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.     

Model Bridging Effects of Asymmetrical Triblock Copolymers

Summary: We have performed Monte Carlo simulations to study the bridging of symmetrical or asymmetrical triblock copolymers confined between two similar or different solid surfaces based on a simple lattice model. The influence of the molecular structure, surface separation, adsorption energy, chain composition, and the chain concentration on the fractions of chains with bridge, loop and dangling configurations are reported in detail. The results show that the largest bridging fraction is given only when symmetrical triblock copolymers are confined between two parallel surfaces with the same adsorption energy. The bridge fraction is decreased so long as the asymmetry of the copolymers or the difference between the two surfaces is enhanced. It was found also that the bridging fraction increases as the adsorption energy increases. The bridging fraction Ω_bridge under different separations, L_z, can be expressed as in various situations. On the other hand, by introducing a symmetry index ν, the influence of molecular structure of copolymers on the bridges can be illustrated approximately by a relation when the two surfaces are similar and the adsorption energy is not too high. Combining the two expressions, data of the bridge fractions for copolymers of different symmetries confined between surfaces with different separations can be described with a single equation, which, in some occasion, can be used for prediction.

Influence of molecular structure on the bridging fraction for .     

Adsorption Behavior of Asymmetrical Triblock Copolymers at the Solid‐Liquid Interface by Monte Carlo Simulation

Summary: Monte Carlo simulation on a simple lattice model has been used to study the adsorption of asymmetrical triblock copolymers from a non‐selective solvent at the solid‐liquid interface. The size distributions of train, loop and tail configurations for those copolymers are obtained as well as other details of the adsorption layer microstructure. Also the influence of adsorption energy and the role of molecular symmetry are investigated. A segment‐density profile, the adsorption amount, the surface coverage, and the adsorption layer thickness have been determined. Finally, it is shown that the adsorption behavior of an asymmetrical copolymer can be predicted from the symmetrical copolymer.

Size distributions of the tail configuration for A_8−kB₂₀A_k.     

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.     

两嵌段共聚高分子在固液界面吸附的Monte Carlo模拟(Ⅱ)──界面浓度分布和吸附量

用MonteCarlo方法对两嵌段共聚高分子在固液界面的吸附进行模拟,获得了固液界面区总链节密度和吸附链节浓度分布、链附着率、表面覆盖率和吸附量等信息,考察了吸附性链节的对比吸附能 ε>_An 和两嵌段共聚高分子中吸附性链节比例f对它们的影响.结果表明,较大时,吸附量先随f的增加而上升,在f=0.4左右达到最大值后逐渐下降.     

Study of hydrogen adsorption on FeTi using molecular dynamics simulations

We have used molecular dynamics simulation to study the adsorption isotherms of molecular hydrogen on FeTi at several temperatures ranging from 60 to 100 K. Adsorption coverage, isosteric heat, and binding energy were calculated at different temperatures and pressures. The results indicated that FeTi can be used as an ideal hydrogen storage material. The surface coverage or total amount of hydrogen adsorbed on FeTi is between 0.28 to 0.35.     

Phase behavior in thin films of cylinder-forming ABA block copolymers: mesoscale modeling

The phase behavior of cylinder-forming ABA block copolymers in thin films is modeled in detail using dynamic density functional theory and compared with recent experiments on polystyrene-block-polybutadiene-block-polystyrene triblock copolymers. Deviations from the bulk structure, such as wetting layer, perforated lamella, and lamella, are identified as surface reconstructions. Their stability regions are determined by an interplay between surface fields and confinement effects. Our results give evidence for a general mechanism governing the phase behavior in thin films of modulated phases.     

Monolayer structure of tetracene on Cu (100) surface: parallel geometry

The geometrical arrangement of tetracene on Cu (100) surface at monolayer coverage is studied by using scanning tunneling microscopy measurement and density functional theory (DFT) calculations. Tetracene molecule is found to be oriented with its molecular plane parallel to the substrate surface, and no perpendicular geometry is observed at this coverage. The molecule is aligned either in the [011] or [011] direction due to the fourfold symmetry of the Cu (100) surface. DFT calculations show that the molecule with the "flat-lying" mode has larger adsorption energy than that with the "upright standing" mode, indicating that the former is the more stable structure. With the flat-lying geometry, the carbon atoms prefer to be placed between surface Cu atoms. The molecular center prefers to be located at the bridge site between two nearest surface Cu atoms.     

