RATESOF MOLECULAR VAPORIZATION OF LINEAR ALKANES
3237
Rates of Molecular Vaporization of Linear Alkanes’
by Leo A. Wall, Joseph H. Flynn, and Sidney Straus Natwnal Bureau of Standards, Polymer Chemistry Section, Washington, D. C. bOP3,f
(Received March 9, 1070)
The rates of molecular vaporization of four linear alkanes, n-nonadecane (GIs), n-tetracosane (C2J, n-hexatricontane (Ch), and n-tetranonacontane (Ch), were measured. The tetranonacontane vaporized without detection of hydrocarbon decomposition products by mass spectral monitoring. The kinetics of the vaporization process showed zero-order behavior as a vaporization process proportional to the surface area should. The Arrhenius slope, +3RT/2, was compared to heats of vaporization of other n-alkanes in the literature. The data show that the heat of vaporization is closely proportional to the two-thirds power of the number n, of carbon atoms in the species and not to the first power. Our results and the majority of the known heats of vaporization are well fitted by the equation, A H , = 13.43naI8- 0.08075T 12.22 kJ/mol. The results suggest a much higher upper limit to the size of species capable of molecular vaporization without decomposition than previously assumed.
+
The molecular vaporization kinetics of hydrocarbons is of importance to an understanding of the decomposition2 of hydrocarbon polymers by weight loss techniques as well as being of fundamental interest in itself. Contemporary studies of polymer decompositions often utilize gravimetric techniques3 for which equipment is now commercially available. In order to better understand the results of our studies of polymer decompositions we have studied gravimetrically the molecular vaporization of four hydrocarbons, n-nonadecane (C19H40),n-tetracosane (CzaH,o), n-hexatricontane (G 6 H 4 , and n-te tranonacon tane (C94H190), both as pure substances and as a component in a mixture with polyethylene. The rate of vaporization of high polymers is controlled in theory by the rate of rupture of the chemical bonds comprising the polymer molecule. Consequently, the rate of vaporization in a high vacuum is proportional to the weight of sample provided the sample is reasonably thin. This behavior is often not observed with polymers of number average molecular weights less than lo4. In theory, of course, molecules small enough to volatilize molecularly should vaporize with a rate proportional only to the exposed surface. With a pure substance and constant surface area, the rate of molecular vaporization would be independent of conversion and hence the “order” of the process might be said to be zero. A solution of miscible substances all vaporizing molecularly could give rates of vaporization with many different dependences on conversion. Such systems may in some aspects duplicate behavior commonly observed in studies2t3of the thermal volatilization of high polymers. In theoretical discussions of the thermal decomposition of high polymers by techniques in which the decomposition products are volatilized, it is assumed that below a critical size, L,molecules evaporate instead of decomposing. This permits one to set the lower limit
in summing over all the molecules in the reactor. Assuming a random decomposition mechanism, the distribution of products from the thermal decomposition of linear polyethylene indicates that this lower limit for tjhe alkanes is 72 methylene unitsO6
Apparatus The apparatus consisted of an electrobalance capable of measuring the weight of sample with an accuracy of at least 275, an electronic recorder, a pyrometric controller and programmer, or alternatively a stepless controller which is capable of holding a constant temperature up to 600” with an accuracy of .t0.5”, and a vacuum system monitored with a Pirani gauge. The furnace is situated inside the vacuum envelope and attains the desired temperature within 3-5 min. The hydrocarbon sample, generally 10 mg in weight, is loaded into a small 190-mg quartz or polytetrafluoroethylene (PTFE) bucket approximately 4 mm i.d. and 10 mm tall, which is hung from the weighing beam by means of a 3-mil tungsten wire. The bucket with the sample is suspended in the center of the -in. furnace opening approximately 1 mm above a calibrated 28gauge chromel-constantan thermocouple. The thermocouple is kept in a fixed position in the exact center of the furnace to record the temperature. This thermocouple was compared to the readings obtained, in a separate series of experiments, from another chromelconstantan thermocouple placed in the sample which is heated by radiation. A t the slow rates of vaporization used, no correction is needed. The thermocouple 1 (1) Based on research supported by the Advanced Research Project
Agency, Washington, D. C. 20301. (2) L. A. Wall, “Pyrolysis,” Analytical Chemistry of Polymers, Vol. 11, G. M. Kline, Ed., Interscience, New York, N. Y., 1962. (3) J. H. Flynn and L. A. Wall, J . Res. N a t . Bur. Stand., Sect. A ,
70, 487 (1966). (4) R. R. Reidhard and J. A. Dixon, J . Org. Chem., 30, 1450 (1965). ( 5 ) R. Simlia and L. A. Wall, J . Potym. Sci., 6 , 39 (1951).
