The Relationship between Wormlike Micelle Scission Free Energy and Micellar Composition: The Case of Sodium Lauryl Ether Sulfate and Cocamidopropyl Betaine

Influence of Surfactant Structure on Polydisperse Formulations of Alkyl Ether Sulfates and Alkyl Amidopropyl Betaines

Surfactants provide detergency, foaming, and texture in personal care formulations, yet the micellization of typical industrial primary and cosurfactants is not well understood, particularly in light of the polydisperse nature of commercial surfactants. Synergistic interactions are hypothesized to drive the formation of elongated wormlike self-assemblies in these mixed surfactant systems. Small-angle neutron scattering, rheology, and pendant drop tensiometry are used to examine surface adsorption, viscoelasticity, and self-assembly structure for wormlike micellar formulations comprising cocoamidopropyl betaine, and its two major components laurylamidopropyl betaine and oleylamidopropyl betaine, with sodium alkyl ethoxy sulfates. The tail length of sodium alkyl ethoxy sulfates was related to their ability to form wormlike micelles in electrolyte solutions, indicating that a tail length greater than 10 carbons is required to form wormlike micelles in NaCl solutions, with the decyl homologue unable to form elongated micelles and maintaining a low viscosity even at 20 wt % surfactant loading with 4 wt % NaCl present. For these systems, the incorporation of a disperse ethoxylate linker does not enable shorter chain surfactants to elongate into wormlike micelles for single-component systems; however, it could increase the interactions between surfactants in mixed surfactant systems. For synergy in surfactant mixing, the nonideal regular solution theory is used to study the sulfate/betaine mixtures. Tail mismatch appears to drive lower critical micelle concentrations, although tail matching improves synergy with larger relative reductions in critical micelle concentrations and greater micelle elongation, as seen by both tensiometric and scattering measurements.

A many-body dissipative particle dynamics parametrisation scheme to study behaviour at air-water interfaces

In this article, we present a general parametrisation scheme for many-body dissipative particle dynamics (MDPD). The scheme is based on matching model components to experimental surface tensions and chemical potentials. This allows us to obtain the correct surface and mixing behaviours of complex, multicomponent systems. The methodology is tested by modelling the behaviour of nonionic polyoxyethylene alkyl ether surfactants at an air/water interface. In particular, the influence of the number of ethylene oxide units in the surfactant head group is investigated. We find good agreement with many experimentally obtained parameters, such as minimum surface area per molecule; and a decrease in the surface tension with increasing surfactant surface density. Moreover, we observe an orientational transition, from surfactants lying directly on the water surface at low surface coverage, to surfactants lying parallel or tilted with respect to the surface normal at high surface coverage. The parametrisation scheme is also extended to cover the zwitterionic surfactant lauryldimethylamine oxide (LDAO), where we provide good predictions for the surface tension at maximum surface coverage. Here, if we exceed this coverage, we are able to demonstrate the spontaneous production of micelles from the surface surfactant layer.

Molecular Insights on Morphology, Composition, and Stability of Mixed Micelles Formed by Ionic Surfactant and Nonionic Block Copolymer in Water Using Coarse-Grained Molecular Dynamics Simulations

The nanoscale association domains are the ultimate determinants of the macroscopic properties of complex fluids involving amphiphilic polymers and surfactants, and hence, it is foremost important to understand the role of polymer/surfactant concentration on these domains. We have used coarse-grained molecular dynamics simulations to investigate the effect of polymer/surfactant concentration on the morphology of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO, i.e., pluronics or poloxamers) block copolymer, and ionic surfactants sodium dodecyl sulfate (SDS), mixed micelles in aqueous solution. The proclivity of the surfactant to form the mixed micelles is also probed using umbrella sampling simulations. In this study, we observed that the core of the pluronic + SDS formed mixed micelles consists of PPO, the alkyl tail of SDS, and some water molecules, whereas the PEO, water, and sulfate headgroups of SDS form a shell, consistent with experimental observations. The micelles are spherical at high-pluronic/low-SDS compositions, ellipsoidal at high-SDS/low-pluronic compositions, and wormlike-cylindrical at high-pluronic/high-SDS compositions. The transitions in micelle morphology are governed by the solvent accessible surface area of mixed aggregates, electrostatic repulsion between SDS-headgroups, and dehydration of PEO and PPO segments. The free energy barrier for SDS escape is much higher in mixed micelles than in pure SDS micelles, indicating a stronger tendency for SDS to form pluronic-SDS mixed micelles.

