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The difference in a polymer series between the enthalpy and Gibbs energy of the glass-like and crystalline states
0082-$950/70/0901-2284507.50/0
Polymez Science U.S.S.R. Vol. 21, pp. 2284-2240. @ Pergamon Preu Ltd. 1980. Printed in Poland
THE, DIFFERENCE IN A POLYMER SERIES BETWEEN THE ENTHALPY AND GIBBS ENERGY OF THE GLASS-LIKE AND CRYSTALLINE STATES* I. B. RABI~OVICa and B. V. LEBEDEV Chemistry Research Institute, N. I. Lobachevskii State University, Gor'ki
(Received I0 J ~ y 1978) By using the results to be found in the literature and our own about the temperature dependence of the heat contents of polymers, their melting temperature T ° and enthalpy z~H~,we estimated the difference in the zero enthalpies H~ (0)--H i (0) of the glass-like and crystalline states of the examined polymers. From the found difference and the zero entropy S~(0) of the polymer glasses published earlier we calculated the respective differences between the Gibbs energies G~(T)--G~(T) for the range from 0°K to the glass temperature T~°. The value of G~ (0) -- G~ (0) was within the range 2-12 kJ.mole -1 for the various polymers; the temperature elevation from 0°K to T~ caused the latter to drop by a factor of 2. The enthalpy and Gibbs energy differences for polymer crystals and glasses chiefly depend on structural differences and those of the properties in these states; the part played by some degree of "tempering" of the polymer glass is relatively small. m y
T H E crystalline state is thermodynamically stable in the case of crystallizing polymers and low mol.wt, substances below their melting point Tin. I n the glass-like state however the relaxation time is very long owing to the high activation energy of rearrangement to the crystals. The properties of polymer glasses do not alter at a measurable rate as long as the external conditions do not change i.e. no force is exerted from the outside). One can therefore say t h a t the polymer glasses are capable of crystallization in principle and exist in a metastable state. In contrast with the analogous metastability of a supercooled liquid, the thermodynamic properties of a polymer glass depend to some extent on the thermal history at a given temperature T and pressure io. This is known to be due to the polymers having been subjected to "tempering" below the Tg and the position of the macromolecules in space is not t h a t existing at the Tg typical for the polymer, but t h a t at some T ~ Tg (the distribution of the macromolecules can change during slow cooling from above the Tg to the experimental temperature and the structure will freeze to t h a t at the Tg of the polymer). The crystals of polymers are known to be normally imperfect. This is true about polymers in the crystalline state and their thermodynamic properties can be found ex-
* Vysokomol. soyed. A21- No. 9, 2025-2030, 1979.
2234
Entha]py and gibbs energy of glass-like and crystalline states
2235
perimentally. Despi~ these features of polymers, it is worth assessing the differences in thermodynamic properties between the true glass-like and crysta|linc states. Thermodynamic equilibrium requires an absolute minimum of the Gibbs energy G at constant temperature and pressure; JG=0, J2G~0. The relative stability in the two states of substances is therefore assessed on the basis of their Gibbs energy and one can therefore get a relative indication of the metastability of the polyIher glass and crystal under given conditions from the difference Gg--Gc. These authors [1] used calorimetric data to assess the entropy difference S~(0)--S~(0) on 14 polymers in the glass-like and crystalline states at T = 0 ° K . Their experimental results and those of other investigators on the temperature dependence of C~ for 18 polymers (at various % crystallinities of the samples of each polymer), their temperature and enthalpy of melting, are being used in this paper to asses the zero enthalpy difference between the glass-like and crystalline states for each of the polymers. As the enthalpy is a function of the state of the system, the enthalpy wil~ be the same whether the liquid was produced from crystals or from the amorphous polymer for T ~ T ~ at a given pressure. We can therefore write Tin°
