Pressure dependence of the second virial coefficient of dilute polystyrene solutions

The pressure derivatives of the second virial coefficients [dA₂/dP; 0.1 ≤ P (MPa) ≤ 35.0] for dilute polystyrene (PS) solutions in good, θ, and poor solvents were measured with static light scattering. The solvent quality improved (dA₂/dP > 0) in the good and poor solvents that we investigated (toluene, chloroform; and methylcyclohexane) but deteriorated (dA₂/dP < 0) in θ solvents (cyclohexane and 50‐50 cis,trans‐decalin). The effects of temperature [22 < T (°C) < 45] and molecular weight [25 × 10³ < weight‐average molecular weight (amu mol^?1) < 900 × 10³] on dA₂/dP for PS/cyclohexane solutions were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3070–3076, 2003     

Time dependence of viscosity of dilute polyisobutylene solutions

Summary Shearing at constant gradient of polyisobutylene (PIB) solutions in viscous polybutene oils results in time dependent changes of their viscosities. Two PIB fractions (M=8·10⁶ and 3.8·10⁶) have been studied in a variety of solvents, covering the viscosity range from 5 to 0.5·10⁻² poise. The overall phenomenon is similar to that already observed for polymethylmethacrylate, polystyrene, and polyethylene oxide solutions in Aroclor. Results have been discussed in terms of polymer molecular weight and concentration, solvent viscosity and gradient. The systems investigated are free from strong polar interactions and tendency toward molecular aggregation; time dependent changes of viscosity are therefore observable also for true molecularly dispersed solutions.

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Zusammenfassung Scherung mit konstantem Geschwindigkeitsgradienten von Polyisobutylen (PIB)-L?sungen in viskosen Polybuten-?len ergibt zeitabh?ngige ?nderungen ihrer Viskosit?ten. Zwei PIB-Fraktionen (M=8·10⁶ und 3,8·10⁶) wurden in einer Vielzahl von L?sungsmitteln untersucht, die den Viskosit?tsbereich von 5 bis 0,5·10⁻² Poise überdeckten. Das ph?nomenologische Erscheinungsbild ist ?hnlich dem schon beobachteten für Polymethylmethacrylat, Polystyrol und Poly?thylenoxid-L?sungen in Aroclor. Die Ergebnisse wurden hinsichtlich des Polymer-Molekulargewichts und der Konzentration, der L?sungsmittelviskosit?t und des Gradienten diskutiert. Die untersuchten Systeme sind frei von starken polaren Wechselwirkungen und von Tendenzen in Richtung auf molekulare Aggregation. Zeitabh?ngige ?nderungen der Viskosit?t sind deshalb auch für wahre molekulardisperse L?sungen beobachtbar.

     

Temperature dependence of the viscosity of dilute poly(β-naphthyl methacrylate) solutions

The temperature dependence of the actual viscosity of dilute poly(β-naphthyl methacrylate) solutions was described by an Arrhenius expression according to Moore's treatment. The apparent activation energy of flow was found to be lower for solutions in benzene, toluene and tetralin than for solvent. In dioxane, a good solvent, the activation energy was nearly constant and close to that for the solvent. The pre-exponential terms were, in all cases, higher for solutions than for the solvents. The decrease in activation energy and increase in pre-exponential term are largely dependent on solvent power: the maximum effect is found in the poorest solvent. This behaviour is discussed in connection with the temperature dependence of the Mark-Houwink and of the Fox-Flory constants obtained from intrinsic viscosity data: the differences in the activation energy of flow and in the pre-exponential term between the solvent and the solutions are related to variation of coil expansion with temperature.     

