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behenyl alcohol by molecular dynamics
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Journal of Industrial and Engineering Chemistry 14 (2008) 804–809 www.elsevier.com/locate/jiec
Computational simulation on steric hindrance between hydrophobic tails of lamellar matrix composed of acyl glutamate/stearyl alcohol/behenyl alcohol by molecular dynamics Dong-Sung Seo a, Jin-Chul Kim b,*, Dong-Pyo Kim a a
Department of Fine Chemical Engineering & Chemistry, Chungnam National University, Daejeon 305-764, Republic of Korea b School of Biotechnology & Bioengineering, Kangwon National University, 192-1 Hyoja 2-dong, Chunchon, Kangwon-do 200-701, Republic of Korea Received 28 February 2008; accepted 6 May 2008
Abstract Monosodium N-stearoyl-L-glutamate (MSSG), an amino acid surfactant, could associate with higher alcohols such as stearyl alcohol (SA) and behenyl alcohol (BA) and they were self-assembled into a lamella in an aqueous phase. When MSSG, SA and BA were assumed to associate each other in molar ratios of 1:1:1, 1:2:1, 1:1:2, 1:2:2 and 1:1:3, the packing parameter of each associate was calculated using molecular dynamics (MD). Among them, only 1:1:1 associate and 1:1:3 one exhibited packing parameters of around 1. According to the result of colloidal stability, however, the lamella composed of 1:1:3 associate was poorly stable while that of 1:1:1 associate was stable. In order to explain why the colloidal stability is not related to the packing parameter, the concept of steric compressibility was introduced. Steric compressibility is a measure of vertical steric hindrance occurred between hydrophobic tails of lamella. The value of steric compressibility, calculated by MD, of 1:1:1 and 1:1:3 associates were 4.7 and 8.2, respectively. That is, the vertical repulsion in the lamella of 1:1:3 associate might be greater than in the lamella of 1:1:1 associate. This would account for why the lamella of 1:1:3 associate is poorly stable even though the packing parameter is almost 1. Besides the condition that packing parameter is to be around 1, the steric compressibility of lamella should be as low as possible to achieve a stable lamella. # 2008 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. Keywords: Lamella; Molecular dynamics; Steric hindrance
1. Introduction Amphiphiles have a hydrophilic head group and a hydrophobic tails and they are called surface-active agents (surfactants). Since most of hydrophobic tails are non-polar linear hydrocarbon chains, surfactants hardly exist as an individual molecule in polar aqueous phase. When a surfactant is dissolved in polar aqueous phase, water molecules surrounding hydrophobic tails are highly ordered and the solution is thermodynamically unstable due to the low entropy of the solution. In order for surfactant molecules to be assembled by hydrophobic interaction of tails, the highly ordered water molecules are to be freed from the tails and thus the degree of freedom of water molecule increases. That is, the assembling of surfactants is an entropy-increasing process.
* Corresponding author. Tel.: +82 33 250 6561; fax: +82 33 253 6560. E-mail address: [email protected] (J.-C. Kim).
Accordingly, the assemblies are formed spontaneously and they are called self-assemblies. It was reported that the shape of selfassemblies depends on the effective volume ratio of head group to tail [1]. In general, the volume ratio is quantitatively expressed as packing parameter (P), defined as V/a0lc (V is the effective hydrocarbon volume of an amphiphilic molecule, a0 is the optimum surface area of the head group, and lc is the fully extended chain length). Amphiphiles having P < 1/3 prefer to form spherical micelles and those having 1/3 < P < 1/2, 1/ 2 < P < 1, P 1, or P > 1 prefer to form rod-like or cylindrical micelles, hexagonal or cubic vesicles, planar lamella bilayers, and inverse cylindrical aggregates, respectively. However, Kratzat and Finkelmann reported that asymmetrically branched nonionic surfactants do not follow the packing parameter model of Israelachvili [2]. In other words, even though the packing parameters are the same, the aggregates of amphiphiles may take different geometric packing shapes, depending on what kind of branched hydrocarbon tails they have. Since it is very difficult to
1226-086X/$ – see front matter # 2008 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2008.05.009
D.-S. Seo et al. / Journal of Industrial and Engineering Chemistry 14 (2008) 804–809
