Anal. Chem. 1997, 69, 4619-4626
Development of a Nonisothermal Knudsen Effusion Method and Application to PAH and Cellulose Tar Vapor Pressure Measurement Vahur Oja and Eric M. Suuberg*
Division of Engineering, Brown University, Providence, Rhode Island 02912
The Knudsen effusion technique has long been employed as an indirect method for determining the vapor pressures of low-volatility materials. The method is tedious and, if not carefully applied, subject to considerable errors in temperature measurement. It is also desirable to shorten the time of measurement in some cases, since when working with either mixtures or thermally labile materials the long time scales of the usual measurement can result in significant changes in composition while waiting for pseudo-steady state to obtain. For these reasons, a new method, based on the traditional Knudsen effusion technique, was developed. The resulting nonisothermal method is a straightforward modification of the usual Knudsen effusion technique, generally requiring few changes in equipment and only a limited change in procedures. The technique has been applied to polycyclic aromatics and pyrolysis tars. Vapor pressures of high molecular weight thermal decomposition products of organic materials (i.e., tars) are often an important parameter in modeling the combustion behavior of such materials (e.g., coals, biomass). The extent to which the tars vaporize, before retrograde reactions reincorporate them into a char, plays a key role in determining the flux of combustibles to the flame, as reflected in advanced pyrolysis models for coal.1-8 It has also been hypothesized that the vapor pressures of tars may play a key role in determining the course of cellulose pyrolysis.9 Unfortunately, few data are available on such complex, lowvolatility materials, mainly from the literature on pure high molecular weight polycyclic aromatic hydrocarbons (PAHs) or, in the case of coals, from modestly characterized, highly hydro(1) Suuberg, E. M. In Chemistry of Coal Conversion; Schlosberg, R., Ed.; Plenum: New York, 1985; Chapter 4. (2) Unger, P. E.; Suuberg, E. M. Proceedings of the 18th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1981; p 1203. (3) Niksa, S. AIChE J. 1988, 34, 790. (4) Niksa, S.; Kerstein, A. Energy Fuels 1991, 5, 647. (5) Fletcher, T.; Kerstein, A.; Pugmire, R.; Solum, M.; Grant, D. Energy Fuels 1992, 6, 414. (6) Solomon, P. R.; Serio, M. A.; Suuberg, E. M. Prog. Energy Combust. Sci. 1992, 18, 133. (7) Solomon, P. R.; Hamblen, D. G.; Carangelo, R. M.; Serio, M. A.; Deshpande, G. V. Energy Fuels 1988, 2, 405. (8) Oh, M. S.; Peters, W. A.; Howard, J. B. AIChE J. 1989, 35, 776. (9) Suuberg, E. M.; Milosavljevic, I. ; Oja, V. Two-Regime Global Kinetics of Cellulose Pyrolysis: The Role of Tar Evaporation. Proceedings of the 26th Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, PA, 1996; p 1515. S0003-2700(97)00262-X CCC: $14.00
© 1997 American Chemical Society
genated coal liquids.10 Uncertainties of an order of magnitude are common. Comparisons of the behavior of various proposed correlations for coal tars are offered elsewhere.5,11 The vapor pressures of primary pyrolysis tars are the principal topic of interest in the work presented here. While the materials of interest are formed and evolve at high temperatures, they are extremely thermally labile. Roughly speaking, when dealing with pyrolysis tars, the temperatures of measurement should not exceed about 250 °C, and even this proved too high in many cases. These tars typically have molecular weights in the range of several hundred daltons. It is difficult to measure their vapor pressures directly because, at the temperatures needed to achieve vapor pressures measurable by standard techniques, the tars will always decompose to some extent. A low-temperature technique is thus required which, in turn, requires one suitable for very low vapor pressures. Among those judged appropriate was the Knudsen effusion method. Initially, the standard Knudsen effusion technique was employed to measure the vapor pressures of pure polycyclic aromatics both because these were thought to represent an important constituent of coal tars and because they are of interest in their own right. Results from an extensive study will be presented elsewhere. It became apparent, however, that the standard technique is difficult to apply to complicated mixtures such as tars. Among other problems was that the rather long time scales of the standard Knudsen effusion technique were not attractive in a mixture whose composition varied with evaporative loss of components. This was the case even when an attempt was made to prepare narrow molecular weight tar fractions for testing. Related to this is the general problem, well known in the petroleum characterization field, of a mixture that exhibits a boiling point distribution. It is necessary to scan a range of temperatures in order to assure complete characterization of the mixture. Typically, mixtures of components exhibiting a wide range of volatility are examined by a nonisothermal distillation procedure, e.g., ASTM D86-96 (Distillation of Petroleum Products), D447-93 (Distillation of Plant Spray Oils), D850-93 (Distillation of Industrial Aromatic Hydrocarbons and Related Materials), and D 1078-95 (Distillation Range of Volatile Organic Liquids). The difficulties in applying these methods have led to various alternative methods, including the well-known “simulated distillation” as performed by gas chromatograph, e.g., D2887-93e1, Boiling Point Distribution of Petroleum Fractions by Gas Chromatography (GC), D5307-92, Determination of Boiling Point Range (10) Tsonopoulos, C.; Heidman, J.; Hwang, S.-C. Thermodynamic and Transport Properties of Coal Liquids; Wiley: New York, 1986. (11) Oja , V.; Suuberg, E. M. ACS Div. Fuel Chem. Prepr. 1996, 41, 82.
