Silica Interfaces

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Atomistic descriptions of the cis-1,4-polybutadiene / silica interfaces Kevin Kempfer, Julien Devemy, Alain Dequidt, Marc Couty, and Patrice Malfreyt ACS Appl. Polym. Mater., Just Accepted Manuscript • DOI: 10.1021/acsapm.8b00274 • Publication Date (Web): 15 Apr 2019 Downloaded from http://pubs.acs.org on April 20, 2019

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ACS Applied Polymer Materials

Atomistic Descriptions of the cis-1,4-Polybutadiene / Silica Interfaces K. Kempfer,†,‡ J. Devémy,† A. Dequidt,† M. Couty,‡ and P. Malfreyt∗,† †Université Clermont Auvergne, CNRS, SIGMA Clermont, Institut de Chimie de Clermont-Ferrand, F-63000 Clermont-Ferrand, France ‡Manufacture Française des Pneumatiques Michelin, 23, Place des Carmes, 63040 Clermont-Ferrand, France E-mail: [email protected]

Abstract Since the early nineteen forties, the silica has been increasingly used in tyre compounds as a complement to carbon blacks. The use of silica offers substantial benefits in tyres such as a low rolling resistance, a better grip on wet and icy roads. Nevertheless, coupling agents must be used to enable the mixing with rubber. The understanding of the action of the silica in the reinforcement process and the role of the coupling agents at the molecular level requires to investigate the interfacial region of the silica surface interacting with polymer chains. We report here detailed atomistic simulations of the interfacial region between different silica surfaces and cis-1,4-polybutadiene polymer chains. We describe the interfacial regions in terms of density, radius of gyration components profiles along the normal to the substrate. We investigate how the nature of the silica surface, the surface density of silanols, the surface coverage of grafted polymer chains and grafted OCTEO impact the molecular arrangements of the interfacial zone and the local properties of polymer chains.

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Introduction Polymers reinforced with nanoparticles have attracted growing interest due the fascinating enhanced properties 1–10 when compared to pure polymers. The addition of inorganic fillers e.g silica, 11–13 carbon black, 14 long glass fibers, 15 flexible nanofibers 16 , hybrid silica/carbon black 17 changes significantly the physical properties of the polymers. 18 Indeed, polymer nanocomposites 1,19,20 exhibit significant improved properties such an increase in the dielectric properties, 7,8,21 thermal conductivity, 6 electromagnetic, 22 modulus, strength, surface hardness and heat resistance. 18 These improved mechanical and thermal performances give to these nanocomposites high industrial potentials in the fields of the medecine, 23 automotive 24 and aerospace. 25 Among a wide variety of inorganic/organic nanocomposites, polymer/silica composites have been extensively studied 19,26–28 and find applications in tires, in drug delivery and cosmetics. In the tire industry, carbon black and silica are used as reinforcing fillers. Carbon black plays a key role in increasing the wear resistance of the tires and also protecting them against ozone and UV damage. Silica nanoparticles can reduce the rolling resistance up to 25%, improves the grip on cold surface and increases the longevity of the tires. A key-challenge for the tire industry is then to understand and to interpret the property enhancements of these polymer nanocomposites from the description of the polymer/filler interfacial region. This is an essential step toward the design of new materials with desired properties. It has been found that strong interactions or chemical bonding between the polymer components and the silica nanoparticles can lead to both reinforcement and toughening. 26 It has been shown from experiments that changing the composition of the interfacial region changes significantly the macroscopic properties of the materials. 29–32 Indeed, the interfacial region plays a major role in the performance of the nanocomposites even if this interface exhibits properties in terms of thickness, structure, composition that are polymer and filler dependent. For example, to enhance the polymer/silica interaction, the coating agent OCTEO (octyltriethoxysilane) can be added to improve the compatibility with the 2


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polymer chains and thus leads to a better mixing of the polymer and the fillers. 33 It is also possible to functionalize the silica surface by grafting polymer chains of the same nature as the polymer matrix 34–36 with different grafting densities, architectures and polymer chain lengths. Recent experimental studies aimed to rationalize the behavior and properties of these polymer nanocomposites. By using dielectric relaxation spectroscopy, Gong et al. have shown that the slow-down of the segmental dynamics of polymer melts is impacted by the size and concentration of the silica nanoparticle. 37 The interfacial region which is also characterized by a bound layer has been recently studied 38 by thermogravimetric analysis (TGA). The main conclusion from this work is that the bound layer extends over a region corresponding in size to the radius of gyration of the polymer chains. The structure and composition of this interfacial region as well as the properties of polymer chains in this layer has been the object of intensive debate 39–44 since there are no direct and local methods for measuring the interfacial properties of the polymer material. Since a detailed knowledge of the impact of the nanoparticles on the polymer chains is critical at a molecular level for a control of the properties of the nanocomposites, the molecular simulation technique has become an essential tool to investigate the structural properties of the polymer/filler interfacial region. We hope in the near future that this technique will help in the development of new materials that is still largely empirical due to the difficulty of experimentally accessing the polymer structure at the polymer/filler interface. 45–49 However, these materials involving complex interactions between the nanoparticles and the polymer chains require a combination of different techniques of simulation to accurately capture the different properties of these composites 50 at different length and time scales. Molecular simulations using atomistic force-fields have been successfully applied to polymers and polymer-based nanocomposites to investigate mainly the structure and the mechanical properties. 51–59 However, these methods using an atomistic description of the interactions find their limitations in the calculation of properties that converge on times exceeding 1 µs.

