Soft Condensed Matter

Introduction

Soft-condensed matter or organised molecular systems or again complex fluids are different expressions of the same domains of complexity and flexibility of matter based on (bio)polymers, surfactants, liquid crystals as well as colloidal particles.

The long-range supramolecular correlation in these systems is studied using the very high brilliance and collimation of the synchrotron radiation beam of the ESRF and by analysing the structural information contained in the small-angle scattering patterns.

Moreover, their corresponding dynamics can be investigated using the spatial coherence properties of synchrotron radiation. The X-ray speckle pattern analysis (photon correlation spectroscopy) is a unique new technique, which was up to now only feasible with laser sources.

The field of soft-condensed matter, which covers several different domains such as life sciences, chemistry, physics and industrial research will obtain much more attention in the future when all the ESRF beamlines are operational.

 

Shear-induced ordering in a micellar cubic crystal

Since the pioneering works of Hoffman (1972) and also of Ackerson and collaborators (1981) on shear-induced transitions in suspensions of charged particles, a lot of work has been done to identify the structural properties of sheared colloidal crystals. Some recent studies have focused on the search of correlation between the mechanical response (rheology) of colloidal suspensions and their structures in shearing fields.

In addition to conventional colloidal crystals, large-size monodisperse particles can also be prepared by using the selective solvent properties of di- or triblock copolymers. Recently, for polystyrene/polyisoprene diblock copolymers as constituents of the polymeric micelles, in decane, a correlation between flow and structural properties has been clearly established for two different types of crystalline arrangement [by Mc Connel et al.].

In almost all the cases mentioned above, when a colloidal crystal is subjected to a shearing field, layers of maximum density and hexagonal symmetry are formed so that the close-packed direction is parallel to the flow velocity, and the overall layers are stacked perpendicular to the shear gradient.

During the last decade, neutron scattering at small-angles has proven to be a very powerful tool in the identification of sheared structures. However, the major drawbacks of such a scattering experiment are on one hand the poor resolution (limited by the 10%-accuracy on the incident neutron wave-length) and the difficulty to probe several planes of the reciprocal space. As far as the latter point is concerned, there have been several attempts to determine the correlation between layers repeatedly stacked in the direction of the velocity gradient, kinetic measurements and in some rare cases, an estimation of the stacking fault probability could be given.

On the ID2 SAXS station the polymers placed under examination are the triblock copolymers (EO)₁₂₇(PO)₄₈ (EO)₁₂₇, where EO denotes a polyethylene oxide chain of m monomers and PO a polypropylene oxide chain of n monomers. In water, these copolymers exhibit a liquid-to-solid transition occurring with increasing temperature or polymer concentration . Using small-angle X-ray scattering (SAXS) experiments, we first stated the polycrystalline nature of the gel and the corresponding symmetry of the lattice. The structure is face-centred cubic (fcc). Applying an oscillating shearing field in a Couette cell results in a layered structure. However, the SAXS spectrometer on ID2 permitted us to explore directly and, for the first time to our knowledge, the scattered intensity along the "tubes" in the direction of the velocity gradient. The results are in excellent agreement with the stacking fault model recently reformulated by Loose and Ackerson: an almost fault-free fcc packing has been observed (Figure 90). Moreover in the stationary shearing regime, a transition between a defect mediated flow and a layering flow was pointed out. Correlation with rheological measurements are in progress.

Publication

[1] O. Diat (a), J. F. Berret (b) and G. Porte (b), Phys. Rev. B. 54 (1996) 22
[2] J. F. Berret (b), F. Molino (b), G. Porte (b), O. Diat (a) and P. Lindner (c), J. Phys.: Condens. Matter, 8 (1996) 9513
[3] F. Molino (b), J. F. Berret (b) and G. Porte (b), submitted to J. Phys.

(a) ESRF
(b) URA 233, University of Montpellier (France)
(c) ILL, Grenoble (France)

 

 

 

X-ray diffraction of photonic colloidal single crystals

Photonic crystals are dielectric composites in which the refractive index varies periodically on distances of the order of optical wavelengths. This causes effects on light analogous to the periodic potential of electrons in atomic crystals. If light is very strongly coupled with the photonic crystal, "photonic band gaps" are expected. These will cause novel phenomena such as inhibition of the spontaneous emission of excited atoms or localisation of photons. A natural way to make photonic crystals is to use suspensions of small solid spheres that perform Brownian motion. Such colloidal particles can spontaneously form bulk crystals with the desired length scales.