describe the various surfactant systems using only P value, the structural parameter (S) of Tanford is used to describe the aggregate of the nonionic surfactants with branched tails [3]. The structure parameter provides the information of the degree of asymmetry in the hydrocarbon parts of surfactant. In this study, monosodium N-stearoyl-L-glutamate (MSSG) and higher alcohols (HAs), such as stearyl alcohol (SA) and behenyl acohol (BA), were assumed to associate each other in various molar ratios, and they behave like one molecule (called MSSG/SA/BA associate). In addition, MSSG/HA associates were assumed to form bilayer structures where the hydrophobic tails of HAs act as a pseudo tail of MSSG. And then, the packing parameters of MSSG/HA associates were calculated by molecular dynamic (MD). Calculated P values could hardly be correlated with the colloidal stabilities of lamellar structures of MSSG/HA associates. As a complementary criterion, steric compressibility (Sc) was calculated to predict the colloidal stabilities. Sc is a measure of vertical steric hindrance occurred between hydrophobic tails of lamellar structures. In order to verify the calculated P value and Sc value could predict what the real systems would be, the colloidal stabilities of MSSG/HA associates were investigated. 2. Experimental 2.1. Materials Monosodium N-stearoyl-L-glutamate (MSSG, MW 435.22) was used as an acyl glutamate, and it was purchased from Ajinomoto Co. Stearyl alcohol (SA, 1-octadecanol, MW 270.48) and behenyl alcohol (BA, 1-docosanol, MW 326.61) were used as higher alcohols and they are obtained from Kokyu Alcohol Kogyo Co. Dipropylene glycol (MW 270.48), a solvent for higher alcohols, was provided by Toshin Kagaku Co. Water was doubly distilled in a Milli-Q water purification system (Millipore Corp.) until the resistivity was 18 MV/cm. All other reagents were in analytical grade. 2.2. MD simulation MD simulations were done with MSSG/SA/BA surfactant systems using DISCOVER simulation package (SGI Indigo 2). Class II consistent force field (CFF91) was employed in MD simulation and it has been successfully used in modeling of carbohydrate molecules under the influence of hydrogen bond [4,5]. Simulation conditions used in this study were summarized in Table 1. The geometry of molecules constituting lamella was optimized by conjugated gradient method. And then, periodic boundary condition was applied to two-dimensional plain. To determine the sizes and the volumes of molecules and to discover the structures of self-assemblies, we adopted hypothetical annealing process where amphiphiles exist in a molecular level at higher temperature, and then they are selfassembled during annealing process. In detail, the dimension of MSSG, and the packing parameter of MSSG/SA/BA associates were calculated under condition that system was annealed from
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Table 1 Computing conditions of MD. Computing program 2D periodic boundary System size Simulated annealing Constant temperature dynamics Computing time
Force-field, CHARM 28a3 version 40 40 Unit system: 8,832 atoms Periodic system: 22,644 atoms Unit system: 500 K ! 300 K Periodic system: 1000 K ! 300 K Unit system: 30 ps Periodic system: 70 ps Unit system: 24–48 h Periodic system: 111.82 h
500 K to 300 K, and MD was executed every 30 ps for 24–48 h. In addition, steric hindrance occurred between hydrophobic tails in lamella were calculated under the condition that system was annealed from 1000 K to 300 K, and MD was executed every 70 ps for 111.82 h. 2.3. Preparation of self-assemblies and observation of colloidal stability 0.5 g of MSSG was added to 20 g of distilled water and it was heated up to 70–80 8C. In parallel, variable amounts of SA and BA were dissolved in 30 g of dipropylene glycol, preheated to the same temperature. And then, the solution of higher alcohols was added to the solution of MSSG. The mixture containing three kinds of amphiphiles was homogenized for 10 min at 1000 rpm using a homo-mixer (HEIDOLPH, DIA 900) and it was further homogenized for 10 min using a sonicator (W-385, Heat Systems-Ultrasonics). The suspension was annealed for 12 h at room temperature. Distilled water was slowly added to the sonicated suspension so that total mass is 100 g. The solution was further homogenized at 1000 bar using a microfluidizer (Microfluidics Co., M-110EH) [6]. The colloidal stabilities of self-assemblies composed of MSSG/SA/ BA were observed at room temperature for 30 days. And the formation of lamella was confirmed by X-ray diffraction (XRD, X’pert APD, Philips).
Fig. 1. Skeleton structures of MSSG, SA and BA in vacuum box.
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3. Results and discussion 3.1. Molecular structures Fig. 1 shows the molecular structures of MSSG, SA and BA, obtained by MD simulation under vacuum box condition. MSSG is a compound obtained by condensation reaction between stearic acid and glutamate. Accordingly, it has stearoyl group (C18) as a hydrophobic hydrocarbon tail and it has two carboxylates in its head group. Head and tail are linked
though amide bond. Carboxylate (Na+ ion-attached COO ! yellow ball) is adjacent to asymmetric carbon of the amino acid residue, and carboxylic acid (hydrogenterminated COOH ! red stick) is spaced from asymmetric carbon by one ethylene group. As a result, the position of carboxylate and carboxylic acid is asymmetric with respect to the hydrocarbon tail axis. On the other hand, since the number of carbon of SA, 18, is the same as that of the tail of MSSG, the tail length of MSSG and that of SA were the same under vacuum box condition. In addition, the whole length of BA, of
Fig. 2. Dimensions necessary for the calculation of cross-sectional area of MSSG tail (a), cross-sectional area of MSSG head (b), and length of MSSG tail (c).
