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1.
Overshoot of shear stress, σ, and the first normal stress difference, N1, in shear flow was investigated for dilute solutions of polystyrene with very high molecular weight in concentrated solution of low M PS. In the case that the matrix was a nonentangled system, behavior of overshoot was similar to that of dilute solution of high M PS in pure solvent. The magnitudes of shear, γσm and γNm, corresponding to the peaks of σ and N1 lay on the universal functions of γ˙τR, respectively, proposed for dilute solutions in pure solvent. Here τR is the Rouse relaxation time for high M PS in the blend evaluated from dynamic modulus at high frequencies. In the case that the matrix was an entangled system, an additional σ peak was observed at high rates of shear at times corresponding to γσm = 2–3. This peak can be assigned to the motion of low M chains in entanglement network. When the matrix was entangled, stress overshoot was observed even at relatively low rates of shear, say γ˙τR < 10−2. This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γσm and γNm values were higher than those expected for entangled chains of monodisperse polymer in pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2043–2050, 2000  相似文献   

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3.
Beginning with a recently proposed expression for the drag force on a single macromolecule pulled with constant velocity through a fluid of long‐entangled molecules (V. R. Mhetar and L. A. Archer, Macromolecules 1998, 31, 6639), we investigate the effect of entanglement loss on polymer dynamics in steady shearing flows. At steady‐state, a balance between the elastic restoring force and viscous drag acting on entangled polymer segments reveals a critical molecular strain γm,c beyond which the drag force exerted on polymer molecules by their neighbors is insufficient to support arbitrarily small orientation angles. Specifically, we find that in fast steady shear flows τ < γ˙ < τ, polymer orientation in the shear plane approaches a limiting angle χc ≈ atau(1/(1 + γm,c)) beyond which flow becomes incapable of producing further molecular alignment. Shear flow experiments using a series of concentrated polystyrene/diethyl phthalate solutions with fixed entanglement spacing, but variable polymer molecular weight 0.94 × 106Mw ≤ 5.48 × 106, reveal a limiting steady‐state orientation angle between 6° and 9° over a range of shear rates; confirming the theoretical result. Orientation angle undershoots observed during start‐up of fast steady shearing flows are also explained in terms of a transient imbalance of elastic restoring force and viscous drag on oriented polymer molecules. Our findings suggest that the Doi–Edwards affine orientation tensor (Q) is not universal, but rather depends on deformation type and deformation history through a balance of elastic force and viscous drag on polymer molecules. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 222–233, 2000  相似文献   

4.
Non-Newtonian shear viscosities were measured over six decades of strain rate k for 13 solutions of both the ionic and nonionic forms of polyacrylamide. By using the Weissenberg rheogoniometer with both the cone-and-plate and the parallel-plate attachments, the normal stress functions σ1 (k2) and σ2(k2) were obtained for four of the solutions. From the measurements of the shear viscosity and the normal stresses at low rates of strain, characteristic times τ and τN, respectively, were determined for each solution. The quantity τ was then used to nondimensionalize the strain rate τk, and when plotted versus the reduced shear viscosity, found successfully to correlate the experimental data for all the polyelectrolyte solutions over the entire range of τk and the data for the concentrated solutions of the nonionic polymer over a smaller range of τk. However, in order to correlate the normal stress data for the polyelectrolyte solutions, a second reduced strain rate (τNk) was used. Thus, two different times were required to correlate all the observed data. The shear viscosity data for the dilute solutions of the nonionic polymer were well represented by the two-parameter, non-Newtonian intrinsic viscosity function that has been computed by Fixman.  相似文献   

5.
Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τRZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τL > τRZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ1) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ2)?1/2, where γ is the magnitude of shear. Contributions to η and Ψ1 from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τst = τ + (τRZ ? τ)/(1 + 0.35τRZ γ˙) instead of τRZ. Here, γ˙ is the rate of shear, and τ is the τRZ value at the infinite dilution limit. η and Ψ1 at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002  相似文献   

