Although impurities are unavoidable in real-world and experimental systems, most numerical studies on nucleation focus on pure (impurity-free) systems. As a result, the role of impurities in phase transitions remains poorly understood, especially for systems with complex free energy landscapes featuring one or more intermediate metastable phases. In this study, we employed Monte Carlo simulations to investigate the effects of static impurities (quenched disorder) of varying length scales and surface morphologies on the crystal nucleation mechanism and kinetics in the Gaussian core model system—a representative model for soft colloidal systems. We first explored how the nucleation free energy barrier and critical cluster size are influenced by the fraction of randomly pinned (or, static) particles (fp) and the size (np) of the pinned region or cluster. Both the nucleation free energy barrier and critical cluster size increase sharply with increasing fp but decrease as np grows for a given fraction of pinned particles, eventually approaching the homogeneous nucleation limit. On examining the impact of impurity’s surface morphology on nucleation kinetics, we observed that the nucleation barrier significantly decreases with increasing the impurity (or, seed) size with crystalline surface morphologies with body-centered cubic showing the greatest facilitation. Interestingly, seeds with random surface roughness had little effect on nucleation kinetics. In addition, the polymorphic identity of particles in the final crystalline phase is influenced by both the seed’s surface morphology and system size. This study further provides crucial insights into the intricate relationship between surface-induced local structural fluctuations and the selection of the polymorphic identity in the final crystalline phase, which is essential for understanding and controlling crystallization processes in experiments.

1.
M.
Aizenman
and
J.
Wehr
,
Phys. Rev. Lett.
62
,
2503
(
1989
).
2.
Y.
Imry
and
S.-k.
Ma
,
Phys. Rev. Lett.
35
,
1399
(
1975
).
3.
L.
Li
,
A. J.
Fijneman
,
J. A.
Kaandorp
,
J.
Aizenberg
, and
W. L.
Noorduin
,
Proc. Natl. Acad. Sci. U. S. A.
115
,
3575
(
2018
).
4.
S.
Deutschländer
,
T.
Horn
,
H.
Löwen
,
G.
Maret
, and
P.
Keim
,
Phys. Rev. Lett.
111
,
098301
(
2013
).
5.
W.
Qi
and
M.
Dijkstra
,
Soft Matter
11
,
2852
(
2015
).
6.
E. N.
Tsiok
,
D. E.
Dudalov
,
Y. D.
Fomin
, and
V. N.
Ryzhov
,
Phys. Rev. E
92
,
032110
(
2015
).
7.
E. N.
Tsiok
,
Y. D.
Fomin
,
E. A.
Gaiduk
, and
V. N.
Ryzhov
,
Phys. Rev. E
103
,
062612
(
2021
).
8.
P.
Jami
,
P.
Chaudhuri
,
C.
Dasgupta
, and
A.
Ghosal
,
Phys. Rev. E
109
,
L062101
(
2024
).
9.
D. W.
Oxtoby
,
J. Phys.: Condens. Matter
4
,
7627
(
1992
).
10.
P. G.
Debenedetti
,
Metastable Liquids: Concepts and Principles
(
Princeton University Press
,
1996
).
11.
P. R.
ten Wolde
and
D.
Frenkel
,
Science
277
,
1975
(
1997
).
12.
T.
Kawasaki
and
H.
Tanaka
,
Proc. Natl. Acad. Sci. U. S. A.
107
,
14036
(
2010
).
13.
A.
Haji-Akbari
and
P. G.
Debenedetti
,
Proc. Natl. Acad. Sci. U. S. A.
112
,
10582
(
2015
).
14.
B. P.
Bhowmik
,
P.
Chaudhuri
, and
S.
Karmakar
,
Phys. Rev. Lett.
123
,
185501
(
2019
).
15.
D.
Mandal
and
D.
Quigley
,
Soft Matter
17
,
8642
(
2021
).
16.
S. P.
Niblett
,
V. K.
de Souza
,
R. L.
Jack
, and
D. J.
Wales
,
J. Chem. Phys.
149
,
114503
(
2018
).
17.
B. P.
Bhowmik
,
R.
Das
, and
S.
Karmakar
,
J. Stat. Mech.: Theory Exp.
2016
,
074003
.
18.
C.
Brito
,
G.
Parisi
, and
F.
Zamponi
,
Soft Matter
9
,
8540
(
2013
).
19.
S.
Chakrabarty
,
S.
Karmakar
, and
C.
Dasgupta
,
Sci. Rep.
5
,
12577
(
2015
).
