Mechanism of the Methylchlorosilane Reaction: Improved Lab Reactor

the mechanism of the MCS reaction has a long history.11 Recent work has focused on the role the various metal promoters play in the reaction.12,13...
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Ind. Eng. Chem. Res. 2003, 42, 3532-3543

Mechanism of the Methylchlorosilane Reaction: Improved Lab Reactor Design and Kinetic Data John M. Bablin, Larry N. Lewis,* Pierre Bui, and Martha Gardner GE Global Research, 1 Research Circle, Niskayuna, New York 12309

An extensive laboratory reaction kinetics study was performed on the “direct process” of methyl chloride and silicon, also commonly referred to as the methylchlorosilane (MCS) reaction. Temperature and concentrations of copper, zinc, and tin were varied. Reaction rate reproducibility and repeatability were improved by increasing temperature homogeneity in our fixed-bed reactor system. A stripped gas chromatograph (GC) oven, a detailed standard operating procedure, and small-diameter fixed-bed reactors were used to achieve good temperature control. The kinetics study incorporated multiple sample points per run as opposed to a single sample. The complete kinetics data set was analyzed with statistical analysis tools (SAS, Minitab). Three silicon utilization windows (0-15%, 15-30%, and g30%) were assumed to determine reaction rate descriptions by so-called transfer functions. The developed model supports a proposal wherein at least two processes exist. The main reaction (the MCS reaction) produces dimethyldichlorosilane (Di) and equimolar amounts of trimethylchlorosilane (mono) and methyltrichlorosilane (Tri). At least one side reaction occurs during the MCS deactivation phase resulting in higher levels of Tri and other byproducts. Introduction The methychlorosilane (MCS) reaction, eq 1 (amounts in weight %), was discovered independently by Rochow1 and Muller2 in the 1940s. Since that time numerous reports have appeared on the kinetics of the MCS reaction. Early kinetics work on MCS was carried out by Bazant and co-workers.3 This group determined that temperature, pressure, and copper concentration were factors in the kinetic expression. The first comprehensive approach to MCS kinetics was by Voorhoeve4 who provided activation values. A review of mostly Russian literature appeared in 1975.5

Until the early 1980s the importance of tin as a critical promoter was not explicitly recognized.6 Thus early kinetic measurements were performed without precise knowledge of the promoter metals added to the bed or present in the silicon. For example, DeCooker et al.7 added various metal promoters to the MCS contact mass but failed to describe the composition of the silicon used in their experiments. Ward and co-workers described the use of tin as a promoter, the synergistic effect of tin and zinc, and, using a fluidized bed reactor, derived an overall reaction rate constant.8 The Ward et al. rate expression is shown in its entirety in Figure 1.

Figure 1. MCS rate expression from Ward et al.8

* To whom correspondence should be addressed. Tel.: (518) 387-7925. Fax: (518) 387-5592. E-mail: [email protected].

The Rethwisch group used a continuous fixed-bed reactor system and determined the reaction rate as a function of catalyst composition.9

10.1021/ie0203330 CCC: $25.00 © 2003 American Chemical Society Published on Web 06/25/2003

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Figure 2. Representation of the role Cu plays in MCS.

The rate expression found by Rethwisch is shown in eq 2 with q ) 1.6 ( 0.1.

-ri )

kiPnMeCl (1 + xKAPMeCl + KBPsilane)m

(2)

where ki ) apparent rate constant, Ki ) adsorption constant, Pi ) partial pressure, n and m are constants with n ) 1, m ) 2. For low conversions KBPsilane , 1

-ri ) kiPqMeCl

Figure 3. MCS proposed mechanism including C-H bond breaking.

