# The Crystallization Kinetics of Polyamide 66 in Non-isothermal and Isothermal Conditions: Effect of Nucleating Agent and Pressure.

J. C. WON [1]

R. FULCHIRON [2][*]

A. DOUILLARD [2]

B. CHABERT [2]

J. VARLET [3]

D. CHOMIER [4]

The crystallization kinetics of virgin and nucleated polyamide 66 was investigated in non-isothermal and isothermal conditions, by use of DSC and high pressure dilatometry. In non-isothermal conditions, at atmospheric pressure, the results were first analyzed using the Ozawa equation, leading to an Avrami exponent of 4 in the case of the virgin grade and 2.1 for the nucleated polyamide. However, experimental and calculated kinetics showed a difference in the ending part of the crystallization, likely due to a large secondary crystallization phenomenon. Thus, the relative crystallinities were normalized to extract the primary crystallization from the whole signal and analyzed using the Douillard/Kim equation. In isothermal conditions, at atmospheric pressure, the Avrami exponents were similar to the values obtained in non-isothermal conditions for both virgin and nucleated grades. Furthermore, the crystallization under pressure was examined in terms of crystallization supercooling. In non-isothermal condition s, the crystallization supercooling ([delta]Tc) increases when the cooling rate increases, but it is not affected by the pressure since the crystallization temperature increase is due to the equilibrium melting temperature rise. In isothermal conditions, the supercooling ([delta]T) rises according to the increase of the pressure for the same crystallization temperature.

INTRODUCTION

Knowledge of the crystallization behavior of semi-crystalline polymers is of a great importance for the manufacture of plastic parts, because physical properties of polymers depend on the crystalline morphology of the material. Practically, industrial processes, like injection molding or compression molding for polymers, are carried out under high pressure. Moreover, many polyamide 66 grades contain nucleating agents in order to accelerate the solidification in the mold and so to increase the manufacturing efficiency. The crystallization kinetics of polyamide 66 has been largely investigated, with or without nucleating agents, at atmospheric pressure [1-4]. Nevertheless it becomes necessary to apprehend the effect of the pressure on the crystallization behavior [5-7].

Besides, as concerns the modeling of the crystallization kinetics, Ozawa (8), Nakamura (9, 10) and other authors (11-16) proposed different models, generally based on an extension of the Avrami equation (17-19) used for isothermal crystallization. Otherwise, Douillard/Kim (15, 16) carried out the modeling of the crystallization kinetics at constant cooling rate by empirical method.

Moreover, it is known that the PA66 crystallization exhibits both primary and secondary crystallizations. The secondary crystallization corresponds to different phenomena and is defined as happening neither by further germination nor by increase of the size of the spherulites. We can consider that it appears at the same time or after the primary crystallization (20-22). Nevertheless, in all cases, it becomes dominant in the final part of the crystallization since this phenomenon is related to the already transformed quantity.

In the present work, the crystallization kinetics of a virgin and a nucleated PA66 grades is studied, in isothermal and non-isothermal conditions and at atmospheric and high pressure.

EXPERIMENTAL

Materials

Two formulations of PA66, supplied by the Rhodia Nyltech Company, have been studied: a virgin grade and a commercial grade nucleated for injection productivity enhancement. The molecular weight of both grades was M[upsilon] = 33,000 g[cdotp][mol.sup.-1], determined by viscosimetry at 30[degrees]C in 90 vol% formic acid.

Thermal Measurements

At atmospheric pressure, the crystallization studies were carried out in non-isothermal and isothermal conditions using a Perkin-Elmer differential scanning calorimeter, DSC-7. The calibration was carried out at different scanning rates using standards such as indium and zinc. In order to specify the best conditions for removing the thermal history, different crystallization experiments at 10[degrees]C[cdotp][min.sup.-1] were first performed with various holding temperature and holding times in the molten state. For a holding time of 10 min, when the holding temperature is below 280[degrees]C, the crystallization temperature increases when the holding temperature decreases. Between 280 and 320[degrees]C the crystallization temperature appears independent of the holding temperature. On the other hand, when the holding temperature is above 330[degrees]C, the crystallization temperature decreases when the holding temperature increases because of the thermal degradation of the polymer. Therefore, for a temperatu re value of 290[degrees]C, the holding time can range between 10 and 15 minutes. Finally, the most appropriate experimental conditions for our studies were as follows:

* Holding temperature of the melting state: 290[degrees]C

* Holding time: 10 minutes

Dilatometric Measurements

The crystallization under pressure was analyzed by measuring the specific volume change using a PVT-100 apparatus from SWO Polymertechnik. With this device, the temperature can range between 30[degrees]C and 420[degrees]C with [+ or -] 0.3[degrees]C of accuracy and the pressure between 200 and 2500 bar with [+ or -] 5% of accuracy. It can work in isobaric or isothermal conditions and in cooling or heating procedures. The specific volume is calculated from the measurement of the length of the cylindrical sample located in the cell. The pressure is ensured by the hydraulic system, which controls the upper mobile piston. Between the pistons and the polymer, polyimide sealings are used to prevent polymer leakage. The pellets of polymer were introduced in the PVT cylindrical cell and then molten at 310[degrees]C during 10 minutes under the desired pressure. This temperature value was chosen higher than for DSC because of higher pressure. The behaviors of the virgin and nucleated grades have been stu died for cooling rates between 2.5[degrees]C . [min.sup.-1] and 15[degrees]C . [min.sup.-1] and for different pressures ranged between 200 and 2000 bar. Real scanning rate values can be calculated afterward from the result files including time. In isothermal conditions, the crystallization of the virgin and nucleated grades was analyzed between 250[degrees]C and 270[degrees]C at 400 and 800 bar.

