Nonisothermal Melt Crystallization Kinetics of PHB/babassu Compounds

PHB has interesting features such as biodegradability, sustainability and durability. However, it has a high cost, in addition to being hard, brittle and thermally unstable during processing. Therefore, it was found convenient to study the crystallization of PHB/20% babassu compounds, with the intention of reducing the cost of the composite, in addition to seeking improvements in thermal properties. In this work, the parameters of melt crystallization were studied for PHB/20% babassu compounds driven at different cooling rates under a nitrogen flow. Subsequently, crystallization parameters were compared for different cooling rates. A kinetic analysis of data obtained for melt crystallization was performed. Among the models studied, Pseudo-Avrami showed the best correlation with experimental data, with discrepancy between +6% and -4%. The Mo model presented a discrepancy between +15% and -8%. A modified Mo model discrepancies are reduced to +3% and -4% within the range of validity of the model.


Introduction
Due to the large amount of synthetic plastic waste produced by modern societies, lack of space in landfills, emission of toxic gases in incineration, and their negative impact on the environment, there is a growing interest in biodegradable polymers to substitute conventional polymeric materials [1][2][3][4][5] . Polyhydroxyalkanoates (PHA) are a family of biopolyesters that could be synthesized by microorganisms from various substrates as carbon sources. Poly(3-hydroxybutyrate) (PHB) is a well-known polymer of this family [6][7] .
PHB is a semicrystalline thermoplastic, biocompatible and biodegradable, naturally produced by bacteria from renewable sources (sugar or starch) [8][9][10][11] . PHB has interesting mechanical and barrier properties, similar to those of polypropylene, and can be processed in conventional industrial equipment [12][13] . However, PHB is thermally unstable at processing temperatures and combines a high crystallinity with a low crystallization rate, characteristics which limit its applications [12][13][14] . Copolymerization of 3-hydroxybutyrate (e.g., with 3-hydroxyvalerate) partially addresses these issues, but the resulting copolymer (PHBV) still exhibits a very narrow processing window. Additives, blends, and composites are other ways to overcome these problems 4,7 .
Recent research on crystallization of PHB in blends and compounds, focused on improving mechanical and thermal properties, have been reported in the literature 15-20-48-50 . Composites with natural fillers are a good option to modify PHB and improve its properties. Vegetable fibers have good mechanical properties, are fairly compatible with the polar matrix of PHB, and, by its very nature, are completely biodegradable and frequently biocompatible and nontoxic 20,21 ; they are inexpensive (compared with the polymer matrix) and naturally abundant.
Among the vegetable fillers, the shell of the fruit of the babassu palm tree is rich in cellulosic fiber, and is a byproduct of extractivist activities centered in the production of oil from the seeds of the fruit. As such, it is a renewable natural resource, obtained without the use of agrochemicals or fertilizers. PHB/babassu compounds are thus very close to the ideal ecofriendly material, if only their properties and processability are found to be reasonable 22 .
The nonisothermal crystallization characteristics of polymeric compounds are important tools to characterize the microstructure of the materials and study filler-matrix interactions. Moreover, crystallization is a key step in many processes, including extrusion and molding. Reliable information about the kinetics of nonisothermal crystallization may be useful in designing and optimizing commercial processes for the production of films, fibers, etc 23 . Differential scanning calorimetry has been employed for some time to generate this information 24 . However there is a lack of quantitative correlations, critically evaluated in terms of its predicting ability, to estimate the evolution of crystallinity and its dependence on time, temperature and rate of cooling.
The objective of the present work is to study the effect of processing time, and the type and initial particle size of the filler, on the nonisothermal crystallization parameters of PHB/20% babassu compounds. In addition, the suitability of two macrokinetic models for nonisothermal melt crystallization (Pseudo-Avrami and Mo) to correlate the experimental results is investigated. A new, improved version of the latter is presented. No attempt is made to "explain" the results of thermal analysis in structural terms, as we believe that without in depth microscopic studies and other characterization techniques, interpretation of DSC results alone are mostly unwarranted speculation.

Materials
The matrix for the compounds, called PHB, is actually the random copolymer of 3-hydroxybutyrate (3HB) and 3-hydroxyvalerate (3HV) containing approximately 4% units of 3HV. It was supplied by PHB Industrial SA (of Serrana SP, Brazil), commercial grade FE-141. According to the manufacturer it has a density of 1.20 g/cm 3 (ASTM D729) and a melt flow rate of 23-25 dg/min (ASTM D1238, 190°C/2.16 kg).
As filler, two types of vegetable fiber were used, taken from the outer (epicarp) and intermediate (mesocarp) layers of the shell of the fruit of the babassu palm tree, codified in the present work as EPI and MESO, respectively. The filler was supplied by a cooperative of local producers, MAPA (São Luis MA, Brazil). Two different granulometries were employed, resulting from screening of the raw materials: one with average particle size between 150 and 75 (code #100) and other with average particle size between 45 and 75 µm (code #200).