Small-angle X-ray scattering has been performed on ID2 to elucidate the structure of colloidal crystals and colloidal particles, since the relevant systems are optically multiple scattering. Many Bragg peaks were observed of single crystals, with lattice parameters of ~ 3700 Å (see Figure 91). On powders, many diffraction rings were detected. At all densities, the Bragg peaks could be indexed as face-centred cubic (fcc) crystals at all densities, which is a favourable structure for photonic crystals. Moreover, the fcc structure agrees with theoretical predictions for dense colloids, but contrasts to previous observations of glass formation or random stacks of hexagonal planes. The large number of Bragg peaks suggests that the Debye-Waller factors are low. Hence the colloidal particles are well ordered, which is favourable for the observation of photonic effects.

Finally, the experiments demonstrate that X-ray diffraction is a powerful tool to investigate systems with length scales comparable to wavelengths of visible light.

Publications

[1] W.L. Vos (a), M. Megens (a), C.M. van Kats (a), and P. Bösecke (b, c), Langmuir (accepted).
[2] M. Megens (a), C.M. van Kats (a), P. Bösecke (b, c), and W.L. Vos (a), J. Appl. Cryst. (1997, at press).
[3] M. Megens (a), C.M. van Kats (a), P. Bösecke (b, c), and W.L. Vos (a), Langmuir (submitted).

(a) Van der Waals-Zeeman Instituut, Universiteit van Amsterdam (The Netherlands)
(b) ESRF
(c) Max Planck Institut, Hamburg (Germany)

 

 

 

Dynamics of polymers studied with coherent X-rays

Photon Correlation Spectroscopy (PCS) is widely used to study the dynamics of soft condensed matter systems such as colloids, polymers and biological samples. It probes the dynamic properties of matter by analysing the temporal correlations of photons scattered by the material. This requires the sample to be illuminated coherently implying the need for an intense coherent photon beam with sufficient transverse (typically 10 µm) and longitudinal (> 100 Å) coherence lengths. This can easily be fulfilled with a laser source giving access to the low frequency dynamics range ( < 10⁶ Hz) but allows only the long wavelength q < 4 x 10^-3 Å^-1 regime in materials not absorbing visible light to be probed. Coherent X-ray beams give access to the dynamics on smaller spatial scales in a q range from 10^-3 Å^-1 up to several Å^-1.

The ID10A branch of the TROIKA beamline can provide a 1.5 Å coherent X-ray beam of 5 x 10⁹ photons/sec with a transverse coherence length of 12 µm and a longitudinal coherence length of 120 Å [1]. This beam was used to study a dispersion of spherical block copolymer micelles in a polymer matrix with the micelles occupying about 30% of the volume. More specifically the sample contained polystyrene (PS) polymers (molecular weight 12700) mixed with 17% by weight of polystyrene-polyisoprene (PS-PI) block polymers (molecular weight 89100). Groups of the copolymer form spherical aggregates (micelles) that have PI cores and PS tails. Each micelle consists of about 300 copolymers and measures about 470 Å across.

This sample is solid below the glass transition temperature of PS (about 360 K) and the micelles scatter a coherent X-ray beam to produce a static speckle pattern, reflecting the exact spatial arrangement of the disorder. Figure 92 (top) shows such a pattern taken at 293 K. At elevated temperatures (T = 393 K > Tg) the polystyrene forms a viscous melt and the corresponding speckle pattern fluctuates on time scales of 50 - 200 sec, consistent with slow Brownian motion of the micelles in the melt and the grainy appearance of the static pattern is blurred as shown in Figure 92 (bottom).

Modelling of the average intensity shows that the average spatial arrangement of the micelles is similar to that of a simple liquid resulting in a peak of the static structure factor at a wavevector close to 2/ d_m, where d_m is the diameter of the micelle.

