Elastic behavior of short compact chains confined in double parallel boundaries

Adsorption of short two-dimensional compact chains confined in the double attractive parallel planar boundaries is investigated by using enumeration calculation method in this paper. First, we calculate the chain size and shape of adsorbed compact chains, such as mean-square end-to-end distance per bond R²/N, mean-square radii of gyration per bond S²_x/N and S²_y/N, shape factor δ and fraction of adsorbed segments f_a to illuminate that how the size and shape of adsorbed compact chains changes during the process of tensile elongation. There are some special behaviors in the chain size and shape for strong attraction interaction. In the meantime, compact chains can reach to the stable state with large distance between two parallel boundaries D. On the other hand, some thermodynamic properties, such as average energy per bond, Helmholtz free energy per bond, elastic force f and energy contribution to elastic f_U are also investigated in order to study the elastic behavior of compact chains adsorbed on the double attractive parallel planar boundaries. These investigations may provide some insights into the thermodynamic behaviors of adsorbed compact chains.     

Elastic behavior of adsorbed polymer chains

Elastic behaviors of single polymer chains adsorbed on the attractive surface are first investigated using Monte Carlo simulation method based on the bond fluctuation model. We investigate the chain size and shape of adsorbed chains, such as mean-square radius of gyration S2, mean-square bond length b2, shape factors sf(i) and delta*, and the orientation of chain segments P2, to illuminate how the shape of polymer chains changes during the process of tensile elongation. There are some special behaviors of the chain size and shape at the beginning of elongation, especially for strong attraction interaction. For example, mean fraction of adsorbed segments decreases abruptly in the region of small elongation ratio and then decreases slowly with increasing elongation ratio. In fact, the chain size and shape also changes abruptly for small elongation ratio with strong attraction interaction. Some thermodynamics properties are also investigated here. Average Helmholtz free energy increases fast for elongation ratio lambda<1.15, especially with strong attraction, and increases slowly for lambda>1.15. Similar behaviors are obtained for average energy per bond. Elastic force (f ) and energy contribution to force (f(U)) are also studied, and we find that elastic force decreases abruptly for lambda<1.15, and there is a minimum of elastic force for strong attraction interaction, then increases very slowly with increasing elongation ratio. However, there are different behaviors for weak attraction interaction. For energy contribution to force (f(U)), there is a maximum value for strong attraction interaction in the region of lambda<1.15. Some comparisons with the atomic force microscopy experiments are also made. These investigations may provide some insights into the elastic behaviors of adsorbed polymer chains.     

Conformational structures and thermodynamic properties of compact polymer chains confined between two parallel plane boundaries

In this paper, the authors investigated the adsorption phenomenon of compact chains confined between two parallel plane boundaries using a pruned‐enriched Rosenbluth method. The authors considered three cases with different adsorption energies of ε = 0, ?1, and ?3 (in units of k_BT) for the confined compact chains of different chain lengths N, respectively. Several parameters were employed to describe the size and shape of compact chain, and some special behaviors in the conformational structures were investigated for the first time. For example, the size and shape of confined compact chains undergo distinct changes in the adsorption cases of ε = ?1 and ?3, and pass through the maximum values at the characteristic distances D_c. The authors found that this characteristic distance D_c could be scaled as D_c～ (N + 1)^ν (ν = 0.56 ± 0.01) in the case of ε = ?3. In addition, the microstructures of chains were investigated, and several significant results were obtained by analyzing the segment density distribution and the mean fractions of segment in tails, trains, bridges, and loops structures. On the other hand, the thermodynamic properties were also investigated for the confined compact chains, such as average energy per bond, Helmholtz free energy per bond, and elastic force per bond. Results show that elastic forces f have different behaviors in three cases, indicating that it is not necessary to exert an external force on the boundaries in the nonadsorption case. At the same time, the average contact energy of compact chain obviously changes when the distance between the two parallel boundaries D increases, which is similar to those of the size and shape parameters. The authors also conclude that these thermodynamic properties of compact chains depend strongly on not only the adsorption energies but also the chain lengths and the confined condition. In addition, several results of the conformational and thermodynamic parameters, such as the segment density distribution and free energy, were compared with the results from the self‐consistent field theory. These investigations may help us to deepen the knowledge about the adsorption phenomenon of confined compact chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2888–2901, 2006     

