Langmuir 2001, 17, 2287-2290
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Heat of Desorption Measured by Means of Electrical Heat Excitation C. Nguyen and D. D. Do* Department of Chemical Engineering, University of Queensland, St Lucia, Queensland 4072, Australia Received September 15, 2000. In Final Form: February 2, 2001 A new method of measuring heat of desorption is proposed in this Letter. The principle of the method is to measure the amount of mass released when a controlled amount of energy is supplied directly to a solid adsorbent. This is in contrast to conventional methods such as microcalorimetry, where heat released upon adsorption is measured. In this method, a quantified heat supply is generated by passing a dc current through a carbon pellet, which is equilibrated with a gas phase confined in a closed vessel. As a consequence of the heating, the particle temperature is increased, resulting in partial desorption of adsorbed molecules. The variations of pellet temperature and the system pressure with respect to time are used to determine the heat of desorption as a function of loading.
1. Introduction Heat released upon adsorption from a gas phase onto a porous solid is one of the important aspects of adsorption study. It is a measure of the strength of solid-fluid interaction and the surface heterogeneity of the solid.1 Different methods of measuring the heat of adsorption are discussed in detail by Rouquerol et al.2 In principle, the methods can be divided into induced and direct methods. An example of the first approach is the method where heat of adsorption is calculated from the dependence of the Henry constant on temperature. This method is convenient; however it is not very reliable and requires elaborate and accurate equilibrium data at low pressures. Among the direct methods most frequently used are microcalorimetry3 and chromatography.4 The main difficulties with these methods are equipment setup and the associated delicate experimental procedures.2 The heat of adsorption is primarily a function of the adsorbate-adsorbent interaction and the heterogeneity of the adsorbent.2 Information concerning the magnitude of the heat of adsorption and its variation with coverage carries information about the gas phase-solid interaction and the pore structure of the solid itself.5 This was used, for example, by Do and Do6 to develop a generalized adsorption isotherm based on the isosteric heat as a function of loading. In this work we propose a new approach for measuring the heat of desorption, which in most cases can be used interchangeably with the heat of adsorption since, more often than not, they are the same. It could be classified as a direct method of measurement, but the difference from the microcalorimetry method is that here heat is used to evoke the partial desorption of the adsorbed molecules and the heat of desorption is calculated from simple coupled heat and mass balance equations. The * Corresponding author. (1) Ruthven, D. M. Principles of adsorption and adsorption processes; John Wiley & Sons: New York, 1984. (2) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powders and Porous Solids; Academic Press: London, 1999. (3) Myer, A. L. In Fundamental of Adsorption II; Liapis, A. I., Ed.; Engineering Foundation: New York, 1987. (4) Gravelle, P. C. J. Therm. Anal. 1978, 14, 53,. (5) Ruthven, D. M. Principles of adsorption and adsorption processes; John Wiley & Sons: New York, 1984. (6) Do, D. D.; Do, H. D. Chem. Eng. Sci. 1997, 52, 297.
philosophy here is that since the amount of heat released is not easy to measure exactly, we choose to use a known energy supply to evoke the mass transfer, which can be monitored more readily. This heat of desorption is an average of the heats corresponding to the loadings before and after the partial desorption of adsorbed molecules. Therefore to determine more accurately the heat of adsorption as a function of loading, the extent of partial desorption should be kept as low as possible. This is quite feasible with our proposed method by simply supplying a small amount of energy into the particle. This will be elaborated in section 2. Heat is introduced into the system by passing a dc current through an adsorbent pellet. The amount of heat generated can be readily controlled by varying the current. It is obvious then that this method is viable to conductive porous materials such as activated carbons. In this paper, the method is tested on the system of ethanol-commercial Ajax activated carbon. 2. Experimental Section Two conducting wires are connected to two ends of a carbon pellet, which is housed in a vacuum-tight chamber. A dc source is connected to the conducting wires to form a closed electrical loop. The particle thus can be heated by passing a dc current through the loop. The pellet temperature is measured using a mini-thermocouple attached to the middle of the pellet, while another mini-thermocouple is used to monitor the temperature of the gas surrounding the pellet. The system pressure is measured by two high-accuracy Baratron transducers, each covering a different range of pressure. Prior to the experiment, the sample is cleaned under ultralow vacuum for 24 h. This process is facilitated by heat generated by passing a dc current through the pellet to maintain the cleaning temperature at 110 °C. When this is completed, the carbon pellet is allowed to cool to the experimental temperature, and then a known quantity of pure adsorbate is introduced into the chamber and sufficient time is allowed for the equilibrium to take place. Once the equilibrium has been reached, partial desorption of the adsorbate is evoked by running a low-voltage dc current through the pellet. The energy generated by the current heats the particle and evaporates some adsorbed molecules. The temperature and pressure changes are recorded for further analysis.
