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.     

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.     

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.     

Solution properties,unperturbed dimensions,and chain flexibility of poly(1‐adamantyl acrylate)

Poly(1‐adamantyl acrylate) (PAdA) exhibits much higher glass transition and degradation temperatures than other polyacrylates. However, the quantitative evaluation of the stiffness of this polymer chain has not been reported previously. In this study, the dilute solution properties and conformational characteristics of PAdA were evaluated using viscometry and scattering techniques. The unperturbed dimensions of this polymer were evaluated using the Burchard–Stockmayer–Fixman extrapolation and the touched‐bead wormlike chain model. The PAdA chain has a comparable persistence length, diameter per bead and characteristic ratio to poly(methyl methacrylate) and polystyrene. All these results indicate that PAdA is less flexible than common polyacrylates. In addition, the second virial coefficients (A₂) of PAdA in different solvents obtained by static light scattering were compared. Among the solvents investigated, tetrahydrofuran is a moderate solvent. Radius of gyration of a polymer sample in the various solvents ranged from 16.8 to 30.3 nm. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1526–1531     

Polystyrene in cyclopentane: Dilute solution properties from the upper critical to the lower critical solution temperature

Dilute solutions of polystyrene in cyclopentane are studied with four narrow-distribution polymer fractions ranging in molecular weight from 1.6 × 10⁵ to 1.8 × 10⁶. Light scattering (total intensity) and viscosity measurements cover a temperature range spanning both “theta” temperatures: the limiting upper critical solution temperature (19.6°C) and the limiting lower critical temperature (154.5°C). Within experimental uncertainty, chain dimensions are the same at the two theta temperatures. Correlations among second virial coefficients, mean-square molecular radii of gyration, and intrinsic viscosities, are analyzed. Temperature and molecular-weight dependences are correlated satisfactorily in terms of the excluded-volume parameter z that is central to the “two-parameter” theories of dilute solution behavior. The data can also be correlated in the framework of the newer renormalization theories.     

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.     

Temperature dependence of limiting viscosity number and radius of gyration of cellulose diacetate in acetone

Acetone solutions of a cellulose diacetate fraction were studied by viscosity and light scattering methods over the range 12.6–50.3². The temperature dependences of the limiting viscosity number [η], the mean-square radius of gyration 〈s²〉, and the second virial coefficient A₂ were determined. The unperturbed mean-square radius of gyration 〈s²〉_o and the expansion factor α, were estimated by using theoretical relations to the interpenetration function. It was found that dln 〈s²〉_o/dT is ?6.4 × 10^?3 deg^?1, while α, is close to unity over the whole temperature range studied. The viscosity results are interpreted to show that the draining effect is not negligible and the Flory viscosity parameter Φ slightly increases with increasing temperature. It is finally concluded that the value of ?6.9 × 10^?3 deg^?1 for dln [η]/dT can be ascribable to the rapid decrease in 〈s²〉_o.     

Properties of cellulose acetate in solution. I. Light scattering,osmometry, and viscometry on dilute solutions

Light-scattering, osmotic pressure, and viscometric studies on fractions of cellulose acetate (degree of substitution 2.45) in three solvents are described. The data yield the dependence of the mean-square radius of gyration 〈s²〉, the second virial coefficient Γ₂, and the intrinsic viscosity [η] on molecular weight M and temperature. The results are interpreted to show that excluded volume effects on 〈s²〉 are negligible, even though Γ₂ is large and dΓ₂/dT is positive. The large experimental value of d In [η]/d In M is interpreted in terms of partial draining effects. Data on 〈s₂〉 and [η] for other cellulose esters in the literature are similarly interpreted. Significant aggregation found in solutions of cellulose acetate in many solvents is 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.     

