Ind. Eng. Chem. Res. 1992,31, 2003-2010 Saeman, J. F. Hydrolysis of cellulose and decomposition of sugars in dilute acid at high temperature. Znd. Eng. Chem. 1945,37(l), 43-52. Saeman,J. F.; Bubl, J. L.; Harris,E. E. Quantitative saccharification of wood and cellulm. Znd. Eng. Chem.,Anal. Ed. 1946,17,35-37. Santini, G. S.;Vaux, W. G.Biochemical conversion of refuse to ethyl-alcohol. AZChE Symp. Ser. 1976, 72 (No. 158), 9s103. Shelef, G.; Green, M.; Kimchie, S.; Maleeter, I. A. "Exploitation of organic wastes in Israel to produce ethanol and by-products"; Final report (in Hebrew); The Technion R&D Foundation La., Haifa, Israel, 1987. Thompson, D. R.;Grethlein, H. E. Design and evaluation of a plug
2003
flow reactor for acid hydrolysis of cellulose. Znd. Eng. Chem. Prod. Res. Dev.1979, 18 (3), 166-169. Titchener, A. L.; Guha, B. K. 'Acid hydrolysis of wood"; Report No. 56,New Zealand Engineering Research and Development Committee, University of Auckland, New Zealand, 1981. Ullal, V. G.;Mutharaaan, R.; Grossmann, E. D. New insights into high solids acid hydrolysis of biomass. Biotech. Bioeng. Symp. 1984,No. 14,69-93. Received for review September 6, 1991 Revised manuscript received March 23, 1992 Accepted April 13, 1992
Partial Least Squares for Mass Spectral Analysis of H2and D2Plasma Scrambling Products Sourav K. Sengupta,+Scott C. Cheeseman,' Steven D. Brown,$and Henry C. Foley*JJ Center for Catalytic Science and Technology, Department of Chemical Engineering, and Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716
The application of the partial least squares (PLS) method to resolve the mass spectrum of hydrogen and deuterium scrambling in a fast flow plasma reactor is reported. Calibration was performed by using a mixture of hydrogen, deuterium, and deuterium hydride, and the model predictions were validated against the experimental results. The calibration model was then extended to actual plasma scrambling experiments, and the effects of power, residence time, pressure, and inlet mole fraction of H2and D2were investigated. While residence time and applied power were found to have no significant effect on the deuterium hydride concentration within the operating regime tested here, changes in pressure and inlet mole fraction affected the conversion of H2and Dzto HD, as expected. The results from this study can be applied toward a more rational design of fast flow plasma or downstream etching reactors used in advanced materials fabrication.
Introduction Due to the increasing importance of plasma technology for materials fabrication and processing, the development of new methods for the quantitation of atoms and free radicals has become increasingly important. QpicaUy, this quantitation has been performed by one or more of the following techniques: calorimetry, electron spin resonance (ESR),vibrational spectroscopy, laser fluorometry, and mass spectrometry. Mass spectrometry is quite versatile, is readily available, and can be used to determine the concentration of atoms and the molecules that result from the plasma reactions. Yet the direct measurement of free radicals by mass spectrometry requires that the analyses be carried out at ultrahigh vacuum in order to avoid recombination within the plasma reactor or in the mass spectrometer. Since the pressure regime in which plasma reactors operate for materials fabrication is orders of magnitude higher than that maintained in ultrahigh vacuum experiments, there is strong motivation to develop new methods of mass spectrometry to analyze and quantitate the products from plasma scrambling processes. In this paper we have utilized partial least squares (PLS) analysis to accomplish this. Background Isotopic labeling and scrambling experiments are used for kinetic measurement of rate constants and to elucidate mechanisms of various reactions. Recently, catalytic scrambling of hydrogen and deuterium has been reported *Author to whom correspondence should be addressed. 'Center for Catalytic Science and Technology,Department of Chemical Engineering. t Department of Chemistry and Biochemistry.