Tin°
Hi (0)+ I C~, ¢ dT+zftt~=H~ (0)+ I C~, a dT, 0
(1)
0
and from it we find T=o
N~ (0)--H~ (0)=
S (C~,,¢--C~,a) dT+dH~,
(2}
0
in which Hi (0), HI (0) are enthalpies of a 100% crystalline and glass-like polymer respectively: at T : 0°K; C°~, e, C°~, a, heat capacities of the polymer in the crystalline and amorphous state respectively; T~, AH~, temperature and entha]py of melting of the 100% crystalline polymer at p : 101.325 kPa. The C~, c : f ( T ) and C~o,a=f(T) functions were calculated by a method based on the extrapolation of the respective experimental results got with polymers of relatively high crystallinity (see Table). The C~:f(T) plots were extrapolated on the basis of the C~ only slightly depending on the crystallinity up to the Tg, and that the C~o of chain polymers is practically linear in the 100300OK range [2]. It is also reckoned that a graphical extrapolation of the curve experimentally produced for a liquid above the T~ (and for a slightly supercoo!ed liquid in a number of cases) is normally described by the heat content of a 100% amorphous polymer present in the highly elastic-state up to the T~ (see diagram)[3]. Extrapolation of the experimental C ~ f ( T ) curves to T = 0 made use of the equation which is the sum of the Debye and Einstein functions; the coefficients were selected for it from the experimental resu!g~. The experimental C~o of tho
4.3 6.3 7.3 1.8 11.7 5.6 2.9
2.4 1.2 8.3 -
3.3 4.8 4.9 1.5 10.0 4.3 l-8
4.3 6.3 7.3 1.8
11.7 5.6 2.9
Polydim&hylsiltrim&hyltmc
Poly-THF
Cie-polybutadiene
Natural rubber
T9wwpolypcn~namer
(Xqolypentenamer
Polyglycolide
2.7
1.8
2.7
PDMS
10.4
13.3
17.0
3.1
24.0
15.2
9.6
8.9
26
11.4
6.2
8.8
11.4
Poly-1,3&oxolane
8
4.1
2.5
3.3
4.1
Polyoxypropylenc
11.1
5.4
3.2
5.4
Polyoxyethylcne
4.3
5.5
0.3
Iaotactic PP
8
3.5
5.1
6.7
PE
6.3
lOOOK 1 200°K
4.7
I 16
0°K 6.7
Polymer
Initial exp. data
ci (a=87; T=20-415 and ~~48; T=80-415 [S, 71; AH;h=8.20; T&=414 [S]; T,“=237 [6] Cp (a=65 and 2-3; T=84-498) [9]; A%=8.97; T&=459; Tic260 [8, 91 c; (a=82; T=13.8-362); AHLz9.66; T:=343; T,“=216 [lo] cp (a=91; T=90-370) [ll]; AH&=8*37; T&=340; To=216 [8] T=90-390); AH$=16.7; Cp (a=58; T&=347; To=209 [la] cp (a=67; 69; T=S-3350); AH&=4*54; T;=246; T;=151 [13] Ci (a=14; 54; 85; 90; T=S-335); AHL=8.49; T$=325; T;=207 [14] VP (a=54; 57; 64; 65; T=5-329); AH&= 11.0; T&=348; T;=186 [15] Vp(a=45 (estimation); T=20-310) [16]; AH&=9.20; Tm=279; T;=165 [S, 161 C%(a=0 and 25; T=l4-320) [17j; AHm=4.39; T”,=301; T;=l99 [17, 181 Ci (a=26; 43; 47; 50; 67; T= 13.8-550); AHm=23*5; T&=501; T;=318 [19] C; (a=34; 39; 40; 50; T=O-325); AH:,=8.93; T&=310; Tic175 [ZO] C$ (a=O; T=O-325); AH&=5*2; %=232; T;=l56 [20]
-I
-
DIFFERENCES BORPOLYMERBIN THE CLASS-LIKE(g) AND CRYSFALLINE(c) STATES; g p= 101.325kPa
kJ*mole-l
H6,AND EWBZOPYS’
T Ui (T)-G:(T),
THE GIBBS ENERGY06, EWRALPY
7.8
4.9 12-4
4.8
Poly-l,3-dioxepane
Poly-B-propiolactono
Polyoctenylene
Poly-4-methylcyclohexene
3-1
8.9
3"9
5.7
7"7
1.4
5.3
2.9
5"3
4-8
12.4
4.9
7.8
16.9t
35.3*
10.0t
20.5
23.4
kJ'm°le-1 10.0
S~(0)--S~(0),
J'm°le-*'°K-*
H~(0)--H~(0), o
0~ (a=75; 77; T=13.8--350); AH~ =16.2; T°.,=337; T&=209 [21] C~ (~----50; T-----80--360); AH~,=14.3 T~=296; T~=189 [22] C~ ( a = 79; T = 13--400); A H ~ = 10.2; T~=366; T~=245 (authors' estimation) C~(a=37; T=8--330); AH°..=16.8; T~ = 308; T~° = 180 (authors' estimation) 0~(g=26; 29; 6--323); AH~----8; 30; T°.. = 256; T~= 198 (authors' estimation)
Initial exp. data
* C°p-heat COntent in the temperature range shown in brackets (°K) for crystalUnity ~, %; JH°m (kJ.mole -x) and T°m ( ° K ) - e n t h a l p y and melting point at g = l O 0 % ; T°,, °K--glass temperature. t Calculated by the authors as described under [3J.
