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Thermodynamics of polymerization of heterocyclic compounds I—The heat capacity, entropy and enthalpy of trioxan
Thermodynamics of Polymerization of Heterocyclic Compounds I The Heat Capacity, Entropy and Enthalpy of Trioxan G. A. CLEGG, T. P. MELIA and A. TYSON A n adiabatic, vacuum calorimeter has been used to measure the heat capacity of trioxan from 8 0 ° K to 310°K. A n approximate extrapolation procedure has been used to estimate heat capacities below 80°K. Entropy and enthalpy values have been derived and are listed at ten degree intervals. Published vapour pressure data have been used to calculate the entropy o/trioxan gas at one atmosphere pressure and 298"16°K. The value obtained 68"09+0.82 cal deg -1 mole -1 compares with that of 68.99+0'01 cal deg -1 mole -1 obtained by statistical methods. The entropy of polymerization of trioxan to crystalline polyoxymethylene, AS°oc", has been calculated as --37"2 cal deg -I mole -1.
As PART Of a general study of the thermodynamics of polymerization of heterocyclic compounds the heat capacities of various monomers and polymers have been measured over the temperature range 80 ° to 310°K. Heat capacities below 80°K can be evaluated using the Kelley, Parks and Huffman extrapolation procedure: and this enables an estimate to be made of the Third Law entropy. The material .studied in this work, trioxan, is a cyclic trimer of formaldehyde which readily undergoes cationic polymerization in solid 2 and liquid ~'4 phases and in solution 3-7 or suspension 3'4'6 to yield high molecular weight polyoxymethylenes. The thermodynamic functions of trioxan gas at one atmosphere pressure over the temperature range 0 ° to 1 000°K have recelatly been calculated by Melia, Bailey and Tyson 8 using the methods of statistical thermodynamics. Vapour pressure data for the sublimation of trioxan are also available 9'1° so the results presented enable a comparison to be made between the statistical and Third Law entropies of trioxan. EXPERIMENTAL Calorimeter The calorimeter used for the heat capacity measurements is of the adiabatic, vacuum type closely resembling that of Scott et al. 11. Temperature measurements were made with a platinum resistance thermometer (R0=25 ohms) calibrated by the National Physical Laboratory. The thermometer was housed in a re-entrant well in the base of the calorimeter. The calorimeter was close wound with 'Eureka' resistance wire which serves as the heater. Temperature rise and heat input were measured on a thermoelectric-free potentiometer of the Diesselhorst type, supplied by H. Tinsley and Co. Ltd. The top, bottom and sides of the adiabatic shield were manually maintained at the temperature of the calorimeter. The calorimeter was
75
G. A. CLEGG, T. P. MELIA and A. TYSON calibrated in the range 80 ° to 320°K using thermochemically pure benzoic acid supplied by British Drug Houses Limited.
Heat capacity measurements Because of its high vapour pressure trioxan was subjected to only 30 minutes degassing under vacuum prior to sealing in the calorimeter. A small quantity of helium gas, sufficient to give a pressure of 500 mm of mercury at room temperature, was sealed in the calorimeter and served to accelerate thermal equilibrium during the experiments. Heat capacity measurements were made over the temperature range 80 ° to 310°K, temperature increments being varied from 5 deg. to 13 deg. K. The magnitude of the temperature increment did not appear to affect the heat capacity value. Temperature equilibrium was reached about seven minutes after the end of a heating period over the whole temperature range. Material Laboratory Reagent grade trioxan supplied by British Drug Houses Limited was purified by sublimation from silver oxide using the method described by Jaacks and KernTM. RESULTS Observed values of the heat capacity, calculated from the relationship
C=(C,-Cc+E)/(M,-Mc)
(1)
