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Molecular dynamics study of ultrathin lubricant films with functional end groups: Thermal-induced desorption and decomposition
Computational Materials Science 93 (2014) 11–14
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Molecular dynamics study of ultrathin lubricant films with functional end groups: Thermal-induced desorption and decomposition B. Li, C.H. Wong ⇑ School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
a r t i c l e
i n f o
Article history: Received 19 February 2014 Received in revised form 9 June 2014 Accepted 14 June 2014
Keywords: Lubricant films Desorption Decomposition Molecular dynamics simulation
a b s t r a c t Molecular dynamics simulation is employed to study the thermal durability and stability of molecularly thin lubricant films with functional end groups. A coarse-grained polymer model that describes intrinsic bond breakage is presented. Using this novel model, we investigated the bead number density profile to quantify the lubricant weight loss that occurs during heat treatment process. The density profile, which was partially computed by a hyperbolic tangent function, reveals that both the liquid–vapor interfacial thickness and the solid–vapor separation increase with temperature. Nonetheless, the liquid phase diminishes at high temperatures and the solid–vapor separation begins to decay as the temperature increases further. We also investigated the lubricant weight and bond loss profiles to provide an insight on the thermal instability of nonfunctional and functional lubricant films. Our simulation results show that the functionality of the lubricant film can greatly influence lubricant desorption albeit a slight effect on lubricant decomposition. For both nonfunctional and functional thin lubricant films, lubricant desorption is the domination depletion process and is attributed as the root for lubricant degradation and failure. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Huge amount of efforts have been directed towards increasing the areal data density of hard disk drive (HDD) systems during past decades. One typical method is to reduce the flying height to obtain greater areal density. For example, the flying height is lowered to about 3.5 nm to yield an areal density of 1 Tb/in2 [1]. Unfortunately, this ultra-low spacing inevitably requires the size of the magnetic grains on the disk to be decreased as well. However, when this happens the thermal fluctuations induce random flipping of the magnetic moment and recording bit loses its stability as the size is shrinked to below the superparamagnetic limit [2]. And one possible approach to delay the thermal limit is by employing heat-assisted magnetic recording (HAMR) technology [3], in which a high anisotropic medium is adopted and is written by the heat produced by a laser beam as well as the field produced by a magnetic head. In this technique, the laser beam temporarily irradiates the magnetic medium to beyond 400 °C which helps lower the medium coercivity and therefore allowing the medium to be easily overwritten. However, the use of laser heating in the HAMR technique introduces critical issues at the head disk
⇑ Corresponding author. Tel.: +65 6790 5913; fax: +65 6792 4062. E-mail address: [email protected] (C.H. Wong). http://dx.doi.org/10.1016/j.commatsci.2014.06.023 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
interface (HDI). For example, the ultrathin perfluoropolyether (PFPE) lubricant on the disk surface is subjected to severe depletion in the form of decomposition and desorption. It is found that the depletion is heavily dependent on the lubricant thickness, bonding ratio, molecular weight, and the laser heating rate [4–7]. At elevated temperature, the depletion in the lubricant is attributed to desorption from and/or decomposition on the disk surface. However, the mechanisms of the lubricant desorption and decomposition are not well understood, especially under rapid laser heating conditions (in the order of 1011 K/s) [7]. Therefore, to understand the mechanism of lubricant depletion under HAMR conditions, it is crucial to investigate the thermal reliability and stability of the ultrathin PFPEs at near-contact HDI.
