Shear small-angle light scattering studies of shear-induced concentration fluctuations and steady state viscoelastic properties

We aimed at elucidating the influence of shear-induced structures (shear-enhanced concentration fluctuations and/or shear-induced phase separation), as observed by rheo-optical methods with small-angle light scattering under shear flow (shear-SALS) and shear-microscopy, on viscoelastic properties in semidilute polystyrene (PS) solutions of 6.0 wt % concentration using dioctyl phthalate (DOP) as a Theta solvent and tricresyl phosphate (TCP) as a good solvent. In order to quantify the effects of the shear-induced structures, we conducted a numerical analysis of rheological properties in a homogeneous solution based on the constitutive equation developed by Kaye-Bernstein, Kearsley, and Zapas (K-BKZ). In the low-to-intermediate shear rate gamma region between tau(w) (-1) and tau(e) (-1), where tau(w) and tau(e) are, respectively, terminal relaxation time and the relaxation time for chain stretching, the steady state rheological properties, such as shear stress sigma and the first normal stress difference N(1), for the PS/DOP and PS/TCP solutions are found to be almost same and also well predicted by the K-BKZ equation, in spite of the fact that there is a significant difference in the shear-induced structures as observed by shear-SALS and shear-microscopy. This implies that the contribution of the concentration fluctuations built up by shear flow to the rheological properties seems very small in this gamma region. On the other hand, once gamma exceeds tau(e) (-1), sigma and N(1) for both PS/DOP and PS/TCP start to deviate from the predicted values. Moreover, when gamma further increases and becomes higher than gamma(a,DOP) (sufficiently higher than tau(e) (-1)), above which rheological and scattering anomalies are observed for PS/DOP, sigma and N(1) for PS/DOP and PS/TCP are significantly larger than those predicted by K-BKZ. Particularly, a steep increase of sigma and N(1) for PS/DOP above gamma(a,DOP) is attributed to an excess free energy stored in the system via the deformation of interface of well-defined domains, which are aligned into the stringlike structure developed parallel to the flow axis, and stretching of the chains connecting the domains in the stringlike structures. Thus, we advocate that the effect of shear-induced structures should be well considered on the behavior of sigma and N(1) at the high gamma region above tau(e) (-1) in semidilute polymer solutions.     

Structure and dynamics of concentration fluctuations in a polymer blend solution under shear flow

The technique of small-angle light scattering (SALS) has been employed to investigate the time-dependent behavior of a single-phase, semidilute solution of polystyrene and polybutadiene in dioctyl phthalate under shear flow. Concentration fluctuations in the polymer blend solution are found to grow with time in the direction of flow, and their orientation angles evolve from 45° from the flow direction toward 0°, with the steady-state value being dependent on shear rate. SALS patterns are simulated using a modified Cahn-Hilliard-Cook model, with an additional collective restoring force to account for polymer elasticity. Predictions from this modified model for the orientation angles of the concentration fluctuations are in excellent agreement with the experimental results. Our model also predicts that the quiescent structure factor has a Gaussian form and that the steady-state orientation of the scattering patterns is dependent on shear rate. These predictions are also in good agreement with our experimental observations. © 1994 John Wiley & Sons, Inc.     

Scattered intensity by a cross-linked polymer blend

Cross-linked mixtures of polystyrene and poly(vinyl methyl ether) exhibit a non-vanishing zero-angle intensity in small-angle neutron scattering experiments. A possible explanation is that fluctuations in composition in the mixture may be frozen by the presence of cross-links. Assuming this, we introduce a screening length κ by the condition that the scattered intensity should not be changed by cross-linking. We find κ² ∼ C/(χ − χ_i), where C is an elastic constant, χ and χ_i, respectively, the inverse temperature and that where cross-linking is performed. When the temperature is varied, we find three regimes. In the first one, the scattered intensity is monotonously decreasing. In the second one, it has a finite maximum. In the last one, the maximum eventually diverges.     

Stress overshoot of polymer solutions at high rates of shear; Polystyrene with bimodal molecular weight distribution

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, γ_σm and γ_Nm, corresponding to the peaks of σ and N₁ lay on the universal functions of γ˙τ_R, respectively, proposed for dilute solutions in pure solvent. Here τ_R 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 γ_σm = 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˙τ_R < 10⁻². This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γ_σm and γ_Nm 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     

Reversible size of shear-induced multi-lamellar vesicles

We have investigated the reversibility in the shear-induced multi-lamellar vesicle (MLV) size during stepwise cycling of the shear rate by employing common rheometry, polarized light microscopy and rheo-optic techniques. We thus address the question whether there is a true MLV steady state, irrespective of history. The system studied, was the nonionic surfactant triethylene glycol decyl ether (C₁₀E₃) with a concentration of 40 wt.% in D₂O and a constant temperature of 25°C. It was found that the MLV size varies reversibly with varying shear rate, and hence there exists a true steady state in the presence of shear flow. The experimental observations of reversibility are however restricted to higher shear rates. Because the transformation of the size results from the shear strain, the process is very slow at lower shear rates, where the steady state cannot be reached within a reasonable experimental time.     

