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.{{cite journal|last=Rényi|first=A.|title=On a one-dimensional problem concerning random space filling|journal= Publ. Math. Inst. Hung. Acad. Sci.|volume=3 |issue=109–127|year=1958|pages=30–36}}

Other early works include those of Benjamin Widom.{{cite journal|last=Widom|first=B. J.|title=Random Sequential Addition of Hard Spheres to a Volume|journal=J. Chem. Phys.|volume=44|issue=10|year=1966|doi=10.1063/1.1726548|pages=3888–3894|bibcode=1966JChPh..44.3888W}}

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.

File:Random Sequential Adsorption Disks1.png

The blocking process has been studied in detail in terms of the random sequential adsorption (RSA) model.{{cite journal|last=Evans|first=J. W.|title=Random and cooperative sequential adsorption|journal=Rev. Mod. Phys.|volume=65|issue=4|year=1993|pages=1281–1329|doi=10.1103/RevModPhys.65.1281|bibcode=1993RvMP...65.1281E|url=https://dr.lib.iastate.edu/bitstreams/e600caa3-d5d0-4f2d-a350-d30212e9abd2/download}} 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 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.Weisstein, Eric W., [http://mathworld.wolfram.com/RenyisParkingConstants.html "Rényi's Parking Constants"], From MathWorld--A Wolfram Web Resource

Then followed the conjecture of Ilona Palásti,{{cite journal|last=Palasti|first=I.|author-link= Ilona Palásti |title=On some random space filling problems|journal= Publ. Math. Inst. Hung. Acad. Sci.|volume=5|year=1960|pages=353–359}}

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,{{cite book|last=Krapivsky|first=P.|author2 = S. Redner|author3 = E. Ben-Naim|title=A Kinetic View of Statistical Physics|publisher = Cambridge Univ. Press.|year=2010}}

$\theta_k = k \int_0^\infty \exp\left(-u - 2 \sum_{j=1}^{k-1} \frac{1-e^{-j u}}{j} \right) du =
k \int_0^1 \exp\left(- 2 \sum_{j=1}^{k-1} \frac{1-v^j}{j} \right) dv$

When $k$ goes to infinity, this gives the Renyi result above. For k = 2, this gives the Flory result $\theta_1 = 1 - e^{-2}$ .

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

File:Random_sequential_adsorption_of_line_segments.png

Saturation coverage of ''k''-mers on 1d lattice systems

class="wikitable"
system ! Saturated coverage $\theta_k$ (fraction of sites filled)
dimers \| $1 - e^{-2} = 0.86466472$ {{cite journal\|last=Flory\|first=P. J.\|title=Intramolecular Reaction between Neighboring Substituents of Vinyl Polymers\|journal = J. Am. Chem. Soc.\|volume=61\|issue=6\|year=1939\|doi=10.1021/ja01875a053\|pages=1518–1521\|bibcode=1939JAChS..61.1518F }}
trimers \| $\frac{3 \sqrt{\pi } (\text{erfi}(2)-\text{erfi}(1))}{2 e^4} \approx 0.82365296$
k = 4 \| $0.80389348$
k = 10 \| $0.76957741$
k = 100 \| $0.74976335$
k = 1000 \| $0.74781413$
k = 10000 \| $0.74761954$
k = 100000 \| $0.74760008$
k = $\infty$ \| $0.74759792$

class="wikitable"

system

! Saturated coverage $\theta_k$ (fraction of sites filled)

dimers

| $1 - e^{-2} = 0.86466472$

{{cite journal|last=Flory|first=P. J.|title=Intramolecular Reaction between Neighboring Substituents of Vinyl Polymers|journal = J. Am. Chem. Soc.|volume=61|issue=6|year=1939|doi=10.1021/ja01875a053|pages=1518–1521|bibcode=1939JAChS..61.1518F }}

trimers

| $\frac{3 \sqrt{\pi } (\text{erfi}(2)-\text{erfi}(1))}{2 e^4} \approx 0.82365296$

k = 4

| $0.80389348$

k = 10

| $0.76957741$

k = 100

| $0.74976335$

k = 1000

| $0.74781413$

k = 10000

| $0.74761954$

k = 100000

| $0.74760008$

k =

\infty

| $0.74759792$

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

class="wikitable"
system ! Saturated coverage $\theta$ (fraction of line filled)
R = 1 \|0.74759792
R = 1.05 \| 0.7544753(62) {{Cite journal \|last1 = Araujo \|first1 = N. A. M. \|last2 = Cadilhe \| first2 = A. \|title = Gap-size distribution functions of a random sequential adsorption model of segments on a line \|journal= Phys. Rev. E \|volume = 73 \|pages = 051602 \|year = 2006 \|issue = 5 \|doi = 10.1103/PhysRevE.73.051602\|pmid = 16802941 \|arxiv = cond-mat/0404422 \|bibcode = 2006PhRvE..73e1602A \|s2cid = 8046084 }}
R = 1.1 \|0.7599829(63)
R = 2 \| 0.7941038(58)

class="wikitable"

system

! Saturated coverage $\theta$ (fraction of line filled)

R = 1

|0.74759792

R = 1.05

| 0.7544753(62) {{Cite journal

|last1 = Araujo |first1 = N. A. M.

|last2 = Cadilhe | first2 = A.

|title = Gap-size distribution functions of a random sequential adsorption model of segments on a line

|journal= Phys. Rev. E

|volume = 73

|pages = 051602

|year = 2006

|issue = 5

|doi = 10.1103/PhysRevE.73.051602|pmid = 16802941

|arxiv = cond-mat/0404422

|bibcode = 2006PhRvE..73e1602A

|s2cid = 8046084

}}

R = 1.1

|0.7599829(63)

R = 2

| 0.7941038(58)

