Determination of the Degradation Mechanism from the Kinetic

3174

J. Phys. Chem. B 2001, 105, 3174-3181

Determination of the Degradation Mechanism from the Kinetic Parameters of Dehydrochlorinated Poly(vinyl chloride) Decomposition K. J. Jordan,† S. L. Suib,*,†,‡,§ and J. T. Koberstein†,§ Institute of Material Science, Department of Chemistry, and Department of Chemical Engineering, UniVersity of Connecticut, Storrs, Connecticut 06269-4060 ReceiVed: September 13, 2000; In Final Form: January 16, 2001

Kinetic theory in regards to the basic understanding of reaction order as it relates to polymer degradation is discussed. This new theory is then tested by determining the kinetic parameters for dehydrochlorinated poly(vinyl chloride) using thermogravimetric analysis. Four different mechanisms of degradation were deduced from four sets of kinetic parameters. The calculated kinetic parameters were apparent reaction order, apparent activation energy, and apparent frequency factor as determined by the original Freeman and Carroll model. The four regions/mechanisms attained by the theory from the data are in order of appearance: final dehydrochlorination; random chain scission; cyclization; coke degradation. The data indicate transition regions between the individual regions where two mechanisms are competing with one another. Also, a method for obtaining the optimal heating rate from a set of heating rates is discussed.

Introduction Several investigators have looked into the determination of kinetic parameters for polymer decomposition.1-10 Of these parameters, the one that has been fundamentally the most difficult to understand has been the reaction order (n). Early investigators used kinetic models which assumed n to be equal to 1.11,12 However, the process of polymer degradation is far too complex with differing mechanisms for different polymers10,13 for this assumption to be held valid for long. Thus, several kinetic models9 have been developed and applied that allow for the determination of n from a polymer degradation system. With n not fixed to a particular value, an extra degree of freedom is allowed for more accurate values of the activation energy (Ea) and frequency factor (k0). Despite the development of these kinetic models, it still remains controversial as to what a particular value for n represents when dealing with a polymer system undergoing thermal degradation. This study gives a fundamental understanding of what information n gives for a specific polymer degradation system. Kinetic Theory Let us begin by first looking at a typical rate expression for a conventional chemical reaction involving microscopic molecules, eq 1, for a reactant molecule going to product where CA is the concentration of a reactant molecule A.

rA ) -

dCA ) kCAn dt

(1)

Most often the concentration is expressed in terms of molarity or moles/volume. Moles are directly proportional to the number of molecules. Thus, eq 1 can be used to measure the number of reactant molecules of A which “disappear” per reaction from * To whom correspondence should be addressed. † Institute of Material Science. ‡ Department of Chemistry. § Department of Chemical Engineering.

the system. Thus, it can be noticed that in the case of an elementary reaction of first-order molecularity that one reactant molecule of A reacts/reaction. This type of reaction is termed first order because n in these reactions takes on a value of 1. The parameter n takes on a value of 2 for reactions having a molecularity of 2, and n ) 3 for the rare reaction in which three molecules collide with one another to form product. Then, for a conventional chemical reaction not involving intermediates, n represents the number of molecules involved in the reaction. Now, our attention is focused on a polymer system undergoing thermal degradation. Since degradation of a polymer system implies bond cleavage, the rate of polymer degradation is proportional to the number of bonds such that we can write a rate equation, eq 2, which is analogous to eq 1.

r)-

dN n kN dt

(2)

The only change is that CA has been replaced by N where N represents the total number of bonds in the polymer system. On the basis of the logic used to understand n for a conventional chemical reaction, it seems that n for a polymer degradation system represents the number of bonds that “disappear” per molecular formation. This analogy is reasonable on the basis of the wide acceptance of molecularity for an elementary chemical reaction. Thus, n for a polymer degradation system fundamentally gives information about the average number of bonds that leave the polymer system per bond cleavage and consequently the type of unstable and/or stable species formed directly from the polymer chain. This approach of understanding the fundamental concept behind the reaction order differs substantially from other methods which basically try to explain the reaction order by looking at the final products. Technically, this conceptualization assumes no side chain scission, but if the side chain is only a small fraction of the repeat unit molecular weight or has the same repeat unit, the error introduced is negligible. The degradation rate of a polymer sample being directly proportional to the number of bonds in the sample raised to the

