Theoretical study on the electrostatic interactions of mixed surfactant systems

Journal of Molecular Structure: THEOCHEM 717 (2005) 53–57 www.elsevier.com/locate/theochem

Theoretical study on the electrostatic interactions of mixed surfactant systems Fu-qiang Shi*, Jing-yi An, Jia-yong Yu The Technical Institute of Physics and Chemistry of the Chinese Academy of Sciences, Beijing Da Tun Road Jia 3, Beijing 100101, China Received 17 August 2004; accepted 4 November 2004 Available online 8 January 2005

Abstract A quantum mechanical study on the electrostatic interactions of mixed surfactant systems was performed, 15 reduced complexes were considered in the gas phase, chloroform solution, and aqueous solution. The geometries were fully optimized in gas phase at the MP2/6-31G(d) level, single points calculations were performed for all the complexes and monomers at the HF/6-31G(d), HF/6-311G(d,p), HF/6-311CCG(d,p), MP2/6-31G(d), MP2/6-311G(d,p), and MP2/6-311CCG(d,p) levels of theory. The influence of solvent was investigated at the MP2/6-311CCG(d,p) level using the polarizable continuum model. q 2004 Elsevier B.V. All rights reserved. Keywords: Surfactant; Gas phase; Electrostatic interaction

1. Introduction Surfactant systems used for practical applications often consist of mixtures of surfactants, either because commercial surfactants are always mixtures or because mixtures of surfactants often show better performance properties than individual ones [1]. Because of this, there has been considerable research on the molecular interactions between different surfactant in their binary mixtures, particularly in relation to the existence of synergy between them. In general the cationic and anionic surface-active agents will mutually precipitate when brought together in aqueous solution. This is due to the formation of the high molecular weight, poorly ionizable salt of the hydrophobic anion with the hydrophobic cation [2]. These ion pairs, usually denoted salt bridges, are involved in large variety of biological processes [3–7]. For the past decade, the interest in ion–pair interactions has been extended to materials science. Thus, remarkable advances in noncovalent chemistry have led to design of new materials consisting of charged polymer chains and oppositely charged small amphiphilic molecules (surfactants) [8–11]. * Corresponding author. Tel.: C86 1064 88165; fax: C86 1064 879375. E-mail address: [email protected] (F.-q. Shi). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2004.11.028

Understanding of the structural and functional roles played by salt bridges cannot be achieved without knowledge of the energetics of this interaction. Accordingly, a number of theoretical studies have been devoted to investigating salt bridges through sophisticated quantum mechanical methods on reduced systems [12–16]. We present here a systematic quantum mechanical study about the geometry and energetics of the electrostatic interaction found in complexes consisted of alkylammonium and alkyl sulfonate. Interaction energies have been computed not only in the gas phase but also in chloroform and aqueous solutions. Results have been compared with those reported for the electrostatic interactions of n-ATMA PALG complexes [17] and PLL n-AS complexes [18].

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2. Methods

Table 1 Chemical constitution of the ion–pair complexes investigated in this work

The structures of both complexes and monomers were determined in the gas phase by full geometry optimizations at the MP2/6-31G(d) level of theory. It should be noted that the 6-31G(d) basis set [18] provides geometries very similar to those obtained with larger basis sets, even in systems constituted by charged monomers. [19] After optimization, frequency calculation was done on each optimized complex to verify that the geometry was a real minimum without any imaginary frequency. To present a systematic study, singlepoint calculations were performed for all the complexes and monomers at the HF/6-31G(d), HF/6-311G(d,p), HF/ 6-311CCG(d,p), MP2/6-31G(d), MP2/6-311G(d,p), and MP2/6-311CCG(d,p) levels of theory. The stabilization energy in the gas phase, Estab,g, was calculated according to Eq. (1).

Complex

Cation

Anion

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CH3 K NHC 3 CH3 K NHC 3 CH3 K NHC 3 CH3 K NHC 3 CH3 K NHC 3

CH3 K SOK 3 CH3 K CH2 K SOK 3 CH3 K ðCH2 Þ2 K SOK 3 CH3 K ðCH2 Þ3 K SOK 3 ðCH3 Þ2 K CHK SOK 3 CH3 K SOK 3 CH3 K SOK 3 CH3 K SOK 3 CH3 K SOK 3 CH3 K SOK 3 CH3 K SOK 3 CH3 K CH2 K SOK 3 ðCH3 Þ2 CHK SOK 3 ðCH3 Þ2 CHK SOK 3 ðCH3 Þ2 CHK SOK 3

Estab;g Z Eab K Ea;comp K Eb;comp

(1)

where Eab corresponds to the total energy of the optimized complex while Ea,comp and Eb,comp are the energies of the isolated monomers with the geometries obtained from the optimization of the complex. The counterpoise (CP) method was applied to correct the basis set superposition error (BSSE) [20]. The CP correction for each monomer was calculated as the difference between the energy of the monomer on the complexed geometry with the basis set of the whole complex and that of the same monomer without ghost orbitals. The distortion energy, Edis, which estimates the relaxation of the monomers on ion–pair formation, was computed by using Eq. (2).

