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Mechanical relaxation studies of the cure of epoxy resins: 2. Activation energy of the γ-process in amine-cured epoxy resins
Mechanical relaxation studies of the cure of epoxy resins: 2. Activation energy of the y-process in amine-cured epoxy resins R. G. C. Arridge H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK
and d. H. Speake NDT Centre, AERE, Harwell, Didcot, Berks, UK (Received 22 February 1972; revised 4 April 1972) Measurements are reported of the activation energy for secondary relaxation (y-relaxation) in amine-cured epoxy resins. Good agreement was found between values determined from the area under the loss modulus/inverse absolute temperature curve and those derived from the shift of the ~,-relaxation in temperature for different measuring frequencies. The energy was found to be dependent on the degree of cure, increasing from about 14 kcal/mol during the early stages of cure to higher values following post cure after gelation, eventually levelling out to a value characteristic of the hardener used (23 kcal/mol for triethylene tetramine, 26 kcal/mol for ethylene diamine). If less than the stoichiometric amount of hardener is used the activation energy is reduced (e.g. to 18k cal/mol for 11 phr TETA). The interpretation of the ~,-relaxation as being due to 'crankshaft' rotation of the -CHz-CH(OH)-CH2-O group with an activation energy of 14 kcal/mol is therefore modified on post curing to become an example of hindered rotation in a double potential well, the additional energy barrier being due to steric effects arising from the increase in crosslink density.
INTRODUCTION The secondary mechanical relaxation in amine-cured epoxy resins, known as the ~,-relaxation, is generally thoughtT M to be caused by a flexible segment -CH~CH(OH)-CH~-O formed during the curing process, although other hypotheses have also been suggested 5, 6. The manner in which the glycidyl segment relaxes is not known but PoganyI has suggested that the group probably rotates in the manner of a crankshaft as outlined by SchatzkiL It is the purpose of this paper to present measurements of the activation energy of the y-process for resins in various states of cure to partly elucidate the mechanism of this relaxation. The usefulness of determining the activation energy of a mechanical relaxation is that it provides a quantitative measure of the magnitude of the relaxation and often an indication of the type and location of the molecular species giving rise to it. There have been many determinations of the activation energy of the major transition but only Kreahling and Klines and Van Hoorn a have put forward any value for the 9t-relaxation. The former found a value of 16 kcal/mol in a system consisting of diglycidyl ether of bisphenol A cured with metaphenylene diamine whereas the figure of
450 POLYMER, 1972, Vol 13, September
14kcal/mol quoted by Van Hoorn is the average of a number of systems each containing the glycidyl ether segment. EXPERIMENTAL The materials and measuring techniques used in this investigation were the same as previously reported 9 in which a commercial diglycidyl ether of bisphenol A (DGEBA) was crosslinked with either ethylene diamine (EDA) or triethylenetetramine (TETA). Varying degrees of cure were achieved by using less than the stoichiometric quantity of curing agent and also by heat treatment. The methods of measurement were a torsion pendulum operating at 0-67 Hz which yielded both the real and imaginary parts of a complex shear modulus, and ultrasonic techniques. These were employed over the frequency range of 10kHz to 2MHz and only the real part of a complex shear modulus was measured. LOSS MODULUS The loss modulus is the imaginary part of a complex modulus and is denoted G". It is related to the storage modulus G' and the loss tangent, tan& The change in loss
Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake
2J
modulus with cure is governed by the same factors as tan8 and indeed plots of G" as a function of temperature for a series of states of cure are similar to those of tan8 but occur at lower temperatures 9. However, the usefulness of the loss modulus is in the determination of the activation energy of the relaxation. Read and Williams z° have put forward a theory which allows the calculation of activation energy from the area beneath a G" versus 1/T plot. Their theory showed that the relationship between area and activation energy is of the following form:
f°
AHZ/
j+
2
"b.