D.-S. Seo et al. / Journal of Industrial and Engineering Chemistry 14 (2008) 804–809
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Table 2 Packing parameters of MSSG calculated by MD with 2D grid sheet superposition. Criteria
Cross-sectional ˚ 2) area of tail (A
˚) Tail length (A
˚ 3) Tail volume (A
Cross-sectional area ˚ 2) of headgroup (A
Headgroup ˚ 3) volume (A
P
0.1 0.05 0.03 0.025
16.59 20.00 21.82 22.27
24.76 24.76 24.76 24.76
410.77 495.20 540.26 551.41
38.18 42.73 46.14 47.27
945.34 1057.99 1142.43 1170.41
0.43 0.47 0.47 0.47
which the number of carbon is 22, was the same as that of MSSG under vacuum box condition. 3.2. Dimension and packing parameter of MSSG The dimension of MSSG having a structure presented in Fig. 1 was calculated by MD, and the results are shown in Fig. 2. In subsequent, the packing parameter of MSSG was determined using the dimension. Fig. 2(a) shows dimensions necessary for the calculation of cross-sectional area of MSSG tail. The radius of a cylinder was calculated using H atom–H atom distance (distance between furthest separated two H ˚ for H, 1.79 A ˚ for C). The atoms) and van der Waals radii (1.2 A ˚ calculated radius was 2.54 A and the cross-sectional area was calculated, assuming that the tail is a cylinder. Fig. 2(b) is dimension necessary for the calculation of cross-sectional area of MSSG head. Assuming that the head is rectangle, the length of vertical side was calculated using distance between H1 ˚ for H, 1.79 A ˚ for atom–O1 atom and van der Waals radii (1.2 A ˚ C, 1.52 A for O), and the length of horizontal side was calculated using distance between O2 atom–O3 atom and the van der Waals radii. As a result of MD simulation, the lengths of ˚ and 5.29 A ˚, vertical and horizontal side were 9.17 A respectively. Fig. 2(c) represents dimensions for the calculation of length of MSSG tail. The calculated length including amide ˚ . Based on dimensions carbon (C18+1 carbon) was 24.76 A
calculated above, the packing parameter of MSSG can be calculated. Assuming that hydrophobic tail is a cylinder, the ˚ ) and the volume could be calculated using the length (24.76 A 3 ˚ ˚ radius (2.54 A) and the value was 466.67 A . Assuming that MSSG head is a rectangle, the cross-section area could be ˚ ) and horizontal calculated using vertical side length (9.17 A ˚ ˚ 2. Accordingly, side length (5.29 A), and the value was 48.51 A the packing parameter p is calculated to be 0.39. Since the packing parameter falls within the value of 1/3 < P < 1/2, MSSG would be assembled into micelles [7]. However, the calculated packing parameter is erroneous, since real geometry of MSSG head group and tail deviate from a rectangle and a cylinder, respectively. In order to make the error small, method of two-dimensional grid search was employed in MD simulation. In two-dimensional grid search, two-dimensional grid sheet is superposed onto a molecule and the number of grid point within van der Waals radii is counted. By doing that, volume and area can be calculated more accurately. The twodimensional grid search method was also applied when calculating the packing parameter of MSSG/SA/BA associates, and when calculating the longitudinal steric hindrance occurred between the ends of hydrophobic tails. Van der Waals’ interaction occurred between the model of MSSG and 10 10 size tip surface (440 tip atoms) was used to determine the crosssection areas of MSSG head and tail. That is, the cross-section areas were calculated by counting the number of tip atoms
Fig. 3. Associations of MSSG/SA (a), MSSG/BA (b) and MSSG/SA/BA (c).
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D.-S. Seo et al. / Journal of Industrial and Engineering Chemistry 14 (2008) 804–809
displaced by van der Waals interaction. Four MD simulations were done depending on the degree of atom displacement. Calculated packing parameters are shown in Table 2. When atom displacement is 0.05 or less than 0.05, the packing parameter is 0.47 and the value is constant with respect to atom displacement. Hence, the packing parameter calculated by twodimensional grid sheet superposition was 0.47. Since this value is also in the range of 1/3 < P < 1/2, MSSG is like to be assembled into micelles or hexagonals in an aqueous phase [7]. 3.3. Proposed types of association and colloidal stability To be assembled into a lamellar structure, MSSG would need a complement molecule such as higher alcohol. A complement molecule could associate with MSSG through the interaction between its head and that of MSSG. It would fill a space under the MSSG head and it could act as a pseudo tail of MSSG. As a result, the tail volume of MSSG/HA associates would be much greater than that of MSSG, while the cross-sectional area of the head of the associate being almost the same as that of MSSG. Circles in Fig. 3 represent carboxyl groups of MSSG and hydroxyl group of higher alcohol, and dotted lines indicate hydrogen bonds between carboxyl group and hydroxyl group. In association type (a), H-terminated carboxyl group of MSSG has hydrogen bond with hydroxyl group of SA, and the length of SA is the same as that of acyl group (C18) of MSSG. In association type (b), hydrogen bond occurs between Na+-attached carboxyl group of MSSG and hydroxyl group of BA, and the length of BA is the same as that of MSSG. In association type (c), H-terminated carboxyl group and Na+-attached carboxyl group of MSSG have hydrogen bonds with hydroxyl group of SA and that of BA, respectively. Among three types of associations, type (c) is the most likely to be assembled into lamellar structure, since the apparent shape is almost rectangle. To verify this hypothesis, MSSG, SA and BAwere combined in molar ratios of 1:1:1, 1:2:1, 1:1:2, 1:2:2 and 1:1:3. The corresponding colloidal suspensions were prepared as described in the Section 2.3. The colloidal stabilities of each sample were observed for 30 days and the results are shown in Table 3. The colloid was stable at room temperature for 30 days when the molar ratio of MSG/SA/BA was 1:1:1. The other combinations resulted in precipitation
Table 3 Stability of MSSG/SA/BA suspensions. Days
1 2 3 5 7 10 20 30
Molar ratios of MSSG/SA/BA 1:1:1
1:1:2
1:2:1
1:2:2
1:1:3
S S S S S S S S
S S S S U – – –
S S S S S S U –
S S S U – – – –
S S U – – – – –
S, stable and translucent; U, precipitation; –, the same as above or precipitate increases.
