J . Phys. Chem. 1986, 90, 6732-6736
Kinetics of a Pressure- Induced Polymerization Reaction of Cyanogen Choong-Shik Yo0 and Malcolm Nicol* Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024 (Received: May 8, 1986)
The kinetics of the conversion of poly-(2,3-diiminosuccinonitrile), a polymeric high pressure form of cyanogen, to paracyanogen have been determined by monitoring Fourier-transform infrared spectra at pressures between 10 and 12 GPa and temperatures between 290 and 350 K. The reaction kinetics can be described by an Avrami equation with exponent, 0.5, and specific rate constant, 0.040 h-II2, at 10 GPa and 297 K. The activation enthalpy and volume are 28 kJ/mol and -3.3 cm3/mol, respectively. A two-step mechanism is suggested that involves diffusive rearrangement of the pDISN chains into a configuration in which 4 + 2 cycloadditions occur between adjacent p-DISN chains.
Introduction Many physical and chemical properties of materials are greatly altered under high pressures as the materials adopt dense, low free energy structures. Most substances undergo polymorphic transformations to more densely packed structures with shorter and/or more intermolecular contacts.' Molecular systems with unsaturated bonds also can achieve denser, more stable structures by polymerizing, that is, by exchanging, in each successive addition of a monomer, a very strong, unsaturated bond and a long, weak intermolecular contact with two strong, short, more saturated bond^.^,^ Whether or not polymerization proceeds to saturated products is influenced by material transport, tophemistry, steric hinderance, and other chemical considerations. Both types of structural accommodations to high pressures occur in the cyanogen system. At low pressures, solid cyanogen undergoes two structural phase transitions; above 3.5 GPa, cyanogen reacts both reversibly and irreversibly." Between 3.5 and 10 GPa, C2N2converts to a linear chain species, identified as poly(2,3diiminosuccinonitrile) or p-DISN. Evidence for this conversion 10 GPa, p-DISN is activated to is described e l ~ e w h e r e .Near ~ convert to a cross-linked paracyanogen that can be recovered at room pressure. Paracyanogen synthesized by this route has a highly metallic luster, is black, and is very thermally and chemically stable. The issues of concern in this study are the kinetics and mechanism of this irreversible transformation. Few kinetic studies of chemical reactions at very high pressures have been and most of these studies have involved polymerizations or explosions. There are several reasons for this situation. Reactions at very high pressures usually occur in the solid state and follow complex mechanisms that yield several products. Even at temperatures and pressures that can be obtained with relative ease, many reactions are too rapid or too complicated to follow by available techniques for monitoring minute samples. Thus, this study of the chemistry of highly compressed cyanogen is the first examination of the kinetics of an organic polymerization above 10 GPa. The polymerization kinetics were followed by monitoring changes of the Fourier-transform infrared (FTIR) spectrum of the sample. These kinetic data were analyzed with Avrami's model for nucleation and/or growth:*-1° x = 1 - exp[-bt"]
(1) where x is the fractional conversion at time, t , after initiation of (1) Bridgman, P. W.; Conant J. B. Proc. Natl. Acad. U.S.A. 1929, 15,680. (2) Weale, K. E. Chemical Reactions at High Pressures; E. & F. N. Spon: London, 1967; p 239. (3) Nicol, M. F.; Yen, G. Z . J . Phys. 1984, 45, C8-163. (4) Yoo, C.-S.; Nicol, M. F. J . Phys. Chem. this issue. ( 5 ) Asano, T.; Lenoble, W. J. Chem. Rev. 1978, 78, 407. (6) LeNoble, W. J. Prog. Phys. Org. Chem. 1967, 5, 207. (7) Nicol, M. F.; Wiget, J. M.; Wu, C. K. J . Polym. Sci. 1980, 18, 1087. (8) Avrami, M. J. Chem. Phys. 1939, 7 , 1103. (9) Avrami, M. J . Chem. Phys. 1940, 8, 212. (10) Avrami, M. J . Chem. Phys. 1941, 9, 177.
the reaction and b and n are parameters related to the specific rate and topochemistry of the reaction. The activation enthalpy, AH*, and activation volume, AV, of the reaction were determined from the dependence of the rate constant, b, on temperature and pressure, respectively. Together with n, these parameters are used to infer possible reaction mechanisms.
