Flow birefringence of short-chain molecules: Cellulose tricarbanilates in benzophenone

Measurements of flow birefringence of cellulose tricarbanilates were carried out on nine fractions (0.27 × 10⁵ < M ≤ 12 × 10⁵) in a temperature range of 55–110°C, with benzophenone as a matching solvent (dn/dc = 0). The ratio of Maxwell constant to intrinsic viscosity, which has been found to be independent of molecular weight for the limiting case of Gaussian molecules, is successfully interpreted as a function of molecular weight in terms of the recent theory of Gotlib and Svetlov (based on the wormlike chain model of Kratky and Porod). From the measurements at 55°C a number of 36.6 monomer units per random link is deduced. This is in accord with results of small-angle x-ray scattering. For the extinction angle curves a clear transition is observed from rodlike to statistical molecules when the molecular weight is increased. At high molecular weights the master curves obtained for anionic polystyrenes and cellulose tricarbanilates coincide. Implications of this observation on the kinetic stiffness of the cellulose tricarbanilate chain are discussed. The intrinsic viscosity-molecular weight relationship is considered. From a comparison with the results of the theory of Eizner and Ptitsyn it is concluded that the cellulose tricarbanilate chain must be highly solvated in benzophenone.     

Measurements of the relaxation spectra of unplasticized poly(vinyl chloride) melts

We have measured the relaxation modulus in the temperature range 150–220°C of two samples of poly(vinyl chloride) resin with different molecular weights. The data were treated by the principle of reduced variables to yield composite curves. The shift factors (a_T) when plotted against reciprocal temperature gave good straight lines from which apparent activation energies were obtained. An apparent activation energy of 50 kcal/mole was obtained for both samples. A relaxation spectrum for each resin was calculated from the relaxation modulus data. These spectra showed a marked molecular weight dependence. The spectra were in the range characteristic of the terminal zone of the entanglement plateau. Zero-shear-rate viscosities were obtained from the integration of relaxation modulus plots. From extrapolation of capillary viscosity data it is shown that the viscosity of the higher molecular weight resin used in this study does not approach its zero-shear value until shear rates less than 10^?3 sec^?1 are reached. The effect of supermolecular flow units is briefly discussed.     

Stress relaxation of monodisperse poly-α-methylstyrene

The viscoelastic properties of monodisperse poly-α-methylstyrenes of molecular weights of 4 × 10⁴ to 50 × 10⁴ were studied by the tensile stress-relaxation method. The relaxation-time spectra as well as the steady-flow viscosity, the steady-state compliance, the maximum relaxation time, and the modulus associated with the maximum relaxation time were determined. The molecular weight dependences of these quantities were compared with the theory of Rouse and Bueche as modified by Ferry, Landel, and Williams, as well as with data on other polymers reported in the literature.     

Temperature dependence of the conformational relaxation time of polymer molecules in elongational flow: Invariance of the molecular weight exponent

Using an elongational flow technique, we have investigated the relationship between the molecular conformational relaxation time and the molecular weight for a solvent whose quality was altered thermally from near θ to a good solvent state. The materials used were closely monodisperse samples of atactic polystyrene. The results show that the relaxation time τ varies with the molecular weight M as τ ∝ M^1.5, independent of the solvent quality, a result which apparently is at variance with the observed molecular weight dependence of intrinsic viscosity. Despite this invariance of the molecular weight exponent with solvent quality, our results also show that the coils do expand when the solvent quality was increased in agreement with the mean-field theory of Flory.     

