Pressure-induced formation of diblock copolymer "micelles" in supercritical fluids. A combined study by small angle scattering experiments and mean-field theory. I. The critical micellization density concept

We developed a simple mean-field theory to describe polymer and AB diblock copolymer phase separation in supercritical (SC) fluids. The highly compressible SC fluid has been described by using a phenomenological hole theory, properly extended to consider the solvent/polymer/vacancy pseudoternary mixture. The model has been applied to describe the phase behavior of AB-diblock copolymers under the assumption of a strong solvent selectivity for just one copolymer chain. In our model the solvent selectivity is a strong function of the external pressure because in compressible fluids vacancies reduce the number of favorable solvent-polymer contacts. The combined effect of the pressure on the average solvent quality and selectivity for a single polymer chain makes the phase behavior of a diblock copolymer in SC fluids quite complex. Small angle neutron and x-ray scattering (SANS and SAXS) measurements have been performed on SC-CO2 solutions of different AB-diblock copolymers containing a perfluorinated chain. The data obtained over a wide range of pressure and temperature confirm our theoretical predictions.     

Sphere-to-rod transition of non-surface-active amphiphilic diblock copolymer micelles: a small-angle neutron scattering study

Micellization behavior of amphiphilic diblock copolymers with strong acid groups, poly(hydrogenated isoprene)-block-poly(styrenesulfonate), was investigated by small-angle neutron scattering (SANS). We have reported previously (Kaewsaiha, P.; Matsumoto, K.; Matsuoka, H. Langmuir 2005, 21, 9938) that this strongly ionic amphiphilic diblock copolymer shows almost no surface activity but forms micelles in water. In this study, the size, shape, and internal structures of the micelles formed by these unique copolymers in aqueous solution were duly investigated. The SANS data were well described by the theoretical form factor of a core-shell model and the Pedersen core-corona model. The micellar shape strongly depends on the hydrophobic chain length of the block copolymer. The polymer with the shortest hydrophobic chain was suggested to form spherical micelles, whereas the scattering curves of the longer hydrophobic chain polymers showed a q-1 dependence, reflecting the formation of rodlike micelles. Furthermore, the addition of salt at high concentration also induced the sphere-to-rod transition in micellar shape as a result of the shielding effect of electrostatic repulsion. The corona thickness was almost constant up to the critical salt concentration (around 0.2 M) and then decreased with further increases in salt concentration, which is in qualitatively agreement with existing theories. The spherical/rodlike micelle ratio was also constant up to the critical salt concentration and then decreased. The micelle size and shape of this unique polymer could be described by the common concept of the packing parameter, but the anomalously stable nature of the micelle (up to 1 M NaCl) is a special characteristic.     

Study of micelle formation by the diblock copolymer poly(styrene-b-dimethyl siloxane) in n-dodecane by small angle x-ray scattering

The diblock copolymer poly(styrene-b-dimethyl siloxane) (PS-PDMS) in n-dodecane forms multimolecular micelles in which insoluble PS blocks associate in a core surrounded by a shell of solvated PDMS blocks. Small angle X-ray scattering data have been obtained for PS-PDMS concentrations in the range 0.5–10%. Intensity data have been interpreted by the Guinier method in order to determine the radius of the PS core of a micelle. Scattering intensities exhibit negative deviations from Porod's law, which is characteristic of a diffuse interfacial layer, permitting the determination of the thickness of the shell of solvated PDMS blocks. Scattering curves for solutions having high PS-PDMS concentrations have a peak maximum indicating ordered arrays of micelles.     

Mixed micelles of fluorocarbon and hydrocarbon surfactants. A small angle neutron scattering study

Mixtures of the partly fluorinated cationic surfactant HFDePC (N-(1, 1,2,2-tetrahydroperfluorodecanyl)-pyridinium chloride and deuterated headgroup) with C16TAC, hexadecyl-trimethylammonium chloride, have been investigated using small angle neutron scattering with contrast matching. Earlier results from this system suggested that a demixing occurred, into two coexisting populations of micelles, hydrocarbon-rich and fluorocarbon-rich, respectively. The present results could be explained by one type of mixed micelles with an inhomogeneous distribution of fluorinated and hydrogenated surfactants within the micelles although a demixing cannot be definitely excluded.     

A small angle neutron scattering study of the sodium di-n-pentyl phosphate micelles in water

Small angle neutron scattering has been used to elucidate the size and shape of a micelle in the sodium di-n-pentyl phosphate (DPP)-water system. The results are summarized as follows. For the DPP micelle, the aggregation number (n) depends on the concentration (n=12, at 7.0 wt% andn=15 at 10.0 wt%). The minimum micelle is spherical and has an aggregation numbern=7. For the DPP-micellar system, it can be assumed that micellar growth and variation from the spherical to probate shape occurs with an increase in concentration above the CMC.     