10.0
G~(T)--G~(T), kJ.mole -1 0°K I 100°K I 200°K
Poly-caprolactam
Polymer
TABLE (cont.)
b0 t~
p-d ~"
o ~,
rn
~c;
• 2238
I . B . RAJBmOWCH a n d B . V. LEBEDEV
polymers in the range from 5-20 to 340-350°K were used in 14 out of 18 cases to calculate the thermodynamic properties (see Table). The determination accuracy was 0.2-0.3% in all cases. The majority of the polymers were cooled from room temperature to that of the determination start before calorimetry at a l°K/hr rate (Table) and then heated at the same rate during the measurement. Some of the AH~n were already l~own for 100% crystalline polymers while they had to be calculated for others from the proportionality of AH~n with a degree of crystallinity a (Samples of the same polymer having differing a-values were produced by always crystallizing them at near T~ directly in the calorimeter at the same rate but the crystallization time varied. We therefore believe t h a t the imperfections of crystalline structure were the same in these samples). The a values were determined from the AC~ ratio of the polymer sample to t h a t of its fully amorphous equivalent; the AC~ is the heat content increase during thawing in which the described ratio approaches the value 1-~ [2]. The found difference in enthalpy between the glass and crystal, and also t h e zero entropy of the glass [1] were used to calculate the respective Gibbs energy difference for the range 0-T~:
G~ (T)--G~ (T)=H~g (T)--H~ (T)--T [S~ (T)--S~ (T)]
(3)
T
H~ (T)--H~ (T)=H& (0)--H~ (0)+ S (C~, ~--C;j, e) dT
(4)
0 T
S~ (T)--S~ (T)=S~ (0)--S~ (0)+ S (C;,,~--C;,,e)dln T
(5)
0
The above equations recall that C~, e--C~, e in the range 0°K-T~, which ~ a s confirmed by the calorimetry by these authors for the C~ of the described polymers at various crystallinitics. The integrals occurring in eqns. (4) and (5) therefore become almost zero for the 0-T~ range and we get
G~° (T)--G~ (T)=H~ (0)--He° (0)--T [S~ (0)--S °e(0)]
(6)
The calculation results from using eqn. (6) and also those of calorimetry, together with the original information, are contained in the Table. The errors ,of estimating the enthalpy and Gibbs energy differences are around 10% of the found value• A comparative assessment of the true differences can point o o o 0 )-He( o 0 ) for example are 10-90% of to the fact that the Sg(0)-Se(0) and Hg( the respective AS~n and ziH~n (AS~AH~n/T~n). One can say on the basis of the results got by Petrie [4] that any "tempering" ,of the glass-like state is unlikely to have any significant effect on the calculated enthalpy and Gibbs energy differences for the glasses and crystals. It also follows from this work [4] that the complete "annealing" (retention at a temperature 10°K below the T~ until no more heat is liberated) of "tempered" polymer samples which is linked with a heat liberation of several hundreds of Joules
Enthalpy and gibbs energy of glad-like and crystalline states
2239
per ma-;s o f the r e p e t i t i v e chain u n i t will be smaller b y more t h a n one p o t e n c y t h a n the H~ (T)-H; (T) difference. One can p r o b a b l y estimate the calculated differences of the t h e r m o d y n a m i c values o f the glass-like a n d crystalline s t a t e s as v a r y i n g b y a r o u n d 10% according to t h e degree o f t e m p e r i n g (according t o t h e t h e r m a l history) o f t h e p o l y m e r glass. ,,,l
,R
,
150
:MN fIN D
!
50
0
100
200
300
7;,°K
The heat content of polytetrahydrofuran. ABe--crystalline; AB--glass; KE-highly elastic; EF--liquid; PMNE--apparent heat content in the melting range; the experimental points of curve AB were produced for samples having the crystallinities (%): 54, 57, 64, and 65; the points of curve BLPD--for the sample of 65~/o crystallinity. I t should be n o t e d t h a t a n increase in the cooling r a t e of p o l y h e x - l - e n e f r o m 4 × 10 -5 to 7 × 10-2°K when s t a r t i n g a t 225°K [5] caused the thawing p o i n t ia c a l o r i m e t r y to increase b y only 2°K, i.e. from 213.5J=l°K to 2 1 5 . 5 ~ 1 ° K .
