Capillary flow behavior of worm‐like micelles studied by small‐angle X‐ray scattering and small angle light scattering

A novel capillary flow device has been developed and applied to study the orientation of worm‐like micelles, among other systems. Small‐angle X‐ray scattering (SAXS) data from micelles formed by a Pluronic block copolymer in aqueous salt solution provides evidence for the formation of worm‐like micelles, which align under flow. A transition from a rod‐like form factor to a less persistent conformation is observed under flow. Flow alignment of worm‐like micelles formed by the low molar mass amphiphile system cetyl pyridinium chloride+sodium salicylate is studied for comparative purposes. Here, inhomogenous flow at the micron scale is revealed by streaks in the small‐angle light scattering pattern perpendicular to the flow direction. Copyright © 2006 John Wiley & Sons, Ltd.     

Crystallization and chain conformation of semicrystalline and amorphous polymer blends studied by wide‐angle and small‐angle scattering

We examine the crystallization and chain conformation behavior of semicrystalline poly(ethylene oxide) (PEO) and amorphous poly(vinyl acetate) (PVAc) mixtures with wide‐angle X‐ray diffraction (WAXD), small‐angle X‐ray scattering (SAXS), and small‐angle neutron scattering (SANS) experiments. For blends with PEO weight fractions (wt_PEO) greater than or equal to 0.3, below the melting point of PEO, the WAXD patterns reveal that crystalline PEO belongs to the monoclinic system. The unit‐cell parameters are independent of wt_PEO. However, the bulk crystallinity determined from WAXD decreases as wt_PEO decreases. The scattered intensities from SAXS experiments show that the systems form an ordered crystalline/amorphous lamellar structure. In a combination of WAXD and SAXS analysis, the related morphological parameters are assigned correctly. With the addition of amorphous PVAc, both the average amorphous layer thickness and long spacing increase, whereas the average crystalline layer thickness decreases. We find that a two‐phase analysis of the correlation function from SAXS, in which the scattering invariant is linearly proportional to the volume fraction of lamellar stacks, describes quantitatively the crystallization behavior of PEO in the presence of PVAc. When wt_PEO is close to 1, the samples are fully spaced‐filled with lamellar stacks. As wt_PEO decreases from 1.0 to 0.3, more PVAc chains are excluded from the interlamellar region into the interfibrillar region. The fraction outside the lamellar stacks, which is completely occupied with PVAc chains, increases from 0 to 58%. Because the radius of gyration of PVAc with a random‐coil configuration determined from SANS is smaller than the average amorphous layer thickness from SAXS, we believe that the amorphous PVAc chains still persist with a random‐coil configuration even when the blends form an ordered structure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2705–2715, 2001     

Conformation of comb‐like liquid crystal polymers in isotropic solution probed by small‐angle neutron scattering

The conformational characteristics of a comb‐like side‐chain liquid crystal polysiloxane (SCLCP), dissolved in deuterated chloroform, were evaluated by small‐angle neutron scattering (SANS) measurements over a wide q range. SANS studies were carried out on specimens with constant backbone length (DP = 198) and variable spacer length (n = 3, 5, and 11), and with constant spacer length (n = 5) and variable DP (45, 72, 127, and 198). The form factor P(q) at high q was analyzed using the wormlike chain model with finite cross‐sectional thickness (R_c) and taking into account the molecular weight polydispersity. The analysis generated values of persistence length in the range l_p = 28–32 Å, considerably larger than that of the unsubstituted polysiloxane chain (l_p = 5.8 Å), with contour lengths per monomer comparable to the fully‐extended polysiloxane backbone (l_m = 2.9 Å). This indicates a relatively rigid SCLCP chain due to the influence of the densely attached mesogenic groups. The SCLCP with n = 11 is more flexible (l_p = 28 Å) than those with n = 3 and n = 5 (l_p = 32 Å). The cross‐sectional thickness increases with spacer length, R_c ～ n^0.21±0.02 (3 ≤ n ≤ 11), and the contour length per monomer decreases with increasing spacer length, l_m ～ n^?0.35±0.01. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2412–2424, 2006     

A revised worm‐like chain model for elasticity of polypeptide chains

The elasticity of polypeptide chains is usually characterized by the worm‐like chain model that was proposed first to describe the elasticity of double‐stranded DNA. However, the molecular dynamics simulation data on the elasticity of the polypeptide chains are deviated significantly away from the theoretical data obtained based on the worm‐like chain model. Here, we provide a revised worm‐like chain model by considering entropic, enthalpic, and hydrophobic effects and the effect of the compressing force applied to the polypeptide chains. The theoretical data obtained based on the revised model are in good agreement with the molecular dynamics simulation data. Additionally, we reveal that, besides the positive‐force regime in the elasticity of polypeptide chains, the negative‐force regime also plays important roles in the biological functions of proteins. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 297–307     

