Random sequential adsorption

Random sequential adsorption (RSA) refers to a process where particles are randomly introduced in a system, and if they do not overlap any previously adsorbed particle, they adsorb and remain fixed for the rest of the process. RSA can be carried out in computer simulation, in a mathematical analysis, or in experiments. It was first studied by one-dimensional models: the attachment of pendant groups in a polymer chain by Paul Flory, and the car-parking problem by Alfréd Rényi.^[1] Other early works include those of Benjamin Widom.^[2] In two and higher dimensions many systems have been studied by computer simulation, including in 2d, disks, randomly oriented squares and rectangles, aligned squares and rectangles, various other shapes, etc.

An important result is the maximum surface coverage, called the saturation coverage or the packing fraction. On this page we list that coverage for many systems.

The blocking process has been studied in detail in terms of the random sequential adsorption (RSA) model.^[3] The simplest RSA model related to deposition of spherical particles considers irreversible adsorption of circular disks. One disk after another is placed randomly at a surface. Once a disk is placed, it sticks at the same spot, and cannot be removed. When an attempt to deposit a disk would result in an overlap with an already deposited disk, this attempt is rejected. Within this model, the surface is initially filled rapidly, but the more one approaches saturation the slower the surface is being filled. Within the RSA model, saturation is sometimes referred to as jamming. For circular disks, saturation occurs at a coverage of 0.547. When the depositing particles are polydisperse, much higher surface coverage can be reached, since the small particles will be able to deposit into the holes in between the larger deposited particles. On the other hand, rod like particles may lead to much smaller coverage, since a few misaligned rods may block a large portion of the surface.

For the one-dimensional parking-car problem, Renyi^[1] has shown that the maximum coverage is equal to

$\theta _{1}=\int _{0}^{\infty }\exp \left(-2\int _{0}^{x}{\frac {1-e^{-y}}{y}}dy\right)dx=0.7475979202534\ldots$

the so-called Renyi car-parking constant.^[4]

Then followed the conjecture of Ilona Palásti,^[5] who proposed that the coverage of d-dimensional aligned squares, cubes and hypercubes is equal to θ₁^d. This conjecture led to a great deal of work arguing in favor of it, against it, and finally computer simulations in two and three dimensions showing that it was a good approximation but not exact. The accuracy of this conjecture in higher dimensions is not known.

For $k$ -mers on a one-dimensional lattice, we have for the fraction of vertices covered,^[6]

$\theta _{k}=k\int _{0}^{\infty }\exp \left(-u-2\sum _{j=1}^{k-1}{\frac {1-e^{-ju}}{j}}\right)du=k\int _{0}^{1}\exp \left(-2\sum _{j=1}^{k-1}{\frac {1-v^{j}}{j}}\right)dv$

When $k$ goes to infinity, this gives the Renyi result above. For k = 2, this gives the Flory ^[7] result $\theta _{1}=1-e^{-2}$ .

For percolation thresholds related to random sequentially adsorbed particles, see Percolation threshold.

Saturation coverage of k-mers on 1d lattice systems

system	Saturated coverage $\theta _{k}$ (fraction of sites filled)
dimers	$1-e^{-2}=0.86466472$ ^[7]
trimers	${\frac {3{\sqrt {\pi }}({\text{erfi}}(2)-{\text{erfi}}(1))}{2e^{4}}}\approx 0.82365296$ ^[6]
k = 4	$0.80389348$ ^[6]
k = 10	$0.76957741$ ^[6]
k = 100	$0.74976335$ ^[6]
k = 1000	$0.74781413$ ^[6]
k = 10000	$0.74761954$ ^[6]
k = 100000	$0.74760008$ ^[6]
k = $\infty$	$0.74759792$ ^[1]

Asymptotic behavior: $\theta _{k}\sim \theta _{\infty }+0.2162/k+\ldots$ .

Saturation coverage of segments of two lengths on a one dimensional continuum

R = size ratio of segments. Assume equal rates of adsorption

system	Saturated coverage $\theta$ (fraction of line filled)
R = 1	0.74759792^[1]
R = 1.05	0.7544753(62) ^[9]
R = 1.1	0.7599829(63) ^[9]
R = 2	0.7941038(58) ^[9]

Saturation coverage of k-mers on a 2d square lattice

system	Saturated coverage $\theta _{k}$ (fraction of sites filled)
dimers k = 2	0.906820(2),^[10] 0.906,^[11] 0.9068,^[12] 0.9062,^[13] 0.906,^[14] 0.905(9),^[15] 0.906,^[11] 0.906823(2),^[16]
trimers k = 3	^[6] 0.846,^[11] 0.8366 ^[12]
k = 4	0.8094 ^[13] 0.81^[11]
k = 5	0.7868 ^[11]
k = 6	0.7703 ^[11]
k = 7	0.7579 ^[11]
k = 8	0.7479,^[13] 0.747^[11]
k = 9	0.7405^[11]
k = 16	0.7103,^[13] 0.71^[11]
k = 32	0.6892,^[13] 0.689,^[11] 0.6893(4)^[17]
k = 48	0.6809(5),^[17]
k = 64	0.6755,^[13] 0.678,^[11] 0.6765(6)^[17]
k = 96	0.6714(5)^[17]
k = 128	0.6686,^[13] 0.668(9),^[15] 0.668^[11] 0.6682(6)^[17]
k = 192	0.6655(7)^[17]
k = 256	0.6628^[13] 0.665,^[11] 0.6637(6)^[17]
k = 384	0.6634(6)^[17]
k = 512	0.6618,^[13] 0.6628(9)^[17]
k = 1024	0.6592 ^[13]
k = 2048	0.6596 ^[13]
k = 4096	0.6575^[13]
k = 8192	0.6571 ^[13]
k = 16384	0.6561 ^[13]
k = ∞	0.660(2),^[17] 0.583(10),^[18]

Asymptotic behavior: $\theta _{k}\sim \theta _{\infty }+\ldots$ .

