Tribological Behavior of Grafted Nanoparticle on Polymer-Brushed

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Tribological Behavior of Grafted Nanoparticle on PolymerBrushed Walls: A Dissipative Particle Dynamics Study Vinh Phu Nguyen, Phuoc Quang Phi, and Seung Tae Choi ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b19001 • Publication Date (Web): 01 Mar 2019 Downloaded from http://pubs.acs.org on March 2, 2019

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ACS Applied Materials & Interfaces

Tribological Behavior of Grafted Nanoparticle on Polymer-Brushed Walls: A Dissipative Particle Dynamics Study

Vinh Phu Nguyen†, Phuoc Quang Phi†, and Seung Tae Choi*,† †School

of Mechanical Engineering, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul 06974, Republic of Korea

Keywords: Polymer brushes, Dissipative Particle Dynamics, coarse-graining, hairy particle, lubrication, mechanical stability

Abstract Two contacting surfaces grafted with polymer brushes have potential applications due to their extraordinary lubricating behavior. However, the polymer brushes may have poor mechanical stability under high normal and shear stresses, which is a challenge for practical usage of polymer brushes systems. In this study, we propose the use of grafted nanoparticles as nano-bearings on polymer brush-coated surfaces to alleviate the harsh working conditions of polymer brushes and to improve their mechanical stability. We have performed dissipative particle dynamics (DPD) simulations to investigate the tribological interaction between grafted nanoparticle and parallel walls with non-charged polymer brushes in the presence of explicit solvent. The influences of several parameters (solvent quality, brush miscibility, etc.) on the tribological behavior of the system are investigated. The grafted nanoparticle obviously acts as nano-bearing that partially replace the

*Corresponding

author. Tel: +82-2-820-5275. Email: [email protected] (Seung Tae CHOI) ACS Paragon Plus Environment

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sliding contact between two brushed walls with rolling contact between the grafted nanoparticle and two brushed walls, and reduce the number of DPD particles withstanding high force. Although the introduction of grafted nanoparticle into polymer-brushed walls increases the friction coefficient by 20-30%, it does not greatly decrease lubrication of the brushed walls, while still help stabilizing the system of polymer brushes to be used with liquids with low viscosity, such as water. The DPD simulation results and analysis performed in this study would be beneficial in designing systems with polymer-brushed surfaces and grafted nanoparticle.

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1.

Introduction

Polymers grafted onto surfaces have important technological and industrial applications including wetting, adhesion, colloidal stabilization, oil recovery, modification of surface, tribology, lubrication, protective coatings, biocompatibility, bio-active and anti-fouling surfaces.1-6 The reason for that wide range of applications is the ability of grafted polymers to control surface properties and surfaces' responses to various stimuli. If the density of grafted polymers is sufficiently high, then the polymer chains have a tendency to stretch in the direction normal to the surface and form a polymer brush to avoid the unfavorable overlapping of the polymers due to elastic energy of the chain, interactions between monomers and interactions between polymers and solvent.7-8 An interesting phenomenon related to polymer brush is that two sliding surfaces can reduce the friction between them up to two or three orders of magnitude if both surfaces are grafted with polymer brush.9-11 The polymer brush structures can store a large amount of solvent and exert a considerable repulsive force on the opposite surface or on opposite brushes even at high compressions, enabling the forming of a fluidic layer between two polymer brushes.12 Due to this fluidic layer and the absence of direct contact between solid surfaces, polymer brushes can greatly reduce the frictional force compared to bare or oillubricated surfaces. The extraordinary lubricating behavior of polymer brushed surfaces, particularly two brushed surfaces compressed against each other, gives rise to a very promising application of polymer-brushbased lubrication, as opposed to oil-based lubrication. The combination of polymer brushes systems with water as a solvent can provide two major advantages. Firstly, the friction is greatly reduced as mentioned above. Secondly, the solvated polymer brushes can support the load instead of hydrodynamic forces, therefore environmentally friendly solvent such as water can be used rather than usual oil-based lubricant despite of water's low viscosity. The polymer-brush-based and water-based lubrication will have positive impact on environmental problems, for example ecotoxicity and renewable lubricants. One of the major problems concerning the lubrication performance of polymer brushes is asperity contact at rough surfaces under high normal loading and shear. These harsh contacts can detach grafted chains, which is detrimental to the mechanical stability of polymer brushes. To overcome the problem of mechanical stability and to realize the lubrication application of the polymer brushes, it is desirable to use solid additives such as TiO2,13-14 ZnS,15-16 Cu,17-18 and CuO14 nanoparticles, as successfully applied in industrial lubricant oils. In