where q is the apparent reaction order. The Dow Corning group also carried out a kinetic investigation of MCS, but there were no numerical details of their results.10 Discussion of the detailed chemical steps in the mechanism of the MCS reaction has a long history.11 Recent work has focused on the role the various metal promoters play in the reaction.12,13 Copper, of course, is the main catalyst in MCS. A crude representation of the role copper plays in MCS is shown in Figure 2.14 Here it is seen that a Cu-Si phase forms. The silicon activated in the Cu-Si phase reacts with MeCl to form a silylene intermediate for which there is experimental evidence.15 Reaction of the copper-centered methylchlorosilylene with a second equivalent of MeCl yields dimethyldichlorosilane (Di). The reaction cycle is completed by re-formation of a Cu-Si phase by copper diffusion to a new silicon atom. Copper diffusion is not rate-limiting in the process in Figure 2 as has recently been discussed.16 In addition to copper, several other metals are essential in the MCS reaction in order to obtain reasonable rate and selectivity for Di. Zinc has been recognized as a key promoter for many years17 as has the aforementioned tin. Lewis and co-workers describe so-called structural (like zinc) and textural (like tin) promoters.18 In a manner similar to tin, phosphorus19 also appears to be a textural promoter. A strong correlation between high selectivity for Di and Cu3Si (eta phase) was reported. Additionally, phosphorus promotes the forma-

tion of eta phase.20 Thus, the copper-catalyzed formation of Di in MCS occurs as shown in Figure 2 with formation and reaction of eta phase facilitated by promoters. In practice, the selectivity for Di in MCS is usually from 80 to 90% with formation of Si-H-containing byproducts as well as disilanes to name a few. It is likely that a second process is involved in formation of byproducts. If one assumes that Di (and equimolar amounts of mono and Tri) occur via the scheme in Figure 2, then a second process (or processes) is responsible for formation of byproducts. Key to understanding byproduct formation is the fact that competitive C-H bond breaking occurs under MCS conditions. Rethwisch recently discussed the issue of coking in the MCS reaction.21 Figure 3 shows a more expanded view of a proposed mechanism for MCS, taking into account some of the consequences of C-H bond breaking. Note that formation of Di (and equimolar mono and Tri) is not considered to be a free radical process18 but that there is a free radical component when C-H bond breaking occurs. This report will discuss our construction of an MCS laboratory reactor that gives improved reproducibility of product formation rates. Experiments are described in which copper, tin, and zinc were varied at different temperatures. We determined the value of these promoters as a function of silicon utilization in the fixedbed reactor. Furthermore, we attempted to re-examine the kinetics of the MCS reaction and investigated the effects of copper, zinc, tin, and temperature on rate of

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Table 1. Contact Mass Preparation; 60-g Batches desired [Cu]

desired Sn/Cu ratio

resultant [Sn] ppm

amount silicon (g)

3000 Sn/Cu - CuCl slurry (g)

0 Sn/Cu CuCl slurry (g)

2.38 2.38 4.75 4.75 4.75 7.13 7.13 7.13

1000 2000 500 1000 2000 330 1000 1330

24 48 24 48 96 24 71 95

58.57 58.57 57.15 57.15 57.15 55.72 55.72 55.72

2.96 5.91 2.95 5.90 11.80 2.92 8.86 11.78

5.96 2.99 14.82 11.87 5.97 23.76 17.82 14.90

Di formation. We determined the kinetic parameters at low silicon conversion and at higher conversion. The C-H bond breaking process is more prevalent at higher silicon conversion so we believe we have separated the contributions of the purely Di forming portion of the process from the byproduct forming portion. Significant improvements in our laboratory reactor design, especially with regard to temperature control, have contributed to our ability to obtain data with improved reproducibility.

Table 2. Contact Mass Preparation for Riffling; 24-g Batches [Zn] ppm

Zn added (mg)

[Cu]

