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 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 hyrophobic than bilayers due to the electrostatic interactions between water molecules and the exposed cationic headgroups.


Introduction
The adsorption of surfactants on heterogeneous solid surfaces is important for the performance of a wide range of industrial and domestic formulations, from fluids for oil extraction 1 and lubricants 2 to laundry detergents 3 and cosmetics. 4 Despite this, the vast majority of experimental and computational studies of surfactant adsorption are conducted using flat homogeneous substrates. 5 It has been shown that nanoscale surface roughness and chemical heterogeneity can strongly impact surfactant performance, so it is important to include these substrate effects in the surfactant design and formulation process. 5 Human hair is one such heterogeneous surface where surfactant adsorption plays an important role in modifying interfacial behaviour. The outer layer of hair, the epicuticle, is protected by a fatty acid monolayer that is primarily composed of 18-methyleicosanoic acid . 6 This layer is crucial to maintaining the hydrophobicity, low friction, and satisfactory look and feel of hair. 6 The 18-MEA layer is covalently bound to the underlying cysteine layer via thioester bonds, 7 and can be partially removed when hair is damaged through chemical treatments such as bleaching, 8 exposed to ultraviolet light, 9 or even rubbed vigorously. 10 These damage processes expose oxidised cysteic acid residues, which results in the formation of negatively charged regions on the hair surface. 11 Microscopic damaged regions 12 are randomly arranged on the epicuticles, leading to heterogeneous surfaces. 13 Due to stronger electrostatic interactions between water molecules and the negatively charged tion of shampoos is to clean the hair, 20 while conditioners repair hair damage to make it easier to comb and improve its feel, shine, and softness. 21 Shampoos contain mostly anionic surfactants due to their superior cleaning performance, 20,22 they have been shown to successfully remove dirt and sebum from the hair surface. 22 Conditioners typically contain mainly cationic surfactants and polymers due to their ability to form strong ionic bonds with negatively-charged regions on the hair surface to act as a repairing agent and remain bound after rinsing and drying. 21 Many experimental studies have investigated the adsorption of anionic surfactants, 23,24 cationic surfactants 23,[25][26][27] and cationic polymers 28-32 on hair.
Chemically damaged and bleached hair shows much higher friction than virgin hair. [33][34][35][36][37][38][39][40] This is due to the removal of the protective 18-MEA layer and its replacement with anionic sulfonate groups. 41 Atomic force microscopy (AFM) experiments showed that the application of a commercial hair conditioner reduced the friction of chemically damaged and bleached hair to levels comparable to virgin hair through adsorption onto the damaged patches. 36 More recent AFM experiments suggested that friction reduction of chemically damaged hair due to treatment with a commercial conditioner was evident below a normal load threshold of 5 nN (corresponding to a mean Hertz pressure, σ ≈ 120 MPa for a 15 nm SiN tip), above which friction was similar to untreated damaged hair. 38 In addition to formulated conditioners, reductions in hair friction have also been observed with simple cationic surfactants. It has been shown that the friction between a single bleached hair and hard rubber can be decreased by increasing the concentration of cetyltrimethylammonium bromide (CTAB). 