Structure and dynamics of water in nonionic reverse micelles: A combined time-resolved infrared and small angle x-ray scattering study

We study the structure and reorientation dynamics of nanometer-sized water droplets inside nonionic reverse micelles (water/Igepal-CO-520/cyclohexane) with time-resolved mid-infrared pump-probe spectroscopy and small angle x-ray scattering. In the time-resolved experiments, we probe the vibrational and orientational dynamics of the O-D bonds of dilute HDO:H(2)O mixtures in Igepal reverse micelles as a function of temperature and micelle size. We find that even small micelles contain a large fraction of water that reorients at the same rate as water in the bulk, which indicates that the polyethylene oxide chains of the surfactant do not penetrate into the water volume. We also observe that the confinement affects the reorientation dynamics of only the first hydration layer. From the temperature dependent surface-water dynamics, we estimate an activation enthalpy for reorientation of 45 ± 9 kJ mol(-1) (11?±?2 kcal mol(-1)), which is close to the activation energy of the reorientation of water molecules in ice.     

Analysis of orientation fluctuation in fluids by small angle X-ray scattering

The small angle X-ray scattering of molecular fluids contains information on particular aspects of their orientational order. Examples are given for the case of the isotropic, nematic and cholesteric phases of mesogenic molecules. It is shown that the distribution of the molecular centers relative to the direction defined by the molecular long axes can be analysed by means of small angle X-ray scattering. An approximate expression for the circulation correlation function is given.     

A neutron scattering study of the structure and water partitioning of selectively deuterated copolymer micelles

We present a scattering study of a selectively deuterated micelle-forming diblock copolymer. The copolymer comprises a partially deuterated polystyrene (d,h-PS) block and an imidazolium-functionalized PS (IL) block. In toluene solutions, the copolymers assemble into elongated micelles where the IL block forms the micelle core. Through dynamic light scattering (DLS) measurements, we obtain the overall size of the micelles. In our small-angle neutron scattering (SANS) studies, we use contrast matching to characterize the IL core and the PS shell of the micelles independently. The PS block forming the micelle shell exhibits either a starlike or brushlike conformation depending upon the size of the core to which it is tethered. We find the IL block to be in an extended conformation, driving the formation of slightly elongated and relatively stiff micelle cores. The elongated micelle core cross-sectional radius and length depend linearly on the length of the IL block. We find that the micelles can sequester a few water molecules for each IL repeat unit; the addition of water slightly increases the cross section of the elongated micelles.     

Light scattering study of solubilization of organic molecules by block copolymer micelles in aqueous media

Block copolymers, when dissolved in a selective solvent, form spherical micelles. These micelles can selectively solubilize organic molecules otherwise insoluble in the pure solvent. In this study, we report solubilization of organic molecules by styrene-methacrylic acid block copolymer micelles in aqueous buffers. A light scattering technique was developed to determine the extent of micellar solubilization. Our results indicate that the extent of micellar solubilization depends on the chemical nature of organic molecules, specifically, on the interactions between the organic compound and polystyrene. A thermodynamic model has been developed to describe micellar solubilization. The theoretical calculation agrees reasonably well with the experimental results for two micellar samples examined. ©1995 John Wiley & Sons, Inc.     

Characteristic lengths and the structure of salt free polyelectrolyte solutions. A small angle neutron scattering study

We have studied salt free semi dilute polyelectrolyte solutions by small angle neutron scattering. Specific labelling associated with an extrapolation method has allowed the separation of the form factor of a single polyelectrolyte chainS ₁(q) and the structure factorS ₂(q). Two lengths are deduced from these two factors: the persistence lengthb _t which characterizes the electrostatic interactions along the chain by a fitting ofS ₁(q) with calculation of the scattering function for a wormlike chain, and fromS ₂(q),q _m ^–1 which characterizes the interactions between chains. These two lengths vary in the same way with the concentration of polyions (b _t C _p ^–1/2 ,q _m ^–1 C _p ^–1/2 ) and a constant relation exists between them: only one length is then necessary to describe the structure of polyelectrolyte soltuion on this semidilute concentration range.Laboratoire Commun CEA-CNRS.     

