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.     

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.     

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.     

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.     

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.     

Aggregation behavior of polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer in N‐methylpyrrolidone

Solution property of hydrogenated polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer (SEBS copolymer) was studied by using static light scattering and dynamic light scattering for cyclohexane and N‐methylpyrrolidone (NMP) solutions. From the values of dimensionless parameters ρ, defined as the ratio of radius of gyration 〈S²〉^1/2 to hydrodynamic radius R_H, and solubility parameters, SEBS copolymer proved to exist as single chain close to random coil in nonpolar cyclohexane, whereas aggregate into the core‐shell micelle consisting of poly(ethylene/butylene) (PEB) core surrounded by PS shell in polar NMP. The core‐shell micelle formed in NMP is composed of 65 polymer chains, having three times larger average chain density (d = 0.12 g cm^?3) than a single polymer chain (d = 0.04 g cm^?3) in cyclohexane. The comparison with the aggregation behaviors in other solvents demonstrated that the aggregate compactness of the copolymer depended largely on solvent polarity, resulting in formation of the highly dense PEB core (R_c = 4.5 nm) and the thick PS shell (ΔR = 22.9 nm) in high‐polar NMP. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 588–594, 2010     

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.     

Polymer deformation in various flows

Using a Langevin-like approach, the deformation of a polymer, modelled as a bead-spring chain, is calculated in simple shear, elongational and Kramers potential flow. Analytic expressions for the mean-square end-to-end distance, radius of gyration, segment-segment distance, static structure factor up to O(q⁴) and the intrinsic elongational viscosity are given. Near equilibrium, preaveraged hydrodynamic interaction is taken into account.     

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.     

Monte Carlo study of star-branched polymers on the tetrahedral lattice. I. Conformation of the macromolecule

The star-branched polymers on the tetrahedral lattice are studied by means of the Monte Carlo method. The influence of solvent quality on the dimensions of the coil is described for both linear and branched polymer systems of different functionality. It has been observed that the ratios of gyration radii 〈S²〉_b/〈S²〉_l are greater than those predicted theoretically for the random-flight model. The fourth reduced moment of S² distribution and the mean-square separation of the branch ends from the center of gravity have been also computed. The changes in segment arrangement in the coil with increasing number of branches have been observed.     

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.     

Effect of polystyrene‐b‐poly(ethylene oxide) on self‐assembly of polystyrene‐b‐poly(N‐isopropylacrylamide) in aqueous solution

Mixed micelles of polystyrene‐b‐poly(N‐isopropylacrylamide) (PS‐b‐PNIPAM) and two polystyrene‐b‐poly(ethylene oxide) diblock copolymers (PS‐b‐PEO) with different chain lengths of polystyrene in aqueous solution were prepared by adding the tetrahydrofuran solutions dropwise into an excess of water. The formation and stabilization of the resultant mixed micelles were characterized by using a combination of static and dynamic light scattering. Increasing the initial concentration of PS‐b‐PEO in THF led to a decrease in the size and the weight average molar mass (〈M_w〉) of the mixed micelles when the initial concentration of PS‐b‐ PNIPAM was kept as 1 × 10^?3 g/mL. The PS‐b‐PEO with shorter PS block has a more pronounced effect on the change of the size and 〈M_w〉 than that with longer PS block. The number of PS‐b‐PNIPAM in each mixed micelle decreased with the addition of PS‐b‐PEO. The average hydrodynamic radius 〈R_h〉 and average radius of gyration 〈R_g〉 of pure PS‐b‐PNIPAM and mixed micelles gradually decreased with the increase in the temperature. Both the pure micelles and mixed micelles were stable in the temperature range of 18 °C–39 °C. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1168–1174, 2010     

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.     

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.     