33 Friction reduction of single hair-hair contacts was also observed using AFM as the concentration of tetradecyltrimethylammonium bromide (TTAB) was increased. 39 Friction reductions with CTAB has also been observed at larger scales in rubbing experiments with a model finger on hair bundles. 42 In addition to friction reduction, cationic surfactants and polymers can also be added to formulations to make hydrophilic bleached hair more hydrophobic. 10,15,39,[43][44][45][46][47] Dynamic and static wetting experiments on bleached hair showed that the water contact angle increased through the deposition of cationic surfactants 6,15,48 Theoretical and numerical models can help in providing insights to surfactant interactions with hair surfaces that are otherwise inaccessible through experiments. Mean-field theory approaches, such as self-consistent field theory (SCF) have been used to predict self-assembly of polymers and surfactants and their adsorption to hair-like surfaces. [49][50][51] These tools ultimately provide useful insights into the equilibrium structure of surfactants in bulk solution and near substrates across a wide range of concentrations and molecular architectures. However, system dynamics and non-equilibrium systems as well as the threedimensional structure of systems cannot be accurately captured with the common mean-field approaches. These factors can be accounted for using molecular simulation techniques, such as molecular dynamics (MD) and dissipate particle dynamics (DPD). For example, DPD has been used to study the adsorption of nonionic n-alkyl poly(ethylene oxide) surfactants on planar hydrophobic surfaces as a model for virgin hair. 52 The adsorption of non-ionic surfactants on chemically heterogeneous surfaces representative of damaged hair has also been studied with DPD. 53 Recently, the adsorption and desorption under shear of cetrimonium chloride (CTAC) and fatty alcohols on 18-MEA monolayers grafted to a planar surface as a model for virgin hair were investigated using DPD. 54 MD simulations with atomisitic resolution have also been used to study the adsorption of fatty acids onto the 18-MEA-covered ultrahigh sulfur proteins. 55 We recently proposed a coarse-grained molecular model to study the wettability of virgin and bleached hair using MD simulations. 56 We used these models to investigate the friction between two hair surfaces at various levels of chemical damage under dry and wet conditions using non-equilibrium molecular dynamics (NEMD) simulations. 41 Recently, a similar coarse-grained MD framework was used to study the adsorption and friction of large biomacromolecules mixed with ionic surfactants on hair surfaces. 57 In this work we study the adsorption of cationic and anionic surfactants onto virgin and bleached hair surfaces using coarse-grained MD simulations. We simulate surfactant adsorption isotherms with bulk systems at concentrations above the critical micelle concentration  Figure 1: Overview of molecules and MARTINI bead types considered in this work: Surfacegrafted molecules a) Cys-18-MEA, b) cysteic acid and free molecules c) CTAB, d) SDS, e) polarizable water, and f) (excess) ions with first hydration shell.
(cmc). Subsequently, we investigate the friction of hair surfaces with adsorbed cationic surfactants using squeeze-out and NEMD simulations at a wide range of contact pressures and sliding velocities. Our NEMD simulation results are compared to previous hair friction experiments with various cationic surfactants. Finally, we carry out nanodroplet wetting simulations to compare the contact angle on surfaces with adsorbed cationic surfactants to previous results on bare model hair surfaces.