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recent years, hairy nanoparticles, or nanoparticles grafted with polymers, have been investigated as new additives for industrial lubricant oils and have exhibited tribological and protective effects that are superior to traditional solid additives.19-21 Therefore, it is sensible to propose that hairy nanoparticles be used as lubricating additives to alleviate harmful working conditions since they can act as nano-ball-bearings and protective layers. Note that similar structure can be found in nature and biological systems, e.g. brush-like surfaces of synovial joints with embedded macromolecules.22-23 There have been several numerical studies on polymer brushes with other entities like macromolecular or nanoparticle inclusions, similar to biological systems or potential application systems of catalysts and sensors based on nanoparticles, nanochannel coated by polymer brushes.24-30 Their motivation focused on investigating the interaction between polymer brushes and inclusions, and the arrangement of inclusions depends on that interaction. Thus, grafted polymers can be used to control nanoparticle distributions. Milchev et al. studied the shearing of polymer brushes to wash out the nanosized inclusions, and also found that those embedded colloids can enhance robustness of polymer brushes under high shear.25 In this study, we propose using well-distributed “hairy”, or grafted nanoparticles instead, and focuses on stabilizing the polymer brushed walls in nanoscale. The polymer brushes with grafted nanoparticles may advance many applications of polymer brushes in colloidal stabilization, biological systems such as synovial joints, tribology, polymer-brushes-based lubrication which replaces oil-based lubrication. Prior to real applications, the effects of hairy nanoparticle on tribological performance and system stability must be studied, preferably by computational simulations as an initial investigation and for providing additional details on the structural and rheological properties of polymer brushes. In this paper, we use the dissipative particle dynamics (DPD) method to study shear deformation of polymer brushes under compression in the presence of grafted nanoparticle. DPD is a coarse-grain method first introduced by Hoogerbrugge and Koelmann,31 and later extended to polymers by Schlijper.32-33 Mesoscale simulation like DPD is a powerful technique to model polymer systems because of soft conservative interactions and thus achievable long time-step. The dissipative and random forces are short-ranged and pairwise additive, and the method also obeys Newton’s third law, exhibits Navier-Stokes behavior, and includes the hydrodynamic interactions. Recently, polymer brushes have been also investigated numerically with DPD simulations. The foundation was established by Malfreyt and Tildesley in 2000,34 who demonstrated the


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correctness of simulation methods and investigated the effects of several parameters on the structure of brushes. Later, shear simulations with periodic boundary conditions were used to derive kinetic friction coefficients, viscosities, brush structure during shear, and the effects of several parameters on these properties.35 DPD simulation in the grand canonical ensemble was applied to study brushes under compression.36 Entanglement effects in compressed brushes was also included by considering the anti-bondcrossing potential, which improves simulation accuracy at high compression.37 From neutral polymer-brushes, DPD simulations were also extended to polyelectrolyte brushes, which bear closer resemblance to real biological lubrication systems.38 The ability to isolate the effects of electrostatic properties is a distinctive advantage of simulations over experiments. These results show that a strong electrostatic interaction does not enhance the lubrication effects of brushes, but rather stabilizes the brushes during highly non-stationary processes. The simulation model includes two solid walls with polymer brushes in nanoscale, a nanoparticle grafted with polymer chains, and a solvent. Compression in the simulation can be obtained by controlling either one of three following system parameters: the total number of particles, the density, or the chemical potential of the solvent to be constant. The constant chemical potential condition represents the grand canonical ensemble and is the most similar one with condition of the surface force apparatus (SFA) where the compressions are measured experimentally.39 Including a constant chemical potential and bond-repulsion into DPD simulations can significantly improve the description of polymer brushes’ structural and frictional behavior in the high compression regime. However, at intermediate and low compression, when the volume is not changed, DPD simulations with and without these effects give quite similar results.36-37 In this study, due to separation created by nanoparticle, the studied system is under low to intermediate compression. Moreover, the separation between the surfaces with the grafted polymer brushes does not change, i.e. the volume does not change, during each simulation, therefore the DPD model for neutral, non-entangled polymer brushes with constant density of the system is applicable for studying the behaviors of our proposed system and effects of several important design parameters. This paper is organized as follows. In section 2, the formulation of DPD method is described. In section 3, we detail the DPD simulation model of the polymer brushes with nanoparticle. Section 4 contains our results:



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the behavior of systems with and without a grafted nanoparticle are compared at different compression ratios and shear rates. The effects of solvent quality, polymer miscibility, grafted chain length, and brush grafting density on tribological performance are also investigated. Section 5 concludes our study.