2. Molecular dynamics simulation and methodology Following our earlier work [8–10], the PFPE lubricant is characterized by a three dimensional coarse-grained polymer model as shown in Fig. 1. Fig. 1(a) presents the schematic view of the polymer model as well as five potentials used in the simulations. Each polymer chain consists of 10 identical beads and has a molecular weight of about 2000 g/mol. And Fig. 1(b) shows the front view of the equilibrated system with lubricant beads N = 6480 at T = 1.0e/kB. The lubricant film spreads uniformly on the disk
12
B. Li, C.H. Wong / Computational Materials Science 93 (2014) 11–14
and similarly, the polar interactions between the end beads can be expressed as
rr c U ebeb ðrÞ ¼ ep exp ; d
Fig. 1. (a) Schematics of the coarse-grained polymer model together with five potentials used in the simulations; (b) isometric view of the equilibrated functional lubricant (epw = ep = 4e) system. The blue beads are end groups, the pink beads are backbone groups, and the yellow flat wall is the disk substrate surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
substrate and has a square area of A = 30r 30r in the x–y plane. A layering film structure is also achieved for the functional lubricant as seen in Fig. 1(b). The PFPE molecules prefer to reside flatly on the disk surface due to strong adhesions (see potential Ueb-wall in Fig. 1(a)) between the functional end beads and the disk, thus forming a parallel and thin layer I. While the free functional end beads above layer I tend to couple to each other as a result of the polar interactions among them (see potential Ueb–eb in Fig. 1(a)), generating a layer II with a thickness about twice of that of the layer I. The characteristics of the layering molecular structure match well with the experimental data [11,12] and the full atomic simulation work [13]. In order to save computation time in our simulations, the disk surface (located at z = 0) is assumed to be a thermally inert, and an infinitely long and deep flat surface. Additionally, the beads are categorized into backbone beads (bbs) or end beads (ebs) to represent different functionalities. In this work, we employed a truncated-shifted ‘‘12-6’’ form of the Lennard-Jones (LJ) potential to compute the van der Waals interactions between all the beads and is computed as
" U LJ ðrÞ ¼ 4e
r12 r
r6 r
r
r cutoff
12
þ
r rcutoff
6 # ;
ð1Þ
where r represents the bead diameter, r depicts the bead distance, e refers to the LJ well depth for the bead interactions and rcutoff = 3.0r is the cutoff distance for the non-bonded potential. By integrating the ‘‘12-6’’ LJ potential, we obtained a summed ‘‘9-3’’ mathematical representation of the LJ potential which describes the interactions between the solid disk (substrate) and all the beads and is expressed as
U wall ðzÞ ¼ ew
2 r9 r3 ; 15 z z
ð2Þ
where ew = 4e represents a relatively strong interaction between the substrate (disk surface) and the bead (lubricant film) [14,15], while z is the vertical distance between the substrate and the bead. The additional polar interactions between the substrate and the end beads can be described using short-range exponential decay functions [14,15] such that
zz c U ebwall ðzÞ ¼ epw exp ; d
ð3Þ
ð4Þ
where epw and ep are the corresponding interaction strengths that are used to qualify the functionality of polar end beads. zc is the critical distance for eb-wall interactions while rc is the critical distance for eb–eb interactions, and d = 0.3r refers to the characteristic short-range decay length for the coupling interaction. Typically, the simulations of lubrications adopted the finitely extensible nonlinear elastic (FENE) potential [16] to describe the bond interaction based on a coarse-grained, bead-spring model. However, the usage of FENE potential is inadequate because it is unable to describe the intrinsic chemical bond breakage. As such, to study lubricant decomposition at elevated temperature, we adopted a quartic bond potential [17,18] to approximate the FENE potential at the potential minimum such that
( U 4 ðrÞ ¼
k4 ðy b1 Þðy b2 Þy2 þ U 0 U0
r < rb ; r > rb
ð5Þ
where r is the distance between two neighboring beads, y = r rb shifts the quartic center from the origin and rb is the cutoff length where the potential goes smoothly to a local maximum. When the bond length exceeds rb, the bond breaks and the quartic term is deactivated to impede the bond from reforming. This potential mimics the FENE potential by setting the following parameters as k4 = 1434.3e/ r4, b1 = 0.7589r, b2 = 0.0, rb = 1.5r, and U0 = 67.2234e [17,18]. In this paper, we incorporated the Langevin thermostat into the MD simulations to investigate lubricant depletion in the form of desorption and decomposition at different temperatures. The temperature of the lubricant system is defined as
X1 2
mv 2 ¼
d NkB T; 2
ð6Þ
where the left-hand side of the equation is the total kinetic energy of the lubricant beads, d = 3 is the dimensionality of the simulation, N equals to the number of beads, and kB is the Boltzmann constant relating the kinetic energy at a microscopic level with calculated temperature T. The system is first relaxed at T = 1.0e/kB for 2500s in a canonical ensemble (NVT). The lubricant is then subjected to a heating rate of 0.0005e/(kBs) by uniformly coupling it to an external heat bath. The system will be kept constant for another 10,000s whenever it is heated up to a desired temperature. The quantities of interest will be time averaged over the next 1000s. Velocity Verlet algorithm is employed to determine the phase-space trajectories and a Verlet neighbor list is reconstructed at every 20 time steps. A free lubricant–vacuum interface is obtained by applying periodic boundary conditions on the x and y directions of the simulation box, while fixing the z direction with a sufficient domain height Lz. 3. Results and discussion Fig. 2(a) shows the number density profiles for functional lubricant films at various temperatures and agrees well with the observations in Ref. [13]. It is observed that the maximum lubricant density occurs near the bottom of the simulation box at z = 0. At low temperatures (T < 2.8e/kB), the maximum density is followed by another two or three peaks before it reaches a stable density value (ql) which represents the bulk liquid phase. However, at T = 1.8e/kB, there is a slight bulge in the liquid density ql due to the characteristic layering structure of PFPE molecules. As shown in Fig. 2(b), when the temperature increases, the layering structure becomes less prominent and the bulge diminishes. Moreover, the lubricant density q(z) in Fig. 2(a) continues to decrease smoothly
B. Li, C.H. Wong / Computational Materials Science 93 (2014) 11–14
13
Fig. 2. (a) Bead number density profiles for functional lubricant films (ep = epw = 4e) at different temperatures as averaged over 1000s; (b) number density profiles for eb and bb at T = 1.8e/kB and T = 2.5e/kB, respectively.