~
I .~r(rnox)
A
co
o
2"4[-
(2r+ 1)9'
(1)
u
2'0
=..
r=0
where A = a constant, A H = the activation energy, R = the gas constant, T = temperature in K, ~o=the measuring frequency, r=relaxation time at temperature T K , r0 = relaxation time at infinite temperature. If the temperature of the maximum loss is denoted T(max), then
o '_o 1.6 %
1,2
A = (G~ (max) - - G~(max))T(max) and
I -150
AH
I
(2)
"rmax= r °exP ( R T ~ a x ) )
I -IIO
I
I
i
I
-70 Tempzroture (°C)
I
I
-30
I
*10
Figure 2 Evaluation of G~tmax) and G~(max)
Gv and G~ are the unrelaxed and relaxed values of shear modulus respectively. Schallamach n showed that tOrmax differs only slightly from unity, which is the value predicted by the single relaxation time model, and also that co70<1 for the frequencies normally encountered, thus a combination of equations (1) and (2) leads to the following result:
9-O m
7"0-
AH= LGRr ~/'(max) _ Gu~'(max)]~
R~r
qo 0,, 4E
/
S'O-
U
¢-
/
-
L~ 3-0--
Thus the area under the G" versus lIT curve and the extrapolated values of Gv and GR at T(max) are the only experimental quantities required. Unfortunately equation (3) is limited in applicability. Two curves of loss modulus are shown in Figure 1 for a system of D G E B A hardened with 11 parts of TETA (by weight) per hundred parts of resin (phr). It is apparent that the curve representing 19°C cure has two widely differing values of loss modulus. This renders the construction of a baseline open to considerable conjecture and for curves of this form no activation energy was calculated. The area under the curve for 159°C cure is well defined and was measured. Measurements of area were made using a planimeter. G~(max) and G~ (max) were found by extrapolation to T(max) using values of Gtr and GR at temperatures at which the baseline of the G" versus lIT curve intersected G", as shown in Figure 2.
\
/
m
l'O--
l
2.0
I
l
4"0
I
6'0
I03
(3)
l
8-0
(K)
T
Figure 1 Loss modulus for two states of cure. O, 2h at 159°C; A, cured at room temperature
RESULTS Values of activation energy are given in Table 1 for cure temperatures above 70°C, where the areas under the loss modulus curves are well defined.
POLYMER, 1972, Vol 13, September
4.51
Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake Table 1 Activation energies for cure temperatures above 70°C
16
Activation
energy
Cure temp, (°C)
(kcal/mol)
76"3 93"9
15"2 17"9
118'0
18"8
159'0
17"8
12
8
The value obtained at a cure temperature of 159°C is lower than the one at 118.8°C and this is due to the onset of degradationlL The results would seem to suggest that the activation energy increases with increasing crosslinking density and this is borne out as shown in the following section. Modulus/temperature curves were also obtained at differing frequencies and it was found that the temperature of the y-relaxation, in a system of D G E B A cured to a true equilibrium state with 11 phr of TETA, moved from about - 4 5 ° C when measured at 0.67 Hz to about 65°C when measured at 1.25 MHz. The good superposition of curves obtained at different frequencies signified that the activation energy of the y-process does not depend on temperature in contrast to the glass/rubber transition where the activation energy is strongly dependent on temperature. Hence equation (2) can be rewritten to yield the activation energy by measuring the shift in temperature of the relaxation when observed at a different frequency. This is expressed as:
AH=(
R
c
4i
I
I o.4
o
I (il~-
I o.8
I
I I. 2
I
1 I. 6
l i t 2 ), fO 3 {K)
Determination of activation energy from data at four
Figure 3
frequencies
co2
1 - - 1 '~1n~--11
(4)
where oJ1, oJ2 are the measuring frequencies and Tz, Ts are the temperatures of the y-relaxation when observed at oJ1 and ~oz respectively. Results are shown in Figure 3, the slope of which yields an activation energy of 17.9kcal/ mol. This is in very good agreement with the value found by the loss modulus analysis on the same resin system.