20.
S.
Chakrabarty
,
S.
Karmakar
, and
C.
Dasgupta
,
Proc. Natl. Acad. Sci. U. S. A.
112
,
E4819
(
2015
).
21.
S.
Chakrabarty
,
R.
Das
,
S.
Karmakar
, and
C.
Dasgupta
,
J. Chem. Phys.
145
,
034507
(
2016
).
22.
R.
Das
,
S.
Chakrabarty
, and
S.
Karmakar
,
Soft Matter
13
,
6929
(
2017
).
23.
S.
Karmakar
and
G.
Parisi
,
Proc. Natl. Acad. Sci. U. S. A.
110
,
2752
(
2013
).
24.
W.
Kob
and
L.
Berthier
,
Phys. Rev. Lett.
110
,
245702
(
2013
).
25.
Y.
Liu
,
H.
Liu
, and
H.
Peng
,
J. Non-Cryst. Solids
601
,
122052
(
2023
).
26.
M.
Ozawa
,
W.
Kob
,
A.
Ikeda
, and
K.
Miyazaki
,
Proc. Natl. Acad. Sci. U. S. A.
112
,
6914
(
2015
).
27.
B. P.
Bhowmik
,
S.
Karmakar
,
I.
Procaccia
, and
C.
Rainone
,
Phys. Rev. E
100
,
052110
(
2019
).
28.
S.
Gokhale
,
K.
Hima Nagamanasa
,
R.
Ganapathy
, and
A.
Sood
,
Nat. Commun.
5
,
4685
(
2014
).
29.
P.
Patel
and
S.
Maitra Bhattacharyya
,
J. Chem. Phys.
160
,
164501
(
2024
).
30.
E.
Anwar
,
P.
Patel
,
M.
Sharma
, and
S.
Maitra Bhattacharyya
,
J. Chem. Phys.
161
,
154501
(
2024
).
31.
D.
Kashchiev
,
Nucleation: Basic Theory with Applications
(
Butterworth-Heinemann
,
2000
).
32.
D. J.
Wales
,
Energy Landscapes: Applications to Clusters, Biomolecules and Glasses
(
Cambridge University Press
,
2003
).
33.
M. E.
Davis
and
R. F.
Lobo
,
Chem. Mater.
4
,
756
(
1992
).
34.
I.
Petrovic
,
A.
Navrotsky
,
M. E.
Davis
, and
S. I.
Zones
,
Chem. Mater.
5
,
1805
(
1993
).
35.
N. J.
Henson
,
A. K.
Cheetham
, and
J. D.
Gale
,
Chem. Mater.
6
,
1647
(
1994
).
36.
V. J.
Anderson
and
H. N. W.
Lekkerkerker
,
Nature
416
,
811
(
2002
).
37.
S. Y.
Chung
,
Y. M.
Kim
,
J. G.
Kim
, and
Y. J.
Kim
,
Nat. Phys.
5
,
68
(
2009
).
38.
R. S.
Singh
,
M.
Santra
, and
B.
Bagchi
,
J. Chem. Phys.
138
,
184507
(
2013
).
39.
R. S.
Singh
and
B.
Bagchi
,
J. Chem. Phys.
139
,
194702
(
2013
).
40.
J. C.
Palmer
,
F.
Martelli
,
Y.
Liu
,
R.
Car
,
A. Z.
Panagiotopoulos
, and
P. G.
Debenedetti
,
Nature
510
,
385
(
2014
).
41.
F.
Smallenburg
,
L.
Filion
, and
F.
Sciortino
,
Nat. Phys.
10
,
653
(
2014
).
42.
A. E. S.
Van Driessche
,
N.
Van Gerven
,
P. H. H.
Bomans
,
R. R. M.
Joosten
,
H.
Friedrich
,
D.
Gil-Carton
,
N. A. J. M.
Sommerdijk
, and
M.
Sleutel
,
Nature
556
,
89
(
2018
).
43.
A.
Cacciuto
,
S.
Auer
, and
D.
Frenkel
,
Nature
428
,
404
(
2004
).
44.
K.
Sandomirski
,
E.
Allahyarov
,
H.
Löwen
, and
S. U.
Egelhaaf
,
Soft Matter
7
,
8050
(
2011
).
45.
L.
Lupi
,
A.
Hudait
, and
V.
Molinero
,
J. Am. Chem. Soc.
136
,
3156
(
2014
).
46.
L.
Lupi
,
B.
Peters
, and
V.
