**4. Energy storage study of IPMC polymer system**

The electro-active IPMC material comprises a central layer possessed by a polymer with the upper and lower layer prepared of higher conductive electrodes.

#### *IPMC Based Flexible Platform: A Boon to the Alternative Energy Solution DOI: http://dx.doi.org/10.5772/intechopen.99434*

The polymer that conquers the central layer has two main attributes: ion selectivity and permeability. These features are accomplished using polymers comprising organic ionic groups involved by covalent bonds to the polymer's backbone. Rely on the sign of the charge of the ionic groups existing in the polymer; it may be penetrable to cationic charge, i.e., positive and anionic charge, i.e., negative, or both. The polymers are commonly used with fixed ionic sulfonate groups for permeable positive ionic charges [35]. Furthermore, it is stated that one of the most standard groups of polymers worked in IPMC is "perfluorinated alkene," and specimens of these polymers are Nafion, Neoseptat, Flemiont or Selemiont, and Aciplext [35]. The electrodes founding the upper and lower layers of IPMCs are electrical conductors, investigated by very low electric resistivity. They are generally platinum (Pt) or silver (Ag) [36]. In the methods of fabrication of an IPMC, the electrodes deposition is presently made on the upper and lower active surfaces in three techniques: the route of "incorporation through reduction" (suffusing reduction methods) [29]; the physical casting procedure and the "direct mounting methods" (natural process assembly). The latter was established to elucidate the main difficulty of the two other manufacturing methods: the poor control in the deposition time of electrodes. The efficacy of the "integration through reduction" methodologies has created this the most worked, despite being the most time-taking and highly expensive [37]. IPMC membranes were fabricated using Nafion 117 polymer that is penetrable to positive ionic charges. The electrodes were deposited by high conducting metal like platinum or gold on the polymer using the "integration by reduction" procedures. Moreover, the disadvantage of holding poor control in the surface features of the electrodes typically reasons IPMC membranes to have different textures. The surface morphology and geometry of the electrodes of the IPMCs must be associated with their enactment, concomitant with the electrodes' electric resistance, and the consequential IPMC dielectric constant. Fundamentally, existing research work uses IPMC materials as actuation elements in electromechanical systems [30, 38–42]. A research was conducted on the capabilities of electro-active IPMC capacitors and the requirement of these possibilities on temperature [43–47]. Numerous IPMC membranes were observed with the same thickness but varying active surface areas. The membranes did not need any electrolyte that is why it is called "dry" strips with those capacitor elements. The polymer constituent of the membranes was acquired from a sheet of Nafion 117 and having a definite thickness. After cutting, a layer of chromium of 5 nm thickness was coated on the polymer surface, followed by a gold layer with a thickness of 100 nm on that same platform. Chromium was used to guarantee good adhesion between the gold and the polymeric matrix. The features of the voltage terminals of the composite material were chronicled within charge and discharge tests. All assays were done when charging the IPMC using a current power source, from which constant current charge was produced. Each IPMC was charged over fixed time using a fixed electric charging current in mA and then allowed to discharge, investigating the material property itself, i.e., how long they hold a charge. Moreover, the obtained results are calculated, and the exhibited capacitance value of specific and areal both have in the very higher range. The charging procedure is happened very fast up to the limit. The operating voltage was also perceived that the operating voltage is set up to that above which the IPMC got disrupted. Some of the used IPMC membranes were cut to test their storage capacitance scalability with their effective surface area. It was witnessed that a lessening of 20% of the surface area amounted to a reduction of 20% of its storage capacitance, such as a linear relationship [48]. Another research work verified a system for producing and storing electrical energy using IPMC devices and polymeric polyvinylidene difluoride (PVDF) piezoelectric devices to feed emitting organic diodes. For the electrical energy storage of IPMC, electro-active devices were worked, also for the production of electrical energy, PVDF piezoelectric elements

were employed, both as-fabricated single and double layers. The feasibility of IPMCs as electric energy storage elements was measured. The experiments were executed concerning the duration of the electrical charge store in the IPMC and reached the voltage level when the charging mechanism occurred at a constant voltage and constant current. Mainly The Nafion polymer is used in the IPMCs. The chromium electrodes were worked with an intermediary layer between the gold and the polymeric matrix, and also, the electrical contact from the gold platform is easy to make up [49, 50]. The storage capability of the IPMC membranes was certified with the integration of lithium ions in their interior structure. This for the initial doping of the IPMCs matrix was executed by dipping the devices in LiCl solution. The fabricated morphology of IPMCs matrix and metal-doped IPMC membranes stored charge in the greatest amount within a particular time window compared to the other storage elements, especially electrolytic capacitors, which exhibited specific and areal capacitances, too high. This work allows us to determine the relatively short electric charge of this material (**Figure 6**).

