Small-angle X-ray scattering study of a poly(oxyphenylethylene)–poly(oxyethylene) diblock copolymer gel under shear flow

 The structure and flow behaviour of a micellar “cubic” phase is studied, using small-angle X-ray scattering (SAXS) and constant stress rheometry on a poly(oxyphenylethylene)–poly(oxyethylene) diblock copolymer in water. The predominant structure is a face-centred cubic (fcc) array of spherical micelles, which under shear undergoes layer sliding to give a scattering pattern from stacked hexagonal close-packed layers. A detailed analysis of the SAXS data indicates the presence of a fraction of grains with a structure distorted from a fcc phase. The additional reflections that characterize this structure can be indexed to a rhombohedral unit cell, space group R3ˉm, with the same volume as the fcc unit cell. The rhombohedral unit cell corresponds to a cubic cell that has been “stretched” along a [111] direction, and it is suggested that such a structure results from the gradient in shear velocity in the Couette cell employed. Shearing at high shear rates leads to a “smearing out” of the reflections, but upon cessation of shear under these conditions a highly oriented SAXS pattern is obtained, which confirms the persistence of rhombohedral ordering. The shear-induced changes in orientation are correlated to a plateau observed in the stress plotted against shear rate, such a plateau being a sign of inhomogeneous flow. Received: 8 September 2000 Accepted: 29 November 2000     

Three-dimensional crystallographic determination of the body-centered-cubic morphologies of shear-aligned block copolymer systems

The texture of ordered phases of block copolymer melts and gels is highly sensitive to shear. In the body-centered-cubic phase of a block copolymer system [polystyrene–poly(ethylene butylene)–polystyrene] mixed with oil, we show how a given textures can be controlled with the application of a specific shear rate and amplitude. The low-amplitude shear texture is dominated by {001} planes perpendicular to the shear gradient and by the [110] axis parallel to the flow direction, that is, the {001}/[110] slip system. Detailed crystallographic studies show that both intermediate-amplitude oscillatory shear and large-amplitude oscillatory shear lead to twin structures with {112} planes sharing neighboring twins and [111] axes parallel to the shear flow. At an intermediate shear amplitude, the ve shear plane, defined by the shear flow direction (v) and shear vorticity direction (e), is parallel to the {112} twin planes. At a high shear amplitude, the orientation is rotated 90°, and this makes the ve shear plane parallel to the {110} crystallographic planes. The crystalline slip system is accordingly ({112 }/[111] + {11 2}/[111]) under intermediate-amplitude shear and ({11 0}/[111] + {1 10}/[111]) under large-amplitude shear. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3095–3101, 2004     

Bond-orientational analysis of hard-disk and hard-sphere structures

We report the bond-orientational analysis results for the thermodynamic, random, and homogeneously sheared inelastic structures of hard-disks and hard-spheres. The thermodynamic structures show a sharp rise in the order across the freezing transition. The random structures show the absence of crystallization. The homogeneously sheared structures get ordered at a packing fraction higher than the thermodynamic freezing packing fraction, due to the suppression of crystal nucleation. On shear ordering, strings of close-packed hard-disks in two dimensions and close-packed layers of hard-spheres in three dimensions, oriented along the velocity direction, slide past each other. Such a flow creates a considerable amount of fourfold order in two dimensions and body-centered-tetragonal (bct) structure in three dimensions. These transitions are the flow analogs of the martensitic transformations occurring in metals due to the stresses induced by a rapid quench. In hard-disk structures, using the bond-orientational analysis we show the presence of fourfold order. In sheared inelastic hard-sphere structures, even though the global bond-orientational analysis shows that the system is highly ordered, a third-order rotational invariant analysis shows that only about 40% of the spheres have face-centered-cubic (fcc) order, even in the dense and near-elastic limits, clearly indicating the coexistence of multiple crystalline orders. When layers of close-packed spheres slide past each other, in addition to the bct structure, the hexagonal-close-packed (hcp) structure is formed due to the random stacking faults. Using the Honeycutt-Andersen pair analysis and an analysis based on the 14-faceted polyhedra having six quadrilateral and eight hexagonal faces, we show the presence of bct and hcp signatures in shear ordered inelastic hard-spheres. Thus, our analysis shows that the dense sheared inelastic hard-spheres have a mixture of fcc, bct, and hcp structures.     