CH3 K CH2 K NHC 3 CH3 ðCH2 Þ2 K NHC 3 ðCH3 Þ2 CHK NHC 3 CH3 K CH2 K NHC 2 K CH3 CH3 K CH2 K NHC K ðCH3 Þ2 CH3 K CH2 K NC K ðCH3 Þ3 CH3 K CH2 K NHC 3 CH3 K ðCH2 Þ2 K NHC 3 CH3 K CH2 K NHC 2 K CH3 CH3 K CH2 K NHC K ðCH3 Þ2

where DDGassoc is the difference between the free energy of solvation of the ion pair, DGsol,ab, and those of the separated monomers, DGsol,a and DGsol,b, in the corresponding solvent. DDGassoc Z DGsol;ab K DGsol;a K DGsol;b All of the calculations were performed with revision A.9 (Table 1) [22].

(5) GAUSSIAN

98,

3. Results and discussion Edis Z ðEa;comp C Eb;comp Þ K ðEa;opt C Eb;opt Þ

(2)

where Ea,opt and Eb,opt are the energies obtained from the geometries optimized for the isolated monomers. Thus, the total interaction energies in the gas phase, Eint,g, were evaluated as the sum of the stabilization and distortion energies. Eint;g Z Estab;g C Edis

(3)

The influence of the corrections for zero-point energy and entropy on Eint,g was investigated for the smaller complexes using frequencies calculated at the MP2/6-31G(d) level. The effect of the solvent (water and chloroform) on the interaction energies was estimated following the polarizable continuum model (PCM) developed by Miertus, Scrocco, and Tomasi [21]. PCM calculations were performed in the framework of the ab initio MP2 level with the 6-311CCG(d,p) basis set and using the gas phase optimized geometries. The interaction energy in aqueous and chloroform solution, Eint,aq/chl, was evaluated by using Eq. (4). Eint;aq=chl; Z Eint;g C DDGassoc

(4)

3.1. Influence of the quantum mechanical method, the basis set, and the BSSE on the stabilization and interaction energies The results in Tables 2 and 4 show that the values of Estab,g and Eint,g calculated using the HF theory are slightly underestimated (w5–8%) with respect to those obtained at the MP2 level. Inspection of the results obtained with the 6-31G(d), 6-311G(d,p), and 6-311CCG(d,p) basis sets indicates that both Estab,g and Eint,g decrease when the size of the basis sets increases. Such energy parameters diminish about 7 kJ/mol, respectively, when the basis set is extended from the 6-31G(d) to the 6-311G(d,p). The introduction of diffuse functions to the 6-311G(d,p) basis set produces a new reduction of about 4 kJ/mol. Comparison between results displayed in Tables 2 and 3 indicates that, in general, the size of the BSSE is about 13–19 kJ/mol larger at the MP2 level than at the HF one. The strength of the Estab,g predicted by MP2 calculations is overestimated by about 20–35 kJ/mol when the BSSE is not corrected.

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Table 2 Stabilization energies computed in the gas phase (Estab,g, kJ/mol) with correction for the basis set superposition error Complex

HF

MP2

6-31G(d)

6-311G(d,p)

6-311CCG(d,p)

6-31G(d)

6-311G(d,p)

