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Stuart Rice is a Frank P. Hixon Distinguished Service Professor in the James Franck Institute and the Department of Chemistry at the University of Chicago.
MYUNG S. JHON
Department of Chemical Engineering and Data Storage Systems Center, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.
CONTENTS
I. Introduction II. Experimentation and Qualitative Analysis A. Scanning Microellipsometry B. Interpretation of L-t plot and D from Phenomenological Transport Model C. Rheological Measurement D. Thermodynamic and Qualitative Description III. Simulation A. SRS Model B. Monte Carlo Simulation with Bead-Spring Model C. Molecular Dynamics Simulation IV. Conclusion Appendix A.1. Background for Hard-Disk Drive (HDD) A.2. Calculation of D(h) from Hydrodynamic Model Acknowledgments References
This chapter presents fundamental scientific tools as well as potential applications relevant to the emerging field of nanotechnology. In particular, understanding the behavior of molecularly thin lubricant films is essential for achieving durability and reliability in nanoscale devices, and the experimentation and theory for the physicochemical properties of ultrathin perfluoropolyether (PFPE) films are reviewed. A method for extracting spreading properties from the scanning microellipsometry (SME) for various PFPE/solid surface pairs and the rheological characterization of PFPEs are examined at length. The interrelationships among SME spreading profiles, surface energy, rheology, and tribology, are discussed as well. Phenomenological theories, including stability analysis and microscale mass transfer, are introduced to interpret ultrathin PFPE film nanostructures qualitatively. In addition, rigorous simulation tools, including a lattice-based simple reactive sphere model, the off-lattice bead-spring Monte Carlo method, and molecular dynamics method, are examined. These tools may accurately describe the static and dynamic behaviors of PFPE films consistent with experimental findings and thus will be suitable for describing the fundamental mechanisms of film dewetting and rupture due to instability arising from nanoscale temperature and pressure inhomogeneities. Nanotribological applications, such as finding an optimal disk lubricant based on a molecule-level interaction of the lubricant with solid surfaces, will be explored.
I. INTRODUCTION
Nanoscale confined polymers are important for their potential industrial applications. The functionalities of polymer chain and solid surfaces are key control factors in determining the material designs for these applications. A fluid confined in a nanoscale system will dramatically alter its structural and dynamic properties. Because of broad technological interest, numerous studies on nanoscale confined fluids have been investigated, both theoretically and experimentally by scientists and engineers from a variety of backgrounds, including data storage, synthetic catalysis, polymer synthesis and physics, tribology, robotics, and medicine. The behavior of materials having constituents with dimensions on the nanometer scale is remarkably different from the behavior in bulk state, which has led to a new paradigm that we now refer to as nanotechnology.
Molecularly thin lubricant film is an important application of nanoscale confined polymeric fluids, and is the focus of this chapter. Ultrathin lubricant films are necessary in high-density data storage to increase the reliability and performance of hard-disk drive (HDD) systems. Spinoff and intermittent contact between the slider (or head) and the lubricated disk [ultrathin perfluoropolyether (PFPE) films are applied to the disk's carbon-overcoated surface, as shown in Fig. 1.1] cause loss and reflow of the lubricant film. The relevant HDD technology is summarized briefly in the end-of-chapter Appendix Section A.I, which provides an overview of how certain information technology devices are controlled by nanoscale chemistry.
The lubricant dynamics can alter the nanoscale aerodynamics of the slider. Conversely, the lubricant morphology and dynamics may be altered because of the presence of the slider. For these types of applications, a molecule-level understanding of the lubricant interaction with nanoscale airbearing and solid surfaces is critical. The HDD industry must cope with problems of lubricant film uniformity, roughness, durability, and stability in order to achieve its goal of increasing areal density.
The commercially available PFPE Z and Zdol (Montedison Co. products) are random copolymers with the linear backbone chain structure
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where X (endgroup) is C[F.sub.3] in PFPE Z and C[F.sub.2]C[H.sub.2]OH in PFPE Zdol. Note that Zdol has hydroxyl groups at both chain ends, which exhibit moderate interactions with solid surfaces, e.g., silica and carbon.
In addition, we examined PFPE ZdolTX with "bulky" endgroups as a potential lubricant, which is shown below:
X = C[F.sub.2]C[H.sub.2]-[(OC[H.sub.2]C[H.sub.2]).sub.1.5]-OH
The structures of PFPE Z, Zdol, and ZdolTX are shown in Figure 1.2. Other PFPEs that have been investigated include Ztetraol and AM2001; Xs are as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The use of additives, such as X1-P, may enhance the reliability of an HDD.