by Nakamura et al. (1987)and Yamada et al. (1989)on Ni(100)single crystals with and without modification by sulfur. In these studies, maw spectrometry has been used to quantify the hydrogen, deuterium, and deuterium hydride concentration. The authors used mass fragments 2, 3, and 4 amu and a "suitable calibration factor" to quantify H2,HD, and D2 However, determinationof the calibration factor was difficult due to double scrambling that takes place, first, within the reactor in the plasma zone and then, again, in the maw spectrometer due to electron impact for ionization. This results in a doubly mixed spectrum of mass fragment ions due to H2,D2,and HD, the resolution of which requires a sophisticated mathematical model. Several methods have been used in the past to convert a set of overlapped spectroscopic data into the concentrations of the components of the mixtures giving rise to such overlapped spectra; this process is known as multivariate calibration. Mathematical methods for calibration include multiple linear regression, principal component regression, ridge regression methods such as the Kalman filter, and partial least squares regression. A number of review articles and books are available in the literature (McClure, 1987). Most of these mathematical methods for multivariate calibration have also been compared in detail by a number of researchers in the past few years (Wold, 1982; Manne, 1987; Hoskuldsson, 1988; Sanchez and Kowalski, 1988). New methods for multivariate calibration have been applied successfullyto mixtures of components with very similar spectra in ultraviolet, infrared, and X-ray spectroscopies (Lindberg et al., 1986;Frank et al., 1983; Haaland and Thomas, 1988;Thomas and Haaland, 1990; Karstang and Eastgate, 1987). The goals of this project were 2-fold: first, to establish a multivariate calibration method based on partial least
0888-5885/92/2631-2003$03.00/00 1992 American Chemical Society
2004 Ind. Eng. Chem. Res., Vol. 31,No. 8,1992 squares modeling of the relation between mass spectra and component concentrations that could be used to quantitate the products of the scrambling of reactant gases in a plasma reactor and, second, to apply this calibration method to study the effect of different process parameters on plasma-induced scrambling of Hz and D,.
Theory Multivariate Calibrations. A multivariate calibration method was developed to create a mathematical model relating the observed mass spectrum of a mixture of gases to the component concentrations for a series of standards. Once the calibration model is determined, the concentrations of the component species can be determined in unknowns. Partial least squares (PLS) modeling was used to perform the chemical calibration and to develop the predictive mathematical model in this work. The details of PLS modeling have been reported in detail (McClure, 1987; Wold, 1982; Manne, 1987; Hoskuldsaon, 1988; Sanchez and Kowalski, 1988; Karstang and Eastgate, 1987; Geladi and Kowalski, 1986a,b;Martens and Naes, 1989), and a few reviews of ita performance in multivariate calibration are available (McClure, 1987; Martens and Naes, 1989). A brief overview of PLS modeling will be given here. The reader is referred to the references for more complete treatments. Partial least squares modeling involves a least-squares regression in latent variables. The latent variables, which describe the variation over a data set, may be obtained by suitable linear transformation of the data set. In PLS regression, two seta of latent variables are used: one set of latent variables describing the dependent variable, often called the "Y block," and the other set of latent variables describing the independent variable, the "X block." With the most common algorithm for PLS regression, the NIPALS algorithm, the pairs of latent variables describing the X and Y blocks are generated one at a time, and the latent variables describing each block are selected to ensure maximum correlation between the pair. Mathematically, this task is accomplished by solving the two truncated eigendecompositionscalled the "outer relations", one in the independent variable X: X = TP' + E (1) and one in the dependent variable Y:
Y=UQ'+F
(2)
subject to the constraint that, for each of the n latent variables U and T extracted from the X and Y blocks, respectively, maximum correlation is present. This correlation is forced by imposing a linear equation in each row of the matrices of latent variables defined by U and T, namely
ui = biti (3) This interrelation of the latent variables of the X and Y blocks is known as the "inner relation." In these equations, matrices P and Q describe the loadings (projections) of the original N seta of measurements of component concentrations and responses in the X and Y blocks on the latent variables. Matrices T and U describe the scoresthe new axea defining the latent variables. Matrices E and F describe the residuals of the paired eigendecompositions; these matricea contain the parta of the X and Y blocks that were not modeled by the set of latent variables selected in T and U. The latent variables are found by examining the variation across a data set, with the first latent variable con-