Analytical Chemistry, Vol. 69, No. 22, November 15, 1997 4619
Distribution of Crude Petroleum Products by GC, D5399-95, Boiling Point Distribution of Hydrocarbon Solvents by GC, and to thermogravimetric methods.12 These ordinary or modified distillation techniques are, again because of the excessive temperatures, not acceptable in our case, even under mild vacuum conditions. In contrast to the these procedures, the working pressure in the Knudsen technique is typically a high vacuum. Moreover, the pressure outside the Knudsen effusion cell is of no consequence, provided that it is below the vapor pressure of the sample by at least an order of magnitude, and as long as the situation in the effusion cell pinhole leak approximates collisionless flow. The nonisothermal Knudsen method will be presented by describing the minor modifications made to the standard isothermal technique, which is described first. EXPERIMENTAL SECTION The Knudsen Effusion Technique for Vapor Pressure Measurement. “Effusion” methods are based on the molecular effusion of a vapor from a surface or through an orifice.13 In the Knudsen method,14,15 a substance of interest effuses through a small pinhole of known area, in an otherwise sealed container or cell, allowing measurement of low vapor pressures in the 1-10-6 Torr range under molecular flow conditions. This ideally requires that pressures inside and outside the sample cell are low enough that the frequency of collisions of vapor molecules with gas phase species are low in comparison with the frequency of collisions with the cell. The measurement of vapor pressure involves determining the rate of loss of molecules of the evaporating substance from the effusion cell under these conditions. Measurements are typically made under isothermal conditions, with weight loss from the cell being recorded as a function of time, generally in a thermogravimetric analysis (TGA)-type apparatus. The basic theory of the effusion method is found in the literature, and is only summarized here.14-16 Using classical gas kinetic theory, Knudsen derived an expression for the slow isothermal flow out of a cell with a small hole in it; the vapor pressure of a material in the cell can be calculated from Knudsen’s original effusion equation:
P1 - P2 ) (m/t)(w1 + w2)/F1/2
(1)
where P1 and P2 are the pressures of saturated vapor inside and of gas outside of the effusion cell, respectively, w1 and w2 are the resistances of the hole in the cell and sample cell itself, respectively, m is the mass lost by effusion over a time t, and F is the density of the vapor at the temperature of experiment. The relation simplifies upon applying several assumptions, including the ideal gas law, that the pinhole leak is the main flow resistance, and assuming P1 . P2, yielding (12) Huang, H.; Wang, K.; Wang. S.; Klein, M.; Calkins, W. H. Prepr. Pap.sAm. Chem. Soc. Div. Fuel Chem. 1996, 41, 87. (13) Dushman, S. In Scientific Foundations of Vacuum Technique, 2nd ed.; Lafferty, J. M., Ed.; Wiley: New York, 1962. (14) Knudsen, M. Ann. Physik. 1909, 28, 999. (15) Knudsen, M. Ann. Physik. 1909, 29, 179. (16) Hollahan, J. J. Chem. Educ. 1962, 39, 23.
