Application of computer simulation free-energy methods to compute the free energy of micellization as a function of micelle composition. 2. Implementation

In this paper, the implementation of the CS-FE/MT model introduced in article 1 is discussed, and computer simulations are performed to evaluate the feasibility of the new theoretical approach. As discussed in article 1, making predictions of surfactant/solubilizate aqueous solution behavior using the CS-FE/MT model requires evaluation of DeltaDeltaG for multiple surfactant-to-solubilizate or surfactant-to-cosurfactant transformations. The central goal of this article is to evaluate the quantitative accuracy of the alchemical computer simulation method used in the CS-FE/MT modeling approach to predict DeltaDeltaG for a single surfactant-to-solubilizate or for a single surfactant-to-cosurfactant transformation. A hybrid single/dual topology approach was used to morph the ionic surfactant sodium dodecyl sulfate (SDS) into the ionic solubilizate ibuprofen (IBU), and a dual topology approach was used to morph the nonionic surfactant octyl glucoside (OG) into the nonionic solubilizate p-aminobenzoate (PAB). In addition, a single topology approach was used to morph the nonionic surfactant n-decyl dimethylphosphine oxide (C10PO) into the nonionic cosurfactant n-decyl methyl sulfoxide (C10SO), the nonionic surfactant octylsulfinyl ethanol (C8SE) into the nonionic cosurfactant decylsulfinyl ethanol (C10SE), and the nonionic surfactant n-decyl methyl sulfoxide (C10SO) into the nonionic cosurfactant n-octyl methyl sulfoxide (C8SO). Each DeltaDeltaG value was computed by using thermodynamic integration to determine the difference in free energy associated with (i) transforming a surfactant molecule of type A into a cosurfactant/solubilizate molecule of type B in a micellar environment (referred to as DeltaG2) and (ii) transforming a surfactant molecule of type A into a cosurfactant/solubilizate molecule of type B in aqueous solution (referred to as DeltaG1). CS-FE/MT model predictions of DeltaDeltaG for each alchemical transformation were made at a number of simulation conditions, including (i) different equilibration times at each value of the coupling parameter lambda, (ii) different data-gathering times at each lambda value, and (iii) simulation at a different number of lambda values. For the three surfactant-to-cosurfactant transformations considered here, the DeltaDeltaG values predicted by the CS-FE/MT model were compared with DeltaDeltaG values predicted by an accurate molecular thermodynamic (MT) model developed by fitting to experimental CMC data. Even after performing lengthy equilibration and data gathering at each lambda value, physically unrealistic values of DeltaDeltaG were predicted by the CS-FE/MT model for the transformations of SDS into IBU and of OG into PAB. However, more physically realistic DeltaDeltaG values were predicted for the transformation of C10PO into C10SO, and reasonable free-energy predictions were obtained for the transformations of C8SE into C10SE and C10SO into C8SO. Each of the surfactant-to-cosurfactant transformations considered here involved less extensive structural changes than the surfactant-to-solubilizate transformations. As computer power increases and as improvements are made to alchemical free-energy methods, it may become possible to apply the CS-FE/MT model to make accurate predictions of the free-energy changes associated with forming multicomponent surfactant and solubilizate micelles in aqueous solution where the chemical structures of the surfactants, cosurfactants, and solubilizates differ significantly.     

Quantifying the hydrophobic effect. 1. A computer simulation-molecular-thermodynamic model for the self-assembly of hydrophobic and amphiphilic solutes in aqueous solution

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.     

Quantifying the hydrophobic effect. 3. A computer simulation-molecular-thermodynamic model for the micellization of ionic and zwitterionic surfactants in aqueous solution

In this article, the validity and accuracy of the CS-MT model introduced in article 1 for oil aggregates and in article 2 for nonionic surfactants is further evaluated by using it to model the micellization behavior of ionic and zwitterionic surfactants in aqueous solution. In the CS-MT model, two separate free-energy contributions to the hydrophobic driving force for micelle formation are computed using hydration data obtained from computer simulation: gdehydr, the free-energy change associated with dehydration, and ghydr, the change in the hydration free energy. To enable straightforward estimation of gdehydr and ghydr for ionic and zwitterionic surfactants, a number of simplifying approximations were made. Reasonable agreement between the CMCs predicted using the CS-MT model and the experimental CMCs was obtained for sodium dodecyl sulfate (SDS), dodecylphophocholine (DPC), cetyltrimethylammonium bromide (CTAB), two 3-hydroxy sulfonate surfactants (AOS-12 and AOS-16), and a homologous series of four DCNA bromide surfactants with a dimethylammonium head attached to a dodecyl alkyl tail and to an alkyl side chain of length CN, having the chemical formula C12H25CNH2N+1N(CH3)2Br, with N = 1 (DC1AB), 2 (DC2AB), 4 (DC4AB), and 6 (DC6AB). For six of these nine surfactants, the CMCs predicted using the CS-MT model are closer to the experimental CMCs than the CMCs predicted using the traditional molecular-thermodynamic (MT) model. For DC2AB, DC4AB, and DC6AB, which are the most structurally complex of the ionic surfactants modeled, the CMCs predicted using the CS-MT model are in remarkably good agreement with the experimental CMCs, and the CMCs predicted using the traditional MT model are quite inaccurate. Our results suggest that the CS-MT model accurately quantifies the hydrophobic driving force for micelle formation for ionic and zwitterionic surfactants in aqueous solution. For complex ionic and zwitterionic surfactants where it is difficult to accurately quantify the hydrophobic driving force for micelle formation using the traditional MT modeling approach, the CS-MT model represents a very promising alternative.     