Resulting Cu/Zn

790 790 790 1580 1580 1580 2380 2380 2380

19 19 19 38 38 38 57 57 57

2.38 4.75 7.13 2.38 4.75 7.13 2.38 4.75 7.13

30 60 90 15 30 45 10 20 30

Experimental Section Preparation of CuCl Based Contact Mass. Prior to using cuprous chloride (Copper (I) Chloride, Alpha Aesar, 99.999% metals basis), the CuCl was ground to a particle size of 2-5 µm by first preparing a mixture of 3:1 hexane/CuCl in a plastic jar containing 1-cm porcelain balls. Because the amount of tin is so low, for convenience and accuracy tin powder (Aldrich, 325 mesh, 99.8%) was added to the CuCl slurry prior to grinding. For this MCS kinetics effort two separate CuCl in hexane slurries were employed: a tin-free slurry and one containing 483 ppm [Sn] (or 3000 parts per million Sn/Cu ratio). The jar was sealed with Teflon tape and placed on a roller mill for 12 to 16 h. A finely dispersed CuCl/Sn suspension resulted and was transferred to a glass 150-mL bottle with a clean stir bar. A contact mass was prepared by blending lab-grind silicon powder, the CuCl/Sn suspension, and additional hexane in order to make the resultant slurry homogeneous. A known amount of the silicon powder was placed in a clean, dry 150-mL quartz reaction thimble. Depending on the desired [Cu] and Sn/Cu ratio, various amounts of the 0 ppm [Sn] and 483 ppm [Sn] suspensions were added together as shown in Table 1. While the CuCl/Sn suspension(s) was stirred by magnetic stir bar, amounts were removed via Pasteur pipet and placed into the silicon until the desired mass was obtained. Finally, an amount of hexane (Merck, GC/LC solvent grade) was added to thoroughly disperse the CuCl. The slurry was then mixed for ∼5 min. This homogenized slurry was then dried free of hexane by sweeping nitrogen over the top of it in a fume hood for at least 2 h. Completing the removal of all the hexane solvent, the semi-dried silicon and CuCl cake was vacuum-dried for at least 1/2 h. The thimble containing the dried mixture was placed in a furnace set at 320 °C, through which argon(g) flowed at ∼200 sccm. Within 1/ hour after applying heat the reduction of CuCl to Cu 2 began, as indicative of the presence of SiCl4 (Q) in the exit gas stream. The exit gas was easily monitored for Q by passing the vent tube through and or over ammonium hydroxide solution (Baker, reagent grade). At the peak of the Q reaction, the exit gas from the furnace became a dense fog. When the fog was no longer visible (after ∼2 h) the Q reaction was determined to

be complete, and the furnace was shut off, opened, and cooled, and the reaction thimble was then removed. The resulting contact mass was weighed, sealed, and then stored in a dry glovebox until further use. Preparation of Contact Mass for MCS Reactor. The lab grind of silicon contains various particle sizes, and silicon grinds are known to segregate in size over the course of time. We also have shown that [Cu] varies according to particle size. For this MCS kinetics effort we decided to use a 3-g MCS bed: large enough to obtain a good reaction rate signal-to-noise ratio and small enough to model the reactor as a differential reactor. Thus, the conversion of MeCl was restricted to 15% conversion per pass. To ensure accuracy and homogeneity of the 3-g MCS bed sizes we employed the use of an eight-cell micro riffler (QuantaChrome, Rotary Micro Riffler) to uniformly divide a larger quantity of mixed solids. Prior to riffling this size contact mass, the promoter zinc (Belmont Industries, zinc dust, 400 mesh) was added to a level of either 790, 1580, or 2380 ppm [Zn]. As shown in Table 2 the resulting Cu/Zn ratio varied with the starting [Cu] in the contact mass even though the absolute [Zn] was the same. The standard operating procedure for final preparation was then to vigorously shake the glovebox-stored contact mass, weigh out the contact mass (∼24 g, less the zinc amount), add the correct amount of Zn, vigorously shake the blend, and then place it in the riffler. After riffling, the eight individual samples (test tubes) were weighed for riffle repeatability to the 3-g amount; a riffle re-run would be performed if a variance greater than 10% by mass occurred. The completed riffled samples were then corked and returned to the glovebox for dry storage. Previously it was found that a contact mass degrades when in contact with ambient air/water vapor. Reactor Apparatus Description. All MCS bench scale experiments require the transfer of heat energy to a reaction mass in the presence of MeCl(g). Prior to this examination of MCS kinetics, the standard reactor design for a fixed- or fluidized-bed MCS reaction involved a tubular heating device. Typically this heating device employed two heat zones of 2 in. i.d. × 8.5 in. height which then transferred heat energy to an MCS

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Figure 4. Typical GE fixed-bed reactor cross section.