6.
We analyze the adsorption of strongly charged polyelectrolytes onto weakly charged surfaces in divalent salt solutions. We include short-range attractions between the monomers and the surface and between condensed ions and monomers, as well correlations among the condensed ions. Our results are compared with the adsorption in monovalent salt solutions. Different surface charge densities (σ), and divalent (m) and monovalent (s) salt concentrations are considered. When the Wigner-Seitz cells diameter (2R) is larger than the length of the rod, the maximum amount of adsorption scales like nmax ∼ σ4/3 in both monovalent and divalent solutions. For homogeneously charged surfaces, the maximum adsorption occurs at s* ∼ σ2 when s* > ϕ, where ϕ is the monomer concentration, the counterpart for divalent salt solution, m* roughly scales as σ2.2 when m* > ϕ. The effective surface charge density has a maximum absolute value at m′ < m*. A discrete surface charge distribution and short-range attractions between monomers and surface charge groups can greatly enhance surface charge inversion especially for high salt concentration. The critical salt concentration for adsorption in divalent salt solution roughly scales as mcbσ1.9, where b is the distance between two neighboring charged monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3642–3653, 2004  相似文献   

7.
Viscosity and normal stress behavior were measured for poly(methyl methacrylate) samples of various average molecular weights in diethyl phthalate solution at 30 and 60°C. All samples conformed approximately to the most probable distriution (M?w/M?n = 2). Concentrations ranged from 0.113 to 0.38 g/ml, and M?w from 53,800 to 1,620,000. Despite considerable evidence in the literature of unusual linear viscoelastic behavior for this polymer, its nonlinear properties appear to be rather conventional. The viscosity–shear rate master curve was similar to that found earlier for concentrated solutions of polystyrene and poly(vinyl acetate) of comparable molecular-weight distribution. The viscosity time constant τo parallels τR, the characteristic time of the Rouse model, although the residual dependence of τoR on concentration and molecular weight appears to be slightly different from that for polystyrene and poly(vinyl acetate). Similar conclusions apply to the recoverable compliance Je,o estimated from the normal stress behavior of each solution, and its relationship to the Rouse model compliance JR.  相似文献   

8.
Orientation angle and stress‐relaxation dynamics of entangled polystyrene (PS)/diethyl phthalate solutions were investigated in steady and step shear flows. Concentrated (19 vol %) solutions of 0.995, 1.81, and 3.84 million molecular weight (MW) PS and a semidilute (6.4 vol %) solution of 20.6 million MW PS were used to study the effects of entanglement loss on dynamics. A phase‐modulated flow birefringence apparatus was developed to facilitate measurements of time‐dependent changes in optical equivalents of shear stress (n12 ≈ Cσ) and first normal stress differences (n1 = n11 ? n22 ≈ CN1) in a planar‐Couette shear‐flow geometry. Flow birefringence results were supplemented with cone‐and‐plate mechanical rheometry measurements to extend the range of shear rates over which entangled polymer dynamics are studied. In slow > ) steady shear‐flow experiments using the ultrahigh MW polymer sample (20.6 × 106 MW PS), steady‐state n12 and n1 results manifest unusual power‐law dependencies on shear rate [n12,ss 0.4 and n1,ss 0.8]. At shear rates in the range τ < < τ, steady‐state orientation angles χSS are found to be nearly independent of shear rate for all but the most weakly entangled materials investigated. For solutions containing the highest MW PS, an approximate plateau orientation angle χp in the range 20–24° is observed; χp values ranging from 14 to 16° are found for the other materials. In the start‐up of fast steady shear flow ˙ ≥ τ), transient undershoots in orientation angle are also reported. The molecular origins of these observations were examined with the help of a tube model theory that accommodates changes in polymer entanglement density during flow. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2275–2289, 2001  相似文献   