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

class="wikitable"
system ! Saturated coverage $\theta_k$ (fraction of sites filled)
dimers k = 2 \| 0.906820(2),{{Cite journal \|last1 = Wang \|first1 = Jian-Sheng \|last2 = Pandey \| first2 = Ras B. \|title = Kinetics and jamming coverage in a random sequential adsorption of polymer chains \|journal= Phys. Rev. Lett. \|volume = 77 \|pages = 1773–1776 \|year = 1996 \|issue = 9 \|doi = 10.1103/PhysRevLett.77.1773\|pmid = 10063168 \|arxiv = cond-mat/9605038 \|bibcode = 1996PhRvL..77.1773W \|s2cid = 36659964 }} 0.906,{{Cite journal \|last1 = Tarasevich \| first1 = Yuri Yu \|last2 = Laptev \| first2 = Valeri V. \|last3 = Vygornitskii \| first3 = Nikolai V. \|last4 = Lebovka \|first4 = Nikolai I. \|title = Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices \|journal= Phys. Rev. E \|volume = 91 \|pages = 012109 \|year = 2015 \| issue = 1 \|doi = 10.1103/PhysRevE.91.012109\| pmid = 25679572 \|arxiv = 1412.7267 \| bibcode = 2015PhRvE..91a2109T \| s2cid = 35537612 }} 0.9068,{{Cite journal \|last1 = Nord \|first1 = R. S. \|last2 = Evans \| first2 = J. W. \|title = Irreversible immobile random adsorption of dimers, trimers, ... on 2D lattices \|journal= J. Chem. Phys. \|volume = 82 \|issue = 6 \|pages = 2795–2810 \|year = 1985 \|doi = 10.1063/1.448279\|bibcode = 1985JChPh..82.2795N \|url = https://lib.dr.iastate.edu/physastro_pubs/446 \|doi-access = free }} 0.9062,{{Cite journal \|arxiv = 1810.06800\|last1 = Slutskii\|first1 = M. G.\|title = Percolation and jamming of random sequential adsorption samples of large linear k-mers on a square lattice\|last2 = Barash\|first2 = L. Yu.\|last3 = Tarasevich\|first3 = Yu. Yu.\|journal = Physical Review E\|year = 2018\|volume = 98\|issue = 6\|page = 062130\|doi = 10.1103/PhysRevE.98.062130\| bibcode=2018PhRvE..98f2130S \|s2cid = 53709717}} 0.906,{{Cite journal \|last1 = Vandewalle\|first1 = N.\|last2 = Galam\|first2 = S.\|last3 = Kramer\|first3 = M.\|title = A new universality for random sequential deposition of needles\|year = 2000\|journal=Eur. Phys. J. B\|volume=14\|issue = 3\|pages = 407–410\|doi=10.1007/s100510051047\|arxiv = cond-mat/0004271\| bibcode=2000EPJB...14..407V \|s2cid = 11142384}} 0.905(9),{{Cite journal \|last1 = Lebovka \|first1 = Nikolai I. \|last2 = Karmazina \| first2 = Natalia \|last3 = Tarasevich \| first3 = Yuri Yu \|last4 = Laptev \| first4 = Valeri V. \|title = Random sequential adsorption of partially oriented linear k-mers on a square lattice \|journal= Phys. Rev. E \|volume = 85 \|pages = 029902 \|year = 2011 \|issue = 6 \|doi = 10.1103/PhysRevE.84.061603\|pmid = 22304098 \|arxiv = 1109.3271 \|bibcode = 2011PhRvE..84f1603L \|s2cid = 25377751 }} 0.906, 0.906823(2),{{Cite journal \|last1 = Wang \| first1 = J. S. \|title = Series expansion and computer simulation studies of random sequential adsorption \|journal= Colloids and Surfaces A \|volume = 165 \|pages = 325–343 \|year = 2000 \| issue = 1–3 \|doi=10.1016/S0927-7757(99)00444-6 \|arxiv = cond-mat/9903139 }}
trimers k = 3 \| 0.846, 0.8366
k = 4 \|0.8094 0.81
k = 5 \|0.7868
k = 6 \|0.7703
k = 7 \|0.7579
k = 8 \|0.7479, 0.747
k = 9 \|0.7405
k = 16 \|0.7103, 0.71
k = 32 \|0.6892, 0.689, 0.6893(4)
k = 48 \|0.6809(5),
k = 64 \| 0.6755, 0.678, 0.6765(6)
k = 96 \| 0.6714(5)
k = 128 \|0.6686, 0.668(9), 0.668 0.6682(6)
k = 192 \| 0.6655(7)
k = 256 \| 0.6628 0.665, 0.6637(6)
k = 384 \| 0.6634(6)
k = 512 \| 0.6618, 0.6628(9)
k = 1024 \|0.6592
k = 2048 \|0.6596
k = 4096 \| 0.6575
k = 8192 \|0.6571
k = 16384 \|0.6561
k = ∞ \|0.660(2),{{Cite journal \|last1 = Bonnier \|first1 = B. \|last2 = Hontebeyrie \| first2 = M. \|last3 = Leroyer \| first3 = Y. \|last4 = Meyers \| first4 = Valeri C. \|last5 = Pommiers \| first5 = E. \|title = Random sequential adsorption of partially oriented linear k-mers on a square lattice \|journal= Phys. Rev. E \|volume = 49 \|pages = 305–312 \|year = 1994 \|issue = 1 \|doi = 10.1103/PhysRevE.49.305\|pmid = 9961218 \|arxiv = cond-mat/9307043 \|s2cid = 131089 }} 0.583(10),{{Cite journal \|last1 = Manna \|first1 = S. S. \|last2 = Svrakic \| first2 = N. M. \|title = Random sequential adsorption: line segments on the square lattice \|journal= J. Phys. A: Math. Gen. \|volume = 24 \|pages = L671–L676 \|year = 1991 \|issue = 12 \|doi = 10.1088/0305-4470/24/12/003\|bibcode = 1991JPhA...24L.671M }}

class="wikitable"

system

! Saturated coverage $\theta_k$ (fraction of sites filled)

dimers k = 2

| 0.906820(2),{{Cite journal

|last1 = Wang |first1 = Jian-Sheng

|last2 = Pandey | first2 = Ras B.

|title = Kinetics and jamming coverage in a random sequential adsorption of polymer chains

|journal= Phys. Rev. Lett.

|volume = 77

|pages = 1773–1776

|year = 1996

|issue = 9

|doi = 10.1103/PhysRevLett.77.1773|pmid = 10063168

|arxiv = cond-mat/9605038

|bibcode = 1996PhRvL..77.1773W

|s2cid = 36659964

}} 0.906,{{Cite journal

|last1 = Tarasevich | first1 = Yuri Yu

|last2 = Laptev | first2 = Valeri V.

|last3 = Vygornitskii | first3 = Nikolai V.

|last4 = Lebovka |first4 = Nikolai I.

|title = Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices

|journal= Phys. Rev. E

|volume = 91

|pages = 012109

|year = 2015

| issue = 1

|doi = 10.1103/PhysRevE.91.012109| pmid = 25679572

|arxiv = 1412.7267

| bibcode = 2015PhRvE..91a2109T

| s2cid = 35537612

}} 0.9068,{{Cite journal

|last1 = Nord |first1 = R. S.

|last2 = Evans | first2 = J. W.

|title = Irreversible immobile random adsorption of dimers, trimers, ... on 2D lattices

|journal= J. Chem. Phys.