Processing
Polymer and filler were dried for 4 h at 60°C immediately before processing in a laboratory internal mixer Haake Rheomix 600 with high intensity (roller type) rotors at 60 rpm, keeping the chamber wall at a constant temperature of 160°C. The initial fill factor was about 70%. Compounds with 80% PHB and 20% (w/w) babassu fiber were prepared at two processing times, 4 min and 8 min, in order to study the combined effect of mixing and matrix degradation 25 .

Thermal Analysis
Tests were conducted in a Mettler-Toledo DSC-1 instrument with 5 to 10 mg samples in standard aluminum crucibles under a constant inert gas (nitrogen) flow of 50 mL/min. The samples were subjected to a three-stage thermal program: heated from ambient temperature (25°C) to 185°C at 16°C/min, cooled at different constant rates (2, 3, 4, 6, 8, 12, 16 e 24 °C/min), and reheated at either 4 or 16°C/min. A common and relatively fast initial heating rate was chosen to minimize matrix degradation and provide a uniform molten material before the critical stage of polymer crystallization from the melt 41 .
Raw time (t), sample temperature (T) and heat flow (J) registered by the instrument at 1 s intervals were integrated, using a suitable virtual baseline (J 0 ) and onset/end points visually determined (t 1 ,t 2 ), for the melt crystallization event during cooling. Custom software was employed to obtain the relative crystallinity (x) and rate of crystallization (c) as functions of time and temperature: is total latent heat of phase change. Time and temperature are related through the constant rate of cooling, φ = |dT/dt|: From the functions x(T) and c(T) a series of characteristic crystallization parameters could be estimated. For example, the crystallization (or fusion) temperature interval is estimated from temperatures at which conversion (x) reaches 0.1% and 99.9 %: (5) and the half-crystallization time: (6) Mass crystallinity recovered during the event is estimated as: where m s is the sample mass, w P is the mass fraction of the polymer (PHB) and Hm 0 D is the latent heat of melting of a 100% crystalline polymer, taken in the present work as 146 J/g 26 .
While considering parameters derived from the experimental data obtained by differential scanning calorimetry, allowance should be made for the relative imprecision of this technique. Following expert recommendation 24 discrepancies below 5% (or ± 1°C in temperatures) will be disregarded.
The thermogravimetric analyzes were conducted on a Shimadzu DTG-60H instrument, using alumina crucible under nitrogen atmosphere, with an approximate mass of 5 mg samples. The samples were heated at a heating rate of 10°C / min from 25 to 600°C for the loads and from 25 to 800°C for the composites. Filler particle distribution and filler/matrix interface were explored by scanning electron microscopy (SEM) with a Shimadzu SSX-550 instrument. Samples consisted of impact test specimens fractured in liquid nitrogen and metallized. Their fracture surface was observed at several magnifications between 500x and 2000x 39 .

Results and Discussions
As reported elsewhere 27,28,30,[39][40][41][42][43][44] PHB crystallizes only partially from the melt during the cooling stage, and the crystallization process is completed during the reheating stage (cold crystallization). However, in PHB compounds with 20% babassu fiber content, full melt crystallization was verified in all tests, suggesting a strong nucleating effect of the filler. Melt crystallization shows simple, fairly symmetric exothermic peaks in the DSC scans.

Effect of filler type, particle size, and processing time on melt crystallization
Some melt crystallization parameters obtained using the procedures described in the previous section are collected in Table 1 for DSC tests performed at two different cooling rates (4 and 16°C/min) on samples processed for two different times (4 and 8 min) and compounded with different filler types (epicarp and mesocarp of babassu fruit) and different initial particle sizes (#100 and #200). Comparisons in graphical form are presented in Figure 1, plots of the normalized melt crystallization peak -the rate of crystallization Eq.(2).
Filler type (epicarp versus mesocarp), even with the same particle size, moderately affected the melt crystallization parameters (Table 1 and Figure 1a). Mesocarp facilitates PHB crystallization, which runs 15% faster and takes place at 2.5°C higher temperature. The 2 to 5% higher crystallinity observed is probably within the expected uncertainty.
It has been shown 29 that the mild processing conditions in the laboratory internal mixer have little effect on filler particle size. Moreover, particle size has a discreet effect on PHB crystallization at 4°C/min (and none at 16°C/min), as shown in Table 1 an Figure 1b. Samples processed for only 4 min correspond to materials that were "just molten" in the mixing chamber; filler dispersion resulting in this case from mixing during the matrix melting process only. Samples processed for 8 min were given an extra 4 min of melt mixing to complete the filler dispersion process. However, the extra time at processing temperature, even under the mild conditions in the internal mixer chamber, is known to result in significant PHB degradation 30 . Notwithstanding, experimental results (Table 1 and Figure 1c) show that processing time did not affect significantly the crystallization parameters.

