# Viscoelastic behavior of poly(cyanate epoxy).

INTRODUCTION

A lot of work has been devoted to the study of anelastic properties of polyepoxies with semiflexible sequences. Various empirical relationships or molecular theories have been proposed for describing the broad relaxation and retardation modes observed in those polymers. Another approach is by thermostimulated creep: in this case, the complex retardation modes are resolved into elementary processes that can be characterized by their retardation times. With this technique, we have previously shown the complexity of localized molecular mobility in polyepoxies such as DGEBA-DDM (1-3), DGEBA-DDA (4) and TG-DDM-DDS (5).

As for the retardation mode associated with the glass transition, it has been characterized by a distribution of retardation times obeying a compensation law with a compensation time of some tens of seconds and a compensation temperature [T.sub.c] [similar to] [T.sub.g] + 10 [degrees] C (6-9). Such behavior has been also observed in thermoplastics with flexible and semiflexible chains with [T.sub.g]s lying in the vicinity of 100 [degrees] C (10).

The need for thermostable polymers prompts materials researchers to consider polymers with rigid chains, i.e., with a much higher [T.sub.g]. Special attention has been paid to thermosets based on cyanate resins (11). They have higher moduli than polyepoxy and [T.sub.g]s from 200 to 290 [degrees] C. Moreover, they are hydrophobic ([less than]1% of water uptake). Finally, during polymerization, they exhibit a low exothermicity. For maintaining polymerization conditions analogous with those of polyepoxy, epoxy has been added to cyanate, giving poly(cyanate epoxy), CE.

In this paper, viscoelastic properties of poly(cyanate epoxy) have been studied by dynamic mechanical analysis (DMA). The dynamic loss compliance deduced from DMA has been compared with the one calculated from thermostimulated creep (TSC) data. We have also extracted from TSC the distribution of the activation enthalpy. Those values have allowed us to identify localized and delocalized movements. The cooperativity of molecular mobility has been also analyzed, and a discussion on the specificity of polymers with rigid chains is presented.

MATERIALS AND METHODS

Materials

Among thermosets, cyanate resins have specific advantages:

* The [T.sub.g] lies in the vicinity of 180 [degrees] C;

* Their water uptake is 1%;

* The polymerization conditions are interesting:

* [approximately]no volatile compounds;

* [approximately]low exothermicity.

The introduction of epoxides allows a lower polymerization temperature and also reduces the cost of resins.

Of major interest are the thermomechanical properties of poly(cyanate epoxy). The rigidity of this thermoset is mainly due to the existence of triazine rings formed by tripolymerization of dicyanate monomers, as shown in Fig. 1. For clarity, the bisphenol A groups are represented by R. The cyclopolymerization is achieved by curing in an autoclave. Sheets 0.5 mm thick were prepared for this study by Hexcel Genin.

Dynamic Mechanical Analysis

Dynamic mechanical analysis (DMA) was performed using the torsion excitation mode. The variation of the G[prime] modulus and tan [Delta] were recorded as a function of temperature at 1 Hz using a Rheometrics RDC 7700. The heating rate was 3 K/min.

Thermostimulated Creep

The principle of thermostimulated creep (TSC) is the following: A static shear stress is applied to the sample, in the torsion mode, at a given temperature T[Sigma]; for 2 min. Then, the sample is quenched in order to freeze this configuration. The stress is cut off and the temperature is increased at a rate of 7 K/min. The return to equilibrium of the sample is followed by recording the rate of change of the deformation [Mathematical Expression Omitted] as a function of temperature. For purposes of comparison, [Mathematical Expression Omitted] has been normalized to the applied stress [Sigma]: [Mathematical Expression Omitted] versus temperature T is designated as TSC spectrum.

The TSC setup used for the experiments is described elsewhere (12).

DYNAMIC MECHANICAL ANALYSIS

In the low temperature region, it is difficult to obtain a significant variation of G[prime] and tan [Delta] for CE. Nevertheless, Fig. 2 shows the existence of a broad relaxation mode with a maximum around -94 [degrees] C. According to the literature nomenclature, it has been designated as the [Beta] mode.

It is interesting to note the value of the static modulus: 2 GPa.

