Moderately concentrated solutions of polystyrene. I. Viscosity as a function of concentration,temperature, and molecular weight

Data on the viscosity η of moderately concentrated solutions of polystyrene are reported. Several solvents were investigated, including cyclopentane solutions over a temperature span between θ_U = 19.5°C and θ_L = 154.5°C. The data were analyzed in terms of a relation giving η as a function of αφM, where α_φ is the expansion factor for the chain dimensions in a solution with volume fraction φ of polymer with molecular weight M. It is shown that values of α_φ so determined decrease as ? lnα_φ/? lnφ = (1 ? 2μ)/6μ for φ greater than φ^* = 0.2M/s³ for moderately concentrated solutions, where s is the root-mean-square radius of gyration and μ = ? ln[η]/? lnM with [η] the intrinsic viscosity.     

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.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

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.     

Excluded volume study of a sulfonate-containing polyelectrolyte in salt solutions

Chain characteristics of a linear sulfonate-containing homopolymer, sodium poly(3-methacryloyloxypropane-1-sulfonate), in aqueous salt solutions (ionic strength, C_s = 0.01N to 5N NaCl) have been investigated by light scattering and intrinsic viscosity. The molecular weight (M?_w)–viscosity relation can be well described by the Mark–Houwink and the Stockmayer–Fixman equations. The coil is highly expanded even in the most concentrated NaCl solution (6N), and no 1:1 electrolyte was found to precipitate this polymer. A linear relation was observed between the viscosity expansion factor, α^3η, and (M?_w/C_s)^1/2. Examination of the data in terms of theories for excluded volume and hydrodynamic interaction suggests that the coil experiences dominant hydrodynamic interaction, corresponding to a nondraining coil, and the second virial coefficient and coil expansion at high C^s can be correlated by the Flory–Krigbaum–Orofino equation. Results for this polymer are compared with those for other polyelectrolytes, and are discussed in terms of chain structure, flexibility, and hydrophobicity.     

Chain dimensions and transport coefficients of sodium poly(isoprenesulfonate) in aqueous sodium chloride

Sodium poly(isoprenesulfonate) (NaPIS) fractions consisting of 1,4‐ and 3,4‐isomeric units (0.44:0.56) and ranging in molecular weight from 4.9 × 10³ to 2.0 × 10⁵ were studied by static and dynamic light scattering, sedimentation equilibrium, and viscometry in aqueous NaCl of a salt concentration (C_s) of 0.5‐M at 25 °C. Viscosity data were also obtained at C_s = 0.05, 0.1, and 1 M. The measured z‐average radii of gyration 〈S²〉_z^1/2, intrinsic viscosities [η], and translational diffusion coefficients D at C_s = 0.5‐M showed that high molecular weight NaPIS in the aqueous salt behaves like a flexible chain in the good solvent limit. On the assumption that the distribution of 1,4‐ and 3,4‐isomeric units in the NaPIS chain is completely random, the [η] data for high molecular weights at C_s = 0.5 and 1 M were analyzed first in the conventional two‐parameter scheme to estimate the unperturbed dimension at infinite molecular weight and the mean binary cluster integral. By further invoking a coarse‐graining of the NaPIS molecule, all the [η] and D data in the entire molecular weight range were then analyzed on the basis of the current theories for the unperturbed wormlike chain combined with the quasi‐two‐parameter theory. It is shown that the experimental 〈S²〉_z, [η], and D are explained by the theories with a degree of accuracy similar to that known for uncharged linear flexible homopolymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2071–2080, 2001     

Lateral thermal expansion of chitin crystals

Measurements of the thermal expansion coefficients (TECs) of chitin crystals in the lateral direction are reported. We investigated highly crystalline α chitin from the Paralithodes tendon and an anhydrous form of β chitin from a Lamellibrachia tube from room temperature to 250 °C, using X‐ray diffraction at selected temperatures in the heating process. For α chitin, the TECs of the a and b axes were α_a = 6.0 × 10⁻⁵ °C⁻¹ and α_b = 5.7 × 10⁻⁵ °C⁻¹, indicating an isotropic thermal expansion in the lateral direction. However, the anhydrous β chitin exhibited an anisotropic thermal expansion in the lateral direction. The TEC of the a axis was constant at α_a = 4.0 × 10⁻⁵ °C⁻¹, but the TEC of the b axis increased linearly from room temperature to 250 °C, with α_b = 3.0–14.6 × 10⁻⁵ °C⁻¹. These differences in the lateral thermal expansion behaviors of the α chitin and the anhydrous β chitin are due to their different intermolecular hydrogen bonding systems. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 168–174, 2001     