9.
We review recent hole growth measurements performed at elevated temperatures in freely-standing polystyrene (PS) films, using optical microscopy and a differential pressure experiment (DPE). In the hole growth experiments, which were performed at temperatures close to the bulk glass-transition temperature of PS, T = 97 °C, we find evidence for nonlinear viscoelastic effects, which markedly affect the growth of holes in freely-standing PS films. The hole radius R initially grew linearly with time t before undergoing a transition to exponential growth characterized by a growth time τ. The time scale τ1 for the decay of the initial transient behavior prior to reaching steady state was consistent with the convective constraint release mechanism of the tube theory of entangled polymer dynamics, while the characteristic hole growth times τ of the holes were consistent with significant reductions in viscosity of over eight orders of magnitude with increasing shear strain rate due to shear thinning. DPE measurements of hole growth on very thin freely-standing films revealed that hole formation and growth occurs only at temperatures that are comparable to or greater than T, even for films for which the Tg value was reduced by many tens of degrees Celsius below the bulk value. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B:Polym Phys 44: 3011–3021, 2006  相似文献   

10.
Samples of a polyelectrolyte poly(methacryloylethyl trimethylammonium methylsulfate), PMETMMS, with molar masses Mw = 22−25 × 106 were examined with viscosity, static light scattering, and conductivity measurements in a water–acetone solvent. Because acetone is a nonsolvent for this polymer the measurements were performed to determine the influence of the solvent composition, the polymer concentration, and the presence of added ions on the conformation of the polyelectrolyte in mixed solvents. The possible influence of a hydrodynamic field on the polymer conformation was also studied. The viscosity of the polymer solutions as a function of polymer concentration, as well as of the solvent composition, was studied using a broad range of shear rates. When the mass fraction of acetone in the solvent, γ, is below 0.5, the solutions show a usual polyelectrolyte behavior. When γ ≥ 0.80, the polymer adopts a compact conformation. This is observed as a decrease of the radius of gyration, Rg, second virial coefficient, A2, the viscosity, and also as a change in the conductivity of the solution. The change in the polymer conformation may be induced also by dilution. When 0.60 ≤ γ < 0.80, a gradual decrease in the polymer concentration leads to a sudden decrease of the reduced viscosity, which indicates a decrease in the particle size. The values of Mw measured by static light scattering were constant in all experiments. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1107–1114, 1998  相似文献   

11.
The steady shear viscosity η(k) and the stress decay function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \eta \left({t,k} \right)$\end{document} (the shear stress divided by the rate of shear k after cessation of steady shear flow) were measured for concentrated solutions of polystyrene in diethyl phthalate. Ranges of molecular weight M and concentration c were 7.10 × 105 to 7.62 × 106 and 0.112–0.329 g/cm3, respectively. Measurements were performed with a rheometer of the cone-and-plate type in the range 10?4 < k < 1 sec?1. The Cox–Merz relation η(k) = |η*(ω)|ω=k was tested with the experimental result (|*(ω)| is the magnitude of the complex viscosity). It was found to be applicable to solutions of relatively low M or c but not to those of high M and c. For the latter η(k) began to decrease at a lower rate of shear than |η*(ω)|ω=k did; the Cox–Merz law underestimated the effect of rate of shear. The stress decay function was assumed to have a functional form \documentclass{article}\pagestyle{empty}\begin{document}$\tilde \eta \left( {t,k} \right) = \sum {\eta _p \left( k \right)e^{ - t/\tau p\left( k \right)} } $\end{document} where τ1 > τ2 > …, and the values of τ1, τ2 η1 and η2 were determined for some solutions. The relaxation times τ1 and τ2 were found to be independent of k and equal to the relaxation times of linear viscoelasticity. At the limit of k → 0, η1 and η2 were approximately 60 and 20–30%, respectively, of η and the non-Newtonian behavior was due to large decreases of η1 and η2 with increasing k. It was shown that η1(k) may be evaluated from the relaxation strength G1(s) for the longest relaxation time of the strain-dependent relaxation modulus with a constitutive model for relatively high cM systems as well as for low cM systems.  相似文献   

12.
Transient and steady-state rheological data are reported for several anionic polystyrene solutions in tritolylphosphate (1. 6 < cMMc < 7). Here c is the concentration of the solution, M is the molecular weight, ρ the density of the undiluted polymer, and Mc the molecular weight between entanglements as determined from zero-shear viscosity. The polystyrene used had Mw = 410,000 and Mw/Mn < 1.06. Data are also given for solutions of polyisobutylene and poly(vinyl acetate) with larger Mw/Mn. 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 ηk, recoverable compliance Rk, the first-normal stress function Nk(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 ηk0, Rk/R0, and Nk(1)/N0(1) should depend on η0R0k, 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.  相似文献   