Methodology Surfactant bulk solutions
We carry out self-assembly MD simulations of the ionic surfactants in aqueous solution to establish equilibrated bulk systems for subsequent surface adsorption simulations. We use CTAB as a model cationic surfactant and sodium dodecyl sulfate (SDS) as a model anionic surfactant. We also consider systems with excess salt (NaCl) to study the effect on self-assembly and adsorption. An overview of all the molecules considered and their coarsegrained bead types is shown in Fig. 1. We employ the MARTINI 2.0 model 58,59 in conjunction with the polarizable MARTINI water model introduced by Yesylevskyy et al. 60 throughout. This combination has been validated previously for the structure, wettability, and frition of virgin and bleached hair surfaces. 41,56 All bulk systems presented in this work were prepared using PACKMOL 61 for both the pre-assembled micelles and randomly distributed molecules and Moltemplate 62 for assembly of the systems.
CTAB is described as a linear chain of four apolar C 1 beads with a terminal positivelycharged Q 0 bead and negativly-charged Q 0 bead representative of the bromide counterions. [63][64][65] For CTAB, we consider bulk concentrations in the range of c 0 = 120 − 973 mM, where c 0 is the concentration prior to any adsorption. The equilibrium bulk concentration is further denoted by c e and can potentially differ from the initial concentration due to surfactant adsorption and therefore depletion from the finite-size bulk. 66 SDS is modelled as three apolar C 1 and a terminal negatively-charged Q a bead with a positively-charged sodium counterion (Q d ). 63,67,68 Initial SDS concentrations in the range of c 0 = 173 − 701 mM are considered.
All simulations were performed in the open-source code LAMMPS. 69 We use the velocity-Verlet 70 integration scheme with a timestep of 5 fs. 58 The fully periodic bulk systems are equilibrated to atmospheric pressure (p = 1 atm) for 0.1 ns in the isothermal-isobaric (NPT) ensemble and are then run in the canonical ensemble (NVT) at T = 300 K for at least 100 ns.
We used a global Nosé-Hoover thermostat 71,72 and barostat 73 with a damping coefficient of 1 ps for the temperature and 3 ps for the pressure.
The standard MARTINI shifted Lennard-Jones (LJ) potentials 58 are used for all nonbonded interactions between non-aqueous, charge-neutral beads. The LJ contributions are smoothly shifted to zero between the cut-off radius r LJ,cut = 0.9 and r LJ,shift = 1.2 nm. 58 All remaining non-bonded interactions are treated in accordance with the extensions in-troduced by the polarizable water model. 60 Short-range electrostatic interactions between charged beads are considered through direct Coulombic potentials below the switching radius of r C,cut = 1.2 nm. Long-range electrostatic interactions are calculated using the particleparticle particle-mesh (PPPM) method at a relative energy tolerance of 10 −5 . 74 The importance of accurate long-range electrostatics to correctly capture the self-assembly and adsorption problems of ionic surfactant solutions has been highlighted in previous surfactant studies using the MARTINI force field. 63,66 Bonds and angles are treated using weak harmonic potentials as in the original MARTINI framework. 58 The SHAKE algorithm 75 is applied to constrain all polarizable water bonds to r = 0.14 nm.
We performed additional simulations with pre-assembled micelles to assess how a variation in micelle aggregation number would affect the micelle stability and adsorption to the hair surface. Aggregation numbers of N ag = 82 for CTAB and N ag = 45 for SDS were chosen in accordance with experiments and previous coarse-grained simulations with standard MARTINI water. 63,[76][77][78][79] The pre-assembled micelles were generated using PACKMOL. 61 For the pre-assembled micelles, we consider low and intermediate concentrations for both CTAB (c 0 = 120 mM and c 0 = 509 mM) and SDS (c 0 = 170 mM and c 0 = 584 mM) used in the self-assembled systems. Micelle stability simulations were run in a fully periodic system for at least 100 ns. Afterwards, we transferred the bulk systems to the hair surfaces and conducted adsorption simulations, as described below.