Crystal orientation in a semicrystalline polymer in relation to deformation of polymer spherulites. III. Small-angle light scattering

Small-angle polarized light scattering from a deformed three-dimensional spherulite is formulated on the basis of the deformation model proposed in Part II of this series. The intensity distribution of scattered light is discussed chiefly for the cross-polarization condition, the so-called H_v polarization, as a function of elongation of the spherulite. In the undeformed state, the scattered intensity distribution forms the typical fourleaf clover pattern, and the intensity decreases with increasing fraction of crystals oriented randomly (type R crystals) within the crystal lamellae of the spherulites. In a system composed of type R crystals and folded-chain crystals (type B crystals) within the lamellae, the four-leaf pattern moves to the horizontal zone near the equator with increasing elongation of the spherulite, and, simultaneously, extends to some extent to the vertical zone near the meridional direction as a parameter measuring the ease of lamellar untwisting increases. In a system composed, in addition to type R and type B crystals, of crystals transformed from type B to type C_a and type C_r due to tilting and unfolding of polymer chains, respectively, within the crystal lamellae an eight-leaf pattern appears, even at small elongation up to about 30%. Each lobe of the eight-leaf pattern undergoes a characteristic change with increasing elongation. In both systems, the scattered intensity increases with sharpening of orientation distribution of crystals within the crystal lamellae.     

一个高粘弹的阴离子蠕虫胶束体系

以频率扫描和稳态剪切实验研究了140 mmol·L^-1羧酸盐gemini 表面活性剂(C₁₄Φ₂C₁₄)在100 mmol·L^-1 NaBr 条件下溶液的流变行为. 在低剪切频率时, 溶液呈现出具有单一松弛时间特性的Maxwell 流体行为.通过活的高分子模型(living polymer model)分析,C₁₄Φ₂C₁₄体系在25℃ 时形成了很长的蠕虫胶束(3.6-6.8μm). 冷冻透射电镜也观察到蠕虫胶束的形成. 这些胶束相互缠绕, 形成了很黏稠的溶液(零剪切粘度高达1.10×10⁴ Pa·s), 外观呈现胶状. 随着温度升高至70℃, 体系的相对粘度仍旧保持很高(1.8×10⁴), 这在阴离子表面活性剂蠕虫胶束溶液中是很少见的. 体系的流动活化能(E_a)约为(141±5) kJ·mol^-1. 利用动态光散射测定了C₁₄Φ₂C₁₄聚集体的尺寸分布, 证实了这个表面活性剂在5-10 mmol·L^-1的低浓度时生成了约100 nm的大聚集体, 这些大聚集体随着表面活性剂浓度的增加很容易转化成棒状直至蠕虫胶束.     

Scattering function and the dynamics of phase separation in polymer mixtures under shear flow

The phenomenological mean-field theory describing concentration fluctuations and spinodal decomposition of binary mixtures of long flexible macromolecules is generalized to mixtures under steady shear flow. This shear flow leads to a partial orientation and stretching of the coils, as well as to an anisotropic deformation of concentration fluctuations. Generalizing the approach of Onuki and Kawasaki, we obtain the collective scattering function describing these concentration fluctuations in the mixture under shear flow. Both the steady-state situation in the one-phase region and the initial stages of spinodal decomposition for concentrations inside of the spinodal curve are considered.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Berlin, March 30–April 3, 1987.     

Light scattering from swollen textured polymer network composites

Light scattering from a swollen textured heterogeneous polymer network is discussed using example of a network composite filled by spherical inclusions anisotropically distributed in the matrix. The dependence of the scattering intensity on the Fourier transform of the correlation function dry-state shear moduli fluctuations has been established. H_v scattering patterns from uniaxial textures and their ratio with the composite anisotropy parameter are analyzed. The sensitivity of the H_v scattering pattern on restrictions during the swelling is emphasized. © 1993 John Wiley & Sons, Inc.     