Appreciable norbornene incorporation in the copolymerization of ethylene/norbornene using titanium catalysts containing trianionic N[CH2CH(Ph)O]33− ligands

The newly synthesized 1‐TiCl (C₃ symmetric) and 2‐TiCl (C_s symmetric) precatalysts in combination with MAO polymerized ethylene, cyclic olefins, and copolymerized ethylene/norbornene in good yields. The catalyst with C₃ symmetry exhibits moderate catalytic activity and efficient norbornene incorporation for E/NBE copolymerization in the presence of MAO [activity = 360 kg polymer/(mol Ti h), ethylene 1 atm, NBE 5 mmol/mL, 10 min], affording poly(ethylene‐co‐NBE)s with high norbornene contents (42.0%) and the C_s symmetric catalyst showed an activity of 420 kg polymer/(mol Ti h), ethylene 1 atm, NBE 5 mmol/mL affording poly(ethylene‐co‐NBE)s with 33.0% norbornene content. The effect of monomer concentration at ambient temperature and constant Al/Ti ratio for the homo and copolymerization was studied in a detailed manner. We found that apart from the electronic environment around the metal center the steric environment provided by the symmetry of the catalyst systems has a considerable influence on the percentage of norbornene content of the copolymer obtained. We also found that with a given catalyst a variable clearly influencing the copolymer microstructure, hence also the copolymer properties, is the monomer concentration at a given feed ratio. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 444–452, 2008     

Synthesis of Heterotelechelic Poly(ethylene glycol)-block-poly(succinimide) Possessing Both Acetal and Tert-Butoxycarbonyl-amino Terminals with Narrow Molecular Weight Distribution

A novel heterotelechelic linear block copolymer of poly(ethylene glycol) (PEG) and poly(succinimide) (PSI) possessing both acetal and tert-butoxycarbonyl-amino (Boc-NH) terminals (Acetal-PEG-b-PSI-NH-Boc) with a narrow molecular weight distribution (MWD) was successfully prepared by the nucleophilic attack of triethylamine (TEA) to the poly(β-benzyl L-aspartate) (PBLA) segment of Acetal-PEG-b-PBLA-NH-Boc. Acetal-PEG-b-PBLA-NH-Boc with MWD of 1.07 was prepared by living anionic ring-opening polymerization of β-benzyl L-aspartate N-carboxy-anhydride with α-acetal-ω-amino PEG as a macroinitiator, followed by Boc protection. The subsequent conversion of PBLA segment to PSI was successfully carried out by reacting with the catalytic amount of TEA. The characterization by ¹H NMR, GPC and IR demonstrates that the formation of poly(succinimide) proceeded completely without any remarkable side reactions. Acetal-PEG-b-PSI-NH-Boc thus obtained may have a potential utility as a targetable drug carrier in the field of drug delivery system.     

Glass and subglass transitions in a series of poly(itaconate ester)s with methyl-terminated poly(ethylene oxide) side chains

A series of poly(itaconate ester)s containing methyl-terminated poly(ethylene oxide) side chains with lengths ranging from 1 to 5 ethylene oxide units has been synthesized. Both heat capacity C_p and dynamic mechanical measurements have been carried out on these polymers using differential scanning calorimetry (DSC) and torsional braid analysis (TBA), respectively. The resulting data for this polymer series are discussed, and comparisons are made with work previously published for the corresponding di-n-alkyl itaconate ester polymers where appropriate.     

Solubilization of C60 by micellization with a thermoresponsive block copolymer in water: Characterization,singlet oxygen generation,and DNA photocleavage

Water‐soluble diblock copolymer, poly(N‐isopropylacrylamide)‐block‐poly(N‐vinyl‐2‐pyrroridone) (PNIPAM_m‐b‐PNVP_n), was found to associate with fullerene (C₆₀), and thus C₆₀ can be solubilized in water. The 63C₆₀/PNIPAM_m‐b‐PNVP_n micelle formed a core‐shell micelle‐like aggregate comprising a C₆₀/PNVP hydrophobic core and a thermoresponsive PNIPAM shell. The C₆₀‐containing polymer micelle formation and its thermoresponsive behavior were characterized using light scattering and ¹H NMR techniques. The hydrodynamic radius (R_h) of the C₆₀‐bound polymer micelle increased with increasing temperature, which was ascribed to the hydrophobic association between dehydrated PNIPAM shells above lower critical solution temperature (LCST). ¹H NMR data suggest that the motion of the PNIPAM block is restricted above LCST due to the dehydration of the PNIPAM shell in water. The generation of singlet oxygen by photosensitization by the C₆₀‐bound polymer micelle was confirmed from photooxidation of 9,10‐anthracenedipropionic acid. Furthermore, DNA was found to be cleaved by visible light irradiation in the presence of the C₆₀‐bound polymer micelle. Therefore, there may be a hope for a pharmaceutical application of the C₆₀‐bound polymer micelle to cancer photodynamic therapy. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

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.