Excluded‐volume effects on the chain dimensions and transport coefficients of sodium poly(styrene sulfonate) in aqueous sodium chloride

Fifteen samples of sodium poly(styrene sulfonate) with weight‐average molecular weights of 3 × 10⁴ to 8 × 10⁵ have been studied by static and dynamic light scattering and viscometry in 0.05 and 0.5 M aqueous NaCl at 25 °C. The measured radii of gyration, translational diffusion coefficients, and intrinsic viscosities at the lower salt concentration exhibit molecular weight dependencies stronger than those predictable for uncharged flexible chains in the good solvent limit. These data and those at the higher NaCl concentration are analyzed, along with previous intrinsic viscosity data covering a broad molecular weight range, in the framework of the quasi‐two‐parameter (QTP) theory with the wormlike chain as the model. It is shown that the relevant theories for the expansion factors in the QTP scheme combined with these theories for the unperturbed wormlike chain are capable of describing the experimental data with a degree of accuracy similar to that known for nonionic flexible polymers. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2728–2735, 2002     

Hydrodynamic interaction effects on intrinsic viscosity of perturbed chains: Experimental results for polystyrene

Experimental measurements of intrinsic viscosity and radii of gyration of monodisperse samples of polystyrene of molecular weights 2.33 X 10⁵, 4.11 X 10⁵, 6.70 X 10⁵, and 2.3 X 10⁶ dissolved in the homologous series of 1-chloroparaffins from butane to undecane are reported. The dependence of the viscosity expansion coefficient α_η on the expansion factor α_s for the radius of gyration is discussed in the light of the results obtained by an expansion of the Fixman theory for perturbed chains to include partial draining. These results give support to the finite chain effect on the hydrodynamics of expanded coils in the usual range of molecular weight. The exponent a in the relation α³_η = α^a_s depends on molecular weight and agrees with recent nondraining theoretical calculation for exceedingly high polymers.     

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.     

Intrinsic viscosity and axial extension ratio of random-coiling macromolecules in a hydrodynamic shear field

The shear dependence of the intrinsic viscosity and the conformation of high molecular weight polyisobutylene in dilute solutions of decahydronaphthalene under shear were determined simultaneously. Experimental variables investigated were the shear rate (0 to 2 × 10³ sec^?1), the molecular weight (1.0 × 10⁷ to 1.7 × 10⁷) and the polymer concentration (1.8 × 10^?4 to 8.4 × 10^?4 g/cc). Correlations allowing concentration and shear rate normalization for any one sample are described. Conformational extention ratios along the orientation direction of the deformed molecule to 1.42 and intrinsic viscosity ratios (sheared to zero shear) to 0.5 were observed.     

Effect of finite number of segments on flow birefringence extinction angle and the determination of internal viscosity and chain relaxation time

Summary The effect of restriction to a finite number of segments in modeling a flexible macromolecule by a linear Gaussian chain is considered. This model with an internal viscosity included has been used byCerf to develop the behavior of the extinction angle in flow birefringence. The consequences of restriction to a finite number of segments together with variable internal hydrodynamic interaction are determined with respect to the behavior of the extinction angle at low flow gradients and the characteristic chain relaxation times. The theoretical behavior of the extinction angle is shown to depend uniquely on the product of the longest characteristic relaxation time and the flowgradient. The relations between both extinction angle and intrinsic viscosity and the longest relaxation time is dependent upon both number of segments and hydrodynamic interaction. Also the relation given byCerf between gradient dependence of extinction angle and internal viscosity is dependent on both number of segments and hydrodynamic interaction. Results are given for a number of segments ranging from 1 to 1000 and for hydrodynamic interaction ranging from the free draining condition to an extreme nonfree draining condition.

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Zusammenfassung Der Einflu? einer Beschr?nkung auf endliche Zahl an Segmenten für die Nachbildung eines flexiblen Makromoleküls durch eineGauβsche Kette wird betrachtet. Dieses Modell mit einer inneren Viskosit?t wurde vonCerf gebraucht, das Verhalten des Extinktionswinkels bei Str?mungsdoppelbrechung zu entwickeln. Die Folgen einer Beschr?nkung auf endliche Segmentzahlen zusammen mit innerer hydrodynamischer Wechselwirkung werden hinsichtlich der Str?mungsdoppelbrechung bei niedrigen Gradienten und der charakteristischen Ketten-Relaxationszeiten ermittelt. Die Beziehung sowohl von Extinktionswinkel wie Intrinsic-Viskosit?t zur l?ngsten Relaxationszeit h?ngt von der Segmentzahl wie von der hydrodynamischen Wechselwirkung ab. Auch die vonCerf angegebene Beziehung zwischen Str?mungsgradient-Abh?ngigkeit des Extinktionswinkels und innerer Viskosit?t ist sowohl von der Segmentzahl wie von der hydrodynamischen Wechselwirkung abh?ngig. Ergebnisse wurden für Segmentzahlen von 1 bis 1000 und für die hydrodynamische Wechselwirkung von freier Durchspülung bis zu fast v?lliger Undurchdringlichkeit des Kn?uels angeführt.