#### **4.1 Electric model representing IPMCs as electrical energy storage elements**

Dependent on the IPMC element mode, a variation of its theoretical model had to be prepared. This section analyses the various aspects and effects of the entire force on the positive ionic charges when the IPMC stores electrical energy. Electrical forces: When a continual electric current is enforced on the IPMC matrix, this leads to the positive ions, which are primarily at rest within the negative ionic polymer charges, to transport in the direction of one electrode. However, the negative ionic costs in the polymer are permanent; they will not be transportable. The gap between the positive and negative ionic charges will then escalate to the genesis of an electric field inside the IPMC matrix; there is a potential difference in its terminals and electrical forces between the IPMC systems. Mass diffusion forces: Mass diffusion forces are important in the experimental stage. When an IPMC membrane is dipped in an electrolyte, the forces for the mass diffusion method contribute to the impregnation of the membrane with the component positive ionic charges of the electrolyte. At the time of positive ionic charges, concentration in the membrane equals outside positive ionic charges. The concentration on the outer surface is residual; a substantial concentration gradient can transfer charges into the polymer matrix. Nafion 117's polymer encompasses negative charges, making the IPMC membrane selective only to positive charges concerned by the electrical forces

**Figure 6.** *Illustration of ionic distribution in the IPMC based system [51].*

between them and the negative fixed charges. Mechanical forces: There are no mechanical pressures forced on the IPMC capacitor. The positive ionic charges current density: regarding the forces' characterisation, one arrives at Eq. (1) for the positive ionic charges current density within the IPMC.

$$J\_{+} \approx -\left(\frac{RT}{K}\right)\nabla\_{\rho\epsilon}^{+} - \left(\frac{q+}{kp}\right)\nabla\_{p\text{mec}}\tag{1}$$

#### **4.2 Discharging and charging of IPMCs at constant current**

The discharge investigation under a resistive load intended to acquire the specific capacitance values Ceq (Fg�<sup>1</sup> ) connected with a specific IPMC membrane, i.e., a capacitive element, and compute each discharge time td and each used electrolyte. To execute a discharge test, it is essential to execute the electrical charging of each IPMC capacitive membrane. However, in every discharge, the test contained two divergent phases: discharging through a resistor and constant voltage charging. The obtained value was selected to have a much low value than the internal IPMC Rdif resistance. This is expected to realise the synchronised use of two membranes of IPMC materials connected in parallel. The upper IPMC electrodes were associated with the positive terminal of the external DC voltage, while the lower electrodes were coupled to its negative terminal. There is a discharge resistance, i.e., Rext is present in between the terminals of the external circuit. Two of the most significant parameters for analysing a device for electrical energy storage are the rated voltage Vn and charging time ts. A series of IPMC charge tests are executed at a constant current to acquire values for those two parameters. The current source has the main benefits of being consistent for quite lower values of current in the mA order, and the voltage is controlled. The usage of the lower current value is for charging the IPMC is vindicated by these for being usable in low-power devices. This voltage source permits the constant current imposition to the IPMC capacitive membrane elements is crucial for the investigations of charging and discharging. The net gain in the current power source is better. The IPMC charging analyses were carried out at a constant current. This value was selected because the thinnest IPMC used in those tests reaches its nominal voltage of 1.5 V.

#### **4.3 Duty cycle**

The quantity of charge–discharge cycles provides the valuable life of a precise electrical energy storage device that can tolerate ago no longer being fit for operation. Those parameters are essential for indicating how long or for how many cycles the elements can be worked for a specific application. To conclude whether altered solute concentrations could enhance the useful life of an IPMC capacitive membrane, numerous consecutive charging and discharging investigation at constant current were executed. This harvests a square waveform of electric current conforming to charging and discharging cycles at fixed current. The waveform was asymmetric because a negative current in the discharge time was introduced, and the IPMC terminal voltage would reach negative values [51].

