ROBUST, REPAIRABLE, HIGH THERMAL CONDUCTANCE HYDROPHOBIC COATINGS

FIELD OF THE INVENTION

The present disclosure relates to hybrid coatings.

BACKGROUND

Surfaces of objects can be modified with coatings to change their liquid wetting properties.

SUMMARY

The invention relates to a hybrid coating that can have superior thermal and chemical properties. The material can be self-healing.

In one aspect, a hybrid coating can include a plurality of structures on a substrate, the plurality of structures creating a void space, and a polymer filling the void space.

In another aspect, a method of altering the properties of a surface can include providing a plurality of structures on a substrate, the plurality of structures creating a void space; and filling the void space with a polymer. In certain circumstances, the method can include healing a defect in the surface. In certain circumstances, the method can include heating the substrate to soften the polymer.

In certain circumstances, the plurality of structures on a substrate can be nanostructures, for example, metal nanostructures or metal oxide nanostructures, on a surface of the substrate.

In certain circumstances, the plurality of structures can form a pattern.

In certain circumstances, the plurality of structures on the substrate have a high thermal conductivity.

In certain circumstances, the plurality of structures can have a height from the substrate. In certain circumstances, the height is slightly larger than a depth of the polymer. In certain circumstances, the polymer does not extend beyond the height. In certain circumstances, the height is slightly smaller than a depth of the polymer, for example, so the polymer extends no more than 500 nm greater than the height.

In certain circumstances, the polymer can be an acrylic polymer, a polyolefin, a hydrophobic polymer, a moderately hydrophilic polymer, a fluorinated polymer, or a siloxane.

In certain circumstances, the polymer can be a low thermal conductivity polymer.

In certain circumstances, the void space can be a porous structure on the substrate.

In certain circumstances, the polymer substantially infuses the porous structure on the substrate.

In certain circumstances, the polymer can include a fluorinated polymer.

In certain circumstances, the substrate can be copper, aluminum or steel.

In certain circumstances, the plurality of structures can be pillars, micronails, nanoblades, parabolic structures, pyramidal structures, triangular structures, pins, walls or channels, cavities, inverse opal structures, or a reverse micronail.

Other aspects, embodiments, and features will be apparent from the following description, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a structure having a heat transfer enhancement compared to robustness of previously developed coatings and polymer infused porous surfaces (PIPS). PIPS enabled the performance. Advantages of PIPS can include enhanced thermal conductivity, improved polymer adhesion, and self-healing via heating. The predominately polymer surface can be hydrophobic and corrosion resistant.

FIG. 2 depicts robustness and performance of surfaces. Heat transfer enhancement compared to filmwise condensation and observed robustness (lifetime) of various hydrophobic surface coatings including lubricant infused surfaces, monolayer promoters, polymers, graphene, and finned and extended surfaces. Coatings that achieve large improvements in performance are thin, limiting heat transfer resistance through but causing the coatings to fail quickly. On the other hand, thick, robust coatings and finned surfaces exhibit minimal performance enhancement. The PIPS introduced in this work achieved both a large enhancement and a long lifetime. (Note that each referenced work may use different condensation conditions, resulting in additional variance in observed enhancement and robustness. All data shown is for condensation of water. Enhancement for other liquids may follow different trends.)

FIG. 3 depicts the history of the development of coatings for enhanced condensation heat transfer.

FIG. 4 depicts poor robustness of thin polymer coatings.

FIGS. 5A-5D depicts fabrication of polymer infused porous surfaces. FIG. 5A shows a top view scanning electron microscope images of copper oxide nanoblades and copper nanowires used in this study. FIG. 5B shows a schematic of fabrication process for PIPS. First, nanostructures were grown directly on the condenser surface. Next, the polymer was infused until the nanostructure was completely filled without covering the surface with additional polymer to prevent additional resistance to heat transfer. FIG. 5C shows a top view scanning electron microscope images of filling copper oxide nanostructures at different stages. Filling was stopped when the polymer completely filled the structure, but had not yet formed a layer on top of the nanostructure. FIG. 5D shows atomic force microscope images as the nanostructure was infused. The final surface had very small roughness, resulting in a smooth, hydrophobic surface (note the relatively small vertical scale).

FIGS. 6A-6B depict heat transfer testing of PIPS. FIG. 6A shows a schematic of environmental chamber for heat transfer coefficient and durability testing of PIPS. A pure vapor ambient was maintained at controlled conditions. PIPS were fabricated directly on copper rods cooled by a chiller, inducing condensation on the surface at a controlled heat flux. A viewport allowed imaging of the surface. FIG. 6B shows a measured condensation heat transfer coefficient. PIPS achieved performance similar to other state of the art coatings for dropwise condensation. However, due to the increased thermal conductivity, performance was not significantly reduced as coating thickness of PIPS with copper nanowires is increased, providing design flexibility. Compared to similar thicknesses of Teflon AF without embedded nanostructures, performance was significantly higher.

FIG. 7A-7C depict durability of polymer infused porous surfaces. FIG. 7A shows the heat transfer coefficient, HTC, on 20 μm Cu nanowire PIPS, CuO nanoblade PIPS, and 2 μm Teflon AF during continuous condensation of steam. Teflon AF performance degrades within 100 hours, while both PIPS show little to no degradation for 200+ days. FIG. 7B shows the mode of degradation of the Teflon AF surface is delamination of the coating, which can be seen in the image after 6 hours. PIPS, on the other hand, continues to exhibit high-quality dropwise condensation even after 200+ days. FIG. 7C shows the contact angles and contact angle hysteresis of CuO nanoblade PIPS was unchanged after 4800+ hours of testing. Hysteresis on Cu Nanowire PIPS, however, increased by 12 degrees. This was not enough to make an observable change to the dropwise condensation performance in FIGS. 7A and 7B; however, it is expected that continued degradation would decrease performance.

FIGS. 8A-8D depict self-healing of polymer infused porous surfaces. FIG. 8A shows that after 4800+ hours of testing, the contact angle hysteresis on Cu Nanoblade PIPS had increased (top row). However, after self-healing by heating, θa was 111.1 degrees and Or was 101 degrees, reducing hysteresis greatly and returning the surface to its original state before degradation. FIG. 8B, left, shows a Cu Nanoblade PIPS surface damaged by laser ablation. The laser removed polymer from the surface and partially destroyed the nanostructure. However, by heating the surface past the melting point of the polymer, the surface largely self-healed (right). FIG. 8C shows advancing and receding contact angle of a Cu Nanoblade PIPS surface. Advancing angle is the upper bound of the bar, whereas receding is the lower bound. After damage of various types, contact angle hysteresis was significantly increased. However, after healing, the original wetting properties are largely recovered. Scraping, i.e., significant damage to the surface and nanostructure, recovered the least. FIG. 8D shows condensation on damaged PIPS and repaired PIPS for the laser ablated surface. The damaged surface has large droplets due to the large contact angle hysteresis. After repair high quality dropwise condensation is recovered.

FIGS. 9A-9C depicts design of PIPS. FIG. 9A shows a schematic of polymer infused porous surfaces. Structured surfaces (depicted with pillars in the schematic) are infused with polymer (white material in schematic). A portion of the polymer was removed in the schematic to reveal the structured surface with characteristic dimensions height, H, diameter, D, and pitch, L. FIG. 9B shows effective thermal conductivity of the coating (dashed blue line) as well as predicted advancing and receding contact angles (black lines) of the surface. FIG. 9C shows surface area enhancement for a surface with pillars and H=10 μm and different solid fractions, φ, as structure pitch is varied. Structure diameter was also varied to maintain constant solid fraction.

