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Nonmonotoic fluctuation-induced interactions between dielectric slabs carrying charge disorder
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10.1063/1.3497039
/content/aip/journal/jcp/133/17/10.1063/1.3497039
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/17/10.1063/1.3497039
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

We consider two semi-infinite net-neutral slabs (half-spaces) of dielectric constant and interacting across a medium of dielectric constant . The monopolar charge disorder (shown schematically by small light and dark patches) is distributed as random patches of finite typical size (correlation length) in a layered structure in the bulk of the slabs and on the two bounding surfaces at . It may be either quenched or annealed.

Image of FIG. 2.
FIG. 2.

(a) Magnitude of the rescaled total force, [Eq. (25)], between two identical net-neutral dielectric slabs in vacuum bearing quenched monopolar charge disorder as a function of the rescaled distance, . The results are plotted here for fixed , (no surface disorder) and bulk disorder variance , and varying disorder correlation lengths , 200, , , and (from top to bottom). Inset shows the ratio of the total force to the pure zero-frequency vdW force (34) between the slabs in the absence of charge disorder for the same range of . (b) Same as (a) but here we fix , , and and vary the bulk disorder variance in the range , , , , and (from top to bottom). Solid curve is the pure vdW force (34). (c) Same as (b) but here we fix , , and and vary the dielectric constant of slabs as (top dotted curve), 10, 40, and 100 (bottom dot-dashed curve). All graphs are plotted in log-log scale.

Image of FIG. 3.
FIG. 3.

(a) Ratio of the total force (30) to the zero-frequency vdW force (34) between two identical net-neutral dielectric slabs in vacuum bearing annealed monopolar charge disorder as a function of the rescaled distance, . The results are plotted here for fixed , (no surface disorder), , and varying disorder correlation length , 200, , and (from top to bottom). Annealed curves are bounded by the perfect conductor result, Eq. (37) (top solid line), for large disorder and the vdW result, Eq. (34) (bottom solid line), for no disorder. (b) Same as (a) but here we have fixed , , , and bulk disorder variance varied in the range , , , , and (from top to bottom). (c) Same as (a) but here we fix , , and and vary the dielectric constant of the slabs as , 10, 40, and 100 (from top). Inset shows a closer view of the curves for and 100 (from top). Top dotted lines correspond to Eq. (37). All graphs are plotted in log-log scale.

Image of FIG. 4.
FIG. 4.

(a) Same as Fig. 3(a) but here we fix , , , and and vary the dielectric constant of the intervening medium as , 10, 20, and 40 (from bottom to top). (b) Same as (a) but here we fix the dielectric constant of the slab as and vary that of the intervening medium as , 40, 60, and 80 (from top to bottom). Top dotted lines correspond to Eq. (37).

Image of FIG. 5.
FIG. 5.

The rescaled magnitude of the (attractive) force, Eq. (30), between two identical net-neutral dielectric slabs bearing annealed monopolar charge disorder in a dielectrically homogeneous system as a function of the rescaled distance, . Here we plot the resulting force for , 10, 40, and 100 (from top to bottom) and for uncorrelated bulk disorder in both slabs with , , and . Top solid line shows the universal limiting expression (37).

Image of FIG. 6.
FIG. 6.

Same as Fig. 3(a) but for two dissimilar dielectric slabs in vacuum with one slab being disorder free and the other slab containing annealed charge disorder of variance , . Here, we fix and vary the disorder correlation length as , 200, , and (from top to bottom). The results in this case are bounded by the limiting values given by Eqs. (34) and (42) [solid lines labeled by and , respectively]; see Eq. (41). The top solid line [labeled by ] is from Eq. (37).

Image of FIG. 7.
FIG. 7.

(a) The rescaled total force, [Eq. (25)], between two dissimilar net-neutral dielectric slabs interacting across a medium of dielectric constant varying in the range , 15, 25, and 40 (dashed curves from bottom). Here, we have fixed the dielectric constant of the slabs as and , which contain uncorrelated quenched disorder of fixed disorder variances and . Inset shows a closer view of the region around the minimum. (b) Same as (a) but plotted for correlated quenched disorder. Here, we fix and vary the correlation length as , 20, 100, 500, and , which is taken to be equal in both slabs . Inset again shows a closer view of the region around the minimum. (c) Same as (a) but for (uncorrelated) annealed disorder obtained from Eq. (30) for , 20, and 40. Inset shows the ratio of the total force to the pure zero-frequency vdW force (18) in the absence of charge disorder for a wider range of separations. The horizontal dotted lines show the limiting expression (37).

Image of FIG. 8.
FIG. 8.

(a) The rescaled total force, [Eq. (25)], between two dissimilar net-neutral dielectric slabs interacting across a medium of dielectric constant varying in the range , 40, 60, and 100 (dashed curves from bottom). Here, we have fixed the dielectric constant of the slabs as and , which contain uncorrelated quenched disorder of fixed disorder variances and . Inset shows a closer view of the region around the maximum. (b) Same as (a) but for annealed disorder obtained from Eq. (30). Inset shows the ratio of the total force to the vdW force (18) for a wider range of separations; here the horizontal dotted lines correspond to Eq. (37). (c) Same as (a) but for one slab being disorder free and the other slab containing annealed charge disorder of variances and (dashed curves from top correspond to , 40, 60, and 100). Inset shows the ratio for a wider range of separations; the horizontal dotted lines correspond to Eq. (42) where should be replaced by

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/content/aip/journal/jcp/133/17/10.1063/1.3497039
2010-11-02
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonmonotoic fluctuation-induced interactions between dielectric slabs carrying charge disorder
http://aip.metastore.ingenta.com/content/aip/journal/jcp/133/17/10.1063/1.3497039
10.1063/1.3497039
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