Lattice Monte Carlo simulations of three-dimensional charged polymer chains

The configurational properties of strongly charged polyelectrolytes accompanied by neutralizing counterions in dilute solutions are simulated using the cooperative motion algorithm on the face-centered-cubic lattice. The full Coulomb potential and the excluded volume condition between different ions/beads are taken into account and the reduced temperature T* is considered the main, variable parameter. The calculations that have been carried out for solutions of both single and several chains indicate a few regions of their behavior: (1) for T*--> infinity, it corresponds to that of neutral, self-avoiding polymers under good solvent conditions; (2) for T* approximately 1, due to the electrostatic interactions being effectively stronger, the chains are more outstretched compared to their size at other temperatures; (3) for T* well below one, the counterion condensation becomes more and more dominant, which gradually leads to strongly collapsed chains; and (4) at the lowest temperatures the chains and counterions assume low-energy configurations in the form of neutral, compact aggregates.     

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.     

Monte Carlo simulations of charged dendrimer-linear polyelectrolyte complexes and explicit counterions

We study complexes composed of one dendrimer of generation G = 4 (G4 dendrimer) with N(t) = 32 charged terminal groups and an oppositely charged linear polyelectrolyte accompanied by neutralizing counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature τ and the chain length N(ch) as the main simulation parameters. Our calculations indicate that there exist three temperature ranges that determine the behavior of such complexes. At τ(complex) stable charged dendrimer-linear polyelectrolyte complexes are formed first, which are subsequently accompanied by selective counterion localization within the complex interior at τ(loc) ≤ τ(complex), and counterion condensation as temperature is further decreased below τ(cond) < τ(loc). In particular, we observe that condensation takes place exclusively on the excess charges in the complex and thus no condensation is observed at the compensation point (N(ch) = N(t)), irrespective of τ. For N(ch) ≠ N(t) the complex is overally charged. Furthermore, we discuss the size and structure of the dendrimer and the linear polyelectrolyte within the complex, as well as spatial distributions of monomers and counterions. Conformations of the chain in the bound state are analysed in terms of loops, trains, and tails.     

Monte Carlo study of surfactant adsorption on heterogeneous solid surfaces

The equilibrium between free surfactant molecules in aqueous solution and adsorbed layers on structured solid surfaces is investigated by lattice Monte Carlo simulation. The solid surfaces are composed of hydrophilic and hydrophobic surface regions. The structures of the surfactant adsorbate above isolated surface domains and domains arranged in a checkerboard-like pattern are characterized. At the domain boundary, the adsorption layers display a different behavior for hydrophilic and hydrophobic surface domains. For the checkerboard-like surfaces, additional adsorption takes place at the boundaries between surface domains.     

Monte Carlo simulations of cross-linked polyelectrolyte gels with oppositely charged macroions

The volume and structural changes upon replacement of oppositely charged network counterions for oppositely charged macroions in cross-linked polyelectrolyte gels have been investigated by Monte Carlo simulations using a coarse-grained model. Initially, the gel deswells, but after an approximately equivalent amount of macroions, the gel starts to swell again. The deswelling effect is greatest for small and highly charged macroions. The role of different network properties on the deswelling has also been examined. The initial deswelling is understood in terms of a replacement of confined counterions with macroions, thereby reducing the osmotic pressure originating from the counterions. At these conditions, macroions are located near network nodes with various degrees of network chains wrapping them. At charge equivalence, a profound change in the network structure has appeared. At these conditions, the cohesive electrostatic interaction and the excluded volume effect of the macroions strongly influence the equilibrium volume of the gel. Our model system reproduces many characteristic experimental observations of polyelectrolyte gels containing oppositely charged surfactants.     

Monte Carlo simulations on the effect of substrate geometry on adsorption and compression

Canonical Monte Carlo simulations were used to study the adsorption and compression of fluid layers on model substrates with cubic, (111) fcc, and graphite geometries. The effect of the relative size of the fluid and substrate molecules on adsorption was considered for strong molecule-surface interactions. In the case of monolayer formation, it was found that the surface geometry and the size of the adsorbate molecules had a significant effect on the structure of the adsorbed layer. These structures varied from well-ordered, commensurate layers to liquid-like structures. Lateral compression was observed for certain fluid to substrate molecule sizes. For the interactions studied in this work, it was found that maximum lateral compression occurred on the cubic surface when adsorbate molecules had a diameter approximately 15% larger than the substrate diameter. In the case of multilayer formation, it was found that second and higher adsorbed layers could compress into the adsorbed layers below them. For cubic substrates, the interlayer compression was predicted analytically with reasonable accuracy, with maximum interlayer compression found for fluid diameters approximately 90% the size of substrate molecule diameters.     