FIG. 10 depicts the effect of variable solid fraction on effective thermal conductivity. Three cases for variable solid fraction along x are considered. Constant solid fraction, such as pillars, linear solid fraction, such as triangular ridges, and parabolic solid fraction, such as cones. For simplicity, the linear and parabolic cases are assumed to go from ϕ=0 at x=0 to ϕ=1 at x=H, whereas the constant solid fraction in this figure is 0.3. The resulting k_eff (x) is shown, and the resulting overall k_eff, i.e., the effective thermal conductivity of the layer assuming it were homogeneous, is calculated and labeled in the figure.

FIG. 11 depicts a COMSOL model of the condenser block with an applied heat flux of ˜100,000 W/m²and a condensation heat transfer coefficient of 120,000 W/m²K. The resulting temperature profile is highly linear, validating this measurement strategy.

FIG. 12 depicts contact angle hysteresis as the surface roughness increases (i.e., nanostructures are exposed due to gradual polymer removal) for a nanostructure solid fraction of 0.4 and 0.05. Due to the larger solid fraction at the surface of Cu Nanowire PIPS, the hysteresis grows more rapidly with removal of the polymer. A primary reason that an increase in the contact angle hysteresis was observed for the Cu Nanowire PIPS and not the CuO Nanoblade PIPS.

FIG. 13 depicts potentiodynamic polarization curves for bare copper and PIPS, measured in 3.5 weight percent NaCl solution. Corrosion rate on PIPS is reduced 2 orders of magnitude.

FIG. 14 depicts contact angle measurement as an image of the custom-built contact angle measurement setup. A syringe added and removed liquid from a droplet on the surface while a camera recorded the contact angle. A light source (not shown) provided illumination of the droplet.

FIG. 15 depicts a surface as described herein.

DETAILED DESCRIPTION OF THE INVENTION

Polymer infused porous surfaces (PIPS) can provide robust, thermally conductive, self-healing coatings for dropwise condensation. The surface includes a plurality of nanostructures infiltrated by a polymer. The material is a hybrid material, meaning it is a composite formed form at least two materials.

Hydrophobic coatings with low thermal resistance promise a significant enhancement in condensation heat transfer performance by promoting dropwise condensation in applications including power generation, water treatment, and thermal management of high-performance electronics. However, coatings with adequate robustness have remained elusive due to a combination of the lack of proper adhesion to substrates and the typically low thermal conductivity of hydrophobic materials necessitating very-thin coatings to achieve high thermal conductance. In this work, both of these issues are addressed simultaneously by infusing hydrophobic polymers into nanostructured surfaces, creating long-lasting condensation heat transfer enhancement via dropwise condensation by infusing a hydrophobic polymer, Teflon AF, into a porous nanostructured surface. This polymer infused porous surface (PIPS) uses the large surface area of the nanostructures to enhance polymer adhesion, while the nanostructures form a percolated network of high thermal conductivity material throughout the polymer and greatly enhance the thermal conductance of the composite. The approach has demonstrated over 700% enhancement in the condensation of steam compared to an uncoated surface. This performance enhancement was sustained for more than 200 days without significant degradation, offering a level of durability appropriate for industrial applications. Furthermore, it is shown that the surfaces are self-repairing upon raising the temperature past the melting point of the polymer, allowing recovery of hydrophobicity.

Referring to FIG. 15, a hybrid coating 10 on substrate 20 can include a plurality of structures 30 creating a void space 60 and a polymer 65 filling the void space. The surface of the polymer 50 and the surface of the structures 40 form an outer surface of the coating.

The substrate can be a glass, metal, inorganic polymer, semiconductor, a ceramic, an organic polymer or other structure. For example, the substrate can be copper, aluminum, steel, or silicon. For example, the polymer can include an acrylic polymer, a polyolefin, a hydrophobic polymer, a moderately hydrophilic polymer, a fluorinated polymer, a siloxane, an organic molecule, silicon dioxide, aluminum oxide, or combinations thereof.

The surface can be on a substrate. The substrate can be a glass, metal, inorganic polymer, semiconductor, a ceramic, an organic polymer or other structure. The surface can be coated or uncoated, for example, with a polar coating or an non-polar coating. The coating can be a polymer coating, a coating of organic material, or an inorganic coating. For example, the coating can include an acrylic polymer, a polyolefin, a fluorinated polymer, an organic polymer, a siloxane, an organic molecule, silicon dioxide, aluminum oxide, or combinations thereof.

The structures can be pillars, micronails, nanoblades, parabolic structures, pyramidal structures, triangular structures, pins, walls or channels, cavities, inverse opal structures, or a reverse micronail. The plurality of structures can be spaced periodically, for example, in square or hexagonal patterns. The structures can be microstructures or nanostructures. The structures can be patterned in a random, periodic or aperiodic manner. The plurality of structures can form a porous surface. The structures form a void space on the surface.

The plurality of structures can have a height from the substrate and the height is slightly larger than a depth of the polymer, the polymer does not extend beyond the height, or the height can be slightly smaller than a depth of the polymer. The structures can have dimensions of 0.1 to 500 microns, for example, 0.2 to 400 microns, 0.3 to 300 microns or 0.5 to 100 microns. The spacing between the microstructures can be between 0.01 to 1000 microns, for example, 0.02 to 500 microns, 0.03 to 250 microns, 0.04 to 100 microns, or 0.05 to 10 microns. The spacing can be 0.1 to 5 microns. Referring to FIG. 9A, without limiting to pillar structures, the structure can have a width, D, 0.01 to 1000 microns, for example, 0.02 to 500 microns, 0.03 to 250 microns, 0.04 to 100 microns, or 0.05 to 10 microns (e.g., 0.1 to 5 microns), and a height, X, of between 1 to 500 microns, for example, 1 to 400 microns or 10 to 300 microns, for example, between 10 to 200 microns, and a spacing between structures, L, of 0.01 to 1000 microns, for example, 0.02 to 500 microns, 0.03 to 250 microns, 0.04 to 100 microns, or 0.05 to 10 microns (e.g., 0.1 to 5 microns). The height of the polymer and the height of the structure can be substantially equal.

The hybrid coating can be self-healing. The polymer can be heated to a softening point or melting point to heal or reform the surface.

A method of altering the properties of a surface can include providing a plurality of structures on a substrate, the plurality of structures creating a void space; and filling the void space with a polymer. The structures can be provided by direct growth, indentation, machining or other mechanical means, or attachment/bonding to form the structures on the surface. A polymer can infuse the void space. For example, the polymer can be applied as a melt to the surface.

The coating can be self-healing. For example, the method can include healing a defect in the surface. Heating the substrate to soften or melt the polymer can heal the polymer portion of the coating, allowing defects to anneal out of the polymer.