     

Solution properties of styrene-p-chlorostyrene diblock copolymers—II. Light scattering studies in a selective solvent

Conformational behaviour of styrene-p-chlorostyrene diblock copolymers in cumene (a good solvent for polystyrene but a θ solvent for poly-p-chlorostyrene) was studied over the temperature range 15–60° by light scattering, osmotic pressure and intrinsic viscosity measurements. Two samples of copolymer (AB-4 and AB-2) were used. The composition of the samples was c. 50 mol% of styrene and the number-average molecular weights were 27.7 × 10⁴ for the AB-4 and 19.5 × 10⁴ for the AB-2. It was found that below 40° the number-average molecular weight of the AB-4 sample seemed to increase gradually with decreasing temperature and around 40°, marked decreases in the osmotic second virial coefficient and intrinsic viscosity were observed. The Zimm plot for the AB-2 sample was fairly normal at 40°. It seems that the temperature where an anomaly becomes evident in Zimm plots is dependent on the molecular weight of the sample. The experimental results for the diblock copolymers could be understood from the view that intermolecular association took place to some extent in the solutions on lowering the temperature giving rise to multi-molecular micelles.     

Flow birefringence and optical anisotropy of poly(N-vinylpyrrolidone) molecules

Concentration dependences of flow birefringence and viscosity of poly(N-vinylpyrrolidone) solutions in water and benzyl alcohol are investigated. The intrinsic anisotropy for a poly(N-vinylpyrrolidone) macromolecular segment, (α₁ ? α₂) = ?(82 ± 8) × 10^?25 cm³, is determined from the results of birefringence measurements in benzyl alcohol. For aqueous solutions, a strong concentration dependence of the specific anisotropy of solution is obtained, a result that may be explained by the heterogeneity of coils. A model allowing for this heterogeneity is suggested. It makes it possible to fit the concentration dependence to a hyperbolic function, to separate contributions of heterogeneity anisotropy and form anisotropy to the birefringence of a solution, and to estimate the segment asymmetry parameter as p = 3.0 ± 0.5.     

A Study of Monodispersed Polydimethylsiloxanes

A series of monodispersed polydimenthylsiloxanes (PDMS) with molecular weights from 3K to 156K were synthesized. The intrinsic viscosity and absolute molecular weight of each monodispersed PDMS was measured and the Mark-Houwink equation for the PDMS series in toluene at 25°C was derived: [eta;]=2.88 × 10^?4 M^0.613. It was proven that the accurate molecular weight determination of polysiloxanes is not possible using polystyrene (PS) standards. It can be achieved either by using a gel permeation chromatographic method with PDMS standards or by a calculation from the Mark-Houwink equation using experimental values of intrinsic viscosity.     

