Thermal Expansion and Glass Transition Temperatures of Amorphous Polymers
Abstract Generated abstract
This paper examines the relationship between volumetric thermal expansion and glass transition temperature in amorphous thermosetting polymers, with emphasis on modified epoxy compounds relevant to insulating structures. Using quartz dilatometry and interferometry, the authors measured expansion coefficients above and below the glass transition for cold-cured ED-5 and hot-cured ED-6 epoxy systems with several modifying additives, then compared calculated products with the Simha and Boyer relations previously established mainly for thermoplastics. The results indicate that increasing modifier content generally lowers the glass transition temperature, that expansion in the highly elastic state is about two to four times greater than in the glassy state, and that the Simha and Boyer equations give satisfactory agreement for the studied thermosetting epoxy compounds.
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PROCEEDINGS
OF THE TOMSK ORDER OF THE OCTOBER REVOLUTION
AND ORDER OF THE RED BANNER OF LABOR
POLYTECHNIC INSTITUTE NAMED AFTER S. M. KIROV
Vol. 282 1974
THERMAL EXPANSION AND GLASS TRANSITION TEMPERATURES OF AMORPHOUS POLYMERS
R. M. KESSENIKH, A. V. PETROV, L. A. KORSHUNOVA
(Presented by the scientific seminar of the Department of Electrical Insulation and Cable Engineering)
The magnitude of the temperature coefficient of volumetric expansion ($\beta$) is of essentially great importance when reinforcing metals with plastics, when casting the windings of electrical machines, etc. A large difference in $\beta$ of the materials used leads to large internal stresses in an insulating structure. These stresses pose a great danger under abrupt temperature changes.
As is known, for polymers a smooth bend is observed in the temperature dependence curves for the temperature coefficient of volumetric expansion, and this smooth bend of the curves is observed in the temperature region in which the time of action or measurement and the relaxation time are approximately equal to one another. In other words, this smooth bend corresponds to the temperature interval of transition from the glassy state to the highly elastic state and is associated with the softening (glass transition) temperature—$T_c$. What has been said applies both to thermoplastic and to thermosetting polymers, with the only difference being that the relaxation times of these two types of polymers differ noticeably.
Many properties of polymers are explained from the point of view of free volume, which is represented as holes of the order of molecular (monomeric) dimensions or as voids associated with the irregularity of packing of the polymer chains. In particular, the coefficient of thermal expansion above $T_c$ is interpreted as an increase in free volume with increasing temperature, and is not associated with the anharmonicity of vibrations characteristic of crystalline solids. In [1] it is shown that the free volume of all polymers at $T_c$ must have a constant value. Developing the indicated proposition, in [2] the value of the fraction of free volume ($f_c$) at the glass transition temperature was established for most polymer systems:
\[ f_c = 0.025 \pm 0.003, \tag{1} \]
where $f_c=\dfrac{v_c}{v}$ ($v_c$ is the free volume, $v$ is the specific volume).
In [2] the theory of reduced variables developed by Williams, Landel, and Ferry (WLF) is presented. The temperature dependence of the relaxation time is related in a definite way to the magnitude of the free volume, which determines the mobility of macromolecules near the glass transition temperature.
The indicated dependence has the form
\[ \lg a_T=-\frac{\left(\dfrac{B}{2.3}\cdot f_c\right)\cdot (T-T_c)} {\dfrac{f_c}{\beta_f}+T-T_c}, \tag{2} \]
where \(a_T\) is the ratio of the relaxation times at temperatures \(T\) and \(T_c\);
\[ \beta_f=\beta_b-\beta_c; \]
\(\beta_f\) is the difference between the coefficients of volume expansion above and below \(T_c\);
\(B\) is a constant close to unity;
\(f_c\) is the fraction of free volume.
Experimental verification of equation (2) in [3] showed that the fraction of free volume is substantially larger than the universal value. The author explains this discrepancy by the fact that in the WLF theory the fraction of free volume was determined from data on dynamic mechanical properties (segmental and molecular mobility are manifested). Meanwhile, if larger structural elements take part in the relaxation process, this will require a larger volume.
