Crystallization of syndiotactic polystyrene.
Polystyrene is commonly used in the atactic form with no crystallinity. There is increasing interest in the syndiotactic form, which crystallizes at higher rates than the isotactic. The resultant properties, high melting point, relatively good mechanical strength (1, 2) above the glass transition, [T.sub.g], and good chemical resistance (3), are related to the amount and morphology of the crystalline fraction. The practical utilization of the material will depend upon the crystallization behavior under conditions of different processing histories.
There is thus considerable interest in understanding the crystallization process of this novel polymer (4-7). Cimmino et al. (4) have described the crystallization kinetics at temperatures close either to the melting temperature or to [T.sub.g]. Wesson (5) has used dynamic crystallization experiments to predict the kinetics of crystallization over a wider temperature range. The parameters that control crystallization were inferred in this latter work from the continuous cooling experiments. The standard methods to estimate such rate controlling parameters involve isothermal experiments that can be directly fitted to theoretical models. The practical application of this kind of modeling lies in its ability to predict the crystallization kinetics in a non-isothermal case, which are more often found in realistic thermomechanical processes. For potential practical cases, this may mean heating from the quenched amorphous state as well as cooling from the melt.
It is the purpose of this paper to examine the process of crystallization in sPS over the temperature range from [T.sub.m] to [T.sub.g] using measurements determined from isothermal experiments. The spherulitic and lamellar morphology was correlated with the different thermal histories. The isothermally determined parameters were used to estimate the crystallization behavior in some typical non-isothermal cases and the quality of the fit compared to other similar work.
The sPS ([M.sub.w] = 3.72 x [10.sup.5]) used for these experiments was supplied by Dr. M. Rogers of Dow Chemical (Canada). A differential scanning calorimeter (DSC) was used for both the crystallization rate measurements and to heat treat many of the specimens (exploiting the precise temperature and heating rate control in the instrument). Specimen mass was kept small for all experiments, to ensure uniform temperature distribution through the sample during heating and cooling scans. The sample mass was approximately 5 mg. The temperature gradient across a sample of this size will be minimal, Fig. 4.13 of Wunderlich (8). To produce amorphous samples, a high cooling rate is required, so samples were quenched in liquid media.
Depending on the practical handling difficulties of small samples, two different techniques were used to prepare the samples for the isothermal and non-isothermal crystallization experiments. For crystallization at high temperatures, samples were melted in a Perkin-Elmer DSC 7 at 340 [degrees] C for 5 min and then rapidly cooled at a nominal rate of 200 C [degrees]/min to the crystallization temperature, [T.sub.c[. For continuous cooling experiments, the sample was cooled at a rate of 10 C [degrees]/min to 50 [degrees] C.
For isothermal crystallization at low temperatures amorphous films were prepared by melting sheets of [less than]0.5 mm thickness at 340 [degrees] C in a tube furnace with a continuous flow of nitrogen for at least 5 min. The thin sheets were then quenched into ice water at 0 [degrees] C. To ensure that the sheets were completely amorphous they were examined between crossed polars in transmitted light in the optical microscope. No birefringent contrast was observed in properly quenched samples. Selected areas were cut from the thin films and heated in the DSC at 80 C [degrees]/min to measure the initial crystallinity using the method of Krzystowczyk et al. (9). The completely amorphous samples were then heated at 200 C [degrees]/min from an initial temperature of 70 [degrees] C to [T.sub.c]. For the non-isothermal tests, the samples were heated from the quenched amorphous state at 10 C [degrees]/min to the melting point.
All the samples were sealed in aluminum pans, and a continuous flow of nitrogen was passed through the sample chamber during the crystallization experiments. The heat evolved during crystallization was recorded as a function of time. Pure indium and zinc were used as reference materials to calibrate the DSC.
