#### 3.1. XRD Analysis

The XRD patterns of TiO

_{2} nanoparticles, pure PDVL, and their composites containing 1, 2, 3, 4, and 5 wt % of TiO

_{2} are shown in

Figure 1. The pattern of the pure anatase phase of TiO

_{2} nanoparticles reveals the main diffraction peaks at 2θ localized at 25.30, 37.80, 48.10, 53.90, 55.00, 62.80, and 70.00°, with those of the rutile phase at 27.4, 36.1, 41.3, and 56.6°, which agrees with the standard spectrum (JCPDS No.: 88-1175 and 84-1286) [

41]. The crystal size of TiO

_{2} particles was evaluated from the Scherrer equation [

42,

43]:

where the X-ray wavelength

λ of Cu Kα radiation is 1.54 Å, the shape factor

K is assigned a value of 0.90, theta is the Bragg angle, and

β is the half-height of angle diffraction. The reflecting peak at 25.3°, which is the (101) characteristic peak of TiO

_{2} anatase, is taken to determine the diameter of an average crystal, and

β is 0.411. Both of the

β values are converted to radians, and using the Scherer formula, the calculated average sizes of the crystallite TiO

_{2} nanoparticles are estimated to be approximately 20 nm. The semi-crystalline structure of pure PDVL is closely related to its chain architecture. The XRD pattern of this polymer has two crystallographic reflections, which are probably indexed to the crystal PDVL structure. The sharp crystalline peaks localized at 2θ 22° and 24° were assigned to diffraction of the (110) and (200) lattice planes, respectively [

44], indicating that the PDVL probably crystallized in the ordinary crystal geometric structure. The crystallographic analysis conducted by Furuhashi indicated that PDVL crystallized with an orthorhombic unit cell structure [

45]. The XRD patterns of the PDVL/TiO

_{2} nanocomposites show only the combined crystallographic reflections of their pure components, indicating the non-formation of new crystalline structures and proving the stability of the crystallinity of the TiO

_{2} nanoparticles in the composite. However, an important depression in the crystallinity of PDVL is observed when the amount of TiO

_{2} nanoparticles incorporated in the composite is increased.

#### 3.4. Thermal Behavior of the PDVL/TiO_{2} Nanocomposite

A uniform thermal history across all specimens was ensured by presenting thermograms with traces of the second run after quenching from temperatures slightly above

T_{g}. As shown in

Figure 4, the thermogram of PDVL shows that

T_{g} and

T_{m} occur at −63 °C and 58 °C, respectively, which is in agreement with the literature [

48,

49]. The thermal curves of PDVL/TiO

_{2} systems show a dependence of the thermal properties on the TiO

_{2} content incorporated in the composite.

Table 2 summarizes the

T_{g}s and

T_{m}s values deducted. As indicated by this table, the glass transition behavior is significantly influenced by the TiO

_{2} content, in which the

T_{g} value of the PDVL in the PDVL/TiO

_{2} system increased from −63 to −47 °C when the TiO

_{2} loading was varied from 0 to 5 wt %. However, as the inorganic content increased, the melting behavior stabilized or slightly decreased, and the

T_{m} value stabilized at approximately 59 °C or increased from 58 °C to 60 °C. The value of ∆

H_{m} decreased from 63 to 52.5 J·g

^{−1}. This finding can be explained by a thermodynamic mixture accompanied by exothermic interactions created between the crystalline structure of PDVL and those of TiO

_{2} nanoparticles, in which the slide chains are considerably reduced, leading to an increase in

T_{g} and a decrease in the enthalpy of melting.

As is well-known for polymer composites, the crystallization temperature of the polymer component depends on its affinity with respect to the filler, the physico-chemical properties of the two components, and crystallization conditions [

50]. The DSC thermograms of pure PDVL and PDVL/TiO

_{2} nanocomposites recorded in the cooling mode are shown in

Figure 5, and the temperatures and the heats of crystallization that were deducted are gathered in

Table 2. The DSC thermogram of pure PDVL exhibits a crystallization temperature at 27 °C, which is slightly lower than that in the literature (29.7–30.4 °C) [

44]. However, no significant change in the

T_{c} value of PDVL is observed when the amount of TiO

_{2} varied from 1 to 5 wt % is incorporated in the polymer matrix. On the other hand, a relatively dramatic depression of the crystallization heat (from 54.3 to 47.3 J∙g

^{−1}) is observed for the same variation of the TiO

_{2} content.