Tailoring wetting behavior during condensation can greatly enhance heat transfer performance for applications including power generation, water purification, and thermal management. See, for example, Beer, J. M. High efficiency electric power generation: The environmental role. Progress in Energy and combustion science 33, 107-134 (2007); Glicksman, L. R. & Hunt Jr, A. W. Numerical simulation of dropwise condensation. International journal of heat and mass transfer 15, 2251-2269 (1972); Schilling, H. Improving the Efficiency of Pulverised Coal Fired Power Generating Plant. VGB KraftwerksTechnik (English edition) 73, 564-576 (1993); Humplik, T. et al. Nanostructured materials for water desalination. Nanotechnology 22, 292001 (2011); Andrews, H., Eccles, E., Schofield, W. & Badyal, J. Three-dimensional hierarchical structures for fog harvesting. Langmuir 27, 3798-3802 (2011); Khawaji, A. D., Kutubkhanah, I. K. & Wie, J.-M. Advances in seawater desalination technologies. Desalination 221, 47-69 (2008); Leach, R., Stevens, F., Langford, S. & Dickinson, J. Dropwise condensation: experiments and simulations of nucleation and growth of water drops in a cooling system. Langmuir 22, 8864-8872 (2006); and Peters, T. B. et al. Design of an integrated loop heat pipe air-cooled heat exchanger for high performance electronics. IEEE Transactions on Components, Packaging and Manufacturing Technology 2, 1637-1648 (2012), each of which is incorporated by reference in its entirety. In fact, the majority of electricity in the United States is produced with steam cycle power plants in which the condensation of water plays a critical role. Industrial condensers are typically manufactured from metals that are highly wetting to water, leading to the filmwise mode of condensation in which the condensate forms a thick liquid film of low thermal conductance on the condenser surface and impedes heat transfer. Conversely, upon rendering the surface of a condenser hydrophobic with a low-surface-energy coating, the condensate forms discrete droplets that nucleate, grow, coalesce, and easily shed in the dropwise mode of condensation. See, for example, Rose, J. Dropwise condensation theory and experiment: a review. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 216, 115-128 (2002), which is incorporated by reference in its entirety. Because condensate is removed from the surface more efficiently, heat and mass transfer performance can be improved by an order of magnitude by transitioning from filmwise to dropwise condensation, which consequently improves overall steam cycle efficiency. See, for example, Schilling, H. Improving the Efficiency of Pulverised Coal Fired Power Generating Plant. VGB KraftwerksTechnik (English edition) 73, 564-576 (1993), which is incorporated by reference in its entirety. Stable dropwise condensation can be formed on ultra-smooth hydrophilic surfaces, which if implemented in a PIPS structure as disclosed herein, the structures would be durable than as described in, for example, H. Cha et al., Dropwise condensation on solid hydrophilic surfaces. Sci. Adv. 6 (2020), doi:10.1126/sciadv.aax0746, which is incorporated by reference in its entirety.

Despite the fact that low-surface-energy coatings for condensation enhancement have been explored for nearly a century (FIG. 3), industry continues to rely on filmwise condensation, primarily due to a lack of durable coatings. See, for example, Penniman, A. L. Patents, 1935; Drew, T., Nagle, W. & Smith, W. The conditions for dropwise condensation of steam. AIChE Transactions 31, 605-621 (1935); Nagle, W. u., Bays, G., Blenderman, L. & Drew, T. Heat-transfer coefficients during dropwise condensation of steam. Trans. AIChE 31, 593-621 (1935); Schmidt, E., Schurig, W. & Sellschopp, W. Versuche fiber die Kondensation von Wasserdampf in Film-und Tropfenform. Technische Mechanik and Thermodynamik 1, 53-63 (1930); Fitzpatrick, J., Baum, S. & McAdams, W. Dropwise condensation of steam on vertical tubes. Trans. AIChE 35, 97-107 (1939); Blackman, L., Dewar, M. & Hampson, H. An investigation of compounds promoting the dropwise condensation of steam. Journal of Applied Chemistry 7, 160-171 (1957); McCormick, J. & Westwater, J. Nucleation sites for dropwise condensation. Chemical Engineering Science 20, 1021-1036 (1965); Umur, A. & Griffith, P. Mechanism of dropwise condensation. Journal of heat transfer 87, 275-282 (1965); Kollera, M. & Grigull, U. Über das Abspringen von Tropfen bei der Kondensation von Quecksilber. Wärme-und Stoffübertragung 2, 31-35 (1969); Boreyko, J. B. & Chen, C.-H. Self-propelled dropwise condensate on superhydrophobic surfaces. Physical review letters 103, 184501 (2009); Marto, P., Looney, D., Rose, J. & Wanniarachchi, A. Evaluation of organic coatings for the promotion of dropwise condensation of steam. International Journal of Heat and Mass Transfer 29, 1109-1117 (1986); Holden, K., Wanniarachchi, A., Marto, P., Boone, D. & Rose, J. The use of organic coatings to promote dropwise condensation of steam. Journal of heat transfer 109, 768-774 (1987); Paxson, A. T., YagUe, J. L., Gleason, K. K. & Varanasi, K. K. Stable dropwise condensation for enhancing heat transfer via the initiated chemical vapor deposition (iCVD) of grafted polymer films. Advanced Materials 26, 418-423 (2014); and Preston, D. J., Mafra, D. L., Miljkovic, N., Kong, J. & Wang, E. N. Scalable graphene coatings for enhanced condensation heat transfer. Nano letters 15, 2902-2909 (2015), each of which is incorporated by reference in its entirety. Prior work has focused on developing numerous types of low-surface-energy coatings including monolayer promoters, organic films, lubricant infused surfaces (LIS), and graphene. See, for example, Blackman, L., Dewar, M. & Hampson, H. An investigation of compounds promoting the dropwise condensation of steam. Journal of Applied Chemistry 7, 160-171 (1957); Vemuri, S., Kim, K., Wood, B., Govindaraju, S. & Bell, T. Long term testing for dropwise condensation using self-assembled monolayer coatings of n-octadecyl mercaptan. Applied thermal engineering 26, 421-429 (2006); Das, A., Kilty, H., Marto, P., Andeen, G. & Kumar, A. The use of an organic self-assembled monolayer coating to promote dropwise condensation of steam on horizontal tubes. Journal of heat transfer 122, 278-286 (2000); Chen, L. et al. n-Octadecanethiol self-assembled monolayer coating with microscopic roughness for dropwise condensation of steam. Journal of Thermal Science 18, 160-165 (2009); Love, J. C., Estroff, L. A., Kriebel, J. K., Nuzzo, R. G. & Whitesides, G. M. Self-assembled monolayers of thiolates on metals as a form of nanotechnology. Chemical reviews 105, 1103-1170 (2005); Marto, P., Looney, D., Rose, J. & Wanniarachchi, A. Evaluation of organic coatings for the promotion of dropwise condensation of steam. International Journal of Heat and Mass Transfer 29, 1109-1117 (1986); Holden, K., Wanniarachchi, A., Marto, P., Boone, D. & Rose, J. The use of organic coatings to promote dropwise condensation of steam. Journal of heat transfer 109, 768-774 (1987); Paxson, A. T., Yagüe, J. L., Gleason, K. K. & Varanasi, K. K. Stable dropwise condensation for enhancing heat transfer via the initiated chemical vapor deposition (iCVD) of grafted polymer films. Advanced Materials 26, 418-423 (2014); Ma, X. et al. Influence of processing conditions of polymer film on dropwise condensation heat transfer. International Journal of Heat and Mass Transfer 45, 3405-3411 (2002); Haraguchi, T., Shimada, R., Kumagai, S. & Takeyama, T. The effect of polyvinylidene chloride coating thickness on promotion of dropwise steam condensation. International Journal of Heat and Mass Transfer 34, 3047-3054 (1991); Anand, S., Paxson, A. T., Dhiman, R., Smith, J. D. & Varanasi, K. K. Enhanced condensation on lubricant-impregnated nanotextured surfaces. Acs Nano 6, 10122-10129 (2012); Weisensee, P. B. et al. Condensate droplet size distribution on lubricant-infused surfaces. International Journal of Heat and Mass Transfer 109, 187-199 (2017); Preston, D. J. et al. Heat transfer enhancement during water and hydrocarbon condensation on lubricant infused surfaces. Scientific reports 8, 540 (2018); Xiao, R., Miljkovic, N., Enright, R. & Wang, E. N. Immersion condensation on oil-infused heterogeneous surfaces for enhanced heat transfer. Scientific reports 3, 1988 (2013); and Preston, D. J., Mafra, D. L., Miljkovic, N., Kong, J. & Wang, E. N. Scalable graphene coatings for enhanced condensation heat transfer. Nano letters 15, 2902-2909 (2015), each of which is incorporated by reference in its entirety. Recent work has also focused on combining these coatings with surface structuring to further enhance hydrophobicity and achieve jumping-droplet condensation. See, for example, Boreyko, J. B. & Chen, C.-H. Self-propelled dropwise condensate on superhydrophobic surfaces. Physical review letters 103, 184501 (2009); Miljkovic, N. et al. Jumping-droplet-enhanced condensation on scalable superhydrophobic nanostructured surfaces. Nano letters 13, 179-187 (2012); Enright, R., Miljkovic, N., Al-Obeidi, A., Thompson, C. V. & Wang, E. N. Condensation on superhydrophobic surfaces: the role of local energy barriers and structure length scale. Langmuir 28, 14424-14432 (2012); Miljkovic, N. & Wang, E. N. Condensation heat transfer on superhydrophobic surfaces. MRS bulletin 38, 397-406 (2013); and Enright, R., Miljkovic, N., Dou, N., Nam, Y. & Wang, E. N. Condensation on superhydrophobic copper oxide nanostructures. Journal of heat transfer 135, 091304 (2013), each of which is incorporated by reference in its entirety. However, robust coatings that achieve significant performance enhancement have not yet been demonstrated (FIG. 2). Instead, adequate lifetimes of organic coatings were only achieved when the coating thickness was large (>4 μm), and, due to the low thermal conductivity of the coatings, the thickness of these coatings significantly reduced the performance enhancement. See, for example, Holden, K., Wanniarachchi, A., Marto, P., Boone, D. & Rose, J. The use of organic coatings to promote dropwise condensation of steam. Journal of heat transfer 109, 768-774 (1987), each of which is incorporated by reference in its entirety. Thinner coatings of various types, which achieved significant performance enhancement, failed quickly. Meanwhile, other forms of enhancement without low-surface-energy coatings have focused on increased heat transfer area through the use of extended surfaces, wicking to promote condensate removal, and fluid-repellent surface structuring that relies only on geometric effects. See, for example, Preston, D. J. et al. Gravitationally driven wicking for enhanced condensation heat transfer. Langmuir 34, 4658-4664 (2018); Wanniarachchi, A., Marto, P. & Rose, J. Film condensation of steam on horizontal finned tubes: effect of fin spacing. Journal of heat transfer 108, 960-966 (1986); Wilke, K. L., Preston, D. J., Lu, Z. & Wang, E. N. Toward condensation-resistant omniphobic surfaces. ACS nano 12, 11013-11021 (2018), each of which is incorporated by reference in its entirety. Unfortunately, the heat transfer enhancement demonstrated with these methods has not been as impressive as strategies incorporating low-surface-energy coatings.