Application of anomalous small‐angle X‐ray scattering to spherical polyelectrolyte brushes

The analysis of spherical polyelectrolyte brushes by anomalous small‐angle X‐ray scattering (ASAXS) is considered. The particles under consideration consist of a solid poly(styrene) core onto which chains of poly(acrylic acid) are grafted. If Rubidium ions are chosen as counterions, ASAXS can be applied to the study of these systems because the absorption edge of Rb (15199.6eV) can be reached by synchrotron radiation. Here we discuss the results to be obtained by the application of ASAXS to spherical polyelectrolyte brushes.     

Multivariable structural characterization of semicrystalline polymer blends by small‐angle light scattering

A new multi‐variable‐measurement approach for characterizing and correlating the nanoscale and microscale morphology of crystal‐amorphous polymer blends with melt‐phase behavior is described. A vertical small‐angle light scattering (SALS) instrument optimized for examining the scattering and light transmitted from structures ranging from 0.5 to 50 μm, thereby spanning the size range characteristic of the initial‐to‐late stages of thermal‐phase transitions (e.g., melt‐phase separation and crystallization) in crystal‐amorphous polymer blends, was constructed. The SALS instrument was interfaced with differential scanning calorimetry (DSC), and simultaneous SALS/DSC/transmission measurements were performed. We show that the measurement of transmitted light and SALS under H_V (cross‐polarized) optical alignments during melting can be used to reliably measure the thermodynamic (e.g., crystal melting and melt‐phase separation temperatures) and structural variables (e.g., crystalline fraction within the superstructures and volume fraction of superstructures) necessary for describing the multiphase behavior of crystal‐amorphous blends in one combined measurement. We also evaluate the orientation correlations of crystalline volume elements within the superstructures. Our results indicate that simultaneous measurement of transmitted light can provide a reliable estimate of the total scattering from density and orientation fluctuations and the melt‐phase separation temperature of polymer blends. For solution‐cast poly(?‐caprolactone)/poly(D,L‐lactic acid) blends, our multivariable measurements during melting provide the parameters necessary to generate a crystal–liquid and liquid–liquid phase diagram and characterize the solid‐state morphology. This opens up the challenge to explore use of our vertical SALS instrument as a rapid and convenient method for developing structure–property relationships for crystal‐amorphous polymer blends. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2714–2727, 2002     

Review of polystyrene diffusion studies in latex particles by small‐angle neutron scattering

This paper reviews small‐angle neutron scattering (SANS) and some results from direct nonradiative energy transfer (DET), for the observation of the diffusion coefficients of polystyrene chains at latex interfaces. To compare SANS with DET, doubly labeled polystyrene with deuterium and fluorescence groups were synthesized, showing that while SANS and DET produce comparable data in terms of diffusion coefficients, both results differ in detail, each having their own advantages. Chain confinement, ionic end groups, and short branch effects on interdiffusion were studied. Large polymer chains confined in small particles have non‐Gaussian shapes that store rubber elastic energy. Rapid, non‐diffusion relaxation is inhibited because the density would be required to become less than normal. Hence confinement effects on the diffusion rate are not significant. Using the DET method, ionic end‐groups were found to increase the early‐time apparent interdiffusion coefficients during film formation. The early‐time apparent diffusion coefficients of polystyrene with varying end‐groups were found to increase as follows: The higher apparent diffusion coefficients of the chains with ionic groups are presumably due to a surface segregation of the end‐groups caused by the polar, aqueous environment during latex synthesis. The interdiffusion behavior of sulfite‐ended polystyrene (M_n ? 300 000 g/mol) with H‐ends, one sulfite end, and two sulfite ends were compared via SANS and DET. The diffusion coefficients of polystyrene with one or two sulfite end groups were five times and ten times lower than that of polystyrene, respectively. The ionic end group effects on the reduced diffusion coefficients are interpreted as the competition between enhancement by the surface segregation of end groups and reduction by end group aggregation. Noting that sulfate end groups diffused faster, while sulfite end groups diffused slower, the effect is complex, and not yet fully resolved. Diffusion coefficients of polystyrene with branches were studied by DET. Short branches work to decrease the T_g and hence increase the diffusion coefficients. However, after the experimental temperature, T, is converted to a normalized temperature, T‐T_g, the diffusion coefficients are found to be almost independent upon the number of branches and the length of branches. The branch length ranged from one‐carbon to 40 carbons. Side chains of entanglement molecular weight or longer may be required to significantly reduce the diffusion coefficient. Copyright © 2002 John Wiley & Sons, Ltd.     