Brownian dynamics simulations of polyelectrolyte adsorption onto charged patterned surfaces

The adsorption of single polyelectrolyte molecules onto surfaces decorated with periodic arrays of charged patches was studied using Brownian dynamics simulations. A free-draining, freely jointed bead-rod chain was used to model the polyelectrolyte, and electrostatic interactions were incorporated using a screened Coulombic potential with the excluded volume accounted for by a hard-sphere potential. The simulations predicted that the polyelectrolyte lies close to the adsorbing surface if the patch length, surface charge density, and screening length are sufficiently large. Chain conformations were found to be very sensitive to patch length, patch spacing, and the nature of the charge on adjacent patches. This is due both to the size of the polymer relative to patch length and spacing and to the structure of the electric field near the surface. In some cases, the component of the radius of gyration parallel to the surface can be made smaller than its free-solution value, which is contrary to what is observed for a uniformly charged surface. Isolated charged patches were also considered, and significant adsorption was observed above a critical surface charge density. The results demonstrate how polyelectrolyte conformations can be controlled by the design of the charged patches and may be useful for applications in which adsorbed polyelectrolyte films play a key role.     

Monte Carlo simulations of phase transitions and adsorption isotherm discontinuities on surface compression

Low temperature, Grand Canonical Monte Carlo simulations were used to study the adsorption of fluid layers on cubic, hexagonal, and atomically smooth substrates to determine the effects of registry and surface compression on the system. The size of the fluid molecules was fixed to be 20% larger than the substrate molecules in order to observe the transition from an expanded to commensurate and finally to an incommensurate monolayer. For relatively weak fluid-substrate interactions, the cubic system underwent a first-order phase transition. As the strength of the fluid-substrate interactions increased, the molecules became fixed at commensurate locations and the transition from low density to commensurate packing became continuous. The strong fluid-substrate interactions lead to the development of a kink in the adsorption isotherm that showed the increased stability of the commensurate phase. This kink became more pronounced as the system temperature was decreased. The hexagonal system showed less dramatic results due to a decrease in the substrate well depth of the relative to the cubic system. The system did experience a first-order phase transition for a weak fluid-substrate interactions and the transition became much more gradual as the fluid-substrate interaction increased. The molecules became fixed to commensurate substrate locations, but the surface was not corrugated sufficiently to have a stable commensurate phase. The atomically smooth substrate showed the first-order phase transition expected of a low temperature system with no effects of registry.     

Adsorption of binary mixtures on two-dimensional surfaces: theory and Monte Carlo simulations

The adsorption of binary mixtures on square lattices is studied by combining theoretical modeling and Monte Carlo (MC) simulations in grand canonical ensemble. The adsorption thermodynamics is analyzed through the total and partial isotherms. Two theoretical models have been used in the present study: (i) the first, which we called cluster approximation (CA), is based on exact calculations of configurations on finite cells. An efficient algorithm allows us to calculate the detailed structure of the configuration space for \(m = l \times l \) cells; and (ii) the second is a generalization of the classical quasi-chemical approximation (QCA) in which the adsorbate is a binary mixture of species \(a\) and \(b\) . Adsorbate–adsorbate lateral interactions are incorporated in the context of the two mentioned approximations. Results from CA and QCA are compared with MC simulations. Close agreement between simulated and theoretical data supports the validity of the theoretical models to describe the adsorption of mixed gases on two-dimensional surfaces.     

Two-dimensional Monte Carlo simulations of ionic and nonionic silane self-assembly on hydrophilic surfaces

Aqueous chemistries have recently been shown to be useful for the deposition of hydrophobic films of nonionic and cationic silanes on hydrophilic substrates for the prevention of stiction in MEMS. The Monte Carlo method is used to simulate in two dimensions the self-assembly of silane films on a hydrophilic surface. We investigate the impact of charged group in cationic silane on the overall structure of the films. We characterize the film structure with spatial pair correlations at each molecular layer of the deposited films. The simulations reveal long-range correlations for the film of cationic silanes. Based on our two-dimensional simulations, we report an average "most probable" structure for the films of nonionic and cationic silanes.     