Estimation and analysis of the rheological properties of a perfluoropolyether through molecular dynamics simulation

Equilibrium and non-equilibrium molecular dynamics simulations of a perfluoropolyether C₈F₁₈O₄ are reported using an atomistic interaction potential. The bulk rheological properties of the perfluoropolyether are investigated through molecular dynamics simulations as a function of both temperature and shear rate. The effect of molecular structure on viscosity is explored in detail. The rotational relaxation time is reported as a function of temperature. Structural properties, including the mean-square end-to-end chain length, the mean-square radius of gyration of chains, and the distribution functions of bond lengths, bond angles, and bond torsional angles are collected and analyzed as functions of shear rate. After an initial plateau, both mean-square end-to-end chain length and mean-square radius of gyration decrease monotonically with increasing shear rate. The behaviors of the rheological and structural properties are explained through an analysis of the individual contributions due to bond stretching, bond bending, and bond torsion, as well as both intramolecular and intermolecular non-bonded interactions. A further analysis is possible through a meticulous breakdown of each contribution into a specific type of mode; e.g., the total bond stretching is comprised of CC, CO, and CF bond stretching terms. In this way, one can relate the shear viscosity to the specific chemical structure of C₈F₁₈O₄.     

Conformation of linear polyethylene in 1-chloronaphthalene: Light scattering characterization of polymers. IV

Light scattering measurements were carried out on a linear polyethylene sample NBS 1475 in 1-chloronaphthalene at 135 and 115°C to determine the weight-average molecular weight, the second virial coefficient A₂, and the z-average mean-square radius of gyration. By use of these results, the system is analyzed in terms of the interpenetration function Ψ for A₂. Observed values of A₂ are rather large but the excluded volume is nevertheless relatively small. Such behavior seem to be similar to that of semiflexible polymers. The characteristic ratio C_n,LS as determined by light scattering is found to be almost twice the literature value of 6.7, which was obtained from viscosity measurements. This discrepancy is explained by comparing the theoretical value of the Flory viscosity parameter Φ at the nondraining limit with values calculated from the light scattering results.     

Rheological Behavior and Scattering Studies of Acrylamide-Based Copolymer Solutions

Summary: In this paper the chemical structure of an acrylamide-N,N-dihexylacrylamide copolymer was established by IR and NMR. Static and dynamic light scattering in formamide were used in order to evaluate the polymer structural parameters, such as weight-average molecular weight (M_w), second virial coefficient (A₂), radius of gyration (R_G), the form factor P(q) and the hydrodynamic radius (R_H). Additionally to the classical characterization, those results indicated the presence of aggregation, showing that formamide is not a very good solvent, as stated in earlier investigations. The rheological behavior in aqueous solutions was evaluated as a function of the salt concentration. The solutions presented an important viscosity increase in the presence of NaCl and did not show any sensitivity to the presence of CaCl₂. This result is in favor of the oil recovery especially in high salinity reservoirs.     

Studies of solution properties of copolymers. II. Copolymer of maleic anhydride and styrene

Styrene and maleic anhydride were copolymerized in benzene. The whole polymer thus obtained was fractionated with acetone and petroleum ether as the solvent and precipitant, respectively. The viscosities and osmotic pressures of the fractions were determined in tetrahydrofuran. The relation between the intrinsic viscosity and the molecular weight, [η] = 5.07 × 10^?5 M?_n^0.81, was obtained in tetrahydrofuran. The unperturbed mean square end-to-end distance was estimated by the Stockmayer-Fixman equation. A theoretical equation for the mean square end-to-end distance for a chain of repeating units of different bond lengths a and b with a fixed valence angle θ and without restriction of internal rotation was presented and applied to this copolymer. In addition, the equation of the mean-square end-to-end distance derived by Wall for trans-polyisoprene without rotational restriction was modified for application to this copolymer. The result evaluated with our equation was about 26% smaller than that from the modified Wall equation. A steric parameter for the present copolymer is defined and discussed in comparison with those of polystyrenesulfone and polystyrene.     

Thermodynamic and conformational properties of polystyrene. III. Dilute solution studies on branched polymers

Light-scattering and viscometric measurements on dilute solutions of five branched polystyrene polymers are reported. The data include studies in decalin as a function of temperature, including the theta temperature, and in toluene. The results for the radius of gyration and the second virial coefficient are not in accord with the two parameter random-flight model. Possible causes of this descrepancy are considered. It is shown that the intrinsic viscosity of branched chains is not uniquely determined by the radius of gyration.     