Pressure dependence of viscosity

We reanalyze the pressure dependence of viscosity of liquids of constant composition under isothermal conditions. Based exclusively on very general considerations concerning the relationship between viscosity and "free volume," we show that, at moderate values of pressure, viscosity increases, as a rule, with increasing pressure, provided the liquid is in stable or metastable (undercooled) equilibrium states. However, even if the behavior of the viscosity is governed by free volume effects, deviations from a positive pressure dependence are possible, when the liquid's thermal expansion coefficient is negative. We derive an equation that allows one to quantitatively determine the pressure dependence of viscosity, which requires, in the simplest case, only the knowledge of the temperature dependence of viscosity at constant pressure, the thermal expansion coefficient, and the isothermal compressibility of the liquid. As an example, the negative pressure dependence of water in the range of temperatures 0-4 degrees C and of several silicate liquids, such as albite, jadeite, dacite, basalts, etc., could be explained in such a way. Other glass-forming liquids initially (for moderate pressures) show a positive pressure dependence of viscosity that changes to a negative one when subjected to high (approximately GPa) isostatic pressure. A detailed analysis of water and already mentioned silicate melts at GPa pressures shows that, in addition to free volume effects, other pressure induced structural transformations may have to be accounted for in a variety of cases. By this reason, the theoretical analysis is extended (i) in order to describe the pressure dependence of viscosity for systems that are in frozen-in thermodynamic nonequilibrium states (glasses, i.e., undercooled liquids below the glass transition temperature Tg) and (ii) to systems which undergo, in addition to variations of the free volume, pressure induced changes of other structural parameters. In such cases a decrease of viscosity with increasing pressure may occur, in principle, even if the thermal expansion coefficient is positive. In this way, the present analysis grants a general tool to estimate the pressure dependence of viscosity and supposedly settles the controversy in the current literature.     

Acoustic absorption and dynamic compressibility studies of dilute and concentrated solutions of polystyrene in toluene and cyclohexane

Acoustic absorption and adiabatic compressibility measurements are reported on solutions of polystyrene (M_n = 89,000) in toluene and cyclohexane. The data in toluene cover a temperature range from 293 to 343°K and a concentration range of 10–400 Kg m^?3 (1–40 wt%). The dependence of acoustic absorption on concentration was found to be linear up to 100 kg m^?3, which corresponds to the concentration at which polymer–polymer interactions cause significant changes in the specific viscosity-concentration relationship. Up to 200 kg m^?3 the data could be fitted to computations based on an artificial separation of the dispersion into contributions from viscoelastic and segmental processes, using parameters obtained from a study of narrow molecular weight distribution samples at 25 kg m^?3. However, neither approach was capable of describing dispersions in the 300, 400 kg m^?3 solutions. The modification of the relaxation spectrum observed at the highest concentrations is ascribed to volume and entropy changes associated with alterations of the local environment around a segment of the polymer chain. These changes have their origin in interchain penetration and polymer–polymer contacts, and indicate that ‘entanglement’ is primarily entropic in effect. The adiabatic compressibility exhibited similar deviations from a simple concentration dependence, and allowed estimation of an incompressible volume increment associated with polymer–polymer interactions in the high-concentration entangled matrix. However, the adiabatic compressibilities of solutions of polystyrene, 10–15 kg m^?3, in cyclohexane showed no deviations from simple behavior in the region of the theta temperature. Measurements of the adiabatic compressibility of polystyrene in mixtures of cyclohexane-toluene have been used to obtain the relative magnitude of solvent and polymer contributions to the excess compressibility.     

Temperature dependence of the conformation of isotactic polystyrene in toluene

In order to obtain information about a possible helix–coil transition of isotactic polystyrene (i-PS) at 80°C in toluene, as has been reported in other solvents, solution properties were examined at temperatures between 10 and 110°C. Use was made of viscometry, high-resolution nuclear magnetic resonance, infrared spectroscopy, calorimetry, and light scattering. No distinct transition was found at 80°C but rather a second-order transition between 62 and 65°C. A similar transition occurred in toluene solutions of atactic polystyrene. The transition may be attributed to a sudden change in the mobility of the phenyl side-group of the polymer. From this study it is concluded that i-PS has a helical conformation in toluene, the mean helix length decreasing smoothly with increasing temperature.     