Surface properties
Coarse-grained MARTINI models are used to describe the surface of virgin and bleached hair. 56 In this study, we consider two surfaces with different degrees of alkyl and sulfonate groups with a combined packing density of 2.73 nm -2 . For virgin hair, we use a random arrangement of 75% alkyl groups and 25% sulfonate groups. For medium bleached hair, we use a random arrangement of 15% alkyl groups and 85% sulfonate groups. These groups are grafted to a flat graphene sheet made up of MARTINI C 1 beads. 80 The MARTINI bead types for the surface-grafted molecules are shown in Fig. 1a)-b). The 18-MEA molecules are represented by a P 5 bead, bonded to a C 5 bead, bonded to five C 5 beads for the alkyl groups. 81 The oxidised cysteic acid molecules are represented by a P 5 bead, bonded to a Q a bead with a charge of -1 for the sulfonate group and a free Q a bead with a charge of +1 for the sodium counterion. A detailed model description of the MARTINI paramters and their validation for hair surface wettability can be found elsewhere. 56 The x × y dimensions of both surfaces are 24 × 21 nm for the adsorption simulations. The surface properties of the two hair models are given in Table 1. The surface energies (polar + non-polar) were calculated using the Owens-Wendt 82 method from previously reported contact angle measurements from coarse-grained MD simulations using the same hair surfaces with water (polar) and n-hexadecane (non-polar). 56 The surface energy is larger for bleached hair than virgin hair, mainly due to the increase in polar contribution. The surface energies in Table 1 are in good agreement with those obtained from wetting experiments on real virgin hair (18.9 mJ m -2 ) and bleached hair (29.8 mJ m -2 ). 48 The virgin hair surface energy is somewhat overestimated in the simulations compared to the experiments, while the bleached hair surface energy is underestimated. The underestimation of the surface energy of the medium bleached hair surface is probably due to the systematically lower water-vapour surface tension of the polarizable MARTINI water model. 60 On the other hand, the n-hexadecane-vapour surface tension with the MARTINI force field is close to experiment. 56,83 The surface charge densities from the simulations are somewhat larger than those from previous experimental measurements of the surface charge density of virgin (−1.5 µC cm -2 ) and bleached (−10.0 µC cm -2 ) hair. 11 However, the density of cysteic acid groups on bleached hair is in good agreement with estimates (ρ SO 3 − = 2.2 nm -2 ) from another experimental study. 12 This suggests that the surface charge measured in the experiments 11 is lower than the simulations due to partial screening of the negative charges by the K + counterions present in solution. The screening effect by Na + counterions is not considered in the simulations surface charge density values reported in Table 1. The charge density for the medium bleached hair surface is very similar to that measured for an SDS monolayer at the hexadecane-water interface (−37.9 µC cm -2 ). 84 The root-mean-square (RMS) roughness of our model surfaces ( This discrepancy between the experiments and simulations is likely a result of the simplified atomically-smooth surfaces used in the simulations. In reality, the underlying disordered protein layer 55 is likely to be rougher than the graphene layer used to represent it in the simulations. Despite this opposite trend, the RMS roughnesses for both model surfaces are quite close to the experimental values using a small scanning area. 85 AFM experiments with larger scan areas (10 × 10 µm) showed higher RMS roughness values, which also increased from 10 nm for virgin hair and hair bleached for 10 minutes to 13 nm for hair bleached for 20 minutes (mean of three locations). 86 These larger area scans also included features such as cuticle edges, which are not considered in the current simulations.
The fractal dimension of the hair surfaces was estimated using a surface roughness spec-tral approach as described by Persson. 87 Approximate experimental fractal dimension of D f = 2.20 for virgin hair (2 × 2 µm scan area), 85 and D f = 2.71 for bleached hair (7 × 7 µm) 13 were estimated from AFM images available in the literature. The larger fractal dimension for the bleached hair model than the virgin hair one is in good agreement with these experimental estimates. This observation suggests that the bleached hair surfaces are more irregular than virgin ones, 88 which is due to the formation of lipid islands as an increasing proportion of alkyl groups are replaced by sulfonate groups. 56 Previous MD simulations of hydrophobic surfaces have shown that wettability is sensitive to the nanoscale RMS roughness, but not the fractal dimension. 89 However, for the current biomimetic surfaces, where hydrophobic groups in virgin hair are replaced by hydrophilic groups in bleached hair, the wettability is expected to be affected by both of these parameters.