1_,
DEPENDENCE OF ACTIVATION ENERGY ON STATE OF CURE The loss modulus analysis suggested that the activation energy decreased with decreasing degree of cure and a detailed investigation was therefore made on the relationship between activation energy and state of cure. Curves of shear modulus as a function of temperature measured at 30 kHz were obtained on the system D G E B A cured with the stoichiometric quantity of TETA at various temperatures. Some of these curves are shown in Figure4. The modulus and temperature were recorded at the point of inflection for each curve. A small section of the cylindrical specimen used in the resonance technique was then inserted into the transit time equipment operating at 1.25MHz. The temperature was then altered until the measured velocity yielded a modulus value identical to that noted at the inflection point. Use of the Arrhenius relationship then allowed calculation of the activation energy. Results are illustrated in Figure 5. It was tempting, although not justifiable, to draw a sigmoid through the points because apart from the results at 25°C and 80°C
452
POLYMER,
1972, V o l 13, S e p t e m b e r
,
-70
-30
*10 "50 Temperoture (°C)
'90
Figure 4 Shear modulus measured at 30kHz for various states of cure. (The anomaly in the curve for room temperature cure is due to post cure during test.) O, Room temperature cure; A, 65°C cure for 2h; x , 100°C cure for 2h; 17,130°C cure for2h
24
0 0
0
I
I
0
0
0
8
o
o
l
20
I
I
6(3 I00 Cure tcrnperotur¢ (°C)
I
140
I
I
IBO
Figure 5 Activation energy of the y-relaxation as a function of cure temperature. Cured 30min at each temperature
Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake +30
0
0
0
the stoichiometric quantity is less than for resins cured with higher concentrations of hardener.
A
L) O
DISCUSSION
*I0 E
-30 I
I 6
I
I I 8 EDA (phr)
I IO
I
I 12
Figure 6 Temperature of the y-relaxation for varying quantities of hardener
28 0
0
o
E20 "6 u O O
<3 12
I
4
6
I
I
8 EDA (phr)
I
I
lO
[
t
t
12
Figure 7 Activation energy of the y-relaxation for different amounts
of hardener
the others lie on a smooth sigmoidal-shaped curve. The determination of activation energies of resins with a small degree of crosslinking is more inaccurate than for fully cured material owing to the greater uncertainty in determining the temperature of inflection on the modulus/ temperature curve. The upper value of about 23 kcal/mol for the fully cured resin is much higher than the value of 17.9 kcal/mol found using four frequencies and the reason for the difference is that a stoichiometric quantity of hardener was used in the former case whereas only 11 phr was used in the latter, resulting in a higher density of crosslinking. This was checked by measuring the activation energy in systems containing varying quantities of hardener in which an equilibrium state of cure has been achieved. EDA was used rather than TETA owing to the greater ease of preparation of specimens utilizing the former constituent. The temperature of the relaxation, determined by the inflection point, was plotted as a function of EDA concentration and is shown in Figure 6. These results are similar in form to those obtained using a torsion pendulum where tanSmax was plotted against cure temperature. The activation energy was determined and results are presented in Figure 7 where it is demonstrated that the activation energy for a resin cured with less than
The results lend striking support for the proposed mechanism of cure outlined in Part 1 a. Here it was postulated that crosslinks are initiated at widely dispersed sites in the network but as the number increase, potentially reactive segments are sterically hindered from diffusing to other reactive sites and to overcome this barrier more thermal energy must be supplied to the network. This mechanism is certainly borne out by the results shown in Figure 5 in which the activation energy is seen to increase until a curing temperature of 140°C is attained when it becomes constant. These results illustrate the importance of knowing the state of cure when determining activation energies and the values of 16kcal/mol reported by Kreahling and Klines, and of 14 kcal/mol by Van Hoorn 4 are not meaningful because these workers failed to realize that an increase in crosslinking density inhibits the yrelaxation, thus increasing the apparent activation energy, and they do not stipulate the state of cure to which