Figure 5. GC-Oven reactor used for MCS kinetics experiments.

reaction mass located in the center of the reactor, as shown in Figure 4. Fluidized-bed reactors used at GE are typically loaded with 18 to 25 g of contact mass in a reactor of a tube diameter 1.75 in. i.d. Conversely, GE fixed-bed reactors use 3-6 g of contact mass in a reactor of a tube diameter 0.5 in. i.d. The effort to produce meaningful kinetic data required us to focus on the use of a fixed-bed reactor because of its reverse frit and bed design, lack of fines loss, and minimal silicon particle-to-particle interaction, all of which are inherent to the GE fluid bed. For all experimental conditions (low MeCl conversion), our fixed-bed reactor can be modeled as a differential reactor to extract kinetics. Note that the reaction has low MeCl utilization per pass and is considered to be pseudo first order in MeCl. Our bed (Si) is somewhat consumed with each pass so we use a normalized rate to include silicon utilization. A gas chromatograph (GC) oven was used as a reactor heating “zone” because it is designed to accurately and quickly maintain a set temperature by employing a lowthermal-inertia heating coil and high-gas-flow fan combination. The continual movement of large volumes of

air across the heated element allows for near-perfect mass-transfer and distribution of the heat energy quickly to the oven contents. Any object placed in the “oven” will equilibrate to the oven temperature set-point to within (0.1% of the desired set-point. Due to the exacting nature of the “forced convection oven” method of transferring and maintaining heat energy to an MCS reaction, the GC oven has allowed us to obtain reproducible product rates from MCS beds composed of any metal and promoter combination. The GC oven used in the described experiments in this report was a Shimadzu GC9A. As shown in Figure 5., the length and width of 14 × 9 in. easily accommodated the existing all-glass fixed-bed apparatus without extensive glassware modifications. Early into the kinetics effort a noticeable pressure rise and then drop occurred during the reaction of some ∼1.5-g bed masses. Further examination of this phenomenon showed that simple hourly tapping of the externally located gas inlet joints caused the bed pressure to quickly rise due to presumed MCS bed particle re-packing. We concluded that nontapped MCS reactions would prematurely stop reacting whereas those

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tapped would continue to utilize bed silicon. Therefore, the MCS reaction heated by GC oven setup incorporated a “clamp-on” continuous vibrator (Vibro Mixer, A. G. furChemie Apparatebau) onto the gas inlet tubing area prior to the heated zone. Reactor Usage. To a clean, tared, fixed-bed reactor a riffled, glovebox-stored MCS bed of known composition (Cu, Zn, and Sn) was added. The weight was recorded along with the bed height (∼ 2.2 to 2.5 cm). An aluminum oxide monolith (∼10 mm × 10 mm) with a center hole and side notch, both of which would accommodate a 1/16-in. diam. thermocouple, was then lowered in the reactor on top of the bed surface. The loaded reactor was placed in the GC oven and then mated to the upper ground-glass joint or the gas-inlet side of the reactor apparatus. A clean 90° elbow joint was then affixed to the reactor exit. The exit of the reactor was now on the exterior of the GC oven so that the socket joint could be attached to the ball joint of the crude collector. A standard condenser atop the collector and exit gas flow indicator completed the apparatus. Grease was applied only to the ball-and-socket joint; we found that dry fitting of the oven-heated ground-glass joints worked best for leak prevention and ease of disassembly. A simple system flow check was performed by applying 40 sccm Ar(g) to the reactor and then counting the bubbles that passed through the flow indicator. Good bubbling greater than 21 counts per 15 s indicated a secure system. Counts under that amount indicated a leak that had to be remedied. Two thermocouples (TCs), mounted and secured through the use of a GC injector septum, were lowered into the bed mass. One thermocouple was placed into the center of the bed just above the frit, and the other was placed against the reactor wall. These TCs along with a TC located next to the reactor in the GC oven allowed us to monitor the GC oven temperature along with any reaction exotherm during the experiment. System backpressure was also monitored during the oven and bed heat-up stage and as the reaction progressed. All four data points were monitored and recorded every five minutes through the use of an Agilent 34790 data-acquisition switch box. Once the system was verified “gastight”, the GC oven was turned on to the desired set point of 300, 315, 330, or 345 °C. The chiller was also turned on to -20 °C. A standard heat-up period of 1 h under 40 sscm Ar(g) flow was followed for all MCS bed masses evaluated. MeCl(g) at a flow of 24 sccm was started through the system at a recorded time t ) 0 along with the start of the continuous vibration of the system through the inlet pipe fitting. Crude collection began at approximately 0.5 g of crude and continued at this frequency in order to obtain product rate data at increments of 5% silicon utilization points. A typical experiment yielded 10-14 crude samples or data points. The end of the MCS reaction produced little crude or no rate, which suggested the stoppage of the experiment. Crude samples were analyzed for the typical MCS products, and the residual MCS bed material was removed from the disassembled reactor system. To ensure a good MCS experimental result and one that captured the true product crude reaction rates, a silicon mass balance was performed. Because we employed the use of a fixed bed reactor, the initial copper catalyst was assumed to remain in the final bed (confirmed by some analyses). Initial added amounts of