from ql to another stable density qv, which represents the density of vapor phase. Between the bulk liquid and vapor phase is the liquid–vapor interface and its density is derived by the van der Waals model for surface tension [19,20] and is computed as
where z0 is qlv(z0) = (ql + qv)/2. The solid–vapor separation d between the vapor phase and the wall is calculated as d = z0 + d/2. As such, we made use of the lubricant molecules that lie above plane z = d to calculate the lubricant weight and bond loss profiles. Furthermore, when the temperature reaches a critical value of Tc = 2.8e/kB (see Fig. 2(a)), the bulk liquid phase diminishes and only one solid–vapor phase is observed. Therefore, at T > Tc the solid– vapor separation d is estimated to be the distance from which the density profile q(z) begins its approach to the constant vapor density qv. Fig. 3 illustrates the solid–vapor separation d for functional
lubricants at different temperatures. Along with the increase in solid–vapor separation d, the liquid–vapor interfacial thickness d also increases with temperature due to the thermal expansion in the density profile when the temperature is below Tc. Nonetheless, at high temperatures (T > Tc), the liquid phase vanishes and the solid–vapor separation d begins to decay slowly while the temperature increases as illustrated in Fig. 3. This is caused by having more molecules entering into the vapor phase. In order to study the durability and thermal stability of molecularly thin lubricant films, the change in lubricant weight at various temperatures is examined and is depicted in Fig. 4. The thermal stability of lubricant desorption is defined as the temperature Tdes at which there is 5% lubricant weight loss. As such, the thermal stability of nonfunctional and functional lubricants are Tdes = 2.0e/kB and Tdes = 2.4e/kB, respectively. Especially, at T = 2.6e/kB, the nonfunctional lubricant evaporates 50% more than the functional lubricant, indicating a more severe lubricant depletion at the HDI. The hysteresis in weight loss profiles for nonfunctional and functional lubricants state that the functionalities (ep and epw ) can strongly affect the lubricant desorption from the disk surface. As the functionalities increase, more PFPE molecules are attached onto the substrate, thereby improving the thermal stability and durability for lubricant
Fig. 3. Liquid–vapor interfacial thickness d and solid–vapor separation d for functional lubricant films (ep = epw = 4e) at various temperatures. Solid lines are the fitted curves.
Fig. 4. Lubricant weight change as a function of temperature for nonfunctional and functional lubricant films, respectively.
1 2
1 2
qlv ðzÞ ¼ ðql þ qv Þ ðql qv Þ tanh
2ðz z0 Þ ; d
ð7Þ
such that d is the liquid–vapor interfacial thickness and is defined as
d¼
ql qv ; ½@ qlv ðzÞ=@zz¼z0
ð8Þ
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B. Li, C.H. Wong / Computational Materials Science 93 (2014) 11–14
Fig. 5. Lubricant bond change as a function of temperature for nonfunctional and functional lubricant films, respectively.