Samples for direct observation using both optical microscopy and electron microscopy were cast from dilute solutions of sPS in o-xylene. For optical examination, a drop of 0.5 wt% solution was placed onto hot phosphoric acid at [approximately]290 [degrees] C. After the solvent evaporated the remaining thin film of the polymer was quenched onto the surface of ice water. The thick portions of the samples were then floated onto either 200 or 50 mesh transmission electron microscope grids. For melt crystallization experiments, the grids (with sPS specimens attached) were cooled in the DSC at rates from 5 [degrees] C/min to 200 [degrees] C/min or the molten thin films were cooled directly from the casting temperature at different rates. The samples crystallized from the amorphous state were either heated from room temperature in the DSC to the crystallization temperature or placed in a tube furnace at 150 [degrees] C. The maximum crystallization temperature used for the solid state experiments was 150 [degrees] C. An oil immersion 100X objective lens was used for the optical microscopy, which revealed the morphology near the spherulite scale. For smaller structures such as lamellae, which were viewed with electron microscopy (JEOL 100 running at 80 KV), the samples were cast from a solution of 0.25 wt%. The thinnest portions of the samples were selected and floated onto 1000 mesh TEM grids.
RESULTS AND DISCUSSION
The measurement of isothermal crystallization rates involves cooling rapidly from the molten state to the temperature of interest, and holding at that temperature while the transformation rate is measured. The crystallization during the transient cooling from the melt to the test temperature is assumed to be negligible. At small undercoolings, the rate of crystallization of sPS increased rapidly with increasing undercooling, as expected. The maximum cooling rate achievable in the DSC was too slow to prevent significant amounts of transient crystallization at temperatures below [approximately]240 [degrees] C. The experiments were thus divided into two regions: those at high crystallization temperatures, in which the specimens were cooled in the DSC directly from the melt; and those at low crystallization temperatures (near the glass transition), in which the specimens were quenched from the melt to a metastable amorphous state, then reheated to the appropriate test temperature.
The underlying assumption is that the molten molecular conformations are frozen by quenching from the melt. This is confirmed by examining the optical micrographs of the quenched films, in which no birefringence is observed after water quenching. Similarly in an earlier study, isotactic polystyrene was shown to have the same growth rates for samples crystallized from the melt or from the amorphous state at a given temperature (10).
The total heat evolved on crystallization is measured using the DSC. This includes the heat resulting from both nucleation and growth processes. Typical experimental crystallization isotherms are shown in Fig. 1 for both temperature regions. The rate constant, k(T), at each temperature was determined using the relation
k(T) = ln 2/[([[Tau].sub.1/2]).sup.n] (1)
where [[Tau].sub.1/2] is the crystallization half time and n is the Avrami index. The value of n for sPS was determined using the standard Avrami (11) analysis.
1 - X(t) = exp(- [kt.sup.n]) (2)
where X(t) is the degree of phase transformed at time t. The Avrami analysis of the isothermal data for crystallinities between 10% and 90% is shown in Fig. 2. The value of n determined for both temperature regions was between 2 and 3. There was a slight difference between n from the high temperatures experiments and n from the low temperature experiments but this difference was considered to be within experimental error. For Eq 1, n was set to 3, which was also the value used by Wesson (5).
In similar studies, Cimmino et al. (4) have also reported that the value of n is between 2 and 3. For both studies, the range of the Avrami analysis was limited to temperatures close to either [T.sub.m] or [T.sub.g]. To predict the crystallization kinetics over a wider temperature range the data must be modeled to determine the thermodynamic parameters of the crystallization process. The kinetics at temperatures that are not accessible experimentally can then be predicted.
Isothermal Crystallization Kinetics
The rate constant can be modeled as having contributions from two temperature dependent processes, nucleation and growth. The temperature dependence of the rate constant then has the form (5)
[Mathematical Expression Omitted] (3)
where the parameters U, A, and [k.sub.o], which are polymer dependent, have been defined by Wesson (5). The influence of diffusive processes is represented by the first term, while the thermodynamic driving force is found in the second term. [Mathematical Expression Omitted] is the equilibrium melting temperature for the crystal and [T.sub.[infinity]] is the temperature (below [T.sub.g]) at which all molecular motion hypothetically ceases. A correction factor (f) is needed for high undercoolings. These parameters have been estimated using continuous cooling experiments in a standard DSC (5). There are inherent difficulties in obtaining accurate values using dynamic experiments of this kind. This becomes clearer on examination of the fitting of the isothermal experiments to the model particularly at low temperatures.