where C, is the gross heat capacity of the calorimeter plus sample, Cc is the heat capacity of the empty calorimeter, M, and Mc are the weights, respectively, of the calorimeter full and empty, and E is a small correction term for the different weights of grease, Wood's metal and copper capillary tube used in the two sets of measurements, are shown in Table 1. Smoothed values of the heat capacity, together with derived values of entropy and enthalpy, are shown in Table 2. The heat capacity data below 90°K were obtained using the Kelley, Parks and Huffman1 procedure. Cyclohexane was chosen as the standard substance for this extrapolation. A cubic equation was fitted to the experimental data in the range 80 ° to 310°K by the method of least squares using a KDF9 English Electric computer. The equation obtained is C=0-2467+ 3-754 × 10-3T-6"192 × 10-~T~+ 1"602 × 10-ST3abs. J deg-~g-x
(2)
Although maximum deviation of the experimental values from the smoothed curve is one per cent (one point), the vast majority lie within +0-2 per cent of the smoothed curve values. Since trioxan sublimes readily at room temperature the heat capacity, C, should be converted to the quantity C•t.. thus making allowance for the fact that C includes some heat of sublimation. This correction can be carded out by means of the equation~s C , , = C - (T/M){d ( V - M~)/dT}(dP/dT) 76
(3)
HEAT CAPACITY, E N T R O P Y A N D E N T H A L P Y OF T R I O X A N
Table 1. Observed values of heat capacity for trioxan Temperature
(°K)
I I
C (abs..l deg -1 g-l)
(OK)
RUN 1
RUN 3
RUN 2 0"5298 0'5615 0"6017 0-6426 0"6802 0-7205 0"7870 0-8265 0"8559 0-8933
85"05 95"12 107-54 121"77 134"93 147-27 171"05 182"35 193"77 204-86
RUN 6 217-79 226"57 233"51 238"34 242"04 245"96 25"0.42 255"42 261-04 267-53 274"40
RUN 4 279"26 290-14 300"75 310-86
0'8909 0"9055 0"9232 0"9476 0"9663 0"9875 1"013 1"060 1"053 1"081 1"119 1"129
203"36 209-37 215-25 221-01 226"87 233-00 239"15 245"29 251"68 258"40 265"23 272-52
0-5355 0"5854 0-6276 0"6694 0"7094 0"7406 0-7798 0-8200
87"10 102-54 117"05 130"68 143"72 156"30 168"63 180"61
C (abs. J deg -1 g-l)
Temperature
1-165 1"211 1"258 1"300
0"9216 0"9877 0"9848 1-000 1"020 1"038 1"038 1"059 1~88 1 "122 1"140
RUN 5 281-53 292-25 303"00 313-37
1-168 1-218 1-252 1-308
where C.t. is the heat capacity of unit mass of trioxan in equilibrium with its own vapour, M is the mass of sample contained in the calorimeter, V is the total volume of the calorimeter, ~ is the specific volume of solid trioxan, T is the temperature in °K, and P is the vapour pressure. This correction has been applied to the smoothed values of the heat capacity shown in Table 2. The term d P / d T in equation (3) was evaluated from the relation-
ship log P (ram H g ) : 10-808 - 2 8 9 4 / T
(4)
which was obtained from the vapour pressure data of Auerbach and Barschall 1°. DISCUSSION
The results obtained in the present investigation together with previously publishedTM vapour pressure data for sofid trioxan can be used to calculate the entropy of trioxan gas at one atmosphere pressure and 298-16°K. The results of this calculation are presented in Table 3. The value obtained for 77
G. A. CLEGG, T. P. M E L I A and A. TYSON
Table 2. Smoothed values of heat capacity, entropy and enthalpy of trioxan Temperature (°K)
C~t (abs. I deg-lg "1)
0 10 20 30 40 50
0 0"014 0"092 0"207 0"303 0"372
0 0.007 0"036 0"095 0"168 0-244
0 0"04 0"51 2"01 4"58 7"97
60 70 80 90 100 110
0"428 0'472 0'511 0"5459 0"5767 0"6065
0"317 0"386 0-452 0"514 0"573 0'629
120 130 140 150 160 170
0"6362 0"6658 0"6955 0"7252 0"7551 0'7854
0'683 0"735 0"786 0-835 0"883 0"929
11"98 16"49 21 "40 26"68 32"29 38"20 44"42 50"93 57"73 64"84 72"24 79 '94
180 190 200 210 220 230
0"8160 0"8471 0"8783 0"9112 0-9444 0'9784
0"975 1"020 1"064 1"108 1"151 1'193
87 "94 96 "26 104"9 113"8 123"1 132"7
240 250 260 270 273"16
1 '013 1"050 1"087 1"125 1"138
1"236 1"278 1"320 1'361 1'373
142-7 153'0 163"6 174"7 178 "2
28O 290 298'16 300 310
1"165 1"205 1'237 1-246 1"289
1"404 1'445 1'477 1'487 1"528
186"2 198"0 208'0 210"3 223"0
Table 3.