taining the largest amount of variation, the second latent variable containing the next largest independent source of variation, and so forth. The goal of PLS modeling is the explanation of all "relevant" variation that occurs in a calibration-variation relating response to component calibration-by including it in the matrices T and U. Unimportant variation occurring in the calibration data will remain in matrices E and F. Thus, PLS modeling involves the reduction of IlEll and IIFII, because the PLS model attempts to explain as much systematic variation as possible in the X and Y blocks of the calibration data. PLS modeling also requires scaling of the latent variables used in the modeling. Scaling associates a weight to each set of latent variables, thereby reducing the underprediction caused by less significant latent variables or overprediction caused by the dominant latent variables. In most cases, it is difficult to associate weights a priori; therefore, in the PLS algorithm used here, the weights were determined as part of the model-building process, and were not preassigned. The goal of PLS modeling is prediction, not just explanation of the calibration data with an equation; however, it is intended to produce minimum variance estimates of the n component concentrations from an unknown, multivariate response. Because of the truncation involved in assigning T and U from variation present in a calibration set, PLS regression is biased, and the number of latent variable pairs used in the PLS model has a significant effect on the quality of the estimates obtained from the modeL Too few latent variables included in the PLS model leads to bias in the component concentration estimates predicted from a multicomponent response, as some important systematic effects have been neglected in the model. On the other hand, when too many latent variables are used in the model, extraneous (noise) variation is incorporated into the PIS model, and the multivariate input data is modeled to both signal and noise. This overfitting leads to decreased precision in the eatimates of component concentrations. Thus, finding the optimal number of latent variables in the model is a critical step in the calibration process when PLS regression is used. The PLS model is optimized by testing it on a set of well-known 'unknowns", so that the predictions can be compared with the true values. Optimization can be accomplished by using a second set of M standards, called a validation set, to test the predictions of trial PLS models with different numbers of latent variables. The metric used to evaluate the quality of the PLS models judges the accuracy of predictions, and not the error in fitting the calibration data. This is conveniently accomplished with the predicted residual error sum of squares (PRESS) statistic: M N
PRESS =
j=1 k = l
-
( ~ j ; g ~-*;g)~
(4)
The PLS model producing minimum PRESS should be the best predictive model over the range of the validation set. Another way of testing the calibration models is to make use of part of the calibration data. This method, called cross-validation, is based on withholding some calibration standards for use in the validation step to come (Wold, 1978). This method for validating a multivariate calibration model is commonly used when a validation set is difficult or very expensive to obtain. In cross-validation, a set of trial calibration models, each with a different number of latent variables, is built using a subset of the available calibration standerds and then tested on the data
Ind. Eng. Chem. Res., Vol. 31, No. 8,1992 2006
that were not used in creating the calibration model. This process is repeated several times, each time withholding different standards for use as the validation data, and building the same set of trial PLS models. The average PRESS statistic obtained for each of the PLS models over all of the predictions is used to judge model quality. As before, the "best" PLS model is taken to be the one with the smallest PRESS value. In this way, the number of latent variables that gives rise to the best predictions within the PLS model, over the range of the cross-validation, is identified. In chemical calibration, an "inverse" calibration model C=KR+e (5) is often used with PLS regression. Here, C is the N X n component concentrationmatrix, R is the P X n response matrix, K is the N X P calibration matrix, and e is an N X n matrix of error. This model differs from the "classical" model commonly used with calibrations based on multiple linear regression in the assumption that the concentration data carries the error. For PLS regression using the inverse calibration model, the X block describes the instrumental response (the mass spectra here), and the Y block describes the concentration of the standards. Use of the inverse model has the advantage of requiring no matrix inversions in the prediction of component concentrations from an unknown response. The assumption of no error in the mass spectral responses can be justified if the number of latent variables is carefully chosen, since the residual matrix E will contain the bulk of the experimental error in that case (Martens and Naes, 1989). Experimental Section Fast Flow Plasma Reactor. The scrambling of hydrogen and deuterium is performed in a fast flow plasma reactor (Figure la). High-purity hydrogen (Matheson, Research Purity, 99.9995%) and deuterium (Matheson, CP grade, 99.99%) enter the reactor through a gas manifold. The flow rates are metered by mass flow controllers (Tylan), and the pressure in the reactor is monitored by a capacitance manometer (Inficon, CM 100). The reactor is a cylindrical quartz tube with an inside