Using quantum chemistry to predict solubilization in detergent micelles

THEO CHEM ELSEVIER

Journal of Molecular

Structure

(Theochem)

394 (1997) 267-270

Using quantum chemistry to predict solubilization in detergent micelles Jo20 P.S. Farah*, Gilson A.R. Lima, Frank H. Quina lmtitrrto de Quimico. lJnivrr.sidade dr Ssio Paula, Cuixo Postal 26077, Sdo Paula, 05599.970 Brazil Received 22 November

1995; accepted 23 January

1996

Abstract Experimental K, values for the solubilization of 66 non-ionic solutes in micelles of the anionic detergent sodium dodecyl sulfate can be reproduced using quantum chemical surrogate parameters, the calculation of which requires only a knowledge of the solute molecular structure. The parameters evaluated include the solute molar volume (V,), the solute HOMO and LLJMO energler. the magnitudes of the charges of the most positive hydrogen and most negative atom of the molecule (q+ and lq_l, respectively), the molecular dipole moment and the solute “dipolarity” (the molecular polarizability divided by V,). The linear resultant solvation free energy relationship (LSER) based on these surrogate parameters (log K, = -0.487 + 1.27q+ -3.76/q_ I+ 2.97V,) is chemically reasonable and consistent with the LSER for micellar solubilization based on experimentally-derived solute parameters. The use of quantum chemical parameters to develop LSERs should thus prove to be a convenient approach for predicting solubilities in organized media from solute molecular structure. 0 1997 Elsevier Science B.V.

Keywords: Atomic charges; Hydrogen bond basicity; Linear free energy relationships; Micelles; MNDO; Solubilization

solvation,

1. Introduction

One of the most fundamental properties of aqueous micellar solutions is their ability to solubilize a wide variety of organic solutes with quite distinct polarities and degrees of hydrophobicity. Although incorporation coefficients (K,) for micelle-water partitioning of solutes can be measured experimentally [ 11, very little is known about the relationship between the molecular structure of the solute and its affinity for a given detergent micelle [2,3 1. Linear solvation free energy relationships (LSERs) have proven to be quite useful for understanding processes that involve the transfer of solutes between two condensed phases. Based on a simple cavity model of * Corresponding

author. E-mail: [email protected]

SO

I66- I280(96)04842-7

[4,5] has proposed the LSER:

logSP=c+a~~~+bCP2+pa~+‘RZ+S(V,/100) (1) where SP refers to the property of interest for a series of solutes in a single solvent medium. In addition to a constant (c) dependent on the property of interest and the choice of standard state, this LSER contains five solute-specific, medium-insensitive parameters whose relative contributions are dictated by five numerical coefficients (a, 6, p, r and s). The five parameters account for solute hydrogen bond acidity ( Ca2) and basicity (c&), solute dipolarity (a& solute polarizability (expressed as the solute’s excess molar refraction, R2) and solute molar volume (V,). Recently, we employed Eq. (1) to correlate solubility data for non-ionic solutes in aqueous micellar

0166.1280/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved PI/

Abraham

268

J.P.S. Furuh et nl./Journal

of MolrcularStructure(Theochem)

solutions of anionic, cationic and non-ionic surfactants [6]. The resultant linear solvation free energy relationships provide interesting insights into the interplay between detergent charge and structure, and the non-hydrophobic factors that contribute to the micellar solubility of organic molecules. In all cases, incorporation is strongly favored by an increase in solute molar volume (V,c) and strongly disfavored by an increase in solute hydrogen bond basicity (C&). Although LSERs of this type provide a useful framework for developing quantitative structuresolubility relationships for organized media, their widespread application is seriously limited by the fact that the requisite solute parameters x (Y?, I&, R2 and ?r?, which must be determined experimentally, are available for only several hundred solutes of rather simple molecular structure [4,5,7]. A potentially more general approach, applicable to any solute of interest, would be to replace Abraham’s experimentally determined solute parameters with parameters that can be calculated solely on the basis of solute molecular structure. One of the most successful attempts to implement this approach is that of Famini and co-workers [8,9], who have found rather good correlations employing LSERs containing six parameters: the solute molar volume and five “surrogate” parameters derived from semi-empirical quantum chemical calculations on the solute of interest. These surrogate parameters include specific atomic charges (q+ of the most positive hydrogen; q_ of the most negative atom), polarizabilities (~2) and the HOMO/LUMO energies of the solute. In the present work, we apply this quantum chemical surrogate approach to the solubilization of non-ionic solutes in anionic micelles of sodium dodecyl sulfate (SDS), and demonstrate that the resultant LSER is chemically reasonable and consistent with that obtained employing the Abraham solute parameters.