An approach to address both the low thermal conductance and poor robustness of hydrophobic coatings simultaneously is demonstrated. A hydrophobic polymer (Teflon AF) was infused into nanostructures grown directly on condenser surfaces. The nanostructures create a large surface area for adhesion and constrain the polymer to the surface, improving durability. Furthermore, because the nanostructures create a percolated network of high thermal conductivity material through the low thermal conductivity polymer, the thermal conductance of the coating is greatly increased. The design and fabrication of these polymer infused porous surfaces (PIPS) is discussed and demonstrate dropwise condensation for more than 200 days with heat transfer performance 5.9-7.5× that of filmwise condensation (FIG. 2). Coatings of this type are self-healing upon raising the temperature of the surface above the polymer melting point, allowing simple recovery of the initial hydrophobicity if degradation or damage does occur.

Results

Design of Polymer Infused Porous Surfaces.

To achieve durable condensation heat transfer enhancement through dropwise condensation with low-surface-energy coatings, multiple design criteria for the proposed polymer infused porous surfaces were considered (see below and FIGS. 9A-9C for greater detail). First, the thermal resistance needs to be sufficiently low as to not impede heat transfer. This resistance scales as H/k, where H is the thickness of the coating and k is the thermal conductivity (FIG. 9B). Therefore, a low resistance was achieved by using the embedded porous structures to enhance thermal conductivity while keeping the overall thickness sufficiently thin. Second, the coating must enable dropwise condensation. Generally, the quality and performance of dropwise condensation is greatest when the advancing contact angle, θ_a, is large (θ_a>90 degrees) and the contact angle hysteresis, i.e., the difference between the advancing contact angle and the receding contact angle, is small (θ_a−θ_r<20 degrees). See, for example, Neumann, A., Abdelmessih, A. & Hameed, A. The role of contact angles and contact angle hysteresis in dropwise condensation heat transfer. International Journal of Heat and Mass Transfer 21, 947-953 (1978), each of which is incorporated by reference in its entirety. The hysteresis is reduced by keeping the solid fraction—in this case, the fraction of nanostructure relative to the polymer—as low as possible. Therefore, the optimal solid fraction can be determined from a balance of increasing effective thermal conductivity and keeping contact angle hysteresis low (FIG. 9B). Finally, coating adhesion must be large enough to prevent delamination of the polymer, which was achieved by utilizing nanostructures with high surface area to constrain and adhere the polymer to the surface (FIG. 9C). See, for example, Awaja, F., Gilbert, M., Kelly, G., Fox, B. & Pigram, P. J. Adhesion of polymers. Progress in polymer science 34, 948-968 (2009), each of which is incorporated by reference in its entirety.

Fabrication of Polymer Infused Porous Surfaces.

Based on the design considerations above, nanostructures were chosen that could be controlled within the blue highlighted rows of Table 2. These nanostructures represent significantly different designs while still promising enhancement, demonstrating the flexibility of PIPS. Specifically, copper oxide nanoblades and copper nanowires (FIG. 5A) were chosen due to the ability to grow them directly on the condenser surfaces with dimensions in the required range (details of fabricated samples in Table 1). See, for example, Enright, R., Miljkovic, N., Dou, N., Nam, Y. & Wang, E. N. Condensation on superhydrophobic copper oxide nanostructures. Journal of heat transfer 135, 091304 (2013); and Wen, R., Xu, S., Ma, X., Lee, Y.-C. & Yang, R. Three-dimensional superhydrophobic nanowire networks for enhancing condensation heat transfer. Joule 2, 269-279 (2018), each of which is incorporated by reference in its entirety. To fabricate PIPS, these nanostructures were grown directly on the condenser surface and then infused with polymer until the entire nanostructure was filled (FIG. 5B). Care was taken not to overfill the nanostructures, given overfilling would create a layer of low-thermal-conductivity polymer on top of the nanostructures, creating additional resistance to heat transfer. As seen in Table 2, only 290 nm of Teflon AF without embedded nanostructures would decrease performance by 10 percent, highlighting the importance of preventing overfilling. The polymer Teflon AF 1600 was chosen for its hydrophobicity and the ease of filling the nanostructure due to its high surface wettability in solution. By spin coating consecutive layers of Teflon AF, the filling was precisely controlled and stopped before overfilling (FIG. 5C). Scanning electron microscope images, water contact angle measurements, and atomic force microscopy were used to determine when filling was complete. After spin coating, the surface was heated above the polymer melting point to ensure proper filling of the nanostructure without voids. This resulted in a predominately Teflon AF surface with very low roughness, ideal for enabling dropwise condensation, as shown in FIG. 5D with atomic force microscope images of a copper oxide surface at the filling stages in FIG. 5C.

TABLE 1

Properties of fabricated surfaces. The geometry and measured advancing

and receding contact angles of all surfaces used in this study.