4620
Analytical Chemistry, Vol. 69, No. 22, November 15, 1997
P)
m 2πRT tA0 M
(
1/2
)
(2)
This result is called the ideal Knudsen equation, in which P is the desired vapor pressure, m the mass loss during the effusion time t, A0 the ideal orifice area, M the substance molecular weight, and T the temperature of the experiment. It is further assumed that the equilibrium vapor pressure of the effusing species is maintained within the cell, that the orifice walls do not intercept an appreciable fraction of molecular current of effusing species entering the hole, that there is no back flux into the orifice exit, and that the number of intermolecular collisions within the orifice is negligible. The above equation has been modified by a number of authors. The refinements have included consideration of the shape of the orifice and cell, nonunity evaporation coefficients, effects due to long mean free path (wall collision effects), effects due to short mean free paths as the flow goes from free molecular to transition to hydrodynamic, and effects due to temperature gradients, surface diffusion, and specular reflection. The working equation used by most workers in the field has the form
P ) 17.1436
m xT/M tAW0
(3)
where P is the vapor pressure in Torr, m is the weight loss in grams during the effusion time t, in seconds, A is the true area of the orifice in squared centimeters, M is the molecular weight of the effusing vapor in grams per mole, T is the temperature in kelvins, and W0 is the Clausing probability factor, obtained by interpolation from the table given by Dushman.13 The Clausing factor is the single most important correction for nonideality. It is the transmission probability for the effusing species and has values in the range from zero to unity. It may be interpreted as a probability that a molecule entering the orifice from the effusion chamber will reach the exterior of the orifice. It is assumed that molecules enter the orifice from an isotropic gas phase from a random direction, according to the cosine law. The values of T, A, and W0 are fixed as experimental parameters, and M is known or measured prior to an experiment. Thus, m/t remains as the experimentally measured quantity from which the vapor pressure is determined. Equation 3 has been utilized to calculate equilibrium vapor pressures of organic compounds by many workers.17-24 Effusion Cell Design. We have developed a Knudsen cell design for our work with PAHs and tars. The design was limited by several special requirements: first, it had to be very light, less than 1 g (determined by the capacity of our microbalance); second, it had to allow using samples of a few tens of milligrams (since we were not be able to produce large quantities of wellcharacterized tars); and third, it had to be inexpensive enough (17) Morecroft, D. W. J. Chem. Eng. 1964, 9, 488. (18) Wiedemann, H. G., Thermochim. Acta 1972, 3, 355. (19) DePablo, R. S. J. Chem. Eng. 1976, 21, 141. (20) DeKruif, C. G. J. Chem. Thermodyn. 1980, 12, 243. (21) Colomina, M.; Jimenes, P.; Perez-Ossorio, R.; Roux, M. V. J. Chem. Thermodyn. 1980, 20, 575. (22) Colomina, M.; Jimenes, P.; Turrion, C. J. Chem. Thermodyn. 1982, 14, 779. (23) Murray, J. J.; Pottie, R. F. Can. J. Chem. 1974, 52, 557. (24) Kelley, J. D.; Rice, F. O. J. Phys. Chem. 1964, 68 (12), 3795.
Figure 1. Schematic of the Knudsen effusion apparatus.
so as to be disposable, to avoid concerns about cleaning. The cells were made in-house out of either brass or stainless steel foil of 25 µm thickness, using an appropriate die. They were sealed by crimping a circular top onto a stamped base. The cell was cylindrical and had approximate dimensions of 0.5 cm height × 0.5 cm diameter, and a volume of 0.4 cm3. The foil cell had a final assembled mass of about 0.1 g. After fabrication, the cells were outgassed under vacuum for several hours at a temperature of at least 300 °C or cleaned by heating in a propane flame. The effusion holes were made in the top plate of the sample cell using a fine drill. The orifice diameter was measured using an optical microscope. The diameter determination is made at room temperature, and thermal expansion should not alter the dimensions of the hole significantly. The Clausing factor is obtained from the hole diameter by interpolation from the table given by Dushman.13 Orifice diameter selection was guided by published results, and examined experimentally. Morecroft17 has shown that the vapor pressure measurement is independent of hole size within the guidelines that the mean free path of the molecules be larger than the orifice diameter. Several different diameters were tested, and it was verified that hole diameter had no effect on the results within the range from 0.6 to 1.1 mm. Larger holes can yield erroneously low apparent values for vapor pressures, owing to self-cooling of the sample and failure to maintain equilibrium.25 Much smaller holes are also undesirable, due to slow effusion rates and other reasons, e.g., small leaks in the cell can cause problems if the effusion hole is small. It was also reported26 that the influence of surface diffusion increases as the radius of the hole decreases. Cell Environment. A schematic of the apparatus is shown in Figure 1. The backpressure in the TGA system was maintained at 10-7 Torr, which has been determined to be sufficient to provide (25) Ribero Da Silva, M.; Monte, M. Thermochim. Acta 1990, 171, 169. (26) Winterbottom, W.; Hirt, J. J. Chem. Phys. 1962, 37, 784.
