Crystallization and fusion kinetics of Poly(butylene terephthalate)/Titanium Dioxide

Abstract In this paper, the crystallization, fusion, and activation energy (Ea) of PBT/TiO2 were thoroughly evaluated using DSC. Increasing the rates shifted the peaks of melt crystallization to lower temperatures while the fusions were almost unaffected. TiO2 hindered the melt crystallization of PBT and lower crystallization rates, i.e., CMAX and K’ were acquired, in general, the crystallinity degree (Xc) was 4% higher in PBT/TiO2 which is in the marginal error. Pseudo-Avrami and Mo models were applied to evaluate the melt crystallization kinetics; both fitted the melt crystallization quite well; deviations were observed at the beginning and the crystallization end most due to the nucleation and spherulites impingement during the secondary crystallization. Ea was evaluated using the Friedman model, considering the values of Ea less energy has to be removed from PBT/TiO2 when compared to PBT, specifically at 1% of TiO2.


Introduction
Polyesters are plastic resins widely used in sundry industrial applications, from the general goods as commodities to the sophisticated products with high technological performance and added value. These resins contribute for almost 18% of the world's polymer production [1] . Among them, one of the most important is poly(butylene terephthalate) (PBT), a thermoplastic, semi-crystalline with excellent processing properties. Its high chemical, thermal and mechanical performances make PBT a potential candidate for many applications in science and technology [2][3][4][5][6][7] .
Literature has reported the crystallization kinetics of PBT upon additives and fillers addition, the second phase addition may promote the heterogeneous nucleation and reduce the crystallization time, speeding up its general processing [8] . However, other properties can be achieved, such as significant improvement in the mechanical properties [9] , antistatic and super-strength characters [10] are examples of synergistic PBT compounds, filled with aluminum oxide (Al 2 O 3 ), epoxide elastomers and carbon nanotubes, for instance.
In order to improve polymers' properties, additives and fillers are commonly added. For instance, Titanium dioxide (TiO 2 ) which is used due to its high thermal and chemical stability, non-toxicity, photo-catalytic character and antibacterial action, for instance [11,12] , the addition of TiO 2 to the compounds may increase the solar reflectance [13] , rigidity [14] , tenacity [15] , synthesize films [16] and increases the degree of crystallinity [17] . Due to these great achievements, adding TiO 2 can be attractive aiming at higher PBT performance, therefore in this work, PBT was doped with TiO 2 , in amounts ranging from 0 to 10% of the weight. Afterwards, the phase transitions, i.e., crystallization and melting were investigated.
Zhou et al. [18] reported TiO 2 effect in nanocomposites of poly(butene 2,5-furan dicarboxylate) (PBF), a biologicalbased polyester similar to PBT, at concentrations up to 7% of the weight; TiO 2 acted as a nucleating agent accelerating the crystallization as well as improving UV resistance. In the present work, as later on discussed at low PBT/TiO 2 contents (1% wt) there was no nucleating effect, suggesting that the deterrent effect of TiO 2 's solid particles was greater than the nucleation ability into PBT matrix during the melt crystallization [5] , investigation of the crystallization kinetics and energetic measurements are presented contributing to scientific and technological databases.
Crystallization and fusion of PBT and PBT/TiO 2 composites were recorded using differential scanning calorimetry (DSC) through non-isothermal scans, and applying several heating/ cooling rates. Crystallization kinetics was evaluated using Pseudo-Avrami and Mo models, measured discrepancies are provided validating the modeling. Additionally, this work reports the activation energy evaluations for crystallization and fusion processes, a methodology rarely reported. The activation energy for the melt crystallization was computed using the Friedman isoconversional model [19] . Regarding the activation energy of fusion, Toda et al. [20] suggested a model for polymer fusion, considering the geometry of melting cylindrical rods, however, the literature reports that for cases of sample overheating during fusion, the most robust isoconversional models for calculation of the crystallization activation energy are also suitable for the evaluation of the activation energy of the fusion, therefore Friedman's isoconversional method was applied in this work [21] . Based on our database, the kinetics of crystallization and its modeling discrepancies, as well as the activation energies evaluation for PBT/ TiO 2 , have been rarely reported for polymers composites.