diameter of 2.2 cm. The reaction zone is inductively coupled with a 2.45-GHz, l-kW CW microwave generator (ASTEX 1OOO) through a waveguide to generate the plasma. The approximate length of the plasma zone is 10 cm with an approximate wall temperature of 800 K. The reactor is evacuated with a high-speed roots blower (Leybold Hereaus,WSU150) and a mechanical backing pump (Leybold Hereaus, W).The ultimate preasure that can be achieved by these pumps is 3 X Torr. The advantage of using a roots blower is that it can accelerate gas-phase species to high linear velocities at a moderately low vacuum. Both conditions are necessary for successful downstream plasma processing and chemistry. The average linear velocity of the gas molecules is on the order of 1 X lo3 cm/s in the plasma zone. The reactor is equipped with a DYCOR residual gas analyzer (-70 eV) to measure the on-line gas-phase composition of the product stream. Simulation Runs with Mixtures of HzyDOand HD. Experiments were performed to deconvolute the mass spectra of known mixtures of hydrogen, deuterium, and deuterium hydride. These teats were conducted by making mixtures of H2,DP,and HD in different proportions in a Pyrex gas manifold (Figure lb) with provisions for attaching three l-L deuterium hydride (Merck Sharp and Dohme, 99.9% purity) flasks, an empty gas holding flask, and the existing hydrogen and deuterium supply lines. The simulation experiments had a dual purpose: to
evaluate the effectiveness of the PLS method and to construct a predictive multivariate calibration model to be used in the determination of the composition of the mixtures from the plasma scrambling experiments. The simulation runs, like any low-pressure experiments, were begun by pumping down the system to its base pressure and simultaneously baking the Pyrex manifold overnight (at approximately 3 X Torr and 100 OC for 8-10 h) to ensure proper outgassing of the system. At the onset of each run the system was pumped down to base pressure and the valve between the manifold (downstream from the gas holding flask) and the pump was closed. Next, one of the valves attached to the deuterium hydride flask was opened and deuterium hydride leaked into the gas holding flask, through the manifold. When the desired pressure level was attained, the valve attached to the deuterium hydride flask was closed and the valve separating the manifold from the hydrogen and deuterium supply lines was opened. The mass flow controllers were used to introduce hydrogen and deuterium. The advantage of using the mass flow controllers was that they restrict the flow of gas in the reverse direction, ensuring negligible back flow of the components from the manifold to the supply lines. After introduction of the second component (which might be hydrogen or deuterium) into the system, the total pressure was recorded using the capacitance manometer, and the difference between the finaland initial pressure was therefore the partial pressure of the second component. The same procedure was repeated for the third component and its partial pressure was recorded. The partial pressures of the three components were then converted to mole fractions. The mixture was finally analyzed by the residual gas analyzer (RGA). The same procedure was repeated for several different pressures and molar ratios of hydrogen, deuterium, and deuterium hydride. Plasma Scrambling Runs. The plasma scrambling runs were comprised of two steps. The frst step involved setting the gas flow rates to the desired molar ratio by adjusting the mass flow controllers and analyzing the mixture with the RGA. In the second step, hydrogen to deuterium inlet molar ratio was maintained exactly the same as in step one, with plasma turned on; the product of scrambling was analyzed downstream from the plasma zone. This allowed both for verification of the initial molar ratio of H2 and D2 in the feed and for calculation of the conversion of H2 and D2 to HD after scrambling in the plasma. Experiments were performed varying the pressure, residence time, inlet molar ratio, and microwave forward and reflected power. While the flow rates, residence times, and molar ratios of H, and Dz were varied, the microwave forward and reflected powers were kept constant at 500 and 200 W,respectively, since the initial runs indicated that the microwave power did not affect the H2-D2 conversion in the range of interest.
Results and Discussion Chemistry of Hydrogen and Deuterium Scrambling. Electrical discharge of hydrogen and deuterium in a low-pressurereactor can cause a plethora of reactions, including vibrational excitation, ionization, dissociation, electronic excitation, dissociative attachment, and superelastic vibrational collisions (Capitelli and Molinari, 1980). However, a microwave discharge typically produces only a weakly ionized plasma, and therefore ionization and dissociative attachment may be considered to have only a small contributionto the total chemistry (Yamane, 1968; Bell, 1972). The elementary gas-phase reactions in a
2006 Ind. Eng. Chem. Res., Vol. 31, No. 8,1992
D2
Ar
H2
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source
D2
AI
HZ
Mass Flow Conmllas
Deutaium Hydride Flisks
Figure 1. (a, top) Schematic diagram of the fast flow plasma reactor with on-line residual gas analyzer. (b, bottom) Schematic diagram of the Pyrex manifold with the three deuterium hydride flasks and a gas holding flask,used for the calibration runs.
