Monte Carlo simulation for the adsorption of symmetric triblock copolymers II. Adsorption layer information

By using Monte Carlo simulation, adsorption of both end-adsorbed and middle-adsorbed symmetric triblock copolymers from a non-selective solvent on an impenetrable surface has been studied. Influences of the adsorption energy, the bulk concentration, the chain composition and the chain length on the adsorption behavior including the surface coverage, the adsorption amount and the layer thickness are presented. It is shown that the total surface coverage for both end-adsorbed and middle-adsorbed copolymers increases monotonically as the bulk concentration increases. The higher the adsorption energy and the more the attractive segments, the higher the total surface coverage is exhibited. Surface coverage θ decreases with increasing the length of the non-attractive segments, but the product of θ and the proportion of the non-attractive segments in a triblock copolymer chain is nearly independent of the chain length. The adsorption amount increases almost monotonically with the bulk concentration. The logarithm of the adsorption amount is a linear function of the reciprocal of the reduced temperature. When the adsorption energy is large, the adsorption amount exhibits a maximum as the composition of the attractive segment increases. The adsorption isotherms of copolymers with different length of the non-attractive segments can be mapped onto a single curve under certain energy indicating that copolymers with different chain length have the same adsorption amount. The adsorption layer thickness for the end-adsorbed copolymers decreases as the energy and the number of adsorbing segments increases. The longer non-attractive segments, the larger adsorbed layer thickness is found. The tails mainly governs the adsorption layer thickness.     

Self-assembled structures of block copolymers in selective solvents reproduced by lattice Monte Carlo simulation

A lattice Monte Carlo (MC) simulation was applied to the study of block copolymers in selective solvent or amphiphilic surfactant solution on the segment level, hydrodynamic interactions being neglected. The code was found to be very efficient, employing a partial reptation mode as the elementary movement of the self-avoiding lattice chains. Typical self-assembled structures of block copolymers such as micelle, lamellae, hexagonal cylinder and bicontinuous networks have been successfully reproduced without any priori specification of structure. Order–disorder and order–order transitions of diblock copolymers are systematically studied by adjusting the temperature, the concentration or the block length ratio in a series computer simulations. The structural differences between micelles composed of ABA and BAB triblock copolymers are also explicitly revealed by direct visualisation of the underlying chain configurations. The simulation results are consistent with the experimental observations in the literature. This simulation approach is thus a very useful tool in the extensive investigation of self-assembled structures. It has the advantage that both micro-domains and chain configurations can be studied with only a comparatively modest call on computational resources.     

Monte Carlo simulation of block copolymers

Monte Carlo simulations deal with crudely simplified but well-defined models and have the advantage that they treat the statistical thermodynamics of the considered model exactly (apart from statistical errors and problems due to finite size effects). Therefore, these simulations are well suited to test various approximate theories of block copolymer ordering, e.g. the self-consistent field theory. Recent examples of this approach include the study of block copolymer ordering at melt surfaces and confinement effects in thin films, adsorption of block copolymers at interfaces of unmixed homopolymer blends, the phase behavior of ternary mixtures of two homopolymers and their block copolymer, and micelle formation in selective solvents.     

Analogy in the adsorption of random copolymers and homopolymers at solid-liquid interface: a Monte Carlo simulation study

The adsorption of random copolymers at solid-liquid interface from a nonselective solvent has been studied by Monte Carlo simulation in a cubic lattice. The polymeric molecules are modeled as self-avoiding linear chains composed of two types of segments A and B. The effects of copolymer composition (A/B ratio), segment-surface interaction, and bulk concentration are examined on the thermodynamic and structural adsorption properties including surface coverage, adsorption amount, adsorption layer thickness, and microscopic density distribution. At a given newly introduced effective adsorption energy, random copolymers are found to behave quantitatively as homopolymers regardless of the copolymer composition and surface affinity. This remarkable analogy provides an efficient way in predicting the adsorption of random copolymers from homopolymers.     