Self-assembly of star ABC triblock copolymer thin films: self-consistent field theory

Microphase separation and morphology of star ABC triblock copolymers confined between two identical parallel walls (symmetric wetting or dewetting) are investigated with self-consistent field theory (SCFT) combined with the "masking" technique to describe the geometric confinement of the films. In particular, we examine the morphology of confined near-symmetric star triblock copolymers under symmetric and asymmetric interactions as a function of the film thickness and the surface field. Under the interplay between the degree of spatial confinement, characterized by the ratio of the film thickness to bulk period, and surface field, the confined star ABC triblock copolymers are found to exhibit a rich phase behavior. In the parameter space we have explored, the thin film morphologies are described by four primary classes including cylinders, perforated lamellae, lamellae, and other complex hybrid structures. Some of them involve novel structures, such as spheres in a continuous matrix and cylinders with alternating helices structure, which are observed to be stable with suitable film thickness and surface field. In particular, complex hybrid network structures in thin films of bulk cylinder-forming star triblock copolymers are found when the natural domain period is not commensurate with the film thickness. Furthermore, a strong surface field is found to be more significant than the spatial confinement on changing the morphology of star triblock copolymers in bulk. These findings provide a guide to designing novel microstructures involving star triblock copolymers via geometric confinement and surface fields.     

Self-assembly behavior of ABA coil-rod-coil triblock copolymers: a Brownian dynamics simulation approach

The self-assembly behavior of ABA coil-rod-coil triblock copolymers in a selective solvent was studied by a Brownian molecular dynamics simulation method. It was found that the rod midblock plays an important role in the self-assembly of the copolymers. With a decrease in the segregation strength, ?(RR), of rod pairs, the aggregate structure first varies from a smecticlike disk shape to a long twisted string micelle and then to small aggregates. The influence of the block length and the asymmetry of the triblock copolymer on the phase behavior were studied and the corresponding phase diagrams were mapped. It was revealed that the variation of these parameters has a profound effect on microstructure. The simulation results are consistent with experimental results. Compared to rod-coil diblock copolymers, the coil-rod-coil triblock copolymers has a larger entropy penalty associated with the interfacial grafting density of the aggregate, leading to a higher ?(RR) value for structural transitions.     

双亲三嵌段共聚物PEO-PPO-PEO在水溶液中相行为的理论研究

用自洽平均场理论的谱方法研究了双亲三嵌段共聚物PEO-PPO-PEO的分子量对其在水溶液相行为的影响. 理论预测了各种溶致液晶相的稳定区域. 通过系统地改变聚合物的分子量, 我们给出了各种PEO-PPO-PEO三嵌段共聚物在水溶液中的相图. 此外, 也研究了分子量对自组装结构各组分浓度分布的影响. 发现在给定的温度下, 聚合物的分子量是体系发生相分离的一个重要驱动力. 我们的理论结果与相关的实验很好地符合.     

Tethered polymer layers: phase transitions and reduction of protein adsorption

The structural and thermodynamic properties of tethered polymer layers formed by spreading diblock copolymers at a solid surface or at a fluid‐fluid interface are studied using a molecular mean‐field theory. The role of the anchoring block in determining the properties of the tethered polymer layer is studied in detail. It is found that both the anchoring and the tethered blocks are very important in determining the phase behavior of the polymer layer. The structures of the coexisting phases, the phase boundaries and the stability of the layer are found to depend on the ratio of molecular weight between the two blocks, the polymer‐interface (surface) interactions and the strength of the interactions between the two blocks. The different phase transitions found are related to experimental observations. The properties of the polymer layers at coexistence reflect the block that is the dominant driving force for phase separation. The ability of the tethered polymer layers, under different conditions, to control protein adsorption to surfaces is also studied. It is found that the most important factors determining the ability of a polymer layer to reduce the equilibrium amount of proteins adsorbed to a surface are the surface coverage of polymer and the surface‐polymer interactions. The polymer chain length plays only a secondary role. For the kinetic control, however, it is found that the potential of mean‐force, and thus the early stages of adsorption, depends strongly on polymer molecular weight. Further, it is found that the molecular factors determining the ability of the tethered polymer layer to reduce the equilibrium amount of protein adsorption are different than those that control the kinetic behavior. Comparisons with experimental observations are presented. The predictions of the theory are in very good agreement with the measured adsorption isotherms. Guidelines for building optimal surface protection for protein adsorption, both kinetic and thermodynamic, are discussed.     

