P. Randall Schunk

Rapid prototyping of patterned functional nanostructures

Living systems exhibit form and function on multiple length scales and at multiple locations. In order to mimic such natural structures, it is necessary to develop efficient strategies for assembling hierarchical materials. Conventional photolithography, although ubiquitous in the fabrication of microelectronics and microelectromechanical systems, is impractical for defining feature sizes below 0.1 micrometres and poorly suited to pattern chemical functionality. Recently, so-called ‘soft’ lithographic approaches have been combined with surfactant and particulate templating procedures to create materials with multiple levels of structural order. But the materials thus formed have been limited primarily to oxides with no specific functionality, and the associated processing times have ranged from hours to days. Here, using a self-assembling ‘ink’, we combine silica–surfactant self-assembly with three rapid printing procedures—pen lithography, ink-jet printing, and dip-coating of patterned self-assembled monolayers—to form functional, hierarchically organized structures in seconds. The rapid-prototyping procedures we describe are simple, employ readily available equipment, and provide a link between computer-aided design and self-assembled nanostructures. We expect that the ability to form arbitrary functional designs on arbitrary surfaces will be of practical importance for directly writing sensor arrays and fluidic or photonic systems.

A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion

Computational fluid mechanics techniques for examining free surface problems in two-dimensional form are now well established. Extending these methods to three dimensions requires a reconsideration of some of the difficult issues from two-dimensional problems as well as developing new formulations to handle added geometric complexity. This paper presents a new finite element formulation for handling three-dimensional free surface problems with a boundary-fitted mesh and full Newton iteration, which solves for velocity, pressure, and mesh variables simultaneously. A boundary-fitted, pseudo-solid approach is used for moving the mesh, which treats the interior of the mesh as a fictitious elastic solid that deforms in response to boundary motion. To minimize mesh distortion near free boundary under large deformations, the mesh motion equations are rotated into normal and tangential components prior to applying boundary conditions. The Navier–Stokes equations are discretized using a Galerkin–least square/pressure stabilization formulation, which provides good convergence properties with iterative solvers. The result is a method that can track large deformations and rotations of free surface boundaries in three dimensions. The method is applied to two sample problems: solid body rotation of a fluid and extrusion from a nozzle with a rectangular cross-section. The extrusion example exhibits a variety of free surface shapes that arise from changing processing conditions. Copyright

Dynamics of low capillary number interfaces moving through sharp features

The success of any nanoimprint process depends upon its ability to exactly reproduce the template pattern. Thus, complete filling of recessed features in the template is an important issue that is controlled by the dynamics of the flow through these sharp structures. At these small scales, capillary forces are large and must be included in the fluid flow model. The mechanism of interface advancement at low capillary number through sharp rectangular features is useful for understanding how and why features fill or trap air. In this study we present a two-dimensional simulation of this feature filling to capture the details of the process, including the viscous and capillary effects. Fluid is injected into the channel between the template and substrate, where the fluid–air interface soon encounters a rectangular feature with some height greater than the channel gap. As the fluid advances through the channel, the shape of the interface is a circular arc due to the strong capillary forces. The interface maint...

Hierarchically Structured Functional Porous Silica and Composite Produced by Evaporation-Induced Self-Assembly