Design of random copolymers with statistically controlled monomer sequence distributions via Monte Carlo simulations

We use Monte Carlo simulations to model the formation of random copolymers with tunable monomer sequence distributions. Our scheme is based on the original idea proposed a few years ago by Khokhlov and Khalatur [Physica A 249, 253 (1998); Phys. Rev. Lett. 82, 3456 (1999)], who showed that the distribution of species B in A-B random copolymers can be regulated by (a) adjusting the coil size of a homopolymer A and (b) chemically modifying ("coloring") monomers that reside at (or close to) the periphery of the coil with species B. In contrast to Khokhlov and Khalatur's work, who modeled the polymer modification by performing the coloring instantaneously, we let the chemical coloring reaction progress over time using computer simulations. We show that similar to Khokhlov and Khalatur's work, the blockiness (i.e., number of consecutive monomers) of the B species along the A-B copolymer increases with increasing degree of collapse of the parent homopolymer A. A simple analysis of the A-B monomer sequences in the copolymers reveals that monomer sequence distributions in homopolymers "colored" under collapsed conformations possess certain degrees of self-similarity, while there is no correlation found among the monomer sequence distributions formed by coloring homopolymers with expanded conformations.     

Lattice Monte Carlo investigations on copolymer systems, 3. Alternating and random copolymers

Alternating and random copolymers in dilute solution are investigated by means of Monte Carlo simulations on a cubic lattice. Each molecule consists of an equal number of A and B segments, either randomly distributed along the chain or forming an alternating sequence. The energy parameters chosen represent selective solvent conditions (the solvent is a good one for monomers of type A and a θ-solvent for B; between A and B repulsive interactions are operative). Comparison with di- and triblock copolymers of equal overall composition reveals that the behaviour of random or alternating copolymers (subject to the same selective solvent) is quite different. Their properties rather resemble those of homopolymers in a solvent of intermediate quality. The absolute chain dimensions (e.g. the mean square radius of gyration, 〈s²〉, and the mean square end-to-end distance, 〈h²〉) of random and alternating copolymers as well as their scaling exponents are significantly larger than those of block copolymers. The ratio between 〈h²〉 and 〈s²〉 as well as the shape of the polymer (expressed by the asphericity δ) are similar to those of athermal polymers indicating that there is no pronounced selectivity of the solvent. In contrast to block copolymers, these parameters exhibit no significant chain-length dependence. The number of the various types of polymer-polymer contacts (A-A, B-B and A-B) is almost independent of the type of contact at least for the solvent conditions investigated. This is in contrast to block copolymers where A-B contacts are widely suppressed and where the number of B-B contacts is approximately twice as high as that of A-A contacts.     

Adsorption of random copolymers on disordered surfaces

Monte Carlo simulations are used to study adsorption of random heteropolymers on disordered substrates. The adsorbent surface is modelled as an impenetrable wall with the random distribution of sites characterised by short-ranged segment-specific interactions with the polymer. Spatial fluctuations in the interaction strength are described as a Gaussian process with zero mean and variance σ₁ which is proportional to the site/segment potential, and to the loading of sites on the surface. In all cases, a moderate depletion in the polymer density is observed at small surface loading. Upon increasing σ₁ the polymer begins to adsorb on the surface. At a certain threshold loading, we observe a sharp second adsorption transition followed by gradual saturation. The transition is interpreted in terms of pattern matching; i.e. the heteropolymers accomodate themselves at surface domains with site distributions that match the configuration and the sequence of the chain when the sequence and surface site distributions are related in a special way. Distinct peaks in heat capacity and compressibility observed at the adsorption transition point to a first order process envisaged in earlier replica/mean-field analysis. These results suggest that random heteropolymers with designed sequence statistics can ‘recognise’ multifunctional disordered surfaces due to statistical pattern-matching.     

Confined crystallization of cylindrical diblock copolymers studied by dynamic Monte Carlo simulations

We report dynamic Monte Carlo simulations of polymer crystallization confined in the cylindrical microdomains of diblock copolymers. The microdomains were prepared via spontaneous microphase separation from homogeneous melt, and the major component was then frozen in a vitreous amorphous state to make a hard confinement to the crystallization of the minor component. We found that during the isothermal crystallization at high temperatures, crystal orientations are dominantly perpendicular to the cylinder axis at the early stage of crystal nucleation and remain to the final state; while if the block junctions are broken before crystallization, crystal orientations are dominantly parallel at the early stage of crystal nucleation, and eventually other orientations take the place of parallel preferences. Analysis of bond orientations in the heterogeneous melts demonstrates the microscopic origin of oriented crystal nucleation.     

