二维高分子链形态的计算机模拟

介绍在“高分子物理实验”教学中新开设的又一个计算机模拟实验，即应用自编的改进型四位置模型，模拟二维空间中的自回避行走链和无规行走链，并验算均方末端距和均方回转半径与聚合度的标度关系，所得结果与de Gennes的理论符合良好。     

具有极性大侧基乙烯基聚合物的分子尺寸和均方二极矩

基于旋转异构态模型和生成矩阵代数方法,重新推导了大侧基聚合物均方回转半径和均方二极矩等基础量公式,应用于对聚乙烯咔唑（PVK）、聚对氯苯乙烯（PPCS）、聚乙烯砒啶（P2VP）和聚乙烯砒咯烷酮（PVP）链构象-构型依赖性质的研究.计算得到其无规链的均方二极矩特征比分别为0.55、0.57、0.48和0.37,均方回转半径特征比分别为2.07、1.74、1.11和1.52,全同链温度系数在？6.1×10？3～2.1×10？3K？1之间,范围比间同和无规链大.比较各特征比变化曲线规律,发现PPCS、PVP和P2VP的基础量分别受聚合物聚合度、规整程度和构象能的影响相对比较明显,而大侧基使PVK的均方二极矩和均方回转半径特征差异显著;对照改进的计算结果表明,在计算均方二极矩和回转半径时考虑极性侧基的方向和尺寸是十分重要的,在聚合物极性和柔性分析中不能忽略极性大侧基的影响.     

聚乙烯型尾形链构象统计的Monte Carlo研究

以聚乙烯型尾形链为例 ,根据链的实际键长、键角和Θ条件下每一链段处于不同旋转异构态的条件概率 ,用MonteCarlo模拟方法生成样本链分子 ,计算了尾形链的均方末端矩及其分量、构象数 ,并与完全计算法及理论推导值作了比较 ,讨论了尾形链构象数和沿边界方向及法线方向均方末端矩分量随链段数n及键角Φ的变化 .     

含引发机制的Ａf—Ａg型缩聚反应Z—均回转半径研究

讨论了含引发机制的Ａf-Ａg型缩聚反应体系Z－均回转半径,利用枝状高分子成键的统计分析,给出组合因子分解公式,并得到均方回转半径的表达式;进一步结合数量分布函数,定义k次高分子半径,并给出计算k次高分子回转半径的循环公式,最后得到凝胶点前Z－均回转半径的解析表达式。     

聚丙烯酸烷基酯侧基差异对链构象性质的影响

针对聚丙烯酸烷基酯侧基形状、极性的不同,基于高分子链的构象-构型统计理论和生成矩阵方法,推出均方电偶极矩和均方回转半径的改进公式,应用于聚丙烯酸甲酯(PMA)链和聚甲基丙烯酸乙酯(PEMA)链等的链构象依赖性质的研究.得到无规PMA4(4态PMA)和PEMA的偶极矩特征比分别为0.63和0.66,温度系数为-0.66×10-3 K-1和1.72×10-3 K-1,无规PMA和PEMA的均方回转半径的特征比分别为1.73和1.43,温度系数为-1.05×10-3 K-1和-1.28×10-3 K-1,均与实验结果符合.而且考虑链规整程度的不同和酯类基团方向等的改变,PMA和PEMA的特征比也呈现较大的差异,尤其对间同构型链PMA4短链,偶极矩及其温度系数均伴有极大值的出现,这些结果表明聚丙烯酸烷基酯侧基对其链构象性质的影响不能忽略.     

聚苯乙烯链规整度与特性粘数的理论研究

应用构象 构型统计理论和旋转异构态模型 ,考虑大侧基对高分子链构型的影响 ,建立高分子溶液特性粘数与链无规程度的关系 ,并应用于大分子量的聚苯乙烯溶液的特性粘数的计算 ,得到特性粘数与全同、间同和无规链分子量的关系 ,并与实验结果进行比较 ,结果较为满意     

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 .     

