April_AMP_Digital

A D V A N C E D M A T E R I A L S & P R O C E S S E S | A P R I L 2 0 2 0 2 0 the terminal boundaries in that direc- tion. It is useful to normalize the re- sistance to the unitized engineering variable known as surface resistivity (ρ s ) described in Equation (6) [10] . Some per- foration patterns will generate values of ρ s that differ with orientation. Equa- tion (7) describes the surface resistivity ρ sw in the direction of W M , and is derived from the global resistance R W and Equa- tion (6). ρ s = R s (W s /L s ) (Eq 6) ρ sw = R W (L M /W M ) (Eq 7) ρ sL = R L (W M /L M ) (Eq 8) Define the boundary conditions for terminal and ground in the direction of L M (see Fig. 7) and execute the anal- ysis to determine the global resistance R L in the direction of L M . Equation (8) de- scribes the surface resistivity ρ sL in the direction of L M and is derived from the global resistance R L and equation (6). EXAMPLE A foraminous copper foil conduc- tor was designed in accord with the parameters described above to have hexagonal shaped holes with a typi- cal length of 1.50 mm (approximate- ly 0.0590 in.) and a typical spacing between adjacent hexagonal shapes of 1.88 mm (0.0741 inch). The multi-cell model size L M = 31.0267 mm (1.221 in.) and W M = 15.6734 mm (0.6171 in.) was selected to include 7x3.5 unitary cells. For 12 µm (0.47 mils) conductor thick- ness, the predicted performance was: ρ sw = 2.8 mΩ/square ρ sL = 2.8 mΩ/square Basis weight = 71 g/m 2 CONDUCTOR FABRICATION A foraminous copper foil was prepared using processes described here. The surface of a thick copper foil was immersed in a persulfate and sul- furic acid etch, to remove surface ox- ides and contaminants, and then rinsed with deionized water. This copper foil was then coated in selected regions with a masking agent. 3M Scotch-Weld Epoxy Adhesive DP100 Plus was used as a quick setting masking agent, to create a patterned surface having hexagonal patterned shapes (feature 104 in Fig. 8) spaced in an hexagonal close-packed arrangement (feature 102). The copper foil was then immersed in a solution of dilute hydrogen peroxide for a peri- od of two minutes and rinsed in deion- ized water. The exposed surface of this copper foil was then treated and plated as follows. Solutionswere created for the plat- ing process. A one-liter aqueous copper plating solution was prepared by mix- ing deionized water 60% by volume, 74 g (2.6 oz) copper sulfate pentahy- drate, and sulfuric acid. A one-liter aqu- eous tin plating solution was prepared by filtering 1 L of tin sulfate through a 1 µm polypropylene filter for 12 h. The copper foil was electroplated with tin by immersing in the tin plating solution at a current density of 12 A/ft 2 for approximately 40 s. The copper foil was then immersed in the copper plat- ing solution for approximately 77 min. at a current density of 10 A/ft 2 followed by immersion in the tin plating solution at a current density of 12 A/ft 2 for ap- proximately 40 seconds. The plated foil was then gently removed from the cop- per substrate surface, resulting in a deli- cately thin conductor having hexagonal perforations. MEASUREMENTS Using a microscope and refer- ring to Fig. 8, each side of the hexag- onal shapes had a typical length of 1.47 mm (0.0577 in.), with a typical spacing between adjacent hexagonal shapes of 1.88 mm (0.0741 in.). The surface resistivity ρ s of the foil was determined from measurements of R W and R L determined per ASTM D4496 as described above using orientations shown in Fig. 5. ρ sw = 2.7 mΩ/square ρ sL = 2.7 mΩ/square The thickness was measured with a micrometer to be 12 µm. The basis weight of the resulting foraminous foil was determined per ASTM D3776-96 [11] to be 73 g/m 2 . All measurements were within 4% of the predicted design values. SUMMARY Attachment of expanded foil to exterior surfaces is a popular choice as a lightning protection conductor in applications such as airplanes, wind generators, and automobiles. The re- sulting form is largely limited to a foil with a foraminous pattern of mar- quise-shaped holes in a hexagonal close-packed pattern. When the shape of the conductor is unconstrained by the fabrication process, design tools can be used to predict the performance of the resulting foil and to optimize the shape of perforations and their arrange- ment to match more closely the desired properties in any direction. Such a con- ductor can provide conductive paths in any desired orientation to manage the electric fields as current moves from at- tachment site to attachment site with optimized weight. Additionally, one can imagine such a construction could be used to enhance RF shielding effects of the skin over a broad frequency spec- trum. A design for conductivity perfor- mance was demonstrated here. Designs to minimize damage at the strike sight or provide enhanced conformability to contoured surfaces are subjects for fu- ture works. ~AM&P Acknowledgement This article was adapted from a paper originally published in the Inter- national Conference on Lightning and Static Electricity 2019. For more information: Larry S. Hebert, lead research specialist, 3M Compa- ny, 3M Center, St, Paul, MN 55144, lshe- bert@mmm.com . References 1. R.B. Greegor, J.D. Morgan, Q.N. Le, and P.K. Ackerman, “Finite Element Fig. 8 — A hexagonal pattern shape.