accuracy in the 10-6 Torr range of vapor pressures.25 A mechanical vacuum pump is used both for pre-evacuating the system and for backing a 4 in. oil diffusion pump. The pumping system is isolated from the main part of the apparatus by a liquid nitrogen trap. An ionization gauge is used for measuring the vacuum maintained in the system, and two thermocouple gauges are used for monitoring preevacuation. The hardest vacuum achieved in this system was 10-8 Torr. The effusion cell is suspended on the arm of a Cahn 2000 recording electrobalance which has a sensitivity 0.5 µg, a capacity of 1.5 g, and a zero stability better than 10 µg. The cell is hung on a 40 cm long, 0.25 mm diameter tungsten wire, ending in a small hook of 0.05 mm diameter tungsten wire. The cell itself hangs inside of an aluminum capsule which surrounds, but does not touch, the cell. The capsule is cylindrical and has a diameter of about 1.5 cm, a length of 4 cm, and a mass of 5 g. The capsule is painted black with high-temperature paint to increase the effectiveness of radiative transfer. Maintaining and measuring the cell temperature with a high accuracy is critical. It has been noted18 that a change of a few tenths of a degree can alter the vaporization rate and lead to significantly erroneous values of vapor pressure, particularly at low temperatures. Most discrepancies in the literature from workers using the Knudsen or related techniques are the result of insufficient attention to temperature measurement. The cellwithin-a-capsule arrangement was found to be necessary in order to improve heat transfer to the cell and to allow accurate measurement of temperature in the immediate vicinity of the cell. We have used it in performing both the traditional isothermal experiments as well as the new continuous nonisothermal experiments. The capsule temperature is measured by a chromel/alumel thermocouple in direct contact with the capsule, at a distance of no more than a few millimeters from the bottom of the cell. The thermocouple is calibrated against a Fisher brand calibrated Analytical Chemistry, Vol. 69, No. 22, November 15, 1997
4621
mercury thermometer, and its signal is continuously recorded with an accuracy of 0.1 K using an Omega DP85 digital indicator and data acquisition system. A cold trap near the orifice of the Knudsen cell is common, in order to condense the vaporized compound and assist in keeping the backpressure low. We have not made provision for a cold trap near the cell and have relied upon high pumping rates and a condenser slightly downstream of the cell to give us the necessary low pressures outside of the cell (see Figure 1). The sometimes troublesome effects of static charges on the glass vacuum enclosure tube could be eliminated by rinsing the outside of the tube with methanol or water. The heating system is entirely outside of the vacuum enclosure and consists of an aluminum block oven surrounded by insulating material. Heat is provided by cartridge heaters embedded in the aluminum. This is a high-mass heating system and offers temperature control comparable to that possible with oil bath systems. It does not have the disadvantage of electromagnetic induction effects, as do ordinary resistance furnaces. Two different heating cartridges are employed for the temperature control system. There is a baseload 300 W heater for coarse regulation and a 50 W heater for precise regulation of temperature. These heating cartridges are regulated by means of an RFL Industries, Inc. temperature controller, which is designed to regulate temperature within a few tenths of a degree. The temperature in the block is measured using a chromel/alumel thermocouple and recorded using an Omega DP85 digital indicator. The Nonisothermal Knudsen Effusion Technique. The nonisothermal Knudsen effusion method was developed in response to the need to scan a wide range of temperatures in a modest time. As the sample cell is in a high vacuum and must receive heat purely by radiation, heat transfer is a key concern. A long time is generally required to reach thermal equilibrium in an isothermal experiment. In our case, the main thermal lag is associated with heating of the 5 g capsule which surrounds the sample cell. This capsule is also in the high-vacuum environment and is heated mainly by radiation from the glass walls of the device and from the heating block. Achieving a new steady state temperature typically requires hours. The advantage of the nonisothermal technique is that it does not require the capsule to reach a steady state temperature. A temperature ramp is imposed by ramping the aluminum block temperature, but the temperature difference between the block and capsule is no longer of concern. The capsule will rise in temperature at a rate which is in some way related to the rise in block temperature, but