Translated by K. A. A-LLEN REFERENCES
1. B. V. LEBEDEV and I. B. RABINOVICH, Dokl. Akad. Nauk SSSR 237: 641, 1977 2. Yu. K. GODOVSKII, Teplofizieheskie metody issledovaniya polimerov. (Thermo-physical Study Methods of Polymers). Izd. p. 127, "Khimiya", 1976 3. B. V. LEBEDEV and I. B. RABINOVICH, Vysokomol. soyed. B18: 416, 1976 (Not translated in Polymer Sic. U.S.S.R.) 4. S. E. B. PETRIE, J. Maeromol. Sci. B12: 225, 1976 5. J. BOURJ)ARRIAT and A. BERTON, Polymer 14: 167, 1973 6. B. WUNDERLICH, J. Chem. Phys. 37: 1203, 1962 7. E. PASSAGLIA and H. K. KEVORKIAN, J. Appl. Polymer Sci. 7: 119, 1963
2240
T . I . BOmSOVA e~ al.
8. B. WUNDERLICH, Fizika makromolekul (Maeromolecular Physics). p. 446, Izd. "Mir", 1976 9. E. PASSAGLIA and H. K, KEVORKIAN, J. Appl. Phys. 84: 90, 1963 10. B. V. LEBEDEV, A. A. YEVSTRONOV and V. I. BELOV, Mezhvuz, sb. Termodinamika organicheskikh soyedinenii (Inter-Univ. Coll.: The Thermo-Dynamics of Organic Compounds). Gor'ki, issue 6, 3, 1977 11. R. H. BEAUMONT, G. CLEGG, G. GEE, J. B. M. HERBERT et al., Polymer, 7: 401, 1966 12. (L A. CLEGG and T. P. MELIA, Polymer 1O: 912, 1969 13. B. V. LEBEDEV, N. N. MUKHINA a n d T. G. KULAGINA, Vysokomol. soyed. A20: 1297, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 6, 1458, 1978) 14. B. V. LEBEDEV, I. B. RABINOVICH, N. K. LEBEDEV a n d N. V. USHAKOV, Dokl. A k a d . N a u k SSSR 239: 1140, 1978 15. B. V. LEBEDEV a n d V. Ya. LITYAGOV, Vysokomol. soyed. A19: 2238, 1977 (Translated in P o l y m e r Sci. U.S.S.R. 19: 10, 2566, 1977) 16. F. S. DAINTON, D. M. EVANS, F. E. HOARE and T. P. MELIA, Polymer 3: 263, 1962 17. N. B E K K E D A H L and H. MATHESON, J. Res. Nat, Bur. Standards 15: 503, 1935 18. L. MANDEL'KERN, Kristallizatsiya polimerov (The Crystallization of Polymers). p. 125, Izd. " K h i m i y a " , 1966 19. B. V. LEBEDEV, A. A. YEVSTRONOV, Ye. G. KIPARISOVA, Ye. B. LYUDVIG a n d G. S. SANINA, Dokl. Akad. N a u k SSSR 236: 669, 1977 20. B. V. LEBEDEV, I. B. RABINOVICH a n d V. Ya. LITYAGOV, ]:)old. Akad. N a u k SSSR 237: 877, 1977 21. B. V. LEBEDEV, A. A. YEVSTRONOV, Ye. G. KIPARiSOVA a n d V. I. BELOV, Vysoko. tool soyed. A2O: 29, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 1, 32, 1978) ~2. W. K. BUSFILD and R. M. LEE, Makromol. Chemie 169: 199, 1973
Polym~ ScienceU.S.S.R.Vol. 21, pp. 2240-2248. O PergamonPress Ltd. 1980. Printed in Poland
0032-3950/79/0901-2240507.50/0
DIELECTRIC STUDY OF THE TRANSITION TEMPERATURES OF CELLULOSES OF DIVERSE SUPERMOLECULAR STRUCTURE* T. I. BoaIsovA, G. A. PETROPAVLOVSKII and N. YE. ~]:OTEL'I~IKOV)~ High Polymers Institute, U.S.S.R. Academy of Sciences
(Received 11 July 1978) The temperature-frequency dependence of the dielectric loss factor have been studied on woed and cotton cellulose samples in their original, micro-crystalline and amorphous states. Three dielectrically active relaxation processes can be ob* Vysokomot. soyed. A21: No. 9, 2031-0237, 1979.