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To simulate these materials on larger time scales, the alternative is to simplify the model and to develop coarse-grained (CG) models. The development of these CG models 60–67 was carried out with the aim of reproducing universal properties of polymer melts. The inability to simulate a monomer of a specific chemical nature prevented any quantitative prediction of properties of interest for the experimentalists. Recently, to address the issue of the generic CG models, top-down 68–71 and bottom-up 50,56,72–74 parameterization schemes have been proposed to derive realistic CG models that have been mainly applied to reproduce the properties of polymer melts. 73,75–78 The extension of these methodologies for the development of realistic CG models for the simulation of the polymer-solid interface is very challenging due to the presence of the surface and few studies have been reported in the literature 58,59,79–82 for the study of this interaction at a mesoscopic level. For both experimentalists and theoreticians who develop CG models with a bottom-up approach, a fine description of the polymer-filler interfacial region is critical at the molecular scale. We propose here to investigate the interaction between cis-,4 polybutadiene (cPB) and silica surfaces by using molecular dynamics (MD) simulations. We focus on various forms of silica that differ by surface characteristic such as cleavage plane, surface density of silanol groups and degree of ionization. In this paper, we also study how the adsorption of polymer chains is modified with the addition of grafted chains of different lengths onto the silica surface. The modifications of the substrate are analyzed through the structural properties of the polymer chains and the density distributions at the interfacial region. We take the route of using the force field developed for the silica surface in 2014 by Emami et al.. 83 This model has been successfully applied to the study of the silica-water interfacial properties. The same force field has also been applied to the interaction between silica surface and various peptides. 84 These are the first simulations that report the study of the adsorption of polymer chains on silica surfaces with this force field.

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Computational details MD simulations of silica interfaces with different surface chemistry in contact with cis-1,4polybutadiene (cPB) polymer chains were considered. At T = 300 K, Peri and Hensley 85 and Armistead et al. 86 have shown experimentally that fully hydroxylized silica surfaces typically hold 4.6 OH nm−2 . These hydroxyl groups are distributed between 1.4 SiOH nm−2 and 1.6 Si(OH)2 nm−2 . They modeled their surface by 30 % and 70 % of two fully hydroxylated surfaces of β-cristobalite cleaved parallel to a (111) and (001) planes, respectively. By following this path, the model silica crystalline structure chosen for this work is the β-cristobalite proposed by Wyckoff 87 in 1925 (space group Fd3m). This structure is available free of charge on the American Mineralogist Crystal Structure Database webpage. The unit cell was replicated in the three space directions and silica slabs were cut out from it in the selected directions. The 3D visualization program VESTA 88 was used for this purpose. The typical size of the silica slab width is about 70 Å by 70 Å by 25 Å. The superficial vacant atoms are hydroxylized to form either isolated silanols, geminal silanols, or siloxane bridges, depending on the surface chemistry 85 we want to examine (Figure 1). From the experimental point of view, IR measurements allow to quantify the amount of these chemical groups on the silica surface. 86,89 The cPB polymer amorphous initial configurations were built using our custom-made polymer generator that ensures an initial realistic gaussian distribution of the end-to-end vector. 90 Unless explicitly specified, 90 free polymer chains of length 240 united-atoms (60 monomers), corresponding to 21 600 united-atoms, are packed together under confinement along z-axis at an initial density of 0.8 g cm−3 . The z-confined polymer melt is placed on top of a given silica surface (beforehand relaxed for 2 ns in the constant-N PT T ensemble where PT is the tangential pressure defined as the half sum of the xx and yy pressure components. Periodic boundary in the three space directions are applied, resulting in an effective polymer melt confined between two silica surfaces along z direction. In addition, we also considered two systems not confined along z, containing 90, 45 cPB amorphous chains of length 240 5



united-atoms (60 monomers), 480 united-atoms (120 monomers) per chain, respectively. These systems were used to compute bulk cis-1,4-polybutadiene properties. The lateral dimension of the surface corresponds to 3 Rg with the longest polymer chain length. In this case, a chain may scarcely interact with its own image. We do not expect any influence on the density profiles and radius of gyrations of the polymer chains.

Figure 1: Chemical structure representations. The force field for the silica was taken from recent work of Emami et al., 83 that is intended to model realistic silica interfaces. In 2014, the same authors demonstrated the robustness of their force field parameters by investigating in details the adsorption of three different peptides on silica surfaces with varying surface chemistry. 84 A united-atom description was chosen to describe the cPB polymer chains. The force field is completely flexible and has been taken from works of Smith and Paul 91 and Tsolou et al.. 92 The octyltriethoxysilane was parametrized using the same united-atom approach. The missing parameters were taken from CFF91 force field. 93 The pairwise cross-interactions were adjusted using geometric mixing rules. The complete set of force field parameters is provided in Tables S1, S2 and S3 in the Supporting Information. All the simulations were conducted with the LAMMPS software. 94 Newton’s equations of motion were integrated using the standard velocity-Verlet integrator with a timestep of 2 fs. The SHAKE algorithm 95 was employed to constrain O−H bonds present at the surface of the silica. The pressure was controlled using Berendsen algorithm 96 with a relaxation 6