10.1021/jp003223k CCC: $20.00 © 2001 American Chemical Society Published on Web 03/31/2001

Dehydrochlorinated PVC Decomposition

J. Phys. Chem. B, Vol. 105, No. 16, 2001 3175

power of the number of bonds in the degradation products (R Nn) is also supported by a probability treatment of polymer degradation in a book by Kelen.14 In the book, he shows that the number of compounds formed from the degradation is directly proportional to the probability that a bond has not been cleaved (i.e. conversion) raised to the power of the number of bonds within the compound. This probability is a function of the number of bonds remaining in the polymer sample.

Since every term on the right-hand side of eq 8 is a constant except for W, it can be simplified further to eq 9, where k′ is the apparent reaction rate constant.

W N+1) N - (M0 - 1) m0 A

(3a)

The first term on the right-hand side of eq 3a represents the total number of repeat units in the polymer system. The term on the left-hand side is needed since the number of bonds in a polymer chain is one less than the number of repeat units in a single polymer molecule. Similarly, the second term on the righthand side takes into account that a bond is lost for every polymer molecule above one in the system. Equation 3a can be easily simplified to eq 4 by distributing the negative sign through the second term on the right-hand side. A reviewer has suggested that eq 3b is a better derivation that utilizes discussed analysis:

)

W 1 W N - 1 M0 ) N - M0 m 0 A M0 m0 A

(3b)

Equation 4 still suffers from having a term, M0, that is difficult

N)

W N - M0 m0 A

(4)

to measure directly. M0 must then be expressed in measurable quantities as in eq 5, where Mn is the number-average molecular weight of the polymer system undergoing degradation.

M0 )

W NA Mn

(5)

If one substitutes eq 5 into eq 4 and factoring out common terms, eq 6 is produced:

N ) WNA

(

1 1 m0 Mn

)

(6)

For high polymers (i.e., those with several repeat units) at the start of the reaction, 1/m0 . 1/Mn. This continues to be true throughout the entire course of degradation for high temperature degradations since relatively small molecules will volatilize from the polymer system. Thus, eq 6 becomes

N)

WNA m0

Wn

dW ) k′Wn dt

-

Fundamentally, eq 2 is a valid rate equation. However, experimentally, it is extremely difficult to measure N directly and accurately. To overcome this problem, a method for measuring the number of bonds indirectly needs to be used. A parameter that is directly proportional to N but experimentally easy to measure is the sample weight, W. Equation 3 relates W to N through the parameters m0, NA, and M0, which represent the repeat unit molecular weight, Avogadro’s number, and the total number of polymer molecules in the system, respectively.

(

n-1

(7)

If eq 7 is substituted into eq 2, upon simplification eq 8 results.

(8)

Though k becomes k′ through the mathematical derivation,

Bond Removal versus Weight Loss

N)

()

NA dW )k dt m0

-

(9)

Ea and n remain the same. This is extremely significant as it allows for the determination of n using weight loss data, while being able to use that same n as if it was determined from bond removal data. Thus, it is possible to experimentally test the kinetic theory developed above. Data Analysis To test the kinetic theory, the original Freeman and Carroll method15 was used. This method was chosen because it is the most fundamental of the methods commonly used to analyze nonisothermal kinetic data. Two equations, eq 9 and the Arrhenius equation, are used to develop kinetic plots which allow for the determination of apparent activation energy and apparent reaction order from the slope and the y-intercept, respectively. This can be seen in eq 10 which is the expression used for the original Freeman and Carroll method:

( dWdt ) )

d log -

d log W

Ea dT +n 2.303R T2 d log W

(10)