Saturation coverage of k-mers on a 2d triangular lattice

system	Saturated coverage $\theta _{k}$ (fraction of sites filled)
dimers k = 2	0.9142(12),^[19]
k = 3	0.8364(6),^[19]
k = 4	0.7892(5),^[19]
k = 5	0.7584(6),^[19]
k = 6	0.7371(7),^[19]
k = 8	0.7091(6),^[19]
k = 10	0.6912(6),^[19]
k = 12	0.6786(6),^[19]
k = 20	0.6515(6),^[19]
k = 30	0.6362(6),^[19]
k = 40	0.6276(6),^[19]
k = 50	0.6220(7),^[19]
k = 60	0.6183(6),^[19]
k = 70	0.6153(6),^[19]
k = 80	0.6129(7),^[19]
k = 90	0.6108(7),^[19]
k = 100	0.6090(8),^[19]
k = 128	0.6060(13),^[19]

Saturation coverage for particles with neighbors exclusion on 2d lattices

system	Saturated coverage $\theta _{k}$ (fraction of sites filled)
Square lattice with NN exclusion	0.3641323(1),^[20] 0.36413(1),^[21] 0.3641330(5),^[22]
Honeycomb lattice with NN exclusion	0.37913944(1),^[20] 0.38(1),^[2] 0.379^[23]

.

Saturation coverage of $k\times k$ squares on a 2d square lattice

system	Saturated coverage $\theta _{k}$ (fraction of sites filled)
k = 2	0.74793(1),^[24] 0.747943(37),^[25] 0.749(1),^[26]
k = 3	0.67961(1),^[24] 0.681(1),^[26]
k = 4	0.64793(1),^[24] 0.647927(22)^[25] 0.646(1),^[26]
k = 5	0.62968(1)^[24] 0.628(1),^[26]
k = 8	0.603355(55)^[25] 0.603(1),^[26]
k = 10	0.59476(4)^[24] 0.593(1),^[26]
k = 15	0.583(1),^[26]
k = 16	0.582233(39)^[25]
k = 20	0.57807(5)^[24] 0.578(1),^[26]
k = 30	0.574(1),^[26]
k = 32	0.571916(27)^[25]
k = 50	0.56841(10)^[24]
k = 64	0.567077(40)^[25]
k = 100	0.56516(10)^[24]
k = 128	0.564405(51)^[25]
k = 256	0.563074(52)^[25]
k = 512	0.562647(31)^[25]
k = 1024	0.562346(33)^[25]
k = 4096	0.562127(33)^[25]
k = 16384	0.562038(33)^[25]

For k = ∞, see "2d aligned squares" below. Asymptotic behavior:^[25] $\theta _{k}\sim \theta _{\infty }+0.316/k+0.114/k^{2}\ldots$ . See also ^[27]

Saturation coverage for randomly oriented 2d systems

system	Saturated coverage
equilateral triangles	0.52590(4)^[28]
squares	0.523-0.532,^[29] 0.530(1),^[30] 0.530(1),^[31] 0.52760(5)^[28]
regular pentagons	0.54130(5)^[28]
regular hexagons	0.53913(5)^[28]
regular heptagons	0.54210(6)^[28]
regular octagons	0.54238(5)^[28]
regular enneagons	0.54405(5)^[28]
regular decagons	0.54421(6)^[28]

2d oblong shapes with maximal coverage

system	aspect ratio	Saturated coverage
rectangle	1.618	0.553(1)^[32]
dimer	1.5098	0.5793(1)^[33]
ellipse	2.0	0.583(1)^[32]
spherocylinder	1.75	0.583(1)^[32]
smoothed dimer	1.6347	0.5833(5)^[34]

Saturation coverage for 3d systems

system	Saturated coverage
spheres	0.3841307(21),^[35] 0.38278(5),^[36] 0.384(1)^[37]
randomly oriented cubes	0.3686(15),^[38] 0.36306(60)^[39]
randomly oriented cuboids 0.75:1:1.3	0.40187(97),^[39]

Saturation coverages for disks, spheres, and hyperspheres

system	Saturated coverage
2d disks	0.5470735(28),^[35] 0.547067(3),^[40] 0.547070,^[41] 0.5470690(7),^[42] 0.54700(6),^[36] 0.54711(16),^[43] 0.5472(2),^[44] 0.547(2),^[45] 0.5479,^[16]
3d spheres	0.3841307(21),^[35] 0.38278(5),^[36] 0.384(1)^[37]
4d hyperspheres	0.2600781(37),^[35] 0.25454(9),^[36]
5d hyperspheres	0.1707761(46),^[35] 0.16102(4),^[36]
6d hyperspheres	0.109302(19),^[35] 0.09394(5),^[36]
7d hyperspheres	0.068404(16),^[35]
8d hyperspheres	0.04230(21),^[35]

Saturation coverages for aligned squares, cubes, and hypercubes

system	Saturated coverage
2d aligned squares	0.562009(4),^[25] 0.5623(4),^[16] 0.562(2),^[45] 0.5565(15),^[46] 0.5625(5),^[47] 0.5444(24),^[48] 0.5629(6),^[49] 0.562(2),^[50]
3d aligned cubes	0.4227(6),^[50] 0.42(1),^[51] 0.4262,^[52] 0.430(8),^[53] 0.422(8),^[54] 0.42243(5)^[38]
4d aligned hypercubes	0.3129,^[50] 0.3341,^[52]