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time of 1 ps and a bulk modulus of 100 MPa. The temperature was maintained by using the Langevin thermostat 97,98 with a relaxation time of 10 ps for the polymer and 100 fs for the silica. The global cutoff for Lennard-Jones and Coulombic interactions (for the silica) was set at 14 Å. No long-range Van der Waals tail correction was added as the materials of interest are heterogeneous by construction. Since modeling realistic long range electrostatic interactions is very time consuming for large system-sizes, we took the route of using a short-range Coulomb potential which only slightly impacts the density of the silica. Indeed, the use of long range corrections amounts to increase the density of the silica by about 10%. In addition, the atoms composing the polymer do not carry any charge and interact with their surrounding environment only through Lennard-Jones interactions. Recently, it was demonstrated 99 in the graphene-water interface that the use of short range Coulomb interactions does not lead to significant differences in the structure of water close to the surface and in the interfacial tension compared to the use of Ewald summation technique. The equilibration procedure consists in three steps lasting in total 20 ns. A first thermalization of the polymer at high temperature 500 K in the constant-N V T ensemble is carried out during 10 ns. Then, the system is cooled down with a linear temperature gradient of 100 K per nanosecond during 2 ns to reach the target temperature 300 K. During these two first steps, the silica is kept frozen. Afterwards, the whole system is relaxed for 8 ns in the constant-N PN T ensemble where PN = Pz is the normal pressure component at 300 K and 0.1 MPa. The last 2 ns of the equilibration are analyzed to check good convergence of both the global thermodynamical properties and the structural characteristics of the polymer. Finally, a production run of 50 ns is performed in the constant-N PN T ensemble. The bulk polymer systems without silica were studied the same way, but in the constant-N P T ensemble. The global thermodynamical properties are computed every 1 ps. The trajectory is stored every 50 ps, i.e 1000 configurations are recorded. Moreover, each quantity measured in the following is averaged over five statistically independent trajectories in order to account for slow decorrelation of the polymer chains at 300 K. 100,101 In other words, five sets of

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1000 configurations are recorded per system. This ensures a better description of the phase space of each system and significantly improves the accuracy of measurement. For instance, Figure S1 of the Supporting Information displays a typical neat density profile of free cPB chains placed on top of a silica substrate with an accuracy of 0.1 Å binsize. We checked that mechanical and thermal stability of polymer/silica composites is reached for each system studied. The normal pressure profiles were obtained by adding local zz components of the per-atom pressure tensor into bins along z-axis with 0.2 Å binsize. The tangential pressure profiles were obtained by adding the local average of xx and yy components of the per-atom pressure tensor into bins along z-axis with 0.2 Å binsize. Both profiles were averaged on-the-fly across the production run with a time span of 100 fs, i.e 500 000 configurations were used. This method corresponds to the so-called IK-1 method. 102 Figure S2a in the Supporting Information demonstrates mechanical equilibrium in the bulk polymer region since both normal and tangential pressure profiles converge to the imposed pressure 0.1 MPa far from the interface. As raised by Varnik et al. 102 in 2000, the strong oscillations of the normal pressure profile in the interfacial region are intrinsic to the IK-1 method (due to the local heterogeneity of the system) and should not be considered. Nevertheless, its integral over z can be taken into account. From this, we checked that the computed global normal pressure hPN i = 0.12 ± 0.03 MPa is indeed in accordance with the imposed pressure for all systems studied. The temperature profiles correspond to the sum of local contributions of each atom to the temperature T =

mv 2 3kB

across the trajectory divided by the total atom

count in each z-bin with 1 Å binsize. Figure S2b shows that the temperature is homogeneous and equal to the imposed temperature 300 K throughout the whole system, especially at the interface. By checking the thermal and mechanical aspects, we ensure that the polymer chains in interaction with the silica surface are in thermodynamic equilibrium, a necessary condition to extract relevant structural properties.

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Results and discussion Bulk cis-1,4-polybutadiene properties The structural properties of monodisperse bulk cPB for different chain lengths at T = 300 K and P = 0.1 MPa are summarized in Table 1. The computed density is about 2 % higher than experimental value. 103,104 The mean square radius of gyration hR2g i of a monodisperse polymer melt is defined 105 such as N

* P m (r − r )2 + i i g hR2g i =

i=1 N P

(1) mi

i=1

N P

rg =

mi r i

i=1 N P

(2) mi

i=1

were N is the number of atoms per polymer chain, mi and r i are the mass and position of the ith atom in the considered chain, r g is the position of the center of mass of the chain, hi is the ensemble average over all chains across the trajectory. The mean square end-to-end vector hR2ee i is then defined 105,106 such as hR2ee i = h(r N − r 1 ) · (r N − r 1 )i

(3)

Both the normalized mean square end-to-end vector and the normalized mean square radius of gyration show deviations of about 5 % with respect to experimental values. 103,104 Their ratio confirms the expected gaussian behavior. 105 These results are consistent with the ones reported earlier using the same force field. 91,92,107–109

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Table 1: Structural and thermodynamic properties of monodisperse bulk cPB melts as function of polymer chain length at T = 300 K and P = 0.1 MPa. C240 and C480 correspond to a chain length of 240 and 480 united-atoms, i.e 60 and 120 repeating units per chain, respectively.

Simulation Unit Density g cm−3 hRee i Å hRg i Å 2 2 hRee i Å 2 hR2g i Å 2 hR2ee i/Ma Å mol g−1 2 h6R2g i/Ma Å mol g−1 − hR2ee i/hR2g i a

Experiment 103,104 0.900 − − − − 0.758 − 6 (theory)

C240 0.918 46 ± 1 19.4 ± 0.2 2437 ± 81 394 ± 8 0.75 ± 0.02 0.73 ± 0.01 6.2 ± 0.1

C480 0.923 64 ± 4 27.3 ± 0.1 4733 ± 525 784 ± 48 0.73 ± 0.08 0.72 ± 0.04 6.0 ± 0.4

M denotes the polymer chain molar mass.

