Introduction

With this work, we wish to contribute to the understanding of the phase transformations and molecular mobility in two glass-forming active pharmaceutical ingredients (APIs): bifonazole and lamotrigine. Bifonazole is an imidazole-based anti-fungal agent with broad spectrum activity against many fungi, molds, yeast and some Gram-positive bacteria [1]. Lamotrigine is an anticonvulsant medication introduced for treatment of seizure disorders and now used to treat epilepsy and bipolar disorder [2]. The research presented here is not, however, intended to address the medical applications of these substances, but rather to study the thermodynamic and kinetic properties upon which their stability and bioavailability depend. Modern medicines are fascinating from a molecular point of view because of the huge diversity of their chemical structures and dimensions, which gives them a great diversity of physical and chemical properties and behaviors, and justifies their frequent polymorphism. Many of them are also good glass-formers displaying a wide range of glass-forming abilities and glass stabilities. This diversity and richness of molecular behaviors gives rise to an increased interest in the study of their different phases and respective interconversions.

In the pharmaceutical field, the amorphous form of drugs is often preferred over crystalline because of the higher solubility and dissolution rate that result from its higher Gibbs energy [3,4,5,6]. However, the amorphous solid tends to crystallize (decrease in the Gibbs energy), tendency which depends in particular on two factors: the degree of molecular mobility [7,8,9,10] and the thermodynamic driving force for crystallization [11]. Knowledge of the amorphous properties is therefore important for defining the most appropriate stabilization procedures and storage conditions.

Furthermore, unit operations on a large-scale batch such as freeze and spray drying may lead to the generation of amorphous systems, while grinding or conventional drying may result in materials which are partially or wholly disordered. In both situations, diagnosing manufacturing irregularities should be part of a quality protocol.

In this work, we use the techniques of differential scanning calorimetry (DSC) to study phase diagram aspects such as thermodynamic transitions and polymorphism, and to characterize the glass transition, while with thermostimulated depolarization currents (TSDC) we will study the slow molecular mobility in the amorphous solid state, in the glass transition region and in the metastable liquid just above Tg of the two glass-forming systems under study.

Experimental

Materials

Bifonazole, (RS)-1-[phenyl(4-phenylphenyl)methyl]-1H-imidazole or 1-(p,α-diphenylbenzyl)imidazole, with molecular formula C22H18N2, molecular mass 310.39 g mol−1 and CAS number 60628-96-8, was provided by TCI, lot number UAVZA-LM with purity of 99.3%.

Lamotrigine, 3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine, with molecular formula C9H7Cl2N5, molecular mass 256. 094 g mol−1 and CAS number 84057-84-1, was provided by Acros, lot number A0374231 with G.P. ≥ 98%.

The chemical structures of these substances are shown in Fig. 1; the acquired samples were used without further purification.

Fig. 1
figure 1

Molecular structures of a bifonazole and b lamotrigine

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Techniques

Differential scanning calorimetry (DSC)

The calorimetric measurements were performed with a 2920 MDSC system from TA Instruments Inc. The samples with ~ 5.0 mg mass were contained in aluminum pans sealed in air. All the measurements were done under helium (Air Liquide N55), at a flow rate of 30 cm3 min−1. Details of the experimental procedures and of the calibration of the temperature and heat flow scales are presented elsewhere [12]. All weightings were performed with a precision of ± 0.1 μg in a Mettler UMT2 ultra-micro balance.

Thermally stimulated depolarization currents (TSDC)

Thermally stimulated depolarization current experiments were carried out with a TSC/RMA spectrometer (TherMold, Stamford, CT, USA) covering the range from − 170 to + 400 °C. A clear and concise explanation of the experimental procedures provided by the technique of thermally stimulated currents is available (see Supplementary data associated with Ref. [13]) and may be useful for the reader unfamiliar with this technique.

