Moderately concentrated solutions of polystyrene. II. Integrated-intensity light scattering as a function of concentration,temperature, and molecular weight

Integrated-intensity light scattering data are reported for moderately concentrated solutions of polystyrene in benzene and in cyclopentane. The benzene system is one for which the second virial coefficient A₂ is large; data obtained over the range 0.5 < A₂Mc < 30, with c the polymer concentration, are analyzed in terms of the (extrapolated) intensity at zero angle and the angular dependence of the intensity. The former is discussed in terms of power law representations based on scaling relations, which are found to represent the data. The latter is discussed in terms of the dependence of the chain dimensions on concentration. With cyclopentane, the behavior is similar for temperatures for which A₂ is near its maximum, but for T near either Θ_U or Θ_L, for which A₂ is zero or small, the angular dependence of the scattering is distinctly different, with the intensity exhibiting a maximum as a function of scattering angle.     

Dependence of viscosity of polystyrene solutions on molecular weight and concentration

Viscosities of solutions of polystyrene in toluene were measured for concentrations up to 400 kg m^?3 at 298 K. Polymers of molecular weights ranging from 8.7 × 10³ to 2.4 × 10⁶ were used. It is observed that viscosity of the polymer solution increases with increasing concentration and molecular weight; the rate of increase is greater at higher values of the two parameters. A master curve for the system is constructed by using the experimental data for viscosity, concentration and molecular weight of the polymer. Regions of various polymer interactions in solution are identified.     

Dependence of viscosity of concentrated polymer solutions upon molecular weight and concentration

Molecular weight M and concentration c dependencies of the zero-shear viscosity (η) were measured over wide ranges of M and c for concentrated solutions of linear and branched poly(vinyl acetate) as well as of polystyrene under θ conditions. The log η versus log M and log η versus log c curves for a given system can be superposed by the horizontal shift along the abscissa, giving smooth master curves. From the shift factors the ratio of two exponents β and α, which appear in the following equation, can be evaluated: η = K′(cρ)^αM^β, where ρ is the density of the solution and K′ is a constant at constant temperature. The evaluated values of β/α for the systems under θ conditions are equal to or very close to 0.50 as was anticipated from the previous work. The above superposition method was also applied to available viscosity data, and it was found that β/α had a good correlation with a in [η] = KM^a. This indicates that the individual molecules in concentrated solutions maintain the same individuality as in dilute solutions, and might be a positive support to the packed sphere model proposed previously by the authors. The effect of solvent on the molecular weight and the concentration dependencies of viscosity was also discussed.     

Moderately concentrated solutions of polystyrene,part 5. Static and dynamic light scattering in bis(2-ethylhexyl) phthalate

Static and dynamic light scattering data are reported on dilute and moderately concentrated solutions of a high molecular weight polystyrene (M_w = 3.61 × 10⁶) in bis(2-ethylhexyl) phthalate under Flory Theta conditions. The data cover a concentration range with 0.03 × [η]c × 3.5, with several concentrations large enough that the product cM^w exceeds the value necessary for entanglement behavior. The results show that a certain intermolecular scattering function H(q, c) often approximated by unity should not be neglected in the evaluation of the correlation length in the static scattering from moderately concentrated solutions of flexible chain polymers. An approximate form for H(q, c) for moderately concentrated solutions is consistent with a soft spherically symmetric repulsive potential among the chains. The dynamic scattering show two distinct groups of relaxation rates at all concentrations, but the interpretation of the two modes changes as the concentration increases from low concentrations ([η]c < 1) to higher concentrations. At low concentrations the slower mode corresponds to mutual diffusion, and the faster mode to intramolecular dynamics. For concentrations with [η]c > 2.4 the slow mode is viscoelastic in origin, and the faster mode is diffusive. The behavior is compared with theoretical predictions in both regimes.     

Viscosity of concentrated solutions of polystyrene and poly(vinyl acetate) (empirical equations)

The viscosity of solutions of polystyrene with M _w from 2.8 × 10⁴ to 7.8 × 10⁵ in toluene and of poly(vinyl acetate) with M _w from 2 × 10⁴ to 1.4 × 10⁵ in butyl acetate at 30–80°C is measured. The dependence of the activation energy of the viscous flow of the solutions on the molecular weight of the polymers and solution concentration is examined. This dependence is approximated by a cubic polynomial for polystyrene solutions and by a quadratic polynomial for poly(vinyl acetate) solutions. The dependences of the solution viscosity on the concentration, molecular weight, and temperature are approximated by exponential equations in which the exponents are sums of polynomials. The coefficients of the polynomials are determined.     

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.     

