Fushan Geng

Bei Hu

Chao Li

Chong Zhao

Olivier Lafon

Julien Trebosc

Jean-Paul Amoureux

Ming Shen

Bingwen Hu

Bei Hu

Julien Trébosc

Bingwen Hu

Anionic Redox and Structural Degradation in Cation-Disordered Rock-Salt Li 1.2 Ti 0.4 Mn 0.4 O 2 Cathode Material Revealed by Solid-State NMR and EPR

    Anionic redox reactions and structural degradation in a cation-disordered rock-salt Li(1.2)Ti(0.4)Mn(0.4)O(2) cathode material revealed by solid-state NMR and EPR

Introduction

To meet the demands for advanced batteries in portable devices and electric vehicles, as well as efficient electrical energy-storage technologies for sustainable power sources, lithium-ion batteries (LIBs) have been developed as one of the most promising solutions. 1,2 However, cathode materials are currently the key bottleneck that limits the energy density and production costs of LIBs. 3,4 The current commercialized cathode materials are mostly layered rock-salt materials, such as LiCoO 2 , 5,6 LiNi x Co y Mn z O 2 (NCM), [7][8][9] and LiNi 0.8 Co 0.15 Al 0.05 O 2 (NCA). 10,11 These materials have a good cycling stability due to the facile insertion of Li ions into the layered structure, but their capacities are limited by the redox activity of transition metal (TM) cations.

Taking advantage of oxygen redox, breakthroughs can be easily achieved in cathode capacity. 12,13 In particular, in the layered rock-salt materials, the oxidation of oxygen at high voltage can be enabled by an excess of Li ions in the TM layers, giving rise to a prevalence of Li-rich layered oxides. [14][15][16] Two types of oxygen redox mechanisms have been suggested: the formation of localized electron holes on oxygen which usually exist in Mn-based systems, 17 and the formation of peroxolike anions (O 2 ) n-(n = 1, 2, 3) in 4d/5d and d 0 /d 10 metal systems. [18][19][20] Both mechanisms lie with the O 2p non-bonding state, corresponding to the Li-O-Li configuration arising from the excess of Li ions.

Nevertheless, undesirable problems arise in Li-rich layered oxides when oxygen takes part in the charge compensation. One of the major issues is the hysteresis between charge and discharge, which lowers the energy efficiency. Another issue is the voltage decay occurring during prolonged cycling, which decreases the energy density even if the charge capacity is maintained. [21][22][23] After several years of research, the origins of these two issues have been primarily related to the anionic redox activity and the migration of TM cations (including the formation of spinel-like structures). [24][25][26][27] These troubles still remain as an obstacle on the way to practical application.

The emerging Li-rich cation-disordered rock-salt (DRX) materials are another competitive option, because the migration of Li ions is more favorable through a unique percolation channel devoid of TM ions, called a 0-TM channel, 28 Furthermore, their electrochemical properties can be easily adjusted owing to the large diversity of the selectable TM ions. In particular, DRX materials commonly incorporate early transition metals with d 0 electronic configuration, which tolerates structural distortion and hence, increases the disorder. 29 Several d 0 cation-based DRX materials have been explored, such as Mo-, 30,31 Nb-, 32 and V-based oxides. 33,34 Nevertheless, a voltage hysteresis is still observed in these materials and their cycle stability is unsatisfactory. Unlike the ordered layered materials which can be hardly fluorinated, 35 fluorine substitution is easily achieved in the local Lirich environments of DRX. [36][37][38] Such strategy was proved to limit the oxygen loss, 31,39 and allows utilizing only reversible TM redox, which alleviate the voltage hysteresis and structural degradation caused by excessive oxygen redox while maintaining the high capacity of Li-rich compounds. 40,41 It is fundamental to understand the structural evolution during charge and discharge for better designing the electrode materials. A few works have investigated the redox behaviors and long-range structural variations in these materials using X-ray absorption spectroscopy (XAS) and X-ray/neutron diffraction (XRD/NPD), respectively, combined with DFT calculations. 32,[42][43][44] However, there is a large variety of local environments in DRX materials. Common diffraction techniques only provide insights into the average structure and hence, do not allow to access crucial information on the structure of these disordered materials. By processing neutron or synchrotron X-ray scattering data, pair distribution function (PDF) analysis is able to provide the short-range structure information. 45 In addition, solid-state NMR (ssNMR) spectroscopy with fast magic angle spinning (MAS) is qualified to probe the atomic-scale local structures, which lack long-range positional order. 45 Moreover, in situ/ex situ NMR can allow the quantification of the Li contents in different surroundings, 46 which would be a very useful information in DRX materials. Furthermore, electron paramagnetic resonance (EPR), which gives information on the local environment of unpaired electrons, can improve our understanding of the redox processes. [47][48][49] Herein, we demonstrate that NMR spectroscopy is a powerful tool for determining the Li and O local environments in DRX materials. With the assistance of EPR spectroscopy, we have clarified the changes in local atomic-scale structures during charge and discharge as well as the redox mechanisms.

Based on this novel information, several strategies are proposed to circumvent the structural degradation during the first cycle and the voltage hysteresis issue.

Results

Material Characterization

17 O-labelled Li 1.2 Ti 0.4 Mn 0.4 O 2 (LTMO) was prepared via high-energy shaker-milling with 17 Oenriched H 2 O, followed by annealing under inert atmosphere. The synchrotron XRD (SXRD) pattern (Fig. 1a) verifies the cubic rock-salt structure (Fm m) of the as-prepared sample with no observable 3 impurities, and the Rietveld refinement gives a lattice parameter of 4.143 Å. The particle size was observed by transmission electron microscopy (TEM). As shown in Fig. S1, the diameter of the asprepared material is ~2 m with good crystallinity, whereas the sample ball-milled with carbon additive is crushed into irregular particles with ~150 nm in size. Such a ball-milling procedure is necessary for DRX materials to insure good electrochemical performances.

The crystal structure is illustrated in Fig. 1b. Each cation (Li + , Ti 4+ , or Mn 3+ ) is directly bonded to six O anions, and vice versa. With regard to the local environments, each cation has 12 nearestneighbor cations with 90° bond pathway through oxygen and 6 next-nearest ones with 180° bond pathway. The presence of paramagnetic Mn 3+ ions near 7 Li or 17 O nuclei shifts their NMR signal.

This paramagnetic shift stems, in general, from the Fermi contact interaction due to the transfer of unpaired electron spin density from the TM d orbitals to the Li/O s orbitals through bond pathways.

Fig. 1c shows the 7 Li spectrum of the pristine material, corresponding to the isotropic projection of magic angle turning phase-adjusted spinning sidebands 2D spectrum (pjMATPASS). 50 The MATPASS sequence separates in two distinct dimensions, the isotropic and anisotropic shifts, in order to improve the spectral resolution. Along the isotropic projection, the position of the peak is purely determined by the isotropic shift. The isotropic projection of LTMO can be simulated as the sum of two components: a broad line centered at 241 ppm spanning over 1000 ppm and a narrow peak resonating at 0.6 ppm. The broad line, denoted P-Li, is assigned to 7 Li nuclei close to paramagnetic Mn 3+ ions, which produces Fermi contact shift, whereas the narrow peak, denoted D-Li, is ascribed to 7 Li nuclei with only diamagnetic Li + and Ti 4+ as neighbor cations. Note that the simulation of P-Li peaks as a single Gaussian-Lorentzian line is an approximation, since there are 90 different possible paramagnetic environments for 7 Li nuclei in LTMO (see Supporting Information).

As pjMATPASS experiment is generally assumed to be quantitative, 50 the integrated intensities of deconvoluted signals in Fig. 1c indicates that the fraction of P-Li and D-Li environments in LTMO are 78.2 and 21.8 %, respectively. However, owing to the short relaxation times for the paramagnetic environments, it should be noted that the pjMATPASS experiment could lead to the underestimate of the P-Li content; and the Li 2 O/Li 2 CO 3 formed in the bulk or at the surface during the synthesis may lead to the overestimate of the diamagnetic Li environment.

The D-Li signal was also acquired by filtering out the rapidly decaying P-Li signal (Fig. S2).

This signal can be simulated as the sum of three components assigned to 7 Li environments rich in Li atoms (0.6 ppm, 33.1%), with even amounts of Li and Ti atoms (-25 ppm, 28.2%), and rich in Ti atoms (-65 ppm, 38.6%), respectively. Likewise, owing to the difference between the T 2 relaxation times, it should be noted that there may be some errors for the relative intensities of these different D-Li signals. Monte Carlo simulations indicated that ca. 35% of Li in LTMO is percolating. 51 The 0-TM percolation channels necessarily have a strong correlation with the Li-rich environments. It can be speculated that a larger amount of the 0-TM channels results from a larger amount of the Li-rich environments.

Another common element in cathode materials, oxygen, has rarely been studied by NMR spectroscopy due to the extremely low natural abundance (0.037%) of 17 O nuclei. 52,53 To circumvent this issue, LTMO has been enriched in 17 O and the acquired 17 O spectra at different fields with different MAS frequencies are shown in Fig. 1d. They exhibit a broad signal with an apparent isotropic peak at ca. 550 ppm. No second-order quadrupolar pattern can be observed since the spectrum is dominated by the distribution of chemical shifts given the large distribution of local environments. The 17 O shifts mainly depends on the nature of the six nearest-neighbor cations. When none of them is a Mn 3+ cation, the position of the peak is determined by the isotropic chemical shift.

Here we try to assign the 17 O shifts in terms of the O coordination environments. For O-Li 6 configuration, where the O atom is totally ionic, a shift of ca. 35 ppm should be observed, similar to that in lithium oxide. 54 However, there is no clear signature of such ionic O environment at ca. 35 ppm in the spectrum, suggesting that O-Li 6 configuration is not likely to form in this DRX material.

Hence the observed strong diamagnetic 7 Li signal mainly results from Li segregation in domains rich in Ti 4+ , Li + and O 2-. When O atoms are bonded to Ti cations, the orbital interactions lead to higher 17 O chemical shifts comparable to 400~800 ppm, which has been measured for Li 2 TiO 3 layered rocksalt and Ti x O y compounds. [55][56][57] The fairly broad isotropic resonance (or overlapping resonances) at ca. 550 ppm is just located in this range, which could well correspond to 17 O nuclei in the O-Li x Ti y environments. The broadening of these resonances could result from strong dipolar interaction due to the presence of nearby paramagnetic Mn ions that are not in the first two coordination shell.