Inclusion complexes of γ-cyclodextrin and carboxyl-modified γ-cyclodextrin with C60: synthesis, characterization and controlled release application via microgels

Carboxyl modified γ-cyclodextrin (CDSA) with a substitution degree of about 9.5 was prepared by the esterification of γ-cyclodextrin (CD) with succinic anhydride in pyridine at 90 °C. The chemical composition and the structure of CDSA were characterized by FT-IR, MALDI-TOF, X-ray diffraction pattern, potentiometric titration and TGA. Modified and native γ-cyclodextrin associate with fullerene (C₆₀) in DMF-toluene mixture resulting 1:1 CDSA:C₆₀ and CD:C₆₀ inclusion complexes. Aqueous solutions of native cyclodextrin, carboxyl-modified cyclodextrin and their inclusion complexes with C₆₀ were used as microgel solvent (or swelling agent) for controlled release application. The release of solutions was induced by shear stress and demonstrated using rheo-optical set-up.     

Elastic and quasielastic light scattering from mixtures of three polymers and a solvent: The effects of polymethylmethacrylate concentration and molecular weight on the properties of polystyrene/polydimethylsiloxane/toluene solutions

Elastic and quasi-elastic light scattering data obtained from PS/PDMS/PMMA/toluene mixtures are reported. Several systems characterized by different concentrations and different molecular weights of PMMA are considered. For each of these systems, a systematic investigation is performed as a function of the scattering angle and the concentration of the PS/PDMS mixture using both techniques. The PMMA does not contribute directly to the scattered light since its increment of refractive index is zero. However the data show that its presence modifies substantially the apparent interaction parameter of PS and PDMS and the single diffusion coefficient of these polymers in the solution. The variations of these quantities with the concentration and molecular weight of PMMA are obtained. The data are analyzed within a simplified model combining based on the random phase approximation and the Rouse dynamics for ternary polymer mixtures. © 1995 John Wiley & Sons, Inc.     

Rheo‐optical studies of the effect of shear flow on the structure of elastomer blends

The effect of shear flow on the structure of a phase‐separated, near‐critical blend of 50/50 (w/w) poly(styrene‐ran‐butadiene) and polybutadiene was studied with two different custom‐built rheo‐optical instruments that combined polymer melt flow and small‐angle light scattering (SALS). The deformation of the phase domains during shear flow was nonaffine, and the SALS patterns evolved from a spinodal ring (SR) pattern to a squashed SR with two high‐intensity lobes, to an H‐pattern, to a butterfly pattern with a dark streak along the equator, and finally to a steady‐state, elliptical pattern. The SALS patterns were explained in terms of a network model, in which the strands of the network first orient in the flow direction, then extend in this direction, and finally break up into droplets aligned in the flow direction. According to this picture, the strands in the vorticity direction do not deform until relatively high strains, after which the periodicity of the network begins to disappear. Supporting this model was the observation that the transitions between the different SALS patterns corresponded to inflections and/or maxima in the shear stress or first normal stress difference. Increasing the shear rate changed the kinetics of the structure evolution and reduced the size of the phase‐separated droplets in the steady state. No evidence was obtained for flow‐induced miscibility. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1725–1738, 2004     

Small-angle neutron scattering from a hexagonal phase under shear

Summary The shear orientation of a micellar hexagonal liquid crystalline phase was investigated by small-angle neutron scattering. The hexagonal phase in the quiescent state showed a symmetrical scattering pattern typical of a polydomain structure. Enhanced scattering along the flow direction was observed during shear and the anisotropy of scattering intensity became stronger with increasing shear rate. The anisotropic scattering pattern corresponds to an orientation perpendicular to the flow direction and can be interpreted as a log-rolling state. The oriented sample did not relax after cessation of shear. The results from small-angle neutron scattering confirm data obtained previously from rheo-small angle light scattering measurements and are discussed in comparison to shear alignment of lyotropic liquid crystalline polymer solutions.     

Dynamic light scattering and small-angle neutron scattering studies on organogels formed with a gelator

Small-angle neutron scattering (SANS) and light scattering studies were carried out on an organogel consisting of a gelator, coded P-1, and dimethyl sulfoxide (DMSO). The gelator was made of an oligosiloxane stem and about eight branches of an amino acid derivative combined with a long alkyl chain. The amino acid part, N-n-pentanoyl-L -isoleucylaminooctadecane, was responsible for intermolecular association via hydrogen bonding between amide groups. After the complete dissolution of P-1 in DMSO at 85 °C, the solution was cooled, and the variations of the scattered light intensity were monitored as a function of the temperature. The scattered intensity increased drastically at about 40 °C when the P-1 concentration (C) was 3.5 g/L, and this indicated gel formation. The SANS results showed that the scattering intensity function was a monotonically decreasing function, regardless of C. A master relationship of the scattering intensity was obtained with respect to C. These scattering studies disclosed the following facts. First, gelation could be monitored as an abrupt increase in the intensity. Second, the gel was composed of randomly oriented bundlelike clusters. Third, the structure factor could be reduced by the gelator concentration, and this indicated the presence of a self-similar structure across the gelation threshold. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1841–1848, 2004     