For the nucleation and growth kinetics model, the overall rate of crystallization k(T) is controlled by the influence of different parameters in different temperature regions. The two principal processes in the model are controlled by the viscosity (which is related to U), and by the thermodynamic driving force (related to A). The crystallization rate will be slow near the melting point and increase with decreasing temperature due to the increasing thermodynamic driving force. At temperatures approaching [T.sub.g], the viscosity of the melt increases and the overall crystallization rate is limited by the molecular mobility. Because sPS crystallizes relatively rapidly, the isothermal measurements are feasible only at the extremes of the crystallization temperature range. However, each of the parameters can be optimally fitted by examining in turn the curve fit in the different temperature ranges.
High Temperature Kinetics
At temperatures approaching the melting point, the mobility of the molecules is high enough that the overall crystallization rate is dominated by the thermodynamic driving force. In this region, k(T) will be insensitive to minor changes in U. As a result, it is possible to determine A and [k.sub.o] from Eq 3 using assigned values for U once [T.sub.[infinity]] and [Mathematical Expression Omitted] are defined. Initially in the present analysis, [Mathematical Expression Omitted] is set equal to ([T.sub.m] + 8 K), which is the same estimate used by Wesson (5). For sPS, [T.sub.m] is approximately 543 K. The value for [T.sub.[infinity]] was taken as ([T.sub.g] - 30 K) where [T.sub.g] = 373 K as determined from DSC measurements. U was varied from 1500 to 4120 cal/mole. The lower bound is the so-called universal value for crystallization, (12) and the upper bound is the Williams-Landel-Ferry constant for bulk fluidity (13). By rearranging Eq 3 and plotting the data in the form [ln(k(T)) + U/R (T - [T.sub.[infinity]])] versus [1/T[Delta]Tf], values for A and [k.sub.o] can be estimated from the slope and the intercept.
The crystallization rate predicted using these model parameters was then plotted in Fig. 3. k(T) is more sensitive to U at the lower temperatures as expected. The best fit between the experimental data from both temperature regions and the predicted k(T) was found for U = 2300 [+ or -] 100 cal/mole, A = 2.95 x [10.sup.5] [K.sup.2] and [k.sub.o] = 4.7 x [10.sup.3] 1/sec. For the entire range of U values investigated, A was found to change by [less than] 10%. As well, regardless of the value of U used in the analysis, the predicted values of k(T) were found to be in close agreement with the experimental data at the high temperatures. In this temperature range the analysis is as expected insensitive to the value of U. The value of A determined from these isothermal experiments is significantly different from the value determined from non-isothermal experiments.
For comparison, k (T) predicted by using the parameters determined with the dynamic (non-isothermal) experiments (5) is shown in Fig. 3 as the dark solid line. The non-isothermally determined parameters predict an overall crystallization rate that fits the present high temperature measurements somewhat better then the low temperature data. At low temperatures the discrepancy is [approximately]3 orders of magnitude. The poor fit at these low temperatures is due to the relatively small value for U estimated from the dynamic experiments. The present analysis shows that to estimate U, the fit with experimental data should be made at low temperatures.
Low Temperature Kinetics
A more reliable estimate of U can be determined by beginning the analysis with the low temperature data. Using a plot of [ln(k(T)) + A/T[Delta]Tf] versus [1/R(T [T.sub.[infinity]])], U and [k.sub.o] were calculated from the slope and intercept respectively. The initial value of the parameter A was taken from the above analysis. The crystallization rate k(T) was then plotted using these values for the crystallization parameters; see Fig. 4.
As expected, the predicted k(T) is more sensitive to changes in A at the higher temperatures. For a range of A values from 2.9 x [10.sup.5] to 4 x [10.sup.5] [K.sup.2], there is agreement between the low temperature crystallization experimental data and the calculated rate constant values. Over this range U was found to be approximately 3072 cal/mole. The best fit at both high and low temperatures was found for U = 3086 cal/mole, A = 3.5 x [10.sup.5] [+ or -] 1 x [10.sup.4] [K.sup.2] and [k.sub.o] [approximately equal to] 1 x [10.sup.6] 1/sec.
Effect of Equilibrium Melting Temperature [Mathematical Expression Omitted]
The separate analysis of the experimental data from the two temperature regions results in different values for U, A, and [k.sub.o]. This inconsistency can be minimized by adjusting the assigned value for the equilibrium melting temperature (approximated initially as 551 K, consistent with Wesson's value). A higher melting point has been reported by Arnauts and Berghmans (14) who determined that [Mathematical Expression Omitted] using the Hoffman-Weeks method (15). But an even higher experimental value of [T.sub.m] has been obtained by Gvozdic and Meier (16) using an extremely careful and slow annealing procedure. The highest melting temperature reported by these authors [Mathematical Expression Omitted] was used to refit the data.
