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     

Phase behavior of pseudo-IPN's of polycarbonate-urethane and polystyrene

The pseudo-IPN's of PCU/PS with different M_n and narrow MWD of the linear PS have been synthesized and characterized. The effect of M_n and composition on the phase morphology of the pseudo-IPN's of PCU/PS has been studied by DSC and SEM. The pseudo-IPN's with ultra-high M_n of the linear PS appeared to possess a single T_g and no SEM-resolvable domains at 35 wt % PS and below. This metastable state may reflect the result of a high extent of entanglement of the linear PS chains with the PCU network and the limited molecular mobility of the linear PS chains with high M_n. © 1993 John Wiley & Sons, Inc.     

Relaxation of shear and normal stresses in step-shear deformation of a polystyrene solution. Comparison with the predictions of the Doi–Edwards theory

The shear stress σ, two components of birefringence, and extinction angle were measured for a concentrated polystyrene solution in step-shear deformation of magnitude of shear 0.3 ≤ γ ≤ 4.0. The stress-optical coefficient did not depend on either γ or time. The first and the second normal-stress differences v₁ and v₂ were evaluated with the use of the stress-optical law. Over a certain range of long times, σ could be factored as σ = γh(γ)G(t) and the quantity h(γ) agreed with the prediction of the Doi–Edwards theory based on the de Gennes tube model of entangled polymer chains. At short times the effect of γ on σ/γ was smaller than at long times. The relaxation spectrum became approximately independent of γ at the short-time end of the rubbery plateau region. The ratios v₁/σ and v₂/v₁ were independent of time and were in quantitative agreement with those predicted by the Doi–Edwards theory: v₁/σ was equal to γ, v₂/v₁ was negative, and |v₂/v₁| decreased with increasing γ.     

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     

Effect of ultrasound on the microstructure of polystyrene in cyclohexane: a synchrotron small-angle X-ray scattering study

Synchrotron small-angle X-ray scattering technique has been used to study the effect of ultrasound on the microstructure of polystyrene (PS) in cyclohexane solutions. The results show that the intramolecular radius of gyration (R _g) decreases with ultrasound, indicating the shrinkage and collapse of PS chains. There is an exponential relationship between R _g and the molecular weight of PS (M _w), and the exponent changes from 0.5 to 0.417, as the ultrasound time is increased. This means that the shape of PS chain changes from random coil to shrunken form. The Kratky plots also confirm the shape transformation of PS chains induced by ultrasound. Moreover, the intermolecular correlation length increases with the ultrasound time, which is indicative of the entanglement of PS chains.     

Insight into shear‐induced modification for improving processability of polymers: Effect of shear rate on the evolution of entanglement state

Many experimental results have revealed that the re‐entanglement kinetics of disentangled polymers is much slower than that predicted by tube theory. This retarded recovery of fully entangled state is of practical significance that shear‐induced modification may offer a way to improve processability for a polymer by reducing viscosity. This work tried to figure out the shear‐rate dependence variation of viscosity in the view of evolution of entanglement state through disentanglement and re‐entanglement, aiming to provide fundamental insights into application prospect of shear‐induced modification in preparing “in‐pellet” disentangled polymers prior to final processing. High‐density polyethylene was sheared on a parallel‐plate rotational rheometer with a linearly increased shear rate. Results showed that higher shear rate could induce further disentanglement, resulting in a lower viscosity with a reduction rate up to 93.7%, larger molecular weight between entanglements M_e , and longer re‐entanglement time. Additionally, less entanglement would give a larger lamellar thickness of sheared samples after nonisothermal crystallization. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 598–606     

Effect of molecular entanglements on craze microstructure in glassy polymers

Thin films of ten glassy polymers are bonded to copper grids and strained in tension to produce crazes, which are then examined in the transmission electron microscope. The average craze fibril extension ratio λ for each polymer is determined from microdensitometer measurements of the mass thickness contrast of the crazes. The extension ratio λ is found to increase approximately linearly with the chain contour length l_e between entanglements, as determined from melt elasticity measurements of the entanglement molecular weight of these polymers. These results are analyzed by comparing them with λ_max, the maximum extension ratio of an entanglement network in which polymer chains neither break nor reptate (i.e., permanent entanglement crosslinks are assumed). The values of λ_max are given by l_e/d where d, the entanglement mesh spacing in the unoriented glass, is computed from d = k(M_e)^1/2 with k determined either from small-angle neutron scattering results on isolated chains in the glass or from coil size measurements in dilute solutions of a θ solvent. The craze extension ratios fall somewhat below λ_max at low λ but increase to well above λ_max for polymers with high l_e. This comparison suggests a significant contribution due to chain breakage (or reptation) in the higher-λ crazes of large-l_e polymers, which may arise from the higher true stresses in the craze fibrils (which for a given applied stress increase proportionally to λ). The results also imply that a useful way to increase the “brittle” fracture stress and decrease the ductile-to-brittle transition temperature of a glassy polymer is to decrease its entanglement contour length l_e.     