Experimental Section The poly(vinyl chloride) (PVC) used for the experiments was obtained from Aldrich Chemical Co., Inc. (product number 18,262-1), and was in powder form. The number-average and weight-average molecular weights as reported on the certificate of analyses were 37 400 and 83 500 g/mol, respectively. The PVC was first pretreated at a temperature of 300 °C for 1 h in a helium atmosphere to remove HCl and form polyene referred to hereafter as de-HCl PVC. The de-HCl PVC was then grounded to sizes between 300 and 590 µm for use in the experiments. A Du Pont Instruments 951 thermogravimetric analyzer (TGA) was used to perform the experiments. The data were collected with a TA Instruments Thermal Analyst 2000 from Du Pont Instruments. The weight recorded with the thermobalance is accurate to four significant figures. For each experiment, a sample of about 10 mg was put in an aluminum pan and placed on the thermobalance of the TGA. Two sets of experiments were carried out in two different atmospheres, helium and hydrogen. Each set was performed at five different heating rates 1, 2, 5, 10, and 20 °C/min. The TGA was programmed to begin the heating rates once the temperature had equilibrated at 200 °C with the final temperature being 500 °C. Each run was carried out in duplicate for averaging and consistency. Results TGA Curves. Figures 1 and 2 show the TGA weight loss curves in helium and hydrogen atmospheres, respectively, as a function of temperature at different heating rates. In helium, it is observed that the conversion increases as the heating rate is

3176 J. Phys. Chem. B, Vol. 105, No. 16, 2001

Jordan et al.

Figure 4. Typical log dW/dt vs log weight plot.

Figure 1. TGA curves for the decomposition of de-HCl PVC in helium.

Figure 5. Nonisothermal kinetic plot in helium at a heating rate of 1 ˚C/min.

Figure 2. TGA curves for the decomposition of de-HCl PVC in hydrogen.


Figure 3. Typical temperature vs log weight plot.

increased. Thus, there is more residual coke remaining in the TGA pan at lower heating rates in the helium atmosphere. While in the hydrogen atmosphere, the conversion is essentially constant regardless of the heating rate and there is no residual coke but rather a black oil residue remains. Raw Data. Typical plots of the raw data generated by the TGA experiments are shown in Figures 3 and 4. Figure 3 shows a typical temperature vs log weight plot while Figure 4 shows a typical log dW/dt vs log weight plot. An equation was fitted to both curves using the data analysis program Sigma Plot 3.0 for the purpose of taking the necessary derivatives for the kinetic plots. Kinetic Plots. The kinetic plots for the degradation of deHCl PVC in a helium atmosphere are shown in Figures 5-9 corresponding to the different heating rates used. It is clear that


Figures 5 and 6 do not yield straight lines. However, Figures 7-9 which correspond to heating rates of 1 and 2 °C/min do yield straight lines consistent with eq 10. Four different linear regions are observed on these kinetic plots corresponding to heating rates of 5, 10, and 20 °C/min. Figure 10 shows the kinetic plot in a hydrogen atmosphere at a heating rate of 5 °C/min. The four linear regions are seen to be discernible in




Figure 11. General location of kinetic regions on a typical TGA curve.


Figure 12. Kinetic parameter determination plot of de-HCl PVC degraded in helium at a heating rate of 5 ˚C/min: region 1.

Figure 10. Nonisothermal kinetic plot in hydrogen at a heating rate of 5 ˚C/min.

the hydrogen atmosphere as well. These four regions from the kinetic plots take place at approximately the same place on all the TGA curves that yield linear plots and their approximate locations are shown in Figure 11. The quantitative analyses of the kinetic plots are shown in Tables 1-3. Discussion TGA Curves. Since the carbon-carbon bond length in deHCl PVC is between that of a single and double bond (explained later), it is expected that its dissociation energy lies approximately midway between the dissociation energies of a carbon-carbon single bond and carbon-carbon double bond. This makes for a carbon-carbon bond that has a higher dissociation energy than the carbon-hydrogen bond. Thus, as the sample is heated from room temperature, a zone is reached where there is enough thermal energy to break the C-H bond but not enough to break the carbon-carbon bond. At low heating rates, the amount of time spent in this zone is considerable and thus much of the hydrogen has left the polymer with the carbon remaining in the polymer. As a result, more


coke is formed with low heating rates rather than with high heating rates. This is not observed in the hydrogen atmosphere as much of the hydrogen that leaves the polymer is quickly replaced by another hydrogen atom. Therefore, the final conversion is independent of the heating rate in the hydrogen atmosphere. Kinetic Plots. At the low heating rates (Figures 5 and 6),