Time‐resolved crystallization study of absorbable polymers by synchrotron small‐angle X‐ray scattering

Changes in the lamellar morphology that occurred during the quiescent isothermal crystallization of absorbable poly(p‐dioxanone) (PDS) and PDS/poly(glycolide) block copolymer were studied by synchrotron small‐angle X‐ray scattering. Important morphological parameters such as the lamellar long period, the thicknesses of the crystal and amorphous phases, and the scattering invariant were estimated as a function of time, and trends observed over a wide range of experimental conditions are discussed. Thicker but more perfect lamellae were detected at higher crystallization temperatures. The breadth of the normalized semilog Lorentz‐corrected intensity peak systematically decreased with increasing temperature. In addition, the values of the crystallization half‐time and the Avrami exponent (n = 2.5), determined from the real‐time changes in the lamellar development, showed superb agreement with the bulk crystallinity data generated from other experimental techniques, such as calorimetry and dielectric relaxation spectroscopy. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 153–167, 2001     

Morphology of polyanhydride copolymers: Time‐resolved small‐angle X‐ray scattering studies of crystallization

Synchrotron small‐angle X‐ray scattering (SAXS) was used to study the isothermal crystallization kinetics of a family of polyanhydride copolymers consisting of 1,6‐bis(p‐carboxyphenoxy)hexane and sebacic acid monomers. In situ SAXS experiments permitted the direct observation of the crystallization kinetics. The structural parameters (the long period, lamellar thickness, and degree of crystallinity) were obtained from Lorentz‐corrected intensity profiles, one‐dimensional correlation functions, and interface distribution functions to form a comprehensive picture of the crystal morphology. The combination of these three analyses provided information not only on the lamellar dimensions but also on the polydispersity (nonuniformity) of these dimensions. Where possible, the crystallization kinetics were interpreted with a modified version of the Avrami equation. The results can be used to perform the rational design of controlled‐drug‐release formulations because crystallinity affects drug‐release kinetics. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 463–477, 2005     

Central small‐angle diffuse scattering from fibers is made of two components

Small‐angle X‐ray and neutron scattering from materials with fibrous texture generally includes a central diffuse scattering that is either diamond‐shaped or shaped like a two‐bladed propeller. The central scattering from fibers of polyacrylonitrile, nylon, and poly(ethylene terephthalate) and in particular the changes seen during deformation and heating have been examined. The result is that all types of central scattering from fibers are best described as having two distinct components, where these components are an extended equatorial streak and an inner nearly isotropic scattering. They arise respectively from objects that do and do not become aligned or elongated during fiber production. Examples of objects that do not become aligned are small spherical voids and solid particles. Objects that do become aligned include internal phase boundaries, and the surfaces of the fibers themselves. The equatorial streak arises from an assembly of such elongated objects preferentially oriented along the fiber axis. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

The solution phase characterization of poly(ferrocenyldimethylsilane)s by small‐angle neutron scattering

A series of monodisperse (M_w/M_n < 1.1) poly(ferrocenyldimethylsilane)s was prepared with number‐averaged degrees of polymerization, 〈z〉_n, of 9, 33, 206, and 506 ( 2 – 5 , respectively), as determined by gel permeation chromatography (GPC). The polymers were studied by small‐angle neutron scattering (SANS) in solution with the aim of obtaining the radius of gyration, R_g, the weight‐averaged molecular weight, M_w, and the polydispersity index, M_w/M_n. Data were collected over the range 0.008 < Q/Å^?1 < 0.5 and for a series of concentrations (weight fraction, w = 0.0063, 0.0125, 0.025, and 0.05). The scattered intensity, I(Q), was fitted to a model based on a Schultz–Zimm distribution of isolated chains with excluded volume. A comparison of the molecular weight and size data determined by GPC and SANS indicated an acceptable agreement between the values for R_g, M_w and M_w/M_n. The results of this study demonstrate the potential utility of SANS to fully characterize metallopolymers, and other polymer systems where traditional methods cannot be applied. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4011–4020     

Characteristics of several kinds of polyethylene gel estimated by small‐angle light scattering under cross polarization