microwave plasma reactor involve the dissociation of diatomic molecules to neutral atoms and can be expressed as H2(v=O) + e H2* + e 2H + e (6) D2(v=O)+ e D2* + e 2D + e (7) HD(v=O) + e HD* + e H + D + e (8) The possible reactions that lead to the depletion of hydrogen and deuterium atoms require three-body collisions, where the quartz wall acta as the third body (MI: 2H + M H2 + M (9) 2D + M D2 + M (10) H + D + M -w HD + M (11) The homogeneous gas-phase recombination reactions can
-- --
+
+
be neglected since, in the pressure regime in which the plasma reactor has been operated in this study, the wall recombination reactions predominate over the homogeneous gas-phase recombination reactions. This simplifies analysis of the chemistry of the plasma scrambling reaction. The products of reaction are deuterium hydride formed by heterogeneous cross-recombination of hydrogen and deuterium atoms on the quartz wall, as well as unreacted and self-recombined hydrogen and deuterium. Figure 2 shows a representative data set obtained with and without plasma at a system pressure of 0.500 Torr and hydrogen and deuterium flow rate of 22.5 cm3(STP)min-'. Simulation Results with H2,Dz, and HD mixtures. The simulation runs play an important role in constructing
Ind. Eng. Chem. Res., Vol. 31, No. 8,1992 2007 Table I. Predicted Residual Error Sum of Squares (PRESS) a s a Function of Increasing Number of
press. (Tom) . ~ 0.10 0.25 0.50 1.00
in
?n
30 M a s Fragments (mu)
40
Figure 2. Representative mass spectra of the products before and after starting the plasma a t an operating preeaure of 0.5 Torr, inlet flow rate of 50 cmS(STP) mi&, and hydrogen to deuterium mole ratio of 0.5
an implicit model using the partial least squares method. In the implicit model building approach a set of known concentrations of components in a mixture, together with its spectral response (called training set), are used to formulate a model. Here, a known set of concentrations and corresponding spectral responses were used to validate the accuracy of the model. The calibration and the validation resulta were obtained from the mass spectral response of the RGA after some preprocessing. The first step in prepmcessing was to select the proper subspace of the mass spectrum. The initial n m s spectral analysis of a mixture of hydrogen, deuterium, and deuterium hydride showed mass peaks between mass numbers 1and 6 amu. It was observed that peaks corresponding to 5 and 6 amu were due to the scrambling of H, and D, in the RGA, a proteas which can occur at higher pressure in the detection chamber. Preliminary analysis of the data showed that these two peaks did not have any correlation with the true concentration of the components. Therefore, mass peaks at 5 and 6 amu were eliminated from the data collected for calibration by reducing the RGA total presawe from -1W7 to 10* Torr. The raw mass spectral data sets were corrected for mass spectral background by subtraction of a blank recorded before each run. This process also reduced the contribution of any variations due to fixed error in the instrument or due to extraneous peaks caused by impurities in the reactor, especially from oil backstreaming from the vacuum pumps. After subtracting the background spectza, the relative mass abundances were obtained by dividing each mass peak ahundance by the cumulative sum of the abundances of all the mass peaks. The normalization removed the discrepancy in the abundances of the individual peaks that could be caused by the change in the RGA head pressure, which is known to be sensitive to the system pressure. The background-subtractedand normalized calibration data set for four different pressures (0.1,0.25,0.5, and 1.0 Torr) was used for PLS modeling. The PLS program, written in MATLAB (Moler et al., 1988), implemented the algorithm given by Geladi and Kowalski (1986a,b). Cross-validation on the calibration data was used to identify the best predictive model over the range of the calibration data The results of the cm-validation study are summarized in Table I. The optimal PLS model found in cross-validation used three latent variables, a result that is larger than that expeded for the three components present as mole fractions (and, therefore, summing
c a l d PRESS values for cumul no. of components 1 2 3 4 , 0.0416 0.8492 0.0386 1.8762 0.0623 0.0762 2.1903 1.5531 0.0641 0.0733 2.7155 0.9853 0.0651 0.0773 1.5888 1.4665