When 17 O nucleus is bonded to Mn ions, the isotropic shift is determined by the Fermi contact interaction which can result in a very large range of paramagnetic shift. The much broader 17 O signal spanning over 7000 ppm (range from -2000 to 5000 ppm) would then be assigned to 17 O in domains containing paramagnetic Mn ions. Since Fermi contact shifts are additive, the isotropic shift of O depends on the number of Mn 3+ among the nearest neighbor cations. The decreasing signal intensity from 550 to 3000 ppm in Fig. 1d indicates that the populations of the O-Mn x (Li/Ti) 6-x (x = 0~6) configurations decrease with increasing x.

Electrochemistry and Redox Processes

The galvanostatic charge and discharge were carried out at 45°C for a better kinetic performance.

Fig. 2a shows the voltage profile of LTMO cycled between 1.5 and 4.8 V, which delivers charge and discharge capacities of 358 and 251 mAh g -1 , respectively, with a low coulombic efficiency of 70.1%.

The theoretical Mn 3+/4+ redox limit of 131.6 mAh g -1 is marked as a vertical dashed line. The sloppy voltage charge profile before this limit is related to the oxidation of Mn 3+ ions, while the oxygen oxidation beyond this limit shows a flatter voltage profile. No voltage plateau can be seen in the discharge curve.

Cyclic voltammetry (CV) was used to discriminate the redox reactions since it is more sensitive than the differential capacity (dQ/dV) curves. The first two CV scans between 1.5 and 4.8 V are shown in Fig. 2b. In the first anode process, two obvious anodic peaks located at ca. 3.8 and 4.5 V are observed, corresponding to the Mn 3+ and O 2-oxidations, respectively. When the scan voltage turns back, a very broad cathodic peak can be discerned at around 4.2 V, which is ascribed to the reduction of oxygen. A strong Mn 4+ reduction peak is observed at ca. 3.3 V, suggesting the good reversibility of the Mn redox. Further reduction of oxygen is evidenced by the two tiny cathodic peaks at around 2.0 and 2.3V. At a low voltage close to 1.5 V, the increasing current density indicates that Mn 3+ begins to be reduced to Mn 2+ , as substantiated by XAS in a previous work. 58 The features of the second CV scan are roughly the same as the first cycle. However, the Mn 3+ oxidation peak drifts to ca. 3.4 V, implying the change of the energy level of Mn 3d orbital. The O reduction is still separated into two parts, and the part after Mn reduction becomes even more obvious at ca. 2.1 V as one peak. Irreversible oxygen loss is supposed to take place in the first oxidation process, as the oxidation peak of O is less intense in the second cycle than in the first one. As a conclusion, the CV results show a good reversibility of the Mn redox but a large voltage hysteresis due to the complicated O redox.

Ex situ 7 Li and 17 O NMR 7 Li and 17 O NMR experiments were employed to analyze the changes in the local environments in LTMO during the first cycle, and the involved redox mechanisms. Fig. 3a shows the 7 Li NMR isotropic spectra of LTMO at different states of charge (SOCs), acquired with the pjMATPASS sequence (The pseudo-2D MATPASS spectra are shown in Fig. S3). These spectra exhibit P-Li and D-Li signals like the pristine sample. The P-Li signal is clearly shifted to high frequency upon charging and shifted back upon discharging, but at the end of the discharge, it does not come back to its initial position. Comparable variations are also observed in the 17 O NMR spectra (Fig. 3b), which were acquired at a high field of 18.8 T in order to reduce the second-order quadrupolar interaction and focus on the paramagnetic shifts. The apparent isotropic peak increases during the charge and decreases during the discharge. Another notable phenomenon is that the spinning sidebands in the 17 O NMR spectra are visible at low SOC but are broadened at high SOC, suggesting a more heterogeneous local environments and/or an enhanced 17 O quadrupolar interaction and/or increased paramagnetic interactions for high voltage charge.

To analyze the modification of Li local environments during charge and discharge, the ex situ 7 Li NMR spectra were also deconvoluted as shown in Fig. S4. However, the use of a single Gaussian-Lorentzian line shape to simulate the P-Li signal leads to inaccuracy on the shifts and integral intensities, and hence we principally focus on the variation tendency. paramagnetic and average 7 Li shifts have steep slopes in the two forms before the Mn 3+/4+ limit, whereas their increase is slower during the oxidation of oxygen. This observation indicates that the magnitude of Fermi contact shifts on 7 Li is different for the unpaired electrons of Mn and O. Therefore, the redox center involved at different SOCs can be recognized from the slope of 7 Li shift. During the discharge process, the 7 Li shifts exhibit low slope corresponding to the multistep oxygen reductions (4.8~3.5 V and 3~1.5 V, except for the Mn 3+ to Mn 2+ reduction near 1.5 V) and steep slope corresponding to the Mn 4+ to Mn 3+ reduction (3.5~3 V) in agreement with the above CV study.

Fig. 3e shows the evolution of the 17 O shifts for the apparent isotropic peaks. A weighted average calculation cannot be applied to the 17 O shifts due to the large anisotropy when using a solid-echo sequence for acquisition. However, the apparent isotropic peak represents the most abundant oxygen environments, and hence it is reasonable to evaluate the changes in oxygen local environments from this peak position. During the oxidation of Mn 3+ to Mn 4+ , the peak drifts from 552 to 660 ppm, and then it drifts to 787 ppm at the plateau of O oxidation. At the last charge stage from 4.5 to 4.8 V, the peak shifts back to 750 ppm. When discharging to 1.5 V, the peak drifts to 606 ppm. Unlike the 7 Li shifts, the slope of 17 O shifts does not significantly vary during the charge and the discharge, which may indicate similar Fermi contact interactions for Mn 4+ -O and (O-O) n-species. However, we notice that an anomaly occurs in both 7 Li and 17 O shifts at the end of charging, since we observe a decrease of the 17 O peak shift and a steep rise in the 7 Li weighted average shift. Such anomaly implies a conversion in the local environment, especially in the electronic structure, and hence EPR experiments were performed to better understand the change in the electronic properties during the charge and the discharge.

Electronic Structure

The molar magnetic susceptibility ( m ) of the pristine sample was measured in order to determine the spin state of Mn 3+ ions (Fig. S5). The sample exhibits a paramagnetic behavior above 50 K which follows the Curie-Weiss law and an antiferromagnetic state at very low temperature, analogous to the cation-disordered Li 1.25 Nb 0.25 Mn 0.5 O 2 sample. 45 A linear fit of the reciprocal magnetic susceptibility ( m -1 ) versus the temperature between 100 and 300 K gives a Weiss temperature of -41.9 K and a Curie constant of 2.46, which corresponds to an effective magnetic moment  eff = 4.44  B . The spin-only magnetic moment for Mn 3+ is 4.9  B in high-spin state (t 2g 3 e g 1 , S = 2) and 2.83  B in low-spin state (t 2g 4 e g 0 , S = 1), suggesting that the Mn 3+ ions in LTMO are in the high-spin state. The slight deviation between the observation and the expected value may be due to the second-order spin-orbit coupling effects. The EPR spectrum, which lacks any signal, shown in Fig. 4a, confirms the valence +3 of Mn ions, because Mn 4+ ions (S = 3/2) gives a broad signal at g ≈ 2.0 while Mn 3+ ions are EPR-silent due to the integer spin. 48 The perpendicular-mode EPR spectra are presented into three distinct subfigures for clarity, corresponding to the Mn oxidation, O oxidation, and reduction, as shown in Fig. 4a-c, respectively.

A prominent broad line resonating at ca. 90 mT (g ≈ 7.5) is observed for all charged samples and is assigned to the ferromagnetic resonance, resulting from significant exchange interaction between the Mn ions once Mn 3+ ions has been oxidized. The molar magnetic susceptibility of two samples, from which ca. 1/3 and 2/3 of Li were extracted, respectively, were further investigated to confirm the ferromagnetism in the charged samples (Fig. S6), and the result shows the presence of short-range ferromagnetism due to the local clusters of Mn ions. As seen in Fig. 4a, the ferromagnetic resonance intensity decreases during the oxidation of Mn 3+ into Mn 4+ . However, no signal of Mn 4+ ions (g ≈ 2.0) can be observed. Two insights into the structure of LTMO can be inferred from these EPR observations. First, Mn ions are clustered in the material, otherwise the Mn 4+ ion surrounded by Li ions should lead to the EPR signal at g ≈ 2.0 due to the lack of exchange interaction. Second, the decrease of the ferromagnetic resonance during the charge indicates that the ferromagnetic interaction between Mn 3+ and Mn 4+ is stronger than between Mn 4+ ions.

At the beginning of oxygen oxidation (C230, Fig. 4b), a new weak signal appears at g ≈ 2.0 is assigned to (O 2 ) n-(n = 1, 2, 3) species. 49,59 As compared to the previous report on the (O 2 ) n-species, 49 the (O 2 ) n-signal in our work is a lot broader, which may be due to the ferromagnetism in the samples (Fig. S9). However, the (O 2 ) n-signal disappears for C310 as oxidation proceeds. Oxygen loss has been attested in LTMO at the latter charging stage, 58 and thus it is suggested that the labile (O 2 ) n- species are further oxidized to O 2 that is released, resulting in the loss of (O 2 ) n-signal. A few (O 2 ) n- species may still exist, but are unobservable due to their weak intensity. When charging to the high voltage of 4.8 V (C358), a signal analogous to the (O 2 ) n-species appears with stronger intensity, which should be ascribed to the localized electron holes on the lone-pair states of O whose other 2p orbitals are bonded to Mn. 17 Moreover, a broad line shape centered at g ≈ 2.0 is superimposed on the EPR line, which is unambiguously identified as the line shape of Mn 4+ ions. It is hence deduced that the electron holes on oxygen disrupt the Mn 4+ -O 2--Mn 4+ superexchange coupling so that a part of the Mn 4+ ions regain the EPR line shape. Additional XPS experiments (Fig. S10) exclude the existence of Mn 2+ ions at the surface of the high-voltage samples which may contribute to the EPR signals at g ≈ 2.0.

The signal of the Mn 4+ ions and the electron holes on oxygen vanish for D60 (Fig. 4c), indicating the reduction of oxygen and the rebuilding of the Mn 4+ -O 2--Mn 4+ superexchange coupling. It can be concluded that the reduction of holes on oxygen is prior to that of Mn 4+ ions. Subsequently, the reduction of Mn 4+ to Mn 3+ is reflected by the change in the ferromagnetic resonance line shape due to the difference in the magnetic property of Mn 3+ and Mn 4+ cations. When discharging to 1.5 V (D251), a new signal centered at g ≈ 2.0 is detected. It is assigned to the half-integer spin Mn 2+ ions, in agreement with the CV curve. The ferromagnetic resonance has not disappeared for the fully discharged sample, indicating that the magnetic ordering is altered in LTMO after electrochemical cycling.