Unusual phenomenon was confirmed in the gelation of polymer solution when branched low molecular weight polyethylene (B‐LMWPE) and ultrahigh molecular weight polyethylene (UHMWPE) solutions were quenched at their gelation temperature. That is, polarized light scattering (Hv scattering) from B‐LMWPE gels containing 95% solvent yielded a four‐leaf clover type as like the scattering from a perfect spherulite under Hv scattering but the corresponding polarized optical microscopy (POM) showed dark image showing no spherulite with Maltese cross color indicating considerable orientation fluctuation between the optical axes with respect to the radial axis of the spherulite. Hv scattering from pristine UHMWPE gels containing more than 99% solvent had an X‐type pattern, which became clearer with time. The corresponding POM images change from being dark, indicating no superstructure, to being slightly brighter, indicating the presence of indistinct superstructures. To analyze this unusual phenomenon of Hv scattering from B‐LMWPE and UHMWPE gels, new models were proposed using a statistical approach and optically anisotropic elements in three‐dimensional space. The theoretical patterns were in agreement with observation. Thus, it came to a conclusion that Hv scattering from the gels is attributed to strong distance correlation between polar and rotational angles of two optically anisotropic elements in the polymer‐rich phase. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Effect of the initial matrix material on the structure of radiation‐grafted ion‐exchange membranes: Wide‐angle and small‐angle X‐ray scattering studies

Seven different fluoropolymer films were used as matrix materials for radiation‐grafted ion‐exchange membranes. The crystallinity and preferred orientation of these membranes were studied with wide‐angle X‐ray scattering, and the lamellar structure of the membranes was examined with small‐angle X‐ray scattering. The crystallinity of poly(vinylidene fluoride) (PVDF)‐based matrix materials varied between 57 and 40%, and the crystallinity of the sulfonated samples varied between 34 and 23%. The lamellar periods of PVDF‐based matrix materials were about 115 Å, and the lamellar periods of poly(ethylene‐alt‐tetrafluoroethylene) and poly(tetrafluoroethylene‐co‐hexafluoropropylene) were 250 and 212 Å, respectively. When the samples were grafted, the lamellar periods increased. Correlation function analysis showed very clearly that the long‐range order decreased because of grafting and sulfonation processes. For those samples that showed good proton conductivity, the lamellar period also increased because of sulfonation. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1539–1555, 2002     

Removal of poly(methyl methacrylate) in diblock copolymers films studied by grazing incidence small‐angle X‐ray scattering

Self‐assembly of diblock copolymers (BCP) into periodic arrays is a promising route to generate templates for the fabrication of nanoscopic elements, when one block is selectively removed. In cylindrical morphology polystyrene‐block‐poly(methyl methacrylate) (PS‐b‐PMMA) copolymer (BCP) films, the efficiency of different processes for removing the PMMA from cylinders is studied using grazing incidence small angle X‐ray scattering (GISAXS), x‐ray reflectivity and critical dimension scanning electron microscopy. The detailed analysis of the GISAXS patterns leads to the determination of the depth of cylindrical holes left by removal of the PMMA. It is found that the combination of a preliminary UV exposure followed by a wet treatment allows to remove totally the PMMA blocks. Furthermore, the optimization of both UV exposition time and solvent allows to preserve the PS matrix and interestingly for nanolithographic applications to decrease the process costs. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1137–1144     

Deformation in lamellar and crystalline structures: in situ simultaneous small‐angle X‐ray scattering and wide‐angle X‐ray diffraction measurements on polyethylene terephthalate fibers

Changes in the lamellar and crystalline structures were followed as a function of applied stress to understand the influence of the interactions between the crystalline and amorphous domains on the fiber properties. We observed a reversible transformation from a structure giving a four‐point small‐angle pattern to a structure giving a two‐point pattern; these structures corresponded to the lamellae with oblique and normal lamellar surfaces, respectively. The characteristics of these two structures such as the stack diameter, stack height, and tilt angle were different and were determined by the processing conditions and did not change when the fiber was elastically deformed. The structure giving a two‐point pattern was probably the load‐carrying lamellar entity in these fibers. The diameter of the lamellar stacks, tilt angle of the lamellae, and the strain in the lamellar spacing appeared to have the most influence on properties such as tenacity and dimensional stability. The long‐spacing strain, which is about the same as the fiber strain, determined the modulus at low elongation as well as ultimate elongation. These indicate that the lamellar stacks have at least as much influence as the interfibrillar chains on fiber properties. Structural features that determine the performance in semicrystalline polymers were investigated by analyzing four generations of polyethylene terephthalate fibers. Some of the fiber properties correlate with changes in the crystalline domains such as the crystalline orientation, size, and unit cell dimensions. Fibers in which the crystalline strain was large because of their strong linkages to the amorphous chains, and better load transfer, had the highest modulus and lowest ultimate elongation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1538–1553, 2003     

