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.     

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.     

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.     

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.     

Mean-square Radius of Gyration of Poly[oxy(1-alkylethylenes)]

Taking account of the influences of both side groups and hetero-atoms in backbone, the mean-square radius of gyration of poly[oxy(1-alkylethylenes)] has been derived by the method of the rotational isomeric state approximation and matrix algebra. Numerical calculation with the parameters available in literature indicated that the dependence of 〈S²〉 on the molecular weight can be expressed as the general formula, 〈S²〉 = aM^b with b = 1 ± 0.02, for poly(oxypropylene), poly[oxy(1-ethylethylene)] and poly[oxy(1-tert-butylethylene)]. © 1997 John Wiley & Sons, Ltd.     

Third-order interaction approximation for linear polymer chains

Third-order interactions imposed by a pair of atoms separated by five bonds are taken into account in computations of the mean-square end-to-end distance and the mean-square radius of gyration for linear polymer chains. The statistical weight matrices are established on the basis of the rotational isomeric state model. The conformational energy of n-hexane is calculated as a function of the C? C bond rotation angles. The third-order interaction energy is obtained by comparison with that of n-pentane. The characteristic ratio of polymethylene is 6.6 in the third-order interaction approximation, which is in agreement with experimental data.     

聚羧酸系高性能减水剂分子在稀溶液中尺寸及其在体积排除色谱表征中表观分子量的模型研究

针对被称为"第一代聚羧酸高性能减水剂"(以下简称为MPEG-type PCE)的甲基丙烯酸(MAA)/烯酸甲酯(MAA-MPEG)梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作:首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱"表观分子量"(又被称为GPC分子量)两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.     

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.     

Intercalation of solvent and polymer in galleries of mobile clay platelets by a Monte Carlo simulation

The intercalation of solvent particles and polymer chains of concentration C_w = 0.2 and C_p = 0.2, respectively, in a layer of (4) clay platelets is studied by a Monte Carlo simulation on a cubic lattice. Polymer chains and platelets are modeled by bond fluctuations. Besides the excluded volume, a set of polymer-clay (cs) and solvent-clay (ws) interactions with (i) cs = 1, ws = −2, (ii) cs = −2, ws = 1 and (iii) cs = ws = −2 are considered. The global dynamics of platelets is constrained due to the presence of three components, i.e., solvent, polymer, and platelets, which retain their interstitial spacing with well-defined galleries. Intercalation of solvent particles and polymer chains (low molecular weight) occurs with their attractive interaction with the platelets, which further reinforces the layered clay morphology. The density profiles of the solvent particles are similar to previous studies with platelets in a mobile solvent. The density profile of polymer chains differs considerably from the platelets in a polymer matrix alone, particularly with its attractive interaction (ii). For the same attractive interaction of solvent and polymer chains with the clay platelets (iii), the solvent particles (the smallest constituents) intercalate the fastest in the clay galleries, whereas the intercalation of polymer chains decreases with their molecular weight. The polymer density profiles, both longitudinal (x) and transverse (y), show maxima peaks around outer platelets (surface) of the layer and decay sharply both in the adjacent galleries and in the bulk. The amplitude of oscillation in the transverse density profiles, a measure of the degree of intercalation, decreases with increasing molecular weight of the polymer. The intercalation of the polymer is driven by its attractive interaction at the low molecular weight, but reduces considerably at high molecular weight because of both entanglement and larger radius of gyration. Variations of the gyration radius of the diffusing polymer chains with molecular weight and interaction with the clay are consistent with the results of their corresponding density profiles. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2487–2500, 2009     

The variations of the configurational and solvency properties of low molecular weight sodium polyacrylate with ionic strength