The degree of crystallinity

X_{c} of pure PDVL and PDVL/TiO

_{2} systems with different TiO

_{2} contents was determined using Equation (2) [

44,

51,

52,

53]:

where ∆

H_{m} is the heat attributed to fusion of PDVL;

$\Delta {H}_{m}^{o}$ is the enthalpy of fusion of 100% crystalline PDVL, which is estimated at 18.8 J·g

^{−1} [

54]; and

w_{f} is the weight fraction of PDVL in the composite. The degree of crystallinity of pure PDVL and those of PDVL/TiO

_{2} nanocomposites obtained by this method are shown in the data in

Table 2. A significant decrease in

X_{c} is observed with increasing TiO

_{2} content, revealing that the crystallinity rate of PDVL is significantly affected by this inorganic filler, notably at 5 wt % in the composite, in which this polymer loses approximately 13% of its crystallinity. This decrease in the crystallinity of PDVL in the nanocomposite is certainly due to the TiO

_{2} nanoparticles being incrusted between the polymer chains, which hinders the crystallization process and the formation of crystallites (

Scheme 1). Comparable results were also obtained by Jiang et al. [

55] using the PCL/SiO

_{2} nanomaterial. On the other hand, the thermograms of the pure PDVL and nanocomposites, realized at cooling rates ranging between 5 and 20 °C·min

^{−1} (shown in

Figure 6), revealed that for all samples, the peak of the crystallization enthalpy shifted toward lower temperatures when the cooling rate increased. The high cooling rate prevents the motion of the macromolecular chains from following the cooling process in time, due to the influence of heat hysteresis, and this fact leads to a lower peak of the crystallization temperature. Therefore, the crystallization process is facilitated by the lower cooling rate.

The variation in the

T_{c} value vs. the PDVL/TiO

_{2} composition at different cooling rates, plotted in

Figure 7, revealed comparable profiles which increased linearly with the TiO

_{2} content. This finding indicates that the incorporation of TiO

_{2} nanoparticles in the PDVL matrix, ranging between 1.0 and 5.0 wt %, accelerates the crystallization process. Comparable results were also observed by Wang et al. [

56] using the PCL/TiO

_{2} nanocomposite, and this phenomenon was attributed to an effect of heterogeneity nucleation of the nanoparticles in the polymer matrix.

#### 3.5. Non-Isothermal Crystallization Kinetics of PDVL and PDVL/TiO_{2} Nanocomposites

The relative degree of crystallinity

X_{T} vs. the crystallization temperature is expressed by Equation (3) [

57]:

where

A_{T} is the area under the thermograms from

T =

T_{o} to

T =

T, and A

_{∞} is the total area under the crystallization curve. Further,

T_{o} and T

_{∞} are the beginning and end of crystallization temperatures taken at the starting and finishing inflections of the crystallization peak, respectively, and

H is the heat of the process. Based on Equation (3),

X_{T} at a specific temperature

T is calculated. During non-isothermal crystallization, the variation of the crystallization time with the crystallization temperature is given by Equation (4):

where

T is the temperature of crystallization at time

t, and

β is the cooling rate in degrees Celsius per minute. The integration of the exothermic peaks during the non-isothermal crystallization process leads to the attainment of the relative degree of crystallinity

X_{T} as a function of temperature.

Figure 8 (on the left) shows the curves obtained for pure PDVL and the PDVL/TiO

_{2} nanocomposite containing 3 wt % of TiO

_{2} as an example. Because crystallization is impeded, all curves have a pattern approximating a sigmoid shape. A typical plot of

X_{t} vs. time for pure PDVL, and this same system plotted using a combination of Equations (3) and (4), are also shown in

Figure 8 (on the right). As in the case of the plots of

X_{T} vs. temperature, all patterns have an approximately sigmoid profile, and their slopes at each point indicate the instantaneous rate of crystallization. As can be seen, the rate of crystallization is almost constant between 20% and 80% of the relative crystallinity, because the profile of these curves in this zone is almost a straight line. At a later stage, the curves tend to become flat due to spherulite impingement [

58].