Upturn effect in the Non-Newtonian intrinsic viscosity of polymer solutions. II. Polyisobutylene in polybutene oil

With an increasing gradient, the intrinsic viscosity of a high molecular weight polyisobutylene (M?_n = 7 × 10⁶) in polybutene oil L.100 (η_s = 5 poise) first drops to a minimum and then rises again. The minimum occurs at β = M[η]₀η_sG/NkT = 240, which is about ten times the value predicted by the dumbbell model. Such a shift to larger gradient is in good agreement with the more realistic necklace model of macromolecules in a good solvent. The increase of intrinsic viscosity after the minimum is nearly linear with the gradient and continues beyond the value at zero gradient. Experiments with capillaries of different length-to-diameter ratios yield identical flow curves so that one may exclude the possibility that the observed upturn is an artifact caused by end effects or time dependence of viscosity.     

Polymerization of vinyl chloride with organolithium compounds. V. Fractionation and solution properties of high molecular weight poly(vinyl chloride)

A sample of high molecular weight poly(vinyl chloride) (PVC) was fractionated by classical precipitation fractionation and gel-permeation chromatography (GPC) on a preparative scale. The fractions thus obtained were characterized by light scattering, viscometry, and by the GPC method. The measured weight-average molecular weights M?_w, intrinsic viscosity [η], and polydispersity index M?_w/M?_n values were used for the determination of the Mark-Houwink equation, [η] = KM^a, for PVC in cyclohexanone (CHX) at 25°C valid for molecular weights from 100,000 to 625,000.     

“Experimentation and modeling for the apparent elongation viscosity of polymer melts with the White–Metzner model”

The measurement of the apparent elongation viscosity (η_e) of several polyolefin melts was conducted in this study by using the isothermal fiber‐spinning method. The White–Metzner (W–M) model was used to analyze the spinning flow of the polymer melts and, thus, the elongation viscosity was predicted at elongation strain rates ranging from 0 to approximately 5 s^?1. The values of the model parameters required in the W–M model were obtained by curve fitting the experimental data obtained from the shear measurements. The elongation viscosity predicted using the W–M model was in good agreement with the experimental results of fiber spinning. In addition, η_e could also be estimated directly from the measured shear viscosity (η_S) with a formulation using the W–M model; the subsequently obtained elongation viscosity and Trouton ratio (T_R) were reasonable within a wide range of strain rates. Based on the experimental and theoretical results, the polyolefin with a high molecular weight was observed to have high elongation viscosity, and the polymer with a broad molecular weight distribution also possessed high η_e. The T_R value of the commercial polypropylene (PP‐1040) began to increase from 3 at a deformation rate of 0.1 s^?1 and grew up asymptotically to 10, whereas the T_R of high‐density polyethylene (HDPE‐606) remained nearly at 3 within the entire range of strain rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Configuration and hydrodynamic properties of fully acetylated salep glucomannan

The polysaccharide of salep orchid tuber was shown to be a glucomannan with a glucose/mannose ratio of 2.6 and an acetyl content of 2.1%. After extraction from the powdered root with water, the triacetate derivative was prepared and its configurational and hydrodynamic properties examined. The polymer yielded a series of fractions from 615 to 4170 in weight-average degree of polymerization. Light-scattering, viscosity, and osmometry experiments were conducted. Intrinsic viscosity results were interpreted according to the hydrodynamic theory of Eizner and Ptitsyn resulting in a value of ζ/η₀ = 20 ± 6 A. for the ratio of monomeric friction coefficient to solvent viscosity and a corresponding value of a = 55 ± 4 A. for the persistence length, closely similar to those reported for other β-1,4-linked polysaccharides. The theoretical Flory coefficient increased with increasing molecular weight but was less than the limiting value of Φ₀ = 2.86 × 10²³ mole^?1. The dependence of the light-scattering radius of gyration of the glucomannan polymer on the contour length showed that the configuration of the heteropolymer was similar to that of other β-1,4-linked polysaccharides which have only glucose or mannose in the main chain. Calculated radii of gyration based on the Porod-Kratky persistence length were found to be smaller than radii found by light scattering on the fractions.     

