Growth transitions and critical behavior in the non-equilibrium aggregation of short, patchy nanorods
Tóm tắt
We have carried out Monte Carlo simulations to study the non-equilibrium aggregation of short patchy nanorods in two dimensions. Below a critical value of patch size (
$$p_c = 0.31675$$
), the aggregates have finite sizes with small radii of gyration,
$$R_g$$
. At
$$p_c$$
, the average radius of gyration shows a power law increase with time such that
$$\sim t^{\gamma }$$
, where
$$\gamma =0.411 \pm 0.006$$
. Above,
$$p_c$$
, the aggregates are fractal in nature and their fractal dimension depends on the value of patch size. These morphological differences are due to the fact that below the critical value of patch size (
$$p_{c}$$
), the growth of the clusters is suppressed and the system reaches an ‘absorbed state.’ Above
$$p_{c}$$
, the system reaches an ‘active state,’ in which the cluster size keeps growing with a fixed rate at long times. Thus, the system encounters a non-equilibrium phase transition. Close to the transition, the growth rate scales as
$$\varGamma (t) \sim t^{-\alpha }$$
, where
$$\alpha = 0.160 \pm 0.030$$
. The long-time growth rate varies as
$$\varGamma (\infty )\sim (p-p_c)^\beta $$
where
$$\beta = 0.279 \pm 0.034$$
. These scaling exponents indicate that the transition belongs to the directed percolation universality class. The patchy nanorods also display a threshold patch size (
$$p_{t}$$
), beyond which the long-time growth rate remains constant. We present geometric arguments for the existence of
$$p_t$$
. The fractal dimension of the aggregates increases from 1.75, at
$$p_c$$
, to 1.81, at
$$p_t$$
. It remains constant beyond
$$p_t$$
.
Tài liệu tham khảo
S.C. Glotzer, M.J. Solomon, Nat. Mat. 6, 557 (2007)
J. Yan, K. Chaudhary, S.C. Bae, J.A. Lewis, S. Granick, Nat. Comm. 4, 1516 (2013)
E. Bianchi, R. Blaak, C.N. Likos, Phys. Chem. Chem. Phys. 13, 6397 (2011)
A. Walther, A.H.E. Muller, Soft Matter 4, 663 (2008)
A. Walther, M. Drechsler, A.H.E. Muller, Soft Matter 5, 385 (2009)
S. Granick, S. Jiang, Q. Chen, Phys. Today 62, 68 (2009)
B.J. Park, T. Brugarolas, D. Lee, Soft Matter 7, 6413 (2011)
J.R. Wolters, J.E. Verweij, G. Avvisati, M. Dijkstra, W.K. Kegel, Langmuir 33, 3270 (2017)
S. Jiang, S. Granick, Langmuir 24, 2438 (2008)
C.E. Snyder, A.M. Yake, J.D. Feick, D. Velegol, Langmuir 21, 4813 (2005)
K.H. Roh, D.C. Martin, J. Lahann, J. Am. Chem. Soc. 128, 6796 (2006)
Q. Chen, J.K. Whitmer, S. Jiang, S.C. Bae, E. Luijten, S. Granick, Science 331, 119 (2011)
A.B. Pawar, I. Kretzschmar, Lagmuir 24, 355 (2008)
A.B. Pawar, I. Kretzschmar, Lagmuir 25, 9057 (2009)
C.S. Dias, N.A.M. Araujo, M.M.T. da Gama, Phys. Rev. E 87, 032308 (2013)
C.S. Dias, N.A.M. Araujo, M.M.T. da Gama, Phys. Rev. E 90, 032302 (2014)
C.S. Dias, N.A.M. Araujo, M.M.T. da Gama, Mol. Phys. 113, 1069 (2015)
M.J. Kartha, A. Sayeed, Phys. Letts. A 380, 2791 (2016)
M.J. Kartha, A.G. Banpurkar, Phys. Rev. E 94, 062108 (2016)
M.J. Kartha, Phys. Letts. A 381, 556 (2017)
W. Bol, Mol. Phys. 45, 605 (1982)