3. Balance Equations 3.1. Heat Balance. The general heat balance equation written for the control volume (the volume of the carbon
10.1021/la0013291 CCC: $20.00 © 2001 American Chemical Society Published on Web 03/17/2001
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Figure 1. Definitions of parameters and the control volume.
pellet) as shown in Figure 1 is
dQ ) dQe + dQs + dQa + dQg + dQd + dQv
(1a)
where Q is the heat supply and the heat terms on the right-hand side represent different heat consumptions: evaporation heat required to desorb molecules (Qe), solid pellet heating (Qs), adsorbed phase heating (Qa), occluded gas phase heating (Qg), loss by conduction via the attached wires (Qd), and loss by convection through the gas phase to the wall of the chamber (Qv). In the case of an electrical energy supply (Q ) UIt), and assuming the gas-phase and cell wall temperatures are equal to the surrounding temperature (Tb ) Tw ) To), the heat balance equation takes the following form:
m C dT + d(UIt) ) dQe + mCs dT + mθC1 dT + F v λAd(T - To) dt + σAv(T - To) dt (1b) It is clear that the fourth term of the right-hand side, which is the heat used to warm the occluded gas phase, is small and can be ignored. Equation 1b rearranged for the evaporation heat in the case of a constant heat supply (UI ) W) is as follows:
dQe ) d(Wt) - Hs dT - mθC1 dT - Ld(T - To) dt Lv(T - To) dt (2) with Hs ) mCs, Ld ) λAd, and Lv ) σAv. 3.2. Mass Balance. Since the change in the temperature of the gas phase is small, a simplified balance for mass transfer between the adsorbed and the gas phase can be written as follows:
m
V dP dθ )dt RTo dt
(3)
4. Results and Discussions 4.1. Heat of Adsorption Calculation. a. Experiment with Vacuum. It is advantageous to conduct heat excitation runs (so-called blank runs) under vacuum conditions to determine the nonadsorption-related parameters. Since there is no gas phase and no adsorption, the evaporation (Qe), adsorbed phase heating (Qa), occluded gas phase heating (Qg), and loss by convection (Qv) become zero. The heat balance eq 2 is thus simplified to
W dt ) Hs dT + Ld(T - To) dt
(4)
from which the following analytical solution can be derived for the particle temperature:
Figure 2. Experimental vacuum run and the temperature model fitting.
T)
W + LdTo - W exp(-Ldt/Hs) Ld
(5)
At long time, i.e., when the steady state is reached, the temperature Ts is calculated as
Ts )
W + LdTo Ld
(6)
from which we can calculate the heat loss coefficient by conduction Ld
Ld )
W Ts - To
(7)
Parameter Hs, which is the heat needed to increase the pellet energy content per 1 deg increase, can be calculated by fitting eq 5 to the temperature response curve obtained under vacuum conditions. b. Experiment with a Gas Phase. It is known that the isosteric heat of desorption E (J/mol) is dependent on loading. The variation rate of the evaporation heat can be h dθ with E h being the expressed as dQe ) d(mEθ) ) mE average of the heat of desorption in the loading range from θ to θ - dθ. The heat balance equation (eq 2) for the case when a gas phase is present takes the form
mE h dθ ) W dt - Hs dT - mθC1 dT - L(T - To) dt (8) with L ) Ld + Lv being the combined heat loss coefficient. Unlike eq 4 for the case of heating under vacuum, this equation does not give an analytical temperature solution. However, the long time solution for temperature and the heat loss coefficient, respectively, would be in the form analogous to those of eqs 6 and 7 with Lv replaced by L. c. Heat of Desorption. The heat required for evaporation is obtained by integrating eq 8 from time 0 to t, and the result is
mE h ∆θ ) Wt - Hs(T - To) -
∫TTmθC1 dT ∫0tL(T - To) dt o
(9)
Moreover, the amount desorbed from the pellet ∆θ can be
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Figure 3. Temperature (left) and pressure (right) responses to a step change in the exciting current of 122 mA (T ) 30 °C; θ ) 4.7 mmol/g).