2.

Dissipative Particle Dynamics Formulation

DPD was first introduced by Hoogerbrugge and Koelman,31 and its theoretical foundation was reinforced by Espanõl and Warren.40 DPD is a coarse-graining technique that sacrifices some atomistic details or accuracy for computational efficiency and has been successfully applied to model polymer brushes34 and their tribological behavior.26, 32, 41-43 The input parameters in a DPD simulation are in dimensionless or reduced units. The normalized distance is r *  r rc , where rc is the cut-off radius. Masses are m*  m m0 , where m0 is the particle mass, in this study all particles have equal mass. The reduced temperature is T *  k BT  , where k B is * the Boltzmann constant and  is the unit energy. The reduced time is t  t

m /  rc2  t  , where   10 ps

is the characteristic time. These reduced units are also similar to those in the previous studies, e.g. unit cut-off radius and unit particle mass used by Groot and Warren,44 Malfreyt and Tildesley,34 and Irfachsyad et al.35 For simplicity, the asterisk (*) notation is usually omitted. In DPD, particles represent groups of atoms interacting with each other through three types of forces: a conservative force F C , a dissipative force F D , and a stochastic (random) force F R , as follows:

fi 

F    F

C ij

ij

i j

i j



 FijD  FijR .

(1)

The conservative force F C is derived from a soft, repulsive potential and takes the following form:





  ai  j 1  rij rîj FijC   0  

if rij  1.0,

(2)

if rij  1.0,


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where ai  j is a repulsive parameter and rîj is the unit vector in the direction of the relative positions vector

rij  ri  r j between two DPD particles. The dissipative force F D and random force F R , which represent viscous friction and thermal noise among DPD particles, respectively, are defined as

 



FijD   D rij rîj  vij rîj ,

(5)

 

(6)

FijR   R rij ij rîj ,

where  D and  R are weight functions vanishing for r  1 ,  is the friction coefficient or dissipation strength between two particles,  is the noise amplitude, ij is a random number of unit variance and zero mean value, and vij  vi  v j is the relative velocity between two DPD particles. Español and Warren40 have shown that the form of  D and  R must satisfy the following relationships for the simulated system to be a canonical ensemble: 2

 D  r    R  r   .

(7)

One of two weight functions  D and  R can be chosen arbitrarily. For simplicity, the following form is used:

1  r 2 2 R     r     r      0 D

if r  1, if r  1.

(8)

The dissipation strength  and noise amplitude  must also satisfy:40



2 . 2k BT

(9)

When the noise amplitude  decreases, the reaction time of the system to temperature change or the relaxation time also decreases. However, if the noise amplitude  increases over some limit, the system temperature can be unstable.44 In this study,   4.5 is the input parameter for all DPD simulations, following recommendation of  and  by Groot and Warren.44



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In Eq. (2), ai  j is a repulsive parameter that determines the interaction strength between two particles of type i and type j. This is one of the most important parameters in any DPD simulation and accounts for the miscibility of DPD particles. Miscibility between particle i and particle j is defined by:

ai  j  ai  j 

1  aii  a j  j  , 2

(4)

where ai  j , ai i , and a j  j are repulsive parameters for non-bonded interactions between i-j particles, i-i particles, and j-j particles, respectively. Negative values of ai  j indicates high miscibility between two types of particles, while positive values indicate immiscibility. Solvent quality a pol  sol influences the miscibility of polymer particles and solvent particles (i = pol, j = sol) in a DPD simulation. In a good solvent, polymer particles are attracted by solvent particles, and a dispersion is more likely to form. Thus, the brushes tend to stretch. On the contrary, in a bad solvent, polymer particles are repelled by the solvent, and the polymer brushes tend to shrink. A good solvent corresponds to negative a pol  sol values, and vice versa for a bad solvent. Similarly, polymer miscibility

a pol1  pol2 (i = pol1, j = pol2) describes how well one polymer species can be dispersed in another. In this case, pol1 corresponds to wall brush polymer particles and pol2 corresponds to nanoparticle brush polymer particles. Because in DPD formulation, the force depends on velocity, the modified velocity Verlet algorithm is used instead of the simple Euler-type algorithm to update the velocities and positions of particles:45

ri  t  t   ri  t   tvi  t  

1  t 2 fi  t  2

(10)

v%i  t  t   vi  t   tfi  t 

(11)

fi  t  t   fi  r  t  t  , v% t  t  

(12)