films at high temperatures expected for HAMR systems. Fig. 5 shows the bond loss profiles for lubricant films at different temperatures. Similarly, the thermal stability of lubricant decomposition Tdec is defined as the temperature at which a 5% bond loss occurs and as a result, we obtained Tdec = 3.1e/kB for nonfunctional lubricant and Tdec = 3.2e/kB for functional lubricant. The slight difference in bond loss profiles shows that the functionalities have a negligible effect on the lubricant decomposition. Since bb and eb share the same size and mass, we therefore employ the same quartic potential in Eq. (5) to account for the bond interaction for all the beads in our simulations. The bond breakage is attributed to the bond potential, but not the functionalities. In addition, if we compare Tdec with Tdes, we find that the lubricant desorption process is more dominant compared to decomposition for both nonfunctional and functional lubricants. In particular, at T = 3.1e/kB only about 32% and 13% lubricant remain on the wall surface for nonfunctional and functional lubricants, respectively. Under such a condition, the lubricant loses its capability to protect the wall from damages due to corrosion and wear. Hence, based on our findings, HDI deterioration and failure is mainly caused by lubricant desorption for PFPE films with molecular weight of about 2000 g/mol. 4. Conclusions In conclusion, we investigated the depletion of lubricant films in terms of thermal-induced desorption and decomposition via
molecular dynamics simulation technique using a coarse-grained, polymer model. A quartic bond potential was adopted to describe the intrinsic bond breakage. Using this novel technique, we calculated the number density profile to reveal the lubricant weight loss during heat treatment. The density profile was partially computed by a hyperbolic tangent function that describes the liquid–vapor interfacial thickness d. We found that both the solid–vapor separation d and interfacial thickness d increase monotonously with temperature. However as the temperature increases beyond T > 2.8e/ kB, the liquid phase diminishes while the solid–vapor separation d decays slowly. Furthermore, the lubricant bond and weight loss profiles were investigated to study the thermal durability and stability of both nonfunctional and functional lubricant films. The study demonstrated that the functionality influences the lubricant desorption greatly, but only a slight effect on the lubricant decomposition. Additionally, we found that lubricant depletion is predominantly caused by desorption rather than decomposition and we attribute lubricant desorption as the root cause for lubricant failure at the HDI for low-molecular weight (2000 g/mol) PFPE lubricants. Therefore, a novel PFPE lubricant suitable for HAMR system should be designed and engineered to overcome the prone to desorption from the disk surfaces. References [1] G. Jing, IEEE Trans. Magn. 39 (2003) 716. [2] S.H. Charap, P.L. Lu, Y.J. He, IEEE Trans. Magn. 33 (1997) 978. [3] W.A. Challener, C.B. Peng, A.V. Itagi, D. Karns, W. Peng, Y.G. Peng, X.M. Yang, X.B. Zhu, N.J. Gokemeijer, Y.T. Hsia, G. Ju, R.E. Rottmayer, M.A. Seigler, E.C. Gage, Nature Photon. 3 (2009) 220. [4] N. Tagawa, H. Andoh, H. Tani, Tribol. Lett. 37 (2010) 411. [5] N. Tagawa, T. Miki, H. Tani, Tribol. Lett. 47 (2012) 123. [6] L. Wu, Nanotechnology 18 (2007) 215702. [7] M.S. Lim, A.J. Gellman, Tribol. Int. 38 (2005) 554. [8] C.H. Wong, B. Li, S.K. Yu, W. Hua, W.D. Zhou, Tribol. Lett. 43 (2011) 89. [9] Y. Li, C.H. Wong, B. Li, S.K. Yu, W. Hua, W.D. Zhou, Soft Matter 8 (2012) 5649. [10] B. Li, C.H. Wong, Polymer 54 (2013) 6008. [11] G.W. Tyndall, P.B. Leezenberg, R.J. Waltman, J. Castenada, Tribol. Lett. 4 (1998) 103. [12] X. Ma, J. Gui, L. Smoliar, K. Grannen, B. Marchon, M.S. Jhon, C.L. Bauer, J. Chem. Phys. 110 (1999) 3129. [13] V. Sorkin, Z.D. Sha, P.S. Branicio, Q.X. Pei, Y.W. Zhang, IEEE Trans. Magn. 49 (2013) 5227. [14] Q. Guo, L. Li, Y.T. Hsia, M.S. Jhon, J. Appl. Phys. 97 (2005) 10P302. [15] Q. Guo, P.S. Chung, M.S. Jhon, H.J. Choi, Macromol. Theory Simul. 17 (2008) 454. [16] R.B. Bird, R.C. Armstrong, D. Hassager, Dynamics of Polymeric Liquids, John Wiley & Sons, New York, 1971. [17] M. Tsige, M.J. Stevens, Macromolecules 37 (2004) 630. [18] M.J. Stevens, Macromolecules 34 (2001) 1411. [19] J.W. Cahn, J.E. Hilliard, J. Phys. Chem. 28 (1958) 258. [20] F.P. Buff, R.A. Lovett, F.H. Stillinger, Phys. Rev. Lett. 15 (1965) 621.