Surfactant adsorption
A single hair surface is brought into contact with the equilibrated bulk solution, similar to a previous coarse-grained MD 66,90 and DPD 52-54 adsorption studies on different surfaces. The bulk is placed approximately 3Å above the surface to avoid initial overlap of the beads.
Excess counterions in the bulk corresponding to the number of hair surface charges were randomly removed for systems with CTAB and added for systems with SDS to maintain an overall charge-neutral system. We also investigated the effect of counterion condensation by

Friction
We further investigate the effect of cationic surfactants on friction between two hair surfaces using NEMD simulations. 92 The methodology for the NEMD simulations is similar to that previously described for water-lubricated hair surfaces. 41 First, squeeze-out simulations between two hair surfaces are performed in a water bath to establish equilibrium contact thickness and composition for a given contact pressure, σ. The cationic surfactant is preadsorbed on the surfaces in the configurations obtained from the adsorption simulations.
We select two surface adsorption densities Γ based on our adsorption study for the virgin and medium bleached hair surface models. The surfaces were duplicated and reflected at an initial distance of 10 nm between the surfaces. This is sufficiently large to accommodate the adsorption structures from both surfaces.
A normal stress of σ = 5− 50 MPa was applied between two hair surfaces of equal surface damage. This range is consistent with our previous estimate of physiologically relevant contact pressures between two hairs. 41 No excess surfactants are present in the bath since we do not expect the surface coverage of surfactants to increase during squeeze-out due to micelle entrapment or further physical adsorption. Very few CTAB molecules were squeezed out from the contact due to the strong affinity to the surfaces. Therefore, only the number of water molecules in the contact was considered a free variable with respect to the normal load applied during squeeze-out.

Contact angle
The wettability of the CTAB-treated hair surfaces is investigated by the deposition of water nanodroplets. CTAB molecules are not present in the water droplet and negligible desorption occurs during the wetting simulations. Thus, we consider the effect of the surfactant on the solid-liquid and solid-vapour surface tensions, but not the liquid-vapour surface tension. 96 This is equivalent to measuring the contact angle of pure water on hair previously treated with cationic surfactant. 15 The methodology for the wetting simulations is the same as we described previously for base virgin and bleached hair surfaces. 56 This was based on a previous study of the wetting of graphene by water and various surfactants using the MARTINI model. 97 The diameter of the initially hemispherical droplet is d = 20 nm, containing 18,121 polarizable water molecules. 56 In our previous study, this droplet size was found to be sufficiently large to be representative of the contact angle of macroscale droplets. 56 Larger hair surfaces with simulation box lengths of L x = 47.6 nm, L x = 41.3 nm were used for the wetting simulations to accommodate droplets with low contact angles. The model surfaces were equilibrated for 10 ns in the canonical (NVT) ensemble, followed by a production run with the droplet added for a further 10 ns. We apply a global Nosé-Hoover thermostat 71,72 with a damping coefficient of 1 ps. We measure the water nanodroplet contact angle at the interface using 10 block averages of 1 ns.

Results and Discussion
Surfactant bulk self-assembly We investigated the implications of using the polarizable MARTINI water model 60 on the aggregation behaviour of the surfactants. Aggregation numbers as a function of the bulk concentration are provided in the Supplementary Material (Table S1). above the second cmc (m = 0.24 mol kg -1 ) obtained using nuclear magnetic resonance (NMR) spectroscopy. 101 Finite-size effects 102 were briefly checked by comparing self-assembly simu- is also worth noting that a systematic underestimation of the aggregation numbers of CTAB and SDS compared to experiments was reported for the standard water model on multiple occasions. 63,64,102 This is in contrast to larger-than-experimental aggregation numbers numbers of SDS above c = 100 mM found during self-assembly simulations with standard MARTINI water and a modified Lennard-Jones potential of the SDS hydrocarbon tails. 104 We conclude that capturing the experimental aggregation numbers of specific surfactant types likely requires fine-tuning of the force field parameters when using either polarizable or non-polarizable water models. This is beyond the scope of the current study, where we are more interested in the adsorption of surfactants on solid surfaces.
We conducted additional bulk and adsorption simulations of larger pre-assembled CTAB (N agg = 82) and SDS (N agg = 45) micelles to investigate if the reduced micelle size due to the force field parameters would have a significant effect on surface adsorption. These micelle sizes were selected based on previous experiments [76][77][78][79] and molecular simulations with standard MARTINI water. 63 The pre-assembled micelles were stable in bulk simulations over more than 100 ns. The adsorption densities and kinetics from pre-assembled and self-assembled micelles were very similar across a wide range of surfactant concentrations, as shown for CTAB in the Supplementary Material (Fig. S1). This indicates that the aggregation number does not seem to be an important consideration for the adsorption of surfactants since micelles tend to break up in the proximity of the surface. We therefore only discuss the results using bulk systems with self-assembled micelles in the remainder of this study.

