Please wait a minute...
 物理化学学报  2018, Vol. 34 Issue (10): 1163-1170    DOI: 10.3866/PKU.WHXB201802271 所属专题： 材料科学的分子模拟
 论文
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
YOSHII Noriyuki1,2,*(),KOMORI Mika2,KAWADA Shinji2,TAKABAYASHI Hiroaki2,FUJIMOTO Kazushi2,OKAZAKI Susumu1,2,*()
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
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
 全文: PDF(1773 KB)   HTML 输出: 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.

Abstract:

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 words: Free energy change    Aggregation pathway    SDS    Micelle    Molecular dynamics calculation

 服务 把本文推荐给朋友 加入引用管理器 E-mail Alert RSS 作者相关文章 YOSHII Noriyuki KOMORI Mika KAWADA Shinji TAKABAYASHI Hiroaki FUJIMOTO Kazushi OKAZAKI Susumu

#### 引用本文:

YOSHII Noriyuki,KOMORI Mika,KAWADA Shinji,TAKABAYASHI Hiroaki,FUJIMOTO Kazushi,OKAZAKI Susumu. 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[J]. 物理化学学报, 2018, 34(10): 1163-1170.

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 Physico-Chimica Sinca, 2018, 34(10): 1163-1170.

#### 链接本文:

 Fig 1  The molecular structure of SDS. Yellow: sulfur atom, red: oxygen atom, cyan: carbon atom, gray: hydrogen atom, and blue: sodium ion. Color online. Fig 2  Δμi0 and Δμi† as a function of aggregation number i. The value of Δμi0 obtained from MD calculation is given in Ref. 7. The black solid line was obtained by fitting the polynomials $\sum\limits_{k = 0} {{a_k}{i^k}}$ to the calculated Δμi0 for two regions (1 ≤ i < 66 and 66 ≤ i ≤ 80). The red solid line shows Δμi† in Eq. (6), where the coefficient α was determined to reproduces the experimental CMC. Table 1  Fitting coefficients, ak, of Δμi0, where Δμi0 is approximated as $\Delta \mu _i^0 = \sum\limits_{k = 0} {{a_k}{i^k}}$. Fig 3  Aggregation number i dependence of Gi† -(i -1) kBT lnX1eq. Gi†: black line, Gi† -(I -1) kBTlnX1eq at 0.5CMC, CMC, and 30CMC are depicted by the blue, red and green lines, respectively. The black dashed line represents (I -1) kBT ln X1eq at CMC. Color online. Fig 4  Free energy landscape, ΔGi+j†, of formation of an (i + j)-mer from i-mer and j-mer. Fig 5  Free energy profile G(l, k) (lower plot of (a)) and Gmix(l, k) (upper plot of (a)), and ΔG(l, k) (lower plot of (b)) and ΔGmix(l, k) (upper plot of (b)) along the aggregation pathways. Note that the scales on the vertical axes are different between (a) and (b). Fig 6  Snapshot of SDS aggregates in solution at elapsed time (a) t = 0 ns, (b) 7 ns, (c) 50 ns, and (d) 100 ns. Colors for atoms are the same as in Fig. 1. Water molecules are not depicted for clarity. Fig 7  Time evolution of (a) maximum aggregation number, i, of aggregates in the independent six aggregation simulations, (b) four largest aggregation numbers for one trajectory, green line in Fig. 7a, and (c) free energy profile G(l, t) of the system evaluated by Eq. (14) for each trajectory. Results of the six independent MD runs are plotted in different colors in (a) and (c).
 1 Tanford C. J. Phys. Chem. 1974, 78, 2469. doi: 10.1021/j100617a012 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. doi: 10.1063/1.457829 5 Christopher P. S. ; Oxtoby D. W. J. Chem. Phys. 2003, 118, 5665. doi: 10.1063/1.1554394 6 Maibaum L. ; Dinner A. R. ; Chandler D. J. Phys. Chem. B 2004, 108, 6778. doi: 10.1021/jp037487t 7 Yoshii N. ; Iwahashi K. ; Okazaki S. J. Chem. Phys. 2006, 124, 184901. doi: 10.1063/1.2179074 8 Pool R. ; Bolhuis P. G. J. Chem. Phys. 2007, 126, 244703. doi: 10.1063/1.2741513 9 Burov S. V. ; Shchekin A. K. J. Chem. Phys. 2010, 133, 244109. doi: 10.1063/1.3519815 10 Verde A. V. ; Frenkel D. Soft Matter 