3.1. Paschen’s Law Ethanol

The behavior of the graphs obtained experimentally for an ethanol (CH₃CH₂H) glow discharge is congruent with a Paschen curve and its ratio (pd - V)^11-16. The ionization generated in the reaction chamber occurs when the electric field between the copper electrodes became sufficiently intense to accelerate the electrons at velocity that allowed the ionization of the ethanol molecules. The ions that were also accelerated in this field released new electrons from the copper electrodes through elastic collisions, and the breakdown occurred when this process became sustainable. From these data, the Paschen curve for ethanol (CH₃CH₂H) was constructed, as shown Fig. 2.

Figure 2 Paschen curve of CH₃CH₂OH at a d=0.5, d=1.0, d=1.5, d=2.0 and d= 2.5 cm. 

When the pd parameters increased beyond the curve’s minimum, the collisions may have been too frequent. In this regime, an electron on its way to the anode may collide with molecules of gas phase so often that a higher input voltage is required to accumulate enough energy to ionize a neutral atom. Therefore, the behavior of the Paschen curve was observed when the pd increased. The uncertainty corresponded to the error propagation of coefficient γ according to Eq. (1) of Paschen’s model and to that obtained with the voltage reading of the multimeter Δ. The minimum breakdown voltage in an ethanol (CH₃CH₂OH) discharge at different pressures occurs as shown in the Table I.

The fitting was made according to Paschen’s model, with the function of Eq. (4) and C = ln(A/ln(1+[1/(])) obtaining the following fitting coefficients, R₂, for ethanol.

The fitting was made according to Paschen’s model, with the function of Eq. (4) and C = ln(A/ln(1+[1/(])) which indicates the processes in which electrons are released from the cathode due to first and second species collisions and photoelectric effect, which are referred to the gamma constant, obtaining the following coefficients C and fitting coefficients, R², for ethanol.

Table II also shows the values obtained from the ratio d/r, where r is the radius of the electrode in the variation of Paschen’s law. The curves show a behavior already known in these types of discharges for which Paschen’s law states that the gas-related dielectric breakdown voltage depends only on the pd value.

However, the results obtained indicate that for the same pd value, the breakdown voltages are different for each of the Paschen curves, which, in turn, correspond to different values of d/r, and this was due to the difference in the distribution of the electric field and the mean free path. This dictates the probability of collision of the electrons with the ethanol atoms, in which case, depending on whether the breakdown voltage is higher or lower, this changes.

3.2. Paschen’s law of methanol

By generating a pressure difference in the reaction chamber, a certain density of gas particles will begin to ionize when the voltage applied between the electrodes is greater than or equal to the breakdown voltage. For this to occur, there must be a free electron or some free electrons that induce ionization by interacting with the neutral particles present between the circular copper electrodes, and these electrons produce an amplification in the concentration of the ions and electrons in the gas.

The different methanol (CH₃OH) Paschen curves were obtained by varying the distance between the electrodes for the pressures (0.07, 0.08, 0.09, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 2.00, 3.00, 4.00, and 5.00 Torr) and they are shown from Figs. 3a) to 3b) In all curves, a decreasing behavior of the voltage as a function of the product is shown between the distance and pressure until the minimum is reached. After this, the voltage increases. The uncertainty corresponds to the error propagation of coefficient γ according to Eq. (1) of Paschen’s model and to that obtained with the reading of the multimeter ΔV.

Figure 3 Paschen curve of methanol (CH₃OH) at a 2a: d=0.5, 2b: d=1.0, 2c: 1.5, 2d: 2.0 and 2e: 2.5 cm. 

The minimum breakdown voltages in the methanol (CH₃OH) discharges at different pressures are shown in Table III.

In Table IV, the fit according to the Paschen model can be seen with the function of Equation (4) and C = ln(A/ln[1+[1/(]) for methanol (CH₃OH).