Surfactant adsorption onto hair surfaces
Cationic surfactants  Tyrode et al. 107 also reported multi-stage adsorption isotherms for CTAB on hydrophilic silicon surfaces. They also identified two plateau regions, the first at a CTAB coverage of around 1 nm −2 and the second at around 3 nm −2 , which the same range seen in Fig. 3 for our model hair surfaces. These works considered surfactant concentrations below and slightly above the cmc, whereas in our simulations the concentrations are all above the cmc due to the significant computational cost of these large-scale explicit solvent simulations. 63 Nonetheless, the plateau adsorption densities reported in this work are similar to those observed experimentally for comparable cationic surfactants on virgin hair 27 and CTAB on other hydrophilic surfaces. 107 We therefore expect that, despite the higher surfactant concentrations and finite-size limitations of the MD adsorption simulations, they provide a useful pathway for obtaining similar equilibrium adsorption configurations as seen experimentally for subsequent MD simulations of friction and wetting.

Anionic surfactants
For SDS, we observe a monotonic increase of the surface coverage with the logarithm of the concentration on both virgin and bleached surfaces, as shown in Fig. 3b). Adsorption of SDS is much weaker than for CTAB, which is primarily driven by hydrophobic attraction phase transitions from spherical micelles to hexagonally-ordered structures would need to be considered, 63 which are beyond the scope of the present study.

Surfactant orientation
The characteristic regions in the adsorption isotherm of CTAB in Fig. 3a) raise questions regarding the transitions in adsorption mechanism as the concentration is increased. Previous analytic models for ionic surfactant adsorption on solid surfaces considered both electrostaticdriven and hydrophobic-driven adsorption at the interface. 27,111,112 The density profiles shown in Fig. 3c)-d) suggest the arrangement of CTAB molecules into distinct layers on the surface.
To give additional insights, we calculated the orientation of surfactants adsorbed on the surface from the MD simulations. This enables us to quantify the fraction of surfactants residing in a monolayer or a bilayer. We use this information to apply a general two-step Langmuir model to the systems with cationic surfactants: 113 where electrostatic (monolayer) and hydrophobic-driven (bilayer) adsorption mechanisms are considered by linear superposition. The adsorption isotherm Γ t of CTAB, consisting of primary electrostatic adsorption and secondary hydrophobic-driven adsorption, Γ el and Γ hyd respectively, is fitted to the individual adsorption densities from our MD simulations.

Effects of ionic background strength
Hair care formulations usually contain around 0.5-2 wt.% salt. 114 The addition of a background electrolyte to the bulk could affect the adsorption of ionic surfactants on the hair surface. To study this effect, we repeated a subset of the CTAB adsorption simulations with coarse-grained sodium Na + and chloride Clions (with their first hydration shell) 59  adsorption. This is likely because, for the high CTAB concentrations studied, the number of surfactant molecules is considerably higher than that of the number of excess sodium ions.
CTAB adsorption densities were much less sensitive to background salt concentration on virgin hair. This supports our previous suggestion that CTAB adsorption on virgin hair is primarily driven by hydrophobic interactions, where charge screening will not play a significant role.

Friction with adsorbed cationic surfactants Shear stress dependence on sliding velocity
We conduct NEMD simulations to quantify the friction between hair surfaces in the presence of adsorbed CTAB molecules. Friction with adsorbed SDS molecules are only briefly considerd, due to the much lower adsorption densities of SDS on the hair surfaces and its potential to quickly desorb during compression, sliding and rinsing. 43,116 A set of friction results from