3178 J. Phys. Chem. B, Vol. 105, No. 16, 2001

Jordan et al. TABLE 1: Nonisothermal Kinetic Parameters He at 5 °C/min 1st region 2nd region 3rd region 4th region 1st region 2nd region 3rd region 4th region

n (Apparent Reaction Order) 4.843 (r2 ) 0.992) 0.1983 (r2 ) 0.995) 3.374 (r2 ) 0.995) 0.7111 (r2 ) 0.997) 7.475 (r2 ) 0.997) 1.147 (r2 ) 0.998) 6.005 (r2 ) 0.995) 1.112 (r2 ) 0.995)

1st region 2nd region 3rd region 4th region Figure 14. Kinetic parameter determination plot of de-HCl PVC degraded in helium at a heating rate of 5 ˚C/min: region 3.

H2 at 5 °C/min

Corrected Weight Loss (%) 0-37.06 0-40.85 37.06-60.00 40.85-64.35 60.00-78.81 64.35-83.68 78.81-100 83.68-100

Ea (Apparent Activation Energy) (kJ/mol) 65.18 51.54 158.5 64.58 243.3 51.77 116.2 13.58

K0′ (Apparent Frequency Factor) (mg1-n/min) Psuedo Isothermal 1st region 3.606 × 10-7 (r2 ) 0.999) 3.170 × 104 (r2 ) 1.000) 2nd region 1.297 × 10-9 (r2 ) 0.989) 2.992 × 102 (r2 ) 0.995) 3rd region 1.766 × 10-9 (r2 ) 1.000) 3.565 × 102 (r2 ) 1.000) 4th region 1st region 2nd region 3rd region 4th region

Freeman and Carroll 9.516 × 10-3 2.257 × 103 4.529 × 107 7.318 × 103 6.623 × 108 3.480 × 102 4.238 × 100 6.698 × 10-1

TABLE 2: Activation Energy (Ea, kJ/mol) Cross-Check in Heliuma nonisothermal


the kinetic test fails due to large amounts of coke formed early in the reaction. This is not the case, however, at the higher heating rates (Figures 7-9), and four different regions are observed. Each region indicates a different mechanism of degradation occurring. There is a problem, however, of which heating rate to choose for the determination of the kinetic parameters as each plot generates different constants (Figures 12-15). One rationale for choosing the best heating rate is to use the lowest heating rate that gives a linear kinetic plot since at higher heating rates the separate mechanisms may merge together convoluting the data. This reasoning would lead to using the data collected at the heating rate of 5 °C/min because the data at 1 and 2 °C/min did not yield linear kinetic plots. Ea Cross-Check. The determination of k0′ also allows for a second rationale, a quantitative rationale, of determining the activation energy from the kinetic data. Since determining k′’s in a nonisothermal experiment gives rate constants at different temperatures, these k′’s can be used as if they were determined from separate sets of isothermal experiments at different temperatures. Thus, the logarithmic form of the Arrhenius equation can then be used for determining kinetic parameters from the data. If the n’s determined from the nonisothermal kinetic plots are accurate, then the Ea’s calculated from both the isothermal and nonisothermal methods should be the same since the same raw data are being used. Upon inspection of Table 2, the best agreement between the two methods in all regions occurs at the heating rate of 5 °C/min in both helium and hydrogen atmospheres. The lone exception is region one

isothermal

absolute diff

3rd region

1 °C/min 241.4 (r2 ) 0.986) 13.49 (r2 ) 0.994)