Experimental and theoretical investigation of the micellar-assisted solubilization of ibuprofen in aqueous media

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.     

Expected improvement in efficient global optimization through bootstrapped kriging

This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the classic ??expected improvement?? (EI) in ??efficient global optimization?? (EGO) through the introduction of an improved estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are compared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer.     

Application-driven sequential designs for simulation experiments: Kriging metamodelling

This paper proposes a novel method to select an experimental design for interpolation in simulation. Although the paper focuses on Kriging in deterministic simulation, the method also applies to other types of metamodels (besides Kriging), and to stochastic simulation. The paper focuses on simulations that require much computer time, so it is important to select a design with a small number of observations. The proposed method is therefore sequential. The novelty of the method is that it accounts for the specific input/output function of the particular simulation model at hand; that is, the method is application-driven or customized. This customization is achieved through cross-validation and jackknifing. The new method is tested through two academic applications, which demonstrate that the method indeed gives better results than either sequential designs based on an approximate Kriging prediction variance formula or designs with prefixed sample sizes.     

A new synthetic method for controlled polymerization using a microfluidic system

While many parallel synthesis methods developed by the pharmaceutical and life science communities are being applied to polymer synthesis, there remains a need to construct "libraries" of polymeric materials that explore a wider range of polymer structures with accuracy, flexibility, and rapid, often small, changes. We report the use of microfluidics to create an environment for continuous controlled radical polymerization. Varying either the flow rate or the relative concentrations of reactants (i.e., stoichiometry) controls the molecular properties of the products. Molecular variables, here molecular weight, can then be varied continuously. Well-defined materials with narrow molecular weight distributions are produced inside the microfluidic reactor and are available for processing, such as further mixing, deposition, or coating on surfaces. Preliminary kinetic data appear to agree well with literature values reported for larger-scale reactions.     

Raman spectroscopic monitoring of droplet polymerization in a microfluidic device

Microfluidic methodologies are becoming increasingly important for rapid formulation and screening of materials, and development of analytical tools for multiple sample screening is a critical step in achieving a combinatorial 'lab on a chip' approach. This work demonstrates the application of Raman spectroscopy for analysis of monomer composition and degree of conversion of methacrylate-based droplets in a microfluidic device. Droplet formation was conducted by flow focusing on the devices, and a gradient of component composition was created by varying the flow rates of the droplet-phase fluids into the microchannels. Raman data were collected using a fiber optic probe from a stationary array of the droplets/particles on the device, followed by partial least squares (PLS) calibration of the first derivative (1600 cm(-1) to 1550 cm(-1)) allowing successful measurement of monomer composition with a standard error of calibration (SEC) of +/-1.95% by volume. Following photopolymerization, the percentage of double bond conversion of the individual particles was calculated from the depletion of the normalized intensity of the C[double bond, length as m-dash]C stretching vibration at 1605 cm(-1). Raman data allowed accurate measurement of the decrease in double bond conversion as a function of increasing crosslinker concentration. The results from the research demonstrate that Raman spectroscopy is an effective, on-chip analytical tool for screening polymeric materials on the micrometre scale.     

Synthesis and characterization of tapered copolymer brushes via surface-initiated atom transfer radical copolymerization

Tapered copolymer brushes of methyl methacrylate (MMA) and 2-hydroxyethyl methacrylate (HEMA) were synthesized via surface-initiated atom transfer radical polymerization (ATRP) by gradual addition of HEMA to a reaction mixture that originally only had MMA as monomer. The copolymer brush grew linearly with polymerization time. The tapered copolymer brushes responded to selective solvent treatments. For the same tapered copolymer brush, pretreating the surface with methylene chloride made the surface more hydrophobic; pretreating the surface with methanol increased the surface hydrophilicity. This change in surface properties was reversible and considered to be caused by the solvent induced rearrangement of the polymer brushes, which is supported by atomic force microscopy images of the surface. Our work demonstrates that the properties of the tapered copolymer brush could be finely tuned by careful control of the composition profile.