Lateral thermal expansion of cellulose Iβ and IIII polymorphs

Measurements of the thermal expansion coefficients (TECs) of cellulose crystals in the lateral direction are reported. Oriented films of highly crystalline cellulose I_β and III_I were prepared and then investigated with X‐ray diffraction at specific temperatures from room temperature to 250 °C during the heating process. Cellulose I_β underwent a transition into the high‐temperature phase with the temperature increasing above 220–230 °C; cellulose III_I was transformed into cellulose I_β when the sample was heated above 200 °C. Therefore, the TECs of I_β and III_I below 200 °C were measured. For cellulose I_β, the TEC of the a axis increased linearly from room temperature at α_a = 4.3 × 10^?5 °C^?1 to 200 °C at α_a = 17.0 × 10^?5 °C^?1, but the TEC of the b axis was constant at α_b = 0.5 × 10^?5 °C^?1. Like cellulose I_β, cellulose III_I also showed an anisotropic thermal expansion in the lateral direction. The TECs of the a and b axes were α_a = 7.6 × 10^?5 °C^?1 and α_b = 0.8 × 10^?5 °C^?1. The anisotropic thermal expansion behaviors in the lateral direction for I_β and III_I were closely related to the intermolecular hydrogen‐bonding systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1095–1102, 2002     

Molecular weight influence on viscosimetric parameters of poly(4-vinylpyridine) polymers

This work describes the effect of the molecular weight on the viscosimetric parameters of poly(4-vinylpyridine) (P4VP) polymers in ethanolic solution. Numerous studies concerning this question have been reported in very separate intervals of molecular weight. We have observed a discordance (discontinuity) in the variation of the intrinsic viscosity as a function of the molecular weight of these polymers ([η]=f(M_w)). In order to establish a general relationship between viscosimetric parameters and M_w, we have considered 10 P4VP samples in a wide interval of molecular weights: 0.75×10⁴ to 153×10⁴. These results have been compared and completed with that of the literature. We have observed that:

(i)

All viscosimetric parameters (intrinsic viscosity [η], Huggins constant k_H, second virial coefficient, viscosimetric expansion coefficient α_η, and critical concentration) change according to a continuous function without a break.

(ii)

The lower is the molecular weight of P4VP; the higher are the variations of the expansion coefficient and the interaction effects.

(iii)

The variation of the intrinsic viscosity versus the molecular weight follows a unique relation in the whole M_w range. In fact, the Berkowitz equation (1), described for a limited range of relatively high M_w (10⁵ to 18.5×10⁵) is extended for all M_w interval values.

(iv)

Empiric laws for [η], k_H, A₂ and C^* and variations as a function of molecular weight were proposed for the P4VP in ethanol.

     

Generalized correlations for molecular weight and concentration dependence of zero-shear viscosity of high polymer solutions

Data are presented to show that two correlations of viscosity–concentration data are useful representations for data over wide ranges of molecular weight and up to at least moderately high concentrations for both good and fair solvents. Low molecular weight polymer solutions (below the critical entanglement molecular weight M_c) generally have higher viscosities than predicted by the correlations. One correlation is η_sp/c[η] versus k′[η], where η_sp is specific viscosity, c is polymer concentration, [η] is intrinsic viscosity, and k′ is the Huggins constant. A standard curve for good solvent systems has been defined up to k′[η]c ≈? 3. It can also be used for fair solvents up to k′[η]c ≈? 1.25· low estimates are obtained at higher values. A simpler and more useful correlation is η_R versus c[η], where η_R is relative viscosity. Fair solvent viscosities can be predicted from the good solvent curve up to c[η] ≈? 3, above which estimates are low. Poor solvent data can also be correlated as η_R versus c[η] for molecular weights below 1 to 2 × 10⁵.     

Mark-Houwink relations for linear polyethylene in 1-chloronaphthalene and 1,2,4-trichlorobenzene

The parameters in the Mark-Houwink relationship, [η] = K′M?_v^a, for linear polyethylene in 1-chloronaphthalene and 1,2,4-trichlorobenzene at 130°C have been estimated. They were found by measuring the limiting viscosity numbers of a series of fractions with molecular weights ranging from less than 10,000 to almost 700,000. The results are for 1-chloronaphthalene, [η] =0.0555 M?_v^0.684 (with a standard error of 0.0064 in K′ and 0.010 in a) and for 1,2,4-trichlorobenzene, [η] = 0.0392M?_v^0.725 (with a standard error of 0.00703 in K′ and 0.015 in a), where [η] is expressed in ml/g. The unperturbed end-to-end distance calculated from the viscosity-molecular weight data agrees with the theoretically expected value.     