Structural Degradation

As evidenced by 7 Li NMR (see Fig. 3c), the Li in paramagnetic environment has a good reversibility during the charge-discharge cycle, while half of the Li in diamagnetic environment is lost. What is at the origin of the degradation of the diamagnetic Li environments? Fig. 5a shows four diffuse scattering patterns around the reciprocal lattices for the pristine LTMO, in accordance with the previous observation on short-range order (SRO). 51 The diffuse scattering patterns preserve their shape and intensity for C150 (Fig. 5b), for which Mn 3+ is oxidized into Mn 4+ , indicating that the charge compensation on Mn ions does not give rise to structural evolution. On the contrary, when charging to 4.8 V (Fig. 5c), the ring-like reciprocal halo indicates the lattice distortions, which should be associated with the formation of (O 2 ) n-species and oxygen release at high voltage. For the fully discharged sample (Fig. 5d), several intensity maxima appear in the diffuse scattering patterns, suggesting a higher SRO after the first cycle, which necessarily involve migration of TM cations.

Since the SRO pattern after Mn oxidation does not change, we speculate that the TM cation migration takes place during O oxidation to relax the distorted lattices, resulting in a local disorder-to-order transition.

To verify this hypothesis, the C358 sample was investigated again after being stored into the glove box for two months. As shown in Fig. 6, after two months, the cubic rock-salt structure was transformed into the rhombohedral structure, which means that the original disordered cations were rearranged into ordered layers. The electronic property of this ordered sample was further investigated by EPR and sXAS (Fig. S12), which indicated that the magnetic coupling was stronger in the rhombohedral structure and the holes on oxygen were refilled. A recent study has suggested a coupling between oxygen redox and TM migration in the layered oxides. 60 In addition, we herein infer that the magnetic ordering transition plays a role in the TM migration as well and the electron spins are prone to alignment in the layers for the rhombohedral structure, which is the alternative (111) plane of the cubic structure. However, the precondition for the TM migration is the existence of vacancies. Upon cycling it is hard to form a long-range order because the vacancies are constantly refilled with Li ions. This dynamic process can only produce a short-range order. The structural degradation must originate from the TM migration during O oxidation, which aggravates the SRO and blocks the 0-TM pathway, resulting in a degradation of electrochemical performance.

Discussion

On the basis of the above investigations, we try now to illuminate the first-cycle anionic redox process in the cation-disordered LTMO, and then correlate it to the structural degradation. Unlike the periodic structure in layered materials, the O environments in DRX materials vary between the different oxygen sub-lattices due to the disordered distribution of cations. 61 Thus, the anionic redox process is complicated. Under the assumption that the cations are randomly distributed, several ) n-and the energy splitting of the |O 2p state. As a result, the energy level of the anti-bonding orbital   is higher than the Mn e g * orbital, resulting in the hysteresis of O reduction in the discharge process. In addition, oxygen loss is easier to occur in the Li 2 TiO 3 -rich environments, as argued by Yabuuchi and coworkers. 62 We further suggest that, accompanied with oxygen release, the TM migration occurs above 4.5 V, resulting in a more serious SRO that impedes the Li diffusion. The irreversible loss of the D-Li environments in the 7 Li NMR spectra could result from the oxygen release and the TM migration. And in the CV curves, we observed the shift of the Mn oxidation peak, indicating that the TM migration is irreversible, which alters the Mn redox potential. When charging to 4.8 V, the O The poor first-cycle reversibility is one of the main issues in the cation-disordered LTMO.

Besides the side reactions, the irreversible oxygen loss and the TM migration could be responsible for it. We noticed that, in similar reports on LTMO, 32,62 the first-cycle reversibility was much better than in our present work. The discrepancy may come from the sample preparation, leading to the difference in the local O environments which have a great influence on the reversibility. Another issue is the hysteresis of the oxygen reduction, which results from the difficulty in reducing the peroxo-like anions stabilized by the d 0 cations. 19 This is an intrinsic shortcoming in all cathodes utilizing anionic redox. Until recently, breakthroughs have been found via superstructure control or by using a O2-type layered structure. [63][64][65] Unfortunately, these methods cannot be applied to DRX due to its disordered nature, and thus the hysteresis of the anionic redox in DRX is still waiting to be resolved. Given the broad diversity of the selectable TM ions in DRX materials, the use of only reversible TM redox seems to be a possible solution. The cation-disordered Li 1.25 Nb 0.25 V 0.5 O 2 shows an ideal symmetric voltage profile with an excellent reversible capacity of 240 mAh g -1 , 34 and hence it looks worth developing DRX materials based on early transition metals. Fluorine substitution is also a versatile strategy to stabilize the O and improve the participation of TM redox. 36,37,41 In a word, increasing the participation of TM redox is a promising approach for the improvement of the performance of DRX materials in terms of practical applications.

Conclusions

In this work, we have investigated the evolution of local environments and electronic structure during the first cycle for LTMO via NMR and EPR spectroscopies. This study allowed us to gain new insights into the oxygen redox process and the related structural degradations. For the first time, The obtained mixture was then pelletized and calcined at 900°C with a heating rate of 5°C min -1 for 10 h under argon flow, followed by furnace cooling to room temperature. The pellets were manually ground into powders and stored in an argon-filled glove box.

Experimental Synthesis

Electrochemistry

The active material was first shaker-milled with Super P carbon for 1 h at a weight ratio of 7.5:1 in order to pulverize the particles and enhance the electronic conductivity. Excess Super P and polyvinylidene difluoride (PVDF) were then added to the milled powder, followed by manual grinding in an agate mortar. N-Methyl-2-pyrrolidone (NMP) was used to form the slurry, which was casted on an Al foil and vacuum-dried at 100°C overnight. The proportion of active material, carbon and binder in the cathode were 75%, 15% and 10%, respectively. 1 M LiPF 6 in a mixture of ethylene carbonate (EC), dimethyl carbonate (DMC) and ethyl methyl carbonate (EMC) (1:1:1 V/V/V) with additive (5%) of fluoroethylene carbonate (FEC) was used as electrolyte. CR2032 coin cells were assembled using Celgard 2300 separators and metallic lithium disks as anode. The mass load was Mn ions in the first two nearest neighbors will produce the paramagnetic shifts on 7 Li nucleus through 90° or 180° interaction. c) 7 Li pjMATPASS NMR spectrum of LTMO at 2.35 T with MAS frequency of 25 kHz. The isotropic resonances can be deconvoluted into P-Li (magenta) and D-Li (cyan) components. d) 17 O MAS NMR spectra of LTMO. By varying fields and MAS frequencies, an apparent isotropic peak is assigned at ca. 550 ppm, and spinning sidebands are indicated with asterisks.

  Fig. 3c shows the variation of the Li contents in P-Li and D-Li local environments during charge and discharge. These molar fractions were calculated from the integrated intensities of P-Li and D-Li signals divided by the masses of the active materials and transients, normalized to that of pristine. At the beginning of charging, P-Li and D-Li contents decrease simultaneously. From C40 to C150 as the delithiation proceeds, the amount of D-Li drops faster than that of P-Li, which is in good agreement with the faster migration of Li ions along the 0-TM percolation channel. 28 At the latter stage of the charge, D-Li sites are almost exhausted. Thus, P-Li ions continue to be extracted. During discharging, P-Li recovers quickly while a large proportion of D-Li is irreversibly lost, suggesting the degradation of the D-Li environments. Besides, the electrochemical removal/decomposition of the Li 2 O/Li 2 CO 3 impurities during cycling may also account for some part of the loss of D-Li. The 7 Li shifts are further analyzed in Fig. 3d by plotting two values: the weighted average shifts and the paramagnetic shifts. The average shift was calculated as the average of the shifts of all the isotropic resonances (P-Li and D-Li) weighted by their intensities (see Supporting Information). The paramagnetic shift is determined by simulating the P-Li signal. These two values corroborate each other to show the variation tendency of local magnetism around Li. As shown in Fig. 3d, both

  typical O coordination environments are illustrated in Fig. 7a. Note that the unhybridized O 2p orbitals (denoted as |O 2p ) stand along the Li-O-Li axis. They have a higher energy level than the hybridized states, and hence the oxygen oxidation preferentially occurs on these |O 2p orbitals. As shown in Fig. 7a, the O-Li 6 , O-TMLi 5 and O-TM 2 Li 4 configurations have three, two and one |O 2p lone pairs, respectively, whereas the O 2p orbitals in O-TM 3 Li 3 and O-TM 6 configurations are all hybridized, and hence are hard to be oxidized. On the basis of the 17 O NMR result, the O-Li 6 configurations barely exist in the cation-disordered LTMO, which is contrary to the random cation distribution. This is in agreement with a recent work by Ceder and coworkers, 51 which suggested that the cations in DRX materials are not randomly distributed due to the presence of SRO. Therefore, the |O 2p states in LTMO can be classified into two types: the |O 2p states under Ti surrounding and the |O 2p states under Mn surrounding. The energy of the |O 2p states under Mn surrounding are the lower than under Ti surrounding, because Mn t 2g orbitals may have a weak π-type interaction with the |O 2p states. Besides the |O 2p states, the energy level of the hybridized O 2p states lies at the bottom, predominating the bonding state between O 2p and TM 3d/4s/4p. The proposed band structure evolution for LTMO upon charging is illustrated in Fig. 7b. When charging to 4.25 V, the electrons are removed from the highest occupied orbital of Mn 3+ , which is the e g * orbital, since the Mn 3+ ions are in high-spin state. With the exhaustion of the e g * electrons beyond 4.25 V, the O 2-ions having |O 2p states under Ti surrounding begins to be oxidized upon charging to 4.5 V. Owing to the less directional bonding with d 0 Ti ions, the unhybridized O 2p orbitals are able to rotate to form -type O-O bonds when losing electrons, 20 leading to formation of peroxo-like anions (O 2

  we have been able to measure the evolution of Li content in different surroundings and the distribution of O local environments in LTMO. Li ions are preferentially removed from the Li-rich regions, in accord with the theory of the 0-TM percolation. Because of the manifold local environments in DRX materials, O redox involves the peroxo-like anions (O 2 ) n-under Ti surrounding and the electron holes on O 2p state under Mn surrounding. An undesirable voltage hysteresis occurs during charge and discharge, which results from the difficulty in reducing the peroxo-like anions owing to their stable O-O bonds. The irreversible loss of Li in the diamagnetic environment is observed by7 Li NMR, indicating the structural degradation after the first cycle. The degradation mechanism could be involved with the oxygen loss and the TM migration at high voltage, which result in a local disorderto-order transition as the aggravation of SRO which further deteriorates the percolating kinetics. Here, we anticipate that utilizing only TM redox can be a promising solution to improve the first-cycle reversibility and counterbalance the voltage hysteresis upon cycling while maintaining the high DRX capacity, by carefully selecting the TM ions or fluorine substitution.

around 3 .