The temperature-dependent relaxation time, τ(T), associated with a given TSDC peak can be calculated using methods described in the literature (supplementary data associated with Ref. [13] or appendix of Ref. [14]). The physical foundations of the TSDC technique are exposed in different classic books [15,16,17], while its applications are explained in several reviews [18,19,20,21,22].

To prepare the sample for the TSDC experiments, ~ 30 mg of the as-received crystalline powder were placed on the lower electrode of the TSDC equipment, introduced into an oven and then melted under vacuum (at T = 165 °C for bifonazole and at T = 235 °C for lamotrigine). The lower electrode/sample assembly was then cooled to room temperature and transferred at normal pressure to the TSC cell, where it was mounted with the upper electrode (7 mm diameter) to form the parallel plate capacitor (thickness of ~ 0.5 mm). Three successive vacuum/helium cycles allowed the TSDC cell to be placed under a helium atmosphere of 1.1 bar and, prior to the experimental measurements, the sample was heated up to the metastable liquid to improve electrical contact with both electrodes (at T = 40 °C for bifonazole and at T = 110 °C for lamotrigine).

Results and discussion

Differential scanning calorimetry

General thermal behavior and polymorphism

Bifonazole

The as-received sample displayed a DSC endothermic peak with maximum at (Tfus)max = 148.7 °C at 10 °C min−1 (onset at (Tfus)on = 145.6 °C), and the corresponding melting enthalpy was ΔHfus = 38.49 kJ mol−1, in good agreement with the published values (see Table 1).

Table 1 Melting temperature, Tfus, and enthalpy of fusion, ΔHfus, of the studied API glass-formers
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Cold crystallization was observed on heating either from the amorphous solid state or from a temperature above Tg (see Fig. 2); at 2.5 °C min−1 it starts at ~ 70 °C, has a maximum rate at ~ 90 °C and ends at ~ 110 °C. The crystal produced by cold crystallization shows an endothermic DSC peak at (Tfus)max = 148.8 °C, with an area corresponding to a melting enthalpy of ΔHfus = 107.9 J g−1 = 33.50 kJ mol−1; the melting temperature is similar to that of the as-received sample, but the different melting enthalpy suggests that we are in the presence of a metastable polymorph (form II), not yet reported in the literature. We further verified that the melting temperature and enthalpy of the crystalline sample obtained by isothermal crystallization from the metastable liquid at 90 °C are exactly the same as that of the crystal obtained by cold crystallization on heating from the amorphous solid. The sample supplied by the manufacturer, with a higher melting enthalpy and a very close melting temperature, will therefore correspond to the most stable polymorph (form I).

Fig. 2
figure 2

a DSC successive scans on heating at 5 °C min−1 for the as-received crystalline form of bifonazole (red line) and for the sample cooled down from the melt down to the glassy state (black line); b DSC successive scans on heating at 10 °C min−1 for the as-received crystalline form of lamotrigine (red line) and for the sample cooled down from the melt down to the glassy state (black line). In both cases, no crystallization was observed on cooling from the melt down to below Tg; the signature of the cold crystallization is clearly shown and the insert displays the detail of the glass transition step signal

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Lamotrigine

The as-received sample displayed a DSC endothermic peak with maximum at (Tfus)max = 218.0 °C (onset at Ton = 216.3 °C), and the corresponding melting enthalpy was ΔHfus = 33.7 kJ mol−1, in reasonable agreement with the values reported in the literature [30, 36] (see Table 1).

No crystallization is observed on cooling from the isotropic liquid; however, cold crystallization is observed starting at Tin ≅ 150 ± 10 °C and maximum speed at Tmax ≅ 175 ± 10 °C for heating rates between 5 and 15 °C min−1 (see Fig. 2). No clear signs of polymorphism were observed in lamotrigine; however, the shape of the endothermic fusion peak often shows an asymmetry (even a slightly noticeable double character) that may indicate the existence of polymorphs with very close melting temperatures.

