The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length p in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be “switched off,” and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown that the variation in the adsorption threshold ϵwallcr with p is compatible with the predicted law ϵwallcrp1/3. In the vicinity of the adsorption threshold, the coils are still three-dimensional, and for large p, the effect of the excluded volume is almost negligible, while for strongly adsorbed chains it is always felt. Near the transition, the decay length of orientational correlations along the chain contour increases gradually from p to 2p. While the latter value is expected for strictly two-dimensional chains from the Kratky–Porod model, this model is inaccurate for the description of lateral chain dimensions of long, strongly adsorbed, semiflexible polymers due to its neglect of excluded volume. The significance of these findings for the interpretation of pertinent experiments is briefly discussed.

1.
C. J.
Fleer
,
M. A.
Cohen-Stuart
,
J. M. M.
Scheutjens
,
T.
Cosgrove
, and
B.
Vincent
,
Polymers at Interfaces
(
Chapman & Hall
,
London
,
1993
).
2.
E.
Eisenriegler
,
Polymers Near Surfaces
(
World Scientific
,
Singapore
,
1993
).
3.
P. G.
de Gennes
,
Adv. Colloid Interface Sci.
27
,
189
(
1987
).
4.
R. R.
Netz
and
D.
Andelman
,
Phys. Rep.
380
,
1
(
2003
).
5.
J.
Baschnagel
,
H.
Meyer
,
J.
Wittmer
,
I.
Kulić
,
H.
Mohrbach
,
F.
Ziebert
,
G. M.
Nam
,
N.-K.
Lee
, and
A.
Johner
,
Polymers
8
,
286
(
2016
).
6.
B.
Liu
,
S.
Salgado
,
V.
Maheshwari
, and
J.
Liu
,
Curr. Opin. Colloid Interface Sci.
26
,
41
(
2016
).
7.
R.
Sinha
,
H. L.
Frisch
, and
F. R.
Eirich
,
J. Chem. Phys.
57
,
584
(
1953
).
8.
R. J.
Rubin
,
J. Chem. Phys.
43
,
2392
(
1965
).
10.
Y.
Lépine
and
A.
Caillé
,
Can. J. Phys.
56
,
403
(
1978
).
11.
P. G.
de Gennes
,
Macromolecules
14
,
1637
(
1981
).
12.
E.
Eisenriegler
,
K.
Kremer
, and
K.
Binder
,
J. Chem. Phys.
77
,
6296
(
1982
).
13.
T.
Kreer
,
S.
Metzger
,
M.
Müller
,
K.
Binder
, and
J.
Baschnagel
,
J. Chem. Phys.
120
,
4012
(
2004
).
14.
S.
Bhattacharya
,
H.-P.
Hsu
,
A.
Milchev
,
V. G.
Rostiashvili
, and
T. A.
Vilgis
,
Macromolecules
41
,
2920
(
2008
).
15.
L. I.
Klushin
,
A. A.
Polotsky
,
H.-P.
Hsu
,
D. A.
Markelov
,
K.
Binder
, and
A. M.
Skvortsov
,
Phys. Rev. E
87
,
022604
(
2013
).
16.
A.
Grosberg
and
A. R.
Khokhlov
,
Statistical Physics of Macromolecules
(
AIP Press
,
New York
,
1994
).
17.
M.
Rubinstein
and
R. H.
Colby
,
Polymer Physics
(
Oxford University Press
,
New York
,
2003
).
18.
G. L.
Brelsford
and
W. R.
Krigbaum
,
Liquid Crystallinity in Polymers: Principles and Fundamental Properties
(
VCH Publishers
,
New York
,
1983
), p.
61
.
19.
H.-P.
Hsu
,
W.
Paul
, and
K.
Binder
,
Macromolecules
43
,
3094
(
2010
).
20.
W.
Reisner
,
J. N.
Pederson
, and
R. H.
Austin
,
Rep. Prog. Phys.
