高度支化共聚物的均方回转半径和支化度的关系

对于聚合物的均方回转半径和支化度的关系, 过去鲜有定量研究, 这是由于具有不同支化度的系列同种聚合物样品较难合成之故. 1982年, Kricheldorf等[1]报道了AB2和AB型单体的共缩聚反应, 这种反应可以方便地通过调节AB2和AB型单体的比例来控制产物的支化度.     

Mean-square radius of gyration of polymer chains

The calculations of the mean-square radius of gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square radius of gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square radius of gyration on the molecular weight can be expressed by the general formula 〈S²〉 = aM^b, which was supported by a number of experimental measurements. A comparison of our expression for the mean-square radius of gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.     

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.     

Improved expression of the mean-square radius of gyration, 3. 1,4-polydienes

The mean-square radii of gyration of cis- and trans-1,4-polybutadiene and corresponding 1,4-polyisoprene were derived using Abe's and Flory's rotational isomeric scheme. Calculations performed using available experimental data showed that the dependence of the mean-square radius of gyration on the molecular weight for these stereoregular polydienes can be expressed as where a and b are constants characteristic of the polymer. This behaviour is analogous to that of vinyl polymers and poly-1,1-disubstituted ethylenes discussed in the preceding papers of the present series. The mean-square radius of gyration of 1,4-polyisoprene with predominantly trans units is more sensitive to stereoirregularity than with predominantly cis units. However, 1,4-polybutadiene chains are comparatively insensitive to the stereochemical composition.     

Poly(styrene-b-isoprene) micelles. Effect of molecular weight on micelle size

Micelles composed of poly(styrene-b-isoprene) formed in heptane were studied using small-angle X-ray scattering (SAXS). Block copolymers of various molecular weights were synthesized via anionic polymerization employing the sequential monomer addition technique. The radii of gyration of these block copolymers were measured from SAXS data using the method of Guinier; it was found that the radius of gyration varies as the 0.5 power of the molecular weight. The form of the SAXS curve was calculated and reasons for using only the lowest angle region for determination of radii of gyration are discussed.     

Improved expression of the mean-square radius of gyration, 2. Poly(1,1-disubstituted ethylene)s

The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s is calculated according to a method already developed for poly(methyl methacrylate), poly(α-methylstyrene) and polyitaconate. During the derivation both the effect of side groups and the masses of skeletal atoms were taken into account. A hypothetical polymer chain was introduced, in which the mass of the substituents on every C^α was considered to be concentrated in their center of mass, and the virtual side bond vector runs from C^α to this center. The mean-square radius of gyration of poly(1,1-disubstituted ethylene)s consists of two parts, one of which is the mean-square radius of gyration of the hypothetical molecule described before and the other is related to the geometrical characteristics of the side groups. Numerical calculations indicated that the dependence of the mean-square radius of gyration of poly(1,1-disubstituted ethylene)s on the molecular weight is analogous to that of vinyl polymers, 〈S²〉 = aM^b, where a and b are constants characteristic of the polymer.     

Configurational-conformational statistics of stereoirregular polystyrene

The dependence of the configurational-conformational characteristics, such as the mean-square end-to-end distance, the mean-square radius of gyration, and the temperature coefficient of the stereoirregular polystyrene chains on the fraction of meso dyads, P_m was investigated, using the periodic condition method. The calculation shows that polystyrene has the most compact chain when P_m = 0.7, and the temperature coefficient of the characteristic ratio of the mean-square end-to-end distance reaches the minimum, −0.89 × 10⁻³ K⁻¹, at P_m = 0.5. The theoretical result of the mean-square radius of gyration for atactic polystyrene, 〈S²〉^1/2 = 0.2245 M^0.5106 shows good agreement with the experimental measurement in both bulk amorphous state and θ-solvent.     

Solution properties and chain conformation characteristics of cellulose tricarbanilate

Fractions of two cellulose tricarbanilate samples were characterized by light-scattering (weight-average molecular weight, second virial coefficient, mean-square radius of gyration), gel permeation chromatography (polydispersity index), and viscometry (intrinsic viscosity) in tetrahydrofuran and acetone. The intrinsic viscosity data were analyzed in terms of the theory developed for the continuous wormlike cylinder model, and the chain parameters (Kuhn statistical segment length λ^?1, chain diameter d, and shift factor M_L) were evaluated. The molecular-weight dependence of the mean-square radius of gyration in tetrahydrofuran was calculated for the Kratky—Porod chain model and compared with the experimental results. Data on the intrinsic viscosity and radii of gyration for other solvents at temperatures from 0 to 100°C were analyzed in the same way, and the effects of solvent and temperature on the statistical segment length were evaluated. Polymer—solvent interaction parameters were estimated from the second virial coefficients.     

