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Journal of Chemical Physics / Volume 136 / Issue 1 / ARTICLES / Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation
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J. Chem. Phys. 136, 014511 (2012); http://dx.doi.org/10.1063/1.3671997 (9 pages)

Free energy profiles for penetration of methane and water molecules into spherical sodium dodecyl sulfate micelles obtained using the thermodynamic integration method combined with molecular dynamics calculations

K. Fujimoto1, N. Yoshii1,2, and S. Okazaki1

1Department of Applied Chemistry, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
2Center for Computational Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

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(Received 14 October 2011; accepted 5 December 2011; published online 6 January 2012)

The free energy profiles, ΔG(r), for penetration of methane and water molecules into sodium dodecyl sulfate (SDS) micelles have been calculated as a function of distance r from the SDS micelle to the methane and water molecules, using the thermodynamic integration method combined with molecular dynamics calculations. The calculations showed that methane is about 6–12 kJ mol−1 more stable in the SDS micelle than in the water phase, and no ΔG(r) barrier is observed in the vicinity of the sulfate ions of the SDS micelle, implying that methane is easily drawn into the SDS micelle. Based on analysis of the contributions from hydrophobic groups, sulfate ions, sodium ions, and solvent water to ΔG(r), it is clear that methane in the SDS micelle is about 25 kJ mol−1 more stable than it is in the water phase because of the contribution from the solvent water itself. This can be understood by the hydrophobic effect. In contrast, methane is destabilized by 5–15 kJ mol−1 by the contribution from the hydrophobic groups of the SDS micelle because of the repulsive interactions between the methane and the crowded hydrophobic groups of the SDS. The large stabilizing effect of the solvent water is higher than the repulsion by the hydrophobic groups, driving methane to become solubilized into the SDS micelle. A good correlation was found between the distribution of cavities and the distribution of methane molecules in the micelle. The methane may move about in the SDS micelle by diffusing between cavities. In contrast, with respect to the water, ΔG(r) has a large positive value of 24–35 kJ mol−1, so water is not stabilized in the micelle. Analysis showed that the contributions change in complex ways as a function of r and cancel each other out. Reference calculations of the mean forces on a penetrating water molecule into a dodecane droplet clearly showed the same free energy behavior. The common feature is that water is less stable in the hydrophobic core than in the water phase because of the energetic disadvantage of breaking hydrogen bonds formed in the water phase. The difference between the behaviors of the SDS micelles and the dodecane droplets is found just at the interface; this is caused by the strong surface dipole moment formed by sulfate ions and sodium ions in the SDS micelles.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. METHOD
    1. Free energy profile
    2. MD calculations
    3. SDS micelle
    4. Dodecane droplet
  3. RESULTS AND DISCUSSION
    1. Mean force
    2. Free energy profile for penetration
    3. Contributions from hydrophobic groups, sulfate ions, sodium ions, and solvent water to Δ G ( r )
      1. Methane
      2. Water
    4. Methane distribution in the SDS micelle solution
  4. CONCLUSION

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KEYWORDS, PACS, and IPC

Keywords

colloids, drops, free energy, hydrogen bonds, molecular dynamics method, molecular moments, organic compounds, solvent effects, surfactants, water

PACS

  • 31.70.Dk

    Environmental and solvent effects

  • 31.15.xv

    Molecular dynamics and other numerical methods

  • 33.15.Kr

    Electric and magnetic moments (and derivatives), polarizability, and magnetic susceptibility

  • 33.15.Fm

    Bond strengths, dissociation energies

  • 82.70.Dd

    Colloids

  • 82.70.Uv

    Surfactants, micellar solutions, vesicles, lamellae, amphiphilic systems, (hydrophilic and hydrophobic interactions)

International Patent Classification (IPC)

  • B01J13/00

    Colloid chemistry, e.g. the production of colloidal materials or their solutions, not otherwise provided for; Making microcapsules or microballoons

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3671997

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (click on thumbnails to view enlargements)

FIG.1
(a) Radial number density profile, ρ(r), of SDS micelles as a function of radial distance from the center of mass of the SDS micelle (green: hydrophobic carbon atom, red: sulfur and oxygen atoms of sulfate ion, blue: water molecule, and brown: sodium ion), (b) the mean force 〈F(r)〉, and (c) the free energy profile, ΔG(r), for penetration of a methane and a water molecule to the SDS micelle as a function of radial distance from the center of mass of the SDS micelle to those of penetrating methane and water molecules (●: methane and ○: water molecule). Open squares in (c) represent data obtained by Matubayasi et al.16 Error bars in (b) and (c) represent 80% confidence intervals. See text for details.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
Cumulative average of force F(r) as a function of simulation time between SDS micelle and penetrating (a) methane and (b) water molecules at distance r = 1.5 nm. Solid and dashed lines are the results of MD calculations starting from two different initial configurations. Straight lines in (a) and (b) represent resultant averages of the mean force 〈F(r)〉.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
Contributions from hydrophobic groups (green), sulfate ions (red), sodium ions (brown), and solvent water (blue) to (a) the mean force 〈F(r)〉 and (b) the free energy profile ΔG(r) for solubilization of methane molecules into SDS micelles. Black closed circle represents the total.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.4
Schematic diagram of solubilization of methane into SDS micelles. The inset shows the number density profile ρ(r) of hydrophobic parts and water in SDS solution. The density of hydrophobic groups of SDS micelles is shown by shades of gray. Darker gray represents higher density. The black dot represents a methane molecule. The green and blue arrows represent mean forces 〈F(r)〉 arising from the hydrophobic groups and solvent water, respectively.

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.5
Contributions from hydrophobic groups (green), sulfate ions (red), sodium ions (brown), and solvent water (blue) to (a) the mean force 〈F(r)〉 and (b) the free energy profile ΔG(r) for penetration of water molecules into SDS micelles. Black open circle represents the total.

FIG.5 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.6
(a) Number density profile of a dodecane droplet solution (green: hydrophobic group; blue: water); contributions from hydrophobic groups (green) and solvent water (blue) to (b) the mean force 〈F(r)〉 and (c) the free energy profile ΔG(r) for transfer of a water molecule into a dodecane droplet. Black open circle represents the total.

FIG.6 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.7
Distribution of methane as a function of radial distance r. ● and ― were calculated from the free energy profile ΔG(r) and 15-ns MD calculations, respectively. - - - is the distribution of space that can accommodate a sphere of diameter 0.3 nm, i.e., a cavity, in the SDS micelle. All are scaled to the same value at r = 1.5 nm. The density of methane molecules per Cartesian space calculated by multiplying by the Jacobian 4πr2 is shown in the inset.

FIG.7 Download High Resolution Image (.zip file) | Export Figure to PowerPoint


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