Ultraslow dynamics in asymmetric block copolymers with nanospherical domains

Low shear rate and low frequency measurements focused on the extremely slow dynamics of a three-dimensional body-centered cubic (BCC) structure of an asymmetric block copolymer under nanophase-separated conditions. The material studied was poly(styrene-b-ethylene-co-butylene-b-styrene) swollen in a hydrocarbon oil selective for the midblock. Transient viscosities during start-up of shear flow at extremely low shear rates are governed by very long relaxation times and by a modulus that is nearly the same as the plateau modulus obtained from oscillatory shear experiments. Only at extremely low shear rates a zero shear viscosity could be attained. Its very high value is close to the viscosity calculated from stress relaxation experiments. The steady shear viscosity decreases by several orders of magnitude when increasing the shear rate. SAXS experiments on samples sheared even at very low rates indicated loss of the BCC order that was present in the annealed samples before shearing. The SAXS profile recorded on such a sample showed a first-order maximum followed by a broad shoulder indicating a liquid-like short-range order of PS nanospheres in the swollen EB matrix.     

Stacking structure of concentrated shear ordered dispersions by two scattering methods

In this paper, the ordering in concentrated charge stabilized colloidal dispersions is considered. Despite the impressive Bragg reflections obtained for shear ordered dispersions by light (LS), small-angle neutron (SANS), and small-angle X-ray scattering (SAXS), a number of open questions remain. Sheared dispersions are usually ordered in layers. For such systems, two questions arise: (1) What is the structure in a layer? (2) What is the stacking structure perpendicular to the layers? The second question requires a method to determine the structure perpendicular to the layers. Although originally interested only in structural aspects, we were forced to consider different methods. Two methods are treated both applicable to neutron and X-ray scattering from concentrated dispersions. One has been used by physicists and chemists for many years to determine the structure of crystals by sample rotation. In colloid science, we have used it previously in neutron and X-ray scattering. A second method is treated here which can be applied in small-angle scattering from a Couette cell. It gives the scattering intensity in a certain direction without sample rotation. Although very useful with the Couette cell, it cannot be found in any of the well-known references on colloid science. A theoretical explanation and experimental examples obtained by synchrotron X-ray scattering from a Couette cell are given in the paper.     

Stacking fault structure in shear-induced colloidal crystallization

We report measurements of the spatial distribution of stacking faults in colloidal crystals formed by means of an oscillatory shear field at a particle volume fraction of 52% in a system where the pair potential interactions are mildly repulsive. Stacking faults are directly visualized via confocal laser scanning microscopy. Consistent with previous scattering studies, shear orders the initially amorphous colloids into close-packed planes parallel to the shearing surface. Upon increasing the strain amplitude, the close-packed direction of the (111) crystal plane shifts from an orientation parallel to the vorticity direction to parallel the flow direction. The quality of the layer ordering, as characterized by the mean stacking parameter, decreases with strain amplitude. In addition, we directly observe the three-dimensional structure of stacking faults in sheared crystals. We observe and quantify spatial heterogeneity in the stacking fault arrangement in both the flow-vorticity plane and the gradient direction, particularly at high strain amplitudes (gamma> or =3). At these conditions, layer ordering persists in the flow-vorticity plane only over scales of approximately 5-10 particle diameters. This heterogeneity is one component of the random layer ordering deduced from previous scattering studies. In addition, in the gradient direction, the stacking registry shows that crystals with intermediate global mean stacking probability are comprised of short sequences of face-centered cubic and hexagonal close-packed layers with a stacking that includes a component that is nonrandom and alternating in character.     

Study on Non-Newtonian Behaviors of Lennard-Jones Fluids via Molecular Dynamics Simulations

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic structure of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here:First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase monotonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.     

Scattering experiments on the structure of concentrated dispersions

 In this work the Couette cell is compared with a more recently constructed disk shear cell. There are distinct advantages of the disk over the Couette cell, in particular, when it comes to the determination of the intensity along certain Bragg rods. Received: 12 December 2000 Accepted: 31 January 2001     

振荡剪切流场下PS/PVME/SiO2复合物的相行为

利用光学显微镜-剪切台联用系统研究了振荡剪切流场下聚苯乙烯（PS）/聚甲基乙烯基醚（PVME）/二氧化硅（SiO₂）纳米粒子复合物的热力学稳定性. 结果表明,小振幅振荡剪切可导致PS/PVME共混物出现类似在稳态流场下的剪切诱导相容及剪切诱导相分离现象. 共混体系存在临界振荡频率ω_c,当振荡频率低于ω_c时,发生剪切诱导相分离（SID）行为,反之发生剪切诱导相容（SIM）行为. SiO₂纳米粒子的加入使复合体系的相容性提高. 存在一个临界SiO₂纳米粒子含量φ_c,当SiO₂纳米粒子含量高于φ_c时,复合体系中不存在临界振荡频率ω_c,低振荡频率下的剪切诱导相分离得到抑制. 此外,复合体系的上述行为与升温速率和共混物组成密切相关.     