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Molecular dynamics study of ultrathin lubricant films with functional end groups: Thermal-induced desorption and decomposition B. Li, C.H. Wong ⇑ School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
a r t i c l e
i n f o
Article history: Received 19 February 2014 Received in revised form 9 June 2014 Accepted 14 June 2014
Keywords: Lubricant films Desorption Decomposition Molecular dynamics simulation
a b s t r a c t Molecular dynamics simulation is employed to study the thermal durability and stability of molecularly thin lubricant films with functional end groups. A coarse-grained polymer model that describes intrinsic bond breakage is presented. Using this novel model, we investigated the bead number density profile to quantify the lubricant weight loss that occurs during heat treatment process. The density profile, which was partially computed by a hyperbolic tangent function, reveals that both the liquid–vapor interfacial thickness and the solid–vapor separation increase with temperature. Nonetheless, the liquid phase diminishes at high temperatures and the solid–vapor separation begins to decay as the temperature increases further. We also investigated the lubricant weight and bond loss profiles to provide an insight on the thermal instability of nonfunctional and functional lubricant films. Our simulation results show that the functionality of the lubricant film can greatly influence lubricant desorption albeit a slight effect on lubricant decomposition. For both nonfunctional and functional thin lubricant films, lubricant desorption is the domination depletion process and is attributed as the root for lubricant degradation and failure. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Huge amount of efforts have been directed towards increasing the areal data density of hard disk drive (HDD) systems during past decades. One typical method is to reduce the flying height to obtain greater areal density. For example, the flying height is lowered to about 3.5 nm to yield an areal density of 1 Tb/in2 [1]. Unfortunately, this ultra-low spacing inevitably requires the size of the magnetic grains on the disk to be decreased as well. However, when this happens the thermal fluctuations induce random flipping of the magnetic moment and recording bit loses its stability as the size is shrinked to below the superparamagnetic limit [2]. And one possible approach to delay the thermal limit is by employing heat-assisted magnetic recording (HAMR) technology [3], in which a high anisotropic medium is adopted and is written by the heat produced by a laser beam as well as the field produced by a magnetic head. In this technique, the laser beam temporarily irradiates the magnetic medium to beyond 400 °C which helps lower the medium coercivity and therefore allowing the medium to be easily overwritten. However, the use of laser heating in the HAMR technique introduces critical issues at the head disk
⇑ Corresponding author. Tel.: +65 6790 5913; fax: +65 6792 4062. E-mail address: [email protected] (C.H. Wong). http://dx.doi.org/10.1016/j.commatsci.2014.06.023 0927-0256/Ó 2014 Elsevier B.V. All rights reserved.
interface (HDI). For example, the ultrathin perfluoropolyether (PFPE) lubricant on the disk surface is subjected to severe depletion in the form of decomposition and desorption. It is found that the depletion is heavily dependent on the lubricant thickness, bonding ratio, molecular weight, and the laser heating rate [4–7]. At elevated temperature, the depletion in the lubricant is attributed to desorption from and/or decomposition on the disk surface. However, the mechanisms of the lubricant desorption and decomposition are not well understood, especially under rapid laser heating conditions (in the order of 1011 K/s) [7]. Therefore, to understand the mechanism of lubricant depletion under HAMR conditions, it is crucial to investigate the thermal reliability and stability of the ultrathin PFPEs at near-contact HDI.