三维吸附紧密高分子单链的力学性质研究

采用PERM(pruned-enriched Rosenbluth method)算法,研究了吸附在界面附近的紧密高分子链力学行为.发现当界面的吸附能比较大时,紧密高分子链从紧贴于吸附界面到逐渐远离的过程中,其外形会经历4种典型的变化.同时紧密高分子链的尺寸大小如/N、xy/N、z/N,形状参数<δ*>,热力学性质如每个键的平均自由能A/N,平均相互作用能/N等,甚至所受外力的大小都会同时做出相应的变化,其出现变化的位置也一致.特别是随着紧密高分子链离开吸附界面的过程中,作用于高分子链上的外力明显出现几个力学平台,这与实验得到的结果完全一致.同时还研究了弱吸附能的情况,在这种情况下实验是很难进行的.     

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.     

拉力诱导下的紧密高分子链相变行为

采用相互作用自回避行走(interacting self-avoiding walks,ISAWS)模型研究了一端固定的紧密高分子链在拉伸过程中的低温相变行为,观察到在拉伸过程中当温度T<0.1时平均拉力会出现一个震荡,随着温度的升高这种震荡现象又渐渐消失,这是由于紧密高分子链在低温时类似于β折叠的"冻结构象"被拉开而引起的.比较吸附条件下和无吸附作用下平均拉力、自由能以及相变行为的差别,发现在吸附条件下在拉伸的初始阶段为了克服表面吸附的相互作用,拉力会出现一个峰.吸附作用也使得外界作用到高分子链上的实际有效拉力减小,造成崩塌相态(collapsed phase)区域面积减少.另外发现在吸附条件下平均拉力还受温度变化的影响.在拉伸的初期由于单体间存在体积排除效应,平均拉力是随着温度的升高而降低,随着拉伸的深入当末端距到达一定长度时平均拉力是随着温度的升高而增加.并同Kumar等人在不考虑吸附作用下拉伸紧密高分子链得到的结果进行了比较.这些研究对于进一步研究外力诱导下吸附紧密高分子的相变有一定的参考价值.     

Elastic behavior of single polymer chains adsorbed on rough surfaces

In this paper, elastic behaviors of single polymer chains adsorbed on the rough surfaces with a substrate and some periodically tactic pillars are investigated by the pruned-enriched-Rosenbluth method (PERM). In our simulation, a single polymer chain is firstly adsorbed on the substrate and then pulled along the z-axis direction, which is vertical to the substrate. We investigate the chain size and shape of polymer chains, such as mean-square radii of gyration per bond 〈S²〉_xy/N, 〈S²〉_z/N and shape factor 〈δ^∗〉 in order to show how the size and shape of adsorbed polymer chains change during the desorption process. Due to the occurrences of separation of the chains from the substrate, farther adsorption on the upper surfaces of pillars and complete separation from the whole rough surfaces in the elastic process, the changes of 〈S²〉_xy/N, 〈S²〉_z/N and 〈δ^∗〉 during the process are complicated. On the other hand, some thermodynamic properties such as average energy per bond, average Helmholtz free energy per bond, elastic force f are investigated, and our aim is to study the elastic behaviors of polymer chains adsorbed on the rough surface during the elasticity process. Elastic force f has some plateaus during the desorption process for strong adsorption interaction. If there is no adsorption interaction, the chains can get away from the rough surfaces spontaneously. These investigations can provide some insights into the elastic behaviors of polymer chains adsorbed on the rough surface.     