it need not track it perfectly. Meanwhile, the sample cell has a view factor of the capsule which approaches 1. Together with the fact that the effusion cell has a much smaller mass, 0.15 g, it thus tracks the capsule temperature well. The long equilibration times associated with isothermal experiments are avoided if an experiment is carried out nonisothermally. The analysis of experimental result was only slightly altered in the nonisothermal experiments. The information on mass as a function of time was converted to a derivative, so that it was possible to relate each recorded sample temperature to an instantaneous value of mass loss rate. This did not fundamentally change the analysis, which was still based on eq 3. Some small degree of data smoothing was sometimes desirable, as is typical when taking derivatives of raw data. 4622
Analytical Chemistry, Vol. 69, No. 22, November 15, 1997
Materials Examined. Anthracene (C14H10, FW ) 178.2, mp ) 215 °C ) 488 K). Anthracene of 99+% purity was obtained from Sigma Chemical Co., Inc. It was used with no further purification. It was customary to begin an experiment by evaporating a few percent of the sample before recording data. After this, reproducible vapor pressures were obtained over a wide range of mass loss, so residual impurities appeared to not be influencing results. Consequently, no further purification of sample was called for. Naphthacene (C18H12, FW ) 228.3, mp ) 357 °C ) 630 K). Naphthacene (or 2,3-benzanthracene) of 98% purity was obtained from Aldrich Chemical Co., Inc., and was also used without further purification, for the reasons cited above. Cellulose Pyrolysis Tar. The preparation of this material has been described in a previous publication.9 The tars were prepared by pyrolyzing cellulose within the folds of a resistively heated wire mesh. In this device, the tars are quickly quenched by rapid mixing with the surrounding cold gas, and tars were collected from the reactor by washing it with methanol or methanol/ tetrahydrofuran (THF) mixtures after an experiment. Tars are operationally defined as room temperature condensable materials. Pure, fresh tar samples were prepared from this solution by evaporation of the methanol in a vacuum oven, at a temperature not exceeding 55 °C. In the range of vapor pressures of relevance here, previous experiments have shown that the solvent and light condensables (e.g., water) are all lost, while components with vapor pressures comparable to that of anthracene are retained to better than 95%. The cellulose tar will be shown below to exhibit a much lower vapor pressure than anthracene (which has a vapor pressure near 2.5 × 10-4 Torr at 55 °C), and should all be retained. The tars were measured to have a number-average molecular weight of between 172 and 184 Da. The elemental composition of the tars was. on average. 46.5% C, 7.1% H, and 46.5% O, all on a weight percent basis. The similarity of tars to levoglucosan (1,6anhydro-β-D-glucopyranose) has been earlier noted (see ref 9). For comparison, the molecular weight of levoglucosan is 162, and its elemental composition is 44.4% C, 6.2% H, and 49.2% O. Thus, the cellulose tar is similar in molecular weight and composition to levoglucosan. RESULTS AND DISCUSSION The Standard Isothermal Knudsen Effusion Method. The reliability of the present implementation of the standard isothermal Knudsen effusion technique was checked using many aromatic compounds. Generally, the results were in very good agreement with literature values. Here, only two examples will be given, and a more extensive compilation of results will be presented elsewhere. Anthracene has been studied by many groups,27-31 and earlier results showed a high degree of consistency, so there is a good basis for comparing the results of the present study. The results obtained in the present study, using the traditional isothermal Knudsen effusion method, are shown in Figure 2. It should be noted that the measurements were all performed with anthracene in the solid phase and, therefore, involve sublimation vapor pressures. They are seen to be in excellent agreement with the (27) Hansen, P. C.; Eckert, C. A. J. Chem. Eng. Data 1986, 31, 1. (28) DeKruif, C. G. J. Chem. Thermodyn. 1980, 12, 243. (29) Kelley, J. D.; Rice, F. O. J. Phys. Chem. 1964, 68, 3794. (30) Macknick, A. B.; Prausnitz, J. M. J. Chem. Eng. Data 1979, 24, 176. (31) Sonnefeld, W. J. Anal. Chem. 1983, 55, 275.
Figure 2. Vapor pressure data for anthracene, showing literature results and results obtained here using the isothermal Knudsen effusion method. O, ref 30; 2, ref 28; 0, ref 27; b, ref 29; 4, ref 31; 9, this study. The correlation equation for the literature data is ln P [Torr] ) 28.549 - 12 082/T [K]. The correlation equation for the data of this study is ln P [Torr] ) 28.388 - 12 024/T [K].