References

^ ^a ^b ^c ^d Rényi, A. (1958). "On a one-dimensional problem concerning random space filling". Publ. Math. Inst. Hung. Acad. Sci. 3 (109–127): 30–36.
^ ^a ^b Widom, B. J. (1966). "Random Sequential Addition of Hard Spheres to a Volume". J. Chem. Phys. 44 (10): 3888–3894. Bibcode:1966JChPh..44.3888W. doi:10.1063/1.1726548.
^ Evans, J. W. (1993). "Random and cooperative sequential adsorption". Rev. Mod. Phys. 65 (4): 1281–1329. Bibcode:1993RvMP...65.1281E. doi:10.1103/RevModPhys.65.1281.
^ Weisstein, Eric W., "Rényi's Parking Constants", From MathWorld--A Wolfram Web Resource
^ Palasti, I. (1960). "On some random space filling problems". Publ. Math. Inst. Hung. Acad. Sci. 5: 353–359.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ Krapivsky, P.; S. Redner; E. Ben-Naim (2010). A Kinetic View of Statistical Physics. Cambridge Univ. Press.
^ ^a ^b Flory, P. J. (1939). "Intramolecular Reaction between Neighboring Substituents of Vinyl Polymers". J. Am. Chem. Soc. 61 (6): 1518–1521. doi:10.1021/ja01875a053.
^ Ziff, Robert M.; R. Dennis Vigil (1990). "Kinetics and fractal properties of the random sequential adsorption of line segments". J. Phys. A: Math. Gen. 23 (21): 5103–5108. Bibcode:1990JPhA...23.5103Z. doi:10.1088/0305-4470/23/21/044. hdl:2027.42/48820.
^ ^a ^b ^c Araujo, N. A. M.; Cadilhe, A. (2006). "Gap-size distribution functions of a random sequential adsorption model of segments on a line". Phys. Rev. E. 73 (5): 051602. arXiv:cond-mat/0404422. Bibcode:2006PhRvE..73e1602A. doi:10.1103/PhysRevE.73.051602. PMID 16802941. S2CID 8046084.
^ Wang, Jian-Sheng; Pandey, Ras B. (1996). "Kinetics and jamming coverage in a random sequential adsorption of polymer chains". Phys. Rev. Lett. 77 (9): 1773–1776. arXiv:cond-mat/9605038. Bibcode:1996PhRvL..77.1773W. doi:10.1103/PhysRevLett.77.1773. PMID 10063168. S2CID 36659964.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ Tarasevich, Yuri Yu; Laptev, Valeri V.; Vygornitskii, Nikolai V.; Lebovka, Nikolai I. (2015). "Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices". Phys. Rev. E. 91 (1): 012109. arXiv:1412.7267. Bibcode:2015PhRvE..91a2109T. doi:10.1103/PhysRevE.91.012109. PMID 25679572. S2CID 35537612.
^ ^a ^b Nord, R. S.; Evans, J. W. (1985). "Irreversible immobile random adsorption of dimers, trimers, ... on 2D lattices". J. Chem. Phys. 82 (6): 2795–2810. Bibcode:1985JChPh..82.2795N. doi:10.1063/1.448279.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ Slutskii, M. G.; Barash, L. Yu.; Tarasevich, Yu. Yu. (2018). "Percolation and jamming of random sequential adsorption samples of large linear k-mers on a square lattice". Physical Review E. 98 (6): 062130. arXiv:1810.06800. Bibcode:2018PhRvE..98f2130S. doi:10.1103/PhysRevE.98.062130. S2CID 53709717.
^ Vandewalle, N.; Galam, S.; Kramer, M. (2000). "A new universality for random sequential deposition of needles". Eur. Phys. J. B. 14 (3): 407–410. arXiv:cond-mat/0004271. Bibcode:2000EPJB...14..407V. doi:10.1007/s100510051047. S2CID 11142384.
^ ^a ^b Lebovka, Nikolai I.; Karmazina, Natalia; Tarasevich, Yuri Yu; Laptev, Valeri V. (2011). "Random sequential adsorption of partially oriented linear k-mers on a square lattice". Phys. Rev. E. 85 (6): 029902. arXiv:1109.3271. Bibcode:2011PhRvE..84f1603L. doi:10.1103/PhysRevE.84.061603. PMID 22304098. S2CID 25377751.
^ ^a ^b ^c Wang, J. S. (2000). "Series expansion and computer simulation studies of random sequential adsorption". Colloids and Surfaces A. 165 (1–3): 325–343. arXiv:cond-mat/9903139. doi:10.1016/S0927-7757(99)00444-6.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j Bonnier, B.; Hontebeyrie, M.; Leroyer, Y.; Meyers, Valeri C.; Pommiers, E. (1994). "Random sequential adsorption of partially oriented linear k-mers on a square lattice". Phys. Rev. E. 49 (1): 305–312. arXiv:cond-mat/9307043. doi:10.1103/PhysRevE.49.305. PMID 9961218. S2CID 131089.
