**3. Results and Discussion**

A previous work by the authors has shown that grafting alcohols of different chain lengths onto the surface of CNCs using TDI as a linker is a relatively simple process for tailoring CNC surface properties [19]. As a result of this grafting, the water contact angle of the modified CNCs increased to 34◦ ± 4, 52◦ ± 3, 104◦ ± 1, or 120◦ ± 5 using ethanol, 1-butanol, 1-hexanol, or 1-octanol, respectively. In comparison, the water contact angle of PBS is 77◦ ± 3. This systematic reduction in hydrophilicity allowed the dispersion of CNCs in hydrophobic matrices such as PBS, which is in general not possible for unmodified CNCs. Moreover, thermomechanical studies showed that the surface modification had a direct positive impact on the reinforcement capabilities of the CNCs, as it improved their interfacial adhesion with PBS. The improvement increased with increasing the chain length of the grafted alcohol. In this paper, we performed further studies to investigate the impact of interfacial adhesion on the crystallization kinetics of PBS using the modified CNCs as filler.

The non-isothermal crystallization and melting behaviors of the neat and CNC-reinforced PBS were studied using DSC at four cooling/heating rates (4, 6, 8, and 10 ◦C/min) (Figure 2 and Table 1). The results showed that crystallization took place at higher temperatures for the reinforced PBS compared to the neat one due to the nucleation activity of the modified CNCs. A similar behavior has been observed for PBS composites using other nanofillers such as carbon nanotubes [39]. It is interesting that the nucleation activity of the modified CNCs was dependent on the chain length of the grafted alcohol. Using a cooling rate of 10 ◦C/min, the crystallization temperature (Tc) of the reinforced PBS was 82.2, 83.4, 84.5, and 86.6 ◦C using CNCs-TDI-Eth, CNCs-TDI-But, CNCs-TDI-Hex, and CNCs-TDI-Oct compared to 74.7 ◦C for neat PBS. This means a stronger interaction between PBS molecular chains and the modified CNCs with higher degrees of hydrophobization. The homogeneity of the crystallization process was also affected by the addition of the CNCs. Compared to the typical single crystallization peak of the neat PBS, the crystallization peak of the reinforced PBS had shoulders on its both sides. These shoulders indicate a special interaction between the CNCs and PBS during nucleation (first

shoulder) and secondary crystallization (second shoulder), which resulted in accelerating both of them. However, the shape of the primary crystallization peak does not look significantly different for the neat and reinforced PBS despite taking place at significantly higher temperatures. This implies that the interaction of the CNCs with PBS changes as crystallization progresses.

**Figure 2.** The crystallization exotherms of neat and reinforced poly(butylene succinate) (PBS (left)) (PBS+CNCs-TDI-Oct (right)) at different cooling rates (4, 6, 8, and 10 ◦C/min).


**Table 1.** The crystallization and melting parameters of neat and reinforced PBS at different cooling rates.

In terms of PBS melting behavior, the melting temperature was not affected by the CNCs (around 115 ◦C for all samples). However, the crystallinity was slightly affected. The PBS samples reinforced by CNCs-TDI-Eth and CNCs-TDI-But showed a slightly lower crystallinity than neat PBS, while those reinforced by CNCs-TDI-Hex and CNCs-TDI-Oct showed higher crystallinity. It was dependent on the alcohol chain length of the modified CNCs, which could be a result of the higher nucleation activity of the modified CNCs with increasing the chain length of the grafted alcohol. Overall, the crystallinity values are in accordance with those reported in the literature [34].

To estimate the nucleation activity of nucleating agents, a simple method was proposed by Dobreva and Gutzow [44]. They proposed the nucleation activity factor φ, which varies from 0 to 1 and represents the ratio between the heterogeneous and homogenous nucleation parameters, B\* and B, respectively (φ = B\*/B). B\* and B can be estimated by plotting lnβ versus the reciprocal of (Tm − Tc) 2 according to the following equation (C is a constant):

$$
\ln \beta = -\frac{B}{\left(T\_m - T\_c\right)^2} + C.
$$

when applied on the crystallization of neat and CNC-reinforced PBS, straight lines were obtained (Figure 3), and the slope was either the B value for the neat PBS or the B\* value for the reinforced PBS. Then, the nucleation activity factor was calculated (Table 2). According to the results, it is clear that PBS nucleation was accelerated in the presence of CNCs in general, as the B\* values of the reinforced PBS were all lower than the B value of neat PBS. Moreover, the nucleation activity was dependent on the surface properties of the CNCs as it increased with increasing the chain length of the grafted alcohol. This implies that stronger PBS/CNCs interfacial adhesion results in stronger nucleation activity, as suggested earlier in Table 1.

**Figure 3.** Nucleation activity determination for the neat and reinforced PBS using Dobreva and Gutzow's method.

**Table 2.** The estimated nucleation activity values for neat and reinforced PBS.


B value for the neat PBS and B\* values for the reinforced PBS.