ELASTIC BEHAVIOR OF PROTEIN-LIKE SINGLE CHAIN

The conformational properties and elastic behaviors of protein-like single chains in the process of tensile elongation were investigated by means of Monte Carlo method. The sequences of protein-like single chains contain two types of residues: hydrophobic (H) and hydrophilic (P). The average conformations and thermodynamics statistical properties of protein-like single chains with various elongation ratio λ were calculated. It was found that the mean-square end-to-end distance r increases with elongation ratio,λ. The tensor eigenvalues ratio of : decreases with elongation ratio λ for short (HP)x protein-like polymers, however, the ratio of : increases with elongation ratioλ,especially for long (H)x sequence. Average energy per bond increases with elongation ratioλ, especially for(H)x protein-like single chains. Helmholtz free energy per bond also increases with elongation ratioλ. Elastic force (f), energy contribution to force (fU) and entropy contribution to force (fs) for different protein-like single chains were also calculated.These investigations may provide some insights into elastic behaviors of proteins.     

Monte Carlo Simulation of Coil-to-Globule Transition of Compact Polymer Chains: Role of Monomer Interacting

Coil-to-globule transitions are fundamental problems existing in polymer science for several decades; however, some features are still unclear, such as the effect of chain monomer interaction. Herein, we use Monte Carlo simulation to study the coil-to-globule transition of simple compact polymer chains. We first consider the finite-size effects for a given monomer interaction, where the short chain exhibits a one-step collapse while long chains demonstrate a two-step collapse, indicated by the specific heat. More interestingly, with the decrease of chain monomer interaction, the critical temperatures marked by the peaks of heat capacity shift to low values. A closer examination from the energy, mean-squared radius of gyration and shape factor also suggests the lower temperature of coil-to-globule transition.     

Translocation of a proteinlike chain through a finite channel

We use the pruned-enriched-Rosenbluth method and the modified orientation-dependent monomer-monomer interaction model to study the translocation of a proteinlike chain through a finite channel. The mean-square radius of gyration per bond /N and shape factor of proteinlike chains with different secondary structures transporting through a finite channel with different channel radii R=1, 2, 3, 4, and 20 are investigated in the translocation. The average Helmholtz free energy per bond A/N and the mechanical force f are also presented. A/N remains unchanged when X(0)<0 and X(0)>1, and decreases monotonously when 0.5/N is also calculated in the process of translocation. An energy barrier is shown. The proteinlike chains must cross this energy barrier when they escape from the channel. The position of the maximum of /N depends on the secondary structures and the channel radius. We also discuss the average contact energy per bond c/N, the average alpha-helical energy per bond h/N, and the average beta-sheet energy per bond b/N.     

Phase transition of short linear molecules adsorbed on solid surfaces from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on strongly attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the layering transitions change with the change of the chain length and with relative strength of the fluid-solid interaction. The critical temperature of the first layering transition, rescaled by the bulk critical temperature, increases slightly with an increase of the chain length. We have found that for longer chains the layering transitions within consecutive layers are shifted toward very low temperatures and that their sequence is finally replaced by a single transition.     

Short chains at solid surfaces: wetting transition from a density functional approach

A microscopic density functional theory is used to investigate the adsorption of short chains on attractive solid surfaces. We analyze the structure of the adsorbed fluid and investigate how the wetting transition changes with the change of the chain length and with the relative strength of the fluid-solid interaction. End segments adsorb preferentially in the first adsorbed layer whereas the concentration of the middle segments is enhanced in the second layer. We observe that the wetting temperature rescaled by the bulk critical temperature decreases with an increase of the chain length. For longer chains this temperature reaches a plateau. For the surface critical temperature an inverse effect is observed, i.e., the surface critical temperature increases with the chain length and then attains a plateau. These findings may serve as a quick estimate of the wetting and surface critical temperatures for fluids of longer chain lengths.     

