聚合物分子量经验分布与理论分布(Ⅰ)——三参数指数分布与Poisson分布

本文通过矩数分析给出了Poisson分布与三参数指数型分布的关系.这是由加聚物买验分布推断反应机理的初步尝试.     

形态分布计算软件的设计及在大学化学教学中的应用

介绍了一种简单的配位平衡体系形态分布计算程序的设计方法,给出了程序中拟牛顿法解方程组的算法,并以铁（Ⅲ）-草酸盐配合物体系作为实际例子,给出了该程序计算所得的铁（Ⅲ）-草酸盐主要配离子形态的分布系数曲线。该软件设计有利于学习“大学化学”课程中复杂的配位平衡计算原理与方法,也为涉及到配合物平衡体系的化学研究提供帮助。     

新型无机离子交换剂焦磷亚硒酸锡的结构研究—径向分布函数法

本文报道了应用径向分布函数(RDF)法研究非晶态无机离子交换剂焦磷亚硒酸锡的结构。由RDF的峰位、谷位等数据计算出该化合物中原子间的距离、平均配位数及短程有序畴等。讨论了焦磷亚硒酸锡的结构参数与离子交换剂选择性间的关系。     

煅烧煤系高岭土粒度分布的分形特征

通过分析煤系高岭土及其煅烧产物的粒度,得出：煤系高岭土的粒度分布具有分形规律,同时发现煤系高岭土的普度变化包括膨胀阶段和收缩阶段,并且与高岭土的结构变化相关,计算不同煅烧温度的煅烧产物的粒度分布分维数,并得出分维数与煅烧的关系曲线,由此关系曲线可较容易地确定出煤系高岭土的煅烧温度。     

针镍矿实验电子密度分布的研究

针镍矿反常的配位数及配位距离使其在矿物学和结构化学方面引起了人们的重视。我们从高分辨的X射线衍射数据得到了它的实验电子密度的分布。从Ni,S原子孤对电子的分布以及它们明显地远离Ni和S的核表明在Ni和S之间是多重的配键,而在Ni和Ni之间是通常的配价键。这个结论与针镍矿中Ni和S的反常配位数、配位多面体的型式、原子间的键距以及它的部分金属特性等是完全符合的。     

无规行走链回转半径几率分布函数的计算

使用无规行走模型,得到了线状分子链回转半径几率分布函数各阶矩的一般表达式。当链段数趋向无穷大时,无规行走链与Gauss链的渐近行为一致。本文还给出了无规行走链回转半径各阶矩的近似计算方法以及2阶矩、4阶矩、6阶矩与链段数关系的严格解析表达式。     

分子动力学模拟全氟辛酸钠在水中的分布

为从微观上探究氟碳型表面活性剂在水中的分布情况,使用全原子分子动力学方法模拟了全氟辛酸钠(Na-PFO)在水中的分布情况。模拟平衡后,PFO^-分布在水/气界面处,且疏水的氟碳链朝向气相,亲水的羧酸根浸在水中,形成层状分布,径向分布函数证明钠离子主要分布在水中的羧酸根附近。羧酸根可与周围的水分子形成氢键,且显负电性的氟原子也可与水分子形成氢键,钠离子与水分子之间具有吸引作用,但不形成氢键;钠离子主要分布于PFO^-的氧原子附近。     

1-辛烯Ziegler-Natta聚合的活性中心多分散性——分子量分布及动力学的研究

本文通过对TiCl_3-Al(C_2H_5)_3聚合1-辛烯产物的双峰型分子量分布曲线用Schulz函数进行拟合、分峰处理,发现这种双峰型分布中的高分子量峰部分由一种活性中心生成,低分子量峰部分则由至少两种活性中心生成.将不同转化率时聚辛烯的分子量分布分峰拟合数据与聚合速率、活性中心数等测定数据相结合,得到了高分子量和低分子量两部分产物相应的活性中心上各自的动力学参数(增长速率常数、活性中心数、链转移常数等)及各自的聚合速率曲线,从而证实了多种活性中心的存在、它们催化特性的差异及与聚合物分子量分布增宽的关系.     

