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X-ray reflectivity theory for determining the density profile of a liquid under nanometre confinement.

Perret E, Nygård K, Satapathy DK, Balmer TE, Bunk O, Heuberger M, van der Veen JF - J Synchrotron Radiat (2010)

Bottom Line: The confinement geometry acts like an X-ray interferometer, which consists of two opposing atomically flat single-crystal mica membranes with an intervening thin liquid film of variable thickness.An expression for the reflected intensity as a function of momentum transfer is given.The total structure factor intensity for the liquid-filled confinement device is derived as a sum of contributions from the inner and outer crystal terminations.

View Article: PubMed Central - HTML - PubMed

Affiliation: Paul Scherrer Institut, Villigen PSI, Switzerland.

ABSTRACT
An X-ray reflectivity theory on the determination of the density profile of a molecular liquid under nanometre confinement is presented. The confinement geometry acts like an X-ray interferometer, which consists of two opposing atomically flat single-crystal mica membranes with an intervening thin liquid film of variable thickness. The X-rays reflected from the parallel crystal planes (of known structure) and the layered liquid in between them (of unknown structure) interfere with one another, making X-ray reflectivity highly sensitive to the liquid's density profile along the confinement direction. An expression for the reflected intensity as a function of momentum transfer is given. The total structure factor intensity for the liquid-filled confinement device is derived as a sum of contributions from the inner and outer crystal terminations. The method presented readily distinguishes the confined liquid from the liquid adsorbed on the outer mica surfaces. It is illustrated for the molecular liquid tetrakis(trimethyl)siloxysilane, confined by two mica surfaces at a distance of 8.6 nm.

No MeSH data available.


Related in: MedlinePlus

Confinement geometry. Left-hand side: stack, (I) single-crystal membranes of mica with N                  3 unit cells, (II) liquid in the gap and (III) condensed liquid on the outer mica surfaces. Right-hand side: molecular structures of muscovite mica, TTMSS and water. The gap width D is defined as the distance between the surface potassium ions of the opposing mica crystals.
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fig2: Confinement geometry. Left-hand side: stack, (I) single-crystal membranes of mica with N 3 unit cells, (II) liquid in the gap and (III) condensed liquid on the outer mica surfaces. Right-hand side: molecular structures of muscovite mica, TTMSS and water. The gap width D is defined as the distance between the surface potassium ions of the opposing mica crystals.

Mentions: A symmetric planar confinement geometry was obtained as follows. A thin single-crystal mica membrane of (001) orientation was cleaved from a large crystal. The micrometre-thin membrane was then cut into two pieces, which were glued onto Invar cylindrical supports with their freshly cleaved faces being exposed. Both supports have rectangular areas cut out, leaving the central part of the membranes unsupported. The two crystals were brought to close proximity and a liquid droplet, in this study TTMSS, was inserted using a syringe. In order to avoid fast evaporation of the liquid the vapour pressure in the chamber was increased by a TTMSS reservoir in a small cuvette. The non-zero vapour pressure gave rise to condensed TTMSS layers on the water-covered outer mica surfaces. Upon fast approach, liquid became trapped and a pocket was formed, which slowly drained out until a flat layered film of typically 300 µm × 300 µm in size was obtained (Perret et al., 2009 ▶). The crossed pair of free-standing mica membranes with liquid in between was aligned such that the focused beam impinges onto the centre of the flat confined film area, which made it possible to measure the X-ray reflectivity from an oriented planar mica–liquid–mica stack. The stack can be regarded as a single crystal having an extended planar vacancy of adjustable thickness which is filled with liquid (Fig. 2 ▶). The assumption of a symmetric geometry is justified by the fact that the mica sheets have the same thickness and that they are surrounded by the same gas environment.


X-ray reflectivity theory for determining the density profile of a liquid under nanometre confinement.

Perret E, Nygård K, Satapathy DK, Balmer TE, Bunk O, Heuberger M, van der Veen JF - J Synchrotron Radiat (2010)

Confinement geometry. Left-hand side: stack, (I) single-crystal membranes of mica with N                  3 unit cells, (II) liquid in the gap and (III) condensed liquid on the outer mica surfaces. Right-hand side: molecular structures of muscovite mica, TTMSS and water. The gap width D is defined as the distance between the surface potassium ions of the opposing mica crystals.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2927908&req=5

fig2: Confinement geometry. Left-hand side: stack, (I) single-crystal membranes of mica with N 3 unit cells, (II) liquid in the gap and (III) condensed liquid on the outer mica surfaces. Right-hand side: molecular structures of muscovite mica, TTMSS and water. The gap width D is defined as the distance between the surface potassium ions of the opposing mica crystals.
Mentions: A symmetric planar confinement geometry was obtained as follows. A thin single-crystal mica membrane of (001) orientation was cleaved from a large crystal. The micrometre-thin membrane was then cut into two pieces, which were glued onto Invar cylindrical supports with their freshly cleaved faces being exposed. Both supports have rectangular areas cut out, leaving the central part of the membranes unsupported. The two crystals were brought to close proximity and a liquid droplet, in this study TTMSS, was inserted using a syringe. In order to avoid fast evaporation of the liquid the vapour pressure in the chamber was increased by a TTMSS reservoir in a small cuvette. The non-zero vapour pressure gave rise to condensed TTMSS layers on the water-covered outer mica surfaces. Upon fast approach, liquid became trapped and a pocket was formed, which slowly drained out until a flat layered film of typically 300 µm × 300 µm in size was obtained (Perret et al., 2009 ▶). The crossed pair of free-standing mica membranes with liquid in between was aligned such that the focused beam impinges onto the centre of the flat confined film area, which made it possible to measure the X-ray reflectivity from an oriented planar mica–liquid–mica stack. The stack can be regarded as a single crystal having an extended planar vacancy of adjustable thickness which is filled with liquid (Fig. 2 ▶). The assumption of a symmetric geometry is justified by the fact that the mica sheets have the same thickness and that they are surrounded by the same gas environment.

Bottom Line: The confinement geometry acts like an X-ray interferometer, which consists of two opposing atomically flat single-crystal mica membranes with an intervening thin liquid film of variable thickness.An expression for the reflected intensity as a function of momentum transfer is given.The total structure factor intensity for the liquid-filled confinement device is derived as a sum of contributions from the inner and outer crystal terminations.

View Article: PubMed Central - HTML - PubMed

Affiliation: Paul Scherrer Institut, Villigen PSI, Switzerland.

ABSTRACT
An X-ray reflectivity theory on the determination of the density profile of a molecular liquid under nanometre confinement is presented. The confinement geometry acts like an X-ray interferometer, which consists of two opposing atomically flat single-crystal mica membranes with an intervening thin liquid film of variable thickness. The X-rays reflected from the parallel crystal planes (of known structure) and the layered liquid in between them (of unknown structure) interfere with one another, making X-ray reflectivity highly sensitive to the liquid's density profile along the confinement direction. An expression for the reflected intensity as a function of momentum transfer is given. The total structure factor intensity for the liquid-filled confinement device is derived as a sum of contributions from the inner and outer crystal terminations. The method presented readily distinguishes the confined liquid from the liquid adsorbed on the outer mica surfaces. It is illustrated for the molecular liquid tetrakis(trimethyl)siloxysilane, confined by two mica surfaces at a distance of 8.6 nm.

No MeSH data available.


Related in: MedlinePlus