**4. Simultaneous sensing and actuating properties in conducting polymers**

The driving reversible electrochemical reaction supports the development of simultaneous sensing and actuating properties by conducting polymer materials and by any electrochemical device based on those materials. The electrochemical working device (based on the electrochemical reaction) senses changes of any physical or chemical variable acting on the polymer reaction rate while working. This is the Le Chatelier principle applied outside equilibrium conditions (Smith, 2004). Therefore, for increasing values of the electrolyte concentrations or of the temperature working under flow of a constant current (constant reaction rate), lower values of the device potential are observed (the reaction is easier) during the transition between the same initial and final oxidation states of the materials. When a greater mechanical work is required (moving faster, applying a higher current, or a higher mechanical stress is needed to move the actuator) the reaction gives increasing potential when the device moves between the same initial and final oxidation states.

Those sensing abilities are intrinsic properties of the reaction. They are characteristics of the material reaction and of any device based on this electrochemical reaction. So, the dual and simultaneous sensing-actuation property is expected to be quantified from electrochemical equations.

The evolution of the conducting polymer film potential with time E(t) during the movement from the same initial oxidation/reduction state to the same final oxidation/reduction state driven by flow of a constant anodic current is given by a stair function (Otero et al., 2012).

$$E\left(t\right) = \sum E\_n\left(t\right)p\_n\left(t\right) = E\_1\left(t\right)p\_1\left(t\right) + E\_2\left(t\right)p\_2\left(t\right) + \dots + E\_n\left(t\right)p\_n\left(t\right) \tag{4}$$

where:

286 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

(potential or current applied), electrolyte and solvents used.

**4. Simultaneous sensing and actuating properties in conducting** 

The driving reversible electrochemical reaction supports the development of simultaneous sensing and actuating properties by conducting polymer materials and by any electrochemical device based on those materials. The electrochemical working device (based on the electrochemical reaction) senses changes of any physical or chemical variable acting on the polymer reaction rate while working. This is the Le Chatelier principle applied outside equilibrium conditions (Smith, 2004). Therefore, for increasing values of the electrolyte concentrations or of the temperature working under flow of a constant current (constant reaction rate), lower values of the device potential are observed (the reaction is easier) during the transition between the same initial and final oxidation states of the materials. When a

reversible electrochemical stimulation (Fig. 1).

anions.

**polymers** 

The reversible conformational movement from a coil like structure to a rod like structure is produced by extraction (oxidation) or injection (reduction) of *n* electrons through *n* consecutive steps of one electron per step, together with movement of balancing counterions. This results in length variation of a free polymer chain in solution but, in polymer films three dimensional changes of volume are observed. The entanglement of the polymer chains in the film gives reversible swelling or shrinking changes of volume under

**Figure 1.** Schematic representation of the reversible volume change associated with the electrochemical reaction in conducting polymer chains during oxidation/reducction during p-doping exchanging

Some mechanical test machines have been developed following length or thickness variations produced by submitting the film to different potential (Bay et al., 2003; Kiefer et al., 2007; Mazzoldi et al., 1998; Spinks et al., 2002) or current (Otero et al., 2006; Otero et al., 2007c) programs. In situ Atomic Force Microscopy (AFM) technique follows film thickness variation during reverse oxidation/reduction processes (Bieńkowski et al., 2011; Cho et al., 2011; Smela & Gadegaard, 2001). In this way, it has been possible to measure a volume difference between reduced and oxidized state up to 35% (Smela & Gadegaard, 1999). The volume change depends on multiple factors such as type of polymer, synthesis conditions

$$p\_n(t) = \mu\left(t - t\_n\right) - \mu\left(t - t\_{n+1}\right) = \begin{cases} 1, t \in \left[t\_n, t\_{n+1}\right] \\ 0, t \notin \left[t\_n, t\_{n+1}\right] \end{cases} \tag{5}$$

Being *tn* the time while the nth electron is removed from every polymeric chain and En(t):

$$\mathrm{E}\_{s}\left(t\right) = \mathrm{E}\_{o} + \left(n - 1\right)\Delta E + \frac{RT}{\left(1 - \alpha\right)F} \left\{ \ln\left(\frac{i\_{s}}{FV}\right) - d\ln\left[A^{-}\right] - c\ln\left(\left[Pol^{\*}\right]\_{\alpha\omega\omega} - \frac{i\_{s}t}{FV}\right) - \ln k\_{s\alpha} \right\} \tag{6}$$

where E0 is the standard potential, ia is the applied current; n is the number of consecutive electrons extracted from a chain; ΔE is the increment observed in the potential when a new electron is extracted from a polymeric chain, R is the universal gas constant (R = 8.314 J K-1 mol-1); α is the symmetry factor; F is the Faraday constant (F=96485 C mol-1); V, the volume of the film; [A- ] the concentration of anions (counterion) in solution; t, the time of current flow; T is the experimental temperature; d and e are the reactions orders related with the concentration of anions in solution or to that of the active centres [Pol\* ] in the film (sites of the polymer where a positive charge will be stored after oxidation) and ka0 is the rate constant or rate coefficient for E=E0.

Therefore, Eqs. 4 and 6 are the sensing equations: the evolution of the device potential during actuation is a function of either, driving (current) and working (temperature, electrolyte concentration and film volume) variables.

Being electrical machines, by integration of Eq. 6 the evolution of the electrical energy consumed by the electrochemical device (Ua) during the actuation time is attained:

$$\begin{aligned} \text{iU}\_{a}\left(t\right) &= i\_{a}\left[\text{E}\left(t\right)dt = i\_{a}t\left\{\text{E}\_{0} + \left(n - 1\right)\Delta\right\} + \frac{RT\dot{\imath}\_{a}t}{\left(1 - \alpha\right)F} \left\{\ln\left(\frac{\dot{\imath}\_{a}}{FV}\right) - d\ln\left[A^{-}\right] - \ln k\_{a0}\right\} + \\ &\frac{RT\dot{\imath}\_{a}}{\left(1 - \alpha\right)} \left\{\ln\left(\left[P\dot{\imath}^{\prime}\right]\_{\text{siai}} - \frac{\dot{\imath}\_{f}t}{FV}\right) - 1\right\} \left\{\left[P\dot{\imath}^{\prime}\right] - \frac{\dot{\imath}\_{f}t}{FV}\right\} \end{aligned} \tag{7}$$

The consumed energy (Ua) after any constant time (t) of current flow is also a sensing function of the same variables. Fig. 2 shows the good agreement between experimental and theoretical results for the consumption of three different charges (from the same initial oxidation/reduction state, three different final oxidation/reduction states are obtained) at different experimental temperatures by flow of a constant anodic current for three different times of current flow.

**Figure 2.** a) Anodic and cathodic experimental (full lines) and theoretical (dotted lines) chronopotentiograms obtained by flow of ±0.75 mA through a 1.6 mg pPy film (10.77 mm x 5.09 mm x 19 μm) at different temperatures (black line: 5ºC; red line: 10ºC; green line: 15ºC; blue line: 20ºC and cyan line: 25ºC) in 1 M LiClO4 aqueous solution. b) Achieved potential after different times of anodic (positive) or cathodic (negative) current flow. c) Consumed electrical energy after the same times of current flow. Reproduced from (Otero et al., 2012), with permission of American Chemical Society).
