**2. Experimental**

are preferred for pulse power applications, because they provide far higher power electric pulses, per weight/volume, than batteries [1, 2]. Moreover, unlike batteries, capacitors are not damaged by providing pulsed power. This robust feature leads to their employment as power load levelers to extend battery life. For example, in satellites, systems designed to transfer high power demand from batteries to a parallel capacitor system can significantly increase

Most research into increasing capacitor energy density is focused on developing graphene,

generation EDLC [3–7]. The theory suggests that capacitors with graphene electrodes could

Recently, a new type of 'supercapacitor' was invented, NP supercapacitors (NPS) with energy density rivaling the best prototype EDLC, but based on an entirely different paradigm [8–14]. Unlike EDLC that gain energy density through the use of high surface area electrodes with low dielectric value, NPS use low surface area electrodes and dielectrics with remarkably high dielectric constants, specifically super dielectric materials (SDM), that is materials with

an 'active phase', such as salt dissolved in a liquid, and an 'inactive' mechanical phase such as anodized titania, T-SDM [8, 9], high surface area porous refractory oxides, Powder-SDM [10–12], or even simple fabrics, Fabric-SDM [13], that hold the active phase in place. The theoretical basis of SDM [8, 9] is that in an electric field the ions in solution travel to create dipoles, which are far longer (ca. 1 μm) than those found in solid dielectrics (ca. 10−4 μm). It is the 'field canceling' effect of dipoles, proportional to length, which leads to increased capacitance, as

It is reasonable to label NPS, a new type of supercapacitor based on the energy storage val-

charge rates, rivaling, perhaps surpassing, the best graphene-based EDLC prototypes [18–20]. One unresolved issue: NPS performance as a function of frequency. Given the theory of NPS requires micron scale ionic migration in a liquid to form giant dipoles, there should be significant performance degradation ('roll-off') with increasing frequency. That is, if not enough time is available in a charge cycle for dipoles to fully form via ion travel, the dielectric value, energy density, etc. will be reduced. Thus, it is important to directly test the performance of NPS as a function of frequency. Given the most likely application, power release over very short times, ca. 0.05 s, special attention should be paid to discharge rate dependence of power and energy. The one study of NPS performance as a function of discharge time was on F-SDM, a variety not found to have particularly high energy density. Significant roll-off of all parameters with decreasing discharge period (roughly equivalent to increasing frequency) was documented. The roll-offs, all parameters, were well fit by simple power law relations over orders of magnitude of discharge time. In the present study, we employed the same method used in the earlier study to characterize performance as a function of discharge period of a variety of high energy density NPS, those employing anodized titania saturated with various aqueous free ion solutions. Once again, significant roll-off was observed as expected and the power

.

/g), electrodes for the next

, a value far less than the current generation

). Notably, current commercial supercapacitors

, although values >1011 are reported. SDM are composed of

for T-SDM with aqueous NaCl solutions at very slow dis-

the conductive material with the highest surface area (~2600 m<sup>2</sup>

have an ultimate energy density of ~800 J/cm<sup>3</sup>

per the classic model of dielectric behavior [15–17].

commercial lithium ion battery (~2200 J/cm<sup>3</sup>

have an energy storage rating of <50 J/cm<sup>3</sup>

dielectric values greater than 10<sup>5</sup>

ues achieved, approx. 400 J/cm<sup>3</sup>

battery and satellite, lifetime.

70 Supercapacitors - Theoretical and Practical Solutions

The NP supercapacitors were constructed of anodized titania foils filled with various aqueous salt solutions. The remaining metal of the original titania was one electrode and a graphitic material served as the other electrode. The performance of these capacitors was characterized using standard galvanostat constant current protocols. All procedures are described below.

Anodization process–Titanium foil anodes (99.99% Sigma Aldrich), approx. 0.05 mm thick, were anodized, as described elsewhere [8, 9, 21–23], in an ethylene glycol solution containing small quantities of ammonium fluoride (0.25% w/w) and water (2.75% w/w), using a titanium cathode (2 cm distant from the anode) at a constant DC voltage of 40 V for 46 min. This process created a layer of cylindrical hollow titania tubes on the parent titanium, average length measured to be 7.7+/−0.4 μm [24], but for purposes of conservative computation of energy density and all other parameters, assumed to be 8 μm in length. The tube diameter was found to be approximately 90 nm, but that figure does not enter the computations. In prior studies employing a nearly identical protocol, but using different anodization time periods, the intent was to create anodized layers/tubes of various lengths in order to test the impact of tube length on dielectric value and energy density. In this study, the intent was to focus only on the impact of the liquid phase composition, thus all the matrix material, that is the anodized titania, was produced using a single protocol and produced nearly identical anodized layers. Typical tubes formed from this process are very regular in structure and densely packed together [8, 9, 23, 24]. They are all oriented with the long axis perpendicular to the surface of the parent foil. No effort was made to crystallize the tubes via a thermal treatment.

