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Open Access
Abstract: A general method to invert parameter distributions of a polydisperse system using data acquired from a small-angle scattering (SAS) experiment is presented. The forward problem, i.e. calculating the scattering intensity given the distributions of any causal parameters of a theoretical model, is generalized as a multi-linear map, characterized by a high-dimensional Green tensor that represents the complete scattering physics. The inverse problem, i.e. finding the maximum-likelihood estimation of the parameter distributions (in free form) given the scattering intensity (either a curve or an image) acquired from an experiment, is formulated as a constrained nonlinear programming (NLP) problem. This NLP problem is solved with high accuracy and efficiency via several theoretical and computational enhancements, such as an automatic data scaling for accuracy preservation and GPU acceleration for large-scale multi-parameter systems. Six numerical examples are presented, including both synthetic tests and solutions to real neutron and X-ray data sets, where the method is compared with several existing methods in terms of their generality, accuracy and computational cost. These examples show that SAS inversion is subject to a high degree of non-uniqueness of solution or structural ambiguity. With an ultra-high accuracy, the method can yield a series of near-optimal solutions that fit data to different acceptable levels.
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Aug 2022
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I22-Small angle scattering & Diffraction
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Andrew
Smith
,
S. G.
Alcock
,
L. S.
Davidson
,
J. H.
Emmins
,
J. C.
Hiller Bardsley
,
P.
Holloway
,
M.
Malfois
,
A. R.
Marshall
,
C. L.
Pizzey
,
S. E.
Rogers
,
O.
Shebanova
,
T.
Snow
,
J. P.
Sutter
,
E. P.
Williams
,
N. J.
Terrill
Open Access
Abstract: Beamline I22 at Diamond Light Source is dedicated to the study of soft-matter systems from both biological and materials science. The beamline can operate in the range 3.7 keV to 22 keV for transmission SAXS and 14 keV to 20 keV for microfocus SAXS with beam sizes of 240 µm × 60 µm [full width half-maximum (FWHM) horizontal (H) × vertical (V)] at the sample for the main beamline, and approximately 10 µm × 10 µm for the dedicated microfocusing platform. There is a versatile sample platform for accommodating a range of facilities and user-developed sample environments. The high brilliance of the insertion device source on I22 allows structural investigation of materials under extreme environments (for example, fluid flow at high pressures and temperatures). I22 provides reliable access to millisecond data acquisition timescales, essential to understanding kinetic processes such as protein folding or structural evolution in polymers and colloids.
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May 2021
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I07-Surface & interface diffraction
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Diamond Proposal Number(s):
[20171]
Open Access
Abstract: Glyceline, a deep eutectic solvent comprising glycerol and choline chloride, is a green nonaqueous solvent with potential industrial applications. Molecular mechanisms of surfactant self-assembly in deep eutectic solvents are expected to differ from those in their constituent polar components and are not well understood. Here we report the observation of self-assembled SDS fractal dendrites with dimensions up to ~ mm in glyceline at SDS concentrations as low as cSDS ~ 0.1 wt%. The prevalence of these dendritic fractal aggregates led to the formation of a gel phase at SDS concentrations above ≥ 1.9 wt% (the critical gelation concentration cCGC). The gel microscopic structure was visualised using polarised light microscopy (PLM); rheology measurements confirmed the formation of a colloidal gel, where the first normal stress difference was negative and the elastic modulus was dominant. Detailed nano-structural characterisation by small-angle neutron scattering (SANS) further confirmed the presence of fractal aggregates. Such SDS aggregation or gelation has not been observed in water at such low surfactant concentrations, whereas SDS has been reported to form lamellar aggregates in glycerol (a component of glyceline). We attribute the formation of the SDS fractal dendrites to the condensation of counterions (i.e. the choline ions) around the SDS aggregates - a diffusion-controlled process, leading to the aggregate morphology observed. These unprecedented results shed light on the molecular mechanisms of surfactant self-assembly in deep eutectic solvents, important to their application in industrial formulation.