Effect of local substrate structure and surface density of silanols 90 cPB free polymer chains of length 240 united-atoms (60 monomers) are placed on top of three different silica slabs as drawn in Figure 2. As shown in Figure 3a, the local density profile of the polymer depends heavily on the structure of the substrate above which it is in contact with. When placed on top of a regular silica β-cristobalite cleaved parallel to a (111) plane with a density of isolated silanols of 4.2 SiOH nm−2 (Figure 2a), denoted as S111 , the density profile of the polymer exhibits strong oscillations with neat peaks at 4.7, 9.3, 14 Å. When placed on top of a regular silica β-cristobalite cleaved parallel to a (001) plane with a density of geminal silanols of 7.3 SiOH nm−2 (Figure 2b), denoted as S001 , this density profile is shifted by about 0.5 Å towards the substrate and the peaks are slightly better defined. This shift can be explained by investigating the density profiles of the silicium and oxygen atoms involved in a silanol group, i.e looking at the boundary atoms of the substrate (Figure 3b). Indeed, for all systems studied, the z-axis origin is defined such as the average position of all silicium atoms involved in a silanol group. The density profile of oxygen atoms engaged in isolated silanols shows one unique peak at about 1.5 Å. In the case of geminal silanols, this peak is split in two peaks with strong overlapping, one peak at 0.8 Å and the other at 1.2 Å,

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with an average position at 1 Å. When placed on top of an annealed silica β-cristobalite cleaved parallel to a (001) plane with a density of mixed isolated and geminal silanols of 4.2 SiOH nm−2 (Figure 2c), denoted as S001d , corresponding to about 45 % dehydration of the surface S001 , the surface becomes less-well defined, leading to a more flat density profile of the polymer shifted towards the surface (see Figure 3a). Thus, the local conformation of the polymer is directly related to the local chemical structure of the substrate. As expected, the more ordered the substrate, the sharpest the polymer density profile. On the other hand, the lower the ordering of the substrate, flatter the polymer density profile. Moreover, the polymer recovers its bulk density at a distance of about 25 Å from the interface when placed on top of regular silica surfaces, whereas this distance is reduced to about 20 Å for the annealed silica surface (less ordered). The end-chains do not show any specificity and follow a similar behavior, as denoted in Figure 3c. To consider the anisotropy of the system, we introduce the normalized parallel hR2g,k i and perpendicular hR2g,⊥ i components of the mean square radius of gyration hR2g i defined 110 such as h

N P

mi (xi − xg )2 + (yi − yg )2 i

i=1

hR2g,k i = h

N P

(4)

mi (xi − xg )2 + (yi − yg )2 + (zi − zg )2 i

i=1

h

N P

mi (zi − zg )2 i

i=1

hR2g,⊥ i = h

N P

(5)

mi (xi − xg )2 + (yi − yg )2 + (zi − zg )2 i

i=1

hR2g,⊥ i = 1 − hR2g,k i

(6)

where xi , yi , zi are the mass and coordinates of the ith atom in the considered chain, xg , yg , zg are the coordinates of the center of mass of the chain. Figure 3d displays these two components as a function of the position of the polymer center of mass (number density profile given in Figure 3c) for different types of substrate and area densities of silanols. The horizontal dashed lines show the values of the parallel (2/3) and perpendicular (1/3) components for

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Figure 2: a) Regular silica β-cristobalite cleaved parallel to a (111) plane with a density of isolated silanols of 4.2 SiOH nm−2 , denoted as S111 . b) Regular silica β-cristobalite cleaved parallel to a (001) plane with a density of geminal silanols of 7.3 SiOH nm−2 , denoted as S001 . c) Annealed silica β-cristobalite cleaved parallel to a (001) plane with a density of mixed isolated and geminal silanols of 4.2 SiOH nm−2 , that corresponds to about 45 % dehydration of the surface S001 . This surface is denoted as S001d .

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Figure 3: Free cPB chains of length 240 united-atoms (60 monomers) placed on top of different types of substrate. The z-axis origin is defined such as the average position of all silicium atoms involved in a silanol group is set at zero as shown in b). The green curve corresponds to the response of the polymer placed on top of the surface S111 . The orange curve corresponds to the response of the polymer placed on top of the surface S001 . The purple curve corresponds to the response of the polymer placed on top of the surface S001d . a) Atomic mass density profiles of free cPB. b) Atomic mass density profiles of silicium (dotted) and oxygen (full) atoms involved in silanol groups. c) End-chain (dotted) and center of mass (full) number density profiles of free cPB. d) Normalized parallel and perpendicular components of the mean square radius of gyration as a function of the position of the polymer center of mass. The horizontal dashed lines show their ideal values 2/3 and 1/3 for bulk polymer.

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ideal gaussian chains, in line with bulk conditions as discussed before (see Table 1). Interestingly, we observe that the type of substrate and surface density of silanols have negligible impact on the parallel and perpendicular components of the mean square radius of gyration. Close to the surface, the parallel component tends to 1, while the perpendicular component decreases to 0, traducing flattening of the polymer chains against the silica surface. The polymer chains recover their bulk behavior at a distance of about 25 Å from the interface.

Effect of free polymer chains length We study the effect of chain length at constant total number of atoms. 90 and 45 cPB free polymer chains of length 240 united-atoms (60 monomers) and 480 united-atoms (120 monomers) per chain, respectively, are placed on top of the surface S111 (Figure 2a). Figure 4a shows a perfect superposition of the local density profiles of the polymer for both chain lengths. The polymer recovers its bulk density at a distance of about 25 Å from the interface. This characteristic depth of perturbation is therefore intrinsic to the substrate / polymer interaction. In particular, it does not depend on the polymer chain length, neither on its global conformational properties. So far, we have focused on the atomic adsorption, which is reflected by the density profiles. It is also possible to consider the chain adsorption using the concept of trains. 111,112 A train is defined as a subchain in direct contact with the surface within a distance of 6 Å from the substrate. 111,112 We characterize in Figure 4b the distributions of train lengths in terms of numbers of united atoms. Figure 4b shows the distributions calculated for 5 independent trajectories and for both polymer chain lengths C240 and C480 . We show that the distribution of train lengths is not sensitive to the chain length with an average of 5.0 atoms per train (number average). In addition, we also compute the normalized parallel hR2g,k i and perpendicular hR2g,⊥ i components of the mean square radius of gyration. Figure 4c reports these two components as a function of the position of the polymer center of mass. The number density profile of 14


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the polymer center of mass is given in Figure 4b for comparison. As noticed before, the chains spread over the substrate close to the interface and recover their bulk behavior far from it. One can notice the normalization of the z-axis by the corresponding bulk mean radius of gyration obtained from simulations of monodisperse bulk cPB for different chain lengths (Table 1). More precisely, the polymer chains recover their isotropic bulk behavior at a distance of about 1 time their corresponding bulk mean radius of gyration hRg ibulk . Our results point out that the global conformational properties of the cPB near a silica substrate are mainly driven by the geometrical confinement along the normal to the substrate.

