Porous metals are employed in thermal management applications thanks to the fact that they conduct heat and electricity well, and because they have a large fluid-accessible surface area. For applications like heat exchangers, for example, the material architecture is often reduced to nanoscale feature sizes. As the pore sizes in these nanomaterials become smaller, the total surface area of the material increases and the distance over which heat or electricity can travel reduces. A team led by Kenneth Goodson at Stanford University has now found that the way heat is conducted in metal inverse opals depends on the pore size in these materials too but with an extra twist: that heat conductivity goes from being diffusive on the microscale to being quasi-ballistic on the nanoscale.

“The transition from diffusive to quasi-ballistic thermal conduction occurs when the size of the conduction pathway becomes comparable to the mean-free path of the thermal energy carriers (electrons in the case of metals),” explains team member and lead author of the study Michael Barako “We can think of an inverse opal as a macro-crystal of spherical pores with well-defined crystallographic characteristics, and the conducting pathway is made up of the volume surrounding these pores. By tuning the pore size in these materials, we can predictably tune the size of the conduction pathway, which allows us to optimize the material’s properties for thermal management applications in the future.”

The researchers obtained their results by modulating the pore size of either copper or nickel inverse opals from 100 nm to 1000 nm. In the case of the nickel material, in which the mean-free path of electrons is around 6 nm, the conduction length scales are much larger than the mean-free path and conduction remains diffusive with conductivity staying about the same, regardless of pore size.

### Quasi-ballistic transport

“When the inverse opal is made of copper, however, which has a mean-free path of 39 nm, the conduction length scales become comparable to the mean-free path and we observe a monotonic decrease in the thermal conductivity with pore size,” Barako tells *nanotechweb.org*. “This is the regime in which the thermal conductivity depends on both the intrinsic material and the system size – and is characteristic of quasi-ballistic transport. We used inverse opals to show that, by adjusting the ‘knob’ on pore size, we could effectively tune the thermal conductivity of the material so that it goes from being diffusive to being quasi-ballistic.”

The materials could be employed to control heat flow in electronics devices, which becomes more important as component dimensions decrease, he adds. “We are currently exploring three different thermal applications for metal inverse opals. The first is in microfluidic heat exchangers for active cooling of high-power microelectronics, in which a fluid is pumped through the inverse opal and heat exchange is accelerated by the large surface area of the material. The second is in thin-film heat pipes for passive cooling of portable electronics, such as smart phones and tablets, where capillary-driven flow through the inverse opal creates an evaporation/condensation loop. The third is in high-rate thermal storage media, where the inverse opal is impregnated with a phase change material to form a composite thermal battery that has both a large storage capacity and can deliver/extract high rates of heat.”

### Functional heat transfer components

The team, reporting its work in *Nano Letters* DOI: 10.1021/acs.nanolett.6b00468, is now busy integrating metal inverse opals into functional thermal devices and measuring key performance metrics at both the material and device levels. “At the material scale, we are examining the thermofluidic properties of metal inverse opals, including hydraulic permeability, capillary pressure and boiling characteristics,” explains Barako. “At the device scale, we are assembling inverse opals into functional heat transfer components, such as diamond heat sinks, silicon microchannels and thermal capacitors.”

The researchers are also working on optimizing the design of their inverse opal-based thermal devices while assessing their performance, such as the rate at which they dissipate heat. “While inverse opals have previously been used in many electrical and electrochemical systems, our work outlines a path forward to integrating thermally-conductive nano-architectures into functional heat transfer devices,” says Barako.