圆环上的无规行走

研究了半径为R的圆环上的无规行走问题,给出了n步末端向量的几率分布ω(θ,n)和均方末端距2>的数学表达式,发现当R²》nl²时,2≈nl²即还原为一维直线上无规行走的结果;而当r²《nl²时,2>≈π²r²/3.还计算了平均末端距<|r|>及k阶矩k>和半径R的关系,同时作了简单的物理讨论。     

端基附壁模型聚合物环形链的构象统计理论

环形链定义为两个端基均附壁的线形聚合物链所得的环 .采用精确计数和蒙特卡罗模拟方法 ,研究了自回避行走 (SAW)模型表示的环形链的构象 ,求得构象数和均方回转半径随链长的变化 .对于二维和三维SAW环形链 ,精确计数的最大链长分别为N =2 9和 1 9.用标度理论处理了数值结果 ,所得的标度指数和其他参数与理论预示值进行了比较 .模拟结果表明 ,SAW环形链限制壁平行方向的尺寸大于垂直方向的尺寸 ,与SAW尾形链尺寸的变化正好相反 .     

聚己内酯-聚丙交酯-聚醚三元共聚高分子微粒及其降解的研究

用乳化－ 溶剂蒸发法制备了聚己内酯－ 聚丙交酯－ 聚醚三元无规共聚物微粒,且与用相同方法制备的聚己内酯（ＰＣＬ） 和聚己内酯－ 聚醚嵌段共聚物微粒的形态进行了比较,讨论了材料的亲水性,以及三元无规共聚物中亲水性聚醚链段的长度及含量对所形成微粒形态的影响。研究结果表明,随着聚合物由疏水性向亲水性转变,所生成微粒的形态则从光滑、多孔、到不规则变化。证明了三元无规共聚物多孔微粒的形成是由于亲水的聚醚链段向水相取向所致。在３７ ℃、ｐＨ７ ．４ 的缓冲液中进行了三元无规共聚物微粒的降解,结果表明,随着降解时间的延长, 三元无规共聚物的分子量逐渐下降,且其中的聚醚链段含量有明显的降低。     

Enhanced spin capturing polymerization: Numerical investigation of mechanism

Simulation on the kinetic scheme of enhanced spin capturing polymerizations (ESCP) were performed to reveal the influence of different parameters, e.g., initiation rate, spin capturing and side reactions on the properties (the monomer conversion, degree of polymerization, polydispersity index, and the fraction of “living” chains) of polymer obtained. The kinetic scheme of ESCP was solved numerically as well as the method of statistical moments of molecular weight distribution was applied to get some numerical expressions for analysis. The simulations showed that fast initiation rate can lead to decrease of living fraction and broadening of molecular weight distribution. Whereas high rate of spin capturing makes the polymer chains shorter but increases living character. And side reactions always decrease livingness of the polymer obtained. Finally in the case of absence of side reaction we were able to formulate criteria for formation of polymer with target molecular weight and quota of living chains via ESCP process. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2546–2556     

Moments and distribution function of polyelectrolyte chains

It is demonstrated that the moments R(2k) of the end-to-end distance distribution function f(r) of charged wormlike chains with excluded volume effects in solution with added salt, in the Debye-Huckel approximation, obey a remarkably simple relation. It is shown that the R(2k) can be expressed as weighted sums of the corresponding moments of ideal wormlike chains. As an application of this method, we show that the Fourier transform of f(r) can also be represented by a superposition of distribution functions of ideal chains. The quantities so calculated are compared with the results of Monte Carlo simulations. Excellent agreement between them is observed.     

Dynamics of adsorbed polymer chains subjected to flow: The dumbbell model

The dumbbell model of an adsorbed polymer segment is analyzed in order to investigate the response of such segments to a velocity gradient imposed at the solid/liquid interface. It is demonstrated that exact expressions for the time-dependent moments of the distribution function describing the conformation can be obtained. Both a dangling end and an attached loop can be represented and several bulk properties of a polymer film subjected to flow are evaluated.     