1 vi  t  t   vi  t   t  fi  t   fi  t  t   2

(13)


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where v%i  t  t  is the predicted velocity at time t  t and  is an empirical parameter. It was found the appropriate value of  ranges from 1/2 to 0.65, and the scheme can use time steps as large as t  0.06 , for which the system temperature is still stable.44 In this study,   0.65 was used for all simulations. From the calculated positions, velocities, and forces for all DPD particles, the stress (pressure) tensor is obtained from the virial theorem:45

P

1 V

  



1

u u  2 r F  , i i

i

ij

i j

ij



(14)

where ui  vi  v  r  is the velocity relative to the stream, v  r  is the stream velocity.

3.

DPD Simulation Model of a Grafted Nanoparticle and Brushed Walls

The simulation model includes two solid walls with polymer brushes, a nanoparticle grafted with polymer chains, and solvent particles in a tetragonal cell. The simulation cell dimensions in reduced units are Lx = Ly = 14.12, and Lz is also fixed to be one between 14.14 and 28.24 in each simulation so the volume is not changed during the shear simulation. Boundary conditions are periodic in the x and y directions but non-periodic in the z direction. To keep wall particles from escaping the box, the outermost layers of the walls are fixed along the z direction. The nanoparticle diameter is 6 in reduced units. The surface coverage and chain length of the wall brushes are 30% and 18 (number of bonds), respectively, and these values range from 15 to 45% and from 2 to 6 for nanoparticle brushes. Solvent particles are filled randomly in the empty spaces between polymer particles to ensure the box has overall density of  rc3  4.0 . The schematic of the simulation model is shown in Fig. 1 (a). The walls and nanoparticle are built from DPD wall particles arranged in a face-centered cubic lattice with lattice constant a = 1 as shown in Fig. 1 (b) and (c), respectively. In addition to the conservative force, dissipative force and random force, the pair force Fij defined in Eq. (1) should also include the bonding interaction force wherever a bond is formed between two particles. In this study, the wall particles are bonded with harmonic springs:32-33







FijS  kS ri  rj  req ,

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(15)

where kS and req are the spring constant and equilibrium spring length between particles, respectively. The spring constant of the walls is set to be kS = 1500 sufficiently large to keep the wall particles in a solid structure, and req = 0.707. The polymer chains are grafted to randomly-selected grafting points on the wall surfaces. The grafting potential is harmonic with kS = 150 and req = 0.85. Bonding potential in a polymer chain is finite extensible nonlinear elastic potential,43 defined as

  1  1 U FENE  r    KR02 ln 1    2   R0  

2

 .  

(16)

To investigate the effects of solvent quality, the same polymer particles are used for wall brushes and nanoparticle brushes, where a pol  sol changes from 20 to 40, while other repulsive parameters ( a pol  pol , asol  sol ,

awall  sol , awall  pol ) are all set to 30. To investigate the effects of polymer miscibility, polymer particles pol1, and pol2 were assigned to wall brushes and nanoparticle brushes, respectively, and a pol1  pol2 changes from 20 to 40 while a pol1  pol1 , a pol2  pol2 , and the remaining repulsive parameters are set to 30. A shear simulation was performed by applying velocities of vx to the upper wall and vx to the lower wall. The shear rate is defined as:

&

2v x , D

(17)

where D is the dimension of the pore or separation distance between the two inner wall surfaces as shown in Fig. 1(a). To characterize the tribological performance and interaction of polymer brushes, kinetic friction coefficient and number of interbrush interactions will be evaluated. The kinetic friction coefficient defined by the timeaverage of the ratio between shear and normal stress (Pxz and Pzz components of the stress tensor in Eq. (14), respectively)35, 38, 42 will help to investigate the friction behavior of the systems under various controlled design parameters. Note that the kinetic friction coefficient can also be determined from the linear slope of shear stress versus normal stress relationship, and it can lead to different results in term of parameter dependency.46 10 ACS Paragon Plus Environment

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However, the overall density of simulation box in this study is fixed through all varied design parameters, thus the two approaches for obtaining kinetic friction coefficient will provide similar friction behaviors. The mutual interactions between polymer brushes then can provide insights for the observed friction behaviors. Although it is a challenge to be quantified experimentally, in simulation there are several quantities that may characterize mutual interactions, such as interpenetration length47 and number of interbrush interactions.26, 38 The number of interbrush interactions defined by number of interbrush monomer contacts is more direct and convenient to calculate, and will be used in this study.