Effect of surface density of grafted polymer chains and grafted polymer chain length The surface S111 is coated on both sides with monodisperse cPB polymer chains of length 120 united-atoms (30 monomers) or 240 united-atoms (60 monomers) per chain at different grafting densities φgf t . The polymer end-chain CH3 united-atom is replaced by a CH2 Si(CH3 )2 group which is chemically grafted onto the silica by removing an hydrogen from a silanol in order to form a new siloxane bridge SiOSi between the vacant silicium atoms of both the silica and the grafted polymer chain. In practice, this process corresponds to the condensation of a functionalized silane with hydroxylized silica with release of water as given in references 46 and 33. The polymer chains are grafted randomly in a symmetrical way on both faces of the silica slab. The selected grafting densities are 0.04, 0.09, 0.17, 0.33, 0.58, 0.84, 1.24, 1.67, and 2.08 chains nm−2 . These grafting rates correspond in the same order to 1, 2, 4, 8, 14, 20, 30, 40, and 50 % grafting of the surface S111 . The total surface density of isolated silanols and grafted polymer chains remains constant equal to 4.2 nm−2 for all systems. Before adding the free polymer chains on top of it, each grafted surface is relaxed for 500 ps at 300 K in the constant-N V T ensemble. In the low grafting density regime (Figure 5a), the free polymer chains can reach the silica surface crossing through the whole grafted polymer brush. The total free/grafted polymer 15



Figure 4: Free cPB chains placed on top of the surface S111 as a function of polymer chain length. The red and blue curves correspond to a polymer chain length of 240 united-atoms (60 monomers) and 480 united-atoms (120 monomers) per chain, denoted as C240 and C480 , respectively. The thickness of the C240 and C480 layers are 5.4hRg i and 3.8hRg i (see Table 1). The z-axis origin is defined such as the average position of all silicium atoms involved in a silanol group. a) Atomic mass density profiles (vertical offset for better view). b) Average number of trains as a function of the number of atoms in the train. The averages are shown for 5 independent trajectories. c) Normalized parallel and perpendicular components of the mean square radius of gyration as a function of the position of the polymer center of mass. The horizontal dashed lines show their ideal values 2/3 and 1/3 for bulk polymers.

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density profile superimposes with the corresponding one built without chemical grafting (Figure S1). It means that grafting few polymer chains onto the silica surface does not have a big impact on the local structure adopted by the polymer in the interfacial region. To be more specific, we compute the brush height h, inspired from earlier works, 113,114 from the first moment of the brush mass density profile by *R L

z

h=2

0

(z − z1 )ρ1 (z) dz R Lz ρ1 (z) dz 0

+ (7)

where z1 is the z-coordinate of the bottom silica surface defined as the average position of all silicium atoms involved in a silanol group (the same relation can be written for the top brush and the top silica surface reversing the sign) and ρ1 (z) is the mass density profile of the bottom brush. This quantity is characteristic of the grafted brush thickness. We also define the free/grafted interpenetration width w expressed as

w = z95 − z5 R z5

ρ1f (z) dz 0 R Lz ρ1f (z) dz 0

(8)

R z95 0

ρ1f (z) dz

0

ρ1f (z) dz

= 0.05 and R Lz

= 0.95

where ρ1f (z) = min (ρ1 (z), ρf ree (z)) outlines the interpenetration area between the bottom brush and the free polymer chains. ρf ree (z) is the mass density profile of the free chains. With this definition of the interpenetration width w, 90 % of the interpenetration area, where both grafted and free polymer chains are well represented, is considered as drawn in Figures 5a and 5b. Indeed, taking the whole interpenetration area into account is less accurate due to the rounding of the density profile when extrapolating it to zero. Additionally, w is computable at any grafting density whatever the shape of the free and grafted density profiles. Since each simulation box contains two interfaces (one on each face of the substrate), two brushes were analyzed at once. For each system, h and w were thus averaged over 10 interfaces. For short grafted chains (30 monomers per chain), below φgf t = 0.17 nm−2 , both the normalized brush 17



Page 18 of 44

height and the interpenetration width exhibit a plateau as drawn in Figure S3. This first regime corresponds to the mushroom regime, 49,115,116 where the grafted polymer chains are far enough in order not to interact with each other. At φgf t = 0.17 nm−2 , the typical distance between two grafted polymer chain anchor points is √ 1

φgf t

= 24.5 Å, while the square root

of the parallel component of the mean square radius of gyration of the grafted chains equals q hR2g,k i = 12.9 ± 0.4 Å, meaning that the grafted chains start to feel each other. When raising the grafting density, both the brush height and the interpenetration width steadily increase traducing stretching of the grafted chains along the normal to the surface due to higher packing. At φgf t = 0.84 nm−2 , the interpenetration width achieves an optimum before decreasing again. In this third regime, the brush becomes so dense that it prevents the free chains from penetrating it as described in Figure 5b. Indeed, in this extreme grafting density regime, no free polymer chain can reach the substrate and the free/grafted polymer interfaces (both bottom and top) become symmetrical along the plane parallel to the substrate centered on z = z50 , where ρ1 (z = z50 ) = ρf ree (z = z50 ). For longer grafted chains (60 monomers per chain), the brush height h and the free/grafted interpenetration width w follow a similar behavior as described before except that the low grafting density plateaus seems to have disappeared. In fact, at φgf t = 0.09 nm−2 , the grafted chains already interact with each other as the average distance between two grafted anchor points √ 1

