Geometry of random sequential adsorption

Hinrichsen, Einar L.; Feder, Jens; Jøssang, Torstein

doi:10.1007/bf01011908

Cited by 473 publications

(374 citation statements)

References 16 publications

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“…In the following subsection, we provide an analytical argument supporting the same scaling form in the high-dimensional limit. It is noteworthy that the best rigorous lower bound on the maximal density [29], derived by considering lattice packings, has the same form as (20). An interesting conjecture due to Palàsti [30] claims that the saturation density for RSA packings of congruent, oriented d-dimensional cubes equals the saturation density φ s = 0.747598 .…”

Section: A Saturation Densitymentioning

confidence: 99%

“…[17]. For 2 ≤ d < ∞, an exact determination of φ(∞) is not possible, but estimates for it have been obtained via computer experiments in two dimensions (circular disks) [18,20] and three dimensions (spheres) [21,22]. However, estimates of the saturation density φ(∞) in higher dimensions have heretofore not been obtained.…”

Section: Introductionmentioning

confidence: 99%

“…The algorithm is checked by reproducing some known results for d = 1, 2 and 3 [17,18,20,21,22]. Although we know that the saturation density φ(∞) is bounded from below by 2 −d [13,14], the manner in which φ(∞) scales with density is not known for d > 3.…”

Section: Introductionmentioning

confidence: 99%

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Random sequential addition of hard spheres in high Euclidean dimensions

2006

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Sphere packings in high dimensions have been the subject of recent theoretical interest. Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in d-dimensional Euclidean space R d in the infinitetime or saturation limit for the first six space dimensions (1 ≤ d ≤ 6). Specifically, we determine the saturation density, pair correlation function, cumulative coordination number and the structure factor in each of these dimensions. We find that for 2 ≤ d ≤ 6, the saturation density φ s scales with dimension as φ s = c 1 /2 d + c 2 d/2 d , where c 1 = 0.202048 and c 2 = 0.973872. We also show analytically that the same density scaling persists in the high-dimensional limit, albeit with different coefficients. A byproduct of this high-dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by φ s ≥ (d + 2)(1 − S 0 )/2 d+1 , where S 0 ∈ [0, 1] is the structure factor at k = 0 (i.e., infinite-wavelength number variance) in the high-dimensional limit.We prove rigorously that a Palàsti-like conjecture (the saturation density in R d is equal to that of the one-dimensional problem raised to the dth power) cannot be true for RSA hyperspheres.We demonstrate that the structure factor S(k) must be analytic at k = 0 and that RSA packings for 1 ≤ d ≤ 6 are nearly "hyperuniform." Consistent with the recent "decorrelation principle," we find that pair correlations markedly diminish as the space dimension increases up to six. We also obtain kissing (contact) number statistics for saturated RSA configurations on the surface of a ddimensional sphere for dimensions 2 ≤ d ≤ 5 and compare to the maximal kissing numbers in these dimensions. We determine the structure factor exactly for the related "ghost" RSA packing in R d and show that its distance from "hyperuniformity" increases as the space dimension increases, approaching a constant asymptotic value of 1/2. Our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions.

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Section: A Saturation Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Random sequential addition of hard spheres in high Euclidean dimensions

2006

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“…In this case, percolation with connectivity defined through particle overlap is never achieved, and for particles having a finite area the deposition terminates to a finite density called the 'jamming limit'. However, if one defines the connectivity rule to require only that particles are within a certain distance of each other to be in the same cluster it is possible to have a percolating cluster [36].…”

Section: Rejection Modelmentioning

confidence: 99%

Fiber deposition models in two and three spatial dimensions

Provatas

Haataja

Asikainen

et al. 2000

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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We review growth, percolation, and spatial correlations in deposition models of disordered fiber networks. We first consider 2D models with effective interactions between the deposited particles represented by simple parametrization. In particular, we discuss the case of single cluster growth, growth of uniformly random networks, and flocculated networks with nontrivial spatial correlations. We also consider a 3D deposition model of flexible fibers that describes the growth of multilayer structures of disordered networks. We discuss the statistical properties of such structures, transport of fluid through the network, and the asymptotics of growth in the limit of infinite thickness.

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“…Moreover, starting from a PD of points, increasing spatial correlation through a hard core interaction, the behavior of the system has been investigated up to the jamming point. Incidentally, the latter is nothing less that the well-known random sequential adsorption (RSA) process [5]. These processes have been characterized mainly through the kinetics of fractional surface coverage, although other morphological descriptors, such as the distribution of the Voronoi tessellation, and the pair distribution function thereof, have been monitored.…”

Section: Introductionmentioning

confidence: 99%

Order and randomness in Kolmogorov–Johnson–Mehl–Avrami-type phase transitions

Fanfoni

Persichetti

Tomellini

2012

J. Phys.: Condens. Matter

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The distribution of points on a 2D domain influences the kinetics of its coverage when a growth law is attached at each point. This implies that the kinetics of space filling can be adopted as a descriptor of the degree of order of the initial point distribution. In this paper, the degree of order of an initial array of points has been changed following two paths: (i) from a regular square lattice, through increasing displacement assigned to each point, towards Poissonian disorder; (ii) from a Poissonian distribution, by introducing a hard core potential with increasing correlation lengths, towards a more ordered lattice. A linear growth law has been attached to the points of the initial array and the kinetics X(X e ), where X e is the extended coverage as defined in the Kolmogorov-Johnson-Mehl-Avrami model, has been monitored. The quantitative analysis has been performed by fitting the kinetics to an equation which we propose for the first time and which has proved to be, in fact, highly suitable for the purpose. The results demonstrate that the gross of variation from order to disorder is obtained for point displacements, u, of the order of a, the latter being the constant of a square lattice. Vice versa, the introduction of a correlation distance in a random distribution provokes at most an order limited to the first neighbors and no real order can ever be reached. Others descriptors have been investigated, all confirming our results. We also developed an analytical description based on the use of the f -functions, as have been defined by Van Kampen, up to the second order terms. Such a description has been shown to work well for u/a < 1 within an interval X e which depends on the value.

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Geometry of random sequential adsorption

Cited by 473 publications

References 16 publications

Random sequential addition of hard spheres in high Euclidean dimensions

Random sequential addition of hard spheres in high Euclidean dimensions

Fiber deposition models in two and three spatial dimensions

Order and randomness in Kolmogorov–Johnson–Mehl–Avrami-type phase transitions

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