4.

Results and Discussion

4.1 The effect of grafted nanoparticle inclusion on stability and tribological performance of polymer brushes One of the disadvantages for polymer brushes in lubrication application is their poor mechanical stability, i.e. polymer brushes can be detached under high normal and shear force. Polymer brushes withstanding high shear motion in general will have sliding contact and align in shear direction, thus the polymer chains from opposite brushes increase their contacts and interaction forces that can exert longitudinal forces on polymer chains and detether polymer brushes. To improve the stability of polymer brushes, grafted nanoparticles as solid additives are proposed in this study, and the DPD simulation result with nanoparticle is shown in Fig. 2, in which one part of the grafted nanoparticle is highlighted with different color to visualize nanoparticle’s motion. Fig. 2 shows that the grafted nanoparticle can prevent direct contact between opposite brushes, and more importantly, they can replace the sliding contact of polymer brushes with rolling contact. Under rolling contact, the two polymer brushes will interact with grafted nanoparticle instead with each other, and due to the flexible rolling motion of the nanoparticle the interaction forces can be reduced dramatically. Note that the interaction forces will depend on the nanoparticle’s chain length and grafting density, which can be tuned to have optimum results. For more quantitative evaluation of the effect of grafted nanoparticle on the mechanical stability of the system, DPD forces acting on DPD particles are analyzed and compared between the systems without nanoparticle and with nanoparticle inclusion. The DPD forces per particle in the simulation cell are shown in Fig. 3 (a) and as a function of z in Fig. 3 (b). In term of mechanical stability, the number of DPD particles having high DPD force is of interest. Therefore, the number of DPD particles having DPD force



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larger than a critical value, Nhf, is counted and plotted as a function of critical DPD force in Fig. 3 (c). Including hairy nanoparticle shows a reduction in the number of DPD particle withstanding high DPD force, which confirms the improvement of mechanical stability of the system with grafted nanoparticle inclusion. Note that Nhf at higher critical DPD force is more important since those DPD particles sustain severer conditions. Fig. 3 (c) also shows that in general the relative reduction of Nhf is better at higher critical DPD force, which is desirable. The asperity contact at rough surfaces may cause more detrimental effect on the polymer brushes, i.e. stress or force concentration due to roughness that can cause polymer chain rupture, and it is needed to be considered in future studies. Fig. 4 (a) and (b) show the snapshots of DPD simulation model of polymer-brushed walls and concentration profiles of polymer brushes in cases: (a) without and (b) with grafted nanoparticle inclusion. It is worth noting that the oscillating concentration profile near the grafting wall originates from the repulsive interaction between polymer particles and wall particles. Another property of the concentration profile is that the profiles of polymer brushes generally show a parabolic shape due to the repulsive force between the opposite polymer brushes, which is in agreement with the result on polymer brushes at moderate grafting density in a good solvent obtained by the self-consistent field (SCF) theory48 and simulations.34-35 A consequence of the parabolic profile is the rapid decay in polymer brush density in the middle of the simulation box. This distribution of concentration profile is a feature of polymer brushes system that enables the forming of a fluidic layer between two polymer brushes and hence reduces the frictional force. Fig. 4 (c) shows the tribological performance in terms of the friction coefficient for polymer brushes with and without grafted nanoparticle inclusion at various values of the distance between the two grafted walls, D, from which the corresponding compression ratio can be calculated. In both cases, the friction coefficient increases as the wall distance decreases and the shear rate increases. The results for brushes without nanoparticle are consistent with those in literature.41-42 The friction coefficient of the system with nanoparticle is always higher that that without nanoparticle. Although the ball-bearing effect of nanoparticle can significantly improve the lubrication behavior of metal surfaces,19 friction increases when combined with brushes. To prevent direct detrimental contact between wall surfaces and nanoparticle, thus enhancing the mechanical stability of the brushes, lubrication performance must be sacrificed somewhat. Fig. 4 (c) shows that 12 ACS Paragon Plus Environment

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the friction coefficient increases by approximately 20-30% due to the presence of nanoparticle in the system. As the polymer brush system provides desirable lubrication, the performance of the polymer brush system with nanoparticle is still found to be satisfactory.