those energies refer. If Figure 5 is assumed to be sigmoidal, then the apparently constant value of about 14kcal/mol for low degrees of cure must be indicative of the energy necessary for the glycidyl ether segment to relax and any value above this represents the extra energy needed to overcome the increasing steric hindrance as more crosslinks are formed. If a crankshaft-type relaxation mechanism is assumed then the lower value certainly agrees well with the value of 13 kcal/mol calculated by Schatzki 7 based on twice the butane potential barrier plus a van der Waals barrier determined from cohesive energy density. However, the relaxation temperature for methylene sequences is about - 120°C when measured at 1 Hz and because the ~,-relaxation in epoxy resin occurs at a higher temperature, owing to the hindrance of the pendant hydroxyl, the activation energy assuming a crankshaft model would be expected to be higher than the 13 kcal/mol proposed by Schatzki. Thus the crankshaft model does not seem to be realistic from energy considerations and it is suggested that the relaxation is governed by hindered rotation in a double potential well whose height above about 14kcal/ mol is determined by the extent of steric hindrance caused by an increase in crosslinking density. It is interesting to note that the form of the curves shown in Figures 6 and 7 is identical adding further weight to the proposed curing mechanism. Also apparent is the fact that the activation energy for the relaxation in a resin fully cured with the stoichiometric quantity of EDA is higher than one cured with TETA, i.e. 26 as compared with 23 kcal/mol. This would seem to signify that the stiffness of the hardener chain influences the relaxing segment. The EDA chain is about half the length of a molecule of TETA and probably less mobile although in both hardeners reactive hydrogen atoms are separated by two (CH2) units. Nonetheless the longer chain is expected to exhibit greater flexibility. Delatycki et al. 5 examined a series of epoxy-diamine networks using a low frequency torsion pendulum and found that the temperature of the ~,-relaxation remained constant for diamines containing up to 12 methylene groups, although the height of the loss modulus/temperature curve decreased with increasing chain length. This suggests that the activation energy of the relaxation
POLYMER,
1972, Vol 13, September
453
Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake decreased with increasing chain length. In view of the results presented in our paper it is surprising that the relaxation temperature remained constant because the change in steric hindrance arising from the change in crosslinking density when the hardener is varied might be expected to shift the relaxation along the temperature axis. This could be checked by employing an ultrasonic test method for measuring the loss modulus where any change in activation energy would be shown up by a spread of relaxation temperatures even though the temperature remained constant in the low frequency test.
is determined by the crosslinking density and is found to be higher in systems where short chains are reacted. ACKNOWLEDGEMENTS This work was supported by the Procurement Executive, Ministry of Defence. We should also like to thank the NDT Centre, Harwell for providing the experimental facilities. REFERENCES
CONCLUSION The dependence of the activation energy of the yrelaxation on the state of cure demonstrates the part played by steric hindrance on the relaxation mechanism. For low degrees of cure the activation energy of the y-process is fairly constant and of the order of 13 kcal/mol. It must be remembered that this value is obtained in a system which has already undergone about 70 % of the total crosslinking reaction. It is unlikely that 100 % of the reaction is ever achieved and so the large part played by steric effects in the later stages is rather surprising. The limiting value of activation energy in a fully cured system
454 POLYMER, 1972, Vol 13, September
1 Pogany, G. A. Polymer 1970, 11, 66 2 May, C. A. and Weir, F. E. SPE Trans. 1962 (July) p 207 3 Kline, D. E. J. Polym. Sci. 1960, 47, 237 4 Van Hoorn, H. J. Appl. Polym. Sci. 1968, 12, 871 5 Delatycki, O., Shaw, J. C. and Williams, J. G. J. Polym. Sci. (.4-2) 1969, 7, 753 6 Cuddihy, E. F. and Moacanin, J. J. Polym. Sci. (4-2) 1970, 8, 1627 7 Schatzki, T. F. J. Polym. Sci. 1962, 57, 496 8 Kreahling, R. P. and Kline, D. E. J. ,4ppl. Polym. Sci. 1969, 13, 2411 9 Arridge, R. G. C. and Speake, J. H. Polymer 1972, 13, 443 10 Read, B. E. and Williams, G. Trans. Faraday Soc. 1961,57,1979 11 Schallamach, A. Trans. Faraday Soc. 1946, A42, 495 12 Pogany, G. A. DPhil Thesis Oxford University, 1966
