Boundary Lubrication Performance of Polyelectrolyte-Surfactant Complexes on Biomimetic Surfaces.

Aqueous mixtures of oppositely charged polyelectrolytes and surfactants are useful in many industrial applications, such as shampoos and hair conditioners. In this work, we investigate the friction between biomimetic hair surfaces in the presence of adsorbed complexes formed from cationic polyelectrolytes and anionic surfactants in an aqueous solution. We apply nonequilibrium molecular dynamics (NEMD) simulations using the coarse-grained MARTINI model. We first developed new MARTINI parameters for cationic guar gum (CGG), a functionalized, plant-derived polysaccharide. The complexation of CGG and the anionic surfactant sodium dodecyl sulfate (SDS) on virgin and chemically damaged biomimetic hair surfaces was studied using a sequential adsorption approach. We then carried out squeeze-out and sliding NEMD simulations to assess the boundary lubrication performance of the CGG-SDS complex compressed between two hair surfaces. At low pressure, we observe a synergistic friction behavior for the CGG-SDS complex, which gives lower shear stress than either pure CGG or SDS. Here, friction is dominated by viscous dissipation in an interfacial layer comprising SDS and water. At higher pressures, which are probably beyond those usually experienced during hair manipulation, SDS and water are squeezed out, and friction increases due to interdigitation. The outcomes of this work are expected to be beneficial to fine-tune and screen sustainable hair care formulations to provide low friction and therefore a smooth feel and reduced entanglement.

Effects of surfactant adsorption on the wettability and friction of biomimetic surfaces.

The properties of solid-liquid interfaces can be markedly altered by surfactant adsorption. Here, we use molecular dynamics (MD) simulations to study the adsorption of ionic surfactants at the interface between water and heterogeneous solid surfaces with randomly arranged hydrophilic and hydrophobic regions, which mimic the surface properties of human hair. We use the coarse-grained MARTINI model to describe both the hair surfaces and surfactant solutions. We consider negatively-charged virgin and bleached hair surface models with different grafting densities of neutral octadecyl and anionic sulfonate groups. The adsorption of cationic cetrimonium bromide (CTAB) and anionic sodium dodecyl sulfate (SDS) surfactants from water are studied above the critical micelle concentration. The simulated adsorption isotherms suggest that cationic surfactants adsorb to the surfaces via a two-stage process, initially forming monolayers and then bilayers at high concentrations, which is consistent with previous experiments. Anionic surfactants weakly adsorb via hydrophobic interactions, forming only monolayers on both virgin and medium bleached hair surfaces. We also conduct non-equilibrium molecular dynamics simulations, which show that applying cationic surfactant solutions to bleached hair successfully restores the low friction seen with virgin hair. Friction is controlled by the combined surface coverage of the grafted lipids and the adsorbed CTAB molecules. Treated surfaces containing monolayers and bilayers both show similar friction, since the latter are easily removed by compression and shear. Further wetting MD simulations show that bleached hair treated with CTAB increases the hydrophobicity to similar levels seen for virgin hair. Treated surfaces containing CTAB monolayers with the tailgroups pointing predominantly away from the surface are more hydrophobic than bilayers due to the electrostatic interactions between water molecules and the exposed cationic headgroups.

Coarse-grained molecular models of the surface of hair.