The glass transition and the dynamic fragility

As far as we know, there are no published studies on the molecular mobility in the amorphous solid state and in the glass transition region for either bifonazole or lamotrigine. In this work, we will use two experimental techniques to obtain information in this field, namely to obtain the glass transition temperature, the activation energy of the structural relaxation and the dynamic fragility for the two glass-formers under study. In this section, we will present results obtained by differential scanning calorimetry, whereas the conclusions of the analysis by thermostimulated depolarization currents will be presented in Section “The glass transformation region”.

In the DSC study, we will determine the activation energy of the structural relaxation, Ea(Tg), from the effect of the heating rate on the temperature location of the glass transition step signal [40, 41]:

$$\frac{{{\text{d}}\left( {\ln q^{ + } } \right)}}{{{\text{d}}\left( {1/T_{\text{x}} } \right)}} = - \frac{{E_{\text{a}} \left( {T_{\text{x}} } \right)}}{R},$$
(1)

where q+ is the heating rate, Tx is the temperature that defines the position of the DSC glass transition step signal, and R is the gas constant. The cooling/heating cycles of the experimental protocol obey the necessary condition that q−/q+ = 1, i.e., the rate of a given cooling is always equal to that of the next heating [40,41,42]. In addition, to define the temperature location of the step signal of the glass transition we considered two different temperatures, namely the temperature of the onset, Ton, and the temperature of the overshoot, Tov: the latter because it can be determined with greater accuracy and the first, Ton, for being the one that as was shown in a recent work [45], is physically more acceptable because it is less affected by physical aging. Therefore, although some authors suggest the use of Tov [43, 44], we will keep in mind that the values of activation energy of the structural relaxation, Ea(Tg), obtained through Eq. (1) based on Ton are physically more acceptable.

Once Ea(Tg) is obtained, the dynamic fragility, m, can be estimated by:

$$m = \frac{{E_{\text{a}} \left( {T_{\text{g}} } \right)}}{{2.303 \times RT_{\text{g}} }},$$
(2)

where the 10 based logarithm defines a scale of dynamic fragility, m, such that the lower limit (extremely strong glasses) corresponds to mmin = 16 [46]; we will use Eq. (2) to calculate mDSC(Tov) and mDSC(Ton) for the two glass-formers under analysis.

Bifonazole

The glass transition temperature of bifonazole measured by DSC was found at TgDSC = 13.8 °C (extrapolated onset on heating at 10 °C min−1), which compares well with the values reported in the literature (see Table 2). On the other hand, the heat capacity jump observed at the glass transition is ΔCP = 0.415 ± 0.026 J °C−1 g−1 in excellent agreement with the published 0.40 value [25].

Table 2 Properties of the glass transition and of the structural relaxation of bifonazole and lamotrigine
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Using the methodology described above for calculating the dynamic fragility based on Eqs. (1) and (2) (see Fig. 3 for lamotrigine), we obtained the values of Ea(Tov) = 336 kJ mol−1 and Ea(Ton) = 402 kJ mol−1 for the activation energy of the structural relaxation of bifonazole.

Fig. 3
figure 3

Dynamic fragility of lamotrigine observed by DSC: “Arrhenius plots” of the logarithm of the heating rate, q+, as a function of 1000/Tov (diamonds, blue in the online edition) and of 1000/Ton (circles, red in the online edition), where Ton is the temperature of the extrapolated onset and Tov is the temperature of the overshoot peak, of the glass transition signature on heating. The experiments were such that the ratio between the heating rate, q+, and the previous cooling rate, q−, was unity: q−/q+ = 1

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With these values in Eq. (2), we obtain mDSC = 61 from Tov and 73 from Ton (see Table 2). It should be noted that the determination of the onset of the stepwise signal of the glass transition at different heating rates was particularly difficult in the case of bifonazole, which resulted in a significant dispersion of the results and led to a greater number of experimental determinations.

