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.     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers I. Configuration distribution and density profiles of adsorbed chains

Monte Carlo simulations for the adsorption of symmetric triblock copolymers from a nonselective solvent at a solid-liquid interface have been performed on a lattice model. In simulations, triblock copolymer molecules are modeled as self-avoiding linear chains composed of m segments of A and n segments of B arranged as A_m/2B_nA_m/2. Either segment A or segment B is attractive, while the other is non-attractive to the surface. The microstructure of the adsorbed layers, including the segment-density profiles and the size distribution of loops, tails and trains are presented. The effect of the adsorption energy, the bulk concentration, the chain composition, as well as the chain length on various adsorption properties has been studied. The results have shown that the size distribution of various configurations is dependent of the adsorption energy, the chain composition and the chain length. The mean length of the loops, trains and tails is insensitive to the bulk concentration. The mean length of the trains increases and that of the tails decreases as the adsorption energy and the length of the attractive segments increase. The mean length of the loops for the end-adsorbed copolymers appears a maximum and that for middle-adsorbed copolymers appears a minimum as the length of attractive segments increases. The length of the non-attractive segments affects mostly the size distribution of the tails. The longer the chain is, the larger the tail appears. The mean length of the tails and loops increases linearly as the length of the non-attractive segments increases, but that of the trains approximately is unchanged.     

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.     

Synthesis and characterization of poly(DTC‐b‐PEG‐b‐DTC) triblock and poly(TMC‐b‐DTC‐b‐PEG‐b‐DTC‐b‐TMC) pentablock copolymers and kinetics of the polymerization

Dihydroxyl capped biodegradable poly(DTC‐b‐PEG‐b‐DTC) (BCB) triblock copolymer and poly(TMC‐b‐DTC‐b‐PEG‐b‐DTC‐b‐TMC) (ABCBA) pentablock copolymer have been synthesized by PEG and BCB copolymer as macroinitiator in the presence of yttrium tris(2,6‐di‐tert‐butyl‐4‐methylphenolate). The copolymers without random segments have been thoroughly characterized by ¹H, ¹³C‐NMR, SEC, and DSC. Molecular weights of the obtained copolymers are dependent on the amount of PEGs and coincide with the theoretical values. The exchange reaction of yttrium alkoxide and hydroxyl end group is essential for controlling the products' molecular weight. Their thermal behaviors are relevant to the chain lengths of PEG and PDTC segments. The Monte Carlo method has been developed to estimate the chain propagation constant and exchange reaction constant. In average, one exchange reaction will occur after approximately six monomer molecules insert into the growing chain. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1787–1796, 2005     

Elastic Behaviors of Adsorbed Protein-like Chains

Elastic behaviors of protein-like chains are investigated by Pruned-Enriched-Rosenbluth method and modified orientation-dependent monomer-monomer interactions model. The protein-like chain is pulled away from the attractive surface slowly with elastic force acting on it. Strong adsorption interaction and no adsorption interaction are both considered. We calculate the characteristic ratio and shape factor of protein-like chains in the process of elongation. The conformation change of the protein-like chain is well depicted. The shape of chain changes from “rod” to “sphere” at the beginning of elongation. Then, the shape changes from “sphere” to “rod”. In the end, the shape becomes a “sphere” as the chain leaves away from the surface. In the meantime, we discuss average Helmoholtz free energy per bond, average energy per bond, average adsorbed energy per bond, average α-helical energy per bond, average β-sheet energy per bond and average contact energy per bond.On the other hand, elastic force is also studied. It is found that elastic force has a long plateau during the tensile elongation when there exists adsorption interaction. This result is consistent with SMFS experiment of general polymers. Energy contribution to elastic force and contact energy contribution to elastic force are both discussed. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

Monte Carlo Computer Simulation of a Single Semi-Flexible Macromolecule at a Plane Surface

Summary: The properties of a single semiflexible mushroom chain at a plane surface with a long-ranged attracting potential are studied by means of lattice Monte Carlo computer simulation using the bond fluctuation model, configurational bias algorithm for chain re-growing and the Wang-Landau sampling technique. We present the diagram of states in variables temperature T vs. strength of the adsorption potential, ε_w, for a quite short semiflexible chain consisting of N = 64 monomer units. The diagram of states consists of the regions of a coil, liquid globule, solid isotropic globule, adsorbed coil and cylinder-like liquid-crystalline globule. At low values of the adsorption strength ε_w the coil–globule and the subsequent liquid–solid globule transitions are observed upon decreasing temperature below the adsorption transition point. At high values of ε_w these two transitions change into a single transition from an adsorbed coil to a cylinder-like liquid-crystalline solid globule. We conclude that for a semiflexible chain the presence of a plane attracting surface favors the formation of a globule with internal liquid-crystalline ordering of bonds.     