Hybrid polyion complex micelles formed from double hydrophilic block copolymers and multivalent metal ions: size control and nanostructure

Hybrid polyion complex (HPIC) micelles are nanoaggregates obtained by complexation of multivalent metal ions by double hydrophilic block copolymers (DHBC). Solutions of DHBC such as the poly(acrylic acid)-block-poly(acrylamide) (PAA-b-PAM) or poly(acrylic acid)-block-poly(2-hydroxyethylacrylate) (PAA-b-PHEA), constituted of an ionizable complexing block and a neutral stabilizing block, were mixed with solutions of metal ions, which are either monoatomic ions or metal polycations, such as Al(3+), La(3+), or Al(13)(7+). The physicochemical properties of the HPIC micelles were investigated by small angle neutron scattering (SANS) and dynamic light scattering (DLS) as a function of the polymer block lengths and the nature of the cation. Mixtures of metal cations and asymmetric block copolymers with a complexing block smaller than the stabilizing block lead to the formation of stable colloidal HPIC micelles. The hydrodynamic radius of the HPIC micelles varies with the polymer molecular weight as M(0.6). In addition, the variation of R(h) of the HPIC micelle is stronger when the complexing block length is increased than when the neutral block length is increased. R(h) is highly sensitive to the polymer asymmetry degree (block weight ratio), and this is even more true when the polymer asymmetry degree goes down to values close to 3. SANS experiments reveal that HPIC micelles exhibit a well-defined core-corona nanostructure; the core is formed by the insoluble dense poly(acrylate)/metal cation complex, and the diffuse corona is constituted of swollen neutral polymer chains. The scattering curves were modeled by an analytical function of the form factor; the fitting parameters of the Pedersen's model provide information on the core size, the corona thickness, and the aggregation number of the micelles. For a given metal ion, the micelle core radius increases as the PAA block length. The radius of gyration of the micelle is very close to the value of the core radius, while it varies very weakly with the neutral block length. Nevertheless, the radius of gyration of the micelle is highly dependent on the asymmetry degree of the polymer: if the neutral block length increases in a large extent, the micelle radius of gyration decreases due to a decrease of the micelle aggregation number. The variation of the R(g)/R(h) ratio as a function of the polymer block lengths confirms the nanostructure associating a dense spherical core and a diffuse corona. Finally, the high stability of HPIC micelles with increasing concentration is the result of the nature of the coordination complex bonds in the micelle core.     

Mean-square radius of gyration of polysiloxanes

The mean-square radius of gyration for polysiloxanes has been derived according to the exact definition. Taking account of the examples of symmetrically substituted poly(dimethylsiloxane) and unsymmetrically substituted poly(methylphenylsiloxane), we find that the dependence of 〈S²〉 on the molecular weight follows the general formula 〈S²〉 = aM^b with b = 1 ± 0.016, which is analogous to the theoretical outcomes for vinyl or vinylidene polymers even though the skeletal bone of polysiloxanes consists of alternating heteroatoms. A numerical comparison of the rigorous expression of the mean-square radius of gyration given in this paper with that reported by Flory shows that the difference is obvious for low-molecular-weight polymer and it gradually declines with increasing degree of polymerization.     

Geometrical characteristics of polyelectrolyte nanogel particles and their polyelectrolyte complexes studied by dynamic and static light scattering

The geometric characteristics of nanogel particles in aqueous solutions were studied by determining their ratios of radius of gyration (mean-square radius; Rg) to hydrodynamic radius (Rh), Rg/Rh, derived from static light scattering and dynamic light scattering experiments, respectively. The various nanogel samples studied included ones composed of lightly cross-linked N-isopropylacrylamide (NIPA) polymer, NIPA-based anionic or cationic copolymers, and amphoteric terpolymers. Polyelectrolyte complexes between anionic or cationic nanogels and oppositely charged polyions or nanogels having opposite charges were also studied. Most NIPA and NIPA-based polyelectrolyte nanogels in a swollen state had Rg/Rh values >0.775, which is the theoretically predicted value for a solid sphere. In a collapsed state, one may expect nanogel particles to be spherical in shape; however, this was not the case for a variety of nanogel samples, either with or without charges. These data were consistent with the idea that the surfaces of these nanogel particles were decorated with attached dangling chains. The Rg/Rh data from polyelectrolyte-nanogel complexes, however, indicated different structures from this. It was found that most of the polyelectrolyte-nanogel complex particles had Rg/Rh approximately 0.775. This suggested that the complexed nanogel particles were spherical in shape and that there were no dangling surface chains.     

不同压力条件下氢化丁腈橡胶的应力弛豫及分子动力学模拟研究

采用分子动力学模拟方法构建了氢化丁腈橡胶的分子链结构并计算出不同压缩比下的均方回转半径,同时对应力弛豫进行了理论预测并与压缩应力弛豫实验结果进行了对比.研究发现,均方回转半径随着压力的增大而逐渐降低,随着温度的增大而逐渐增大;在不同压力下,应力均随着时间的增大而逐渐降低而且当时间达到一定程度后应力降低逐渐平缓;计算结果表明压力增大或低温下均方回转半径小、弛豫时间长,体系越表现出弹性特征,此结果表明可用均方回转半径的变化来定量描述橡胶材料体系的应力弛豫变化,分子模拟得到的应力弛豫规律与实验结果有较好吻合.     

