Please wait a minute...
Acta Phys. -Chim. Sin.  2018, Vol. 34 Issue (10): 1163-1170    DOI: 10.3866/PKU.WHXB201802271
Special Issue: Molecular Simulations in Materials Science
Free Energy Change of Micelle Formation for Sodium Dodecyl Sulfate from a Dispersed State in Solution to Complete Micelles along Its Aggregation Pathways Evaluated by Chemical Species Model Combined with Molecular Dynamics Calculations
Noriyuki YOSHII1,2,*(),Mika KOMORI2,Shinji KAWADA2,Hiroaki TAKABAYASHI2,Kazushi FUJIMOTO2,Susumu OKAZAKI1,2,*()
1 Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
2 Department of Applied Chemistry, Nagoya University, Nagoya 464-8603, Japan
Download: HTML     PDF(1773KB) Export: BibTeX | EndNote (RIS)       Supporting Info


Surfactant molecules, when dispersed in solution, have been shown to spontaneously form aggregates. Our previous studies on molecular dynamics (MD) calculations have shown that ionic sodium dodecyl sulfate molecules quickly aggregated even when the aggregation number is small. The aggregation rate, however, decreased for larger aggregation numbers. In addition, studies have shown that micelle formation was not completed even after a 100 ns-long MD run (Chem. Phys. Lett. 2016, 646, 36). Herein, we analyze the free energy change of micelle formation based on chemical species model combined with molecular dynamics calculations. First, the free energy landscape of the aggregation, ΔGi+j, where two aggregates with sizes i and j associate to form the (i + j)-mer, was investigated using the free energy of micelle formation of the i-mer, Gi, which was obtained through MD calculations. The calculated ΔGi+j was negative for all the aggregations where the sum of DS ions in the two aggregates was 60 or less. From the viewpoint of chemical equilibrium, aggregation to the stable micelle is desired. Further, the free energy profile along possible aggregation pathways was investigated, starting from small aggregates and ending with the complete thermodynamically stable micelles in solution. The free energy profiles, G(l, k), of the aggregates at l-th aggregation path and k-th state were evaluated by the formation free energy $\sum\limits_i {{n_i}\left( {l, k} \right)G_i^\dagger } $ and the free energy of mixing $\sum\limits_i {{n_i}(l, k){k_B}Tln({n_i}(l, k)/n(l, k))} $, where ni(l, k) is the number of i-mer in the system at the l-th aggregation path and k-th state, with $n\left( {l, k} \right) = \sum\limits_i {{n_i}\left( {l, k} \right)} $. All the aggregation pathways were obtained from the initial state of 12 pentamers to the stable micelle with i = 60. All the calculated G(l, k) values monotonically decreased with increasing k. This indicates that there are no free energy barriers along the pathways. Hence, the slowdown is not due to the thermodynamic stability of the aggregates, but rather the kinetics that inhibit the association of the fragments. The time required for a collision between aggregates, one of the kinetic factors, was evaluated using the fast passage time, tFPT. The calculated tFPT was about 20 ns for the aggregates with N = 31. Therefore, if aggregation is a diffusion-controlled process, it should be completed within the 100 ns-simulation. However, aggregation does not occur due to the free energy barrier between the aggregates, that is, the repulsive force acting on them. This may be caused by electrostatic repulsions produced by the overlap of the electric double layers, which are formed by the negative charge of the hydrophilic groups and counter sodium ions on the surface of the aggregates.

Key wordsFree energy change      Aggregation pathway      SDS      Micelle      Molecular dynamics calculation     
Received: 25 December 2017      Published: 13 April 2018
Fund:  This work was supported by FLAGSHIP2020, MEXT within Priority Study 5 (Development of New Fundamental Technologies for High-Efficiency Energy Creation, Conversion/Storage and Use) Using Computational Resources of the K Computer Provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research Project (hp170241). This work was also funded by MEXT KAKENHI Grant Number 17K04758 (N.Y.)
Corresponding Authors: Noriyuki YOSHII,Susumu OKAZAKI     E-mail:;
Cite this article:

Noriyuki YOSHII,Mika KOMORI,Shinji KAWADA,Hiroaki TAKABAYASHI,Kazushi FUJIMOTO,Susumu OKAZAKI. Free Energy Change of Micelle Formation for Sodium Dodecyl Sulfate from a Dispersed State in Solution to Complete Micelles along Its Aggregation Pathways Evaluated by Chemical Species Model Combined with Molecular Dynamics Calculations. Acta Phys. -Chim. Sin., 2018, 34(10): 1163-1170.