Electrophoretic flow of interacting polymer chains: Effects of temperature,polymer concentration,and porosity

Using a Monte Carlo simulation in three dimensions, we studied the variation of the root-meansquare (rms) displacement (R_rms) of polymer chains with time and the rates of their mass transfer (j) as a function of biased field (B), polymer concentration (p), chain length (L_c), porosity (p_s), and temperature (T). In homogeneous/annealed system, the rms displacement of the chains shows a drift-like behavior, R_rms ∼ t, in the asymptotic time regime preceded by a subdiffusive power-law (R_rms ∼ t^k, with k < 1/2) at high p. The subdiffusive regime expands on increasing L_c and p but reduces on increasing T or B. In quenched porous media, the drift-like behavior of R_rms persists at low barrier concentration (p_b) and high T. However, at high p_b and/or low T, chains relax into a subdrift and/or subdiffusive behavior especially with high p or long L_c. Flow of chains is measured via an effective permeability (σ) using a linear response assumption. In annealed system, σ increases monotonically with B at high T and low p but varies nonmonotonically at low T, high p and high L_c. We find that σ decays with L_c, σ ∼ L, where α depends on B, p and T with a typical value a α ∼ 0.43−0.64 for p = 0.1-0.3 at B = 0.5. Further, σ decays with p, σ ∼ − Cp with a decay rate C sensitive to T and B. In quenched porous media, even at low pb and high T, σ varies nonmonotonically with bias, i.e., the increase of σ is followed by decay on increasing the bias beyond a characteristic value (B_c). This characteristic bias seems to decrease logarithmically with barrier concentration, B_c ∼ −klnp_b. The prefactor k depends on the chain length, k ≈ 0.35 for shorter chains (L_c = 20, 40) and ≈ 0.15 for longer chains (L_c = 60). Scaling dependence of σ on L_c similar to that in annealed system is also observed in porous media with different values of exponent α. The current density shows a nonlinear power-law response, j ∼ B^σ, with a nonuniversal exponent δ ≈ 1.10−1.39 at high temperatures and low barrier concentrations.     

Graftlike interpolymer complexes from poly(2‐vinylpyridine) and end‐sulfonic acid polystyrene and polyisoprene: Intermediates to noncovalently bonded block copolymer‐like micelles

The complexation between narrow molecular weight distribution poly(2‐vinylpyridine) (P2VP) and polystyrene (suPS) or polyisoprene (suPI) end‐functionalized with one sulfonic acid group was examined in tetrahydrofuran dilute solutions by a combination of static and dynamic laser light scattering. Both apparent weight‐average molecular weight (M_w,app) and hydrodynamic radius (R_h) of the complexes exhibited a maximum at a certain molar ratio of suPS chains to P2VP monomeric units. This indicated that the P2VP backbone may be saturated by the grafted end‐functionalized chains because of repulsion between the grafted chains. By changing the molar mass of P2VP from 100,000 to 30,000 g/mol, the values of M_w,app and R_h decreased. When suPI was used instead of suPS, similar trends were observed. In the latter case, it was possible to prepare block copolymer‐like micelles by transferring the P2VP/suPI blend solutions in decane, which is a selective solvent for PI. The non‐covalent‐bonded polymeric micelle characteristics were investigated as a function of sulfonic acid/2‐vinylpyridine units ratio as well as temperature. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2454–2461, 2003     