227.9

2nd region

2 °C/min 16.01 (r2 ) 0.998) 113.8 (r2 ) 0.979)

97.8

5 °C/min 1st region 65.19 (r2 ) 0.992) 172.0 (r2 ) 0.999) 2nd region 158.5 (r2 ) 0.995) 174.6 (r2 ) 0.989) 3rd region 243.3 (r2 ) 0.997) 242.1 (r2 ) 1.000) 4th region 116.2 (r2 ) 0.995) 130.9 (r2 ) 0.999)

106.8 16.1 1.2 14.7

10 °C/min 71.94 (r2 ) 0.993) 154.4 (r2 ) 0.999) 127.3 (r2 )0.997) 129.7 (r2 ) 0.992)

82.5 2.4

1st region 4th region

20 °C/min 1st region 44.38 (r2 ) 0.983) 228.8 (r2 ) 0.998) 2nd region 113.9 (r2 ) 0.998) 177.7 (r2 ) 0.985) 3rd region 7.094 (r2 )0.995) 11.20 (r2 ) 1.000) 4th region 37.35 (r2 ) 0.995) 31.95 (r2 )0.995)

184.4 63.8 4.11 5.40

aRegions in which the kinetic plots were nonlinear are not shown (i.e. r2 g 0.980).

in the helium atmosphere where 10 °C/min gives the best agreement. This gives quantitative evidence that the best heating rate among the rates used experimentally for determining kinetic data is 5 °C/min for de-HCl PVC. Given that even at a heating rate of 5 °C/min the Ea’s are not quite the same, the optimal heating rate is probably somewhere near 5 °C/min. Thus, it is possible to use this Ea cross-check as a means for determining which heating rate to use for determining polymer degradation kinetics. Corrected Weight Loss. If the weight losses in both atmospheres are normalized by adjusting for the differences in conversion, it can then be seen as shown in Table 1 that the four regions occur for the most part at the same percent weight loss. At most, there is only a 5% difference for the two atmospheres as to the ending of a region and the beginning of



TABLE 3: Activation Energy (Ea, kJ/mol) Cross-Check in Hydrogena nonisothermal

isothermal

CHART 2: Backbone Structure of de-HCl PVC

absolute diff


1 °C/min 77.25 (r2 ) 0.992) 132.8 (r2 ) 0.998) 112.5 (r2 )0.988) 78.52 (r2 ) 0.982)

55.5 34.0


2 °C/min 81.79 (r2 ) 1.000) 109.1 (r2 ) 0.997) 227.4 (r2 ) 0.997) 222.4 (r2 ) 0.996)

27.3 5.0

1st region 2nd region 3rd region 4th region

5 °C/min 51.55 (r2 ) 0.995) 66.55 (r2 ) 1.000) 64.58 (r2 ) 0.997) 45.80 (r2 ) 0.995) 51.78 (r2 ) 0.998) 51.86 (r2 ) 1.000) 13.59 (r2 ) 0.995) 12.34 (r2 ) 1.000)

15.00 18.78 0.08 1.25

1st region 3rd region 4th region

10 oC/min 6.113 (r2 ) 0.994) 31.23 (r2 ) 1.000) 14.68 (r2 ) 0.999) 58.67 (r2 ) 0.992) 8.085 (r2 ) 0.999) 22.87 (r2 ) 0.994)

25.12 44.99 14.78

1st region 2nd region 3rd region 4th region

20 oC/min 34.48 (r2 ) 1.000) 166.5 (r2 ) 0.997) 84.71 (r2 ) 0.998) 301.2 (r2 ) 0.999) 54.52 (r2 ) 0.996) 152.9 (r2 ) 0.998) 42.18 (r2 ) 0.995) 127.4 (r2 ) 0.997)

132.0 216.5 98.4 85.2

aRegions in which the kinetic plots were nonlinear are not shown (i.e. r2 g 0.980).

