Sow-Hsin Chen

Analysis of small angle neutron scattering spectra from polydisperse interacting colloids

In this paper, we outline a simple procedure for analyzing small angle neutron scattering (SANS) spectra from interacting colloids containing a continuous distribution of particle sizes. In particular, the effects of polydispersity on the apparent interparticle structure factor S′(Q) observed by SANS is investigated. We find that the oscillations in S′(Q) are significantly damped in comparison to those of the true structure factor S(Q). When our procedure is extended to the analysis of SANS spectra from nonspherical particles, we find that orientational averaging affects S′(Q) in a qualitatively similar way. The applicability of the procedure to the analysis of real data is demonstrated with spectra taken from water‐in‐oil microemulsions, ionic micelles, and interacting proteins.

Pressure dependence of fragile-to-strong transition and a possible second critical point in supercooled confined water

By confining water in nanopores of silica glass, we can bypass the crystallization and study the pressure effect on the dynamical behavior in deeply supercooled state using neutron scattering. We observe a clear evidence of a cusplike fragile-to-strong (FS) dynamic transition. Here we show that the transition temperature decreases steadily with an increasing pressure, until it intersects the homogenous nucleation temperature line of bulk water at a pressure of 1600 bar. Above this pressure, it is no longer possible to discern the characteristic feature of the FS transition. Identification of this end point with the possible second critical point is discussed.

Evidence of the existence of the low-density liquid phase in supercooled, confined water

By confining water in a nanoporous structure so narrow that the liquid could not freeze, it is possible to study properties of this previously undescribed system well below its homogeneous nucleation temperature TH = 231 K. Using this trick, we were able to study, by means of a Fourier transform infrared spectroscopy, vibrational spectra (HOH bending and OH-stretching modes) of deeply supercooled water in the temperature range 183 < T < 273 K. We observed, upon decreasing temperature, the building up of a new population of hydrogen-bonded oscillators centered around 3,120 cm−1, the contribution of which progressively dominates the spectra as one enters into the deeply supercooled regime. We determined that the fractional weight of this spectral component reaches 50% just at the temperature, TL ≈ 225 K, where the confined water shows a fragile-to-strong dynamic cross-over phenomenon [Ito, K., Moynihan, C. T., Angell, C. A. (1999) Nature 398:492–494]. Furthermore, the fact that the corresponding OH stretching spectral peak position of the low-density-amorphous solid water occurs exactly at 3,120 cm−1 [Sivakumar, T. C., Rice, S. A., Sceats, M. G. (1978) J. Chem. Phys. 69:3468–3476.] strongly suggests that these oscillators originate from existence of the low-density-liquid phase derived from the occurrence of the first-order liquid–liquid (LL) phase transition and the associated LL critical point in supercooled water proposed earlier by a computer molecular dynamics simulation [Poole, P. H., Sciortino, F., Essmann, U., Stanley, H. E. (1992) Nature 360:324–328].

The violation of the Stokes–Einstein relation in supercooled water

By confining water in nanopores, so narrow that the liquid cannot freeze, it is possible to explore its properties well below its homogeneous nucleation temperature TH≈ 235 K. In particular, the dynamical parameters of water can be measured down to 180 K, approaching the suggested glass transition temperature Tg≈ 165 K. Here we present experimental evidence, obtained from Nuclear Magnetic Resonance and Quasi-Elastic Neutron Scattering spectroscopies, of a well defined decoupling of transport properties (the self-diffusion coefficient and the average translational relaxation time), which implies the breakdown of the Stokes–Einstein relation. We further show that such a non-monotonic decoupling reflects the characteristics of the recently observed dynamic crossover, at ≈225 K, between the two dynamical behaviors known as fragile and strong, which is a consequence of a change in the hydrogen bond structure of liquid water.

Light scattering from water droplets in the geometrical optics approximation.

The geometrical optics approach is used to derive i(1)(theta) = |S(1)(theta)|(2) and i(2)(theta) = |S(2)(theta)|(2), the angular intensity functions for light scattered by a spherical water droplet of a radius comparable with or larger than the wavelength of light. In contrast to previously published results, these functions are obtained in closed form and as functions of the scattering angle theta, which greatly enhance their usefulness in numerical work and in the reduction of large sphere scattering data. The range of validity of these expressions is investigated by graphical comparison of calculated angular intensity patterns with those obtained from rigorous Mie theory. Our main objective is to study the feasibility of using the geometrical optics expressions as a basis for practical laser water droplet sizing work. A criterion is established for the range of applicability of the relationship I(theta,R) = K(theta)R(2), which relates the scattering intensity at a particular angle theta to the radius R of the droplet. Accuracy of the laser water droplet sizing technique is thus quantitatively established.

