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Scission free energies for wormlike surfactant micelles: Development of a simulation protocol, application and validation for personal care formulations Huan Wang, Xueming Tang, David Michael Eike, Ronald G. Larson, and Peter H. Koenig Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b03552 • Publication Date (Web): 15 Dec 2017 Downloaded from http://pubs.acs.org on December 28, 2017
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Scission free energies for wormlike surfactant micelles: Development of a simulation protocol, application and validation for personal care formulations Huan Wang,1 Xueming Tang,2 David M. Eike, 3 Ronald G. Larson, 2 Peter H. Koenig3,§ 1 University of Cincinnati Simulation Center, 2728 Vine Street, Cincinnati OH 45220, USA Department of Chemical Engineering, 2800 Plymouth Road, University of Michigan, Ann Arbor, MI 48109, USA 3 Computational Chemistry, Modeling and Simulation, The Procter & Gamble Company, 8611 Beckett Road, West Chester, OH 45069, USA 2
§ Correspondence: e-mail:
[email protected], phone (513) 634 8958, FAX: (513) 634 8564 Abstract We present a scheme to calculate wormlike micelle scission free energies from a potential of mean force (PMF) derived from a Weighted Histogram Analysis Method (WHAM) applied to coarse grained dissipative particle dynamics (DPD) simulations. In contrast to previous related work, we use a specially chosen external potential based on a reaction coordinate that reversibly drives surfactants out of the nascent scission location. For the application to a model body wash formulation, we predict how addition of NaCl and small molecules such as perfume raw materials (PRMs) affect scission energies. The results show qualitative agreement and correct trends compared to recently determined scission energies for the same system; however, a more rigorous parameterization of the underlying DPD potential is required for quantitative agreement. Introduction Surfactant solutions containing self-assembled structures including spherical or elongated worm-like micelles are the main effective ingredients of detergents and personal care products and have been widely studied in recent years. The structure of these micelles depends on multiple factors such as salt concentration, surfactant composition, temperature and solvent.1–4 Understanding how these factors contribute to micelle solution properties would greatly improve formulation design and provide a better understanding of the physics behind micelle solutions. Rheological properties of wormlike micellar solutions have similarities to those of long entangled polymers.5,6 Several theories have been developed that treat wormlike micelles as living/equilibrium polymers,7–9 which break and rejoin in thermal equilibrium. Borrowing the tube concept from entangled polymers, Cates and coworkers developed a model that links the rheology of wormlike micellar solutions to properties of micelles, such as their length and rate of breakage. In recent years, improvements have been made to the original Cates theory that allow more quantitative predictions of micelle properties from rheological experiments.10 The “Pointer Algorithm,” a simulation method that incorporates some additional physics neglected in the original Cates model, has seen successfully applied to obtaining rheological properties of worm-like micelles.11–13 The simple geometric packing parameter of Israelachvili, Mitchell and Ninham14 can be used to infer trends in rheological properties and phase diagrams for single surfactants and simple mixtures. Recently, Dhakal et al.15 presented a scheme to analyze micelle shapes including a measure to assess the local 1 ACS Paragon Plus Environment
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curvature of aggregates. Applied to simulations of surfactant self-assembly, these kinds of tools can provide a more quantitative assessment than the manual classification of micelle shapes (e.g. spherical, rodlike micelles, bilayers). It can also be used to build empirical models linking micelle shapes to macroscopic observables.15 Despite these advances, we are looking for a more general and systematic way to predict macroscopic rheological properties from microscopic structure. Properties at the molecular and micellar scale can be linked to the macroscopic scale through the scission energy (really free energy) Esciss. In Cates’ theory, the average micelle length , which is a thermodynamic property of the micelle solution, can be inferred from Esciss according to the following equation:
~Φ/ /
(1)
The scission energy represents the excess free energy for introduction of a pair of hemispherical endcaps into a worm-like micelle, thus breaking the micelle in two. The prefactor describes the scaling of the micelle length with increasing micelle volume fraction Φ. More recently, the prefactor was derived in more detail from the law of mass action, which also provides a way to determine scission energies from small angle neutron scattering16 and rheological analysis.13
≈
. 8 $%& exp ( ) 2() *
(2)
, , ,d, N. are the average molecular mass of the surfactant, surfactant mole fraction, surfactant Here, density, micelle diameter, and Avogadro constant, respectively. Here, we present a novel method to directly determine micelle scission energy Esciss using molecular dynamics simulations, and demonstrate that it is suitable and robust. We then predict and interpret scission energy simulations of a model body wash with different levels of salt additions and the addition of perfume raw materials. We show that these predictions agree well with rheological experiments and simulations results obtained though the Pointer Algorithm calculated in a recent paper.13 Furthermore, using scission energies, we demonstrate the ability of the simulations to describe the non-linear effect of multiple additives in controlling the viscoelastic properties. Materials and methods System compositions The model body wash formulations studied here are analogous to the BW-1EO formulations used in a previous study.13 Specifically, we study an 11 wt. % BW-1EO aqueous solution consisting of a mixture of 9.85 wt. % SLE1S, 1.15 wt. % CAPB with various level of salt concentrations, and perfume raw materials (PRMs). “SLE1S” designates a commercial sodium lauryl ether sulfate with a distribution of the number of ethylene-oxide groups with an average of 1.0; “CAPB” (cocamidopropyl betaine, all chemical structures are included in the Supplementary Information) is a zwitterionic cosurfactant. Note that, typically, CAPB is prepared by reacting chloroacetic acid with the amide of dimethylaminopropylamine and lauric acid, with subsequent neutralization with sodium hydroxide. Commercial samples of CAPB therefore typically include some NaCl. For comparison against experimental data, compositions specified below account for both NaCl introduced by CAPB raw 2 ACS Paragon Plus Environment
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material as well as NaCl explicitly added to the formulation. For range finding, we simulated formulas at 0.5, 2.5 and 5.0 wt% NaCl. For a limited number of samples, we also ran simulations at salt levels of 0.83, 0.95, 1.20 and 1.45 wt% NaCl for comparison against previous experimental results. Some of our systems here include a model perfume accord (“ACCORD”) to make the compositions more relevant to typical body washes. ACCORD is a simplified depiction of a typical commercial perfume (with typically dozens of PRMs). Our model accord is composed of the following PRMs (weight fractions in percentages, with molecular structures listed inSupplementary Information): heliotropin (15.4%), linalool (23.3%), allyl amyl glycolate (13.5%), undecavertol (25.6%), beta-ionone (11.5 %), and synambran (10.7). In addition, each of the following compounds were separately added to some formulations at a level of 0.025 mol/l (abbreviations in parenthesis): dipropylene glycol (DPG), cumene, linalool, and isopropyl myristate (IPM). Dissipative Particle Dynamics simulations We use coarse grained dissipative particle dynamics (DPD) simulations to probe the structure and dynamics of micelles on length scales of 10’s of nms. Over the last two decades since its introduction,17–19 DPD has become a popular method for simulating self-assembling and amphiphilic molecules.20–27 In DPD, typically, a soft-repulsive potential is used to describe the specific interactions between spherical beads that represent different molecular groups, where a “molecular group” is a collection of 3-5 heavy atoms per bead. Each bead (or particle) interacts with neighboring particles i, j through pairwise forces obeying Newton’s equations of motion: (3) / = 1(2 4 + 2 6 + 2 7 ) &
38&
&3
&3
&3
Here, 2&34 , 2&36 and 2&37 are the conservative, dissipative and random forces respectively. The latter two forces provide a Langevin thermostat through fluctuation and dissipation of energy:
2&36 = −:;6
