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．     

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.     

RUTHENIUM COORDINATION COMPOUNDS WITH POLYPYRIDINES V．DNA－BINDING STUDIES OF Ru（Ⅱ）COORDINATION COMPOUNDS WITH（2－PHENYL－）IMIDAZO［f］1，10－PHENANTHROLINE

ＲＵＴＨＥＮＩＵＭＣＯＯＲＤＩＮＡＴＩＯＮＣＯＭＰＯＵＮＤＳＷＩＴＨＰＯＬＹＰＹＲＩＤＩＮＥＳＶ．ＤＮＡ－ＢＩＮＤＩＮＧＳＴＵＤＩＥＳＯＦＲｕ（Ⅱ）ＣＯＯＲＤＩＮＡＴＩＯＮＣＯＭＰＯＵＮＤＳＷＩＴＨ（２－ＰＨＥＮＹＬ－）ＩＭＩＤＡＺＯ［ｆ］１，１０－...     

PARAMAGNETIC AND DIAMAGNETIC DICOPPER（Ⅱ） COMPLEXES WITH DI－SCHIFF BASE DERIVED FROM 2－HYDROXY－1－NAPHTHALDEHYDE AND1，3－DIANINO－2－PROPANOL

ＰＡＲＡＭＡＧＮＥＴＩＣＡＮＤＤＩＡＭＡＧＮＥＴＩＣＤＩＣＯＰＰＥＲ（Ⅱ）ＣＯＭＰＬＥＸＥＳＷＩＴＨＤＩ－ＳＣＨＩＦＦＢＡＳＥＤＥＲＩＶＥＤＦＲＯＭ２－ＨＹＤＲＯＸＹ－１－ＮＡＰＨＴＨＡＬＤＥＨＹＤＥＡＮＤ１，３－ＤＩＡＮＩＮＯ－２－ＰＲＯＰＡＮＯＬ...     

RUTHENIUM COORDINATION COMPOUBNDS WITH POLYPYRIDINES Ⅳ SYNTHESIS AND CHARACTERIZATION OF （2－PHENYL）IMIDAZO［f］ 1， 10－PHENANTHROLINE AND THEIR Ru（Ⅱ） COORDINATION COMPOUNDS

ＲＵＴＨＥＮＩＵＭＣＯＯＲＤＩＮＡＴＩＯＮＣＯＭＰＯＵＢＮＤＳＷＩＴＨＰＯＬＹＰＹＲＩＤＩＮＥＳⅣＳＹＮＴＨＥＳＩＳＡＮＤＣＨＡＲＡＣＴＥＲＩＺＡＴＩＯＮＯＦ（２－ＰＨＥＮＹＬ）ＩＭＩＤＡＺＯ［ｆ］１，１０－ＰＨＥＮＡＮＴＨＲＯＬＩＮＥＡＮＤＴＨＥＩ...     

SYNTHESIS OF NEW AMMONIUM-METAL (DNID)_2 COMPLEXES WITH LONG ALKYL CHAIN

ＳＹＮＴＨＥＳＩＳ　ＯＦ　ＮＥＷ　ＡＭＭＯＮＩＵＭ－ＭＥＴＡＬ（ＤＮＩＤ）＿２　ＣＯＭＰＬＥＸＥＳ　ＷＩＴＨ　ＬＯＮＧ　ＡＬＫＹＬ　ＣＨＡＩＮＪｉｎＸｉｎｇＰＡＮ；ＹｕｎＱｉＬＩＵａｎｄＤａｏＢｅｎＺＨＵ（ＩｎｓｔｉｔｕｔｅｏｆＣｈｅｍｉｓｔｒｙ．Ａ...     

聚环氧氯丙烷聚氨酯／聚（甲基丙烯酸甲酯－苯乙烯）IPN的研究

改变聚（甲基丙烯酸甲酯－苯乙烯）（Ｐ（ＭＭＡ－ｃｏ－Ｓｔ）中甲基丙烯酸甲酯的含量（Ｗ_（ＭＭＡ）），通过一步法合成出聚环氧氯丙烷聚氨酯（ＰＵ（ＰＥＣＨ）／Ｐ（ＭＭＡ－ｃｏ－Ｓｔ）ＩＰＮ．ＤＳＣ、ＴＥＭ和动态粘弹谱研究结果表明：当Ｐ（ＭＭＡ－ｃｏ－Ｓｔ）中Ｗ_（ＭＭＡ）大于０．６时，ＩＰＮ仅有一个Ｔｇ；当Ｗ_（ＭＭＡ）小于０．４时，ＩＰＮ有２个Ｔ_ｇ，ＴＥＭ上出现相区，Ｐ（ＭＭＡ－ｃｏ－Ｓｔ）溶度参数（δ）及δ的氢键作用分量（δｈ）与相态、力学性能有密切关系。     