Theoretical foundation of X-ray and neutron reflectometry

Abstract This review attempts to give a systematic exposition of the theoretical foundation underlying surface depth profiling at the molecular level using X-ray and neutron specular reflectometry. It covers the fundamentals of X-ray and neutron interactions with matter, the direct theory of specular reflection from stratified media, the inverse theory of specular reflection for obtaining the surface depth profile from measured specular reflection data, and demonstration of how the theories can be used in practice. The part on X-ray and neutron interactions with matter begins with the basic quantum mechanical and classical electromagnetic descriptions of scattering, discusses the important concepts of scattering and absorption cross sections, the scattering length density and the refractive index of matter, and derives the one-dimensional Helmholtz wave equation which fully describes the specular reflection of slow neutrons and X-rays from a macroscopic stratified medium. The direct theory begins with the development of the solution of the Helmholtz wave equation in the form of a discrete formulation, namely, Parratts recurrence relation, and proceeds to several continuous formulations, such as the Born and distorted wave Born (DWBA) approximations, the small-curvature approximation (SCA), the modified WKB approximation (MWKB) and the weighted-superposition approximation (WSA), and ends with a discussion about the effect of surface roughness. The inverse theory presents methods for the reconstruction of the depth profile of the surface scattering length density from a set of specular reflection data. This includes the feasibility of data inversion, some simple examples of analytic data inversion, a matrix-iteration method (MIM), and a groove-tracking method (GTM). For demonstration of the use of the theories, we give an example of neutron reflectivity data analyses, from which the surface-layering phenomenon in bicontinuous microemulsions is revealed.

Observation of the density minimum in deeply supercooled confined water

Small angle neutron scattering (SANS) is used to measure the density of heavy water contained in 1D cylindrical pores of mesoporous silica material MCM-41-S-15, with pores of diameter of 15 ± 1 Å. In these pores the homogenous nucleation process of bulk water at 235 K does not occur, and the liquid can be supercooled down to at least 160 K. The analysis of SANS data allows us to determine the absolute value of the density of D2O as a function of temperature. We observe a density minimum at 210 ± 5 K with a value of 1.041 ± 0.003 g/cm3. We show that the results are consistent with the predictions of molecular dynamics simulations of supercooled bulk water. Here we present an experimental report of the existence of the density minimum in supercooled water, which has not been described previously.

The anomalous behavior of the density of water in the range 30 K < T < 373 K

The temperature dependence of the density of water, ρ(T), is obtained by means of optical scattering data, Raman and Fourier transform infrared, in a very wide temperature range, 30 < T < 373 K. This interval covers three regions: the thermodynamically stable liquid phase, the metastable supercooled phase, and the low-density amorphous solid phase, at very low T. From analyses of the profile of the OH stretching spectra, we determine the fractional weight of the two main spectral components characterized by two different local hydrogen bond structures. They are, as predicted by the liquid–liquid phase transition hypothesis of liquid water, the low- and the high-density liquid phases. We evaluate contributions to the density of these two phases and thus are able to calculate the absolute density of water as a function of T. We observe in ρ(T) a complex thermal behavior characterized not only by the well known maximum in the stable liquid phase at T = 277 K, but also by a well defined minimum in the deeply supercooled region at 203 ± 5 K, in agreement with suggestions from molecular dynamics simulations.

Cluster formation in two-Yukawa fluids.

We present a different and efficient method for implementing the analytical solution of Ornstein-Zernike equation for two-Yukawa fluids in the mean spherical approximation. We investigate, in particular, the conditions for the formation of an extra low-Q peak in the structure factor, which we interpret as due to cluster formation in the two-Yukawa fluid when the interparticle potential is composed of a short-range attraction and a long-range repulsion. We then apply this model to interpret the small angle neutron scattering data for protein solutions at moderate concentrations and find out that the presence of a peak centered at Q=0 (zero-Q peak) besides the regular interaction peak due to charged proteins implies an existence of long-range attractive interactions besides the charge repulsion.

Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

It is becoming common practice to partition glass-forming liquids into two classes based on the dependence of the shear viscosity η on temperature T. In an Arrhenius plot, ln η vs 1/T, a strong liquid shows linear behavior whereas a fragile liquid exhibits an upward curvature [super-Arrhenius (SA) behavior], a situation customarily described by using the Vogel–Fulcher–Tammann law. Here we analyze existing data of the transport coefficients of 84 glass-forming liquids. We show the data are consistent, on decreasing temperature, with the onset of a well-defined dynamical crossover η×, where η× has the same value, η× ≈ 103 Poise, for all 84 liquids. The crossover temperature, T×, located well above the calorimetric glass transition temperature Tg, marks significant variations in the system thermodynamics, evidenced by the change of the SA-like T dependence above T× to Arrhenius behavior below T×. We also show that below T× the familiar Stokes–Einstein relation D/T ∼ η-1 breaks down and is replaced by a fractional form D/T ∼ η-ζ, with ζ ≈ 0.85.