Flow-induced scission of wormlike micelles in nonionic surfactant solutions under shear flow

We investigate flow-induced scission of wormlike micelles with dissipative particle dynamics simulations of nonionic surfactant solutions under shear flow. To understand flow-induced scission in terms of micellar timescales, we propose a method to evaluate the longest relaxation time of unentangled surfactant micelles from the rotational relaxation time and the average lifetime at equilibrium. The mean squared displacement of surfactant molecules provides evidence that the longest relaxation time estimated by the proposed method serves as the characteristic timescale at equilibrium. We also demonstrate that the longest relaxation time plays an essential role in flow-induced scission. Using conditional statistics based on the aggregation number of micelles, we examine the statistical properties of the lifetime of wormlike micelles. We then conclude that flow-induced scission occurs when the Weissenberg number defined as the product of the longest relaxation time and the shear rate is larger than a threshold value.

Structural properties of cationic surfactant-fatty alcohol bilayers: insights from dissipative particle dynamics

Bilayers, self-assembled by cationic surfactants and fatty alcohols in water, are the basic units of lamellar gel networks - creamy formulations extensively used in cosmetics and pharmaceutics. Mesoscopic modelling and study of the bilayers formed by single- or double-tail cationic surfactants (CTAC or DHDAC), and fatty alcohols (FAs) in the lamellar fluid and gel phases were employed. Fatty alcohols with alkyl tail equal to or greater than the surfactant alkyl tail, i.e., C₁₆FA or C₁₈FA and C₂₂FA, were considered. A model formulation was explored with the FA concentration greater than that of the surfactant and the structure of the fluid and gel bilayers in tensionless state characterised via the density profiles across the bilayers, orientational order parameters of the surfactant and FA chains, intrinsic analysis of the bilayer interfaces, and bending rigidity. The intrinsic analysis allows identification and quantification of the coexistence of the interdigitated and non-interdigitated phases present within the gel bilayers. The FA chains were found to conform the primary scaffolding of the bilayers while the surfactant chains tessellate bilayer monolayers from their water-hydrophobic interface. Further, the overlap of the FA chains from the apposed monolayers of the fluid bilayers rises with increasing FA length. Finally, the prevalence of the non-interdigitated phase over the interdigitated phase within the gel bilayers becomes enhanced upon the FA length increase with a preference of the surfactant chains to reside in the non-interdigitated phase rather than the interdigitated phase.

Heads or tails? The synthesis, self-assembly, properties and uses of betaine and betaine-like surfactants

Betaines are a key class of zwitterionic surfactant that exhibit particularly favorable properties, making them indispensable in modern formulation. Due to their composition, betaines are readily biodegradable, mild on the skin and exhibit some antimicrobial activity. Vital to their function, these surfactants self-assemble into diverse micellar geometries, some of which contribute to increased solution viscosity, and their surface activity results in strong detergency and foaming. As such, their behavior has been exploited in various applications from personal care (including shampoos and liquid soaps) to specific industrial fields (such as enhanced oil recovery). This review aims to inform the reader of the diverse range of different betaine and betaine-like surfactants that have been actively researched over the past three decades. Synthesis as well as both chemical and physical characterization of betaine surfactants are discussed, including small-angle scattering studies that indicate self-assembly structures and rheological data that demonstrates texture and flow. Stimulus responsive systems and exotic betaine analogs with enhanced functionality are also covered. Crucially, the connection between surfactant molecular architecture and function are highlighted, exemplifying precisely why zwitterionic betaine and related surfactants are so uniquely functional.

Comparison of equilibrium techniques for the viscosity calculation from DPD simulations

Dissipative Particle Dynamics (DPD) is a powerful mesoscopic modelling technique that is routinely used to predict complex fluid morphology and structural properties. While its ability to quickly scan the conformational space is well known, it is unclear if DPD can correctly calculate the viscosity of complex fluids. In this work, we estimate the viscosity of several unentangled polymer solutions using both the Einstein and Green-Kubo formulas. For this purpose, an Einstein relation is derived analogous to the revised Green-Kubo formula suggested by Jung and Schmid, J. Chem. Phys., 2016, 144, 204104. We show that the DPD simulations reproduce the dynamical behaviour predicted by the theory irrespectively of the values of the conservative and friction parameters used and estimate a Schmidt number compatible to that of a fluid system. Moreover, we observe that the Einstein method requires shorter trajectories to achieve the same statistical accuracy as the Green-Kubo formula. This work shows that DPD can confidently be used to calculate the viscosity of complex fluids and that the statistical accuracy of short trajectories can be improved by using our revised Einstein formula.