Experimental Section These experiments were performed with a diamond-anvil cell of Bassett's design" with type-IIa diamonds with 0.8-mm culets. Cyanogen (Matheson, 98.5% purity) was loaded into 0.25" holes in Inconel gaskets by the indium-dam techniqueI2J3 at temperatures between 248 and 252 K,which were attained by immersing the cell in a dry ice-ethanol solution. Details of the loading procedure are given e l ~ e w h e r e . ~ Before each kinetic run, the pressure on the sample was raised to about 9.0 GPa and held while the pressure was measured by the ruby luminescence technique14 and the infrared spectrum of the starting material was recorded. In a few runs, samples were held near 9.0 GPa for 2-3 days. During this extended preparation, the starting material did not appear to alter, and the subsequent kinetics were not changed. Each reaction was initiated by jumping the pressure to the desired value, which was quickly measured. The cell was then positioned in the FTIR spectrometer, and the reaction was essentially continuously followed for 20 h to as many as 150 h. At the end of the kinetic run, the pressure was redetermined. During a typical run, the pressure dropped by 0.2-0.5 GPa, which is comparable to the instrumental resolution for pressure measurements. Polymerization is expected to increase the density of the sample and, at constant applied load, would be expected to reduce the pressure by this amount, although relaxation of the stressed gasket and other components of the cell also contribute to the pressure change. The average of the pressures before and after the kinetic run was taken as the reaction pressure. Finally, the pressure was increased to 12 GPa, and an infrared spectrum of completely reacted material was recorded. For runs above room temperature, the sample was heated by an external electrical heater that was turned on at a fixed, preset current as soon as the cell was mounted in the FTIR spectrometer. The temperature of the sample was measured with a copperconstantan thermocouple that was welded to the small indium dam, 6-mm in diameter and 2-mm thick, in order to minimize differences between the measured temperatures and that of the sample. Experiments with different samples showed that, under these conditions: (a) stable temperatures were attaned within 20 min (1 1) Bassett, W. A,; Ming, L. C. In The Physics and Chemistry of Minerals and Rocks; Strens, R. G., Ed.; Wiley: New York, 1973; p 366. (12) Liebenberg, D. H. Phys. Lett. 1979, 73A, 74. (13) Mills, R. L.; Liebenberg, D. H.; Bronson, D. H.; Schmidt, L. C. Rev. Sci. Instrum. 1980, 51, 74. (14) Barnett, J. D.; Block, S.; Piermarini, G. J. Reo. Sci. Instrum. 1973, 44, 441.
0022-3654/86/2090-6732$01.50/00 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 25, 1986 6733
u z a
WAVE NUMB E R
Figure 2. Measured FTIR spectra (lowest trace) at 9 GPa before kinetic run and (top trace) during kinetic run and (middle trace) difference
spectrum used to compute fractional conversion.
P,and temperatures, T , were determined from A,(P,T), the in0.0 )OO
WAVENUMBE R Figure 1. FTIR spectra of paracyanogen at 297 K and several times. Each spectrum was scanned for 2.7 h with 15-s time delay between spectra.
after the heater was turned on; (b) the temperatures and heating currents were reproducibly related; (c) the temperature difference between the indium dam and the back side of one of the diamonds did not exceed 2 K; and (d) the temperature did not fluctuate more than 0.5 K during the time required to obtain an infrared spectrum. Thus, only part of the first 2.7-h scan of the infrared spectrum was at temperatures below the reported reaction temperature. Infrared spectra were determined with Matteson Cygnus 2 spectrometer. The diamond cell and heater were mounted on a fixed stage whose position was precalibrated to give the maximum interferogram voltage. Spectra usually were acquired during 2.7 h by accumulating lo4 scans at 8-cm-' resolution and pausing for 15 s between spectra. The reaction time was taken when the spectrum was completed. The overall reaction period greatly exceeded the acquisition time for a spectrum. Thus, differences between the real and measured reaction times were negligible except for the first few spectra, for which the measured degrees of conversion systematically were slightly low. Poor signal-to-noise ratios and long scanning periods also limited the precision of the experimental data.
