超级球随机顺序吸附的形态和动力学：从六足到立方体
Morphology and Kinetics of Random Sequential Adsorption of Superballs: From Hexapods to Cubes
摘要：
超级球代表一类颗粒，其形状由${|x|}^{2p}+{|y|}^{2p}+{|z|}^{2p} \le R^{2p}$定义，其中$p\in(0,\infty)$是“变形参数”。$0<p<0.5$代表六足状（凹八面体状）颗粒族，而对于$0.5\leq p<1$和$p>1$，分别具有凸八面体状和立方体状颗粒族，其中$p=1,\;0.5$和$\infty$代表球体、八面体和立方体。胶体沸石悬浮液，催化和吸附，以及生物医学磁性纳米颗粒只是超级球包装的几个应用。我们介绍了一种通用的方法来模拟随机顺序吸附的超级球，我们称之为“低熵”算法，与传统的算法，代表了一个“高熵”的方法。这两种算法分别产生干扰分数$ϕ_\infty(p)$和$ν(p)$的精确估计，该指数表征长时间吸附动力学$t$，$ϕ(\infty)-ϕ(t)\sim t^{-ν(p)}$。精确估计的$ϕ_\infty(p)$和$ν(p)$，并显示出在协议，在某些特殊的限制，与现有的分析和数值结果。
英文摘要：
Superballs represent a class of particles whose shapes are defined by ${|x|}^{2p}+{|y|}^{2p}+{|z|}^{2p} \le R^{2p}$, with $p\in(0,\infty)$ being the "deformation parameter". $0<p<0.5$ represents a family of hexapodlike (concave octahedrallike) particles, while for $0.5\leq p<1$ and $p>1$ one has, respectively, families of convex octahedrallike and cubelike particles, with $p=1,\;0.5$ and $\infty$ representing spheres, octahedra, and cubes. Colloidal zeolite suspensions, catalysis, and adsorption, as well as biomedical magnetic nanoparticles are but a few of the applications of packing of superballs. We introduce a universal method for simulating random sequential adsorption of superballs, which we refer to as "low-entropy" algorithm, in contrast with the conventional algorithm that represents a "high-entropy" method. The two algorithms yield, respectively, precise estimates of the jamming fraction $ϕ_\infty(p)$ and $ν(p)$, the exponent that characterizes the kinetics of adsorption at long times $t$, $ϕ(\infty)-ϕ(t)\sim t^{-ν(p)}$. Precise estimates of $ϕ_\infty(p)$ and $ν(p)$ are obtained and shown to be in agreement, in some special limits, with the existing analytical and numerical results.
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