URL:     OR

1 ≤ i ≤ 66 66 ≤ i ≤ 80
a0 4.11 × 10-21 7.11 × 10-21
a1 -5.51 × 10-21 -4.81 × 10-21
a2 3.73 × 10-22 1.21 × 10-22
a3 -1.73 × 10-23 -1.21 × 10-24
a4 4.24 × 10-25 4.00 × 10-27
a5 -5.31 × 10-27 -
a5 3.24 × 10-29 -
a7 -7.65 × 10-32 -
1 Tanford C. J. Phys. Chem. 1974, 78, 2469.
2 Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed. ; Academic Press: London, UK, 1992.
3 Everett, D. H. Basic Principles of Colloid Science; The Royal Society of Chemistry: London, UK, 1988.
4 Puvvada S. ; Blankschtein D. J. Chem. Phys. 1990, 92, 3710.
5 Christopher P. S. ; Oxtoby D. W. J. Chem. Phys. 2003, 118, 5665.
6 Maibaum L. ; Dinner A. R. ; Chandler D. J. Phys. Chem. B 2004, 108, 6778.
7 Yoshii N. ; Iwahashi K. ; Okazaki S. J. Chem. Phys. 2006, 124, 184901.
8 Pool R. ; Bolhuis P. G. J. Chem. Phys. 2007, 126, 244703.
9 Burov S. V. ; Shchekin A. K. J. Chem. Phys. 2010, 133, 244109.
10 Verde A. V. ; Frenkel D. Soft Matter 2010, 6, 3815.
11 Bernardino K. ; de Moura A. F. J. Phys. Chem. B 2013, 117, 7324.
12 Marrink S. J. ; Tieleman D. P. ; Mark A. E. J. Phys. Chem. B 2000, 104, 12165.
13 Lazaridis T. ; Mallik B. ; Chen Y. J. Phys. Chem. B 2005, 109, 15098.
14 Tieleman D. P. ; van der Spoel D. ; Berendsen H. J. C. J. Phys. Chem. B 2000, 104, 6380.
15 Bond P. J. ; Cuthbertson J. M. ; Deol S. S. ; Sansom M. S. P. J. Am. Chem. Soc. 2004, 126, 15948.
16 Jusufi A. ; Hynninen A.-P. ; Panagiotopoulos A. Z. J. Phys. Chem. B 2008, 112, 13783.
17 Sanders S. ; Sammalkorpi M. ; Panagiotopoulos A. Z. J. Phys. Chem. B 2012, 116, 2430.
18 Sammalkorpi M. ; Karttunen M. ; Haataja M. J. Phys. Chem. B 2007, 111, 11722.
19 Cheong D. ; Panagiotopoulos A. Z. Langmuir 2006, 22, 4076.
20 Pool R. ; Bolhuis P. G. J. Phys. Chem. B 2005, 109, 6650.
21 Pool R. ; Bolhuis P. G. Phys. Rev. Lett. 2006, 97, 018302.
22 Pool R. ; Bolhuis P. G. Phys. Chem. Chem. Phys. 2006, 8, 941.
23 Kawada S. ; Komori M. ; Fujimoto K. ; Yoshii N. ; Okazaki S. Chem. Phys. Lett. 2016, 646, 36.
24 Fujimoto K. ; Kubo Y. ; Kawada S. ; Yoshii N. ; Okazaki S. Mol. Simul. 2017, 43, 13.
25 Lifshitz I. M. ; Slyozov V. V. J. Phys. Chem. Solids 1961, 19, 35.
26 Szabo A. ; Schulten K. ; Schulten Z. J. Chem. Phys. 1980, 72, 4350.
27 Moore, W. J. Physical Chemistry, 4th ed. ; Prentice Hall, Inc. : Upper Saddle River, NJ, USA, 1972.
28 Everett D. H. Colloids Surf. 1986, 21, 41.
29 Yoshii N. ; Okazaki S. Chem. Phys. Lett. 2006, 425, 58.
30 Yoshii N. ; Okazaki S. Chem. Phys. Lett. 2006, 426, 66.
31 Aniansson E. A. G. ; Wall S. N. J. Phys. Chem. 1974, 78, 1024.
32 Kestin J. ; Sokolov M. ; Wakeham W. A. J. Phys. Chem. Ref. Data 1978, 7, 941.
33 The value obtained in Eq. (1) of Ref. 28 was used.
34 Russel W. B. ; Saville D. A. ; Schowalter W. R. Colloidal Dispersions Cambridge, UK: Cambridge University Press, 1989.
35 Kawada S. ; Fujimoto K. ; Yoshii N. ; Okazaki S. J. Chem. Phys. 2017, 147, 084903.
[1] Ping-Ping ZHOU,Xi XI,Bing-Lei SONG,Xiao-Mei PEI,Zheng-Gang CUI. Rheological Behavior of Trimeric Anionic Surfactant/Cationic Additive Mixed Systems[J]. Acta Phys. -Chim. Sin., 2016, 32(9): 2309-2317.