The effect of concentration,temperature, and molecular weight on the dynamics of rigid-rod molecules in semi-dilute solutions

The dynamics of rigid-rod-like molecules are studied using rheo-optical techniques. Measurements of flow birefringence as a function of shear rate are utilized to understand the scaling behavior of rotational diffusivity with respect to concentration and temperature. The concentration scaling exponent increases with increasing concentration and the scaling laws are valid in narrow concentration windows. The Doi-Edwards (DE) scaling law D_r ∼ c⁻², holds at very high concentrations (cL³ > 150). The concentration scaling exponent decreases dramatically with increasing temperature at concentrations, cL²d > 1. Scaling of rotational diffusivity, with respect to temperature and solvent viscosity in the semidilute regime, does not follow the predictions of DE theory (and related caging ideas). On the contrary, a model proposed by Fixman was found to explain both the temperature and concentration dependence of the rotational diffusivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 181–190, 1998     

Effect of temperature and molecular weight on enthalpy relaxation in polystyrene

Isothermal enthalpy relaxation in polystyrene was measured as a function of temperature and molecular weight on a differential scanning calorimeter. Relaxation spectra were derived from the data and expressed as a distribution of relaxation times. For a given molecular weight the relaxation spectra at different temperatures could not be superimposed by a shift in time. The relaxation curves of samples of different molecular weights could be superimposed only when the difference between the temperature at which the relaxation was monitored (T_a) and their respective T_g was the same. The relaxation spectrum at any temperature for a given molecular weight was also expressed as a distribution of energies. The average energy represented by this distribution was associated with an activation energy required for the motion of a chemical repeat unit. The activation energy extracted from the temperature shift in the relaxation spectra corresponded to the motion of a statistical unit (Kuhn's segment) in polystyrene.     

Product distribution of peroxynitrite decay as a function of pH, temperature, and concentration.

The decay of peroxynitrite [O=NOO(-), oxoperoxonitrate(1-)] was examined as a function of concentration (0.050-2.5 mM), temperature (5-45 degrees C), and pH (2.2-10.0). Below 5 degrees C and pH 7, little amounts of the decomposition products nitrite and dioxygen are formed, even when the peroxynitrite concentration is high (2.5 mM). Instead, approximately > or =90% isomerizes to nitrate. At higher pH, decomposition increases at the expense of isomerization, up to nearly 80% at pH 10.0 at 5 degrees C and 90% at 45 degrees C. Much less nitrite and dioxygen per peroxynitrite are formed when the peroxynitrite concentration is lower; at 50 microM and pH 10.2, < or =40% decomposes. In contrast to two other reports (Pfeiffer, S.; Gorren, A. C. F.; Schmidt, K.; Werner, E. R.; Hansert, B.; Bohle, D. S.; Mayer, B. J. Biol. Chem. 1997, 272, 3465-3470, and Coddington, J. W.; Hurst, J. K.; Lymar, S. V. J. Am. Chem. Soc. 1999, 121, 2438-2443), we find that the extent of decomposition is dependent on the peroxynitrite concentration.     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

Polarized and depolarized dynamic light scattering of concentrated polystyrene solutions

Polarized and depolarized dynamic light scattering have been used to examine the dynamics of concentrated polystyrene solutions in dioctyl phthalate and toluene. Time-temperature superposition of the depolarized intensity correlation functions gave master curves covering more than 10 decades on the time scale. Polarized correlation functions are resolved into relaxational and diffusive components having different temperature dependences. When the relaxation rate of the concentration fluctuations approaches the reorientational relaxation rate, the concentration fluctuations become q-independent i.e. the diffusional relaxation is rate-determined by the backbone mobility. With a small molecule solvent as toluene, however, a part of the concentration fluctuations relaxes faster than the orientational relaxation, i.e., the diffusion occurs in the free volume within the “frozen” network.     

Molecular sieving of lambda phage DNA in polyacrylamide solutions as a function of the molecular weight of the polymer.

Electrophoresis of lambda phage DNA was carried out in solutions at various concentrations of uncrosslinked polyacrylamide of 0.6, 1, 5 and 9 x 10(6) molecular weight (Mw) with narrow Mw distribution. By inspection of mobilities in the various concentration ranges, it appears that mobilities decrease, and retardation increases, with increasing Mw. The relation between electrophoretic retardation and the Mw of the polymer was also interpreted (i) in the manner previously applied to nonlinear Ferguson plots and compatible with the Ogston model; and (ii) empirically, on the basis of the first derivatives of the functions describing the Ferguson plots at the polymer concentrations used. Interpretation (i) shows that the retardation increases linearly in the order of 0.6, 1, 5 and 9 x 10(6) Mw of polyacrylamide. Interpretation (ii) shows a nonlinear increase of retardation in the Mw range 5 to 9 x 10(6), and a decrease in retardation as Mw is raised from 0.6 to 5.0 x 10(6). Hypothetically, interpretation (ii) can be explained mechanistically by a progressive change, as the polymer size is increased, from a collision with the surface of the polymer fiber to one occurring after permeation in the interior of a random-coiled fiber. Interpretation (i) may fail to detect that change due to the large difference between DNA mobility in solutions of the smallest polymer and the free mobility. DNA peak detection in all of the four size classes of polyacrylamide in solution is limited to relatively narrow ranges of polymer concentration.(ABSTRACT TRUNCATED AT 250 WORDS)     