Among the many models that have been developed to study the kinetics of isothermal crystallization, there are very few that are suitable for non-isothermal kinetics, such as those proposed by Jeziorny [

57], Ziabicki [

58], and Ozawa [

59]. In the present investigation, the Ozawa equation, which is written as

is adopted to investigate the non-isothermal crystallization of the virgin PDVL and PDVL/TiO

_{2} hybrid nanomaterials, using 5, 10, 15, and 20 °C·min

^{−1} cooling rates, in which this relationship is an extension of the Avrami equation [

60]:

This equation was originally used for the conversion of isothermal crystallization to non-isothermal crystallization, by assuming that the sample is cooled at a constant cooling rate. The term X_{t} represents the relative degree of crystallinity as a function of the crystallization time t. k and k_{T} are the constants of the crystallization kinetics rate and the cooling function of non-isothermal crystallization at a certain temperature T, respectively. Further, n and m are the isothermal Avrami and the non-isothermal Ozawa exponents, respectively, and depend on the size of the crystal growth. β is the cooling rate.

When

m or

n is close to 3, this value indicates a crystalline growth in bulk or in three dimensions, whereas a value of

m or

n closer to 1 indicates surface growth. An intermediate

n value between 1 and 3 indicates that both surface and internal crystallizations occur simultaneously [

61]. Both parameters are determined from the linearized Equation (6) as follows:

Plots of

ln[−

ln(1 −

X_{t})] vs.

ln(

β) of virgin PDVL and the PDVL/TiO

_{2} systems containing different TiO

_{2} loadings are shown in

Figure 9. A straight line is obtained, indicating that the Ozawa equation (Equation (7)) perfectly describes the main process of non-isothermal crystallization of pure PDVL and also that of the PDVL/TiO

_{2} system for all given compositions. The slope and the intercept of these curves yields the Ozawa exponent (

m) and crystallization kinetics rate (

k_{T}), respectively. The values of

m and

k_{T} of the pure polymer and composites are summarized in

Table 3 and reveal that the average value of

m for pure PDVL is close to 2. This finding indicates that the crystal evolves by growing in both dimensions, with a linear growth rate, a heterogeneous nucleation [

62], and a thermal nucleation [

63]. According to Desio et al. [

64], a thermal nucleation implies that the nucleation rate does not contribute to the activation energy. However, the

m values of the composites, which range from 1.60 to 3.10, slightly increase with the crystallization temperature, which is explained by the simultaneous appearance of two and three dimensional spherulitic growth. On the other hand, as for pure PDVL, the

k_{T} value for each composite, of which the logarithm was between 3.38 and 7.32, increased with increasing the

T_{c} value. These values indicate that the incorporation of a quantity of TiO

_{2} nanoparticles ranging from 1.0% to 5.0% by weight in the PDVL matrix only slightly modifies the nucleation mechanism and the morphology of crystal growth.

The half time

t_{1/2} toward complete crystallization of the pure PDVL and composites plotted in

Figure 10A is deducted at 50% crystallinity of the curves of

Figure 9, indicating the variation of

X_{t} vs. time. These data reveal that the values of

t_{1/2} were depressed following the same logarithmic profile when the cooling rate increased. A similar change in

t_{1/2} was also observed by Wei et al. [

65] using PCL/TiO

_{2} nanocomposites. Indeed, the

t_{1/2} values obtained at 5 °C·min

^{−1} were approximately 2–5 times those at 20 °C·min

^{−1}, depending on the inorganic amount incorporated in the PDVL matrix. As can be seen, the

t_{1/2} value of the sample containing 1 wt % TiO

_{2} dramatically decreased from 14.28 to 65.40 s when the cooling rate varied from 5 to 20 °C·min

^{−1}, whereas samples with TiO

_{2} content below 2 wt % decreased with a comparable trend.

Figure 10B, in which

t_{1/2} is presented vs. the TiO

_{2} content in the composite, reveals a lower dynamic of the crystallization process (

t_{1/2} maximum) when 1 wt % of TiO

_{2} content was incorporated in the PDVL matrix, notably at the lowest cooling rate. In contrast,

t_{1/2} reaches a minimum with 2 wt % of the filler in the composite, indicating a higher dynamic of the crystallization process, notably using the highest cooling rate. Another slowdown of the crystal growth, but less important, is also observed at 3–4 wt % of TiO

_{2} in the composite depending on the cooling rate used. This finding can be explained by the fact that at relatively low TiO

_{2} loadings, the filler cluster in the polymer matrix cannot restrict the motion of the PDVL macromolecular chains, but acts during the non-isothermal crystallization process as a heterogeneous nucleating agent and therefore increases the crystallization rate. However, at a higher TiO

_{2} loading, the titanium dioxide nanoparticles cluster to form a barrier that restricts the thermal motion of the PDVL macromolecules and therefore negatively impacts upon crystal formation. As a result, the incorporation of a large amount of TiO

_{2} in the PDVL matrix can delay the overall crystallization process.

