We report a surprising result, established by numerical simulations and analytical arguments for a one-dimensional lattice model of random sequential adsorption, that even an arbitrarily small imprecision in the lattice-site localization changes the convergence to jamming from fast, exponential, to slow, power-law, with, for some parameter values, a discontinuous jump in the jamming coverage value. This finding has implications for irreversible deposition on patterned substrates with pre-made landing sites for particle attachment. We also consider a general problem of the particle (depositing object) size not an exact multiple of the lattice spacing, and the lattice sites themselves imprecise, broadened into allowed-deposition intervals. Regions of exponential vs. power-law convergence to jamming are identified, and certain conclusions regarding the jamming coverage are argued for analytically and confirmed numerically.

1.
J. W.
Evans
, “
Random and cooperative sequential adsorption
,”
Rev. Mod. Phys.
65
,
1281
1311
(
1993
).
2.
P.
Schaaf
,
J.-C.
Voegel
, and
B.
Senger
, “
From random sequential adsorption to ballistic deposition: A general view of irreversible deposition processes
,”
J. Phys. Chem. B
104
,
2204
2214
(
2000
).
3.
J.
Talbot
,
G.
Tarjus
,
P. R.
Van Tassel
, and
P.
Viot
, “
From car parking to protein adsorption: An overview of sequential adsorption processes
,”
Colloids Surf., A
165
,
287
324
(
2000
).
4.
V.
Privman
,
J.-S.
Wang
, and
P.
Nielaba
, “
Continuum limit in random sequential adsorption
,”
Phys. Rev. B
43
,
3366
3372
(
1991
).
5.
A.
Cadilhe
,
N. A. M.
Araujo
, and
V.
Privman
, “
Random sequential adsorption: From continuum to lattice and pre-patterned substrates
,”
J. Phys.: Condens. Matter.
19
,
065124
(
2007
).
6.
J. J.
González
,
P. C.
Hemmer
, and
J. S.
Høye
, “
Cooperative effects in random sequential polymer reactions
,”
Chem. Phys.
3
,
228
238
(
1974
).
7.
Y.
Pomeau
, “
Some asymptotic estimates in the random parking problem
,”
J. Phys. A
13
,
L193
L196
(
1980
).
8.
R. H.
Swendsen
, “
Dynamics of random sequential adsorption
,”
Phys. Rev. A
24
,
504
508
(
1981
).
9.
D.
Xia
,
D.
Li
,
Y.
Luo
, and
S. R. J.
Brueck
, “
An approach to lithographically defined self-assembled nanoparticle films
,”
Adv. Mater.
18
,
930
933
(
2006
).
10.
K. M.
Chen
,
X.
Jiang
,
L. C.
Kimerling
, and
P. T.
Hammond
, “
Selective self-organization of colloids on patterned polyelectrolyte templates
,”
Langmuir
16
,
7825
7834
(
2000
).
11.
E.
Kumacheva
,
R. K.
Golding
,
M.
Allard
, and
E. H.
Sargent
, “
Colloid crystal growth on mesoscopically patterned surfaces: Effect of confinement
,”
Adv. Mater.
14
,
221
224
(
2002
).
12.
S. B.
Darling
, “
Mechanism for hierarchical self-assembly of nanoparticles on scaffolds derived from block copolymers
,”
Surf. Sci.
601
,
2555
2561
(
2007
).
13.
P. C.
Lewis
,
E.
Kumacheva
,
M.
Allard
, and
E. H.
Sargent
, “
Colloidal crystallization accomplished by electrodeposition on patterned substrates
,”
J. Dispersion Sci. Technol.
26
,
259
265
(
2005
).
14.
M.
Elimelech
,
J. Y.
Chen
, and
Z. A.
Kuznar
, “
Particle deposition onto solid surfaces with micropatterned charge heterogeneity: The ‘hydrodynamic bump’ effect
,”
Langmuir
19
,
6594
(
2003
).
15.
A.
Katsman
,
M.
Beregovsky
, and
Y. E.
Yaish
, “
Formation and evolution of nickel silicides in silicon nanowires
,”
Nano Stud.
8
,
139
152
(
2013
).
16.
A.
Katsman
,
M.
Beregovsky
, and
Y. E.
Yaish
, “
Evolution of nickel silicide intrusions in silicon nanowires during thermal cycling
,”
J. Appl. Phys.
113
,
084305
(
2013
).