RESULTS AND DISCUSSION

Non-isothermal Crystallization at Atmospheric Pressure

Several crystallization experiments were carried out with cooling rates from 2 to 30[degrees]C . [min.sup.-1]. When the cooling rate increases, the crystallization onset temperature decreases. The relative crystallinity for a temperature T was calculated by the integration of the crystallization peak (2):

X(T) = [[[integral].sup.T].sub.[T.sub.i]] (dH/dT)dT/[[[integral].sup.[T.sup.f]].sub.[T.sub.i]] (dH/dT)dT (1)

where [T.sub.i] and [T.sub.f] are the temperatures, respectively, of the onset and the end of the crystallization.

Figure 1 shows the evolution of the relative crystallinity versus temperature for different cooling rates. As expected, the onset temperature of crystallization for the nucleated grade is higher than for the virgin grade. Indeed, the nucleating agent increases the quantity of activated germs, which leads to a higher value for the starting crystallization temperature (23). Nevertheless, for the nucleated grade, the crystallization spreads on a larger temperature domain than for the virgin grade.

First, the Ozawa theory was applied for the crystallization modeling of polyamide 66.

1 - X(T) = exp [- K(T)/[[phi].sup.n]] (2)

where K(T) is the rate constant for the primary crystallization depending only on the temperature, [phi] is the cooling rate and n is the Avrami exponent. The parameters of Eq 2 were obtained by plotting Ln(-Ln(1-X(T)) versus Ln[phi] for different temperatures leading to straight lines of slope n and origin coordinate LnK(T).

For this analysis, the relative crystallinity X(T) was voluntarily limited between 5% and 50% to avoid the disruption caused by the secondary crystallization (4). For the virgin grade, we obtained an average value of n of 3.9 [+ or -] 0.6, which is in agreement with the sporadic germination and the spherulitic growth (n = 4) (24). Nevertheless in this case, the values of n appear scattered. For the nucleated grade, we obtained a value of 2.1 [+ or -] 0.2, lower than the theoretical value n = 3, generally expected for instantaneous germination due to the nucleating agent. However, the practically constant value of n (Fig. 2) means that the crystallization process is not changed in the considered temperature range. The rate constant K(T) is shown in Fig. 3.

The relative crystallinity curves calculated with Eq 2 do not entirely correspond to experimental results (see Fig. 1) because the Ozawa theory does not account for the secondary crystallization, which can occur while the primary crystallization is not finished (21, 22). However, the beginning of the crystallization is well fitted by the model, especially for the virgin grade.

The experimental relative crystallinity curves were also analyzed by means of the Douillard/Kim equation (16, 25):

X(T) = exp[f(T)]/1 + exp [f(T)], with f(T) = [alpha](T - [T.sub.c*MAX]) (3)

where f(T) = [alpha][T - [T.sub.C*MAX]) with [T.sub.C*MAX] corresponding to the temperature of the crystallization peak maximum (cooling rate dependent), and [alpha] being a cooling rate dependent parameter. From this equation, the plot of ln[X(T)/1-X(T)] versus T should lead to a straight line of slope [alpha]. Practically, in the case of our experimental results, this kind of plot exhibited two linear parts of different slopes (Fig. 4). It was assumed that the linear part in the higher temperature range was mainly characteristic of the primary crystallization, the other linear part being linked to the secondary crystallization process (much slower). Thus, the intersection of the two straight lines (see curve (a) in Fig. 4) was considered as the end of the primary crystallization. So, the relative crystallinity curves were renormalized in such a way that they became equal to unity for the temperature corresponding to this intersection.

Then, the equation of Douillard/Kim was applied on the normalized relative crystallinity curves. As shown in Fig. 5, the coefficient [alpha] decreases in absolute value when the cooling rate increases which corresponds to a narrower crystallization temperature range. The variation of this coefficient with the temperature can be described by:

[alpha] = [C.sub.1] + [C.sub.2]ln[phi] (4)

where [phi] is the cooling rate.

The temperature of the exothermic peak maximum [T.sub.C*MAX] according to the cooling rate is shown in Fig. 6. The evolution of [T.sub.C*MAX] can be well fitted by a second order polynomial of ln([phi]) (Douillard/Kim (16) used a linear function), as follows:

[T.sub.C*MAX] = [C.sub.3] + [C.sub.4]ln[phi] + [C.sub.5][(ln[phi]).sup.2] (5)

From Eqs 3, 4 and 5, the primary crystallization curves were calculated. As shown in Fig. 7, experimental plots are well described by the model, especially in the case of the virgin grade. However, for the nucleated grade, the agreement between experimental and calculated curves is slightly poorer.