Polymez Science U.S.S.R. Vol. 21, pp. 2284-2240. @ Pergamon Preu Ltd. 1980. Printed in Poland
THE, DIFFERENCE IN A POLYMER SERIES BETWEEN THE ENTHALPY AND GIBBS ENERGY OF THE GLASS-LIKE AND CRYSTALLINE STATES* I. B. RABI~OVICa and B. V. LEBEDEV Chemistry Research Institute, N. I. Lobachevskii State University, Gor'ki
(Received I0 J ~ y 1978) By using the results to be found in the literature and our own about the temperature dependence of the heat contents of polymers, their melting temperature T ° and enthalpy z~H~,we estimated the difference in the zero enthalpies H~ (0)--H i (0) of the glass-like and crystalline states of the examined polymers. From the found difference and the zero entropy S~(0) of the polymer glasses published earlier we calculated the respective differences between the Gibbs energies G~(T)--G~(T) for the range from 0°K to the glass temperature T~°. The value of G~ (0) -- G~ (0) was within the range 2-12 kJ.mole -1 for the various polymers; the temperature elevation from 0°K to T~ caused the latter to drop by a factor of 2. The enthalpy and Gibbs energy differences for polymer crystals and glasses chiefly depend on structural differences and those of the properties in these states; the part played by some degree of "tempering" of the polymer glass is relatively small. m y
T H E crystalline state is thermodynamically stable in the case of crystallizing polymers and low mol.wt, substances below their melting point Tin. I n the glass-like state however the relaxation time is very long owing to the high activation energy of rearrangement to the crystals. The properties of polymer glasses do not alter at a measurable rate as long as the external conditions do not change i.e. no force is exerted from the outside). One can therefore say t h a t the polymer glasses are capable of crystallization in principle and exist in a metastable state. In contrast with the analogous metastability of a supercooled liquid, the thermodynamic properties of a polymer glass depend to some extent on the thermal history at a given temperature T and pressure io. This is known to be due to the polymers having been subjected to "tempering" below the Tg and the position of the macromolecules in space is not t h a t existing at the Tg typical for the polymer, but t h a t at some T ~ Tg (the distribution of the macromolecules can change during slow cooling from above the Tg to the experimental temperature and the structure will freeze to t h a t at the Tg of the polymer). The crystals of polymers are known to be normally imperfect. This is true about polymers in the crystalline state and their thermodynamic properties can be found ex-
* Vysokomol. soyed. A21- No. 9, 2025-2030, 1979.
2234
Entha]py and gibbs energy of glass-like and crystalline states
2235
perimentally. Despi~ these features of polymers, it is worth assessing the differences in thermodynamic properties between the true glass-like and crysta|linc states. Thermodynamic equilibrium requires an absolute minimum of the Gibbs energy G at constant temperature and pressure; JG=0, J2G~0. The relative stability in the two states of substances is therefore assessed on the basis of their Gibbs energy and one can therefore get a relative indication of the metastability of the polyIher glass and crystal under given conditions from the difference Gg--Gc. These authors [1] used calorimetric data to assess the entropy difference S~(0)--S~(0) on 14 polymers in the glass-like and crystalline states at T = 0 ° K . Their experimental results and those of other investigators on the temperature dependence of C~ for 18 polymers (at various % crystallinities of the samples of each polymer), their temperature and enthalpy of melting, are being used in this paper to asses the zero enthalpy difference between the glass-like and crystalline states for each of the polymers. As the enthalpy is a function of the state of the system, the enthalpy wil~ be the same whether the liquid was produced from crystals or from the amorphous polymer for T ~ T ~ at a given pressure. We can therefore write Tin°