Monte Carlo simulations of a charged dendrimer with explicit counterions and salt ions

Static properties of a dendrimer with generation g = 5 with positively charged terminal groups in an athermal solvent are studied by lattice Monte Carlo simulations using the cooperative motion algorithm as the tossing scheme. The calculations are performed both for a salt-free system with neutralizing counterions and for a small amount of added monovalent and divalent salt. The full Coulomb potential and the excluded volume interactions between ions and beads are taken explicitly into account with the reduced temperature tau, the number of salt cations (anions) n(s), and salt valence z(s) as the simulation parameters. The bahaviour of the systems is analyzed by the mean effective charge per end-bead , Coulomb mean energy , mean-square radius of gyration , pair correlation functions g(alphabeta), and charge density rho(ch). The simulations show that for n(s)> or = 0 and decreasing tau: (a) there is encapsulation in the dendrimer and condensation onto the terminal groups of anions accompanied by a monotonic decrease in and and by subsequent swelling and shrinking of the molecule; (b) encapsulation, condensation and shrinking are the most significant and swelling weaker for |z(s)| = 2; (c) penetration of salt cations into the dendrimer is minor when compared to that of anions; (d) rho(ch) is reduced and becomes negative close to the center of mass of the dendrimer and on its periphery; (e) for the considered n(s) > 0, unlike divalent salt ions the monovalent ones cause slight effects when compared to the salt-free case.     

Monte Carlo simulations of hydrogen adsorption in alkali-doped single-walled carbon nanotubes

Monte Carlo simulations and Widom's test particle insertion method have been used to calculate the solubility coefficients (S) and the adsorption equilibrium constants (K) in single-walled (10,10) armchair carbon nanotubes including single nanotubes, and nanotube bundles with various configurations with and without alkali dopants. The hydrogen adsorption isotherms at room temperature were predicted by following the Langmuir adsorption model using the calculated constants S and K. The simulation results were in good agreement with experimental data as well as the grand canonical Monte Carlo simulation results reported in the literature. The simulations of nanotube bundle configurations suggest that the gravimetric hydrogen adsorption increases with internanotube gap size. It may be attributed to favorable hydrogen-nanotube interactions outside the nanotubes. The effect of alkali doping on hydrogen adsorption was studied by incorporating K+ or Li+ ions into nanotube arrays using a Monte Carlo simulation. The results on hydrogen adsorption isotherms indicate hydrogen adsorption of 3.95 wt% for K-doping, and 4.21 wt% for Li-doping, in reasonable agreement with the experimental results obtained at 100 atm and room temperature.     

Polyion adsorption onto catanionic surfaces. A Monte Carlo study

The adsorption of a single and negatively charged polyion with varying flexibility onto a surface carrying both negative and positive charges representing a charged membrane surface has been investigated by using a simple model employing Monte Carlo simulations. The polyion was represented by a sequence of negatively charged hard spheres connected with harmonic bonds. The charged surface groups were also represented by charged hard spheres, and they were positioned on a hard surface slightly protruding into the solution. The surface charges were either frozen in a liquidlike structure or laterally mobile. With a large excess of positive surface charges, the classical picture of a strongly adsorbed polyion with an extended and flat configuration emerged. However, adsorption also appeared at a net neutral surface or at a weakly negatively charged surface, and at these conditions the adsorption was stronger with a flexible polyion as compared to a semiflexible one, two features not appearing in simpler models containing homogeneously charged surfaces. The presence of charged surface patches (frozen surface charges) and the ability of polarization of the surface charges (mobile surface charges) are the main reasons for the enhanced adsorption. The stronger adsorption with the flexible chain is caused by its greater ability to spatially correlate with the surface charges.     

Monte Carlo modeling of chiral adsorption on nanostructured chiral surfaces and slit pores

Adsorptive separation of chiral molecules is a powerful technique that has long been used in the chemical and pharmaceutical industries. An important challenge in this field is to design and optimize new adsorbents to provide selective discrimination of enantiomers. In this article, we introduce an off-lattice model of chiral adsorption on nanostructured surfaces and slit pores with the aim of predicting their enantioslective properties. The concept presented here involves finding the optimal chiral pattern of active sites on the pore walls that maximizes the difference between the binding energies of the enantiomers. Our initial effort focuses on chiral molecules that do not have specific interactions with the pore surface. One candidate meeting this requirement is 1,2-dimethylcyclopropane (DMCP), a chiral hydrocarbon whose interaction with a model pore surface was described using the Lennard-Jones potential. To model the adsorption of DMCP, we used the Monte Carlo simulation method. It was demonstrated that the separation of the enantiomers of DMCP is hardly obtainable because of the smoothness of the potential energy surface for molecules physisorbed in the pore. However, the simulated results allowed the identification of key factors that influence the binding of the enantiomers of DMCP to the pore walls with a special distribution of active sites. This information will be useful in future considerations of the adsorption of more complex chiral molecules.     