These geometries were chosen to test a range of designs that were

expected to provide enhancement using standard fabrication methods.

2 μm and 20 μm Teflon AF coatings with no nanostructure were

also fabricated on bare copper as reference. Note the copper surface

had an oxide layer that was not removed before coating.

Nanostructure
Nanostructure/
H
ϕ
θ_a
θ_r

Solid Fraction
Polymer
[μm]
(x = 0)
[deg]
[deg]

—
—/Teflon AF
2
0
107.2
106

—
—/Teflon AF
20
0
106.7
105

Constant
Cu Nanowires/
5
0.4
108
92

Teflon AF

Constant
Cu Nanowires/
20
0.4
105.1
89

Teflon AF

Parabolic
CuO Nanoblades/
1.5
~0
108.2
103.2

Teflon AF

Heat Transfer Coefficient Testing.

The resulting surfaces consisted predominately of Teflon AF. This resulted in a high quality, hydrophobic surface with large advancing contact angle and low contact angle hysteresis (Table 1). These surfaces were tested under conditions typical in a power plant condenser. An environmental chamber (FIG. 6A) was used to control a pure vapor ambient for condensation. Experiments were run at ˜60° C. saturated vapor conditions and a heat flux of 100 kW/m²was applied to the surfaces. All surfaces, including PIPS, were fabricated directly on copper rods connected to a chiller loop, allowing accurate control over the condensation heat flux applied to the surfaces. Thermocouples embedded in the copper rod were used to extrapolate the heat flux as well as the heat transfer coefficient (see below). This chamber allowed for simultaneous visualization of surfaces and monitoring of heat transfer performance during testing.

The heat transfer coefficient (HTC) of dropwise condensation, h_c, on the high thermal conductance PIPS was comparable to that observed in the literature for previously developed thin, non-robust coatings for dropwise condensation (FIG. 6B). The shaded region shows the expected performance of dropwise condensation at the tested conditions using a correlation developed by Rose based on experimental measurements of heat transfer at various temperatures and heat fluxes (133-142 kW/m²-K predicted), while the filmwise performance was measured to be ˜16 kW/m²K on a bare copper condenser, close to the expected performance calculated using Nusselt Film Theory. See, for example, Rose, J. Some aspects of condensation heat transfer theory. International communications in heat and mass transfer 15, 449-473 (1988), each of which is incorporated by reference in its entirety. The model lines show the expected performance including the added thermal resistance of the different PIPS coatings (see below). Because PIPS has enhanced thermal conductance, the overall thickness could be increased significantly without decreasing heat transfer performance, whereas a Teflon AF-only coating significantly reduced performance at a thickness of only 2 micrometers. In fact, PIPS with copper nanowires demonstrated heat transfer performance near that expected of dropwise condensation even at thicknesses up to 20 μm, whereas a Teflon AF only coating this thick had performance worse than filmwise condensation. The observed values for PIPS tended to be less than the expected values, although within the uncertainty. This discrepancy was attributed to two factors: first, the equations used to estimate effective thermal conductivity of PIPS tend to overpredict the true value; second, although care was taken to not overfill the Teflon AF in the nanostructures, any overfilling that does occur would reduce dropwise heat transfer performance due to the additional thermal resistance the overfilling creates.

The 20 μm thick Cu nanowire PIPS, the CuO nanoblade PIPS, and the 2 μm Teflon AF coating, all of which showed enhancement over filmwise condensation, were then tested for robustness by continuously condensing on the surface at ˜60° C. saturated vapor conditions and a heat flux of ˜100 kW/m². To ensure a pure water vapor ambient, vacuum was pulled on the system once per week to remove any buildup of non-condensable gases (SI). The heat transfer coefficient of the 2 μm Teflon AF coating started with a 4.7× enhancement over filmwise condensation, but degradation of performance started within hours (FIG. 7A). This degradation was caused by delamination of the Teflon AF, resulting in a film of water forming in the delaminated regions (FIG. 7B) and ultimately resulting in complete failure within 100 hours, although it is noted there are strategies to moderately improve lifetime before failure for polymer coatings on bare surfaces that were not pursued in this work. See, for example, Wilke, K. Tailoring wetting behavior at extremes, Massachusetts Institute of Technology, (2019), which is incorporated by reference in its entirety. PIPS, however, did not show any significant degradation based both on the heat transfer measurement and the surface imaging after 4800+ hours of testing (FIGS. 7A-7B). After testing the CuO Nanoblade PIPS contact angles and contact angle hysteresis remained unchanged, while hysteresis on the Cu Nanowire PIPS increased from 16.1 degrees to 28.5 degrees (FIG. 7C). This was not due to delamination of the polymer. Rather, this increase in hysteresis was attributed to the larger solid fraction of the Cu Nanowire PIPS resulting in a larger sensitivity to nanostructure becoming exposed as degradation at the surface occurs (see below and FIG. 12). It may also be in part because CuO nanoblade PIPS are more resistant to corrosion than Cu nanowire PIPS (see below and Table 3).

The continuous condensation study demonstrated the increased durability of PIPS, with no degradation observed on CuO nanoblade PIPS and minor degradation of contact angle on Cu Nanowire PIPS with little to no effect on heat transfer performance. However, continued degradation or incidental mechanical damage would be expected to reduce performance. Therefore, it was also demonstrated that, because the surface was prepared using a polymer that can melt, a simple mechanism for self-healing exists. Self-healing surfaces are generally split into two categories: autonomic, which heal automatically when damaged, and non-autonomic, which require an external trigger to heal, such as heat or light. See, for example, Hager, M. D., Greil, P., Leyens, C., van der Zwaag, S. & Schubert, U. S. Self-healing materials. Advanced Materials 22, 5424-5430 (2010); and Blaiszik, B. J. et al. Self-healing polymers and composites. Annual Review of Materials Research 40, 179-211 (2010)), each of which is incorporated by reference in its entirety. PIPS fall into the second category, where applying heat to re-flow the polymer repairs damage to the polymer due to capillary effects reducing surface roughness. By heating the surface to 330° C. for 30 minutes, the contact angle hysteresis on the 20 μm Cu nanowire PIPS is once again reduced, as shown in FIG. 8A. To further demonstrate self-healing, surfaces were intentionally damaged more significantly than what was observed in durability testing. FIG. 8B shows a CuO nanoblade PIPS damaged using laser ablation. The laser, which was used to create a grid of damaged lines on the surface, created roughly 100 μm wide damaged sections where the polymer was largely removed from the embedded nanoblades. However, during self-healing the polymer reflowed and repaired the surface, thereby recovering the original wetting properties. In FIG. 8C, the advancing and receding contact angles of damaged and repaired CuO nanobloade PIPS are shown. The advancing contact angle is the upper bound of the box, whereas the receding contact angle is the lower bound. The original, undamaged surface was hydrophobic with small hysteresis. The surface was then damaged in different ways. Laser ablation, as shown in FIG. 8B, removed much of the polymer but did not completely destroy the underlying nanostructure; scraping using a multiblade cross hatch cutting tool (ISO 2409:2007) destroyed both the polymer, nanostructure, and underlying surface; and chemical damage (achieved here by placing the surface in an oxygen plasma for 3 minutes) removed fluorination (and thus hydrophobicity) at the surface of the coating but left the underlying polymer and structure undamaged. See, for example, Morra, M., Occhiello, E. & Garbassi, F. in High Energy Density Technologies in Materials Science 161-168 (Springer, 1990), which is incorporated by reference in its entirety. After repair, the original contact angles were largely recovered for all types of damage, where the level of physical damage to the surface and nanostructure determined how well the surface could be repaired. Because chemical damage did not destroy the structure at all, the original contact angles were completely recovered, whereas with scraping, which caused significant damage to the surface, the wetting properties were only partially recovered. The recovery of surface wetting properties and dropwise condensation behavior is demonstrated in FIG. 8D. The white lines in FIG. 8D are the grid of laser damage. Due to the large contact angle hysteresis of the damaged surface, droplets on the surface grow large and begin to spread, covering the surface. However, after repair, small, highly mobile droplets and dropwise condensation were once again achieved due to the recovery of original wetting properties.

