Introduction

Poly(lactic acid) (PLA) is a linear, semicrystalline and biodegradable aliphatic polyester that can be produced from lactic acid by fermentation of renewable resources [1–3] and used as ecofriendly material [4–6]. PLA has good mechanical properties such as high mechanical strength, thermoplasticity and processability. However, PLA has some drawbacks that limit its wide application as a technical material, namely a relatively low impact resistance and low crystallization rate [7]. Thus, several modifications have been proposed to overcome these drawbacks, which include plasticization of PLA. The use of natural and/or biodegradable plasticizers, which are characterized by low toxicity, good compatibility and low migration, with biodegradable polymers, has attracted a lot of attention [8–12]. Compatibility between polymer and plasticizer is an important factor in choosing the external plasticizer, in order to produce a homogeneous and stable composition with reduced tendency for plasticizer migration [13, 14]. In a previous study, Moataz et al. used jojoba oil as a green plasticizer for PLA. They demonstrated that the elongation at a break point and Izod impact strength improve from 3.0 to 74 % and 12.9 ± 0.7 to 23.8 ± 1.6 kJ m−2 with the addition of 7 mass% jojoba oil respectively, resulting in a toughened PLA [15].

Generally, it is well accepted that the mechanical and physical properties of the semicrystalline polymers are governed by the morphology and supermolecular structure, which in turn is dominated by crystallization temperature and whether crystallization is performed from melt or from glassy state (histories). The crystallization behavior of neat PLA is extensively studied, especially the crystallization kinetics [16–19]; the isothermal melting mechanism [20–22]; the dimension of the crystal growth [16–22]; the effects of annealing on the thermal properties, morphology and mechanical properties of PLA films [23]; and the effects of thermal treatment on compression-molded PLA [24, 25].

In order to increase the crystallization rate three routes can be considered. The first one is to add a nucleating agent that will lower the surface free energy barrier toward nucleation and thus initiates crystallization at higher temperature upon cooling. A second possibility is to add a plasticizer which will increase the polymer chain mobility and will enhance the crystallization rate by reducing the energy required during crystallization for the chain folding process. The third possibility is to play with the molding conditions, in particular molding temperature and cooling time. The incorporation of plasticizer or/and nucleating agent [8, 26–30] into PLA matrix significantly change its crystallization behavior and therefore alter its physical and mechanical properties. In order to describe the macroscopic evolution of crystallinity under both isothermal and nonisothermal conditions (during the primary crystallization process), a number of mathematical models have been proposed [31–37]; among them, the so-called Avrami model is commonly used to analyze crystallization kinetics [33, 34]. It was reported that the PLA had a three-phase structure made of crystalline phase and two amorphous fractions [38–41]. In addition to the mobile amorphous fraction made of polymer chains that mobilize at the glass transition, a second fraction, the so-called rigid amorphous fraction, is the result of strong restrictions of amorphous chain segment mobility. The absolute value of the rigid amorphous fraction depends on whether it is formed during melt or cold crystallization and it was found to be around 10–35 % of the overall sample mass [41, 42]. Dielectric technique has widely been applied to monitor the kinetics of both cold and melt crystallization of semicrystalline polymers, including PLA [43–49]. In fact, the technique is particularly sensitive to the changes in the mobility of the different phases during the chain reorganization at the earlier stages.

This works aims to investigate the influence of the jojoba oil, as natural plasticizer, on the nonisothermal cold crystallization behavior of PLA. The molecular dynamics of the plasticized PLA was investigated by dielectric technique.

Experimental

Materials

The commercially available injection grade linear PLA, Ingeo™ 3001D, was supplied in pellet form by NatureWorks® LLC (Minnetonka, USA). The PLA has a density of 1.24 g cm−3 and a melt flow index of 15 dg min−1 (190 °C/2.16 kg). The jojoba oil, a commercial grade, was purchased from Egyptian Natural Oil Company NATOIL (Cairo, Egypt).

Sample preparation

The neat PLA and jojoba oil were predried in vacuum oven at 80 °C for 24 h before use. PLA and jojoba oil were mixed together with different weight ratios of 100/0, 97/3 and 93/7 in a Prism Eurolab 16 co-rotating twin-screw extruder (Thermo Scientific). PLA containing 3.0 and 7.0 mass% jojoba oil are denoted here as PLA-3JO and PLA-7JO, respectively.