We present a coarse-grained molecular model of the surface of human hair, which consists of a supported lipid monolayer, in the MARTINI framework. Using coarse-grained molecular dynamics (MD) simulations, we identify a lipid grafting distance that yields a monolayer thickness consistent with both atomistic MD simulations and experimental measurements of the hair surface. Coarse-grained models for fully-functionalised, partially damaged, and fully damaged hair surfaces are created by randomly replacing neutral thioesters with anionic sulfonate groups. This mimics the progressive removal of fatty acids from the hair surface by bleaching and leads to chemically heterogeneous surfaces. Using molecular dynamics (MD) simulations, we study the island structures formed by the lipid monolayers at different degrees of damage in vacuum and in the presence of polar (water) and non-polar (n-hexadecane) solvents. We also use MD simulations to compare the wetting behaviour of water and n-hexadecane droplets on the model surfaces through contact angle measurements, which are compared to experiments using virgin and bleached hair. The model surfaces capture the experimentally-observed transition of the hair surface from hydrophobic (and oleophilic) to hydrophilic (and oleophobic) as the level of bleaching damage increases. By selecting surfaces with specific damage ratios, we obtain contact angles from the MD simulations that are in good agreement with experiments for both solvents on virgin and bleached human hairs. To negate the possible effects of microscale curvature and roughness of real hairs on wetting, we also conduct additional experiments using biomimetic surfaces that are co-functionalised with fatty acids and sulfonate groups. In both the MD simulations and experiments, the cosine of the water contact angle increases linearly with the sulfonate group surface coverage with a similar slope. We expect that the proposed systems will be useful for future molecular dynamics simulations of the adsorption and tribological behaviour of hair, as well as other chemically heterogeneous surfaces.

Rates of cavity filling by liquids.

Understanding the fundamental wetting behavior of liquids on surfaces with pores or cavities provides insights into the wetting phenomena associated with rough or patterned surfaces, such as skin and fabrics, as well as the development of everyday products such as ointments and paints, and industrial applications such as enhanced oil recovery and pitting during chemical mechanical polishing. We have studied, both experimentally and theoretically, the dynamics of the transitions from the unfilled/partially filled (Cassie-Baxter) wetting state to the fully filled (Wenzel) wetting state on intrinsically hydrophilic surfaces (intrinsic water contact angle <90°, where the Wenzel state is always the thermodynamically favorable state, while a temporary metastable Cassie-Baxter state can also exist) to determine the variables that control the rates of such transitions. We prepared silicon wafers with cylindrical cavities of different geometries and immersed them in bulk water. With bright-field and confocal fluorescence microscopy, we observed the details of, and the rates associated with, water penetration into the cavities from the bulk. We find that unconnected, reentrant cavities (i.e., cavities that open up below the surface) have the slowest cavity-filling rates, while connected or non-reentrant cavities undergo very rapid transitions. Using these unconnected, reentrant cavities, we identified the variables that affect cavity-filling rates: (i) the intrinsic contact angle, (ii) the concentration of dissolved air in the bulk water phase (i.e., aeration), (iii) the liquid volatility that determines the rate of capillary condensation inside the cavities, and (iv) the presence of surfactants.

Computer simulations of colloidal gels: how hindered particle rotation affects structure and rheology.

The effects of particle roughness and short-ranged non-central forces on colloidal gels are studied using computer simulations in which particles experience a sinusoidal variation in energy as they rotate. The number of minima n and energy scale K are the key parameters; for large K and n, particle rotation is strongly hindered, but for small K and n particle rotation is nearly free. A series of systems are simulated and characterized using fractal dimensions, structure factors, coordination number distributions, bond-angle distributions and linear rheology. When particles rotate easily, clusters restructure to favor dense packings. This leads to longer gelation times and gels with strand-like morphology. The elastic moduli of such gels scale as G'∝ω0.5 at high shear frequencies ω. In contrast, hindered particle rotation inhibits restructuring and leads to rapid gelation and diffuse morphology. Such gels are stiffer, with G'∝ω0.35. The viscous moduli G'' in the low-barrier and high-barrier regimes scale according to exponents 0.53 and 0.5, respectively. The crossover frequency between elastic and viscous behaviors generally increases with the barrier to rotation. These findings agree qualitatively with some recent experiments on heterogeneously-surface particles and with studies of DLCA-type gels and gels of smooth spheres.

Automated Measurement of Spatially Resolved Hair-Hair Single Fiber Adhesion.