S OT -- S O 0 (abs. J deg-lg -1)
I-1oT -- H 0° (abs. J g-l)
Entropy of trioxan gas at 1 atm pressure and 298.16°K calculated from heat capacity and vapour pressure data on the solid
Source of data
Entropy contribution (cal deg. K -I mole -1)
S o - - S O (Kelley, Parks and Huffman 90
11-06 + 0'55
0
extrapolation) 298.16
f
20'73 _+0"06
c~at./T
9o
ASagsq6 (sublimation) A S = R In 12"7/760
44.39 + 0"20 --8.09+0-01
Entropy of gas at 298'16°K
68"09 + 0"82 78
HEAT CAPACITY, ENTROPY AND ENTHALPY OF TRIOXAN the e n t r o p y of t r i o x a n gas, 68"09+0"82 c a l d e g -a m o l e -x, is in r e a s o n a b l e a g r e e m e n t with that of 68"99+0"01 cal deg -~ m o l e -z calculated b y M e l i a , Bailey a n d T y s o n 8 using the m e t h o d s of statistical t h e r m o d y n a m i c s . T h e e n t r o p y change, A ~ , , associated with the p o l y m e r i z a t i o n of one m o l e of t r i o x a n gas, at one a t m o s p h e r e pressure a n d 298.16°K, to crystalline p o l y o x y m e t h y l e n e can be o b t a i n e d b y s u b t r a c t i n g the e n t r o p y of the gaseous m o n o m e r f r o m that of the crystalline p o l y m e r x~ (31.8 c a l d e g -a m o l e -a) at the same t e m p e r a t u r e . T h e value o b t a i n e d is - 3 7 . 2 cal deg -1 m o l e -~. A similar value ( - 3 5 ' 9 cal deg -z m o l e -a) has been f o u n d for the p o l y m e r i z a t i o n of cyclohexane to polyethylene ~5'16.
G. A. Clegg and A. Tyson thank the University ol Sal[ord for the award o[ maintenance grants. We are also indebted to the Science Research Council/or a grant in aid of this investigation. Department o] Chemistry and Applied Chemistry, University o] Salford (Received April 1967) REFERENCES a KELLEY, K. K., PARKS,G. S. and HUFFMAN,H. M../. phys. Chem. 1929, 33, 1802 2 SACK,H. Belg. Pat. No. 612 792 (1962) 3 HUt~IN, D., SUMMIT,E. and BER~DXNELU, F. M. U.S. Pat. No. 2 989 507 (1961) Htro6IN, D., SUMMXT,E. and BERmUJINELLT,F. M. U.S. Pat. No. 2 989 506 (1961) 5 HtmGIN, D., SUMMIT,E. and BERARDINELLI,F. M. U.S. Pat. No. 2 989 508 (1961) 6 Htn~iN, D., SUMMIT,E. and BERm~OINELLI,F. M. U.S. Pat. No. 2 989 505 (1961) 7 SCrn~EIDER,A. K. U.S. Pat. No. 2 795 571 (1961) s MELIA,T. P., BAILEY,D. and TYSON, A. J. appl. Chem. 1967, 17, 15 0 FRANK, C. F., see WALKER, J. F. Formaldehyde, 3rd ed., p 193. Reinhold: New York, 1964 10AtmRBACH, F. and BnRSCRALL, H. Studien iiber Formaldehyde--Die Festen Polymeren des Formaldehydes, p 38. Springer: Berlin, 1907 n Scoa-r, R. B., MEYERS, C. H., RANDS, R. D., BPJCKWEDDE, F. D. and BEKKEDAHL, N. J. Res. Nat. Bur. Stand. 1945, 35, 39 1~J~CKS, V. and KEea~, W. Makromol. Chem. 1962, 52, 37 t3 HOGE, H. J. J. Res. Nat. Bur. Stand. 1946, 36, 111 1~DAIrCrON, F. S., EVANS, D. M., HOA~, F. E. and MEHA, T. P. Polymer, Lond. 1962, 3, 263 as DAIrCrON, F. S., EVANS, D. M., HOARE, F. E. and MEUA, T. P. Polymer, Lond. 1962, 3, 277 a6DAINTON, F. S., DEVLIN, T. R. E. and SMALL, P. A. Trans. Faraday Soc. 1955, 51, 1710
79
