Dynamic mechanical properties of moderately concentrated polystyrene solutions

The storage (G′) and loss (G″) shear moduli have been measured in the frequency range from 0.04 to 630 Hz for solutions of narrow distribution polystyrenes with molecular weights (M) 19,800 to 860,000, and a few of poly(vinyl acetate), M = 240,000. The concentration (c) range was 0.014–0.40 g/ml and the viscosities of the solvents (diethyl phthalate and chlorinated diphenyls) ranged from 0.12 to 70 poise. Data at different temperatures (0–40°C) were combined by the method of reduced variables. Two types of behavior departing from the usual frequency dependence describable by the Rouse-Zimm-Tschoegl theories were observed. First, for M ? 20,000, the ratio (G″ ? ωη_s)/G′ in the neighborhood of ωτ₁ = 1 was abnormally large and the steady-state compliance J was abnormally small, especially at the lowest concentrations studied. Here ω is circular frequency, η_s solvent viscosity, and τ₁ terminal relaxation time. Related anomalies have been observed by others in undiluted polymers at still lower molecular weights. Second, at the highest concentrations and molecular weights, a “crossover” region of the logarithmic frequency scale appeared in which G″ ? ωη_s < G′. The width of this region is a linear function of log c; the frequency dependence under these conditions can be represented by a sequence of Rouse relaxation times grafted on to a sequence of Zimm relaxation times. For each molecular weight, the terminal relaxation time τ₁ was approximately a single function of c for different solvents of widely different η_s. At lower concentrations, τ₁ was close to the Rouse prediction of 6ηM/π²cRT, where η is the steady-flow viscosity; but at higher concentrations, τ₁ was proportional to η/c² and corresponded, according to a recent theory of Graessley, to an average molecular weight of 20,000 between entanglement coupling points in the undiluted polymer.     

RADIATION CROSSLINKING OF BRANCHED POLY (VINYL ACETATE)

In the present work, radiation crosslinking of different branched poly (vinyl acetate) have beemstudied and the validity of the relationship between sol fraction and radiation dose: R(S+S~(1/2)=1/U_(1qo)+p′_o/q_oR~βto branched poly(vinyl acetate) have been assured.     

Viscoelasticity of nanobubble‐inflated ultrathin polymer films: Justification by the coupling model

The nanobubble inflation method is the only experimental technique that can measure the viscoelastic creep compliance of unsupported ultrathin films of polymers over the glass–rubber transition zone as well as the dependence of the glass transition temperature (T_g) on film thickness. Sizeable reduction of T_g was observed in polystyrene (PS) and bisphenol A polycarbonate by the shift of the creep compliance to shorter times. The dependence of T_g on film thickness is consistent with the published data of free‐standing PS ultrathin films. However, accompanying the shift of the compliance to shorter times, a decrease in the rubbery plateau compliance is observed. The decrease becomes more dramatic in thinner films and at lower temperatures. This anomalous viscoelastic behavior was also observed in poly(vinyl acetate) and poly (n‐butyl methacrylate), but with large variation in the change of either the T_g or the plateau compliance. By now, well established in bulk polymers is the presence of three different viscoelastic mechanisms in the glass–rubber transition zone, namely, the Rouse modes, the sub‐Rouse modes, and the segmental α‐relaxation. Based on the thermorheological complexity of the three mechanisms, the viscoelastic anomaly observed in ultrathin polymer films and its dependence on chemical structure are explained in the framework of the Coupling Model. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

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.     

Zero shear viscosity in miscible polymer blends of polystyrene and poly(2,6-dimethylphenylene ether)

The dynamic viscosities of blends of high molecular weight, narrowmolecular-weight distributed polystyrene and poly(2, 6-dimethylphenylene ether) are studied. The zero shear viscosity η_o depends on the weight average molecular weight M̄_w and on the average entanglement molecular weight M̄_e in the blend according to η_o ≈︁ M̄^3.4 _w(blend)/M̄^2.4_e(blend).     

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.     

Interpretation of differences in temperature and pressure dependences of density and concentration fluctuations in amorphous poly(phenylmethyl siloxane)

Differences in the temperature and pressure dependences of the relaxation times of a slow diffusional process and the α structural relaxation pose an interesting problem. This feature, observed by dynamic light scattering in amorphous poly(phenylmethyl siloxane), is related to another basic feature of lack of thermorheological simplicity discovered by Plazek in polystyrene, poly(vinyl acetate), and amorphous polypropylene. A quantitative explanation based on the predictions of a general coupling theory of relaxations has been found. The coupling theory also predicts the Kohlrausch fractional exponential time correlation function exp[?(tτ^*)^1?n] at long times, as observed by photon correlation spectroscopy, and crossover to an exponential time dependence exp–(t/τ₀) at short times, as frequently assumed in Brillouin scattering. An additional relation between τ^* and τ₀ predicted by the theory is confirmed also by the experimental data.     