Adsorption of copolymers in a selective nanoslit: a hybrid density functional theory

A hybrid density functional theory (DFT) is developed for adsorption of copolymers in a selective nanoslit. The DFT incorporates a single-chain simulation for the ideal-gas free energy functional with two weighted density approximations for the residual free energy functional. The theory is found to be insensitive to the width parameter used in the weighted density. Theoretical predictions are in excellent agreement with simulation results in the segment density profiles and the adsorption configurations including tail, loop, and train for copolymers with various sequences over a wide range of surface affinity. The bridge conformation is also observed in multiblock copolymers. Ordered assembly is facilitated in copolymers with longer chain/block and at stronger attraction between segment B and the slit wall. While diblock copolymer shows the longest tail, alternating copolymer has the shortest. As the attraction between segment B and the slit wall increases, the average size and fraction decrease for tail, but increase for loop and train.     

Monte Carlo studies of tethered chains

Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent conditions. The simulations spanned a wide range of chain lengths, N (100–1000, i.e., up to molecular weights of a few hundred thousands), and anchoring densities, σ (2 × 10⁻⁴ to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage σ* = σπR is the most appropriate variable that quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R_g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for σ* > 8. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:2449–2461, 2009     

Adsorption of Semiflexible Chains on Nanostriped Surfaces: Monte Carlo Simulations

Monte Carlo simulations were carried out to investigate the adsorption of semiflexible chains from a semidilute solution to substrates with periodic stripes of width w. The chains are made of fused N = 10 monomers of diameter σ interacting with each other through excluded volume interactions and with the stripes via a square‐well potential of depth ε and width σ. The surface coverage was found to increase upon increasing the chain stiffness and decreases on increasing the width of the stripes. At small w, more flexible chains are adsorbed than stiff chains. Analysis of the radius of gyration for the chains showed that when w < 8σ, the component along the stripe direction is significantly larger than the others. Orientational order parameter reveals that, for small w, chains have preference to align along the stripe direction.

     

Symmetric diblock copolymers in nanopores: Monte Carlo simulations and strong-stretching theory

We have performed lattice Monte Carlo simulations to study the self-assembled morphology of symmetric diblock copolymers in nanopores. The pore diameter and surface preference are systematically varied to examine their effects on the chain conformations, structures of various morphologies, and their phase transition. Various ensemble-averaged profiles and quantities are used to provide detailed information about the system. The simulation results are also compared with the predictions of a strong-stretching theory commonly used in the literature. Such comparisons reveal the deficiencies of this theory in describing the morphologies under cylindrical confinement, and call for further theoretical studies using more accurate formalisms.     

Adsorption of a binary mixture of adhesive fluids in planar pores: a Monte Carlo study

Grand canonical Monte Carlo simulation is used to study the adsorption of a binary sticky hard-sphere fluid mixture in planar pores. The wall-component 1 and wall-component 2 contact densities are determined to calculate the pressure as a function of the composition of the mixture and the separation between the walls. From these data dependence of the solvation force between the plates on pore width is estimated. The simulation results are compared with the predictions of the Percus-Yevick approximation for planar pores. The density profiles of particular components show interesting shapes stemming from the interplay between the steric effects and the competitive adhesion among all possible species pairs. It is shown that narrowing of the pore causes selective partitioning of individual components of the mixture between the bulk phase and the interior of the pore. The agreement between the two methods is better at wider pores and for the component comprised of weakly adhesive particles.     

Monte Carlo simulation studies of polymer systems

Polymers molecules in solution or melt are more or less flexible and continuously change their shape and size. Thus, characteristic properties of the system fluctuate around statistical mean values which are dependent on the concentration of the solution, on the quality of the solvent used, and on the specific structure of the molecules, e.g. linear or star-branched. The most direct approach to these quantities on a molecular level are computer simulations. Due to restrictions of computer power fully atomistic simulations of macromolecules are presently still at the beginning but several arguments justify the use of simplified models. The most efficient way dealing with polymer systems are Monte Carlo simulations based on lattice chains, at least as long as static properties are of interest only. In the present paper a short introduction to the field is given and selected examples are presented in order to demonstrate the usefulness of these methods.     