 3 5 mg cm -2 based on active materials. Charge/discharge tests were carried out on a Land CT2001A autocycler at 45°C. The coin cells were cycled to various SOCs and then disassembled carefully inside the glove box to obtain the electrodes which were washed with dimethyl carbonate (DMC) to remove the residual electrolyte. Cyclic voltammetry (CV) test was conducted on a CHI 660e electrochemical workstation within the voltage window of 1.5~4.8 V.

Fig. 1

 1 Fig. 1 Crystal structure and local environment of LTMO. a) Synchrotron X-ray diffraction (SXRD,  = 0.68888 Å) pattern and Rietveld refinement of the as-synthesized LTMO. b) Crystal structure of LTMO. Left: unit cell of LTMO and the Li-O cube of 0-TM channel. Li diffusion through an intermediate tetrahedral site with no TM ions around has the lowest migration barrier. Right: local environment of Li.Mn ions in the first two nearest neighbors will produce the paramagnetic shifts on7 Li nucleus through 90° or 180° interaction. c)7 Li pjMATPASS NMR spectrum of LTMO at 2.35 T with MAS frequency of 25 kHz. The isotropic resonances can be deconvoluted into P-Li (magenta) and D-Li (cyan) components. d)17 O MAS NMR spectra of LTMO. By varying fields and MAS frequencies, an apparent isotropic peak is assigned at ca. 550 ppm, and spinning sidebands are indicated with asterisks.

Fig. 2

 2 Fig. 2 Electrochemical performance of LTMO half-cell. a) Galvanostatic charge and discharge curve for the first cycle at 10 mA g -1 at 45°C. The crosses (+) denote the states of charge (SOCs) for the NMR and EPR characterizations. b) Cyclic voltammogram for the first two scans at a scan rate of 0.02 mV s -1 .

Fig. 3

 3 Fig.3Ex situ7 Li pjMATPASS (a) and17 O MAS (b) NMR spectra of LTMO at different SOCs. The7 Li and 17 O NMR spectra were acquired at a static magnetic field of 2.35 and 18.8 T, respectively. The cycled samples are named as "C/DX", where "C" and "D" stands for charge and discharge, respectively, and X is the cut-off capacities in mAh g -1 . c) Normalized P-Li and D-Li contents in LTMO electrodes at different SOCs. d) Weighted average and paramagnetic7 Li shifts of LTMO at different SOCs. Note that the weighted average shift should never exceed the paramagnetic shift for the same sample, and if not, it is caused by the deviation between the asymmetric spectral line shape and the single Gaussian-Lorentzian line shape in the fitting of paramagnetic shifts. e) Isotropic17 O shifts of LTMO at different SOCs. Galvaniostatic charge and discharge curves are displayed in the background of the subfigures.

Fig. 4

 4 Fig. 4 Ex situ perpendicular-mode CW-EPR spectra of LTMO during the processes of (a) Mn oxidation, (b) O oxidation, and (c) reduction. These EPR measurements were performed at 1.8 K and the results at room temperature are displayed in Fig. S7. The corresponding parallel-mode CW-EPR spectra are displayed in Fig. S8. Signal intensities are normalized based on the mass of each material scraped from the electrodes. The sharp signals centered at ~345 mT (g ≈ 2.0) stem from the delocalized electrons in the conductive carbon black, which can be regarded as an external reference although it may cover up similar signals. The variation on the conductive carbon signals at high voltage is unclear, probably due to the side reaction of carbon oxidation.

Fig. 5

 5 Fig. 5 Fast Fourier transforms (FFT) of the TEM images of: the pristine sample (a), C150 (b), C358 (c), and D251 (d). The direction of observation is along the zone axis [100]. The respective original

Fig. 6

 6 Fig. 6 Synchrotron X-ray diffraction (SXRD,  = 1.240618 Å) pattern of C358 stored in the glove box for two months. The reflection peaks can be indexed to the rhombohedral structure with R m 3 space group.

Fig. 7 a

 7 Fig. 7 a) Typical O coordination environments in LTMO. b) Schematic of the proposed band structure evolution for LTMO in the first charge process.

  2-ions having |O 2p states under Mn surrounding starts to be oxidized. Because the partially filled d orbitals which have a strong directionality prevent the rotation of O 2p orbitals, the oxidation at 4.8 V creates localized holes on |O 2p states instead of the O-O bond. The holes on |O 2p states are quite unstable and are easy to cause further structural rearrangement. During discharging, electrons would fill the empty bands from low to high. The holes on |O 2p states are first refilled, showing a small voltage hysteresis. The Mn 4+ ions are reduced next. The Mn e g * band has shifted higher due to the TM migration, leading to a lower Mn 3+/4+ redox potential. The O-O bonds are broken at last due to the high energy of the anti-bonding orbital   , giving rise to a large voltage hysteresis. After the first whole cycle, the local structure in LTMO is changed and the Li and O environments do not return to the pristine state.

  Stoichiometric amounts of Li 2 O (Aladdin, 99.99%; 7% excess), TiO 2 (anatase, Aladdin, 99%), and Mn 2 O 3 (Alfa Aesar, 98%) with the goal of 0.01 mol of Li 1.2 Ti 0.4 Mn 0.4 O 2 were shaker-milled in a 45-

	mL zirconia grinding bowl with two 8-mm-diameter yttria-stabilized zirconia balls for 30 minutes
	together with 0.5 mL of H 2 17 O (35~40% 17 O, Cambridge Isotope), using a SPEX 8000M Mixer/Mill.

Journal of Materials Chemistry A

Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 21872055, 21902049, 21703068, 21874045) and Shanghai Sailing Program (19YF1413000). Chevreul Institute

Characterization

The powder XRD pattern of the 17 O-labelled Li 1.2 Ti 0.4 Mn 0.4 O 2 was recorded at the synchrotron beam line BL14B at Shanghai Synchrotron Radiation Facility (SSRF). Rietveld refinement of the synchrotron XRD (SXRD) pattern was executed with the FullProf Suite software.

Morphological features and lattice fringes of the samples were observed using a high-resolution transmission electron microscope (HRTEM, FEI, TECNAI G2 F20). HRTEM Images were analyzed and processed by the Gatan DigitalMicrograph program. 7 Li NMR experiments were performed on a 100 MHz Bruker Avance NMR spectrometer operating at a static magnetic field of 2.35 T and equipped with a 2.5 mm triple resonance HXY MAS probe used in double-resonance mode. 7 Li NMR spectra were acquired at a MAS frequency of 25 kHz using zirconia rotors. Temperature regulation was carried out by measuring the paramagnetic shift of protons in a mixture of ferrocene and nickelocene. 66 The actual temperature of the samples was 309 K under the test condition. We carried out rotor-synchronized Hahn-echo (π/2-τ-π-τ-acq)

and pjMATPASS experiments with a π/2 pulse length of 1.8 μs. The recycle delay was 70 ms, which was long enough to reach thermal equilibrium. The 7 Li isotropic shifts were externally referenced to the signal of 1 M LiCl aqueous solution at 0 ppm. The 7 Li signals were simulated using the DMFIT program. 67 17 O NMR experiments were performed on a 400 MHz Bruker Avance II NMR spectrometer operating at a static magnetic field of 9.4 T and equipped with a 2.5 mm triple-resonance HXY MAS probe and a 800 MHz Bruker Avance Neo NMR spectrometer operating at a static magnetic field of 18.8 T and equipped with a 1.3 mm triple-resonance HXY MAS probe. The 2.5 and 1.3 mm rotors were spun at a MAS frequency of 30 and 60 kHz, respectively. The temperature was calibrated using the same approach as that employed for experiments at 2.35 T. The actual temperature of the samples was 314 and 316 K in the case of 2.5 and 1.3 mm rotors, respectively.

The 17 O spectra were acquired using a rotor-synchronized solid-echo sequence (π/2-τ-π/2-τ-acq) with a π/2 pulse length of 1.5 and 1.08 μs for the acquisition at 9.4 and 18.8 T, respectively. The recycle delay was 10 ms. The 17 O isotropic shifts were externally referenced to the signal of pure liquid water at 0 ppm. Magnetic susceptibility measurements were carried out on a Quantum Design Magnetic Properties Measurement System (MPMS) with a Superconducting Quantum Interference Device (SQUID) magnetometer.

Continuous-wave (CW) X-band EPR spectra were recorded on a Bruker EMX plus 10/12 spectrometer equipped with an Oxford ESR910 Liquid Helium cryostat and a dual-mode microwave cavity. The perpendicular-mode EPR spectra were acquired at a microwave frequency of 9.647~9.649 GHz and room temperature or temperature of 1.8 K using a microwave power of 2 mW and a modulation amplitude of 2 G. The parallel-mode EPR spectra were acquired at a microwave frequency of 9.405~9.408 GHz and room temperature or temperature of 1.8 K using a microwave power of 2 mW and a modulation amplitude of 2 G. Soft X-ray absorption spectroscopy (sXAS) measurements were recorded at the synchrotron beam line BL08UA at SSRF.

Conflicts of interest

There are no conflicts to declare.

(FR 2638), Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation, Hauts-de-France Region and FEDER are acknowledged for supporting and funding partially this work.

Financial support from the IR-RMN-THC Fr3050 CNRS for conducting the research is gratefully acknowledged. We also acknowledge the support from the Steady High Magnetic Field Facilities of High Magnetic Field Laboratory (CAS) for the EPR and MPMS tests, and the support from Shanghai Synchrotron Radiation Facility for the SXRD (BL14B) and sXAS (BL08UA) experiments. We would like to thank Herve Vezin for inspirational discussion on EPR experiments and Bertrand Doumert for assistance in NMR experiments.

Table of contents entry

The structural evolution of the cation-disordered rock-salt Li 1.2 Ti 0.4 Mn 0.4 O 2 is investigated by solidstate NMR and Electron paramagnetic resonance (EPR) spectroscopy during the first cycle. The formation of stable O-O bonds coordinated by Ti ions leads to the voltage hysteresis. The structural degradation is related to the oxygen loss and transition metal migration.