Method of determination of dielectric relaxation characteristics of plasticized polystyrenes on the basis of calorimetric glass temperature

The dielectric loss measurements of different polystyrenes (fractions and blends) with different molecular weights (M _n 2000–125000 g/mol) were carried out in the frequency range 10^–2–10⁶ Hz and the temperature range of the glass process (60°–135°C, depending on the molecular weight). The measurements of the pure fractions showed that the half-width of the glass relaxation process of the different polystyrenes can be correlated by a straight line, if they are plotted versus the relaxation frequency maxima of the glass process, regardless of the difference in both their molecular weight and glass transition temperature. Moreover, the fine structure of the shape of the glass process of polystyrenes with different molecular weights was found to be the same when the glass process appears at the same relaxation frequency range. The addition of oligostyrenes or low molecular <10% wt additives to the high molecular weight polystyrene did not influence the shape of the glass process. The calorimetric glass transition temperature of polystyrene was found to be only dependent on the number average molecular weight as well as on the number of end groups, but not on the molecular weight distribution. The obtained experimental results were correlated to develop a method for the estimation of the dielectric relaxation characteristics (relaxation frequency as well as the shape parameters) of the glass process of plasticized polystyrenes based on the calorimetric glass transition temperature. A method for the analysis of the dielectric relaxation curves of mixtures of label and polymer is suggested.     

Infinite-dilution viscoelastic properties of sodium poly(styrene sulfonate)

The storage and loss shear moduli G′ and G″ of dilute solutions of two samples of sodium poly(styrene sulfonate) with molecular weights (M) of 3.28 × 10⁵ have been measured. The Birnboim–Schrag multiple-lumped resonator technique was used in the frequency range 100–8000 Hz, and the intrinsic moduli were obtained by extrapolation to infinite dilution. Measurements were performed over the temperature range from 1.0 to 25.0°C in aqueous solvents containing from 0 to 60% by weight glycerol and from 0.001 to 0.005M added salt. The large intrinsic viscosities indicated high extension of the polymer, and the frequency dependences of G′ and G″ were matched well by hybrid relaxation spectra combining rodlike and coil-like behavior. In a solvent containing 0.001M sodium ion and no glycerol, the end-over-end rotational relaxation times for the two molecular weights corresponded to proportionality to the 1.7 power of M. With increasing molecular weight, ionic strength, and/or glycerol concentration, the polyelectrolyte appeared to become less extended, and its behavior more nearly coil-like.     

Conformation of poly(methacrylic acid) in alcohol–water mixtures. III. Dependence on molecular weight

Poly(methacrylic acid) has been studied in 0.002N HCl–ethanol mixtures as a function of molecular weight. A different dependence on molecular weight is noted at different alcohol concentrations. Since the intrinsic viscosity passes through a series of extrema with changes in alcohol concentration, the dependence on molecular weight has been considered in two regions of alcohol concentration in particular. The region of the first minimum and the region of the second minimum (or overall maximum). In the region of the first minimum, intrinsic viscosity is proportional to M^½, just as in 0.002N HCl. The Huggins coefficient k′ is large (ca. 60) but drops to about 10 when the molecular weight exceeds 320,000. In the region of the second minimum the dependence on molecular weight is complex. Intrinsic viscosity is proportional to molecular weight both at low and at high molecular weight and thus indicates freely draining structures. There is a conformational contraction, however, at molecular weight about 320,000 leading from one type of structure to the other. The structure at higher molecular weight may involve a specially strong bond between specifically grouped segments in the chain. The positions of the extrema along the alcohol concentration axis are not molecular weight dependent, particularly above 320,000. Results available for molecular weight dependence in methanol agree well with this picture. The present results confirm prediction inherent in the model of Silberberg and Priel and Silberberg.     

Electric birefringence in solutions of cellulose carbanilate as a function of molecular weight

Electro-optical, dynamo-optical and hydrodynamic properties of solutions of some fractions of cellulose carbanilate (CC) in dioxan have been investigated. In a variable electric field, strong dispersion of the Kerr effect is observed, indicating the dipole-orientational mechanism of electrical birefringence and its relaxation. A comparison of relaxation times of fractions with their molecular weights and intrinsic viscosities indicates that the mechanism responsible for the Kerr effect is the rotation of the molecule as a whole in an electric field (a kinetically rigid molecule). The dependence of relaxation time on molecular weight (M) shows that, with increase in M, the conformation of the CC molecule changes from a slightly curved rod to a rigid Gaussian coil. The same conclusion may be drawn from a study on the dependence of the equilibrium value of the Kerr constant on M. In the Gaussian range (high M), the Kerr effect depends on the longitudinal (with respect to the chain) component of the dipole moment formed by the CO bonds in the glucoside ring. At low M, the transverse components of the monomer dipoles begin to play an important part in birefringence.     