A Molecular Dynamics Simulation on the Self‐Assembly of ABC Triblock Copolymers, 1. Effects of Block Composition in Symmetric Triblock Copolymers

The self‐assembly of ABC triblock copolymers in the microphase‐separated state is investigated using an isothermal‐isobaric molecular dynamics simulation. For the validation of our simulation scheme, ABA triblock copolymers are also simulated. We examine the effect of the composition (f_B) of symmetric triblock copolymers on the morphology realized in these copolymers, keeping other parameters fixed. For ABA triblock copolymers, the transition from lamellar to cylindrical morphologies is observed with increasing the composition from f_B = 0.5 to f_B = 0.75, and such behavior is supported by calculation results of scattering patterns. These simulated results agree well with experimental and theoretical ones, validating our simulation method. More complex structures are predicted for ABC triblock copolymers. If midblock B is the minor component, its structures are changed from lamellar, cylindrical, to spherical morphology at the interface between A/C lamellae as f_B decreases. For ABC triblock copolymers with the midblock B as the major component, the morphology of end blocks in the matrix composed of the midblock is changed from tricontinuous to spherical structures as f_B increases.     

Coverage-dependent adsorption geometry of octithiophene on Au(111)

The adsorption behavior of α-octithiophene (8T) on the Au(111) surface as a function of 8T coverage has been studied with low-temperature scanning tunneling microscopy, high resolution electron energy loss spectroscopy as well as with angle-resolved two-photon photoemission and ultraviolet photoemission spectroscopy. In the sub-monolayer regime 8T adopts a flat-lying adsorption geometry. Upon reaching the monolayer coverage the orientation of 8T molecules changes towards a tilted configuration, with the long molecular axis parallel to the surface plane, facilitating attractive intermolecular π-π-interactions. The photoemission intensity from the highest occupied molecular orbitals (HOMO and HOMO - 1) possesses a strong dependence on the adsorption geometry due to the direction of the involved transition dipole moment for the respective photoemission process. The change in molecular orientation as a function of coverage in the first molecular layer mirrors the delicate balance between intermolecular and molecule/substrate interactions. Fine tuning of these interactions opens up the possibility to control the molecular structure and accordingly the desirable functionality.     

环形嵌段共聚物的胶束化行为模拟简

利用Monte Carlo模拟,对比了相同组成下环形二嵌段共聚物AB和线形三嵌段共聚物ABA在选择性溶剂中的胶束化行为. 结果发现,相同链组成的环形和线形嵌段共聚物的临界胶束浓度(cmc)的差别与A嵌段的比例(fA)及B嵌段间的吸引强度(ε)密切相关. 在fA较小、ε较大的情况下,相应环形嵌段共聚物的cmc值更小;而在fA较大、ε较小的情况下,线形嵌段共聚物的cmc值更小. 为了进一步理解胶束化行为同fA及ε的关系,计算了胶束化过程中熵和势能部分对自由能的贡献. 结果表明,在所研究的fA和ε范围内,环形嵌段共聚物形成胶束时的熵损失更小,因而从熵贡献角度来看,环形嵌段共聚物更易发生胶束化. 而从势能贡献角度来看,当fA较小、ε较大时,环形嵌段共聚物形成胶束时势能有较大程度的降低,对自由能的贡献更大,因而此时环形嵌段共聚物更易发生胶束化. 而当fA较大、ε较小时,线形嵌段共聚物形成胶束时势能有较大程度的降低,对自由能的贡献更大,因而此时线形嵌段共聚物更易发生胶束化. 由此可见,对体系的胶束化自由能进行系统分析,有助于更好地理解环形和线形嵌段共聚物的胶束化行为.     

嵌段序列对线型ABC三嵌段高分子微相分离动力学的影响

用动态密度泛函理论研究了嵌段序列对线型ABC三嵌段高分子微相分离动力学机理的影响. 针对一个典型的线型ABC三嵌段高分子, 通过系统地改变各嵌段的体积分数, 我们给出了嵌段序列为ABC 和BAC时, 关于微相分离机理的三元相图. 发现除各嵌段的平均组分、相互作用能外, 嵌段序列也影响其微相分离的机理和最终的相结构. 此外, 嵌段序列的变化还导致了三元相图对称性的破缺.     