SYNTHESIS AND ~（183）W NMR CHARACTERIZATION OF P_4W_（30）Al_4（H_2O）_2O_（112）~（20－） HETEROPOLYANION

ＳＹＮＴＨＥＳＩＳ　ＡＮＤ　~（１８３）Ｗ　ＮＭＲ　ＣＨＡＲＡＣＴＥＲＩＺＡＴＩＯＮ　ＯＦ　Ｐ_４Ｗ_（３０）Ａｌ_４（Ｈ_２Ｏ）_２Ｏ_（１１２）~（２０－）　ＨＥＴＥＲＯＰＯＬＹＡＮＩＯＮＳＹＮＴＨＥＳＩＳＡＮＤ~（１８３）ＷＮＭＲＣＨＡＲＡＣＴＥＲＩＺ?..     

STUDIES OF FAR－INFRARED SPECTRA AND SOLID－SOLID PHASE TRANSITION IN ［n－C_nH_（2n＋1）NH_3］_2 CuX_4 LAYER COMPOUNDS WITH n＝7－12，16

ＳＴＵＤＩＥＳＯＦＦＡＲ－ＩＮＦＲＡＲＥＤＳＰＥＣＴＲＡＡＮＤＳＯＬＩＤ－ＳＯＬＩＤＰＨＡＳＥＴＲＡＮＳＩＴＩＯＮＩＮ［ｎ－Ｃ_ｎＨ_（２ｎ＋１）ＮＨ_３］_２ＣｕＸ_４ＬＡＹＥＲＣＯＭＰＯＵＮＤＳＷＩＴＨｎ＝７－１２，１６￥ＮｉｎｇＧＵＯ（Ｄｅｐａｒｔ?..     

STUDIES ON THE SYNTHESIS AND REACTIONS OF N－（1－OXO－4－CARBONYL－2，6，7－TRIOXA－1－PHOSPHABICYCLO ［2．2．2］ OCTANE）－N＇－ARYL THIOUREAS

ＳＴＵＤＩＥＳＯＮＴＨＥＳＹＮＴＨＥＳＩＳＡＮＤＲＥＡＣＴＩＯＮＳＯＦＮ－（１－ＯＸＯ－４－ＣＡＲＢＯＮＹＬ－２，６，７－ＴＲＩＯＸＡ－１－ＰＨＯＳＰＨＡＢＩＣＹＣＬＯ［２．２．２］ＯＣＴＡＮＥ）－Ｎ’－ＡＲＹＬＴＨＩＯＵＲＥＡＳＹｕＧｕｉＬＩ；Ｘｕ...     

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     

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 .     

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     

简立方格点自避行走所模拟的高分子链吸附和塌缩

采用复合Markov链法 ,针对简立方格点上的自避行走模型 ,研究了同时具有对壁的吸附作用ε1 和最近邻相互作用ε2 的高分子链的热力学性质 .相互作用能量参数ε1 和ε2 分别联系于参数α和 β .令链长N=10 0 ,由这种MonteCarlo方法可得出链的自由能FN(α ,β) ,热容2 FN(α ,β) /2 α和2 FN(α ,β) /2 β ,吸附点平均数〈m〉/N ,最近邻相互作用对平均数〈n〉/N和均方末端距对壁的垂直分量RZ2 .除已有方法由热容数据可绘出α β相图外 ,建议由结构参数〈m〉/N ,〈n〉/N和RZ2 绘制相图 ,并发现二者基本一致 .所得相图表明 ,存在 4个相区 ,分别是解吸 膨胀相 (DE) ,吸附 膨胀相 (AE) ,解吸 紧密相 (DC)和吸附 紧密相 (AC) .在伸展区和塌缩区 ,随着吸附作用的增强 ,会出现吸附相转变 .在解吸区和吸附区 ,随着自相互作用的增大 ,也将出现塌缩相转变 .相图出现了两个三相点 ,即AE AC DC三相点和AE DE DC三相点     

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 .     