4.2 Shear rate and kinetic friction Under shear deformation, the grafted polymer chains on wall brushes are tilted away from the normal direction in their original equilibrium configuration and are aligned in the shear direction, as shown in Fig. 5. As the shear rate increases, the tilting degree of the polymer chains with respect to the walls also increases. Usually the system of polymer brushes without nanoparticle under stationary shear motion will have two regions dependent on shear rate.49 In the region of small shear rate, the shear force as well as kinetic friction coefficient increase linearly with the shear rate, as is the case of Newtonian fluids. In the region of large shear rate, the shear thinning effect is observed, where the shear force and kinetic friction coefficient increase more and more slowly as the shear rate increases, in other words, the kinetic friction coefficient increases sublinearly with the shear rate. Note that even at nanoscale, it has been shown that relationship between friction and shear speed follows the Stribeck curve, i.e. including boundary lubrication, mixed lubrication and hydrodynamic lubrication regimes,50 but this study is limited to stationary shear motion of polymer brushes in hydrodynamic lubrication regime with a thin liquid layer formed between them. In our system of polymer brushes with nanoparticle, the kinetic friction coefficient increases linearly with low shear rates (smaller than 0.01) and sublinearly with high shear rates (larger than 0.04), as show in Fig. 4 (c) of double-logarithmic relations for different compression ratios. The shear thinning effect at high shear rates may originate from the competition between the shear rate and the relaxation rate of the polymer brushes. Due to the complicated interactions between nanoparticle and polymer brushes, the polymer brushes do not have enough time to relax and go through structural changes, which can reduce interaction between polymer brushes and nanoparticle and cause the shear thinning effect.



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4.3 Solvent quality and brushes miscibility The kinetic friction coefficient decreases from 0.006 to 0.002 as a pol  sol increases from -4 to 4, as shown in Fig. 6. This tendency is similar to the results presented by Irfachsyad et al.35 and can also be explained by the structural changes of the brushes. Negative a pol  sol values correspond to good solvent conditions that favor the stretching of polymer brushes, while positive a pol  sol values will cause the brushes to shrink. For

a pol  sol  4 , both the wall brushes and nanoparticle brushes expand and contract vigorously. This gives rise to a larger number of inter-brush interactions, which explains the relatively high friction coefficient (0.006). On the contrary, the polymer and solvent particles will prefer to be surrounded by the same type of particles when

a pol  sol  4 , thus solvent particles are repelled from the brushes. This will cause polymer chains to stay very close to the grafting surfaces and create a solvent-rich region between them. Therefore, the level of inter-brush contact reduces significantly, which explains the relatively lower kinetic friction coefficient (0.002). Although good solvent causes the friction coefficient to increase, it is still desirable for mechanical stability of the system, since good solvent also causes polymer brushes to be stretched and store solvent, which will reduce harmful effect and possibility of damage for polymer brushes. Similar to solvent quality, the miscibility of wall brushes and nanoparticle brushes also influences the kinetic friction coefficient by changing the brush structure and number of inter-brush interactions. It means that there is always a trade-off between tribological behavior and stability of the polymer brushes with grafted nanoparticle, so in design of real application one should decide the acceptable degree of lubricating behavior reduction in order to gain the mechanical stability improvement. Fig. 7 show that kinetic friction decreases as the miscibility of polymer increases. However, as a pol1 pol 2 increases beyond 0, the friction coefficient curve becomes stationary. The number of inter-brush interactions is strongly correlated with changes in frictional behavior (Fig. 7). The effects of miscibility ( a pol1 pol 2  4 ) are considerably weaker than that of a good solvent. This difference is due to the fact that solvent quality affects all polymer particles in the box, while the miscibility of brushes only affects those in the contact region. Therefore, the brushes stretch and shrink more vigorously when solvent quality changes than when brush miscibility changes. As the brushes become less


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miscible, their mutual repulsion increases. However, that repulsion is not enough to further decrease the height of the brushes due to the stronger effects of solvent condition. By comparing the case of a good solvent and high brush miscibility, it was found that although the number of inter-brush interactions is much lower in the presence of a good solvent, the friction coefficient is much higher.