Results and Discussion The vibrational spectra of cyanogen and its pressure-induced reaction products at various pressures are discussed e l ~ e w h e r e . ~ Typical spectra reflecting growth of the polymer at 10.7 GPa and 297 K are shown in Figure 1. The spectra were scanned from 400 to 6000 cm-'; however, the major changes were between 900 and 1900 cm-', the region of the -C=N- stretching mode. At pressures greater than 11.7 GPa, the reaction was too rapid to follow by these techniques. Runs a t temperatures above 334 K were limited by pronounced and unpredictable drops of pressure. Spectra measured during the kinetic runs were corrected for background absorption and absorption by the starting material by subtracting the spectrum measured at 9 GPa before the kinetic run, see Figure 2. Fractional conversions, x, at times, t, pressures,
tegrated intensities of the corrected spectra between 900 and 1900 cm-', as follows: x ( t ) = A,(P,T)/As.(P,T)
As a practical matter, A24(12,T), the integrated intensity of the spectrum measured at 12 GPa after the reaction had run for 24 h was substituted for A,(P,T) instead of waiting for each reaction to go to completion at presurre P. Both visible observations and mass spectral analyses of recovered samples indicated that conversion was 100% complete at 12 GPa within much less than 24 h. Indeed, at 12.0 GPa and room temperature, the integrated absorption intensity saturated without further changes in less than 3 h. This substitution introduces small systematic errors in the computed degrees of conversion and rate constants but should not affect the qualitative features of the kinetics. Figure 3 shows the experimental conversion curves for several pressures (a) and temperatures (b and c). Not surprisingly, increasing the pressure and/or the temperature accelerates the reaction and increases the overall product yield. The data are moderately scattered; however, much of the scatter can be explained by four factors. (1) The data were corrected for absorption by starting material as discussed above. (2) Uncertainties in A,(P,T) were caused by substituting A24(12,T); these are greater for slower than for faster conversions. (3) Many of the slower runs were interrupted from time-to-time by detector and source fluctuations that generated offsets in the data for these experiments. (4)Compression or distortion of the gasket and cell during an experiment can change the optical path lengths through the sample. The parameters of Avrami's equation, b and n, may readily be determined by least-squares fitting of the data to the linear equation obtained by taking the double logarithm ofg eq 1: In [-ln (1 - x)] = In b
+ n In t
Plots of the fits obtained for several pressures (a) and temperatures (b and c) in Figure 4 show that the slopes of the linear fits are independent of pressure and temperature to within 20%. Thus, the kinetics can be described by an Avrami model with a constant exponent. The values of b and n determined for individual expeiments are given in Table I. The values of b increase with the temperature and pressure, while the experimental n's and the shapes of the conversion curves suggest that 1 / 2 is the most appropriate integral or half-integral value of the Avrami exponent.
The Journal of Physical Chemistry, Vol. 90, No. 25, 1986
Yo0 and Nicol
0 0 0.4
LN ( T I ME)
T I M E (HRS)
i 1 h h
" z i I "
T I M E (HRS)
0. 6 W
> z 0
x 0.2 0.0
T I M E (HRS)
Figure 3. Kinetic data for the polymerization reaction at various pressures and temperatures: (a, top) = at 297 K and different pressures (11.7, 11.4, 11.1, 10.7, and 10.0 GPa from top down); (b, middle) and (c, bottom) at 10.0 and 10.7 GPa, respectively, and different temperatures (338, 328, 317, 307, and 297 K from the top down).
Figure 4. Linearized Avrami plots at various pressures and temperatures: (a, top) at 297 K and different pressures (1 1.7, 11.4, 11.1, 10.7, and 10.0 GPa from top down); (b, middle) and (c, bottom) at 10.0 and 10.7 GPa, respectively, and different temperatures (338, 328, 317, 307, and 297 K from top down).
TABLE I: Avrami Exponents n and Rate Constants b Determined by the Least-Sqaures Linear Fits at Various Temperatures and Pressures pressure. GPa temp,K 10.0 10.7 11.1 11.4 11.7 Avrami Exponents, n
TABLE 11: Avrami Rate Constants for an Exponent of pressure, GPa temp, K 10.0 10.7 11.1 11.4
297 307 317 328 338
0.440 0.497 0.489 0.589 0.575
297 307 317 328 338
0.057 0.078 0.099 0.111 0.146
0.513 0.514 0.495 0.561 0.603
Avrami Rate Constant, b 0.063 0.094 0.117 0.154 0.197
The overall agreement among the experimental results and the fits is reasonably good, despite some large differences for a few samples and at short times. In addition to the sources of scatter discussed above, there are three significant sources for these differences: (1) The relative difference between the measured
297 307 317 328 338
0.040 0.075 0.088 0.147 0.184
0.065 0.094 0.113 0.191 0.242
and true reaction time is larger for the earlier spectra, and the corresponding measured degrees of conversion are low. (2) The average pressure is slightly lower than the initial reaction pressure, and this increases the conversion rates near the beginning of a run. (3) The temperature during the first scan is lower than the recorded temperature; this causes lower conversion rates. These effects are limited to the first, and sometimes second, spectra and should not affect the overall results. By constraining n to be 1/2, another linear form of Avrami's equation can be used to examine the pressure and temperature dependences of b: -In (1 - x ) = -bt1I2
The Journal of Physical Chemistry, Vol. 90, No. 25, 1986 6735
1 . 5 k
1 -0.50 -0.25
SQRT ( T I ME (HRS)
Figure 6. Plot of In k vs. 1/T at 10.0 (upper) and 10.7 GPa (lower).