to a constant) in the mixture. When p m u r e was included in the Y-block data, the cross-validation model did not result from four latent variables. A possible explanation is that the composition of the mixture is the molar ratio of the three components and it can be represented by the normalized relative abundances, whereas the system pressure does not have a one to one correspondence with the relative abundances. It is probable that additional latent variables would be needed to predict the total pressure. Since the primary objective of our study was to use the PLS model to ascertain the molar ratio of Hz, D,, and HD after plasma smambling,no further attempt was made to predict the system pressure in the PLS model. After cross-validation was complete, the weight matrix, concentration and spectral loading matrices, inner relationship, and spectral response and concentration residual matrices were obtained from the optimal PLS model with three latent variables (based on the PRESS values). These parameters were then used to evaluate the unknown concentration of the components in the mixture before and after plasma scrambling. The PLS model, developed during the cross-validation, was also tested by a separate validation step. Results for validation at the four different pressure conditions are plotted in Figure 3. In this figure the mole fractions of HD predicted from the PLS calibration model are plotted against experimentally observed concentrations. The straight lines in the validation plots are the theoretical prediction lines; had there been no error in prediction, all the points would have fallen on the straight line. It can be inferred from the validation plots that the PLS model predicts the experimental results quite well, except at the lower and higher end of the spectrum. These deviations could be due to two reasons. A t the low-concentrationend, lack of fit may be due to the lack of sensitivity of the RGA when the concentration of at least one of the components in the mixture is low. A t the high-pressure end the deviation may result from secondary scrambling and ionmolecule reactions in the mass spectrometer leading to the formation of HDz+and DHz+. Plasma Scrambling of Hydrogen and Deuterium. The last part of the study involved the analysis of the data obtained from the actual scrambling experiments. This was done with the predictive PLS model constructed earlier from the calibration data set. The model was used to predict concentrations from a set of spectral responses from mixtures of unknown composition. The results of these predictions were used to study the effects of input molar ratios of hydrogen and deuterium, system pressure, and effective input power on the conversion of H,-D, to
HD. Effects of Process Parameters. Figure 4 shows the effect of net input power (the difference between the forward and reflected power) on HD conversion at constant pressure (0.5 Torr), residence time (3 X 1W2 s), and input molar ratio of hydrogen to deuterium (31). As expected, the input power density did not have any effect on the conversion under the operating conditions tested. This
2008 Ind. Eng. Chem. Res., Vol. 31, No.8,1992 C
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observation is in agreement with the results reported by Bell (1972). Bell showed that the conversion of dihydmgen to atomic hydrogen increases asymptotically with power density, so that above a certain power level there is no appreciable change in the concentration of atomic hydrogen with further increases in power density. Therefore, if the operating power density falls in the flat section of the curve, as it does in our case, the conversion is independent of the applied power. The excess power is dissipated by conduction, convection, and radiation, part of
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which increases the reactor wall temperature (Morin and Hawley, 1987). The effects of residence time on deuterium hydride concentration, parametric in praure, are plotted in Figure 5. The inlet mole fraction of hydrogen and deuterium were kept constant at 0.5 while three different pressures were selected, viz.,0.1, 0.25, and 0.5 Torr, to study the effect of residence time. The range of residence time
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sumption of hydrogen and deuterium atoms within the plasma zone. Apparently, the plasma zone is more backmixed than the afterglow region, and so conversion is actually lower with longer residence times in this zone. Conversely, with higher convective velocities and shorter residence times in the reactor, conversion of the diatomic molecules to active atomic species is higher. As a result, concentration of the atomic species entering the afterglow region of the reactor is higher, leading to a higher deuterium hydride concentration in the product stream. This is in agreement with results reported by other researchers (Bell, 1972; Mearns and Ekinci, 1977).