4.4 Chain length and surface coverage of nanoparticle brushes After the determination of types of polymer brushes and solvent for the system, i.e. the solvent quality and the miscibility of wall brushes and nanoparticle brushes are fixed, we also need to consider design parameters of grafted nanoparticle such as their chain length and surface coverage. These parameters can further increase or decrease the friction coefficient and may affect the distribution of grafted nanoparticles. In this section, those parameters are studied, and qualitative analyses are given. As the grafted chain length increases, the particle becomes more “hairy” and the kinetic friction coefficient increases from 0.0025 to greater than 0.0035 (Fig. 8). However, as the chain length increases beyond 4 (number of bonds), the friction coefficient saturates. Fig. 8 shows that the number of inter-brush interactions increases constantly as the chain length increases. In this case, the increased number of inter-brush interaction for chain length longer than 4 is not correlated with changes in the friction coefficient. Similar to grafted chain length, as the grafting density increases, the grafted nanoparticle becomes hairier as surface coverage increases. The kinetic friction coefficient increases continuously from 0.003 to 0.004 throughout the range of surface coverage values (Fig. 9). Fig. 9 shows that the number of inter-brush interactions nearly saturates at 2000. At such a number of inter-brush interactions, this kinetic friction coefficient is larger than that in the case of a long chain length (N = 6), but is significantly smaller than in the case of a good solvent. The unexpected observation is that a larger number of inter-brush interactions in this case do not explain why the friction coefficient is much lower than the case of a good solvent, similar to the results regarding brush miscibility. Since bare nanoparticles have a strong tendency to agglomerate, they are kept dispersed by grafting the nanoparticle surface with polymer chains, which produces steric repulsion between nanoparticles. However, the results of this section showed that increasing in chain length and surface coverage, which helps dispersion of nanoparticles, will also reduce the lubricating behavior of the system. For



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the usage of grafted nanoparticles, the dependence of dispersion and distribution of them on the degree of coverage should be investigated to find the minimum or optimum values for their design parameters.

4.5 Toward practical applications for lubrication We have used DPD method to simulate the system of polymer brushes with hairy nanoparticle as additive. The role of grafted nanoparticle as nano-bearing between polymer brushes is studied, and the effects of interaction parameters between different types of particles as well as grafting parameters (coverage, chain length) are investigated. Polymer brushes have attracted increasing interest in various applications due to its ability for surface modification. With the advance of controlled radical polymerization from surface methods such as atom transfer radical polymerization (ATRP), nitroxide-mediated polymerization (NMP), and reversible addition−fragmentation chain transfer (RAFT),51-53 it is possible to control the density of polymer brushes and their chain conformation. It is recognized that the polymer brushes can reduce friction between two solid surfaces enormously,9-10 and recently Chen et al. have shown that polyzwitterionic brushes grafted on two mica sheets (the separation D is in order of several nanometers to several tens of nanometers) with water as solvent can have lubrication performance comparable to or even better than natural synovial joints.11 Another variation of polymer brush is hairy nanoparticles, or grafted nanoparticles. One of the main obstacles to application of nanoparticles is their tendency of agglomeration, therefore polymer chains are grafted onto nanoparticle's surface to improve the dispersion. Many types of nanoparticle such as metal oxides, carbon, silica, etc. and their tribological performances have been investigated.13-18 Among them, grafted silica nanoparticles not only have good tribological behavior but also are environmental friendly and economically. We can propose the application of such system as polyzwitterionic brushes with water as solvent and grafted silica nanoparticles as additives. Even if the grafted nanoparticle may increase the friction coefficient between polyzwitterionic brushes by 20-30%, the resulted lubrication performance is still comparable to synovial joints,11 which is very satisfactory. One interesting aspect raising from our study is that despite the usual improvement of grafted nanoparticle on traditional oil-based lubrication, in polymer brushes system we have the trade-off between lubrication performance and stability. The obtained simulation results can be used as a guideline for real application, and the simulation method can be adopted for more specific and detail 16 ACS Paragon Plus Environment

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studies if needed. Since only one grafted nanoparticle with periodic boundary conditions is considered in DPD simulations, the dispersion or agglomeration of multiple nanoparticle, which can depend on the applied shear rate and grafted polymer chains of nanoparticle, remains to be studied further. The combination of polymer brushes with well-dispersed grafted nanoparticles gives a promising application for lubrication, provided that the ability to control and modify polymer grafted on surface is improved rapidly. It can lead to a wide range of aqueous lubrication application, which has many advantages over conventional oil-based lubricant, especially in environmental aspect.