Stability and Diffusion Properties of Insulin in Dissolvable Microneedles: A Multiscale Simulation Study

Microneedle (MN) technology has been proven to be promising to become an effective drug delivery route of insulin for diabetes treatment, with the advantages of high delivery efficiency, convenient management, and minimal risk of infection. However, efforts are still required to verify the insulin activity in MNs for further clinical application. Moreover, it is also essential to study the diffusion properties of insulin to understand the ability of various MN materials to control insulin release. Herein, we have combined all-atom molecular dynamics simulation and coarse-grained dissipative particle dynamics to systematically study insulin's structural stability and diffusion coefficient in polyvinyl alcohol and hyaluronic acid solutions. The all-atom simulation reveals the dissimilarities in the interaction mode between insulin and the two polymers. It also points out that the presence of the two polymers would not irreversibly impact the secondary structure of insulin, thereby ensuring regular insulin expression in vivo. Mesoscopic simulation results manifest that the diffusion coefficient of insulin in hyaluronic acid (HA) solution is greater than that of the polyvinyl alcohol (PVA) system. Meanwhile, through the study of insulin centroid trajectory, we have claimed two different diffusion mechanisms of insulin in polymer solution: The movement of insulin in the HA and water solution follows the Brownian motion rule. In comparison, the hopping effect of insulin has been observed in the PVA solution due to poor intermolecular affinity as well as lower polymer water solubility. By summarizing different diffusion mechanisms, this study can provide theoretical guidance for preparing insulin-loaded dissolvable MNs.

Salt- and pH-Dependent Viscosity of SDS/LAPB Solutions: Experiments and a Semiempirical Thermodynamic Model

We present novel data on the composition-, pH-, and salt-dependent zero shear viscosity of the commercially important mixture of anionic sodium dodecyl sulfate (SDS) and zwitterionic lauramidopropyl betaine (LAPB). We show via proton NMR experiments that the notionally zwitterionic LAPB exhibits a large pK_a shift in the presence of SDS and can become partially cationic at formulation-relevant pH ranges of 4.5-6.0-that is, the binary system is effectively a ternary system. This has a pronounced effect on the viscosity of the system at low pH, especially if the fraction of LAPB is high. We use theoretical arguments to motivate a semiempirical but practical approach to model the viscosity of the mixtures using thermodynamic parameters such as the excess chemical potentials or activity coefficients of the surfactants. We demonstrate this using an augmented regular solution theory-based mixed micelle thermodynamic model and develop robust regression models using Bayesian approaches. We also show how the pK_a shift from NMR experiments can be used to parameterize the thermodynamic model. This framework should be extensible to other arbitrary surfactant mixtures in the future and hence will be of broad interest for the development of surfactant formulations for household, personal care, and other applications.

Critical Micelle Concentrations in Surfactant Mixtures and Blends by Simulation

We explore the use of coarse-grained dissipative particle dynamics simulations to predict critical micelle concentrations (CMCs) in polydisperse surfactant mixtures and blends. By fitting pseudo-phase separation models (PSMs) to aqueous solutions of binary surfactant mixtures at selected compositions above the CMC, we avoid the need for expensive simulations of more complex multicomponent mixtures performed as a function of dilution. The approach is demonstrated for sodium laureth sulfate (SLES) surfactants with polydispersity in the ethoxylate spacer. For this system, we find a modest degree of cooperativity in micelle formation, which we attribute to the reduced repulsion between charged headgroups for surfactants with dissimilar ethoxylate spacer lengths. However, this is insufficient to explain the lowered CMC often observed in commercial SLES samples, which we attribute to the presence of small amounts of unsulfated alkyl ethoxylates and/or traces of salt.

Where are those lipid nano rings?

Highly curved toroidal micelles with diameters as small as 100 nm have been successfully constructed by self-assembly of amphiphilic block copolymers. These structures may have potential applications in gene or drug delivery. Experimental observations suggest that toroidal micelles likely originate from spherical or disc-like micelles which are tricked into forming toroidal micelles upon external stimuli ('smart' materials). Since self-assembly of polymeric and lipid surfactants is guided by the same physical principles, we hypothesize that 'smart' lipid surfactants can be equivalently tricked into forming highly curved toroidal micelles that are tenfold smaller (≃10 nm diameter). Paradoxically, these 'nano rings' have never been observed. Using coarse-grained molecular dynamics (MD) simulations in conjunction with a state-of-the-art free energy calculation method (a string method), we illustrate how a thermo-responsive lipid surfactant is able to form toroidal micelles. These micelles originate from disc-like micelles that are spontaneously perforated upon heat shocking, thereby supporting a longstanding hypothesis on the possible origin of polymeric toroidal micelle phases observed in experiments. We illustrate that kinetically stable 'nano rings' are substantially shorter lived than their tenfold larger polymeric analogs. The estimated life-time (milliseconds) is in fact similar to the characteristic breaking time of the corresponding worm-like micelle. Finally, we resolve the characteristic finger print which 'nano rings' leave in time-resolved X-ray spectra and illustrate how the uptake of small DNA fragments may enhance their stability. Despite a shared kinetics of self-assembly, length scale dependent differences in the life-time of surfactant phases can occur when phases are kinetically rather than thermodynamically stable. This results in the apparent absence or presence of toroidal micelle phases on different length scales. Our theoretical work precisely illustrates that the universality of surfactants nevertheless remains conserved even at different length scales.