Figure 3. Vapor pressures for naphthacene, showing literature results and results obtained here using the isothermal Knudsen effusion method. 0, ref 28; 4, ref 32; 9, this study. The correlation equation for the data of this study is ln P [Torr] ) 28.768 - 15 165/T [K].
previously published data. All of the data are well approximated by the Clausius-Clapeyron equation, with a constant enthalpy of sublimation:
ln P ) ln R - ∆Hs/RT
(4)
Constancy of the enthalpy of sublimation over the modest range of temperatures examined here is a common observation. The mean of all of the literature data can be represented by ln R ) 28.549 and ∆Hs/R ) 12 082 K, where the units of P are Torr. This mean was obtained by using each group’s recommended correlation applied to the maximum and minimum temperatures of the study. This procedure is admittedly somewhat arbitrary but captures the essence of the data, as the resulting correlation line shows. The data for naphthacene are shown in Figure 3. Again, the results obtained by the standard isothermal technique are seen to be in excellent agreement with values from the literature.20,32 As in the case of anthracene, these experiments involved sublimation of the naphthacene. The results are also well represented by the correlating eq 4. The mean for the data is ln R ) 28.768 and ∆Hs/R ) 15 165 K. (32) Stephenson, R. M.; Malanowski, S. Handbook of the Thermodynamics of Organic Compounds; Elsevier: Amsterdam, 1987.
Figure 4. Results of the application of the nonisothermal Knudsen effusion technique to anthracene. The results were obtained at roughly 5 K/min heating and cooling rates. The dashed line shows the true correlation, from Figure 2.
It has been thus clearly established that the standard technique has been implemented in a reliable manner. The Nonisothermal Knudsen Effusion Method. The reliability of the nonisothermal Knudsen effusion technique was shown using the same two test materials as above. Figure 4 shows the results for anthracene which were obtained in a single experiment in which the sample was subjected to a cycle of first heating and then cooling. Both heating and cooling took place at rates of approximately 5 K/min. The results are compared with the mean of the isothermal data, shown as the dashed line. There is a significant deviation of the nonisothermal results from the isothermal technique data. The observation that the heating data underpredict and the cooling data overpredict the real vapor pressures suggests that the cell temperature is lagging the surrounding capsule temperature. This indicates a significant transport limitation in the capsule-to-cell heat transport process. The thermocouple indicates the true capsule temperature, but this temperature is above the true cell temperature during heating. Thus, the whole vapor pressure curve is shifted to higher-thanactual temperatures. During cooling, the capsule will decrease in temperature more quickly than does the cell, and the shift is reversed. The problem may be analyzed in terms of a simple heat transfer model. The change in capsule temperature may be approximated by a linear function of time:
Tcapsule ) T0 + bt
(5)
It is this capsule temperature which is experimentally measured. The variation of cell temperature (Tcell) with time may be calculated from
mcC (dTcell/dt) ) qrad - qsublimation
(6)
where mc is the mass of cell + sample, C is the mass heat capacity of the cell + sample, qrad is the net rate of radiative heat transfer to the cell from its surroundings, and qsublimation is the enthalpy demand associated with sublimation of the sample. The radiative heat transfer term may be modeled as
qrad ) σAcc [(Tcapsule)4 - (Tcell)4] Analytical Chemistry, Vol. 69, No. 22, November 15, 1997
(7) 4623
Figure 5. Calculated deviation of cell temperature from measured capsule temperature in nonisothermal effusion experiments. The solid line indicates perfect agreement, the short-dashed curve is for 0.01 K/s heating rate, and the long-dashed curve is for 0.05 K/s heating rate.
Figure 6. Vapor pressure measurements on anthracene using the nonisothermal Knudsen effusion technique in heating mode at a heating rate of 0.8 K/min. The dashed straight line is the correlation of Figure 2. The solid straight line is the fit to the nonisothermal data. The correlation equation is ln P [Torr] ) 28.715 - 12 122/T [K].
Table 1. Parameters Used in Modeling the Rise in Cell Temperature surface area of cell mass of cell + sample heat capacity of cell + sample emissivity of cell initial temperature enthalpy of sublimation preexponential in eq 4 corrected orifice area molecular mass of sample
Ac mc C c Tcell ) Tcapsule ∆H R AW0 M
heating rates
b
1.2 cm2 0.1 g 0.45 J/(g K) 0.5 323 K 101 kJ/mol 3.22 × 1012 Torr 0.477 mm2 178 g/mol (anthracene) 0.01, 0.05 K/s
where σ ) 5.669 × 10-8 W/(m2 K4) is the Stefan-Boltzmann constant, Ac is the geometrical surface area of the sample cell, and c is emissivity. This approximation assumes that the view factor of the cell for the capsule enclosure is essentially unity. The term for the enthalpy loss due to sublimation can be estimated by rearranging eq 2 to obtain the mass loss rate (r ) m/t). Then,
qsublimation ) (r/M)∆Hs
(8)
r ) PAW0 [M/2πRT]1/2
(9)
and
where the Clausing factor W0 has been introduced to eq 2, as discussed above. Substituting eq 4 for P, and then eqs 5 and 7-9 into eq 6, it is possible to calculate the cell temperature as a function of time. The actual solution was implemented using a fourth-order Runge-Kutta method, and the result is shown in Figure 5 for typical values of the parameters. The actual parameter values used are shown in Table 1. If the capsule temperature is increased at 0.05 K/s ()3 K/min), then there is a significant steady lag of cell temperature behind the measured capsule temperature. The deviation would be approximately 3-4 K throughout the temperature region of interest. This is the origin of the deviation exhibited in Figure 4. The cell simply cannot keep up with the capsule. If the capsule heating rate is decreased to 0.01 K/s (0.6 K/min), then the 4624 Analytical Chemistry, Vol. 69, No. 22, November 15, 1997
Figure 7. Vapor pressure measurements on naphthacene using the nonisothermal Knudsen effusion technique in cooling mode at a rate of 0.8 K/min. The dashed straight line is the correlation of data shown in Figure 3. The solid straight line is the fit to the nonisothermal data. The correlation equation is ln P [Torr] ) 30.347 - 15 742/T [K].
