Model-free analysis of neutron reflectivity data from polymer thin films with the simulated annealing technique

Kunz, Klaus; Reiter, J.M.; Götzelmann, A.; Stamm, Manfred

doi:10.1021/ma00068a038

Cited by 28 publications

(12 citation statements)

References 3 publications

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“…Fitting of experimental data requires varying model parameters until an appropriate merit function is minimized. Fitting of reflectivity data involves some special considerations. ,− Because of the strong variation in intensity across the q-range of the reflectivity data, familiar merit functions such as χ 2 will largely ignore the higher- q region where all of the relevant interference effects appear. It is therefore necessary to use merit functions that reduce the dominance of the numerically larger low- q data.…”

Section: Resultsmentioning

confidence: 99%

Interfacial Density Profiles of Polar and Nonpolar Liquids at Hydrophobic Surfaces

2020

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A density-depleted region ("gap") is known to exist between water and hydrophobic surfaces. Using X-ray reflectivity, we have observed similar gaps between hydrophobic self-assembled monolayers (SAMs) and four other polar liquids. For these liquids and for water, the observed electron density depletion is nonzero and is in most cases slightly greater than the depletion attributable to the layer of hydrogen atoms at the SAM surface. On the other hand, the observed X-ray reflectivity from the interfaces between SAMs and three nonpolar liquids studied can be explained either without gaps or with smaller gaps. Thus, polar liquids (including but not limited to water) stand away from even the terminal hydrogen atoms at hydrophobic surfaces, while nonpolar liquids interpenetrate the terminal region. There is no consistent correlation between the sizes of the gaps and the liquid−SAM contact angles, the relative polarities of the polar liquids, or their bulk densities.Article pubs.acs.org/Langmuir

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Section: Resultsmentioning

confidence: 99%

Interfacial Density Profiles of Polar and Nonpolar Liquids at Hydrophobic Surfaces

2020

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“…In contrast to previous attempts to solve the reflectivity inverse problem using stochastic methods (Laub & Kuhl, 2006;Kunz et al, 1993;Zhou & Chen, 1993;Sivia et al, 1991), here we take advantage of the concurrent fit of multiple solvent contrasts, thus avoiding the need for a 'good initial guess' for the profiles or for a set of criteria for identifying physically reasonable profiles among different candidates. Despite the fact that only examples at the solid/liquid interface were showcased in the previous sections, the methodology is also directly applicable at the air/liquid interface without any modifications.…”

Section: Discussionmentioning

confidence: 99%

“…The defined score function f has essentially two contributions, one from the squared difference between the experimental and theoretical q 4 -weighted reflectivities and a second one from the squared difference of their logarithms. Many different forms of f have been tested, including log R, Rq 4 , log Rq 4 and P ðR exp À RÞ 2 = min ðR exp ; RÞ 2 (Kunz et al, 1993). It was found that while Rq 4 gave the best results, there is some noticeable bias towards high q.…”

Section: Algorithmmentioning

confidence: 99%

“…Hohage et al (2008) introduced an iterative algorithm for profile reconstruction based on regularization methods. Kunz et al (1993) and Laub & Kuhl (2006) combined aspects of simulated annealing with special parameterization of the SLD profile, de Haan & Drijkoningen (1994) used genetic algorithms for model fitting, and Sivia et al (1991) implemented maximum entropy methods for obtaining 'free-form' solutions, while Zhou & Chen (1993) proposed a groove-tracking method for SLD reconstruction. A common feature of all these approaches is that they treat the case of single contrast measurements that cannot yield a unique density profile, while successful reconstructions usually depend on a good initial guess about the profile or on constraints based on prior knowledge about the system.…”

Section: Introductionmentioning

confidence: 99%

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Model-independent recovery of interfacial structure from multi-contrast neutron reflectivity data

Koutsioubas

2019

J Appl Cryst

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Neutron specular reflectivity at soft interfaces provides sub-nanometre information concerning the molecular distribution of thin films, while the application of contrast variation can highlight the scattering from different parts of the system and lead to an overall reduction in fitting ambiguity. Traditional modelling approaches involve the construction of a trial scattering length density profile based on initial speculation and the subsequent refinement of its parameters through minimization of the discrepancy between the calculated and measured reflectivity. In practice this might produce an artificial bias towards specific sets of solutions. On the other hand, direct inversion of reflectivity data, despite its ability to provide a unique solution, is subject to limitations and experimental complications. Presented here is an integrated indirect Fourier transform/simulated annealing method that, when applied to multiple solvent contrast reflectivity data and within the limits of finite spatial resolution, leads to reliable reconstructions of the interfacial structure without the need for any a priori assumptions. The generality of the method permits its straightforward application in common experimental contrast-variation investigations at the solid/liquid and air/liquid interface.

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“…Several different 'model-independent' approaches for the reconstruction of interfacial structure from reflectivity measurements have been reported, based either on experimental (Majkrzak & Berk, 1998;Majkrzak et al, 2003Majkrzak et al, , 2000 or on numerical/stochastic methods (Pedersen, 1992;Hohage et al, 2008;Kunz et al, 1993;Zhou & Chen, 1993;Koutsioubas, 2019). However, the vast majority of investigations in the literature rely traditionally on model-dependent refinements, where the interface is modelled as a stratified medium (succession of slabs) with prior knowledge about the system being embodied in the bounds and relations between the sld, thickness and roughness of each slab.…”

Section: Introductionmentioning

confidence: 99%

anaklasis: a compact software package for model-based analysis of specular neutron and X-ray reflectometry data sets

Koutsioubas

2021

J Appl Cryst

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anaklasis constitutes a set of open-source Python scripts that facilitate a range of specular neutron and X-ray reflectivity calculations, involving the generation of theoretical curves and the comparison/fitting of interfacial model reflectivity against experimental data sets. The primary focus of the software is twofold: on one hand to offer a more natural framework for model definition, requiring minimum coding literacy, and on the other hand to include advanced analysis methods that have been proposed in recent work. Particular attention is given to the ability to co-refine reflectivity data and to the estimation of model-parameter uncertainty and covariance using bootstrap analysis and Markov chain Monte Carlo sampling. The compactness and simplicity of model definition together with the streamlined analysis do not present a steep learning curve for the user, an aspect that may accelerate the generation of reproducible, easily readable and statistically accurate reports in future neutron and X-ray reflectivity related literature.

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Model-free analysis of neutron reflectivity data from polymer thin films with the simulated annealing technique

Cited by 28 publications

References 3 publications

Interfacial Density Profiles of Polar and Nonpolar Liquids at Hydrophobic Surfaces

Interfacial Density Profiles of Polar and Nonpolar Liquids at Hydrophobic Surfaces

Model-independent recovery of interfacial structure from multi-contrast neutron reflectivity data

anaklasis: a compact software package for model-based analysis of specular neutron and X-ray reflectometry data sets

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