Achieving Super Sensitivity in Capacitive Strain Sensing by Electrode Fragmentation

Achieving Super Sensitivity in Capacitive Strain Sensing by Electrode Fragmentation

Item Type Article

Authors Nesser, Hussein;Lubineau, Gilles

Citation Nesser, H., & Lubineau, G. (2021). Achieving Super Sensitivity in Capacitive Strain Sensing by Electrode Fragmentation. ACS Applied Materials & Interfaces. doi:10.1021/acsami.1c07704 Eprint version Post-print

DOI 10.1021/acsami.1c07704

Publisher American Chemical Society (ACS) Journal ACS Applied Materials & Interfaces

Rights This document is the Accepted Manuscript version of a Published Work that appeared in final form in ACS Applied Materials &

Interfaces, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://pubs.acs.org/doi/10.1021/

acsami.1c07704.

Download date 2023-11-29 19:51:43

Link to Item http://hdl.handle.net/10754/670301

Supporting information

Achieving Super Sensitivity In Capacitive Strain Sensing By Electrode Fragmentation

Hussein Nesser and Gilles Lubineau*

King Abdullah University of Science and Technology (KAUST), Physical Sciences and Engineering Division (PSE), COHMAS Laboratory, Thuwal 23955-6900, Saudi Arabia.

E-mail:

KEYWORDS: Strain sensor, Wireless detection, Capacitive behavior, Fragmented electrodes, Dielectric materials, Transmission line model

1. Capacitive strain sensor sensitivity

Figure S1. Chart summarizing the gauge factor (GF) of the previously reported capacitive sensors

and our work’s position compared to what is available.

The majority of existing works on capacitive sensors take advantage of the direct relationship between capacity and geometry. Figure S1 clarifies that all works based on the geometric effect (change in sensor dimensions under mechanical load) have a GF that does not exceed 1 (red line, Figure S1) ^1–13. The initial capacitance is given by 𝐶₀=𝑒₀𝑒_𝑟^𝜔_𝑑⁰₀^𝑙0, where e0 and er are the vacuum permittivity and the dielectric constant for the dielectric layer, respectively. l0 is the initial length;

ω0 is the initial width; and d0 is the initial thickness (i.e., distance between the two electrodes).

When the sensor is stretched in one direction with strain ε, the structure length increases to (1 + ε)l0, while the dielectric layer width and thickness decrease to (1 − νelectrodeε)ω0 and (1 − νdielectricε)d0, respectively, where νelectrode and νdielectric are the Poisson’s ratios for the stretchable

electrodes and the dielectric layer, respectively. However, the change in the sensor dimensions affects the capacitance change, as illustrated in Equation (1):

0 0 (1)

0

0

(1 ) (1 )

(1 )

electrode r

dielectric

v l

C e e

v d

 

 

 

The difference in the Poisson’s ratios between the through thickness direction and the in-plane direction is not usually considered as that for this type of flexible sensor. The electrode and the dielectric material almost have the same Poisson’s ratio. In this case, the sensor capacitance changes according to 𝐶=𝐶₀(1 +𝜀) due to the variation of the device geometry.

Some studies proposed new mechanisms to achieve a GF higher than 1 (e.g., wrinkled gold-film electrode, electron transport mechanism, and interdigitated capacitor) ^14–18. However, this capacitive strain sensor sensitivity is still insufficient for detecting the very low strain (<1%) in some applications. We succeeded herein in surpassing all the current results by obtaining the highest GF for capacitive strain sensors. This work represents a qualitative leap in the potential of capacitive sensors compared to pre-existing sensors.

2. Telegraph’s equation

We first review the transmission line model and the calculation details inspired by the telegraph’s equation to fully understand the origin of the voltage dissipation and attenuation in the dielectric capacitor.

Figure S2.a depicts the general form of the transmission line model of our flexible capacitor based on fragmented electrodes. The capacitor behaves like a composition of smaller capacitors in parallel. Every segment (∆z) consists of an ideal capacitance C′DE in parallel with the dielectric resistance R′DE to model the dielectric material, representing the leakage and the current losses of the capacitor that are minimal for well-insulating polymers. Figure S2.a illustrates that

the dielectric’s electrical components are in series with the electrodes. R′e is the electrode resistance that varies with strain. The capacity of the fragmented electrodes, C′e, is the sum of the capacity of every crack on the electrodes and results from the insulating zone between the conductive blocks. For barely opened cracks and high dielectric insulation, we can simplify these circuits by ignoring the electrode capacitance (Ce) and the dielectric material resistance (RDE) in the model. The top and bottom electrode resistances can be combined as two resistances in series.

Consequently, each segment is modelled based on the capacitance per unit length ∆zC′ similar to C′DE and the resistance per unit length ∆zR′ similar to R′e.

Figure S2. (a) The transmission line is a distributed model representing the fragmented electrode- based sensor as an infinite series of lumped circuits repeated every ∆z. (b) Distributed element model for a transmission line showing the voltage and current distribution on one segment.