Molinero
,
J. Chem. Phys.
145
,
211910
(
2016
).
47.
P.
Pedevilla
,
M.
Fitzner
,
G. C.
Sosso
, and
A.
Michaelides
,
J. Chem. Phys.
149
,
072327
(
2018
).
48.
49.
J. R.
Espinosa
,
C.
Vega
,
C.
Valeriani
,
D.
Frenkel
, and
E.
Sanz
,
Soft Matter
15
,
9625
(
2019
).
50.
N. N.
Lata
,
J.
Zhou
,
P.
Hamilton
,
M.
Larsen
,
S.
Sarupria
, and
W.
Cantrell
,
J. Phys. Chem. Lett.
11
,
8682
(
2020
).
51.
M.
Fitzner
,
P.
Pedevilla
, and
A.
Michaelides
,
Nat. Commun.
11
,
4777
(
2020
).
52.
T.
Yuan
,
R. S.
DeFever
,
J.
Zhou
,
E. C.
Cortes-Morales
, and
S.
Sarupria
,
J. Phys. Chem. B
127
,
4112
(
2023
).
53.
P. M.
Piaggi
,
A.
Selloni
,
A. Z.
Panagiotopoulos
,
R.
Car
, and
P. G.
Debenedetti
,
Faraday Discuss.
249
,
98
(
2024
).
54.
M. B.
Davies
,
M.
Fitzner
, and
A.
Michaelides
,
Proc. Natl. Acad. Sci. U. S. A.
118
,
e2025245118
(
2021
).
55.
G.
Díaz Leines
and
J.
Rogal
,
Phys. Rev. Lett.
128
,
166001
(
2022
).
56.
R.
Becker
and
W.
Döring
,
Ann. Phys.
416
,
719
(
1935
).
57.
J.
Frenkel
,
Kinetic Theory of Liquids
(
Dover
,
New York
,
1955
).
58.
C.
Desgranges
and
J.
Delhommelle
,
J. Am. Chem. Soc.
133
,
2872
(
2011
).
59.
M. H.
Nielsen
,
S.
Aloni
, and
J. J.
De Yoreo
,
Science
345
,
1158
(
2014
).
60.
M.
Sleutel
and
A. E. S.
Van Driessche
,
Proc. Natl. Acad. Sci. U. S. A.
111
,
E546
(
2014
).
61.
M.
Santra
,
R. S.
Singh
, and
B.
Bagchi
,
J. Phys. Chem. B
117
,
13154
(
2013
).
62.
R. S.
Singh
and
B.
Bagchi
,
J. Chem. Phys.
140
,
164503
(
2014
).
63.
K.
Kratzer
and
A.
Arnold
,
Soft Matter
11
,
2174
(
2015
).
64.
D.
Eaton
,
I.
Saika-Voivod
,
R. K.
Bowles
, and
P. H.
Poole
,
J. Chem. Phys.
154
,
234507
(
2021
).
65.
D.
James
,
S.
Beairsto
,
C.
Hartt
,
O.
Zavalov
,
I.
Saika-Voivod
,
R. K.
Bowles
, and
P. H.
Poole
,
J. Chem. Phys.
150
,
074501
(
2019
).
66.
M.
Fitzner
,
G. C.
Sosso
,
F.
Pietrucci
,
S.
Pipolo
, and
A.
Michaelides
,
Nat. Commun.
8
,
2257
(
2017
).
67.
A. K.
Metya
and
V.
Molinero
,
J. Am. Chem. Soc.
143
,
4607
(
2021
).
68.
M.
Fitzner
,
G. C.
Sosso
,
S. J.
Cox
, and
A.
Michaelides
,
J. Am. Chem. Soc.
137
,
13658
(
2015
).
69.
F.
Artusio
and
R.
Pisano
,
Int. J. Pharm.
547
,
190
(
2018
).
70.
H.
Barron
,
G.
Opletal
,
R.
Tilley
, and
A. S.
Barnard
,
Nanoscale
9
,
1502
(
2017
).
71.
N.
Hiranuma
,
N.
Hoffmann
,
A.
Kiselev
,
A.
Dreyer
,
K.
Zhang
,
G.
Kulkarni
,
T.
Koop
, and
O.
Möhler
,
Atmos. Chem. Phys.
14
,
2315
(
2014
).
72.
H.
Wang
,
H.-B.
Li
,
N.
Lin
,
J.
Wang
,
R.
Xu
, and
X.
Zhao
,
J. Phys. Chem. C
125
,
5056
(
2021
).
73.