Irene Adroher-Benítez

Tatiana I Morozova

Gabriel Catalini

Nicolás A García

Jean-Louis Barrat

Gustavo S Luengo

Fabien Léonforte

Effect of polymer architecture on the adsorption and coating stability on heterogeneous biomimetic surfaces

This study aims to investigate the physical properties that govern polymer adsorption and desorption on chemically structured surfaces. These surfaces are considered biomimetic of natural ones that specifically exhibit a combination of hydrophobic and hydrophilic domains, like those found on hair surfaces. Understanding these processes is especially crucial when designing and developing new eco-sustainable polymers for industrial applications such as cosmetic products. In this work, we developed computational models of the hair surface and two polymers with different architectures. The first polymer studied was a semi-flexible, linear polysaccharide of natural origin, which offers potential for sustainable formulations. The second, and more complex model, was a stiff, comb-like cationic polyelectrolyte similar to petroleum-based polymers traditionally used in hair care cosmetics. We conducted coarse-grained molecular dynamics simulations to study the adsorption of the polymers onto the substrate and we found that increasing polymer concentration enhanced adsorption. The branched copolymer led to a thicker coating and exhibited a more random coverage pattern compared to the linear polymer. Furthermore, we analyzed the stability of the polymer coating by running Brownian dynamics simulations of the adsorbed polymers under a linear shear flow. These simulations revealed a correlation between flow strength and polymer desorption, thereby highlighting the importance of low desorption time for performing coatings in cosmetic applications. Despite both polymer types presenting improved resistance with longer polymer chains, the branched polymer layer exhibited higher stability. This finding demonstrates the key role of polymer architecture in assessing the coating formation, properties and performance of new eco-sustainable polymers in industrial applications.

Introduction

Research in eco-friendly cosmetic formulations is a growing field due to an increasing consumer demand for innovative products that establish a compromise between efficiency and sustainability. It is critical to align this research with the principles of green chemistry, [START_REF] Anastas | Green Chemistry: Principles and Practice[END_REF] emphasizing the design and production of safe, biodegradable, and efficient polymers, and minimizing the use of harmful compounds. Certain ingredients currently used in cosmetic products, like silicones and cationic polyelectrolytes, such as polyquaterniums, [START_REF] Hössel | Conditioning polymers in today's shampoo formulations -efficacy, mechanism and test methods[END_REF] present considerable ecological challenges. [START_REF] Cumming | Ecotoxicities of polyquaterniums and their associated polyelectrolyte-surfactant aggregates (PSA) to Gambusia holbrooki[END_REF] These difficulties have driven the cosmetic industry to improve sustainability in their formulations. However, transitioning from existing polymers to greener alternatives is non-trivial, as the new components must meet the performance standards expected by consumers. Still, progress has been made in this direction, since some polysaccharides have already been incorporated into makeup formulations. [START_REF] Luengo | Surface science of cosmetic substrates, cleansing actives and formulations[END_REF] Indeed, carbohydrates represent promising sources of sustainable monomers. Despite the economic challenges they pose when competing with petrochemical-derived polymers, there are many opportunities to improve their value in high-demand applications through targeted property enhancements. [START_REF] Zhu | Sustainable polymers from renewable resources[END_REF] Recognizing these opportunities, the cosmetic industry has been actively conducting research on the synthesis and application of such green polymers. [START_REF] L'haridon | Ecodesign of cosmetic formulae: methodology and application[END_REF] Certainly, an interdisciplinary collaboration between fundamental and applied research is crucial for achieving this objective.

A part of this effort must be dedicated to identifying the physical parameters that govern polymer adsorption onto hair-like substrates. The first challenge is therefore to have a good knowledge of the hair surface, which is made of many layers. [START_REF] Bouillon | The Science of Hair Care[END_REF] The most external layer, that acts as physical and chemical protection for the hair, is called the F-layer. [START_REF] Robbins | Chemical and Physical Behavior of Human Hair[END_REF] It is formed by fatty acids and it is hydrophobic. [START_REF] Bhushan | Biophysics of Human Hair: Structural, Nanomechanical, and Nanotribological Studies[END_REF] This layer can be partially damaged by several factors, including ageing and external aggressions such as solar radiation, bleaching, and various treatments. [START_REF] Thibaut | Chronological ageing of human hair keratin fibres[END_REF][START_REF] Maddar | Nanoscale surface charge visualization of human hair[END_REF][START_REF] Wang | Effect of Surface Treatments on the Nanomechanical Properties of Human Hair[END_REF][START_REF] Durkan | Nanometre-scale investigations by atomic force microscopy into the effect of different treatments on the surface structure of hair[END_REF] The cuticle degradation exposes hydrophilic layers of hair, resulting in a surface that exhibits both hydrophobic and hydrophilic areas. [START_REF] Korte | Distribution and Localization of Hydrophobic and Ionic Chemical Groups at the Surface of Bleached Human Hair Fibers[END_REF][START_REF] Weiand | Coarse-grained molecular models of the surface of hair[END_REF] Surface heterogeneity can significantly influence the dynamics of molecule adsorption, thereby affecting the physical properties of the resulting coatings. [START_REF] Pastore | Influence of wall heterogeneity on nanoscopically confined polymers[END_REF][START_REF] Klebes | The Role of Chemical Heterogeneity in Surfactant Adsorption at Solid-Liquid Interfaces[END_REF] In the context of cosmetics, the diverse physicochemical characteristics across different regions of the hair surface make uniform polymer adsorption a considerable challenge. Addressing this substrate complexity, Llamas et al. [START_REF] Llamas | Adsorption of polyelectrolytes and polyelectrolytes-surfactant mixtures at surfaces: a physico-chemical approach to a cosmetic challenge[END_REF] conducted experimental research on the adsorption of polymer and surfactant mixtures for personal care products, focusing on the interaction with different hair surfaces. They introduced systems capable of adhering to negatively charged surfaces, paving the way for new methods of applying cosmetic ingredients.

The equilibrium properties of polymer coatings and the dynamics of polymer adsorption have sustained interest from the scientific community for years. Pioneering experimental work, such as the study conducted by Frantz and Granick on the adsorption-desorption kinetics of polymers at a solid surface, [START_REF] Frantz | Kinetics of polymer adsorption and desorption[END_REF] has provided insight into the factors that influence the dynamics of adsorbed polymer chains. However, theoretical and computational methods can offer some advantages over experimental research, including reduced cost and time, or improved precision and scalability. For instance, Polotsky and Ivanova conducted a series of analytical studies on the adsorption of single polymer chains onto stripe-patterned surfaces to investigate the adsorptiondesorption transition. They developed different theoretical models for homopolymers [START_REF] Polotsky | Adsorption of a homopolymer chain onto a heterogeneous stripe-patterned surface studied using a directed walk model of the polymer[END_REF][START_REF] Polotsky | Effect of bending stiffness on the polymer adsorption onto a heterogeneous stripe-patterned surface[END_REF] and copolymers, [START_REF] Ivanova | Random copolymer adsorption onto a periodic heterogeneous surface: A partially directed walk model[END_REF] and analyzed the effect of parameters such as temperature, chain stiffness or polymer composition on the adsorption on these heterogeneous surfaces. Milchev and Binder 23 conducted molecular dynamics simulations to clarify how chain stiffness influences the adsorption transition and structural properties of adsorbed semiflexible polymer chains. With a focus in cosmetic applications, Banerjee et al. [START_REF] Banerjee | Modeling of Polyelectrolyte Adsorption from Micellar Solutions onto Biomimetic Substrates[END_REF] investigated the deposition of cationic polyelectrolytes from micellar solutions containing surfactants onto hair-like surfaces. Using self-consistent field calculations, they found that polyelectrolyte adsorption is typically governed by the molecular details of the species in solution as well as the specificities of the surface. They highlighted the critical role of molecular modeling in optimizing the adsorption processes in industrial applications. Molecular dynamics was also used by Zhou et al. [START_REF] Zhou | Dynamic Propagation Depth in Substrate-Supported Polymer Films: A Molecular Dynamics Simulation[END_REF] to investigate how the strength of substrate attraction and polymer chain length affected the behavior of adsorbed and non-adsorbed chains in substrate-supported thin films. They found an influence zone beyond which the diffusion of polymer chains remained unaffected by the substrate. The adsorbed polymer layer comprised a fraction of weakly adsorbed chains with tails that extended vertically, penetrating the non-adsorbed chains. Interestingly, the ends of these chains were found to have a notable impact on the dynamics of the free polymers in the bulk.

Studying the rheological effects of polymer adsorption and desorption in flowing systems represents a relevant area of interest, especially within the context of hair and skin cleaning products. These cosmetics are typically applied under the influence of a shear flow. In general, it is expected that the flow enhances the desorption of the adsorbed polymer layers, while hydrodynamic forces could potentially inhibit the adsorption of polymer chains onto surfaces from flowing solutions. [START_REF] Lee | Adsorption and desorption of flexible polymer chains in flowing systems[END_REF] Recent computational studies have made progress in understanding polymer adsorption and desorption in flowing systems. Panwar and Kumar 27 utilized coarse-grained Brownian dynamics simulations to analyze the adsorption of a polyelectrolyte onto an oppositely charged surface. They examined adsorption behavior with respect to screening length in presence and absence of shear flow. Under shear flow, they observed the polymer chain aligning with the flow direction, increasing surface contact. An investigation by Ibáñez-García et al. [START_REF] Ibáñez-García | Brownian dynamics simulations of confined tethered polymers in shear flow: the effect of attractive surfaces[END_REF] focused on how attractive surfaces affect the stretching of confined tethered polymers under shear flow. They observed unique stationary cyclic dynamics, varying with the shear flow intensity and surface potential strength. Their results indicated that a stronger attractive potential decreased polymer stretching, deviating from scaling predictions for non-adsorbed polymers. They also found the shear flow intensity to enhance the adsorption process. Šindelka et al. [START_REF] Šindelka | Interactions of cationic surfactant-fatty alcohol monolayers with natural human hair surface: Insights from dissipative particle dynamics[END_REF] employed dissipative particle dynamics simulations for study of the interaction between two main components of personal care products and the human hair surface. Their work included analysis both above and below the fluid-gel transition temperature and both in-and out-of-equilibrium conditions. Interestingly, under shear stress, they found that beyond a certain threshold, both types of adsorbed layers began to lose their attached molecules. In the fluid layers, this was due to increased shear overpowering the hydrophobic interactions, while in the gel lay-ers, it resulted from the collapse of the hair lipid brush, causing a significant desorption.