and d. H. Speake NDT Centre, AERE, Harwell, Didcot, Berks, UK (Received 22 February 1972; revised 4 April 1972) Measurements are reported of the activation energy for secondary relaxation (y-relaxation) in amine-cured epoxy resins. Good agreement was found between values determined from the area under the loss modulus/inverse absolute temperature curve and those derived from the shift of the ~,-relaxation in temperature for different measuring frequencies. The energy was found to be dependent on the degree of cure, increasing from about 14 kcal/mol during the early stages of cure to higher values following post cure after gelation, eventually levelling out to a value characteristic of the hardener used (23 kcal/mol for triethylene tetramine, 26 kcal/mol for ethylene diamine). If less than the stoichiometric amount of hardener is used the activation energy is reduced (e.g. to 18k cal/mol for 11 phr TETA). The interpretation of the ~,-relaxation as being due to 'crankshaft' rotation of the -CHz-CH(OH)-CH2-O group with an activation energy of 14 kcal/mol is therefore modified on post curing to become an example of hindered rotation in a double potential well, the additional energy barrier being due to steric effects arising from the increase in crosslink density.
INTRODUCTION The secondary mechanical relaxation in amine-cured epoxy resins, known as the ~,-relaxation, is generally thoughtT M to be caused by a flexible segment -CH~CH(OH)-CH~-O formed during the curing process, although other hypotheses have also been suggested 5, 6. The manner in which the glycidyl segment relaxes is not known but PoganyI has suggested that the group probably rotates in the manner of a crankshaft as outlined by SchatzkiL It is the purpose of this paper to present measurements of the activation energy of the y-process for resins in various states of cure to partly elucidate the mechanism of this relaxation. The usefulness of determining the activation energy of a mechanical relaxation is that it provides a quantitative measure of the magnitude of the relaxation and often an indication of the type and location of the molecular species giving rise to it. There have been many determinations of the activation energy of the major transition but only Kreahling and Klines and Van Hoorn a have put forward any value for the 9t-relaxation. The former found a value of 16 kcal/mol in a system consisting of diglycidyl ether of bisphenol A cured with metaphenylene diamine whereas the figure of
450 POLYMER, 1972, Vol 13, September
14kcal/mol quoted by Van Hoorn is the average of a number of systems each containing the glycidyl ether segment. EXPERIMENTAL The materials and measuring techniques used in this investigation were the same as previously reported 9 in which a commercial diglycidyl ether of bisphenol A (DGEBA) was crosslinked with either ethylene diamine (EDA) or triethylenetetramine (TETA). Varying degrees of cure were achieved by using less than the stoichiometric quantity of curing agent and also by heat treatment. The methods of measurement were a torsion pendulum operating at 0-67 Hz which yielded both the real and imaginary parts of a complex shear modulus, and ultrasonic techniques. These were employed over the frequency range of 10kHz to 2MHz and only the real part of a complex shear modulus was measured. LOSS MODULUS The loss modulus is the imaginary part of a complex modulus and is denoted G". It is related to the storage modulus G' and the loss tangent, tan& The change in loss
Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake
2J
modulus with cure is governed by the same factors as tan8 and indeed plots of G" as a function of temperature for a series of states of cure are similar to those of tan8 but occur at lower temperatures 9. However, the usefulness of the loss modulus is in the determination of the activation energy of the relaxation. Read and Williams z° have put forward a theory which allows the calculation of activation energy from the area beneath a G" versus 1/T plot. Their theory showed that the relationship between area and activation energy is of the following form:
f°
AHZ/
j+
2
"b.