Using this higher value for [Mathematical Expression Omitted], both the high and low temperature measured crystallization rates could be simultaneously fitted to Eq. 2, for common values of U, A, and [k.sub.o]; see Fig. 5. The best fit in this case was found for U = 2950 cal/mole, A = 5.45 x [10.sup.5] [K.sup.2] and [k.sub.o] = 0.64 x [10.sup.8] 1/sec. The parameter A in particular, was found to be very sensitive to the value of [Mathematical Expression Omitted]. For example, a 10 K increase in the assigned melting temperature resulted in an increase of [approximately]50%.
Model Sensitivity at Low Temperatures
The crystallization rates predicted using the above activated rate process parameters can clearly fit the experimental isothermal measurements closely, Fig. 5, at both high and low temperatures. The crystallization rates predicted from the non-isothermal experiments were plotted originally as [[Tau].sub.1/2] = [(ln 2/K(T)).sup.1/n] by Wesson (5), and shown as the dashed line in Fig. 5. This was compared with the present work, for which the similarly calculated prediction is shown as a dotted line. For both [[Tau].sub.1/2] curves, n was assumed to be equal to 3. It is obvious that there is a large difference in predicted crystallization rates at the low temperatures, and that the values predicted over this temperature range in the present study are very close to the actual experimental isothermal data.
The process that controls the overall crystallization rate changes between high and low temperatures. It is thus expected that the crystalline morphology will be affected by the temperature at which the amorphous to crystalline transformation occurs. The analogy is found in metals, in which the phase distributions (size and shape) vary with cooling rates from the melt. The physical properties of the crystalline/amorphous composite will be strongly dependent on the phase distributions.
There is a clear distinction between the morphology of samples crystallized at low and high temperatures. These differences are evident in both the spherulitic and the lamellar morphologies. Clearly visible spherulites are observed in sPS crystallized at high temperatures by slow cooling from the melt, as shown in Fig. 6. The low temperature optical micrographs show, instead of the familiar Maltese cross contrast, a fine, granular texture with birefringent entities [approximately]0.5-2.0 [[micro]meter] in size [ILLUSTRATION FOR FIGURE 7 OMITTED]. The primary nucleation density can be estimated by counting the number of spherulites or birefringent entities per unit area. This gives values of 5 x [10.sup.5]/[mm.sup.2] at low temperatures, and much smaller density of [approximately][10.sup.4]/[mm.sup.2] at high temperatures.
Within the high temperature transformation region, the spherulitic morphology changes with rate of cooling from the melt. At the slowest cooling rate used ([less than]5C [degrees] /min), the predominant microstructure is that shown in Fig. 6 (a), in which the crystalline orientation is only locally uniform, similar to samples isothermally crystallized at high temperatures (4). At cooling rates greater than this, accessible using the DSC (5 to 200 C [degrees] /min), the spherulites show a classical contrast, Fig. 6 (b), with a typical size of 10 to 50 [[micro]meter] diameter. The relatively large areas of uniform contrast within the individual spherulites indicate uniform molecular orientation. For faster cooling rates (air quenching), the volume fraction of spherulites decreases (as expected for lower total crystallinities), and the nuclei have not developed to full spherulitic size, being typically [approximately]2-10 [[micro]meter] in diameter; see Fig. 8. The most rapidly cooled samples (quenched from the melt in cooled agitated ice water) showed no birefringent structure, indicating completely amorphous material.
A more revealing difference in morphology was found in examining the lamellar structure using transmission electron microscopy. The samples crystallized at high and low temperatures showed distinct differences related to the differences in rate controlling crystallization processes. At high temperatures the lamellae were arranged into a classical sheaf like morphology seen in Fig. 9. The lamellae had thicknesses in the range from 9 to 25 nm [ILLUSTRATION FOR FIGURE 10 OMITTED]. The thinnest lamellae are found in "loops" of entrapped material formed by the bends in the thicker lamellae as they grow outward from the center of the sheaf. These thin lamellae are visible in Fig. 10 and the loops of entrapped material are visible in both Figs. 9 and 10. The average interlamellar spacing (9-25 nm) is larger at these high temperatures than at low transformation temperatures (5-14 nm) as shown in Fig. 11, as expected for the relatively high melt diffusivities. The lamellae remain closely parallel over extended distances and grow coherently over large distances. The viscosity is low enough that the molecules can arrange themselves in crystalline arrays that more closely approximate the expected equilibrium structures.
