Figure 1

The contact density ${\rho }_c\left(x\right)$ of a fluid of hard spheres with radius $R$ and packing fraction ${\eta }_s=0.3$ at a hard spherocylinder with length $L=10R$ and radius $R_c=3R$ so that the contact density occurs at $R_{sc}=4R$. The path on the parallel surface of contact of the spherocylinder is parametrized by $x$, as is indicated by the dotted line in the inset. Note that the inset is not drawn to scale. According to the curvature expansion the contact value ${\rho }_c\left(x\right)$ jumps at $x=L∕2$, where the cylindrical and the spherical parts meet, as shown by the full line. The symbols denote data from Monte Carlo simulations for ${\eta }_s=0.3$.Reuse & Permissions

Figure 2

Depletion interaction between an oblate (a) [prolate (b)] ellipsoid with half-axes $(10,10,4)R$ [$(4,4,10)R$] and a sphere with $R_a=10R$. The center of the inserted sphere approaches the north pole of the fixed ellipsoid normal to the surface. Both particles touch if $u=R_a$. The symbols denote results obtained by approach (i), for which we employ FMT for convex objects, and the lines denote corresponding results from approach (ii), for which we use the curvature expansion. As both approaches involve approximations of very different nature, the excellent agreement is very likely to be due to the fact that the systematic error is very small in both approaches. We verified this observation also for ellipsoids with different half axes. For these data the depletion agent is a fluid of hard spheres with radius $R$ modeled via the White Bear version of FMT. The bulk packing fraction is ${\eta }_s=0.3$. Note that the insets here and in the following figures are not drawn to scale.Reuse & Permissions

Figure 3

Depletion interaction between two oblate ellipsoids with half-axes $(10,10,4)R$. The inserted particle approaches the north pole of the first ellipsoid perpendicular to its surface. $\gamma$ denotes the angle between the $z$ axis and the large half axis of the inserted ellipsoid (see the inset). If both ellipsoids are aligned (as drawn in the inset), i.e., $\gamma =90°$, the minimal separation of the centers is $z_{min}=8R$, while for $\gamma =0$ it is $z_{min}=14R$; $z_{min}(\gamma =60°)\approx 9.53R$ and $z_{min}(\gamma =30°)\approx 12.57R$. The positions of the extrema and the zeros are basically independent of $\gamma$. The solvent is a fluid of hard spheres with radius $R$ and bulk packing fraction ${\eta }_s=0.3$ and is modeled via the White Bear density functional.Reuse & Permissions

Figure 4

Depletion potential for the same setup as in Fig. 3 with fixed $\gamma =90°$. The angle $\alpha$ characterizes the straight line along which the center of the inserted ellipsoid is moved away from its contact position at the north poles (see the inset). The abscissa measures the normal (i.e., minimal) distance $u$ of the center of the inserted ellipsoid from the surface of the fixed one. For small $\alpha$ the depletion potentials almost coincide due to the oblate shape $(10,10,4)R$ of the fixed ellipsoid.Reuse & Permissions

Figure 5

Entropic torque between two oblate ellipsoids with half-axes $(10,10,4)R$ immersed in a solvent of hard spheres with radius $R$ as sketched in the inset. The angle $\gamma$ parametrizes the rotation of the inserted ellipsoid and $\Delta z$ denotes the distance between the centers. The ellipsoids are aligned such that the vector connecting their centers runs through the north poles of the fixed (lower) ellipsoid. For this setup the entropic torque $M$ is given by $M=-\partial W∕\partial \gamma$ [23]. If $\mathrm{\Delta }z>8R$, the inserted (upper) ellipsoid can be rotated as indicated in the inset and experiences an entropic torque. Positive values of $M$ mean that the ellipsoid is pushed toward larger values of $\gamma$. The curves end if the two ellipsoids overlap due to the geometrical constraint. Note that the visible discontinuities in the first derivative of the curves for $\mathrm{\Delta }z=12R$ and $\mathrm{\Delta }z=14R$ are not artifacts. They occur if both ellipsoids come so close that just a single small sphere with radius $R$ fits in between their surfaces. For $\mathrm{\Delta }z=16R$ the distance between the ellipsoids is large enough so that this effect does not occur.Reuse & Permissions