The adhesion force between individual human hair fibers in a crosshair geometry was measured by observing their natural bending and adhesive jumps out of contact, using optical video microscopy. The hair fibers' natural elastic responses, calibrated by measuring their natural resonant frequencies, were used to measure the forces. Using a custom-designed, automated apparatus to measure thousands of individual hair-hair contacts along millimeter length scales of hair, it was found that a broad, yet characteristic, spatially variant distribution in adhesion force is measured on the 1 to 1000 nN scale for both clean and conditioner-treated hair fibers. Comparison between the measured adhesion forces and adhesion forces modeled from the hairs' surface topography (measured using confocal laser profilometry) shows they have a good order-of-magnitude agreement and have similar breadth and shape. The agreement between the measurements and the model suggests, perhaps unsurprisingly, that hair-hair adhesion is governed, to a first approximation, by the unique surface structure of the hairs' cuticles and, therefore, the large distribution in local mean curvature at the various individual contact points along the hairs' lengths. We posit that haircare products could best control the surface properties (or at least the adhesive properties) between hairs by directly modifying the hair surface microstructure.

Nonmonotonic Scission and Branching Free Energies as Functions of Hydrotrope Concentration for Charged Micelles.

Using coarse-grained molecular dynamics simulations and an umbrella sampling method that uses local surfactant density as a reaction coordinate, we directly calculate, for the first time, both the scission and branching free energies of a model charged micelle [cationic cetyltrimethylammonium chloride (CTAC)] in the presence of inorganic and organic salts (hydrotropes). We find that while inorganic salt only weakly affects the micelle scission energy, organic hydrotropes produce a strong, nonmonotonic dependence of both scission energy and branching on salt concentration. The nonmonotonicity in scission energy is traced to a competition between electrostatic screening of the repulsions among the surfactant head groups and thinning of the micellar core, which result from attachment of the hydrotropes to the micelle surface. We are able to correlate the nonmonotonicity in the scission energy of CTAC micelles with the peak observed experimentally in viscosity versus hydrotrope concentration and the location of this peak in CTAC solutions.

Scission Free Energies for Wormlike Surfactant Micelles: Development of a Simulation Protocol, Application, and Validation for Personal Care Formulations.

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 parametrization of the underlying DPD potential is required for quantitative agreement.

Probing Additive Loading in the Lamellar Phase of a Nonionic Surfactant: Gibbs Ensemble Monte Carlo Simulations Using the SDK Force Field.

Understanding solute uptake into soft microstructured materials, such as bilayers and worm-like and spherical micelles, is of interest in the pharmaceutical, agricultural, and personal care industries. To obtain molecular-level insight on the effects of solutes loading into a lamellar phase, we utilize the Shinoda-Devane-Klein (SDK) coarse-grained force field in conjunction with configurational-bias Monte Carlo simulations in the osmotic Gibbs ensemble. The lamellar phase is comprised of a bilayer formed by triethylene glycol mono- n-decyl ether (C10E3) surfactants surrounded by water with a 50:50 surfactant/water weight ratio. We study both the unary adsorption isotherm and the effects on bilayer structure and stability caused by n-nonane, 1-hexanol, and ethyl butyrate at several different reduced reservoir pressures. The nonpolar n-nonane molecules load near the center of the bilayer. In contrast, the polar 1-hexanol and ethyl butyrate molecules both load with their polar bead close to the surfactant head groups. Near the center of the bilayer, none of the solute molecules exhibits a significant orientational preference. Solute molecules adsorbed near the polar groups of the surfactant chains show a preference for orientations perpendicular to the interface, and this alignment with the long axis of the surfactant molecules is most pronounced for 1-hexanol. Loading of n-nonane leads to an increase of the bilayer thickness, but does not affect the surface area per surfactant. Loading of polar additives leads to both lateral and transverse swelling. The reduced Henry's law constants of adsorption (expressed as a molar ratio of additive to surfactant per reduced pressure) are 0.23, 1.4, and 14 for n-nonane, 1-hexanol, and ethyl butyrate, respectively, and it appears that the SDK force field significantly overestimates the ethyl butyrate-surfactant interactions.