In contrast, at low crystallization temperatures ([less than] 150 [degrees] C), the lamellae do not grow as coherently, being on the whole less parallel, see Fig. 11, than in the samples crystallized at high temperatures. The classical sheaf-like structures observed for near-equilibrium microstructures are not observed here. The birefringent structures observed in the optical micrographs are seen here as small bundles of nearly parallel lamellae ([approximately]1 [[micro]meter] is extent).
The spherulitic/lamellar morphology that develops thus depends on the crystallization temperature. Comparison with other work studying morphology (17) suggests that the molecular weight effect is most likely related to the overall mobility of the molecule.
Predicting Non-Isothermal Crystallization Kinetics
The crystallization parameters determined from the isothermal experiments can be used to predict nonisothermal or dynamic cooling behavior. The latter, of course, is of direct practical importance in modeling crystallization behavior under realistic processing conditions. For sPS, the possibility of quenching to amorphous at readily accessible cooling rates means that the crystallization behavior from the quenched structure is also of importance to practical processes. This has been recognized in earlier work by Chan and Isayev (18) on poly(ethylene terephthalate), in which the parameters derived from isothermal experiments were used to predict non-isothermal crystallization behavior for material crystallized in both regimes. The fitting methods were similar to those used by Patel and Spruiell on nylon-6 crystallizing only from the melt (19). The general approach used in this earlier work is followed here. It should be noted that in sPS, Wesson has approached the problem in the inverse direction, estimating the isothermal crystallization parameters from experiments on dynamically cooled samples (5). The collective consensus is that the Nakamura model, which relates the isothermal transformation kinetics to the dynamically cooled crystallization kinetics, is the one that fits the experimental observations best.
The Nakamura model (20) predicts the normalized mass fraction that has crystallized as a function of temperature during a dynamic cooling process:
X(T)/[X.sub.[infinity]] = 1 - exp [-[([integral of] k(T) dT/R).sup.n]] (4)
Where R = dT/dt (t is time), and K(T) is related to the isothermal rate constant through the expression K(T) = k[(T).sup.1/n]. This form of the Nakamura equation has been used by Wesson (5) to determine isothermal crystallization parameters for sPS from dynamic cooling experiments. Inherent in Eq 4 is the assumption that the nucleation rate and the growth rates have the same temperature dependence.
Using the kinetics parameters obtained from the isothermal experiments earlier (U = 2950 cal/mole, A = 5.45 x [10.sup.5] [K.sup.2] and [k.sub.o] = 0.64 x [10.sup.8] 1/sec), the fraction of crystalline phase that is predicted by the Nakamura model to appear during cooling from the melt is shown in Fig. 12(a). The equivalent crystallization behavior on heating from the quenched amorphous state can be predicted from the same isothermal kinetics parameters (following the discussion earlier) and is shown in Fig. 12(b). These are compared in these Figures to the experimentally determined crystalline fractions. The heating and cooling rates in these non-isothermal experiments are 10 C [degrees] /min.
For cooling from the melt the model agrees with the experimental data; Fig. 12(a). Only toward the completion of crystallization, at low temperatures, do the predicted values deviate slightly from the experimental values. The maximum difference at these low temperatures, in terms of a simple horizontal temperature shift, is [approximately]3 [degrees] C. This is smaller than the discrepancy seen in the earlier work of poly(ethylene terephthalate) (18). Chan and Isayev have invoked an "induction time index" as a correction to obtain an improved fit. In the present work on sPS, the initial fit seems adequate without this additional correction term.
The isothermally determined parameters may also be used to predict the non-isothermal crystallization kinetics from the quenched amorphous state; Fig. 12(b). The difference between prediction and experiment is significantly larger than was found in Fig. 12(a) for the melt crystallized case. The possible origins of this discrepancy have been discussed by Chan and Isayev (18). Basically, the assumptions on which the Nakamura model is based - namely, that the crystallization progresses under isokinetic conditions and that the number of activated nuclei is constant - are considered not to be rigorously valid for large temperature changes (18). In any case the discrepancy is small and for practical purposes may be considered insignificant.