Figure 6. Di rates using “old” reactor system.

Zn and Sn were of low significant mass values (up to 8 mg) along with any MCS reaction generating and bed depositing carbon as to impact the mass balance. All crude collected was assumed to have ∼22% silicon by weight on average. Therefore, the remaining bed weight was used to calculate unreacted silicon and added with that silicon collected in the crude. This total was compared to that of the initial charge of the starting MCS bed mass. Typically any mass balance of less than 90% required a repeat of the experiment and the inspection, cleaning, or replacement of the crude collection glassware. Chiller coolant efficiency was also a typical suspect in low-yielding mass balance experiments and would require cleaning or replacement as needed. Results and Discussion New Reactor System: Improved MCS Rates. The adaptation of the GC oven and vibrator to the reactor system along with micro-riffling and glovebox storage of contact mass bed samples allowed for dramatic improvement in MCS rate reproducibility. As shown in Figure 6, the prior fixed-bed reactor system (pictured in Figure 4 above) resulted in product rates of Di that were unusable for a MCS kinetics study. In this set of five experiments, the same micro-riffled contact mass (4.75% Cu, 30:1 Cu/Zn, 48 ppm Sn) was run using the standard operating procedure for the GE fixed-bed reactor. As shown, the rate for the product of main interest, Di, at the 20% silicon utilization point varied from 2 to 8 mg Di/g silicon min. Previous MCS data collected when using a 6-g MCS mass (above) resulted in product crude values that were reproducible for Di, Tri, mono, and etc. Even though we attained reproducibility for % Di, Tri, mono, etc., from the same bed composition, overall crude rates, as expressed in grams of crude per gram of silicon per hour, were significantly different from run to run. Upon experimental examination of the heating area between the reaction tube and the heater internal wall we discovered that temperature variances occurred anywhere from an additional 10 to 40 °C horizontally and vertically from the active MCS bed during the reaction. Further probing of the heater wall demonstrated the existence of localized “hot spots”. Several remedies to correct the nonuniformity of temperature due to the heater apparatus included the following: increasing insulation, adding more surface area of either SnO (tin oxide) or Nichrome wire (for more watts per length of heater), adding an internal air re-circulation device (fan), clamping of a metal jacket around the glass

Ind. Eng. Chem. Res., Vol. 42, No. 15, 2003 3537 Table 4. Bed Compositions and Temperatures

Figure 7. Di rates using “new” reactor system. Upper curves were at 330 °C, lower curves were at 300 °C. Table 3. Comparison of Di Rates Using Old and New Reactor System MCS at 300 °C

MCS at 330 °C

Di rate (mg Di/g Si-min)

old

new

old

new

mean standard dev.