Understanding the friction between hair fibers and polymer-coated hair surfaces is also of significant scientific and industrial importance. The degree of friction influences the tactile sensation, manageability, and combing of hair, which are primary factors in consumer perception of hair care products. Recently, Weiand et al. [START_REF] Weiand | Nanoscale friction of biomimetic hair surfaces[END_REF] investigated the nanoscale friction between biomimetic hair surfaces using experiments and coarse-grained molecular dynamics simulations. In the simulations, friction was monitored between hair surfaces with different levels of chemical damage. They found that the increase in nanoscale friction in chemically damaged hair is primarily due to changes in the hair surface chemistry, not because of changes in either its roughness or damage beneath the surface. On the other hand, Coscia et al. [START_REF] Coscia | Shearing friction behaviour of synthetic polymers compared to a functionalized polysaccharide on biomimetic surfaces: models for the prediction of performance of eco-designed formulations[END_REF] investigated the tribological behavior of diffferent polymers in surfactant solutions in contact with the hair surface, comparing the aggregation behaviour and lubrication properties of a generic functionalized polysaccharide with two petroleum-based polyelectrolytes used in shampoo formulations.

In our previous work, we examined the adsorption of hydrophilic flexible homopolymers to surfaces that chemically mimic human hair. [START_REF] Morozova | Adsorption and Desorption of Polymers on Bioinspired Chemically Structured Substrates[END_REF] By merging experimental imaging data with coarse-grained molecular dynamics simulations, we explored the impact of polymer chain length and concentration on the adsorption process. We observed that an increase in concentration led to longer polymer tails and loops, reducing the length of the chain sections attached to the surface. We also tested the stability of these polymers under a linear shear flow. Advancing from this foundation, our current study serves as a natural extension, introducing more complex and realistic polymer models to verify the robustness of the computational framework. Our research includes the effect of different polymer architectures, concentrations, and chain length on polymer adsorption. Simulations of rinsing under a linear shear flow were also performed. By considering various flow strengths, we systematically probed the desorption dynamics. This investigation represents a significant step in the construction of models for complex macromolecules interacting with realistic biological surfaces, with the ultimate goal of promoting the design of more eco-friendly industrial products.

The structure of this manuscript is as follows. After this introduction, we detail the models and methodologies employed in our study. This includes descriptions of the substrate and polymer models we have developed, as well as the simulation techniques implemented to model polymer adsorption. The subsequent section presents our findings in the context of the various variables explored, namely polymer architecture, monomer concentration, chain length, and flow strength. We provide interpretations and discuss these results. Finally, we draw conclusions and propose possible directions for future research.

Model and methods

Substrate model

The essential simulation setup consisted of a polymer solution with a substrate at the bottom of the simulation box. Based in real dynamic Chemical Force Microscopy images, the substrate was modeled to represent a realistic bleached human hair surface. [START_REF] Korte | Distribution and Localization of Hydrophobic and Ionic Chemical Groups at the Surface of Bleached Human Hair Fibers[END_REF] Therefore, 60% was composed of damaged areas, which were hydrophilic, while 40% was composed of healthy hydrophobic zones. Figure 1 shows the substrate model used in this work. It was made of spherical beads with the same size as polymer beads, labeled as G (hydrophilic) and H (hydrophobic). For more detailed information regarding the construction of this model, we refer the interested reader to to the previously published paper by Morozova et al. [START_REF] Morozova | Adsorption and Desorption of Polymers on Bioinspired Chemically Structured Substrates[END_REF]

Linear polymer

Branched polymer

A B C D E F G H

Polymer models

We developed two polymer models that correspond to a semi-flexible linear polymer of natural origin and a stiff branched polymer with a bottle-brush structure, similar to those currently used in cosmetic formulations. The former was modeled after chitosan, a linear polysaccharide composed of randomly distributed deacetylated and acetylated units. For the latter, we took inspiration from polyquaterniums, a family of polycationic polymers with quaternary ammonium centers.

Linear block copolymer

We modeled a semi-flexible linear block copolymer where each bead represents a monomer: either Dglucosamine (GlcN) or N-acetylglucosamine (GlcNac) proving the notion of the length-scale in simulations as the size of the monomer is approximately 0.5 nm. [START_REF] Ma | New Insights into chitosan-DNA interactions using isothermal titration microcalorimetry[END_REF] In this model, GlcN units are described by positively charged A beads, while hydrophobic electroneutral B beads stand for GlcNac monomers [START_REF] Tsereteli | An accurate coarsegrained model for chitosan polysaccharides in aqueous solution[END_REF] (see Figure 1). In experiments, polymers like chitosan are composed of 80% GlcN. In our model we have preserved this same fraction of A beads, which are randomly distributed along the chain. We considered good solvent conditions for the chains, resulting in a purely repulsive Weeks-Chandler Andersen (WCA)-type interaction among all monomers

U WCA (r ij ) = 4ε σ r ij 12 - σ r ij 6 +ε, r ij < r c = 2 1/6 σ, (1
) where ε is the interaction strength, and r ij is the distance between i and j monomers. For distances r ij ≥ r c , U WCA (r ij ) = 0. In addition, neighboring monomers were connected via the finitely extensible nonlinear elastic (FENE) potential

U FENE (r ij ) = - 1 2 κr 2 0 ln 1 - r ij r 0 2 , ( 2
)
where we employed the standard Kremer-Grest parameters to prevent unphysical bond crossing, i.e. the maximum bond extension is set to r 0 = 1.5σ, and κ = 30ε/σ 2 is the spring constant. [START_REF] Grest | Molecular Dynamics Simulation for Polymers in the Presence of a Heat Bath[END_REF] Chitosan is a semiflexible polymer with persistence length of approximately l p ≃ 9 nm for the chain composition investigated. [START_REF] Brugnerotto | Overview on structural characterization of chitosan molecules in relation with their behavior in solution[END_REF] Thus, we introduced a bending potential of the harmonic form

U (θ) bend = 1 2 k(θ -θ 0 ) 2 , (3)
where θ 0 = 2π, and the potential constant k = 18 ε/rad 2 . The value of k was chosen in a such a way, that the resulting l p of a chain in simulations is close to the experimental value, i.e., l sim p = 18σ. Furthermore, under experimental conditions, i.e., pH 4.5, chitosan is positively charged through the protonation of its GlcN monomers. [START_REF] Tsereteli | An accurate coarsegrained model for chitosan polysaccharides in aqueous solution[END_REF] Hence, we assumed that each A bead carries a positive elementary charge, z A = +1. We used the experimentally determined value of the surface charge of a hydrophilic zone of bleached hair 11 to estimate the charge of hydrophilic G beads. According to our calculations, each G bead has z G = -0.11 elementary charge. Since under experimental conditions the aqueous solution contains salt ions, we described the effective interaction between two charged beads through the Debye-Hückel screened electrostatic potential,

U DH = z A z G l B r e -κr , (4)
where

l B = e 2 4πεε 0 k B T
is the Bjerrum length, and κ is the inverse Debye length. We adopted experimental values of l B = 0.7 nm, and 1/κ = 1.0 nm. Lastly, the excluded-volume interactions between charged A beads and two types of the substrate beads, as well as between hydrophobic B beads and G (hydrophilic) substrate beads, are given by WCA poten-tial introduced above. Interaction between hydrophobic monomers and hydrophobic beads of the substrate includes attractive part and is described by the Lennard-Jones (LJ) potential

U LJ (r ij ) = 4ε ms σ r ij 12 - σ r ij 6 , r ij < 3σ, (5)
where the value of the energy well was taken from our former study of the homopolymer adsorption and results in ε ms = 0.3ε. [START_REF] Morozova | Adsorption and Desorption of Polymers on Bioinspired Chemically Structured Substrates[END_REF]

Branched bottle-brush copolymer

We also modeled a cationic polyelectrolyte like those currently used in hair cosmetics. It has a stiff comblike architecture in which each monomer is made of 17 beads. Figure 1 (right) shows a dimer of this polymer. The backbone of the chain is made of amphiphilic C beads, while the branches contain charged hydrophilic D beads, hydrophobic E and electroneutral F beads. As for the other polymer model, we considered good solvent conditions, that results in a purely repulsive interactions among all monomers modeled via WCA potential. Neighboring monomers are connected via FENE potential. Amphiphilic C beads of the monomer interact via LJ potential with all substrate beads with the strength ε ms = 0.3ε. Charged D beads interact only with charged beads of the substrate (G) using Debye-Hückel potential, where the charge for D beads z D = 1.4 is adopted. All other interactions between monomeric and substrate beads are described by the excluded-volume interactions (WCA potential). In Table 1 we summarize all monomer types employed in this study.

Table 1: Description of monomer beads employed including their physical nature and type of attractive interaction with the substrate.

Name Polymer Physical nature Interactions

A Linear Charged U DH B Hydrophobic U LJ C Branched Amphiphilic U LJ D Charged U DH E Hydrophobic U LJ F Neutral U WCA

Simulations

With these two polymer families and the modeled substrate we performed coarse-grained molecular dynamics simulations with implicit solvent. The simulation box had periodic boundary conditions in x and y directions and was confined in z direction, normal to the surface. All the simulations were performed within the canonical N V T ensemble. To model the dynamics of the polymers in bulk and adsorbing onto the substrate we used a Langevin thermostat, while the effect of a linear shear flow on the adsorbed polymer chains was simulated applying Brownian dynamics. Simulations were run by means of the simulation package HOOMD-blue. [START_REF] Anderson | General Purpose Molecular Dynamics Simulations Fully Implemented on Graphics Processing Units[END_REF] Table 2 summarizes the sets of system parameters explored in the simulations, namely: polymer architecture, concentration and length to study the adsorption onto the substrate, as well as flow strength to test the stability of the adsorbed layer. First, as described above, we chose two distinct polymer types with different architectures: a semi-flexible linear block copolymer, henceforth referred to as the linear polymer, and a stiff comb-like cationic polyelectrolyte, which we shall designate as the branched polymer. We studied three monomer concentrations ranging from dilute solutions to semidilute ones, c/c * = {0.1, 0.5, 1.0}, being c * the overlap concentration,

c * = N 4 3 πR 3 g0 , ( 6
)
where N is the number of monomers per chain and R g0 is the polymer gyration radius at infinite dilution. To assess the effect of the degree of polymerization on the dynamics of polymer adsorption and on the stability of the polymer coating, we considered three different polymer lengths, characterized by the number of monomers per chain, N = {150, 250, 500}. To have statistically significant results, for each system configuration we ran three independent simulations. The stability of the resulting polymer coating was analyzed applying a linear shear flow along the x-axis to the adsorbed polymers chains. Theoretical and computational details of these calculations can be found in our former work. [START_REF] Morozova | Adsorption and Desorption of Polymers on Bioinspired Chemically Structured Substrates[END_REF] To examine the desorption of polymer chains under applied shear flow, we selected a sample from all the adsorption simulations we conducted, as summarized in Table 2. The concentration was set to c/c * = 1.0, based on the assumption that the density within the adsorbed polymer layer is uniform, a requirement for solving the Brinkman equation. [START_REF] Brinkman | A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles[END_REF][START_REF] Milner | Hydrodynamic penetration into parabolic brushes[END_REF] The polymerization degrees studied during the desorption simulations were the same as those used in the adsorption simulations, namely N = {150, 250, 500} monomers per chain. To characterize the strength of the flow we used the Weissenberg number Wi = γτ 0 , where γ is the ap-plied shear rate and τ 0 is the chain relaxation time at infinite dilution. [START_REF] Dealy | Structure and rheology of molten polymers[END_REF] Further details regarding the computation of τ 0 are provided in the Supplementary Information. Since the Weissenberg number provides the degree of anisotropy generated by the flow, we assume that Wi > 1 implies a strong shear flow, while Wi ≤ 1 indicates a weak perturbation.