Measurements

Thermal behavior and crystallization kinetics of the neat PLA and PLA/JO blends were performed using a differential scanning calorimeter (DSC Q20, TA instrument, USA) under purge of nitrogen (50 mL min−1). Temperature calibration was carried out using an indium standard. The sample weight was about 8–10 mg, and a new sample was used for each measurement to avoid degradation during the thermal analysis. For each measurement, sample of about 8.0 mg was placed in aluminum pan and heated to 190 °C, where it was held for 3.0 min to erase the thermal history, and then rapidly cooled to 20 °C with cooling rate of 40 °C min−1. This allowed to obtain DSC curves of amorphous glassy material for different heating ramps. No remarkable exothermic event except the glass transition for all the investigated samples can be observed during the cooling process at the cooling rate of 40 °C min−1. This indicates that the neat PLA and plasticized PLA are not able to melt crystallized under such cooling condition even at a cooling rate 20 °C min−1 (see Supplemental information). For nonisothermal crystallization, the glassy amorphous samples were heated from 20 to 190 °C at different heating rates (5, 10, 15 and 20 °C min−1), and the glass transition temperature (T g), the cold crystallization temperature (T p) and the melting temperature (T m) as well as the melting (ΔH m) and the crystallization enthalpies (ΔH cc) were determined.

Dielectric measurements were performed on Polymer Laboratories Dielectric Thermal Analyzer (PLDETA), which gives directly the dielectric constant, ε′, and dielectric loss, ε″. Dielectric measurements of wholly amorphous (first run) and crystallized samples (second run) were undertaken in temperature range from 20 to 150 °C at frequency range 0.2–100 kHz with a heating rate of 1.0 °C min−1. Amorphous samples were obtained by rapid cooling of the molten polymer layers between stainless steel electrodes (30 mm in diameter), kept at 190 °C for 3 min, to a room temperature. Semicrystalline samples were obtained by heating the amorphous samples from 25 to 140 °C at heating rate 1.0 °C min−1 and then annealed at 90 ± 1.0 °C for 2.0 h to attain equilibrium crystallinity. For frequency scan sweep of the amorphous samples, the frequency values were chosen within the range from 300 Hz to 100 kHz, in such a way that each spectrum was collected in a time that does not exceed 90 s to avoid the significant change in the crystallinity during the measurements. For all measurements, an appropriate Teflon spacer was used to control the sample thickness of 0.10–0.12 mm.

Results and discussion

Nonisothermal crystallization behavior

Figure 1a, c shows the DSC thermographs of neat PLA and plasticized PLA with 3 and 7 mass% jojoba oil at different heating rates. The glass transition temperature (T g), the cold crystallization (T p) and the melting temperatures (T m) are clearly seen. These values as well as the cold crystallization enthalpy (ΔH cc) and melting enthalpy (ΔH m) at different heating rates are summarized in Table 1. Also listed in this table the degree of crystallinity (χ c %) of these samples calculated using the following equation:

$$X_{\text{c}} \,\% = 100 \times \frac{{\Delta H_{\text{m}} }}{{w \cdot \Delta H_{\text{m}}^{\text{o}} }}$$
(1)