2.14 1.28

3.07 0.30

5.24 2.00

8.68 0.74

reactor zone to increase heat conductivity toward MCS bed (or to dampen out temperature zones). We determined that none of the described remedies proved fruitful toward obtaining uniform heating of the fixed bed reactor. The same contact mass was run in the new reactor system as previously described and pictured in Figure 5. Results of five MCS experiments run at two different temperatures, 300 and 330 °C, are shown in Figure 7. These results clearly demonstrate the improvement of the reactor system with regards to MCS rate reproducibility (in mg Di/g Si min). A final comparison of data, Table 3, shows that the standard deviation of an equal number of runs (3) at two different temperatures led to improved standard deviation due to the new reactor system. Kinetics: Experimental Methodology, Selected Bed Compositions, and Experiment Totals. Experience in analyzing MCS experimental results influenced our decision to incorporate random, triplicate runs of the same bed metals composition (Cu, Zn, and Sn) at a given bed-reaction temperature. This protocol allowed for verification that an MCS experimental result, product crude rates for Di, Tri, mono, and residue, for a specific bed composition was statistically significant. Significant differences from previous experimental results (>20 to 40%) required additional runs at that temperature. The protocol is different from previous MCS reports from this lab.16 Previously we have reported the value of a product (like Di) at a particular % Si utilization (like 20%). However, here we report the rate of the particular product formation for a set of conditions. For this MCS kinetics study the influence of temperature and the concentration(s) of copper, zinc, and tin were examined, Table 4. It has been widely accepted that catalyst and promoter ratios are important in MCS reactivity and crude selectivity. We decided that with careful advanced planning the typical operating ranges for these ratios could be examined during this kinetics effort. The kinetics effort required a total of 94 individual MCS experiments. A quality check of this effort was the

[Cu] wt %

[Zn] (ppm)

[Sn] (ppm)

Cu/Zn

Sn/Cu

temperature(s)

2.38 2.38 2.38 2.38

790 1580 2380 790

24 24 24 48

30 15 10 30

1000 1000 1000 2000

315/345 315/345 315/345 315/345

4.75 4.75 4.75 4.75 4.75

1580 790 1580 2380 1580

24 48 48 48 96

30 60 30 20 30

500 1000 1000 1000 2000

315/345 315/345 300/315/330/345 315/345 315/345

7.13 7.13 7.13 7.13 7.13

790 790 1580 2380 2380

24 71 71 71 95

90 90 45 30 30

330 1000 1000 1000 1330

315/345 315/345 315/345 315/345 315/345

Table 5. Silicon Mass-Balance Results [Cu]

number of runs

mass balance (%)

std. dev.

2.38 4.75 7.13 all

24 38 32 94

92.80 94.00 94.14 93.74

1.77 3.12 2.23 2.69

overall silicon mass-balance of these runs. Table 5 details the results at each [Cu] and shows that the result of all 94 runs was an acceptable 93.7%. Product Rates: Di. A typical kinetics run generated 10-15 crude samples. These samples were analyzed using the standard MCS GC protocol for the crude components. The weight percent result for each crude sample was normalized to mg of component per g of silicon remaining in the bed for the total elapsed run time, instantaneous rate of Di. Rate of Di, in mg of Di per g of silicon remaining in the bed per min, was expressed as function of silicon utilization. The resulting expression was then verified by conducting repeat experiments at four different temperatures, and these results for Di rate, the major crude component, were quite reproducible. The comparisons of the other product rates, Tri, mono, and residue, further demonstrated the exceptional reproducibility of the new GC oven-MCS reactor system. Equations - Assumptions for Data Analysis. Because of the design of the fixed bed reactor shown in Figure 4 we assumed that no copper left the bed. Our assumption was supported by previous results of multiple spent-bed metal analyses. Therefore, a mathematical function can express how each initial starting copper concentration increased as the elemental silicon was converted into silanes. Figure 8 shows the change in bed copper concentration as a function of silicon utilization. However, from previous data of spent-bed metals analyses, the element zinc does transport through the glass frit and will leave the bed. This loss of zinc was significant in magnitude. A set of six bed analyses of the same experimental bed makeup, 4.75% Cu with 30 mg of zinc to start, were best fit to a function that related the percent Zn remaining in the bed to silicon utilization. We made the assumption that this relationship would hold true for all [Cu]s, [Zn]s, and temperatures. The zinc loss function is shown in Figure 9. The model for Zn decay was %Zn loss ) 1 - 0.0117 × SiUt (r2 ) 0.84). The combination of both functions (Figures 8 and 9), the loss of zinc along with the increase of copper in the

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Figure 8. Copper concentration as a function of Si utilization.