Crystallization studies of isotactic polypropylene containing nanostructured polyhedral oligomeric silsesquioxane molecules under quiescent and shear conditions

Crystallization studies at quiescent and shear states in isotactic polypropylene (iPP) containing nanostructured polyhedral oligomeric silsesquioxane (POSS) molecules were performed with in situ small‐angle X‐ray scattering (SAXS) and differential scanning calorimetry (DSC). DSC was used to characterize the quiescent crystallization behavior. It was observed that the addition of POSS molecules increased the crystallization rate of iPP under both isothermal and nonisothermal conditions, which suggests that POSS crystals act as nucleating agents. Furthermore, the crystallization rate was significantly reduced at a POSS concentration of 30 wt %, which suggests a retarded growth mechanism due to the molecular dispersion of POSS in the matrix. In situ SAXS was used to study the behavior of shear‐induced crystallization at temperatures of 140, 145, and 150 °C in samples with POSS concentrations of 10, 20, and 30 wt %. The SAXS patterns showed scattering maxima along the shear direction, which corresponded to a lamellar structure developed perpendicularly to the flow direction. The crystallization half‐time was calculated from the total scattered intensity of the SAXS image. The oriented fraction, defined as the fraction of scattered intensity from the oriented component to the total scattered intensity, was also calculated. The addition of POSS significantly increased the crystallization rate during shear compared with the rate for the neat polymer without POSS. We postulate that although POSS crystals have a limited role in shear‐induced crystallization, molecularly dispersed POSS molecules behave as weak crosslinkers in polymer melts and increase the relaxation time of iPP chains after shear. Therefore, the overall orientation of the polymer chains is improved and a faster crystallization rate is obtained with the addition of POSS. Moreover, higher POSS concentrations resulted in faster crystallization rates during shear. The addition of POSS decreased the average long‐period value of crystallized iPP after shear, which indicates that iPP nuclei are probably initiated in large numbers near molecularly dispersed POSS molecules. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2727–2739, 2001     

Bis(1,3,4‐trimethylpyridinium) tetrachloridocuprate(II) and bis(1,3,4‐trimethylpyridinium) tetrabromidocuprate(II): an examination of the A2CuX4Fdd2 structure type

The title bis(1,3,4‐trimethylpyridinium) tetrahalidocuprate(II) structures, (C₈H₁₂N)₂[CuCl₄], (I), and (C₈H₁₂N)₂[CuBr₄], (II), respectively, consist of flattened [CuX₄]²⁻ tetrahedral complex anions and planar 1,3,4‐trimethylpyridinium cations. Chloride compound (I) is a rare example of an A₂CuCl₄ structure with an elongated unit cell in the polar space group Fdd2. The [CuCl₄]²⁻ anions have twofold rotational symmetry and are arranged in distorted hexagonal close‐packed (hcp) layers, which are interleaved with layers of cations, each in a four‐layer repeat sequence, to generate the elongated axis. The organic cations stack along [101] or [10] in alternating layers. The methyl groups meta on the cation ring and the larger of the trans Cl—Cu—Cl angles both face the same direction along the polar axis and are the most prominent features determining the polarity of the structure. Bromide compound (II) crystallizes in a centrosymmetric structure with a similar layer structure but with only a two‐layer repeat sequence. Here, symmetry‐inequivalent cations are segregated into alternating layers with cations, forming hcp layers of inversion‐related cation pairs in one layer and parallel stacks of cations in the other. The change in space group when the larger Br⁻ ion is present suggests that the 1,3,4‐trimethylpyridinium ion has a minimal size to allow the Fdd2 A₂CuX₄ structure type.     