Materials
PBT 195 Valox was supplied by Sabic company (Bergen op zoom Netherlands), with density of 1.31 g cm -3 . TiO 2 was purchased from Evonik Degussa Co. with surface area of 50 m 2 /g and a 75:25 ratio of anatase and rutile, with an average crystal size of 25 to 94 nm.

Compounding
PBT compounds with 1, 5, and 10% of the weight of TiO 2 were prepared in a Haake Rheomix 600 (Germany) laboratory internal mixer fitted with high-intensity rotors type rollers, at 240 °C, 60 rpm during 10 min.

Scanning electron microscopy (SEM)
Scanning electron microscopy images were captured using a LEO 1430 unit, from Zeiss (USA). The specimens were previously fractured in liquid nitrogen to avoid plastic deformation, afterwards, coated with a carbon layer aiming to avoid the charges accumulation.

Differential scanning calorimetry
The phase transitions, i.e., crystallization and fusion, as well as the thermal properties were monitored with a DSC Q20 from TA Instruments (USA). Specimens weighing approximately 3 mg were experimented in closed aluminum pans under nitrogen gas flow of 50 mL/min. The applied thermal cycle consisted of: heating from 25 °C to 270 °C, isotherm at 270 °C for 3 minutes, cooling from 270 °C to 20 °C and re-heating from 20 °C to 270 °C using constant heating/cooling/reheating rates of 5, 10, 20, and 30 °C/min. Figure 1 displays a typical DSC scan together with an applied thermal cycle illustrated as a dotted red line. The investigated phase transitions are presented and coded as F 1 : first fusion; C 1 : melt crystallization; and F 2 : second fusion.

Integration and conversion during crystallization and fusion measurements
The crystallizable mass conversion during crystallization or fusion, x = x (t), was estimated using Equation 1, through the energy flow between the starting and ending points previously defined.
where: J is the heat flow of the phase transition and ' t the time for partial conversion; J 0 is an adequate baseline and E 0 (Equation 2) refers to the total exchanged heat between the specimen and the neighborhood during the event [22] .
the crystallization or fusion rate c = c (t) was computed using Equation 3 [22] .
The degree of crystallinity X c developed during the event was evaluated using Equation 4: In this work, the equilibrium melting enthalpy used for PBT was 140 J/g and the equilibrium melting temperature was 0 226 Figure 2 shows SEM image of PBT/10% TiO 2 where the white dots are TiO 2 which are well dispersed in PBT matrix as a result of the proper compounding parameters. The applied magnification was 10.000 x.

Melt crystallization (C1) measurements
Relative crystallinity (X rel ) and crystallization rate (dx/dt) as temperature functions for PBT and PBT/1% TiO 2 using the investigated cooling rates are displayed in Figure 3. The Supplementary Material presents plots for PBT/5% TiO 2 , and PBT/10% TiO 2 (please see Figure S3 and S4).
Sigmoidal behavior was verified for X rel plots in Figure 3a and 3b characterizing the phase transition without discontinuities, commonly observed in polymers [24] . The dα/dt showed bell shape, increasing at the beginning of crystallization which is related to nucleation and primary crystallization, reaching the top and decreasing afterwards configuring the secondary crystallization and spherulites impingement [25] .
Sigmoids obtained from the higher cooling rates are displaced to lower temperatures due to the time effect, i.e., upon higher cooling rates exists less time for the nucleation, and crystal growth occurs at lower temperatures [26] . The crystallization rates increase for the higher cooling rates as may be confirmed from the heights of the bellshaped curves. Quantitative data for the crystallization rates is tabled in the Supplementary Material (Table S1). Concerning the TiO 2 addition in general, sigmoids of PBT/ TiO 2 were displaced to lower temperatures, nevertheless, the filler effect is nonlinear, and this topic is further discussed in terms of activation energy. Figure 4a and b presents the sigmoids collected for F 1 and F 2 , respectively, the corresponding melting rates are also shown within the plots. In general, the fusion is less sensitive to the heating rates and TiO 2 addition which is evidenced as subtle bell peaks displacement. During the first fusion, both compounds presented quite similar melting rates and molten fraction profiles, light dissimilarity was verified for PBT/ 10% TiO 2 that melted in a lower temperature range. The readers may find additional molten fraction plots in the Supplementary Material, please see Figure S2 and Figure S8.