calculated using the relationship m∆θ ) V/RTo ∆P, which is derived from the mass balance equation. Substitution into eq 9 gives
V ∆PE h ) Wt - Hs(T - To) RTo
∫TTmθC1 dT ∫0tL(T - To) dt o
(10)
The first two terms of the right-hand side are readily calculated while the other two, which represent the energies used to warm the adsorbed phase and the heat loss to surrounding, respectively, can be obtained by numerical integration. 4.2. Application for the System Ethanol-Ajax AC. The proposed model is tested on the system of Ajax AC pellet-ethanol at 30 °C. a. Vacuum Measurement. The vacuum run is used to estimate the specific heat of the solid pellet. During the experiment, the sample chamber is kept under dynamic vacuum to ensure the best vacuum condition. The temperature response for a current step change of 50.9 mA (or power supply of 2.76 mW) is shown in Figure 2, where the fitting of eq 5 is also presented. The fitting gives an optimized pellet internal energy per degree of 5.5 × 10-2 J/deg. This is compared with a value of 3.0 × 10-3 J/deg calculated by assuming that the pellet is made of graphite, the specific heat of which is available in the literature.7 There are a few possible reasons for the discrepancies between these two values. First, porous carbon may have a larger specific capacity than graphite does. Second, the metal connections attached to the particle are also warmed during the experiment. Last, it is quite possible that the temperature measured by the thermocouple is lower than the real pellet temperature, meaning the calculated heat loss coefficient is higher than its real value. b. Ethanol Desorption. Ethanol vapor is dosed in increments into the chamber to get different adsorption loadings at 30 °C. After equilibrium has been reached, an electrical current is introduced to excite the system. The response to the excitation is recorded as the pressure and temperature vary with time. Figure 3, for example, shows the temperature and pressure responses upon a current excitation of 112 mA when θ ) 4.7 mmol/g. As seen, the temperature response is quite similar to that of the vacuum experiment. This allows us to use the form of eq 5 to (7) Perry, H.; Green D. Perry’s Chemical Engineers’ Handbook, 7th ed.; McGraw-Hill: New York, 1997.
Figure 4. Heat generated as a sum of the heat loss, solid and liquid warming heats, and evaporation heat (T ) 30 °C; θ ) 4.7 mmol/g). Table 1. Calculated Heat of Ethanol Desorption at Different Loadings loading (mmol/g)
heat consumed (J/mmol)
loading (mmol/g)
heat consumed (J/mmol)
1.5 1.7 8.3
43 44 33
9.0 9.4
26 17
describe the temperature data. The fitting parameters are marked with a dash to distinguish from those of the vacuum experiment. It is found that the temperature response in Figure 3 can be described with the form of eq 5 with L′ ) 2.3 × 10-3 J/s, To′ ) 30 °C, and Hs′ ) 0.115 J/deg. The curve fitting result is then used in calculating different terms of the right-hand side of eq 10. The use of eq 5 is also advantageous in the sense that it gives an analytical solution for the rate of temperature change dT/ dt, which is needed in evaluating different heat terms of eq 10. Results of the calculation for the case of θ ) 4.74 mmol/g are shown in Figure 4. Heats of desorption calculated for several ethanol loadings on Ajax AC are shown in Table 1. In general, heat of desorption decreases with loading. The heat of desorption from the smallest pores (occurring at low loadings) is about twice as high as the potential energy change calculated for adsorption on a flat surface (22.5 kJ/mol), which is consistent with the potential theory of
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Everett and Powl8 for slit pores. As the pressure (and the loading) increases, desorption takes place in larger pores, where the potential energy enhancement is less pronounced. At high loadings, the heat required approaches the liquid condensation heat at the same temperature (19 kJ/mol at 30 °C).7 5. Conclusions A method of measuring heat consumption upon desorption is presented in this paper. The heat of desorption can be measured by the direct heat supply method presented in this paper. The principles of this method are straightforward and, with some assumptions, a simple analysis is possible. The method has a potential to be a tool in measuring heat of desorption at different loadings. The principle of heat excitement using an electrical current makes the technique relevant for other methods such as the frequency response analysis, and this is a subject for our further research. Nomenclature a b
subscript denoting adsorbed phase subscript denoting bulk gas phase
(8) Everett, D.; Powl, J. C. J. Chem. Soc., Faraday Trans. 1 1976, 72, 619.
Letters d g m s t v w A C E P Q T V σ λ F θ
subscript denoting heat loss by conduction subscript denoting gas phase within the pellet sample mass subscript denoting solid properties time subscript denoting heat loss by convection subscript denoting cell wall effective areas for heat exchange heat capacity heat of adsorption pressure heat temperature bulk gas volume heat loss coefficient through the wires heat loss coefficient by convection pellet density adsorption loading pellet porosity
Acknowledgment. Support from the Australian Research Council is gratefully acknowledged. LA0013291