The Journal of Physical Chemistry. Vola74, N o . 17, 1970
L. A. WALL,J. H. FLYNN, AND S. STRAUS
3238 mm from the bucket gives the temperature of the samples to within i1". Identical experiments can be repeated to within =!=l%.The experiments are carried out when the Pirani gauge indicates pressures of approximately 1 p or lower. The sample is essentially vaporizing into a perfect vacuum. Hydrocarbon Samples. Four linear hydrocarbons were studied, namely n-tetranonacontane, C94H190, a white powder which melts at 114" ; n-hexatriacontane, C3RH74,a milky-white solid having a melting point -70" ; n-tetracosane, C24H60, a milky-white flaky solid whose melting point is about 47-48" ; and n-nonadecane (n-pristane), CleH4,, a soft opaque solid which melts at about 28". A thermogravimetric run (TGA) was performed on each hydrocarbon from room temperature to a temperature at which evaporation was complete. The rate of rise in temperature was 1.5"/min. The isothermal experiments were carried out in greater detail, especially with C36H74. Rate experiments were conducted at temperatures constant to within ~ 0 . 2 " . The effects of the following variations in the experimental techniques were investigated: (a) size of sample, 1 mg, 2 mg, 4 mg, 10 mg, 20 mg; (b) material of bucket holding sample, quartz or PTFE; (e) height of bucket, 5 mm or 10 mm; (d) i.d. of bucket, 2 mm, 3 mm, 4 mm; (e) with or without liquid nitrogen around glass envelope around heater. Size of Sample. Rate experiments were performed on the C36H74 sample in a 4-mm i d . quartz bucket, 10 mm tall, with sample sizes varying from 1 mg to 20 mg. All the C36H74 samples were preheated for 1 hr at 100" and then raised quickly to the vaporization temperature, in about 2 min time, for all the isothermal experiments. If the samples were raised initially to the vaporization temperature, ranging from 129 to 153", about 30% or more of the sample would erupt from the bucket. This is a result of the final degassing of the sample as it becomes conditioned to the highvacuum environment. With some of the alkanes the isothermal rate curves had an initial rapid portion followed by a flat portion as shown in Figure 1. Here we show several isothermal rate curves for C36H74 using 10-mg samples. The value for the horizontal portion of the curve is taken as the characteristic vaporization rate. At 138", variations in the initial sample size produced the results shown in Table I. If the effective Table I: Effect of Initial Sample Size on the Vaporization Rates of n-Hexatricontane a t 138" Size, mg
Rate, mg/min
%bin
1 2 4 10 20
0.20 0.20 0.26 0.30 0.38
1.96 1.00 0.63 0.30 0.19
The Journal of Physical Chemistry, V d , .74?N o . 17, 1070
\
\' \
\
Tc
.,E.
1.0, \
' \
\ \
0
\
'. 153'C
'.'\.