Free-radical copolymerizations of 1,2-dichloroethylenes. Evidence for chain transfer by chlorine atom elimination

Trialkylboron–oxygen, an active, low-temperature free-radical initiator, has been employed to investigate the effects of very low temperatures on the copolymerizations of vinyl acetate with cis and trans-1,2-dichloroethylenes. The low temperatures favor the propagation rate relative to the transfer rate, such that high molecular weight copolymers containing substantial quantities of 1,2-dichloroethylene can be prepared. The molecular weights of the copolymers depend only on the amounts of 1,2-dichloroethylene in the copolymers, regardless of the isomer which takes part in the copolymerization. Since the double bond of the trans isomer is about six times as reactive as that of the cis isomer, this indicates that the dominating chain transfer reaction occurs by chlorine atom elimination subsequent to the addition of the dichloroethylene unit to the growing free radical chain. It is suggested that a similar chain-transfer mechanism occurs in the polymerization of vinyl chloride, wherein an infrequent head-to-head placement of monomer unit is followed by ejection of a chlorine atom to form an olefinic bond and termination of that growing chain. The presence of the 1,2-dichloroethylene unit in the copolymer increases the glass transition temperature approximately 1°C per weight per cent copolymerized with the vinyl acetate.     

Influence of temperature and headgroup size on condensed-phase patterns in langmuir monolayers of some oxyethylenated nonionic surfactants

The surface phase behavior in Langmuir monolayers of some oxyethylenated nonionic surfactants of the general formula C16En, with n = 1, 2, 3, and 4, at the air-water interface has been studied by film balance and Brewster angle microscopy (BAM) over a wide range of temperatures. The C16E4 monolayers cannot show any indicative features of phase transition because of strong dipolar as well as hydration-induced repulsive interactions between the bulky headgroups. On the other hand, the monolayers of C16E1, C16E2, and C16E3 show a sharp cusp point followed by a pronounced plateau region in their respective isotherms with subsequent formation of a variety of structures in the two-phase coexistence region between the liquid expanded (LE) and liquid condensed (LC) phases at different temperatures. As usually observed, the domains of C16E1, which bears only one ethylene oxide (EO) unit in the headgroup, are circular at lower temperatures while fractal at higher temperatures. On the other hand, those for C16E2 and C16E3 are initially found to be irregular structures, which attain increasingly compact shape with increasing temperature, and finally become circular when the subphase temperature is 26 and 15 degrees C for C16E2 and C16E3, respectively. It is concluded that a higher degree of dehydration around the headgroup region appreciably reduces the headgroup size, which imparts to the molecules an increase in hydrophobicity, thereby a closer molecular packing. Consequently, the line tension of the interface increases, showing compact structures at higher temperatures. Since C16E1 bears only one EO unit in its headgroup, the dehydration effect cannot appreciably raise its hydrophobicity to overcome the increases in thermal motion and chain flexibility of the molecules. Rather, increases in subphase temperature result in a decrease in the line tension of the interface, giving fractal structures at higher temperatures.     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

Surface phase behavior in Langmuir monolayers of diethylene glycol mono-n-hexadecyl ether at the air-water interface

The surface phase behavior of condensed-phase domains formed during a first-order phase transition in Langmuir monolayers of diethylene glycol mono-n-hexadecyl ether at the air-water interface has been investigated by Brewster angle microscopy and polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS). A variety of two-dimensional (2D) structures are observed just after the appearance of the phase transition at different temperatures. At 10 and 15 degrees C, the domains are found to be small nuclei of irregular structures. Spiral structures are observed at 20 and 22 degrees C, while striplike structures at 24 degrees C. The spiral domains attain increasingly compact shape with increasing temperature, and finally become circular at >or=26 degrees C. Increases in temperature result in dehydration in the ethylene oxide chain, which increases the hydrophobicity, and impart to the molecules a longer-chain-like character. As a result line tension increases with increasing temperature, which probably outweighs the dipole-dipole repulsions showing circular domains at higher temperatures. The PM-IRRAS measurement reveals that the nu(as)(CH(2)) mode moves to lower wave numbers indicating that the LE-LC (liquid expanded-liquid condensed) phase transition during the compression of the monolayer involves changes in the conformational order of the molecules with a preferential increase in the planner trans zigzag conformation of the hydrocarbon chains. The nu(as)(CH(2)) mode in the LC region of the isotherm shows a constant value around 2917.8 cm(-1) indicating a stable state of the monolayer with an almost all-trans conformation of the hydrocarbon chains. The downward band at 1124 cm(-1) assigned to the nu(as)(C-O-C) mode indicates that the corresponding transition dipole moment is oriented perpendicular to the water surface.     

