Abstract
We study the condensations of dumbbell-like counterions onto an oppositely charged cylinder at weak and strong electrostatic coupling strengths. Performing extensive Monte Carlo simulations, we show that the condensation characteristics of the dumbbell ions can be understood by viewing dumbbell ions of length d as point ions with an effective valency depending on the radial distance r from the cylinder’s axis. In terms of the condensation behavior, dumbbell ions behave as two independent point ions if r ≪ d, but act as a single point ion with twofold valency when r ≫ d. Such a distance-dependent effective valency as a characteristic of ions of extended structures explains a unique feature in the condensed counterion fraction and heat capacity at both weak and strong coupling strengths.
Similar content being viewed by others
References
J-L. Barrat and J-F. Joanny, Adv. Chem. Phys. 94, 1 (1996).
V. A. Bloomfield, Biopolymers 31, 1471 (1991).
V. A. Bloomfield, Curr. Opin. Struct. Biol. 6, 334 (1996).
N. Grønbech-Jensen, R. J. Mashl, R. F. Bruinsma and W. M. Gelbart, Phys. Rev. Lett. 78, 2477 (1997).
R. Podgornik, D. Rau and V. A. Parsegian, Biophys. J. 66, 962 (1994).
T. E. Angelini, H. Liang, W. Wriggers and G. C. L. Wong, Proc. Natl. Acad. Sci. U.S.A. 100, 8634 (2003).
G. C. Wong et al., Science 288, 2035 (2000).
B-Y. Ha and A. J. Liu, Phys. Rev. Lett. 79, 1289 (1997).
M. L. Henle and P. A. Pincus, Phys. Rev. E 71, 060801 (2005).
M. Sayar and C. Holm, Phys. Rev. E 82, 031901 (2010).
H. Boroudjerdi et al., Phys. Rep. 416, 219 (2005).
J. W. Klein and B. R. Ware, J. Chem. Phys. 80, 1334 (1984).
A. Popov and D. A. Hoagland, J. Polym. Sci. B: Polym. Phys. 42, 3616 (2004).
N. V. Brilliantov, D. V. Kuznetsov and R. Klein, Phys. Rev. Lett. 81, 1433 (1998).
H. Schiessel and P. Pincus, Macromolecules 31, 7953 (1998).
R. Golestanian, M. Kardar and T. B. Liverpool, Phys. Rev. Lett. 82, 4456 (1999).
Y. W. Kim and W. Sung, Phys. Rev. Lett. 91, 118101 (2003).
E. Koculi, C. Hyeon, D. Thirumalai and S. A. Woodson, J. Am. Chem. Soc. 129, 2676 (2007).
E. Koculi, N-K. Lee, D. Thirumalai and S. A. Woodson, J. Mol. Biol. 341, 27 (2004).
R. M. Fuoss, A. Katchalsky and S. Lifson, Proc. Natl. Acad. Sci. U.S.A. 37, 579 (1951).
T. Alfrey, P. W. Berg and H. Morawetz, J. Polym. Sci. 7, 543 (1951).
M. Le Bret and B. H. Zimm, Biopolymers 23, 287 (1984).
G. S. Manning, J. Chem. Phys. 51, 924 (1969).
G. S. Manning, J. Chem. Phys. 51, 3249 (1969).
F. Oosawa, Polyelectrolytes (Marcel Dekker, New York, 1971).
Y. Levin, Physica A 257, 408 (1998).
A. L. Kholodenko and A. L. Beyerlein, Phys. Rev. Lett. 74, 4679 (1995)
Y. Y. Suzuki, J. Phys.: Condens. Matter 16, S2119 (2004).
A. Deshkovski, S. Obukov and M. Rubinstein, Phys. Rev. Lett. 86, 2341 (2001).
M. L. Henle, C. D. Santangelo, D. M. Patel and P. A. Pincus, Europhys. Lett. 66, 284 (2004).
B. O’Shaughnessy and Q. Yang, Phys. Rev. Lett. 94, 048302 (2005).
M. Deserno, C. Holm and S. May, Macromolecules 33, 199 (2000).
Q. Liao, A. V. Dobrynin and M. Rubinstein, Macromolecules 36, 3399 (2003).
A. Naji and R. R. Netz, Phys. Rev. Lett. 95, 185703 (2005).
A. Naji and R. R. Netz, Phys. Rev. E 73, 056105 (2006).
M. Cha, J. Yi and Y. W. Kim, Eur. Phys. J. E 40, 70 (2017).
M. Cha, J. Yi and Y. W. Kim, Sci. Rep. 7, 10551 (2017).
L. C. Gosule and J. A. Schellman, Nature 259, 333 (1976).
D. J. Needleman et al., Proc. Natl. Acad. Sci. U.S.A. 101, 16099 (2004).
J. Pelta, F. Livolant and J-L. Sikorav, J. Biol. Chem. 271, 5656 (1996).
E. Raspaud, M. O. de la Cruz, J-L. Sikorav and F. Livolant, Biophys. J. 74, 381 (1998).
J. C. Butler, T. Angelini, J. X. Tang and G. C. L. Wong, Phys. Rev. Lett. 91, 028301 (2003).
Y. W. Kim, J. Yi and P. Pincus, Phys. Rev. Lett. 101, 208305 (2008).
S. May, A. Iglic, J. Rescic, S. Maset and K. Bohinc, J. Phys. Chem. B 112, 1685 (2008).
M. Kanduc et al., J. Phys.: Condens. Matter 21, 424103 (2009).
A. Naji, M. Kanduc, J. Forsman and R. Podgornik, J. Chem. Phys. 139, 150901 (2013).
D. Dean, J. Dobnikar, A. Naji and R. Podgornik, Electrostatics of Soft and Disordered Matter (Pan Stanford Publishing, Singapore, 2014).
S. Dutta and Y. S. Jho, Phys. Rev. E 93, 012504 (2016).
M. Cha, S. Ro and Y. W. Kim, Phys. Rev. Lett. 121, 058001 (2018).
R. R. Netz and H. Orland, Eur. Phys. J. E 1, 203 (2000).
R. R. Netz, Eur. Phys. J. E 5, 557 (2001).
A. Moreira and R. R. Netz, Phys. Rev. Lett. 87, 078301 (2001).
For various polyelectrolytes, typical values of the surface charge density and the radius are given as σs = 0.17 e/nm2 (F-actin), 0.38 e/nm2 (microtubule) and R = 3.7 nm (F-actin), 12.5 nm (microtubule), which gives parameters in the range of Ξ = 0.5 ∼ 30 and ξ = 3 ∼ 60 for mono- to tri-valent counterions, respectively.
A. Moreira and R. R. Netz, Eur. Phys. J. E 8, 33 (2002).
D. Andelman, in Soft Condensed Matter Physics in Molecular and Cell Biology, edited by W. C. K. Poon and D. Andelman (Taylor & Francis, New York, 2006).
A. Naji and R. R. Netz, Eur. Phys. J. E 13, 43 (2004).
Acknowledgments
This research was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (Grant No. NRF-2020R1A2C1014826). S. R. was supported by the National Research Foundation of Korea (2019R1A6A3A03033761).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cha, M., Ro, S. & Kim, Y.W. Condensation of Rodlike Counterions on a Charged Cylinder. J. Korean Phys. Soc. 77, 811–818 (2020). https://doi.org/10.3938/jkps.77.811
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.77.811