Consequently, it may be assumed that, in studying different relaxation processes, one can determine the corresponding free volumes that ensure the jumps of different structural elements. On the other hand, the free volume must depend on the packing density of the molecules. In the WLF theory such a regularity has not been established; however, the mathematical apparatus of this theory makes it possible to describe molecular motions in polymer systems [3].
In [4], on the basis of the relationship between free volume and the glass-transition temperature, the authors established the following regularities:
\[ (\beta_b-\beta_c)\cdot T_c=0.12, \qquad \beta_b\cdot T_c=0.2, \tag{3} \]
where \(\beta_b\) is the coefficient of volume expansion above \(T_c\);
\(\beta_c\) is the coefficient of volume expansion below \(T_c\);
\(T_c\) is the glass-transition temperature in degrees Kelvin.
Although the universal expression (3) has been checked sufficiently well for thermoplastic polymers, no such experiment has been carried out for thermosetting polymers. In connection with the above, we have performed a study of the thermal expansion and glass-transition temperatures of modified epoxy compounds of hot and cold curing. The experimental data obtained made it possible to calculate the universal constants according to equation (3).
The study was carried out on epoxy compounds based on ED-5 resin cured with polyethylene polyamine (PEPA), and ED-6 resin cured with methyltetrahydrophthalic anhydride. DEG-1, MGF-9, and DBTF were used as modifying additives. The thermal expansion and glass-transition temperatures of the cold- and hot-cured compounds were measured by means of a quartz dilatometer and a Linnick-system IZK-50 interferometer. The heating rate was 1 deg/min. The relative measurement error was 0.4° C/min. The results of the study of \(\beta\) and the glass-transition temperatures, as well as the calculated data for the universal constants, are summarized in Table 1 (cold-
Table 1
Calculation of the Simha and Boyer coefficients for cold-cured epoxy compounds
| No. | Composition | $T_c$, K | $\beta_{\mathrm{v}}\cdot 10^6$, deg$^{-1}$ | $\beta_{\mathrm{c}}\cdot 10^6$, deg$^{-1}$ | $\Delta\beta\cdot 10^6$, deg$^{-1}$ | $\Delta\beta\cdot T_c$ | $\gamma_{\mathrm{v}}\cdot T_c$ |
|---|---|---|---|---|---|---|---|
| 1 | ED-5, 100 parts by weight; GETA—10 parts by weight, pure | 367 | 504 | 144 | 360 | 0,132 | 0,182 |
| 2 | —, DBGF—10 parts by weight | 331 | 685 | 198 | 487 | 0,160 | 0,233 |
| 3 | —, DBGF—20 parts by weight | 329 | 645 | 300 | 345 | 0,135 | 0,121 |
| 4 | —, DBGF—30 parts by weight | 311 | 660 | 375 | 285 | 0,089 | 0,205 |
| 5 | —, DBGF—40 parts by weight | 309 | 540 | 300 | 240 | 0,074 | 0,167 |
| 6 | —, DEG-1, 10 parts by weight | 348 | 450 | 150 | 300 | 0,105 | 0,157 |
| 7 | —, DEG-1, 20 parts by weight | 346 | 390 | 180 | 210 | 0,073 | 0,135 |
| 8 | —, DEG-1, 30 parts by weight | 334 | 510 | 150 | 360 | 0,120 | 0,170 |
| 9 | —, DEG-1, 40 parts by weight | 325 | 450 | 180 | 270 | 0,0877 | 0,146 |
| 10 | —, DEG-1, 50 parts by weight | 210 | 645 | 480 | 165 | 0,051 | 0,200 |
| 11 | —, DEG-1, 100 parts by weight | 298 | 600 | 135 | 465 | 0,132 | 0,179 |
| 12 | —, MGF-9, 10 parts by weight | 328 | 510 | 150 | 360 | 0,118 | 0,167 |
| 13 | —, MGF-9, 20 parts by weight | 326 | 516 | 300 | 216 | 0,071 | 0,168 |
| 14 | —, MGF-9, 30 parts by weight | 322 | 570 | 300 | 270 | 0,087 | 0,184 |
| 15 | —, MGF-9, 40 parts by weight | 318 | 645 | 300 | 345 | 0,110 | 0,205 |
Table 2
Calculation of the Simha and Boyer coefficients for hot-cured epoxy compounds