Isothermal Crystallization at Atmospheric Pressure

The isothermal crystallization kinetics was described by the well-known Avrami equation.

X(t) = 1 - exp(-[kt.sup.n]) (6)

where k is the rate constant which depends on the temperature and n is the Avrami exponent. The parameters of Eq 6 were obtained by plotting Ln(- Ln(1 -X(t)) versus Lnt for different temperatures leading to straight lines of slope n and origin coordinate LnK. As previously, values of relative crystallinity lower than 50% were considered. Table 1 displays the Avrami exponent (n) and the rate constant k. As expected, the rate constant decreases when the crystallization temperature increases and the half-crystallization time ([t.sub.1/2]) increases very rapidly with the crystallization temperature.

For the virgin grade, an average value of n = 4.0 [+ or -] 0.3 was obtained, consistent with the theoretical value (n = 4) and the results of non-isothermal experiments. For the nucleated grade, a value of n of 1.7 [+ or -] 0.2 was obtained, which is lower than the theoretical value (n = 3). This seems to be due to the experimental difficulty to define the beginning of the crystallization because it appeared very rapidly. However, this value is close to the value obtained for non-isothermal crystallization. Figure 8 shows the experimental and calculated curves. The crystallization is well described by the model for the first 50% of relative crystallinity.

Non-isothermal Crystallization

Under High Pressure

In non-isothermal conditions, at constant cooling rate, the crystallization temperature ([T.sub.c]) increases with the pressure. As an example, the PVT diagram obtained with a cooling rate of 9.4[degrees]C/min is shown in Fig. 9.

From the PVT diagrams, the relative crystallinity curves were calculated by the following ratio:

X(T) = [V.sub.a] - [V.sub.T]/[V.sub.a] - [V.sub.s] (7)

where [V.sub.a] is the specific volume of the liquid state extrapolated at the temperature T, [V.sub.s] is the specific volume of the solid state extrapolated at the temperature T and [V.sub.T] is the specific volume measured at the temperature T.

Besides, it should be noticed that from an experimental point of view, the assessment of accurate relative crystallinity curves using the specific volume measurements at constant cooling rate is difficult for different reasons. First, because of the great diameter of the PVT cell and the poor thermal conductivity of polymers, a thermal gradient arises in the sample while it is cooled, leading to an error on the temperature scale: the average sample temperature is higher than the measured temperature at its periphery. Obviously the faster the cooling, the greater the error. Second, the baseline coming from the extrapolation of the solid state specific volume is sometimes ambiguous because of the nonlinearity of this part of the curve. For these reasons, modeling the results using the Ozawa or the Douillard/Kim equation is not presented in this paper. Nevertheless, the trends of the pressure effect on the crystallization kinetics can be deduced from these experimental results.

Relative crystallinity curves are plotted in Fig. 10. The effect of the nucleating agent clearly appears considering the crystallization temperature, which is 10[degrees]C higher than for the virgin grade. The increase of crystallization temperature by the nucleating agent is the same whatever the pressure. Moreover, the variation of crystallization onset temperature ([T.sub.c]) according to the cooling rate for different pressures is shown in Fig. 11 for the virgin grade.

The evolution of [T.sub.c] with the pressure can be explained by the evolution of the equilibrium melting temperature ([T.sub.f][degrees]) according to the pressure. The crystallization kinetics of polymer is governed by two phenomena: the first is a thermodynamic interfacial phenomenon between crystal and amorphous phase. The second is the transport phenomenon due to diffusion of the polymer chain in the amorphous phase. When the crystallization temperature is not very low compared to the melting temperature, the former phenomenon is predominant in the crystallization kinetics, and it is controlled by the supercooling ([delta]T = [T.sub.f][degrees] - T). Generally, when the pressure increases, the entropy of the liquid decreases so that the free enthalpy of liquid increases leading to an increase of the equilibrium melting temperature. Besides, the melting behavior of the samples crystallized under different pressures at the same cooling rate was analyzed by DSC with a heating rate of 10[degrees]C[min.sup.- 1] All the melting peaks were similar and could be superimposed. These results will be presented elsewhere [26]. From these experiments, it was reasonably concluded that these samples were crystallized in the same supercooling conditions. Furthermore, when the cooling rate increases the crystallization supercooling increases which leads to the decrease of the crystallization temperature. As shown in Fig. 11, the effect of the pressure on the crystallization temperature is constant whatever the cooling rate (the shift between the curves is constant along the cooling rate axis); reflecting the pressure independent crystallization supercooling.

Isothermal Crystallization Under High Pressure

In a similar way, for isothermal conditions, the relative crystallinity versus time is obtained from:

X(t) = [V.sub.0] - V(t)/[V.sub.0] - [V.sub.[infinity]]

where [V.sub.0] is the initial specific volume (liquid state), [V.sub.[infinity]] is the specific volume at the end of the experiment (solid state) and V(t) is the specific volume measured at time t.

The crystallization kinetics was described by the Avrami theory (Eq 6). The obtained Avrami exponent (n) is between 1.3 and 2.0 for virgin grade and between 0.7 and 1.4 for the nucleated grade as shown in Table 2.