φgf t

= 32.8 Å is lower

than twice the square root of the parallel component of the mean square radius of gyration q of the grafted chains hR2g,k i = 17.3 ± 1.6 Å. In the same way, the interpenetration width is also shifted towards lower grafting densities with an optimum at φgf t = 0.58 nm−2 . Moreover, the longer the grafted chains, the thicker the brush, leading to higher interpenetration rates with the free polymer. All the values of height, interpenetration, components of radius of gyration are given in Tables S4 and S5 for two polymer chain lengths at different grafting densities. The corresponding density profiles are represented in Figures S4 and S5 in the Supporting Information. Moreover, de Gennes 117 already proposed a theoretical explanation of the phenomena we

18


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Figure 5: Atomic mass density profiles of free C240 (green) and grafted C120 (yellow) cPB polymer chains. The total free and grafted cPB mass density profile is shown in blue. The z-axis origin is defined such as the average position of all silicium atoms involved in a silanol group is set at zero. a) φgf t = 0.33 nm−2 . b) φgf t = 1.67 nm−2 .

19



observed. He distinguished three regimes : • UnStretched Mixed (USM) at low surface covering, in which the free and grafted chains are mixed without constraint. This regime corresponds to the mushroom regime. • Stretched Medium (SM) when increasing the grafting density, in which the grafted coils start to overlap, leading to their slight stretching. • UnMixed Streched (UMS) at high grafting density, in which the free chains are expelled from the grafted brush. Aubouy et al. have proposed in 1995 scaling laws as a function of the grafting density, but for free chains shorter than the grafted ones. 118 Two years later, Gay generalized the approach whatever the chain length. 119 In the UMS regime, the theory gives h ∝ Mgf t φgf t 1/3

−1/3

and w ∝ Mgf t φgf t . Figure 6 shows the validity of these scaling laws at high φgf t , i.e in the UMS regime, in accordance with the theoretical predictions. Figures 7a and 7b show the normalized parallel hR2g,k i and perpendicular hR2g,⊥ i components of the mean square radius of gyration of the free and grafted polymer chains as a function of the chain center of mass. At low surface coverage φgf t = 0.33 nm−2 , the free chains exhibit similar behavior than with the bare surface (Figure 3d). The profiles of the normalized parallel hR2g,k i and perpendicular hR2g,⊥ i components of the mean square radius of gyration of the grafted chains also follow a similar trend. Near the substrate, the parallel component tends to 1 whereas the perpendicular component reaches 0. Moving away from the surface, the parallel component increases continuously while the perpendicular component decreases in a symmetrical way. Both components do not reach their respective characteristic bulk plateaus. This result demonstrates that the grafted chains adopt both flattened and stretched configurations with however different probabilities as outlined by the number density profiles of the free and grafted polymer center of masses displayed in Figure 7c. At extreme surface density of grafted polymer chains φgf t = 1.67 nm−2 , we observe a drastic alteration of the global conformations adopted by the free and grafted chains. The normalized parallel hR2g,k i and perpendicular hR2g,⊥ i components of the mean square radius 20


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Figure 6: Free cPB chains of length 240 united-atoms (60 monomers) placed on top of the surface S111 grafted with cPB chains as function of surface density of grafted polymer chains φgf t and grafted polymer chain length. a) Grafted brush height h and b) free-grafted interpenetration width w 1/3 −1/3 normalized by the UnMixed Streched (UMS) behavior, i.e by Ngf t φgf t and Ngf t φgf t , respectively. Ngf t denotes the number of monomers per grafted chain (30 and 60). Both h and w were computed using equations (7) and (8). The horizontal line corresponds to the UMS behavior.

21



of gyration of the grafted polymer extend to larger distances from the substrate traducing further stretching of the grafted chains along z-axis. The number density profile of the position of the center of mass in Figure 7c corroborates this claim, showing the displacement of the distribution of the z-position of the center of mass up to 4 nm far from the substrate. Next, we observe in Figure 7c that the center of mass of the free and grafted polymer chains do not overlap anymore at φgf t = 1.67 nm−2 . Indeed, the higher the grafting density, the more impermeable the grafted brush will become. Figure 7b shows that the normalized parallel hR2g,k i component of the mean square radius of gyration of the free chains increases to 0.85 whereas the perpendicular component decreases to 0.15 approaching the free/grafted interface. These conformational changes reflect partial flattening of the free chains against the grafted polymer brush. In other words, the grafted polymer brush act as a low permeable surface for the free polymer. Again, the free chains recover their isotropic bulk behavior at a distance of about 1 time their corresponding bulk mean radius of gyration hRg ibulk from the plane parallel to the substrate centered on the free/grafted polymer region, i.e where ρ1 (z = z50 ) = ρf ree (z = z50 ).