75
,
106601
(
2012
).
21.
S.
Fraden
,
Observation, Prediction, and Simulation of Phase Transitions in Complex Fluids
(
Kluwer Academic Publishers
,
Dordrecht
,
1995
), p.
113
.
22.
M.
Hase
and
K.
Yoshikawa
,
J. Chem. Phys.
124
,
104903
(
2006
).
23.
C. R.
Safinya
,
I.
Koltover
, and
J.
Raedler
,
Curr. Opin. Colloid Interface Sci.
3
,
69
(
1998
).
24.
B.
Maier
and
J. O.
Rädler
,
Phys. Rev. Lett.
82
,
1911
(
1999
).
25.
B.
Maier
and
J. O.
Rädler
,
Macromolecules
33
,
7185
(
2000
).
26.
A.
Kato
,
E.
Shindo
,
T.
Sakaue
,
A.
Tsuji
, and
K.
Yoshikawa
,
Biophys. J.
97
,
1678
(
2009
).
27.
C.
Rivetti
,
M.
Guthold
, and
C.
Bustamante
,
J. Mol. Biol.
264
,
919
(
1996
).
28.
J.
Moukhtar
,
E.
Fontaine
,
C.
Faivre-Moskalenko
, and
A.
Arneodo
,
Phys. Rev. Lett.
98
,
178101
(
2007
).
29.
K.
Rechendorff
,
G.
Witz
,
J.
Adamcik
, and
G.
Dietler
,
J. Chem. Phys.
131
,
095103
(
2009
).
30.
N.
Mücke
,
K.
Klenin
,
R.
Kirmse
,
M.
Bussiek
,
H.
Herrmann
,
M.
Hafner
, and
J.
Langowski
,
PLoS One
4
,
e7756
(
2009
).
31.
J.
Moukhtar
,
C.
Faivre-Moskalenko
,
P.
Milani
,
B.
Audit
,
C.
Vaillant
,
E.
Fontaine
,
F.
Mongelard
,
G.
Lavorel
,
P.
St-Jean
,
F.
Argoul
, and
A.
Arnoedo
,
J. Phys. Chem. B
114
,
5125
(
2010
).
32.
D.
Welch
,
M. P.
Lettinga
,
M.
Ripoll
,
Z.
Dogic
, and
G. A.
Vliegenthart
,
Soft Matter
11
,
7507
(
2015
).
33.
N.
Gunari
,
M.
Schmidt
, and
A.
Janshoff
,
Macromolecules
39
,
2219
(
2006
).
34.
M.
Sahl
,
S.
Muth
,
R.
Branscheid
,
K.
Fischer
, and
M.
Schmidt
,
Macromolecules
45
,
5167
(
2012
).
35.
K.
Binder
,
H.-J.
Butt
,
G.
Floudas
,
H.
Frey
,
H.-P.
Hsu
,
K.
Landfester
,
U.
Kolb
,
A.
Kühnle
,
M.
Maskos
,
K.
Müllen
,
W.
Paul
,
M.
Schmidt
,
H. W.
Spiess
, and
P.
Virnau
,
From Single Molecules to Nanoscopically Structured Materials
(
Springer
,
Cham
,
2014
), p.
115
.
36.
H.-P.
Hsu
,
W.
Paul
, and
K.
Binder
,
J. Phys. Chem. B
115
,
14116
(
2011
).
37.
L.
Grebikova
,
S.
Kozhuharov
,
P.
Maroni
,
A.
Mikhaylov
,
G.
Dietler
,
A. D.
Schlüter
, and
M.
Ullner
,
Nanoscale
8
,
13498
(
2016
).
38.
S. S.
Sheiko
,
B. S.
Sumerlin
, and
K.
Matyjaszewki
,
Prog. Polym. Sci.
33
,
759
(
2008
).
39.
H.-P.
Hsu
,
W.
Paul
, and
K.