Assembly of capacitors—All the capacitors employed were a standard parallel plate construction, consisting of an electrode composed of the unanodized section of the original titania foil, the dielectric consisting of the anodized section (2 × 1 cm) filled with an free ion containing aqueous solution, and a positive electrode of Grafoil, a form of compressed graphite. The tubes in the anodized layer were filled with solution simply by placing them in a beaker filled with the solution for 50 min at room temperature. Three different ion precursors were used: sodium nitrate (NaNO<sup>3</sup> ), ammonia chloride (NH<sup>4</sup> Cl), and potassium hydroxide (KOH). Capacitors were constructed from aqueous solutions of the three salts, specifically three weight percent concentrations of each salt, 10, 20, and 30%, for a total of nine capacitors. A 'control study' employing distilled water was run as well.

After the salt solution saturation, the capacitor had one electrode, the metallic component of the anodized titanium foil, and a compound dielectric in the form of the titania tubes filled with aqueous solution. Placing a Grafoil sheet (2 × 1 cm) on top of the open tube end of the anodized film completed the capacitor. Specifically, a rectangle of Grafoil (compressed natural graphite, 99.99% carbon [25, 26]) 0.3 mm thick was placed on top. The metallic part of the anodized foil was connected to the negative terminal of the galvanostat, and the Grafoil sheet connected to the positive terminal. The final volume used in subsequent calculations was that of the dielectric section, 8 μm × 2 cm × 1 cm. Greater detail is given elsewhere [24].

### **2.1. Electrical measurement**

All parameters, including energy density, power density, capacitance, and dielectric values, were derived from 'constant current' galvanostat data (BioLogic Model SP 300 Galvanostat, Bio-Logic Science Instruments SAS, Claix, France). Operated in constant current charge/discharge mode over a selected voltage range (2.3–0.1 V), the data can be employed directly to determine capacitance as a function of voltage from the slope of voltage as a function of time, that is, for constant current:

$$\mathbf{C} = \frac{d\boldsymbol{q}}{dt}/\frac{dV}{dt} = \mathbf{I}/\frac{dV}{dt}$$

Clearly for capacitance which is not a function of voltage, this equation predicts a perfect saw tooth voltage vs. time pattern. In fact, in this and earlier studies, it was found that the capacitance is a function of voltage, leading to 'irregular wave forms' [8–13]. As discussed in earlier work, this indicates that the capacitance is voltage dependent, specifically decreasing as voltage increases. For this reason, the capacitance reported herein is for the voltage region between 0.1 and ~0.8 V. In this voltage regime, the voltage vs. time relationship was always found to be nearly linear for all discharge times greater than 0.001 s indicating constant capacitance over this voltage region. In all cases, it was found that capacitance decreases with increasing voltage as a function of discharge time. The shorter the discharge time the more pronounced the departure from constant capacitance (**Figure 1**).

Given the variability of capacitance with voltage, energy cannot be computed directly from 'capacitance', but it can be determined directly from the constant current data. Specifically, energy was determined from the integrated area under the total discharge curve (volt seconds) multiplied by the constant current. Power was determined by dividing the directly determined energy, by the time required, during discharge, for the voltage to go from the maximum to the minimum value. Energy and power density were then determined by dividing energy or power by the volume of the dielectric.

Methods to determine energy and power density that require the use of data 'extrapolated' beyond the voltage range actual measured can lead to severe errors, generally overestimates. For example, impedance spectroscopy measures the dielectric constant over a narrow voltage range, generally 0 ± 15 mV [27, 28], and provides little reliable information about energy storage characteristics. Determining the energy storage/power production of most capacitors requires a collection of data over the full voltage operating range [29–31].

a wide range of current values over the range 5–250 mA. In all cases, the charging current was the same magnitude as the discharge current, but of opposite sign. For each capacitor studied nine different currents in this range were used to determine capacitive behavior over approximately four orders of magnitude of the discharge time. At each selected constant current at least 10 complete cycles were recorded and generally 20. Averaged data from these cycles are reported. As noted, in all cases, the voltage was in the range 2.3–0.1 V. The finding that linear power law data

**Figure 1.** Deviation from voltage independent capacitance. (Top) For relatively long discharge times (>1 s), the capacitance is nearly independent of voltage to nearly 2 V, as illustrated by the dashed line nearly matching data over a

from ideal behavior, capacitance independent of voltage, becomes more pronounced (sample: NH<sup>4</sup>

100 mA). For all discharge times studied, the capacitance was nearly constant below 0.8 V.