^ Manna, S. S.; Svrakic, N. M. (1991). "Random sequential adsorption: line segments on the square lattice". J. Phys. A: Math. Gen. 24 (12): L671–L676. Bibcode:1991JPhA...24L.671M. doi:10.1088/0305-4470/24/12/003.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q ^r Perino, E. J.; Matoz-Fernandez, D. A.; Pasinetti1, P. M.; Ramirez-Pastor, A. J. (2017). "Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice". Journal of Statistical Mechanics: Theory and Experiment. 2017 (7): 073206. arXiv:1703.07680. Bibcode:2017JSMTE..07.3206P. doi:10.1088/1742-5468/aa79ae. S2CID 119374271.{{cite journal}}: CS1 maint: numeric names: authors list (link)
^ ^a ^b Gan, C. K.; Wang, J.-S. (1998). "Extended series expansions for random sequential adsorption". J. Chem. Phys. 108 (7): 3010–3012. arXiv:cond-mat/9710340. Bibcode:1998JChPh.108.3010G. doi:10.1063/1.475687. S2CID 97703000.
^ Meakin, P.; Cardy, John L.; Loh, John L.; Scalapino, John L. (1987). "Extended series expansions for random sequential adsorption". J. Chem. Phys. 86 (4): 2380–2382. doi:10.1063/1.452085.
^ Baram, Asher; Fixman, Marshall (1995). "Random sequential adsorption: Long time dynamics". J. Chem. Phys. 103 (5): 1929–1933. Bibcode:1995JChPh.103.1929B. doi:10.1063/1.469717.
^ Evans, J. W. (1989). "Comment on Kinetics of random sequential adsorption". Phys. Rev. Lett. 62 (22): 2642. Bibcode:1989PhRvL..62.2642E. doi:10.1103/PhysRevLett.62.2642. PMID 10040048.
^ ^a ^b ^c ^d ^e ^f ^g ^h Privman, V.; Wang, J. S.; Nielaba, P. (1991). "Continuum limit in random sequential adsorption". Phys. Rev. B. 43 (4): 3366–3372. Bibcode:1991PhRvB..43.3366P. doi:10.1103/PhysRevB.43.3366. PMID 9997649.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ Brosilow, B. J.; R. M. Ziff; R. D. Vigil (1991). "Random sequential adsorption of parallel squares". Phys. Rev. A. 43 (2): 631–638. Bibcode:1991PhRvA..43..631B. doi:10.1103/PhysRevA.43.631. PMID 9905079.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ Nakamura, Mitsunobu (1986). "Random sequential packing in square cellular structures". J. Phys. A: Math. Gen. 19 (12): 2345–2351. Bibcode:1986JPhA...19.2345N. doi:10.1088/0305-4470/19/12/020.
^ Sutton, Clifton (1989). "Asymptotic packing densities for two-dimensional lattice models". Stochastic Models. 5 (4): 601–615. doi:10.1080/15326348908807126.
^ ^a ^b ^c ^d ^e ^f ^g ^h Zhang, G. (2018). "Precise algorithm to generate random sequential adsorption of hard polygons at saturation". Physical Review E. 97 (4): 043311. arXiv:1803.08348. Bibcode:2018PhRvE..97d3311Z. doi:10.1103/PhysRevE.97.043311. PMID 29758708. S2CID 46892756.
^ Vigil, R. Dennis; Robert M. Ziff (1989). "Random sequential adsorption of unoriented rectangles onto a plane". J. Chem. Phys. 91 (4): 2599–2602. Bibcode:1989JChPh..91.2599V. doi:10.1063/1.457021. hdl:2027.42/70834.
^ Viot, P.; G. Targus (1990). "Random Sequential Addition of Unoriented Squares: Breakdown of Swendsen's Conjecture". EPL. 13 (4): 295–300. Bibcode:1990EL.....13..295V. doi:10.1209/0295-5075/13/4/002. S2CID 250852782.
^ Viot, P.; G. Targus; S. M. Ricci; J. Talbot (1992). "Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior". J. Chem. Phys. 97 (7): 5212. Bibcode:1992JChPh..97.5212V. doi:10.1063/1.463820.
^ ^a ^b ^c Viot, P.; G. Tarjus; S. Ricci; J.Talbot (1992). "Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior". J. Chem. Phys. 97 (7): 5212–5218. Bibcode:1992JChPh..97.5212V. doi:10.1063/1.463820.
^ Cieśla, Michał (2014). "Properties of random sequential adsorption of generalized dimers". Phys. Rev. E. 89 (4): 042404. arXiv:1403.3200. Bibcode:2014PhRvE..89d2404C. doi:10.1103/PhysRevE.89.042404. PMID 24827257. S2CID 12961099.
^ Ciesśla, Michałl; Grzegorz Pająk; Robert M. Ziff (2015). "Shapes for maximal coverage for two-dimensional random sequential adsorption". Phys. Chem. Chem. Phys. 17 (37): 24376–24381. arXiv:1506.08164. Bibcode:2015PCCP...1724376C. doi:10.1039/c5cp03873a. PMID 26330194. S2CID 14368653.
^ ^a ^b ^c ^d ^e ^f ^g ^h Zhang, G.; S. Torquato (2013). "Precise algorithm to generate random sequential addition of hard hyperspheres at saturation". Phys. Rev. E. 88 (5): 053312. arXiv:1402.4883. Bibcode:2013PhRvE..88e3312Z. doi:10.1103/PhysRevE.88.053312. PMID 24329384. S2CID 14810845.