Abstract Recently so-called soft lithography approaches [Angew. Chem. Int. Ed. 37 (1998) 550] have been combined with surfactant [Adv. Mater. 9 (1997) 811, Nature 390 (1997) 674] and particulate [Science 282 (1998) 2244] templating procedures to create oxides with multiple levels of structural order. But the materials thus formed have been limited primarily to oxides with no specific functionality, and the associated processing times have ranged from hours to days. Using self-assembling inks we have combined evaporation-induced (silica/surfactant) self-assembly [Adv. Mater. 11 (1999) 579] with rapid prototyping techniques like micro-pen lithography [Science 283 (1999) 661, Mat. Res. Soc. Symp. Proc. 542 (1999) 159], ink-jet printing [Adv. Mater. 11 (1999) 734, Mat. Sci. Eng. C5 (1998) 289], and dip coating on micro-contact printed substrates to form hierarchically organized structures in seconds. By co-condensation of tetrafunctional silanes (Si(OR) 4 ) with tri-functional organosilanes ((RO) 3 SiR ′ ) [Chem. Commun. (1999) 1367, Chem. Commun. (1997) 1769, J. Am. Chem. Soc. 119 (1997) 4090] or bridged silsesquioxanes (RO) 3 Si–R ′ –Si(OR) 3 ) or by inclusion of organic additives, we have selectively derivatized the silica framework with functional R ′ ligands or molecules. The rapid-prototyping procedures we describe are simple, employ readily available equipment, and provide a link between computer-aided design and self-assembled functional nanostructures. We expect that the ability to form arbitrary functional designs on arbitrary surfaces will be of practical importance for directly writing sensor arrays and fluidic or photonic systems.

Free-Meniscus Coating Processes

When faced with depositing a liquid film on a surface, laboratory scientists usually rely on free coating by withdrawal or drainage, or so-called free-meniscus coating. Simplistic and inexpensive, these techniques abound in the research and development of materials that can be deposited in the liquid state. What has come to be known as dip coating (Deryagin and Levi 1964; Ruschak 1976; Scriven 1988), viscous lifting (Van Rossum 1958), or drag-out (Landau and Levich 1942) begins with immersing a substrate in a vessel filled with liquid. Withdrawal of the substrate from the liquid, if managed properly, can result in a thin coherent liquid film, as shown in Fig. 13.1b. Alternatively, the liquid in the vessel can be drained around the substrate. This technique is often referred to as coating-by-drainage (Jeffreys 1930; Van Rossum 1958; Groenveld 1971) and is diagrammed in Fig. 13.1c. Recourse is sometimes taken from dip coating to coating-by-drainage when limited vertical space prevents substrate withdrawal (cf. Ashley and Reed 1984) or when coating small, short substrates to avoid the local thickening obtained when the trailing edge is withdrawn (Schroeder 1969). Although most often dip coating is operated as a batch process, it can be made continuous (Fig. 13.1d) when the substrate is a long, flexible sheet or filament (Deryagin and Levi 1964; Scriven 1988); however, sustaining a continuous coating process requires the addition of make-up liquid to the vessel. In any case, the physics of batch dip coating, continuous dip coating, and coating-by-drainage are essentially the same, differing only in the frame of reference in which the flat part of the meniscus is stationary.

Sol—gel derived ceramic films — fundamentals and applications

Sol-gel processing begins with a colloidal dispersion, or sol, of particles or polymers in a liquid. Through subsequent chemical cross-linking, electrostatic destabilization, evaporation or some combination thereof, the fluid sol may be transformed into a rigid gel, which is a substance containing a continuous solid skeleton enclosing a continuous liquid phase. This sol-to-gel transition allows the solid phase to be shaped into films, fibers, microspheres or monoliths. Of these various forms, amorphous (or partially crystalline) thin films represent the earliest commercial application of sol-gel technology [1]. Thin films (normally less than 1 μm in thickness) use little in the way of raw materials and may be processed without cracking, overcoming the major disadvantage of sol-gel processing of bulk materials. Early applications of sol-gel coatings as optical films were reviewed by Schroeder [2]. Since then, many new uses of sol-gel films have appeared in electronic, protective, membrane and sensor applications [3–15]. Most often the as-deposited films are amorphous, but depending on composition and thermal history, they may subsequently crystallize: ferroelectric PLZT (lead lanthanum zirconate titanate) and nonlinear optic LiNbO3 are excellent examples of crystalline films derived from amorphous precursors [16–18].