Thixotropic organogels based on a simple N-hydroxyalkyl amide: rheological and aging properties

The thixotropic properties ofthermoreversible organogels composed ofN-3-hydroxypropyl dodecanamide and various apolar fluids have been investigated by X-ray scattering, light microscopy, and rheo-optics experiments. This revealed that gel formation occurs via a precipitation process. Depending upon the cooling rate, large interconnected aggregates are formed and induce an elastic behavior. When submitted to a shear flow, these aggregates disentangled and became aligned in the direction of the velocity. Nevertheless, shear does not alter the structure of the individual aggregate and connections between the aggregates are quickly rebuilt due to gravity and thermal fluctuations when the applied flow is stopped. The alignment under flow and the reformation of the connections after the cessation of the shear induces the thixotropic behavior.     

Light scattering by cellulose. III. Morphology of wood

Radial, tangential and cross cuts of Eastern spruce are examined by a solid-state light-scattering method which allows study of light scattering due to fluctuations in density and fluctuations in anisotropy. All of the samples investigated show well-defined scattering maxima which are related to their anisotropic texture with limited contributions from random density fluctuations. The radial cuts give rise to scattering similar to that by a grating with orthogonal characteristic spacings. The gratinglike character is due mainly to the pit structure and their periodic spacings, which can be deduced from the “unit-cell” dimensions of the scattering pattern. The scattered intensity is maximum when the fiber direction is at 45° to the polarization direction; when it is either horizontal or vertical, a distinct “spherulitic” scattering is observed from which size and asymmetry of the pits can be deduced.     

The effect of phase‐separated morphology on the rheological properties of polystyrene/poly(vinyl methyl ether) blend

The effect of phase‐separated morphology on the rheological properties of polystyrene/poly(vinyl methyl ether) (PS/PVME) blend was investigated by optical microscopy (OM), light scattering (LS) method, and rheology. The blend had a lower critical solution temperature (LCST) of 112°C obtained by turbidity experiment using LS at a heating rate of 1°C/h. Three different blend compositions (critical 30/70 PS/PVME by weight) and two off‐critical (50/50 and 10/90)) were prepared. The rheological properties of each composition were monitored with phase‐separation time after a temperature jump from a homogeneous state to the preset phase‐separation temperature. For the 30/70 and 50/50 blends, it was found that with phase‐separation time, the storage and loss moduli (G′ and G″) increased at shorter times due to the formation of co‐continuous structures resulting from spinodal decomposition. Under small oscillatory shearing, shear moduli gradually decreased with time at longer phase‐separation times due to the alignment of co‐continuous structures toward the flow direction, as verified by scanning electron microscopy. However, for the 10/90 PS/PVME blend, the rheological properties did not change with phase‐separation times. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 889–906, 1999     

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     

Dispersion stability and rheological behavior of suspensions of polystyrene coated fumed silica particles in polystyrene solutions

Polystyrene coated silica（SiO₂@PS） core-shell composite particles with averaged diameter of about 290 nm were prepared by in situ emulsion polymerization of styrene on the surface ofγ-methacryloxypropyltrimethoxysilane grafted SiO₂ nanoparticles of 20-50 nm in diameter.Rheological behavior and dispersion stability of SiO₂@PS suspension in 10 wt%PS solution were compared with suspensions of untreated SiO₂ and silane modified SiO₂ nanoparticles.Suspensions of the untreated and the silane modified SiO₂ exhibited obvious shear thinning.The SiO-2@PS suspension exhibits shear viscosity considerably smaller than suspensions of untreated and silane modified SiO₂ at low shear rates.Transmission electron microscopy showed that the composite particles can uniformly and stably disperse in PS solution compared to other suspensions,implying that the PS shell can effectively enhance the particle compatibility with PS macromolecules in solution.     

Effect of disorder in the twist angle on light scattering by a three-dimensional spherulite

Light scattering patterns are calculated for imperfect three-dimensional spherulites with fluctuations in the twist angle. The fluctuations are described in terms of a parameter characterizing the distance correlation function. Cases are considered in which (i) the principal axis of the scattering element makes a constant angle with the radius but there is disorder in the twist angle about the axis, and (ii) there is combined twist disorder and orientation disorder of the scattering elements. Calculations suggest that the disorder in the twist angle may lead to a decrease in the higher-order variation of scattered intensity with scattering angle and deviation from the four-leaf-clover-type scattering characteristic of a perfect spherulite at lower scattering angles. On the other hand, disorder in orientation has little effect on the scattering pattern.