Fig. 4. X-ray diffraction of MSSG/SA/BA (1:1:1) suspension.
for the same period. The stability was in the order of 1:1:1 > 1:2:1 > 1:1:2 > 1:2:2 > 1:1:3. 3.4. X-ray diffraction Fig. 4 shows XRD peak of the colloidal suspension, of which the molar ratio is 1:1:1. A strong peak was observed at 2u of 21.558. This value corresponds to d-spacing of 0.4124 nm. It was reported that lamellar structure composed of higher alcohol and surfactant exhibited a strong peak around 2u of 21.48 [8]. This peak is due to d-spacing between oxygen–oxygen atoms of hydroxyl groups, when the two kinds of amphiphiles form a lamellar structure. Accordingly, it is believed that the combination of MSSG, SA and HA in molar of 1:1:1 led to the formation of lamellar structures. Similar XRDs were obtained with the other combination, indicating that all the combinations in Table 3 could form a lamellar structure. 3.5. Packing parameters of MSSG/SA/BA associates As shown in Table 3, the colloidal stability was quite different depending on the combinations. To illuminate those phenomena, the packing parameters of associates with several combination ratios were calculated by MD simulation and the results are shown in Table 4. When molar ratio was 1:1:1, the packing parameter was 0.98. The value was the closest to 1 among the combinations. In fact, the 1:1:1 combination was the most stable among the samples tested. In case molar ratio was 1:1:3, the packing parameter was almost the same as that of the combination of 1:1:1 but the colloidal stability was the worst. When molar ratio was 1:2:1, the packing parameter deviated the Table 4 Packing parameters of MSSG/SA/BA associates. ˚ 3) (A
Molar ratios
Vtotal
1:1:1 1:1:2 1:2:1 1:2:2 1:1:3
17626.58 12351.00 18239.09 15328.19 10712.16
tail
atotal
head
829.89 538.79 600.78 542.37 529.13
˚ 2) (A
˚) ltail (A
Pa
21.63 20.68 21.12 21.50 20.86
0.98 1.11 1.44 1.31 0.97
Vtotal tails, tail volume of associate; atotal head, cross-sectional head area of associate; ltail, tail length of associate; Pa, packing parameter of associate.
D.-S. Seo et al. / Journal of Industrial and Engineering Chemistry 14 (2008) 804–809 Table 5 Steric compressibility of lamella composed of MSSG/SA/BA associates.
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most from 1 but the colloidal stability ranked the second. Therefore, there seems to be no good correlation between packing parameter and colloidal stability.
lamella of 1:1:1 associate. This would account for why the lamella of 1:1:3 associate is poorly stable even though the packing parameter of 1:1:3 associate is almost 1. On the other hand, the packing parameter of 1:2:1 associate, 1.44, was much greater than 1 but the Sc value was secondly low. The lower Sc value could account for why the lamella of 1:2:1 associate is quite stable despite of its greater packing parameter. Following the above results, the integral stability of lamellar structures would depend on not only the packing parameter of molecular associate but also the vertical steric compressibility of lamella, which is composed of molecular associate. In order to achieve a stable bilayer, the packing parameter of molecular associate is to be close to 1 and the steric compressibility of bilayers is as low as possible. 1:1:1 associate could meet two criteria for stable lamellar structure.
3.6. Steric compressibility
4. Conclusions
To explain conflicting phenomena (the colloidal stability strongly depends on the molar ratio of associates but it is not directly related to the packing parameter), the concept of ‘‘steric compressibility’’ was introduced. Steric compressibility (Sc) is defined as follows:
Monosodium N-stearoyl-L-glutamate (MSSG), an amino acid surfactant, could associate with higher alcohols such as stearyl alcohol (SA) and behenyl alcohol (BA) to form lamella in an aqueous phase. The integral stability of lamellar structures would depend on not only the packing parameter of MSSG/SA/ BA associate but also the vertical steric compressibility of lamella. Accordingly, the steric compressibility, along with packing parameter, could be used to predict the colloidal stability of lamella.
Molar ratios
Pa
˚) lass (A
˚) lfix (A
˚) Dl (A
Sc (%)
1:1:1 1:1:2 1:2:1 1:2:2 1:1:3
0.98 1.11 1.44 1.31 0.97
22.65 22.64 22.33 22.65 22.79
21.63 20.68 21.12 20.68 21.06
1.02 1.96 1.21 1.97 0.73
4.72 9.48 5.73 9.53 8.21
Pa, packing parameter of associate; lass: tail length of associate; lfix, tail length of MSSG in associate; Dl, difference in tail length (lass lfix); Sc, steric compressibility.
steric compressibility ðSc ; %Þ ¼
associated tail length fixed tail length 100 fixed tail length
where, fixed tail length is the tail length of MSSG in MSSG/SA/ BA associate, and associated tail length is the tail length of MSSG/SA/BA associate. Accordingly, Sc is a measure of vertical steric hindrance occurred between hydrophobic tails of lamellar structure. Due to the difference in the tail length of amphiphiles, which constitute a lamellar structure, a vertical repulsion force could be developed, leading to the destabilization of the lamella. Sc of a lamella composed of MSSG/SA/BA associates was calculated by MD simulation and the results are summarized in Table 5. The packing parameters of 1:1:1 and 1:1:3 associates are almost 1 (Table 4). However, the Sc values of 1:1:1 and 1:1:3 associates in lamella are 4.7 and 8.2, respectively (Table 5). It means that the vertical repulsion in the lamella of 1:1:3 associate might be greater than in the
References [1] (a) J.N. Israelachvili, D.J. Mitchell, B.W. Ninham, J. Chem. Soc. Faraday Trans. 72 (1976) 1525; (b) J.Y. Kim, Y.H. Park, J.S. Kim, K.T. Lim, Y.T. Jeong, J. Ind. Eng. Chem. 13 (2007) 1023. [2] K. Kratzat, H. Finkelmann, J. Colloid Interface Sci. 181 (1996) 542. [3] C. Tanford, The Hydrophobic Effect, Wiley–Interscience, New York, 1973. [4] J.R. Maple, M.J. Hwang, T.P. Stockfish, U. Dinur, M. Waldman, C.S. Ewing, A.T. Hagler, J. Comput. Chem. 15 (1994) 162. [5] J.R. Maple, U. Dinur, A.T. Hagler, Proc. Natl. Acad. Sci. 85 (1988) 5350. [6] K.-C. Kang, H.-B. Pyo, J.-D. Lee, N.-H. Jeong, J. Ind. Eng. Chem. 10 (2004) 4. [7] J.N. Israelachvili, Colloids Surf. A: Physicochem. Eng. 91 (1994) 1. [8] S. Fukushima, M. Yamaguchi, F. Harusawa, J. Colloid Interface Sci. 59 (1977) 159.