A measurement of the static structure factor is included in Figure 93 (solid line). The fluctuations in a speckle pattern can be quantified via the normalised time correlation function g(q,t). For simple translational diffusion g(q,t) = A(q) exp(-2t) + 1, and the correlation rate = q²D depends upon the diffusion coefficient D(q) and quadratically on the wavevector.

Time correlation spectra, taken on the sample at different wavevectors, reveal that the diffusion coefficient itself is strongly dependent on the wavevector. This is illustrated in Figure 93 showing the wavevector dependence of the inverse diffusion coefficient 1/D(q) for two measurements at 393 K and 398 K. The inverse diffusion coefficient shows a marked maximum at the maximum of the static structure factor. This result illustrates that the diffusion coefficient essentially measures the rate at which density fluctuations of wavelength 2/q decay, and its value depends on a complex interplay between the forces acting on the particles: the Brownian forces arising from collisions with liquid molecules; direct interactions between the particles and indirect hydrodynamic interactions transmitted through the liquid.

Publications

[1] G. Grübel (a), D. Abernathy (a), Proceedings of the "10th ICFA Beam Dynamics Panel Workshop on 4th Generation Light Sources", WGS 2-101, Grenoble (1996).
[2] S.G. J. Mochrie (b), A.M. Mayes (b), A.R. Sandy (c), M. Sutton (d), S. Brauer (c), G.B. Stephenson (e), D.L. Abernathy (a) and G. Grübel (a), Phys. Rev. Lett., 78, 1275 (1997).

(a) ESRF
(b) Department of Physics, MIT, Cambridge (USA)
(c) APS, Argonne National Laboratory, Argonne (USA)
(d) Department of Physics, McGill University, Montreal (Canada)
(e) Materials Science Division, Argonne National Laboratory, Argonne (USA)

 

 

 

The disorder-to-order transition in block copolymers under the influence of pressure

In general, polymers show no or little tendency to mix on a molecular level. The reason is the nearly vanishing contribution of entropy to the free energy of mixing. An interesting phenomenon results when two polymers are chemically connected to form a block copolymer. The repulsive interaction between the constituent blocks now leads to supramolecular order: the different blocks form domains which order on lattices with well-defined symmetry and lattice constants of the order of several nanometers. Such structures may be investigated with small-angle X-ray scattering. The small-angle camera on ID2 makes it possible to obtain scattering patterns in a very short time and at high resolution which enables a detailed study of the line shape and its dependence on external parameters.

It was observed recently [1] that at a pressure of 1 bar the order-to-disorder transition of a polystyrene/polyisoprene diblock copolymer was accompanied by a density discontinuity. The density of the ordered state was lower than that of the disordered state. The Clausius-Clapeyron equation then implies a shift of the transition temperature to lower values with increasing pressure. We have therefore measured the variation of structure with pressure at a temperature just below the transition temperature of 1 bar. The results are shown in Figure 94. At 1 bar the scattering pattern exhibits a narrow peak of high intensity as a result of the lamellar order. The second order peak is suppressed due to the nearly symmetric composition of the block copolymer. Increase of pressure broadens the peak and lowers its intensity, thus indicating the transition to the disordered state. At high pressure, however, this trend is reversed and the systems return to the ordered state. Figure 95 displays the variation of the peak width D and the maximum intensity I(q*) with p. Measurements at different temperatures indeed reveal a decrease of the transition temperature with pressure [2]. The opposite behaviour has been found for high pressure [3] above 25 bar. It remains an open question whether the existence of a minimum in the pressure dependence of the transition temperature is a specific phenomenon for a certain class of block copolymers or a general feature.

Publication

B. Steinhoff (a), M. Rüllmann (a), M. Wenzel (a), M. Junker (a), I. Alig(a), R. Oser (b), B. Stühn (b), G. Meier (c), O. Diat (d), P. Bösecke (d), H. Stanley (d), to be published.