Scientists and engineers working in the information storage industries (e.g., Seagate, Hitachi, and Maxtor) have conducted numerous studies on PFPEs and their thin-film properties. Several academic institutions in the United States [University of California (Berkeley, Computer Mechanics Laboratory; San Diego, Center for Magnetic Recording Research), Ohio State University (Computer Microtribology and Contamination Laboratory), and Carnegie Mellon University (Data Storage Systems Center)] have been actively investigating the role of lubricants and their applications to data storage systems. The Data Storage Institute in Singapore, the largest such institute outside the United States, is involved in nanotribology research relevant to data storage as well. However, despite the plethora of research topics, we will focus only on fundamental scientific issues and our own findings regarding to data storage applications in this review. We will discuss the details of the PFPE experiments, qualitative analysis, and full-scale simulation. Although we will concentrate on selected highlights from our research, other topics will be touched on briefly.
Although not discussed in detail in this chapter, the scientific tools we explored and developed may be applicable to other areas of nanotechnology, such as nanocomposites. The nanocomposites have emerged as a new class of materials during the 1990s. For example, confined polymers solidify at temperatures well above the glass transition temperature as the intercalation rate slows down due to the increased affinity between the polymers and inorganic plate surface. It has been suggested that the timescale of the intercalation process is relatively insensitive to the molecular weight of the polymer when compared to the diffusion coefficient in the confined slit. Various types of nanocomposites have been synthesized and characterized by our research group. In addition to the well-known conventional composite (blend system), these nanocomposites can be classified into two distinct structures: intercalated and exfoliated (Fig. 1.3). Specific interactions through modified functional groups on polymer chains, tethered surface modifiers, and silicate surfaces play important roles in determining the molecular architecture for nanocomposites.
Using a variety of commercial and well-characterized polymers, intercalation has led to a wide variety of nanophase hybrids, many of which had not been previously synthesized using the traditional intercalation approaches. The intercalated nanocomposites are composed of macromolecules that are confined on a lengthscale that is small in comparison to the unperturbed molecular dimensions in a bulk state. The energetic cost of perturbing chains is compensated by the topological "entanglement" constraints imposed on the chains.
Thermal and mechanical properties have been drastically improved by nanocomposites dispersed with inorganic clays in a polymer matrix, which is characterized by nanometer lengthscale domains. These nanocomposite systems can be similarly examined by the methodology reported in this chapter.
Section A.1 of the Appendix discusses the background for the hard-disk drive (see also Figs. 1.4 and 1.5).
II. EXPERIMENTATION AND QUALITATIVE ANALYSIS
In this section, we will study spreading profiles measured from scanning microellipsometry (SME) and its relationship to various experiments, especially rheology, surface energy, and tribology. Phenomenological theory will be developed to interpret the various experiments as well as interrelation among experiments. Rheology of polymer melts and solutions and stability analysis based on thermodynamics will be studied at length as well.
Section A.2 of the Appendix discusses calculation of the film-thickness-dependent diffusion coefficient from a hydrodynamic model.
A. Scanning Microellipsometry
Figure 1.2 illustrates the various PFPEs. To demonstrate the essence of the spreading phenomena, we examined the "thought experiments" for different lubricant-surface and lubricant-lubricant interactions. This is sketched in Figure 1.6. O'Connor et al. were the first to systematically carry out spreading experiments using SME to monitor monodisperse PFPE films on silica as they spread with time. Later, Ma et al. reproduced and carefully examined these results for various carbon surfaces. Novotny, in actuality, pioneered the investigation of PFPEs, although his work mainly dealt with polydisperse PFPE samples. Our coworkers carefully examined and extended the earlier work of Novotny by investigating the spreading of monodisperse PFPEs ([M.sub.w]/[M.sub.n] < 1:1, where, [M.sub.n] and [M.sub.w] are number average and weight average molecular weight, respectively) on silica and various carbon surfaces in a controlled temperature and humidity environment.