17.
M.
Beregovsky
,
A.
Katsman
,
E. M.
Hajaj
, and
Y. E.
Yaish
, “
Diffusion formation of nickel silicide contacts in SiNWs
,”
Solid-State Electron.
80
,
110
117
(
2013
).
18.
M.
Palma
,
J.
Levin
,
V.
Lemaur
,
A.
Liscio
,
V.
Palermo
,
J.
Cornil
,
Y.
Geerts
,
M.
Lehmann
, and
P.
Samorì
, “
Self-organization and nanoscale electronic properties of azatriphenylene-based architectures: A scanning probe microscopy study
,”
Adv. Mater.
18
,
3313
3317
(
2006
).
19.
J. A.
Liddle
,
Y.
Cui
, and
P.
Alivisatos
, “
Lithographically directed self-assembly of nanostructures
,”
J. Vac. Sci. Technol. B
22
,
3409
3414
(
2004
).
20.
T. W.
Odom
,
V. R.
Thalladi
,
J. C.
Love
, and
G. M.
Whitesides
, “
Generation of 30-50 nm structures using easily fabricated, composite PDMS masks
,”
J. Am. Chem. Soc.
124
,
12112
12113
(
2002
).
21.
J.
Joo
,
B. Y.
Chow
, and
J. M.
Jacobson
, “
Nanoscale patterning on insulating substrates by critical energy electron beam lithography
,”
Nano Lett.
6
,
2021
2025
(
2006
).
22.
M. D.
Kelzenberg
,
S. W.
Boettcher
,
J. A.
Petykiewicz
,
D. B.
Turner-Evans
,
M. C.
Putnam
,
E. L.
Warren
,
J. M.
Spurgeon
,
R. M.
Briggs
,
N. S.
Lewis
, and
H. A.
Atwater
, “
Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications
,”
Nat. Mater.
9
,
239
244
(
2010
).
23.
C.-A.
Fustin
,
G.
Glasser
,
H. W.
Spiess
, and
U.
Jonas
, “
Site-selective growth of colloidal crystals with photonic properties on chemically patterned surfaces
,”
Adv. Mater.
15
,
1025
1028
(
2003
).
24.
J. Y.
Chen
,
J. F.
Klemic
, and
M.
Elimelech
, “
Micropatterning microscopic charge heterogeneity on flat surfaces for studying the interaction between colloidal particles and heterogeneously charged surfaces
,”
Nano Lett.
2
,
393
396
(
2002
).
25.
H. B.
Yin
,
T.
Brown
,
J. S.
Wilkinson
,
R. W.
Eason
, and
T.
Melvin
, “
Submicron patterning of DNA oligonucleotides on silicon
,”
Nucleic Acids Res.
32
,
e118a
(
2004
).
26.
W. R.
Childs
and
R. G.
Nuzzo
, “
Decal transfer microlithography: A new soft-lithographic patterning method
,”
J. Am. Chem. Soc.
124
,
13583
13596
(
2002
).
27.
A.
Balck
,
M.
Michalzik
,
L.
Al-Halabi
,
S.
Dübel
, and
S.
Büttgenbach
, “
Design and fabrication of a lab-on-a-chip for point-of-care diagnostics
,”
Sens. Transducers J.
127
,
102
111
(
2011
).
28.
T.
Ogawa
,
Y.
Takahashi
,
H.
Yang
,
K.
Kimura
,
M.
Sakurai
, and
M.
Takahashi
, “
Fabrication of Fe3O4 nanoparticle arrays via patterned template assisted self-assembly
,”
Nanotechnology
17
,
5539
5543
(
2006
).
29.
N. A.
Bernotski
,
X.
Xiong
,
K.
Wang
,
N. E.
Jewell-Larsen
, and
K. F.
Böhringer
, “
Formation of two-dimensional colloidal sphere arrays on micro-patterns
,” in
Proceedings of the 2nd Annual Conference on Foundations of Nanoscience: Self-Assembled Architectures and Devices (FNANO)
,
Snowbird, UT, USA
,
24–28 April 2005
.
30.
N. V.
Dziomkina
and
G. J.
Vancso
, “
Colloidal crystal assembly on topologically patterned templates
,”
Soft Matter
1
,
265
279
(
2005
).
31.
M.-H.
Wu
,
C.