|volume = 82

|issue = 6

|pages = 2795–2810

|year = 1985

|doi = 10.1063/1.448279|bibcode = 1985JChPh..82.2795N

|url = https://lib.dr.iastate.edu/physastro_pubs/446

|doi-access = free

}} 0.9062,{{Cite journal |arxiv = 1810.06800|last1 = Slutskii|first1 = M. G.|title = Percolation and jamming of random sequential adsorption samples of large linear k-mers on a square lattice|last2 = Barash|first2 = L. Yu.|last3 = Tarasevich|first3 = Yu. Yu.|journal = Physical Review E|year = 2018|volume = 98|issue = 6|page = 062130|doi = 10.1103/PhysRevE.98.062130| bibcode=2018PhRvE..98f2130S |s2cid = 53709717}}

0.906,{{Cite journal |last1 = Vandewalle|first1 = N.|last2 = Galam|first2 = S.|last3 = Kramer|first3 = M.|title = A new universality for random sequential deposition of needles|year = 2000|journal=Eur. Phys. J. B|volume=14|issue = 3|pages = 407–410|doi=10.1007/s100510051047|arxiv = cond-mat/0004271| bibcode=2000EPJB...14..407V |s2cid = 11142384}}

0.905(9),{{Cite journal

|last1 = Lebovka |first1 = Nikolai I.

|last2 = Karmazina | first2 = Natalia

|last3 = Tarasevich | first3 = Yuri Yu

|last4 = Laptev | first4 = Valeri V.

|title = Random sequential adsorption of partially oriented linear k-mers on a square lattice

|journal= Phys. Rev. E

|volume = 85

|pages = 029902

|year = 2011

|issue = 6

|doi = 10.1103/PhysRevE.84.061603|pmid = 22304098

|arxiv = 1109.3271

|bibcode = 2011PhRvE..84f1603L

|s2cid = 25377751

}} 0.906, 0.906823(2),{{Cite journal

|last1 = Wang | first1 = J. S.

|title = Series expansion and computer simulation studies of random sequential adsorption

|journal= Colloids and Surfaces A

|volume = 165

|pages = 325–343

|year = 2000

| issue = 1–3

|doi=10.1016/S0927-7757(99)00444-6

|arxiv = cond-mat/9903139

}}

trimers k = 3

| 0.846, 0.8366

k = 4

|0.8094 0.81

k = 5

|0.7868

k = 6

|0.7703

k = 7

|0.7579

k = 8

|0.7479, 0.747

k = 9

|0.7405

k = 16

|0.7103, 0.71

k = 32

|0.6892, 0.689, 0.6893(4)

k = 48

|0.6809(5),

k = 64

| 0.6755, 0.678, 0.6765(6)

k = 96

| 0.6714(5)

k = 128

|0.6686, 0.668(9), 0.668 0.6682(6)

k = 192

| 0.6655(7)

k = 256

| 0.6628 0.665, 0.6637(6)

k = 384

| 0.6634(6)

k = 512

| 0.6618, 0.6628(9)

k = 1024

|0.6592

k = 2048

|0.6596

k = 4096

| 0.6575

k = 8192

|0.6571

k = 16384

|0.6561

k = ∞

|0.660(2),{{Cite journal

|last1 = Bonnier |first1 = B.

|last2 = Hontebeyrie | first2 = M.

|last3 = Leroyer | first3 = Y.

|last4 = Meyers | first4 = Valeri C.

|last5 = Pommiers | first5 = E.

|title = Random sequential adsorption of partially oriented linear k-mers on a square lattice

|journal= Phys. Rev. E

|volume = 49

|pages = 305–312

|year = 1994

|issue = 1

|doi = 10.1103/PhysRevE.49.305|pmid = 9961218

|arxiv = cond-mat/9307043

|s2cid = 131089

}} 0.583(10),{{Cite journal

|last1 = Manna |first1 = S. S.

|last2 = Svrakic | first2 = N. M.

|title = Random sequential adsorption: line segments on the square lattice

|journal= J. Phys. A: Math. Gen.

|volume = 24

|pages = L671–L676

|year = 1991

|issue = 12

|doi = 10.1088/0305-4470/24/12/003|bibcode = 1991JPhA...24L.671M

}}

Asymptotic behavior:

$\theta_k \sim \theta_\infty + \ldots$ .

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

class="wikitable"
system ! Saturated coverage $\theta_k$ (fraction of sites filled)
dimers k = 2 \|0.9142(12),{{Cite journal \|last1 = Perino \|first1 = E. J. \|last2 = Matoz-Fernandez \| first2 = D. A. \|last3 = Pasinetti1 \| first3 = P. M. \|last4 = Ramirez-Pastor \| first4 = A. J. \|title = Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice \|journal= Journal of Statistical Mechanics: Theory and Experiment \|volume = 2017 \|pages = 073206 \|year = 2017 \|issue = 7 \|doi = 10.1088/1742-5468/aa79ae\|arxiv = 1703.07680\|bibcode = 2017JSMTE..07.3206P \|s2cid = 119374271 }}
k = 3 \|0.8364(6),
k = 4 \|0.7892(5),
k = 5 \|0.7584(6),
k = 6 \|0.7371(7),
k = 8 \|0.7091(6),
k = 10 \|0.6912(6),
k = 12 \|0.6786(6),
k = 20 \|0.6515(6),
k = 30 \|0.6362(6),
k = 40 \|0.6276(6),
k = 50 \|0.6220(7),
k = 60 \|0.6183(6),
k = 70 \|0.6153(6),
k = 80 \|0.6129(7),
k = 90 \|0.6108(7),
k = 100 \|0.6090(8),
k = 128 \|0.6060(13),

class="wikitable"

system

! Saturated coverage $\theta_k$ (fraction of sites filled)

dimers k = 2

|0.9142(12),{{Cite journal

|last1 = Perino |first1 = E. J.

|last2 = Matoz-Fernandez | first2 = D. A.

|last3 = Pasinetti1 | first3 = P. M.

|last4 = Ramirez-Pastor | first4 = A. J.