大分子固液界面吸附行为的数字模拟研究方法

介绍了随机数字模拟方法在研究链状大分子吸附行为的一般原理,以立方格子模型的自避行走为例,分析了模型的建立、初始位形的产生以及分子链运动的处理方法.回顾了随机数字模拟方法在研究大分子界面吸附行为方面的发展状况.预测了随机数字模拟方法在大分子吸附行为研究方面的应用前景.     

Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

Properties of star-branched and linear chains in confined space: a computer simulation study

We studied the properties of simple models of linear and star-branched polymer chains confined in a slit. The polymer chains were built of united atoms and were restricted to a simple cubic lattice. Two macromolecular architectures of the chain linear and star-branched with three branches (of equal length) were studied. The excluded volume was the only potential introduced into the model and thus, the system was athermal. The chains were put between two parallel and impenetrable surfaces. Monte Carlo simulations with a sampling algorithm based on chain’s local changes of conformation were carried out. The differences and similarities in the global size and the structure and of linear and star-branched chains were shown and discussed.     

Monte Carlo simulation of the local ordering of water molecules. I. Binary spatial correlations

The pair distribution functions (DFs) of the oxygen and hydrogen atoms over space around one of the water molecules were calculated during Monte Carlo simulation (Metropolis procedure for the NVT ensemble at normal density and 300 K). An analysis of the isosurfaces of the DF_OO and DF_OH constructed around the selected water molecule for several fixed values of local density allowed us to obtain detailed information about the most probable localization of water molecules in the second and third coordination spheres.     

Sphere‐to‐cylinder transition in dilute solutions of diblock copolymers

AB diblock copolymers dissolved in a selective solvent for block B spontaneously self‐assemble into spherical or cylindrical micelles with an A core surrounded by a corona of the B block. Using a Monte Carlo lattice model, we find that the sphere‐to‐cylinder transition can be fully described in terms of a packing parameter that depends on the relative cross sections of the two blocks. The latter can be varied either by a block length being changed or by the B block being allowed to adopt an ordered conformation (e.g., helical). The model results are in good agreement with experimental observation. They also shed some light onto the molecular origins of the ease of processing and exceptional mechanical properties of spider dragline. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 890–895, 2002     

Computer simulation analysis of conductivity of supported polydisperse systems

Effects of the support texture and the supported phase distribution on the conductivity of an individual grain or a granulated system have been analyzed theoretically. Experimental criteria are discussed, which allow one to judge the porous structure and sites of localization of a conducting component on the basis of the concentration dependence of the conductivity.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1449–1453, August, 1995.The authors are grateful to the International Science Foundation for partial financial support of this work (Project No. M 63000).     

Thermally induced phase transition in helical comblike poly(beta-peptide)s: an atomistic simulation

Atomistic Monte Carlo (MC) simulations have been used to study a thermally induced phase transition in poly(alpha-octadecyl-beta,L-aspartate). Simulations were performed by using the parallelized version of Configurational Bias MC algorithm adapted to study comblike polymers. A total of 1.15. 10(6) steps were carried out for a molecular system constituted by 6240 atoms/pseudoatoms. Results were consistent with available experimental observations. The limitations of atomistic simulations to study large length-scale phenomena are discussed.     