Stress overshoot of polymer solutions at high rates of shear

Overshoot of shear stress, σ, and the first normal stress difference, N₁, in shear flow were investigated for polystyrene solutions. The magnitudes of shear corresponding to these stresses, γ_σm and γ_Nm, for entangled as well as nonentangled solutions were universal functions of γ˙τ_eq, respectively, and γ_Nm was approximately equal to 2γ_σm at any rate of shear, γ˙. Here τ_eq = τ_R for nonentangled systems and τ_eq = 2τ_R for entangled systems, where τ_R is the longest Rouse relaxation time evaluated from the dynamic viscoelasticity at high frequencies. Only concentrated solutions exhibited stress overshoot at low reduced rates of shear, γ˙τ_eq < 1. The behavior at very low rates, γ˙τ_eq < 0.2, was consistent with the Doi–Edwards tube model theory for entangled polymers. At high rates, γ˙τ_eq > 1, γ_σm and γ_Nm were approximately proportional to γ˙τ_eq. At very high rates of shear, the peak of σ is located at t = τ_R, possibly indicating that the polymer chain shrinks with a characteristic time τ_R in dilute solutions. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1917–1925, 2000     

Strain criterion in nonlinear creep and recovery in concentrated polymer solutions

Transient and steady-state rheological data are reported for several anionic polystyrene solutions in tritolylphosphate (1. 6 < cM/ρM_c < 7). Here c is the concentration of the solution, M is the molecular weight, ρ the density of the undiluted polymer, and M_c the molecular weight between entanglements as determined from zero-shear viscosity. The polystyrene used had M_w = 410,000 and M_w/M_n < 1.06. Data are also given for solutions of polyisobutylene and poly(vinyl acetate) with larger M_w/M_n. The results give a critical strain γ′ ∝ c⁻¹ such that linear viscoelastic behavior was obtained in a simple shear deformation with shear less than γ′. A simplified version of the constitutive equation of Bernstein, Kearsley, and Zapas is used with an empirical strain function F (γ) which contains γ′ as a parameter to discuss transient and steady-state behavior in terms of the distribution of relaxation (or retardation) times determined for linear viscoelastic responce. Features of the dependence of the steady-state viscosity η_k, recoverable compliance R_k, the first-normal stress function N_k⁽¹⁾ on shear rate k are discussed in terms of F (γ) and the distribution of relaxation times to conclude that the latter plays a dominant role in the behavior observed in the range of k usually studied. The results predict that the reduced functions η_k/η₀, R_k/R₀, and N_k⁽¹⁾/N₀⁽¹⁾ should depend on η₀R_0k, and that the functional form depends markedly on the distribution of relaxation times, at least in the range η₀R₀k < 10². Comparison with the mechanistic model of Doi and Edwards shows a similar F (γ) but substantial differences in the reduced functions caused by a very narrow distribution of relaxation times in the model.     

Grafting of monodisperse low-molecular-weight polystyrene onto cellulose acetate

Well-defined low-molecular-weight polystyrene was grafted onto cellulose acetate in a homogeneous solution. The grafting was performed by esterifying the free hydroxyls in the cellulose acetate (acetyl DS 2.5) with anionically prepared polystyrene having a carboxylic acid group at one end of the chain. The carboxylic acid end group of the polystyrene was activated by either conversion to the corresponding acid chloride, or by reaction with trifluoroacetic anhydride. Pyridine and the more active 4-dimethylaminopyridine were used as catalysts in the esterifications. The polystyrene contents of the copolymers varied between 10 and 80% and the molecular weights of the polystyrene grafts were 2500, 12,100 and 17,100 (M?_w/M?_n = 1.1).     

Gel-permeation chromatography: X. Molecular weight detection by low-angle laser light scattering

Effluent from a gel-permeation chromatographic column has been simultaneously and continuously monitored with a differential refractometer and a low-angle laser light-scattering (LALLS) photometer. This provides a true and direct determination of molecular weight distribution rather than through a calibration method as obtained by conventional GPC techniques. Computer assisted data reduction provides a rapid determination of M?_w, M?_n, M?_z, M?_w/M?_n, as well as a plot of molecular weight distribution. Samples of very narrow molecular weight distribution (MWD) polystyrene from Pressure Chemicals Co. and relatively wide MWD samples of poly(methyl methacrylate) in chloroform have been characterized.     