In the experiments of O'Connor et al., monodisperse fractions of Z and Zdol, which were fractionated via supercritical fluid extraction in C[O.sub.2], were dip-coated onto the surface of silicon wafers. Film thickness was controlled by altering the PFPE concentration and draw rate as shown in Figure 1.7. For example, a draw rate of 6 mm/s with a PFPE concentration of 2 g/L generated a 50- thin film. An SME apparatus (its components are shown in Fig. 1.8) was used to measure the thickness of the film as it spread with time. The coated wafer was placed on a pedestal-like plate, housed in an environmental chamber with slits for passage of the incident and reflected beams. The chamber was mounted on a stage, which translated the sample across the beam area, and the thickness profile measurements were performed under a controlled temperature and humidity environment. The spreading profile obtained from SME is highly dependent on the PFPE-surface interactions, and provides a fingerprint for each pairing.
Typical SME thickness profiles for monodisperse Z and Zdol, as analyzed by O'Connor et al., are shown in Figures 1.9(a) and 1.9(b). As the film spreads with time, the spreading front travels along the surface of the silicon wafers. A sharp "spike" for the Z profile in Figure 1.9(a) was observed to decay over time. The spreading of Zdol exhibits a characteristic shoulder with a height on the order of the radius of gyration for the PFPE molecules, and the PFPE molecules separate from the initial film layer at a sharp boundary. In addition, Zdol appears to experience partial "dewetting" as indicated by the rough appearance of the SME scan beyond 2 mm [Fig. 1.9(b)]. This dewetting phenomenon (investigated for "mogul" dynamics of nanoscale thin lubricant films) could become very important for airbearing design.
Similarly, Figures 1.10(a) and 1.10(b) represent Z and Zdol spreading experiments on amorphous carbon disks performed by Ma et al. a few years after the observations made by O'Connor et al. Again, the Z front (unlike O'Connor et al., they used polydisperse sample) traveled along the surface, gradually decreasing in height, and the Zdol profile showed a characteristic shoulder or layering structure. However, mass buildup for Z was not observed, and dewetting characteristics for Zdol were somewhat suppressed. Although the main features are similar, the major differences between the profiles in Figures 1.9 and 1.10 are the accumulation of mass at the leading edge of the profile shown in Figure 1.9(a) and also the severe dewetting characteristic shown in Figure 1.9(b). These phenomena clearly demonstrate the relevance of surface-energy-driven flow effects at nanometer-scale spreading processes, and could become important in establishing the design criteria for nanodevices or sensors. Figure 1.11 shows experimentation performed by Ma et al. for various carbon surfaces (amorphous/hydrogenated/nitrogenated), illustrating the fingerprint for the various surface/PFPE molecular coupling. Note that Cazabat et al. initially found a layered structure for polydimethylsiloxane (PDMS, without polar endgroups) in non-HDD applications and the spreading behavior of aqueous media containing a variety of nonionic surfactants has been investigated.
The spontaneous spreading of liquid films on solid surfaces described above has gained a considerable attention. We examined the thickness-dependent diffusion coefficient D(h), extracted from the experimental SME via two methods. The first method utilizes the spreading data at constant height (isoheight), while the second method utilizes the entire spreading profile. The first method does not assume spreading is a diffusion process, whereas the second method does. The length L, along which the leading edge of the advancing lubricant front traveled, is defined as the difference between the initial position of the leading edge and its position in each of the subsequent profiles. To determine the spreading rate, L and the corresponding times t obtained from the profiles [Fig. 1.9] are plotted in Figure 1.12. The two piecewise straight lines in the log-log plot fit the data for the entire range of t (i.e., L [varies] [t.sup.[alpha]]); that is, [alpha] [congruent to] 1 for short times (regime I), and after a gradual transition, [alpha] [congruent to] 1/2 (regime II; diffusion region). Therefore, the surface diffusion coefficient D is estimated from the data in regime II (L [varies] [t.sup.1/2]) using the relationship D = [L.sup.2]/t. We developed a second method called the Boltzmann-Matano interface method, which is more accurate for the purely diffusive process. Ma et al. successfully employed this method as the spreading profiles they measured exhibit neither a severe mass buildup at the front nor dewetting. Because the distance of the migration of the film front is very small compared to the length of the boundary, the spreading can be described by the standard non-Fickian diffusion equation
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1)
where [nabla] is the "del" (nabla) operator and h(x, t) is the film thickness.
One can extract the diffusion coefficient from the Boltzmann-Matano technique (1D analysis):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)
See Figure 1.13 for a schematic representation of h and the coordinates x and z.
(Continues...)
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