In the high temperature region, a relaxation mode is observed in the vicinity of the [T.sub.g], as shown in Fig. 3: its maximum Is located around 212 [degrees] C. It must be noted that the corresponding variation of G[prime] is strongly asymmetric. The temperature position together with the magnitude indicate that it corresponds to the anelastic manifestation of the [T.sub.g] that Is usually designated as the [Alpha] mode.

THERMOSTIMULATED CREEP

Complex TSC Spectra

For observing the low temperature relaxation mode, the shear stress has been applied at T[Sigma] = 50 [degrees] C. As shown in Fig. 4, a complex relaxation mode is observed at - 120 [degrees] C: because of its temperature position and low magnitude, it has been associated with the [Beta] mode.

For the high temperature relaxation mode, the loading stress has been applied at T[Sigma] = 230 [degrees] C. Then, a reproducible relaxation mode is observed at 224 [degrees] C (cf. Fig. 5). It is the a mode associated with [T.sub.g].

Elementary TSC Spectra

The complex [Beta] and [Alpha] modes have been resolved into elementary TSC peaks.

[Beta] Mode

The fractional loading procedure has been applied in the temperature range - 150 [degrees] C to 30 [degrees] C so that i varies from 1 to 25: the series of elementary peaks are represented in Fig. 6.

[Alpha] Mode

The explored temperature range is 110-240 [degrees] C so that i varies from 1 to 27. The series of elementary peaks shown by Fig. 7 have an envelope that is analogous with the complex TSC peak (cf. Fig. 5).

Activation Parameters

Each elementary spectrum can be analysed by making the hypothesis of a monokinetic process. Then, the analysis gives the real compliance [Delta][J.sub.1], and the retardation time [[Tau].sub.i](T). By plotting [[Tau].sub.i](T) on an Arrhenius diagram, we have found that for both [Beta] and [Alpha] modes, all the elementary retardation times follows an Arrhenius law:

[[Tau].sub.i](T) = [[Tau].sub.oi] exp [Delta][H.sub.i]/kT (1)

where [[Tau].sub.oi] is the pre exponential factor, and [Delta][H.sub.i] is the activation enthalpy.

[[Tau].sub.oi] and [Delta][H.sub.i] are valid around [T.sub.mi], temperature of the TSC maximum for the i process. By analogy with dynamic mechanical relaxation, we can associate an equivalent frequency [f.sub.ieq] to [[Tau].sub.i] ([T.sub.mi]) by the following relationship: [f.sub.ieq] [equivalence] 1/2[Pi][[Tau].sub.i]([T.sub.mi]) It is important to note that [f.sub.ieq] remains quasiconstant when i varies so that [f.sub.eq] [similar to] [10.sup.-3] Hz can be considered as the equivalent frequency of the complex spectrum.

DISCUSSION

Comparison of Relaxation and Retardation Modes

The parameters extracted from the analysis of elementary TSC spectra allow us to calculate the complex compliance or the complex modulus as a function of angular frequency [Omega] and temperature T. We will show here the loss compliance [J[double prime].sub.TSC]. For each i elementary process, [J[double prime].sub.i] is obtained by using the Kelvin-Voigt model:

[J[double prime].sub.iTSC]([Omega], T) = [Delta][J.sub.i][Omega][[Tau].sub.i](T) / 1 + [[[Omega][[Tau].sub.i](T)].sup.2]

Then, by making the summation over all the elementary processes, the loss compliance [J[double prime].sub.TSC] of the polymer is obtained: [J[double prime].sub.TSC]([Omega], T) = [[Sigma].sub.i][J[double prime].sub.i]([Omega], T).

Low Temperature Mode

For the [Beta] mode, [J[double prime].sub.TSC] (T) has been calculated for various frequencies: Fig. 8 shows the isofrequency 1 Hz (solid line).

In dynamic mechanical relaxation, [J[double prime].sub.DMA] can be calculated from G[prime] and tan [Delta] since

[J[double prime].sub.DMA] = 1 / G[prime] tan [Delta] / 1 + [(tan [Delta]).sup.2]

From the isofrequencies 1 Hz of G[prime] and tan [Delta], [J[double prime].sub.DMA] has been calculated at 1 Hz; it is plotted for comparison in Fig. 8 (dashed line).

Before any quantitative comparison, it is important to note that TSC is sensitive only to anelastic phenomena since a driving force is necessary to recover the strain; tan [Delta] given by DMA reflects all types of damping, including hysteresis phenomena, which cannot be observed by DSC.