振荡剪切场下PS/PVME共混物的相分离动力学研究——相分离的依时性及应力响应

利用自制的激光散射流变仪研究了聚苯乙烯/聚甲基乙烯基醚(PS/PVME)(重量比30/70)二元共混物在振荡剪切场下的相分离动力学过程.在特定的振荡频率和应变振幅条件下,共混物的相分离具有显著的周期特性和各向异性.在同一个振荡相位角条件下,相分离在早期符合经典的Cahn-Hilliard线性理论.在相分离过程中,流动方向上的特征波数qxm表现出明显的受迫振荡特征而涡流方向上的qzm却没有;同时,两个方向上的特征波数qm平均值都未随时间发生变化,说明特定振荡频率和应变振幅的振荡剪切对特定尺寸的浓度涨落具有选择作用.研究还发现,体系的应力响应可以反映出相分离的阶段性过程,例如当相分离早期结束时,表征弹性的第一法向应力差出现了峰值.     

Effect of Shear Flow on the Polymeric Gels Formed by Macroscopic Phase Separation

Summary: Shear‐induced phase behavior of poly(ethylene oxide‐b‐(DL ‐lactic acid‐co‐glycolic acid)‐b‐ethylene oxide) (PEO‐PLGA‐PEO) triblock copolymers in water is investigated using rheology and small‐angle neutron scattering equipped with an in situ Couette shear cell. For gels formed by the macroscopic phase separation, the steady shear experiment reveals that the flow‐induced anisotropy on a nanometer length scale at a critical shear rate and the phase separation on a larger length scale are successively induced with a further increase in the shear rate. In particular, the hard gels show a memory effect inscribed by a pre‐high shear in contrast to the soft gels.

2D SANS patterns clearly show the memory effect of the hard gels at a pre‐high shear.     

Structural Changes in Block Copolymer Solutions under Shear Flow as Determined by Non‐Equilibrium Molecular Dynamics

Summary: A non‐equilibrium molecular dynamics computer simulation on microsegregated solutions of symmetrical diblock copolymers is reported. As the polymer concentration increases, the system undergoes phase transitions in the following order: body centered cubic (BCC) micelles, hexagonal (HEX) cylinders, gyroid (GYR) bicontinuous networks and lamellae (L), which are the same morphology reported for block copolymer melts. Structural classification is based on the patterns of the anisotropic static structure factor and characteristic 3‐dimensional images. The systems in the BCC micellar (ρσ³ = 0.3) and HEX cylindrical (ρσ³ = 0.4) phases were then subjected to a steady planar shear flow. In weak shear flow, the segregated domains in both systems tend to rearrange into sliding parallel close‐packed layers with their normal in the direction of the shear gradient. At higher shear rates, both systems adopt a perpendicular lamellar structure with the normal along the neutral direction. A further increase in the shear rate results in a decrease in lamellar spacing without any further structural transitions. Two critical shear rate values that correspond to the demarcation of different structural behaviors were found.

Shear‐induced BCC‐LAM phase transition.     

Orientation-induced crystallization in isotactic polypropylene melt by shear deformation

Development of orientation-induced precursor structures (nuclei) prior to crystallization in isotactic polypropylene melt under shear flow was studied by in-situ synchrotron small-angle X-ray scattering (SAXS) and rheo-optical techniques. SAXS patterns at 165°C immediately after shear (rate = 60 s⁻¹, t_s = 5 s) showed emergence of equatorial streaks due to oriented structures (microfibrils or shish) parallel to the flow direction and of meridional maxima due to growth of the oriented layer-like structures (kebabs) perpendicular to the flow. SAXS patterns at later times (t = 60 min after shear) indicated that the induced oriented structures were stable above the nominal melting point of iPP. DSC thermograms of sheared iPP samples confirmed the presence of two populations of crystalline fractions; one at 164°C (corresponding to the normal melting point) and the other at 179°C (corresponding to melting of oriented crystalline structures). Time-resolved optical micrography of sheared iPP melt (rate = 10 s⁻¹, t_s = 60 s, T = 148°C) provided further information on orientation-induced morphology at the microscopic scale. The optical micrographs showed growth of highly elongated micron size fibril structures (threads) immediately after shear and additional spherulities nucleated on the fibrils at the later stages. Results from SAXS and rheo-optical studies suggest that a stable scaffold (network) of nuclei, consisting of shear-induced microfibrillar structures along the flow direction superimposed by layered structures perpendicular to the flow direction, form in polymer melt prior to the occurance of primary crystallization. The scaffold dictates the final morphological features in polymer.     