First (F1) and second (F2) fusion measurements
Regarding F 2 , the investigated compounds presented quite similar sigmoid and melting profiles, nevertheless, contrarily to F 1 , F 2 peaks displayed complex character which may be linked to distinct morphologies and crystals perfection [27] ; it seems there are smaller/imperfect crystals that melt in the temperature range from 200 to 220 o C while the most perfect/bigger melt between 220 and 240 o C [28,29] . It is supposed there was crystal reordering during the melt crystallization and second heating which promoted the development of higher perfected crystals, similar trend is reported in the literature for PP, PET, Nylon 1212 [30][31][32] , for instance. Apparently, TiO 2 addition did not significantly change the F 2 trend, however during F 2 higher melting rates were verified suggesting easier melting, deeper discussion related to this topic and its relationship with the activation energy for melting is further on presented.
The degrees of crystallinity computed for F 1 and F 2 are displayed in Figure 5. In general, X c decreased with increasing the heating rate, specifically for the heating rates higher than 10 o C/min, since for higher heating rates there is reduced time for the crystal formation. The thermal environment changes rapidly hindering or interfering in the crystals' nucleation and growth, hence producing shorter or imperfect crystallites [33] .  Regarding TiO 2 addition, the composites presented a slight increase in Xc, i.e., approximately 4% higher.

Melt crystallization kinetics -Pseudo Avrami
Aiming to further analyzing the non-isothermal melt crystallization, the kinetics of crystallization of neat PBT and PBT/TiO 2 composites was analyzed. The relative crystallinity as crystallization time function was computed as the exothermic peak areas ratio using Equation 5: where: c dH dt is the released heat; rel X is the relative crystallinity measured from the peak integration as the ratio between the total and partial peak's area, 0 t and t ∞ are the onset and end melt crystallization times.

Pseudo-Avrami modeling
Avrami [33][34][35][36][37] developed a macrokinetic model to investigate the isothermal crystallization, based on microkinetics approaches. The Avrami model considers the relative crystallinity x as time function τ computed in the event starting according to Equation 6: K = K(Τ) and n = n(Τ) are the Avrami's parameters. K is the rate constant evaluated considering the nucleation and crystalline growth rates, and n is the Avrami exponent which is related with the crystallite geometry [37][38][39][40] . Nonisothermal crystallization data, acquired using constant cooling rates may be correlated through an expression formally identical to Avrami Equation 7: Nevertheless, when using this model for nonisothermal crystallization investigations the parameters K' and n' are the heating rate φ functions, and not of temperature as in the Avrami model. Therefore, our researcher group has named Pseudo-Avrami [25,26] .
The relative crystallinity of PBT and PBT/TiO 2 composites are displayed in Figure S9 which presents the theoretical (solid lines) and experimental (symbols) data. All plots displayed sigmoidal shapes characterizing continuous phase transition as commonly observed in polymers. Plots in Figure S9 present reasonable fits without huge deviation between the experimental and theoretical data. Only for PBT/10% TiO 2 cooled at 5 °C/min presented deviation at the end of the primary crystallization. It can be verified that the experimental relative crystallinity developed subtly higher than the theoretical predictions, in general, when using rates lower than 10 o C/min and higher than 20 o C/min higher deviations are computed, which may be linked to the noise and time-lag effects, additionally, for PBT/10% TiO 2 it is supposed to be also linked to the TiO 2 addition influence. Nevertheless, in general, Pseudo-Avrami described the crystallization of PBT and PBT/TiO 2 composites in  a reasonable mode. The sigmoids may be divided into three stages, i.e., the first stage due to the nucleation, the second stage due to the primary crystallization which takes place at an accelerated rate with a high amount of mass transformation, and the third stage due to the secondary crystallization that is slower and more prominent for the slower cooling rates. It is related to crystallite impingement when the crystallization is finishing [37,41] .
As above verified for the crystallization rates, increasing the cooling rates displaced the sigmoids to higher times (lower temperatures), in general upon higher cooling rates the specimen crystallizes faster nevertheless the developed crystallites are shorter and/or imperfects, thus depending on the desired morphology the cooling rates may be a proper tool to attain it. As mentioned, the sigmoids may be divided into three stages, i.e., nucleation, primary crystallization, and secondary crystallization, related to the discrepancy between theoretical and experimental data the higher deviation was verified during the begging, 0 < X rel < 10% and the crystallization ending, i.e., X rel > 80%.
From the sigmoids presented in Figure S9 the Pseudo-Avrami plots were built and are presented in Figure 6, through the plots of Y versus ln τ according to Equation 6. Linearity deviation was mainly verified when the crystallization was beginning and when it was finishing as illustrated. Clearly, Pseudo-Avrami plots may be divided into three stages: 1 stnucleation, 2 nd -primary crystallization, and 3 rd -secondary crystallization, corroborating with presented data in Figure S9.
The discrepancy between theoretical and experimental data was measured and data are presented in Figure 7 for PBT/1% TiO 2 . In general, the higher deviation was verified for higher cooling rates, and for the beginning and ending of crystallization as mentioned. Whether the analysis is concentered between 20% < X rel < 80% the discrepancy goes down as demonstrated in Figure 7b, confirming Pseudo-Avrami fits quite well the crystallization from the melting of PBT and PBT/TiO 2 composites. Figure 8 presents the crystallization rate constant (K') and maximum crystallization rate (C max ) as the cooling rate function for the investigated compounds, both parameters are related to the crystallization rate and through the displayed data they increased with the cooling rates, i.e., theoretical and experimental crystallization rates followed similar trend [26,[42][43][44][45] . For a given cooling rate, the crystallization rate was higher for neat PBT indicating somehow TiO 2 decreased PBT's crystallizability, i.e., decreased PBT's ability to fast crystallize and hinder the transformation mechanisms, i.e., nucleation, primary and secondary crystallization, possibly changing the activation energy for the crystallization as further on investigated. In the Supplementary Material, in Table S2 the readers find the Pseudo-Avrami exponent and the R 2 parameter.