Monte Carlo studies of a novel X-ray tube anode design

When energetic electrons are incident on high atomic number absorbers, a substantial fraction is back-scattered. This phenomenon is responsible for several undesirable effects in X-ray tubes, in particular a reduction in the X-ray output. The extent of this shortfall has been estimated by using Monte Carlo simulation to start electrons at increasing depth inside the anode, the results indicating that an output enhancement of nearly 50% could be achieved in principle if the electrons wasted in back-scatter events could be trapped inside a tungsten anode. To test this idea a further set of simulations were done for a novel anode geometry. Results showed that X-ray tube efficiencies might be substantially enhanced by this approach.     

Adsorption of copolymers aggregates: from kinetics to adsorbed layer structure

We examined the adsorption, on hydrophobic and hydrophilic surfaces, of 4 rake-type poly(dimethyl siloxane) (PDMS) copolymers varying the amount of poly(ethylene glycol) (PEG) graft arms from 41 to 72%. The copolymers formed large aggregates in solution, complicating their adsorption kinetics and layer structures. We found the adsorption process always to be dominated by the adsorption of large aggregates, with strongly bound layers resistant to rinsing in adsorbing buffer. Adsorbed amounts were nearly independent of the substrate. However, subtleties in the adsorption kinetics suggested different layer structures for the different systems. On hydrophilic silica, aggregates adsorbed at the transport limited rate until surface saturation, and associated interfacial structures were likely retained. On the hydrophobic surface, a subset of the copolymers exhibited retarded late stage adsorption kinetics suggestive of brush formation. This work demonstrates how subtle differences in adsorption kinetics provide insight into potential interfacial layer structures.     

Adsorption and morphology transition of surfactants on hydrophobic surfaces: a lattice Monte Carlo study

In this work, we first show that there are only five independent interchange parameters in the surfactant-solvent-interface system in Larson's model, and then adsorption and morphology transition of surfactants on hydrophobic surfaces are studied by extensive lattice Monte Carlo simulations. In our simulations, we found that there exist six adsorbed morphologies: (1) premature admicelle, (2) hemisphere, (3) hemisphere-hemicylinder mixture, (4) wormlike hemicylinder, (5) perforated monolayer, and (6) monolayer. The surface morphologies and the amount of adsorption on hydrophobic surfaces are found to be affected obviously by two interchange parameters. One is the attractive interaction between tail groups and surface (chiTS), and the other is the solubility of head groups in bulk (chiHW). Phase diagrams in chiHW versus chiTS planes for surfactants with different hydrophobicities (chiTW) and for surfactants with different molecular structures are determined in this work, from which the transitions of surface morphologies and adsorption behaviors are discussed.     

Gibbs系综Monte Carlo模拟甲烷的吸附平衡

在263、298和313 K下,对甲烷在1.91 nm的活性炭孔中的吸附平衡进行了Gibbs系综Monte Carlo(GEMC)模拟的研究.改进了GEMC方法,使之可用于模拟指定压力下的吸附平衡.通过改进的GEMC模拟,得到了在1.91 nm的活性炭中甲烷在263、298和313 K时的吸附等温线;发现263 K时的超额吸附量要大于298 K、313 K时的超额吸附量; 且不同温度下的超额吸附等温线均存在一最大超额吸附.263 K时,超额吸附量在5.0 MPa时出现最大值;而298 K、313 K时超额吸附量则在7.0 MPa时出现最大值.此工作为不同温度下天然气吸附存贮过程的开发及设计提供了依据.     

Monte Carlo simulation for the micellar behavior of amphiphilic comb-like copolymers

Micellar behaviors in 2D and 3D lattice models for amphiphilic comb-like copolymers in water phase and in water/oil mixtures were simulated. A dynamical algorithm together with chain reptation movements was used in the simulation. Three-dimension displaying program was pro-grammed and free energy was estimated by Monte Carlo technigue. The results demonstrate that reduced interaction energy influences morphological structures of micelle and emulsion stems greatly; 3D simulation showing can display more direct images of morphological structures; the amphiphilic comb-like polymers with a hydrophobic main chain and hydrophilic side chains have lower energy in water than in oil.     

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