i -0. -0. 0.
SQRT ( T I M E (HRS)) 95
-0.50 -0. 25 0. 00 0
SQRT ( T I M E (HRS))
Figure 5. Linearized Avrami plots with n restricted to
Figure 7. Plot of In k vs. P at 297 K.
for the various
pressures and temperatures: (a, top) at 297 K and different pressures (11.7, 11.4, 11.1, 10.7, and 10.0 GPa from top down); (b, middle) and (c, bottom) at 10.0 and 10.7 GPa, respectively, and different temperatures (338 328, 317, 307, and 297 K from top down).
Plots of the data in this linear form are shown in Figure 5 for several pressures (a) and temperatures ( b and c), and the rate constants obtained from least-squares fits to this one-parameter equation are given in Table 11. These fits are reasonable, although not so good as with the two-parameter equation. The activation energy and volume for the reaction calculated from these data
are 28 kJ/mol and -3.3 cm3/mol, respectively. Figures 6 and 7 show that the relevant semilogarithmic plots of these rate constants vs. 1 / T at 10.0 and 10.7 GPa and vs. P a t 297 K are reasonable. The stoichiometry of the overall reaction and the values of n, LW, and AV provide clues about the steps that must be included in the mechanism and which of these steps may be rate determining. The signs of AfP and AV are expected for condensation reactions; however, the magnitude of AV is smaller by a factor of 3 from what might be expected for a cycloaddition on the basis of studies at pressures of the order of 1 GPa. Solid-state reactions can be represented as combinations of two fundamentally different types of elementary steps:15(a) transport of reactants to the reactive sites, and (b) breaking and/or forming of chemical bonds. In this context, the production of paracyanogen can be represented by the somewhat idealized twwtep mechanism shown in eq 5 . p-DISN prepared from solid cyanogen probably is not favorably positioned for growth of paracyanogen. Thus, the first step in this mechanism involves diffusion (in the general context that includes activated reorientation or similar “random(15) Roghavan, V.; Cohtn, M. In Treatise in Solid Stare Chemistry, Hannay, B., Ed.; Prentice-Hall: New York, 1975; Vol. V, p 67.
J . Phys. Chem. 1986, 90, 6736-6740
of activation for cycloadditions are -10 ~ m ~ / m o l . ~ * ~ ~ ~ Another interesting observation can be made by extrapolating these data to lower pressures and temperatures. Figure 8 is a plot of the measured fractional conversion to paracyanogen after 50 h at several pressures and temperatures. On this time scale, polymerization is efficient above 10.7 GPa at 283 K, 10.0 GPa at 287 K, and 9.6 GPa at 293 K. This trend indicates that the pressure at which rapid polymerization begins decreases by about 1 GPa for every 30 K increase in temperature. Extrapolation of this trend to atmospheric pressure suggests that the pyrolytic synthesis of paracyanogen that is reported to occur above 620 K at low pressures follows the same mechanism.
30 W 2
a s t -
Summary The kinetics of formation paracyanogen from p-DISN have been measured between 290 and 350 K at 10 to 12 GPa by monitoring the growth of the -C=N- absorption bands between 900 and 1900 cm-]. The experimental data can be explained by Avrami rate law with an exponent of 0.5 and rate constant of 0.057 h-1’2at 297 K and 10.0 GPa. The activation volume and enthalpy are -3.30 cm3/mol and 28 kJ/mol, respectively. A two-step mechanism is suggested that involves diffusion of the p-DISN chains into an arrangement in which 4 + 2 cycloadditions occur between adjacent p-DISN chains.