Mo and co-workers modeling
Mo and co-workers [45,46] developed a model to correlate non-isothermal crystallization parameters in polymers tested using constant cooling/heating rates, assuming the needed time τ to reach a given level of relative crystallinity due to the cooling/heating rate φ, according to Equation 8:  Figure S12c shows sigmoids for PBT/5% TiO 2 where symbols are the experimental data acquired during cooling, and the solid lines are the theoretical data computed according to Mo model. Plots presented quite good fits between experimental and theoretical data with subtle deviation at the crystallization extremes, i.e., beginning and ending, i.e., possibly linked with the nucleation and spherulites impingement, following a similar trend as already observed for Pseudo-Avrami model. From these sigmoids Mo plots were built and presented in Figure S11d for PBT/10% TiO 2 and 10% < X rel < 90% from an overview of these data may be suggested Mo is adequate to modeling PBT and PBT/TiO 2 composites. Plots for other compounds are displayed in the Supplementary Material; please see the Figure S11 and Figure S12. Figure 9 shows the discrepancy between the theoretical and experimental data for PBT/10%TiO 2 evaluated using Mo model, following a similar trend as already observed for Pseudo-Avrami. A huger deviation was observed at the beginning and end of crystallization, nevertheless if assumed the range 20 < X rel < 80% the deviation is quite low, i.e., less than 5% which confirms Mo model describes very well the crystallization from the melt of PBT compounds [41,47] .
Mo parameters F and α were measured using Equation 9 and are graphically presented in Figure 10 [47,48] . In the Supplementary Material, Table S3 the readers find the R 2 parameter for the investigated compounds.
F increased with the degree of crystallization, i.e., for higher crystallinity much energy must be supplied to the system; a quite similar trend was observed for PP/PET blends as reported by Zhu et al. [49] . Related to TiO 2 addition, PBT composites displayed higher F suggesting that with the crystallization development the composites need much energy [50][51][52] .
Mo exponent slowly increased with the degree of crystallinity suggesting crystalline structures more complexes were produced with the crystallization advance, i.e., nuclei are formed, as crystallization advance new macromolecules are added, progressing to the fibrils and then to the spherulites, which increase in size and can become more crystalline with the crystallization improvement, their crystallinity also depending on the applied crystallization parameters (time, temperature, cooling/heating rates), which can be used to control the whole crystallization. Parameters reported in the present paper may be used as proper tools to control the crystallization rate and the degree of crystallinity of PBT and PBT/TiO 2 composites.
The following section presents the calculations for the activation energy for the melt crystallization and for the fusions.