Conformational statistics of polymer chain terminally attached to wall (III) —NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface, the polymer chain forms the “loop” conformation. Investigation has been made on the conformational statistics of a model loop chain by the normal random walk (NRW) on a lattice confined in the half-infinite space. Based on the conformational distribution function of the NRW model tail chain, it is easy to deduce an analytical formula expressing the conformational number of the model loop chain. It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power functionN ^-2/3 when the chain lengthN→οο. The same result -was obtained by means of the recursion equation. The ratio of the mean square end-to-end distanceh ² for the model loop chain to its mean square bond lengthl ² is 2N/3. Compared with the free chain with the same lengthN, the mean square end-to-end distance of the model loop chain contracts to a certain extent. The basic relationships deduced were supported by the exact enumeration and Monte Carlo simulations. Project supported by the National Natural Science Foundation of China.     

Conformational properties and dynamics of molecular bottle‐brushes: A cellular‐automaton‐based simulation

Extensive computer simulation was performed using the bond‐fluctuation model and cellular‐automaton (CA)‐based simulation technique to probe the equilibrium structure and dynamical behavior of comb‐branched polymers in which the flexible side chains of a given length are placed regularly along the backbone and the number of branches increases linearly with total molecular weight. By applying very efficient CA algorithm – the “lattice molecular dynamics” (LMD) method – we have been able to study the properties of sufficiently large structures (up to 5880 monomeric units). Depending on the length of main and side chains as well as on interbranch spacing, we have calculated mean chain dimensions, local fractal dimensionalities, particle scattering functions, time autocorrelation functions, etc. The following main conclusions may be drawn from the results presented in our study: (i) The critical exponent, governing the mean size of the main chain, remains unchanged from its value known for a 3d self‐avoiding walk (SAW). On the other hand, two‐dimensional branched macromolecules with one‐sided branches are effectively in a collapsed state even under conditions of a good solvent, forming specific helical superstructures. (ii) Comparison of the simulated data with the predictions of the scaling model indicates that the latter is valid in describing the mean dimensions of the backbone as a function of side‐chain length and interbranch spacing. (iii) The excluded volume interaction between side chains dramatically slows down the relaxation of the backbone chain.     

Growing self avoiding walk trees

The Growing self avoiding walk model (GSAW) was proposed to explain statistical mechanics of the growth process in polymerization. Close examination of the model reveals that it is suited only for addition polymerization where only one monomer unit is added to the growing polymer chain. In this paper we propose a model for step growth or condensation polymerisation, where all of the monomer is converted first to dimer, all dimers are converted to tetramer etc. In the calculation of probabilities of the walker taking a step in a specified direction in the GSAW model the probability is the reciprocal of the number of steps available if the walker looks one step ahead. It is seen that our model for condensation polymerization GSAW can be generalized to the walker looking a finite number of steps ahead (instead of one only) for the purpose of calculation of probabilities. This is explained in detail in the first section of the paper. In the second section of the paper we explain the use of the Depth first search (DFS) algorithm in the calculation of probabilities and moments for the generalized growing self avoiding walk model. In the third section of the paper we report the exact values of the mean square end to end distances and relevant survival probabilities for the model. When GSAW was first proposed there was a controversy over whether it belonged to the same universality class as the True self avoiding walk $\left( \upsilon =\frac{2}{d+1}\right) $ or that of the self avoiding walk $\left( \upsilon =\frac{3}{d+2}\right) $ . At that time it was conclusively shown that the GSAW model cannot belong to the same universality class as the true self avoiding walk model. However it was never conclusively shown that $\upsilon =\frac{3}{d+2}$ for GSAW. In this paper we propose two methods of studying this problem. One method is rigorous analysis of the DFS algorithm. We explain how this algorithm can be used to study restricted random walks with finite memory and self avoiding walks. The second method proposed by us is a detailed analysis of the generalised GSAW model proposed by us. This paper is to be viewed as an introductory paper on a new model that should be of interest to both chemists and mathematicians.     

DYNAMIC MONTE CARLO STUDY ON THE CORRELATION BETWEEN SHAPE AND SIZE OF LINEAR POLYMER CHAINS

The correlation between shape and size of linear chains on the simple cubic lattice is investigated using a dynamicMonte Carlo technique. A positive correlation between the asphericity parameter A and the square of the end-to-end distanceR~2, as well as that between A and the square of the radius of gyration S~2, is found for both RW and SAW chains, indicatingthat a chain conformation of small size is usually more spherical than one of large size. The result can explain why the shapeof the SAW chain deviate much more from a sphere than that of the RW chain, and can also explain the similar dependenceof size and shape on chain stiffness and on the distance of the first bead of a chain from an infinitely large flat surface.