Contact Angle and Adhesion Dynamics and Hysteresis on Molecularly Smooth Chemically Homogeneous Surfaces.

Measuring truly equilibrium adhesion energies or contact angles to obtain the thermodynamic values is experimentally difficult because it requires loading/unloading or advancing/receding boundaries to be measured at rates that can be slower than 1 nm/s. We have measured advancing-receding contact angles and loading-unloading adhesion energies for various systems and geometries involving molecularly smooth and chemically homogeneous surfaces moving at different but steady velocities in both directions, ±V, focusing on the thermodynamic limit of ±V → 0. We have used the Bell Theory (1978) to derive expressions for the dynamic (velocity-dependent) adhesion energies and contact angles suitable for both (i) dynamic adhesion measurements using the classic Johnson-Kendall-Roberts (JKR, 1971) theory of "contact mechanics" and (ii) dynamic contact angle hysteresis measurements of both rolling droplets and syringe-controlled (sessile) droplets on various surfaces. We present our results for systems that exhibited both steady and varying velocities from V ≈ 10 mm/s to 1 nm/s, where in all cases but one, the advancing (V > 0) and receding (V < 0) adhesion energies and/or contact angles converged toward the same theoretical (thermodynamic) values as V → 0. Our equations for the dynamic contact angles are similar to the classic equations of Blake & Haynes (1969) and fitted the experimental adhesion data equally well over the range of velocities studied, although with somewhat different fitting parameters for the characteristic molecular length/dimension or area and characteristic bond formation/rupture lifetime or velocity. Our theoretical and experimental methods and results unify previous kinetic theories of adhesion and contact angle hysteresis and offer new experimental methods for testing kinetic models in the thermodynamic, quasi-static, limit. Our analyses are limited to kinetic effects only, and we conclude that hydrodynamic, i.e., viscous, and inertial effects do not play a role at the interfacial velocities of our experiments, i.e., V < (1-10) mm/s (for water and hexadecane, but for viscous polymers it may be different), consistent with previously reported studies.

Liquid-liquid equilibria for soft-repulsive particles: improved equation of state and methodology for representing molecules of different sizes and chemistry in dissipative particle dynamics.

Three developments are presented that significantly expand the applicability of dissipative particle dynamics (DPD) simulations for symmetric and non-symmetric mixtures, where the former contain particles with equal repulsive parameter for self-interactions but a different repulsive parameter for cross-interactions, and the latter contain particles with different repulsive parameters also for the self-interactions. Monte Carlo and molecular dynamics simulations for unary phases covering a wide range of repulsive parameters and of densities for single-bead DPD particles point to deficiencies of the Groot and Warren equation of state (GW-EOS) [J. Chem. Phys. 107, 4423 (1997)]. A revised version, called rGW-EOS, is proposed here that is significantly more accurate over a wider range of parameters/densities. The second development is the generalization of the relationship between the Flory-Huggins χ parameter and the repulsive cross-interaction parameter when the two particles involved have different molecular volumes. The third aspect is an investigation of Gibbs ensemble Monte Carlo simulation protocols, which demonstrates the importance of volume fluctuations and excess volumes of mixing even for equimolar symmetric mixtures of DPD particles. As an illustrative example, the novel DPD methodology is applied to the prediction of the liquid-liquid equilibria for acetic anhydride/(n-hexane or n-octane) binary mixtures.

Predicting proton titration in cationic micelle and bilayer environments.