As PART Of a general study of the thermodynamics of polymerization of heterocyclic compounds the heat capacities of various monomers and polymers have been measured over the temperature range 80 ° to 310°K. Heat capacities below 80°K can be evaluated using the Kelley, Parks and Huffman extrapolation procedure: and this enables an estimate to be made of the Third Law entropy. The material .studied in this work, trioxan, is a cyclic trimer of formaldehyde which readily undergoes cationic polymerization in solid 2 and liquid ~'4 phases and in solution 3-7 or suspension 3'4'6 to yield high molecular weight polyoxymethylenes. The thermodynamic functions of trioxan gas at one atmosphere pressure over the temperature range 0 ° to 1 000°K have recelatly been calculated by Melia, Bailey and Tyson 8 using the methods of statistical thermodynamics. Vapour pressure data for the sublimation of trioxan are also available 9'1° so the results presented enable a comparison to be made between the statistical and Third Law entropies of trioxan. EXPERIMENTAL Calorimeter The calorimeter used for the heat capacity measurements is of the adiabatic, vacuum type closely resembling that of Scott et al. 11. Temperature measurements were made with a platinum resistance thermometer (R0=25 ohms) calibrated by the National Physical Laboratory. The thermometer was housed in a re-entrant well in the base of the calorimeter. The calorimeter was close wound with 'Eureka' resistance wire which serves as the heater. Temperature rise and heat input were measured on a thermoelectric-free potentiometer of the Diesselhorst type, supplied by H. Tinsley and Co. Ltd. The top, bottom and sides of the adiabatic shield were manually maintained at the temperature of the calorimeter. The calorimeter was
75
G. A. CLEGG, T. P. MELIA and A. TYSON calibrated in the range 80 ° to 320°K using thermochemically pure benzoic acid supplied by British Drug Houses Limited.
Heat capacity measurements Because of its high vapour pressure trioxan was subjected to only 30 minutes degassing under vacuum prior to sealing in the calorimeter. A small quantity of helium gas, sufficient to give a pressure of 500 mm of mercury at room temperature, was sealed in the calorimeter and served to accelerate thermal equilibrium during the experiments. Heat capacity measurements were made over the temperature range 80 ° to 310°K, temperature increments being varied from 5 deg. to 13 deg. K. The magnitude of the temperature increment did not appear to affect the heat capacity value. Temperature equilibrium was reached about seven minutes after the end of a heating period over the whole temperature range. Material Laboratory Reagent grade trioxan supplied by British Drug Houses Limited was purified by sublimation from silver oxide using the method described by Jaacks and KernTM. RESULTS Observed values of the heat capacity, calculated from the relationship
C=(C,-Cc+E)/(M,-Mc)
(1)
where C, is the gross heat capacity of the calorimeter plus sample, Cc is the heat capacity of the empty calorimeter, M, and Mc are the weights, respectively, of the calorimeter full and empty, and E is a small correction term for the different weights of grease, Wood's metal and copper capillary tube used in the two sets of measurements, are shown in Table 1. Smoothed values of the heat capacity, together with derived values of entropy and enthalpy, are shown in Table 2. The heat capacity data below 90°K were obtained using the Kelley, Parks and Huffman1 procedure. Cyclohexane was chosen as the standard substance for this extrapolation. A cubic equation was fitted to the experimental data in the range 80 ° to 310°K by the method of least squares using a KDF9 English Electric computer. The equation obtained is C=0-2467+ 3-754 × 10-3T-6"192 × 10-~T~+ 1"602 × 10-ST3abs. J deg-~g-x