Coil-globule transition: Self-assembly of a single polymer chain

The coil collapse problem is of interest not only because it represents the simplest model of protein folding, but also because of its fundamental importance as related to polymer nanostructures and fractionation. It is extremely difficult to observe the coil-to-globule transition experimentally because at finite concentrations in a poor solvent, the macromolecules tend to aggregate due to phase separation when the collapsed state is being achieved. In the mid-1980s, two-stage kinetics of a single-chain collapse was proposed theoretically.^1,2 The first successful experimental observation of a two-stage coil-to-globule transition was achieved by quenching a dilute solution of polystyrene (PS) in cyclohexane.³ By using a thinnest capillary tube cell with a wall thickness of 0.01 mm and a diameter of 5 mm for dynamic light scattering, two relaxation times, τ_crum for the crumpled globule state and τ_eq for the compact globule state, were determined⁴ for the first time. The relaxation times were much slower than expected. From the size of the crumpled globule and that of the compact globule and by assuming the intraglobular density to be uniform, the volume fraction of the PS chain in the crumpled globule state, ϕ_crum, and that in the compact globule state, ϕ_comp, can be estimated, with ϕ_crum = 0.02 and ϕ_comp ∼ 0.24-0.4 at 28°C for polystyrene in cyclohexane. The results imply that a single-chain globule contains a large amount of solvent. It should also be noted that ϕ_comp is temperature dependent, i.e., one would have to go to hypothetically low temperatures in order to squeeze out all the solvent (cyclohexane) in the compact PS globule. The single-chain coil collapse state could be achieved under equilibrium conditions by using a high molecular weight, M_w ∼ 1.08 × 10⁷ g/mol; M_w/M_n < 1.06) poly(N-isopropylacrylamide) (PNIPAM) in water,<⁵ even though the ten million molecular weight for PNIPAM was substantially lower than that for polystyrene (M_w ∼ 50 × 10⁶ g/mole).⁶ Under equilibrium conditions, it was feasible to determine both the hydrodynamic radius R_h and the radius of gyration R_g. The ratio of R_g/R_h changed from 1.45 to 0.77, clearly demonstrating the transition from the theta coil state to the compact globule state. At the maximum value of the scaled expansion factor α_s³ |τ| M_w^1/2, R_g/R_h = 1.33 where α_s = R_g/R_g (θ) and τ = |T-θ| / θ with θ being the theta temperature. In the compact globule, R_g/R_h was of the order of 0.7, implying that the PNIPAM compact globule in water still contained ∼80% water, of the same order of magnitude as the PS compact globule in cyclohexane at 7° below its theta temperature (35°C).     

Diffuse interface between polymers: Structure and kinetics

The interfacial structure and diffusion kinetics of two compatible polymers, poly(methyl methacrylate) and poly(vinylidene fluoride) are studied in the melt. The interdiffusion rates of the two components are found to be unequal, giving unequal diffusion coefficients, a net mass flow across the interface, and an asymmetric interfacial composition profile. The structure and kinetics confirm the predictions of the reptation theory. The interfacial thickness d grows with t^1/2, and the interdiffusion coefficient is proportional to M^?2, where t is the time and M is the molecular weight. The scaling law for the interfacial thickness is therefore d ∝ M^?1t^1/2. The number of chains per unit area crossing the original interface reaches a constant value independent of diffusion time after a short induction time on the order of the tube disengagement time (about 0.1–10 s in the present cases depending on the molecular weights). The adhesive bond strength σ is scaled by σ ∝ t^1/4M^?1/2 and σ/σ∞ ∝ t^1/4M^?1/2 [1- (M_c/M)]^?1, where σ _∞is the σ at infinite molecular weight and M_c is the entanglement molecular weight.     

Dynamic light scattering of polystyrene single chains in a semidilute solution of poly(methyl methacrylate) and benzene

Translational diffusion and internal motion have been observed by dynamic light scattering of optically labeled single chains of polystyrene (PS) in a semidilute solution of poly(methyl methacrylate) and benzene for the case in which the dimension R_g of the PS chain is comparable to the correlation length of the matrix solution. The molecular weight M_w dependence of the hydrodynamic radius R_h is expressed as R_h ～ M, while R_h ～ M in pure benzene. The average linewidth Γ for internal motions (KR_g > 1) appears to depend on the magnitude K of the scattering vector approximately as Γ ∝ K⁴ at higher KR_g ( > 1), in contrast with the fact that Γ ∝ K³ approximately for KR_g > 1 in pure benzene. The scaling law for the K dependence of Γ does not hold in low-molecular-weight PS owing to the K dependence of Γ /K² for KR_g < 1.     

Polymer Chain Conformation on Deuterated Polystyrene Nanoparticles Investigated by SANS

We previously reported that grafted polystyrene (PS) chains on silica nanoparticles at a low grafting density show similar conformations to free PS chains in the same solvent, THF (diameter ?50 nm, Colloid.poly.Sci. (2013), 291, 9, 2087–2099). As an extension of our previous study we choose an organic nanoparticle (deuterated polystyrene, dPS) instead of inorganic nanoparticle to see the impact of the substrate material on chain conformation. Additionally, a wider range of molecular weights were prepared to investigate the conformation feature of grafted PS chains more in detail. Small angle neutron scattering (SANS) experiments were performed to characterize PS grafted dPS particles in good solvent condition, with deuterated toluene and deuterated THF as solvent. To get insight into the conformation of the grafted PS layer we apply a scaling law describing the dimension of free PS polymer in good solvent condition to the obtained thickness of the grafted PS layer. We find an overall agreement with the scaling law where the thickness of the grafted PS layer is slightly larger than 2R_g of the free polymer chains in the respective solvent giving hint for semi dilute polymer brush (SDPB) situation.     