|title = Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice

|journal= Journal of Statistical Mechanics: Theory and Experiment

|volume = 2017

|pages = 073206

|year = 2017

|issue = 7

|doi = 10.1088/1742-5468/aa79ae|arxiv = 1703.07680|bibcode = 2017JSMTE..07.3206P

|s2cid = 119374271

}}

k = 3

|0.8364(6),

k = 4

|0.7892(5),

k = 5

|0.7584(6),

k = 6

|0.7371(7),

k = 8

|0.7091(6),

k = 10

|0.6912(6),

k = 12

|0.6786(6),

k = 20

|0.6515(6),

k = 30

|0.6362(6),

k = 40

|0.6276(6),

k = 50

|0.6220(7),

k = 60

|0.6183(6),

k = 70

|0.6153(6),

k = 80

|0.6129(7),

k = 90

|0.6108(7),

k = 100

|0.6090(8),

k = 128

|0.6060(13),

Saturation coverage for particles with neighbors exclusion on 2d lattices

class="wikitable"
system ! Saturated coverage $\theta_k$ (fraction of sites filled)
Square lattice with NN exclusion \| 0.3641323(1),{{Cite journal \|last1 = Gan \|first1 = C. K. \|last2 = Wang \| first2 = J.-S. \|title = Extended series expansions for random sequential adsorption \|journal= J. Chem. Phys. \|volume = 108 \|pages = 3010–3012 \|year = 1998 \|issue = 7 \|doi = 10.1063/1.475687\|arxiv = cond-mat/9710340 \|bibcode = 1998JChPh.108.3010G \|s2cid = 97703000 }} 0.36413(1),{{Cite journal \|last1 = Meakin \|first1 = P. \|last2 = Cardy \| first2 = John L. \|last3 = Loh \| first3 = John L. \|last4 = Scalapino \| first4 = John L. \|title = Extended series expansions for random sequential adsorption \|journal= J. Chem. Phys. \|volume = 86 \|issue = 4 \|pages = 2380–2382 \|year = 1987 \|doi = 10.1063/1.452085}} 0.3641330(5),{{Cite journal \|last1 = Baram \| first1 = Asher \|last2 = Fixman \| first2 = Marshall \|title = Random sequential adsorption: Long time dynamics \|journal= J. Chem. Phys. \|volume = 103 \|issue = 5 \|pages = 1929–1933 \|year = 1995 \|doi = 10.1063/1.469717\| bibcode = 1995JChPh.103.1929B }}
Honeycomb lattice with NN exclusion \| 0.37913944(1), 0.38(1), 0.379{{Cite journal \|last1 = Evans \|first1 = J. W. \|title = Comment on Kinetics of random sequential adsorption \|journal= Phys. Rev. Lett. \|volume = 62 \|pages = 2642 \|issue = 22 \|year = 1989 \|doi = 10.1103/PhysRevLett.62.2642\|pmid = 10040048 \|bibcode = 1989PhRvL..62.2642E \|url = https://lib.dr.iastate.edu/physastro_pubs/418 }}

class="wikitable"

system

! Saturated coverage $\theta_k$ (fraction of sites filled)

Square lattice with NN exclusion

| 0.3641323(1),{{Cite journal

|last1 = Gan |first1 = C. K.

|last2 = Wang | first2 = J.-S.

|title = Extended series expansions for random sequential adsorption

|journal= J. Chem. Phys.

|volume = 108

|pages = 3010–3012

|year = 1998

|issue = 7

|doi = 10.1063/1.475687|arxiv = cond-mat/9710340

|bibcode = 1998JChPh.108.3010G

|s2cid = 97703000

}} 0.36413(1),{{Cite journal

|last1 = Meakin |first1 = P.

|last2 = Cardy | first2 = John L.

|last3 = Loh | first3 = John L.

|last4 = Scalapino | first4 = John L.

|title = Extended series expansions for random sequential adsorption

|journal= J. Chem. Phys.

|volume = 86

|issue = 4

|pages = 2380–2382

|year = 1987

|doi = 10.1063/1.452085}} 0.3641330(5),{{Cite journal

|last1 = Baram | first1 = Asher

|last2 = Fixman | first2 = Marshall

|title = Random sequential adsorption: Long time dynamics

|journal= J. Chem. Phys.

|volume = 103

|issue = 5

|pages = 1929–1933

|year = 1995

|doi = 10.1063/1.469717| bibcode = 1995JChPh.103.1929B

}}

Honeycomb lattice with NN exclusion

| 0.37913944(1), 0.38(1), 0.379{{Cite journal

|last1 = Evans |first1 = J. W.

|title = Comment on Kinetics of random sequential adsorption

|journal= Phys. Rev. Lett.

|volume = 62

|pages = 2642

|issue = 22

|year = 1989

|doi = 10.1103/PhysRevLett.62.2642|pmid = 10040048

|bibcode = 1989PhRvL..62.2642E

|url = https://lib.dr.iastate.edu/physastro_pubs/418

}}

Saturation coverage of <math> k \times k </math> squares on a 2d square lattice

class="wikitable"
system ! Saturated coverage $\theta_k$ (fraction of sites filled)
k = 2 \| 0.74793(1),{{Cite journal \|last1 = Privman \|first1 = V. \|last2 = Wang \| first2 = J. S. \|last3 = Nielaba \| first3 = P. \|title = Continuum limit in random sequential adsorption \|journal= Phys. Rev. B \|volume = 43 \|pages = 3366–3372 \|year = 1991 \|issue = 4 \|doi = 10.1103/PhysRevB.43.3366\|pmid = 9997649 \|bibcode = 1991PhRvB..43.3366P }} 0.747943(37), 0.749(1),{{Cite journal \|last1 = Nakamura \|first1 = Mitsunobu \|title = Random sequential packing in square cellular structures \|journal= J. Phys. A: Math. Gen. \|volume = 19 \|pages = 2345–2351 \|year = 1986 \|issue = 12 \|doi = 10.1088/0305-4470/19/12/020\|bibcode = 1986JPhA...19.2345N }}
k = 3 \| 0.67961(1), 0.681(1),
k = 4 \| 0.64793(1), 0.647927(22) 0.646(1),
k = 5 \| 0.62968(1) 0.628(1),
k = 8 \| 0.603355(55) 0.603(1),
k = 10 \| 0.59476(4) 0.593(1),
k = 15 \| 0.583(1),
k = 16 \| 0.582233(39)
k = 20 \| 0.57807(5) 0.578(1),
k = 30 \| 0.574(1),
k = 32 \| 0.571916(27)
k = 50 \| 0.56841(10)
k = 64 \| 0.567077(40)
k = 100 \| 0.56516(10)
k = 128 \| 0.564405(51)
k = 256 \| 0.563074(52)
k = 512 \| 0.562647(31)
k = 1024 \| 0.562346(33)
k = 4096 \| 0.562127(33)
k = 16384 \| 0.562038(33)

class="wikitable"

system

! Saturated coverage $\theta_k$ (fraction of sites filled)

k = 2

| 0.74793(1),{{Cite journal

|last1 = Privman |first1 = V.

|last2 = Wang | first2 = J. S.

|last3 = Nielaba | first3 = P.

|title = Continuum limit in random sequential adsorption

|journal= Phys. Rev. B

|volume = 43

|pages = 3366–3372

|year = 1991

|issue = 4

|doi = 10.1103/PhysRevB.43.3366|pmid = 9997649

|bibcode = 1991PhRvB..43.3366P

}} 0.747943(37), 0.749(1),{{Cite journal

|last1 = Nakamura |first1 = Mitsunobu

|title = Random sequential packing in square cellular structures

|journal= J. Phys. A: Math. Gen.