C% C ~ ? I E ? S I ; F /
Figure 8. Plot of fractional conversion x after 50 h as a function of pressure and temperature: for pressure at 297 K (solid line) and for temperature at 10.7 (---) and 10.0GPa (---)
walk” steps) which brings the p-DISN chains into configurations where the second step cycloadditions between adjacent p-DISN chains can procede. Model calculations16 indicate that, when the value of n is the mechanism involves a diffusion-controlled one-dimensional growth process; and empirical evidence suggests that the values of n for reactions controlled by diffusion are between 0.53 and 0.58.17 These observations are not inconsistent with the first step in eq 5. The volume of activation for diffusion, however, should be positive; thus, a subsequent step with a large negative volume of activation must be rate-limiting. The cycloaddition in the second step of this mechanisms satisfies this requirement; typical volumes
Acknowledgment. Support provided for this work by grants from the U S . National Science Foundation (DMR83-18812) and Los Alamos Branch of the University of California Institute of Geophysics and Planetary Physics (No. 028) are gratefully appreciated. Registry No. Paracyanogen, 2521 5-76-3; poly(2,3-diiminosuccinonitrile) (SRU), 104619-15-0.
(16) Hulbert, S . F. J . Br. Ceram. Sac. 1969, 6, 11. (17) Brown. W. E.: Dollimore. D.: Galwev. A. K. In ComDrehensioe Chemical Kinetics, Bamford, C . H.; Tipper, Cy F. H., Eds.; Elsivier: New York, 1980; Vol. 22, p 71.
(18) Jenner, G. Angew Chem., Inr. Edit. Engl. 1975, 14, 137. (19) Van der Meer, R.; German, A. L.; Heikens, D. J . Polym. Sci. 1977, 15, 1765.
On the Glass Transition and Viscosity of P,05 S. W. Martint and C. A. Angell* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: May 19, 1986)
The calorimetric glass transition temperature Tgfor pure anhydrous P2Os melted in sealed Si02ampules at 1000 “C has been obtained directly for the first time with differential scanning calorimetry, and the increase in heat capacity at Tg has been determined. Tgmeasured in this way is 57 K higher than the value quoted in the literature, which is probably based on an Arrhenius law extrapolation of viscosity data to 9 = lOI3 P. Combining the high-temperature viscosity data with the common observation that, for oxide glasses, 7 = 10l2P at the DSC Tg,we find that the P,O, viscosity obeys an Arrhenius law over at least 6 decades of 7. Furthermore, the intercept at 1 / T = 0 coincides with the common point of T,-reduced viscosity plots for a wide variety of liquids recently used in establishing the “strong” vs. “fragile” classification of glass-forming liquids. On this basis, P2Os behaves as the archetypal “strong” liquid. However, the value of C,,(liquid)/C,(glass) at T,, 1.27, is larger than expected on this basis since other “strong” liquids show smaller values, e.g., GeO, (1.09) and BeF2 (no AC, detected). The dependence of Tgon heating rate has been determined and shows that enthalpy relaxation in the transition region has, within error, the same activation energy (43.9 kcal/mol) as for viscous flow.
Introduction In the course of studying the glass-forming characteristics of the binary system Li20-P20,1 we became aware that no welldefined measurement of the glass transition temperature of P 2 0 5 has ever been recorded in the literature, although it is one of the three primary “glass formers.” The value that is quoted,2 T8 = 262 “C, is apparently based on the Arrhenius law extrapolation
Sohio Research Fellow, January 1984-January 1985. Present Address: Department of Materials Science & Engineering, Iowa State University, Ames, Iowa 5001 1 .
of viscosity data reported by Cormia et aL3 in the temperature range 545-645 OC. A comparable value has been reported by Ray,2bbut no details of the determination were given. Over the limited temperature range of their study Cormia et aL3 found the viscosity obeyed the Arrhenius law with the pa(1) (a) Martin, s. w.; Angell, C . A. J . Nan-Cryst. Solids 1986, 83, 185. (b) Martin, S . W.; Angell, C. A,, to be published. (2) (a) Sakka, S . ; McKenzie, J. D. J . Non-Cryst. Solids 1971, 6, 145. (b) Ray, N. H. J. Non-Cryst. Solids 1974, 15, 423. (3) Cormia, R. L.; Mackenzie, J. D.; Turnbull, D. J. J . Appl. Phys. 1963, 34(4), 2245.
0 1986 American Chemical Society