(375u) Multi-Scale Modeling of Head Disk Interface

Multi-scale modeling has recently become a new paradigm of the engineering field by providing a novel methodology of integrated system design criteria and potentially gives several orders of magnitude advances in new technology by providing rigorous physical models of the inter-scale phenomena. The head disk interface (HDI) in hard disk drive system, which includes atomic, molecular, mesoscopic, and continuum levels, can be used as a benchmark for multi-scale modeling. Integration of HDI requires three component technologies shown in Fig. 1: top level (longest in time and length scales) includes continuum theory while just below this level, one often investigates the Boltzmann transport equation (BTE) to describe continuum based molecular lubrication theory and the Cattaneo equation description for mesoscale mass transfer for examining the static and dynamic response of lubricant nano film as well as microscale heat conduction in media (especially important for heat assisted magnetic recording system). Furthermore, at the bottom level (shortest in time and length scales), one develops Monte Carlo/molecular dynamics (MD) to investigate nanostructured conformation and dynamic behavior of molecularly thin lubricant film. As an integration of HDI multi-scale subsystems, three approaches can be employed: top to bottom, bottom to top, and middle-out. The conventional top to bottom approach was used in airbearing simulation by hybridizing continuum theory with BTE to describe a slip flow using the Knudsen number (Kn) [1, 2]. On the other hand, conventional bottom to top approach has been applied to the dynamic coupling of the lubricant film with continuum air shear in an ad hoc manner.

In this study, we will introduce novel multi-scale modeling based on the lattice Boltzmann method (LBM) as the centerpiece of our middle-out approach. Kim et al. [3] developed a novel, accurate, fast, robust, and parallelizable computational tool based on the LBM, which provides an efficient solution of the BTE and is easy to hybridize with bottom level theory including the MD used in lubricant nano film [4, 5]. Since the LBM is originated from the BTE description for high Kn flows, we can easily couple the LBM with continuum fluid flow & thermal flow to describe transport processes occurring inside the system. We utilize a coarse-graining procedure to simplify the atomic scale model to a coarse-grained bead-spring model and a simple reactive sphere model (SRS) [6]. Furthermore, the LBM can be constructed from the SRS model to describe lubricant dynamics by applying ?spins? or ?internal structures? on the spherical particles, which provides polarity on PFPEs. Calculations based on ab-initio methods as well as density functional theory will be used to determine the intramolecular (stretching, bending, torsional) force field parameters by directly using the ab-initio hessian matrix. The PFPE-PFPE dimer potential and PFPE-amorphous carbon surface interactions as a function of the end group structure (e.g., Zdol and Ztetraol) will be examined to calculate the intermolecular force field parameters, which will determine the potential energy function of the end group in classical molecular dynamics model as well as equilibrium PFPE-PFPE and PFPE-carbon surface geometry as a function of the PFPE structures. Our multi-scale framework stems from a novel middle-out approach in modern multi-scale modeling, using LBM as a base formulation and marches towards the continuum (top) and molecular (bottom) levels.

[1] S. Fukui and R. Kaneko, ?Analysis of Ultra-thin Gas Film Lubrication Based on Linearized Boltzmann Equation (Influence of Accommodation Coefficient),? JSME Int. J. 30, 1660 (1987).

[2] S.-C. Kang, R.M. Crone, and M.S. Jhon, ?A New Molecular Gas Lubrication Theory Suitable for Head-Disk Interface Modeling,? J. Appl. Phys. 85(8), 5594-5596 (1999).

[3] W.T. Kim, M.S. Jhon, Y. Zhou, I. Staroselsky, and H. Chen, ?Nanoscale Air Bearing Modeling via Lattice Boltzmann Method,? J. Appl. Phys. 97, 10P304 (2005).

[4] Q. Guo, L. Li, Y.-T. Hsia, and M.S. Jhon, ?A Spreading Study of Lubricant Film via Optical Surface Analyzer and Molecular Dynamics,? IEEE Trans. Mag. 42(10), 2528-2530 (2006).

[5] Q. Guo, L. Li, Y.-T. Hsia, and M.S. Jhon, ?Stability Analysis of Ultrathin Lubricant Films via Surface Energy Measurements and Molecular Dynamics Simulation,? J. Appl. Phys. 97, 10P302 (2005).

[6] X. Ma, C.L. Bauer, M.S. Jhon, J. Gui, and B. Marchon, "Monte Carlo Simulations of Liquid Spreading on a Solid Surface: Effect of End-group Functionality," Phys. Rev. E, 60, 5795 (1999).