Consequently, J[double prime] (DMA) is overestimated, leading to a difference with J[double prime] (TSC), which is relatively important because of the low internal friction for secondary relaxation. Moreover, the discrepancy observed on the low temperature side can be explained by the lack of sensitivity of measurements in this temperature range.

The position of the [Beta] peak from DMA and TSC is coherent.

High Temperature Mode

The comparison of [J[double prime].sub.TSC] (T) (solid line) and [J[double prime].sub.DMA] (T) (dashed line) at 1 Hz for the [Alpha] mode is represented in Fig. 9. The shift of 4 [degrees] for the positions of the loss peaks can be associated with the difference in the thermal history due to experimental procedures: Indeed, for recording TSC, the loading stress is applied at 230 [degrees] C for 2 min so that the curing process goes on.

The shift of the [Alpha] peak can be approximated by an Arrhenius equation: the corresponding apparent activation enthalpy is 4.2 eV. This value is close from the activation enthalpy of peak 19, which is close to the maximum.

Localization of Molecular Mobility

Starkweather (13) has proposed a criterion for identifying localized and delocalized movements: for localized movements, the activation entropy is negligible so that the activation enthalpy is given by:

[Delta]H = kT ln{kT / 2[Pi][f.sub.eq]h} (2)

where h is the Planck's constant.

For delocalized movements, the activation enthalpy is increased because of the entropic term.

We have plotted in Figs. 10 and 11 the temperature variation of the activation enthalpy deduced form TSC elementary spectra for the [Beta] and [Alpha] modes, respectively. We have also indicated (dashed line) the Eyring-Starkweather line (Eq 2).

Most of the experimental points corresponding to the [Beta] mode are well described by the Eyring-Starkweather line: the corresponding processes are localized. Contrarily, most of the experimental points belonging to the [Alpha] mode diverge from the Eyring-Starkweather line: this mode corresponds to delocalized movements. Such a result has been also observed in a wide series of polymers.

Cooperativity of Molecular Mobility

For cooperative modes, the relaxation times follow a compensation law:

[[Tau].sub.i](T) = [[Tau].sub.c] exp{[Delta][H.sub.i]/k(1/T - 1/[T.sub.c])} (3)

where [[Tau].sub.c] is the compensation time and [T.sub.c] is the compensation temperature.

In that case, ln [[Tau].sub.oi] is a linear function of [Delta][H.sub.i]. So, for identifying cooperative movements, the experimental points have been reported on a compensation diagram where ln [[Tau].sub.oi] is plotted as a function of [Delta][H.sub.i]. Figures 12 and 13 correspond, respectively, to the [Beta] and [Alpha] modes. In both cases, the compensation lines have been indicated (dashed line). Note that i indicated in the vicinity of the experimental points varies always in a monotonous manner on a compensation line. Evidently, the [Beta] mode has a fine structure: four sub modes can be distinguished; they have been designated as [[Beta].sub.1], [[Beta][double prime].sub.2], [[Beta][prime].sub.2] and [[Beta].sub.2] in the order of increasing temperature. Contrarily, the [Alpha] mode has no fine structure since the experimental points that do not belong to the compensation line (open dots) are at random.

Origin of Molecular Mobility

[Beta] Mode

First, the origin of the localized [Beta] mode will be discussed.

[[Beta].sub.1] sub mode. It is constituted of elementary processes situated between -138 and -180 [degrees] C and the activation enthalpy ranging between 0.32 and 0.57 eV. It is interesting to note here that such a sub mode has been found in other polymers containing diphenylpropane groups (1-5, 14-17). Vibrations of phenyl groups in diphenylpropane units might be involved in this sub mode.

[[Beta][double prime].sub.2] sub mode. The constituting elementary processes are located in the temperature range -109, -90 [degrees] C and the corresponding activation enthalpies vary only by 0.1 eV. This sub mode that is only found in poly(cyanate epoxy) has not been assigned to a definite entity.

[[Beta][prime].sub.2] sub mode. The elementary peaks constituting this sub mode are situated between -88 and -67 [degrees] C; the activation enthalpies vary from 0.48 to 0.61 eV. An analogous sub mode has been observed in other poly epoxies(TGDDM/DDS and DGEBA/DDM). The molecular mobility seems to involve the opening site where polymerization takes place (1-5).