The Avrami exponent (n) deviates from the theoretical values and the crystallization rate constant is scattered. However, it seems that the germination is already effective before the beginning of the isothermal experiment because of the cooling to the desired temperature, which takes a relatively long time with the PVT device. So, the initial time can be erroneous. He and Zoller (6) tried to introduce a correction factor ([t.sub.0]) in the time scale, which leads to:

X(t) = 1 - exp {-k[(t + [t.sub.0]).sup.n]} (9)

The value of n was fixed to n 3 and the crystallization rate constant k and the correction time [t.sub.0] were adjusted. The crystallization rate constant (k) for two pressures is shown in Fig. 12, where a linear evolution of Ink appears versus the temperature. Nevertheless, the calculated relative crystallinity shown in Fig. 13 is in agreement with the experimental curves. Moreover, in isothermal conditions, the crystallization supercooling increases with the pressure. In Fig. 12 the horizontal shift between the two pressures (400 bar and 800 bar) corresponds to the increment of supercooling [26].

CONCLUSION

The crystallization of a virgin and a nucleated grade of polyamide 66 was studied in non-isothermal and isothermal conditions at different pressures. When the nucleating agent is added, the crystallization temperature increases the same amount whatever the pressure.

At atmospheric pressure, in non-isothermal conditions, The Ozawa model cannot describe the entire crystallization of polyamide 66 because of the secondary crystallization. However, the onset zone of crystallization is well predicted by the model.

After a normalization of the relative crystalline curves, the Douillard/Kim equation was successfully applied to describe the primary crystallization process for both virgin and nucleated polyamides. However, the results are better for the virgin grade.

In isothermal conditions, at atmospheric pressure, the virgin polyamide 66 was fitted with the Avrami equation leading to n = 4. In the case of the nucleated polyamide 66, the obtained Avrami exponent n = 1.7 is weaker than the generally expected value of 3 for nucleated polymers. This discrepancy seems to be due to a difficult determination of the crystallization beginning time.

Under high pressure, in non-isothermal conditions, the crystallization temperature change due to the pressure increase is explained by the increase of the equilibrium melting temperature so that the crystallization supercooling remains unchanged for a constant cooling rate.

In isothermal conditions under pressure, the obtained Avrami exponent n was weaker whatever the pressure and the temperature for both virgin and nucleated grades, compared to those obtained at atmospheric pressure. Nevertheless, using an Avrami exponent of 3 and introducing a correction time, the crystallization kinetics for the virgin polyamide was well described. Moreover, the pressure increase for a same crystallization temperature leads to an increase of the super-cooling because of the rise of the equilibrium melting temperature. Therefore, the obtained rate constant for the Avrami equation is shifted on the temperature scale when the pressure is increased.

ACKNOWLEDGMENT

The authors would like to thank the Rhodia Nyltech Company for its financial support and material supply.

(1.) Korea Research Istitute of Chemical Technology Advanced Materials Division P.O. Box 107, Yusong, Taejon 305-606, Korea

(2.) Laboratoire des Materiaux Polymeres et des Biomateriaux UMR CNRS #5627 Universite Lyon 1 Bat ISTIL, 43, Bd 11 Novembre 1918 69622 Villeurbanne Cedex, France

(3.) CRL -- Rhodia-Recherches 85 av. des Freres Perret, BP 62 69192 Saint Fons Cedex, France

(4.) Rhodia-Engineering-Plastics Avenue Ramboz, BP 64 69192 Saint Fons Cedex, France

(*.) To whom correspondence should be addressed.

REFERENCES

(1.) A. Savolainen, J. Polym. Sci.: Symp., 42. 885 (1973).

(2.) N. Klein, D. Selivansky, and G. Marom, Polym. Camp., 16, 189 (1995).

(3.) B. Chabert and J. Chauchard, Ann. Chim. Fr., 16, 173 (1991).

(4.) B. Chabert, J. Chauchard, and J. Cinquin, Makromol. Chem., Macromol. Symp., 9, 99 (1987).

(5.) J. He and P. Zoller, ANTEC 92, 1144 (1992).

(6.) J. He and P. Zoller, J. Polym. Sci. B: Polyrn. Phys., 32, 1049 (1994).

(7.) K. Kishore and R Vasanthakumari, High Temperatures -- High Pressures, 16, 241 (1984).

(8.) T. Ozawa, Polymer, 12, 150 (1971).

(9.) K. Nakamura, T. Watanabe, K. Katayama, and T. Amano, J. Appl. Polym, Sci. 16, 1077(1972).

(10.) K. Nakumara, K. Katayama, and T. Amano, J. Appl. Polym. Sci., 17, 1031 (1973).

(11.) M. R. Kamal and E. Chu, Polym. Eng. Sci., 23, 27 (1983).

(12.) R. M. Patel and J. E. Spruiell Polym. Eng. Sci. 31, 730 (1991).

(13.) P. Cebe, Polym. Eng. Sci., 28, 1192 (1988).

(14.) C. R. Choe and K. H. Lee, Polym. Eng. Sci, 29, 801 (1989).