(a) Deutsches Kunststoff-Institut, Darmstadt (Germany)
(b) Fakultät für Physik, Freiburg (Germany)
(c) MPI für Polymerforschung, PO 3148, Mainz (Germany)
(d) ESRF

Reference

[1] H. Kasten, B. Stühn, Macromolecules 1995, 28, 4777
[2] B. Steinhoff et al, Macromolecules, submitted
[3] D. Hajduk et al, Macromolecules, 1996, 29, 1473

 

 

 

X-ray absorption spectroscopy investigations of the hydrophobic hydration of noble gases

One challenging area of aqueous solution chemistry, where investigation of local structure correlations has long eluded direct experimental study, is the characterisation of the hydration of non-polar solutes. These solutes do not favour the aqueous environment and the term given to their dissolution is hydrophobic hydration. This very fundamental process of hydration of a non-polar moiety is of great importance in many areas of biological, chemical and medical science. It has thus attracted a significant quantity of scientific investigation, although direct structural studies of these important processes have for a long time remained impossible - the dislike of the non-polar moiety for the aqueous environment results in very low solute concentrations which are beyond the capabilities of most direct experimental structural probes. These difficulties thus drove the majority of investigations towards indirect methods such as thermodynamic studies or computer simulation. Conventional theory relates the observed phenomena associated with hydrophobic hydration to an increase in ordering of liquid water in the hydration shell of the solute, to that found in the bulk solvent.

The noble gases, Ne, Ar, Kr and Xe are ideal non-polar solutes, and the structure adopted by liquid water when hydrating these atoms is consequently a perfect example of hydrophobic hydration. The first experimental attempt to directly measure the hydration structure of a noble gas atom was the neutron scattering study of Broadbent and Nielson, who made use of isotopic substitution and first order difference techniques to investigate the first hydration shell of argon. Their results were far from perfect, but a reasonable estimate of the hydration structure was made. Their experience, however, illustrated the impracticality of detailed studies by this technique as a function of thermodynamic state.

X-ray absorption spectroscopy (XAS) is a powerful method to investigate the average local structure around heavy atoms (Z > 20) in an aqueous environment and has been pursued for many years. The recent developments and availability of third generation synchrotron radiation sources now allow this long-established field to be extended to cover non-ambient thermodynamic states and to address some of the remaining more challenging problems. The main experimental difficulties lie in the necessity to confine the sample in a pressure vessel whose X-ray windows are sufficiently transparent to the radiation at the given edge under investigation (i.e. Kr K-edge E ~ 14.32 keV). We point out that the use of single crystal diamond windows for XAS is hampered by the presence of several Bragg reflections appearing during the energy scan. A specific cell design has been developed at the ESRF to withstand pressures up to 200 bar and operate in automatic mode in the 5-150 °C temperature range. The body of the cell is constructed from three stainless steel pieces (Figure 96), which delimit an internal cavity sealed with an epoxy resin layer that becomes thicker and of conical profile at the level of the X-ray windows. The size of cavity and windows are optimised for each solvent-solute system.

The high brilliance of the synchrotron radiation source, the beam stability during energy scan, and a high rate of harmonic rejection, are essential characteristics for a successful absorption experiment through the small aperture available for X-rays. The BM29 spectrometer at the ESRF meets these requirements and we successfully measured X-ray absorption spectra of krypton and xenon in water with an excellent signal to noise ratio in the 10⁴ range, comparable to that obtained for standard reference foils. This is essential to evidence the weak structural signal originating from the surrounding H₂O molecules. An example of the spectra for the Kr in H₂O system is reported in Figure 97. The various lines correspond to the absorption of the cell, the cell + water and the cell + water + krypton at various pressures.

The spectra have been analysed with an advanced scheme and the structural contribution to the signal, shown in Figure 98 for 100 bar and 47 °C, has been interpreted in terms of a Kr-O partial radial distribution function. With the present XAS investigation we were able to reveal experimentally, for the first time, a well defined Kr-O correlation peak centred at 3.8 Å indicating the existence of a reasonably well-ordered hydration shell around the gas atom.

These results have laid the necessary foundations for a systematic investigation of hydrophobic hydration of Kr and Xe as a function of pressure, temperature and the presence of ionic cosolutes. These are studies which are planned for the near future.

Publication

A. Filipponi (a), D.T. Bowron (b), C. Lobban (b) and J.L. Finney (b), Phys. Rev. Lett., 79, 1293 (1997).

(a) ESRF
(b) Department of Physics and Astronomy, University College London, (UK)