Lamotrigine

In the absence of published studies on the lamotrigine glass transition, the values of the dynamic properties presented below cannot be compared with others. The glass transition temperature measured by DSC was found at TgDSC = 94.3 °C, and the heat capacity jump at the glass transition was ΔCP = 0.468 ± 0.014 J °C−1 g−1.

On the other hand, using the methodology described before, the activation energy of the structural relaxation of lamotrigine was found to be Ea(Tov) = 530 kJ mol−1 and Ea(Ton) = 655 kJ mol−1 (see Fig. 3). With these values in Eq. (2), we obtained mDSC = 72 from Tov and 89 from Ton (see Table 2). Remember that the values of Ea(Tg) and mDSC obtained on the basis of the extrapolated onset temperature, Ton, are physically more credible because they are less distorted by aging.

Thermally stimulated depolarization currents

The information presented above and collected by DSC on the dynamic fragility of our two glass-formers can be further elucidated by the TSDC technique. For this purpose, the temperature ranges of the amorphous solid state and of the glass transformation were scanned with partial polarization (or narrow polarization window) experiments.

The glass transformation region

Figure 4 shows some of the results obtained in the glass transition region of bifonazole; these are depolarization peaks, I(T), obtained by partial polarization (or narrow polarization window) experiments, each corresponding to a narrowly distributed mobility. The general appearance of the figure is similar to that found in other glass-formers [48]: while the polarization window ΔT is within the temperature range of the amorphous solid, the partial polarization experiment is capable of retaining some polarization in the freezing step, which is depolarized on the next heating ramp giving rise to a depolarization current peak; in contrast, if the polarization window is in the liquid range, all the polarization created by the field in the polarization step will disappear when it is withdrawn, hence the relative configuration of the different depolarization peaks, with increasing area as the polarization window approaches Tg and with a sharply decreasing area when that temperature is reached and exceeded.

Fig. 4
figure 4

Partial polarization peaks in the glass transformation region of bifonazole, obtained with polarization temperatures, TP, from − 7 to + 9 °C. The PP peak with higher intensity (red in the online edition), obtained with Tp = 5 °C, is located at TM = (Tg)TSDC = 8 °C. The other experimental conditions were: strength of the polarizing electric field, E = 350 V mm−1; polarization time, tP = 5 min.; width of the polarization window, ΔT = 2 °C; heating rate, q = 6 °C min−1. The insert shows the τ(T) versus 1/T lines corresponding to the depolarization I(T) peaks shown in the main figure; the thicker line, red in the online edition, is that which corresponds to the peak I(T) of higher intensity, and it is from this line that the activation energy of structural relaxation, Ea(TM), and the dynamic fragility, m, are calculated

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The peak with higher intensity in Fig. 4 (red in the online edition) has very special features; one is that the temperature of its maximum, TM, corresponds to the glass transition temperature provided by TSDC, TM = TgTSDC [48]; we thus have for bifonazole TgTSDC = 8 °C, a value a little smaller than that obtained by DSC (see Table 2). Another feature of this peak, the most intense among the peaks of Fig. 4, is that it results from the depolarization of the motional modes of the structural relaxation with higher activation energy [48, 49]; for this reason, this depolarization peak is the one chosen for the calculation of the dynamic fragility in TSDC [14, 50].

The temperature-dependent relaxation time, τ(T), of each narrowly distributed mobility can be calculated from the raw experimental result, I(T) (see supplementary data associated with Ref. [13] or appendix of Ref. [14]), and each τ(T) line contains the complete kinetic information about the respective motional mode. The τ(T) lines corresponding to the peaks of the main Fig. 4 are shown in the insert, and the thicker line (red in the online edition) corresponds to the highest intensity peak of the main figure. From the τ(T) line of the highest intensity peak, located at TM in the glass transition region, we can easily calculate Ea(TM) and then the dynamic fragility, mTSDC, from Eq. (2). The activation energy of the structural relaxation was found to be Ea(Tg) = 494 kJ mol−1 for lamotrigine, and the fragility index, from Eq. (2), is mTSDC = 72. Table 2 shows the values of the glass transition temperature, TgTSDC, and of the dynamic fragility, mTSDC, for the two systems studied.

