2.4.2. Elasticity Measurements

Elasticity determination is essential to obtain linear length change (strain) results. In all available commercial muscle analyzers, only the calibration of the force sensor is performed by a defined weight, which will provide uncertainties in real measurements due to the fact that the elastic modulus of an ionic actuator changes during charging/discharging cycles [34,35]. The elasticity estimation of an artificial muscle is based on Hooke's law (Equation (3)):

$$F = -kX \tag{3}$$

where, *F* is the force needed to extend or compress an object by some distance *X* and k is a constant factor characterizing object elasticity. If a derivative of the force is taken with respect to distance, Equation (4) is obtained:

$$k = -\frac{\partial F}{\partial X} \tag{4}$$

The idea was to perform a known movement with LAS and measure the changes of force. Figure S2 shows the block diagram of the software with the respective steps in the description of the algorithm.

#### 2.4.3. Initialization and Experiments with the Potentiostat

The potentiostat controls the electrochemical processes of ionic actuators, which translate the electrical signal (potential, current) to shape change, which is measured as force (weight change) or strain (length change).

The initialization process of the potentiostat is based on three steps: (a) reading the variables describing how the experiment will be performed, (b) setting up the potentiostat for the experiment, and (c) starting the experiment. The setup variables are directly read from the user interface from user-controllable variables. The experiment type is selected by the user from a set of three: cyclic

voltammetry (CV), chronoamperometry (CA), and chronopotentiometry (CP). The block diagram for the potentiostat is shown in Figure S3a, strain and stress measurements have the same basic structure.

#### 2.4.4. Strain and Stress Measurements

Strain experiments also include an additional muscle length controlling logic, as the upper clamp is moved by the LAS plate to maintain constant force during the scan. The magnitude of the required movement by the LAS constitutes the isotonic strain. In order to keep a constant force, a proportional controller (P controller) is implemented, as presented in Equation (5), which derives from Equation (4):

$$
\Delta X = -k' \Delta F \tag{5}
$$

where, the gain k´= (k + uk), and uk is the uncertainty of k. The addition of uk to k assures that no faulty steps are done in a case when *k* - *uk*. The input (ΔF) is the difference between the measured force and the set state (force value which the P controller is intended to track). The output is a step size (ΔX) needed to maintain the muscle in the set state of force. The gain (k) for the P controller is the elasticity coefficient of a muscle, whose strain is to be measured. The minimum steps size that the LAS can carry out is Δlmin = 0.5 μm. In case the ΔF is smaller then:

$$
\Delta F\_{\min} = \frac{\Delta l\_{\min}}{-k'} \tag{6}
$$

No movement is carried out since it would require a step size < Δlmin. In such cases, the electroactive material has linear displacement below the resolution of the LAS, the actual force can differ from the set value and is equal to ΔFmin. The detailed description of the block diagram for strain measurement is given in Figure S3b.

The automated multiple stress or strain measurement process is shown in Figure 2a and the user interface of the isotonic (displacement) and isometric (force) electro-chemo-measurement software (IIECMS) [33] is presented in Figure 2b. The IIECMS program is designed for measurement automation with the additional function of avoiding user errors in mislabeling or accidentally selecting wrong settings for the experiments.

**Figure 2. a:** Block diagram of the automated multiple stress or strain measurement processes, and **b**: Layout of the graphical user interface (single force experiment) of the developed software.

The block diagram of the automated measurement process (Figure 2a) reads the experiment list and coe fficients from a previously generated .txt file. Coe fficients, which describe the experiments, are extracted and placed into a temporary array. The program enters into a for-loop, where the potentiostat is initialized and the user-selected measurement is executed. The number of cycles in the for-loop is equal to the amount of experiments on the list.

The graphical user interface (GUI) in Figure 2b shows three main sections. Section 1 includes all controls, such as general settings, file direction and names, potentiostat settings, and motor controls/elasticity measurement. Section 2 includes a set of indicators of experiment progress, such as ongoing experiment and experiment list info's. In Section 3, four graphs are included that plot measurement data.