[2] Xing-Zhong GUO,Li DING,Huan YU,Jia-Qi SHAN,Hui YANG. Construction and Preparation Mechanism of Hierarchically Porous SiO2 Monoliths[J]. Acta Phys. -Chim. Sin., 2016, 32(7): 1727-1733.
[3] Chuan-Hong HAN,Pei-Pei GENG,Yan GUO,Xiao-Xiao CHEN,Xiao-Dong GUO,Jun-Hong ZHANG,Jie LIU,Xi-Lian WEI. Thermoresponsive Properties of a Mixed Aqueous Solution of Cationic Surfactant and Organic Acid[J]. Acta Phys. -Chim. Sin., 2016, 32(4): 863-871.
[4] Wei-Ju HAO,Jun-Qi ZHANG,Ya-Zhuo SHANG,Shou-Hong XU,Hong-Lai LIU. Preparation of Fluorescently Labeled pH-Sensitive Micelles for Controlled Drug Release[J]. Acta Phys. -Chim. Sin., 2016, 32(10): 2628-2635.
[5] Ye-Chang LU,Wen-Hong LI,Yong-Qiang ZHANG,Xue-Feng LI,Jin-Feng DONG. In-situ Viscosity of Hydrolyzed Polyacrylamides and Surfactant Worm-Like Micelle Solutions in Microscale Capillaries[J]. Acta Phys. -Chim. Sin., 2016, 32(1): 365-372.
[6] Xiao-Hong ZHANG,Hong-Yan XU,Ling-Ling GE,Rong GUO. Mixed Micelle of Surface Active Ionic Liquid Lauryl Isoquinolinium Bromide and Nonionic Surfactant Triton X-100 in Aqueous Solutions[J]. Acta Phys. -Chim. Sin., 2016, 32(1): 356-364.
[7] Hui-Yong WANG,Hong-Pei LI,Guo-Kai CUI,Zhi-Yong LI,Jian-Ji WANG. Recent Progress in Self-Assembly of Ionic Liquid Surfactants and Its Regulation and Control in Aqueous Solutions[J]. Acta Phys. -Chim. Sin., 2016, 32(1): 249-260.
[8] LIANG Ju, LAI Dan-Yu, WU Wen-Lan, LI Guo-Zhi, LI Jun-Bo, FANG Cai-Lin. Self-Assembly and Acid-Responsive Behavior of Three Amphiphilic Peptides[J]. Acta Phys. -Chim. Sin., 2015, 31(4): 722-728.
[9] DENG Yong-Hong, LIU You-Fa, ZHANG Wei-Jian, QIU Xue-Qing. Formation of Colloidal Spheres from a Lignin-Based Azo Polymer[J]. Acta Phys. -Chim. Sin., 2015, 31(3): 505-511.
[10] Yi-Xiu. HAN,Hong. ZHOU,Yong-Qiang. WEI,Yong-Jun. MEI,Hang. WANG. Effect of TBAB/KCl on Constructing Anionic Wormlike Micelles[J]. Acta Phys. -Chim. Sin., 2015, 31(11): 2124-2130.
[11] Jie. YANG,Yu-He. LI,Hai-Long. HU. Finely Controlling the Diameter of the TiO2 Nanowire Array by Micelles in the Reversed Micelle Reaction under Hydrothermal Condition[J]. Acta Phys. -Chim. Sin., 2015, 31(11): 2207-2212.
[12] XU Bo-Shen, ZHAO Ying, SHEN Xian-Liang, CONG Yue, YIN Xiu-Mei, WANG Xin-Peng, YUAN Qing, YU Nai-Sen, DONG Bin. Dissipative Particle Dynamics Simulation of Multicompartment Micelles Self-Assembled from a Blend of Triblock Copolymers and Diblock Copolymers in an Aqueous Solution[J]. Acta Phys. -Chim. Sin., 2014, 30(4): 646-653.
[13] LIU Ying, MENG Xiang-Guang, YU Wei-Feng, LI Xiao-Hong, PENG Xiao. Hydrolysis of Methyl-β-D-cellobioside Catalyzed by Functional Micelles with Glutamic Acid under Mild Conditions[J]. Acta Phys. -Chim. Sin., 2013, 29(10): 2263-2270.
[14] XIE Dan-Hua, ZHAO Jian-Xi, LIU Lin, YOU Yi, WEI Xi-Li`s\vl VE`s\vl" target="_blank" class="txt_zhaiyao">A Highly Viscoelastic Anionic Wormlike Micellar System[J]. Acta Phys. -Chim. Sin., 2013, 29(07): 1534-1540.
[15] CHEN Mei-Ling, WANG Li-Xiang, CHEN Shan-Shan, LIU Xiao-Ya. Surface Hydrophilicity of Spherical Micelle from Self-Assembly of Random Copolymer: A Dissipative Particle Dynamics Simulation[J]. Acta Phys. -Chim. Sin., 2013, 29(06): 1201-1208.