Journal of Industrial and Engineering Chemistry 14 (2008) 804–809 www.elsevier.com/locate/jiec
Computational simulation on steric hindrance between hydrophobic tails of lamellar matrix composed of acyl glutamate/stearyl alcohol/behenyl alcohol by molecular dynamics Dong-Sung Seo a, Jin-Chul Kim b,*, Dong-Pyo Kim a a
Department of Fine Chemical Engineering & Chemistry, Chungnam National University, Daejeon 305-764, Republic of Korea b School of Biotechnology & Bioengineering, Kangwon National University, 192-1 Hyoja 2-dong, Chunchon, Kangwon-do 200-701, Republic of Korea Received 28 February 2008; accepted 6 May 2008
Abstract Monosodium N-stearoyl-L-glutamate (MSSG), an amino acid surfactant, could associate with higher alcohols such as stearyl alcohol (SA) and behenyl alcohol (BA) and they were self-assembled into a lamella in an aqueous phase. When MSSG, SA and BA were assumed to associate each other in molar ratios of 1:1:1, 1:2:1, 1:1:2, 1:2:2 and 1:1:3, the packing parameter of each associate was calculated using molecular dynamics (MD). Among them, only 1:1:1 associate and 1:1:3 one exhibited packing parameters of around 1. According to the result of colloidal stability, however, the lamella composed of 1:1:3 associate was poorly stable while that of 1:1:1 associate was stable. In order to explain why the colloidal stability is not related to the packing parameter, the concept of steric compressibility was introduced. Steric compressibility is a measure of vertical steric hindrance occurred between hydrophobic tails of lamella. The value of steric compressibility, calculated by MD, of 1:1:1 and 1:1:3 associates were 4.7 and 8.2, respectively. That is, the vertical repulsion in the lamella of 1:1:3 associate might be greater than in the lamella of 1:1:1 associate. This would account for why the lamella of 1:1:3 associate is poorly stable even though the packing parameter is almost 1. Besides the condition that packing parameter is to be around 1, the steric compressibility of lamella should be as low as possible to achieve a stable lamella. # 2008 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. Keywords: Lamella; Molecular dynamics; Steric hindrance
1. Introduction Amphiphiles have a hydrophilic head group and a hydrophobic tails and they are called surface-active agents (surfactants). Since most of hydrophobic tails are non-polar linear hydrocarbon chains, surfactants hardly exist as an individual molecule in polar aqueous phase. When a surfactant is dissolved in polar aqueous phase, water molecules surrounding hydrophobic tails are highly ordered and the solution is thermodynamically unstable due to the low entropy of the solution. In order for surfactant molecules to be assembled by hydrophobic interaction of tails, the highly ordered water molecules are to be freed from the tails and thus the degree of freedom of water molecule increases. That is, the assembling of surfactants is an entropy-increasing process.
* Corresponding author. Tel.: +82 33 250 6561; fax: +82 33 253 6560. E-mail address: [email protected] (J.-C. Kim).
Accordingly, the assemblies are formed spontaneously and they are called self-assemblies. It was reported that the shape of selfassemblies depends on the effective volume ratio of head group to tail [1]. In general, the volume ratio is quantitatively expressed as packing parameter (P), defined as V/a0lc (V is the effective hydrocarbon volume of an amphiphilic molecule, a0 is the optimum surface area of the head group, and lc is the fully extended chain length). Amphiphiles having P < 1/3 prefer to form spherical micelles and those having 1/3 < P < 1/2, 1/ 2 < P < 1, P 1, or P > 1 prefer to form rod-like or cylindrical micelles, hexagonal or cubic vesicles, planar lamella bilayers, and inverse cylindrical aggregates, respectively. However, Kratzat and Finkelmann reported that asymmetrically branched nonionic surfactants do not follow the packing parameter model of Israelachvili [2]. In other words, even though the packing parameters are the same, the aggregates of amphiphiles may take different geometric packing shapes, depending on what kind of branched hydrocarbon tails they have. Since it is very difficult to
1226-086X/$ – see front matter # 2008 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2008.05.009
D.-S. Seo et al. / Journal of Industrial and Engineering Chemistry 14 (2008) 804–809