#### **3. Results on Model Systems and Discussion**

The IIECMS program was adapted on real sample measurements. Two di fferent types of test samples were measured (conducting polymers PPy/DBS and MWCNT-CDC fibers) to show isotonic and isometric measurement results. In the case of the conducting polymer, the isotonic length change or displacement amplitude was more than 20 times higher (referred to as high signal-to-noise ratio ca. 20 dB) than the actuation resolution of the LAS ( Δlmin = 0.5 μm). The second measurement represents a situation where the displacement amplitude is comparable to Δlmin (referred to as low signal-to-noise ratio) and a measurement resolution refining technique is described.

Over 50 di fferent isometric and istotonic measurements were made on ionic material samples, meaning about 200 h of measurement time. The minimum data acquisition period of this measurement setup was 160 ms.

#### *3.1. Characterization of Ionic Actuator Materials*

In the case of PPy/DBS, the DBS- counterions are immobilized during electropolymerization [36] and upon discharging, their negative charge is compensated by (solvated) cations, as shown before [37,38]. In the case of MWCNT-CDC fibers, the actuation mechanism is based on the charging of the electric double layer (non-Faradaic actuator) [10]. Figure 3 shows the scanning electron microscopy (SEM) images of the two di fferent electroactive materials applied in this work.

**Figure 3.** Scanning electronic microscopy (SEM) images of **a**: Polypyrrole Doped with Dodecylbenzene-Sulfonate (PPy/DBS) surface (scale bar 30 μm) with inset—the cross-section (scale bar 10 μm), and **b**: MWCNT-CDC fiber surface (scale bar 5 μm) with inset—cross-section (scale bar 50 μm).

The surface of the PPy/DBS film (Figure 3a) showed a typical cauliflower structure [39], with the cross-section showing a thickness of 18.5 μm. The diameter of the MWCNT-CDC fiber, as measured from the cross section (inset in Figure 3b), was 149.6 μm, the solid particles partly seen represent CDC surrounded by MWCNT material [10] (marked in Figure 3b). The conductivity of the PPy/DBS films was 0.5 ± 0.04 S cm<sup>−</sup><sup>1</sup> while MWCNT-CDC fiber had 13.5 ± 7 S cm<sup>−</sup>1, in line with those shown before [10]. When it comes to linear actuation measurements, the mechanical properties, such as brittleness and elasticity, are important [13]. PPy/DBS films were easy to handle for fixing them on the force sensor and the upper clamp (Figure 2a), while the MWCNT-CDC fiber was very brittle and required extremely delicate handling.

#### *3.2. High Signal-to-Noise Ratio Isotonic and Isometric Measurements*

The performance of the setup was demonstrated on PPy/DBS samples in LiTFSI-PC solution in the potential range of 0.65 to −0.6 V under isometric (Figure 4a) and isotonic (Figure 4b) modes. This relates to case one, where isotonic length change or displacement amplitude is about 2 orders of magnitude larger than the minimal step size of the LAS ( Δlmin= 0.5μm).

**Figure 4.** Cyclic voltammetry measurements (scan rate 5 mV s<sup>−</sup>1, 3 cycles) of PPy/DBS films in LiTFSI-PC electrolyte in voltage potential (dashed) range 0.65 to -0.6V showing in **a**: isometric (measured force, black line), and **b**: isotonic (measured displacement, black line) results against time.