[[Beta].sub.2] sub mode. The values of [T.sub.mi] for the constituting peaks range from -65 to -24 [degrees] C, and the activation enthalpies are between 0.55 and 0.89 eV. Analogous sub modes are observed in polyepoxy (1-5) but it is difficult to assign them to definite entities.

The processes constituting the [Beta] mode can be excited by frequencies in the kHz range around room temperature. This means that, upon impact, the corresponding molecular mobility dissipates energy in a reversible way.

[Alpha] Mode

The second part of this discussion on the origin of molecular mobility is devoted to the delocalized [Alpha] mode.

It is important to note here that the cooperativity is very well obeyed, since 17 elementary processes follows the compensation law. The values of the compensation parameters are also interesting: the compensation time - [[Tau].sub.c] = 0.03 s - is low regarding the values of [[Tau].sub.c] for polymers with flexible chain (10). Such values of [[Tau].sub.c] are observed when strong interactive forces intervene.

The compensation temperature for CE is [T.sub.c] = 243 [degrees] C, i.e. [T.sub.c] [similar to] [T.sub.g] + 63 [degrees] C. For polymers with flexible chains, the lag between [T.sub.c] and [T.sub.g] is [approximately]30 [degrees] C (10). Since the compensation temperature is close to the maximum temperature of the TSC peak, the width of this peak is restricted despite the broad distribution of activation enthalpy.

With the cooperative [Alpha] mode, we are dealing with movement that propagates along the chain. According to the model of Hoffman, Williams, and Passaglia (18), the larger the activation enthalpy, the larger the mobile unit. The rigidity of poly(cyanate epoxy) is probably responsible for the delocalization of the movement.

An interpretation of the compensation law on the basis of a theoretical model describing the molecular mobility of amorphous polymers has been proposed by Perez et al. (19). In this theory, the width of the distribution function of relaxation times is minimum at the compensation temperature. Rather high values of activation enthalpy (1.42 to 5.22 eV) and low values of the pre-exponential factor ([10.sup.-17] to [10.sup.-52] s) might be explained by low values of correlation parameter. The strong correlation predicted by this theory perfectly reflects the very rigid structure of poly(cyanate epoxy).

CONCLUSION

The viscoelastic behavior of a thermostable thermoset poly(cyanate epoxy) has been analyzed by dynamic mechanical analysis and thermostimulated creep.

The low temperature relaxation and retardation modes are due to localized movements involving tie points or phenyls in diphenylpropane groups. Cooperative sub-modes can be distinguished. From the extracted parameters, we have seen that dissipative processes take place in the kHz region at room temperature.

The high temperature relaxation and retardation modes correspond to the anelastic manifestation of the [T.sub.g]. The activation enthalpy distribution is very broad, indicating a strong delocalization of molecular mobility. The compensation phenomenon in polymers with rigid chains is characterized by compensation parameters with low values of [[Tau].sub.c] and large values of lag between [T.sub.c] and [T.sub.g].

REFERENCES

1. J. Boye, J. J. Martinez, C. Lacabanne, B. Chabert, and J. F. Gerard, Annales des Composites, 13 (1990).

2. J. Boye, J. J. Martinez, D. Chatain, and C. Lacabanne, J. Thermal Anal., 37, 1795 (1991).

3. J. Boye, PhD thesis, Universite Paul Sabatier, Toulouse, France (1990).

4. A. Dufresne, PhD thesis, Universite Paul Sabatier, Toulouse, France (1991).

5. L. Michel, PhD thesis, Universite Paul Sabatier, Toulouse, France (1990).

6. J. Boye, J. J. Martinez, C. Lacabanne, B. Chabert, and J. F. Gerard, in Basic Features of the Glassy State, p. 350, World Scientific Pub. Co. (1990).