|volume = 19

|pages = 2345–2351

|year = 1986

|issue = 12

|doi = 10.1088/0305-4470/19/12/020|bibcode = 1986JPhA...19.2345N

}}

k = 3

| 0.67961(1), 0.681(1),

k = 4

| 0.64793(1), 0.647927(22) 0.646(1),

k = 5

| 0.62968(1) 0.628(1),

k = 8

| 0.603355(55) 0.603(1),

k = 10

| 0.59476(4) 0.593(1),

k = 15

| 0.583(1),

k = 16

| 0.582233(39)

k = 20

| 0.57807(5) 0.578(1),

k = 30

| 0.574(1),

k = 32

| 0.571916(27)

k = 50

| 0.56841(10)

k = 64

| 0.567077(40)

k = 100

| 0.56516(10)

k = 128

| 0.564405(51)

k = 256

| 0.563074(52)

k = 512

| 0.562647(31)

k = 1024

| 0.562346(33)

k = 4096

| 0.562127(33)

k = 16384

| 0.562038(33)

For k = ∞, see "2d aligned squares" below.

Asymptotic behavior:

$\theta_k \sim \theta_\infty + 0.316/k + 0.114/k^2 \ldots$ .

Saturation coverage for randomly oriented 2d systems

class="wikitable"
system ! Saturated coverage
equilateral triangles \|0.52590(4)
squares \| 0.523-0.532,{{cite journal\|last=Vigil\|first=R. Dennis\|author2 = Robert M. Ziff\|title=Random sequential adsorption of unoriented rectangles onto a plane\|journal=J. Chem. Phys.\|volume=91\|issue=4\|year=1989\|doi=10.1063/1.457021\|pages=2599–2602\|bibcode=1989JChPh..91.2599V\|hdl=2027.42/70834\|hdl-access=free}} 0.530(1),{{cite journal\|last=Viot\|first= P.\|author2 = G. Targus\|title=Random Sequential Addition of Unoriented Squares: Breakdown of Swendsen's Conjecture\|journal=EPL\|volume=13\|issue=4\|year=1990\|doi=10.1209/0295-5075/13/4/002\|pages=295–300\|bibcode=1990EL.....13..295V\|s2cid= 250852782}} 0.530(1),{{cite journal\|last=Viot\|first= P.\|author2 = G. Targus\|author3 = S. M. Ricci \|author4=J. Talbot\|title=Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior\|journal=J. Chem. Phys.\|volume=97\|issue=7\|year=1992\|doi=10.1063/1.463820\|pages=5212\|bibcode=1992JChPh..97.5212V}} 0.52760(5){{Cite journal\|last=Zhang\|first=G.\|date=2018\|title=Precise algorithm to generate random sequential adsorption of hard polygons at saturation\|journal=Physical Review E\|volume=97\|issue=4\|pages=043311\|doi=10.1103/PhysRevE.97.043311\|pmid=29758708\|arxiv=1803.08348\|bibcode=2018PhRvE..97d3311Z\|s2cid=46892756}}
regular pentagons \|0.54130(5)
regular hexagons \|0.53913(5)
regular heptagons \|0.54210(6)
regular octagons \|0.54238(5)
regular enneagons \|0.54405(5)
regular decagons \|0.54421(6)

class="wikitable"

system

! Saturated coverage

equilateral triangles

|0.52590(4)

squares

| 0.523-0.532,{{cite journal|last=Vigil|first=R. Dennis|author2 = Robert M. Ziff|title=Random sequential adsorption of unoriented rectangles onto a plane|journal=J. Chem. Phys.|volume=91|issue=4|year=1989|doi=10.1063/1.457021|pages=2599–2602|bibcode=1989JChPh..91.2599V|hdl=2027.42/70834|hdl-access=free}} 0.530(1),{{cite journal|last=Viot|first= P.|author2 = G. Targus|title=Random Sequential Addition of Unoriented Squares: Breakdown of Swendsen's Conjecture|journal=EPL|volume=13|issue=4|year=1990|doi=10.1209/0295-5075/13/4/002|pages=295–300|bibcode=1990EL.....13..295V|s2cid= 250852782}}

0.530(1),{{cite journal|last=Viot|first= P.|author2 = G. Targus|author3 = S. M. Ricci |author4=J. Talbot|title=Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior|journal=J. Chem. Phys.|volume=97|issue=7|year=1992|doi=10.1063/1.463820|pages=5212|bibcode=1992JChPh..97.5212V}} 0.52760(5){{Cite journal|last=Zhang|first=G.|date=2018|title=Precise algorithm to generate random sequential adsorption of hard polygons at saturation|journal=Physical Review E|volume=97|issue=4|pages=043311|doi=10.1103/PhysRevE.97.043311|pmid=29758708|arxiv=1803.08348|bibcode=2018PhRvE..97d3311Z|s2cid=46892756}}

regular pentagons

|0.54130(5)

regular hexagons

|0.53913(5)

regular heptagons

|0.54210(6)

regular octagons

|0.54238(5)

regular enneagons

|0.54405(5)

regular decagons

|0.54421(6)

2d oblong shapes with maximal coverage

class="wikitable"
system ! aspect ratio ! Saturated coverage
rectangle \| 1.618 \| 0.553(1){{cite journal\|last=Viot\|first=P.\|author2 = G. Tarjus\|author3 = S. Ricci\|author4 = J.Talbot\|title=Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior\|journal = J. Chem. Phys.\|volume=97\|issue=7\|year=1992\|doi=10.1063/1.463820\|pages=5212–5218\|bibcode=1992JChPh..97.5212V}}
dimer \| 1.5098 \| 0.5793(1){{cite journal\|last=Cieśla\|first=Michał\|title=Properties of random sequential adsorption of generalized dimers\|journal = Phys. Rev. E\|volume=89\|issue=4\|year=2014\|doi=10.1103/PhysRevE.89.042404\|pmid=24827257\|pages=042404\|arxiv=1403.3200\|bibcode=2014PhRvE..89d2404C\|s2cid=12961099}}
ellipse \| 2.0 \| 0.583(1)
spherocylinder \| 1.75 \| 0.583(1)
smoothed dimer \| 1.6347 \| 0.5833(5){{cite journal\|last=Ciesśla\|first=Michałl\|author2 = Grzegorz Pająk \| author3 = Robert M. Ziff\| title=Shapes for maximal coverage for two-dimensional random sequential adsorption\|journal = Phys. Chem. Chem. Phys.\|volume=17\|issue=37\|year=2015\|doi=10.1039/c5cp03873a\|pmid=26330194\|pages=24376–24381\|arxiv=1506.08164\|bibcode=2015PCCP...1724376C\|s2cid=14368653}}