#### 3.6. Activation Energy

The activation energy of crystallization

E_{ac} is generally used to indicate the crystallization ability of polymers. Indeed, the lower the

E_{ac} value, the higher the crystallization ability. In this work, the Kissinger equation [

66] expressed below is used to estimate the

E_{ac} values of pure PDVL and its composites:

where

R and

T_{c} are the gas constant and the top of the crystallization temperature peak, respectively. The variation of

ln(

β/

T_{c}^{2}) vs. 1/

T_{c} for pure PDVL and its composites is plotted in

Figure 11 and is linear for all samples, and

E_{ac} is deducted from the slope of each pattern with a correlation coefficient

R^{2} exceeding 0.996. As shown in the data of

Table 3, at any composition, the crystallization activation energy has negative values, indicating that the crystallization is an exothermic process. Furthermore,

E_{ac} for the pure PDVL is −214.10 kJ·mol

^{−1} and was surpassed by a maximum of −324.25 kJ·mol

^{−1} when 4 wt % of TiO

_{2} was added to the PDVL polymer matrix. According to Yang et al. [

67], the more negative

E_{ac} is, the more heat is released for crystallization and the more crystallization is favored. In other words, the incorporation of 4 wt % of TiO

_{2} nanofiller in the PDVL polymer matrix greatly facilitated the crystallization of PDVL in the composite. This fact is gradually amortized with the addition of supplementary amounts of TiO

_{2} in the nanocomposite. In general, the increase in the absolute value of

E_{ac} should be due to the increase in the transportability of the PDVL chains, owing to the incorporation of TiO

_{2} in the polymer matrix. The incorporation of TiO

_{2} nanocomposite into the PDVL matrix could have heterogeneous nucleation effects; therefore, in this situation the hindrance effect of this load is not negligible. In the case of the incorporation of a small amount of TiO

_{2} in the PDVL matrix, the heterogeneous effect is not obvious, while the chain mobility of the polymer decreases even more. In addition, the absolute values of

E_{ac} of the PDVL/TiO

_{2} nanocomposites are higher than that of pure PDVL. On the other hand, when the TiO

_{2} content in the nanocomposite increased, its heterogeneous effect became even more important, despite the reduced mobility of the PDVL macromolecule chains.

#### 3.7. Effective Energy Barrier

According to Vyazovkin [

68], the Kissinger equation generally gives unspecified values of the activation crystallization energy, because the dependence of the temperature on the overall flow cannot be correctly described by a single Arrhenius graph on an extended temperature. On the other hand, the variation of the effective activation energy of the relative crystallinity (

X_{t}) has an additional parameter that is used to detect the change in the crystallization process that probably occurs in processes such as polymer crystallization. This dependence was very useful for the detection and elucidation of complicated dynamics in the polymeric materials. In this investigation, the Friedman differential iso-conversional equation [

69], as expressed below, was employed to evaluate the effective energy barrier

E_{X}:

where

Ln(

dX/

dt) represents the logarithm of the instantaneous crystallization rate of the polymer or composite as a function of time taken at a certain conversion

X.

T_{X,i} is the set of temperatures linked to the conversion

X obtained at different selected cooling rates. The index

i refers to a given individual cooling rate.

In the Friedman equation, the function of the instantaneous crystallization rate of the polymer (

X_{t}) is obtained from the integration of the measured crystallization rates, which is initially differentiated with regard to time to obtain

dX/

dt. In addition, from the selection of the appropriate degree of crystallinity, the

dX/

dt values at a certain conversion

X are correlated to the corresponding crystallization temperature

T_{X}, and

E_{x} is deducted from the slope of the linear curve presented in

Figure 12, indicating the variation of

Ln(

dX/

dt)

_{Xi} vs. the inverse of

T_{X}. The variation in

E_{x} of pure PDVL and the composites vs. the obtained

X_{t} are plotted in

Figure 13. As shown in these curve profiles, the effective energy barriers of pure PDVL and PDVL/TiO

_{2} nanocomposites have large negative values, and linearly increase with the extent of conversion and decrease in temperature. Comparable results were also observed by Wei et al. [

65] using PCL as the polymer matrix, and this fact was attributed to the great difficulty of the polymer to crystallize as the crystallization progresses.