7. J. Boye, J. J. Martinez, Ph. Demont, and C. Lacabanne, Thermochimica Acta, 192, 147 (1991).

8. J. Boye, J. J. Martinez, C. Lacabanne, P. Perret, B. Chabert, and J. F. Gerard. Polymer, 30, 2, 323 (1992).

9. C. Lavergne, A. Dufresne, D. Chatain, and C. Lacabanne, J. Thermal Anal., 40, 705 (1993).

10. C. Lacabanne, A. Lamure, G. Teyssedre, A. Bernes, and M. Mourgues, J. Non Crystalline Solids, 172-174, 884 (1994).

11. V. P. McConnell, Adv. Compos. J., 28-37 (1992).

12. J. C. Monpagens, D. Chatain, C. Lacabanne, and P. Gautier, J. Polym. Sci. Phys. Ed., 15, 541 (1977).

13. M. L. Williams, R. F. Landel, and J. D. Ferry, J. Am. Chem. Soc., 77, 3701 (1955).

14. H. W. Starkweather, Macromolecules, 23, 328 (1990).

15. V. B. Gupta, L. T. Drzal, and C. Y. C. Lee, J. Macromol. Sci., B22, 4-6, 435 (1985).

16. T. Takahama, C. S. Wu, A. Chen, S. Pangrele, and P. H. Geil, Polym. Compos., 7, 348 (1986).

17. J. E. Fried, A. Letton, and W. J. Welsh, Polymer, 31, 1032 (1990).

18. J. D. Hoffman, G. Williams, and E. Passaglia, J. Polym. Sci., Part C14, 141 (1965).

19. J. Perez and J. Y. Cavaille, J. Phys., III 5, 791 (1995).

A lot of work has been devoted to the study of anelastic properties of polyepoxies with semiflexible sequences. Various empirical relationships or molecular theories have been proposed for describing the broad relaxation and retardation modes observed in those polymers. Another approach is by thermostimulated creep: in this case, the complex retardation modes are resolved into elementary processes that can be characterized by their retardation times. With this technique, we have previously shown the complexity of localized molecular mobility in polyepoxies such as DGEBA-DDM (1-3), DGEBA-DDA (4) and TG-DDM-DDS (5).

As for the retardation mode associated with the glass transition, it has been characterized by a distribution of retardation times obeying a compensation law with a compensation time of some tens of seconds and a compensation temperature [T.sub.c] [similar to] [T.sub.g] + 10 [degrees] C (6-9). Such behavior has been also observed in thermoplastics with flexible and semiflexible chains with [T.sub.g]s lying in the vicinity of 100 [degrees] C (10).

The need for thermostable polymers prompts materials researchers to consider polymers with rigid chains, i.e., with a much higher [T.sub.g]. Special attention has been paid to thermosets based on cyanate resins (11). They have higher moduli than polyepoxy and [T.sub.g]s from 200 to 290 [degrees] C. Moreover, they are hydrophobic ([less than]1% of water uptake). Finally, during polymerization, they exhibit a low exothermicity. For maintaining polymerization conditions analogous with those of polyepoxy, epoxy has been added to cyanate, giving poly(cyanate epoxy), CE.

In this paper, viscoelastic properties of poly(cyanate epoxy) have been studied by dynamic mechanical analysis (DMA). The dynamic loss compliance deduced from DMA has been compared with the one calculated from thermostimulated creep (TSC) data. We have also extracted from TSC the distribution of the activation enthalpy. Those values have allowed us to identify localized and delocalized movements. The cooperativity of molecular mobility has been also analyzed, and a discussion on the specificity of polymers with rigid chains is presented.

MATERIALS AND METHODS

Materials

Among thermosets, cyanate resins have specific advantages:

* The [T.sub.g] lies in the vicinity of 180 [degrees] C;

* Their water uptake is 1%;

* The polymerization conditions are interesting:

* [approximately]no volatile compounds;

* [approximately]low exothermicity.

The introduction of epoxides allows a lower polymerization temperature and also reduces the cost of resins.

Of major interest are the thermomechanical properties of poly(cyanate epoxy). The rigidity of this thermoset is mainly due to the existence of triazine rings formed by tripolymerization of dicyanate monomers, as shown in Fig. 1. For clarity, the bisphenol A groups are represented by R. The cyclopolymerization is achieved by curing in an autoclave. Sheets 0.5 mm thick were prepared for this study by Hexcel Genin.

Dynamic Mechanical Analysis

Dynamic mechanical analysis (DMA) was performed using the torsion excitation mode. The variation of the G[prime] modulus and tan [Delta] were recorded as a function of temperature at 1 Hz using a Rheometrics RDC 7700. The heating rate was 3 K/min.