Knowledge of the protonation behavior of pH-sensitive molecules in micelles and bilayers has significant implications in consumer product development and biomedical applications. However, the calculation of pKa's in such environments proves challenging using traditional structure-based calculations. Here we apply all-atom constant pH molecular dynamics with explicit ions and titratable water to calculate the pKa of a fatty acid molecule in a micelle of dodecyl trimethylammonium chloride and liquid as well as gel-phase bilayers of diethyl ester dimethylammonium chloride. Interestingly, the pKa of the fatty acid in the gel bilayer is 5.4, 0.4 units lower than that in the analogous liquid bilayer or micelle, despite the fact that the protonated carboxylic group is significantly more desolvated in the gel bilayer. This work illustrates the capability of all-atom constant pH molecular dynamics in capturing the delicate balance in the free energies of desolvation and Coulombic interactions. It also shows the importance of the explicit treatment of ions in sampling the protonation states. The ability to model dynamics of pH-responsive substrates in a bilayer environment is useful for improving fabric care products as well as our understanding of the side effects of anti-inflammatory drugs.

Self-assembly and bilayer-micelle transition of fatty acids studied by replica-exchange constant pH molecular dynamics.

Recent interest in the development of surfactant-based nanodelivery systems targeting tumor sites has sparked our curiosity in understanding the detailed mechanism of the self-assembly and phase transitions of pH-sensitive surfactants. Toward this goal, we applied a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with the hybrid-solvent scheme and pH-based replica-exchange protocol, to study the de novo self-assembly of 30 and 40 lauric acids, a simple model titratable surfactant. We observed the formation of a gel-state bilayer at low and intermediate pH and a spherical micelle at high pH, with the phase transition starting at 20-30% ionization and being completed at 50%. The degree of cooperativity for the transition increases from the 30-mer to the 40-mer. The calculated apparent or bulk pKa value is 7.0 for the 30-mer and 7.5 for the 40-mer. Congruent with experiment, these data demonstrate that CpHMD is capable of accurately modeling large conformational transitions of surfactant systems while allowing the simultaneous proton titration of constituent molecules. We suggest that CpHMD simulations may become a useful tool in aiding in the design and development of pH-sensitive nanocarriers for a variety of biomedical and technological applications.

Nanoscale friction of biomimetic hair surfaces.

We investigate the nanoscale friction between biomimetic hair surfaces using chemical colloidal probe atomic force microscopy experiments and nonequilibrium molecular dynamics simulations. In the experiments, friction is measured between water-lubricated silica surfaces functionalised with monolayers formed from either octadecyl or sulfonate groups, which are representative of the surfaces of virgin and ultimately bleached hair, respectively. In the simulations, friction is monitored between coarse-grained model hair surfaces with different levels of chemical damage, where a specified amount of grafted octadecyl groups are randomly replaced with sulfonate groups. The sliding velocity dependence of friction in the simulations can be described using an extended stress-augmented thermally activation model. As the damage level increases in the simulations, the friction coefficient generally increases, but its sliding velocity-dependence decreases. At low sliding velocities, which are closer to those encountered experimentally and physiologically, we observe a monotonic increase of the friction coefficient with damage ratio, which is consistent with our new experiments using biomimetic surfaces and previous ones using real hair. This observation demonstrates that modified surface chemistry, rather than roughness changes or subsurface damage, control the increase in nanoscale friction of bleached or chemically damaged hair. We expect the methods and biomimetic surfaces proposed here to be useful to screen the tribological performance of hair care formulations both experimentally and computationally.

Atomistic simulations of pH-dependent self-assembly of micelle and bilayer from fatty acids.

Detailed knowledge of the self-assembly and phase behavior of pH-sensitive surfactants has implications in areas such as targeted drug delivery. Here we present a study of the formation of micelle and bilayer from lauric acids using a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with conformational sampling in explicit solvent and the pH-based replica-exchange protocol. We find that at high pH conditions a spherical micelle is formed, while at low pH conditions a bilayer is formed with a considerable degree of interdigitation. The mid-point of the phase transition is in good agreement with experiment. Preliminary investigation also reveals that the effect of counterions and salt screening shifts the transition mid-point and does not change the structure of the surfactant assembly. Based on these data we suggest that CpHMD simulations may be applied to computational design of surfactant-based nano devices in the future.

