Nowadays one of the popular research topics in the world is modeling the global warming process[1,2] and reducing green house gases which cause the ozone layer depletion and the global warming. These harmful phenomena come from more absorption of infrared light due to the green house gases such as carbon dioxide, methane, nitrous oxide, chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs), hydrochlorofluorocarbons (HFCs), perfluorocarbons (PFCs), etc[3-5]. Among these chemicals, CFCs that had a lot of uses with refrigerators and air conditioners, have been already replaced by HFCs. PFCs are used as CFC substitutes for cleaning or printing electronic circuit boards, hybrid ICs, etc. However, PFCs which are more stable than CFCs, are not decomposed until they soar up above the stratosphere and thus are considered significant global warming compounds. Thus one needs to be concerned with the emission and life of PFCs in the atmosphere.

Among the PFCs, the light PFCs (i.e., CF₄ and C₂F₆) are the most potentially damaging due to their long atmospheric lifetime. The atmospheric lifetimes of CF₄ and C₂F₆ are estimated to be 50,000 years and 10,000 years, respectively[6]. The main usage of PFCs is the CVD chamber cleaning, dry etching, heat transfer medium and coolant in the semiconductor processing. The total amount of PFC emission is small compared to CO₂, but PFCs contribute to the global warming as much as 6,500 to 9,200 times the same amount of CO₂. Considering the long-lived contribution of PFCs to the global warming, their emissions should be treated somehow to reduce their entry into the atmosphere in the semiconductor industry[7-9].

There are many approaches to reduce and eliminate PFCs emissions from industrial processes. Potential methods are as follows: recovery/recycle of PFCs[10]; conversion of PFCs to non-PFCs[11,12]; process optimization using reconfiguration and endpoint detection[13]; replacement of PFCs with non- PFCs[14]. Among these control technologies, recovery/recycle methods are currently the most available and cost-efficient ways for treating PFCs gases from emissions of industrial processes. In general, the potential technologies are condensation, absorption, adsorption, and membrane separation[15-19].

For recovery of volatile organic gases, adsorption is a useful method because it offers some recognized advantages. These include the possibility of recovery of raw materials for recycling and a high removal efficiency at a low concentration of adsorbates. Furthermore, this technology often demands low energy costs. It is also important to select the proper adsorbent for the development of an efficient adsorption process. Single-walled carbon nanotubes (SWNTs) can serve as good nanoscale vessels for encapsulation of tetrafluoromethane at 300 K and operating external pressure of 1 bar[20]. However, from an economic point of view, activated carbon is suitable adsorbent for commercial processes such as pressure swing adsorption[21,22].

In this work, the adsorption quantity of CF₄ and C₂F₆ on activated carbon (20 to 40 mesh) were experimentally measured at various temperatures under low pressures of CF₄ and C₂F₆ up to 20.7 kPa by the constant volume method. The objective of this study is to find the heats of adsorption from the two step model which consists of Langmuir model for the first layer adsorption and then Freundlich physisorption.

The adsorbents used in the experiments were activated carbon (20 to 40 mesh) supplied by Darco Co. Their physical properties were measured using an automatic volumetric sorption analyzer (ASAP2010, Micromeritics Instrument Co.) and pycnometer (Accupyc2375, Micromeritics Instrument Co.). These physical properties are given in Table 1. We used 20 to 40 mesh activated carbon only because smaller particles (or larger mesh) takes less time to reach equilibrium due to faster diffusion into pores. The physical data for another size range (10 to 20 mesh) are, although its activated carbon was not used for this study, presented in Table 1 for comparison. The adsorbents (CF₄ and C₂F₆) were provided by Dae-Han gas Co. and Daikin industry Co. The physical properties of their products are good enough to be used in real processes and the prices are also economical. Their purity was 99.99％ and 99.999％, respectively.

A volumetric type apparatus was used to determine the equilibrium isotherms for the single component systems[8,9]. A schematic diagram of the apparatus is shown in Figure 1. It was composed of an adsorption cell, a loading cell, a vacuum pump, gas cylinders, water bath with temperature controller, pressure transducer (PT), thermocouple (TC), and displays. Figure 2 displays a flow diagram of the experiment procedure.

The internal volume of the various parts of the system was accurately measured by expanding helium gas. Before each experiment, the adsorbent was outgassed overnight in a vacuum at a pressure lower than 10⁻⁴ kPa at 423 K. Adsorption isotherms of pure components on various adsorbents were measured at temperatures; 303 K, 323 K, 343 K and pressures up to 20.7 kPa. A static equilibrium technique was used for the measurement of the pure gas adsorption isotherms. The sample gas was introduced into the adsorption cell containing the weighed adsorbent sample. The amount of gas adsorbed was hence determined by performing a material balance on the number of moles present in the gas and the adsorbed phase before and after the addition of a new dose of gas to the adsorption cell using the ideal gas P-V-T relationships.

Adsorbed phase moles are

where n_L and n_A are moles of gas in the loading cell and the adsorption cell, respectively. Subscripts 1 and 2 are the before and after supply of PFC gas to the adsorption cell, respectively. The moles of gas (n_A2) was measured at adsorption equilibrium.

The adsorbed amount q is

where w is mass of adsorbent.

We employ the two step model of adsorption for data analysis of the present adsorption experiments. This model applies Langmuir isotherm model until the first layer of adsorbate is covered. Thus this first step is a sort of chemical reaction between the gas phase adsorbent and the solid phase adsorbate. After all the possible spots of adsorbate are covered, the gas phase adsorbent may deposit right on the already-adsorbed spots. This second step may be taken as Freundlich physisorption. Another way of interpretation of the second step is the phase change to a condensed phase. Although most isotherms (for instance, Langmuir, Sips, and Toth isotherms) would fit the experimental data for CF₄ and C₂F₆ in the experimental pressure range (under 20.7 kPa), the two step model is theoretically more reasonable and good enough to predict the adsorbed amounts.