In this case, during the crystallization process, the diffusion of the crystallization chain segments during the progression of the fusion to the growth front is prevented by the rejection of the segments of the polymer chain. Similar shapes were also obtained for polyethylene terephthalate (PET) and polypropylene/SiO

_{2} nanocomposites [

70].

Considering the data in

Figure 13, it is noteworthy that the nanocomposites exhibit higher values, indicating that the crystallization is hindered compared with that of PCL, except for the sample containing 3 wt % of TiO

_{2}, in which the crystallization process occurs at approximately the same or at slightly lower rates than the neat polymer. The tendency of the effective energy barrier evaluated using the iso-conversional method perfectly agrees with that obtained by the aforementioned Kissinger’s route.

#### 3.8. TGA Analysis

In contrast to poly (δ-caprolactone) and poly(L-lactic acid), which are linear aliphatic polyesters, only a few investigations on the degradation behavior of PDVL have been reported [

71,

72]. In this work, the thermal degradation of pure PDVL and PDVL/TiO

_{2} nanocomposites was performed by the TGA method, and the thermograms obtained in nitrogen gas atmosphere are grouped in

Figure 14. As shown in the thermal curve of pure PDVL, only one main decomposition step, which starts at 225 °C, is attributed to the formation of 4-pentanoic acid and carbon dioxide, similar to that observed during the thermal decomposition of the analogous PCL [

73]. The curve profiles of the composites reveal an important shift of the onset of the decomposition of PDVL from 225 °C to 265 °C with increasing TiO

_{2} loading, thereby indicating a significant improvement in its thermal stability. The thermograms of the PDVL/TiO

_{2} systems also showed a second decomposition step, which started at 372 °C for the PDVL/TiO

_{2}-1 nanocomposite containing 1 wt % of TiO

_{2} nanoparticles, and dramatically shifted to 400 °C for that containing 5 wt % of TiO

_{2}. During this step, this material lost between 15 and 40 wt % of its weight, which was volatilized depending on the amount of nanofiller in the PDVL matrix. An unexpected observation in the form of a second decomposition step can be seen in the PDVL/TiO

_{2} nanocomposite thermograms. This step started at 400–420 °C, and was completed at 420 and 475 °C depending on the amount of TiO

_{2} incorporated in the nanocomposite. During this step, the degradation of this hybrid material slowed down, and between 5 and 35 wt % of the material was degraded depending on its PDVL/TiO

_{2} composition. The presence of TiO

_{2} nanoparticles in this temperature range seems to interact with the residual sample to produce new molecules. This suggestion can also explain the increase in weight loss during this step, as the TiO

_{2} content in the nanocomposite increases.

The activation energy

E_{a} of the pure PDVL and PDVL/TiO

_{2} nanocomposites was estimated from the first stage of the thermal decomposition using the integral method proposed by Broido [

74]:

where

Y represents the fraction of the sample not yet decomposed, and

w_{o},

w_{∞}, and

w_{T} are the initial weight, final weight, and the weight at a certain temperature, respectively. The variation of

$Ln[Ln\left(\frac{1}{Y}\right)]$ versus the inverse of temperature plotted for pure PDVL and the nanocomposites in

Figure 15 is linear, thus the

E_{a} of the thermal decomposition process was deduced from the respective slopes. As can be seen from these curve profiles, the activation energy of pure PDVL was determined as 79.0 kJ·mol

^{−1}, which is lower than that reported in the literature (101 ± 10 kJ·mol

^{−1}) [

73]. The activation energy increased to reach a maximum of 103.1 kJ·mol

^{−1} when the TiO

_{2} content in the nanocomposite is 2.0 wt %, beyond which it decreased to reach a minimum of 83.1 kJ·mol

^{−1} with the PDVL/TiO

_{2} system containing 5 wt % of TiO

_{2}. This finding indicates that the addition of a small amount of TiO

_{2} nanoparticles to this polymer enhanced the thermal stability of PDVL, notably when the percentage of TiO

_{2} in the composite is 2 wt %. The decrease in the

E_{a} value when the nanofiller loading the composites increased is probably due to the lower energy required for bond scission and the unzipping of PDVL/TiO

_{2} nanocomposites.