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May 2021
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B21-High Throughput SAXS
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Diamond Proposal Number(s):
[21035]
Abstract: We report a small-angle neutron scattering (SANS) study of semidilute aqueous solutions of sodium carboxymethyl cellulose (NaCMC), in the presence of mono- (Na+) and divalent salts (Mg2+, Ca2+, Zn2+, and Ba2+). A degree of substitution of 1.3 is selected to ensure that, in salt-free solution, the polymer is molecularly dissolved. We find that Na+ and Mg2+ salt addition yields H-type phase behavior, while Ca2+, Zn2+, and Ba2+ instead yield a mixed H/L-type phase behavior dependent on the NaCMC concentration (cp), in the decreasing order of the salt concentration required to induce turbidity (at a fixed cp). Charge screening by addition of NaCl induces the disappearance of the characteristic polyelectrolyte correlation peak and eventually yields scattering profiles with a q–1 dependence over nearly 3 decades in the wavenumber q. By fitting a descriptive model to data with excess Na+, we obtain a correlation length ξ′ = 1030 cp–0.72 Å with cp in g L–1. Addition of Mg2+, which does not interact specifically with NaCMC carboxylate groups, yields an analogous screening behavior to that of Na+, albeit at lower salt concentrations, in line with its higher ionic strength. At low salt concentration, addition of specifically interacting Ca2+, Zn2+, and Ba2+ yields a comparatively greater screening of the polyelectrolyte correlation peak, and at concentrations above the phase boundary, results in excess scattering at low-q, compatible with the formation of 20–40 nm clusters. This behavior is interpreted as due to the reduction in charge density along the chain, promoting interchain association and multichain domain formation resulting in visible turbidity. Overall, drawing analogies with NaCMC at a lower degree of substitution, where hydrophobic association takes place, our findings provide a framework to describe the solution structure and phase behavior of NaCMC in salt-free and salt solutions.
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Feb 2020
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I22-Small angle scattering & Diffraction
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Diamond Proposal Number(s):
[18402]
Abstract: Understanding structure-property relationships is critical for the development of new drug delivery systems. This study investigates the properties of Pluronic smart hydrogel formulations for future use as injectable controlled drug carriers. The smart hydrogels promise to enhance patient compliance, decrease side effects and reduce dose and frequency. Pharmaceutically, these systems are attractive due to their unique sol-gel phase transition in the body, biocompatibility, safety and injectability as solutions before transforming into gel matrices at body temperature. We quantify the structural changes of F127 systems under controlled temperature after flow, as experienced during real bodily injection. Empirical formulae combining the coupled thermal and shear dependency are produced to aid future application of these systems. Induced structural transitions measured in-situ by small angle x-ray and neutron scattering reveal mixed oriented structures that can be exploited to tailor the drug release profile.
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Dec 2019
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I07-Surface & interface diffraction
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Diamond Proposal Number(s):
[8117]
Abstract: The crystallization of poly(3-hexylthiophene) (P3HT) to form nanowires has attracted considerable interest because this process significantly increases the hole mobility when compared to amorphous P3HT, leading to improved performance in photovoltaic and other organic electronic devices. However, full characterization of the crystallization self-assembly of the polymer chains in solution has not been achieved yet, due to limited use of
in−situ
not destructive techniques. Here, we investigate the ageing-driven formation and evolution of regioregular (rr) P3HT nanostructures in chlorobenzene solution using small angle neutron scattering (SANS) and UV–Vis spectroscopy. We have monitored how the shape of the rr-P3HT aggregates evolves. The initial states for rr-P3HT chains are the random coils, which straighten to form rods. These subsequently π - π stack to form 2D lamellae, which further stack to create nanowires. The formation of nanowires is promoted both by the length of ageing and by low temperatures (
4∘C
). Temperatures above
>40∘C
reverse the formation of nanowires. Additionally, atomic force microscopy (AFM) and grazing incidence wide angle x-ray scattering (GIWAXS) reveal that the nanowires can be successfully aligned during deposition by off-axis spin coating. Finally, the anisotropic conductivity of the aligned rr-P3HT nanowire films is reported. This is significant for applications such as gas sensing or organic thin film transistors, where increased conductivity and controlled nanostructure are desirable.
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Nov 2019
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I22-Small angle scattering & Diffraction
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Gregory N.
Smith
,
Silvia
Ahualli
,
Angel V.
Delgado
,
David A. J.
Gillespie
,
Roger
Kemp
,
Jocelyn
Peach
,
Jonathan C.
Pegg
,
Sarah
Rogers
,
Olga
Shebanova
,
Nathan
Smith
,
Julian
Eastoe
Diamond Proposal Number(s):
[9753]
Abstract: The electrophoresis of a well-established model system of charged colloids in nonpolar solvents has been studied as a function of particle volume fraction at constant surfactant concentration. Dispersions of poly(12-hydroxystearic acid)-stabilized poly(methyl methacrylate) (PMMA) latexes in dodecane were prepared with added Aerosol OT surfactant as the charging agent. The electrophoretic mobility (µ) of the PMMA latexes is found to decrease with particle concentration. The particles are charged by a small molecule charging agent (AOT) at finite concentration, and this makes the origin of this decrease in µ unclear. There are two suggested explanations. The decrease could either be due to the reservoir of available surfactant being exhausted at high particle concentrations or the interactions between the charged particles at high particle number concentrations. Contrast-variation small-angle neutron scattering measurements of PMMA latexes and deuterated AOT-d34 surfactant in latex core contrast-matched solvent were used to study the former, and electrokinetic modeling were used to study the latter. As the same amount of AOT-d34 is found to be incorporated with the latexes at all volume fractions, the solvodynamic and electrical interactions between particles are determined to be the explanation for the decrease in mobility. These measurements show that, for small latexes, there are interactions between the charged particles at all accessible particle volume fractions and that it is necessary to account for this to accurately determine the electrokinetic ζ potential.