temperature deviation decreases to about 1K under steady conditions. The beneficial effects of decrease of capsule heating rate are borne out by the experimental results obtained at an 0.8 K/min heating rate, shown in Figure 6. There is, in this case, reasonably good agreement between the results obtained from the nonisothermal and isothermal techniques. It is noted that the nonisothermal technique gives results that are, again, just a bit below the isothermal results (by typically less than 10%). The difference could be further decreased by further decreasing the heating rate, at the expense of increasing the analysis time. This was not pursued here with this material, only because it was recognized that, in application to tar systems, such small systematic errors would be unimportant in comparison to the variability of the material itself. It also needs to be noted that the “jaggedness” of the vapor pressure curves derived using the nonisothermal method is a consequence of the amplification of “noise” in the mass signal, as a result of taking its time derivative. There was a minimum of smoothing performed on the raw data used in obtaining Figures 4 and 6. It is clearly appropriate to draw a straight line through the data of Figure 6, as has been done. Figure 7 shows the results of the isothermal technique applied to naphthacene in “cooling” mode. As can be seen in Figure 7,
Figure 8. Vapor pressure measurements on naphthacene using the nonisothermal Knudsen effusion technique in heating mode at a rate of 0.8 K/min. The dashed straight line is the correlation of data shown in Figure 3. The heavy straight line is the fit to the nonisothermal data. The correlation equation is ln P [Torr] ) 30.277 15 742/T [K].
Figure 9. Vapor pressures of levoglucosan (ref 9) and cellulose tars. The open and closed squares and solid correlation line represent the results of two different sets of experiments on cellulose tars, using the isothermal Knudsen effusion method. The circles and dashed line represent the results for levoglucosan, using the isothermal Knudsen effusion method. The crosses all represent the results of the nonisothermal Knudsen effusion method applied to cellulose tars. The two different types of crosses are used in order to highlight a brief cooling and reheating excursion at around 1/T ) 0.00273 K-1. The correlation of the data on levoglucosan gives ln P [Torr] ) 32.391 14 452/T [K]. The correlation line shown for cellulose gives ln P [Torr] ) 38.233 - 16 253/T [K].
there is, again, good agreement between the results of isothermal and nonisothermal methods. Comparably good results were obtained in the heating mode; these results are shown in Figure 8. Thus, the reliability of the nonisothermal method appears to be established. Nonisothermal Method Applied to Cellulose Pyrolysis Tars. We have previously reported the vapor pressure of primary cellulose pyrolysis tar.9 The earlier results had been obtained using the isothermal Knudsen effusion method. Figure 9 compares the results of both the isothermal and nonisothermal techniques applied to cellulose tars. For comparison, earlier published data on the vapor pressure of levoglucosan are also indicated.9 The data on levoglucosan are typical of the data obtained on pure compounds. They show a very constant and reproducible behavior, throughout the measured range of temperatures, which here extended up to approximately 386 K. The data on cellulose tar are markedly different. The data that have been obtained using
the standard isothermal technique are shown as individual points, through which a correlation line has been drawn. The choice was made here to show only points obtained below 373 K, because it has been earlier observed that high-temperature exposures, in excess of this maximum temperature, result in reactions which tend to alter the nature of the tar.9 The cellulose tar is seen to exhibit a vapor pressure which is comparable to but a bit higher than that for levoglucosan, which has been reported to be a majority constituent of the tar in some cases.9 A detailed analysis of the cellulose tar was not performed here to verify this. Molecular weight, gel permeation chromatographic (GPC), and elemental composition data all support the conclusion that the tar material is similar to levoglucosan or a single glucose residue, but it is almost surely a complex mixture of many similar types of materials. The nonisothermal vapor pressure determinations provide additional insight into the behavior of the tars. The observed behavior is typical of what is seen with complex mixtures. In the nonisothermal experiments, the temperature of the tar sample was initially raised to 363 K, prior to beginning actual data collection. This was necessary because, in spite of the attempts to completely dry the sample prior to the experiment, there was always a residue of 2-5% of very volatile components left