6-311CCG(d,p)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

K469.6 K468.3 K467.5 K467.2 K467.3 K456.3 K451.3 K447.4 K449.2 K422.7 K355.8 K455.6 K449.5 K446.6 K421.2

K461.7 K460.4 K459.5 K459.1 K459.4 K449.3 K444.3 K440.6 K442.0 K419.3 K352.4 K448.4 K442.4 K439.5 K417.7

K457.3 K456.7 K455.9 K455.7 K456.4 K444.7 K439.6 K436.0 K437.5 K415.5 K349.4 K444.5 K440.2 K437.7 K416.1

K493.7 K492.3 K491.4 K491.1 K490.0 K482.2 K477.7 K473.9 K474.9 K451.0 K375.7 K481.2 K487.5 K484.2 K460.8

K485.6 K484.3 K483.2 K482.8 K481.7 K475.6 K471.1 K467.9 K466.0 K449.0 K370.6 K474.3 K466.9 K462.3 K444.6

K478.6 K478.8 K478.2 K478.1 K477.5 K469.1 K464.5 K461.6 K460.0 K444.7 K368.7 K469.1 K464.5 K460.8 K444.0

3.2. Energetics of the electrostatic interaction of alkylammonium alkyl sulfonate ion pairs complexes in the gas phase Comparison among complexes 1–5 indicates that Estab,g and Eint,g are nearly not affected by the size of the alkyl group connected with the sulfonate group, this is always the case for different basis sets and methods. The Estab,g and Eint,g computed at the 6-311CCG(d,p) level decreases are about 2.4 kJ/mol when the size of the alkyl group connected with the sulfonate groups inceases form methyl to butyl. This is because that less electrons in sulfonate group transfer to the alkyl group, therefore the geometry has little influence on Estab,g and Eint,g. Through inspecting 6, 7, and 8, it can be found that Estab,g and Eint,g approximately decrease 10 kJ/mol when the size of the alkyl group connected with the ammonium cation increases form methyl to ethyl and that Estab,g and Eint,g approximately decreased 4 kJ/mol when the size of the alkyl groups increases form ethyl to

propyl. Moreover, the Estab,g and Eint,g approximately decrease 3 kJ/mol as ammonium cation shifts from a to b position of propyl group. All these happen because electrons transfer from N to C more easily than they do from N to H, which leads to the electrostatic interactions weakened. Comparison among complexes 9–11 indicates that the electrostatic interactions weaken when methyl group substitutes H atom. This is because the methyl groups that are connected to the N atom leads to the increase of distance between ammonium cation and sulfonate group. 3.3. Geometry of the alkylammonium alkyl sulfonate ion pairs complexes in the gas phase The optimized intermolecular geometries are displayed in Fig. 1a. Inspection of Fig. 1a reveals that the sulfate group is symmetrically arranged with respect to the cation, as can be inferred from the same values found between the two H/O intermolecular distances.

Table 3 Stabilization energies computed in the gas phase (Estab,g, kJ/mol) without correction for the basis set superposition error Complex

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

HF

MP2

6-31G(d)

6-311G(d,p)

6-311CCG(d,p)

6-31G(d)

6-311G(d,p)

6-311CCG(d,p)

K479.6 K478.3 K477.4 K477.1 K477.0 K469.5 K464.7 K460.9 K462.6 K438.7 K370.4 K467.9 K462.6 K459.8 K436.7

K474.6 K472.8 K471.8 K471.5 K470.8 K465.3 K460.5 K457.0 K456.1 K435.0 K366.0 K462.3 K457.0 K453.7 K431.6

K464.3 K463.6 K462.9 K462.8 K463.7 K453.0 K448.4 K444.8 K445.7 K424.6 K355.9 K452.5 K449.3 K446.7 K425.2

K517.3 K516.0 K515.1 K514.8 K513.4 K511.8 K507.9 K504.4 K504.7 K485.0 K409.1 K509.8 K517.6 K514.0 K494.1

K514.5 K512.4 K511.1 K510.8 K508.2 K510.1 K506.1 K503.1 K497.7 K484.8 K401.3 K505.1 K499.1 K493.6 K477.1

K498.2 K498.6 K498.3 K498.3 K498.1 K491.7 K488.4 K485.7 K484.0 K472.4 K390.0 K491.3 K489.0 K485.4 K471.7

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Fig. 1. Optimized geometries of the alkylammonium alkyl sulfonate ion pairs 2 and 11 (only the atoms involved in the intermolecular interaction have been explicitly represented, the remaining atoms of the alkyl groups being symbolized by large spheres). Intermolecular distances are given in nm.

The optimized geometry verifies greatly as the H atom is substituted by methyl group. The distance between the cation and the anion, which was represented by the distance between N (alkylammonium) and S (alkyl sulfonate), increases from 0.3064 to 0.3858 nm. The distance between N (alkylammonium) and S (alkyl sulfonate) closes to that between N (alkylammonium) and S (alkyl sulfate)[18] and so do electrostatic interactions. In complex 11, the H atoms of alkyltrimethylammonium cations and the O atoms of alkyl sulfonate are interlacedly arranged; this shows that the electrostatic interactions are stronger than the H-bond interactions. 3.4. Effect of the solvent in the formation of the ion pair Table 5 shows the DGsol, DDGassoc, and Eint in water and chloroform for the 15 ion pairs investigated in this work. In all cases, the solvation of the complexes was worse than that of the isolated ions, which led to positive DDGassoc values. Furthermore, the magnitude of such repulsive energy term increases with the polarity of the solvent. Thus, the solvation of the isolated ions in water is favored by strong electrostatic interactions between the bulk solvent and the