Tin°
Hi (0)+ I C~, ¢ dT+zftt~=H~ (0)+ I C~, a dT, 0
(1)
0
and from it we find T=o
N~ (0)--H~ (0)=
S (C~,,¢--C~,a) dT+dH~,
(2}
0
in which Hi (0), HI (0) are enthalpies of a 100% crystalline and glass-like polymer respectively: at T : 0°K; C°~, e, C°~, a, heat capacities of the polymer in the crystalline and amorphous state respectively; T~, AH~, temperature and entha]py of melting of the 100% crystalline polymer at p : 101.325 kPa. The C~, c : f ( T ) and C~o,a=f(T) functions were calculated by a method based on the extrapolation of the respective experimental results got with polymers of relatively high crystallinity (see Table). The C~:f(T) plots were extrapolated on the basis of the C~ only slightly depending on the crystallinity up to the Tg, and that the C~o of chain polymers is practically linear in the 100300OK range [2]. It is also reckoned that a graphical extrapolation of the curve experimentally produced for a liquid above the T~ (and for a slightly supercoo!ed liquid in a number of cases) is normally described by the heat content of a 100% amorphous polymer present in the highly elastic-state up to the T~ (see diagram)[3]. Extrapolation of the experimental C ~ f ( T ) curves to T = 0 made use of the equation which is the sum of the Debye and Einstein functions; the coefficients were selected for it from the experimental resu!g~. The experimental C~o of tho
4.3 6.3 7.3 1.8 11.7 5.6 2.9
2.4 1.2 8.3 -
3.3 4.8 4.9 1.5 10.0 4.3 l-8
4.3 6.3 7.3 1.8
11.7 5.6 2.9
Polydim&hylsiltrim&hyltmc
Poly-THF
Cie-polybutadiene
Natural rubber
T9wwpolypcn~namer
(Xqolypentenamer
Polyglycolide
2.7
1.8
2.7
PDMS
10.4
13.3
17.0
3.1
24.0
15.2
9.6
8.9
26
11.4
6.2
8.8
11.4
Poly-1,3&oxolane
8
4.1
2.5
3.3
4.1
Polyoxypropylenc
11.1
5.4
3.2
5.4
Polyoxyethylcne
4.3
5.5
0.3
Iaotactic PP
8
3.5
5.1
6.7
PE
6.3
lOOOK 1 200°K
4.7
I 16
0°K 6.7
Polymer
Initial exp. data
ci (a=87; T=20-415 and ~~48; T=80-415 [S, 71; AH;h=8.20; T&=414 [S]; T,“=237 [6] Cp (a=65 and 2-3; T=84-498) [9]; A%=8.97; T&=459; Tic260 [8, 91 c; (a=82; T=13.8-362); AHLz9.66; T:=343; T,“=216 [lo] cp (a=91; T=90-370) [ll]; AH&=8*37; T&=340; To=216 [8] T=90-390); AH$=16.7; Cp (a=58; T&=347; To=209 [la] cp (a=67; 69; T=S-3350); AH&=4*54; T;=246; T;=151 [13] Ci (a=14; 54; 85; 90; T=S-335); AHL=8.49; T$=325; T;=207 [14] VP (a=54; 57; 64; 65; T=5-329); AH&= 11.0; T&=348; T;=186 [15] Vp(a=45 (estimation); T=20-310) [16]; AH&=9.20; Tm=279; T;=165 [S, 161 C%(a=0 and 25; T=l4-320) [17j; AHm=4.39; T”,=301; T;=l99 [17, 181 Ci (a=26; 43; 47; 50; 67; T= 13.8-550); AHm=23*5; T&=501; T;=318 [19] C; (a=34; 39; 40; 50; T=O-325); AH:,=8.93; T&=310; Tic175 [ZO] C$ (a=O; T=O-325); AH&=5*2; %=232; T;=l56 [20]
-I
-
DIFFERENCES BORPOLYMERBIN THE CLASS-LIKE(g) AND CRYSFALLINE(c) STATES; g p= 101.325kPa
kJ*mole-l
H6,AND EWBZOPYS’
T Ui (T)-G:(T),
THE GIBBS ENERGY06, EWRALPY
7.8
4.9 12-4
4.8
Poly-l,3-dioxepane
Poly-B-propiolactono
Polyoctenylene
Poly-4-methylcyclohexene
3-1
8.9
3"9
5.7
7"7
1.4
5.3
2.9
5"3
4-8
12.4
4.9
7.8
16.9t
35.3*
10.0t
20.5
23.4
kJ'm°le-1 10.0
S~(0)--S~(0),
J'm°le-*'°K-*
H~(0)--H~(0), o
0~ (a=75; 77; T=13.8--350); AH~ =16.2; T°.,=337; T&=209 [21] C~ (~----50; T-----80--360); AH~,=14.3 T~=296; T~=189 [22] C~ ( a = 79; T = 13--400); A H ~ = 10.2; T~=366; T~=245 (authors' estimation) C~(a=37; T=8--330); AH°..=16.8; T~ = 308; T~° = 180 (authors' estimation) 0~(g=26; 29; 6--323); AH~----8; 30; T°.. = 256; T~= 198 (authors' estimation)
Initial exp. data
* C°p-heat COntent in the temperature range shown in brackets (°K) for crystalUnity ~, %; JH°m (kJ.mole -x) and T°m ( ° K ) - e n t h a l p y and melting point at g = l O 0 % ; T°,, °K--glass temperature. t Calculated by the authors as described under [3J.