Thermogravimetric analysis (TGA)
The thermogravimetric analyzes were conducted in a Shimadzu DTG-60H instrument, using alumina crucible under nitrogen atmosphere, with an approximate mass of 5 mg samples. The samples were heated at a heating rate of 10°C / min from 25 to 600°C for the loads and from 25 to 800°C for the composites.

Effect of cooling rate on melt crystallization
The sample of PHB/20% babassu epicarp #100 processed for 8 min was selected for in depth analysis of the melt crystallization process. Figure 3 shows the relative crystallinity (fraction crystallized) and crystallization rate computed by integration of the DSC output, in tests performed at eight different cooling rates. As discussed in the Experimental section, the melts were obtained in all tests by heating the sample from ambient temperature to 185°C at the uniform rate of 16°C/min. Table 2 collects some important crystallization parameters, whose dependence on the cooling rate is depicted graphically in Figure 4.
The trends observed are as expected: crystallization temperature decreases and crystallization rate increases as   cooling rate increases, with an almost logarithmic dependence, while crystallinity remains approximately constant. An interesting fact -that could be exploited if these results are to be used in process simulation -is the regularity of the temperature and rate dependencies on cooling rate, and wider data dispersion for the crystallinty and half-crystallization time.

Crystallization kinetics
Crystallization macrokinetic models are useful to correlate experimental data. Even the most "theoretical" of them -the Avrami model for isothermal crystallization -is being described as such: "all in all, the Avrami analysis is rather a convenient representation of experimental data than a way of obtaining physical insights in the polymer crystallization kinetic" 31,32 . One of the major uses may be to insert them "into processing and manufacturing protocols to rationally develop and control commercial processes in which crystallization is one among several concurrent phenomena" 23 . Consequently, the value of macrokinetic models lies more on how well they predict the experimental data from which they are derived, less in the structural or microscopic interpretation of the model parameters.
In the operating conditions of a process, the cooling rates may or may not be greater than the experimental ones. However we are limited with the capacity of the equipment.

Pseudo Avrami model
The simplest model to correlate the relative crystallinity x with time since the onset of the crystallization event τ = t -t 1 in nonisothermal melt or cold crystallization events, measured at constant heating/cooling rate is formally based in the well-known Avrami equation: developed for isothermal crystallization processes. K' and n' are the parameters of the model, which are functions of the heating/cooling rate. These parameters have no connection with the true Avrami parameters (that are functions of the Pseudo-Avrami model should be taken as an empirical correlation for macroscopic nonisothermal data; its parameters have no microkinetical or structural meaning at all. Figure 5 shows an example of Pseudo-Avrami plot. Notice that the interval selected for the linear regression was carefully adjusted, with the aid of the right axis scale, to include the most relevant zone, roughly 1 to 95% conversion. Table 3 shows the parameters estimated in this way, which are presented graphically -as functions of the cooling rate -in Figure 6. Uncertainty of the individual parameter values is very low (between 0.1 and 1%) but for the model to be really useful in processing calculations, the parameters should be expressed by function valid for any cooling rate (within the interval tested). Parameter K may be represented as a simple function: and exponent n is almost constant (independent of the cooling rate), albeit with a significant dispersion (within 5%):n=0.405±0.220, as can be seen in Figure 6.
Model predictions should be tested against experimental data to assess the validity of the model. Figure 7 compares the relative crystallinity measured and predicted by the Pseudo-Avrami model in three particular cases, showing a good fitting.
For a more quantitative analysis the relative discrepancy between model and experimental data defined as: (10) is plotted against the conversion in Figure 8 for all tests performed. Pseudo-Avrami model results in estimates of relative crystallinity within + 6% and -4% of the experimental data. Pseudo-Avrami overestimates the conversion during the first half of the melt crystallization process and underestimates it during the second half.