NEMD simulations at intermediate SDS adsorption densities is shown in the Supplementary
Material (Fig. S5). Adsorbed SDS molecules do provide considerable friction reductions compared to the water case, which is primarily due to enhanced electrostatic repulsion between the sliding surfaces. However, concentrated SDS solutions can cause damage to the hair cuticle surfaces, 108,109 which is not accounted for in our current simulations framework. This is likely to increase the surface roughness and remove some of the protective 18-MEA layer, which could perhaps play a more significant role than the enhanced electrostatic repulsion effect simulated here.
On the other hand, CTAB is not expected to damage the hair surface, so its effects on friction can be fully captured by the current simulation framework. We selected two points from each CTAB adsorption isotherm, corresponding to points c)-f) in Fig. 4 Table 2.
We analysed the structure of the contact during sliding to investigate the molecularscale mechanisms linked to friction reduction with CTAB. Mass density, charge density and velocity profiles of the contact at v s = 1 m s -1 are shown in Fig. 8. We also report During sliding, the structure of confined CTAB molecules differs considerably from that on single hair surfaces (Fig. 3). For the single surfaces, we observed CTAB bilayer on the virgin hair surface at high coverages, where a significant amount of surfactant molecules were oriented with their cationic group facing towards the bulk. Converesly, once a dynamic equilibrium is reached during sliding simulations, most CTAB molecules are oriented with the hydrophobic tail facing the centre of the contact, as shown in Fig. 8. We analyzed the mass density profiles at the beginning and at equilibrium of both compression and sliding simulations, as shown in the Supplementary Material (Fig. S7). The bilayer is observed even after compression of the two surfaces but disappears during the first 5-10 ns of sliding, shown that multilayers are easily removed and show similar friction behaviour to monolayers. 118 The tendency for surfactants to desorb from the hair surface under shear has also been reported both experimentally 38 and in DPD simulations. 54 The charge density profiles in Fig. 8  The charge density and velocity profiles for virgin hair at high surfactant coverage suggest that there is a non-negligible fraction of CTAB molecules that are not adsorbed to either of the sliding surfaces. Here, the combined CTAB and lipid surface coverage is above the value of a pristine 18-MEA monolayer, suggesting that the surface is somewhat over-saturated.
We briefly investigated the mobility fraction 121 of cationic surfactants at the interface shown in the Supplementary Material (Fig. S9). During sliding, there is a much higher mobility fraction of the CTAB surfactants on virgin hair surfaces at Γ = 2.0µMm -2 than the other surface-coverage combinations, which confirms our hypothesis of an over-saturation. The mobility fraction is not sensitive to the sliding velocity for any of the surfaces or CTAB coverages. The mean-square-displacement (MSD) of cationic beads (Q 0 ) on CTAB in the directions normal to the sliding direction (y and z) also confirmed an increased mobility of surfactants for virgin hair at high CTAB concentrations (Fig. S10 in the ESI).
We also investigated the order within the adsorbed CTAB films.