A thermally induced transition from a body-centred to a face-centred cubic lattice in a diblock copolymer gel

 A transition from a body-centred cubic structure at room temperature to a face-centred cubic structure at higher temperature has been observed in a solution of a poly(oxyethylene)-poly(oxybutylene) diblock copolymer. The ordered micellar structures were confirmed using small-angle X-ray scattering by preparing oriented domains via steady shearing in a Couette cell. The effect of shear in generating highly oriented, twinned cubic domains is discussed. Received: 13 January 1998 Accepted: 22 January 1998     

Growth of single-crystalline Ni and Co nanowires via electrochemical deposition and their magnetic properties

Single-crystalline Ni nanowires have been successfully fabricated with anodic aluminum oxide as template by electrodeposition. Structural characterization (X-ray diffraction, XRD, and high-resolution transmission electron microscopy, HRTEM) shows that the single-crystalline Ni nanowire has a preferred orientation along the [220] direction. The effects of electrochemical deposition conditions on the structure of Ni nanowires are systematically studied to investigate the growth mechanism. Possible reasons for the growth of the single-crystalline Ni nanowires were discussed on the basis of electrochemistry and thermodynamics. These single-crystalline Ni nanowires have exhibited excellent magnetic properties (large anisotropy, large coercivity, and high remanence). By a similar process, single-crystalline Co nanowires with hexagonal close-packed (hcp) structure were achieved, also having large anisotropy, large coercivity (1.8 kOe), and high remanence ratio (80.8%).     

The combinatorics of cation-deficient close-packed structures

Pólya's enumeration theorem is used to derive an algorithm for counting all hexagonal close-packed structures with a unit cell of given size, having composition MX₂, where X is an hcp anion, M is an octahedrally coordinated cation, and no face sharing is permitted between octahedra. Generalizations of this algorithm to enumerate ordered derivatives of these structures, hcp structures with tetrahedral instead of octahedral cations, and similar structures having different stacking sequences among the close-packed layers are sketched.     

Shear-induced rotations in a weakly anchored nematic liquid crystal

We analyse the instability dynamics of a nematic liquid crystal under steady plane Couette flow. Weak anchoring for molecules of the nematic at the boundaries with an easy axis perpendicular to the flow plane is assumed. Orientation of the director along the easy axis is our basic state. Previously (Tarasov et al., 2001, Liq. Cryst. 28, 833), it was found that the critical shear rate of the primary instability of the basic state strongly decreases with anchoring strength. In the present study our interest was to examine the effect of the anchoring strength on the nematic dynamics in the regime with a slightly supercritical shear rate. It was found that for weaker anchoring the director rotates more strongly and the relaxation time of the amplitude of the basic state perturbations significantly increases. Results obtained can be used for experimental measurements of the anchoring strengths.     

Birefringence banding in a micellar solution or the complexity of heterogeneous flows

We have investigated the shear flow behavior of a classical viscoelastic equimolar wormlike micellar system made of cetyltrimethylammonium bromide and potassium bromide in the semidilute regime using mechanical and optical measurements. The experimental flow curve of this surfactant solution exhibits, above a critical shear rate, a well-defined stress plateau, characteristic of a flow of the shear-banding type. We first focus on the rheological and rheo-optical transient response of the sample after the sudden start-up of flow. The time-dependent stress profiles are strongly similar to those observed on various other systems with the occurrence of an overshoot at short times followed by a stretched exponential relaxation toward the steady state on a long time scale. This behavior is then correlated to the temporal evolution of the birefringence intensity and the extinction angle; the latter exhibits an undershoot just after the inception of the flow. Using direct visualizations of the sheared sample and spatially resolved flow birefringence across the gap of the Couette cell, we have been able to highlight a peculiar banding structure made up of three distinct regions: two layers of homogeneous but strongly differing orientations located against the walls, separated by a mixed layer, the width of which can reach half of the gap as a function of the effective applied shear rate. The induced structures contained in the band adjacent to the inner moving cylinder are found to be almost fully aligned along the flow direction. The relative proportions of each region are derived from the orientation profiles and compared to the predictions of the lever rule. The results suggest that orientation bands and shear bands are not linked in an obvious way, and the observed band structure can finally be interpreted as the coexistence either of three distinct "phases" or of only two homogeneous phases separated by an interface which can be broad, or thin and fluctuating.