Effect of grafted silanes In this next subsection, we consider the surface S111 coated with both monodisperse C120 polymer chains at different grafting densities φgf t from 0.04 to 0.84 chains nm−2 and octyltriethoxysilane (better known under its commercial name Dynasylan OCTEO) at a constant grafting density φOCT EO = 0.84 nm−2 . Octyltriethoxysilanes are commonly used within this concentration range in the rubber industry as surface modifier of inorganic fillers, typically silica nanoparticles, in order to improve their compatibility with the organic polymer, leading to better dispersion of the nanoparticles inside the polymer matrix. Each octyltriethoxysilane is grafted onto the substrate through condensation of one of its alkoxysilane with hydroxylized silica with release of ethanol 33,46 as drawn in Figure S8a. As before, 90 free C240 cPB polymer chains are placed on top of each grafted surface. The properties of the brushes 22


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Figure 7: Free C240 cPB chains placed on top of the surface S111 grafted with C120 cPB for different surface density of grafted polymer chains φgf t . The z-axis origin is defined such as the average position of all silicium atoms involved in a silanol group is set at zero. a,b) Normalized parallel (dotted) and perpendicular (full) components of the mean square radius of gyration of free C240 (green) and grafted C120 (yellow) cPB as a function of the position of the polymer center of mass at different surface coverages. The horizontal dashed lines show their ideal values 2/3 and 1/3 for bulk polymer. c) Center of mass number density profiles of free C240 (dotted) and grafted C120 (full) cPB at different surface coverages.

23



in terms of height and interpenetration are given in Table S6 as a function of the grafting density. At φgf t = 0.09 nm−2 and φOCT EO = 0.84 nm−2 , we report in Figure 8b the computed local density profiles of the octyltriethoxysilanes and both the free and grafted polymer chains. The total density profile, corresponding this time to the sum of these three profiles, do not superimpose anymore with the reference built from the interaction between the free polymer chains and the bare silica surface (Figure S1). The density profiles of the equivalent system without silane are given for comparison in Figure 8a. Unsurprisingly, the OCTEO density profile confirms that these short silanes are concentrated in the first 1 nm thick layer far from the substrate. Yet, they have a huge impact on the local conformation adopted by the polymer chains. In fact, the maximum intensity of the first adsorption peak of the density profile of the free polymer chains is reduced from 1.17 g cm−3 down to 0.28 g cm−3 in presence of OCTEO at φOCT EO = 0.84 nm−2 with respect to the same system without any grafted silane. As well, the maximum intensity of the first adsorption peak of the density profile of the grafted polymer chains is reduced from 0.36 g cm−3 down to 0.16 g cm−3 . The second adsorption peak at 9.1 Å and the ones following are only slightly impacted by the presence of grafted octyltriethoxysilane, traducing again the tight range of these short silanes. Next, we compute as before the grafted polymer brush height h and the free/grafted polymer interpenetration width w. Interestingly, at φgf t = 0.09 nm−2 and φOCT EO = 0.84 nm−2 , the grafted brush height is increased from 22.7 ± 3.5 Å up to 27.8 ± 1.2 Å, traducing stretching of the grafted polymer chains (Figure 9a). At this realistic surface coverage, these results confirm the role of the octyltriethoxysilane, that is to prevent the polymer chains from reaching the substrate. The interpenetration width follows a similar behavior with a value increasing from 21.0 ± 3.7 Å up to 24.7 ± 2.2 Å (Figure 9b). In fact, although the grafted brush height increases in presence of grafted octyltriethoxysilanes, these silanes do not fully prevent the free polymer chains to reach the silica interface, naturally leading to an increase of the interpenetration width. The same conclusions can be made at φgf t = 0.04 nm−2

24


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and φgf t = 0.17 nm−2 (the corresponding density profiles are provided in Figure S6 in the Supporting Information).

Figure 8: Atomic mass density profiles of free C240 (green), grafted C120 (yellow) cPB and grafted octyltriethoxysilane (pink). The total grafted octyltriethoxysilane, free and grafted cPB mass density profile is shown in blue. The z-axis origin is defined such as the average position of all silicium atoms involved in a silanol group is set at zero. a) φgf t = 0.09 nm−2 . b) φgf t = 0.09 nm−2 , φOCT EO = 0.84 nm−2 .

A similar effect of the octyltriethoxysilanes is found at φgf t = 0.58 nm−2 and φOCT EO = 0.84 nm−2 as plotted in Figure S7 in the Supporting Information. The maximum intensity of the first adsorption peak of the density profile of the grafted polymer chains is reduced from 1.20 g cm−3 down to 0.54 g cm−3 , while the first adsorption peak of the free polymer chains almost totally disappeared. For the same reason than in the low grafted regime, i.e less space in the 1 nm thick layer due to the octyltriethoxysilanes, h increases from 27.8 ± 1.2 Å up to

25



Page 26 of 44

36.2 ± 1.0 Å (Figure 9a). Again, the same conclusion can be made at φgf t = 0.33 nm−2 and φgf t = 0.84 nm−2 (the corresponding data comes with the Supporting Information). However, at these higher grafting polymer rates, w is not altered anymore by the presence of silanes as plotted in Figure 9b. This structural modification is attributed to the change of regime of the grafted polymer. Indeed, at φgf t = 0.17 nm−2 , the square root of the parallel component of the mean square radius of gyration of the grafted chains in presence of octyltriethoxysilanes q q equals hR2g,k i = 12.4 ± 0.3 Å (without OCTEO hR2g,k i = 12.9 ± 0.4 Å), while the typical distance between two grafted polymer chain anchor points remains equal to √ 1

φgf t

= 24.5 Å.

In this mushroom regime, the grafted polymer chains are thereby too far to prevent the free q polymer chains from passing through the grafted brush. At φgf t = 0.33 nm−2 , hR2g,k i = q 11.8 ± 0.4 Å in presence of octyltriethoxysilanes whereas hR2g,k i = 12.4 ± 0.4 Å without OCTEO, but the average distance between two grafted chains √ 1

φgf t

= 17.3 Å is not twice

this radius anymore. The grafted chains start to interact with each other and exhibit a brush behavior. The major interaction of the free polymer chains with their surrounding environment is therefore almost entirely reduced to the interaction with the grafted brush. The free chains do not see anymore the octyltriethoxysilanes as they are drowned in the grafted brush. In short, despite its small size, the octyltriethoxysilane plays a determing role. The conformations of the free and grafted polymer chains are strongly impacted by its presence at the top of the substrate.