Thermodynamics of Adsorption and Micellization of Triblock Copolymers of Oxyethylene and Oxybutylene in Aqueous Medium Using Surface Tensiometry

The aqueous solutions of three triblock copolymers based on polyoxyethylene and polyoxybutylene of the type E_mB₁₀E_m have been analyzed by surface tension measurements. Surface activity of these triblock copolymers was studied by measuring surface parameters, like surface excess concentration, Γ₂, area per molecule of polymer and standard Gibb's free energy of adsorption, Δ^oG_ads, at various temperatures in the range of 20 to 50°C. The Effect of block length of hydrophilic portion of triblock copolymers on surface activity was investigated in this work. Miceller behavior of these triblock copolymers was also investigated using above technique. Critical micelle concentration (CMC) was determined from the plot of surface tension versus log of concentration in the range of temperature of 20–50°C. Thermodynamic parameters, standard free energy of micellization, Δ^oG_mic, standard enthalpy of micellization, Δ^oH_mic, and standard entropy of micellization, Δ^oS_mic were calculated from CMC value using closed association model in this range of temperature. Self assembly behavior of triblock copolymer E₂₀B₁₀E₂₀ was compared with E₃₀B₁₀E₃₀ and E₄₈B₁₀E₄₈ triblock copolymer. Effect of temperature on surface and miceller properties of the triblock copolymers was also studied.     

不同覆盖度下Li原子在Si(001)表面上的吸附构型和电子结构

采用基于赝势平面波基组的密度泛函理论, 对不同Li原子覆盖度下Li/Si(001)体系的吸附构型、电子结构以及吸附Li原子对表面性质的影响进行了系统研究. 计算结果表明, 在所考察的覆盖度范围内, Li原子倾向于吸附在相邻两个Si-Si二聚体之间各种对称性较高的空穴位, 其中覆盖度为0.75 ML(monolayer)时具有最小的平均吸附能. 由能带结构分析结果可知, 随着覆盖度的增大, Si(001)表面存在由半导体→导体→半导体的变化过程. 在覆盖度为1.00 ML时, 由于表层二聚体均受到显著破坏, 使得体系带隙明显增大. 吸附后, 有较多电子从Li原子转移到底物, 导致Si(001)表面功函显著下降, 并随着覆盖度的增加表面功函呈现振荡变化. 此外, 从热力学稳定性角度上看, 覆盖度为0.75 ML的Li/Si(001)表面较难形成.     

水在金红石型TiO2（110）表面〈001〉阶梯边缘吸附的第一性原理研究

利用第一性原理计算方法,研究了水在金红石型TiO2（110）表面及〈001〉阶梯边缘处的吸附．关于水在（11O）表面上的吸附,研究表明,对不同的吸附率,水都是以分子模式吸附在表面．关于水在〈001〉9梯边缘处的吸附,研究表明,其吸附模式和吸附率有密切的联系．当水的吸附率为一个单层（1ML）时,分子吸附和解离吸附对应的吸附能分别为0．92和0．60eV,分子吸附模式更稳定．当吸附率降为1／2ML时,分子吸附和解离吸附所对应的吸附能分别为0．86和0．84eV,两种吸附模式都可能存在．在表面上,不同吸附模式的吸附能随吸附率变化趋势是一致的．而在〈001〉阶梯边缘处,对于不同的吸附模式,吸附能随吸附率的变化呈现出不同的变化趋势．这是由在〈001〉阶梯边缘处低吸附率时解离模式的独特结构引起的．     

Interfacial rheology and conformations of triblock copolymers adsorbed onto the water-oil interface

The conformation and the dilatational properties of three non-ionic triblock PEO-PPO-PEO (where PEO is polyethyleneoxide and PPO is polypropyleneoxide) copolymers of different hydrophobicity and molecular weight were investigated at the water-hexane interface. The interfacial behavior of the copolymers was studied by combining dilatational rheology using the oscillating drop method and ellipsometry. From the dilatational rheology measurements the limiting elasticity values, E(0), of the Pluronics as function of surface pressure, Π, and adsorption time were obtained, i.e. E(0)(t) and E(0)(Π). Here, it is shown that E(0)(t) depends on the number of PEO units and on the bulk concentration, showing maximum and minimum surface elasticity values which indicate conformational changes in the interfacial layer. Furthermore, in the framework of the polymer scaling law theory, conformational transitions were discussed in E(0) vs. Π plots. In a dilute regime (Π<14 mN m(-1)) at the water-hexane interface, E(0)=2Π fits well all the data, which indicates a two-dimensional "stretched chain" conformation. Increasing Π, two other interfacial transitions could take place. The different behavior of Pluronic copolymers could be also described by the local minima of E(0), which depends on the hydrophobicity of the copolymers. Conformational transitions observed by interfacial rheology were compared to ellipsometric data. Experimental results were discussed and explained on the basis of two- and three-dimensional copolymer structure taking into account that PPO chains could be partially immersed in hexane and water.