Microstructural Degeneracy associated with a Two-Point Correlation Function and its Information Content

Two-point correlation functions provide crucial yet incomplete characterization of microstructures because different microstructures may have the same correlation function. In an earlier Letter [Phys. Rev. Lett. 108, 080601 (2012)], we addressed the degeneracy question: What is the number of microstructures compatible with a specified correlation function? We computed this degeneracy, i.e., configurational entropy, in the framework of reconstruction methods, which enabled us to map the problem to the determination of ground-state degeneracies. Here, we provide a more comprehensive presentation and additional results. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically an energy profile corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of this profile is a measure of the roughness of the energy landscape, which can be used as a proxy for ground-state degeneracy. The relationship between roughness metric and ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the degeneracy of a variety of microstructures, including hard disks and Poisson point processes as well as those with known degeneracies (single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the information content of any two-point correlation function, which makes our results broadly applicable to any field in which correlation functions are employed.Comment: Accepted for publication in Physical Review

Inelastic Neutron Scattering Analysis with Time-Dependent Gaussian-Field Models

Converting neutron scattering data to real-space time-dependent structures can only be achieved through suitable models, which is particularly challenging for geometrically disordered structures. We address this problem by introducing time-dependent clipped Gaussian field models. General expressions are derived for all space- and time-correlation functions relevant to coherent inelastic neutron scattering, for multiphase systems and arbitrary scattering contrasts. Various dynamic models are introduced that enable one to add time-dependence to any given spatial statistics, as captured e.g. by small-angle scattering. In a first approach, the Gaussian field is decomposed into localised waves that are allowed to fluctuate in time or to move, either ballistically or diffusively. In a second approach, a dispersion relation is used to make the spectral components of the field time-dependent. The various models lead to qualitatively different dynamics, which can be discriminated by neutron scattering. The methods of the paper are illustrated with oil/water microemulsion studied by small-angle scattering and neutron spin-echo. All available data - in both film and bulk contrasts, over the entire range of $q$ and $\tau$- are analyzed jointly with a single model. The analysis points to static large-scale structure of the oil and water domains, while the interfaces are subject to thermal fluctuations. The fluctuations have an amplitude around 6 nm and contribute to 30 % of the total interface area.Comment: The following article has been accepted by Journal of Chemical Physics. After it is published, it will be found at https://aip.scitation.org/journal/jcp

Tuning thermal, morphological, and physicochemical properties of Thermoplastic Polyurethanes (TPUs) by the 1,4-butanediol (BDO)/dipropylene glycol (DPG) ratio

Thermoplastic polyurethanes (TPUs) are versatile polymers presenting a broad range of properties as a result of their countless combination of raw materials—in essence, isocyanates, polyols, and chain extenders. This study highlights the effect of two different chain extenders and their combination on the structure–property relationships of TPUs synthesized by reactive extrusion. The TPUs were obtained from 4,4-diphenylmethane diisocyanate (MDI), polyester diols, and the chain extenders 1,4-butanediol (BDO) and dipropylene glycol (DPG). The BDO/DPG ratios studied were 100/0, 75/25, 50/50, 25/75, and 0/100 wt.%. The TPUs were characterized by size exclusion chromatography (SEC), Fourier-transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS), UV–vis spectroscopy, and physical-mechanical properties. The results indicate that DPG promotes compatibility between rigid (HS) and flexible (SS) segments of TPUs. Consequently, increasing DPG content (>75 wt.%) reduced the organization of the rigid segments and the degree of phase separation, increasing the polydispersity of the interdomain distance and the transparency in the UV–visible spectrum of the TPUs. Furthermore, increasing DPG content also reduced the amount of hydrogen bonds present in the rigid phase, reducing or extinguishing its glass transition temperature (TgHS) and melting temperature (Tm), and increasing the glass transition temperature of the flexible phase (TgSS). Therefore, increasing DPG content leads to a deterioration in mechanical properties and hydrolysis resistance

SAXS analyses of biphasic, distorted, lamellar morphologies using clipped Gaussian random fields: application to ethylene copolymers and segmented blockcopolymers

status: publishe

CONEX, a program for angular calibration and averaging of two-dimensional powder scattering patterns

CONEX is a Windows application for converting series of two-dimensional X-ray powder patterns measured on flat two-dimensional detectors into one-dimensional scattering patterns. It is based on the rigorous use of scattering patterns of calibration samples to determine the three-dimensional position of the detector, with respect to the sample and to the beam. This enables correction of the data for geometric distortions, even when the detector is highly tilted and not centred on the beam.status: publishe

Stochastic analysis of capillary condensation in disordered mesopores

Most mesoporous materials of practical interest are inherently disordered, which has a significant impact on the condensation and evaporation of vapours in their pores. Traditionally, the effect of disorder is theoretically analyzed in a perturbative approach whereby slight elements of disorder (constriction, corrugation) are added to geometrically ideal pores. We propose an alternative approach, which consists of using a stochastic geometrical model to describe both the porous material and the condensate within the pores. This is done through a multiphase generalisation of the standard Gaussian random field model of disordered materials. The model parameters characterising the condensate provide a low-dimensional approximation of its configuration space, and we use a Derjaguin–Broekhoff–de Boer approximation to calculate the free-energy landscape. Our analysis notably questions the existence of vapour-like metastable states in realistically disordered mesoporous materials. Beyond capillary condensation, our general methodology is applicable to a broad array of confined phenomena

Role of co-reactants during the formation of silica gels assessed by in situ SAXS

status: publishe

The structure and thermal stability of amylose−lipid complexes: A case study on amylose−glycerol monostearate

Three different crystalline amylose-glycerol monostearate (GMS) complexes with increasing thermal stability can be distinguished: type I, type IIa, and type IIb. All complexes consist of GMS-loaded amylose helices that pack hexagonally into lamellar habits. The complex melting points are proportional to the thickness of the lamellae and depend on the amount of water in the system. For type I complexes, SAXS experiments reveal folded amylose chains and a lamellar thickness governed by the presence of two stretched lipid molecules per amylose helix. In the conversion from type I to type IIa complexes, the short amylose chains unfold and assume a stretched conformation, which increases the number of aligned lipid molecules within the helices to four. In type IIb complexes, another pair of lipid molecules is added. The derived quantitative relation between crystal layer thickness, water content and melting point for amylose-GMS complexes also predicts the melting points of other amylose-monoacyl glycerol complexes. © 2014 American Chemical Society.status: publishe