All this kinetic information regarding the slow molecular motions in the amorphous solid state and in the glass transition can be condensed into a graph of Ea(Tm) versus Tm, which is currently called “relaxation map,” where each motional mode (corresponding to each depolarization peak I(T)) is characterized by its location on the temperature axis and by its activation energy. Figure 5 shows such a relaxation map for the two studied glass-forming liquids.

Fig. 5
figure 5

TSDC relaxation map of the two studied glass-forming APIs: activation energy, Ea(Tm), of the partial polarization components of the different relaxations as a function of the peak’s location, Tm. The correspondence between the dots and the glass-formers is as follows: bifonazole (diamonds, blue in the online edition), and lamotrigine (circles, red in the online edition). The arrows indicate TgTSDC, the glass transition temperature provided by TSDC. The dotted line describes the zero entropy behavior. The points in the proximity of the zero entropy line correspond to the local, secondary relaxations, while the points in the vicinity of TgTSDC, displaying a strong and continuous deviation from that line, refer to the cooperative modes of the α-relaxation

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The results for the peaks I(T) of Fig. 4, relative to the glass transition relaxation of bifonazole, correspond to some of the blue diamonds between 5 and 10 °C with activation energies in the range of 250 to 500 kJ mol−1. In each group of points corresponding to a given glass-former in Fig. 5, the coordinates of the point with higher Ea can be used to estimate the dynamic fragility; we can qualitatively infer that the Ea(TM) value is close for bifonazole and lamotrigine, whereas the glass transition temperature is substantially higher in lamotrigine compared to bifonazole; it follows that given Fig. 5 and bearing in mind Eq. (2), the dynamic fragility of bifonazole is predictably higher than that of lamotrigine, which is confirmed by the values given in Table 2.

The secondary relaxations

The partial polarization peaks obtained in the amorphous solid state showed very low dielectric strength in lamotrigine compared with bifonazole, which certainly arises from more active dipolar mobility in the amorphous solid state of this latter glass-former. Figure 6 shows some results of PP experiments carried out on the glassy bifonazole.

Fig. 6
figure 6

Partial polarization peaks of the secondary mobility of bifonazole. The experimental conditions were: heating rate, q = 4 °C min−1, strength of the polarizing electric field, E = 350 V mm−1; polarization time, tP = 5 min.; width of the polarization window, ΔT = 2 °C; the polarization temperatures of the different experiments varied from − 75 to − 30 °C every five degrees

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The points corresponding to the mobility modes of the secondary relaxations of our two glass-forming systems are shown in the relaxation map (Fig. 5) in the close vicinity of the dashed line, the so-called zero entropy line (ZEL) or Starkweather line [51,52,53]. The equation of this line can be written as:

$$\frac{1}{{E_{\text{a}} }} = \frac{{rhN_{\text{A}} }}{{R^{2} T_{\text{m}}^{3} e}}\exp \left( {\frac{{E_{\text{a}} }}{{RT_{\text{m}} }}} \right)$$
(3)

with Ea in J mol−1 and Tm in K, and it defines an effective lower limit for the activation energy of the viscoelastic relaxations [53]; in Eq. (3) h, NA and R are, respectively, the Planck, Avogadro and ideal gas constants, e is the Neper number, and r is the heating rate of the depolarization ramp of the TSDC experiment. The zero entropy line is obtained by equating the Arrhenius and Eyring equations and considering the Eyring’s activation entropy equal to zero: ΔS≠ = 0 (see Supplementary Materials for an explanation of the rationale for Eq. (3)); this imposition of a zero activation entropy corresponds to setting the lower limit of the activation energy of the viscoelastic relaxations.