Molecular characteristics of functional polysaccharides

The molecular characteristics of sodium hyaluronate and amylose in various solvents are discussed by summarizing our recent studies. Data for the intrinsic viscosity and the radius of gyration are analyzed on the basis of the wormlike or helical wormlike chain, with excluded-volume effects taken into account by the Yamakawa-Stockmayer-Shimada theory. The unperturbed hyaluronate molecule in 0.2 M or 0.5 M aqueous NaCl is shown to behave like a wormlike chain with Kuhn's segment length of about 8 nm. Amylose in the unperturbed state is more flexible, regardless of the kind of solvent, its stiffness parameter being about one half that for the hyaluronate chain, but it assumes an irregular helical conformation similar to what is predicted by conformation analysis.     

Molecular properties of poly(carboxybetaine) in solutions with different ionic strengths and pH values

Viscometry and dynamic and static light scattering are employed to study the molecular properties of water-soluble poly(carboxybetaine), that is, poly(2-(diallyl(methyl)ammonium) acetate). It is shown that, in solutions with pH 1, the polymer behaves as a polyelectrolyte. In media with pH 6 and 13, an increase in the concentration of sodium chloride increases the intrinsic viscosity of the polymer and the hydrodynamic radius of its macromolecules, thereby indicating the antipolyelectrolyte effect typical of polymer zwitterions. In water and 0.1 M NaOH, the second virial coefficient of the polymer is close to zero, while exponent ν, which relates the sizes of macromolecules to their molecular masses, is 0.5. In 1 M NaCl, the second virial coefficient becomes positive, while exponent increases to 0.58. The Kuhn segment lengths of poly(carboxybetaine) molecules are 6.3 and 6.6 nm in water and 1 M NaCl, respectively. An increase in the hydrodynamic radius of macromolecules with the ionic strength of the solution is due to the shielding of attraction between zwitterions belonging to polybetaine monomer units located far apart along a macromolecular chain.     

Molecular chain properties of poly (N-isopropyl acrylamide)

A series of poly( N-isopropyl acrylamide) (PNIPAM) samples with molecular weight ranging from 2.23×10~4 to 130×10~4 and molecular weight distribution M_w/M_n≤1.28 were obtained by free radical polymerization and repeat precipitation fractionation. The molecular weight M_w, second virial coefficient A_2 as well as the mean-square-root radius of gyration 〈S~2〉 for PNIPAM samples in tetrahydrofuran (THF) were determined by light scattering, and the relations were estimated at A_2 ∞ M_w~0.25) and 〈S~2〉~(1/2)=1.56×10~(-9) M_w~(0.56). The intrinsic viscosity for THF solution and methanol solution of PNIPAM samples was measured and the Mark-Houwink equations were obtained as [η]=6.90×10~(-5) M~(0/73) (THF solution) and [η]=1.07×10~(-4) M~(0.71) (methanol solution). The above results indicate that both THF and methanol are good solvents for PNIPAM. The limit characteristic ratio C_∞ for PNIPAM in the two solutions was determined to be 10.6 by using Kurata-Stockmayer equation, indicating that the f     

一种手性甲壳型液晶高分子的稀溶液行为及链刚性

用激光光散射和粘度法研究了一系列窄分子量分布的新的手性甲壳型液晶聚合物P1～P6的溶液行为及其链刚性.研究发现四氢呋喃是聚合物P1～P6的良溶剂.在四氢呋喃溶液中,聚合物P1～P6的特性粘数[η]和均方根旋转半径z12对重均分子量Mw的依赖关系分别是[η]=(2.75±0.05)×10-3Mw0.78±0.02和z12=(1.53±0.04)×10-2Mw0.60±0.01.按照YamakawaFujiiYoshizaki蠕虫状圆筒模型的粘度理论和BohdaneckyBushin表达式,求得聚合物的单位围长摩尔质量ML=(29.8±1.0)×102nm,构象保持长度q=(15.4±3.0)nm.q和MHS方程指数α的值说明这类在结构上属于侧链型液晶高分子的聚合物在良溶剂四氢呋喃中呈现比较伸展的刚性链构象,其链刚性与半刚性主链液晶高分子的相似.     

On the theory of dilute polyelectrolyte solutions: Extensions,refinements, and experimental tests

We synthesize a quantitative theory for the radius of gyration, second virial coefficient, intrinsic viscosity, and friction coefficient for polyelectroytes in dilute solution from existing treatments of electrostatic and hydrodynamic interactions within and among wormlike chains. Comparison with data for K-PSS demonstrates the importance of accounting for nonlinearities in the electrostatics and the finite diameter of the polymer backbone.