class="wikitable"

system

! aspect ratio

! Saturated coverage

rectangle

| 1.618

| 0.553(1){{cite journal|last=Viot|first=P.|author2 = G. Tarjus|author3 = S. Ricci|author4 = J.Talbot|title=Random sequential adsorption of anisotropic particles. I. Jamming limit and asymptotic behavior|journal = J. Chem. Phys.|volume=97|issue=7|year=1992|doi=10.1063/1.463820|pages=5212–5218|bibcode=1992JChPh..97.5212V}}

dimer

| 1.5098

| 0.5793(1){{cite journal|last=Cieśla|first=Michał|title=Properties of random sequential adsorption of generalized dimers|journal = Phys. Rev. E|volume=89|issue=4|year=2014|doi=10.1103/PhysRevE.89.042404|pmid=24827257|pages=042404|arxiv=1403.3200|bibcode=2014PhRvE..89d2404C|s2cid=12961099}}

ellipse

| 2.0

| 0.583(1)

spherocylinder

| 1.75

| 0.583(1)

smoothed dimer

| 1.6347

| 0.5833(5){{cite journal|last=Ciesśla|first=Michałl|author2 = Grzegorz Pająk | author3 = Robert M. Ziff| title=Shapes for maximal coverage for two-dimensional random sequential adsorption|journal = Phys. Chem. Chem. Phys.|volume=17|issue=37|year=2015|doi=10.1039/c5cp03873a|pmid=26330194|pages=24376–24381|arxiv=1506.08164|bibcode=2015PCCP...1724376C|s2cid=14368653}}

Saturation coverage for 3d systems

class="wikitable"
system ! Saturated coverage
spheres \| 0.3841307(21), 0.38278(5), 0.384(1){{cite journal\|last=Meakin\|first=Paul\|title=Random sequential adsorption of spheres of different sizes\|journal = Physica A\|volume=187\|issue=3\|year=1992\|doi=10.1016/0378-4371(92)90006-C\|pages=475–488\|bibcode=1992PhyA..187..475M}}
randomly oriented cubes \|0.3686(15),{{Cite journal\|last1=Ciesla\|first1=Michal\|last2=Kubala\|first2=Piotr\|date=2018\|title=Random sequential adsorption of cubes\|doi=10.1063/1.5007319\|pmid=29331110\|journal=The Journal of Chemical Physics\|volume=148\|issue=2\|pages=024501\|bibcode=2018JChPh.148b4501C}} 0.36306(60){{Cite journal\|last1=Ciesla\|first1=Michal\|last2=Kubala\|first2=Piotr\|date=2018\|title=Random sequential adsorption of cuboids\|doi=10.1063/1.5061695\|journal=The Journal of Chemical Physics\|volume=149\|issue=19\|pages=194704\|pmid=30466287\|bibcode=2018JChPh.149s4704C \|s2cid=53727841 }}
randomly oriented cuboids 0.75:1:1.3 \|0.40187(97),

class="wikitable"

system

! Saturated coverage

spheres

| 0.3841307(21), 0.38278(5), 0.384(1){{cite journal|last=Meakin|first=Paul|title=Random sequential adsorption of spheres of different sizes|journal = Physica A|volume=187|issue=3|year=1992|doi=10.1016/0378-4371(92)90006-C|pages=475–488|bibcode=1992PhyA..187..475M}}

randomly oriented cubes

|0.3686(15),{{Cite journal|last1=Ciesla|first1=Michal|last2=Kubala|first2=Piotr|date=2018|title=Random sequential adsorption of cubes|doi=10.1063/1.5007319|pmid=29331110|journal=The Journal of Chemical Physics|volume=148|issue=2|pages=024501|bibcode=2018JChPh.148b4501C}} 0.36306(60){{Cite journal|last1=Ciesla|first1=Michal|last2=Kubala|first2=Piotr|date=2018|title=Random sequential adsorption of cuboids|doi=10.1063/1.5061695|journal=The Journal of Chemical Physics|volume=149|issue=19|pages=194704|pmid=30466287|bibcode=2018JChPh.149s4704C |s2cid=53727841 }}

randomly oriented cuboids 0.75:1:1.3

|0.40187(97),

Saturation coverages for disks, spheres, and hyperspheres

class="wikitable"
system ! Saturated coverage
2d disks \| 0.5470735(28),{{cite journal\|last=Zhang\|first=G.\|author2=S. Torquato\|title=Precise algorithm to generate random sequential addition of hard hyperspheres at saturation\|journal=Phys. Rev. E\|volume=88\|issue=5\|year=2013\|doi=10.1103/PhysRevE.88.053312\|pmid=24329384\|pages=053312\|arxiv=1402.4883\|bibcode=2013PhRvE..88e3312Z\|s2cid=14810845}} 0.547067(3),{{cite journal\|last1=Cieśla\|first1=Michał\|last2=Ziff\|first2=Robert\|title=Boundary conditions in random sequential adsorption \|journal=Journal of Statistical Mechanics: Theory and Experiment\|volume=2018\|issue=4 \|year=2018\|pages=043302\|doi=10.1088/1742-5468/aab685\|arxiv=1712.09663\|bibcode=2018JSMTE..04.3302C \|s2cid=118969644}} 0.547070,{{cite journal\|last=Cieśla\|first=Michał\|author2=Aleksandra Nowak\|title=Managing numerical errors in random sequential adsorption\|journal=Surface Science\|volume=651\|year=2016\|pages=182–186\|doi=10.1016/j.susc.2016.04.014\|bibcode=2016SurSc.651..182C}} 0.5470690(7),{{cite journal\|last=Wang\|first=Jian-Sheng\|title=A fast algorithm for random sequential adsorption of discs\|journal=Int. J. Mod. Phys. C\|volume=5\|issue=4\|year=1994\|pages=707–715\|arxiv = cond-mat/9402066\|doi=10.1142/S0129183194000817\|bibcode=1994IJMPC...5..707W\|s2cid=119032105}} 0.54700(6),{{cite journal\|last=Torquato\|first=S.\|author2=O. U. Uche\|author3=F. H. Stillinger\|title=Random sequential addition of hard spheres in high Euclidean dimensions\|journal=Phys. Rev. E\|volume=74\|issue=6\|year=2006\|doi=10.1103/PhysRevE.74.061308\|pmid=17280063\|pages=061308\|arxiv=cond-mat/0608402\|bibcode=2006PhRvE..74f1308T \|s2cid=15604775}} 0.54711(16),{{cite journal\|last=Chen\|first=Elizabeth R.\|author2=Miranda Holmes-Cerfon\|title=Random Sequential Adsorption of Discs on Surfaces of Constant Curvature: Plane, Sphere, Hyperboloid, and Projective Plane\|journal=J. Nonlinear Sci.\|volume=27\|issue=6\|year=2017\|doi=10.1007/s00332-017-9385-2\|pages=1743–1787\|arxiv=1709.05029\|bibcode=2017JNS....27.1743C\|s2cid=26861078}} 0.5472(2),{{cite journal\|last=Hinrichsen\|first=Einar L.\|author2=Jens Feder\|author3 = Torstein Jøssang\|title=Random packing of disks in two dimensions\|journal=Phys. Rev. A\|volume=41\|issue=8\|year=1990\|doi=10.1103/PhysRevA.41.4199\|pages=4199–4209\|bibcode=1990PhRvA..41.4199H}} 0.547(2),{{cite journal\|last=Feder\|first=Jens\|title=Random sequential adsorption\|journal=J. Theor. Biol.\|volume=87\|issue=2\|year=1980\|doi=10.1016/0022-5193(80)90358-6\|pages=237–254\|bibcode=1980JThBi..87..237F }} 0.5479,
3d spheres \| 0.3841307(21), 0.38278(5), 0.384(1)
4d hyperspheres \| 0.2600781(37), 0.25454(9),
5d hyperspheres \| 0.1707761(46), 0.16102(4),
6d hyperspheres \| 0.109302(19), 0.09394(5),
7d hyperspheres \| 0.068404(16),
8d hyperspheres \| 0.04230(21),