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Ind. Eng. Chem. Res., Vol. 31, No. 8, 1992 2009
c--0
Pressure (Torr)
Figure 6. Effect of preeeure on deuterium hydride concentration at constant inlet flow rate of 50 cm3(STP) m i d ; (*) inlet mole fraction H2 = 0.7, inlet mole fraction Dz= 0.3; (0)inlet mole fraction H2 = 0.6, inlet mole fraction Dz= 0.45; ( 0 )inlet mole fraction Hz= 0.5, inlet mole fraction Dz = 0.5; (A) inlet mole fraction Hz= 0.4, inlet mole fraction Dz= 0.6; (W) inlet mole fraction H2 = 0.3; inlet mole fraction D2= 0.7. X covered in this set of experiments was 4 X s. The residence time in this range was found to have no significant effect on the conversion of H2-D2 to HD. The change in pressure from 0.1 to 0.5 TORhad very little effect on the deuterium hydride concentration. The average change in deuterium hydride concentration, from 0.1 to 0.25 Torr and from 0.25 to 0.5 Torr is roughly about 0.1 mole fraction. Interestingly, the same trend was observed when Bell's (1972) model was used to calculate the hydrogen atom concentration. At short residence time (less than 0.1 s) Bell's model also predicted small changes in the hydrogen atom concentration with comparable changes in pressure. The effect of pressure on deuterium hydride concentration, parametric in mole fraction, is shown in Figure 6. The HD mole fraction has been plotted against pressure at a constant inlet flow rate of 50 cm3(STP) min-' while the inlet hydrogen and deuterium mole fractions were varied between 0.3 and 0.7. The general trend of these curves shows that at lower pressure (less than 0.5 Torr) there is very little change in deuterium hydride concentration. The effect is more dramatic at higher pressure, where, with an increase in deuterium inlet mole fraction, a sharp drop in HD concentration is observed. The rate of generation of hydrogen and deuterium atoms depends on the concentrations of H2 and D2,the average electron density, and the dissociation rate constants. The experimental results of Higo et al. (1982) showed that the cross section for dissociation (which is a measure of the rate constant) of hydrogen is higher than that for deuterium. It is to be expected that the change will be more pronounced for lower hydrogen concentration. This effect becomes obvious when the inlet mole fractions of the two reacting gases are varied. The maximum deuterium hydride concentration shifta from 0.4 inlet hydrogen mole fraction at 0.1 Torr to 0.4 inlet deuterium mole fraction at 1.0 Torr. The drop in production of deuterium hydride at higher pressure can be rationalized in terms of system pressure, space velocity, and the rate of generation and consumption of the atomic species. An increase in pressure increases the rate of generation of atomic hydrogen and deuterium. However, at a constant inlet flow rate an increase in pressure also reduces the space velocity, i.e., increases the residence time, thereby increasing the time for the con-
Conclusions The partial least squares method for multivariate calibration has been successfully applied to the resolution of mass spectral data that result from the scrambling of H2 and Dp The validation result showed that the model prediction fits reasonably well with the experimental data. The deuterium hydride concentrations from the plasma scrambling were found to be in the expected regime, and as expected, they showed only slight dependence on residence time and effective input power. Unlike residence time and net input power, pressure and inlet mole fraction have a significant effect on the concentration of deuterium hydride in the operating regimes tested here. The results obtained from this study can be used to develop a detailed reaction engineering model for scrambling of H2-D2 in a fast flow plasma reactor. The results of the scrambling experiments can have an impact in understanding the mechanistic pathways and intrinsic kinetics of more complex systems, such as plasma scrambling of methane and deuterium. It can also find potential application in the systematic design of plasma reactors for electronic materials processing where determination of atomic and free radical concentrations is important. Acknowledgment Support for this research was provided to H.C.F. by the National Science Foundation in the form of a Presidential Young Investigator Award (CBT-8657614). Allied-Signal Corporation is thanked for providing industrial matching funds. S.D.B. gratefully acknowledges support from the Division of Chemical Sciences, Office of Basic Energy Sciences, of the US Department of Energy (Grant DEFG02-ER13542) for support of this research. Registry No. Hz, 1333-74-0;Dz,7782-39-0.
Literature Cited Bell, A. T. A model for the dissociation of hydrogen in an electric discharge. Znd. Erg. Chem. Fundam. 1972, I1 (2), 209-215. Capitelli,M.; Molinari, E. Kinetica of dissociationprocess in plasmas in the low and intermediatepreeeure range. In Topics in Current Chemistry: Plasma Chemistry Z4 Veprek, S., Venugopalan, M., Eds.; Springer-Verlag: New York, Berlin, 1980, pp 59109. Frank, I. E.; Kalivas, J. H.; Kowalski, B. R. Partial least squares solutions for multicomponent analysis. Anal. Chem. 1983, 55, 1800-1804. Geladi, P.; Kowalski, B. R. Partial least squares regression (PLS): a tutorial. Anal. Chim. Acta 1986a, 185,l-17. Geladi, P.; Kowalski, B. R. A n example of 2-block predictive partial least squares regression with simulated data. Anal. Chim. Acta 1986b, 185,1932. Haaland, D. M.; Thomas, E. V. Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information. Anal. Chem. 1988,60,1193-1202. Higo, M.; Kamata, S.;Ogawa, T. Electron impact diseociation of molecular hydrogen and deuterium: iaotope effect on the emission