Computer simulation of polymer networks: mesoscopic heterogeneity of the structure and topological parameters

Samples of networks of reacting bi- and trifunctional monomers have been obtained by the dynamic Monte Carlo method for the two dimensional lattice model. Systems with various densities and numbers of chemical junctions have been studied. The steady-state structural factor, the number of the degree of conversion, and topological parameters of samples appear to depend strongly on the initial (random) spatial configuration and the size of the Monte Carlo base cell. Deviations of structural parameters calculated by ensemble and time averaging are statistically significant, which makes it possible to classify networks of this type as so-called non-ergodic fortuitous media that exhibit this property for scales of 10² nm. Newly developed facilities for topological analysis allow one to observe the kinetics of changes in individual components of the system: trees, circuits, and other more complex structures.Papers presented in the section Physical Chemistry of this issue are based on the materials delivered at the XII Seminar on Intermolecular Interactions and Conformation of Molecules, Khar'kov, October 3–8, 1994.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1226–1232, July, 1995.The work was financially supported by the Russian Foundation for Basic Research (Project No. 9503-08170a).The authors are grateful for Professor J. G. H. Joosten of Leiden University for helpful critical comments.     

Monte Carlo Study of Heteroarm Star Copolymers in Good and Selective Solvents

Lattice Monte Carlo simulations of conformations of hereroarm star copolymers A_nB_n in selective solvents were performed using a special variant of the Siepman and Frenkel algorithm. The effects of solvent quality, the number and lengths of blocks on the collapse of the insoluble block A, segregation of the two types of blocks and the behavior of the soluble blocks B were studied mainly for “hairy” stars containing high numbers of long arms. The simulation shows that insoluble blocks collapse in strongly selective solvents and the gravity centers of soluble and insoluble blocks separate which suggests the possibility of the formation of non‐spherical structures.

Snapshots of star a in a very bad solvent (T = 3.00) for blocks A. There are two different views of the star with a total number of arms f = 16 and number of segments N = 300.     

Physical association of polymers with nanotubes

We use a coarse-grained Monte Carlo model to further investigate the association of polymers with carbon nanotubes (CNTs). Previous studies have shown ordered helical wrapping conformations for a range of investigated parameters. Such adsorbed conformations allow the polymers to spiral up and down the surface of the nanotube, retaining their helical state. We analyze the helical pitch of such conformations, and relate it to nanotube radius and chain stiffness using a simple model. The model reveals that the helical pitch is approximately determined by the matching between the radius of curvature of the helix with the average bending angle of the polymer, determined by its persistence length. In addition, we simulate adsorption of block and triblock copolymers (BCPs) whose different blocks are differentiated by their degree of association with the nanotube (hydrophobic or polar). The hydrophobic blocks of the copolymers initially adsorb in both helical and random conformations of the hydrophobic block, depending on which part of the chain (center or ends) adsorbs first on the CNTs surface. In both configurations, however, the polar block extends away from the nanotube, forming loops and tails for triblock and diBCPs, respectively. Such configurations may improve the interfacial adhesion in polymer–CNTs composites. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2711–2718, 2008     

Graphoepitaxial assembly of cylinder forming block copolymers in cylindrical holes

The graphoepitaxial assembly of cylinder‐forming block copolymers assembled into holes is investigated through theoretically informed coarse grained Monte Carlo simulations (TICG MC). The aim is to identify conditions leading to assembly of cylinders that span the entire thickness of the holes, thereby enabling applications in lithography. Three hole geometries are considered, including cylinders, elliptical cylinders, and capsule‐shaped holes. Four distinct morphologies of cylinder forming poly(styrene‐b‐methyl methacrylate) (PS‐b‐PMMA) block copolymers are observed in cylinders and elliptical holes, including cylinders, spheres, partial cylinders, and wall‐bound cylinders. Additional morphologies are observed in capsule‐shaped holes. PMMA cylinders that extend through the entire hole are found with PMMA‐wetting surfaces; a weak wetting condition is needed on the bottom of the hole and a strong wetting condition is necessary on the sides of the hole. Simulated are also used to explore the morphologies that arise when holes are overfilled, or when PMMA homopolymers are added in blends with copolymers. We find that overfilling can alter considerably the morphological behavior of copolymers in cylinders and, for blends; we find that when the homopolymer concentration is >10%, the range of conditions for formation of PMMA cylinders that extend through the entire hole is increased. In general, results from simulations (TICG) are shown to be comparable to those of self‐consistent (SCFT) calculations, except for conditions where fluctuations become important. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 430–441