CHART 1: Backbone of the Resonance Structures of de-HCl PVC

the next. Thus, the basic modes of degradation are the same in the two atmospheres. Reaction Order. Since helium is an inert atmosphere, these data will give better intrinsic values than the hydrogen atmosphere and thus will be investigated first. Region one is believed to be due to the final stage of de-HCl in which the HCl that was not removed during the initial de-HCl is removed. The removal of HCl leads to the formation of other hydrocarbons most of which are benzene.13,16-22 Kinetic theory arguments given above suggest that the evolution of benzene from the polymer chain would lead to a reaction order of 6 since benzene has six bonds in its structure. However, HCl is also being evolved and the molecular weight of HCl is only about three times the repeat unit molecular weight of de-HCl PVC (Chart 1) and thus should lower the reaction order somewhat. As seen in Table 1, this is indeed the case. After region one is complete, the de-HCl PVC is now a threedimensional cross-linked polymer network absent of all chlorine. The next degradation mechanism, which occurs in region two, must be random chain scission of the carbon-carbon bonds. Once these bonds are cleaved, the random chain scission process continues in a fashion similar to polyethylene. This can be understood by considering the structure of the de-HCl PVC. When the conjugated polymer has a large number of repeat units, π bond overlapping occurs in the polyene (de-HCl PVC) structure. π bond overlapping develops in planar molecules with alternating single and double bonds. These systems create bonding orbitals in which a continuous bonding π-molecular network is maintained both above and below the plane of the atoms. This gives rise to resonance in the polyene molecule indicating that the polyene is a hybrid of two equally contributing resonance structures as shown in Chart 1. The polyene is an average of these two structures as shown in Chart 2 with all bonds having equal length. This length is between the length

of a single and double bond. Chart 2 makes it more apparent that the bonds in the de-HCl PVC are the same making the molecule similar to polyethylene, which also has all of its backbone bond lengths equal to one another. The major difference between the backbone of polyethylene and de-HCl PVC is the increased electron density between carbon atoms which accounts for the different backbone bond lengths among the two polymers. During the random chain scission of polyethylene, a side reaction occurs which is due to an intramolecular chain transfer reaction.23-25 This side reaction is responsible for C3’s being the most abundant compounds produced on a molar basis during the degradation of polyethylene. Given the structural similarities between polyethylene and de-HCl PVC, it can be expected that the random chain scission of de-HCl PVC should lead to the formation of C3’s. Thus, n for region two should be near 3 since three bonds are removed in the creation of C3’s. Table 1 shows that in fact n is near 3. However, C3’s are not a major component of the product distribution from de-HCl PVC degradation. This is best explained that while the C3 compounds formed during polyethylene degradation are stable, the C3’s formed during the degradation of de-HCl PVC are not. This is because the electron density between carbon atoms is much greater in the case of the latter making them unstable. These unstable species react with other species to decrease their electron density forming mainly aromatic compounds, a process which is thermodynamically favorable. In region three, the de-HCl PVC is no longer a highly crosslinked network and probably resembles more a system of lightly cross-linked star polymers. With the polyene chain now shorter, the electron delocalization brought about by the π bond overlapping is reduced and the bonding network resembles more an alternating sequence of single and double bonds (although the single bond length is shorter than normal and the double bond length is longer than normal).26 Also, there is now more free space for the cyclization/aromatization process to occur by polymer chains folding back on themselves. This process would be expected to yield an n of at least 6 since benzene is the primary compound produced but most likely a little higher than 6 since other aromatics (i.e. toluene, xylene, naphthalene, etc.) are also formed. If one checks Table 1, it is seen that n for this region is well above 6. Region four characterizes the end of the degradation which leads mainly to coke. Understanding that coke is a hydrogen deficient material, only aromatics and unsaturated aliphatics can be formed as products in this region. Taking into account that structural coke resembles fused aromatic rings, acetylene as a significant product can be removed from consideration. Of the aromatics, cyclopentadiene and benzene need the least amount of hydrogen to form. Since the material in this region is hydrogen deficient, these two compounds would be formed preferentially to other aromatics, and with benzene being the more thermodynamically stable of the two, it likely prevails. Table 1 shows that the n in this region is almost exactly 6 meaning that benzene almost exclusively formed in this region. The structure of the de-HCl PVC at the end of each region is shown in Scheme 1. The n’s in the hydrogen atmosphere are much lower than those in the helium atmosphere (Table 1). This can be understood realizing that n is measured by a weight loss method. Yet, there is a weight “gain” in hydrogen with de-HCl PVC