10.0
G~(T)--G~(T), kJ.mole -1 0°K I 100°K I 200°K
Poly-caprolactam
Polymer
TABLE (cont.)
b0 t~
p-d ~"
o ~,
rn
~c;
• 2238
I . B . RAJBmOWCH a n d B . V. LEBEDEV
polymers in the range from 5-20 to 340-350°K were used in 14 out of 18 cases to calculate the thermodynamic properties (see Table). The determination accuracy was 0.2-0.3% in all cases. The majority of the polymers were cooled from room temperature to that of the determination start before calorimetry at a l°K/hr rate (Table) and then heated at the same rate during the measurement. Some of the AH~n were already l~own for 100% crystalline polymers while they had to be calculated for others from the proportionality of AH~n with a degree of crystallinity a (Samples of the same polymer having differing a-values were produced by always crystallizing them at near T~ directly in the calorimeter at the same rate but the crystallization time varied. We therefore believe t h a t the imperfections of crystalline structure were the same in these samples). The a values were determined from the AC~ ratio of the polymer sample to t h a t of its fully amorphous equivalent; the AC~ is the heat content increase during thawing in which the described ratio approaches the value 1-~ [2]. The found difference in enthalpy between the glass and crystal, and also t h e zero entropy of the glass [1] were used to calculate the respective Gibbs energy difference for the range 0-T~:
G~ (T)--G~ (T)=H~g (T)--H~ (T)--T [S~ (T)--S~ (T)]
(3)
T
H~ (T)--H~ (T)=H& (0)--H~ (0)+ S (C~, ~--C;j, e) dT
(4)
0 T
S~ (T)--S~ (T)=S~ (0)--S~ (0)+ S (C;,,~--C;,,e)dln T
(5)
0
The above equations recall that C~, e--C~, e in the range 0°K-T~, which ~ a s confirmed by the calorimetry by these authors for the C~ of the described polymers at various crystallinitics. The integrals occurring in eqns. (4) and (5) therefore become almost zero for the 0-T~ range and we get
G~° (T)--G~ (T)=H~ (0)--He° (0)--T [S~ (0)--S °e(0)]
(6)
The calculation results from using eqn. (6) and also those of calorimetry, together with the original information, are contained in the Table. The errors ,of estimating the enthalpy and Gibbs energy differences are around 10% of the found value• A comparative assessment of the true differences can point o o o 0 )-He( o 0 ) for example are 10-90% of to the fact that the Sg(0)-Se(0) and Hg( the respective AS~n and ziH~n (AS~AH~n/T~n). One can say on the basis of the results got by Petrie [4] that any "tempering" ,of the glass-like state is unlikely to have any significant effect on the calculated enthalpy and Gibbs energy differences for the glasses and crystals. It also follows from this work [4] that the complete "annealing" (retention at a temperature 10°K below the T~ until no more heat is liberated) of "tempered" polymer samples which is linked with a heat liberation of several hundreds of Joules
Enthalpy and gibbs energy of glad-like and crystalline states
2239
per ma-;s o f the r e p e t i t i v e chain u n i t will be smaller b y more t h a n one p o t e n c y t h a n the H~ (T)-H; (T) difference. One can p r o b a b l y estimate the calculated differences of the t h e r m o d y n a m i c values o f the glass-like a n d crystalline s t a t e s as v a r y i n g b y a r o u n d 10% according to t h e degree o f t e m p e r i n g (according t o t h e t h e r m a l history) o f t h e p o l y m e r glass. ,,,l
,R
,
150
:MN fIN D
!
50
0
100
200
300
7;,°K
The heat content of polytetrahydrofuran. ABe--crystalline; AB--glass; KE-highly elastic; EF--liquid; PMNE--apparent heat content in the melting range; the experimental points of curve AB were produced for samples having the crystallinities (%): 54, 57, 64, and 65; the points of curve BLPD--for the sample of 65~/o crystallinity. I t should be n o t e d t h a t a n increase in the cooling r a t e of p o l y h e x - l - e n e f r o m 4 × 10 -5 to 7 × 10-2°K when s t a r t i n g a t 225°K [5] caused the thawing p o i n t ia c a l o r i m e t r y to increase b y only 2°K, i.e. from 213.5J=l°K to 2 1 5 . 5 ~ 1 ° K .