(15.) R. D. Wesson, Polym. Eng. Sci, 34, 1157(1994).

(16.) J. H. Kim, A. Dauillard, A. Vautrin, and B. Chabert, Sci. Eng. Comp. Mat, 4(1), 3 (1995).

(17.) M. Avrami, J. Chem. Phys., 7, 1103 (1939).

(18.) M. Avrami, J. Chem. Phys., 8, 212 (1940).

(19.) M. Avrami, J. Chem. Phys., 9, 177(1941).

(20.) E. M. Woo and J.-M. Chen, J. Polym. Sci. B: Polym. Phys., 33, 1985 (1995).

(21.) W. Dietz, Colloid Polym. Sci, 259, 413 (1981).

(22.) F. C. Perez-Cardenas, L. F. Del Castillo and R. VeraGraziano, J. Appl. Polym. Sci, 43, 779 (1991).

(23.) B. Wunderlich, Macromolecular Physics: Vol. 2: Crystal. Nucleation, Growth. Annealing, Academic Press, London (1976).

(24.) L. Mandelkern, Crystallization of Polymers, McGraw-Hill, New York (1964).

(25.) J. H. Kim, Conception et realisation des composites en polypropylene renforce par les fibres de verre: etude et modelisation de la cristallisation 202 p, Thesis, University of Bourgogne (1995).

(26.) J. C. Won, R. Fulchiron, A. Douillard, B. Chabert, J. Varlet, and D. Chomier, J. Appl. Polym. Sci, in press (2000).

R. FULCHIRON [2][*]

A. DOUILLARD [2]

B. CHABERT [2]

J. VARLET [3]

D. CHOMIER [4]

The crystallization kinetics of virgin and nucleated polyamide 66 was investigated in non-isothermal and isothermal conditions, by use of DSC and high pressure dilatometry. In non-isothermal conditions, at atmospheric pressure, the results were first analyzed using the Ozawa equation, leading to an Avrami exponent of 4 in the case of the virgin grade and 2.1 for the nucleated polyamide. However, experimental and calculated kinetics showed a difference in the ending part of the crystallization, likely due to a large secondary crystallization phenomenon. Thus, the relative crystallinities were normalized to extract the primary crystallization from the whole signal and analyzed using the Douillard/Kim equation. In isothermal conditions, at atmospheric pressure, the Avrami exponents were similar to the values obtained in non-isothermal conditions for both virgin and nucleated grades. Furthermore, the crystallization under pressure was examined in terms of crystallization supercooling. In non-isothermal condition s, the crystallization supercooling ([delta]Tc) increases when the cooling rate increases, but it is not affected by the pressure since the crystallization temperature increase is due to the equilibrium melting temperature rise. In isothermal conditions, the supercooling ([delta]T) rises according to the increase of the pressure for the same crystallization temperature.

INTRODUCTION

Knowledge of the crystallization behavior of semi-crystalline polymers is of a great importance for the manufacture of plastic parts, because physical properties of polymers depend on the crystalline morphology of the material. Practically, industrial processes, like injection molding or compression molding for polymers, are carried out under high pressure. Moreover, many polyamide 66 grades contain nucleating agents in order to accelerate the solidification in the mold and so to increase the manufacturing efficiency. The crystallization kinetics of polyamide 66 has been largely investigated, with or without nucleating agents, at atmospheric pressure [1-4]. Nevertheless it becomes necessary to apprehend the effect of the pressure on the crystallization behavior [5-7].

Besides, as concerns the modeling of the crystallization kinetics, Ozawa (8), Nakamura (9, 10) and other authors (11-16) proposed different models, generally based on an extension of the Avrami equation (17-19) used for isothermal crystallization. Otherwise, Douillard/Kim (15, 16) carried out the modeling of the crystallization kinetics at constant cooling rate by empirical method.

Moreover, it is known that the PA66 crystallization exhibits both primary and secondary crystallizations. The secondary crystallization corresponds to different phenomena and is defined as happening neither by further germination nor by increase of the size of the spherulites. We can consider that it appears at the same time or after the primary crystallization (20-22). Nevertheless, in all cases, it becomes dominant in the final part of the crystallization since this phenomenon is related to the already transformed quantity.

In the present work, the crystallization kinetics of a virgin and a nucleated PA66 grades is studied, in isothermal and non-isothermal conditions and at atmospheric and high pressure.

EXPERIMENTAL

Materials

Two formulations of PA66, supplied by the Rhodia Nyltech Company, have been studied: a virgin grade and a commercial grade nucleated for injection productivity enhancement. The molecular weight of both grades was M[upsilon] = 33,000 g[cdotp][mol.sup.-1], determined by viscosimetry at 30[degrees]C in 90 vol% formic acid.