The configurational and solvency properties of low molecular weight sodium polyacrylate have been determined for a wide range of ionic strength solutions, from intrinsic viscosity data in the polymer literature.The variations of the polymer properties with ionic strength (I) are described very well by simple mathematical expressions. Thus, a linear relationship was found between the solvency parameter and 1/I ^(1/2), while the variations of the expansion factor and the radius of gyration with 1/I ^(1/2) were described by second order polynomials.LowI solutions (i.e. < 0.01) have a high solvency for sodium polyacrylate. In such solutions the polymer is in a highly expanded configuration. Thus, the radius of gyration of a typical, low molecular weight (ca. 5000 g mol^–1) sodium polyacrylate approaches the limiting value of ca. 4.5 nm atI<0.01.Conversely, high ionic strength solutions (i.e. >0.10) have a low solvency for sodium polyacrylate. In such solutions the polymer is in a virtually unexpanded configuration. Thus, the radius of gyration of a typical, low molecular weight sodium polyacrylate approaches the limiting value of ca. 2.0 nm atI>0.10.     

Star‐shaped polymers by Ru(II)‐catalyzed living radical polymerization. II. Effective reaction conditions and characterization by multi‐angle laser light scattering/size exclusion chromatography and small‐angle X‐ray scattering

Star poly(methyl methacrylate)s (P*) of various arm lengths and core sizes were synthesized in high yields by the polymer linking reaction in Ru(II)‐catalyzed living radical polymerization. The yields of the star polymers were strongly dependent on the reaction conditions and increased under the following conditions: (1) at a higher overall concentration of arm chains ([P*]), (2) with a larger degree of polymerization (DP) of the arm chains (arm length), and (3) with a larger ratio (r) of linking agents to P* (core size). In particular, the yields sharply increased in a short time at a higher temperature, in a polar solution, and at a higher complex concentration after the addition of linking agents. These star polymers were then analyzed by multi‐angle laser light scattering to determine the weight‐average molecular weight (3.8 × 10³ to 1.5 × 10⁶), the number of arm chains per molecule (f = 4–63), and the radius of gyration (R_z = 2–22 nm), which also depended on the reaction conditions (e.g., f and R_z increased as [P*], DP, and r increased). Small‐angle X‐ray scattering analyses of the star polymers showed that they consisted of spheres for which the radius of the microgel core was 2.7 nm. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2245–2255, 2002     

Off-lattice Monte Carlo studies on size and shape of isolated polymer chains with isotactic and syndiotactic attached side groups

Chains containing side groups were generated with up to 102 bonds in the backbone for both iso- and syndiotactic arrangements. The mean-square end-to-end distance <h ²>, the mean-square radius of gyration <r ²> and the ratios <l _i ² >/<l ₁ ² > of the axes of inertia were investigated. It could be shown that the mean size and shape of such chains are not influenced by the kind of stereoregularity.Dedicated to Prof. Dr. K. Ueberreiter on the occasion of his 70th birthday.     

Rheological measurements and light-scattering experiments of dilute solutions of high molecular polystyrene. Light-scattering of flowing polymer solutions

We describe the behavior of dilute polymer solutions by means of light-scattering under shear flow. Solution properties of polystyrene in benzene over a wide range of molecular weight has been studied to determine the coefficientsa andK of the Mark-Houwink relationship and to estimate the rheological conditions with regard to light-scattering experiments of flowing polymer solutions. The investigations were carried out to measure the shear-rate dependence of macromolecules in solution, e.g., to observe an orientation and changing of the mean-square radius of gyration.     

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.     

Free‐radical polymerization of methyl methacrylate with a tetrafunctional peroxide initiator

This study examined the use of a new tetrafunctional peroxide initiator in the bulk free‐radical polymerization of methyl methacrylate. The objective was to investigate the effect of using a multifunctional initiator through an examination of the rates of polymerization and the polymer properties. The molecular weights and radii of gyration were obtained with a size exclusion chromatograph equipped with an online multi‐angle laser light scattering detector. The performance of the tetrafunctional initiator was compared to that of a monofunctional counterpart [tert‐butylperoxy 2‐ethylhexyl carbonate (TBEC)]. The results showed that the new tetrafunctional peroxide initiator produced a faster rate of polymerization than TBEC at an equivalent concentration but also generated a polymer of a lower molecular weight. This trend was the opposite of what was observed in a previous study with styrene. When TBEC was used at a concentration four times that of the new tetrafunctional peroxide initiator, both produced equal rates of polymerization and similar molecular weights. The degree of branching was also investigated with radius‐of‐gyration plots. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5647–5661, 2004     