where w is weight fraction of PLA and \(\Delta H_{\text{m}}^{\text{o}}\) is the enthalpy of fusion of 100 % crystalline PLA, and it has a value of 93 J g−1 [24]. As shown from Table 1, the plasticized PLA shows a single glass transition, slightly lower than that of neat PLA, which was found to decrease with increasing plasticizer content. As it is expected, the peak cold crystallization shifts to higher temperature as a heating rate increases, meaning that the higher the heating rate the higher the temperature that the crystallization process started and completed. The addition of plasticizer significantly promoted recrystallization behavior of the PLA. This is a typical behavior of the plasticized thermoplastics, where the plasticizers promote the crystallinity due to the increase in the chain mobility. The higher plasticizer concentration shifted the crystallization peak to a lower temperature. This can be associated with two different phenomena. The first one is the increased chain mobility at low temperature associated with the depression of the T g. This T g reduction enables crystallization to start at a lower temperature upon heating. A second phenomenon is the reduced crystallization induction period due to the presence of crystalline nuclei already formed during the cooling process. A double melting is observed for neat and plasticized PLA. The peak at the lower temperature faded while the peak at the higher temperature became dominant with decreasing the heating rate. Such a double-melting behavior has also been observed by other authors for PLA systems [50–52] and reflects the melting process of crystals having different degrees of perfection; the lower- and higher-melting peaks may be corresponded to the melting of less and more perfect crystallites, respectively. The melting temperature of PLA does not significantly change in the presence of the plasticizer. A comparison between the enthalpy of crystallization and the melting enthalpy indicated that the enthalpy of crystallization is lower than that of melting. A more careful observation of the thermograms reveals the presence of a small exothermic peak prior to the major melting peak, especially at lower heating rate 5 °C min−1, which is characteristic of the α′ phase of PLA [53], could be one explanation of this difference.

Fig. 1
figure 1

DSC curves for the neat and plasticized PLA at different heating rates following a rapid cooling after being heated to 190 °C

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Table 1 Thermal characteristics of the samples evaluated as determined by DSC
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Nonisothermal crystallization kinetics

From the DSC curves, the relative crystallinity (X T) as a function of temperature can be calculated from:

$$X_{T} = \frac{{\mathop \int \nolimits_{{T_{0} }}^{T} \left( {{\text{d}}H_{\text{cc}} /{\text{d}}T} \right){\text{d}}T}}{{\Delta H_{\text{cc}} }}$$
(2)

where T o and T represent the onset and an arbitrary temperature, respectively, and dH cc is the enthalpy of cold crystallization released during an infinitesimal temperature range dT, and ΔH cc is the overall enthalpy of cold crystallization for a specific heating condition.

Assuming that the sample experiences the same thermal history designated by the DSC furnace, the relation between crystallization time t and sample temperature T can be formulated as follows:

$$t = \frac{{\left( {T_{\text{o}} - T} \right)}}{\phi }$$
(3)

where ϕ is the heating rate employed for the nonisothermal cold crystallization. The plots of the degree of crystallinity as a function of time X t versus t for the neat and plasticized PLA cold crystallized nonisothermally at various heating rates are shown in Fig. 2. For each heating run, X t increases exponentially with increasing crystallization time and finally levels off. The time taken to complete crystallization reduced with increasing heating rate, and the relative crystallinity of plasticized PLA was higher than that of neat PLA at a given time.

Fig. 2
figure 2

Relative degree of crystallinity as a function of time at various heating rates for neat and plasticized PLA. The symbols represent experimental data while the continuous line represents the results of the theoretical Avrami model

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An important parameter which can be taken from the X t curves is the half-time of cold crystallization t 1/2, which is the time interval from the onset of the cold crystallization to the time at 50 % completion (Table 2). The obtained t 1/2 values decrease with increasing heating rate, indicating that the samples cold crystallize faster when the heating rate is increased. In addition, at the same heating rate, t 1/2 values of the plasticized PLA are lower than that of neat sample, confirming that the presence of jojoba oil enhances the crystallization process. The reciprocal value of t 1/2 (i.e., 1/t 1/2 time−1) signifies the cold crystallization rate. Comparison of the 1/t 1/2 values for the neat and plasticized PLA, as given in Table 2, revealed that the cold crystallization rate of the neat PLA is lower than plasticized PLA and increased with increasing the jojoba oil content.

Table 2 Nonisothermal crystallization parameters of neat and plasticized PLA
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It is of great interest to evaluate the effect of jojoba oil on the crystallization rate of PLA in the plasticized samples quantitatively. A crystallization rate parameter (CRP), corresponding to the crystallization rate of polymers, was proposed by Zhang and co-workers [54, 55]. The CRP can be determined by the slope of a linear plot of 1/t 1/2 versus heating rate, and a higher slope means a faster crystallization rate. Figure 3 shows the plots of 1/t 1/2 versus heating rate for all the samples. The obtained CRP values are included in Table 2. The CRP values of the PLA loaded with jojoba oil are higher than that of neat one and increased with increasing content of jojoba oil, indicating that the rate of crystallization of PLA is promoted with incorporation of jojoba oil.