'
063
0.90 0,30
01 0
143'C
-
138%
I
1.0
0.5 C
Figure 1. Rate of vaporization of n-hexatricontane (CaeHl4). Quartz bucket (10 X 4) mm i.d., 10-mgsample, activation energy 29.0 kcal.
surface area for vaporization remained constant and no foaming took place, then the rate in mg/min should have been constant. All things considered, they are nearly constant since it is seen that the rate varies less than a factor of 2 for a 20-fold variation in initial sample weight. Influence of Bucket Material. As variations due to sample size were thought to be partially the result of the sample wetting the wall of the bucket, a series of runs was carried out comparing quartz and PTFE buckets of the same dimensions, 4 mm i.d. and 10 mm long. Results at 148" are shown in Table 11. On the assumption that the hydrocarbon does not wet the PTFE vessel, a lower rate was anticipated and was observed. The results also show that the small variation due to sample size is independent of small changes in temperature and bucket material. Thus to calculate rates per unit area one would ignore meniscus corrections and take the experimental areas as 1rr2 where T is the radius of our bucket, in this case 0.2 em. Such rates are considered to be accurate to well within a factor of 2. Table 11: Effect of Bucket Material on the Rate of Vaporization of n-Hexatricontane at 148' PTBE,
Size, mg
Quartz, mg/min
mg/min
4 10 20
0.052 0.069 0.074
0.034 0.050 0,057
The effect of bucket dimensions is shown in Table 111. PTFE buckets were used because they could be readily machined to the desired dimensions. Larger diameter buckets were not tried because we preferred to keep sample weights small. On the other hand, experiments with smaller buckets were impractical either because the bucket was too small for the sample or because during the degassing stage of the experiment the sample
RATESOF MOLECULAR VAPORIZATION OF LINEARALKANES
3239
erupted from the bucket. With the 4-mm i d . bucket, increasing the height by a factor of 5 changed the rate by a factor of 2. Variation in inner diameter of the bucket gave rates nearly proportional to the ar2 area. Table I11 : Effect of PTFE Bucket Dimensions on the Rate of Vaporization of n-Hexatricontane a t 148' Bucket dimension Ht, i.d., mm
mm
2 3 5 10 5 10
4 4 4 4 3 3
10-mg sample, mg/min
20-mg sample, mg/min
0.4
-
0.084 0,050 0.070
0.091 0.057
0,025
Rates of Vapoyixation. Figure 1 shows the rates of vaporization of 10 mg of n-hexatricontane from a 4 X 10 mm quartz bucket. The horizontal portions of the curves are taken as the experimental rate at the indicated temperature. The activation energy is 28 kcal/ mol, 1 kcal is equivalent to 4.1840 kJ, and the midtemperature of the experiments, T , is 145". The result obtained for nonadecane (n-pristane) at 35" was 18 kcal/mol, for n-tetracosane at 75" was 22 kcal/mol, and for n-tetranonacontane at 342" was 45 kcal/mol. Since avariation in the rate of a factor of 2 will be produced by a 0.41 kcal change in activation energy a t 27" and by a 0.55 kcal change at 127", it is believed that these results are accurate to better than f1%. In view of the relatively small temperature range of the experiments, temperature control is probably more important than most of the factors mentioned above. The rates of vaporization per unit area of vaporizing surface are probably not known to better than 50%. For practical estimates one can take the cross-sectional area of the bucket as the area of the vaporizing surface. In Figure 2 we show the rates of vaporization of the tetranonacontane a t four temperatures and the Arrhenius plot for the data, the diagonal line, which gives a value of 46 kcal/mol for the activation energy. The rate is given as the fraction per minute of the sample evaporating from the quartz bucket, 4-mm i d . X 10 mm tall. The sample weight was 10 mg. The rate was very constant over the range of conversion shown. Figure 3 shows the rates of vaporization of 1 mg nhexatricontane from 9 mg of low-density polyethylenea (DYJT Union Carbide Plastics Co.). A few attempts to use a high-density, Le., linear polyethylene, were not successful because of difficulties in making a homogeneous mixture. The samples were prepared by mixing the components in xylene at about 100' and casting films. The results in Figure 2 were less reproducible since the total weight of material vaporized was 1 mg
-
0 3
0.116 0.108
I
.O 1.0
.5
Figure 2. Rate of vaporization of tetranonacontane (CorHloo) and Arrhenius plot of data, activation energy 45 kcnl/mol. Quartz bucket 10 x 4-mm i.d., 10-mg sample.