^ ^a ^b ^c ^d ^e ^f Torquato, S.; O. U. Uche; F. H. Stillinger (2006). "Random sequential addition of hard spheres in high Euclidean dimensions". Phys. Rev. E. 74 (6): 061308. arXiv:cond-mat/0608402. Bibcode:2006PhRvE..74f1308T. doi:10.1103/PhysRevE.74.061308. PMID 17280063. S2CID 15604775.
^ ^a ^b Meakin, Paul (1992). "Random sequential adsorption of spheres of different sizes". Physica A. 187 (3): 475–488. Bibcode:1992PhyA..187..475M. doi:10.1016/0378-4371(92)90006-C.
^ ^a ^b Ciesla, Michal; Kubala, Piotr (2018). "Random sequential adsorption of cubes". The Journal of Chemical Physics. 148 (2): 024501. Bibcode:2018JChPh.148b4501C. doi:10.1063/1.5007319. PMID 29331110.
^ ^a ^b Ciesla, Michal; Kubala, Piotr (2018). "Random sequential adsorption of cuboids". The Journal of Chemical Physics. 149 (19): 194704. Bibcode:2018JChPh.149s4704C. doi:10.1063/1.5061695. PMID 30466287. S2CID 53727841.
^ Cieśla, Michał; Ziff, Robert (2018). "Boundary conditions in random sequential adsorption". Journal of Statistical Mechanics: Theory and Experiment. 2018 (4): 043302. arXiv:1712.09663. Bibcode:2018JSMTE..04.3302C. doi:10.1088/1742-5468/aab685. S2CID 118969644.
^ Cieśla, Michał; Aleksandra Nowak (2016). "Managing numerical errors in random sequential adsorption". Surface Science. 651: 182–186. Bibcode:2016SurSc.651..182C. doi:10.1016/j.susc.2016.04.014.
^ Wang, Jian-Sheng (1994). "A fast algorithm for random sequential adsorption of discs". Int. J. Mod. Phys. C. 5 (4): 707–715. arXiv:cond-mat/9402066. Bibcode:1994IJMPC...5..707W. doi:10.1142/S0129183194000817. S2CID 119032105.
^ Chen, Elizabeth R.; Miranda Holmes-Cerfon (2017). "Random Sequential Adsorption of Discs on Surfaces of Constant Curvature: Plane, Sphere, Hyperboloid, and Projective Plane". J. Nonlinear Sci. 27 (6): 1743–1787. arXiv:1709.05029. Bibcode:2017JNS....27.1743C. doi:10.1007/s00332-017-9385-2. S2CID 26861078.
^ Hinrichsen, Einar L.; Jens Feder; Torstein Jøssang (1990). "Random packing of disks in two dimensions". Phys. Rev. A. 41 (8): 4199–4209. Bibcode:1990PhRvA..41.4199H. doi:10.1103/PhysRevA.41.4199.
^ ^a ^b Feder, Jens (1980). "Random sequential adsorption". J. Theor. Biol. 87 (2): 237–254. Bibcode:1980JThBi..87..237F. doi:10.1016/0022-5193(80)90358-6.
^ Blaisdell, B. Edwin; Herbert Solomon (1970). "On random sequential packing in the plane and a conjecture of Palasti". J. Appl. Probab. 7 (3): 667–698. doi:10.1017/S0021900200110630.
^ Dickman, R.; J. S. Wang; I. Jensen (1991). "Random sequential adsorption of parallel squares". J. Chem. Phys. 94 (12): 8252. Bibcode:1991JChPh..94.8252D. doi:10.1063/1.460109.
^ Tory, E. M.; W. S. Jodrey; D. K. Pikard (1983). "Simulation of Random Sequential Adsorption: Efficient Methods and Resolution of Conflicting Results". J. Theor. Biol. 102 (12): 439–445. Bibcode:1991JChPh..94.8252D. doi:10.1063/1.460109.
^ Akeda, Yoshiaki; Motoo Hori (1976). "On random sequential packing in two and three dimensions". Biometrika. 63 (2): 361–366. doi:10.1093/biomet/63.2.361.
^ ^a ^b ^c Jodrey, W. S.; E. M. Tory (1980). "Random sequential packing in R^n". Journal of Statistical Computation and Simulation. 10 (2): 87–93. doi:10.1080/00949658008810351.
^ Bonnier, B.; M. Hontebeyrie; C. Meyers (1993). "On the random filling of R^d by non-overlapping d-dimensional cubes". Physica A. 198 (1): 1–10. arXiv:cond-mat/9302023. Bibcode:1993PhyA..198....1B. doi:10.1016/0378-4371(93)90180-C. S2CID 11802063.
^ ^a ^b Blaisdell, B. Edwin; Herbert Solomon (1982). "Random Sequential Packing in Euclidean Spaces of Dimensions Three and Four and a Conjecture of Palásti". Journal of Applied Probability. 19 (2): 382–390. doi:10.2307/3213489. JSTOR 3213489. S2CID 118248194.
^ Cooper, Douglas W. (1989). "Random sequential packing simulations in three dimensions for aligned cubes". J. Appl. Probab. 26 (3): 664–670. doi:10.2307/3214426. JSTOR 3214426. S2CID 124311298.
^ Nord, R. S. (1991). "Irreversible random sequential filling of lattices by Monte Carlo simulation". Journal of Statistical Computation and Simulation. 39 (4): 231–240. doi:10.1080/00949659108811358.