The dependence Ea(Tm) described in Eq. (3) is almost linear over a relatively wide temperature range (see Supplementary Materials) which allows us to use as a reasonable approximation of the zero entropy line the equation:

$$E_{\text{ZEL}} = 37RT_{\text{m}}$$
(4)

for a heating rate of 4 °C min−1 and in the temperature range between 65 and 425 K. Looking at the relaxation map of Fig. 5, we find that the motional modes of the bifonazole secondary relaxation (Fig. 6) have activation energies between ~ 55 and ~ 75 kJ mol−1 and are detected in the wide temperature range from − 75 to +  5 °C; lamotrigine’s secondary motional modes, on the other hand, are only detected in the very close proximity of the glassy transformation, in the narrow range between 50 and 75 °C, and show activation energies between ~ 87 and ~ 97 kJ mol−1. In fact, lamotrigine has a rigid molecular structure that does not allow changes in the orientation of dipolar parts of the molecule in relation to each other. In bifonazole, the stiffness is not as strong, as the benzyl-imidazole moiety can rotate around the carbon–carbon bond that connects it to the biphenyl fraction. In addition, there are intermolecular hydrogen bonds in lamotrigine, which is not the case with bifonazole. These differences in the occurrence of secondary relaxations result, at least in part, from the differences between the two glass-forming substances in terms of molecular rigidity and intensity of intermolecular interactions. It is important to note that all the relaxations detected by TSDC below the glass transition region are found to obey the zero entropy line, i.e., have activation energies given by Eq. (4) and zero activation entropy (Arrhenius pre-factor τ0 = 10−13–10−14 s or, in terms of frequency, f0 = 1012–1013 Hz). This is so for very different glass-formers, both polymeric [54, 55] and low molecular mass [56,57,58,59], and also for positionally or orientationally disordered glasses [46, 60] and for ionic liquids [61, 62]. However, studies of the secondary molecular mobility in the amorphous solid state, in particular those of dielectric relaxation spectroscopy (DRS), show the existence of various types of motion [63] with distinct signatures, namely with kinetics where the pre-exponential Arrhenius factor differs significantly from τ0 = 10−13 s. So far, there is no attempt in the literature to reconcile the two dielectric techniques, i.e., to explain the apparent divergence of their results with regard to secondary relaxations; we believe we can look into this matter in the near future. Note finally that introducing Eq. (4) into the definition of the dynamic fragility (Eq. (2)) leads to m = 16 which is the limiting value of dynamic fragility for very strong glasses (see Section “The glass transition and the dynamic fragility”); the dynamic fragility of a glass-forming system thus appears in TSDC as proportional to the departure (at Tg) of the points of α-relaxation from the zero entropy line.

Conclusions

The thermal behavior and polymorphism of bifonazole and lamotrigine were investigated by DSC. Both are easily amorphizable by cooling from the liquid and both undergo cold crystallization. A polymorph of bifonazole not yet reported in the literature was obtained by cold crystallization; in contrast, no clear evidence of lamotrigine polymorphism was found: In this case, we only reported observations that cast suspicion on the possible existence of polymorphism. DSC was also used to study the glass transition by determining its temperature, Tg, activation energy Ea(Tg) (and dynamic fragility, mDSC) as well as the associated heat capacity jump, ΔCp(Tg).

The TSDC study provided experimental values of the glass transition temperature, TgTDSC, and of the dynamic fragility, mTSDC, in reasonable agreement with those obtained by DSC. A secondary relaxation was also characterized by TSDC. The absence of other dynamic studies on these glass-formers does not allow the comparison of our results with those of other techniques, namely with dielectric spectroscopy. On the other hand, attention was drawn to the general need to understand in their mutual relationship the TSDC and DRS results on the secondary relaxations.