端基附壁高分子链的构象统计理论——Ⅱ.SAW尾形链

研究了SAW尾形链,采用精确计数和Monte Carlo模拟方法求得d维(d=2,3)SAW尾形链的构象数C_1~d和均方末端距[h_1~d(N)]~2及其分量随链长N的变化关系.发现它们与自由SAW链一样都服从标度律,从模拟数据拟合求出了这些SAW尾形链的临界指数.还表明短链SAW在壁的法向与NRW尾形链一样有所伸展,均方末端距的法向分量几乎是平行分量的2倍;但随N→∞,链自回避效应对壁的作用有所屏蔽,这与NRW尾形链有明显不同.     

端基附壁高分子链的构象统计理论——Ⅲ.NRW环形链

当线形高分子链两端被固体壁吸附后,形成了“环形链”。采用半空间格点中的普通随机行走(NRW)模型讨论了环形链构象的统计理论。在NRW尾形链构象分布函数的基础上,容易推导出NRW环形链构象数的公式。当链长N→∞时,环形链构象数与自由链构象数之比随N~(-3/2)而变化。用递归方程也导出了同样的结果。环形链的均方末端距(?)与均方键长l~2之比为2N/3,与长度相同的自由链比较,有一定收缩。所导出的基本关系得到了精确计数和Monte Carlo模拟的支持。     

近壁模型高分子链的计算机模拟

采用简立方格点上的普通无规行走 (NRW)和自避行走 (SAW )为模型链 ,研究了不可穿透的刚性壁附近高分子的构象性质 ,得出近壁链的构象熵和尺寸随一端点与壁之间距离z0 的变化 .所用的计算机模拟技术包括精确计数和MonteCarlo模拟 .数值结果表明 ,近壁链的构象熵降低遵循一种简单规律 ,即当链长愈长或一端愈接近于壁时 ,与长度相同的自由链相比 ,链因壁限制所致构象熵的降低愈大 .当链十分接近于壁时 ,其均方末端距〈R2 〉(尤其是与壁垂直的分量〈R2z〉)大于自由链的相应值 ;随z0 增大 ,〈R2 〉及〈R2z〉开始减小 ,通过某一极小值 ,然后上升 ;当z0 →∞时 ,趋于自由链的极限值 .换言之 ,近壁模型链的线团经历一个收缩再逐渐扩张的过程     

模型高分子尾型链的构象统计理论

基于金刚石格点上受限于半空间的随机行走，借概率论中的反射原理推导出了模型高分子尾型链的构象分布．得到了链长为Ｎ的模型尾型链的允许构象数Ｃ１（Ｎ）和末端距分布函数．在四选择模型中，发现Ｃ１（Ｎ）／４Ｎ与Ｎ－１／２成正比．模型尾型链在与壁正交方向上的均方末端距分布与平行方向比较扩张至２倍，而后者与自由链对应的分量相等．这些解析结果得到了精确计数和ＭｏｎｔｅＣａｒｌｏ模拟计算机“实验”的支持．     

金刚石格点上自避行走尾形链的构象统计理论

研究了金刚石格点上自避随机行走（ＳＡＷ）尾形链，采用精确计数和ＭｏｎｔｅＣａｒｌｏ模拟方法求得该ＳＡＷ尾形链的构象数Ｃ（Ｄ）１（Ｎ）和均方末端距［ｈ（Ｄ）１（Ｎ）］２及其分量随链长Ｎ的变化关系．发现它们与自由ＳＡＷ链一样都服从标度律，从这些量的计算机实验数据拟合求出了金刚石格点上ＳＡＷ尾形链的临界指数和格点指数．计算结果还表明短链ＳＡＷ在壁的法向与ＮＲＷ尾形链一样有所伸展，均方末端距的法向分量几乎是平行分量的２倍；但随Ｎ→∞，链自回避效应对壁的作用有所屏蔽．这些都与简立方格子模型上得到的结果一致．     

平行板间高分子链构象熵的动力学Monte Carlo模拟

用动力学Monte Carlo方法模拟了受限于两平行板之间的高分子链,并用扫描法计算了链的构象熵S,研究了构象熵相对于自由链的减小量(S0-S)与平行板间距D和高分子链长n的关系.结果证实了de Gennes的自由能标度关系,并给出了标度关系适用的范围.当D非常小时,高分子链受到强烈限制,S0-S与n成正比,表明单链节受到平行板的平均排斥作用力与链长无关.随着D增大,平行板对构象熵的影响越来越弱,单链节受到平行板的平均排斥作用力随链长的增长而增大.当D比较大时,平行板对构象熵的影响近似可以忽略,高分子链构象熵与自由空间中的结果一致.     

端基附壁高分子模型链的塌缩转变

借MonteCarlo和模拟退火方法研究了端基附壁高分子尾形链在不同温度下的形态变化 ,链的模型采用有最近邻相互吸引作用的自避行走 .计算机实验结果表明 ,对于端基附壁的高分子尾形链 ,与自由链一样 ,当温度逐渐降低时高分子链会发生从松散的无规线团到紧密球体的塌缩转变 .计算机模拟得到了端基附壁链的均方末端距及其分量 ,均方回转半径及分布随温度的变化 .由于刚性壁的影响 ,使得有限链长的高分子尾形链与自由链相比 ,其表示链尺寸 温度关系的曲线要稍低 .模拟还发现 ,在高温时壁对链形状的影响比较大 ,壁垂直方向上尺寸明显大于平行方向的尺寸 ,后者接近于自由链的尺寸分量 .然而 ,低于θ温度时 ,尤其是完全塌缩之后 ,壁对链形状的影响已经很小 .     