13.
It is known that topological restraints by “chain entanglements” severely affect chain dynamics in polymer melts. In this field-cycling NMR relaxometry and fringe-field NMR diffusometry study, melts of linear polymers in bulk and confined to pores in a solid matrix are compared. The diameter of the pore channels was 10 nm. It is shown that the dynamics of chains in bulk dramatically deviate from those observed under pore constraints. In the latter case, one of the most indicative signatures of the reptation model is verified 28 years after its prediction by de Gennes: The frequency and molecular mass dependencies of the spin-lattice relaxation time obey the power law T!M0 v3/4 on a time scale shorter than the longest Rouse relaxation time τR. The mean squared segment displacement in the pores was also found to be compatible to the reptation law < r2>∝ M−1/2t1/2 predicted for τR < t < τd, where τd is the so-called disengagement time. Contrary to these findings, bulk melts of entangled polymers show frequency and molecular mass dependencies significantly different from what one expects on the basis of the reptation model. The data can however be described with the aid of the renormalized Rouse theory.  相似文献   

14.
The properties of thin supported polymer films can be dramatically impacted by the substrate upon which it resides. A simple way to alter the properties of the substrate (chemistry, rigidity, dynamics) is by coating it with an immiscible polymer. Here, we describe how ultrathin (ca. 2 nm) hydrophilic polymer layers of poly(acrylic acid) and poly(styrene sulfonate) (PSS) impact the aging behavior and the residual stress in thin films of poly(butylnorbornene‐ran‐hydroxyhexafluoroisopropyl norbornene) (BuNB‐r‐HFANB). The aging rate decreases as the film thickness (h) is decreased, but the extent of this change depends on the adjacent layer. Even for the thickest films (h > 500 nm), there is a decrease in the aging rate at 100 °C when BuNB‐r‐HFANB is in contact with PSS. In an effort to understand the origins of these differences in the aging behavior, the elastic modulus and residual stress (σR) in the films were determined by wrinkling as a function of aging time. The change in the elastic modulus during aging does not appear to be directly correlated with the densification or expansion of the films, but the aging rates appear to roughly scale as hσR1/3. These results illustrate that the physical aging of thin polymer films can be altered by adjacent polymers. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 992–1000  相似文献   

15.
Formation of wormlike micelles (WLMs) in an aqueous mixture of polyoxyethylene cholesteryl ether (ChEOn; where n = 20 and 30) and polyoxyethylene dodecyl ether (C12EOm; where m = 3 and 4) has been reported; rheological and small angle X-ray scattering (SAXS) measurements have been performed in the micellar solutions of ChEOn as a function of C12EOm for the structural elucidation. When lipophilic cosurfactant, C12EOm is added to the micellar solutions of ChEOn, it favors the sphere-to-cylinder transition due to the penetration of C12EOm in the palisade layer of ChEOn micelle accompanying an increase in viscosity. When the concentration of C12EOm is increased, entangled network of WLMs is formed. A strong shear thinning has been observed in highly viscous samples indicating the presence of transient networks. Such samples exhibited viscoelastic behavior and could be described by the Maxwell model with a single stress relaxation mode. A maximum is observed in zero-shear viscosity-C12EOm plot. With further addition of C12EOm, viscosity declines and ultimately a phase separation occurs with the formation of turbid solution of vesicular dispersion. This decline has been interpreted in terms of micellar branching induced by an increase in endcap energy, E c (which is compensated by the formation of branch points, having a mean curvature opposite to that of endcaps). The C12EOm induced one-dimensional micellar growth has been confirmed by SAXS.  相似文献   