At the demonstrated heat transfer performance and lifetime of PIPS, the coating enables a regime of surface wetting-based enhancement not previously achieved (FIG. 7A), where adequate lifetimes were demonstrated without sacrificing heat transfer enhancement. This enhancement was achieved by creating polymer infused porous surfaces that address the typical challenges associated with using low-surface-energy coatings. The composite surfaces developed here (FIGS. 5A-5D), consisting of a high-thermal conductivity nanostructure filled with a hydrophobic polymer, create a predominately polymer surface. This approach renders the surface hydrophobic, while the nanostructures embedded within the polymer enhance the thermal conductivity, not only reducing constraints on the coating thickness but also greatly enhancing the adhesion of the coating for improved lifetime. Furthermore, the choice of nanostructure and polymer allow the surface to be self-healing via heating. Not only are PIPS robust, high performance coatings, but they can also be easily repaired to damage that does not significantly destroy the nanostructures or underlying condenser surface.

Methods

Fabrication of Surfaces

The fabrication procedure for PIPS is shown in FIGS. 5A-5D. Each step is described in further detail here.

Growth of CuO Nanoblades

The copper surfaces were first polished (SCRUBS Metal Polish Towel), cleaned with detergent (Alconox Detergent Powder), placed in an ultrasonic bath with isopropanol for 10 min, rinsed with deionized (DI) water, placed in 2 M hydrochloric acid for 30 seconds, rinsed with DI water, and then dried with compressed air. CuO nanoblades were then grown by immersing the cleaned rods in alkaline solution composed of NaClO₂, NaOH, Na₃PO₄.12H₂O, and DI water (3.75:5:10:100 wt %) at 96° C. for 1 hour. Based on literature characterization of this oxidation process and atomic force microscopy images, the CuO nanoblades have thickness of h≈1.5 μm, solid fraction at the surface ϕ(x=0)≈0.023, and surface area enhancement of ≈10³⁴. The random orientation of the nanoblades also physically constrains the polymer to the surface, i.e., in order to delaminate the polymer coating must be significantly deformed. This growth process is self-limiting, thus thicker CuO nanoblades could not be made with this process.

Growth of Cu Nanowires

Copper nanowires were grown using a two-step templated electrodeposition process. The copper surfaces were first polished (SCRUBS Metal Polish Towel), cleaned with detergent (Alconox Detergent Powder), placed in an ultrasonic bath with isopropanol for 10 min, rinsed with deionized (DI) water, placed in 2 M hydrochloric acid for 30 seconds, rinsed with DI water, and then dried with compressed air. A 50 μm thick anodized aluminum oxide nanoporous membrane with pore diameter of 160 nm and solid fraction of 0.16 (InRedox), or 200 nm pore diameter and solid fraction of 0.4 (Sterlitech) was placed on the copper surface. In the first electrodeposition step, a piece of filter paper was then placed on top of the membrane and wetted with electrolyte (Elevate Cu Electrolyte 10). Finally, a piece of copper the same size as the surface (1 in diameter disk) was placed on top of the filter paper. The entire stack was clamped together and placed in the electrolyte. A constant current was then applied (2.5 mA for InRedox templates, 10 mA for Sterlitech templates) for one hour to bond the template to the copper surface. The clamp, filter paper, and second piece of copper were removed, leaving only the template bonded to the copper sample surface. The sample was then placed back into the electrolyte for the second electrodeposition step. A constant current was applied (2.5 mA for InRedox templates, 10 mA for Sterlitech templates), where the electrodeposition time controlled the thickness of the nanowire layer. A growth rate of 1.5 μm-2 μm per hour was observed. After the desired thickness was reached, the surface was removed from the electrolyte, rinsed with DI water, and placed in 2 M NaOH solution for 3 hr to remove the AAO, leaving copper nanowires behind.

Infusion of Teflon AF

After growth of CuO nanoblades or Cu nanowires, Teflon AF 1601 (6% solution, Chemours) was spin coated on the surfaces at 1000 rpm. After spin coating, the surface was heated in argon to 330° C. with a ramp rate of 30° C. per minute, held at 330° C. for 30 minutes, and then allowed to cool to room temperature. This heating process allowed the spin coated layer to melt, and wick into the nanostructured surface. This spin coating process was then repeated until the nanostructure was completely filled, i.e., the number of spin coats was changed depending on nanostructure thickness and solid fraction, where each spin coat deposited 1 μm of Teflon AF or less. When the nanostructure was nearly filled the thickness deposited was reduced to 100 nm each spin coat by using a diluted solution (3%) of Teflon AF 1601 to prevent overfilling.

Contact Angle Measurements

A custom-built experimental setup was used to measure contact angle (FIG. 14). The air and liquid temperature remained close to the surrounding laboratory temperature. A syringe pump (Micro4, World Precision Instruments) was used to add and remove water from a droplet on the surface. Note that the liquid was added and removed slowly enough that there was no dynamic effect on the contact angle, i.e., the capillary number was small. A DSLR camera (EOS Rebel T3, Cannon) and macro lens were used to collect images of the droplet advancing on the surface. Lighting of the droplet was supplied with a light source (Intenselight C-HGFI, Nikon) and lens (C-HGFIB, Nikon). Contact angle was extracted from the images using ImageJ.

Self-Healing: Damage and Repair

The PIPS surface was damaged in three different ways. First was laser ablation using a commercial laser cutter (Epilog Laser Zing 24). The laser power was set to 15% and cutting speed to 100%. The laser cutter then produced a 10×10 grid of lines spaced 1 mm apart. This removed the polymer but did not completely destroy the nanostructure. Scraping was achieved using a multiblade cross hatch cutting tool (ISO 2409:2007), which destroyed both the polymer and nanostructure. Chemical damage was achieved by placing the surface in a plasma chamber (790 series, Plasmatherm) for 3 minutes, which removed fluorination (and thus hydrophobicity) at the surface of the coating but left the underlying polymer and structure undamaged. See, for example, Morra, M., Occhiello, E. & Garbassi, F. in High Energy Density Technologies in Materials Science 161-168 (Springer, 1990), which is incorporated by reference in its entirety.

Corrosion Testing

The potentiodynamic polarization curves were measured in 1 liter of 3.5 weight percent NaCl solution. 1 cm²surfaces were used for the tests. The surface was first allowed to sit in the solution for 15 minutes before starting the test. Voltage was then swept at a rate of 0.1 mV/s from 250 mV below to 250 mV above the open circuit voltage and the current monitored. Using Tafel extrapolation, the corrosion current was then determined. See, for example, McCafferty, E. Validation of corrosion rates measured by the Tafel extrapolation method. Corrosion Science 47, 3202-3215 (2005), which is incorporated by reference in its entirety.

