Surfactant micellization and micellar solubilization in aqueous solution can be modeled using a molecular-thermodynamic (MT) theoretical approach; however, the implementation of MT theory requires an accurate identification of the portions of solutes (surfactants and solubilizates) that are hydrated and unhydrated in the micellar state. For simple solutes, such identification is comparatively straightforward using simple rules of thumb or group-contribution methods, but for more complex solutes, the hydration states in the micellar environment are unclear. Recently, a hybrid method was reported by these authors in which hydrated and unhydrated states are identified by atomistic simulation, with the resulting information being used to make MT predictions of micellization and micellar solubilization behavior. Although this hybrid method improves the accuracy of the MT approach for complex solutes with a minimum of computational expense, the limitation remains that individual atoms are modeled as being in only one of two states-head or tail-whereas in reality, there is a continuous spectrum of hydration states between these two limits. In the case of hydrophobic or amphiphilic solutes possessing more complex chemical structures, a new modeling approach is needed to (i) obtain quantitative information about changes in hydration that occur upon aggregate formation, (ii) quantify the hydrophobic driving force for self-assembly, and (iii) make predictions of micellization and micellar solubilization behavior. This article is the first in a series of articles introducing a new computer simulation-molecular thermodynamic (CS-MT) model that accomplishes objectives (i)-(iii) and enables prediction of micellization and micellar solubilization behaviors, which are infeasible to model directly using atomistic simulation. In this article (article 1 of the series), the CS-MT model is introduced and implemented to model simple oil aggregates of various shapes and sizes, and its predictions are compared to those of the traditional MT model. The CS-MT model is formulated to allow the prediction of the free-energy change associated with aggregate formation (gform) of solute aggregates of any shape and size by performing only two computer simulations-one of the solute in bulk water and the other of the solute in an aggregate of arbitrary shape and size. For the 15 oil systems modeled in this article, the average discrepancy between the predictions of the CS-MT model and those of the traditional MT model for gform is only 1.04%. In article 2, the CS-MT modeling approach is implemented to predict the micellization behavior of nonionic surfactants; in article 3, it is used to predict the micellization behavior of ionic and zwitterionic surfactants.

Surfactants can be used to increase the solubility of poorly soluble drugs in water and to increase drug bioavailability. In this article, the aqueous solubilization of the nonsteroidal, antiinflammatory drug ibuprofen is studied experimentally and theoretically in micellar solutions of anionic (sodium dodecyl sulfate, SDS), cationic (dodecyltrimethylammonium bromide, DTAB), and nonionic (dodecyl octa(ethylene oxide), C12E8) surfactants possessing the same hydrocarbon "tail" length but differing in their hydrophilic headgroups. We find that, for these three surfactants, the aqueous solubility of ibuprofen increases linearly with increasing surfactant concentration. In particular, we observed a 16-fold increase in the solubility of ibuprofen relative to that in the aqueous buffer upon the addition of 80 mM DTAB and 80 mM C12E8 but only a 5.5-fold solubility increase upon the addition of 80 mM SDS. The highest value of the molar solubilization capacity (chi) was obtained for DTAB (chi = 0.97), followed by C12E8 (chi = 0.72) and finally by SDS (chi = 0.23). A recently developed computer simulation/molecular-thermodynamic modeling approach was extended to predict theoretically the solubilization behavior of the three ibuprofen/surfactant mixtures considered. In this modeling approach, molecular-dynamics (MD) simulations were used to identify which portions of ibuprofen are exposed to water (hydrated) in a micellar environment by simulating a single ibuprofen molecule at an oil/water interface (modeling the micelle core/water interface). On the basis of this input, molecular-thermodynamic modeling was then implemented to predict (i) the micellar composition as a function of surfactant concentration, (ii) the aqueous solubility of ibuprofen as a function of surfactant concentration, and (iii) the molar solubilization capacity (chi). Our theoretical results on the solubility of ibuprofen in aqueous SDS and C12E8 surfactant solutions are in good agreement with the experimental data. The ibuprofen solubility in aqueous DTAB solutions was somewhat overpredicted because of challenges associated with accurately modeling the strong electrostatic interactions between the anionic ibuprofen and the cationic DTAB. Our results indicate that computer simulations of ibuprofen at a flat oil/water interface can be used to obtain accurate information about the hydrated and the unhydrated portions of ibuprofen in a micellar environment. This information can then be used as input to a molecular-thermodynamic model of self-assembly to successfully predict the aqueous solubilization behavior of ibuprofen in the three surfactant systems studied.