Lattice Monte Carlo simulations of three-dimensional charged polymer chains. II. Added salt

The configurational properties of strongly charged polyelectrolytes accompanied by counterions and salt ions in dilute solutions are simulated using the cooperative motion algorithm on the face-centered-cubic lattice. The calculations indicate that both positive and negative ions condense on the chains at sufficiently low temperatures and their amount depends on the concentration of added salt. As the temperature decreases from high to low, the chains undergo conformational changes from neutral-like, self-avoiding polymers by more outstretched forms to compact globules. The observed extension of the chains at intermediate temperatures is also affected by the amount of salt. Furthermore, configurations with the lowest energies recorded at the lowest temperatures are aggregates of single or more entangled chains and ions of both types.     

Self-recognition and aggregation between diblock (charged/neutral) polyelectrolytes by Monte Carlo simulations

The self-recognition between oppositely charged polyelectrolyte-neutral diblock copolymers and aggregate formation is investigated by Monte Carlo simulations. Both matched lengths and charge numbers are critical conditions for self-recognition. The optimum self-recognition occurs between oppositely charged chains with matched charged block lengths and charge numbers. The size of aggregates increases, as the total length and the ratio of charged to neutral beads become larger. Polyelectrolyte networks were observed in some cases containing unmatched chains. The molecular configurations of the entire chains and of the charged and neutral blocks as well as the radial distribution functions of the charged beads are also investigated.     

Adsorption of proteins onto charged surfaces: A Monte Carlo approach with explicit ions

A computer model has been developed to simulate the adsorption of proteins onto charged surfaces displaying an electric double layer. Coadsorption of ions onto the surface is included by means of explicit ions. Only electrostatic interactions are considered. Monte Carlo simulations in the canonical ensemble of the enzyme cutinase and 15 variants (modeled from the X-ray tertiary structure of the wild-type) were performed. Adsorption free energies for all variants were calculated by the thermodynamic integration method. Distributions of the electric moment and the vector pointing toward the protein active site and parallel to its central β-sheet were determined to elucidate the mean orientation of the protein with respect to the surface as a function of its distance from the surface. It was found that the free energy of adsorption varied linearly with the total charge of the protein, while the electric moment (dipole moment) had a second-order but significant effect. Though an increase of the electric moment generally resulted in a slightly increased affinity of the protein for the surface, close to the surface the mean force acting on the protein clearly varied linearly with the strength of the electric moment, such that a clear correlation between the latter and the protein orientation with respect to the surface could be established. Wild-type cutinase displayed the highest affinity for the charged surface amongst all proteins having the same total charge, even though it did not have the largest electric moment. © 1996 by John Wiley & Sons, Inc.     

Antibody adsorption and orientation on hydrophobic surfaces

The orientation of a monoclonal, anti-streptavidin human IgG1 antibody on a model hydrophobic, CH(3)-terminated surface (1-dodecanethiol self-assembled monolayer on gold) was studied by monitoring the mechanical coupling between the adsorbed layer and the surface as well as the binding of molecular probes to the antibodies. In this study, the streptavidin antigen was used as a probe for the Fab portions of the antibody, while bacteria-derived Protein G' was used as a probe for the Fc region. Bovine serum albumin (BSA) acted as a blocking protein. Monolayer coverage occurred around 468 ng/cm(2). Below 100 ng/cm(2), antibodies were found to adsorb flat-on, tightly coupled to the surface and unable to capture their antigen, whereas the Fc region was able to bind Protein G'. At half-monolayer coverage, there was a transition in the mechanism of adsorption to allow for vertically oriented antibodies, as evidenced by the binding of both Protein G' and streptavidin as well as looser mechanical coupling with the surface. Monolayer coverage was characterized by a reduced level in probe binding per antibody and an even less rigid coupling to the surface.