[Renyi58-1] Rényi, A. (1958). "On a one-dimensional problem concerning random space filling". Publ. Math. Inst. Hung. Acad. Sci. 3 (109–127): 30–36.

[Widom66-2] Widom, B. J. (1966). "Random Sequential Addition of Hard Spheres to a Volume". J. Chem. Phys. 44 (10): 3888–3894. Bibcode:1966JChPh..44.3888W. doi:10.1063/1.1726548.

[Evans93-3] Evans, J. W. (1993). "Random and cooperative sequential adsorption". Rev. Mod. Phys. 65 (4): 1281–1329. Bibcode:1993RvMP...65.1281E. doi:10.1103/RevModPhys.65.1281.

[4] Weisstein, Eric W., "Rényi's Parking Constants", From MathWorld--A Wolfram Web Resource

[Palasti60-5] Palasti, I. (1960). "On some random space filling problems". Publ. Math. Inst. Hung. Acad. Sci. 5: 353–359.

[KrapivskiRednerBenNaim10-6] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ Krapivsky, P.; S. Redner; E. Ben-Naim (2010). A Kinetic View of Statistical Physics. Cambridge Univ. Press.

[Flory39-7] Flory, P. J. (1939). "Intramolecular Reaction between Neighboring Substituents of Vinyl Polymers". J. Am. Chem. Soc. 61 (6): 1518–1521. doi:10.1021/ja01875a053.

[ZiffVigil90-8] Ziff, Robert M.; R. Dennis Vigil (1990). "Kinetics and fractal properties of the random sequential adsorption of line segments". J. Phys. A: Math. Gen. 23 (21): 5103–5108. Bibcode:1990JPhA...23.5103Z. doi:10.1088/0305-4470/23/21/044. hdl:2027.42/48820.

[AraujoCadilhe06-9] Araujo, N. A. M.; Cadilhe, A. (2006). "Gap-size distribution functions of a random sequential adsorption model of segments on a line". Phys. Rev. E. 73 (5): 051602. arXiv:cond-mat/0404422. Bibcode:2006PhRvE..73e1602A. doi:10.1103/PhysRevE.73.051602. PMID 16802941. S2CID 8046084.

[WangPandey96-10] Wang, Jian-Sheng; Pandey, Ras B. (1996). "Kinetics and jamming coverage in a random sequential adsorption of polymer chains". Phys. Rev. Lett. 77 (9): 1773–1776. arXiv:cond-mat/9605038. Bibcode:1996PhRvL..77.1773W. doi:10.1103/PhysRevLett.77.1773. PMID 10063168. S2CID 36659964.

[TarasevichLaptevVygornitskiiLebovka14-11] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ Tarasevich, Yuri Yu; Laptev, Valeri V.; Vygornitskii, Nikolai V.; Lebovka, Nikolai I. (2015). "Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices". Phys. Rev. E. 91 (1): 012109. arXiv:1412.7267. Bibcode:2015PhRvE..91a2109T. doi:10.1103/PhysRevE.91.012109. PMID 25679572. S2CID 35537612.

[NordEvans85-12] Nord, R. S.; Evans, J. W. (1985). "Irreversible immobile random adsorption of dimers, trimers, ... on 2D lattices". J. Chem. Phys. 82 (6): 2795–2810. Bibcode:1985JChPh..82.2795N. doi:10.1063/1.448279.

[SlutskiiBarashTarasevich18-13] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ Slutskii, M. G.; Barash, L. Yu.; Tarasevich, Yu. Yu. (2018). "Percolation and jamming of random sequential adsorption samples of large linear k-mers on a square lattice". Physical Review E. 98 (6): 062130. arXiv:1810.06800. Bibcode:2018PhRvE..98f2130S. doi:10.1103/PhysRevE.98.062130. S2CID 53709717.

[VandewalleGalamKramer00-14] Vandewalle, N.; Galam, S.; Kramer, M. (2000). "A new universality for random sequential deposition of needles". Eur. Phys. J. B. 14 (3): 407–410. arXiv:cond-mat/0004271. Bibcode:2000EPJB...14..407V. doi:10.1007/s100510051047. S2CID 11142384.

[LebovkaKarmazinaTarasevichLaptev11-15] Lebovka, Nikolai I.; Karmazina, Natalia; Tarasevich, Yuri Yu; Laptev, Valeri V. (2011). "Random sequential adsorption of partially oriented linear k-mers on a square lattice". Phys. Rev. E. 85 (6): 029902. arXiv:1109.3271. Bibcode:2011PhRvE..84f1603L. doi:10.1103/PhysRevE.84.061603. PMID 22304098. S2CID 25377751.

[Wang00-16] Wang, J. S. (2000). "Series expansion and computer simulation studies of random sequential adsorption". Colloids and Surfaces A. 165 (1–3): 325–343. arXiv:cond-mat/9903139. doi:10.1016/S0927-7757(99)00444-6.

[BonnierHontebeyrieLeroyerMeyersPommiers94-17] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j Bonnier, B.; Hontebeyrie, M.; Leroyer, Y.; Meyers, Valeri C.; Pommiers, E. (1994). "Random sequential adsorption of partially oriented linear k-mers on a square lattice". Phys. Rev. E. 49 (1): 305–312. arXiv:cond-mat/9307043. doi:10.1103/PhysRevE.49.305. PMID 9961218. S2CID 131089.

[MannaSvrakic91-18] Manna, S. S.; Svrakic, N. M. (1991). "Random sequential adsorption: line segments on the square lattice". J. Phys. A: Math. Gen. 24 (12): L671–L676. Bibcode:1991JPhA...24L.671M. doi:10.1088/0305-4470/24/12/003.

[PerinoMatozFernandezPasinetti1Ramirez-Pastor17-19] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ ^o ^p ^q ^r Perino, E. J.; Matoz-Fernandez, D. A.; Pasinetti1, P. M.; Ramirez-Pastor, A. J. (2017). "Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice". Journal of Statistical Mechanics: Theory and Experiment. 2017 (7): 073206. arXiv:1703.07680. Bibcode:2017JSMTE..07.3206P. doi:10.1088/1742-5468/aa79ae. S2CID 119374271.{{cite journal}}: CS1 maint: numeric names: authors list (link)

[GanWang98-20] Gan, C. K.; Wang, J.-S. (1998). "Extended series expansions for random sequential adsorption". J. Chem. Phys. 108 (7): 3010–3012. arXiv:cond-mat/9710340. Bibcode:1998JChPh.108.3010G. doi:10.1063/1.475687. S2CID 97703000.

