Started by Lauren Hartle, Fall 2011.

"Stretchable Microfluidic Radiofrequency Antennas", Kubo, M., Li, X., Kim, C., Hashimoto, M., Wiley, B.J., Ham, D., and Whitesides, G.M., Advanced Materials, 2010, 22, 2749-2752.

## Introduction

The paper describes improvements made to the design of stretchable antennae. Flexible microfluidic channels injected with a liquid metal form the foundation of the technology. Unlike conventional antennae, which are punched out of metal sheets, flexible, stretchable antennae are more resistant to damage, better conform to arbitrary installation surfaces, and offer tunable frequency when the antenna is stretched. Current PDMS antennae stretch up to 40%, far below the theoretical 160% strain achievable by bulk PDMS. Whitesides, et al. propose the following solution: use PDMS to provide mechanical support to sensitive and/or rigid components and use a softer elastomer to construct the other components. This design provides mechanical stability where necessary, while using the PDMS stiffness "transition" to reduce stress concentration at the interfaces between rigid and soft components.

## Methods

### Fabrication

A half-wave dipole antenna, consisting of two identical branches (dimensions 32.5mm x 3mm x 200um) with electrical connectors positioned in the middle. The liquid metal component was eutectic gallium indium alloy (EGaIn: 75.5% Ga, 24.5% In), and the stiff/soft polymeric components were PDMS and Ecoflex, respectively. The intended resonant frequency of the antenna was roughly 1GHz. Figure 1 shows a schematic of the device. Table 1 shows the relevant mechanical properties of PDMS and Ecoflex.

### Performance Evaluation

A structure of pure PDMS, and an Ecoflex/PDMS "hybrid" were evaluated for radiation efficiency, "tunability" and "reliability". The efficiency with which the device radiated incident signals was evaluated at different strains by comparing the incident to "reflected" power. As Figure 2 shows, not only did the hybrid structures survive up to 120% without damage or malfunction (unlike pure PDMS structures, which mechanically failed at 20% strain), but between 90 and 99% efficiency was maintained at maximum strain. Relative reflected power is given in units of decibels, with "−30 dB, −20 dB and −10 dB" corresponding to "99.9 %, 99 % and 90 %" efficiency.

A half-wave dipole antenna has a resonant frequency determined by the antenna length, l, and the "effective dielectric constant of the medium", $\epsilon_{eff}$.

$f = \frac{143}{l\sqrt{\epsilon_{eff}}}$

Upon stretching to 2.2 times the initial length, the resonance frequency reduced from 1.53 GHz to 0.738 GHz. Upon release, the frequency returned to its initial value. Figure 3 shows the relevant data and images of the antenna at different strain levels.

To determine the cyclability of the device, the antenna was stretched to 50% strain and released 100 times. Virtually no change in the reflected power was observed after 100 cycles. Figure 4 shows a plot of reflected power vs frequency after 0, 10, 50, and 100 cycles.

## Conclusions/Soft Matter Connection

Researchers in the Whitesides group successfully demonstrate proof-of-concept for a flexible, stretchable antenna composed of EGaIn injected into a hybrid PDMS/Ecoflex microfluidic channel structure. The antenna shows improved extensibility and tunability, and shows little degradation after 100 cycles. The paper demonstrates several important concepts in soft matter: 1) adding functionality (like tenability) to classically rigid devices through designs integrating soft materials, 2) an understanding of the impact of mechanics on durability and adhesion: a material providing a transition in stiffness permits weaker adhesion and prevents cracking, and 3) the use of soft materials brings the possibility of simple and inexpensive production.