Thermal Measurements

At atmospheric pressure, the crystallization studies were carried out in non-isothermal and isothermal conditions using a Perkin-Elmer differential scanning calorimeter, DSC-7. The calibration was carried out at different scanning rates using standards such as indium and zinc. In order to specify the best conditions for removing the thermal history, different crystallization experiments at 10[degrees]C[cdotp][min.sup.-1] were first performed with various holding temperature and holding times in the molten state. For a holding time of 10 min, when the holding temperature is below 280[degrees]C, the crystallization temperature increases when the holding temperature decreases. Between 280 and 320[degrees]C the crystallization temperature appears independent of the holding temperature. On the other hand, when the holding temperature is above 330[degrees]C, the crystallization temperature decreases when the holding temperature increases because of the thermal degradation of the polymer. Therefore, for a temperatu re value of 290[degrees]C, the holding time can range between 10 and 15 minutes. Finally, the most appropriate experimental conditions for our studies were as follows:

* Holding temperature of the melting state: 290[degrees]C

* Holding time: 10 minutes

Dilatometric Measurements

The crystallization under pressure was analyzed by measuring the specific volume change using a PVT-100 apparatus from SWO Polymertechnik. With this device, the temperature can range between 30[degrees]C and 420[degrees]C with [+ or -] 0.3[degrees]C of accuracy and the pressure between 200 and 2500 bar with [+ or -] 5% of accuracy. It can work in isobaric or isothermal conditions and in cooling or heating procedures. The specific volume is calculated from the measurement of the length of the cylindrical sample located in the cell. The pressure is ensured by the hydraulic system, which controls the upper mobile piston. Between the pistons and the polymer, polyimide sealings are used to prevent polymer leakage. The pellets of polymer were introduced in the PVT cylindrical cell and then molten at 310[degrees]C during 10 minutes under the desired pressure. This temperature value was chosen higher than for DSC because of higher pressure. The behaviors of the virgin and nucleated grades have been stu died for cooling rates between 2.5[degrees]C . [min.sup.-1] and 15[degrees]C . [min.sup.-1] and for different pressures ranged between 200 and 2000 bar. Real scanning rate values can be calculated afterward from the result files including time. In isothermal conditions, the crystallization of the virgin and nucleated grades was analyzed between 250[degrees]C and 270[degrees]C at 400 and 800 bar.

RESULTS AND DISCUSSION

Non-isothermal Crystallization at Atmospheric Pressure

Several crystallization experiments were carried out with cooling rates from 2 to 30[degrees]C . [min.sup.-1]. When the cooling rate increases, the crystallization onset temperature decreases. The relative crystallinity for a temperature T was calculated by the integration of the crystallization peak (2):

X(T) = [[[integral].sup.T].sub.[T.sub.i]] (dH/dT)dT/[[[integral].sup.[T.sup.f]].sub.[T.sub.i]] (dH/dT)dT (1)

where [T.sub.i] and [T.sub.f] are the temperatures, respectively, of the onset and the end of the crystallization.

Figure 1 shows the evolution of the relative crystallinity versus temperature for different cooling rates. As expected, the onset temperature of crystallization for the nucleated grade is higher than for the virgin grade. Indeed, the nucleating agent increases the quantity of activated germs, which leads to a higher value for the starting crystallization temperature (23). Nevertheless, for the nucleated grade, the crystallization spreads on a larger temperature domain than for the virgin grade.

First, the Ozawa theory was applied for the crystallization modeling of polyamide 66.

1 - X(T) = exp [- K(T)/[[phi].sup.n]] (2)

where K(T) is the rate constant for the primary crystallization depending only on the temperature, [phi] is the cooling rate and n is the Avrami exponent. The parameters of Eq 2 were obtained by plotting Ln(-Ln(1-X(T)) versus Ln[phi] for different temperatures leading to straight lines of slope n and origin coordinate LnK(T).

For this analysis, the relative crystallinity X(T) was voluntarily limited between 5% and 50% to avoid the disruption caused by the secondary crystallization (4). For the virgin grade, we obtained an average value of n of 3.9 [+ or -] 0.6, which is in agreement with the sporadic germination and the spherulitic growth (n = 4) (24). Nevertheless in this case, the values of n appear scattered. For the nucleated grade, we obtained a value of 2.1 [+ or -] 0.2, lower than the theoretical value n = 3, generally expected for instantaneous germination due to the nucleating agent. However, the practically constant value of n (Fig. 2) means that the crystallization process is not changed in the considered temperature range. The rate constant K(T) is shown in Fig. 3.

The relative crystallinity curves calculated with Eq 2 do not entirely correspond to experimental results (see Fig. 1) because the Ozawa theory does not account for the secondary crystallization, which can occur while the primary crystallization is not finished (21, 22). However, the beginning of the crystallization is well fitted by the model, especially for the virgin grade.

The experimental relative crystallinity curves were also analyzed by means of the Douillard/Kim equation (16, 25):

X(T) = exp[f(T)]/1 + exp [f(T)], with f(T) = [alpha](T - [T.sub.c*MAX]) (3)

where f(T) = [alpha][T - [T.sub.C*MAX]) with [T.sub.C*MAX] corresponding to the temperature of the crystallization peak maximum (cooling rate dependent), and [alpha] being a cooling rate dependent parameter. From this equation, the plot of ln[X(T)/1-X(T)] versus T should lead to a straight line of slope [alpha]. Practically, in the case of our experimental results, this kind of plot exhibited two linear parts of different slopes (Fig. 4). It was assumed that the linear part in the higher temperature range was mainly characteristic of the primary crystallization, the other linear part being linked to the secondary crystallization process (much slower). Thus, the intersection of the two straight lines (see curve (a) in Fig. 4) was considered as the end of the primary crystallization. So, the relative crystallinity curves were renormalized in such a way that they became equal to unity for the temperature corresponding to this intersection.