0.6
I\\ \
I
\
- \\\
1
I
J
0
0.5
1.0
C
Figure 3. Rate of vaporization of n-hexatricontane from polyethylene (DYJT). C = 1.0 corresponds to 1 mg of n-hexatricontane vaporized from 9 mg of polyethylene.
instead of 10 mg as in Figures 1 and 2. However, the activation energy of this process shown in Figure 2 is 27 kcal/mol and the diagonal character of the curved is what one expects for a vaporization rate proportional to the concentration of the volatile component in the polymer. The failure of the curves to intercept the abscissa at C = 1.0 is due to the difficulty of weighing 1 mg precisely. Finally, in Figure 4 we show various (6) L.A. Wall and 8. Straw, J . Polym. Sci., 44, 313 (1960). The Journal of Physical Chemistry, Vol. 76, N o . 17,IS70
L. A. WALL,J. H. FLYNN, AND S. STRAUS
3240
the preceding relationship the Arrhenius slope is found to be d l n (dnldt) - _T _ -AE, d(l/T) 2 R
(4)
From our rate measurements then we can obtain according to kinetic theory the internal energy, AE,, for vaporization and also the enthalpy AHv. If the apparent Arrhenius activation energy is designated as E", then Figure 4. Thermogravimetric study of paraffins; 1.5o/min temperature rise.
and
programmed temperature studies of the volatilization of three of the pure hydrocarbons, a mixture of two of them, and some closely related common substances, paraffin wax and beeswax. The results are striking in their apparent sensitivity to the purity of the sample. The pure substances give comparatively vertical curves, while the impure substances tend to produce curves spread over a large temperature range. The mixture has a flat plateau when the volatilization of the lighter component ceases and before the temperature needed for the heavier component is attained.
Discussion According to kinetic theory, the rate of condensation, dnldt, of a vapor in moles per sec is given by7 dn _ dt
apA (2 nMR T) "'
where a is the accomodation coefficient, assumed here to be 1, p the pressure, dyn/cm2, of the substance in the gas phase; A the surface area, cmZ; M the molecular weight; R the gas constant in ergs/deg K, and T the absolute temperature. Since, when a vapor and liquid phase are in equilibrium, the rate of vaporization equals the rate of condensation, we can write the same equation for the rate of vaporization except that now p is the equilibrium vapor pressure at the temperature T. The rate of vaporization we are concerned with is that measured under vacuum conditions and is sometimes referred to as the maximum rate of vaporization. Since the vapor pressure, in atmospheres, is the equilibrium constant for the process, we may write pv =
,-AFv/RT
= eASv/Re-AE~/RT -PAV/RT
e
(2)
For one mole of vapor, PAV = R T , and hence the rate of volatilization, can be written as
where dw/dt is the rate of vaporization in g/sec assuming that a the accommodation coefficient is 1. From The Journal of Physkal ChemistTy, Vol. 74, No. 17, 1970
AH,
= E"
+ 3RT -2-
since E" =
-R d In (dnldt) d(l/T)
Using these relations and our observed apparent activation energies, values were calculated for the enthalpies of vaporization A H y at the mean temperature of our experiments. For n-pristane, n-tetracosane, n-hexatricontane, and n-tetranonacontane the values were 18, 23, 29, and 47, respectively, and did notJ appear to be in line with literature values at first sight. In order to compare our experimental data with those in the literature and evaluate our experimental technique, we reviewed and recalculated values of AHv from data8-16 in the published literature. The most extensive source of original data was