Crystallization of isotactic polystyrene from dilute solutions

The overall rate of crystallization of isotactic polystyrene from dilute solutions, 1% by weight, in trans-decalin and benzyl alcohol was studied as a function of temperature using dilatometry. These solvents were chosen because the dissolution temperatures of crystalline isotactic polystyrene are practically the same in both solvents. The overall rate of crystallization as a function of crystallization temperature showed a maximum in both solvents at about 50°C. At lower crystallization temperatures the rate of crystallization is much lower. The overall rate of crystallization of isotactic polystyrene in benzyl alcohol is far larger than in trans-decalin at the same undercooling throughout the temperature range, which is in apparent contradiction to present crystallization theories. At very large undercooling (T_c lower than about 0°C) the solutions of isotactic polystyrene in both solvents quickly become “rigid” gels. Surface replicas of freeze-etched gels indicate that a fringed micelle type of crystallization takes place at these low temperatures. The transition from folded chain crystallization to fringed micelle crystallization may be due to a stiffening of the polymer chain below about 50°C, with a reduced rotational mobility of the phenyl groups on the chain. If very dilute solutions, below 0.5% by weight, are crystallized at these low temperatures no gels were formed but fibrous crystals are produced which could be observed under the polarizing microscope.     

Viscosimetric study of polystyrene polymacromonomer dilute solutions

The viscosimetric behaviour of poly(ω-norbornenyl polystyrene) polymacromonomers is studied in dilute solutions as a function of the degree of polymerisation and the branch molar mass. We emphasise the fact that the exact molar mass characterisation using scattering techniques is illusory, owing to a strong intermolecular contribution in the scattering distribution, as evidenced by neutron scattering. Two characteristic behaviours are evidenced in the viscosimetric dependence versus molar mass of the polymacromonomer and are attributed to their global conformation when they could be considered as spherically or cylindrically symmetric. Moreover for the branch of higher molar mass used an unexplained deviation appears between the two behaviours. Received: 6 May 2000 Accepted: 6 September 2000     

Degradation on freezing dilute polystyrene solutions in p-xylene

Chain scission was observed during the crystallization of p-xylene in dilute polystyrene solutions. Degradation yields were determined by gel permeation chromatography, as a function of the number of freeze-and-thaw cycles, polymer concentration, and initial polymer molecular weight (M). The rate constant for chain scission K_c increases with the polymer chain length, from 0.021%/cycle at M = 110·10³ to 4.7%/cycle at M = 8.5·10⁶. Over the two decades range of investigated molecular weights, K_c follows an empirical scaling law of the form K_c ～ (M ? M_lim)^1.17578, where M_lim is a limiting molecular weight ? 29,000 g. mol^?1 below which no degradation could be induced. Some propensity for midchain scission was detected, although this tendency was much weaker in comparison to flow-induced degradation. A chain scission model based on crack propagation failed to reproduce the experimental results. To explain the observed dependence of K_c with the square of the radius of gyration, an interfacial stress transmission mechanism between the crystallization fronts and the polymer coil has been proposed. © 1994 John Wiley & Sons, Inc.     

Analysis of viscosity abnormalities of polyelectrolytes in dilute solutions

It was found that the interface effects in viscous capillary flow influenced the process of viscosity measurement greatly,and the abnormal viscosity behaviors of polyelectrolytes as well as neutral polymers in dilute solution region were ascribed to interface effect.According to this theory,we have reviewed the previous viscosity data of derivatives of poly-2- vinylpyridine reported by Maclay and Fuoss first.Then,the abnormal viscosity behaviors of a series of sodium polystyrene sulfonate samples with various molecular weights in dilute aqueous solutions were studied further.The solute adsorption behaviors and structural information of polymers have been discussed carefully.     

Counterion and solvent effects on the dilute solution viscosity of polystyrene ionomers

We present an analysis of data on the intrinsic viscosity [η] of sulfo-polystyrene ionomers in several solvents for a variety of sulfonation levels and counterions. For solvents of low dielectric constant, 2 < ε < 18, [η] decreases from the base polymer value [η]₀ with increasing substitution level. This behavior was attributed to intramolecular association of ionic dipoles. The ratio [η]/[η]₀ was found to depend on a single reduced variable α_Aα_Sx, where x is the fractional substitution, α_A depends only on the counterion, and α_S ∝ ε^?1 depends only on the solvent. For solvents of high dielectric constant, 36 < ε < 47, [η] increases approximately as x³, and counterion effects are small. This behavior was attributed to ionic dissociation, giving rise to a polyelectrolyte effect. Implications of the low ε results are discussed in relation to association-induced gelation behavior and possible generalizations of the reduced variables approach.     

