- Editors' Suggestion
- Access by Xinjiang University
Physical interpretation of the partition function for colloidal clusters
Phys. Rev. E 98, 032608 – Published 24 September, 2018
DOI: https://doi.org/10.1103/PhysRevE.98.032608
Abstract
Colloidal clusters consist of small numbers of colloidal particles bound by weak short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well described by a statistical mechanical model originally developed for molecules. To explain why this model fits experimental data so well, we derive the partition function classically, with no quantum-mechanical considerations. Then, by comparing and contrasting the derivation in particle coordinates with that in center-of-mass coordinates, we physically interpret the terms in the center-of-mass formulation, which is equivalent to the high-temperature partition function for molecules. We discuss, from a purely classical perspective, how and why cluster characteristics such as the symmetry number, moments of inertia, and vibrational frequencies affect the equilibrium probabilities.
Physics Subject Headings (PhySH)
Article Text
References (33)
- R. W. Perry, M. C. Holmes-Cerfon, M. P. Brenner, and V. N. Manoharan, Phys. Rev. Lett. 114, 228301 (2015).
- R. W. Perry and V. N. Manoharan, Soft Matter 12, 2868 (2016).
- G. Meng, N. Arkus, M. P. Brenner, and V. N. Manoharan, Science 327, 560 (2010).
- R. W. Perry, G. Meng, T. G. Dimiduk, J. Fung, and V. N. Manoharan, Faraday Discuss. 159, 211 (2012).
- S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954).
- A. Vrij, Pure Appl. Chem. 48, 471 (1976).
- H. N. W. Lekkerkerker and R. Tuinier, Colloids and the Depletion Interaction (Springer Science + Business Media, Dordrecht, 2011).
- R. S. Hoy, J. Harwayne-Gidansky, and C. S. O'Hern, Phys. Rev. E 85, 051403 (2012).
- P. J. Yunker, Z. Zhang, M. Gratale, K. Chen, and A. G. Yodh, J. Chem. Phys. 138, 12A525 (2013).
- R. S. Hoy, Phys. Rev. E 91, 012303 (2015).
- F. Calvo, J. P. K. Doye, and D. J. Wales, Nanoscale 4, 1085 (2012).
- A. Malins, S. R. Williams, J. Eggers, H. Tanaka, and C. P. Royall, J. Phys.: Condens. Matter 21, 425103 (2009).
- N. Arkus, V. N. Manoharan, and M. P. Brenner, Phys. Rev. Lett. 103, 118303 (2009).
- D. J. Wales, Chem. Phys. Chem. 11, 2491 (2010).
- R. S. Hoy and C. S. O'Hern, Phys. Rev. Lett. 105, 068001 (2010).
- N. Arkus, V. N. Manoharan, and M. P. Brenner, SIAM J. Discrete Math. 25, 1860 (2011).
- J. W. R. Morgan and D. J. Wales, Nanoscale 6, 10717 (2014).
- M. Holmes-Cerfon, SIAM Rev. 58, 229 (2016).
- Y. Kallus and M. Holmes-Cerfon, Phys. Rev. E 95, 022130 (2017).
- M. Holmes-Cerfon, Annu. Rev. Condens. Matter Phys. 8, 77 (2017).
- D. Frenkel, in Soft Condensed Matter Physics in Molecular and Cell Biology, edited by W. C. K. Poon and D. Andelman (CRC, Boca Raton, 2006), pp. 19–48.
- M. E. Cates and V. N. Manoharan, Soft Matter 11, 6538 (2015).
- J. P. Sethna, Statistical Mechanics: Entropy, Order Parameters, and Complexity (Oxford University Press, Oxford, 2006).
- M. K. Gilson and K. K. Irikura, J. Phys. Chem. B 114, 16304 (2010).
- D. R. Herschbach, H. S. Johnston, and D. Rapp, J. Chem. Phys. 31, 1652 (1959).
- S. Boresch and M. Karplus, J. Chem. Phys. 105, 5145 (1996).
- E. B. Wilson, Jr., J. Decius, and P. C. Cross, Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover, New York, 1980).
- G. Meng, J. Paulose, D. R. Nelson, and V. N. Manoharan, Science 343, 634 (2014).
- A. Wilson, Thermodynamics and Statistical Mechanics (Cambridge University Press, Cambridge, 1957).
- M. Cates, available at http://www.condmatjournalclub.org/wp- content/uploads/2012/12/JCCM_DECEMBER2012_01.pdf.
- R. W. Perry, Internal dynamics of equilibrium colloidal clusters, Ph.D. thesis, Harvard University, 2015.
- L. Hong, A. Cacciuto, E. Luijten, and S. Granick, Langmuir 24, 621 (2008).
- Q. Chen, J. K. Whitmer, S. Jiang, S. C. Bae, E. Luijten, and S. Granick, Science 331, 199 (2011).