Poly(2,6-diphenyl-1,4-phenyl oxide): Characterization by gel-permeation chromatography,light scattering,and solution viscosity

Ten unfractionated poly(2,6-diphenyl-1,4-phenylene oxide) samples were examined by gel permeation chromatography (GPC) and intrinsic viscosity [η] at 50°C in benzene, by intrinsic viscosity at 25°C in chloroform, and by light scattering at 30°C in chloroform. The GPC column was calibrated with ten narrow-distribution polystyrenes and styrene monomer to yield a “universal” relation of log ([η]M) versus elution volume. GPC-average molecular weights, defined as M?gpc = \documentclass{article}\pagestyle{empty}\begin{document}$\Sigma w_i [\eta ]_i M_i /\Sigma w_i [\eta ]_i$\end{document}, w_i denoting the weight fraction of polymer of molecular weight M_i, were computed from the GPC and [η] data on the polyethers. The M?GPC were then compared with the weight-average M?_w from light scattering. The intrinsic viscosity (dl/g) versus molecular weight relations for the unfractionated poly(2,6-diphenyl-1,4-phenylene oxides) determined over the molecular weight range 14,000 ≤ M?_w ≤ 1,145,000 are log [η] = ?3.494 + 0.609 log M?_w (chloroform, 25°C) and log [η] = ?3.705 + 0.638 log M?_w (benzene, 50°C). The M?_w(GPC)/M?_n(GPC) ratios for the polymers in the molecular weight range 14,000 ≤ M?_w ≤ 123,000 approximate 1.5 according to computer integrations of the GPC curves with the use of the “universal” calibration and the measured log [η] versus log M?_w relation. The higher molecular weight polymers (326,000 ≤ M?_w ≤ 1,145,000) show slightly broadened distributions.     

Effect of concentration of the crosslinking agent and diluent during polymerization on the viscoelastic spectra of poly(2-hydroxyethyl methacrylate) networks

The effect of concentration of the crosslinking agent (ethylene dimethacrylate) and diluent (water) during the crosslinking copolymerization on the shape and position of retardation spectra in the dry state has been investigated for poly(2-hydroxyethyl methacrylate) networks. With increasing water content during network formation, the maxima of the retardation spectra, L_m, increase and the position of the spectra is shifted toward shorter retardation times, τ. The results are in quantitative agreement with the modified Rouse–Mooney (R–M) molecular theory and suggest the influence of deformation due to the diluent during network formation on the viscoelastic behavior. With increasing content of the crosslinking agent, the retardation spectra are shifted toward longer times. At a constant reference temperature T₀ = 115°C the retardation time, τ_m, at the maxima of the spectra increases with increasing content of effective chains in the network, ν_e. However, after a correction for the effect of the monomeric frictional coefficient, ξ, τ_m/ξ decreases with increasing v_e at a rate which agrees quantitatively with the R–M theory. The slope of the retardation spectra in the main transition region and the value of their maxima decrease with increasing v_e; a comparison of these dependences with theory leads to the most probable distribution of submolecules in the chains. The contribution of long retardation times to the equilibrium compliance, J_e, of the systems under investigation was estimated; it was shown that the application of the Thirion–Chasset extrapolation method for the determination of J_e of loose networks requires a certain type of dependence of the retardation or relaxation spectra on τ.     

Studies of branching in polyvinyl acetate

Batch polymerizations of vinyl acetate were conducted at 60°C and 72°C, and rate constants for branching were established from the variation of M?_n and M?_w with extent of conversion. The calculated branching densities (branch points per polymer molecule) are slightly higher at 72°C for all conversions. Selected samples were saponified and reacetylated to determine the amount of branching through the acetate group. Changes in M?_n, M?_w, and [η] indicate 63%, 75%, and 70%, respectively, of saponificable branches. These percentages are independent of branching density in the original polymer. Molecular weights extrapolated to zero conversion appear to be unchanged by saponification and reacetylation, showing that short chain branching through the acetate group is absent, or at least very infrequent.     

Rheological studies of moderately concentrated polystyrene solutions in the vicinity of the θ temperature. II. Shear-rate dependence for different thermodynamic conditions

The viscosity data of moderately concentrated polystyrene solutions in trans-decalin (TD) (θ solvent, θ temperature 21°C) and toluene (TL) (good solvent) reported in Part I are discussed in terms of Graessley's entanglement theory. Under good solvent conditions, Graessley's master curve provides an excellent fit up to high shear rates, whereas in the vicinity of the θ conditions the data have to be modified by a parameter η_fric introduced by Ito and Shishido. The characteristic time of mechanical response to flow of chains approximately given by the shift factor τ₀ is found in good solvents to be on the order of the Rouse relaxation time. In poor solvents, close to demixing, τ₀ tends to much higher values, indicating a reduced chain mobility. The influence of temperature on the viscosity decreases with increasing shear. The resulting apparent energy of activation of flow shows very small or even negative values at high shear rates. This behavior can be explained by the modified Graessley theory, however, in a quite natural way.     