Binder
,
Macromol. Theory Simul.
20
,
510
(
2011
).
40.
I. V.
Mikhailov
,
A. A.
Darinskii
,
E. B.
Zhulina
,
O. V.
Borisov
, and
F. A.
Leermakers
,
Soft Matter
11
,
9367
(
2015
).
41.
F.
Dutertre
,
K.-T.
Bang
,
B.
Loppinet
,
I.
Choi
,
T.-L.
Choi
, and
G.
Fytas
,
Macromolecules
49
,
2731
(
2016
).
42.
F.
Dutertre
,
K.-T.
Bang
,
E.
Vereroudakis
,
B.
Loppinet
,
S.
Yang
,
S.-Y.
Kang
,
G.
Fytas
, and
T.-L.
Choi
,
Macromolecules
52
,
3342
(
2019
).
43.
D.
Messmer
,
C.
Böttcher
,
H.
Yu
,
A.
Halperin
,
K.
Binder
,
M.
Kröger
, and
A. D.
Schlüter
,
ACS Nano
13
,
3466
(
2019
).
44.
Monte Carlo and Molecular Dynamics Simulations in Polymer Science
, edited by
K.
Binder
(
Oxford University Press
,
New York
,
1995
).
45.
T. M.
Birshtein
,
E. B.
Zhulina
, and
A. M.
Skvortsov
,
Biopolmyers
18
,
1171
(
1979
).
46.
A. R.
Khokhlov
,
F. F.
Ternovsky
, and
E. A.
Zheligovskaya
,
Macromol. Theory Simul.
2
,
151
(
1993
).
47.
H.-P.
Hsu
and
K.
Binder
,
Macromolecules
46
,
2496
(
2013
).
48.
A. R.
Khokhlov
and
A. N.
Semenov
,
Macromolecules
17
,
2678
(
1984
).
49.
P. J.
Flory
,
Statistical Mechanics of Chain Molecules
(
Interscience
,
New York
,
1969
).
50.
O.
Kratky
and
G.
Porod
,
J. Colloid Sci.
4
,
35
(
1949
).
51.
A. C.
Maggs
,
D. A.
Huse
, and
S.
Leibler
,
Europhys. Lett.
8
,
615
(
1989
).
52.
A. N.
Semenov
,
Eur. Phys. J. E
9
,
353
(
2002
).
53.
M.
Deng
,
Y.
Jiang
,
H.
Liang
, and
J. Z. Y.
Chen
,
J. Chem. Phys.
133
,
034902
(
2010
).
54.
T.
Odjik
,
Macromolecules
16
,
1340
(
1983
).
56.
J.
Moon
and
H.
Nakanishi
,
Phys. Rev. A
44
,
6427
(
1991
).
57.
H.-P.
Hsu
,
W.
Paul
, and
K.
Binder
,
Europhys. Lett.
92
,
28003
(
2010
).
58.
H.-P.
Hsu
,
W.
Paul
, and
K.
Binder
,
Europhys. Lett.
95
,
68004
(
2011
).
59.
A.
Huang
,
A.
Bhattacharya
, and
K.
Binder
,
J. Chem. Phys.
140
,
214902
(
2014
).
60.
A.
Huang
,
A.
Bhattacharya
, and
K.
Binder
,
J. Chem. Phys.
143
,
243102
(
2015
).
61.
J.
des Cloizeaux
and
G.
Jannink
,
Polymers in Solution: Their Modeling and Structure
(
Clarendon Press
,
Oxford
,
1990
).
62.
A.
Milchev
and
K.
Binder
,
Phys. Rev. Lett.
123
,
128003
(
2019
).
63.
L.
Schäfer
,
A.
Ostendorf
, and
J.
Hager
,
J. Phys. A: Math. Gen.
32
,
7875
(
1999
).
64.
H.
Benoit
and
P.
Doty
,
J. Phys. Chem.
57
,
958
(
1953
).
65.