[MeakinCardyLohScalapino87-21] Meakin, P.; Cardy, John L.; Loh, John L.; Scalapino, John L. (1987). "Extended series expansions for random sequential adsorption". J. Chem. Phys. 86 (4): 2380–2382. doi:10.1063/1.452085.

[BaramFixman-22] Baram, Asher; Fixman, Marshall (1995). "Random sequential adsorption: Long time dynamics". J. Chem. Phys. 103 (5): 1929–1933. Bibcode:1995JChPh.103.1929B. doi:10.1063/1.469717.

[Evans-23] Evans, J. W. (1989). "Comment on Kinetics of random sequential adsorption". Phys. Rev. Lett. 62 (22): 2642. Bibcode:1989PhRvL..62.2642E. doi:10.1103/PhysRevLett.62.2642. PMID 10040048.

[PrivmanWangNielaba-24] ^ ^a ^b ^c ^d ^e ^f ^g ^h Privman, V.; Wang, J. S.; Nielaba, P. (1991). "Continuum limit in random sequential adsorption". Phys. Rev. B. 43 (4): 3366–3372. Bibcode:1991PhRvB..43.3366P. doi:10.1103/PhysRevB.43.3366. PMID 9997649.

[BrosilowZiffVigil91-25] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l ^m ⁿ Brosilow, B. J.; R. M. Ziff; R. D. Vigil (1991). "Random sequential adsorption of parallel squares". Phys. Rev. A. 43 (2): 631–638. Bibcode:1991PhRvA..43..631B. doi:10.1103/PhysRevA.43.631. PMID 9905079.

[Nakamura86-26] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ Nakamura, Mitsunobu (1986). "Random sequential packing in square cellular structures". J. Phys. A: Math. Gen. 19 (12): 2345–2351. Bibcode:1986JPhA...19.2345N. doi:10.1088/0305-4470/19/12/020.

[Syutton89-27] Sutton, Clifton (1989). "Asymptotic packing densities for two-dimensional lattice models". Stochastic Models. 5 (4): 601–615. doi:10.1080/15326348908807126.

[Zhang18-28] ^ ^a ^b ^c ^d ^e ^f ^g ^h Zhang, G. (2018). "Precise algorithm to generate random sequential adsorption of hard polygons at saturation". Physical Review E. 97 (4): 043311. arXiv:1803.08348. Bibcode:2018PhRvE..97d3311Z. doi:10.1103/PhysRevE.97.043311. PMID 29758708. S2CID 46892756.

[VigilZiff89-29] Vigil, R. Dennis; Robert M. Ziff (1989). "Random sequential adsorption of unoriented rectangles onto a plane". J. Chem. Phys. 91 (4): 2599–2602. Bibcode:1989JChPh..91.2599V. doi:10.1063/1.457021. hdl:2027.42/70834.

[ViotTargus90-30] Viot, P.; G. Targus (1990). "Random Sequential Addition of Unoriented Squares: Breakdown of Swendsen's Conjecture". EPL. 13 (4): 295–300. Bibcode:1990EL.....13..295V. doi:10.1209/0295-5075/13/4/002. S2CID 250852782.

[ViotTargusRicciTalbot92-31] Viot, P.; G. Targus; S. M. Ricci; J. Talbot (1992). "Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior". J. Chem. Phys. 97 (7): 5212. Bibcode:1992JChPh..97.5212V. doi:10.1063/1.463820.

[ViotTarjusRicciTalbot92-32] Viot, P.; G. Tarjus; S. Ricci; J.Talbot (1992). "Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior". J. Chem. Phys. 97 (7): 5212–5218. Bibcode:1992JChPh..97.5212V. doi:10.1063/1.463820.

[Ciesla14-33] Cieśla, Michał (2014). "Properties of random sequential adsorption of generalized dimers". Phys. Rev. E. 89 (4): 042404. arXiv:1403.3200. Bibcode:2014PhRvE..89d2404C. doi:10.1103/PhysRevE.89.042404. PMID 24827257. S2CID 12961099.

[CieslaPajakZiff15-34] Ciesśla, Michałl; Grzegorz Pająk; Robert M. Ziff (2015). "Shapes for maximal coverage for two-dimensional random sequential adsorption". Phys. Chem. Chem. Phys. 17 (37): 24376–24381. arXiv:1506.08164. Bibcode:2015PCCP...1724376C. doi:10.1039/c5cp03873a. PMID 26330194. S2CID 14368653.

[ZhangTorquato13-35] ^ ^a ^b ^c ^d ^e ^f ^g ^h Zhang, G.; S. Torquato (2013). "Precise algorithm to generate random sequential addition of hard hyperspheres at saturation". Phys. Rev. E. 88 (5): 053312. arXiv:1402.4883. Bibcode:2013PhRvE..88e3312Z. doi:10.1103/PhysRevE.88.053312. PMID 24329384. S2CID 14810845.

[TorquatoUcheStillinger06-36] ^ ^a ^b ^c ^d ^e ^f Torquato, S.; O. U. Uche; F. H. Stillinger (2006). "Random sequential addition of hard spheres in high Euclidean dimensions". Phys. Rev. E. 74 (6): 061308. arXiv:cond-mat/0608402. Bibcode:2006PhRvE..74f1308T. doi:10.1103/PhysRevE.74.061308. PMID 17280063. S2CID 15604775.