Surfactant Effects in Coating Processes

Free surfaces and laminar viscous flow are the features common to all coating flows which are susceptible to the effects of surfactant additives. Surfactants can change drastically the interfacial physics and chemistry of aqueous solution — and more rarely organic solutions — because they preferentially concentrate, or adsorb, at interfaces. The surfactant concentration there can be orders of magnitude larger than in the bulk liquid, depressing surface tension far below that of the solvent. If the liquid flows in such a way that fluid elements moving along the surface undergo rapid compression or expansion (area change), then the surface composition changes. If the surface deformation is not everywhere the same, neither is the surface concentration: there are concentration gradients. Concentration gradients make surface tension gradients. The consequence is in the balance of forces at the interface: the depression of capillary forces and the induction of surface tension gradients can stabilize the flow, lead to large changes in interfacial shape, and sometimes induce unsteady flow.

Iterative Solvers and Preconditioners for Fully-Coupled Finite Element Formulations of Incompressible Fluid Mechanics and Related Transport Problems

Finite element discretization of fully-coupled, incompressible flow problems with the classic mixed velocity-pressure interpolation produces matrix systems that render the best and most robust iterative solvers and preconditioners ineffective. The indefinite nature of the discretized continuity equation is the root cause and is one reason for the advancement of pressure penalty formulations, least-squares pressure stabilization techniques, and pressure projection methods. These alternatives have served as admirable expedients and have enabled routine use of iterative matrix solution techniques; but all remain plagued by exceedingly slow convergence in the corresponding nonlinear problem, lack of robustness, or limited range of accuracy. The purpose of this paper is to revisit matrix systems produced by this old mixed velocity-pressure formulation with two approaches: (1) deploying well-established tools consisting of matrix system reordering, GMRES, and ILU preconditioning on modern architectures with substantial distributed or shared memory, and (2) tuning the preconditioner by managing the condition number using knowledge of the physical causes leading to the large condition number. Results obtained thus far using these simple techniques are very encouraging when measured against the reliability (not efficiency) of a direct matrix solver. Here we demonstrate routine solution for an incompressible flow problem using the Galerkin finite element method, Newton-Raphson iteration, and the robust and accurate LBB element. We also critique via an historical survey the limitations of pressure-stabilization strategies and all other commonly used alternatives to the mixed formulation for acceleration of iterative solver convergence. The performance of the new iterative solver approaches on other classes of problems, including fluid-structural interaction, multi-mode viscoelasticity, and free surface flow is also demonstrated.

A computational model for doctoring fluid films in gravure printing

The wiping, or doctoring, process in gravure printing presents a fundamental barrier to resolving the micron-sized features desired in printed electronics applications. This barrier starts with the residual fluid film left behind after wiping, and its importance grows as feature sizes are reduced, especially as the feature size approaches the thickness of the residual fluid film. In this work, various mechanical complexities are considered in a computational model developed to predict the residual fluid film thickness. Lubrication models alone are inadequate, and deformation of the doctor blade body together with elastohydrodynamic lubrication must be considered to make the model predictive of experimental trends. Moreover, model results demonstrate that the particular form of the wetted region of the blade has a significant impact on the models ability to reproduce experimental measurements.

Transformation of a close-packed Au nanoparticle/polymer monolayer into a large area array of oriented Au nanowires via E-beam promoted uniaxial deformation and room temperature sintering.

Transformation of 2D Au nanoparticle (NP) arrays into large scale, ordered, and oriented nanorod/nanowire arrays supported on a transferrable polymer film has been accomplished. E-beam irradiation followed by room temperature aging of a suspended Au NP/polymethylmethacrylate (PMMA) polymer close packed monolayer results in one-dimensional nanoparticle aggregation, reorientation, and sintering into a high density array of oriented Au nanowires with coherent single-crystal-like interfaces. Molecular dynamics simulations of alkane-thiol capped Au NPs, interacting through the Vincent potential and undergoing 2D Poisson compression, account semiquantitatively for the qualitative features of the transformation. This fabrication approach should be extendable to directing 1D aggregation of highly anisotropic nanostructures in arbitrary NP systems.