#### **4.4 Holding time**

Preferably, a device for electrical energy storing should deliver all of the electrical energy previously-stored irrespective of the time at which it was stored. The IPMC electromechanical model delineates that the electric charge in the IPMC system is related to the terminals voltage in Eq. (2). This designates that the electric charge stored in an IPMC is directly proportional to the voltage between its terminals, as in a capacitor.

$$\mathbf{Q} = \frac{\mathbf{3}ebl}{\mathbf{5}d} \text{ V} \tag{2}$$

The experimental methods for assessing the conservation of electrical charge in IPMC capacitive elements had two dissimilar parts; whole charging of the IPMC following the analysis of its voltage at subsequent instants of time [52]. When the IPMC rated voltage is reached, the current source was turned off. The terminals voltages of the membrane were then calculated by varying times. The IPMC material depicts capacitive behaviour, and the value of its capacitance relies on the dielectric constant as in Eq. (3).

$$\mathbf{C\_{eq}} = \frac{3ebl}{5d} \tag{3}$$

The specific capacitance Ceq\_e (F kg�<sup>1</sup> ) of a given IPMC membrane is measured by Eq. (4), where r is the equivalent mass density of the IPMC membrane.

$$\text{Ceq\\_e} = \frac{\text{Ceq}}{m} = \left(\frac{3\epsilon b l}{5d}\right) \cdot \frac{1}{(\rho.b.l.d)} = \frac{3\epsilon}{\rho d^2} \tag{4}$$

The dielectric constant value of the as-fabricated IPMC capacitive system is affected by the electrolyte used and the negative ionic charge density of existing connections to the polymeric morphology. Therefore, the connexion between the dielectric constants of two different IPMC membranes, if assembled in the same electrolyte, is only depicted by the ratio existing within the negative ionic charges density in the same element, which in turn will rely on the volume of the IPMC system (*b.l.d*) and the ionic charges density of the polymeric matrix used, k, stated by the following relation in Eq. (5).

$$a \lnot b.b.l.d.\tag{5}$$

The significant time evolution of the voltage at resistance Rext throughout the IPMC discharge is given by Eq. (6), where U is the voltage at the preliminary instant, Rext is the electrical discharge resistance, and Ceq is the equivalent capacitance of the IPMC element.

$$\mathfrak{G}(\mathbf{t}) = \mathbf{U}\mathcal{A}^{-\frac{t}{\overline{\mathcal{R}\_{\text{ext}}}\mathcal{L}\_{\text{eq}}}} \tag{6}$$

The primary technique contained the numerical approximation of the voltage curves acquired experimentally via Eq. (6). The methodologies of nonlinear least squares with the help of the confidence region algorithm were introduced to assess Ceq. The Rext had a value in the range kΩ. As the regression curve calculated was not a better approximation of the experimental data curve. Eq. (6) for the capacitance of IPMC equivalent presumes only a single capacitive effect in IPMC membranes. This is delineated for the transportation of positive ionic charges in between the polymer matrix, and it's accumulated along the whole surface of the electrode with a negative polarity (**Figure 7**).

Moreover, when the low-frequency is applied electrical signals like 0.1 Hz in this proportion of electro-active material, the positive ionic charges circulated the inner side of the IPMC matrix quickly gathered the nearby zone of the negative electrode, and consecutively the capacitive double layer is formed. The outcomes of

*IPMC Based Flexible Platform: A Boon to the Alternative Energy Solution DOI: http://dx.doi.org/10.5772/intechopen.99434*

experimental analysis, however, depicted the capacitive effect of higher potentiality. On the basis of the physical model formerly manifested for the IPMC materials, it was noted that the capacitive effect was only corroborated with the formation of electric dipoles in between the positive ionic charges and fixed ionic charges those are located in between the double layer region and the positive electrode. In conclusion, there are two distinct capacitive effects: one is for the genesis of the double layer, and another is associated with the produced electric dipoles. To interpret for the two capacitive effects in the time frame of the voltage, an amendment was made to Eq. (6), containing the sum of a second exponential component linked with a second time constant, as Eq. (7) shows [52].

$$\mathcal{S}\left(\mathbf{t}\right) = \mathbf{a}.e^{\overline{\tau}} + b.e^{\overline{\tau}} \tag{7}$$

The model now reflects two-time constants: a short time constant *τ* 1 and a slow time constant *τ* 2. The sum of those parameters a and b is equal to the IPMC voltage at the initial stage of the discharging methods. The capacitance value is obtained related with each time constant from Eqs (8) and (9). One of that time constants is associated with the capacitive effect in the IPMC linked with the electric dipole arrangement and which zone in the polymer resembles the region between the positive ionic charges and the fixed ionic charges. On the contrary, the second constant is allied with the double layer.