Fig. 3
figure 3

Plots of reciprocal of t 1/2 as a function of heating rate for neat and plasticized PLA

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To quantitatively describe the nonisothermal crystallization kinetics, a number of models have been proposed in the literature [31–37, 56]. The most common approach is that based on the Avrami equation proposed by Jeziorny [34, 57]:

$$X_{\text{t}} = 1 - \exp \left( { - K_{\text{t}} t^{\text{n}} } \right)$$
(4)

where X t is the relative degree of crystallinity, K t is the crystallization rate constant depending on nucleation and growth rate, and n is the Avrami exponent depending on the nature of nucleation and growth geometry of the crystals [33]. In order to estimate the Avrami parameters, K t and n, a nonlinear curve-fitting procedure based on the Levenberg–Marquardt method was employed in this work using OriginPro 2016 software. The estimated values of K t and n with those of the r 2 parameter are included in Table 2. Using these values for K t and n, the relative crystallinity as a function of time can be calculated using Eq. (2). The theoretical lines thus produced are also plotted in Fig. 2 and compared to the experimental data. As it can be seen, the fit is well, meaning that the Avrami model is adequate to describe the nonisothermal crystallization kinetics of neat and plasticized PLA. Some minor deviations appear only for data that correspond to low (<5 %) or high (>90 %) relative degrees of crystallinity. At longer crystallization time, the deviation between the calculated trace from experimental data is probably due to the occurrence of impeded secondary crystallization that usually takes place in polymer crystallization at high conversions. The K t and n parameters do not have the same physical meaning as in the isothermal crystallization, because the temperature varies constantly in nonisothermal crystallization. This affects the rates of both nuclei formation and spherulite growth ascribed to their temperature dependence. Therefore, the crystallization rate constant K t should be corrected adequately. Assuming a constant heating rate, the final form of crystallization rate constant can be corrected as suggested by Jeziorny [57] as follows:

$$\log K_{\text{c}} = \frac{{\log K_{\text{t}} }}{\phi }$$
(5)

It can be seen that the values of n for neat PLA were larger than that of plasticized PLA, which indicated that the addition of low molecular weight jojoba oil influences the mechanism of nucleation and the growth of PLA. The average n values of the PLA, PLA-3JO and PLA-7JO are 4.08, 3.28 and 3.09, respectively, suggesting that the nonisothermal cold crystallization of the plasticized PLA follows a heterogeneous nucleation and three-dimensional spherulitic growth, as occurring in the neat PLA [58]. Similar to the case of 1/t 1/2, the values of crystallization rate constant K c are found to be dependent on the heating rate and the content of jojoba oil in the plasticized PLA samples. The K c increased with increasing the heating rate and the content of jojoba oil at the same heating rate.

Activation energy of nonisothermal cold crystallization

The crystallization activation energy (E a) is the activation energy required to transport molecular segments across the phase boundary to the crystallization surface [59]. It is an important parameter associated with nonisothermal cold crystallization. In a nonisothermal crystallization, the activation energy E a can be derived from the variation of crystallization peak temperature T p with heating rates by the Kissinger approach [60] as follows:

$$\frac{{{\text{d}}\ln \left( {\phi /T_{\text{p}}^{2} } \right)}}{{{\text{d}}\left( {1/T_{\text{p}} } \right)}} = - \frac{{E_{\text{a}} }}{R}$$
(6)

where ϕ is the heating rate, T p is the cold crystallization peak temperature, and R is the universal gas constant. Plots of \(\ln \left( {\phi /T_{\text{p}}^{2} } \right)\) versus 1/T p of all samples are shown in Fig. 4, and they are fitted to straight lines. The E a values calculated from the slopes are found to be 76.9 ± 1.1, 77.8 ± 4.0 and 78.3 ± 5.6 kJ mol−1 for PLA, PLA-3JO and PLA-7JO, respectively. The comparable E a of neat and plasticized PLA suggested that presence of jojoba oil did not significantly affect the energy required to transport molecular segments to the crystallization surface.