Activation Energy ( a E ) -Melt crystallization
The conversion rate of a chemical reaction is commonly reported as the product of a temperature-dependent rate constant K(T) and a function of the f(x) conversion characteristic of the reaction mechanism, as shown in Equation 10: Isoconversional models are more applied to determine the activation energy of crystallizations. Friedman's model [53,54] is based on the logarithmic of the conversion rate assuming a constant rate K(T) defined by Arrhenius, which is shown in Equation 11: Where A is a pre-exponential factor constant and R = 8.314 J K -1 mol -1 is the universal gas constant. Transformations from the amorphous/disordered state to the crystalline state in polymeric melt are considered  complex reactions; therefore Equations 10 and 11 must be generalized to: Generally, a E is a function of conversion (in this case it is a function of (X rel ) and Equation 12 can be converted to the logarithmic form: , this treatment repeated for the different values of X rel results in a E as function of X rel . This method was applied in this work for X rel ranging between 0 and 1.0 as shown in Figure 11.
As can be seen from Figure 11, all activation energies are negative, indicating that energy has to be removed from the system in order to promote the melt crystallization.
Considering the absolute values of the activation energies, less energy has to be removed from the system for the TiO 2 / PBT compounds when compared to neat PBT. The only   exception from this behavior is the composition with 10% TiO 2 load in the range 0-30% of relative crystallinity, which could be attributed to a measurement error. The fact that all the curves of a E versus X rel show up as almost parallel lines indicates that there is no significant change in the melt crystallization mechanism when adding the TiO 2 . The effect of filler is also nonlinear. A quite similar nonlinear shifting of activation energy curves was reported by Ries et al. [55] for the cold and melt crystallization of PHB/ZnO composites.

Activation energy ( a E ) -First fusion
In contrast to crystallization kinetics, fusion kinetics has been rarely investigated [56] . Few studies report polymer fusion kinetics by means of isoconversional kinetic models [57][58][59] . A differential or integral isoconversional method may be applied depending on the nature of the experimental data. If the reported data are from DSC measurements, therefore, Friedman's differential isoconversional method [53,54] may be used.
Toda et al. [20,60] proposed a nucleation model for polymer fusion which fusion starts with melting the cylindrical cores. However, Friedman's isoconversional model is powerful to study the fusion kinetics and evaluate a E under superheating [61] . In those situations, a decrease in s of the fusions upon temperature increase is expected [62] . This behavior was mostly observed in this work.
The numerical optimization method [63] is based on the data of Friedman analytical method. The acquired data from the Friedman method such as E(x) and A(x) are numerically optimized, the best fit between the experimental plots is obtained through non-linear optimization based on the least squares method. For fusion, this model-free method was the most suitable in this work, due to the better R 2 of the analytical plot, which ranged from 0,932 to 0,996. a E s were computed using the numerical optimization method and plotted as molten fraction function. Figure 12 shows a E for the first fusion of PBT and PBT/TiO 2 composites. Neat PBT fusion requires the highest activation energy; while the lowest a E was observed for PBT/1%TiO 2 then a further increase in filler content raises the activation energy again. This behavior is similarly nonlinear as the trend verified for the melt crystallization.

Activation energy ( a E ) -Second fusion
a E for the second fusion of investigated compounds was measured using the numerical optimization method, similarly to the first fusion. This method based on the Friedman model presented quite high R 2 , i.e., 0,975 < R 2 < 0,996. Plots are presented in the Supplementary Material, please see Figure S14.
Acquired a E s are plotted as molten fraction (X m ) function and shown in Figure 13. All investigated compounds presented a similar profile, i.e., a E decreased upon the fusion advance, the only exception observed was an increase in for X m > 95% until the end of fusion. In the final stages of the second fusion, the verified trend for a E was: E 95%PBT > E 90%PBT > E 99%PBT > E 100%PBT . During the second melting, there were no significant variations in a E with TiO 2 addition and similarly to the first melting, there was no linear trend between TiO 2 and the computed a E . From Figure 12 and Figure 13 it may be verified that the second fusion character is quite different from the first one, as the first fusion is related to the quenched material from the mixing while the second fusion is related with the melt crystallized material, hence the second fusion was computed during the second heating with different thermal history and mainly distinct morphology altogether would be conducting to different activation energy as displayed in Figure 13