The transmission line theory is based on telegrapher equations to analyse the electrical signal in a dielectric capacitor. The sensor is modelled by an electrical circuit divided into an infinitesimal segment with length dz at position z. The input for each segment at position z is the voltage V(z,t) and the current i(z,t). The output at position z + ∆z is the voltage V(z + ∆z,t) and the current i(z +

∆z,t). The transmission line equations are presented as follows by applying Kirchhoff’s laws to the model shown in Figure S2.b and taking the limit as ∆z → 0:

 

, '

( , ) v z t

R i z t z

 

 (1)

 

, '

 

, i z t v z t

z C t

 

 

  (2)

Combining equations (1) and (2) and considering a sinusoidal steady-state condition lead to

 

2

2

2 ( ) 0

d V z

d z  V z  (3)

The solutions of this differential equation represent the general form of the voltage solution:

   

( , ) ^{j t z j t z}

V z t V e^{  } V e^{  } (4)

where, ω is the angular frequency of the input voltage, and is the wave propagation constant 𝛾 equal to

' '

j C R

   (5)

V⁺ and V⁻ represent the voltage magnitudes of the waves traveling along the transmission line in forward and backward directions; 𝑉0 is the input voltage magnitude; and 𝐿 is the sensor length.

The voltage magnitudes V⁺ and V⁻ can be calculated from the boundary conditions. For z = 0, the voltage is maximal and equal to the input voltage V0:

(6)

V0 V^V^

For z = L, the current 𝑖(𝑧+∆𝑧,𝑡) does not exist at the end of the line. Therefore, V⁺ can be deduced using Equation (6):

(7)

0

(1 ) 2

1 (1 )

z

V V

e ^









  



The propagation constant is a complex number depending on the capacity per unit length C′ and the electrode resistance per unit length R′.

The voltage equation represented in Equation (4) can be simplified by knowing that the voltage vanishes in a high-value electrode resistance per unit length and/or for high frequency. Thus, we can assume that >>> . Using this condition and the expression of V𝛾 _2𝐿^{1 +}, we can deduce that 𝑉⁺ =

. is a complex number with real and imaginary parts, and V0 is a real number that 𝑉₀ and 𝑉^― = 0 𝛾

allows replacing 𝑒^―𝛾𝑧 with 𝑟𝑒𝑎𝑙

{

𝑒^―𝛾𝑧

}

; therefore, the voltage equation as a function of the z- direction can be written as follows:

0 (8)

( ) ^z

V z V e^

3. CNT paper fabrication

The CNT paper was realized using the filtration method shown in Figure S3. First, a 0.5 wt.%

SWCNT doped with 2.7 wt.% COOH groups (CheapTubes) was dispersed in methanesulfonic acid (CH3SO3H, Sigma Aldrich) to create a liquid solvent. The SWCNT/ CH3SO3H solvent was sonicated using a Brason 8510 sonicator (250 W; Thomas Scientific) for 60 min then stirred for 12 h at 500 rpm. A volume of 12 g of the solvent dispersion was vacuum-filtered through a ceramic filtration membrane (pore size: 20 nm, Whatman). CH3SO3H was then removed from the solution after 12 h to obtain an SWCNT paper of 47 mm or 80 mm diameter and 90 µm thickness. These parameters are controllable by changing the SWCNT concentration in the acid solution or by adjusting the solvent quantity.

Figure S3. Photograph of the filtration system and image of an 8 cm-diameter CNT paper.

4. Layer arrangement and structuring

The parallel plate capacitor was created by arranging the layers on top of each other. First, the capacitor's bottom electrodes represented by a strip of laser-engraved SWCNT paper were transferred onto a 0.5 mm-thick PDMS substrate. We connected the first copper wire to the SWCNT paper strips with silver epoxy and poured the second layer of PDMS precursor of equal weight onto the existing two layers. We repeated this process of CNT paper integration to produce the top electrode and its electrical connection. The third layer of PDMS was deposited onto the previous layers to fully encapsulate the SWCNT papers. Each layer of PDMS was cured at 70 °C in an oven for 2 h. This process produced a dielectric layer sandwiched between two fragmented electrodes protected by two PDMS layers on both sides. Finally, we cut these laminated layers using a laser cutting machine to obtain the final structure.

5.

Fabrication of the flexible CNT electrodes

Figure S4. (a) Fabrication methods of the non-cracked CNT film. (b) Image of a flexible sensor

with non-cracked CNT electrodes.

The filtration method was suitable for the thick CNT layer fabrication. The flexible electrodes should be very thin to avoid cracking during stretching. Figure S4 shows the different steps for the indirect printing method used to create the 1 µm-thick CNT film. First, we prepared the solution by dispersing 2 wt.% SWCNT in methanesulfonic acid (CH3SO3H). Next, the solution was sonicated for 60 min and stirred for 12 h at 500 rpm until we obtained ink consistency. The ink was printed on a flexible filtration membrane (pore size: 20 nm, Whatman). Subsequently, CH3SO3H was removed from the solution using a vacuum chamber. The printing will be performed through a fine needle that will be controlled in three directions and by the quantity of ink coming out. The CNTs were then dried to form a uniform film of the CNT network with a thickness ranging

from one to several micrometres. Next, the filter containing the CNT film was cast on top of the uncured PDMS, followed by curing at 65 ° C for 15 min. When the filter was peeled off, the CNT film was bonded to the cured PDMS, allowing us to obtain the bottom electrodes. This process was repeated twice to form the parallel plate capacitor with stretchable and non-cracked electrodes.

6. Influence of cracks in the electrodes to the capacitance variation

0 10 20 30 40

-100 -80 -60 -40 -20 0 20

 C /C ( % )

Strain (%)

1 MHz Without cracks

With cracks

Figure S5. Comparison of the sensitivity of devices with and without fragmented electrodes

7. Durability at high strain

Figure S6. Dynamic durability of the sensor for 2000 loading-unloading cycles at 40% strain, 1 mm/s velocity and 10 KHz interrogation frequency.

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