Thermostimulated Creep

The principle of thermostimulated creep (TSC) is the following: A static shear stress is applied to the sample, in the torsion mode, at a given temperature T[Sigma]; for 2 min. Then, the sample is quenched in order to freeze this configuration. The stress is cut off and the temperature is increased at a rate of 7 K/min. The return to equilibrium of the sample is followed by recording the rate of change of the deformation [Mathematical Expression Omitted] as a function of temperature. For purposes of comparison, [Mathematical Expression Omitted] has been normalized to the applied stress [Sigma]: [Mathematical Expression Omitted] versus temperature T is designated as TSC spectrum.

The TSC setup used for the experiments is described elsewhere (12).

DYNAMIC MECHANICAL ANALYSIS

In the low temperature region, it is difficult to obtain a significant variation of G[prime] and tan [Delta] for CE. Nevertheless, Fig. 2 shows the existence of a broad relaxation mode with a maximum around -94 [degrees] C. According to the literature nomenclature, it has been designated as the [Beta] mode.

It is interesting to note the value of the static modulus: 2 GPa.

In the high temperature region, a relaxation mode is observed in the vicinity of the [T.sub.g], as shown in Fig. 3: its maximum Is located around 212 [degrees] C. It must be noted that the corresponding variation of G[prime] is strongly asymmetric. The temperature position together with the magnitude indicate that it corresponds to the anelastic manifestation of the [T.sub.g] that Is usually designated as the [Alpha] mode.

THERMOSTIMULATED CREEP

Complex TSC Spectra

For observing the low temperature relaxation mode, the shear stress has been applied at T[Sigma] = 50 [degrees] C. As shown in Fig. 4, a complex relaxation mode is observed at - 120 [degrees] C: because of its temperature position and low magnitude, it has been associated with the [Beta] mode.

For the high temperature relaxation mode, the loading stress has been applied at T[Sigma] = 230 [degrees] C. Then, a reproducible relaxation mode is observed at 224 [degrees] C (cf. Fig. 5). It is the a mode associated with [T.sub.g].

Elementary TSC Spectra

The complex [Beta] and [Alpha] modes have been resolved into elementary TSC peaks.

[Beta] Mode

The fractional loading procedure has been applied in the temperature range - 150 [degrees] C to 30 [degrees] C so that i varies from 1 to 25: the series of elementary peaks are represented in Fig. 6.

[Alpha] Mode

The explored temperature range is 110-240 [degrees] C so that i varies from 1 to 27. The series of elementary peaks shown by Fig. 7 have an envelope that is analogous with the complex TSC peak (cf. Fig. 5).

Activation Parameters

Each elementary spectrum can be analysed by making the hypothesis of a monokinetic process. Then, the analysis gives the real compliance [Delta][J.sub.1], and the retardation time [[Tau].sub.i](T). By plotting [[Tau].sub.i](T) on an Arrhenius diagram, we have found that for both [Beta] and [Alpha] modes, all the elementary retardation times follows an Arrhenius law:

[[Tau].sub.i](T) = [[Tau].sub.oi] exp [Delta][H.sub.i]/kT (1)

where [[Tau].sub.oi] is the pre exponential factor, and [Delta][H.sub.i] is the activation enthalpy.

[[Tau].sub.oi] and [Delta][H.sub.i] are valid around [T.sub.mi], temperature of the TSC maximum for the i process. By analogy with dynamic mechanical relaxation, we can associate an equivalent frequency [f.sub.ieq] to [[Tau].sub.i] ([T.sub.mi]) by the following relationship: [f.sub.ieq] [equivalence] 1/2[Pi][[Tau].sub.i]([T.sub.mi]) It is important to note that [f.sub.ieq] remains quasiconstant when i varies so that [f.sub.eq] [similar to] [10.sup.-3] Hz can be considered as the equivalent frequency of the complex spectrum.

DISCUSSION

Comparison of Relaxation and Retardation Modes

The parameters extracted from the analysis of elementary TSC spectra allow us to calculate the complex compliance or the complex modulus as a function of angular frequency [Omega] and temperature T. We will show here the loss compliance [J[double prime].sub.TSC]. For each i elementary process, [J[double prime].sub.i] is obtained by using the Kelvin-Voigt model:

[J[double prime].sub.iTSC]([Omega], T) = [Delta][J.sub.i][Omega][[Tau].sub.i](T) / 1 + [[[Omega][[Tau].sub.i](T)].sup.2]

Then, by making the summation over all the elementary processes, the loss compliance [J[double prime].sub.TSC] of the polymer is obtained: [J[double prime].sub.TSC]([Omega], T) = [[Sigma].sub.i][J[double prime].sub.i]([Omega], T).