J. D.
Weeks
,
D.
Chandler
, and
H. C.
Andersen
,
J. Chem. Phys.
54
,
5237
(
1971
).
66.
G. S.
Grest
and
K.
Kremer
,
Phys. Rev. A
33
,
3628
(
1986
).
67.
S. A.
Egorov
,
A.
Milchev
, and
K.
Binder
,
Phys. Rev. Lett.
116
,
187801
(
2016
).
68.
S. A.
Egorov
,
A.
Milchev
,
P.
Virnau
, and
K.
Binder
,
Soft Matter
12
,
4944
(
2016
).
69.
A.
Milchev
,
S. A.
Egorov
, and
A.
Nikoubashman
,
J. Chem. Phys.
149
,
174909
(
2018
).
70.
A.
Milchev
,
A.
Nikoubashman
, and
K.
Binder
,
Comput. Mater. Sci.
166
,
230
(
2019
).
71.
J.
Kierfeld
,
O.
Niamploy
,
V.
Sa-Yakanit
, and
R.
Lipowsky
,
Eur. Phys. J. E
14
,
17
(
2004
).
72.
T. A.
Kampmann
,
H.-H.
Boltz
, and
J.
Kierfeld
,
J. Chem. Phys.
139
,
034903
(
2013
).
73.
T. A.
Kampmann
and
J.
Kierfeld
,
J. Chem. Phys.
147
,
014901
(
2017
).
74.
S.
Naderi
and
P.
van der Schoot
,
J. Chem. Phys.
141
,
124901
(
2014
).
75.
B.
de Braaf
,
M. O.
Menegon
,
S.
Paquai
, and
P.
van Schoot
,
J. Chem. Phys.
147
,
244901
(
2017
).
76.
A. M.
Skvortsov
,
L. I.
Klushin
,
A. A.
Polotsky
, and
K.
Binder
,
Europhys. Lett.
104
,
18003
(
2013
).
77.
A.
Milchev
and
K.
Binder
,
Europhys. Lett.
106
,
58001
(
2014
).
78.
A.
Milchev
,
S. A.
Egorov
, and
K.
Binder
,
Soft Matter
10
,
5974
(
2014
).
79.
A.
Milchev
,
S. A.
Egorov
, and
K.
Binder
,
Soft Matter
13
,
1888
(
2017
).
80.
A.
Milchev
and
K.
Binder
,
Nanoletters
17
,
4924
(
2017
).
81.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulation of Liquids
, 2nd ed. (
Oxford University Press
,
Oxford
,
2017
).
82.
L.
Andersen
,
C.
Lorenz
, and
J.
Travesset
,
J. Comput. Phys.
227
,
5342
(
2008
).
83.
J.
Glaser
,
T. D.
Nguyen
,
J. A.
Anderson
,
P.
Liu
,
F.
Spiga
,
J. A.
Millan
,
D. C.
Morse
, and
S. C.
Glotzer
,
Comput. Phys. Commun.
192
,
97
(
2015
).
84.
A.
Nikoubashman
,
A.
Milchev
, and
K.
Binder
,
J. Chem. Phys.
145
,
234903
(
2016
).
85.
K.
Binder
and
D. W.
Heermann
,
Monte Carlo Simulation in Statistical Physics. An Introduction
(
Springer
,
Berlin
,
1988
).
86.
P. C.
Hohenberg
and
B. I.
Halperin
,
Rev. Mod. Phys.
49
,
435
(
1977
).
87.
N.-K.
Lee
and
A.
Johner
,
Macromolecules
48
,
7681
(
2015
).
88.
C.-T.
Lee
and
E. M.
Terentjev
,
Phys. Rev. E
100
,
032501
(
2019
).
89.
J. Z. Y.
Chen
,
Progr. Polym. Sci.
54-55
,
3
46
(
2016
).
90.
A. D.
Sokal
, in Ref. 43, Chap. 2.
91.
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