~
I .~r(rnox)
A
co
o
2"4[-
(2r+ 1)9'
(1)
u
2'0
=..
r=0
where A = a constant, A H = the activation energy, R = the gas constant, T = temperature in K, ~o=the measuring frequency, r=relaxation time at temperature T K , r0 = relaxation time at infinite temperature. If the temperature of the maximum loss is denoted T(max), then
o '_o 1.6 %
1,2
A = (G~ (max) - - G~(max))T(max) and
I -150
AH
I
(2)
"rmax= r °exP ( R T ~ a x ) )
I -IIO
I
I
i
I
-70 Tempzroture (°C)
I
I
-30
I
*10
Figure 2 Evaluation of G~tmax) and G~(max)
Gv and G~ are the unrelaxed and relaxed values of shear modulus respectively. Schallamach n showed that tOrmax differs only slightly from unity, which is the value predicted by the single relaxation time model, and also that co70<1 for the frequencies normally encountered, thus a combination of equations (1) and (2) leads to the following result:
9-O m
7"0-
AH= LGRr ~/'(max) _ Gu~'(max)]~
R~r
qo 0,, 4E
/
S'O-
U
¢-
/
-
L~ 3-0--
Thus the area under the G" versus lIT curve and the extrapolated values of Gv and GR at T(max) are the only experimental quantities required. Unfortunately equation (3) is limited in applicability. Two curves of loss modulus are shown in Figure 1 for a system of D G E B A hardened with 11 parts of TETA (by weight) per hundred parts of resin (phr). It is apparent that the curve representing 19°C cure has two widely differing values of loss modulus. This renders the construction of a baseline open to considerable conjecture and for curves of this form no activation energy was calculated. The area under the curve for 159°C cure is well defined and was measured. Measurements of area were made using a planimeter. G~(max) and G~ (max) were found by extrapolation to T(max) using values of Gtr and GR at temperatures at which the baseline of the G" versus lIT curve intersected G", as shown in Figure 2.
\
/
m
l'O--
l
2.0
I
l
4"0
I
6'0
I03
(3)
l
8-0
(K)
T
Figure 1 Loss modulus for two states of cure. O, 2h at 159°C; A, cured at room temperature
RESULTS Values of activation energy are given in Table 1 for cure temperatures above 70°C, where the areas under the loss modulus curves are well defined.
POLYMER, 1972, Vol 13, September
4.51
Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake Table 1 Activation energies for cure temperatures above 70°C
16
Activation
energy
Cure temp, (°C)
(kcal/mol)
76"3 93"9
15"2 17"9
118'0
18"8
159'0
17"8
12
8
The value obtained at a cure temperature of 159°C is lower than the one at 118.8°C and this is due to the onset of degradationlL The results would seem to suggest that the activation energy increases with increasing crosslinking density and this is borne out as shown in the following section. Modulus/temperature curves were also obtained at differing frequencies and it was found that the temperature of the y-relaxation, in a system of D G E B A cured to a true equilibrium state with 11 phr of TETA, moved from about - 4 5 ° C when measured at 0.67 Hz to about 65°C when measured at 1.25 MHz. The good superposition of curves obtained at different frequencies signified that the activation energy of the y-process does not depend on temperature in contrast to the glass/rubber transition where the activation energy is strongly dependent on temperature. Hence equation (2) can be rewritten to yield the activation energy by measuring the shift in temperature of the relaxation when observed at a different frequency. This is expressed as:
AH=(
R
c
4i
I
I o.4
o
I (il~-
I o.8
I
I I. 2
I
1 I. 6
l i t 2 ), fO 3 {K)
Determination of activation energy from data at four
Figure 3
frequencies
co2
1 - - 1 '~1n~--11
(4)
where oJ1, oJ2 are the measuring frequencies and Tz, Ts are the temperatures of the y-relaxation when observed at oJ1 and ~oz respectively. Results are shown in Figure 3, the slope of which yields an activation energy of 17.9kcal/ mol. This is in very good agreement with the value found by the loss modulus analysis on the same resin system.