Then, the equation of Douillard/Kim was applied on the normalized relative crystallinity curves. As shown in Fig. 5, the coefficient [alpha] decreases in absolute value when the cooling rate increases which corresponds to a narrower crystallization temperature range. The variation of this coefficient with the temperature can be described by:

[alpha] = [C.sub.1] + [C.sub.2]ln[phi] (4)

where [phi] is the cooling rate.

The temperature of the exothermic peak maximum [T.sub.C*MAX] according to the cooling rate is shown in Fig. 6. The evolution of [T.sub.C*MAX] can be well fitted by a second order polynomial of ln([phi]) (Douillard/Kim (16) used a linear function), as follows:

[T.sub.C*MAX] = [C.sub.3] + [C.sub.4]ln[phi] + [C.sub.5][(ln[phi]).sup.2] (5)

From Eqs 3, 4 and 5, the primary crystallization curves were calculated. As shown in Fig. 7, experimental plots are well described by the model, especially in the case of the virgin grade. However, for the nucleated grade, the agreement between experimental and calculated curves is slightly poorer.

Isothermal Crystallization at Atmospheric Pressure

The isothermal crystallization kinetics was described by the well-known Avrami equation.

X(t) = 1 - exp(-[kt.sup.n]) (6)

where k is the rate constant which depends on the temperature and n is the Avrami exponent. The parameters of Eq 6 were obtained by plotting Ln(- Ln(1 -X(t)) versus Lnt for different temperatures leading to straight lines of slope n and origin coordinate LnK. As previously, values of relative crystallinity lower than 50% were considered. Table 1 displays the Avrami exponent (n) and the rate constant k. As expected, the rate constant decreases when the crystallization temperature increases and the half-crystallization time ([t.sub.1/2]) increases very rapidly with the crystallization temperature.

For the virgin grade, an average value of n = 4.0 [+ or -] 0.3 was obtained, consistent with the theoretical value (n = 4) and the results of non-isothermal experiments. For the nucleated grade, a value of n of 1.7 [+ or -] 0.2 was obtained, which is lower than the theoretical value (n = 3). This seems to be due to the experimental difficulty to define the beginning of the crystallization because it appeared very rapidly. However, this value is close to the value obtained for non-isothermal crystallization. Figure 8 shows the experimental and calculated curves. The crystallization is well described by the model for the first 50% of relative crystallinity.

Non-isothermal Crystallization

Under High Pressure

In non-isothermal conditions, at constant cooling rate, the crystallization temperature ([T.sub.c]) increases with the pressure. As an example, the PVT diagram obtained with a cooling rate of 9.4[degrees]C/min is shown in Fig. 9.

From the PVT diagrams, the relative crystallinity curves were calculated by the following ratio:

X(T) = [V.sub.a] - [V.sub.T]/[V.sub.a] - [V.sub.s] (7)

where [V.sub.a] is the specific volume of the liquid state extrapolated at the temperature T, [V.sub.s] is the specific volume of the solid state extrapolated at the temperature T and [V.sub.T] is the specific volume measured at the temperature T.

Besides, it should be noticed that from an experimental point of view, the assessment of accurate relative crystallinity curves using the specific volume measurements at constant cooling rate is difficult for different reasons. First, because of the great diameter of the PVT cell and the poor thermal conductivity of polymers, a thermal gradient arises in the sample while it is cooled, leading to an error on the temperature scale: the average sample temperature is higher than the measured temperature at its periphery. Obviously the faster the cooling, the greater the error. Second, the baseline coming from the extrapolation of the solid state specific volume is sometimes ambiguous because of the nonlinearity of this part of the curve. For these reasons, modeling the results using the Ozawa or the Douillard/Kim equation is not presented in this paper. Nevertheless, the trends of the pressure effect on the crystallization kinetics can be deduced from these experimental results.

Relative crystallinity curves are plotted in Fig. 10. The effect of the nucleating agent clearly appears considering the crystallization temperature, which is 10[degrees]C higher than for the virgin grade. The increase of crystallization temperature by the nucleating agent is the same whatever the pressure. Moreover, the variation of crystallization onset temperature ([T.sub.c]) according to the cooling rate for different pressures is shown in Fig. 11 for the virgin grade.