Fig. 4
figure 4

Kissinger plots of the neat PLA and plasticized PLA cold crystallized nonisothermally with various heating rates

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Dielectric relaxation of amorphous and crystallized samples

Figure 5 shows comparative isochronal plots of the dielectric constant (ε′) and the dielectric loss (ε″) around glass transition temperatures of the amorphous (first run) and semicrystalline (second run) neat PLA and plasticized PLA at 100.0 kHz. The isochronal plots of dielectric constant (ε′) and loss (ε″) at various frequencies of the wholly amorphous neat PLA and PLA-3JO, as a representative plasticized PLA sample, are represented in Figs. 6 and 7. For all amorphous samples, a gradual increase in the ε′ is observed above 61 °C, which corresponds to the onset of the glass–rubber relaxation of the PLA matrix; this rise in ε′ is accompanied by a narrow peak in ε″ corresponding to α-relaxation of the wholly amorphous phase of the PLA (denoted as α am). At temperature above 83 °C, a sudden decrease in ε′ is observed that reflects the onset of cold crystallization and this is followed by a faint second relaxation (denoted as α sc) which assigned to the constrained segmental motions of the amorphous fraction confined between crystalline lamellae [43–48, 61, 62].

Fig. 5
figure 5

Isochronal plots of a dielectric permittivity (ε′) and b dielectric loss (ε″) of the amorphous and semicrystalline neat and plasticized PLA at 100 kHz

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Fig. 6
figure 6

Isochronal plots of a dielectric constant and b dielectric loss of amorphous and crystallized neat PLA at some selected frequencies

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Fig. 7
figure 7

Isochronal plots of a dielectric constant and b dielectric loss of amorphous and crystallized PLA-3JO at some selected frequencies

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Comparison of the neat PLA with that of those of the plasticized PLA samples revealed that the increment of the ε′, associated with the glass–rubber transition, increases with increasing the content of jojoba oil and the drop in ε′ due to crystallization starts at lower temperature. This may be attributed to increasing the segmental mobility of PLA chains as a result of increasing their free volume due to loosened molecular packing of the PLA chains in the presence of jojoba. This observation is in agreement with the DSC data for the quenched samples that show enhanced cold crystallization of PLA in the presence of jojoba. Compared with the neat PLA, the loss peaks of the plasticized PLA, as the polymer chains experience much wider spectrum of segmental relaxation environments, exhibit a less intense and broaden. Both the α am and α sc-relaxation processes shifted toward higher temperatures when the frequency increased (Figs. 6 and 7). The observed increase in dielectric constant and loss above T g, especially at lower frequencies and higher temperatures, might be related to the increase in ionic conductivity and/or electrode polarization [63].

For nonisothermal crystallized samples (second scan), an increment in the ε′ is observed around glass–rubber transition, which does not interfere with the effects of the cold crystallization during first scan. Additionally, the ε″ loss peaks became less intense and broadened due to the loss of dipoles that became immobilized as a result of the cold crystallization process and thus will not contribute to the dielectric response of the material. In contact to the amorphous, the loss peaks slightly shifted to higher temperature with increasing jojoba oil. It is also remarkable that the position of the ε″ peak maximum for both the amorphous and crystallized shifted to lower temperature with increasing the content of the jojoba oil. Moreover, the intensity of ε′ and the loss peaks decreased with increasing the jojoba oil content.

Dielectric analysis

Figure 8 shows frequency dependence of ε″ for totally amorphous and semicrystalline of the neat and plasticized PLA at 80 °C (>T g). This temperature allows observing the α-relaxation process in the amorphous and crystallized samples. It can be clearly seen that both the loss peaks of the α am and α sc-relaxations of the PLA are amplified by the addition of jojoba. For the initially amorphous samples, the loss peak shifted to higher frequency (which means that the corresponding relaxation becomes faster) as the content of jojoba increase, probably due to the plasticization effect induced by the presence of jojoba oil. Regarding the crystallized samples, the loss peaks are less intense and broad, as expected for semicrystalline polymers [44–48, 64, 65], and their positions slightly shifted to higher temperature as the content of jojoba increase.