Rheological studies of moderately concentrated polystyrene solutions. I. A new method for the extrapolation of the zero-shear viscosity

Measurements of the viscosity coefficient η of solutions of polystyrene (M_w = 6.0 × 10⁵ and 1.77 × 10⁶) in trans-decalin (TD, θ solvent) and toluene (TL, good solvent) as function of shear rate (11?10⁴ s^?1), concentration (4.24?11.21 wt %), and temperature (10–50°C) are reported. As a new theoretically grounded method for the determination of the zero-shear viscosity η₀ it is proposed to plot η as a function of $\left({\eta \dot \gamma} \right)^3$. The intercepts of the straight lines obtained by this procedure give η₀ in good agreement with directly measured values.     

Adsorption of gelatin to a polystyrene/water interface as a function of concentration, pH, and ionic strength

The technique of neutron reflection has been used to investigate the adsorption of alpha-enriched gelatin from aqueous solution onto spun polystyrene substrates. Neutron reflection can provide information about the distribution of material perpendicular to an interface as well as total adsorbed amounts. The adsorbed layers were found to have maximum density at the surface, decaying with distance into solution. The adsorbed amount, layer thickness, and density were all seen to increase with solution concentration. Temperature was found to have little effect on adsorption. Thicker, less dense layers were observed at high pH and thinner, denser layers were observed at low pH, but the total adsorbed amount did not change significantly. The presence of sodium chloride had little effect on the adsorbed layers. The results are discussed in the context of other studies and the known amino acid sequence of alpha-gelatin.     

Viscosity of poly(vinyl acetate) and its concentrated solutions

Data on the viscosity of poly(vinyl acetate) (PVOAc) and its concentrated solutions in diethyl phthalate (DEP) and cetyl alcohol (CeOH) are examined over the molecular weight range 8 × 10³ < M < 1.3 × 10⁶, the range 0.15 < φ < 1.0 of the volume fraction φ of polymer, the temperature range 308 to 430°K for PVOAc and its solutions in DEP, and at 396°K in CeOH. The latter is the θ temperature for dilute solutions of PVOAc in CeOH. The data are analyzed with the relation η = KX_c(αφM/M_c)^a exp[1/β(T – T₀)], where a is 1 or 3.4 for αφM less than or greater than a constant M_c, respectively, and X_C, is a constant. The expansion factor α_φ of the chain dimension is found to be essentially unity for φ > ca. 0.25, increasing with decreasing φ for smaller φ. Both β and T₀ depend on φ, and T₀ also depends on M at low M.     

Polymerization beyond the gel point. I. The molecular weight of sol as a function of the extent of reaction

Theoretical expressions for describing the weight-average molecular weights of the soluble fractions from polymerizations obtained beyond the gel point were tested experimentally. The theory of branching processes and a recursive approach essentially based on the method of Macosko and Miller were found to be virtually equivalent. The soluble fractions produced from the stoichiometric polymerization of 1,3,5-benzenetriacetic acid (BTA) with decamethylene glycol (DMG) gave molecular weights and distributions in excellent qualitative agreement with the theory. The results are interpreted in terms of intramolecular cyclization, diffusion, and the presence of microgel particles.     

The drawing behavior of linear polyethylene. I. Rate of drawing as a function of polymer molecular weight and initial thermal treatment

The drawing behavior of a series of linear polyethylene homopolymers with weight-average molecular weight (M?_w) ranging from 67,800 to ～3,500,000 and variable distribution (M?_w/M?_n = 5.1?20.9) has been studied. Sheets were prepared by two distinct routes: either by quenching the molten polymer into cold water or by slow cooling below the crystallization temperature (～120°C) followed by quenching into cold water. When the samples (2 cm long) were drawn in air at 75°C using a crosshead speed of 10 cm/min it was found that for low M?_w polymers the initial thermal treatment has a dramatic effect on the rate at which the local deformation proceeds in the necked region. At high M?_w such effects are negligible. An important result was that comparatively high draw ratios (λ > 17) and correspondingly high Young's moduli could be obtained for a polymer with M?_w as high as 312,000. It is shown how some of the structural features of the initial materials (mainly studied by optical microscopy, small-angle x-ray scattering and low-frequency laser Raman spectroscopy) can be interpreted in terms of the molecular weight and molecular weight distribution of the polymers. Although crystallization and morphology can be important at low M?_w, it suggested that the concept of a molecular network which embraces both crystalline and noncrystalline material is more helpful in understanding the drawing behavior over the whole range of molecular weights.