Figure 4a shows the force (weight change) results of the isometric measurements of PPy/DBS films driven by cyclic voltammetry. The maximum stress for this film was found in range of 0.9 MPa. In the case of PPy/DBS, which in general is a typical cation-driven actuator due to the immobile DBSions left in the PPy network, the actuation in LiTFSI-PC is a special phenomenon where the DBS-Li+ ion pairs partly become undissociated in propylene carbonate solvent due to its aprotic nature [13,40]. Therefore, new places of the PPy/DBS film are oxidized and the solvated counter ions TFSI- can enter the film and swell the film at oxidation (expansion, seen in Figure 4b). Our setup was easily able to detect and distinguish between the two processes taking place during one charging cycle. During the first scan (Figure 4a), the potential went from 0.65 to −0.6 V and the force decreased, then increased and finally showed a small decrease at −0.65 V. The contraction corresponds to a small cation involvement during reduction (seen in Figure 4b of displacement measurements, maximum strain in range of 0.6%). During the next cycles, the force was reduced, corresponding to increased displacement (strain). In both displacement and force graphs, creep [24] can be detected, which means that the "neutral" position of the linear PPy/DBS actuator changes, a relatively common behavior for ionic electroactive materials [41]. The phase shift (Figure 4b) of displacement in respect to the driving signal voltage is due to the participation of cations, which in the initial phase of a cycle lead to volume contraction, before the anions take over [13].

Upon very careful observation, one can see some noise appearing in Figure 4b, for example at position 200 s, 700 s, and 1200 s. The noise is introduced when the actual elasticity coe fficient, which is used for P controller, temporarily di ffers from the measured value. This is due to the ion–matrix interactions. In extreme cases, when the elasticity coe fficient is measured to be much lower, the P controller (Equation (6)) starts to generate. The elastic coe fficient, k, was calculated from Equation (3), giving for PPy/DBS, before charging/discharging, the value of 239 mg/μm and after charging/discharging (50 actuation cycles), the value of 134 mg/μm. As it has been shown previously, the elastic modulus of conducting polymers changes during actuation cycles [42] was also effected by the nature of the solvent applied [43]. Therefore, as seen from the above results, the determination of the elastic coefficient to operate isotonic measurements is needed in order to measure meaningful data.

#### *3.3. Low signal-to-Noise Ratio (SNR) Isotonic Measurements*

To examine materials which have very low displacement amplitude, comparable to Δlmin (near 0 dB, SNR) MWCNT-CDC fibers were applied in isotonic displacement measurements conducted with cyclic voltammetry (scan rate 5 mV s<sup>−</sup>1) but with the same electrolyte and potential range seen in Figure 4b. The results are presented in Figure 5.

**Figure 5.** MWCNT-CDC fiber under cyclic voltammetry (scan rate 5 mV s<sup>−</sup><sup>1</sup> (3 cycles), potential range 0.65 to −0.6 V) in LiTFSI-PC electrolyte. **a**: Near 0 dB SNR isotonic displacement measurement results (black line) and force sensor data fused with measurements data (red points) with voltage (dashed, blue). **b**: Fused and shifted isotonic measurements (red points) after being processed by slack correction algorithm with voltage (dashed, blue) compared to isotonic displacement (original LAS position measurements). **c**: Near 0 dB SNR strain measurement data correction algorithm. LAS and force sensor data (inputs) are fused via Equation (7). Then 0.5 um and 0.7 um gaps are eliminated, and resulted data is outputted.

Figure 5 shows the case where the displacement (isotonic measurements) of the ionic electroactive material is in the limitation of the measurement setup. Figure 5a shows the raw measurements of MWCNT-CDC actuators under the cyclic voltammetric technique, which shows a rough estimate about the specimen's isotonic actuation properties. The graph in Figure 5a in the present form cannot be used in further data analysis. To give a better interpretation of the results, the force sensor data can be fused with isotonic displacement measurements. We know from the elastic coefficient measurements that the change in force is proportional to the change of length, therefore the fusion can be implemented as Equation (7):

$$L\_{fuscd\_n} = L\_{LAS\_n} + k(F\_n - F\_{set}) \tag{7}$$

where, *n* is the index of the measurement data sample, *LLASn* is the isotonic displacement measured by LAS's controller, *Fn* is the measured force, and *Fset* is a set force which is constant throughout the experiment. Taking a closer look at the fused measurements shown in Figure 5a, there is some sort of ambiguous slack in the LAS actuation system, for example in the range of 310 s to 320 s, in the form of a 0.5 μm gap (comparable with Δlmin) between the measurement points, whereas similar gaps appear at other time steps as well. We assume that the slack might be a combination of the slack in the muscle samples clamping system, the internal properties of the samples, and the LAS controller position measurement or actuation errors. We assume that since the combined slack is comparable with Δlmin, it is most likely caused by the LAS controller error. Figure 5b shows the fused isotonic displacement (red points) after being processed by a slack correction algorithm in comparison to the original LAS position measurements. Figure 5c gives the data correction algorithm in the near 0 dB SNR displacement measurements by using two cycles, where the first removed the 0.5 μm gaps and the second the 0.7 μm gaps. After applying this algorithm, the results of the displacement measurements of MWCNT-CDC fibers can be interpreted.