Analysis of these values allows better understanding of the discharge in a methanol atmosphere. For regions where the minimum pressure is low and the mean free path is large, the probability of electron collision with methanol atoms is lower, and a higher voltage is required for ionization. In regions where the pressure is high and, therefore, the mean free path is small, there will be a higher incidence of collision between the electrons and atoms.

3.3 Paschen’s Law of Ethanol-methanol mixture

The Paschen curves were obtained from the 50% ethanol-methanol mixture in which the distance between the electrodes was varied (0.5-2.5 cm) (Figs. 4 to 4) In all curves, a decreasing behavior of the voltage as a function of the product between the distance and pressure is shown until the minimum is reached. This is followed by an increase, which, as mentioned before, is a characteristic of glow discharges at low pressures. The uncertainty corresponds to the error propagation of coefficient γ according to (1) of Paschen’s model and to that obtained with the voltage reading of the multimeter ΔV.

Figure 4 Paschen curve of the mixture at 50 % at a 2a: d=0.5, 2b: d=1.0, 2c: 1.5, 2d: 2.0 and 2e: 2.5 cm. 

Table V illustrates the fitting, according to the Paschen model, with the function of Eq. (4 and C = ln(A/ln[1+[1/(]) for the mixture (50% CH₃CH₂OH-50 % CH₃OH).

The minimum breakdown voltage at the 50 % ethanol-methanol mixture discharge at different pressures is displays in Table VI.

Usually, the function of the breakdown voltage is a smooth curve with a minimum as shown in Figs. 2 and 3 The behavior of these graphs allows the appreciation of the minimum voltage from which the breakdown of a gas (ethanol, methanol, and a 50% mixture) can occur under electric fields (produced in this experiment using an external voltage source and circular copper electrodes). Figure 5 shows the minimums obtained during ethanol, methanol, and the 50 % mixture discharges at different distances (0.5-2.5 cm), the behavior of ethanol and the 50 % mixture of ethanol and methanol are similar between 0.5 to 2.0 electrodes gap, showing a minimum breakdown voltage a 1.0 cm of electrodes gap. While the behavior of methanol displays an increasing trend. The similarity of the ethanol and mixture could be due to same tendency of the first and second Townsend coefficients, which can be seen from the B and C values. So, it can infer that the behavior of the mixture is mainly influenced by ethanol.

Figure 5 The minimum breakdown voltage at different gaps between the electrodes in ethanol (CH₃CH₂OH) and methanol (CH₃OH) discharges and a 50 % mixture of both. 

3.4. Modification to Paschen’s Law of Ethanol

The effect of the electrode separation length (d) and electrode radius (r) on the dielectric breakdown voltage is analyzed in the following Paschen curves. These curves are obtained experimentally for a luminescent discharge of ethanol, methanol, and a 50 %mixture of both at five different separation distances between the electrodes (0.5-2.5 cm) and three different radii (1.5, 2.0, and 2.5 cm). The Paschen curves and different d/r values corresponding to each curve are shown from Figs. 6a to 6e.

Figure 6 Paschen curves of CH₃OH at r = 1.5, 2.0, and 2.5 cm and a 2a: d=0.5, 2b: d=1.0, 2c: 1.5, 2d: 2.0 and 2e: 2.5 cm 

Each of the above graphs exhibits the same behavior of the Paschen curve made with a copper electrode of 2.5 cm radius in an ethanol-ionized atmosphere. These curves show intersections at different pressures due to the length of the average free path of the electrons and the first ionization coefficient α. This is an exponential function of the electric field produced by the difference of the potential between the electrodes since it represents the number of free electrons that is capable of producing an electron per unit of average free path length in the direction of the applied electric field. Together, these curves cause the intersection between the graphs with different radii (1.5, 2.0, and 2.5 cm).

3.5. Modification to Paschen’s Law of Methanol

The Paschen curves and different d/r values corresponding to a methanol light discharge at five different electrode distances (0.5-2.5 cm) and three different radii (1.5, 2.0, and 2.5 cm) are shown from Figs. 7a) to 7e).