class="wikitable"

system

! Saturated coverage

2d disks

| 0.5470735(28),{{cite journal|last=Zhang|first=G.|author2=S. Torquato|title=Precise algorithm to generate random sequential addition of hard hyperspheres at saturation|journal=Phys. Rev. E|volume=88|issue=5|year=2013|doi=10.1103/PhysRevE.88.053312|pmid=24329384|pages=053312|arxiv=1402.4883|bibcode=2013PhRvE..88e3312Z|s2cid=14810845}}

0.547067(3),{{cite journal|last1=Cieśla|first1=Michał|last2=Ziff|first2=Robert|title=Boundary conditions in random sequential adsorption

|journal=Journal of Statistical Mechanics: Theory and Experiment|volume=2018|issue=4

|year=2018|pages=043302|doi=10.1088/1742-5468/aab685|arxiv=1712.09663|bibcode=2018JSMTE..04.3302C |s2cid=118969644}}

0.547070,{{cite journal|last=Cieśla|first=Michał|author2=Aleksandra Nowak|title=Managing numerical errors in random sequential adsorption|journal=Surface Science|volume=651|year=2016|pages=182–186|doi=10.1016/j.susc.2016.04.014|bibcode=2016SurSc.651..182C}}

0.5470690(7),{{cite journal|last=Wang|first=Jian-Sheng|title=A fast algorithm for random sequential adsorption of discs|journal=Int. J. Mod. Phys. C|volume=5|issue=4|year=1994|pages=707–715|arxiv = cond-mat/9402066|doi=10.1142/S0129183194000817|bibcode=1994IJMPC...5..707W|s2cid=119032105}}

0.54700(6),{{cite journal|last=Torquato|first=S.|author2=O. U. Uche|author3=F. H. Stillinger|title=Random sequential addition of hard spheres in high Euclidean dimensions|journal=Phys. Rev. E|volume=74|issue=6|year=2006|doi=10.1103/PhysRevE.74.061308|pmid=17280063|pages=061308|arxiv=cond-mat/0608402|bibcode=2006PhRvE..74f1308T |s2cid=15604775}}

0.54711(16),{{cite journal|last=Chen|first=Elizabeth R.|author2=Miranda Holmes-Cerfon|title=Random Sequential Adsorption of Discs on Surfaces of Constant Curvature: Plane, Sphere, Hyperboloid, and Projective Plane|journal=J. Nonlinear Sci.|volume=27|issue=6|year=2017|doi=10.1007/s00332-017-9385-2|pages=1743–1787|arxiv=1709.05029|bibcode=2017JNS....27.1743C|s2cid=26861078}}

0.5472(2),{{cite journal|last=Hinrichsen|first=Einar L.|author2=Jens Feder|author3 = Torstein Jøssang|title=Random packing of disks in two dimensions|journal=Phys. Rev. A|volume=41|issue=8|year=1990|doi=10.1103/PhysRevA.41.4199|pages=4199–4209|bibcode=1990PhRvA..41.4199H}} 0.547(2),{{cite journal|last=Feder|first=Jens|title=Random sequential adsorption|journal=J. Theor. Biol.|volume=87|issue=2|year=1980|doi=10.1016/0022-5193(80)90358-6|pages=237–254|bibcode=1980JThBi..87..237F }}

0.5479,

3d spheres

| 0.3841307(21), 0.38278(5), 0.384(1)