(2)
Although maximum deviation of the experimental values from the smoothed curve is one per cent (one point), the vast majority lie within +0-2 per cent of the smoothed curve values. Since trioxan sublimes readily at room temperature the heat capacity, C, should be converted to the quantity C•t.. thus making allowance for the fact that C includes some heat of sublimation. This correction can be carded out by means of the equation~s C , , = C - (T/M){d ( V - M~)/dT}(dP/dT) 76
(3)
HEAT CAPACITY, E N T R O P Y A N D E N T H A L P Y OF T R I O X A N
Table 1. Observed values of heat capacity for trioxan Temperature
(°K)
I I
C (abs..l deg -1 g-l)
(OK)
RUN 1
RUN 3
RUN 2 0"5298 0'5615 0"6017 0-6426 0"6802 0-7205 0"7870 0-8265 0"8559 0-8933
85"05 95"12 107-54 121"77 134"93 147-27 171"05 182"35 193"77 204-86
RUN 6 217-79 226"57 233"51 238"34 242"04 245"96 25"0.42 255"42 261-04 267-53 274"40
RUN 4 279"26 290-14 300"75 310-86
0'8909 0"9055 0"9232 0"9476 0"9663 0"9875 1"013 1"060 1"053 1"081 1"119 1"129
203"36 209-37 215-25 221-01 226"87 233-00 239"15 245"29 251"68 258"40 265"23 272-52
0-5355 0"5854 0-6276 0"6694 0"7094 0"7406 0-7798 0-8200
87"10 102-54 117"05 130"68 143"72 156"30 168"63 180"61
C (abs. J deg -1 g-l)
Temperature
1-165 1"211 1"258 1"300
0"9216 0"9877 0"9848 1-000 1"020 1"038 1"038 1"059 1~88 1 "122 1"140
RUN 5 281-53 292-25 303"00 313-37
1-168 1-218 1-252 1-308
where C.t. is the heat capacity of unit mass of trioxan in equilibrium with its own vapour, M is the mass of sample contained in the calorimeter, V is the total volume of the calorimeter, ~ is the specific volume of solid trioxan, T is the temperature in °K, and P is the vapour pressure. This correction has been applied to the smoothed values of the heat capacity shown in Table 2. The term d P / d T in equation (3) was evaluated from the relation-
ship log P (ram H g ) : 10-808 - 2 8 9 4 / T
(4)
which was obtained from the vapour pressure data of Auerbach and Barschall 1°. DISCUSSION
The results obtained in the present investigation together with previously publishedTM vapour pressure data for sofid trioxan can be used to calculate the entropy of trioxan gas at one atmosphere pressure and 298-16°K. The results of this calculation are presented in Table 3. The value obtained for 77
G. A. CLEGG, T. P. M E L I A and A. TYSON
Table 2. Smoothed values of heat capacity, entropy and enthalpy of trioxan Temperature (°K)
C~t (abs. I deg-lg "1)
0 10 20 30 40 50
0 0"014 0"092 0"207 0"303 0"372
0 0.007 0"036 0"095 0"168 0-244
0 0"04 0"51 2"01 4"58 7"97
60 70 80 90 100 110
0"428 0'472 0'511 0"5459 0"5767 0"6065
0"317 0"386 0-452 0"514 0"573 0'629
120 130 140 150 160 170
0"6362 0"6658 0"6955 0"7252 0"7551 0'7854
0'683 0"735 0"786 0-835 0"883 0"929
11"98 16"49 21 "40 26"68 32"29 38"20 44"42 50"93 57"73 64"84 72"24 79 '94
180 190 200 210 220 230
0"8160 0"8471 0"8783 0"9112 0-9444 0'9784
0"975 1"020 1"064 1"108 1"151 1'193
87 "94 96 "26 104"9 113"8 123"1 132"7
240 250 260 270 273"16
1 '013 1"050 1"087 1"125 1"138
1"236 1"278 1"320 1'361 1'373
142-7 153'0 163"6 174"7 178 "2
28O 290 298'16 300 310
1"165 1"205 1'237 1-246 1"289
1"404 1'445 1'477 1'487 1"528
186"2 198"0 208'0 210"3 223"0
Table 3.