$$\mathbf{C1} = \frac{\pi \mathbf{1}}{\text{Rext}} \tag{8}$$

$$\text{C2} = \frac{\pi \text{2}}{\text{Rect}} \tag{9}$$

Using the revised model, a substantial enhancement was achieved, allowing assessing the value of capacitances C1 and C2 and the time constants connected with each type of IPMC system and for each type of electrolyte. The fact that the maximum capacitance was accomplished when using electrolytes with lower solute concentrations can be elucidated by the encapsulation effect [53]. The encapsulation effect ascends from the circumstance that the maximum number of electric dipoles designed in the polymer matrix is attained for a given solute concentration of the electrolyte. A definite limited number of electric dipoles will relate to a maximum yield of the dielectric constant of the IPMC matrix. Since the capacitance concomitant with an IPMC is correlated to the dielectric constant using Eq. (9), it follows that the capacitance will incline to a maximum value at high solute concentrations. It should be recollected that *τ* 1 is associated with the polymer region where the creation of electric dipoles in between positive ionic charges and fixed ionic charges happens and the region that will establish the characteristic times of charging and discharging of each IPMC system. However, an IPMC membrane having a higher thickness does not signify a greater time constant but directly proportional to the effective surface area. The difference in surface areas also delineates the alteration in results between the IPMC with the same thickness. Therefore, the secondlargest surface area of the IPMC membrane in the research would be predictable to have higher yields than were acquired.

#### **4.5 Discharge time**

For an RC circuit, the load voltage during discharge of the capacitor over resistance is correctly given by Eq. (10).

$$\theta(\mathbf{t}) = \mathbf{U}\mathbf{0}.e^{-\frac{t}{\mathbb{R}^{C}}} \tag{10}$$

The discharging time constant *τ* is given by eqn

$$
\pi = R.\mathbf{C} \tag{11}
$$

Replacing Eq. (11) into Eq. (9.20), one arises at the voltage at time t given by Eq. (12).

$$\mathcal{S}(\mathbf{t}) = \frac{U\mathbf{0}}{\mathbf{e}} \approx \mathbf{0}.\mathbf{3}\mathbf{\tilde{c}}\mathbf{8}U\mathbf{o} \tag{12}$$

The instantaneous at which the IPMC voltage reaches the value calculated by Eq. (12) is measured from all the experimental results. It was depicted that the majority of IPMC membranes offered results in the order of hundreds of seconds. Incrementing the values with enhancing electrolyte solute concentrations were also found. This system had the lowest surface area among the IPMC matrix analysed, thus having fewer electric dipoles along the electrodes of this matrix. The IPMC doublecapacitance model undertakes two different capacitive effects; one is related with a fast time constant *τ*1 and with the other a slow time constant *τ*2. The significance of each time constants in the IPMC capacitor process is related to the frequency of the circuit in that it will be implanted. The capacitance C1 is leading in the case of high frequencies. Contrariwise, in low frequencies, the capacitance C2 will hold huge prominence in the operation of the IPMC capacitor. However, different functional features rely on the frequency operation of the circuit in which the IPMC is implanted; it is crucial to envisage its energy depending on the envisioned mode of operation. To calculate that percentage of the total stored energy can be free if high frequencies are used, the power degenerate in the resistive load in the time interval consistent to the first time constant—that is, from the initial time of the discharge until the time instant *τ*1—was calculated. Within these essays, two charging times importances had been taken care of analogous to two different time instants in the charging methods of the IPMC. The first time moment t corresponds to the instant at which the IPMC voltage value at its terminals is approximately 63% of the final value U, as shown in Eq. (13).

$$\mathcal{S}(\mathbf{r}) = \mathbf{U} \left( \mathbf{1} - \frac{\mathbf{1}}{\mathbf{e}} \right) \approx \mathbf{0}. \mathbf{632}U \tag{13}$$

*IPMC Based Flexible Platform: A Boon to the Alternative Energy Solution DOI: http://dx.doi.org/10.5772/intechopen.99434*

The second time instant is related to when the across IPMC terminals voltage equals 95% of its final value. These two moments were selected to depict the effect of the two-time constants of the system forecasted by the attuned electrical model. The best times were usually realised for higher solute concentrations, with the maximum having reached for IPMC using the higher electrolyte solute concentration. The charge time values are alike to the period of the cut-off frequency an IPMC element replies to mechanically. The charging time of an IPMC element is directly associated with its frequency response; meanwhile, this time interval resembles the time needed for much of the positive ionic charges stored inside the element is located on one of its electrodes, establishing dipole electric ionic in between positive and negative electric charges. Thus, one can authorise two charging time constants: a fast constant, which impacts the early charge stages, and a slow constant, with greater effect in the remaining moments. For cases of constant current charging, the model that expresses this fact is given by Eq. (14), where Umax is the IPMC voltage at the end of charging and the sum of the constants a and b is equal to 1.