Park
, and
G. M.
Whitesides
, “
Generation of submicrometer structures by photolithography using arrays of spherical microlenses
,”
J. Colloid Interface Sci.
265
,
304
309
(
2003
).
32.
J. L.
Graya
,
R.
Hull
, and
J. A.
Floro
, “
Periodic arrays of epitaxial self-assembled SiGe quantum dot molecules grown on patterned Si substrates
,”
J. Appl. Phys.
100
,
084312
(
2006
).
33.
B.
Päivänranta
,
T.
Saastamoinen
, and
M.
Kuittinen
, “
A wide-angle antireflection surface for the visible spectrum
,”
Nanotechnology
20
,
375301
(
2009
).
34.
E. S.
Loscar
,
R. A.
Borzi
, and
E. V.
Albano
, “
Fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media
,”
Phys. Rev. E
68
,
041106
(
2003
).
35.
Z.
Adamczyk
,
P.
Weroński
, and
E.
Musiał
, “
Colloid particle adsorption at random site (heterogeneous) surfaces
,”
J. Colloid Interface Sci.
248
,
67
75
(
2002
).
36.
Z.
Adamczyk
,
B.
Siwek
,
P.
Weroński
, and
E.
Musiał
, “
Irreversible adsorption of colloid particles at heterogeneous surfaces
,”
Appl. Surf. Sci.
196
,
250
263
(
2002
).
37.
Z.
Adamczyk
,
K.
JaszczółT
,
A.
Michna
,
B.
Siwek
,
L.
Szyk-Warszyńska
, and
M.
Zembala
, “
Irreversible adsorption of particles on heterogeneous surfaces
,”
Adv. Colloid Interface Sci.
118
,
25
42
(
2005
).
38.
X.
Jin
,
N.-H. L.
Wang
,
G.
Tarjus
, and
J.
Talbot
, “
Irreversible adsorption on nonuniform surfaces: The random site model
,”
J. Phys. Chem.
97
,
4256
4258
(
1993
).
39.
D.
Milošević
and
N. M.
Švrakić
, “
Irreversible deposition on disordered substrates
,”
J. Phys. A
26
,
L1061
L1066
(
1993
).
40.
D.
Stojiljković
,
J. R.
Šćepanović
,
S. B.
Vrhovac
, and
N. M.
Švrakić
,
J. Stat. Mech.
2015
,
P06032
.
41.
N. A. M.
Araújo
,
A.
Cadilhe
, and
V.
Privman
, “
Morphology of fine-particle monolayers deposited on nanopatterned substrates
,”
Phys. Rev. E
77
,
031603
(
2008
).
42.
M. C.
Bartelt
and
V.
Privman
, “
Kinetics of irreversible monolayer and multilayer adsorption
,”
Int. J. Mod. Phys. B
5
,
2883
2907
(
1991
).
43.
E.
Burgos
and
H.
Bonadeo
, “
On the car parking problem
,”
J. Phys. A
20
,
1193
1204
(
1987
).
44.
E. L.
Hinrichsen
,
J.
Feder
, and
T.
Jøssang
, “
Geometry of random sequential adsorption
,”
J. Stat. Phys.
44
,
793
827
(
1986
).
45.
J. W.
Evans
,
D. A.
Burgess
, and
D. K.
Hoffman
, “
Irreversible random and cooperative processes on lattices: Spatial correlations
,”
J. Math. Phys.
25
,
3051
3063
(
1984
).
46.
V.
Privman
, “
Finite-size scaling theory
,” in
Finite Size Scaling and Numerical Simulation of Statistical Systems
, edited by
V.
Privman
(
World Scientific
,
Singapore
,
1990
), Chap. I, pp.
1
98
.
47.
M. C.
Bartelt
and
V.
Privman
, “
Kinetics of irreversible adsorption of mixtures of pointlike and fixed-size particles: Exact results
,”
Phys. Rev. A
44
,
R2227
R2230
(
1991
).
48.
J.-S.
Wang
,
P.
Nielaba
, and
V.
Privman
, “
Collective effects in random sequential adsorption of diffusing hard squares
,”
Mod. Phys. Lett. B
7
,
189
196
(
1993
).
49.
J.-S.
Wang
,
P.
Nielaba
, and
V.
Privman
, “
Locally frozen defects in random sequential adsorption with diffusional relaxation
,”
Physica A
199
,
527
538
(
1993
).
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