Figure 9. Zinc concentration as a function of Si utilization.

bed, effected the Cu/Zn ratio at any given silicon utilization. This Cu/Zn ratio function can also be obtained for each starting [Cu] at the three different [Zn]s used. Note that the results in Figures 8 and 9 are empirically verified and relate to the instantaneous concentration of Cu and Zn during the course of the reaction. One referee suggested that the data be fit using y ) 1/(a + bx). The suggested fitting model gives results virtually identical to those presented here (data fit using above equation and the suggested alternative agree with an R2 value of >0.99). Kinetics Results and Analysis. Modeling Approach. We assumed first order kinetics with respect to methyl chloride (and basically also to Si by normalizing the rate by Si weight remaining) for the product(s) Di, Tri, mono, and residue rates. Therefore, the following rate expression was employed for all products:

silane(rate) ) K1[MeCl] where

K1 ) koexp(-Ea/RT)

The science of MCS has led to the general understanding of the roles of the copper catalyst and promoters tin and zinc. It is well-known that these metals influence reaction rate by moderating the activation energy.22 Levels of these elements are incorporated into our model through the use of the activation energy coefficient Ea:

Ea ) f(Cu, Cu/Zn, Sn/Cu) Previous kinetic models used an average reaction rate determined over an entire experimental run. As shown in the experimental rate results for Di, Tri, mono, and residue, the MCS reaction is nonlinear and can be thought of as a quick initiation phase, followed by a steady-state period, and ending with a deactivation stage. Mindful of this, we abandoned a single sample collection for a given run time and opted for multiple samples at different times in an effort to capture the MCS reaction time profile. Because of the nature of the data collection protocol, the statistical treatment of the data employed a “repeated measures” analysis23 to test for significant effects

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in the models. One assumption of standard regression analysis is that the underlying errors of the model are independent. However, when collecting rate measurements over time within a single reaction, it is expected that rate measurements that are next to each other will be more correlated than rate measurements taken farther apart. Thus, a repeated measures analysis, which would take into account this underlying correlation structure over time, was needed. In our experiments, “time” is tracked by silicon utilization (SiUt). A single experiment gives a distinct set of data. Si Ut was used instead of time because rate depends on Si. When we calculate rate we divide by silicon. We assume 1st order in Si. Using Si Ut allows us to normalize and compare different experiments. The first-stage model for Cu at an instantaneous point in time was fitted as a standard linear model using the Minitab statistical program24 (“Start Cu” was the amount of Cu in a fresh bed):

EndCu ) 0.988 StartCu + 0.111 SiUt (0.00186 SiUt × StartCu) - 0.00464 SiUt2 + (0.000399 SiUt2 × StartCu) + 0.000047 SiUt3 (r2 ) 0.99) (see Figure 8). For the second stage of the model, we assume that the underlying covariance structure has a time-series component to it because we expect measurements that are closer to each other in time will be more correlated than measurements that are farther apart. However, many of these structures assume that measurements are collected at equally spaced time intervals, but ours were random. We can view this process as a spatial process in one dimension. The specific structure used in this analysis is called a spatial power law defined as:23

cov(yt1,yt2) ) σ2F|t1-t2| where F is an autoregressive parameter assumed to satisfy |F| e 1. This covariance structure is taken into account when testing the significance of the effects. PROC Mixed in SAS Version 8.0.125 can be used to fit these types of models. Kinetics Results First Attempt. The above models have been fit with the second stage modeling done in a piecewise manner. All data 30% SiUt were grouped together. The second stage of the modeling then follows the repeated measures analysis for the linearized first-order kinetic model as described above. However, a model for Tri at >30% SiUt could not be fit. It is suspected this may happen because two paths for making Tri may be initiated in by this SiUt regime. The coefficients with significant p-values ( 30% increased Cu results in a strong decrease in Di rate. The Cu/Zn, Sn/Cu, and % Cu effects on Di rate, of course, are not necessarily the same as the overall rate of chlorosilane production. For example, the coefficients for Di rate at