Mechanism of the transition between lamellar and gyroid phases formed by a diblock copolymer in aqueous solution

The mechanism of the transition from a lamellar phase to a gyroid phase in an aqueous solution of a diblock copolymer has been studied by time-resolved synchrotron small-angle X-ray scattering. The transition occurs via a metastable perforated lamellar structure. The perforations initially have liquidlike ordering before developing hexagonal packing. The transient phase of irregularly perforated layers is revealed by the development of diffuse scattering peaks, just below the Bragg peaks of the lamellar structure. The diffuse scattering is modeled by Monte Carlo simulations of perforated layers. Following the formation of perforations, Bragg peaks characteristic of a hexagonal structure signal an ordering into a hexagonal lattice (with the concomitant loss of diffuse scattering). Computer simulations based on a dynamic density functional model reproduce these features. The hexagonal perforated lamellar phase is rapidly replaced by the gyroid phase. The domain spacing of the gyroid phase is larger than that of the perforated lamellar structure. The perforated lamellar and gyroid phases coexist for a defined period. The reverse transition from gyroid to lamellae occurs directly, with no transient or metastable intermediates.     

Time evolution of density fluctuation in supercritical region. I. Non-hydrogen-bonded fluids studied by dynamic light scattering

The time evolution of the density fluctuation of molecules inhomogeneously dispersing in a mesoscopic volume is investigated by dynamic light scattering in several fluids in supercritical states. This study is the first time-domain investigation to compare the dynamics of density fluctuation among several fluids. The samples used are non-hydrogen-bonded fluids in the supercritical states: CHF(3), C(2)H(4), CO(2), and xenon. These four molecules have different properties but are of similar size. Under these conditions, the relationship between dynamic and static density inhomogeneities is studied by measuring the time correlation function of the density fluctuation. In all cases, this function is characterized by a single exponential function, decaying within a few microseconds. While the correlation times in the four fluids show noncoincidence, those values agree well with each other when scaled to a dimensionless parameter. From the results of this scaling based on the Kawasaki theory and Landau-Placzek theory, the relation between dynamics and static structures is analyzed, and the following four insights are obtained: (i) viscosity is the main contributor to the time evolution of density fluctuation; (ii) the principle of corresponding state is observed by the use of time-domain data; (iii) the Kawasaki theory and the Landau-Placzek theory are confirmed to be applicable to polar, nonpolar, and nondipolar fluids that have no hydrogen bonding, at temperatures relatively far from critical temperature; and (iv) the density fluctuation correlation length and the value of density fluctuation are estimated from the time-domain data and agree with the values from other experiments and calculations.     

A small angle X-ray scattering study of polyethylene fibres,using the two-dimensional correlation function

Summary By Fourier transformation of the intensity distribution in the small angle X-ray scattering diagram of a polymer fibre one obtains the corresponding two-dimensional correlation function. This is compared with correlation functions calculated on the basis of different models of the semi-crystalline morphology. Here, two steps may be distinguished: in the first, the correctness of a model may be checked with the aid of qualitative features, such as the relative positions and sizes of positive and negative areas; in the second a quatitative agreement is pursued by fixing the various parameters involved. This method was applied to cold drawn low density polyethylene before and after annealing at different temperatures. In the case of the non-annealed sample, the microparacrystalline model, discussed byHosemann andLoboda-Cackovic (J. Appl. Cryst.11, 540 (1978)) was found to give the best fit. Annealing at 80 °C or higher temperatures seems to lead to what has been indicated as a three-dimensional chess-board structure; it consists of fibrils in which crystalline and amorphous regions alternate in such a way that the crystalline regions in a fibril are adjacent to amorphous regions in neighbouring fibrils.

---

Zusammenfassung Durch Fourier-Transformation der Intensitätsverteilung im Kleinwinkelstreudiagramm von Polymerfasern bekommt man die zugehörige zweidimensionale Korrelationsfunktion. Diese wird verglichen mit Korrelationsfunktionen, die für verschiedene Modelle der teilkristallinen Morphologie berechnet wurden.Hier werden zwei Schritte unterschieden. Im ersten Schritt wird die Richtigkeit eines Modells überprüft mit Hilfe von qualitativen Merkmalen, wie z. B. die relativen Lagen und Größen der positiven und negativen Bereiche. Im zweiten Schritt wird eine quantitative Übereinstimmung dadurch angestrebt, daß die unterschiedlich bezüglichen Parameter festgestellt werden. Diese Methode wurde angewandt bei kaltverstrecktem Polyäthylen niedriger Dichte, sowohl vor wie nach Temperung bei verschiedenen Temperaturen. Im Falle einer nicht getemperten Probe zeigte sich, daß das mikrokristalline Modell, vorgeschlagen von Hosemann und Loboda-Cackovic (J. Appl. Cryst.11, 540 (1978)), am besten zutrifft. Temperung bei 80°C oder bei höheren Temperaturen scheint zu einer Struktur zu führen, die als dreidimensionale Schachbrett-Struktur bezeichnet wurde. Sie besteht aus Fibrillen, in denen kristalline und amorphe Bereiche abwechseln, und zwar so, daß die kristallinen Bereiche in einer Fibrille nur von amorphen Bereichen in nächstliegenden Fibrillen umgeben sind.