酸度分布-吸收光谱法用于灰色体系中食用色素的定量分析

利用合成色素随ｐＨ变化的人分布分数曲线和吸收光谱构成两维波谱信息,建立了灰色体系中色素的定量分析方法。约束背景双线性分解法（ＣＢＢＬ）结合数值遗传算法（ＮＧＡ）用于两维矩阵的数据处理。推导了型体总数与两维矩阵的有效秩之间的关系。吸光度矩阵的主成分数根据残余矩阵的残差平方和噪声水平相比较 确定,对标准样品及模拟灰色体系样品的研究表明该法确定的主成分数与理论值一致。对胭脂红、日落黄和柠檬黄的模拟灰色休     

从聚丙烯流动曲线估算分子量分布

聚丙烯的控制降解技术由于能够带来很好的经济效益，国内外都在进行研究．其中分子量分布是一个重要数据，它对于聚丙烯的注塑、纺丝、薄膜等加工过程都有重要的影响．分子量分布一般用重均分子量Mw和数均分子量Mn之比D=Mw/Mn来表征，称为分子量分布指数．它可以     

Distribution of functional groups grafted onto an ethylene-propylene copolymer

A theoretical model, based on the binomial (Bernoullian) distribution function, was employed for the prediction of functional group distribution in an ethylene-propylene copolymer randomly grafted by maleic anhydride. Using the experimentally determined graft level and molecular weight distribution function, the fraction of polymer molecules with given number of functional groups was calculated. The result was checked experimentally by a fluorescence method based on the excimer formation of pyrene fluorophores attached to the anhydride pendants. The time-resolved fluorescence from the pyrene-labeled copolymer yielded the fraction of polymer molecules with a single functional group. The fraction of singly labeled molecules was compared to the calculated functional group distribution and a reasonable agreement was found between the two. The distribution of grafted maleic anhydride was found to be apparently random among polymer molecules. The distribution of distances was calculated between randomly attached consecutive functional groups along the polymer backbone also. The result indicated that the distance distribution function (similar to a decaying exponential) is dominated by short distances. © 1996 John Wiley & Sons, Inc.     

Molecular Weight Distribution of Living Radical Polymers

Summary: The molecular weight distribution formed in an ideal living radical polymerization is considered theoretically. It was found that the hypergeometric function that combines the most probable and the Poisson distribution represents a fundamental distribution of the living radical polymers. The number‐ and weight‐average molecular weights are derived for this fundamental distribution, together with those for polymerizations in a batch and in a continuous stirred tank reactor. These average molecular weight functions are obtained based on the arithmetic calculations without deriving the distribution functions. The effect of the monomer transfer reactions on the formed MWD is also considered. The present study clarifies the relationship between the reaction mechanism and the formed molecular weight distribution as well as the fundamental characteristics of living radical polymers.

Calculated number fraction distribution N(r) development with (dashed) and without (solid) the monomer transfer reactions.     

THE DISTRIBUTION FUNCTION OF RESIDUE-RESIDUE CONTACTS IN PROTEIN MOLECULES

In protein molecules each residue has a different ability to form contacts.In this paper,we calculated the number of contacts per residue and investigated the distribution of residue-residue contacts from 495 globular protein molecules using Contacts of Structural Units(CSU)software.It was found that the probability P(n)of amino acid residues having n pairs of contacts in all contacts fits Gaussian distribution very well.The distribution function of residue-residue contacts can be expressed as:P(n)=P_0+aexp[-b(n-n_c)~2].In our calculation,P_0=-0.06,α=11.4,b=-0.04 and n_c=9.0.According to distribution function,we found that those hydrophobic(H)residues including Leu,Val,Ile,Met,Phe,Tyr,Cys,and Trp residues have large values of the most probable number of contact n_c,and hydrophilic(P)residues including Ala,Gly,Thr, His,Glu,Gln,Asp,Asn,Lys,Ser,Arg,and Pro residues have the small ones.We also compare with Fauchere-Pliska hydrophobicity scale(FPH)and the most probable number of contact n_c for 20 amino acid residues,and find that there exists a linear relationship between Fauchere-Pliska hydrophobicity scale(FPH)and the most probable number of contact n_c, and it is expressed as:n_c=a+b×FPH,here α=8.87,and b=1.15.It is important to further explain protein folding and its stability from residue-residue contacts.     

Polymer Distribution Change During Irreversible Depolymerization by Chain‐End Scission

The change in polymer distribution during depolymerization in which monomer molecules are severed one by one from the chain ends, is considered. Assuming irreversible depolymerization and equal reactivity of all the chain ends, a general formula to calculate the MWD is proposed. After the removal of monomers severed from the chains, the MWDs of depolymerized polymers always approach the most probable distribution whose PDI is practically equal to 2. It may appear to be counterintuitive, but the average MWs of polymers may increase during chain scission when the initial distribution is broader than the most probable (PDI > 2). The interpretation of the MWD data of polymers during depolymerization, such as those obtained by GPC, are not straightforward especially for the initial broad MWDs.

     

The Fischer-Tropsch Synthesis: Molecular Weight Distribution of Primary Products and Reaction Mechanism

An evaluation of literature data concerning the production of hydrocarbons and alcohols by the Fischer-Tropsch procedure indicates that the molecular weight distribution of the primary products can be described by the Schulz-Flory equation (“normal” or “most probable” distribution). It follows that the highest attainable selectivity for a given molecular weight range can be calculated. A reaction mechanism is suggested.     