Shear stress dependence on normal stress
We also consider the effect of different contact pressures on the shear stress. For this purpose, the sliding velocity is kept constant at v s = 0.1 m s -1 , while varying the normal stress, σ = 5 − 50 MPa. Fig. 7c) and d) show the shear stress, τ , as a response to the normal stress, σ for the three degrees of CTAB coverage. We calculate the friction coefficient, µ, from the slope of the linear fits shown in Fig. 7c) and d), τ = µ · σ + τ 0 , where τ 0 is the loadindependent Derjaguin offset due to adhesion. 41 Table 2 Fig. 7c-d), which suggests that stick-slip phenomena are partially eliminated. This closely resembles the observations from AFM experiments where the signal error was found to be largest for KOH-damaged hair, followed by conditioned KOH-damaged and untreated virgin hair. 38 We also related the total surface coverage ρ t from surfactants and 18-MEA, as summarized in Table 2, to the CoF at v s = 0.1 m s -1 . Fig. 9 shows a consistent decrease in friction as well as in the amplitude of the shear stress oscillation (prevalence of stick-slip events) with increasing lipid coverage for both virgin and medium bleached hair surfaces. The overlap between the two profiles at different degrees of damage clearly motivates that the presence of the hydrophobic tails (from either the 18-MEA or CTAB) exposed on each surface dominates the friction reductions, as the surface heterogeneity is reduced and damaged surface patches are repaired.  Ref. 56 are also included for comparison. Table 2 further shows a summary of contact angles at the various degrees of CTAB coverage.
On virgin hair, moderate CTAB adsorption (Γ = 1.1 µM m -2 ) leads to a moderate increase of the contact angle to θ = 106.1°compared to the bare surfaces, θ = 102.2°. The majority of free surfactant molecules adsorbs to the few damaged patches on the surface, therefore increasing the contact angle to nearly the value reported for a pristine monolayer (θ = 120°). 56 At elevated surfactant concentrations on virgin hair, the contact angle decreases to θ = 79.6°. This decrease in θ is attributed to the adsorbed CTAB bilayer. In this bilayer configuration, a significant fraction of CTAB molecules is oriented with their hydrophilic cationic sites exposed towards the bulk, thus increasing the affinity of water to the surface.
The decrease in contact angle on virgin hair is in good agreement with experimental wetting measurements of virgin hair with adsorbed proteolipids. 15 The agreement with these wetting experiments also suggest that the observed bilayer might be resistant to being rinsed off when being locally wetted at macroscopic timescales.
The presence of cationic surfactants on the surface restores the hydrophobicity of the medium bleached surface, as indicated by the increase in contact angles to θ = 71.6°and  15 Treatment of bleached and permed hair with K-peptide and K-protein also led to moderate increases in advancing contact angle from dynamic wetting force measurements. 124 In contrast, virgin hair wetting was largely unaffected by treatment of these molecules. 124 The observed increase in water contact angle and decrease in the CoF on bleach damaged hair surfaces treated with CTAB demonstrate that cationic surfactants can restore the hydrophobicity and low friction properties of the virgin hair surface.

Conclusions
In this study, we have investigated the adsorption, friction and wettability of ionic surfactants on virgin and chemically bleached model hair surfaces using coarse-grained MD simulations. For virgin hair, which contains 75% alkyl groups and 25% sulfonate groups, adsorption of cationic surfactants occurs through both electrostatic and hydrophobic-driven adsorption. At low concentrations, CTAB forms a complete monolayer where the hydrophobic tailgroups point away from the surface due to electrostatic attraction between the cationic headgroup and the anionic sulfonate groups. At higher concentrations, CTAB forms a bilayer due to hydrophobic interactions between the hydrophobic tailgroups of the adsorbed CTAB molecules.
On medium bleached hair, which contains 15% alkyl groups and 85% sulfonate groups, CTAB adsorption is dominated by electrostatic attraction between the anionic sulfonate groups and the cationic headgroup of the cationic surfactant. At low concentrations, CTAB forms a partial monolayer, while a complete monolayer is formed at higher concentrations.
We also highlighted that the the background salt concentration significantly reduces CTAB adsorption to the surface at low CTAB concentrations. Water nanodroplet wetting simulations confirmed that cationic surfactants effectively restore the hydrophobic character of untreated hair after bleaching. On virgin hair, moderate levels of CTAB adsorption further increased the hydrophobicity of the surface due to electrostatic adsorption of surfactants to the few available damaged sites on the surface. Excessive CTAB adsorption on virgin hair led to a slight decrease in contact angle induced by the formation of a bilayer. On medium bleached hair, the contact angle monotonically increased with higher adsorption densities due to the formation of a CTAB monolayer with increasing surface coverage. Our results are in excellent agreement with experimental friction and wetting measurements on hair and show why hair conditioners based on cationic surfactants are effective at repairing chemically damaged hair fibres.
Our simulations also highlight that the structure of surfactants during sliding of two hair surfaces in contact is perturbed in comparison to the structure on a single hair surface. We expect the results of this study to be applicable to further screening of more complex and

Conflict of interest statement
There are no conflicts to declare. Supporting Information Available