P.
Grosfils
and
J. F.
Lutsko
,
Crystals
11
,
4
(
2020
).
74.
M.
Camarillo
,
J.
Oller-Iscar
,
M. M.
Conde
,
J.
Ramírez
, and
E.
Sanz
,
J. Chem. Phys.
160
,
134505
(
2024
).
75.
S. J.
Cox
,
S. M.
Kathmann
,
B.
Slater
, and
A.
Michaelides
,
J. Chem. Phys.
142
,
184704
(
2015
).
76.
F. H.
Stillinger
,
J. Chem. Phys.
65
,
3968
(
1976
).
77.
S.
Prestipino
,
F.
Saija
, and
P. V.
Giaquinta
,
Phys. Rev. E
71
,
050102
(
2005
).
78.
J.
Russo
and
H.
Tanaka
,
Soft Matter
8
,
4206
(
2012
).
79.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
(
Academic Press
,
2001
).
80.
L. A.
Fernández
,
V.
Martín-Mayor
,
B.
Seoane
, and
P.
Verrocchio
,
Phys. Rev. Lett.
108
,
165701
(
2012
).
81.
G. M.
Torrie
and
J. P.
Valleau
,
J. Comput. Phys.
23
,
187
(
1977
).
82.
P. R.
ten Wolde
,
M. J.
Ruiz-Montero
, and
D.
Frenkel
,
J. Chem. Phys.
104
,
9932
(
1996
).
83.
S.
Auer
and
D.
Frenkel
,
Adv. Polym. Sci.
173
,
149
(
2005
).
84.
P. J.
Steinhardt
,
D. R.
Nelson
, and
M.
Ronchetti
,
Phys. Rev. B
28
,
784
(
1983
).
85.
W.
Lechner
and
C.
Dellago
,
J. Chem. Phys.
129
,
114707
(
2008
).
86.
J.
Russo
and
H.
Tanaka
,
Sci. Rep.
2
,
505
(
2012
).
87.
S.
Chakrabarty
,
M.
Santra
, and
B.
Bagchi
,
Phys. Rev. Lett.
101
,
019602
(
2008
).
88.
M.
Santra
,
R. S.
Singh
, and
B.
Bagchi
,
J. Stat. Mech.: Theory Exp.
2011
,
P03017
.
89.
E.
Curcio
,
G.
Di Profio
, and
E.
Drioli
,
J. Cryst. Growth
310
,
5364
(
2008
).
90.
X.
Yao
,
Q.
Liu
,
B.
Wang
,
J.
Yu
,
M. M.
Aristov
,
C.
Shi
,
G. G.
Zhang
, and
L.
Yu
,
J. Am. Chem. Soc.
144
,
11638
(
2022
).
91.
Q.
Zhang
,
J.
Li
,
Z.
Wang
, and
J.
Wang
,
Phys. Chem. Chem. Phys.
25
,
25480
(
2023
).
92.
S.
Hussain
and
A.
Haji-Akbari
,
J. Chem. Phys.
154
,
014108
(
2021
).
93.
S.
Hussain
and
A.
Haji-Akbari
,
J. Chem. Phys.
156
,
054503
(
2022
).
94.
Y.
Chen
,
Z.
Yao
,
S.
Tang
,
H.
Tong
,
T.
Yanagishima
,
H.
Tanaka
, and
P.
Tan
,
Nat. Phys.
17
,
121
(
2021
).
95.
W.
Gispen
,
G. M.
Coli
,
R.
van Damme
,
C. P.
Royall
, and
M.
Dijkstra
,
ACS Nano
17
,
8807
(
2023
).
96.
M.
Hermes
,
E. C. M.
Vermolen
,
M. E.
Leunissen
,
D. L. J.
Vossen
,
P. D. J.
van Oostrum
,
M.
Dijkstra
, and
A.
van Blaaderen
,
Soft Matter
7
,
4623
(
2011
).
97.
T.
Sugiyama
,
K.-i.
Yuyama
, and
H.
Masuhara
,
Acc. Chem. Res.
45
,
1946
(
2012
).
98.
G. C.
Sosso
,
P.
Sudera
,
A. T.
Backes
,
T. F.
Whale
,
J.
Fröhlich-Nowoisky
,
M.
Bonn
,
A.
Michaelides
, and
E. H.
Backus
,
Chem. Sci.
13
,
5014
(
2022
).
99.
Y.
Qiu
and
V.
Molinero
,
Crystals
7
,
86
(
2017
).
You do not currently have access to this content.