X‐ray diffraction study of the thermal expansion behavior of cellulose triacetate I

Highly crystalline samples of cellulose triacetate I (CTA I) were prepared from highly crystalline algal cellulose by heterogeneous acetylation. X‐ray diffraction of the prepared samples was carried out in a helium atmosphere at temperatures ranging from 20 to 250 °C. Changes in seven d‐spacings were observed with increasing temperature due to thermal expansion of the CTA I crystals. Unit cell parameters at specific temperatures were determined from these d‐spacings by the least squares method, and then thermal expansion coefficients (TECs) were calculated. The linear TECs of the a, b, and c axes were α_a = 19.3 × 10^?5 °C^?1, α_b = 0.3 × 10^?5 °C^?1 (T < 130 °C), α_b = ?2.5 × 10^?5 °C^?1 (T > 130 °C), and α_c = ?1.9 × 10^?5 °C^?1, respectively. The volume TEC was β = 15.6 × 10^?5 °C^?1, which is about 1.4 and 2.2 times greater than that of cellulose I_β and cellulose III_I, respectively. This large thermal expansion could occur because no hydrogen bonding exists in CTA I. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 517–523, 2009     

Light-scattering characterization of poly(ethylene terephthalate)

By using a closed-circuit filtration system, we have succeeded in clarifying poly(ethylene terephthalate) (PET) dissolved in hexafluoroisopropanol (HFIP). Such static properties as the radius of gyration R_g, the weight-average molecular weight M_w, and the second virial coefficient A₂ and such dynamic properties as the translational diffusion coefficient D, or its equivalent hydrodynamic radius R_h, and the second (diffusion) virial coefficient k_d were determined for several PET samples of different molecular weights by using light-scattering intensity and linewidth measurements. An empirical relation between D_o (or R_h) and M_w was established: R_h = (1.77±0.15)X10^?2 M with R_h and M_w expressed in units of nanometers and grams per mole, respectively. The empirical exponent α_D(ca. 0.58±0.01) is in good agreement with the less precisely determined intrinsic viscosity/molecular weight exponent α_η (ca. 0.71±0.02). Several intensity correlation functions were measured very precisely using long accumulation times. A Laplace inversion was performed using the singular-value decomposition technique. The approximate molecular weight distribution (MWD) determined by light-scattering spectroscopy was in reasonable agreement with a completely independent determination of MWD using gel permeation chromatography (GPC). It was interesting to note, though not surprising, that GPC showed emphasis on lower-molecular-weight fractions, while light-scattering emphasized higher-molecular-weight fractions. The agreement further strengthens some complementary aspects of the two techniques.     

Intrinsic viscosity of polymers of low molecular weight

Experimental evidence concerning the dependence of the intrinsic viscosity [η] on molecular weight M in the low molecular weight range (from oligomers to M = 5 × 10⁴) has been collected in a variety of solvents for about ten polymers, i.e., polyethylene, poly(ethylene oxide), poly(propylene oxide), polydimethylsiloxane, polyisobutylene, poly(vinylacetate), poly(methyl methacrylate), polystyrene, poly-α-methylstyrene, and some cellulose derivatives. In theta solvents, the constancy of the ratio [η]Θ/M^0.5 extends down to values of M much lower than those predicted by current hydrodynamic theories. In good solvents, and on decreasing M, the polymers examined, with the exception of polyethylene and some cellulose derivatives, show a decrease in the exponent a of the Mark-Houwink equation [η] = KM^a. This upward curvature gives rise to the existence of a more or less extended linear region where the equation [η] = K₀M^0.5 is obeyed. Below the linear range, i.e., for even shorter chains, the exponent a can increase, i.e., polydimethylsiloxane, or decrease below 0.5, i.e., poly(ethylene oxide), depending on the particular chain properties. These different dependences have been discussed in terms of: (a) variations of thermodynamic interactions with molecular weight; (b) variations of conformational characteristics (as for instance the ratio) 〈r0²/nl²〉, where 〈r0²〉 is the unperturbed mean square end-to-end distance and n is the number of bonds each of length l; (c) hydrodynamic properties of short chains.     

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.     

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.