For the second step of physisorption or condensation, the enthalpy change of adsorption (−ΔH₂) can be calculated by the Clausis-Clapeyron equation

where P is the pressure, T is the temperature, and R is the gas constant.

If the difference in the heat capacity of the adsorbate in adsorbed and vapor phases can be neglected,

−ΔH₂ is independent of temperature and Eq. (3) may be integrated directly to yield.

Assuming that the above approximation concerning the heat capacity is valid, a plot of ln P versus 1/T should yield a linear plot with slope (ΔH₂)/R. This provides a simple and useful method for the determination of the heat of adsorption for CF₄ and C₂F₆.

As for the first step of the two step model, one can derive the Langmuir isotherm by considering the reaction between empty active surface spots and the gas phase molecules. Langmuir isotherm is derived as

where K is the equilibrium constant for the reaction of the second step and q_max is the maximum amount of the first layer adsorption.

One cannot determine from the experimental adsorption isotherms when the first step is finished and when the adsorption process evolutes to the second step because this change of adsorption mechanism is not clearly being made. While the first step is still going on, the second step may move in. Rather than using the general form of Langmuir isotherm, Eq. (5), one can calculate the asymptotic slope of the adsorption isotherm curve at zero pressure and obtain the heat of adsorption from the simplified form of Eq. (5) at zero pressure. At zero pressure the adsorbed amount (q) is proportional to the pressure. These initial slopes are listed in Table 2 for the present investigation.

Adsorption experiments of CF₄ and C₂F₆ were performed on activated carbon in the pressure lower than 21 kPa, maintaining the temperature at 293.15 K, 303.15 K, 313.15 K, 323.15 K, and 333.15 K. The adsorption amounts of CF₄ and C₂F₆ increased with increasing pressure and decreased with increasing temperature. These experiments are a typical gas solid reaction and thus samples of solid should be variant from each other when they are newly prepared, which causes experimental data very difficult to reproduce. We should admit that data spread is inevitable in the present research and that every data point should be taken as entailing an error. Figure 3 is a typical data set of experiments with error bars. The solid line going through the data points were carefully drawn. Other isotherm figures that will appear later are results similarly obtained and should be understood to have error bars with them, which were left out for clarity of lines and points. Figures 4 and 5 are displays of the equilibrium amounts adsorbed with respect to the pressure at the above-mentioned temperatures. One can see that adsorption is more favorable with lower temperature and higher pressure, which is a typical adsorption characteristic. Figures 4 and 5 allow us to determine the equilibrium pressure at any selected adsorbed quantity. In the present investigation four values (0.05, 0.10, 0.15, 0.20 mol/kg) of adsorbed quantity (q) were picked out and then the corresponding pressures were read from Figures 4 and 5. Those results of (P, T) in Figure 4 for CF₄ are displayed in Figure 6. The straight line fitting the data points in Figure 6 gave us the slope to find the heat of adsorption (−ΔH₂) for CF₄.

Similarly we could choose three different values (0.2, 0.4, 0.6 mol/kg) of adsorbed quantity and produce Figure 7 using the results of (P, T) in Figure 5 for C₂F₆, In the same way as with CF₄ the slope was measured and we could find the heat of adsorption (−ΔH₂) for C₂F₆. These enthalpy changes for the second step of the two step model are listed in Table 3.

We could measure the initial slope of each curve in Figures 4 and 5 and have them listed in Table 2. The equilibrium constant, K, in Eq. (5) is the ratio of adsorption coefficient to desorption coefficient, and has the relationship with temperature as

At very low pressure Eq. (5) reduces to a straight line with the initial slope of Kq_max. We assume the maximum amount of the first layer, q_max, is independent of temperature. Then the logarithm of the initial slope versus 1/T should give a straight line as long as the heat of adsorption, −ΔH₁, is constant over the range of experimental temperature. We produced Figure 8 for this purpose and measured the slopes of the data points in Figure 8. Consequently, the heats of adsorption for the first step are 25.9 kJ/mol for CF₄ and 38.7 kJ/mol for C₂F₆.

When we compare the heats of adsorption of the first step and the second in Table 3, we see that −ΔH₁ is about 3 times as large as −ΔH₂ for CF₄. This is very reasonable in the sense that the first step of the present adsorption model is a kind of chemical reaction between the active solid surface and the gas phase molecule while the second step is a physisorption. It is a well-known fact that condensation requires a lot less heat release than chemical reaction. However, this reasoning breaks down with C₂F₆ because −ΔH₁ is practically the same as −ΔH₂ for C₂F₆. Thus the two step model is totally agreeable with CF₄. The first step for C₂F₆ may be interpreted as just a physical condensation and could not be differentiated from the second step.

Static equilibrium adsorption experiments were performed to measure the amounts of CF₄ and C₂F₆ adsorbed on activated carbons, using a volumetric method at various temperatures between 293.15 K and 323.15 K in the low pressure range up to 21 kPa. From these data we could calculate the heats of adsorption of CF₄ and C₂F₆ on activated carbon using the two-step model which employs the Langmuir-type chemisorption in the first step and the next step of Freundlich physisorption. With CF₄ the heats of adsorption are 25.9 kJ/mol for the first step and 11.8 kJ/mol for the second step. The heats of adsorption of C₂F₆ were obtained in the same way and they are 38.7 and 38.2 kJ/mol.