Clustering effect In practice, silanes are subject to both hydrolysis and self condensation reactions. 33,46,120 Thus, as the octyltriethoxysilane holds three alkoxysilane functions each able to react (see Figure S8), its addition to a rubber-filler mixture leads to a wide range of OCTEO-based clusters grafted onto the surface of the filler. To model this phenomenon, we prepared three model silica surfaces coated with octyltriethoxysilane at constant total number of grafted 26


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Figure 9: Free C240 cPB chains placed on top of the surface S111 grafted with octyltriethoxysilane

at φOCT EO = 0.84 nm−2 and C120 cPB as function of surface density of grafted polymer chains φgf t (green). The reference without OCTEO is shown in blue (Figure S3). a) Grafted brush height h. b) Free-grafted interpenetration width w.

27



octyltriethoxysilanes but distributed differently. On the one hand, single octyltriethoxysilanes are grafted uniformly and randomly onto the silica at φOCT EO = 0.84 nm−2 (Figure S8a) corresponding to a single condensation of each silane with the hydroxylized silica with release of water. On the other hand, the same amount of OCTEO are grouped either by pair or by triplet as drawn in Figures S8b and S8c to mimic partial self condensation. These groups are then grafted by one anchor onto the substrate to reproduce a condensation reaction. No cPB chains were grafted. Next, these newly created surfaces are brought in contact with 90 free C240 cPB polymer chains and relaxed in constant-N PN T ensemble following the same protocol as described before. As shown in Figure S8, the local density profiles of the free polymer only depend a little on the clustering of the silanes. They exhibit similar oscillations with clear peaks at 4.7, 9.3, and 14 Å. Nevertheless, the intensity of the first adsorption peak of the free polymer chains differs depending on the system studied. Indeed, in the case of a uniformly homogeneous coating of single silanes, the maximum intensity of the first peak reaches 0.42 g cm−3 (Figure S8a) whereas this value increases up to 0.67 g cm−3 and 0.73 g cm−3 if putting the free polymer in contact with an interface holding clusters of octyltriethoxysilanes (Figures S8b and S8c). We attribute this effect to a less homogeneous distribution of the grafted octyltriethoxysilanes due to clustering. Indeed, even though the coating remains random and as uniform as possible, the higher the degree of clustering, the more uneven the surface becomes. This last assumption is well described in Figure S8c looking at the top view of the coated substrate, where one can clearly distinguish two areas of interest : a locally highly coated area in the bottom left corner and a locally raw substrate in the top right corner. Consequently, we expect the free polymer chains to reach easily the substrate in this last less crowded region as shown in a previous section (Figure 2) and to have more troubles reaching the substrate in the highly coated area. The density profile we provide is calculated over the whole surface area and therefore corresponds to an average density profile. We observed similar results (not shown here) with single silanes when the surface coverage is not evenly distributed.

28


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Conclusions As underlined in the introduction of this paper, the understanding of the action of the silica and the role of the coupling agents at the molecular level is fundamental to explain the reinforcement process in tyre technology or other rubber applications. Indeed, understanding the polymer/filler interface in the nanostructured materials, the resulting structure of the fillers and the reinforcement mechanisms responsible of properties enhancement are key challenges for the tire industry. An atomistic description of the polymer/filler interface is therefore an essential first step in interpreting experiments and macroscopic properties. Various interfacial regions between silica surfaces and cis-1,4-polybutadiene polymer chains have been carefully investigated at the atomistic scale by using classical molecular simulations. These atomistic simulations were not possible a few years ago (less than a decade ago) because of the prohibitive computing time required to model polymers of a reasonable chain length (long enough to exhibit self-similarity and to adopt realistic conformations). The simulations reported here will be of great help to experimentalists who need a detailed description of the interface to interpret their experiments and also to those who want to develop realistic coarse grain models. Here we have taken advantage of using a recent force field for the silica surfaces to investigate the impact of different parameters on the structure of polymer chains close to the surface. The first conclusion from this work is that the structure of polymer chains is slightly impacted by the nature of the substrate and the surface density of silanols. In addition, we observe that the polymer chains recover their bulk-properties at a distance of about 2 nm from the silica substrate. The second conclusion is that the nature of the interfacial region in terms of height, overlap between free and grafted chains, local structure, is strongly impacted by the grafting density. We have also established dependencies of the brush height and interpenetration width on the surface coverage. The third important conclusion of this work is the change of the density profiles of polymer chains as OCTEO is grafted onto the silica leading to drastic conformational changes of the free and grafted cis-1,4-polybutadiene 29



polymer chains. We complete this study by investigating the impact of the clustering of OCTEO. The clusters behave as dense brushes that prevent the free polymer chains from penetrating them but allow the polymer to reach the substrate in their surrounding areas. This structural characteristic is only accessible to molecular simulations.

Acknowledgments Computations have been performed using the facilities of the supercomputer Mésocentre Clermont Auvergne. This work was partially funded by the Investissements d’Avenir program "Développement de l’Economie Numérique” through the SMICE project. We kindly thank Florent Goujon who helped us with the development of our custom-made polymer generator and with the use of the POV-Ray tool that we employed to build the different high-quality pictures produced for this paper.

Supporting Information Available All the force field parameters used to model silica, cis-1,4-polybutadiene and silanes come with this paper. For each system studied, tables containing the key structural properties as well as the density profiles are also furnished.

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