S OT -- S O 0 (abs. J deg-lg -1)
I-1oT -- H 0° (abs. J g-l)
Entropy of trioxan gas at 1 atm pressure and 298.16°K calculated from heat capacity and vapour pressure data on the solid
Source of data
Entropy contribution (cal deg. K -I mole -1)
S o - - S O (Kelley, Parks and Huffman 90
11-06 + 0'55
0
extrapolation) 298.16
f
20'73 _+0"06
c~at./T
9o
ASagsq6 (sublimation) A S = R In 12"7/760
44.39 + 0"20 --8.09+0-01
Entropy of gas at 298'16°K
68"09 + 0"82 78
HEAT CAPACITY, ENTROPY AND ENTHALPY OF TRIOXAN the e n t r o p y of t r i o x a n gas, 68"09+0"82 c a l d e g -a m o l e -x, is in r e a s o n a b l e a g r e e m e n t with that of 68"99+0"01 cal deg -~ m o l e -z calculated b y M e l i a , Bailey a n d T y s o n 8 using the m e t h o d s of statistical t h e r m o d y n a m i c s . T h e e n t r o p y change, A ~ , , associated with the p o l y m e r i z a t i o n of one m o l e of t r i o x a n gas, at one a t m o s p h e r e pressure a n d 298.16°K, to crystalline p o l y o x y m e t h y l e n e can be o b t a i n e d b y s u b t r a c t i n g the e n t r o p y of the gaseous m o n o m e r f r o m that of the crystalline p o l y m e r x~ (31.8 c a l d e g -a m o l e -a) at the same t e m p e r a t u r e . T h e value o b t a i n e d is - 3 7 . 2 cal deg -1 m o l e -~. A similar value ( - 3 5 ' 9 cal deg -z m o l e -a) has been f o u n d for the p o l y m e r i z a t i o n of cyclohexane to polyethylene ~5'16.
G. A. Clegg and A. Tyson thank the University ol Sal[ord for the award o[ maintenance grants. We are also indebted to the Science Research Council/or a grant in aid of this investigation. Department o] Chemistry and Applied Chemistry, University o] Salford (Received April 1967) REFERENCES a KELLEY, K. K., PARKS,G. S. and HUFFMAN,H. M../. phys. Chem. 1929, 33, 1802 2 SACK,H. Belg. Pat. No. 612 792 (1962) 3 HUt~IN, D., SUMMIT,E. and BER~DXNELU, F. M. U.S. Pat. No. 2 989 507 (1961) Htro6IN, D., SUMMXT,E. and BERmUJINELLT,F. M. U.S. Pat. No. 2 989 506 (1961) 5 HtmGIN, D., SUMMIT,E. and BERARDINELLI,F. M. U.S. Pat. No. 2 989 508 (1961) 6 Htn~iN, D., SUMMIT,E. and BERm~OINELLI,F. M. U.S. Pat. No. 2 989 505 (1961) 7 SCrn~EIDER,A. K. U.S. Pat. No. 2 795 571 (1961) s MELIA,T. P., BAILEY,D. and TYSON, A. J. appl. Chem. 1967, 17, 15 0 FRANK, C. F., see WALKER, J. F. Formaldehyde, 3rd ed., p 193. Reinhold: New York, 1964 10AtmRBACH, F. and BnRSCRALL, H. Studien iiber Formaldehyde--Die Festen Polymeren des Formaldehydes, p 38. Springer: Berlin, 1907 n Scoa-r, R. B., MEYERS, C. H., RANDS, R. D., BPJCKWEDDE, F. D. and BEKKEDAHL, N. J. Res. Nat. Bur. Stand. 1945, 35, 39 1~J~CKS, V. and KEea~, W. Makromol. Chem. 1962, 52, 37 t3 HOGE, H. J. J. Res. Nat. Bur. Stand. 1946, 36, 111 1~DAIrCrON, F. S., EVANS, D. M., HOA~, F. E. and MEHA, T. P. Polymer, Lond. 1962, 3, 263 as DAIrCrON, F. S., EVANS, D. M., HOARE, F. E. and MEUA, T. P. Polymer, Lond. 1962, 3, 277 a6DAINTON, F. S., DEVLIN, T. R. E. and SMALL, P. A. Trans. Faraday Soc. 1955, 51, 1710
79