1_,
DEPENDENCE OF ACTIVATION ENERGY ON STATE OF CURE The loss modulus analysis suggested that the activation energy decreased with decreasing degree of cure and a detailed investigation was therefore made on the relationship between activation energy and state of cure. Curves of shear modulus as a function of temperature measured at 30 kHz were obtained on the system D G E B A cured with the stoichiometric quantity of TETA at various temperatures. Some of these curves are shown in Figure4. The modulus and temperature were recorded at the point of inflection for each curve. A small section of the cylindrical specimen used in the resonance technique was then inserted into the transit time equipment operating at 1.25MHz. The temperature was then altered until the measured velocity yielded a modulus value identical to that noted at the inflection point. Use of the Arrhenius relationship then allowed calculation of the activation energy. Results are illustrated in Figure 5. It was tempting, although not justifiable, to draw a sigmoid through the points because apart from the results at 25°C and 80°C
452
POLYMER,
1972, V o l 13, S e p t e m b e r
,
-70
-30
*10 "50 Temperoture (°C)
'90
Figure 4 Shear modulus measured at 30kHz for various states of cure. (The anomaly in the curve for room temperature cure is due to post cure during test.) O, Room temperature cure; A, 65°C cure for 2h; x , 100°C cure for 2h; 17,130°C cure for2h
24
0 0
0
I
I
0
0
0
8
o
o
l
20
I
I
6(3 I00 Cure tcrnperotur¢ (°C)
I
140
I
I
IBO
Figure 5 Activation energy of the y-relaxation as a function of cure temperature. Cured 30min at each temperature
Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake +30
0
0
0
the stoichiometric quantity is less than for resins cured with higher concentrations of hardener.
A
L) O
DISCUSSION
*I0 E
-30 I
I 6
I
I I 8 EDA (phr)
I IO
I
I 12
Figure 6 Temperature of the y-relaxation for varying quantities of hardener
28 0
0
o
E20 "6 u O O
<3 12
I
4
6
I
I
8 EDA (phr)
I
I
lO
[
t
t
12
Figure 7 Activation energy of the y-relaxation for different amounts
of hardener
the others lie on a smooth sigmoidal-shaped curve. The determination of activation energies of resins with a small degree of crosslinking is more inaccurate than for fully cured material owing to the greater uncertainty in determining the temperature of inflection on the modulus/ temperature curve. The upper value of about 23 kcal/mol for the fully cured resin is much higher than the value of 17.9 kcal/mol found using four frequencies and the reason for the difference is that a stoichiometric quantity of hardener was used in the former case whereas only 11 phr was used in the latter, resulting in a higher density of crosslinking. This was checked by measuring the activation energy in systems containing varying quantities of hardener in which an equilibrium state of cure has been achieved. EDA was used rather than TETA owing to the greater ease of preparation of specimens utilizing the former constituent. The temperature of the relaxation, determined by the inflection point, was plotted as a function of EDA concentration and is shown in Figure 6. These results are similar in form to those obtained using a torsion pendulum where tanSmax was plotted against cure temperature. The activation energy was determined and results are presented in Figure 7 where it is demonstrated that the activation energy for a resin cured with less than
The results lend striking support for the proposed mechanism of cure outlined in Part 1 a. Here it was postulated that crosslinks are initiated at widely dispersed sites in the network but as the number increase, potentially reactive segments are sterically hindered from diffusing to other reactive sites and to overcome this barrier more thermal energy must be supplied to the network. This mechanism is certainly borne out by the results shown in Figure 5 in which the activation energy is seen to increase until a curing temperature of 140°C is attained when it becomes constant. These results illustrate the importance of knowing the state of cure when determining activation energies and the values of 16kcal/mol reported by Kreahling and Klines, and of 14 kcal/mol by Van Hoorn 4 are not meaningful because these workers failed to realize that an increase in crosslinking density inhibits the yrelaxation, thus increasing the apparent activation energy, and they do not stipulate the state of cure to which those energies refer. If Figure 5 is assumed to be sigmoidal, then the apparently constant value of about 14kcal/mol for low degrees of cure must be indicative of the