2. Methodology The HOMO/LUMO energies, atomic charges, and molecular dipole moment and polarizabilities of the solute molecules were calculated for fully optimized geometry (keyword FORCE) using the MNDO hamiltonian, as implemented in the MOPAC 93 package [lo]. Statistical treatment of the data and multiple

regression Macintosh

394 (1997) X7-270

analyses were 7 100 Computer.

performed

on a Power

3. Results and discussion 3.1. The primup

data set

Solute incorporation coefticients are expressed as pseudophase incorporation coefficients, K,, defined as

[II where ]S,i,] and [S,,] are the stoichiometric concentrations of solute in the micellar and aqueous phases, respectively, and Co is the analytical concentration of micellized detergent, equal to the total detergent concentration minus the critical micelle concentration (cmc). The dimensions of K, are thus I mol-‘. Methods for determining K, and the appropriate formulae for conversion of K, values into other equivalent forms can be found in the review of Sepulveda et al. [ 11. The final data set was derived from a critical compilation of literature K, values for incorporation of 66 non-ionic solute molecules in micellar SDS [6]. These solutes cover a wide range of chemical structural types, including simple gases and aliphatic hydrocarbons (six molecules), halo carbons (six molecules), aromatic hydrocarbons and substituted benzenes (11 molecules), aliphatic alcohols (14 molecules), phenols and naphthols (1 1 molecules), ketones (eight molecules), ethers (one molecule), carboxylic acids and derivatives (seven molecules), and anilines (two molecules). 3.2. The LSERs In the present work, seven parameters potentially relevant to solute-solvent interactions were selected for the development of a corresponding “quantum chemical” LSER of the general form: log Ks=c+aq+

+biq_~+hE,,,,+kE,,,,,

+mD+d7rr+e(V,/lOO)

(3)

One of these, Abraham and McGowan’s 11I] solute molar volume V, (in cm3 mol-‘), was also used by Abraham and co-workers [4,5,7], and can be

For this purpose. it is instructive to compare Eq. (4) with the LSER reported previously [6] for these same data based on the five Abraham solute parameters:

calculated directly from the solute structure. The other six parameters were derived from semi-empirical quantum chemical calculations on the solute employing the MNDO method with full geometry optimization. These include the solute HOMO and LUMO energies (EHOMOand ELUMo,respectively), the magnitudes of the charges of the most positive hydrogen and most negative heteroatom of the molecule (CJ+and k-1, respectively), the molecular dipole moment (D) and the equivalent of Famini’s “dipolarity” rr, equal to the molecular polarizability divided by V,. Standard multiple linear regression analysis [ 121 of the K, data for solubilization in SDS employing these seven parameters resdts in the relationship: log K,= -0.487+

log K, = -0.62 -0.08

r=0.9689;

(n=66;

F=316)

The coefficients of the parameters EHoMO, ELUMO,D and KF are essentially zero and not statistically significant (Table l), as confirmed by stepwise regression analysis [ 121. Fig. 1 illustrates the overall agreement between the values of log K, determined experimentally and calculated from Eq. (4). Goodness-of-fit is a necessary, but not sufficient condition for the validity of Eq. (4) as a LSER. If the parameters selected do, in fact, mirror specific properties of the solubilization environment of the solute, the magnitudes and signs of the coefficients of the resultant regression equation should be compatible with the process of transferring a solute and its cavity from bulk water to the micellar pseudophase. I Summary of

r=0.9895;

sd=0.13,

(5) F=575)

for which only the coefficient of the 1 CY,term is not statistically significant. In both Eqc. (4) and (5), the dominant factor favoring micellar incorporation is the solute molar volume. The large positive V, coefficient clearly reflects the fact that it is much easier to create a cavity in the micelle than in warer, owing to the high cohesive energy density of water. Eq. (5) shows that micellar solubilization is only weakly dependent on solute dipolarity (the 7rr? term) and solute excess molar refraction (the R2 term); this is compatible with the finding that the dipole moment and dipolarity terms are unimportant in Eq. (4). The principal factor favoring partitioning to the aqueous phase is solute hydrogen bond basicity, as evidenced by the large negative coefficient of the I& term in Eq. (5). In contrast, incorporation of solutes into SDS micelles is unaffected by solute hydrogen bond acidity (the statistically insignificant 1 CY?term). This indicates that, relative to the solubilization site(s) in the micelle, bulk water is a much better hydrogen bond donor, but a comparable hydrogen bond acceptor. Micellar solubilization is independent of the solute HOMO/ LUMO energies, which were chosen to reflect

1.27q+ -3.761c/_ I+2.97(V,/lOO)

sd=0.21;

- 0.57a2

+0.3X?? +3.25(V,/lOO)

(4) (n=66;

1 CY?- 1.84 I&

Table

the

standarderrors and partial

F balueh ol‘the coefficients

of the full equatmn for log K, (Eq. (3). retaming all term<). of the linal

LSER (Eq. (4)) and of the relationshIp hetwren solute hydrogen bond hasicity and the atomic charges (Eq. (6))

Term

Full equatmn Coef.