N. Kern, D. Frenkel, J. Chem. Phys. 118, 9882 (2003)
A. Giacometti, F. Lado, J. Largo, G. Pastore, F. Sciortino, J. Chem. Phys. 131, 174114 (2009)
F. Sciortino, A. Giacometti, G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)
M. Tripathy, K.S. Schweizer, J. Phys. Chem. B 117, 373 (2013)
J.L.C. Domingos, F.M. Peeters, W.P. Ferreira, Phys. Rev. E 96, 012603 (2017)
T.A. Witten, L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)
W. Sun, W. Wang, Y. Gu, X. Xu, G. Gong, Fuel 191, 106 (2017)
Y. Sawada, A. Dougherty, J.P. Gollub, Phys. Rev. Lett. 56, 1260 (1986)
H. Eba, K. Sakurai, J. Electroanal. Chem. 571, 149 (2004)
D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shraiman, C. Tang, Rev. Mod. Phys. 58, 977 (1986)
B. Gerß, N. Osterloh, S.C. Heidorn, K. Morgenstern, Cryst. Growth Des. 15, 3046 (2015)
S. Douezan, F. Brochard-Wyart, Soft Matter 8, 784 (2012)
P.L. Niemeyer, L., H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)
R.M. Brady, R. Ball, Nature 309, 225 (1984)
L. Deng, Y. Wang, Z.C.O. Yang, J. Comm. Theor. Phys 58, 895 (2012)
F.L. Braga, O.A. Mattos, V.S. Amorin, A.B. Souza, Physica A 429, 28 (2015)
Y. Iwashita, Y. Kimura, Soft Matter 9, 10694 (2013)
Y. Iwashita, Y. Kimura, Soft Matter 10, 7170 (2014)
K. Chaudhary, Q. Chen, J.J. Juarez, S. Granick, J.A. Lewis, J. Am. Chem. Soc. 134, 12901 (2012)
E.G. Noya, C. Vega, J.P.K. Doye, A.A. Louis, J. Chem. Phys. 132, 234511 (2010)
A.A. Shah, B. Schultz, K.L. Kohlstedt, S.C. Glotzer, M.J. Solomon, Langmuir 29, 4688 (2013)
T. Vissers, A.T. Brown, N. Koumakis, A. Dawson, M. Hermes, J. Schwarz-Linek, A.B. Schofield, J.M. French, V. Koutsos, J. Arlt et al., Sci. Adv. 4, 1170 (2018)
M. Jurasek, R. Vacha, Soft Matter 13, 7492 (2017)
A. Rupela, M.O. Menegon, C. Wu, P.v d Schoot, E. Grelet, Phys. Rev. Lett. 122, 128008 (2019)
D.A. Matoz-Fernandez, D.H. Linares, A.J. Ramirez-Pastor, J. Chem. Phys. 128, 214902 (2008)
D. Nieckarz, P. Szabelski, J. Phys. Chem. C 117, 11229 (2013)
W. Rzysko, D. Nieckarz, P. Szabelski, Adsorption 25, 75 (2019)
S.G. Alves, S.C. Ferreira, Phys. Rev. E 73, 051401 (2006)
I.R. Nogueira, S.G. Alves, S.C. Ferreira, Physica A 390, 4087 (2011)
S.C. Ferreira, S.G. Alves, A.F. Brito, J.G. Moreira, Phys. Rev. E 71, 051402 (2005)
W. Wang, Y. Chau, Soft Matter 5, 4893 (2009)
A. Chandra, M.K. Shukla, P.C. Mishra, S. Chandra, Phys. Rev. E 51, R2767 (1995)
J. Parkinson, K.E. Kadler, A. Brass, Phys. Rev. E 50, 2963 (1994)
J.R. Rothenbuhler, J.R. Huang, B.A. DiDonna, A.J. Levine, T.G. Mason, Soft Matter 5, 3639 (2009)
S. Tolman, P. Meakin, Phys. Rev. A 40, 428 (1989)
H.K. Janssen, Z. Physik. B: Condens. Matter 42, 151 (1981)
P. Grassberger, Z. Physik. B Condens. Matter 47, 365 (1982)
R. Ziff, E. Gulari, Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986)
M. Kohl, R.F. Capellmann, M. Laurati, S.U. Egelhaaf, M. Schmiedeberg, Nat. Commun. 7, 11817 (2016)
P. Grassberger, Math. Biosci. 63, 151 (1983)
M. Henkel, H. Hinrichsen, S. Lubeck, Non-Equilibrium Phase Transitions, vol. 1 (Springer, Berlin, 2008)
M.K. Hassan, D. Alam, Z.I. Jitu, M.M. Rahman, Phys. Rev. E 96, 050101(R) (2017)