5 Conclusion In this study, we propose using grafted nanoparticles as nano-bearings on polymer brushed walls in nanoscale, of which the tribological behavior was analyzed with DPD simulation, a mesoscale simulation technique. Since the DPD simulations are carried out in the low to intermediate compressions, the effect of entanglement between polymer chains is negligible and dismissed in this study, however it should be taken into account if high compression is considered. Embedding grafted nanoparticle between two brushed walls can prevent detrimental contact between two walls at compression as shown from simulation results, i.e. the sliding contact between polymer brushes can be replaced by the rolling contact with hairy nanoparticle and the number of DPD particles withstanding high force is reduced. However, the friction coefficient increases by 2030% compared to brushed walls without grafted nanoparticle. The reduced lubrication performance due to the inclusion of grafted nanoparticle is still very satisfactory, thanks to the extraordinary lubrication of the polymer brush system. The solvent quality has the strongest effect on the brush structures and kinetic friction coefficient, similar to results from previous studies. Miscibility between polymer brushes and grafted polymer chains on the nanoparticle will increase the kinetic friction coefficient, while immiscibility will not decrease it. The repulsion of brushes in the case of immiscibility is not strong enough to further reduce the height of polymer brushes for a given solvent quality. In those cases, the number of inter-brush interactions is strongly correlated with the kinetic friction coefficient. The grafting density and chain length of grafted polymers on nanoparticle, which prevent their agglomeration, also affect the kinetic friction coefficient. However, their effect is much weaker than the effect of solvent quality. As the chain length further increases beyond a specific



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value, it does not change the kinetic friction coefficient much. These qualitative results show that there is a trade-off between tribological behavior and stability of the polymer brushes with grafted nanoparticle. One should pay attention this behavior when designing a practical system. The present results may provide insights that are helpful in designing and developing lubrication materials with grafted nanoparticle for practical applications, such as joint treatment and industrial water-based lubricants. Note that the current simulation models consider only one grafted nanoparticle with periodic boundary conditions, therefore the dispersion and clustering of multiple nanoparticle depending on the applied shear rate and grafted polymer chains need to be investigated further. This study can be extended in direction of simulation of asperity contact at rough surfaces, that will cause detrimental effect on polymer brushes, and incorporating chain rupture or de-tethering accordingly.

Acknowledgement This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (Ministry of Science and ICT) (No. NRF-2017R1A2B4012081) and by the Nano-Material Technology Development Program through NRF, funded by the Korean government (Ministry of Science and ICT) (No. NRF-2016M3A7B4910531).

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Figure Captions

Figure 1. (a) Schematic illustration of tribological interaction between polymer-brushed walls with grafted nanoparticles as nano bearings under sliding motion. (b) Modeling of wall and polymer brush, (c) modeling of nanoparticle. Figure 2. Snapshots of DPD simulation on polymer brushes with grafted nanoparticle inclusion under shear deformation at various shear timesteps: (a) 0, (b) 3000, (c) 6000. One part of the nanoparticle is highlight with different color for visualization of nanoparticle’s motion. Figure 3. (a) DPD forces per particle in the simulation cell. (b) DPD force as a function of z. (c) Number of DPD particles withstanding high DPD force. Only DPD forces acting on polymer brush particles are considered. Figure 4. Concentration profiles in cases: (a) without nanoparticle inclusion and (b) with nanoparticle inclusion. (c) Friction coefficient for polymer brushes with and without grafted nanoparticle as a function of shear rate at different values of the wall distance. Figure 5. Snapshots of DPD simulations on polymer brushed walls with a grafted nanoparticle in a tetragonal unit cell (a) at equilibrium, and under shear deformation at shear rate (b) & 0.1 , (c) & 0.5 . Figure 6. (a) Kinetic friction coefficient and number of interbrush interactions as a function of solvent quality. (b) Concentration profiles for a pol  sol  4 (dotted line), a pol  sol  0 (dashed line), and a pol  sol  4 (solid line). (c) Snapshots for several values of solvent quality. Figure 7. (a) Kinetic friction coefficient and number of interbrush interactions as a function of miscibility of polymer. (b) Concentration profiles for a pol1 pol 2  4 (dotted line), a pol1 pol 2  0 (dashed line), and

a pol1 pol 2  4 (solid line). (c) Snapshots for several values of miscibility of polymer.



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Figure 8. (a) Kinetic friction coefficient and number of interbrush interactions as a function of grafted chain length. (b) Concentration profiles for N  1 (dotted line), N  3 (dashed line), and N  6 (solid line). (c) Snapshots for several values of grafted chain length. Figure 9. (a) Kinetic friction coefficient and number of interbrush interactions as a function of surface coverage. (b) Concentration profiles for C  15% (dotted line), C  30% (dashed line), and C  45% (solid line). (c) Snapshots for several values of surface coverage.


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Figure for table of contents 190x275mm (300 x 300 DPI)



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Tribological Behavior of Grafted Nanoparticle on Polymer-Brushed

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