Viscoelastic behavior of low molecular weight polystyrene

The shear creep and creep recovery behavior of narrow molecular weight distribution polystyrene samples of low molecular weight, 1.1 × 10³, 3.4 × 10³, and 1.57 × 10⁴ are reported as a function of temperature, near and above the glass temperature. Time-temperature equivalence for the total creep compliance is found to be nonapplicable, and in fact the steady-state recoverable compliance, J_e, is a strong function of temperature. The time-scale shift factors for the recoverable compliance are analyzed in the light of free volume theory. Viscosity data are presented for samples with molecular weights between 1.1 × 10³ and 6.0 × 10⁵. The temperature dependence of the characteristic time constant ηJ_e can be explained in terms of free volume concepts whereas that of viscosity η cannot. Effects of residual molecular weight heterogeneity are demonstrated.     

Flow birefringence and conformational characteristics of polyamide hydrazide molecules in dimethylsulphoxide

Flow birefringence (FB) and intrinsic viscosity of 19 samples of aromatic polyamide hydrazide (PAH) in dimethylsulphoxide (DMS), previously characterized by their weight-average molecular weights by the light scattering method, have been investigated. The molecular-weight dependence of reduced birefringence according to theory [12] was used to determine the optical anisotropy of a monomer unit Δa = (200 ± 20) 10^?25cm³ and the length of the Kuhn segment $\text{A = (250 ± 30)}\text{A}\text{?}$ of PAH molecules. The second independent evaluation of rigidity of the PAH chain $\text{A = (240 ± 30)}\text{A}\text{?}$ was obtained according to the theory of rotational friction of rigid wormlike chains by using the coefficients of rotational diffusion of PAH molecules determined from the characteristic values of orientation angles of FB. The value of rigidity of the PAH chain obtained by this method is in good agreement with the data on molecular dimensions obtained by light scattering.     

Molecular dimensions of polydipropylsiloxamer

The molecular dimensions of polydipropylsiloxamer were studied by intrinsic viscosity measurements in toluene and in 2-pentanone. The relationships between the molecualr weight and the intrinsic viscosity were found to be: [η]_25°C., toluene = 4.35 × 10^?4 M^0.58; [η]_θ(10°C.), toluene = 1.09 × 10^?3 M^0.5; [η]_θ(76°C.), 2-pentanone = 8.71 × 10^?4 M^0.5. This held reasonably well for molecular weights from 25,000 to 3000,000. The root-mean-square end-to-end length ratio, (r₀² /M)^1/2 as calculated from the constant K, exceeds the free rotation value by approximately 100%. The disparity is greater than that found with polydimethylsiloxamer, indicating a lower degree of flexibility for the polydipropylsiloxamer. This is largely due to the short range steric interaction between near neighboring units of the chain. Gel permeation chromatography was also employed to demonstrate the lower degree of flexibility for polydipropylsiloxamer as compared with polydimethylsiloxamer.     

Dilute solution properties of a polyurethane. I. Linear polymers

A linear polyurethane of high molecular weight was prepared in solution by the polyaddition of equimolar amounts of ethylene glycol and methylene bis(4-phenyl isocyanate). The polymer was fractionated by using a direct sequential extraction procedure, with a solvent–nonsolvent system consisting of N,N′-dimethylformamide (DMF) and acetone (A). The resulting fractions were characterized by viscosity and lightscattering measurements. The relationship between the intrinsic viscosity and molecular weight was found in DMF at 25°C. to be [η] = 3.64 × 10^?4M^0.71. The unperturbed polymer chain dimensions were determined from intrinsic viscosity measurements carried out under experimentally determined theta conditions.