Mean Square Density Fluctuation Research Articles

Density fluctuations in amorphous pharmaceutical solids. Can SAXS help to predict stability?

The analytical potential of X-ray small-angle scattering (SAXS) combined with simultaneous wide-angle diffraction (WAXS) has been explored on the example of three active pharmaceutical ingredients, (desvenlofaxine, simvastatin, and sulfamerazine, resp.) with the aim of identifying quantitative parameters obtained from SAXS that allow to describe the nano-structural characteristics of different amorphous forms and to monitor the processes of amorphisation and ageing. Cryo-milling, co-milling with polymer, melting and melt-quenching have been used for amorphisation of initially crystalline powders. In parallel to SAXS, the WAXS patterns have been obtained to fingerprint the crystalline state. The SAXS results demonstrate strong, systematic nanostructure variations in amorphous samples obtained by different milling conditions, or by melt-quenching. It has been found that the mean-square density fluctuation, directly obtained from the SAXS invariant, is a sensitive and robust parameter to characterize the degree of nano-heterogeneity, which is related to entropy and hence thermodynamic stability. The SAXS curves also allow estimates of amorphous domain sizes of different density. The propensity to recrystallize or to remain amorphous, respectively, upon ageing has been found to depend on the existence of domains in the starting amorphous materials.

SYSTEMATIC EFFECTS ON THE GENUS TOPOLOGY OF THE LARGE-SCALE STRUCTURE OF THE UNIVERSE

Large-scale structure of the universe is a useful cosmological probe of the primordial non-Gaussianity and the expansion history of the universe because its topology does not change with time in the linear regime in the standard paradigm of structure formation. However, when the topology of iso-density contour surfaces is measured from an observational data, many systematic effects are introduced due to the finite size of pixels used to define the density field, non-linear gravitational evolution, redshift-space distortion, shot noise (discrete sampling), and bias in the distribution of the density field tracers. We study the various systematic effects on the genus curve to a great accuracy by using the Horizon Run 2 simulation of a {\Lambda}CDM cosmology. We numerically measure the genus curve from the gravitationally evolved matter and dark matter halo density fields. It is found that all the non-Gaussian deviations due to the systematic effects can be modeled by using a few low-order Hermite polynomials from H0 to H4. We compare our results with the analytic theories whenever possible, and find many new terms in the Hermite series that are making significant contributions to the non-Gaussian deviations. In particular, it is found that the amplitude drop of the genus curve due to the non-linear gravitational evolution can be accurately modeled by two terms H0 and H2 with coefficients both proportional to \sigma_0^2, the mean-square density fluctuation.

Structure analysis of regenerated cellulose hydrogels by small-angle and ultra-small-angle x-ray scattering.

Absolute intensities Deltai(q) of small-angle x-ray scattering (SAXS) and ultra-small-angle x-ray scattering (USAXS) were measured in a wide range of scattering vector q from 2x10(-4) to 0.5 A(-1) for transparent (VI-P) and translucent (VI-L) cellulose hydrogels prepared by coagulation and regeneration of viscose in acid solutions with and without acetone, respectively. We obtained the scattering intensities at very small q conveniently by desmearing the combined data measured by SAXS and USAXS. The plot of Deltai(q)q(2) versus log(10) q showed a peak at -2.5<log(10) q<-1.0. By assuming a two-phase model with the high-density phase (phase 1) composed of only cellulose and with the low-density phase (phase 2) composed of cellulose dispersed in water, volume fractions of phase 1 in VI-P and VI-L were determined to be 0.18 and 0.09, respectively, from the mean-square fluctuation of electron density determined as integral of (Deltai(q)q(2)dq). By fitting the observed scattering profile with the theoretical particle scattering functions of spheres, the average diameter of the high-density region including crystallite was determined to be 120 A for VI-P and 80 A for VI-L. Similar analyses were applied also to freeze-dried VI-P. These results were consistent with those obtained by the wide-angle x-ray-diffraction measurement and also with the observation by scanning probe microscopy.

Physical aging in poly(methyl methacrylate) glass: densification via density fluctuation

The physical aging in poly(methyl methacrylate) during annealing just below T g was investigated by light scattering and oscillating-DSC in which a sinusoidal temperature rise was imposed over the conventional linear temperature rise. Light scattering intensity decreased monotonously with increasing scattering angle. The intensity was found to increase rapidly and then to decrease gradually with annealing time t a. The correlation length and the mean-square density fluctuations by Debye–Bueche plot increased at an early stage and then decreased with t a. The width of the glass transition, obtained by the Fourier transform treatment of the oscillated DSC heat flow, increased with t a at an early stage and then decreased. The endothermic peak, given by the non-reversing part of the oscillating DSC heat flow, appeared even at an early stage of the aging. These results suggest that: (1) as-quenched PMMA glass is partially densified to yield an inhomogeneity in density with a correlation length about 200 nm; (2) by the annealing, the density fluctuations grow at first by a decrease in density at the low density regions and an expansion of the low density regions to increase the correlation length; and (3) the densification then proceeds at the low density regions to reduce the correlation length and to get higher density as a whole, by approaching a rather homogeneous glassy state.