The derivation of the characteristic function and the spectral density distribution of a Hamiltonian of N‐coupled morse oscillators: The large N‐limit

This paper reports a derivation of the characteristic function and the frequency function of spectral density distribution of a Hamiltonian representing a system of N‐coupled Morse oscillators. The procedure utilized previously evaluated large‐N expressions for spectral density distribution moments. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Dynamics of macromolecular chains. II. Orientation relaxation generated by elementary three-bond motions and notion of an independent kinetic segment

In the preceding paper, general equations were established for the motions of chains confined to a tetrahedral lattice. In the present paper, bond orientation correlation and autocorrelation functions are explicitly calculated for the case where only three-bond elementary motions are considered. Effects due to the chain end are analyzed and the relaxation time distribution function is established. The expressions obtained reflect the influence of the chain structure. Finally, to characterize the dynamic behavior of chains in orientation relaxation experiments, the notion of an independent kinetic segment is proposed.     

Functions of moments in the elution dynamics of adsorption

An exact solution obtained for the direct problem concerning the elution dynamics of adsorption in terms of the model of an equilibrium adsorption layer using the gamma function is analyzed. Analytical expressions derived for the functions of moments comprise adsorbent layer lengths, mobile phase velocities, and adsorption constants. The functions are found to be interrelated via the slope coefficients of linear equations. The correctness of the results obtained is confirmed by good agreement between the theory and experimental data presented as tabulated values of the moments measured previously for the elution dynamics of Freon 13B1 adsorption on active carbon layers of different lengths.     

THE SPATIAL DISTRIBUTION AND MOMENTS OF CIRCULAR FREELY JOINTED CHAIN

The spatial distribution function and second moments of circular freely jointed chain are derived based on an analytical method. The circular Gauss chain, which is simple for long chains, is compared with the circular freely jointed chain, which is exact for short chains. It is shown that the Gauss chain model predicts a more compact configurational distribution than the exact freely jointed chain. The two chain models, however, become closer to each other when the chain length increases. It is found that the difference of the mean square radius of gyration calculated with these two chain models is a constant, independent of the chain length.     

The behavior of the form factor in two dimensions for linear polymers in different regimes

Off-lattice Monte Carlo simulations employing the PIVOT algorithm are used to generate ideal and excluded volume linear polymers in two dimensions. The form factor at small and large wave vectors is calculated from the resulting configurations and compared to the exact equation for ideal chains and to both scaling and renormalization group predictions for excluded volume chains. It is found that using the des Cloizeaux form for the distance distribution function in an analytic calculation of the form factor leads to close agreement with the Monte Carlo data and that simple expressions for both the small and large wave vector expansions reproduce the essential features of the form factor.     

Mass dissolution of polydisperse set of particles in a flow system

A mathematical model of continuous dissolution of salts based on a dynamic equation for crystal size distribution function was considered. A stationary solution was obtained by the moments method. For a nonstationary state, an evolution equation for the undersaturation of solution was derived. An approximate analytical method of solving this equation, which is in good agreement with the numerical solution, was proposed. The notion of the coefficient of continuous dissolution efficiency was introduced and analytical expressions for this value were obtained. The stability of the stationary solution was analyzed.Translated from Kolloidnyi Zhurnal, Vol. 66, No. 6, 2004, pp. 793–801.Original Russian Text Copyright © 2004 by Moshinskii.     

Molecular weight distribution in random branching of polymer chains

Analytical expressions for the average molecular weights of randomly branched polymer molecules with any primary chain distribution are developed. A full molecular weight distribution (MWD) function is also derived for the case where primary chains conform to the most probable distribution. This MWD function can be separated into the fractional MWDs containing k branch points; therefore, very detailed information on the structure of randomly branched polymers can be obtained. The average molecular weights of the polymer fraction containing k branch points are linear functions of the number of branch points k, and the distribution becomes narrower as k increases. The heterogeneity in the distribution of branch points can make the weight-average degree of polymerization larger, although it is impossible to form a gel molecule only via branches (T-shaped junctions) without assistance of crosslinkages (H-shaped junctions).