In this article, the validity and accuracy of the CS-MT model is evaluated by using it to model the micellization behavior of seven nonionic surfactants in aqueous solution. Detailed information about the changes in hydration that occur upon the self-assembly of the surfactants into micelles was obtained through molecular dynamics simulation and subsequently used to compute the hydrophobic driving force for micelle formation. This information has also been used to test, for the first time, approximations made in traditional molecular-thermodynamic modeling. In the CS-MT model, two separate free-energy contributions to the hydrophobic driving force are computed. The first contribution, gdehydr, is the free-energy change associated with the dehydration of each surfactant group upon micelle formation. The second contribution, ghydr, is the change in the hydration free energy of each surfactant group upon micelle formation. To enable the straightforward estimation of gdehydr and ghydr in the case of nonionic surfactants, a number of simplifying approximations were made. Although the CS-MT model can be used to predict a variety of micellar solution properties including the micelle shape, size, and composition, the critical micelle concentration (CMC) was selected for prediction and comparison with experimental CMC data because it depends exponentially on the free energy of micelle formation, and as such, it provides a stringent quantitative test with which to evaluate the predictive accuracy of the CS-MT model. Reasonable agreement between the CMCs predicted by the CS-MT model and the experimental CMCs was obtained for octyl glucoside (OG), dodecyl maltoside (DM), octyl sulfinyl ethanol (OSE), decyl methyl sulfoxide (C10SO), decyl dimethyl phosphine oxide (C10PO), and decanoyl-n-methylglucamide (MEGA-10). For five of these surfactants, the CMCs predicted using the CS-MT model were closer to the experimental CMCs than the CMCs predicted using the traditional molecular-thermodynamic (MT) model. In addition, CMCs predicted for mixtures of C10PO and C10SO using the CS-MT model were significantly closer to the experimental CMCs than those predicted using the traditional MT model. For dodecyl octa(ethylene oxide) (C12E8), the CMC predicted by the CS-MT model was not in good agreement with the experimental CMC and with the CMC predicted by the traditional MT model, because the simplifying approximations made to estimate gdehydr and ghydr in this case were not sufficiently accurate. Consequently, we recommend that these simplifying approximations only be used for nonionic surfactants possessing relatively small, non-polymeric heads. For MEGA-10, which is the most structurally complex of the seven nonionic surfactants modeled, the CMC predicted by the CS-MT model (6.55 mM) was found to be in much closer agreement with the experimental CMC (5 mM) than the CMC predicted by the traditional MT model (43.3 mM). Our results suggest that, for complex, small-head nonionic surfactants where it is difficult to accurately quantify the hy...

Molecular-thermodynamic descriptions of micellization in aqueous media can be utilized to model the self-assembly of surfactants possessing relatively simple chemical structures, where it is possible to identify a priori what equilibrium position they will adopt in the resulting micellar aggregate. For such chemical structures, the portion of the surfactant molecule that is expected to be exposed to water upon aggregate self-assembly can be identified and used as an input to the molecular-thermodynamic description. Unfortunately, for many surfactants possessing more complex chemical structures, it is not clear a priori how they will orient themselves within a micellar aggregate. In this paper, we present a computational approach to identify what portions of a surfactant molecule are hydrated in a micellar environment through the use of molecular dynamics simulations of such molecules at an oil/water interface (modeling the micelle core/water interface). The local environment of each surfactant segment is determined by counting the number of contacts of each segment with the water and oil molecules. After identifying the hydrated and the unhydrated segments of the surfactant molecule, molecular-thermodynamic modeling can be performed to predict: (i) the free-energy change associated with forming a micellar aggregate, (ii) the critical micelle concentration (CMC), and (iii) the optimal shape and size of the micellar aggregate. The computer simulation results were found to be sensitive to the atomic charge parameters utilized during the simulation runs. Two different methods of assigning atomic charges were tested, and the computer simulation and molecular-thermodynamic modeling results obtained using both sets of atomic charges are presented and compared. The combined computer simulation/molecular-thermodynamic modeling approach presented here is validated first by implementing it in the case of anionic (sodium dodecyl sulfate, SDS), cationic (cetyltrimethylammonium bromide, CTAB), zwitterionic (dodecylphosphocholine, DPC), and nonionic (dodecyl poly-(ethylene oxide), C 12 E 8 ) surfactants possessing relatively simple chemical structures and verifying that good predictions of CMCs and micelle aggregation numbers are obtained. In the case of C 12 E 8 , the challenges and limitations associated with simulating a single, polymeric E 8 moiety at the oil/water interface to model its behavior at the micelle/water interface are discussed. Subsequently, the combined modeling approach is implemented in the case of the anionic surfactant 3-hydroxy sulfonate (AOS) and of the nonionic surfactant decanoyl-n-methylglucamide (MEGA-10), which possess significantly more complex chemical structures. The good predictions obtained for these two surfactants indicate that the combined computer simulation/molecular-thermodynamic modeling approach presented here extends the range of applicability of molecular-thermodynamic theory to allow modeling of the micellization behavior of surfactants possessing more complex chemical structures.