3180 J. Phys. Chem. B, Vol. 105, No. 16, 2001 SCHEME 1: Proposed Structure of de-HCl PVC at the End of Each Region

SCHEME 2: Series and Parallel View of de-HCl PVC Degradation

Jordan et al. Arrhenius equation to be used to determine k0′’s for each region as if isothermal experiments had been performed at each temperature. The parameter k0′ may be thought of as the rate constant at infinite temperature. According to this reasoning, it is expected that the k0′’s in hydrogen should be higher than those in helium. Table 1 is seen to be consistent with this idea. Further inspection of the k0′’s in Table 1 shows that in their respective atmospheres the k0′’s in regions two and three are of the same order of magnitude while region one has k0′ values that are 2 orders of magnitude higher. This indicates consistency in the experimental data obtained from the degradation. The k0′’s can also be calculated directly from the Freeman and Carroll method by using the equation ln(dW/dt) ) ln k0′ + n ln W - E/RT and are listed in Table 1 as an average for the region.9 It is quite apparent that the two methods yield very different k0′’s in the four regions. If one desires to reconstruct the TGA curves, the k0′’s from the Freeman and Carroll method must be used. However, the k0′’s from the psuedoisothermal approach are on the same order of magnitudes as the rate constants for the respective regions and atmospheres and thus should be used for comparison between the k0′’s. Conclusion

(an unsaturated polymer) being the starting material since it reacts with hydrogen giving a reaction order which does not correlate with the number of bonds removed from the reaction. Activation Energy. Using helium as the atmosphere that gives more intrinsic data, it is noticed from Table 1 that region one gives the lowest Ea. This is expected since the mechanism in this region is a continuation of what occurred during the initial de-HCl. Region two is expected to have a lower Ea than region three because in region two there is only chain scission while in region three there is chain backbiting as well as chain scission. Thus, there is a comparison of two energetic processes to one as Table 1 is consistent with this reasoning. Producing compounds from coke is a very energetic process, and subsequently, region four should be expected to yield a large Ea. Yet, this is not the case upon inspecting Table 1. This phenomenon may be due to a catalytic effect occurring as the hydrogen reacts with the coke. The Ea’s in the hydrogen atmosphere are significantly lower than those in helium (Table 1) indicating a catalytic effect is associated with hydrogenation of unsaturated polymers. In the study of physical chemistry, it is generally well-known that for a conventional chemical reaction among microscopic molecules that if the activation energy changes with a change in temperature then there has been a shift in the controlling mechanism of reaction. This seems to also be the case with macroscopic molecules undergoing degradation as well. Thus, the increase in activation energy with the increase in temperature in going to region three from region two indicates that the two mechanisms within those regions are parallel routes to the formation of the material at the beginning of region four. While the decrease in the activation energy in going from regions two and three to four indicates the mechansim within region four is the next route in the series rather than a parallel or competing mechanism. This is shown pictorially in Scheme 2. Frequency Factor. Now that the reaction orders have been determined, we can use eq 9 to determine different k′’s. Due to the heating rate used in the experiments these k′’s are at different temperatures. This allows the use of the log form of the