Figure 5a,b results in expansion at discharging (−0.65 V) in the propylene carbonate solvent, which was explained [10] by the anions being nearly immobile, whereas at discharging the (solvated) cations (Li+) balance the negative charge bringing along the length change of the actuator [44]. In the case of the MWCNT-CDC fiber studied in this research, the main expansion also appeared at discharging with displacement in the range of 2 μm (equivalent to 0.2% strain). It was also found that small expansion at oxidation in the range of 0.3 μm appeared, which we assume relies on a small expansion accompanying the charging process of the EDL formed [45].

## *3.4. Uncertainty Evaluation*

The uncertainty of force measurements depends on the components [46] which are used in the force calculations. Since force is calculated based on Equation (2), the combined uncertainty is shown in Equation (8):

$$\mu = \sqrt{\left(\frac{\partial F}{\partial \mathbf{C}} u\_{\mathbf{c}}\right)^2 + \left(\frac{\partial F}{\partial \mathbf{U}\_B} u\_{\mathbf{U}\_B}\right)^2 + \left(\frac{\partial F}{\partial \mathbf{U}} u\_{\mathbf{U}}\right)^2 + u\_{\mathbf{F}d}^2} \tag{8}$$

where, *uC* is the uncertainty of the voltage-to-milligram coefficient, *uUB* is the uncertainty of the bias voltage, *uU* is the uncertainty of the potential measured from the force sensor, and *uFd* is the uncertainty caused by the drift of force measurements. The expanded uncertainty of stress and strain measurements is stated as the standard uncertainty of measurement multiplied by the coverage factor *k* = 2, which for a normal distribution corresponds to a coverage probability of approximately 95%. The uncertainty of the force measurements is proportional to the voltage values measured from the force sensor, which can be seen from Equation (2). This means that small force amplitude signals have higher accuracy, whereas with the growth of signal amplitude, the measurement uncertainty increases. Figure 6 shows the case of small amplitudes in force (mg) for MWCNT-CDC fibers.

**Figure 6.** Cyclovoltammetric (scan rate 5 mV s<sup>−</sup>1, 3r<sup>d</sup> cycle) isometric measurement results of MWCNT-CDC fibers in LiTFSI-PC electrolyte at potential range 0.65 to -0.6V, showing the force measurements (mg) (black line) and the uncertainty (B type) of the force measurements (mg) (red dotted).

The MWCNT-CDC fiber (Figure 6) showed change in force in the range of 30.5 mg, which is translated to stress in the range of 17 kPa. There is a small decrease in force from the starting point of 33 mg to the end point (22.8 mg) of 10.2 mg. The decrease in maximum force belongs to the creep effect, which can appear if mixed ion involvement appears, which is also seen in recent research [47].

The discharging, therefore, leads to the decrease in force which is translated into displacement knowing the elastic coefficient of the MWCNT-CDC fiber (*k* = 13.5 mg/μm). According to the uncertainty measurement in Figure 6 based on Equation (8), the coefficient uc was estimated to be 16.8 g/V and *u*UB = *u*U = 0.005 mV. The most important contributor to displacement measurement error is the resolution of the LAS position estimation system, which is 0.5 μm, therefore, the B type uncertainty of strain measurements without the assistance of data fusing (Equation (8)) is *k* 0.5 μm √3 - 0.6 μm. The data fusion contributes marginally (usually <0.05 μm) to the uncertainty of strain measurements, but it clarifies the interpretation of the results.