EFFECTS OF SECONDARY STRUCTURE ON ELASTIC BEHAVIOR OF PROTEIN-LIKE CHAINS

The elastic behavior of protein-like chains was investigated by using the Pruned-Enriched-Rosenbluth Method (PERM).Three typical protein-like chains such as all-α,all-β,and α+β(α/β) proteins were studied in our modified orientation dependent monomer-monomer interaction (ODI) model.We calculated the ratio of /N and shape factor <δ*> of protein-like chains in the process of elongation.In the meantime,we discussed the average energy per bond ＜U＞/N,average contact energy per bond ＜U＞c/N,average helical energy per bond ＜U＞h/N and average sheet energy per bond ＜U＞b/N.Three maps of contact formation,α-helix formation,β-sheet formation were depicted.All the results educe a view that the helix structure is the most stable structure,while the other two structures are easy to be destroyed.Besides,the average Helmholtz free energy per bond ＜A＞/Nis was presented.The force f obtained from the free energy was also discussed.It was shown that the chain extended itself spontaneously first.The force was studied in the process of elongation.Lastly,the energy contribution to elastic force fu was calculated too.It was noted that fu for all-β chains increased first,and then decreased with x0 increasing.     

磁性高分子链的磁性质和构象性质的Monte Carlo模拟

采用退火 (Annealing)MonteCarlo方法 ,从高温到低温顺序模拟了简立方格点上考虑最近邻Ising相互作用的磁性高分子链在不同温度的磁性质和构象性质 .磁性高分子链在低温下存在自发磁矩 ,无限长链的临界温度Tc=1 77± 0 0 5J kB.在临界温度附近 ,高分子链经历了从伸展的无规线团到紧缩球体的塌缩相变 .对链的尺寸、形状、近邻数及能量的分析表明 ,高分子链的构象性质从温度Tc=1 77开始发生较明显的变化 ,这表明高分子Ising链的相变是Ising相互作用和链节运动协同作用的结果 .     

Study of size-dependent glass transition and Kauzmann temperatures of tin dioxide nanoparticles

The size and shape effects on melting, glass transition, and Kauzmann temperatures of SnO₂ nanoparticles using Lindemann??s criterion have been studied. The melting temperature of SnO₂ nanoparticles decreases as the size of the particle decreases. As the particle size increases, melting temperature increases and approaches to the melting temperature 1,903?K of bulk irrespective of the shape. The glass transition and Kauzmann temperatures are analyzed through the size effect on the melting temperature. The glass transition and Kauzmann temperatures decrease with the decrease in size of SnO₂ nanoparticles.     

Effect of branching and confinement on star-branched polymeric systems

The effect of confinement, number of branches (functionality), and size of the molecules on various properties as a function of temperature of star-branched polymers confined between two walls was studied using Monte Carlo simulations with the parallel tempering technique. The coil-to-globule transition and the liquidlike to solidlike transition, similar to those observed for linear chains, were characterized in all systems by changes in the heat capacity, internal energy, and radius of gyration. The transitions were also characterized by the most probable isomeric structure at a given temperature. The radius of gyration of the star polymers was smaller than the values of linear chains when the number of arms f increased. For star chains with more than f=5 arms the values of the radius of gyration, and therefore the size of the molecules, were similar for every condition of confinement studied, especially at higher temperatures. As confinement was increased, the difference in the radius of gyration of linear chains and star polymers became even larger. The coil-to-globule transition temperatures shifted to higher temperatures as the size of the chains and the number of arms in a molecule were increased. Effects of confinement were higher on the properties of the system at the smallest separations (less than twice the monomer diameter), where the coil-to-globule transition shifted to lower temperatures. The liquidlike to solidlike transition was present at almost the same temperature for different conditions of confinement, chain size, and number of arms. The behavior of the systems for separations between the walls greater than five bead diameters was similar to the behavior in the unconfined case. Hence, no considerable effect of confinement was found above this separation.