Translated by K. A. A-LLEN REFERENCES
1. B. V. LEBEDEV and I. B. RABINOVICH, Dokl. Akad. Nauk SSSR 237: 641, 1977 2. Yu. K. GODOVSKII, Teplofizieheskie metody issledovaniya polimerov. (Thermo-physical Study Methods of Polymers). Izd. p. 127, "Khimiya", 1976 3. B. V. LEBEDEV and I. B. RABINOVICH, Vysokomol. soyed. B18: 416, 1976 (Not translated in Polymer Sic. U.S.S.R.) 4. S. E. B. PETRIE, J. Maeromol. Sci. B12: 225, 1976 5. J. BOURJ)ARRIAT and A. BERTON, Polymer 14: 167, 1973 6. B. WUNDERLICH, J. Chem. Phys. 37: 1203, 1962 7. E. PASSAGLIA and H. K. KEVORKIAN, J. Appl. Polymer Sci. 7: 119, 1963
2240
T . I . BOmSOVA e~ al.
8. B. WUNDERLICH, Fizika makromolekul (Maeromolecular Physics). p. 446, Izd. "Mir", 1976 9. E. PASSAGLIA and H. K, KEVORKIAN, J. Appl. Phys. 84: 90, 1963 10. B. V. LEBEDEV, A. A. YEVSTRONOV and V. I. BELOV, Mezhvuz, sb. Termodinamika organicheskikh soyedinenii (Inter-Univ. Coll.: The Thermo-Dynamics of Organic Compounds). Gor'ki, issue 6, 3, 1977 11. R. H. BEAUMONT, G. CLEGG, G. GEE, J. B. M. HERBERT et al., Polymer, 7: 401, 1966 12. (L A. CLEGG and T. P. MELIA, Polymer 1O: 912, 1969 13. B. V. LEBEDEV, N. N. MUKHINA a n d T. G. KULAGINA, Vysokomol. soyed. A20: 1297, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 6, 1458, 1978) 14. B. V. LEBEDEV, I. B. RABINOVICH, N. K. LEBEDEV a n d N. V. USHAKOV, Dokl. A k a d . N a u k SSSR 239: 1140, 1978 15. B. V. LEBEDEV a n d V. Ya. LITYAGOV, Vysokomol. soyed. A19: 2238, 1977 (Translated in P o l y m e r Sci. U.S.S.R. 19: 10, 2566, 1977) 16. F. S. DAINTON, D. M. EVANS, F. E. HOARE and T. P. MELIA, Polymer 3: 263, 1962 17. N. B E K K E D A H L and H. MATHESON, J. Res. Nat, Bur. Standards 15: 503, 1935 18. L. MANDEL'KERN, Kristallizatsiya polimerov (The Crystallization of Polymers). p. 125, Izd. " K h i m i y a " , 1966 19. B. V. LEBEDEV, A. A. YEVSTRONOV, Ye. G. KIPARISOVA, Ye. B. LYUDVIG a n d G. S. SANINA, Dokl. Akad. N a u k SSSR 236: 669, 1977 20. B. V. LEBEDEV, I. B. RABINOVICH a n d V. Ya. LITYAGOV, ]:)old. Akad. N a u k SSSR 237: 877, 1977 21. B. V. LEBEDEV, A. A. YEVSTRONOV, Ye. G. KIPARiSOVA a n d V. I. BELOV, Vysoko. tool soyed. A2O: 29, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 1, 32, 1978) ~2. W. K. BUSFILD and R. M. LEE, Makromol. Chemie 169: 199, 1973
Polym~ ScienceU.S.S.R.Vol. 21, pp. 2240-2248. O PergamonPress Ltd. 1980. Printed in Poland
0032-3950/79/0901-2240507.50/0
DIELECTRIC STUDY OF THE TRANSITION TEMPERATURES OF CELLULOSES OF DIVERSE SUPERMOLECULAR STRUCTURE* T. I. BoaIsovA, G. A. PETROPAVLOVSKII and N. YE. ~]:OTEL'I~IKOV)~ High Polymers Institute, U.S.S.R. Academy of Sciences
(Received 11 July 1978) The temperature-frequency dependence of the dielectric loss factor have been studied on woed and cotton cellulose samples in their original, micro-crystalline and amorphous states. Three dielectrically active relaxation processes can be ob* Vysokomot. soyed. A21: No. 9, 2031-0237, 1979.