To shed more light on the interaction between the modified CNCs and PBS, the crystallization kinetics of the composite samples were studied using the Avrami model [45]. It is one of the most commonly used models to describe the crystallization process of semi-crystalline polymers. It expresses the relative crystallinity of a polymer (*X*(*t*)) as a function of time (*t*) according to the following equation (where Z is the crystallization rate constant and n is the Avrami exponent) [46]:

$$X(t) = 1 - \exp\left(-Zt^n\right).$$

The Avrami exponent describes the mechanism of the crystallization process, and it is a term of two components: the dimensionality of crystal growth (nd) and the time dependence of nucleation (nn). The value of nd can be 1, 2, or 3 depending on if the crystal growth takes place in 1D, 2D, or 3D, respectively. The value of nn is close to 1 when nucleation is homogenous and close to 0 when nucleation is heterogeneous. As a result, the value of n is in the range from 1 to 4 (nd + nn) [47]. The crystallization rate constant and Avrami exponent can be estimated from the slope and intercept of the logarithmic version of Avrami equation [48]:

$$
\ln[-\ln(1 - X(t))] = n\ln t + \ln Z\_{-}
$$

The crystallization profiles of PBS and reinforced PBS at different cooling rates were all sigmoidal similar to the profiles of many other semi-crystalline polymers (Figure 4) [49]. The sigmoidal shape represents the different stages of crystallization. At first, nucleation takes place (first 60 s) followed by a rapid crystal growth (next 60–120 s) and ends by secondary crystallization (the last 30–60 s) [50]. Expectedly, crystallization took a shorter time to completion using higher cooling rates. It was also observed that the heterogeneity of crystallization seen in Figure 2 for the reinforced PBS did not significantly affect the smoothness of its crystallization profile because the relative crystallinity is cumulative. During the nucleation stage (first 60 s), the reinforced PBS samples reached higher relative crystallinity compared to neat PBS as a result of the nucleation action of the CNCs. This may explain the right shoulder of the crystallization peak of the reinforced PBS samples (Figure 2). However, crystallization took a longer time as a result of the hindrance imposed on the motion of the PBS chains by the surrounding CNCs (impeding effect).

**Figure 4.** Plots of relative crystallinity with time at different cooling rates for neat PBS (left) and PBS+CNCs-TDI-Oct (right).

To quantitatively assess the impact of the CNCs on PBS crystallization, the Avrami kinetic parameters were estimated by plotting the logarithmic version of the Avrami equation (Figure 5 and Table 3). The crystallization of the reinforced PBS samples followed the Avrami model better than neat PBS. It deviated mainly in the beginning due to the slow nucleation of neat PBS (as also observed in Figure 2) and due to ignoring the role of secondary crystallization in the Avrami model [46]. In the reinforced PBS samples, the nucleation activity of the CNCs compensated for this deviation by accelerating PBS nucleation. The Avrami exponent for the neat PBS decreased upon CNC reinforcement, indicating increased crystallization heterogeneity. Avrami exponent values close to 4 imply a three-dimensional crystal growth and homogeneous nucleation (neat PBS), while values closer to 3 implies also three-dimensional growth but following a heterogeneous nucleation (reinforced PBS). This is in accordance with the crystallization curves of the neat and reinforced PBS in Figure 2. When it comes to the crystallization rate constant (Z), it was lower for the reinforced PBS samples compared to the neat PBS due to the hindrance imposed by the CNCs on the migration and diffusion of the PBS chains to the growing crystals [51]. This was also evident from the higher half-time of crystallization (t <sup>1</sup> 2 ) values. This hindrance became less significant by reducing the hydrophilicity of the CNCs. It was the highest for the PBS sample reinforced by CNCs-TDI-Eth and diminished for the sample reinforced by CNCs-TDI-Oct. This may imply an optimum interfacial adhesion between PBS and CNCs-TDI-Oct, which supported a hindrance-free mobility of PBS chains during crystallization.

**Figure 5.** Avrami curves describing the crystallization of neat PBS (left) and PBS+CNCs-TDI-Oct (right) at different cooling rates.


**Table 3.** Avrami crystallization kinetics parameters of neat and reinforced PBS at different cooling rates.

It is possible to estimate the average activation energy (*Ea*) of crystallization for neat and reinforced PBS following Kissinger's method (*R* is the universal gas constant and β*<sup>o</sup>* is the exponential factor):

$$
\ln \beta = -\frac{E\_a}{R \bullet T\_c} + \ln \beta\_o.
$$

The estimated crystallization activation energy of neat PBS was 169 ± 5 kJ/mol (Figure 6). This value is in accordance with the values reported in the literature [36]. It increased to 266 ± 16 kJ/mol when PBS was reinforced by CNCs-TDI-Eth. This implies that crystallization was hindered, although the addition of the modified CNCs in general facilitated PBS nucleation. However, the activation energy was dependent on the surface properties of the CNCs. It decreased with increasing the chain length of the grafted alcohol. The activation energy was 236 ± 8, 225 ± 5, and 196 ± 11 kJ/mol using CNCs-TDI-But, CNCs-TDI-Hex, and CNCs-TDI-Oct, respectively. These conclusions agree with those made based on the estimated Avrami kinetics parameters (Table 2).

**Figure 6.** Kissinger plot to determine the activation energy of crystallization of neat and reinforced PBS.

In summary, the crystallization behavior of PBS was significantly affected by the addition of CNCs, which was dependent on their surface properties (Table 4). In general, CNC addition increased PBS crystallization temperature as a result of the nucleation activity of CNCs. The nucleation activity of the CNCs increased with the increase in their contact angle upon hydrophobization, which could be a result of the improved interaction between PBS and CNCs. Despite the significant improvement in PBS nucleation, its crystallization kinetics were slower as indicated by the drop of Z value and increase of t <sup>1</sup> 2 and Ea. This outcome indicates that the impeding effect of the CNCs was stronger than their nucleation activity, which as a result hindered the molecular motion of PBS chains and decelerated overall crystallization. However, the impeding effect of CNCs became less significant with reducing their hydrophilicity. In terms of the PBS melting temperature and crystallinity, the CNCs did not have a significant impact on them.


**Table 4.** Summary of the impact of CNC surface properties on the crystallization of PBS (at 10 ◦C/min).

\* Contact angle of the CNCs not the composite.