Nonane and Hexanol Adsorption in the Lamellar Phase of a Nonionic Surfactant: Molecular Simulations and Comparison to Ideal Adsorbed Solution Theory.

Adsorption of n-nonane/1-hexanol (C9/C6OH) mixtures into the lamellar phase formed by a 50/50 w/w triethylene glycol mono-n-decyl ether (C10E3)/water system was studied using configurational-bias Monte Carlo simulations in the osmotic Gibbs ensemble. The interactions were described by the Shinoda-Devane-Klein coarse-grained force field. Prior simulations probing single-component adsorption indicated that C9 molecules preferentially load near the center of the bilayer, increasing the bilayer thickness, whereas C6OH molecules are more likely to be found near the interface of the polar and nonpolar moieties, swelling the bilayer in the lateral dimension. Here, we extend this work to binary C9/C6OH adsorption to probe whether the difference in the spatial preferences may lead to a synergistic effect and enhanced loadings for the mixture. Comparing loading trends and the thermodynamics of binary adsorption to unary adsorption reveals that C9-C9 interactions lead to the largest enhancement, whereas C9-C6OH and C6OH-C6OH interactions are less favorable for this bilayer system. Ideal adsorbed solution theory yields satisfactory predictions of the binary loading.

Molecular dynamics simulations of ionic and nonionic surfactant micelles with a generalized Born implicit-solvent model.

In recent years, all-atom and coarse-grained models have been developed and applied to simulations of micelles and biological membranes. Here, we explore the question of whether a combined all-atom representation of surfactant molecules and continuum description of solvent based on the generalized Born model can be used to study surfactant micelles. Specifically, we report the parameterization of the GBSW model with a surface-area dependent nonpolar solvation energy term for dodecyl sulfate, dodecyl tetramethylammonium, and dodecyl triethyleneglycol ether molecules. In the parameterization procedure,the atomic Born radii were derived from the radial distribution functions of solvent charge and refined targeting the potential of mean force of dimer interactions from explicit-solvent simulations. The optimized radii were then applied in molecular dynamics simulations of the ionic and nonionic micelles.We found that the micelles are stable but more compact and rigid than in explicit solvent as a consequence of the drastic reduction in solvation and mobility of surfactant monomers within the micelle. Based on these data and our previous work, we suggest that in addition to a more accurate description of the nonpolar solvation energy, the ruggedness in the short-range interactions due to solvent granularity is a critical feature that needs to be taken into account to accurately model processes such as micelle formation and protein folding in implicit solvent. Finally, the explicit-solvent data presented here offers new insights into different conformational behavior of ionic and nonionic micelles which is valuable for understanding hydrophobic assemblies and of interest to the detergent industry.

The shape and dynamics of deformations of viscoelastic fluids by water droplets.

Many studies on the deformation of soft films by liquids confirmed the increase in the radius of the deformation and the decrease in the apparent contact angle. However, due to the thinness, the dynamics of the deformation could not be observed until the thermodynamic equilibrium. Thus, the dynamics on thick soft materials was studied until equilibrium to contrast the effect of different interfacial energy between different soft materials and water. Therefore, we prepared two different polymeric fluids with similar rheology by cross-linking monomers, yet with different contact angles with water. Sometime after water droplets were placed on these thick polymers, 3D profiles of the deformation were recorded. Though the effect of the surface tension was not verified, the same trend in the dynamics was observed as with thin films, except for the decrease in the radius after the initial increase. The three-phase boundaries (TPBs) were found not at the apex of the ridges formed during the transition to equilibrium. By calculating the surface tensions and angles of each interface at the equilibrium, we found that the temporary imbalance among surface tensions induced the slip of the TPBs toward the center of water droplets, thus dislocating the TPBs and decreasing the radius.