Tube dilation process in star‐branched cis‐polyisoprenes

In current tube models for entanglement, the tube representing the topological constraint is considered to move with time. This tube motion results in the constraint release (CR) as well as the dynamic tube dilation (DTD), and an importance of DTD has been argued for entangled star chains. Under these backgrounds, this article examines the validity of the DTD molecular picture for the star chains. For monodisperse star chains having noninverted type‐A (parallel) dipoles in respective arms, the normalized viscoelastic and dielectric relaxation functions μ(t) and Φ(t) were found to obey a relationship μ(t) ≅ [Φ(t)]² if the tube actually dilates in the time scale of the star relaxation. For 6‐arm star cis‐polyisoprene (PI) chains (having those type‐A dipoles), dielectric and viscoelastic measurements were conducted to test this DTD relationship. Both viscoelastic and dielectric properties exhibited characteristic behavior expected from DTD models (assuming the arm retraction in the dilating tube), the exponential increase of the relaxation time and broadening of the relaxation mode distribution with increasing arm molecular weight M_a. However, in the range of M_a examined, M_a ≤ 8M_e (M_e = entanglement spacing), the above DTD relationship was not valid for a dominant part of the slow relaxation (and the models failed in this sense). Thus, for star chains at least in this range of M_a, the simple DTD picture assuming very rapid CR motion (rapid equilibration in the dilated tube) did not explain the slow relaxation behavior of star chains. This result in turn suggested the importance of the CR motion in this behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1024–1036, 2000     

A study of shear-stress relaxation anomalies in binary mixtures of monodisperse polystyrenes

We report measurements of the nonlinear relaxation moduli after a step-shear strain of polystyrene solutions with nearly monodisperse and with bidisperse distributions of molecular weight. We find, as have others, that for monodisperse solutions with M/M_e > 60, there are anomalies, such as an unusually low nonlinear modulus and a kink in a plot of shear stress versus time after the step strain. Here M is the polymer molecular weight and M_e is the entanglement molecular weight. We find that in the bidisperse solutions the anomalies persist as long as M_w/M_e > 60, where M_w is the weight-averaged molecular weight of the bidisperse solution. The persistence of the anomalies in bidisperse solutions disagrees with a theory of Marrucci and Grizzuti that attributes the anomalies to strain inhomogeneities similar to shear banding. The Marrucci-Grizzuti theory predicts that as little as 10% short chains in the bidisperse mix should eliminate the anomalies, whereas in the experiments reported here at least 30% is required. Nevertheless the way in which the anomalies disappear at high strains when one increases the fraction of low-molecular-weight component is qualitatively similar to the theoretical predictions and supports the notion that strain inhomogeneities occur in these systems. © 1992 John Wiley & Sons, Inc.     

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.     

Effect of polystyrene‐b‐poly(ethylene oxide) on self‐assembly of polystyrene‐b‐poly(N‐isopropylacrylamide) in aqueous solution

Mixed micelles of polystyrene‐b‐poly(N‐isopropylacrylamide) (PS‐b‐PNIPAM) and two polystyrene‐b‐poly(ethylene oxide) diblock copolymers (PS‐b‐PEO) with different chain lengths of polystyrene in aqueous solution were prepared by adding the tetrahydrofuran solutions dropwise into an excess of water. The formation and stabilization of the resultant mixed micelles were characterized by using a combination of static and dynamic light scattering. Increasing the initial concentration of PS‐b‐PEO in THF led to a decrease in the size and the weight average molar mass (〈M_w〉) of the mixed micelles when the initial concentration of PS‐b‐ PNIPAM was kept as 1 × 10^?3 g/mL. The PS‐b‐PEO with shorter PS block has a more pronounced effect on the change of the size and 〈M_w〉 than that with longer PS block. The number of PS‐b‐PNIPAM in each mixed micelle decreased with the addition of PS‐b‐PEO. The average hydrodynamic radius 〈R_h〉 and average radius of gyration 〈R_g〉 of pure PS‐b‐PNIPAM and mixed micelles gradually decreased with the increase in the temperature. Both the pure micelles and mixed micelles were stable in the temperature range of 18 °C–39 °C. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1168–1174, 2010     

The influence of shear rate, temperature and chain conformation on the critical concentration c

 When viscometry is used, a crossover phenomenon is observed separating the dilute solutions into extremely dilute solutions and dilute solutions. The critical concentration c ^**, determined from this crossover phenomenon, strongly depends on the shear rate in the solution. At very high values of shear rate the critical concentration c ^** becomes very low and depends only on the contour length of the elongated chains of different polymers. An increase of the temperature induces an increase of c ^** because the relaxation time of the chains decreases. If a polymer adopts a rodlike conformation (in a given solvent at a given temperature) the excluded volume of its chains increases and its critical concentration c ^** decreases. Received: 14 October 1996 Accepted: 3 March 1997