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Nakamura, J.; Yamada, T.; Tanaka, K. H2-D2isotope exchange reaction on a Ni(100) surface modified by sulfur-effects of a surface compounds involving oxygen. Surf. Sci. 1987, 185, L515L519. Sanchez, E.; Kowalski, B. R. Tensorial calibration: 1. First order calibration. J. Chemom. 1988,2,247-263. Thomas, E. V.; Haaland, D. M. Comparison of multivariate calibration methods for quantitative spectral analysis. Anal. Chem. 1990,62,1091-1099. Wold, S. Cross-validatory estimation of the number of components in factor and principal components models. Technometn'cs 1978, 20, 397. Wold, H. Soft modelling. The basic design and some extensions. In Systems Under Indirect Observation; Joereskog, H., Wold, H., Eds.; North-Holland: Amsterdam, 1982;Vol. 11, pp 1-54. Yamada, T.; Nakamura, J.; Matauo, I.; Toyoshima, I.; Tanaka, K. Catalytic isotope scrambling of H2 + D2 and the formation of surface compounds involving oxygen on Ni(100) modified by sulfur. Surf. Sci. 1989,207,323-343. Yamane, M. Hydrogen ions in the positive column of a hydrogen glow discharge. J. Chem. Phys. 1968,49,4624-4632. Received for review September 16,1991 Revised manuscript received March 3, 1992 Accepted March 23,1992
Effects of Ionic Size Difference on Thermodynamic and Transport Properties of Uniunivalent Molten Salt Mixtures Yutaka Tada,* Setsuro Hiraoka, Yasuhiko Katsumura, and Ikuho Yamada Department of Applied Chemistry, Nagoya Institute of Technology, Nagoya 466, J a p a n
Effects of ionic size difference on the enthalpy, molar volume, surface tension, electrical conductivity, and viscosity of uniunivalent molten salt mixtures were investigated, based on the law of corresponding states. The Helmholtz free energy of the mixture was expanded around that of a hypothetical pure molten salt, whose pair potential was the sum of the hard-sphere potential and the effective Coulomb potential, with the core-repulsive potential differences (ionic size differences). The thermodynamic and transport properties of the mixtures were correlated in the corresponding states with the second-order perturbation term with respect to the ionic size difference. Mixing quantities of the properties were evaluated using the corresponding states correlations with the term of the ionic size difference better than those without the term, in particular in the mixtures which include lithium ion. The ionic size difference increased the mixing quantities of the thermodynamic properties and decreased those of the transport properties. 1. Introduction
A law of corresponding states is one of useful and practical methods for predicting physical properties of molten salt mixtures. The pair potential of molten salt is expressed by the sum of Coulomb, core-repulsion,dipole-dipole (dispersion),induced-dipoleion, and dipole quadrupole interactions. It is important in the law of corresponding states how the pair potential is simplified, what are chosen as the characteristic parameters, and which order of the perturbation terms is included. Harada et al. (1983) simplified the pair potential to the sum of soft-sphere repulsion and effective Coulomb potential. The core repulsion was postulated to be the same for unlike-charged ions and for like-charged ions, on the basis of the assumption of hiss et aL (1961)that the short range repulsion between like ions contributes little to the confiiational integral. The effective Coulomb potential incorporated effects of the dispersion and polarizability. Harada et al. scaled the soft-sphere potential to a hardsphere potential such that the Helmholtz energy of the molten salt with the simplified potential is equal to that of a hypothetical molten salt whose pair potential is the
s u m of the hard-sphere potential and the effective Coulomb potential. They showed that the thermodynamic properties of pure uniunivalent molten salts were correlated in the corresponding states, using the effective Coulomb potential parameter and the hard-sphere diameter as the characteristic parameters. Tada et al. (1988) used the potential simplified by Harada et al. to show that the transport properties of the pure molten salts were correlated in the corresponding states with the simplified potential parameters, the hardsphere diameter, and the characteristic mass, which was obtained by expanding the autocorrelation function of the dynamical quantity for the transport property with the mass difference of anion and cation. As for the mixtures, Lantelme and Turq (1979) investigated mixtures of LiBr-KBr on the basis of molecular dynamics, using the Tosi-Fumi (Tosi and Fumi, 1964) pair potential which consists of core-repulsion, Coulomb, dipole-dipole, and dipole-quadrupole interactions. They showed that many properties of the mixtures were satisfactorily described by the Tosi-Fumi potential and that the contribution of the ionic polarization was relatively
0888-5885f 92f 2631-2010$03.00f 0 0 1992 American Chemical Society