$$\theta(\tau) = \text{Umax}\left(\mathbf{1} - a e^{\frac{-t}{\tau \Lambda}} - b e^{\frac{-t}{\tau \Lambda}}\right) \tag{14}$$

#### **4.6 Nominal voltage and number of charge: discharge cycle**

To assess an IPMC matrix system's electric power density over the maximum energy stored for each IPMC, the rated voltage must know first. It has been contemplated that the nominal voltage of an IPMC polymer matrix to the extreme potential variance can happen at its terminals deprived of the electrolysis of the solvent. Electrolysis of water is a physical circumstance investigated by the water decomposition into its basic elements, namely oxygen molecules and hydrogen ions. This incident has the effect of concentration lowering of solvent present in the IPMC, reducing the ionic mobility within the IPMC. Moreover, the H+ ions formation enhances the density of positive ionic charges, leading to a temporary increment in the ionic current density. If an adequately high electric field is extended, the polymer matrix electro-active IPMC membrane material interruption may still happen, that instigating permanent destruction to the material. The target is to inspect the association between the number of charge–discharge cycles and the solute concentration of a given IPMC polymer matrix. Different IPMCs were evaluated rely on the electric energy originally stored in certain IPMCs equated with the values at the end of the limited number of charge–discharge cycles of the IPMC. It is noted that these results were also equated with all solute concentrations considered. The methodologies introduced to relate the stored energy at the initial and end of a test relates to the square of the voltage at IPMC terminals. After a particular time, the outcomes for the decrease in stored electric energy were calculated as a solute concentration function. When the IPMC system is charged up to a definite maximum voltage, and after a few seconds, the entire system allows for discharge typically without external influence, and the total charge dissipation has occurred consecutively. The entire time taken for discharge is fully its charge storing capabilities. The primary rapid decrement in the voltage is due to the downfall of the double layer shaped by the positive ionic charges and the electric ones on the electrodes. The electrical energy stored in a capacitive system is given by Eq. (15).

$$\mathbf{E} = \frac{1}{2} . C.V^2 \tag{15}$$

In the time interval, the main incident was the reorganisation effect of the electric dipoles formed by ionic charges in the IPMC polymer matrix system.

As a result, the voltage at the IPMC lessened significantly. This voltage drop can be elucidated by evaporation of electrolyte, i.e., water in this case. However, the IPMC does not encapsulate; the evaporation of water will play a vital role in these circumstances [53]. As the solvent vaporises, this took away positive ionic charges, so the electric charge decreased within the IPMC system and the decreased number of electric dipoles. In some cases, it was observed that the membrane had dried, probably having some water in the matrix inside, which elucidates the presence of a residual voltage at its terminals. The energy density of stored electrical energy: It has been calculated that this type of capacitive element—the IPMC material possesses that is similar in nature to that of classic capacitors when used for energy storage. It is known, electrical energy is measured from the rated voltage and the capacitance. The power is proportional to the nominal voltage square directly, and, in turn, the rated voltage is proportional to the IPMC element thickness directly since the electrolysis of the solvent is catalysed by the electric field present within the IPMC system matrix. The energy density is exhibited by the ratio between the extreme energy the IPMC can store and its respective mass. It has also been seen that the response that incrementing the thickness of the IPMC does not impact energy density enhancement. This is a significant response that depicts that the price of a membrane of electro-active IPMC material becomes high prominently with the thickness. It is crucial to mention that the electrolyte a solution of salt and water for research purposes. If an electrolyte having a higher dielectric constant, like an electrolyte composed of lithium and propylene, had been introduced, it would be anticipated that the electric energy storage capacity of the IPMC materials matrix would be prominently enhanced. Lithium ions (Li2+) developing the solute of the electrolyte has a lesser atomic radius than sodium ions (Na+ ) and thus have higher ion transportation capabilities within a membrane of IPMC material, which accelerates the ion interaction between the sulfonate ions (SO3�) and the positively charged ions attached to the polymer structure [54]. Moreover, this electrolyte's degree of evaporation is very low, which advances the preservation time of the electric charge of a capacitive IPMC material matrix.