Fig. 8
figure 8

Dielectric loss spectra of neat and plasticized PLA at 80 °C: a amorphous and b crystallized samples

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A more detailed analysis of the dielectric relaxation can be performed using the Havriliak–Negami (HN) equation [66]:

$$\varepsilon^{*} = \varepsilon_{\infty } + \frac{\Delta \varepsilon }{{\left( {1 + \left( {i\omega \tau_{0} } \right)^{\text{a}} } \right)^{\text{b}} }}$$
(7)
$$\Delta \varepsilon = \varepsilon_{0} - \varepsilon_{\infty }$$
(8)

where ε0 and ε∞ are limiting low- and high-frequency dielectric constants, respectively, ω is the angular frequency, τ 0 is so-called Havriliak–Negami relaxation time and the exponents “a” and “b” are the shape parameters which characterize the width and the asymmetry of the loss curves. For the frequency-dependent conductivity contribution, conduction effects are treated in the usual way by adding contribution of \(\sigma_{0} /\varepsilon_{0} \omega^{s}\) to the dielectric loss where σ 0 is related to the dc conductivity of the sample and ε 0 is the dielectric permittivity of vacuum (8.854 × 10−12 F m−1). The parameter (0 < s ≤ 1.0) describes for s = 1 Ohmic and for s < 1.0 non-Ohmic effects in the conductivity [67]. The shape of the α sc-relaxation seems to be symmetric; the fitting parameter “b” was fixed at b = 1.0. In all preliminary fittings of the α am-relaxation process of amorphous samples, the parameter b was always found to be around 0.55. In Fig. 8, the lines going through the experimental points represent fitting result and the fitting parameters extracted from each relaxation are summarized in Table 3. It can be seen that the estimated symmetric shape parameter “a” for amorphous samples decreased from 0.79 to 0.59, while for the crystallized samples decreased from 0.49 to 0.41 with increasing the content of jojoba oil from 0.0 up to 7.0 %. This decrease is related to some changes in the morphological structure of PLA as a result of incorporation of jojoba oil, where the mobile amorphous and rigid amorphous fractions of PLA become more heterogeneous as the result of the presence of jojoba, and this in turn would give rise to different modes of segmental motions and, accordingly, to broad distribution relaxation times. The data listed in Table 3 demonstrated that the dielectric relaxation strength, Δε, of the α am and α sc of the relaxation processes increased as the content of the jojoba oil increases, and this is also evident from the evolution of the peak height in the ε″ spectra for the raw data. Since the dielectric strength of the α-relaxation is characteristic of the mobile phase, the same interpretation is adopted for the increment of the dielectric strength in the plasticized samples as a result of plasticization. The fraction of the mobile amorphous segments (X maf) in the crystallized samples that relax, at a given temperature, can be calculated by:

$$X_{\text{maf}} \left( T \right) = \Delta \varepsilon_{\text{sc}} \left( T \right)/\Delta \varepsilon_{\text{am}} \left( T \right)$$
(9)

where Δε sc and Δε am are the relaxation strength of the crystallized and fully amorphous samples, respectively [62]. The values obtained are included in Table 3 and are used to calculate the rigid amorphous fraction (X raf) based on a three-phase model, \(X_{\text{raf}} = 1 - X_{\text{maf}} - X_{\text{c}}\), where X c is the absolute crystalline fraction [calculated from DSC, Eq. (1)]. The X raf value of the neat PLA is found to be 0.29, in a good agreement with the value reported by Henricks et al. [42] using DSC technique. They demonstrated that the value of X raf was 0.3 at the maximum crystallinity for the both cold- and melt-crystallized samples. As can be seen in Table 3, the X raf values of PLA decreased with increasing the content of jojoba oil.