Low Temperature Mode

For the [Beta] mode, [J[double prime].sub.TSC] (T) has been calculated for various frequencies: Fig. 8 shows the isofrequency 1 Hz (solid line).

In dynamic mechanical relaxation, [J[double prime].sub.DMA] can be calculated from G[prime] and tan [Delta] since

[J[double prime].sub.DMA] = 1 / G[prime] tan [Delta] / 1 + [(tan [Delta]).sup.2]

From the isofrequencies 1 Hz of G[prime] and tan [Delta], [J[double prime].sub.DMA] has been calculated at 1 Hz; it is plotted for comparison in Fig. 8 (dashed line).

Before any quantitative comparison, it is important to note that TSC is sensitive only to anelastic phenomena since a driving force is necessary to recover the strain; tan [Delta] given by DMA reflects all types of damping, including hysteresis phenomena, which cannot be observed by DSC.

Consequently, J[double prime] (DMA) is overestimated, leading to a difference with J[double prime] (TSC), which is relatively important because of the low internal friction for secondary relaxation. Moreover, the discrepancy observed on the low temperature side can be explained by the lack of sensitivity of measurements in this temperature range.

The position of the [Beta] peak from DMA and TSC is coherent.

High Temperature Mode

The comparison of [J[double prime].sub.TSC] (T) (solid line) and [J[double prime].sub.DMA] (T) (dashed line) at 1 Hz for the [Alpha] mode is represented in Fig. 9. The shift of 4 [degrees] for the positions of the loss peaks can be associated with the difference in the thermal history due to experimental procedures: Indeed, for recording TSC, the loading stress is applied at 230 [degrees] C for 2 min so that the curing process goes on.

The shift of the [Alpha] peak can be approximated by an Arrhenius equation: the corresponding apparent activation enthalpy is 4.2 eV. This value is close from the activation enthalpy of peak 19, which is close to the maximum.

Localization of Molecular Mobility

Starkweather (13) has proposed a criterion for identifying localized and delocalized movements: for localized movements, the activation entropy is negligible so that the activation enthalpy is given by:

[Delta]H = kT ln{kT / 2[Pi][f.sub.eq]h} (2)

where h is the Planck's constant.

For delocalized movements, the activation enthalpy is increased because of the entropic term.

We have plotted in Figs. 10 and 11 the temperature variation of the activation enthalpy deduced form TSC elementary spectra for the [Beta] and [Alpha] modes, respectively. We have also indicated (dashed line) the Eyring-Starkweather line (Eq 2).

Most of the experimental points corresponding to the [Beta] mode are well described by the Eyring-Starkweather line: the corresponding processes are localized. Contrarily, most of the experimental points belonging to the [Alpha] mode diverge from the Eyring-Starkweather line: this mode corresponds to delocalized movements. Such a result has been also observed in a wide series of polymers.

Cooperativity of Molecular Mobility

For cooperative modes, the relaxation times follow a compensation law:

[[Tau].sub.i](T) = [[Tau].sub.c] exp{[Delta][H.sub.i]/k(1/T - 1/[T.sub.c])} (3)

where [[Tau].sub.c] is the compensation time and [T.sub.c] is the compensation temperature.

In that case, ln [[Tau].sub.oi] is a linear function of [Delta][H.sub.i]. So, for identifying cooperative movements, the experimental points have been reported on a compensation diagram where ln [[Tau].sub.oi] is plotted as a function of [Delta][H.sub.i]. Figures 12 and 13 correspond, respectively, to the [Beta] and [Alpha] modes. In both cases, the compensation lines have been indicated (dashed line). Note that i indicated in the vicinity of the experimental points varies always in a monotonous manner on a compensation line. Evidently, the [Beta] mode has a fine structure: four sub modes can be distinguished; they have been designated as [[Beta].sub.1], [[Beta][double prime].sub.2], [[Beta][prime].sub.2] and [[Beta].sub.2] in the order of increasing temperature. Contrarily, the [Alpha] mode has no fine structure since the experimental points that do not belong to the compensation line (open dots) are at random.

Origin of Molecular Mobility

[Beta] Mode

First, the origin of the localized [Beta] mode will be discussed.