4d hyperspheres

| 0.2600781(37), 0.25454(9),

5d hyperspheres

| 0.1707761(46), 0.16102(4),

6d hyperspheres

| 0.109302(19), 0.09394(5),

7d hyperspheres

| 0.068404(16),

8d hyperspheres

| 0.04230(21),

Saturation coverages for aligned squares, cubes, and hypercubes

class="wikitable"
system ! Saturated coverage
2d aligned squares \| 0.562009(4),{{cite journal\|last=Brosilow\|first=B. J.\|author2 = R. M. Ziff\|author3 = R. D. Vigil\|title=Random sequential adsorption of parallel squares\|journal=Phys. Rev. A\|volume=43\|issue=2\|year=1991\|doi=10.1103/PhysRevA.43.631\|pages=631–638\|pmid=9905079\|bibcode=1991PhRvA..43..631B}} 0.5623(4), 0.562(2), 0.5565(15),{{cite journal\|last=Blaisdell\|first=B. Edwin\|author2 = Herbert Solomon\|title=On random sequential packing in the plane and a conjecture of Palasti\|journal=J. Appl. Probab.\|volume=7\|issue=3\|year=1970\|doi=10.1017/S0021900200110630\|pages=667–698}} 0.5625(5),{{cite journal\|last=Dickman\|first=R.\|author2 = J. S. Wang\|author3 = I. Jensen\|title=Random sequential adsorption of parallel squares\|journal=J. Chem. Phys.\|volume=94\|issue=12\|year=1991\|doi=10.1063/1.460109\|pages=8252\|bibcode=1991JChPh..94.8252D}} 0.5444(24),{{cite journal\|last=Tory\|first=E. M.\|author2 = W. S. Jodrey\|author3 =D. K. Pikard\|title=Simulation of Random Sequential Adsorption: Efficient Methods and Resolution of Conflicting Results\|journal=J. Theor. Biol.\|volume=102\|issue=12\|year=1983\|doi=10.1063/1.460109\|pages=439–445\|bibcode=1991JChPh..94.8252D}} 0.5629(6),{{cite journal\|last=Akeda\|first=Yoshiaki\|author2 = Motoo Hori\|title=On random sequential packing in two and three dimensions\|journal=Biometrika\|volume=63\|issue=2\|year=1976\|doi=10.1093/biomet/63.2.361\|pages=361–366}} 0.562(2),
3d aligned cubes \| 0.4227(6),{{cite journal\|last=Jodrey\|first=W. S.\|author2=E. M. Tory\|title=Random sequential packing in R^n\|journal= Journal of Statistical Computation and Simulation\|volume=10\|issue=2\|year=1980\|pages = 87–93\|doi=10.1080/00949658008810351}} 0.42(1),{{cite journal\|last=Bonnier\|first=B.\|author2=M. Hontebeyrie\|author3=C. Meyers\|title=On the random filling of R^d by non-overlapping d-dimensional cubes\|journal=Physica A\|volume=198\|issue=1\|year=1993\|pages = 1–10\|doi=10.1016/0378-4371(93)90180-C\|arxiv=cond-mat/9302023\|bibcode=1993PhyA..198....1B\|s2cid=11802063}} 0.4262,{{cite journal\|last=Blaisdell\|first=B. Edwin\|author2=Herbert Solomon\|title=Random Sequential Packing in Euclidean Spaces of Dimensions Three and Four and a Conjecture of Palásti\|journal=Journal of Applied Probability\|volume=19\|issue=2\|year=1982\|pages = 382–390\|doi=10.2307/3213489\|jstor=3213489\|s2cid=118248194 }} 0.430(8),{{cite journal\|last=Cooper\|first=Douglas W.\|title= Random sequential packing simulations in three dimensions for aligned cubes\|journal=J. Appl. Probab.\|volume=26\|issue=3\|year=1989\|pages = 664–670\|doi=10.2307/3214426\|jstor=3214426\|s2cid=124311298 }} 0.422(8),{{cite journal\|last=Nord\|first=R. S.\|title= Irreversible random sequential filling of lattices by Monte Carlo simulation\|journal= Journal of Statistical Computation and Simulation\|volume=39\|issue=4\|year=1991\|pages = 231–240\|doi=10.1080/00949659108811358}} 0.42243(5)
4d aligned hypercubes \| 0.3129, 0.3341,

class="wikitable"

system

! Saturated coverage

2d aligned squares

| 0.562009(4),{{cite journal|last=Brosilow|first=B. J.|author2 = R. M. Ziff|author3 = R. D. Vigil|title=Random sequential adsorption of parallel squares|journal=Phys. Rev. A|volume=43|issue=2|year=1991|doi=10.1103/PhysRevA.43.631|pages=631–638|pmid=9905079|bibcode=1991PhRvA..43..631B}}

0.5623(4), 0.562(2), 0.5565(15),{{cite journal|last=Blaisdell|first=B. Edwin|author2 = Herbert Solomon|title=On random sequential packing in the plane and a conjecture of Palasti|journal=J. Appl. Probab.|volume=7|issue=3|year=1970|doi=10.1017/S0021900200110630|pages=667–698}}

0.5625(5),{{cite journal|last=Dickman|first=R.|author2 = J. S. Wang|author3 = I. Jensen|title=Random sequential adsorption of parallel squares|journal=J. Chem. Phys.|volume=94|issue=12|year=1991|doi=10.1063/1.460109|pages=8252|bibcode=1991JChPh..94.8252D}}

0.5444(24),{{cite journal|last=Tory|first=E. M.|author2 = W. S. Jodrey|author3 =D. K. Pikard|title=Simulation of Random Sequential Adsorption: Efficient Methods and Resolution of Conflicting Results|journal=J. Theor. Biol.|volume=102|issue=12|year=1983|doi=10.1063/1.460109|pages=439–445|bibcode=1991JChPh..94.8252D}}

0.5629(6),{{cite journal|last=Akeda|first=Yoshiaki|author2 = Motoo Hori|title=On random sequential packing in two and three dimensions|journal=Biometrika|volume=63|issue=2|year=1976|doi=10.1093/biomet/63.2.361|pages=361–366}}

0.562(2),

3d aligned cubes

| 0.4227(6),{{cite journal|last=Jodrey|first=W. S.|author2=E. M. Tory|title=Random sequential packing in R^n|journal= Journal of Statistical Computation and Simulation|volume=10|issue=2|year=1980|pages = 87–93|doi=10.1080/00949658008810351}}

0.42(1),{{cite journal|last=Bonnier|first=B.|author2=M. Hontebeyrie|author3=C. Meyers|title=On the random filling of R^d by non-overlapping d-dimensional cubes|journal=Physica A|volume=198|issue=1|year=1993|pages = 1–10|doi=10.1016/0378-4371(93)90180-C|arxiv=cond-mat/9302023|bibcode=1993PhyA..198....1B|s2cid=11802063}}

0.4262,{{cite journal|last=Blaisdell|first=B. Edwin|author2=Herbert Solomon|title=Random Sequential Packing in Euclidean Spaces of Dimensions Three and Four and a Conjecture of Palásti|journal=Journal of Applied Probability|volume=19|issue=2|year=1982|pages = 382–390|doi=10.2307/3213489|jstor=3213489|s2cid=118248194 }}

0.430(8),{{cite journal|last=Cooper|first=Douglas W.|title= Random sequential packing simulations in three dimensions for aligned cubes|journal=J. Appl. Probab.|volume=26|issue=3|year=1989|pages = 664–670|doi=10.2307/3214426|jstor=3214426|s2cid=124311298 }}

0.422(8),{{cite journal|last=Nord|first=R. S.|title= Irreversible random sequential filling of lattices by Monte Carlo simulation|journal= Journal of Statistical Computation and Simulation|volume=39|issue=4|year=1991|pages = 231–240|doi=10.1080/00949659108811358}}

0.42243(5)

4d aligned hypercubes

| 0.3129, 0.3341,

References

Category:Chemistry

Category:Materials science

Category:Colloidal chemistry

Random sequential adsorption

Saturation coverage of ''k''-mers on 1d lattice systems

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

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

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

Saturation coverage for particles with neighbors exclusion on 2d lattices

Saturation coverage of <math> k \times k </math> squares on a 2d square lattice

Saturation coverage for randomly oriented 2d systems

2d oblong shapes with maximal coverage

Saturation coverage for 3d systems

Saturation coverages for disks, spheres, and hyperspheres

Saturation coverages for aligned squares, cubes, and hypercubes

See also

References