Friedel–crafts crosslinking methods for polystyrene modification. IV. Macromolecular structure of crosslinked particles

Crosslinked polystyrene particles were prepared by Friedel–Crafts suspension crosslinking of polystyrene using 2,4-dichloromethyl-2,5-dimethyl benzene as crosslinking agent. The polymer was dissolved in nitrobenzene and reaction occurred in a 70 wt % aqueous solution of ZnCl₂ with poly(vinyl alcohol) as a suspending agent. The spherical particles produced were swollen in toluene, chloroform, and tetrahydrofuran to determine their equilbrium polystyrene volume fraction. Analysis of the crosslinked macromolecular structure gave values of number-average molecular weight between crosslinks of M?_c = 900–5900 increasing as the nominal crosslinking ratio X decreased from 0.75 to 0.0625 mol of crosslinking agent per mole of polystyrene repeating unit. Porosimetric analysis contributed to the understanding of the importance of the pore structure for swelling behavior.     

Living cationic polymerization of 2-vinyloxyethyl phthalimide: Synthesis of poly(vinyl ether) with pendant primary amino functions

Cationic polymerization of 2-vinyloxyethyl phthalimide ( 1 ) in CH₂Cl₂ at ?15°C with hydrogen iodide/iodine (HI/I₂) as initiator led to living polymers of a narrow molecular weight distribution (M?_w/M?_n = 1.1–1.25). The number-average molecular weight of the polymers was in direct proportion to monomer conversion and could be controlled in the range of 1000–6000 by regulating the 1 /HI feed ratio. However, when a fresh monomer was supplied to the completely polymerized reaction mixture, the molecular weight of the polymers was not directly proportional to monomer conversion. The polymerization of 1 by boron trifluoride etherate (BF₃OEt₂) in CH₂Cl₂ at ?78°C gave polymers with relatively high molecular weight (M?_w > 20,000) and broad molecular weight distribution (M?_w/M?_n ～ 2). The HI/I₂-initiated polymerization of 1 was an order of magnitude slower than that of ethyl vinyl ether, probably because of the electron-withdrawing phthalimide pendant. Hydrazinolysis of the imide functions in poly( 1 ) gave a water-soluble poly(vinyl ether) ( 3 ) with aliphatic primary amino pendants.     

Well‐defined amphiphilic graft copolymer consisting of hydrophilic poly(acrylic acid) backbone and hydrophobic poly(vinyl acetate) side chains

A series of well‐defined amphiphilic graft copolymers containing hydrophilic poly(acrylic acid) (PAA) backbone and hydrophobic poly(vinyl acetate) (PVAc) side chains were synthesized via sequential reversible addition‐fragmentation chain transfer (RAFT) polymerization followed by selective hydrolysis of poly(tert‐butyl acrylate) backbone. A new Br‐containing acrylate monomer, tert‐butyl 2‐((2‐bromopropanoyloxy)methyl) acrylate, was first prepared, which can be polymerized via RAFT in a controlled way to obtain a well‐defined homopolymer with narrow molecular weight distribution (M_w/M_n = 1.08). This homopolymer was transformed into xanthate‐functionalized macromolecular chain transfer agent by reacting with o‐ethyl xanthic acid potassium salt. Grafting‐from strategy was employed to synthesize PtBA‐g‐PVAc well‐defined graft copolymers with narrow molecular weight distributions (M_w/M_n < 1.40) via RAFT of vinyl acetate using macromolecular chain transfer agent. The final PAA‐g‐PVAc amphiphilic graft copolymers were obtained by selective acidic hydrolysis of PtBA backbone in acidic environment without affecting the side chains. The critical micelle concentrations in aqueous media were determined by fluorescence probe technique. The micelle morphologies were found to be spheres. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6032–6043, 2009     

Synthesis of poly(vinyl acetate)‐b‐polystyrene and poly(vinyl alcohol)‐b‐polystyrene copolymers by cobalt‐mediated radical polymerization

Well‐defined poly(vinyl acetate) macroinitiators, with the chains thus end‐capped by a cobalt complex, were synthesized by cobalt‐mediated radical polymerization and used to initiate styrene polymerization at 30 °C. Although the polymerization of the second block was not controlled, poly(vinyl acetate)‐b‐polystyrene copolymers were successfully prepared and converted into amphiphilic poly(vinyl alcohol)‐b‐polystyrene copolymers by the methanolysis of the ester functions of the poly(vinyl acetate) block. These poly(vinyl alcohol)‐b‐polystyrene copolymers self‐associated in water with the formation of nanocups, at least when the poly(vinyl alcohol) content was low enough. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 81–89, 2007