Mo model
A macrokinetic model attributed to Mo 35-37 correlates the rate of heating/cooling φ = |dT/dt| to the time measured since the onset of crystallization, τ = t -t 1 , with data obtained at constant relative crystallinity: Mo model, despite claims of its authors (that it should be taken as motivation, not proof) is a purely empirical correlation procedure, whose justification cannot be sought in "theory" but in the model's ability to represent experimental data within an acceptable level of discrepancy.
Mo parameters, F and α, are function of the conversion x. The model may be used to correlate both cold and melt crystallization results. However, since nonisothermal DSC tests are usually conducted at constant heating/cooling rate, experimental results taken at several values of φ must be interpolated to extract from them the information at constant relative crystallinity. Formally: Once the interpolated results are computed, Mo parameters could be estimated from a linear regression on the expression derived from Eq.(11): (12) Figure 9 shows Mo plot for PHB crystallization in PHB/20% bassssu fiber (epicarp #100) compounds at nine different values of the conversion, and Table 4 collects Mo parameters thus estimated.
Uncertainty in the parameters is very reasonable (1.8% for lnF, 3.5 to 5% for α) but still significantly higher than Pseudo-Avrami parameters. However, the dependence of Mo parameters with relative crystallinity, shown graphically in Figure 10, is very smooth (compare Figure 10b with Figure 6b). The smoothness of the relationship recommends Mo model for applications in which the parameters must be estimated for arbitrary values of the conversion, such as process simulation.
Parameter F may be represented as cubic expression on x:  and exponent α as linear function of the same : Variable x in the previous expression is expressed as fraction, 0 < x < 1 (not percentage).
However, proof of utility of any empirical model consists on the goodness of fit between model prediction and experimental data. It is in this area that Mo model is found wanting. In the first place, Mo model is unable to represent the experimental data for the onset and end of the crystallization process. Mo model, whatever the parameters be, doesn't lead to a true sigmoid x = x(T), and exhibits -unlike experimental data -finite rates of crystallization in the limits x → 0 and x → 1. It can be shown, starting from Eq.(11) and after a long series of mathematical manipulations, that the differential form of the Mo model, with both parameters depending on conversion, is given by: (13) .
. From Eq.(13), in general: (14) Moreover, fitting at intermediate values of the relative crystallinity -even with best parameters -is not particularly good, as shown in Figure 11 for the system tested, which shows a typical behavior 38 .
The quantitative differences between predicted and experimental values is better appreciated defining a discrepancy function, equivalent to Eq.(10), and plotting it against the relative crystallinity. For Mo model we chose the difference between predicted and experimental crystallization time needed to reach a given level of conversion, and using the half-crystallization time, Eq.(6), as a characteristic value: (15) Figure 12 shows such a plot. Discrepancies are highly cooling rate dependent and vary between +15% and -8% within the range of validity of the model (5-95% conversion).
A small modification of the model may improve dramatically its performance. A modified Mo model is defined by: (16) where the new parameter σ -a function of the heating/ cooling rate -is selected to match predicted and experimental crystallization times for x = 50%. Table 5     dx 0 shows the discrepancy in crystallization times as a function of the conversion. Discrepancies are reduced to +3% and -4% within the range of validity of the model, as can be seen in Figure 14.
Discrepancies below the reproducibility of experimental data and smooth dependence of parameters on the cooling rate made the modified Mo model the best choice to correlate relative crystallinity with crystallization time for PHB/20% babassu compounds, except during the initial (x < 5%) and final (x > 95%) stages of the process.

Scanning electron microscopy (SEM)
Scanning electron microscopy studies of biodegradable composites show that the charges are significantly different.
The babassu mesocarp is formed by relatively uniform and isometric particles of diameter between 20-50 micrometers as shown in Figure 15.
On the other hand, the epicarp shows a heterogeneous morphology with the presence of anisotropic particles as bundles of fibers, as shown in Figure 16.
Lemos et. al (2017) performed a detailed study on the structure of babassu fiber, in addition to wood and sugarcane fibers, using characterization techniques such as surface  Figures 15 and 16. Santana et al. (2010) show the importance of the chemical treatment of the fiber to improve the adhesion between the polymer matrix and the load and how the treatment acts in different parts of the babassu: epicarp and mesocarp. This topic will be covered in more detail in the next article.

Conclusions
A detailed study by DSC of the noinsothermal melt crystallization of PHB in PHB/20% vegetable fiber (babassu) compounds prepared by melt mixing was presented. It was found that initial particle size and processing time have little effect on the crystallization characteristics of the polymer, while the origin of the fiber (epicarp or mesocarp of the   fruit) moderately affects them. It was also found that -unlike what is reported elsewhere for neat PHB -the crystallization process is completed during the cooling stage in PHB/ babassu compound, the filler acting probably as an effective nucleating agent. Cooling rate, while affecting crystallization temperature and rate as was expected, has no effect on the degree of crystallinity developed in the event.
Pseudo-Avrami kinetic model correlates well experimental data over the whole conversion interval, with deviations of 5%. However, uncertainty of interpolated data is highly affected by rough dependence of model parameters on cooling rate. The opposite behavior was found for the model proposed by Mo and collaborators: deviations are relatively large (±15%), but interpolation is facilitated by the smooth dependence of the parameters on relative crystallinity. A modification of the original Mo model is proposed, which enhances its predictive capabilities (± 4% over the interval from 5% to 95% conversion). The modified Mo model is thus recommended as reliable predictive algorithm to correlate nonisothermal melt crystallization kinetics for the system under study.