Table 3 Dielectric fitting parameters at 80 °C and calculated rigid amorphous fraction of the neat and plasticized PLA crystallized isothermally at 80 °C
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Typical temperature dependence of the relaxation time (τ = 1/2πf) for α am and α sc-relaxation processes for the amorphous and crystallized samples is shown in Fig. 9; these data are taken from the isochronal dielectric loss curves (T max) at different frequencies and can be described by the Vogel–Fulcher–Tammann (VFT) relation [68–70], expressed by:

$$\tau = \tau_{0} \exp \left( {\frac{B}{{T - T_{0} }}} \right)$$
(10)

where τ 0 is a pre-exponential factor, B is an activation parameter, and T 0 is a so-called Vogel temperature at which the main-chain motions are virtually frozen. The pre-exponential in Eq. (5) is sometimes identified with vibrational lifetimes [71], and thus a constant value of τ 0 = 1 × 10−14 s was used for fitting data of all samples. The parameters extracted from the fit of these relaxation modes are included in Table 3. It is clear that the relaxation time follows the VFT relation regardless of the presence and/or absence of crystalline phase and plasticizer. The obtained T 0 and B values of the amorphous neat PLA are 294 and 1269 K, respectively, in agreement with previous measurement [62]. A small increase in B value on going from amorphous to semicrystalline is observed, while T 0 remains the same. Regarding the changes in the VFT parameters for the amorphous and constrained segmental modes (α am and α sc) of the plasticized PLA, the results revealed that the B values decreased with increasing the content of the plasticizer. The T 0 of crystallized samples is higher than that of amorphous samples.

Fig. 9
figure 9

Temperature dependences of the relaxation times for the α am and α sc-relaxation processes for neat PLA and plasticized PLA, and solid lines are the VFT fit

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The dynamic fragility index, m, which describes the increase in the relaxation times as temperature comes closer to T g is introduced by Angell [72]. Values of m are calculated by Eq. (6) using the VFT parameters (T 0 and B) are given in Table 3.

$$m = \left| {\frac{{{\text{d}}\left( {\log \tau } \right)}}{{{\text{d}}\left( {T_{\text{ref}} /T_{0} } \right)}}} \right|_{{T = T_{\text{g}} }} = \frac{{BT_{\text{ref}} }}{{2.303\left( {T_{\text{ref}} - T_{\text{o}} } \right)^{2} }}$$
(11)

where T ref is a reference temperature when the segmental relaxation time (τ) is 100 s.

As shown in Table 3, the obtained m values are within the extreme values found in the fragility compilation made by Qin and McKenna on a variety of polymers [73] and comparable to the values reported previously for PLA and other bio-based polymers [74]. The m value obtained for neat and plasticized PLA can be considered as relatively fragile, which is by the way a classical behavior for macromolecules with Van der Waals or hydrogen bonds interactions between chains [72, 74]. Compared plasticized PLA with neat PLA revealed that the plasticized samples seem to be less fragile. A small decrement of the m values with increasing the content of jojoba is also observed. The decrease in these values may be attributed to an increase in the amorphous molecular mobility as the result of plasticization effect of jojoba oil.

Conclusions

The nonisothermal cold crystallization behavior PLA plasticized with jojoba was studied using differential scanning calorimetry. The results showed that the cold crystallization temperature (T p) of the PLA decreased, while the melting peak did not significantly change with increasing the jojoba content. Avrami–Jeziorny model was applied to analyze the nonisothermal crystallization process; according to the obtained data, the Avrami exponent (n) indicated that both neat PLA and plasticized PLA follow a heterogeneous nucleation and three-dimensional spherulitic growth. Comparison of half-life crystallization times and the rate constant (K c) revealed that the rate of crystallization of PLA increased with increasing the jojoba content. The incorporation of jojoba in PLA did not significantly change the kinetic energy of the crystallization.

The dielectric spectra of the amorphous plasticized PLA showed that two main α-relaxation one corresponding to the wholly amorphous phase (α am) and the other, which appeared at relatively higher temperature, is assigned to the constrained amorphous phase (α sc) between crystalline lamellae. The intensity of the ε″ maxima of both α am and α sc increased with increasing the content of jojoba oil and shifted to lower temperature as the result of plasticization effect of jojoba. The dielectric data were fitted reasonably well to the semiempirical HN equation. The broadness of the relaxation peaks and the dielectric strength of the both the amorphous and semicrystalline samples increased with increasing the content of jojoba. From the temperature dependence of the relaxation times of the α-processes, the Vogel–Fulcher–Tammann parameters were estimated. The structural relaxation analysis revealed a classical polymeric “fragile” behavior for neat and plasticized PLA, and the fragility index slightly decreased with increasing the jojoba. The difference may be associated with the increase in chains mobility, due to plasticization effect of jojoba.