvent conditions, and, thus, the chains interacted with the excluded volume only. The force field used consisted of a simple contact potential acting between polymer segments and confining surfaces. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on local changes of chain's conformation. The influence of the temperature and the size of the slit on the dynamic behavior of chains was studied. It appeared that, at certain conditions, chain jumps between the confining surfaces were observed.

Properties of Heteropolymer Linear Brushes

We studied a simplified model of a polymer brush. It consisted of linear chains, which were restricted to a simple cubic lattice. Chain macromolecules consisted of a sequence of two different kinds of segments were arranged in a specific sequence. The chains were grafted to an impenetrable surface, i.e., they were terminally attached to the surface with one end. The number of chains was varied from low to high grafting density. The model system was studied at different solvent qualities from good to poor solvent. The properties of this model system were studied by means of Monte Carlo simulation. The sampling Metropolis-type algorithm was based on local changes of chain's conformations. The structure of the brush film was analyzed and the roughness of the surface was determined. The distribution of both types of segments was given for different grafting densities.

Hybridization at a Surface: The Role of Spacers in DNA Microarrays

Flexible spacer chains are utilized to enhance the hybridization of terminally anchored oligonucleotide probes of DNA microarrays. A polymer physics approach identifies an underlying mechanism and yields guidelines for the optimal spacer length in terms of the effect on the equilibrium state. For low grafting densities, the dominant effect arises because of the decimation in the number of accessible chain configurations due to the impenetrable surface. Opposing trends are found for long targets and for short targets. At higher grafting densities, different brush regimes introduce an extra hybridization penalty. A novel brush regime is obtained for long neutral spacers and short targets at intermediate ionic strength where the chain stretching is due to the electrostatic interactions between the probes.

Imaging Simulation of Polarimetric SAR for a Comprehensive Terrain Scene Using the Mapping and Projection Algorithm

A novel approach to polarimetric image simulation for synthetic aperture radar (SAR) observation over comprehensive terrain scenes is developed based on mapping and projection principles. It incorporates penetrable and impenetrable objects, volumetric and surface scatterers in the imaging space with extinction, attenuation, shadowing, and multiple-scattering effects. Scattering of the vegetation canopy is modeled as a layer of random nonspherical particles by using the vector radiative transfer model, and scattering from the ground surface and building objects is calculated by using the integral equation method. As an example, polarimetric SAR images at L-band and C-band and the different spatial resolutions for a virtual terrain scene composed of tree canopies, farmland, buildings, rough land surface, hills, and rivers are simulated. The imaging simulation results demonstrate the feasibility of the mapping and projection approach and the potential utilities of SAR imaging simulation