the compilation made by Stull.8* Direct calorimetric or Knudsen technique measurements were available for only a limited number of alkanes, C?to CI8, and only at a single temperature. The bulk of the AHv values obtained were from vapor pressure vs. temperature data either in its original form or in the form of the Antoine equation. Examples of the latter are found in ref 8. Greatest weight was given to AHv values determined from original vapor pressure data through the slopes of (7) I. Langmuir, Phys. Rev., 2 , 329 (1913). D.R. Stull, Ind. Eng. Chem., 39, 517 (1947); (b) F.D.Rossini, et al., API Research Project 41 (1952). (9) W.M. Masee, Red. Trav. Chim. Pays-Bas, 6 7 , 197 (1949). (10) E.Morawetz and S. Sunner, Acta Chem. Scand., 17, 473 (1963). (11) C. B. Willingham, W. J. Taylor, J. M. Piznocco, and F. D. Rossini, J . Res. Nat. Bur. Stand., 35, 219 (1945). (12) R. W.Shiessler and F. C. Whitmore, Ind. Eng. Chem., 47, 1660 (1955). (13) A. F. Forziatti, W. R. Norris, and F. D. Rossini, J . Res. Nat. Bur. Stand., 43, 556 (1949). (14) H.T. Coach, W. Kosicki, and B. H. Sage, J. Chem. Eng. Data, 8, 347 (1963). (15) R. S. Bradley and A. D. Shellard, Proc. Roy. Soc., Ser. A , 198, 239 (1949). (16) H. S. Myers and M. R. Fenski, Ind. Eng. Chem., 47, 1652 (1955). (8). (a)
RATESOF MOLECULAR VAPORIZATION OF LINEAR ALKANES
3241 5
IIO
30 -
25
-
20
-
15
-
IO
-
AHV
-0 ~~
5
15
IO
20
30
20
Figure 5 . Heats of vaporization of linear alkanes as a function of the number of carbon atoms. T: 0, 0 ; El, 50; A, 100; A, 150; V, 200.
log p us. l / T plots at selected temperatures, viz., 0, 50, 100, 150, 200, and 250” using the Clapeyron equation corrected for the compressibility factor AZ. The relationship is d 1% P A H , = 2.303RAZd 1/T
:L
0
1
I
1
I
2
4
6
8
I
IO
’ 4
at 25”. Since no values of P vs. T data above 1 atm pressure were used in deriving AH, values, A 2 was always >0.95, The error associated with this method should be no greater than 1.5% at 1 atm. The calculated AH, values were first plotted as a linear function of the number of carbon atoms, n, in the alkanes. Over a range of species with 4 to 24 carbon atoms the plots for several different temperatures did not yield straight lines; see Figure 5. The data appear to be best fitted by straight lines for every eight or so consecutive species as shown. With the coordinates used in Figure 5, no smooth curves over the entire range would be completely satisfactory. The breaks in linearity seem to occur at about every 7-8 carbon atoms. This suggested a coiling or folding of the vaporizing molecules as was predicted by Langmuir.’* Also, HugginsIg in 1939 predicted that the heats of vaporization of linear alkanes should vary as the z / 3 power of the number of carbon atoms. Therefore, we plotted the data as a function of n2/’; see Figure 6. It is evident from Figure 6 that at a given temperature the variation in heats of vaporization for the linear alkanes is very closely approximated by linear function of the power of the
4- 2.92
(8)
in kcal/mol, where T is in degrees Kelvin. A modification of eq 8 giving A H , in kJ/mol is AH, = 1 3 . 4 3 ~ ~-” ~0.08075T
(7)
I
I2
number of carbon atoms. The straight lines shown in Figure 6 are given by the relationship A H , = 3.21n’’’ - 0.0193T
Estimates of A 2 as a function of T/Tb are tabulated1’ in the literature. This tabulation is apparently based on the relationship = 1.0 - 0 . 0 5 ~ ( a t m )
40 I’
5-
n
E RT
n
+ 12.22
@a)