16.
Shear-induced structures were investigated for both ultrahigh molecular weight atactic polystyrene (UHMWaPS) and linear polyethylene (UHMWPE) solutions, which were entangled but homogeneous without shear flow, as a function of shear rate ( ) or time after a step-up shear flow. For the PE solutions, the shear flow was imposed at 124 °C which is higher than the nominal melting temperature Tnm of the solution without shear flow. At sufficiently high shear rates both solutions commonly formed highly optically anisotropic string-like structures which are composed of a series of phase-separated domains interconnected by bundles of stretched chains and aligned along the flow direction. After cessation of the shear flow the string-like structures completely disappeared in the UHMWaPS solution, recovering a homogeneous solution, while the UHMWPE solution exhibited shish-kebab structure. The results reveal a new kinetic pathway for shish-kebab formation for the entangled crystallizable solution sheared at T > Tnm which involves first formation of the phase-separated string-like domains and subsequent crystallization into shish from the bundles of stretched chain and then kebab in the demixed domains composed of essentially random coils.  相似文献   

17.
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 × 105Mw ≤ 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 (Mw ≥ 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  相似文献   

18.
This paper presents a nonlinear viscoelastic model for polymer nanocomposites and the computed model response to large amplitude oscillatory shear flow. The model predicts the stress in a mixture of entangled polymer chains, with different convective constraint release (CCR) rates for free chains and nanoparticle‐attached chains, through an averaging scheme which is consistent with double reptation in the Marrucci–Ianniruberto constitutive equation. The nonlinear response of the mixture is evaluated both numerically in terms of Q and by an asymptotic analysis in terms of four frequency dependent parameters of medium amplitude oscillatory shear (MAOS) as well as the intrinsic nonlinearity parameter Q0 . In the case of free polymer chains alone, the MAOS signatures are comparable to those of the Giesekus model with the notable difference of a minimum in the elastic parameter [e1] at De >1. The viscous nonlinear parameters of the mixture model depart significantly from those of the free chains, especially in mixtures where the CCR parameter for attached chains is larger than that for the free chains: [v1] has a prominent minimum and [v3] has a prominent maximum near De = 2/c, the low frequency plateau region, along with a higher Q0 compared to the matrix at all Deborah numbers. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 62–76  相似文献   

19.
The concomitant appearance of crystallites and nanocavities under uniaxial strain is investigated by X‐ray scattering in a model natural rubber system. The nanocavities appear after crystallization and only when the true stress is above a critical cavitation stress σCav. The presence of crystallites alone does not influence the calculation of the void volume fraction ?void. The nanocavities formed are 20–50 nm in size with a constant aspect ratio. The presence of filler shifts the critical crystallization extension ratio λCry, λCav, and σCav to lower values. The clear correlation between σCav and the crystallinity at the onset of cavitation χC(λCav) implies that the crystallites take most of the mechanical loading thus delaying the cavitation in the amorphous phase. Under cyclic loading, nanocavitation is significant only in the first loading and in the successive loadings if the extension ratio is above its maximum historical value. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1125–1138  相似文献   

20.
The reverse osmosis (RO) separation of aqueous organic solutions, such as alcohols, amines, aldehydes, acids,ketones, and esters etc., by PAA (polyacrylic acid)/PSF (polysulfone) composite membrane has been studied. It was foundthat the separation results for aliphatic alcohols, amines and aldehydes are satisfactory, the solute rejection (R_a) and thevolume fluxes of solutions (J_v) for 1000 ppm ethanol, ethylamine and ethyl aldehyde are 66.2%, 61.0%, 84.0% and 0.90×10~(-6), 0.35×10~(-6), 0.40×10~(-6) m~3/m~2·s, respectively, at 5.0 MPa and 30℃. R_a increased with increasing molecular weights ofalcohols, amines and aldehydes, and the R_a for n-amyl alcohol, n-butylamine and n-butyl aldehyde reached 94.3%, 88.6%and 96.0%, respectively. Satisfactory separation results (R_a>70%) for ketones, esters, phenols and polyols have beenobtained with the PAA/PSF composite membrane. The effect of operating pressure on the properties of reverse osmosis hasalso been investigated. Analysis of experimental data with Spiegler-Kedem's transport model has been carried out and themembrane constants such as reflection coefficient σ, solute and hydraulic permeabilities ω and L_p for several organic soluteshave been obtained.  相似文献   

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