Figure 7 Paschen curves of CH₃OH at r = 1.5, 2.0, and 2.5 cm and a 2a: d=0.5, 2b: d=1.0, 2c: 1.5, 2d: 2.0 and 2e: 2.5 cm 

The behavior of the graphs allows the visualization of the minimum dielectric strength at the lowest pressures so that the number of collisions of the electron atoms and methanol is minimal. Therefore, only a limited number of ions are produced because of the inelastic collisions resulting from α processes.

3.6. Modification of the Paschen curves with 50 % ethanol- 50 % methanol

The Paschen curves corresponding to the modification of the Paschen law are made experimentally using a luminescent discharge of the 50 % ethanol-methanol mixture at five different separation distances between the electrodes (0.5-2.5 cm) and three different radii (1.5, 2.0, and 2.5 cm) are display form Figs. 8a) to 8e), respectively.

Figure 8 Paschen curves of CH₃OH 50 % and CH₃CH₂OH 50 % at r = 1.5, 2.0, and 2.5 cm and a 2a: d=0.5, 2b: d=1.0, 2c: 1.5, 2d: 2.0 and 2e: 2.5 cm 

Paschen’s law without the modification dictates that the dielectric breakdown voltage in our reaction chamber depends only on the value of the pressure (p) multiplied by the distance (d). However, in the graphs shown above, it is evident that for the same pd value, the breakdown voltages are different for the different Paschen curves that correspond to different d/r values. Therefore, these curves clearly illustrate the deviations from Paschen’s law.

The analysis of the behavior of these graphs allows the visualization of each region. On the left-hand side, there is not much difference in the breaking voltages for each of the three curves made experimentally, but on the right-hand side, the breakdown voltage presents a greater degree of variation. When the electrode radius is small (1.5 cm), all the ions cannot interact with the cathode to produce secondary electrons that result from 𝛾 processes, and the corresponding breakdown voltages are larger. When the electrode radius is large, the area of the uniform electric field is also large and is directly proportional to its increase and the loss of ions will be less. This explains the decrease in breakdown voltages for low d/r values, as shown in the graphs above. In Fig. 8a) the curve at r = 2.5 cm and d/r = 0.2 does not follow the trend of the other two cases at low pd values, that may be due to the low ratio of distance and radius of the electrodes, which produces an intense electric field affecting the first and second Townsend coefficients and the breakdown voltage.

3.7. Optical emission spectroscopy

To characterize the glow discharge, the optical emission spectrum was obtained (Fig. 9), and the main lines and bands present in each case were identified. The spectra were obtained (200 and 900 nm) of the discharges are presented for Ethanol (CH₃CH₂OH) and Methanol (CH₃OH) and the mixture of both respectively at 50 %. According to the assignment, the ethanol plasma spectra are characterized by bands and lines due to the species CHO (357.01 nm, 367.898 nm, 379.78 nm), O₂ (391.01 nm), CO (411.70 nm, 450.02 nm, 457.95 nm, 482.62 nm, 519.82 nm, 606.99 nm), CH (430.40 nm), OH (433.89 nm), CO₂ (464.44 nm, 468.89 nm), H_β (485.844 nm), H₂ (493.07 nm), O⁺₂ (559.87 nm) and H_α (656.22 nm), where species obtained as a result of some processes among which dissociation stands out (R1 - R3).

Figure 9 Optical emission spectra of a discharge of Ethanol, Methanol and a mixture of both at 50 %. 

Methanol plasma spectra are characterized by bands and lines due to CH (488.90 nm), CO (Angstrom s. B¹Σ-A¹Π), H_β, and H_α species (R4 - R6).

In the present experiment, the line or band with the highest intensity observed by OES measurement was the species H_α. The presence of C₂ and CH species in ethanol discharge can be taken as an indication of the formation of solid carbon and hydrocarbons since these species are typically found as intermediate radicals in the formation mechanism of these products.