双烯化合物类单体合成支化聚合物的支化结构的研究

分别以二乙烯基苯(DVB)、双甲基丙烯酸二缩三乙二醇酯(tri-EGDMA)和1,6-双马来酰亚胺基正己烷(BMIH)为支化单体,采用原子转移自由基聚合合成支化聚苯乙烯;以先核后臂法合成的星状支化聚苯乙烯为参照对合成的支化聚合物的支化形态进行研究.采用气相色谱(GC)、核磁共振氢谱(1H-NMR)和三检测凝胶渗透色谱(TD-SEC)测定了苯乙烯的转化率,聚合物分子量及其分布,特性黏数和均方回转半径.实验结果表明3个支化聚合反应体系内悬垂双键是逐步消耗的,不存在明显的成核过程.反应前期,以形成带有悬垂双键的初级链和轻度支化聚合物为主,聚合物分子量随单体转化率逐步上升;反应后期,悬垂双键聚合导致的分子之间的偶合更加明显,使得聚合物分子量快速上升,合成得到的都是无规支化聚合物.     

The nonlinear change in conformation of polyelectrolyte macromolecules in saltless water-organic solvent

High molecular weight polyelectrolyte: poly(dimethylaminoethyl methacrylate) [PDMAEMA] with molecular weights M_W = 28.0×10⁶, 20.0×10⁶, 15.0×10⁶ was investigated in dilute solution by light scattering, flow birefringence and viscometry (at different rate gradients) in a water-acetone system by varying the weight fraction of acetone r in the mixture. At r=0.76 the polymer undergoes a reversible coil-globule transition accompanied by a drastic decrease in intrinsic viscosity [n], mean-square radius of gyration R²_z^1/2 and second virial coefficient A₂, with no change in molecular weight. The coil asymmetry parameter p (p=2.5 at r=0.50) decreases with increasing r and attains unity (completely symmetrical particle) at the transition point (r=0.76). The anomalous behavior of the viscosity of PDMAEMA-water-acetone solutions, detected near the transition point (r=0.6+0.7), is interpreted by formation of local knots of compactization on the molecular chain under the influence of a hydrodynamic field.     

Dilute solution characterization of polyfluoroalkoxyphosphazenes

Results from the dilute solution characterization of polyfluoroalkoxyphosphazenes in Freon ether (E2) solutions are reported. Anomalous viscosity data suggest that polymer aggregation sometimes occurs in E2 and may be caused by the presence of relatively few anomalous polar groups on the polymer backbone. Since small amounts of acetone added to the E2 solutions inhibit aggregate formation, samples are also characterized in an E2-acetone mixed solvent. Light scattering and osmometry indicate that E2 and E2-acetone (9.09% by volume) are theta solvents for the polymers. High molecular weights (M?_w < 3 × 10⁶) and unusually broad molecular weight distributions (M?_w/M?_n < 16) are found. One polymer is fractionated by extracting solutions in 1,1,2-trichloro-1,2,2-trifluoroethane with acetone. Although the samples are highly polydisperse, intrinsic viscosities correlate with number-average molecular weights satisfying the Mark-Houwink relation with the exponent a ≈ 1/2. The z-average mean-square radius of gyration increases linearly with molecular weight so that 〈S²〉_g/M?_w ≈ 0.098. Because of the large polydispersity and unknown form of the distribution function, a quantitative interpretation of characterization results relating dilute solution parameters to polymer skeletal structure is not possible. The tentative conclusion is that the fluoroalkoxy-substituted phosphazene polymers are relatively linear and therefore that the broad distribution of molecular weights must be due to some polymerization mechanism other than branching.     

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.