2. Molecular dynamics simulation and methodology Following our earlier work [8–10], the PFPE lubricant is characterized by a three dimensional coarse-grained polymer model as shown in Fig. 1. Fig. 1(a) presents the schematic view of the polymer model as well as five potentials used in the simulations. Each polymer chain consists of 10 identical beads and has a molecular weight of about 2000 g/mol. And Fig. 1(b) shows the front view of the equilibrated system with lubricant beads N = 6480 at T = 1.0e/kB. The lubricant film spreads uniformly on the disk
12
B. Li, C.H. Wong / Computational Materials Science 93 (2014) 11–14
and similarly, the polar interactions between the end beads can be expressed as
rr c U ebeb ðrÞ ¼ ep exp ; d
Fig. 1. (a) Schematics of the coarse-grained polymer model together with five potentials used in the simulations; (b) isometric view of the equilibrated functional lubricant (epw = ep = 4e) system. The blue beads are end groups, the pink beads are backbone groups, and the yellow flat wall is the disk substrate surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
substrate and has a square area of A = 30r 30r in the x–y plane. A layering film structure is also achieved for the functional lubricant as seen in Fig. 1(b). The PFPE molecules prefer to reside flatly on the disk surface due to strong adhesions (see potential Ueb-wall in Fig. 1(a)) between the functional end beads and the disk, thus forming a parallel and thin layer I. While the free functional end beads above layer I tend to couple to each other as a result of the polar interactions among them (see potential Ueb–eb in Fig. 1(a)), generating a layer II with a thickness about twice of that of the layer I. The characteristics of the layering molecular structure match well with the experimental data [11,12] and the full atomic simulation work [13]. In order to save computation time in our simulations, the disk surface (located at z = 0) is assumed to be a thermally inert, and an infinitely long and deep flat surface. Additionally, the beads are categorized into backbone beads (bbs) or end beads (ebs) to represent different functionalities. In this work, we employed a truncated-shifted ‘‘12-6’’ form of the Lennard-Jones (LJ) potential to compute the van der Waals interactions between all the beads and is computed as
" U LJ ðrÞ ¼ 4e
r12 r
r6 r
r
r cutoff
12
þ
r rcutoff
6 # ;
ð1Þ
where r represents the bead diameter, r depicts the bead distance, e refers to the LJ well depth for the bead interactions and rcutoff = 3.0r is the cutoff distance for the non-bonded potential. By integrating the ‘‘12-6’’ LJ potential, we obtained a summed ‘‘9-3’’ mathematical representation of the LJ potential which describes the interactions between the solid disk (substrate) and all the beads and is expressed as
U wall ðzÞ ¼ ew
2 r9 r3 ; 15 z z
ð2Þ
where ew = 4e represents a relatively strong interaction between the substrate (disk surface) and the bead (lubricant film) [14,15], while z is the vertical distance between the substrate and the bead. The additional polar interactions between the substrate and the end beads can be described using short-range exponential decay functions [14,15] such that
zz c U ebwall ðzÞ ¼ epw exp ; d
ð3Þ
ð4Þ
where epw and ep are the corresponding interaction strengths that are used to qualify the functionality of polar end beads. zc is the critical distance for eb-wall interactions while rc is the critical distance for eb–eb interactions, and d = 0.3r refers to the characteristic short-range decay length for the coupling interaction. Typically, the simulations of lubrications adopted the finitely extensible nonlinear elastic (FENE) potential [16] to describe the bond interaction based on a coarse-grained, bead-spring model. However, the usage of FENE potential is inadequate because it is unable to describe the intrinsic chemical bond breakage. As such, to study lubricant decomposition at elevated temperature, we adopted a quartic bond potential [17,18] to approximate the FENE potential at the potential minimum such that
( U 4 ðrÞ ¼
k4 ðy b1 Þðy b2 Þy2 þ U 0 U0
r < rb ; r > rb
ð5Þ
where r is the distance between two neighboring beads, y = r rb shifts the quartic center from the origin and rb is the cutoff length where the potential goes smoothly to a local maximum. When the bond length exceeds rb, the bond breaks and the quartic term is deactivated to impede the bond from reforming. This potential mimics the FENE potential by setting the following parameters as k4 = 1434.3e/ r4, b1 = 0.7589r, b2 = 0.0, rb = 1.5r, and U0 = 67.2234e [17,18]. In this paper, we incorporated the Langevin thermostat into the MD simulations to investigate lubricant depletion in the form of desorption and decomposition at different temperatures. The temperature of the lubricant system is defined as
X1 2
mv 2 ¼
d NkB T; 2
ð6Þ
where the left-hand side of the equation is the total kinetic energy of the lubricant beads, d = 3 is the dimensionality of the simulation, N equals to the number of beads, and kB is the Boltzmann constant relating the kinetic energy at a microscopic level with calculated temperature T. The system is first relaxed at T = 1.0e/kB for 2500s in a canonical ensemble (NVT). The lubricant is then subjected to a heating rate of 0.0005e/(kBs) by uniformly coupling it to an external heat bath. The system will be kept constant for another 10,000s whenever it is heated up to a desired temperature. The quantities of interest will be time averaged over the next 1000s. Velocity Verlet algorithm is employed to determine the phase-space trajectories and a Verlet neighbor list is reconstructed at every 20 time steps. A free lubricant–vacuum interface is obtained by applying periodic boundary conditions on the x and y directions of the simulation box, while fixing the z direction with a sufficient domain height Lz. 3. Results and discussion Fig. 2(a) shows the number density profiles for functional lubricant films at various temperatures and agrees well with the observations in Ref. [13]. It is observed that the maximum lubricant density occurs near the bottom of the simulation box at z = 0. At low temperatures (T < 2.8e/kB), the maximum density is followed by another two or three peaks before it reaches a stable density value (ql) which represents the bulk liquid phase. However, at T = 1.8e/kB, there is a slight bulge in the liquid density ql due to the characteristic layering structure of PFPE molecules. As shown in Fig. 2(b), when the temperature increases, the layering structure becomes less prominent and the bulge diminishes. Moreover, the lubricant density q(z) in Fig. 2(a) continues to decrease smoothly
B. Li, C.H. Wong / Computational Materials Science 93 (2014) 11–14
13
Fig. 2. (a) Bead number density profiles for functional lubricant films (ep = epw = 4e) at different temperatures as averaged over 1000s; (b) number density profiles for eb and bb at T = 1.8e/kB and T = 2.5e/kB, respectively.