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Oct 2017
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I22-Small angle scattering & Diffraction
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Gregory N.
Smith
,
Samuel D.
Finlayson
,
David
Gillespie
,
Jocelyn
Peach
,
Jonathan
Pegg
,
Sarah
Rogers
,
Olga
Shebanova
,
Ann
Terry
,
Steven P.
Armes
,
Paul
Bartlett
,
Julian
Eastoe
Abstract: Hypothesis: Poly(methyl methacrylate) (PMMA) latexes in nonpolar solvents are an excellent model system to understand phenomena in low dielectric media, and understanding their internal structure is critical to characterizing their performance in both fundamental studies of colloidal interactions and in potential industrial applications. Both the PMMA cores and the poly(12-hydroxystearic acid) (PHSA) shells of the latexes are known to be penetrable by solvent and small molecules, but the relevance of this for the properties of these particles is unknown. Experiments: These particles can be prepared in a broad range of sizes, and two PMMA latexes dispersed in n-dodecane (76 and 685 nm in diameter) were studied using techniques appropriate to their size. Small-angle scattering (using both neutrons and X-rays) was used to study the small latexes, and analytical centrifugation was used to study the large latexes. These studies enabled the calculation of the core densities and the amount of solvent in the stabilizer shells for both latexes. Both have consequences on interpreting measurements using these latexes. Findings:The PHSA shells are highly solvated (∼85% solvent by volume), as expected for effective steric stabilizers. However, the PHSA chains do contribute to the intensity of neutron scattering measurements on concentrated dispersions and cannot be ignored. The PMMA cores have a slightly lower density than PMMA homopolymer, which shows that only a small free volume is required to allow small molecules to penetrate into the cores. Interestingly, the observations are essentially the same, regardless of the size of the particle; these are general features of these polymer latexes. Despite the latexes being used as a model physical system, the internal chemical structure is complex and must be fully considered when characterizing them.
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Oct 2016
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I22-Small angle scattering & Diffraction
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Diamond Proposal Number(s):
[11969]
Abstract: Molecular self-assembly primarily occurs in solution. To better understand this process, techniques capable of probing the solvated state are consequently required. Small-angle scattering (SAS) has a proven ability to detect and characterize solutions, but it is rarely applied to more complex assembly shapes. Here, small-angle X-ray and neutron scattering are applied to observe toroidal assemblies in solution. Combined analysis confirms that the toroids have a core–shell structure, with a π-conjugated core and an alkyl shell into which solvent penetrates. The dimensions determined by SAS agree well with those obtained by (dried-state) atomic force microscopy. Increasing the number of naphthalene units in the molecular building block yields greater rigidity, as evidenced by a larger toroid and a reduction in solvent penetration into the shell. The detailed structural analysis demonstrates the applicability of SAS to monitor complex solution-based self-assembly.
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Jul 2016
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I22-Small angle scattering & Diffraction
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Abstract: A series of eight sodium sulfonic acid surfactants with differently branched tails (four double-chain sulfosuccinates and four triple-chain sulfocarballylates) were studied as charging agents for sterically stabilized poly(methyl methacrylate) (PMMA) latexes in dodecane. Tail branching was found to have no significant effect on the electrophoretic mobility of the latexes, but the number of tails was found to influence the electrophoretic mobility. Triple-chain, sulfocarballylate surfactants were found to be more effective. Several possible origins of this observation were explored by comparing sodium dioctylsulfosuccinate (AOT1) and sodium trioctylsulfocarballylate (TC1) using identical approaches: the inverse micelle size, the propensity for ion dissociation, the electrical conductivity, the electrokinetic or ζ potential, and contrast-variation small-angle neutron scattering. The most likely origin of the increased ability of TC1 to charge PMMA latexes is a larger number of inverse micelles. These experiments demonstrate a small molecular variation that can be made to influence the ability of surfactants to charge particles in nonpolar solvents, and modifying molecular structure is a promising approach to developing more effective charging agents.
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Nov 2015
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