The complete workflow of this study is summarized in Figure 2. First, the adsorption of the polymer solution onto the heterogeneous substrate was simulated. Non-adsorbed polymers were then removed to obtain the resulting coating. Subsequently, a linear shear flow was applied to the adsorbed layer. Figure 2(c) shows the desorbed polymers colored in pink. The final state of the coating with the remaining adsorbed polymers is presented in Figure 2(d). It is worth noting that during the simulation of a linear shear flow applied to the system, the longest polymer chains were stretched under strong flow regimes which led to polymer selfinteraction within the simulation box. To address this issue, the simulation box was duplicated in the flow direction.

Results and discussion

To ensure that the results obtained from the simulation of two distinct polymer types with different architectures were comparable, we first conducted simulations of polymers in solution for all the system configurations explored in this study. We measured the radius of gyration in bulk, as shown in Figure 3, and confirmed that the sizes of the polymers were similar for a given degree of polymerization N . The obtained results allow us to confidently compare the behavior of these two polymer types and gain insights into the properties of the adsorbed layers. Additionally, by fitting the data to a linear function we determined the value of the radius of gyration of the polymer at infinite dilution R g0 from the y-intercept, used in the calculation of the overlap concentration in equation ( 6). After confirming that both types of polymers were of comparable size, we proceeded to examine their adsorption strength with the substrate. To do so, we calculated the mean potential energy u ads between a monomer from an adsorbed chain and the substrate. This calculation was performed on the polymer coatings obtained at the end of the adsorption simulations, after all nonadsorbed chains had been removed from the simulation box. The results revealed that the adsorption strength per monomer for both polymer models was nearly identical: u ads = (0.46 ± 0.02)ε for the linear polymers and u ads = (0.44 ± 0.01)ε for the branched polymers. The similarity in adsorption strength suggests that any observed differences in the properties of the coatings formed by these polymers could be attributed to other factors, such as differences in polymer architecture.

As the first step in the characterization of the polymer coatings, we started by computing the concentration profiles of the adsorbed chains as a function of the distance to the substrate. These profiles are plotted in Figure 4(a) at three different concentrations for three types of polymers with N = 500 monomers per chain: the linear and branched copolymers modeled in this study, and the linear flexible homopolymers analyzed in our previous study. [START_REF] Morozova | Adsorption and Desorption of Polymers on Bioinspired Chemically Structured Substrates[END_REF] To enable comparison of the resulting layers, the distance in the figure is normalized by the mean radius of gyration of chains in solution.

We found that the shape of the profiles remained constant with concentration for all polymer types, while polymer adsorption increased with concentration. Nevertheless, we could expect the concentration to reach a threshold value that saturates the substrate, preventing more polymers to adsorb. When comparing the polymer types, it was observed that the semi-flexible linear copolymer generated a significantly less thick coating with respect to the average chain length compared to the flexible homopolymer and the branched copolymer. This is because both the linear homopolymer and the branched copolymer, when adsorbed on the substrate, still had long tails that were not adsorbed, contributing to the concentration profile far from the substrate. Conversely, for the linear copolymer, the portion of chain adsorbed onto the substrate was larger, leading to shorter tails in comparison to the average size of the polymers in solution. These findings demonstrate the importance of considering not only polymer architecture but also the specific monomer-substrate interaction in understanding the adsorption dynamics and properties of polymer coatings. Figure 4(b) contains the concentration profiles normalized by the bulk concentration of the three polymer solutions at c/c * = 1.0 as a function of the absolute distance to the substrate. The rapid rise in the concentration profiles at small distances confirms that, in all cases, chains exhibit a preference for adsorption onto the substrate rather than dispersion in the bulk. Furthermore, the concentration profiles also indicate that the branched copolymer is notably more voluminous than the linear polymers, which contributes to the formation of a thicker polymer layer.

To determine the uniformity of the polymer coverage on the substrate, we performed a novel analysis method. The simulation box was partitioned into several slabs along z-axis and the monomer density profile was calculated in each point in the slab. These profiles were then integrated over the slab thickness to obtain two-dimensional density profiles, which were averaged over multiple snapshots of the simulation trajectory. Further details, including an explanatory figure of this slab analysis method, can be found in the Supporting Information. Figure 5 shows the results obtained by dividing each adsorbed polymer layer into four slabs of equal thickness. The first slab starts at a distance zero from the substrate and the last slab ends at a distance h ads , which is the average thickness of the adsorbed polymer layer. It is observed that as the chain length increases, the polymer coating becomes denser and it is easier to keep track of the chains at further slabs from the surface due to reduced mobility and longer tails. For branched polymers the effect of chain length is more significant due to their bulkier nature. Analysis of the slabs close to the substrate shows that for short chains the branched polymers can accommodate in the substrate, while for chains with N > 150 mobility seems to be significantly restricted due to overcrowded substrate. The figure also reveals that linear polymers exhibit a higher degree of memory of the substrate compared to the branched ones. The linear chains adhere more strongly to the hydrophilic areas of the substrate and clearly follow its heterogeneous pattern, resulting in a clear correlation between the polymer layer and the substrate. This effect is particularly evident for long chains. Conversely, branched polymers show a more homogeneous distribution on the substrate. This effect can be attributed to the difference in the chain architecture between linear and branched copolymers, as well as to the specific monomer-substrate interactions. The linear chains have a semi-flexible structure and are made mostly of positively charged monomers, so they are strongly attracted by the hydrophilic beads of the substrate and can also easily adapt to the pattern. Instead, the stiff and voluminous structure of branched polymers limits their mobility and the intricate architecture of each monomer leads to a more complex overall monomer-substrate interaction. Figure 6(a) displays the mean radius of gyration of the adsorbed polymers normalized by the bulk values as a function of chain length N for three different concentrations. We found that the radius of gyration is larger for polymers when they are adsorbed on the substrate than when they are free in bulk, in all cases. This increase in size can be attributed to the change of the chain geometry when adsorbed. We also observed that the degree of polymerization of the chains does not make a significant difference in any case, except for very long branched polymers at very low concentrations. To further understand the change in the geometry of the polymers when adsorbing, we examine Figure 6(b), which shows the diagonal components of the gyration tensor. These quantities provide information about the dimension of the polymer along the Cartesian axes. The component G zz is normal to the substrate and, since we are considering only adsorbed chains, it is expected to have a low value in most cases. Indeed, as seen in Figure 6(b), the G zz components are typically the smallest. With in-creasing concentration, we have already mentioned that the adsorption of polymers was enhanced. Therefore, the G zz component increases due to chains having to compete for the available space on the substrate, thus leading to larger tails and chain loops in the z direction. On the other hand, the gyration tensor components G xx and G yy that are parallel to the substrate show a decrease with increasing concentration. Since for large concentrations chains were crowded together on the substrate, their geometry became more rounded and there were no preferred orientations. However, the case of the longest branched polymers at the lowest concentration is noteworthy, as the G xx component is very large. This occurred because only a small number of polymers were adsorbed, which allowed the chains to fully adsorb onto the substrate. Additionally, it is important to note that since the sample size was smaller in these cases, it is possible that the stretching of the chains was overestimated.

In the following, we analyze the effect of applying a linear shear flow on the adsorbed polymer layer. Figure 7 contains the final values of the diagonal components of the gyration tensor after running the rinsing simulations. The data is normalized by the G xx , G yy and G zz values computed for the adsorbed polymer coating before applying the shear flow, already shown in Figure 6(b). In this way the first thing we can observe is that the component G zz normal to the substrate always decreases with respect to its initial value when the flow is applied, while the parallel and vorticity components (G xx and G yy ) experience very different changes. G xx is the component in the direction of the flow and it always have a higher value after the rinsing than before. On the other hand, for the component in the vorticity direction we always observe G yy /G 0 yy ∼ 1. This general trend can be attributed to the effect of the flow applied in the x-direction. It causes the adsorbed structures, such as chain tails and loops, to tilt towards the surface, thereby altering their overall geometry. Consequently, the diagonal component of the gyration tensor in the flow direction increases while the component in the normal direction decreases. In addition, depending on how stretched where the chains originally, the component in the vorticity direction may slightly increase or decrease. When analyzing the effect of flow strength, we observe significant differences between weak and strong shear flow regimes, particularly for branched polymers. In all cases an increase in flow strength resulted in more pronounced changes on the geometry of the adsorbed polymers. However, within the same regime, the variation in Weissenberg numbers does not appear to have a significant impact on the trend of the values in the plot. Figure 7 also reveals that the way the flow affects the adsorbed coating highly depends on the polymer architecture. Linear polymers were found to be responsive to the flow in all scenarios, even under weak flow conditions. The flow stretched the chains and tilted them towards the substrate, leading to a nearly flat coating with no polymer tails normal to the substrate in the strong flow regime. In this case, the chains were accommodated on the substrate aligned with the flow direction, which explains the high increase of G xx for the longest chains. On the other hand, the branched polymers were practically unaffected by the flow in the weak regime, which can be attributed to the denser and bulkier adsorbed layer they had created compared to the linear polymers. Indeed, the degree of polymerization plays an important role in the behavior of these polymers under strong flow regime. In Figure 7(d) we can observe that as chain length N increases the diagonal components of the gyration tensor approach their original values, that is, the initial polymer coating is less affected by the applied shear flow for longer chains. Nevertheless, below we will discuss the effect that simulation time may have if we had run the simulations for longer times. The analysis of the time evolution of the fraction of adsorbed polymers can provide important insights into the dynamics of polymer coatings under shear flow. Figure 8 shows the ratio between the number of adsorbed chains at a given time and the initial value of polymers adsorbed on the substrate for all the system configurations considered in this study, listed in Table 2: linear and branched copolymers of three different chain lengths and under weak (Wi = {0.5, 1.0}) and strong (Wi = {5, 10}) flow regimes. The evolution of the system was found to be more time demanding under weak flow conditions and for longer polymer chains. In particular, the branched polymer was observed to evolve at a much slower rate compared to the linear polymers, requiring a longer time to reach a steady state due to its more complex architecture. As a consequence, it was impossible to carry out the simulations of the branched polymers under shear flow for the same amount of time with respect to the polymer relaxation time at infinite dilution τ 0 than for the linear polymers. However, this is not necessarily a drawback, since our aim is to compare the behavior of two different types of polymers with cosmetic applications in mind. To ensure a fair comparison, we report the absolute simulation times in Figure 8. Additionally, we include the value of the chain relaxation time at infinite dilution τ 0 for the smallest polymers to provide context for the overall simulation time. From the plots, we can see that some chains desorbed from the substrate in all cases studied, with a stronger flow leading to more detachment. The linear polymers desorbed much faster than the branched polymers, and stronger flows resulted in even faster desorption. Both linear and branched polymers resulted in more stable coatings when longer chains were used. Lastly, the branched copolymer was found to be more resistant to the applied shear flow in all regimes. These findings are noteworthy because while given a certain flow strength the final count of adsorbed polymers may not differ significantly for very long simulation times, the characteristic desorption time at which polymers detach from the substrate plays a crucial role in the performance of polymer coatings for cosmetic applications. Further details about the final fraction of adsorbed polymers can be found in Figure 9, where the ratio between the final and initial number of adsorbed chains is plotted as a function of the degree of polymerization N for the four different flow strengths applied to the systems, characterized by the Weissenberg number. As previously mentioned, in all cases the length of the polymer chains was found to increase the stability of the polymer coatings. The final number of adsorbed chains clearly depends on the strength of the applied shear flow, although within the same regime there are not significant differences for the two values of Wi considered. While both polymer types desorb similarly under a weak shear flow, the combined effect of chain length and architecture was found to play an determinant role in the stability of the polymer coating in the strong flow regime. Except the smallest branched polymers under very strong shear flow, all the systems preserved more than 50% of the adsorbed chains. In addition, the layer formed by the largest branched polymers seemed to be unaltered for all the applied flows.