from ql to another stable density qv, which represents the density of vapor phase. Between the bulk liquid and vapor phase is the liquid–vapor interface and its density is derived by the van der Waals model for surface tension [19,20] and is computed as
where z0 is qlv(z0) = (ql + qv)/2. The solid–vapor separation d between the vapor phase and the wall is calculated as d = z0 + d/2. As such, we made use of the lubricant molecules that lie above plane z = d to calculate the lubricant weight and bond loss profiles. Furthermore, when the temperature reaches a critical value of Tc = 2.8e/kB (see Fig. 2(a)), the bulk liquid phase diminishes and only one solid–vapor phase is observed. Therefore, at T > Tc the solid– vapor separation d is estimated to be the distance from which the density profile q(z) begins its approach to the constant vapor density qv. Fig. 3 illustrates the solid–vapor separation d for functional
lubricants at different temperatures. Along with the increase in solid–vapor separation d, the liquid–vapor interfacial thickness d also increases with temperature due to the thermal expansion in the density profile when the temperature is below Tc. Nonetheless, at high temperatures (T > Tc), the liquid phase vanishes and the solid–vapor separation d begins to decay slowly while the temperature increases as illustrated in Fig. 3. This is caused by having more molecules entering into the vapor phase. In order to study the durability and thermal stability of molecularly thin lubricant films, the change in lubricant weight at various temperatures is examined and is depicted in Fig. 4. The thermal stability of lubricant desorption is defined as the temperature Tdes at which there is 5% lubricant weight loss. As such, the thermal stability of nonfunctional and functional lubricants are Tdes = 2.0e/kB and Tdes = 2.4e/kB, respectively. Especially, at T = 2.6e/kB, the nonfunctional lubricant evaporates 50% more than the functional lubricant, indicating a more severe lubricant depletion at the HDI. The hysteresis in weight loss profiles for nonfunctional and functional lubricants state that the functionalities (ep and epw ) can strongly affect the lubricant desorption from the disk surface. As the functionalities increase, more PFPE molecules are attached onto the substrate, thereby improving the thermal stability and durability for lubricant
Fig. 3. Liquid–vapor interfacial thickness d and solid–vapor separation d for functional lubricant films (ep = epw = 4e) at various temperatures. Solid lines are the fitted curves.
Fig. 4. Lubricant weight change as a function of temperature for nonfunctional and functional lubricant films, respectively.
1 2
1 2
qlv ðzÞ ¼ ðql þ qv Þ ðql qv Þ tanh
2ðz z0 Þ ; d
ð7Þ
such that d is the liquid–vapor interfacial thickness and is defined as
d¼
ql qv ; ½@ qlv ðzÞ=@zz¼z0
ð8Þ
14
B. Li, C.H. Wong / Computational Materials Science 93 (2014) 11–14
Fig. 5. Lubricant bond change as a function of temperature for nonfunctional and functional lubricant films, respectively.