The final conversion of de-HCl PVC in helium is dependent upon the heating rate used to carry out the degradation while no dependency is observed when the degradation is carried out in a hydrogen atmosphere. The experimental n’s indicate that the kinetic theory presented is an accurate depiction of how best to interpret n’s for polymer systems undergoing thermal degradation. Four regions of degradation were observed for deHCl PVC: final stage of de-HCl; random chain scission with subsequent recombination; cyclization/aromatization; degradation from coke formation. The Ea’s were lower in hydrogen while, conversely, the k0′’s were higher in hydrogen. A method for determining which heating rate is the best heating rate for evaluating polymer degradation kinetics from the Freeman and Carroll method was shown and relies upon the matching of Ea’s as determined by nonisothermal and pseudoisothermal kinetic plots. Acknowledgment. K.J.J. and S.L.S. thank the National Science Foundation’s (NSF) Division of Graduate Education and Research Development for a traineeship fellowship (GER9354903) in support of this research. References and Notes (1) Klaric, I.; Roje, U.; Stipanelov, N. J. Appl. Polym. Sci. 1999, 71, 833-839. (2) Marcilla, A.; Beltran, M. Polym. Degrad. Stab. 1998, 60, 1-10. (3) Marcilla, A.; Beltran, M. Polym. Degrad. Stab. 1997, 55, 73-87. (4) Marcilla, A.; Beltran, M. Polym. Degrad. Stab. 1996, 53, 251260. (5) Marcilla, A.; Beltran, M. Polym. Degrad. Stab. 1995, 48, 219229. (6) Jimenez, A.; Berenguer, V.; Lopez, J.; Sanchez, A. J. Appl. Polym. Sci. 1993, 50, 1565-1573. (7) Basan, S.; Olgun, G. Thermochim. Acta 1986, 106, 169-178. (8) Basan, S.; Olgun, G. Thermochim. Acta 1986, 106, 179-182. (9) Allen, N. S. Degradation and Stabilisation of Polyolefins; Applied Science Pub.: Oxford, U.K., 1983; pp 154-162. (10) Anderson, D. A.; Freeman, E. S. J. Polym. Sci. 1961, 54, 253260. (11) Standard Test Methods for Arrhenius Kinetic Constants for Thermally Unstable Materials (ANSI/ASTM E698-79); ASTM: Philadelphia, PA, 1979. (12) Standard Test Methods for Decomposition Kinetics by ThermograVimetry (ANSI/ASTM E1641-94); ASTM: Philadelphia, PA, 1994. (13) Chatterjee, N.; Basu, S.; Palit, S. K.; Maiti, M. M. J. Polym. Sci., Part A: Polym. Chem. 1994, 32, 1225-1236.

Dehydrochlorinated PVC Decomposition (14) Kelen, T. Polymer Degradation; Van Nostrand Reinhold: New York, 1983; pp 62-68. (15) Freeman, E. S.; Carroll, B. J. Phys. Chem. 1958, 62, 394-397. (16) Shun-Myung Shin; Yoshioka, T.; Okuwaki, A. Polym. Degrad. Stab. 1998, 61, 349-353. (17) Utschick, H.; Matuschek, G.; Namendorf, Ch.; Kettrup, A. Thermochim. Acta 1998, 310, 191-198. (18) Muller, J.; Dongmann, G. J. Anal. Appl. Pyrolysis 1998, 45, 5974. (19) Beltran, M.; Marcilla, A. Eur. Polym. J. 1997, 33, 7, 1135-1142.

J. Phys. Chem. B, Vol. 105, No. 16, 2001 3181 (20) Yassin, A. A.; Sabaa, M. W. J. Macromol. Sci., ReV. Macromol. Chem. Phys. 1990, C30 (3, 4), 513-514. (21) Wypych, J. PolyVinyl Chloride Degradation; Elsevier Science Pub. BV: Amsterdam, 1985; pp 104-111. (22) Kelen, T. J. Macromol. Sci., Chem. 1978, A12 (3), 349-360. (23) Kiran, E.; Gillham, J. K. J. Appl. Poly. Sci. 1976, 20, 2045-2068. (24) Tsuchiya, Y.; Sumi, K. Polym. Lett. 1968, 6, 357-361. (25) Tsuchiya, Y.; Sumi, K. J. Polym. Sci. 1968, 6, 415-424. (26) Loudon, G. M. Organic Chemistry, 2nd ed.; Benjamin/Cummings Pub: Reading, MA, 1988; p 583.

Determination of the Degradation Mechanism from the Kinetic

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