Const. (1+

Eq. (3) Std. error

Pamal F

Coef.

-0.77

Eq. (6) Std. error

Pamal F

Coef.

PO.487 9.4

0.28 0.10

I81 852

0.43

9.7

Iq_l V,/lOO

-3.92 3.06

0.43 0.14

83.6 471

E HOMO

-0.02

0.02

I .6”

0.02

I I”

_

_

0.04

0.002”

_

_

0.002

0.001 J

D

0.03

-0.002

BF ‘I Indater

< 0.001

value with no statistical

slgniticance

-3.765 2.967

Partial F

0.0372

I

I.34

ELI’W

I.269

Std. error

0.4

I

0.2I

x.9

I.S.55

0.14

123

-0.62 _ _

_

270

J.P.S. Furah et al.Nourrd

of Moleculur

Structure (Throchm)

394 (1997)

267-270

In summary, we have shown here that experimental solubilization of non-ionic solutes can be reproduced using quantum chemical surrogate parameters, the calculation of which requires only a knowledge of the solute molecular structure. The resultant LSER for micellar solubilization based on these surrogate parameters is chemically reasonable and consistent with the LSER based on experimentally-derived solute parameters. The use of quantum chemical parameters to develop LSERs should thus prove to be a convenient approach for predicting solubilities in organized media from solute molecular structure. K, values for the micellar

-1

0

1 log

2 K,

3

4

@w)

Acknowledgements

Fio I. Comparison of calculated (Eq. (4)) and experimental K, vaf;es [6] for solubilization of non-ionic solutes in anionic SDS micelles.

covalent contributions to the solute hydrogen bond basicity/acidity [9]. Cramer et al. [9] have suggested that Iq-I and q+ are associated with the electrostatic components of the solute hydrogen bond basicity and acidity, respectively. In the light of Eq. (5), one would thus expect the coefficient of the Iq_l term in Eq. (4) to be large and negative, and the q+ term to be absent. Although this expectation is indeed confirmed for lq-I, the q, term does contribute to Eq. (4) and is statistically significant. The origin of this apparent discrepancy is readily resolved by examination of the correlation of Abraham’s solute hydrogen bond basicity [4,5,7] with the calculated atomic charges, which gives the relationship: ~.pz=o.037+1.551q_l-o.629+ (n=66;

r=0.828;

sd=O.ll;

(6) F=68.9)

The physical meaning of Eq. (6) is that, for a protonbearing heteroatom such as hydroxyl or phenolic oxygen, the proportionality between the hydrogen bond basicity and the negative charge of the heteroatom is modulated by the adjacent positive charge of the attached hydrogen atom. Thus, when the relationship in Eq. (6) is taken into account, Eqs. (4) and (5) lead to identical conclusions as to the nature of the dominant factors involved in the solubilization of non-ionic solutes by SDS micelles.

This work was supported by grants from the Fundac 20 de Amparo a Pesquisa do Estado de Sao Paulo FAPESP (Projects 91/0480-l and 1994/3505-3) and PADCT-FINEP (Project No. 65-92-0063-00). The use of the computational facilities of CENAPAD-SP/ UNICAMP, CESUP-UFRGS, LSI-Poli-USP and CCE-USP is gratefully acknowledged.

References [I] L. Seplilveda. E. Lissi and F. Quina. Adv. Colloid Interface Sci.. 25 (1986) I-57. [2] D. Attwood and A.T. Florence, Surfactant Systems. Their Chemistry, Pharmacy and Biology. Chapmann and Hall, London, 1984. [3] W. Blokzijl and J.B.F.N. Engberts, Angew. Chem. Int. Ed. Engl., 32 (1993) 1.54.5-1579. [4] M.H. Abraham. Chem. Sot. Rev., 22 (1993) 73-83. [S] M.H. Abraham, Pure Appl. Chem., 65 (1993) 2503-25 12. [6] F.H. Quma, E.O. Alonso and J.P.S. Farah, J. Phys. Chem.. 99 (1995) I 1708~1I714. [7] M.H. Abraham. H.S. Chadha, G.S. Whiting and R.C. Mitchell. J. Pharm. Sci., 83 (1994) 1085-I 100. [8] G.R. Famini, C.A. Penskl and L.Y. Wilson, J. Phys. Org. Chem., 5 (1992) 395-408. [9] C.J. Cramer. G.R. Famini and A.H. Lowrey, Act. Chem. Res., 26 (1993) 599-605. [IO] J.J.P. Stewart, MOPAC 93.00 Manual, Fujitsu Limited. Tokyo, Japan, 1993. [I I] M.H. Abraham and J.C. McGowan, Chromatographia. 23 (1987)243-246. [ 121 N.R. Draper and H. Smith, Applied Regression Analysis, Wiley, New York, 1981.