in the sample. This may have been some residual solvent or perhaps moisture picked up during handling in air. This material was observed to very quickly be driven off during the initial heating, and it was concluded that this portion could not be meaningfully included in the vapor pressure curves. In Figure 9, the actual amount of the preexperiment loss was 3.4%. The initial curvature on cooling from 363 K shows the continued loss of higher volatility materials. It is difficult to define a dividing line between what is thought to be solvent residue or moisture and actual volatile tar components, but there does not appear to be very much of these materials. Thus, meaningful nonisothermal data collection is seen to begin at a temperature of approximately 363 K (1/T ) 0.002 75). The initially scattered behavior quickly settles down into a welldefined curve, as the sample is cooled at a rate of 0.8 K/min to a temperature of approximately 352 K (1/T ) 0.002 84). The close approach of the nonisothermal curve to the isothermal data is already seen during this initial scan. During this cooling cycle, the sample lost an additional 13% of its mass. Following cooling, the sample is reheated at a rate of 0.8 K/min to a temperature of 366 K, at which it is momentarily cooled, and then heating is continued up to 389 K (1/T ) 0.002 57), at which temperature the experiment gave evidence of thermal alteration of the tar by what are thought to be reaction processes (this aspect will not be discussed here). The trajectory of the heating curve is seen to be different from that which was observed during cooling. This indicates that there is a shift in the composition of the tar that takes place during exposure to the higher temperature portions of the experiment. The lower temperature portions of the cooling and heating curves overlap quite closely, as would be expected since the rate of mass loss at the lower temperatures is quite low, and the composition does not change very much. The shift toward lower vapor pressure as heating is continued is expected, due to the loss of the lower molecular weight components. During this period of heating, the sample lost roughly another 25% of its mass. The value of the nonisothermal technique is clearly evident in identifying this real aspect of the process. The isothermal method data Analytical Chemistry, Vol. 69, No. 22, November 15, 1997
4625
might reveal the same trend, but there is a danger that subtle shifts could be missed, as they are lost in normal data scatter. The data taken from the isothermal experiments define a straight line which essentially bisects the two actual vapor pressure curves. The brief cooling and heating excursion around 366 K shows that the changes that take place in composition generally are still reasonably slow at the very low vapor pressures involved. The vapor pressures measured during this brief temperature swing are independent of the thermal history of the sample. After the heating was reinitiated at a rate of 0.8 K/min, it continued up to 389 K. There is continued evidence of the curvature of the vapor pressure curve for cellulose tar toward the curve measured for levoglucosan. There is an abrupt flattening of the vapor pressure curve near 389 K which, again, we believe marks the occurrence of reactions (supported by differential scanning calorimetry and GPC characterizations). After the reactions, the vapor pressure of the tars is still close to but lower than the vapor pressure of levoglucosan. It is possible to construct a classical boiling point curve from the above data using a knowledge of the mass loss at any time, combined with the correlation that applies to the appropriate segment of the vapor pressure curve. In this case, it may be seen that the variation in boiling point at, for example ln P ) -6 (P ) 2.48 mTorr) would only be from about 362 to 373 K, for about
4626
Analytical Chemistry, Vol. 69, No. 22, November 15, 1997
40% of the tar. Cellulose tar does not show a large variation in vapor pressure with mass loss because it contains species that, for the most part, have quite comparable molecular weights and compositions. Since this paper is devoted to issues of technique, as opposed to issues related to characterization of cellulose tars, further discussion of these results is deferred to a manuscript devoted to the latter topic. CONCLUSIONS The nonisothermal Knudsen effusion method has been shown to be a useful and reliable method for measuring the vapor pressures of pure components and complex mixtures. It is considerably faster and more convenient than the conventional isothermal Knudsen effusion method. ACKNOWLEDGMENT The financial support of the U.S. Department of Energy, under Grant DE-FG22-92PC92544, is gratefully acknowledged. Received for review March 7, 1997. Accepted August 15, 1997.X AC970262S X
Abstract published in Advance ACS Abstracts, October 1, 1997.