describe the various surfactant systems using only P value, the structural parameter (S) of Tanford is used to describe the aggregate of the nonionic surfactants with branched tails [3]. The structure parameter provides the information of the degree of asymmetry in the hydrocarbon parts of surfactant. In this study, monosodium N-stearoyl-L-glutamate (MSSG) and higher alcohols (HAs), such as stearyl alcohol (SA) and behenyl acohol (BA), were assumed to associate each other in various molar ratios, and they behave like one molecule (called MSSG/SA/BA associate). In addition, MSSG/HA associates were assumed to form bilayer structures where the hydrophobic tails of HAs act as a pseudo tail of MSSG. And then, the packing parameters of MSSG/HA associates were calculated by molecular dynamic (MD). Calculated P values could hardly be correlated with the colloidal stabilities of lamellar structures of MSSG/HA associates. As a complementary criterion, steric compressibility (Sc) was calculated to predict the colloidal stabilities. Sc is a measure of vertical steric hindrance occurred between hydrophobic tails of lamellar structures. In order to verify the calculated P value and Sc value could predict what the real systems would be, the colloidal stabilities of MSSG/HA associates were investigated. 2. Experimental 2.1. Materials Monosodium N-stearoyl-L-glutamate (MSSG, MW 435.22) was used as an acyl glutamate, and it was purchased from Ajinomoto Co. Stearyl alcohol (SA, 1-octadecanol, MW 270.48) and behenyl alcohol (BA, 1-docosanol, MW 326.61) were used as higher alcohols and they are obtained from Kokyu Alcohol Kogyo Co. Dipropylene glycol (MW 270.48), a solvent for higher alcohols, was provided by Toshin Kagaku Co. Water was doubly distilled in a Milli-Q water purification system (Millipore Corp.) until the resistivity was 18 MV/cm. All other reagents were in analytical grade. 2.2. MD simulation MD simulations were done with MSSG/SA/BA surfactant systems using DISCOVER simulation package (SGI Indigo 2). Class II consistent force field (CFF91) was employed in MD simulation and it has been successfully used in modeling of carbohydrate molecules under the influence of hydrogen bond [4,5]. Simulation conditions used in this study were summarized in Table 1. The geometry of molecules constituting lamella was optimized by conjugated gradient method. And then, periodic boundary condition was applied to two-dimensional plain. To determine the sizes and the volumes of molecules and to discover the structures of self-assemblies, we adopted hypothetical annealing process where amphiphiles exist in a molecular level at higher temperature, and then they are selfassembled during annealing process. In detail, the dimension of MSSG, and the packing parameter of MSSG/SA/BA associates were calculated under condition that system was annealed from
805
Table 1 Computing conditions of MD. Computing program 2D periodic boundary System size Simulated annealing Constant temperature dynamics Computing time
Force-field, CHARM 28a3 version 40 40 Unit system: 8,832 atoms Periodic system: 22,644 atoms Unit system: 500 K ! 300 K Periodic system: 1000 K ! 300 K Unit system: 30 ps Periodic system: 70 ps Unit system: 24–48 h Periodic system: 111.82 h
500 K to 300 K, and MD was executed every 30 ps for 24–48 h. In addition, steric hindrance occurred between hydrophobic tails in lamella were calculated under the condition that system was annealed from 1000 K to 300 K, and MD was executed every 70 ps for 111.82 h. 2.3. Preparation of self-assemblies and observation of colloidal stability 0.5 g of MSSG was added to 20 g of distilled water and it was heated up to 70–80 8C. In parallel, variable amounts of SA and BA were dissolved in 30 g of dipropylene glycol, preheated to the same temperature. And then, the solution of higher alcohols was added to the solution of MSSG. The mixture containing three kinds of amphiphiles was homogenized for 10 min at 1000 rpm using a homo-mixer (HEIDOLPH, DIA 900) and it was further homogenized for 10 min using a sonicator (W-385, Heat Systems-Ultrasonics). The suspension was annealed for 12 h at room temperature. Distilled water was slowly added to the sonicated suspension so that total mass is 100 g. The solution was further homogenized at 1000 bar using a microfluidizer (Microfluidics Co., M-110EH) [6]. The colloidal stabilities of self-assemblies composed of MSSG/SA/ BA were observed at room temperature for 30 days. And the formation of lamella was confirmed by X-ray diffraction (XRD, X’pert APD, Philips).
Fig. 1. Skeleton structures of MSSG, SA and BA in vacuum box.
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3. Results and discussion 3.1. Molecular structures Fig. 1 shows the molecular structures of MSSG, SA and BA, obtained by MD simulation under vacuum box condition. MSSG is a compound obtained by condensation reaction between stearic acid and glutamate. Accordingly, it has stearoyl group (C18) as a hydrophobic hydrocarbon tail and it has two carboxylates in its head group. Head and tail are linked
though amide bond. Carboxylate (Na+ ion-attached COO ! yellow ball) is adjacent to asymmetric carbon of the amino acid residue, and carboxylic acid (hydrogenterminated COOH ! red stick) is spaced from asymmetric carbon by one ethylene group. As a result, the position of carboxylate and carboxylic acid is asymmetric with respect to the hydrocarbon tail axis. On the other hand, since the number of carbon of SA, 18, is the same as that of the tail of MSSG, the tail length of MSSG and that of SA were the same under vacuum box condition. In addition, the whole length of BA, of
Fig. 2. Dimensions necessary for the calculation of cross-sectional area of MSSG tail (a), cross-sectional area of MSSG head (b), and length of MSSG tail (c).