[MeakinJullien92-37] Meakin, Paul (1992). "Random sequential adsorption of spheres of different sizes". Physica A. 187 (3): 475–488. Bibcode:1992PhyA..187..475M. doi:10.1016/0378-4371(92)90006-C.

[CieslaKubala18a-38] Ciesla, Michal; Kubala, Piotr (2018). "Random sequential adsorption of cubes". The Journal of Chemical Physics. 148 (2): 024501. Bibcode:2018JChPh.148b4501C. doi:10.1063/1.5007319. PMID 29331110.

[CieslaKubala18b-39] Ciesla, Michal; Kubala, Piotr (2018). "Random sequential adsorption of cuboids". The Journal of Chemical Physics. 149 (19): 194704. Bibcode:2018JChPh.149s4704C. doi:10.1063/1.5061695. PMID 30466287. S2CID 53727841.

[CieslaZiff18-40] Cieśla, Michał; Ziff, Robert (2018). "Boundary conditions in random sequential adsorption". Journal of Statistical Mechanics: Theory and Experiment. 2018 (4): 043302. arXiv:1712.09663. Bibcode:2018JSMTE..04.3302C. doi:10.1088/1742-5468/aab685. S2CID 118969644.

[CieslaNowak16-41] Cieśla, Michał; Aleksandra Nowak (2016). "Managing numerical errors in random sequential adsorption". Surface Science. 651: 182–186. Bibcode:2016SurSc.651..182C. doi:10.1016/j.susc.2016.04.014.

[Wang94-42] Wang, Jian-Sheng (1994). "A fast algorithm for random sequential adsorption of discs". Int. J. Mod. Phys. C. 5 (4): 707–715. arXiv:cond-mat/9402066. Bibcode:1994IJMPC...5..707W. doi:10.1142/S0129183194000817. S2CID 119032105.

[ChenHolmesCerfon-43] Chen, Elizabeth R.; Miranda Holmes-Cerfon (2017). "Random Sequential Adsorption of Discs on Surfaces of Constant Curvature: Plane, Sphere, Hyperboloid, and Projective Plane". J. Nonlinear Sci. 27 (6): 1743–1787. arXiv:1709.05029. Bibcode:2017JNS....27.1743C. doi:10.1007/s00332-017-9385-2. S2CID 26861078.

[HinrichsenFederJossang-44] Hinrichsen, Einar L.; Jens Feder; Torstein Jøssang (1990). "Random packing of disks in two dimensions". Phys. Rev. A. 41 (8): 4199–4209. Bibcode:1990PhRvA..41.4199H. doi:10.1103/PhysRevA.41.4199.

[Feder80-45] Feder, Jens (1980). "Random sequential adsorption". J. Theor. Biol. 87 (2): 237–254. Bibcode:1980JThBi..87..237F. doi:10.1016/0022-5193(80)90358-6.

[BlaisdellSolomon70-46] Blaisdell, B. Edwin; Herbert Solomon (1970). "On random sequential packing in the plane and a conjecture of Palasti". J. Appl. Probab. 7 (3): 667–698. doi:10.1017/S0021900200110630.

[DickmanWangJensen91-47] Dickman, R.; J. S. Wang; I. Jensen (1991). "Random sequential adsorption of parallel squares". J. Chem. Phys. 94 (12): 8252. Bibcode:1991JChPh..94.8252D. doi:10.1063/1.460109.

[ToryJodreyPickard83-48] Tory, E. M.; W. S. Jodrey; D. K. Pikard (1983). "Simulation of Random Sequential Adsorption: Efficient Methods and Resolution of Conflicting Results". J. Theor. Biol. 102 (12): 439–445. Bibcode:1991JChPh..94.8252D. doi:10.1063/1.460109.

[AkedaHori76-49] Akeda, Yoshiaki; Motoo Hori (1976). "On random sequential packing in two and three dimensions". Biometrika. 63 (2): 361–366. doi:10.1093/biomet/63.2.361.

[JodreyTory80-50] Jodrey, W. S.; E. M. Tory (1980). "Random sequential packing in R^n". Journal of Statistical Computation and Simulation. 10 (2): 87–93. doi:10.1080/00949658008810351.

[BonnierHontebeyrieMeyers93-51] Bonnier, B.; M. Hontebeyrie; C. Meyers (1993). "On the random filling of R^d by non-overlapping d-dimensional cubes". Physica A. 198 (1): 1–10. arXiv:cond-mat/9302023. Bibcode:1993PhyA..198....1B. doi:10.1016/0378-4371(93)90180-C. S2CID 11802063.

[BlaisdellSolomon82-52] Blaisdell, B. Edwin; Herbert Solomon (1982). "Random Sequential Packing in Euclidean Spaces of Dimensions Three and Four and a Conjecture of Palásti". Journal of Applied Probability. 19 (2): 382–390. doi:10.2307/3213489. JSTOR 3213489. S2CID 118248194.

[Cooper89-53] Cooper, Douglas W. (1989). "Random sequential packing simulations in three dimensions for aligned cubes". J. Appl. Probab. 26 (3): 664–670. doi:10.2307/3214426. JSTOR 3214426. S2CID 124311298.

[Nord91-54] Nord, R. S. (1991). "Irreversible random sequential filling of lattices by Monte Carlo simulation". Journal of Statistical Computation and Simulation. 39 (4): 231–240. doi:10.1080/00949659108811358.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

[41]

[42]

[43]

[44]

[45]

[46]

[47]

[48]

[49]

[50]

[51]

[52]

[53]

[54]