Concentration dependence of the diffusion coefficient of polydisperse polystyrene in dilute solution

The concentration dependence of the diffusion coefficients (D) of two different polystyrenes in toluene was measured. The concentration dependence of D of a standard monodisperse sample (M = 498,000) for concentrations up to 1 · 25 g/dl is not linear. The dependence is adequately described by the theory of dilute polymer solutions up to about 0·7 g/dl and the second virial coefficients of the osmotic pressure can be evaluated. For a polystyrene sample having a broad molecular weight distribution, the concentration dependence of four different average diffusion coefficients was determined so indirectly characterizing the molecular weight distribution. These dependences are not linear and differ from each other owing to the different sensitivity of the individual averages to high-molecular and low-molecular weight fractions. The apparent distribution of the diffusion coefficients becomes narrower with increasing concentration. When evaluating polydispersity from the free diffusion data obtained in good solvents, it is necessary to determine directly the differential diffusion coefficients; an extrapolation of the integral diffusion coefficients can be misleading.     

Conformation analysis of freeze-dried isotactic polystyrene from dilute solutions

Fourier transform infrared spectra of freeze-dried samples of isotactic polystyrene (i-PS) from dilute solutions were analyzed. The 698, 1452, 1493 and 1601 cm⁻¹ bands increased in sharpness and intensity as the solution concentration decreased, indicating that the freeze-dried sample is in a more dilated state. When the freeze-dried i-PS was annealed at 100°C, all aforementioned bands broadened and their heights depressed, accompanied with a significant change of the bands at 981 and 906 cm⁻¹.     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006     

Thermal diffusion of dilute polymer solutions: the role of solvent viscosity

We have performed measurements of the thermal diffusion coefficient D(T) in the dilute limit on polystyrene in cyclo-octane, cyclohexane, benzene, toluene, tetrahydrofuran, ethyl acetate, and methyl ethyl ketone and of poly(dimethyl-siloxane) in toluene. These data have been combined with literature data to test various theoretical predictions. The viscosity is identified as the dominating and only relevant solvent parameter. On the polymer side, the size or mass of an effective correlated segment determines the strength of the Soret effect. Large and heavy effective segments, as found in stiffer chains, lead to higher D(T).     

Concentration dependence of ionic transport in dilute organic electrolyte solutions

Ion transport is studied in dilute organic liquid electrolyte solutions in which close cation-anion interactions are minimized either through steric hindrance imposed by the bulky tetrabutylammonium cation or by strong solvation of alkali metal cations by DMSO or 1-propanol. In these solutions, the molar conductivity does not appear to depend on either the solvent viscosity or the size of the solvated charge carrier in a manner consistent with Walden's rule. The molar conductivities plotted as a function of the solvent dielectric constant from epsilon = 5.48 to 63.5 appear to lie on a smooth curve for a set of 0.0055 M solutions of tetrabutylammonium trifluoromethanesulfonate in a variety of aprotic solvents. The molar conductivity smoothly increases with increasing dielectric constant to a maximum at roughly epsilon = 33 and then decreases with further increase of the dielectric constant. The conductivity appears to depend only on the dielectric constant and not the specific functional group in this broad family of solvents. A similar plot for a series of linear alcohols as solvents also led to a smooth curve, although the values of the molar conductivity were lower than values in the aprotic solvents by almost an order of magnitude at corresponding values of the solvent dielectric constant.     

Incompatibility of polymer solutions. II. Concentration and angle dependence of the light scattering in the system polystyrene + polyisobutylene + toluene

Light scattering experiments are described on the system polystyrene (PS) + polyisobutylene (PIB) + toluene at constant temperature. At a fixed concentration of the nearly “invisible” PIB the light scattering at various angles was measured as a function of varying PS concentration up to the region of incompatibility. For interpretation of the results use is made of an extension of the classical fluctuation theory for multicomponent systems to finite scattering angles. The experimental data can be described qualitatively with this theory. Addition of a second polymer has little influence on the size of the other polymer. The variation of the light scattering with the wavelength can be explained in terms of the (negative) adsorption of one polymer by the other.