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Table 2 Packing parameters of MSSG calculated by MD with 2D grid sheet superposition. Criteria
Cross-sectional ˚ 2) area of tail (A
˚) Tail length (A
˚ 3) Tail volume (A
Cross-sectional area ˚ 2) of headgroup (A
Headgroup ˚ 3) volume (A
P
0.1 0.05 0.03 0.025
16.59 20.00 21.82 22.27
24.76 24.76 24.76 24.76
410.77 495.20 540.26 551.41
38.18 42.73 46.14 47.27
945.34 1057.99 1142.43 1170.41
0.43 0.47 0.47 0.47
which the number of carbon is 22, was the same as that of MSSG under vacuum box condition. 3.2. Dimension and packing parameter of MSSG The dimension of MSSG having a structure presented in Fig. 1 was calculated by MD, and the results are shown in Fig. 2. In subsequent, the packing parameter of MSSG was determined using the dimension. Fig. 2(a) shows dimensions necessary for the calculation of cross-sectional area of MSSG tail. The radius of a cylinder was calculated using H atom–H atom distance (distance between furthest separated two H ˚ for H, 1.79 A ˚ for C). The atoms) and van der Waals radii (1.2 A ˚ calculated radius was 2.54 A and the cross-sectional area was calculated, assuming that the tail is a cylinder. Fig. 2(b) is dimension necessary for the calculation of cross-sectional area of MSSG head. Assuming that the head is rectangle, the length of vertical side was calculated using distance between H1 ˚ for H, 1.79 A ˚ for atom–O1 atom and van der Waals radii (1.2 A ˚ C, 1.52 A for O), and the length of horizontal side was calculated using distance between O2 atom–O3 atom and the van der Waals radii. As a result of MD simulation, the lengths of ˚ and 5.29 A ˚, vertical and horizontal side were 9.17 A respectively. Fig. 2(c) represents dimensions for the calculation of length of MSSG tail. The calculated length including amide ˚ . Based on dimensions carbon (C18+1 carbon) was 24.76 A
calculated above, the packing parameter of MSSG can be calculated. Assuming that hydrophobic tail is a cylinder, the ˚ ) and the volume could be calculated using the length (24.76 A 3 ˚ ˚ radius (2.54 A) and the value was 466.67 A . Assuming that MSSG head is a rectangle, the cross-section area could be ˚ ) and horizontal calculated using vertical side length (9.17 A ˚ ˚ 2. Accordingly, side length (5.29 A), and the value was 48.51 A the packing parameter p is calculated to be 0.39. Since the packing parameter falls within the value of 1/3 < P < 1/2, MSSG would be assembled into micelles [7]. However, the calculated packing parameter is erroneous, since real geometry of MSSG head group and tail deviate from a rectangle and a cylinder, respectively. In order to make the error small, method of two-dimensional grid search was employed in MD simulation. In two-dimensional grid search, two-dimensional grid sheet is superposed onto a molecule and the number of grid point within van der Waals radii is counted. By doing that, volume and area can be calculated more accurately. The twodimensional grid search method was also applied when calculating the packing parameter of MSSG/SA/BA associates, and when calculating the longitudinal steric hindrance occurred between the ends of hydrophobic tails. Van der Waals’ interaction occurred between the model of MSSG and 10 10 size tip surface (440 tip atoms) was used to determine the crosssection areas of MSSG head and tail. That is, the cross-section areas were calculated by counting the number of tip atoms
Fig. 3. Associations of MSSG/SA (a), MSSG/BA (b) and MSSG/SA/BA (c).
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displaced by van der Waals interaction. Four MD simulations were done depending on the degree of atom displacement. Calculated packing parameters are shown in Table 2. When atom displacement is 0.05 or less than 0.05, the packing parameter is 0.47 and the value is constant with respect to atom displacement. Hence, the packing parameter calculated by twodimensional grid sheet superposition was 0.47. Since this value is also in the range of 1/3 < P < 1/2, MSSG is like to be assembled into micelles or hexagonals in an aqueous phase [7]. 3.3. Proposed types of association and colloidal stability To be assembled into a lamellar structure, MSSG would need a complement molecule such as higher alcohol. A complement molecule could associate with MSSG through the interaction between its head and that of MSSG. It would fill a space under the MSSG head and it could act as a pseudo tail of MSSG. As a result, the tail volume of MSSG/HA associates would be much greater than that of MSSG, while the cross-sectional area of the head of the associate being almost the same as that of MSSG. Circles in Fig. 3 represent carboxyl groups of MSSG and hydroxyl group of higher alcohol, and dotted lines indicate hydrogen bonds between carboxyl group and hydroxyl group. In association type (a), H-terminated carboxyl group of MSSG has hydrogen bond with hydroxyl group of SA, and the length of SA is the same as that of acyl group (C18) of MSSG. In association type (b), hydrogen bond occurs between Na+-attached carboxyl group of MSSG and hydroxyl group of BA, and the length of BA is the same as that of MSSG. In association type (c), H-terminated carboxyl group and Na+-attached carboxyl group of MSSG have hydrogen bonds with hydroxyl group of SA and that of BA, respectively. Among three types of associations, type (c) is the most likely to be assembled into lamellar structure, since the apparent shape is almost rectangle. To verify this hypothesis, MSSG, SA and BAwere combined in molar ratios of 1:1:1, 1:2:1, 1:1:2, 1:2:2 and 1:1:3. The corresponding colloidal suspensions were prepared as described in the Section 2.3. The colloidal stabilities of each sample were observed for 30 days and the results are shown in Table 3. The colloid was stable at room temperature for 30 days when the molar ratio of MSG/SA/BA was 1:1:1. The other combinations resulted in precipitation
Table 3 Stability of MSSG/SA/BA suspensions. Days
1 2 3 5 7 10 20 30
Molar ratios of MSSG/SA/BA 1:1:1
1:1:2
1:2:1
1:2:2
1:1:3
S S S S S S S S
S S S S U – – –
S S S S S S U –
S S S U – – – –
S S U – – – – –
S, stable and translucent; U, precipitation; –, the same as above or precipitate increases.