Tilted lamellae in an affinely deformed 3D macrolattice and elliptical features in small‐angle scattering

Lamellar reflections in small‐angle X‐ray and neutron scattering patterns of uniaxially drawn semicrystalline polymers appear to fall on elliptical or hyperbolic arcs. We attribute this to a 3D lattice of tilted lamellae, a macrolattice. Affine deformation of this lattice, such as during uniaxial draw, moves and spreads the reflections along elliptical arcs, and nonaffine deformation, such as during rolling, moves and spreads the reflections along an arc that deviates from an ellipse. Discrete reflections are the product of two functions: the elliptical trace that is the Fourier transform of the affinely deformed lattice and the radial streak that is the Fourier transform of the individual lamella in the reciprocal space. Four‐point patterns are obtained if the lamellar‐surface normal is tilted away from the fiber‐axis, and two‐point patterns if it is not. This model is used to discuss the transformation between four‐ and two‐point patterns and other changes in lamellar morphology that occur during drawing and annealing of oriented semicrystalline polymers. The deformation of the macrolattice of crystalline lamellae, need not be correlated to the tilt of the lamellae. The tilt of the lamellae is shown to be important. It reflects the cross‐sectional area mismatch at the lamellar surface between crystalline stems and amorphous chains segments, and this indicates the internal strain in the interfibrillar amorphous regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1277–1286, 2006     

Probing multiple melting behaviors in poly(ethylene naphthalene 2,6‐dicarboxylate) with different thermal histories by simultaneous wide‐angle and small‐angle X‐ray scattering

A simultaneous wide‐angle and small‐angle X‐ray scattering study of two poly(ethylene naphthalene 2,6‐dicarboxylate) samples crystallized from the glassy state at different annealing temperatures for different annealing times was carried out with synchrotron radiation. Either single or dual melting was induced in the samples, as confirmed by differential scanning calorimetry (DSC). The correlation function and interface distribution function were calculated to evaluate microstructural parameters such as the long spacing, the thickness of the amorphous and crystalline phases, and the width of the size distributions. The sample with dual melting behavior exhibited an abrupt increase of all microstructural parameters at temperatures above the melting of the lowest endotherm, whereas the sample revealing a single melting endotherm did not show such a sudden change. This finding agrees with the concept that the appearance of two melting peaks in DSC traces can be explained by the dual lamellar stacking model. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 881–894, 2001     

Probing the use of small‐angle light scattering for characterizing structure of titanium dioxide/low‐density polyethylene nanocomposites

Small‐angle light scattering (SALS) measurements were used to study the structure of titanium dioxide (TiO₂)/low‐density polyethylene (LDPE) nanocomposites. The results showed that the scattering from LDPE crystalline structures and the scattering from TiO₂ nanoparticles can be resolved and separated. It is shown that the independent effects of crystallization conditions and the presence of nanoparticle aggregates on the spherulitic structure of the LDPE matrix can be determined by analyzing the scattering patterns using the methods proposed. From the SALS results, we conclude that the nanoparticle surface chemistry affects both nucleation of spherulites and their structure particularly under rapid cooling conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1084–1095, 2006     

The equatorial small‐angle scattering during the straining of poly(ether ester) and its analysis

A method for the quantitative analysis of two‐dimensional (2D) small‐angle X‐ray scattering (SAXS) patterns with fiber symmetry by successive information filtering is proposed and applied to a series of images recorded during a straining experiment of a two‐phase polymer sample at a synchrotron beamline. The studied equatorial scattering is similar to the frequently discussed void scattering, but originates from an ensemble of rodlike soft domains (needles) in the sample, orientated in the direction of strain. The intensity is extracted and projected onto the equatorial plane, the ideal two‐phase structure is extracted, and the 2D chord distribution is computed. This curve describes a 2D two‐phase morphology made from needle cross‐sections embedded in matrix material. Because interparticular correlation is found to be weak in the chord distribution, pure particle scattering is assumed. Modeling the needle cross‐sections by circular disks leads to a simple theory, which allows the deconvolution of a disk diameter distribution from the chord distribution. It is shown how parameters of the disk diameter distribution can be computed without deconvolution. For the selected poly(ether ester) thermoplastic elastomer the study of the soft domain needles indicates strain‐induced hardening. While for low elongation ϵ the soft needles are more compressible than the microfibrillar matrix, saturation is observed for ϵ > 2.5. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 975–981, 1999