方阱链状分子临界性质的Monte Carlo模拟

在巨正则系综下对阱宽为λ=1.5,链长分别为4、8、16的方阱链状流体实施Monte Carlo模拟,采用建立在完整标度基础上的无偏的Q-参数方法,通过histogram reweighting技术以及有限尺寸标度理论得到了热力学极限下该系列流体的临界温度和临界密度.模拟结果表明,方阱链流体的临界温度随着链长的增加而升高.并且不同链长方阱流体的临界温度均低于已报道的结果.由于本文所采用的完整标度的无偏性,我们估计的临界点更加准确.并且流体的临界温度与链长之间的关系与Flory-Huggins理论相一致.我们还预测了无限链长方阱流体的临界温度,比已有结果略高.     

基于格子链的缩聚反应的动态Monte Carlo模拟

采用描述自回避格子链的键长涨落模型, 以动态Monte Carlo方法对AB型单体的线型缩聚反应动力学过程进行了模拟. 通过该方法可以得到反应过程中链的瞬时构象, 还可以得到反应程度、聚合度、分子量分布及其随时间的演化. 模拟得到了合理的结果, 同时验证了无规线团尺寸与平均链长的标度关系, 表明该方法用于研究逐步聚合反应过程是可行的, 并且与一般的研究聚合反应的Monte Carlo方法相比, 还能够同时得到构象等空间信息. 还比较了不同大小的模拟体系所得到的分子量和多分散系数的异同, 讨论了有限元胞效应.     

嵌段高分子尾形链构象性质的Monte Carlo研究

基于简立方格点模型对AB两嵌段高分子尾形链的构象性质及其链节的空间分布进行了MonteCarlo模拟.结果表明,链的尺寸、形状和链节的空间分布等统计性质和B链节与平面壁之间的相互吸引能有关.随着B链节与壁之间的吸引能的增加,链的尺寸和形状均呈现出先下降后升高的变化趋势,而且B链节的比例越大,这种变化越明显.     

Conformational statistics of polymer chain terminally attached to wall (II)

The SAW tail chains were studied. The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations, including the exact enumeration and Monte Carlo method. These two basic quantities obeyed the relations deduced from the scaling law. The critical exponents and the lattice indexes were given by fitting the data of the computer experiments. It has been shown that there is a certain extension in the size of the SAW tail chains as well as the NRW tail chains in the direction normal to the wall. The normal component of the mean square end-to-end distance is almost twice as large as the parallel component of the short chain SAW. However, as N →∞, the effect of the wall on the chain conformation becomes a little weak because of the self-avoiding behavior for the model. That is quite different from the case of the NRW tail chain. Project supported by the National Natural Science Foundation of China     

Decomposing bridging adhesion between polyelectrolyte layers into single molecule contributions

A novel approach to analyze the force response of multiple polymer strands, which are bridged between two surfaces, is proposed. The response of single polymer strands is experimentally accessible by measuring the force upon separation of two polymer-coated surfaces with the atomic force microscope. Our approach is based on the decomposition of the stretching and desorption sequence into contributions of independently bridged chains and of the elimination of loops formed on the opposite surface during contact. This approach was applied to investigate the bridging adhesion of surfaces coated with poly(vinylamine) (PVA). The force response of single PVA molecules was described on the basis of a recently proposed model, which accounts for the discrete chain character of the polymer at higher extension forces. As exemplary results, we determined the length distributions of the individual chains and the loop number distribution of these bridging chains on the polyelectrolyte-coated surfaces. The former were compared with scaling theories of polymer adsorption.     

界面层中模型高分子链构象的统计理论

高分子自由链在溶液、熔体或固体中的构象有完整的理论和实验工作 ,已是成熟的知识[1～ 4] .近年来 ,受限大分子构象的探索已成为新的热点[5] .界面是一种最简单的限制 ,将对其附近的高分子产生显著的影响 .除理论家的重视以外 ,界面附近高分子构象问题还与许多应用领域相关 .例如 ,液体高分子的表面张力 ,固体高分子的粘附 ,滑移 ,磨蚀等力学特性 ,甚至它们的光学和电学性质都与界面上的组成和分子构象相关[6] .ｄｅＧｅｎｎｅｓ[7] 最早强调界面附近的分子链构象问题的重要性 .他首先从理论上猜测长链的链端若与界面有强吸引作用 ,则它们…     

Lois d'échelles dans les interfaces couvertes de polymères

In this note, we adress the problem of theoretically describing interfaces covered with long polymer chains. The usual observable for this problem is the monomer volume fraction, , as a function of the distance from the surface, z. However, this function is not always relevant. For example, when the interface is made of a strongly attached polymer chain in the absence of any solvent: the -profile is flat and does not give us any insight into the intimate organization of the layer. We suggest that the function S, defined e.g. as an integral of the loop size distribution, is a powerful tool. In particular, we use this function S and straightforward scaling arguments to recover two important results concerning reversibly and irreversibly adsorbed polymer layers.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Scaling of the viscosity of the Lennard-Jones chain fluid model, argon, and some normal alkanes

In this work, we have tested the efficiency of two scaling approaches aiming at relating shear viscosity to a single thermodynamic quantity in dense fluids, namely the excess entropy and the thermodynamic scaling methods. Using accurate databases, we have applied these approaches first to a model fluid, the flexible Lennard-Jones chain fluid (from the monomer to the hexadecamer), then to real fluids, such as argon and normal alkanes. To enlarge noticeably the range of thermodynamics conditions for which these scaling methods are applicable, we have shown that the use of the residual viscosity instead of the total viscosity is preferable in the scaling procedures. It has been found that both approaches, using the adequate scaling, are suitable for the Lennard-Jones chain fluid model for a wide range of thermodynamic conditions whatever the chain length when scaling law exponents and prefactors are adjusted for each chain length. Furthermore, these results were found to be well respected by the corresponding real fluids.