2010, 6, 3815. doi: 10.1039/C0SM00011F 11 Bernardino K. ; de Moura A. F. J. Phys. Chem. B 2013, 117, 7324. doi: 10.1021/jp312840y 12 Marrink S. J. ; Tieleman D. P. ; Mark A. E. J. Phys. Chem. B 2000, 104, 12165. doi: 10.1021/jp001898h 13 Lazaridis T. ; Mallik B. ; Chen Y. J. Phys. Chem. B 2005, 109, 15098. doi: 10.1021/jp0516801 14 Tieleman D. P. ; van der Spoel D. ; Berendsen H. J. C. J. Phys. Chem. B 2000, 104, 6380. doi: 10.1021/jp001268f 15 Bond P. J. ; Cuthbertson J. M. ; Deol S. S. ; Sansom M. S. P. J. Am. Chem. Soc. 2004, 126, 15948. doi: 10.1021/ja044819e 16 Jusufi A. ; Hynninen A.-P. ; Panagiotopoulos A. Z. J. Phys. Chem. B 2008, 112, 13783. doi: 10.1021/jp8043225 17 Sanders S. ; Sammalkorpi M. ; Panagiotopoulos A. Z. J. Phys. Chem. B 2012, 116, 2430. doi: 10.1021/jp209207p 18 Sammalkorpi M. ; Karttunen M. ; Haataja M. J. Phys. Chem. B 2007, 111, 11722. doi: 10.1021/jp072587a 19 Cheong D. ; Panagiotopoulos A. Z. Langmuir 2006, 22, 4076. doi: 10.1021/la053511d 20 Pool R. ; Bolhuis P. G. J. Phys. Chem. B 2005, 109, 6650. doi: 10.1021/jp045576f 21 Pool R. ; Bolhuis P. G. Phys. Rev. Lett. 2006, 97, 018302. doi: 10.1103/PhysRevLett.97.018302 22 Pool R. ; Bolhuis P. G. Phys. Chem. Chem. Phys. 2006, 8, 941. doi: 10.1039/B512960E 23 Kawada S. ; Komori M. ; Fujimoto K. ; Yoshii N. ; Okazaki S. Chem. Phys. Lett. 2016, 646, 36. doi: 10.1016/j.cplett.2015.12.062 24 Fujimoto K. ; Kubo Y. ; Kawada S. ; Yoshii N. ; Okazaki S. Mol. Simul. 2017, 43, 13. doi: 10.1080/08927022.2017.1328557 25 Lifshitz I. M. ; Slyozov V. V. J. Phys. Chem. Solids 1961, 19, 35. doi: 10.1016/0022-3697(61)90054-3 26 Szabo A. ; Schulten K. ; Schulten Z. J. Chem. Phys. 1980, 72, 4350. doi: 10.1063/1.439715 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. doi: 10.1016/0166-6622(86)80081-6 29 Yoshii N. ; Okazaki S. Chem. Phys. Lett. 2006, 425, 58. doi: 10.1016/j.cplett.2006.05.004 30 Yoshii N. ; Okazaki S. Chem. Phys. Lett. 2006, 426, 66. doi: 10.1016/j.cplett.2006.05.038 31 Aniansson E. A. G. ; Wall S. N. J. Phys. Chem. 1974, 78, 1024. doi: 10.1021/j100603a016 32 Kestin J. ; Sokolov M. ; Wakeham W. A. J. Phys. Chem. Ref. Data 1978, 7, 941. doi: 10.1063/1.555581 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. doi: 10.1063/1.4998549
 [1] KABIR-UD-DIN, RUB Malik Abdul, NAQVI Andleeb Z.. 不同浓度和温度时无机盐和尿素对抗抑郁剂药物丙咪嗪盐酸盐的胶束化行为的影响[J]. 物理化学学报, 2012, 28(04): 885-891. [2] AZUM Naved, NAQVI Andleeb Z., AKRAM Mohd., KABIR-UD-DIN. 混合胶束中Gemini阳离子表面活性剂14-s-14与常规表面活性剂的协同作用: 连接臂及反离子效应[J]. 物理化学学报, 2010, 26(06): 1565-1569. [3] AKRA MMohd, ZAIDI Neelam Hazoor, KABIR-UD-DIN. 阳离子胶束对[Gr(III)-(Gly-Gly)]2+与茚三酮反应动力学的影响[J]. 物理化学学报, 2008, 24(12): 2207-2213. [4] KABIR-UD-DIN;ALI Mohd. Sajid;KHAN Zaheer. 硫酸溶液中胶束催化Ce(IV)氧化D-甘露糖[J]. 物理化学学报, 2008, 24(05): 810-816. [5] ALAMMd. Sayem;KABIR-UD-DIN. 电解质对两性药物分子盐酸氯丙嗪的胶团生长的影响[J]. 物理化学学报, 2008, 24(03): 411-415. [6] 宗晔;王宇;林昌健 . 高负载率纳米Pt-Ru/C催化剂的制备和表征[J]. 物理化学学报, 2006, 22(11): 1305-1309. [7] 倪文彬;刘天晴;郭荣. SDS对镍在HNO3/Cl-/H2O体系中电化学振荡行为的影响[J]. 物理化学学报, 2006, 22(04): 502-506. [8] 姜蓉;赵剑曦;张国城;游毅. C12-2-En-C12•2Br与SDS混合水溶液的胶团化研究[J]. 物理化学学报, 2005, 21(01): 6-9. [9] 徐建新;刘天晴;郭荣. SDS/n-C5H11OH/H2O溶致液晶中SDS分子的扩散特性[J]. 物理化学学报, 2003, 19(04): 364-367. [10] 方云;刘雪锋;夏咏梅;杨扬;蔡琨;徐廷穆;赵宪英. 稳态荧光探针法测定临界胶束聚集数[J]. 物理化学学报, 2001, 17(09): 828-831. [11] 海明潭;韩布兴;闫海科. 顺磁共振和紫外光谱法研究SDS-PEO体系的相互作用[J]. 物理化学学报, 2001, 17(04): 338-342. [12] 郭荣;范国康;刘天晴;焦新安. SDS胶束体系中亚甲蓝与血清白蛋白的相互作用[J]. 物理化学学报, 2001, 17(02): 185-188. [13] 张向东, 刘岩, 孙锦玉, 刘祁涛. 胶束溶液中某些氨基酸和二肽的解离常数[J]. 物理化学学报, 2000, 16(04): 351-355. [14] 张晓宏, 范愉, 吴世康. SDS对PEO-PPO-PEO嵌段共聚物溶液行为的影响[J]. 物理化学学报, 1999, 15(05): 390-397. [15] 张元勤, 曾宪诚, 余孝其, 田安民. SDS胶束对孔雀绿褪色反应的影响[J]. 物理化学学报, 1998, 14(02): 147-153.