Application of computer simulation free-energy methods to compute the free energy of micellization as a function of micelle composition. 1. Theory

The widespread use of surfactant mixtures and surfactant/solubilizate mixtures in practical applications motivates the development of predictive theoretical approaches to improve fundamental understanding of the behavior of these complex self-assembling systems and to facilitate the design and optimization of new surfactant and surfactant/solubilizate mixtures. This paper is the first of two articles introducing a new computer simulation-free-energy/molecular thermodynamic (CS-FE/MT) model. The two articles explore the application of computer simulation free-energy methods to quantify the thermodynamics associated with mixed surfactant/cosurfactant and surfactant/solubilizate micelle formation in aqueous solution. In this paper (article 1 of the series), a theoretical approach is introduced to use computer simulation free-energy methods to compute the free-energy change associated with changing micelle composition (referred to as DeltaDeltaGi). In this approach, experimental critical micelle concentration (CMC) data, or a molecular thermodynamic model of micelle formation, is first used to evaluate the free energy associated with single (pure) surfactant micelle formation, g(form,single), in which the single surfactant micelle contains only surfactant A molecules. An iterative approach is proposed to combine the estimated value of gform,single with free-energy estimates of DeltaDeltaGi based on computer simulation to determine the optimal free energy of mixed micelle formation, the optimal micelle aggregation number and composition, and the optimal bulk solution composition. After introducing the CS-FE/MT modeling framework, a variety of free-energy methods are briefly reviewed, and the selection of the thermodynamic integration free-energy method is justified and selected to implement the CS-FE/MT model. An alchemical free-energy pathway is proposed to allow evaluation of the free-energy change associated with exchanging a surfactant A molecule with a surfactant/solubilizate B molecule through thermodynamic integration. In article 2 of this series, the implementation of the CS-FE/MT model to make DeltaDeltaGi free-energy predictions for several surfactant/solubilizate systems is discussed, and the predictions of the CS-FE/MT model are compared with the DeltaDeltaGi predictions of a molecular thermodynamic model fitted to relevant experimental data.     

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.     

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.     

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.     

On the shape of bottle-brush macromolecules: systematic variation of architectural parameters

We measured the form factor of bottle-brush macromolecules under good solvent conditions with small-angle neutron scattering and static light scattering. The systems under investigation are brushes, synthesized via the grafting-from route, built from a poly(alkyl methacrylate) backbone to which poly(n-butyl acrylate) side chains are densely grafted. The aim of our work is to study how the systematic variation of structural parameters such as the side chain length and backbone length change the conformation of the polymer brushes in solution. All spectra can be consistently described by a model, considering the bottle-brush polymers as flexible rods with internal density fluctuations. Parameters discussed are (1) the contour length per main chain monomer l(b), (2) the fractal dimension of the side chains Ds, as well as (3) the fractal dimension D, and (4) the Kuhn length lambdak of the overall brush. l(b)=0.253+/-0.008 nm is found to be independent of the side chain length and equal to the value found for the bare main chain, indicating a strongly stretched conformation for the backbone due to the presence of the side chains. The fractal dimension of the side chains is determined to be Ds=1.75+/-0.07 which is very close to the value of 10.588 approximately 1.70 expected for a three-dimensional self-avoiding random walk (3D-SAW) under good solvent conditions. On larger length scales the overall brush appears to be a 3D-SAW itself (D=1.64+/-0.08) with a Kuhn-step length of lambdak=70+/-4 nm. The value is independent of the side chain length and 46 times larger than the Kuhn length of the bare backbone (lambdak=1.8+/-0.2 nm). The ratio of Kuhn length to brush diameter lambda(k)d>or=20 determines whether lyotropic behavior can be expected or not. Since longer side chains do not lead to more persistent structures, lambda(k)d decreases from 8 to 4 with increasing side chain length and lyotropic behavior becomes unlikely.     

Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping

This paper proposes a novel method to select an experimental design for interpolation in random simulation, especially discrete event simulation. (Though the paper focuses on Kriging, this design approach may also apply to other types of metamodels such as non-linear regression models and splines.) Assuming that simulation requires much computer time, it is important to select a design with a small number of observations (or simulation runs). The proposed method is therefore sequential. Its novelty is that it accounts for the specific input/output behavior (or response function) of the particular simulation at hand; i.e., the method is customized or application-driven. A tool for this customization is bootstrapping, which enables the estimation of the variances of predictions for inputs not yet simulated. The method is tested through two classic simulation models, namely the expected steady-state waiting time of the M/M/1 queuing model, and the mean costs of a terminating (s, S) inventory simulation. For these two simulation models the novel design indeed gives better results than a popular alternative design, namely Latin Hypercube Sampling (LHS) with a prefixed sample.     

Magnetization and magnetoresistance of amorphous FexB1−x in high magnetic fields

The magnetization and magnetoresistance of ferromagnetic melt-quenched amorphous Fe_xB_1?x has been measured. The magnetization indicates no saturation to fields above 30 tesla. The absolute value of the negative magnetoresistivity increases by a factor of five with decreasing B content from x = 0.25 to 0.15. These results are discussed in terms of different models of the resistivity minimum behaviour of amorphous alloys.