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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

Variables used for the calculation of the structure factor amplitude. Left-hand side: the liquid’s layer positions d                  m away from the centre of the gap, d                  k away from the outmost mica unit cell centre and c the mica unit-cell height are indicated with arrows. Right-hand side: the number of mica unit cells in each mica membrane is N                  3. The gap width D is defined as the distance between the surface potassium ions of the opposing mica crystals.
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fig3: Variables used for the calculation of the structure factor amplitude. Left-hand side: the liquid’s layer positions d m away from the centre of the gap, d k away from the outmost mica unit cell centre and c the mica unit-cell height are indicated with arrows. Right-hand side: the number of mica unit cells in each mica membrane is N 3. The gap width D is defined as the distance between the surface potassium ions of the opposing mica crystals.

Mentions: Fig. 3 ▶ illustrates the variables used for the calculations below. The total structure factor F(q ⊥) for the confinement device is written as a sum of contributions from the regions I, II and III indicated in Fig. 3 ▶, Here, F I is the structure factor for the pair of columns of mica unit cells, F II that of the confined liquid and F III that of liquid condensed on the outer mica surfaces. The squared modulus (‘structure factor intensity’) is given by Below we provide theoretical expressions for these structure factor terms as well as for the interference terms and . We will argue that ≃ 0.


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)

Variables used for the calculation of the structure factor amplitude. Left-hand side: the liquid’s layer positions d                  m away from the centre of the gap, d                  k away from the outmost mica unit cell centre and c the mica unit-cell height are indicated with arrows. Right-hand side: the number of mica unit cells in each mica membrane is N                  3. 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

fig3: Variables used for the calculation of the structure factor amplitude. Left-hand side: the liquid’s layer positions d m away from the centre of the gap, d k away from the outmost mica unit cell centre and c the mica unit-cell height are indicated with arrows. Right-hand side: the number of mica unit cells in each mica membrane is N 3. The gap width D is defined as the distance between the surface potassium ions of the opposing mica crystals.
Mentions: Fig. 3 ▶ illustrates the variables used for the calculations below. The total structure factor F(q ⊥) for the confinement device is written as a sum of contributions from the regions I, II and III indicated in Fig. 3 ▶, Here, F I is the structure factor for the pair of columns of mica unit cells, F II that of the confined liquid and F III that of liquid condensed on the outer mica surfaces. The squared modulus (‘structure factor intensity’) is given by Below we provide theoretical expressions for these structure factor terms as well as for the interference terms and . We will argue that ≃ 0.

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