energy necessary for the glycidyl ether segment to relax and any value above this represents the extra energy needed to overcome the increasing steric hindrance as more crosslinks are formed. If a crankshaft-type relaxation mechanism is assumed then the lower value certainly agrees well with the value of 13 kcal/mol calculated by Schatzki 7 based on twice the butane potential barrier plus a van der Waals barrier determined from cohesive energy density. However, the relaxation temperature for methylene sequences is about - 120°C when measured at 1 Hz and because the ~,-relaxation in epoxy resin occurs at a higher temperature, owing to the hindrance of the pendant hydroxyl, the activation energy assuming a crankshaft model would be expected to be higher than the 13 kcal/mol proposed by Schatzki. Thus the crankshaft model does not seem to be realistic from energy considerations and it is suggested that the relaxation is governed by hindered rotation in a double potential well whose height above about 14kcal/ mol is determined by the extent of steric hindrance caused by an increase in crosslinking density. It is interesting to note that the form of the curves shown in Figures 6 and 7 is identical adding further weight to the proposed curing mechanism. Also apparent is the fact that the activation energy for the relaxation in a resin fully cured with the stoichiometric quantity of EDA is higher than one cured with TETA, i.e. 26 as compared with 23 kcal/mol. This would seem to signify that the stiffness of the hardener chain influences the relaxing segment. The EDA chain is about half the length of a molecule of TETA and probably less mobile although in both hardeners reactive hydrogen atoms are separated by two (CH2) units. Nonetheless the longer chain is expected to exhibit greater flexibility. Delatycki et al. 5 examined a series of epoxy-diamine networks using a low frequency torsion pendulum and found that the temperature of the ~,-relaxation remained constant for diamines containing up to 12 methylene groups, although the height of the loss modulus/temperature curve decreased with increasing chain length. This suggests that the activation energy of the relaxation
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Mechanical relaxation of epoxy resin cure (2): R. G. C. Arridge and J. H. Speake decreased with increasing chain length. In view of the results presented in our paper it is surprising that the relaxation temperature remained constant because the change in steric hindrance arising from the change in crosslinking density when the hardener is varied might be expected to shift the relaxation along the temperature axis. This could be checked by employing an ultrasonic test method for measuring the loss modulus where any change in activation energy would be shown up by a spread of relaxation temperatures even though the temperature remained constant in the low frequency test.
is determined by the crosslinking density and is found to be higher in systems where short chains are reacted. ACKNOWLEDGEMENTS This work was supported by the Procurement Executive, Ministry of Defence. We should also like to thank the NDT Centre, Harwell for providing the experimental facilities. REFERENCES
CONCLUSION The dependence of the activation energy of the yrelaxation on the state of cure demonstrates the part played by steric hindrance on the relaxation mechanism. For low degrees of cure the activation energy of the y-process is fairly constant and of the order of 13 kcal/mol. It must be remembered that this value is obtained in a system which has already undergone about 70 % of the total crosslinking reaction. It is unlikely that 100 % of the reaction is ever achieved and so the large part played by steric effects in the later stages is rather surprising. The limiting value of activation energy in a fully cured system
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1 Pogany, G. A. Polymer 1970, 11, 66 2 May, C. A. and Weir, F. E. SPE Trans. 1962 (July) p 207 3 Kline, D. E. J. Polym. Sci. 1960, 47, 237 4 Van Hoorn, H. J. Appl. Polym. Sci. 1968, 12, 871 5 Delatycki, O., Shaw, J. C. and Williams, J. G. J. Polym. Sci. (.4-2) 1969, 7, 753 6 Cuddihy, E. F. and Moacanin, J. J. Polym. Sci. (4-2) 1970, 8, 1627 7 Schatzki, T. F. J. Polym. Sci. 1962, 57, 496 8 Kreahling, R. P. and Kline, D. E. J. ,4ppl. Polym. Sci. 1969, 13, 2411 9 Arridge, R. G. C. and Speake, J. H. Polymer 1972, 13, 443 10 Read, B. E. and Williams, G. Trans. Faraday Soc. 1961,57,1979 11 Schallamach, A. Trans. Faraday Soc. 1946, A42, 495 12 Pogany, G. A. DPhil Thesis Oxford University, 1966