Fig. 4. X-ray diffraction of MSSG/SA/BA (1:1:1) suspension.
for the same period. The stability was in the order of 1:1:1 > 1:2:1 > 1:1:2 > 1:2:2 > 1:1:3. 3.4. X-ray diffraction Fig. 4 shows XRD peak of the colloidal suspension, of which the molar ratio is 1:1:1. A strong peak was observed at 2u of 21.558. This value corresponds to d-spacing of 0.4124 nm. It was reported that lamellar structure composed of higher alcohol and surfactant exhibited a strong peak around 2u of 21.48 [8]. This peak is due to d-spacing between oxygen–oxygen atoms of hydroxyl groups, when the two kinds of amphiphiles form a lamellar structure. Accordingly, it is believed that the combination of MSSG, SA and HA in molar of 1:1:1 led to the formation of lamellar structures. Similar XRDs were obtained with the other combination, indicating that all the combinations in Table 3 could form a lamellar structure. 3.5. Packing parameters of MSSG/SA/BA associates As shown in Table 3, the colloidal stability was quite different depending on the combinations. To illuminate those phenomena, the packing parameters of associates with several combination ratios were calculated by MD simulation and the results are shown in Table 4. When molar ratio was 1:1:1, the packing parameter was 0.98. The value was the closest to 1 among the combinations. In fact, the 1:1:1 combination was the most stable among the samples tested. In case molar ratio was 1:1:3, the packing parameter was almost the same as that of the combination of 1:1:1 but the colloidal stability was the worst. When molar ratio was 1:2:1, the packing parameter deviated the Table 4 Packing parameters of MSSG/SA/BA associates. ˚ 3) (A
Molar ratios
Vtotal
1:1:1 1:1:2 1:2:1 1:2:2 1:1:3
17626.58 12351.00 18239.09 15328.19 10712.16
tail
atotal
head
829.89 538.79 600.78 542.37 529.13
˚ 2) (A
˚) ltail (A
Pa
21.63 20.68 21.12 21.50 20.86
0.98 1.11 1.44 1.31 0.97
Vtotal tails, tail volume of associate; atotal head, cross-sectional head area of associate; ltail, tail length of associate; Pa, packing parameter of associate.
D.-S. Seo et al. / Journal of Industrial and Engineering Chemistry 14 (2008) 804–809 Table 5 Steric compressibility of lamella composed of MSSG/SA/BA associates.
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most from 1 but the colloidal stability ranked the second. Therefore, there seems to be no good correlation between packing parameter and colloidal stability.
lamella of 1:1:1 associate. This would account for why the lamella of 1:1:3 associate is poorly stable even though the packing parameter of 1:1:3 associate is almost 1. On the other hand, the packing parameter of 1:2:1 associate, 1.44, was much greater than 1 but the Sc value was secondly low. The lower Sc value could account for why the lamella of 1:2:1 associate is quite stable despite of its greater packing parameter. Following the above results, the integral stability of lamellar structures would depend on not only the packing parameter of molecular associate but also the vertical steric compressibility of lamella, which is composed of molecular associate. In order to achieve a stable bilayer, the packing parameter of molecular associate is to be close to 1 and the steric compressibility of bilayers is as low as possible. 1:1:1 associate could meet two criteria for stable lamellar structure.
3.6. Steric compressibility
4. Conclusions
To explain conflicting phenomena (the colloidal stability strongly depends on the molar ratio of associates but it is not directly related to the packing parameter), the concept of ‘‘steric compressibility’’ was introduced. Steric compressibility (Sc) is defined as follows:
Monosodium N-stearoyl-L-glutamate (MSSG), an amino acid surfactant, could associate with higher alcohols such as stearyl alcohol (SA) and behenyl alcohol (BA) to form lamella in an aqueous phase. The integral stability of lamellar structures would depend on not only the packing parameter of MSSG/SA/ BA associate but also the vertical steric compressibility of lamella. Accordingly, the steric compressibility, along with packing parameter, could be used to predict the colloidal stability of lamella.
Molar ratios
Pa
˚) lass (A
˚) lfix (A
˚) Dl (A
Sc (%)
1:1:1 1:1:2 1:2:1 1:2:2 1:1:3
0.98 1.11 1.44 1.31 0.97
22.65 22.64 22.33 22.65 22.79
21.63 20.68 21.12 20.68 21.06
1.02 1.96 1.21 1.97 0.73
4.72 9.48 5.73 9.53 8.21
Pa, packing parameter of associate; lass: tail length of associate; lfix, tail length of MSSG in associate; Dl, difference in tail length (lass lfix); Sc, steric compressibility.
steric compressibility ðSc ; %Þ ¼
associated tail length fixed tail length 100 fixed tail length
where, fixed tail length is the tail length of MSSG in MSSG/SA/ BA associate, and associated tail length is the tail length of MSSG/SA/BA associate. Accordingly, Sc is a measure of vertical steric hindrance occurred between hydrophobic tails of lamellar structure. Due to the difference in the tail length of amphiphiles, which constitute a lamellar structure, a vertical repulsion force could be developed, leading to the destabilization of the lamella. Sc of a lamella composed of MSSG/SA/BA associates was calculated by MD simulation and the results are summarized in Table 5. The packing parameters of 1:1:1 and 1:1:3 associates are almost 1 (Table 4). However, the Sc values of 1:1:1 and 1:1:3 associates in lamella are 4.7 and 8.2, respectively (Table 5). It means that the vertical repulsion in the lamella of 1:1:3 associate might be greater than in the
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