[[Beta].sub.1] sub mode. It is constituted of elementary processes situated between -138 and -180 [degrees] C and the activation enthalpy ranging between 0.32 and 0.57 eV. It is interesting to note here that such a sub mode has been found in other polymers containing diphenylpropane groups (1-5, 14-17). Vibrations of phenyl groups in diphenylpropane units might be involved in this sub mode.

[[Beta][double prime].sub.2] sub mode. The constituting elementary processes are located in the temperature range -109, -90 [degrees] C and the corresponding activation enthalpies vary only by 0.1 eV. This sub mode that is only found in poly(cyanate epoxy) has not been assigned to a definite entity.

[[Beta][prime].sub.2] sub mode. The elementary peaks constituting this sub mode are situated between -88 and -67 [degrees] C; the activation enthalpies vary from 0.48 to 0.61 eV. An analogous sub mode has been observed in other poly epoxies(TGDDM/DDS and DGEBA/DDM). The molecular mobility seems to involve the opening site where polymerization takes place (1-5).

[[Beta].sub.2] sub mode. The values of [T.sub.mi] for the constituting peaks range from -65 to -24 [degrees] C, and the activation enthalpies are between 0.55 and 0.89 eV. Analogous sub modes are observed in polyepoxy (1-5) but it is difficult to assign them to definite entities.

The processes constituting the [Beta] mode can be excited by frequencies in the kHz range around room temperature. This means that, upon impact, the corresponding molecular mobility dissipates energy in a reversible way.

[Alpha] Mode

The second part of this discussion on the origin of molecular mobility is devoted to the delocalized [Alpha] mode.

It is important to note here that the cooperativity is very well obeyed, since 17 elementary processes follows the compensation law. The values of the compensation parameters are also interesting: the compensation time - [[Tau].sub.c] = 0.03 s - is low regarding the values of [[Tau].sub.c] for polymers with flexible chain (10). Such values of [[Tau].sub.c] are observed when strong interactive forces intervene.

The compensation temperature for CE is [T.sub.c] = 243 [degrees] C, i.e. [T.sub.c] [similar to] [T.sub.g] + 63 [degrees] C. For polymers with flexible chains, the lag between [T.sub.c] and [T.sub.g] is [approximately]30 [degrees] C (10). Since the compensation temperature is close to the maximum temperature of the TSC peak, the width of this peak is restricted despite the broad distribution of activation enthalpy.

With the cooperative [Alpha] mode, we are dealing with movement that propagates along the chain. According to the model of Hoffman, Williams, and Passaglia (18), the larger the activation enthalpy, the larger the mobile unit. The rigidity of poly(cyanate epoxy) is probably responsible for the delocalization of the movement.

An interpretation of the compensation law on the basis of a theoretical model describing the molecular mobility of amorphous polymers has been proposed by Perez et al. (19). In this theory, the width of the distribution function of relaxation times is minimum at the compensation temperature. Rather high values of activation enthalpy (1.42 to 5.22 eV) and low values of the pre-exponential factor ([10.sup.-17] to [10.sup.-52] s) might be explained by low values of correlation parameter. The strong correlation predicted by this theory perfectly reflects the very rigid structure of poly(cyanate epoxy).

CONCLUSION

The viscoelastic behavior of a thermostable thermoset poly(cyanate epoxy) has been analyzed by dynamic mechanical analysis and thermostimulated creep.

The low temperature relaxation and retardation modes are due to localized movements involving tie points or phenyls in diphenylpropane groups. Cooperative sub-modes can be distinguished. From the extracted parameters, we have seen that dissipative processes take place in the kHz region at room temperature.

The high temperature relaxation and retardation modes correspond to the anelastic manifestation of the [T.sub.g]. The activation enthalpy distribution is very broad, indicating a strong delocalization of molecular mobility. The compensation phenomenon in polymers with rigid chains is characterized by compensation parameters with low values of [[Tau].sub.c] and large values of lag between [T.sub.c] and [T.sub.g].

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Title Annotation: | French Research on Structural Properties of Polymers |
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Author: | Ponteins, P.; Medda, B.; Demont, P.; Chatain, D.; Lacabanne, C. |

Publication: | Polymer Engineering and Science |

Date: | Oct 1, 1997 |

Words: | 3006 |

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