聚二甲基硅氧烷链的均方迥转半径

采用旋转异构态模型，用ＭｏｎｔｅＣａｒｌｏ方法计算了聚二甲基硅氧烷（Ｐｏｌｙｄｉｍｅｔｈｙｌｓｉｌｏｘａｎｅ）链考虑侧基（ＣＨ３）的均方通转半径。其结果为＜Ｓ２＞／Ｍ＝７．８５×１０－２：（ｇ·ｍｏｌ）与实验结果（７．７×０．３）×１０－２（ｇ·ｍｏｌ）符合得很好。这种方法可进一步研究高分子链的构象性质。     

Self-association dynamics and morphology of short polymeric PBA-b/co-PAA surfactants

The self-association characteristics of very short and well-defined poly(butyl acrylate)-b-poly(acrylic acid) (PBA-b-PAA) block copolymers in water have been studied. The diblocks are asymmetric with the PBA block longer than the PAA block, giving rise to hollow sphere morphology. This is affirmed by experimental data and theoretical evaluations of the hydrophilic and hydrophobic domain sizes, as well as a value close to 1 for the ratio of the hydrodynamic to the gyration radius of the micelles. Besides, the untypically short PBA blocks (polymerization number around 15) render the micelles dynamic. Indications in support include among others the following: the CMC (critical micellar concentration) values depend, together with the aggregation numbers and the micellar sizes, on the block lengths, as predicted by theory; above the CMC their sizes are concentration-independent, while the micelles disappear below CMC. A comparison was also made with a random PBA-co-PAA copolymer of similar length, which self-associates at an apparent CMC 1 order of magnitude larger than those of the block copolymers, but the size of the formed micelles depends on the concentration.     

DIMENSIONS OF ATACTIC POLY（α-METHYLSTYRENE） CHAINS WITH SIDE GROUPS

An improved configurational-confomational statistical method is developed and the mean-square radius of gyration for atactic poly(α-methylstyrene)(PαMS)chains is studied,in which the effect of large side groups is considered. The deduced formulas,based on the rotational isomer state theory,are used to investigate the configuration-dependent properties of the atactic polymer chain,and the statistical correlation of the unperturbed polymer chain dimension and structure parameters are calculated.For the fraction of meso dyads w_m=0.4,the dependence of the radius of gyration R_g and the intrinsic viscosity[η]on the molecule mass M are R_g=2.63×10~(-2) M~(0.50) nm and[η]=7.36×10~(-2) M~(0.497),respectively, which are in agreement with the previous experimental data for the PαMS samples.A small hump is detected in the curve of the characteristic ratio of the unperturbed mean-square radius of gyration versus the chain length for short PαMS chains.The R_g increases linearly with the temperature T,and the effects of the chain length and the tacticity on the temperature coefficient are remarkable.These are quite different from the results for PαMS chains not considering side groups or for the monosubstituted polystyrene chain.     

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.     

Micellization of styrene/butadiene/styrene block copolymers in mixed solvents

Dilute solutions of three block copolymers, styrene/butadiene/styrene in the mixed selective solvents dioxane/different alcohols is studied at different temperatures. The molecular weight, second virial coefficient and radius of gyration in all selective solvents are also determined. From these measurements it is concluded that a maximum in the dissymmetry of the system for all the selective solvents used is observed. This maximum is observed at higher temperatures for concentrated solutions. Similarly, this maximum is also shifted to lower temperature by using strong precipitants in selective solvents. The milky opalescence is observed for all the selective solvents either by lowering the temperature of the system or by increasing the ratio of the precipitant in the selective solvent.     

关于聚乙烯分子链均方回转半径的进一步讨论

本文考虑到氢原子的影响, 用矩阵代数的方法重新推导了聚乙烯分子链的均方回转半径。在我们得到的公式中若忽略氢原子的质量时, 就简化到Flory的公式。具体数值计算得到聚乙烯分子链均方回转半径对分子量的依赖关系是:〈S^2〉^1^/^2=0.44M^1^/^2比较θ-溶剂的实验数据: ⅹ〈S^2〉^1^/^2~w=0.45±0.08M^1^/^2~w是符合得很好的。     

线性聚合物链的m级相互作用近似

导出了线性聚合物链ｍ级相互作用近似统计权重矩阵的递推公式,它满足构象统计的矩阵代数法所要求的连接条件。按作为四元组转动的Ｃ－Ｃ键旋转角的函数计算了正庚烷的构象能。研究了聚乙烯（ＰＥ）链由相隔六键的原子间所施加的四级相互作用对均方末端距和均方回转半径的特征比的影响,结果表明考虑四级相互作用,ＰＥ键的特征比要比三级相互作用近似的小。