Diffusion on a honeycomb lattice: Real-space renormalization-group approach

A two-dimensional lattice-gas model with honeycomb symmetry is investigated by using the real-space renormalization group (RSRG) approach with a number of RSRG transformations based on clusters of different symmetries and sizes (up to 42 sites). The accuracy of calculations is found to be a nonmonotonic function of the size of a cluster, and to depend strongly on its symmetry. The highest obtained accuracy with respect to the determination of the critical value of the pair interaction parameter is 0.38%. The phase diagram of the Ising antiferromagnetic spin model and of the corresponding lattice-gas model is constructed with this accuracy. The ordered phase in the lattice system is shown to appear in the very narrow density interval, $0.447lnl0.553.$ In addition, the coverage dependence of the chemical diffusion coefficient and mean-square density fluctuations are studied at temperatures below the critical one. Both quantities are demonstrated to exhibit singularities at the critical coverages. The type of singularities (in particular, the critical slowdown of diffusion) is in agreement with the predictions of the scaling theory and also with recent results obtained for a model treating the effect of surface reconstruction on diffusion.

Homogeneous buoyancy-generated turbulence

Using a theoretical analysis of fundamental equations and a numerical simulation of the flow field, the statistically homogeneous motion that is generated by buoyancy forces after the creation of homogeneous random fluctuations in the density of infinite fluid at an initial instant is examined. It is shown that analytical results together with numerical results provide a comprehensive description of the 'birth, life, and death' of buoyancy-generated turbulence. Results of numerical simulations yielded the mean-square density mean-square velocity fluctuations and the associated spectra as functions of time for various initial conditions, and the time required for the mean-square density fluctuation to fall to a specified small value was estimated.

Small-angle X-ray scattering study of glassy GeO2

A small-angle X-ray scattering study of glassy GeO2 is reported. Data were obtained from 4π sinθ/λ = 0.05 to 2.0 using a Kratky camera. The SAXS intensity decreased monotonically with decreasing angle from the main diffraction peak, and was not noticeably changed by hydrofluoric acid surface treatment or various annealing treatments. The intensity scattered at the smallest angle was 49±2.5 e.u. molec−1. Extrapolated to zero angle, the intensity corresponds to root-mean-square density fluctuations of 10−12 V−1/2 cm−3/2, a value close to that expected from the thermodynamic fluctuation theory of liquids. A parallel study of fused silica has indicated mean-square density fluctuations similar to those found in GeO2. The results are taken as evidence contrary to representations of structure based on specific arrays differing significantly from the interconnecting material.

Statistical properties of turbulent density fluctuations

The cross-correlation technique has been used to obtain statistical properties of scalar density fluctuations. Two schlieren instruments with their optical beams intersecting in the turbulent field each give a signal proportional to the density gradient in the flow direction but integrated along the beam path. Cross-correlation of the two signals gives an area integral of the density-gradient covariance. For locally isotropic conditions the area integration can exactly compensate for the two gradients giving a result proportional to the local mean-square density fluctuation at the beam intersection point.Experiments performed in the shear layer of a subsonic jet show results which tend to verify the principles of crossed-schlieren measurement. Intensity levels are close to those predicted assuming density fluctuations are related isentropically to local, incompressible pressure fluctuations.

Small-angle X-ray scattering and scattering of visible light by phase-separated glasses

Modern theory and the experimental method of small angle X-ray scattering (SAXS) permit one to find, without any a priori suppositions and with sufficient accuracy, a series of integral structural characteristics of the sub-micro-inhomogeneous (supra-molecular) structure of glass. The temperature dependence of the principal characteristics gives the possibility of describing the change of a glass structure during its heat treatment with great reliability. For example, the area of the geometrical surface separating two phases has been determined, and the change of the “bidispersive structure” with the heat treatment has been studied; it was thereby proved that the high dispersive structure is a result of the terminal velocity of cooling from high temperatures and that it also has a phase-separation nature (the secondary phase separation).Two methods—SAXS and scattering of visible light—have been used as experimental checks of the theory of spinodal decomposition, taking as an example sodium silicate glass, containing 12.5 % sodium oxide. Disagreement of the experimental results with the theoretical predictions has been found. This fact has been explained by the dependence of the diffusion coefficient and some other parameters upon the concentration which have been disregarded in the approximate variant of the theory. The main SAXS characteristics of the inhomogeneous glass structure have been defined, viz., the mean-square electron density fluctuation, the effective size and area of inhomogeneous regions and the distance between their centres.