Capillary Kinetics of Thin Polymer Films in Permeable Microcavities
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1022-II01-02
Capillary Kinetics of Thin Polymer Films in Permeable Microcavities Kahp Y Suh School of Mechanical and Aerospace Engineering, Seoul National University, San 56-1, SillimDong, Kwanak-Gu, Seoul, 151-742, Korea, Republic of
ABSTRACT We present a Poiseuille model that can explain the rate of capillary rise of thin polymer films in permeable microcavities. In comparison to the traditional Poiseuille formulation, two unique features of the system were considered: the permeable nature of the enclosure and the effect of thin polymer films that are confined to the substrate. The model predicts that the rate is inversely proportional to the channel width, contrary to what the original Poiseuille model predicts, and it is proportional to the initial film thickness, which the original model cannot account for. The modified model is in satisfactory agreement with experimental data.
INTRODUCTION Capillarity is involved in many practical systems such as wetting and repellency of woven fibers, paper products, and porous solids, wicking, and cleaning action in detergent baths. Polymer melt can be regarded as a Newtonian fluid and the no-slip boundary condition be applied if the shear rate is sufficiently small. A typical example is capillary force lithography (CFL), which has recently been developed for patterning polymers above their glass transition temperatures (Suh, et al., 2001). When a patterned PDMS mold is placed on a polymer film spin-coated onto a substrate and heated above the glass transition temperature, capillarity forces the polymer melt into the void of the channel. In contrast to the ìforcedî capillary flow in the conventional extrusion process, the flow in this case is ìspontaneousî without any external force. In this spontaneous flow, the rate of capillary rise is very small due to the high viscosity of polymer melt and the shear rate is accordingly small. A similar situation can be found in high temperature nanoimprint lithography (NIL) if a negative mold is used (Scheer, et al., 1998). For a smooth, uniform (laminar) flow of a fluid in a narrow cylindrical tube, which is the classical capillary system, the Poiseuille equation can be used to relate the volumetric flow rate to various characteristics of the fluid and the capillary system. The volumetric flow rate, dV/dt, is given by dV / dt = πr 4 P / 8ηz
(1)
where r is the radius of the tube, η is the viscosity of the fluid, z is the distance of fluid movement in the tube in time, t, and P is the pressure drop across the distance z. In Eq. (1), the polymer melt is a Newtonian fluid and the no-slip boundary condition is used. In the original
Poiseuille formulation, the pressure drop, P, is replaced by Laplace pressure (= γcosθ/L), which yields dz / dt = Lγ cos θ / 8ηz
(2)
where L is the half channel width, γ is the surface tension of the polymer and θ is the equilibrium contact angle at the three-phase contact line. Our experiments revealed that the original Poiseuille formulation fails when it is applied to the capillary rise of thin polyme
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