films at high temperatures expected for HAMR systems. Fig. 5 shows the bond loss profiles for lubricant films at different temperatures. Similarly, the thermal stability of lubricant decomposition Tdec is defined as the temperature at which a 5% bond loss occurs and as a result, we obtained Tdec = 3.1e/kB for nonfunctional lubricant and Tdec = 3.2e/kB for functional lubricant. The slight difference in bond loss profiles shows that the functionalities have a negligible effect on the lubricant decomposition. Since bb and eb share the same size and mass, we therefore employ the same quartic potential in Eq. (5) to account for the bond interaction for all the beads in our simulations. The bond breakage is attributed to the bond potential, but not the functionalities. In addition, if we compare Tdec with Tdes, we find that the lubricant desorption process is more dominant compared to decomposition for both nonfunctional and functional lubricants. In particular, at T = 3.1e/kB only about 32% and 13% lubricant remain on the wall surface for nonfunctional and functional lubricants, respectively. Under such a condition, the lubricant loses its capability to protect the wall from damages due to corrosion and wear. Hence, based on our findings, HDI deterioration and failure is mainly caused by lubricant desorption for PFPE films with molecular weight of about 2000 g/mol. 4. Conclusions In conclusion, we investigated the depletion of lubricant films in terms of thermal-induced desorption and decomposition via
molecular dynamics simulation technique using a coarse-grained, polymer model. A quartic bond potential was adopted to describe the intrinsic bond breakage. Using this novel technique, we calculated the number density profile to reveal the lubricant weight loss during heat treatment. The density profile was partially computed by a hyperbolic tangent function that describes the liquid–vapor interfacial thickness d. We found that both the solid–vapor separation d and interfacial thickness d increase monotonously with temperature. However as the temperature increases beyond T > 2.8e/ kB, the liquid phase diminishes while the solid–vapor separation d decays slowly. Furthermore, the lubricant bond and weight loss profiles were investigated to study the thermal durability and stability of both nonfunctional and functional lubricant films. The study demonstrated that the functionality influences the lubricant desorption greatly, but only a slight effect on the lubricant decomposition. Additionally, we found that lubricant depletion is predominantly caused by desorption rather than decomposition and we attribute lubricant desorption as the root cause for lubricant failure at the HDI for low-molecular weight (2000 g/mol) PFPE lubricants. Therefore, a novel PFPE lubricant suitable for HAMR system should be designed and engineered to overcome the prone to desorption from the disk surfaces. References [1] G. Jing, IEEE Trans. Magn. 39 (2003) 716. [2] S.H. Charap, P.L. Lu, Y.J. He, IEEE Trans. Magn. 33 (1997) 978. [3] W.A. Challener, C.B. Peng, A.V. Itagi, D. Karns, W. Peng, Y.G. Peng, X.M. Yang, X.B. Zhu, N.J. Gokemeijer, Y.T. Hsia, G. Ju, R.E. Rottmayer, M.A. Seigler, E.C. Gage, Nature Photon. 3 (2009) 220. [4] N. Tagawa, H. Andoh, H. Tani, Tribol. Lett. 37 (2010) 411. [5] N. Tagawa, T. Miki, H. Tani, Tribol. Lett. 47 (2012) 123. [6] L. Wu, Nanotechnology 18 (2007) 215702. [7] M.S. Lim, A.J. Gellman, Tribol. Int. 38 (2005) 554. [8] C.H. Wong, B. Li, S.K. Yu, W. Hua, W.D. Zhou, Tribol. Lett. 43 (2011) 89. [9] Y. Li, C.H. Wong, B. Li, S.K. Yu, W. Hua, W.D. Zhou, Soft Matter 8 (2012) 5649. [10] B. Li, C.H. Wong, Polymer 54 (2013) 6008. [11] G.W. Tyndall, P.B. Leezenberg, R.J. Waltman, J. Castenada, Tribol. Lett. 4 (1998) 103. [12] X. Ma, J. Gui, L. Smoliar, K. Grannen, B. Marchon, M.S. Jhon, C.L. Bauer, J. Chem. Phys. 110 (1999) 3129. [13] V. Sorkin, Z.D. Sha, P.S. Branicio, Q.X. Pei, Y.W. Zhang, IEEE Trans. Magn. 49 (2013) 5227. [14] Q. Guo, L. Li, Y.T. Hsia, M.S. Jhon, J. Appl. Phys. 97 (2005) 10P302. [15] Q. Guo, P.S. Chung, M.S. Jhon, H.J. Choi, Macromol. Theory Simul. 17 (2008) 454. [16] R.B. Bird, R.C. Armstrong, D. Hassager, Dynamics of Polymeric Liquids, John Wiley & Sons, New York, 1971. [17] M. Tsige, M.J. Stevens, Macromolecules 37 (2004) 630. [18] M.J. Stevens, Macromolecules 34 (2001) 1411. [19] J.W. Cahn, J.E. Hilliard, J. Phys. Chem. 28 (1958) 258. [20] F.P. Buff, R.A. Lovett, F.H. Stillinger, Phys. Rev. Lett. 15 (1965) 621.