charged solutes, while in chloroform, the strength of such interactions decreases. The Eint,aq and Eint,chl values were obtained by adding the Eint,g estimated at the MP2/ 6-311CCG(d,p) level (Table 4) to the DDGassoc term computed in water and chloroform, respectively (Eq. (4)). The results indicate that the complexation process is less favorable in chloroform solution than in the gas phase. Thus, a comparison between the Eint,chl and Eint,g values reveals that the strength of the binding is about 75% weaker in the former environment than in the latter one. However, it should be emphasized that in chloroform solution the unfavorable DDGassoc term is counterbalanced by the gas phase contribution leading in all cases to negative Eint,chl values. According to the results displayed in Table 5, the binding of an alkylammonium cation to an alkyl sulfate anion in chloroform solution to form the corresponding ion pair is favored by about 64–107 kJ/mol. Conversely, this process is destabilized in aqueous solution by 13–34 kJ/ mol.

4. Summary High-level ab initio calculations including electron correlation show that in the gas phase the electrostatic interaction characteristic of alkyltrimethylammonium sulfonate complexes is about 40 kJ/mol weaker than that of n-ATMA PALG complexes and the electrostatic interaction characteristic of alkylammonium sulfonate complexes is about equal to that of PLL n-AS complexes There are much difference between alkyltrimethylammonium sulfonate complexes and alkylammonium sulfonate complexes. The Eint,g predicted at the highest computational level employed for the systems under study is approximately K454 kJ/mol. Calculations in solution show that the bulk solvent plays a crucial role in the binding process. Results indicate that the destabilization induced by solvent is smaller for PLL, n-AS

Table 4 Interaction energies computed in the gas phase (Eint,g, kJ/mol) Complex

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

HF

MP2

6-31G(d)

6-311G(d,p)

6-311CCG(d,p)

6-31G(d)

6-311G(d,p)

6-311CCG(d,p)

K436.9 K435.3 K434.3 K433.8 K434.1 K425.6 K420.9 K416.7 K427.6 K394.5 K346.3 K425.0 K418.6 K423.2 K392.8

K429.9 K428.5 K427.4 K426.9 K427.2 K419.3 K414.7 K410.5 K421.0 K391.9 K343.8 K418.8 K412.1 K416.5 K389.9

K426.6 K425.8 K424.8 K424.5 K424.9 K415.9 K411.2 K407.1 K418.0 K389.4 K341.8 K416.0 K411.2 K416.1 K389.6

K468.3 K466.5 K465.3 K464.9 K463.8 K459.0 K454.9 K450.8 K458.3 K429.4 K367.5 K457.8 K477.2 K479.3 K451.8

K459.2 K457.8 K456.5 K456.0 K454.6 K451.5 K447.4 K443.9 K447.4 K426.3 K362.0 K450.1 K441.9 K442.0 K420.8

K454.6 K454.4 K453.8 K453.6 K452.2 K447.3 K443.1 K439.9 K444.3 K424.4 K362.1 K447.3 K442.1 K443.2 K422.9

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Table 5 Free energy of solvation and interaction energy in chloroform and aqueous solutions and the difference between the free energy of solvation of the ion pair and separated monomers Complex

DGsol,chl

DDGassoc

Eint,chl

DGsol,aq

DDGassoc

Eint,aq

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

K36.4 K36.1 K33.8 K32.6 K38.6 K39.0 K35.2 K38.0 K27.8 K29.2 K43.9 K39.7 K30.8 K27.4 K26.1

358.0 355.0 354.7 353.4 348.7 346.2 345.5 336.4 342.5 325.1 297.5 342.3 342.9 335.9 321.2

K96.6 K99.4 K99.2 K100.2 K103.5 K101.2 K97.6 K103.6 K101.8 K99.2 K64.6 K105.0 K99.2 K107.3 K101.7

K87.4 K88.7 K84.0 K85.4 K84.6 K85.0 K95.8 K83.8 K69.2 K68.0 K98.6 K87.5 K74.4 K67.8 K68.7

386.3 381.5 387.8 380.5 386.2 472.4 457.9 458.5 463.7 439.6 384.3 466.4 476.4 462.2 436.1

26.4 21.7 28.6 21.6 28.7 25.0 14.7 18.6 19.4 15.2 22.1 19.1 34.3 19.0 13.2

than for complexes under study. Thus the attractive energetic contribution in the gas phase partially compensates the destabilizing effect of the solvent. Our calculations predict that in chloroform solution the binding is favoured by about 100 kJ/mol for complexes while only 12 kJ/mol for complexes while only 12 kJ/mol for n-ATMA PALG complexes [17] and about 108 kJ/mol for PLL, n-AS complexes [18]. In aqueous solution, the binding is unfavored for both types of complexes.

Acknowledgements This work was supported by the Chinese National Key Basic Research Development Program (No. G19990225).

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