The evolution of [T.sub.c] with the pressure can be explained by the evolution of the equilibrium melting temperature ([T.sub.f][degrees]) according to the pressure. The crystallization kinetics of polymer is governed by two phenomena: the first is a thermodynamic interfacial phenomenon between crystal and amorphous phase. The second is the transport phenomenon due to diffusion of the polymer chain in the amorphous phase. When the crystallization temperature is not very low compared to the melting temperature, the former phenomenon is predominant in the crystallization kinetics, and it is controlled by the supercooling ([delta]T = [T.sub.f][degrees] - T). Generally, when the pressure increases, the entropy of the liquid decreases so that the free enthalpy of liquid increases leading to an increase of the equilibrium melting temperature. Besides, the melting behavior of the samples crystallized under different pressures at the same cooling rate was analyzed by DSC with a heating rate of 10[degrees]C[min.sup.- 1] All the melting peaks were similar and could be superimposed. These results will be presented elsewhere [26]. From these experiments, it was reasonably concluded that these samples were crystallized in the same supercooling conditions. Furthermore, when the cooling rate increases the crystallization supercooling increases which leads to the decrease of the crystallization temperature. As shown in Fig. 11, the effect of the pressure on the crystallization temperature is constant whatever the cooling rate (the shift between the curves is constant along the cooling rate axis); reflecting the pressure independent crystallization supercooling.

Isothermal Crystallization Under High Pressure

In a similar way, for isothermal conditions, the relative crystallinity versus time is obtained from:

X(t) = [V.sub.0] - V(t)/[V.sub.0] - [V.sub.[infinity]]

where [V.sub.0] is the initial specific volume (liquid state), [V.sub.[infinity]] is the specific volume at the end of the experiment (solid state) and V(t) is the specific volume measured at time t.

The crystallization kinetics was described by the Avrami theory (Eq 6). The obtained Avrami exponent (n) is between 1.3 and 2.0 for virgin grade and between 0.7 and 1.4 for the nucleated grade as shown in Table 2.

The Avrami exponent (n) deviates from the theoretical values and the crystallization rate constant is scattered. However, it seems that the germination is already effective before the beginning of the isothermal experiment because of the cooling to the desired temperature, which takes a relatively long time with the PVT device. So, the initial time can be erroneous. He and Zoller (6) tried to introduce a correction factor ([t.sub.0]) in the time scale, which leads to:

X(t) = 1 - exp {-k[(t + [t.sub.0]).sup.n]} (9)

The value of n was fixed to n 3 and the crystallization rate constant k and the correction time [t.sub.0] were adjusted. The crystallization rate constant (k) for two pressures is shown in Fig. 12, where a linear evolution of Ink appears versus the temperature. Nevertheless, the calculated relative crystallinity shown in Fig. 13 is in agreement with the experimental curves. Moreover, in isothermal conditions, the crystallization supercooling increases with the pressure. In Fig. 12 the horizontal shift between the two pressures (400 bar and 800 bar) corresponds to the increment of supercooling [26].

CONCLUSION

The crystallization of a virgin and a nucleated grade of polyamide 66 was studied in non-isothermal and isothermal conditions at different pressures. When the nucleating agent is added, the crystallization temperature increases the same amount whatever the pressure.

At atmospheric pressure, in non-isothermal conditions, The Ozawa model cannot describe the entire crystallization of polyamide 66 because of the secondary crystallization. However, the onset zone of crystallization is well predicted by the model.

After a normalization of the relative crystalline curves, the Douillard/Kim equation was successfully applied to describe the primary crystallization process for both virgin and nucleated polyamides. However, the results are better for the virgin grade.

In isothermal conditions, at atmospheric pressure, the virgin polyamide 66 was fitted with the Avrami equation leading to n = 4. In the case of the nucleated polyamide 66, the obtained Avrami exponent n = 1.7 is weaker than the generally expected value of 3 for nucleated polymers. This discrepancy seems to be due to a difficult determination of the crystallization beginning time.

Under high pressure, in non-isothermal conditions, the crystallization temperature change due to the pressure increase is explained by the increase of the equilibrium melting temperature so that the crystallization supercooling remains unchanged for a constant cooling rate.

In isothermal conditions under pressure, the obtained Avrami exponent n was weaker whatever the pressure and the temperature for both virgin and nucleated grades, compared to those obtained at atmospheric pressure. Nevertheless, using an Avrami exponent of 3 and introducing a correction time, the crystallization kinetics for the virgin polyamide was well described. Moreover, the pressure increase for a same crystallization temperature leads to an increase of the super-cooling because of the rise of the equilibrium melting temperature. Therefore, the obtained rate constant for the Avrami equation is shifted on the temperature scale when the pressure is increased.

ACKNOWLEDGMENT

The authors would like to thank the Rhodia Nyltech Company for its financial support and material supply.

(1.) Korea Research Istitute of Chemical Technology Advanced Materials Division P.O. Box 107, Yusong, Taejon 305-606, Korea

(2.) Laboratoire des Materiaux Polymeres et des Biomateriaux UMR CNRS #5627 Universite Lyon 1 Bat ISTIL, 43, Bd 11 Novembre 1918 69622 Villeurbanne Cedex, France

(3.) CRL -- Rhodia-Recherches 85 av. des Freres Perret, BP 62 69192 Saint Fons Cedex, France

(4.) Rhodia-Engineering-Plastics Avenue Ramboz, BP 64 69192 Saint Fons Cedex, France

(*.) To whom correspondence should be addressed.

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Author: | WON, J. C.; FULCHIRON, R.; DOUILLARD, A.; CHABERT, B.; VARLET, J.; CHOMIER, D. |
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Publication: | Polymer Engineering and Science |

Geographic Code: | 1USA |

Date: | Sep 1, 2000 |

Words: | 3667 |

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