Continuous Condensation Testing

Before condensation testing all thermocouples (ungrounded J-type, Omega) were calibrated to ±0.1° C. in a water bath (Lauda recirculating chiller). Surfaces for testing were prepared directly on 1 inch diameter copper rods that extended through the walls of an environmental chamber. These rods were connected to a chilling loop, which was used to set condensation heat flux. The environmental chamber was evacuated to less than 1 Pa to remove all non-condensable gases. Steam was then added via a boiler filled with degassed DI water. Steam conditions were set to 60° C. by heaters in the boiler, and the chamber walls were maintained at this temperature using heaters applied directly to the chamber walls. Steam pressure was monitored (Baratron Capacitance Manometer, MKS). Chiller temperature was set to produce roughly 100 kW/m²heat flux at the condenser surface, extrapolated from temperatures measured by 5 thermocouples embedded along the length of the copper cylinder. Fitting the temperature profile in the copper cylinder also allowed the surface subcooling, and condensation heat transfer coefficient, to be calculated. For long term testing, vacuum was periodically pulled on the chamber to ensure non-condensable gases did not accumulate over time.

Designing Polymer Infused Porous Surfaces

To achieve durable condensation heat transfer enhancement through dropwise condensation with low-surface-energy coatings, multiple design criteria for the proposed polymer infused porous surfaces were considered. The first is that the coating must not add significant resistance to heat transfer, i.e., the thermal conductance must be high. Thermal conductance scales as k/H, where k and H are the thermal conductivity and the thickness of the coating, respectively. Historically, because low-surface-energy coatings tend to have low thermal conductivity, this has been achieved by using very thin coatings (H<4 μm). At these small thicknesses, adhesion of polymers is poor, resulting in inadequate robustness. Therefore, improving adhesion of the coating, as well as improving thermal conductivity such that thicker coatings may be used would both benefit coating lifetime and heat transfer performance. Second is the ability of the low-surface-energy coating to promote dropwise condensation, for which the wetting behavior on the surface is important. Generally, the quality and performance of dropwise condensation is greatest when the advancing contact angle, θ_a, is large (θ_a>90 degrees) and the contact angle hysteresis, i.e., the difference between the advancing contact angle and the receding contact angle, is small (θ_a−θ_r<20 degrees). See, for example, Neumann, A., Abdelmessih, A. & Hameed, A. The role of contact angles and contact angle hysteresis in dropwise condensation heat transfer. International Journal of Heat and Mass Transfer 21, 947-953 (1978), which is incorporated by reference in its entirety. In this section the design rational for surface types chosen in this study is discussed.

PIPS form a composite material consisting of low thermal conductivity polymer and a higher thermal conductivity nanostructure, and the composite material has a surface composed of highly wetting nanostructure and hydrophobic polymer. Therefore, any nanostructure exposed at the surface will affect the wettability of the surface, which would affect the quality of dropwise condensation. Previous works have developed expressions for the expected advancing and receding contact angles of composite surfaces, θ_aand θ_r, respectively (See, for example, Choi, W., Tuteja, A., Mabry, J. M., Cohen, R. E. & McKinley, G. H. A modified Cassie-Baxter relationship to explain contact angle hysteresis and anisotropy on non-wetting textured surfaces. Journal of Colloid and Interface Science 339, 208-216 (2009), which is incorporated by reference in its entirety)

cos θ_a=cos θ_polymer (S1)

cos θ_r=√{square root over (1−ϕ(x=0))}cos θ_polymer+(1−√{square root over (1−ϕ(x=0))})cos θ_ns (S2)

where ϕ(x=0) is the solid fraction of the nanostructure at the surface exposed to the liquid and θ_polymerand θ_nsare the contact angle of the polymer and nanostructure material, respectively. In order to minimize contact angle hysteresis, solid fraction of the nanostructure at the surface should remain small (FIG. 9B). There is also the possibility to overfill the nanostructure with polymer, thereby creating a polymer only surface. However, because the overfilled polymer would have low thermal conductivity, it would create significant resistance to heat transfer and should be kept thin. Therefore, in this work, overfilling was avoided and instead design the surface such that the solid fraction is low enough that contact angle hysteresis is less than 20 degrees (ϕ(x=0)<0.4).

The network of nanostructure inside the polymer also enhances the thermal conductivity. In fact, because the nanostructure is grown on the surface, it inherently creates a continuous, percolated network of high thermal conductivity material through the entire thickness of the layer, forming parallel heat transfer paths. In this scenario, the effective thermal conductivity, k_eff, of the layer can be estimated as (See, for example, Burger, N. et al. Review of thermal conductivity in composites: mechanisms, parameters and theory. Progress in polymer science 61, 1-28 (2016); MANTLE, W. J. & CHANG, W. S. Effective thermal conductivity of sintered metal fibers. Journal of Thermophysics and Heat Transfer 5, 545-549, doi:10.2514/3.299 (1991); and Singh, B., Dybbs, A. & Lyman, F. Experimental study of the effective thermal conductivity of liquid saturated sintered fiber metal wicks. International Journal of Heat and Mass Transfer 16, 145-155 (1973), each of which is incorporated by reference in its entirety)

k
_eff(x)=ϕ(x)k_ns+(1−ϕ(x))k_polymer (S3)

where k_nsand k_polymerare the thermal conductivities of the nanostructure and polymer, respectively, and x is the location within the layer with x=0 located at the exposed surface. To start, in FIG. 9B, nanostructures were considered with constant solid fraction throughout the layer thickness made of copper (k_ns=386 W/mK). Effective thermal conductivity can be enhanced orders of magnitude over that of the polymer (k_polymer=0.29 W/mK) even with relatively small solid fractions of nanostructure. Therefore, a balance exists between the thermal conductivity enhancement and the contact angle hysteresis, motivating the use of nanostructures with intermediate solid fractions.

To enhance adhesion of polymers to a surface, surfaces are often roughened, increasing the total surface area the polymer is in contact with. See, for example, Awaja, F., Gilbert, M., Kelly, G., Fox, B. & Pigram, P. J. Adhesion of polymers. Progress in polymer science 34, 948-968 (2009), which is incorporated by reference in its entirety. In the case of pillars, the surface area enhancement is

$\begin{matrix} Surface Area Enhancement = \frac{L^{2} + π DH}{L^{2}} & (S 4) \end{matrix}$

where L is the pitch and D is the diameter of the pillar, as shown in FIG. 9A. The surface area enhancement is shown in FIG. 9C for different solid fractions, ϕ (for pillars ϕ=(πD²/4)/L²), and a height of 10 μm. H=10 μm was chosen as a representative case given thickness should remain relatively small to limit the thermal resistance the coating adds. The surface area enhancement in this scenario is maximized by moving to smaller pitch, i.e., tall slender structures, where significant enhancement is only reached when structure pitch is hundreds of nanometers. Therefore, this work uses nanostructures.

However, given many nanostructures do not form a constant solid fraction, the effect of varied solid fraction throughout the coating was considered. Three scenarios were evaluated—constant, linear, and parabolic solid fractions throughout the layer—where k_eff(x) is shown along x (FIG. 10). For the constant solid fraction, ϕ=0.3 was used as it falls within the middle of our expected target range from FIG. 9B, whereas for linear and parabolic solid fractions ϕ(x=0)=0 and ϕ(x=H)=1 was assumed. The resulting average effective conductivity, k_eff, of the entire coating, i.e., the effective conductivity if the coating was treated as a homogeneous medium along x, is labeled in FIG. 10 for these scenarios. All types of nanostructure greatly enhanced the thermal conductivity over the polymer; however, constant solid fraction is most effective, followed by linear, and then parabolic. Parabolic performs the worst due to the small amount of nanostructure near x=0, resulting in a low effective thermal conductivity.