| No. | Composition | $T_c$, °K | $\beta_{\mathrm{v}}\cdot 10^{6}$, deg$^{-1}$ | $\beta_c\cdot 10^{6}$, deg$^{-1}$ | $\Delta\beta\cdot 10^{6}$, deg$^{-1}$ | $\Delta\beta\cdot T_c$ | $\beta_{\mathrm{v}}^{3}\cdot T_c$ |
|---|---|---|---|---|---|---|---|
| 1 | ED-6, 100 parts by weight; MTGFA—62 parts by weight, pure | 368 | 504 | 150 | 344 | 0,127 | 0,186 |
| 2 | ED-6, 100 parts by weight; DBTP—10 parts by weight, pure | 337 | 570 | 270 | 300 | 0,101 | 0,192 |
| 3 | ED-6, 100 parts by weight; DBTP—20 parts by weight, pure | 331 | 685 | 180 | 505 | 0,167 | 0,223 |
| 4 | ED-6, 100 parts by weight; DBTP—30 parts by weight, pure | 309 | 720 | 426 | 306 | 0,095 | 0,223 |
| 5 | ED-6, 100 parts by weight; DBTP—40 parts by weight, pure | 304 | 795 | 405 | 390 | 0,119 | 0,242 |
| 6 | ED-6, 100 parts by weight; DET—1 10 parts by weight, pure | 341 | 555 | 153 | 402 | 0,137 | 0,190 |
| 7 | ED-6, 100 parts by weight; DET—1 20 parts by weight, pure | 329 | 600 | 195 | 405 | 0,133 | 0,1975 |
| 8 | ED-6, 100 parts by weight; DET—1 30 parts by weight, pure | 328 | 600 | 180 | 420 | 0,138 | 0,197 |
| 9 | ED-6, 100 parts by weight; DET—1 40 parts by weight, pure | 330 | 660 | 174 | 486 | 0,160 | 0,218 |
| 10 | ED-6, 100 parts by weight; DET—1 50 parts by weight, pure | 321 | 630 | 189 | 441 | 0,142 | 0,202 |
| 11 | ED-6, 100 parts by weight; DET—1 100 parts by weight, pure | 290 | 1050 | 150 | 900 | 0,261 | 0,305 |
| 12 | ED-6, 100 parts by weight; MGF—9 10 parts by weight, pure | 343 | 480 | 150 | 330 | 0,1134 | 0,165 |
| 13 | ED-6, 100 parts by weight; MGF—9 20 parts by weight, pure | 322 | 615 | 240 | 375 | 0,121 | 0,198 |
| 14 | ED-6, 100 parts by weight; MGF—9 30 parts by weight, pure | 316 | 630 | 270 | 360 | 0,114 | 0,199 |
| 15 | ED-6, 100 parts by weight; MGF—9 40 parts by weight, pure | 310 | 645 | 450 | 195 | 0,061 | 0,200 |
curing) and 2 (hot curing). Comparing the calculated data obtained on the basis of our experiments with the data of the Simcha and Boyer equation (3), one may conclude that our calculated results (Tables 1 and 2) are in satisfactory agreement with the universal data of equation (3). Therefore, knowing the glass-transition temperatures, it is possible to calculate the temperature coefficients of volumetric expansion. Thus, the Simcha and Boyer equation is universal also for thermosetting polymers.
Conclusions
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The temperature coefficients of volumetric expansion and the glass-transition temperatures of modified epoxy compounds of hot and cold curing have been studied.
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With an increase in the weight parts of modifiers, a decrease in the glass-transition temperatures of epoxy compounds is observed.
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The coefficients of thermal volumetric expansion of epoxy compounds in the highly elastic state are 2–4 times greater than the coefficients of volumetric expansion of the compounds in the glassy state.
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The experimental and calculated data of Simcha and Boyer are in satisfactory agreement.
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The Simcha and Boyer equation is universal for thermosetting epoxy modified compounds.
Literature
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T. Fox, P. Flory. J. Appl. Phys. 21, 581, 1950.
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D. Ferry. Viscoelastic Properties of Polymers, IL, 1963.
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Yu. S. Lipatov. Physical Chemistry of Filled Polymers. Kiev, “Naukova Dumka,” 1967.
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V. Simcha, R. Boyer. J. of Chem. Physics. 37, No. 5, 1962.