The crystallization parameters that control the overall crystallization kinetics have been determined using isothermal experiments. The model has been fitted simultaneously to the data at both high and low temperatures of crystallization, which has not previously been done. Compared with earlier work, which used a dynamic cooling model, the present work predicts values that appear to fit the measured isothermal data much better (U = 2950 cal/mole, A = 5.45 x [10.sup.5] [K.sup.2] and [k.sub.o] = 0.64 x [10.sup.8] 1/sec). The most important difference with the earlier work was to use a higher estimate for the equilibrium melting temperature [Mathematical Expression Omitted].
The spherulitic and lamellar morphologies for samples crystallized at high and low temperatures showed significant differences, which were qualitatively consistent with the differences in rate controlling process predicted from the kinetics analysis.
Isothermal crystallization experiments have been used to estimate the parameters that control the rate of crystallization from the melt, and from the quenched amorphous state in sPS. These kinetics parameters have been used to predict the crystallization behavior in a non-isothermal experiments. The predictions were found to agree with the measured curves for crystallization from the melt. For crystallization from the amorphous solid, the predicted rates underestimates the measured crystallization rates. The discrepancy may be due to the assumptions on which the model is based.
The authors would like to acknowledge the financial support provided by the Ontario Centre for Materials Research and by the Natural Sciences and Engineering Research Council of Canada. Useful discussions were held with Dr. M. Rogers and Mr. R.J. Collacott.
1. F. DeCandia, R. Russo, and V. Vittoria, J. Polymer Sci. C, 28, 47 (1990).
2. F. DeCandia, G. Romano, R. Russo, and V. Vittoria, Colloid Polym. Sci., 268, 720 (1990).
3. V. Vittoria, R. Russo, and F. DeCandia, J. Macromol. Sci. Phys., B28, 419 (1989).
4. S. Cimmino, E. Di Pace, E. Martuscelli, and C. Silvestre, Polymer, 32, 1080 (1991).
5. R. D. Wesson, Polym. Eng. Sci., 34, 1157 (1994).
6. A. J. Pasztor, Jr., B. G. Landes, and P. J. Karjala, Thermochimica Acta, 177, 187 (1991).
7. F. DeCandia, A. Ruvolo Filho, and V. Vittoria, Colloid Polym. Sci., 269, 650 (1991).
8. B. Wunderlich, in Thermal Analysis, p. 153, Academic Press, San Diego (1990).
9. D. H. Krzystowczyk, X. Niu, R. D. Wesson, and J. R. Collier, Polym. Bull., 33, 109 (1994).
10. B. C. Edwards and P. J. Phillips, Polymer, 15, 351 (1974).
11. M. J. Avrami, J. Chem. Phys. 7, 1103 (1939).
12. J. D. Hoffman, G. T. Davies, and J. I. Lauritzen, Jr., in Treatise on Solid State Chemistry Vol. 3, p. 497, N. B. Hannay, ed., Plenum, New York (1976).
13. J. D. Ferry, Viscoelastic Properties of Polymers, 2nd Ed., Wiley, New York (1970).
14. J. Arnauts and H. Berghmans, Polym. Commun., 31, 343 (1990).
15. J. D. Hoffman and J. J. Weeks, J. Chem. Phys., 42, 4301 (1965).
16. N. V. Gvozdic and D. J. Meier, Polym. Commun., 32, 493 (1991).
17. O. Greis, Y. Xu, T. Asano, and J. Petermann, Polymer, 30, 590 (1989).
18. T. W. Chan and A. I. Isayev, Polym. Eng. Sci., 34, 461 (1994).
19. R. M. Patel and J. E. Spruiell, Polym. Eng. Sci., 31, 730 (1991).
20. K. Nakamura, K. Katayama, and T. Amano, J. Appl. Polym. Sci., 17, 1031 (1973).
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|Title Annotation:||First Symposium on Oriented Polymers|
|Author:||Lawrence, S. St.; Shinozaki, D.M.|
|Publication:||Polymer Engineering and Science|
|Date:||Nov 1, 1997|
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