The n”’ function is highly acceptable on the physical basis that a linear molecule will find it energetically easier to vaporize when coiled into a sphere than as a long extended molecule. The spherical model entails the rupturing of a minimum amount of van der Waals bonding during the vaporization process. According to this model and the above equation the increment in AH, per carbon atom or methylene group decreases with the size of the molecule. By differentiating eq 8 with respect to n, it follows that the increment in A H , per carbon atom is found. A(AH,) = 2.14n-”a
Thus, the increment at lo3carbon atoms is 214 cal/mol. I n Table IV we summarize our experimental data and show the numerical agreement between the experimental activation energies and values calculated from the equation in kcal/mol E,
=
3.21n”’
=
0.0223T
+ 2.92
(8b)
Both the experimental and calculated values are com(17) S. H. Fishtine, Ind. Eng. Chem., 5 5 , 51 (1963). (18) I. Langmuir, “Third Colloid Symposium Monograph,” The Chemical Catalog Co., Kew York, N. Y., 1925, pp 53-64. (19) M. L. Huggins, J . Phys. Chem., 43, 1083 (1939).
T h e Journal of Physical Chemistry, VoE. 74, N o . 17, 1970
L. A. WALL,J. H. FLYNN,AND S. STRAUS
3242 Table IV : Activation Energies for the Molecular Vaporization of n-Alkanes
Alkane
%-Pristane n-Tetracosane n-Hexatricontane n-Tetranonacontane
n
19 24 36 94
M
268 338 506 1318
Rate, g/cm2 -cy, kcal/moh ?, a m X 106 Exptl Eq 8b OC
6.0 6.8 7.5 12.0
18 21 29 46
18.9 21.9 28.6 55.6
35 75 145 345
pared at the mean experimental temperature, T, see last column. The agreement is very good particularly for the three smaller compounds and supports our premise that correct values of the energies of vaporization can be obtained quickly with the presently available equipment. The low result for the largest species, the Cg4,is still quite good considering the degree of extrapolation involved. At such a high n value one suspects that eq 8 will give high values since one anticipates spheres of greater density, the greater the value of n. Experimental rates of vaporization at the temperature given in last column are also listed. The rate of decompositionZoof polyethylene is usually measured in the region of 400" and is proportional to the weight of polymer, not to surface area. The products of thermal volatilization of linear polyethylene
The Journal of Phyaical Chemistry, Vol. 74, N o . 17,1970
assuming a random mechanism indicate6 that 72-carbon atom species are about the minimum size that decompose before evaporating. From eq 8 it follows that the internal energy AEV for vaporization a t 400" is for n = 72, 43.5 kcal, for n = 129, 70 kcal, and for n = 154, 80 kcal. The value 43.5 kcal is near to the activation energy values of the possible free radical reactions constituting the overall thermal decomposition mechanism. The actual overall activation energy for thermal decomposition is about 70 kcal and the usual carbon-carbon bond dissociation energy is 80 kcal. These results show that molecular vaporization of linear alkanes comprised of 100 or so carbon atoms can occur without decomposition. For several experiments with the Cg4compound a gravimetric apparatus with an attached mass spectrometer capable of monitoring masses from 12 to 120 was used and no hydrocarbons from the Cgrsample were observed. This supports, as does the observed kinetic behavior, the conclusion that the Cg4volatilized molecularly without appreciable thermal decomposition. Acknowledgment. The n-tetran~nacontane~ sample used in this work was a greatly appreciated gift to the National Bureau of Standards from the American Viscose Corp. (20) L. A. Wall, S. L. Madorsky, D. W. Brown, S. Straus, and R. Simha, J. Amer. Chem. Sac., 76, 3430 (1954).