Cl 30%; charge rate: 10 mA). (Bottom) As the discharge time decreases, the deviation

Performance of Aqueous Ion Solution/Tube-Super Dielectric Material-Based Capacitors as…

http://dx.doi.org/10.5772/intechopen.71003

73

Cl 30%; charge rate:

broad voltage range. (sample: NH<sup>4</sup>

Galvanostats operated in the constant current mode do not permit selection of frequency. In order to obtain capacitance as a function of frequency, the current is changed. In essence increasing the current decreases the period required to charge/discharge. Hence, each capacitor was tested over

Performance of Aqueous Ion Solution/Tube-Super Dielectric Material-Based Capacitors as… http://dx.doi.org/10.5772/intechopen.71003 73

anodized foil was connected to the negative terminal of the galvanostat, and the Grafoil sheet connected to the positive terminal. The final volume used in subsequent calculations was that

All parameters, including energy density, power density, capacitance, and dielectric values, were derived from 'constant current' galvanostat data (BioLogic Model SP 300 Galvanostat, Bio-Logic Science Instruments SAS, Claix, France). Operated in constant current charge/discharge mode over a selected voltage range (2.3–0.1 V), the data can be employed directly to determine capacitance as a function of voltage from the slope of voltage as a function of time,

> *dt* / \_\_\_ *dV dt* <sup>=</sup> I/

more pronounced the departure from constant capacitance (**Figure 1**).

requires a collection of data over the full voltage operating range [29–31].

Clearly for capacitance which is not a function of voltage, this equation predicts a perfect saw tooth voltage vs. time pattern. In fact, in this and earlier studies, it was found that the capacitance is a function of voltage, leading to 'irregular wave forms' [8–13]. As discussed in earlier work, this indicates that the capacitance is voltage dependent, specifically decreasing as voltage increases. For this reason, the capacitance reported herein is for the voltage region between 0.1 and ~0.8 V. In this voltage regime, the voltage vs. time relationship was always found to be nearly linear for all discharge times greater than 0.001 s indicating constant capacitance over this voltage region. In all cases, it was found that capacitance decreases with increasing voltage as a function of discharge time. The shorter the discharge time the

Given the variability of capacitance with voltage, energy cannot be computed directly from 'capacitance', but it can be determined directly from the constant current data. Specifically, energy was determined from the integrated area under the total discharge curve (volt seconds) multiplied by the constant current. Power was determined by dividing the directly determined energy, by the time required, during discharge, for the voltage to go from the maximum to the minimum value. Energy and power density were then determined by dividing

Methods to determine energy and power density that require the use of data 'extrapolated' beyond the voltage range actual measured can lead to severe errors, generally overestimates. For example, impedance spectroscopy measures the dielectric constant over a narrow voltage range, generally 0 ± 15 mV [27, 28], and provides little reliable information about energy storage characteristics. Determining the energy storage/power production of most capacitors

Galvanostats operated in the constant current mode do not permit selection of frequency. In order to obtain capacitance as a function of frequency, the current is changed. In essence increasing the current decreases the period required to charge/discharge. Hence, each capacitor was tested over

\_\_\_ *dV dt*

of the dielectric section, 8 μm × 2 cm × 1 cm. Greater detail is given elsewhere [24].

**2.1. Electrical measurement**

72 Supercapacitors - Theoretical and Practical Solutions

that is, for constant current:

<sup>C</sup> <sup>=</sup> *dq*\_\_\_

energy or power by the volume of the dielectric.

**Figure 1.** Deviation from voltage independent capacitance. (Top) For relatively long discharge times (>1 s), the capacitance is nearly independent of voltage to nearly 2 V, as illustrated by the dashed line nearly matching data over a broad voltage range. (sample: NH<sup>4</sup> Cl 30%; charge rate: 10 mA). (Bottom) As the discharge time decreases, the deviation from ideal behavior, capacitance independent of voltage, becomes more pronounced (sample: NH<sup>4</sup> Cl 30%; charge rate: 100 mA). For all discharge times studied, the capacitance was nearly constant below 0.8 V.

a wide range of current values over the range 5–250 mA. In all cases, the charging current was the same magnitude as the discharge current, but of opposite sign. For each capacitor studied nine different currents in this range were used to determine capacitive behavior over approximately four orders of magnitude of the discharge time. At each selected constant current at least 10 complete cycles were recorded and generally 20. Averaged data from these cycles are reported. As noted, in all cases, the voltage was in the range 2.3–0.1 V. The finding that linear power law data could fit the data collected in this fashion (see Results) demonstrates the efficacy of this method for determination of frequency response. An error analysis of this approach available elsewhere [13] suggests that all data for energy and power density is accurate to within 10% absolute.