     

Determination of the structure factor for concentrated silica dispersions using small angle x-ray scattering. II. Experiment

The structure factor of a number of silica suspensions in cyclohexane, with concentrations ranging from 0.01 to 0.714 gcm^–3, has been determined with small angle x-ray scattering, using a Kratky camera. The experimental structure factor is compared with a theoretical one for which polydispersity effects on the particle scattering factor and on the structure are explicitly taken into account.Analysis of the scattered intensity at a scattering angle=0 shows that the particles in the suspension interact like hard spheres, with a specific hard sphere volume of 0.61 cm³g^–1. A comparison of the experimentally determined structure factor with the structure factor found by a model calculation for a polydisperse system, using the experimental particle size distribution, showed a general agreement. The height of the first maximum agreed well for all concentrations, however its position varied stronger with concentration in the experimental curves. A possible explanation of this effect is given.     

On the role of block copolymer additives for calcium carbonate crystallization: small angle neutron scattering investigation by applying contrast variation

The role of the double-hydrophilic block copolymer poly(ethylen glycol)-block-poly(methacrylic acid) (PEG-b-PMAA) on the morphogenesis of calcium carbonate (CaCO3) was studied by applying the contrast variation small angle neutron scattering technique. The morphology and size of CaCO3 crystals is strongly affected by the addition of PEG-b-PMAA. In order to determine the partial scattering functions of the polymer and CaCO3 mineral, we developed both an experimental and theoretical approach with a sophisticated method of their determination from the scattering intensity. Partial scattering functions give detailed information for each component. In particular, the partial scattering function of the polymer, Spp, shows a monotonic slope with Q(-2 to -3) where the scattering vector Q is low (Q < 0.01 Angstrom(-1)), which is a clear evidence that the polymer within the CaCO3 mineral has a mass fractal dimension. The other partial scattering functions reflected the geometry of the CaCO3 particles or the "interaction" of polymer and CaCO3 on a microscopic scale, which leads to a coherent view with Spp.     

L-tryptophan transport through a hydrophobic liquid membrane using AOT micelles: dynamics of the process as revealed by small angle X-ray scattering

Hydrophobic liquid membranes have a high technological potential in many fields of separation science. The dynamics of these systems is very complex and still not fully understood. In this work we studied the effect of the incorporation of cationic and anionic L-tryptophan at pH 1.8 and 10.0, respectively, in Aerosol-OT reverse micelles performing small angle X-ray scattering experiments. The use of a synchrotron radiation source allowed efficient in situ data acquisition. Several insights on L-tryptophan transport dynamics through hydrophobic membranes containing AOT could be obtained from these SAXS experiments, such as amino acid site localization and changes in the reverse micelle sizes.     

Water distributions in polystyrene-block-poly[styrene-g-poly(ethylene oxide)] block grafted copolymer system in aqueous solutions revealed by contrast variation small angle neutron scattering study

We develop an experimental approach to analyze the water distribution around a core-shell micelle formed by polystyrene-block-poly[styrene-g-poly(ethylene oxide (PEO)] block copolymers in aqueous media at a fixed polymeric concentration of 10 mg/ml through contrast variation small angle neutron scattering (SANS) study. Through varying the D(2)O/H(2)O ratio, the scattering contributions from the water molecules and the micellar constituent components can be determined. Based on the commonly used core-shell model, a theoretical coherent scattering cross section incorporating the effect of water penetration is developed and used to analyze the SANS I(Q). We have successfully quantified the intramicellar water distribution and found that the overall micellar hydration level increases with the increase in the molecular weight of hydrophilic PEO side chains. Our work presents a practical experimental means for evaluating the intramacromolecular solvent distributions of general soft matter systems.     

A study of helix formation in polydimethysiloxane by Raman scattering

Depolarization ratios ρ of the Raman bands due to CH₃ stretching at 2907 cm^?1 and the Si? O skeletal mode at 491 cm^?1 have been measured in polydimethylsiloxane gum as a function of temperature from 100°C to ?45°C. Below 0°C the changes in p have been interpreted in terms of the formation of helical regions in the gum. The enthalpy of helix formation ΔH has been determined as 3200 ± 600 cal/mole. An upper limit on the entropy change, ΔS, of 16 ± 3 e.u./mole and minimum values of helix content at different temperatures have been found. The Raman spectrum of crystalline polydimethylsiloxane is presented.