Computing the Trivariate Chain Length/Degree of Branching/Number of Combination Points Distribution for Radical Polymerization with Transfer to Polymer and Recombination Termination

Summary: Polymer molecules made by radical polymerization with transfer to polymer and recombination termination contain branch points (connecting branch arms to backbones) and combination points (connecting various molecular structures). The trivariate chain length/degree of branching/number of combination points distribution (CLD/DBD/CPD) was calculated using a two‐dimensional version of a previously used pseudo‐distribution approach. This yielded the CPD moments for given chain length n and number of branches i. Both DBD and CPD at given chain length resemble a binomial distribution. For the construction of the full DBD and CPD a set of orthogonal polynomials, the Krawtchouk polynomials, in combination with the binomial distribution was employed. A first‐order Krawtchouk approximation enabled to compute the full CLD/DBD/CPD from the three CPD moments as a function of n and i. Results agree well with those from a Monte Carlo (MC) simulation method. However, the large scatter due to the small numbers of molecules collected in the MC method at longer chain lengths prevents comparison in this range.

Solutions of 3D CLD/DBD/CPD: CPD at constant chain length (20 000) and number of branch points (20).     

线型高聚物分子量分布函数的另一种推导方法

针对自由基聚合歧化终止和偶合终止两类机理生成的线型高聚物,应用统计物理的基本原理,对其分子量分布重新进行了理论推导,其方法简洁清晰,无须任何附加假定,导出FlorySchulz分布.结果有助于从另一方面理解FlorySchulz分布的物理学基础.     

Effect of interchange reactions on the molecular weight distribution of poly(ethylene terephthalate): A Monte Carlo simulation

The effect of the interchange reactions of poly(ethylene terephthalate) (PET) on its molecular weight distribution (MWD) was analyzed using a Monte Carlo simulation method. Three kinds of motions, which correspond to the direct ester(SINGLEBOND)ester interchange reaction, alcoholysis, and internal alcoholysis in polyester, were performed in this simulation: bond flip, end attack, and backbite. Two systems with two different types of nonequilibrium distribution (monodisperse and bimodal distribution) were initially prepared. The initial biases from equilibrium MWD are rapidly relaxed to an equilibrium MWD as the reaction progresses. The MWD at equilibrium is well described by the most probable MWD proposed by Flory. From the polydispersity data, it is concluded that about 0.3 interchanges per segment are sufficient to equilibrate the nonequilibrium system. For the validity of the simulation, the variation of MWD of the mixtures of two PETs having different molecular weights were monitored using gel permeation chromatography. The agreement between simulation and experiment is remarkably good. © 1996 John Wiley & Sons, Inc.     

Numerical model for the investigation of countercurrent chromatography

A numerical model is developed to describe the separation process of countercurrent chromatography (CCC) in this work. The theory of countercurrent extraction table (TCCET) is first proposed to calculate concentration distributions of chemical components in the CCC, which is essential for a numerical model to describe the dynamic equilibrium of mass transfer. According to the theory of countercurrent extraction, the concentration in chromatography obeys binomial distribution, while the outflow from the n-th stage is a negative binomial distribution. As a result of the central limit theorem, they will obey normal distribution for sufficiently large n. Row-stage ratio (R(RS)) is then defined to determine the K value or retention time because it has a linear relationship to K value and retention time. The stage for a certain K value can be subsequently obtained with a very simple form, n(k)=1/(2piq(k)X(2)(k, max)), which can be calculated from the peak height obtained from experiments. Finally, the actual stage for a separation chromatogram can be acquired with using this simple expression. The agreement between theoretic and experimental results is quite satisfactory in the normal-phase and reversed-phase elution mode.     

Simultaneous Deconvolution of the Molecular Weight and Chemical Composition Distribution of Polyolefins Made with Ziegler-Natta Catalysts

Heterogeneous Ziegler-Natta catalysts produce polyolefins that have broad distributions of molecular weight (MWD) and chemical composition (CCD). For such broad distributions, mathematical models are useful to quantify the information provided by polyolefin analytical techniques such as high-temperature gel permeation chromatography (GPC), temperature rising elution fractionation (TREF), and crystallization analysis fractionation (CRYSTAF). In this paper, we developed a mathematical model to deconvolute the MWD and CCD of polyolefins simultaneously, using Flory's most probable distribution and the cumulative CCD component of Stockmayer's distribution. We have applied this procedure to “model” polyolefin resins and to one industrial linear low-density polyethylene (LLDPE) resin. The proposed methodology is able to deconvolute theoretical distributions even when random noise is added to the MWDs and CCDs, and it can be used to calculate the minimum number of active site types on heterogeneous Ziegler-Natta catalysts.