Conclusions
PBT/TiO 2 compounds were successfully melting mixed; according to SEM images, TiO 2 nanoparticles are well dispersed in the PBT matrix without evidence of agglomeration. The melt crystallization, fusions, and activation energy ( ) a E were evaluated based on DSC scans. Upon the integration of the DSC scans, the thermal events were visualized as sigmoids, indicating continuous phase transformation. Higher cooling rates shifted the sigmoides of the melt  crystallization to lower temperatures, while the fusions were almost insensible to the heating rates. Pseudo-Avrami and Mo models fit the melt crystallization kinetics quite well with subtle deviation only verified at the beginning and end of the crystallization, nevertheless quite high R 2 parameters were acquired. Standard negative activation energies were computed for the melt crystallization and positive activation energies for the fusions; the Friedman model was applied to both phase transition evaluations and high R 2 values suggest that they are a proper methodology. As expected, the activation energies decrease upon temperature increase for all filler contents.

Supplementary Material
Supplementary material accompanies this paper. Figure S1. Typical DSC scan for PBT, collected during applied thermal cycles for the heating/cooling/re-heating of 10 o C/min. Dotted red line is the applied thermal program. Solid blue line the heat flow signal with the investigated phase transitions, i.e., F 1 . Figure S2. The half melt crystallization time τ 1/2 (dashed line) and melt crystallization rate (solid line) of produced compounds as function of tested cooling rates. Figure S3. Relative crystallinity (solid line) and Crystallization rate (dotted line) as temperature function. Compounds and cooling rates indicated. Figure S4. Relative crystallinity (solid line) and Crystallization rate (dotted line) as temperature function. Compounds and cooling rates indicated. Figure S5. Molten fraction (solid line) and Melting rates (dotted line) as temperature function of F 1 . Compounds and cooling rates indicated. Figure S6. Molten fraction (solid line) and Melting rates (dotted line) as temperature function of F 2 . Compounds and cooling rates indicated. Figure S7. Pseudo-Avrami plots of neat and PBT/TiO 2 cooled at indicated cooling rates illustrating crystallization development in three stages. Figure S8. Pseudo-Avrami plots of composites a) PBT/1%TiO 2 , b) PBT/5%TiO 2 and c) PBT/10%TiO 2 computed for the indicated cooling rates. Figure S9. Relative crystallinity of a) neat PBT, b) PBT/1%TiO 2, c) PBT/5%TiO 2 and d) PBT/10%TiO 2 at displayed cooling rates. The theoretical data are solid lines and the experimental are symbols. Figure S10. Discrepancy for the whole melt crystallization of a) neat polymer, b) PBT/5%TiO 2 and c) PBT/10%TiO 2 at indicated cooling rates. And Discrepancy for the melt crystallization between 20% < X rel < 80% of d) neat polymer, e) PBT/5%TiO 2 and f) PBT/10%TiO 2 . Plots built according to Pseudo-Avrami model. Figure S11. Mo plots for the melt crystallization of a) neat PBT, b) PBT with 1%TiO 2, c) PBT/5%TiO 2, and d) PBT/10%TiO 2 at indicated degree of crystallinity. Figure S12. Relative crystallinity for the melt crystallization of a) neat PBT, b) PBT/1%TiO 2, c) PBT/5%TiO 2, and d) PBT/10%TiO 2 at indicated cooling rates. Figure S13. Deviation between theoretical and experimental data during the melt crystallization evaluated using Mo model (cooling rates indicated) of a) neat PBT, b) PBT/1%TiO 2 and c) PBT/5%TiO 2 . And discrepancy evaluated for 0 < X rel < 80% of d) neat PBT, e) PBT/1%TiO 2 and f) PBT/5%TiO 2 . Figure S14. for the second fusion of PBT and PBT/TiO 2 composites using the numerical optimization method Table S1. Melt crystallization data for indicated compositions and rates. Table S2. Pseudo-Avrami expoent (n'), R 2 and degree of crystallinity (X c %) for the investigated compounds.