Based on calculated effective thermal conductivities, a critical thickness, H_crit, was defined beyond which the coating would degrade dropwise heat transfer performance by 10 percent or more. This critical thickness was estimated using a thermal resistance network

$\begin{matrix} \frac{1.1}{h_{drop}} = \frac{1}{h_{drop}} + \frac{H_{crit}}{k_{eff}} & (S 5) \end{matrix}$

where h_dropis the heat transfer coefficient of dropwise condensation. An estimated value of h_drop=100 kW/m²K was taken. The resulting critical thicknesses, along with expected contact angle hysteresis are shown in Table 2 for different nanostructure solid fractions and materials. Without using nanostructures, Teflon AF coatings can only be 0.29 μm thick before reducing condensation heat transfer by more than 10%, highlighting the strict design constraints on these coating types. Adding high thermal conductivity copper nanostructures increases this critical thickness significantly without increasing contact angle hysteresis beyond 20 degrees, whereas adding lower thermal conductivity nanostructure such as copper oxide increases the critical thickness much less.

To prove the validity and flexibility of PIPS, two designs were chosen and are highlighted in blue in the table. Parabolic copper oxide nanostructures with H=1.5 μm, based on copper oxide nanoblades, and copper pillars with a solid fraction of 0.4 and two thickness, H=5 and 20 μm, were used.

Heat Transfer Measurement

To determine the condensation heat flux and condenser surface temperature, temperatures were recorded at evenly-spaced thermocouples mounted within the copper condenser block; these temperatures were input into the 1-dimensional form of Fourier's law to determine the heat flux, and, from a corresponding thermal resistance network for the copper block, the surface temperature was determined. The copper block was insulated with a polyetherimide sleeve to minimize heat transfer at the sidewalls, shown in FIG. 6A in the main text. In order to justify the use of the 1-dimensional Fourier's law in this case, a COMSOL model of the insulated copper condenser block (FIG. 11) was created. The resulting temperature profile was confirmed to be highly linear, allowing use of the 1-dimensional form of Fourier's law to determine heat flux.

Expected Dropwise Heat Transfer Performance with PIPS Resistance.

The PIPS coating adds a thermal resistance, thus lowering the expected performance compared to dropwise condensation without PIPS. Using a serial thermal resistance model, the expected performance was modeled as

$\begin{matrix} \frac{1}{h_{expected}} = \frac{1}{h_{drop}} + \frac{H_{PIPS}}{k_{eff}} & (S6) \end{matrix}$

where H_PIPSis the thickness of the pips layer, h_dropis the dropwise heat transfer coefficient (133 kW/m²K is used in this case based on correlations by Rose (See, for example, Rose, J. Some aspects of condensation heat transfer theory. International communications in heat and mass transfer 15, 449-473 (1988), which is incorporated by reference in its entirety)), and h_expectedis the performance including the PIPS layer, which is plotted in FIG. 6B.

Contact Angle Hysteresis with Surface Degradation.

If polymer is removed from the PIPS during condensation, this may gradually expose nanostructure, changing the wettability of the surface, where the equation for the receding contact angle must account for the exposed nanostructure (inset of FIG. 12). To model expected behavior, a roughness factor, r, was add to Eq. S2 to account for exposed nanostructures increasing the surface area above that of the solid fraction,

cos θ_r=√{square root over (1−ϕ(x=0))}cos θ_polymer+r(1√{square root over (1−ϕ(x=0))})cos θ_ns (S7)

For the pillar nanostructures shown in FIG. 9A, this roughness factor can be estimated by

$\begin{matrix} r = \frac{\frac{π D^{2}}{4} + π DX}{\frac{π D^{2}}{4}} & (S8) \end{matrix}$

where X is the length of exposed pillar/nanostructure. In FIG. 12, the expected hysteresis is shown as the roughness factor is increased for two nanostructure solid fractions. The higher solid fraction has a significantly higher increase in hysteresis as nanostructure is exposed. One can theorize this is the reason Cu nanowire PIPS had observable hysteresis increase after testing, while Cu nanoblade PIPS did not.

Corrosion Resistance.

Because PIPS coatings are primarily non-reactive, low-surface-energy polymer at their outermost surface, they reduce surface corrosion significantly. In FIG. 13, the potentiodynamic polarization curves for bare copper, CuO nanoblade PIPS, and Cu nanowire PIPS with ϕ=0.4, measured in 3.5 weight percent NaCl solution are shown. Using Tafel extrapolation, the corrosion current, I_corr, can be determined. This current was then used to determine the corrosion rate, CR, of the surfaces as

$\begin{matrix} C R = \frac{I_{corr} K \cdot EW}{ρ A} & (S9) \end{matrix}$

where K is a constant that defines the units of corrosion rate (K=3272 mm/A-cm-year to find corrosion rate in mm/year), EW is the equivalent weight of the copper, ρ is the density, and A is the area of the tested surface. The corresponding corrosion rates are shown in Table 3. The corrosion rate of CuO nanoblade PIPS was more than two orders of magnitude less than a bare copper surface, providing significant surface protection. The higher corrosion rate of Cu nanowire PIPS may have contributed to the larger increase of contact angle hysteresis during continuous condensation testing.

Uncertainty Propagation

This section presents the method used for uncertainty propagation of the experimental results. The method for determining uncertainty is described in NIST Technical Note 1297. Individual measurements are assumed to be uncorrelated and random. Therefore, the uncertainty, U, in a calculated quantity, Y, is determined as

$\begin{matrix} U = \sqrt{\sum_{i} {(\frac{\partial Y}{\partial X_{i}})}^{2} U_{x}^{2}} & (S10) \end{matrix}$

where X is the measured variable, and U_xis the uncertainty in the measured variable. Table 4 summarizes the uncertainty associated with each experimental measurement that was then propagated according to Equation S10 to determine uncertainty.

TABLE 2

Critical thickness and expected contact angle hysteresis. Different

possible nanostructure type, materials, and designs are considered.

The resulting critical thickness, surface solid fraction, and expected

advancing and receding contact angles are shown. Critical thickness

is the thickness at which the thermal resistance of the composite

hydrophobic layer is expected to reduce condensation heat transfer

by 10%. Underlined are designs that were chosen for this study.

Nanostructure

H_crit
ϕ
θ_a
θ_r

Type
Material
[μm]
(x = 0)
[deg]
[deg]

None
—
0.29
0
114
114

(Teflon AF)

Parabolic
Copper
6.6
0
114
114

Linear
Copper
52
0
114
114

Constant
Copper
56.6
0.15
114
107.3

Constant

Copper

154.7
0.4

114

95.1

Parabolic

Copper Oxide

1.53

0

114

114

Constant
Copper Oxide
3.2
0.15
114
107.3

TABLE 3

Corrosion current and rate of copper

and copper oxide nanoblade PIPS.

Surface
I_corr(A/cm²)
CR (mm/year)

Bare Copper
1.08E−5
0.25

Bare CuO
6.31E−6
0.15

PIPS: CuO Nanoblade
8.17E−8
0.0019

PIPS: 20 μm Cu Nanowire
1.58E−7
0.0036

TABLE 4

Uncertainties corresponding to experimental measurements. Uncertainty

in vapor temperature and surface heat flux are primarily caused by

fluctuations in the chamber conditions due to PID control of heaters

and chillers, as opposed to the measurement via thermocouples.

Experimental Measurement
Uncertainty

Steam vapor temperature in environmental chamber
2°
C.

Surface heat flux
10,000
W/m²

Contact angle measurement (θ)
5
degrees

Calibrated J-type thermocouples in copper rod
0.1°
C.

Details of one or more embodiments are set forth in the accompanying drawings and description. Other features, objects, and advantages will be apparent from the description, drawings, and claims. Although a number of embodiments of the invention have been described, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. It should also be understood that the appended drawings are not necessarily to scale, presenting a somewhat simplified representation of various features and basic principles of the invention.

ROBUST, REPAIRABLE, HIGH THERMAL CONDUCTANCE HYDROPHOBIC COATINGS

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