Conclusions

Developing novel sustainable formulations presents significant challenges for the industry, since replacing harmful polymers by others with natural origin is not straightforward. For cosmetic applications polysaccharides may be viable alternatives, but identifying suitable molecules requires additional research into their physical and chemical attributes. Most importantly, discerning the physical properties that influence polymer adsorption to hair-like surfaces is crucial. To investigate this issue, we generated a computational substrate mimicking a real microscopy of the external F-layer of the hair and we created models of two polymers with different architecture. We implemented coarse-grained molecular dynamics simulations with implicit solvent to observe polymer adsorption on the substrate and we executed Brownian dynamics simulations of the adsorbed polymers under a linear shear flow to evaluate the stability of the polymer coating. We characterized the polymer coating by computing concentration profiles of adsorbed polymers as a function of their distance from the substrate. Our data indicated that higher polymer concentration increased adsorption, and polymer chains showed a clear tendency to adsorb onto the substrate. Notably, the shape of the density profiles did not depend on the concentration but on the polymer type, and the branched copolymer yielded a thicker coating. To assess the uniformity of polymer coverage on the substrate, we conducted an innovative analysis, splitting the simulation box into slabs and computing twodimensional density profiles. This analysis revealed the heterogeneous substrate pattern in the case of the linear copolymer, whereas the branched copolymer exhibited more random coverage. When assessing coating stability, we tracked the fraction of adsorbed polymers over time and found that even under weak shear flow, some chains desorbed. Under strong flow conditions, the rate and magnitude of polymer desorption increased significantly. This is a key result since desorption time can significantly impact cosmetic applications. We also noted that longer polymer chains resulted in more resistant coatings for both linear and branched polymers, although the branched layer was found to be more stable.

The findings of our study emphasize that the architecture of polymers, whether linear or branched, plays a critical role in their adsorption onto heterogeneous substrates. Interestingly, even polymers with comparable properties in bulk such as gyration radius, and similar adsorption energies with a given substrate, can display distinct behavior due to differences in architecture. This is particularly evident when evaluating their resistance to applied shear flow. Hence the transition towards sustainable new formulations in industry is not as simple as replacing a synthetic polymer with a natural one and expecting similar results. This change requires thorough research in both polymer physics and chemistry to identify feasible polymers that can effectively replace harmful ingredients without compromising performance. Our study highlights the importance of considering not only the simple bulk properties of polymers, such as density or texture, but also their structural design, as well as the chemical complexity of the target substrate, when seeking sustainable alternatives for industrial applications.

Future studies could enhance our understanding of polymer coatings in several ways. Introducing surface roughness into the substrate model could offer a more realistic approximation of natural surfaces, providing more accurate predictions of polymer adsorption and desorption. Refinement of simulations could also involve the incorporation of additional ingredients, such as surfactants. Given their prevalence in cosmetic and industrial formulations, surfactants could substantially alter adsorption dynamics and influence the stability of polymer layers. Thus, their inclusion would provide a more detailed understanding of multi-component solutions. Furthermore, exploring the friction behavior of adsorbed polymer layers could provide insights into the sensory effects associated with different polymer coatings, a factor of critical importance in cosmetic applications.

Figure 1 :

 1 Figure 1: Computational models for the (left) linear and (right) branched polymers. Snapshots on top show (left) a section of the linear polymer with 15 beads, each one representing one monomer, and (right) a dimer of the branched polymer with 17 beads per monomer. Bottom pictures show a single polymer composed by N=150 monomers adsorbed onto the heterogeneous substrate.

Figure 2 :

 2 Figure 2: Snapshots of different stages of the simulations for linear polymers of length N = 250 at concentration c/c * = 1.0. (a) Adsorption of the polymer solution on the substrate. (b) Resulting adsorbed polymer layer. (c) Simulation of the applied shear flow on the adsorbed layer, where desorbed polymers have been colored in pink. (d) Final state of the coating with the remaining adsorbed polymers.

Figure 3 :

 3 Figure 3: Radius of gyration of both polymer types as a function of concentration for different chain lengths. Left plot represents the linear polymer, while the right plot represents the branched polymer. The red triangles, green circles, and blue squares in each plot correspond to the data for the chains with degree of polymerization N = 500, N = 250, and N = 150, respectively.

Figure 4 :

 4 Figure 4: Concentration profiles of polymers as a function of the distance from the substrate. (a) Profiles of only the adsorbed polymers for three polymer types with a chain length of N = 500 at three different concentrations. (b) Concentration profile of the three different polymer solutions normalized by the bulk concentration at c/c * = 1.0.

Figure 6 :

 6 Figure 6: (a) Mean radius of gyration of the adsorbed polymers normalized by their values in bulk as a function of chain length. (b) Diagonal components of the gyration tensor as a function of chain length (N ) for three different concentrations. Green symbols correspond to c = 0.1c * , orange symbols to c = 0.5c * and violet symbols to c = 1.0c * . Filled squares, circles and triangles represent Gxx at the three mentioned concentrations, while empty squares, circles and triangles represent Gyy. The values for Gzz are indicated with empty diamonds, pentagons and inverted triangles.

Figure 7 :

 7 Figure 7: Diagonal components of the gyration tensor after applying a shear flow to the adsorbed polymers normalized by the initial value as a function of chain length. Left plots (a,c) show results for linear copolymers and right plots (b,d) for branched ones. Results under weak shear flow regime are shown colored in blue in top pannels (a,b), while strong flow is represented by red symbols in bottom panels (c,d). For each regime, two different Weissenberg numbers have been considered. Within each color, the light shade corresponds to the smallest Weissenberg number, while the intense shade corresponds to the highest Wi. The symbol scheme for each panel is as follows: squares represent Gxx, circles represent Gyy, and triangles represent Gzz.

Figure 8 :

 8 Figure 8: Fraction of adsorbed polymers on the heterogeneous substrate as a function of time. Left plots (a,c) show results for linear copolymers and right plots (b,d) for branched ones. Evolution under weak shear flow regime is shown in top pannels (a,b), while strong flow corresponds to bottom panels (c,d). For each regime, two different flows have been applied, characterized by the Weissenberg number. The color scheme for each panel is as follows: blue squares represent N = 150, green circles represent N = 250, and red triangles represents N = 500. Within each color, the light shade corresponds to the smallest Weissenberg number, while the intense shade corresponds to the highest Wi. As a guide, the relaxation time at infinite dilution τ0 of chains of length N = 150 is indicated by a vertical dashed line.

Figure 9 :

 9 Figure 9: Fraction of adsorbed polymers on the heterogeneous substrate as a function chain length for different flow strengths, characterized by the Weissenberg number.

Table 2 :

 2 Polymer architecture, concentration and length, as well as Weissenberg numbers explored in the simulations performed in this study.

	Simulation Polymer	c/c *	N	Wi
	Adsorption	Linear Branched	0.1 0.5 1.0	150 250 500
	Desorption	Linear Branched	1.0	150 250 500	0.5 1.0 5 10

https://doi.org/10.26434/chemrxiv-2023-rjdwp ORCID: https://orcid.org/0000-0001-7997-8471 Content not peer-reviewed by ChemRxiv. License: CC BY-NC-ND 4.0

Acknowledgement This research was supported by L'Oréal Research and Innovation. This work was performed using the the GRICAD infrastructure, supported by Grenoble research communities, and HPC resources from GENCI-IDRIS (Grant 2021-A0100912435 and 2022-AD010912435R1). I.A.B. acknowledges María Zambrano Grant funded by MCIN/AEI and NextGen-erationEU/PRTR (C21.I4.P1), and the Precompetitive Research Projects Program of the University of Granada Research Plan. N.A.G. thanks PICT 2019-02257.

Figure 5: 2D monomer density profiles obtained by dividing the polymer coating in four slabs of height one fourth of the average thickness of the adsorbed polymer layer (h ads ). For each system configuration, the first slab starts at a distance zero from the substrate and the last slab ends at a distance h ads . The color scale represents the total monomer density, with warmer colors indicating higher density. Note that the color scale limits vary across panels, with the maximum and minimum values adjusted to best show the range of density in each panel. In this figure we have selected one system for each polymer family and chain length at concentration c/c * = 0.5.

Conflicts of interest

G.S.L and F.L are full employees of L'Oréal involved in research activities.

Author Contributions

Supporting Information Available

The Supporting Information file (PDF) includes additional information on the analysis methods used in this study. Specifically, it provides further details on the computation of the chain relaxation time, the description of the gyration tensor, and the slab analysis employed to assess the uniformity of substrate coverage.