Multiscale Modeling of the Effects of Salt and Perfume Raw Materials on the Rheological Properties of Commercial Threadlike Micellar Solutions.

We link micellar structures to their rheological properties for two surfactant body-wash formulations at various concentrations of salts and perfume raw materials (PRMs) using molecular simulations and micellar-scale modeling, as well as traditional surfactant packing arguments. The two body washes, namely, BW-1EO and BW-3EO, are composed of sodium lauryl ethylene glycol ether sulfate (SLEnS, where n is the average number of ethylene glycol repeat units), cocamidopropyl betaine (CAPB), ACCORD (which is a mixture of six PRMs), and NaCl salt. BW-3EO is an SLE3S-based body wash, whereas BW-1EO is an SLE1S-based body wash. Additional PRMs are also added into the body washes. The effects of temperature, salt, and added PRMs on micellar lengths, breakage times, end-cap free energies, and other properties are obtained from fits of the rheological data to predictions of the "Pointer Algorithm" [ Zou , W. ; Larson , R.G. J. Rheol. 2014 , 58 , 1 - 41 ], which is a simulation method based on the Cates model of micellar dynamics. Changes in these micellar properties are interpreted using the Israelachvili surfactant packing argument. From coarse-grained molecular simulations, we infer how salt modifies the micellar properties by changing the packing between the surfactant head groups, with the micellar radius remaining nearly constant. PRMs do so by partitioning to different locations within the micelles according to their octanol/water partition coefficient POW and chemical structures, adjusting the packing of the head and/or tail groups, and by changing the micelle radius, in the case of a large hydrophobic PRM. We find that relatively hydrophilic PRMs with log POW < 2 partition primarily to the head group region and shrink micellar length, decreasing viscosity substantially, whereas more hydrophobic PRMs, with log POW between 2 and 4, mix with the hydrophobic surfactant tails within the micellar core and slightly enhance the viscosity and micelle length, which is consistent with the packing argument. Large and very hydrophobic PRMs, with log POW > 4, are isolated deep inside the micelle, separating from the tails and swelling the radius of the micelle, leading to shorter micelles and much lower viscosities, leading eventually to swollen-droplet micelles.

Molecular dynamics simulations of sodium dodecyl sulfate micelles in water-the effect of the force field.

Molecular dynamic (MD) simulations of preassembled sodium dodecyl sulfate (SDS) micelles are carried out using three versions of GROMOS, as well as CHARMM36, OPLS-AA, and OPLS-UA force fields at different aggregation numbers and box sizes. The differences among force fields have little effect on the overall micelle structure of small aggregates of size 60 or 100, but for micelles of an aggregation number of 300 or higher, bicelle structures with ordered tails, rather than the more realistic rodlike or cylindrical micelles with disordered tails, occur when using versions of GROMOS45A3 or the OPLS-AA force fields that are adapted to model the sulfate head group atoms using methods given in the literature. We find that the Lennard-Jones (L-J) parameters for the sodium ions and the ionic oxygens of the SDS head group, as well as the water model, control the transition to bicelles, regardless of other L-J parameters. A closer binding of the sodium ions to the head group ionic oxygens screens the electrostatic repulsions more strongly, resulting in condensation of SDS head groups, leading to unphysical bicelles for GROMOS45A3 or the OPLS-AA force fields, when the aggregation number is large. A telltale sign that the sodium-oxygen interaction is too strong shows up in high nearest neighbor peaks (height >8 and height >20 for micelles with 60 and 100 surfactants, respectively) in the radial distribution functions (RDFs) of sodium ions to ionic oxygens. In the 100-surfactant micelles, the high RDF peak is accompanied by "crystal-like" layering of sodium ions onto the surface of the micelle. The distance between the sodium ions and micelle also depends on the number of waters binding to sodium ions in the presence of surfactant head groups, which depends on both the sodium ion and water models, and for the same sodium model increases as the water model is changed in the order: TIP4P, SPC/E, SPC, and TIP3P.