3.1. Preparation of Polymorph III
The high-temperature polymorph (polymorph III) was prepared by heating the initial anhydrous βCD (polymorph I) to 508 K in argon flow in TG/DSC experiment. Corresponding TG/DSC curves are given in
Figure 1. During the first heating of polymorph I, an endothermic effect is observed with onset point at 495 K (
Figure 1). The enthalpy of such effect is ΔH
tr = 16.5 kJ mol
-1. This effect is absent in the second heating run for the product of polymorph I heating to 508 K and cooling (
Figure 1) and no peaks of phase transition can be seen in the corresponding DSC cooling curve in a separate TG/DSC experiment (Figures A7, A8), what indicates irreversibility of the observed transition.
According to TG data, βCD has no mass loss in the range of 473–513 K (
Figure 1). Thus, the endothermic process at these temperatures corresponds to a polymorphic transition leading to the formation of the new polymorph III. For this high-temperature polymorph III, the onset point of thermal destruction is 526 K, which is by 8 K lower than that of the initial form. The lower thermal stability of polymorph III can be explained by its higher energy than that of the initial βCD form.
To differentiate the endothermic polymorphic transition at 495 K from the thermal degradation of βCD, the dependence of the observed transition on heating rate was determined in DSC experiment and corresponding activation energy E
a was calculated using model-free and optimal model methods.[
29,
30] The experimental data and description of calculation details are given in Appendix A. For this transition, model-free Ozawa-Flynn-Wall and Friedman methods give the activation energy E
a of 430 and 350 kJ mol
-1, respectively, in the conversion range of 0.1–0.7. The optimal thermokinetic model is the Prout-Tompkins equation with E
a = 430 kJ mol
-1 and process order of n = 1.92. These E
a values are in 3-4 times higher than the activation energy E
a =105 kJ mol
-1 of the βCD thermal degradation reaction,[
31] which confirms a different nature of the observed endothermic effect.
The structural changes upon polymorphic transition were studied using the powder X-ray diffraction method. For this, diffraction patterns were determined for polymorph I, polymorph III and products of its saturation with water vapor having relative humidity of 33% (water activity a
w = 0.33), its recrystallization in water vapors at a
w = 1.0 (both at 298 K) and from aqueous solution (
Figure 2). Polymorph III for this experiment was prepared by two methods: by heating polymorph I to 508 K and cooling in argon flow and, in a larger scale, by heating to 505 K and cooling in air. Both methods give the samples with nearly the same PXRD pattern (
Figure 2b,c, A9).
The diffractograms obtained indicate an essentially different packing of high-temperature polymorph III (
Figure 2b,c) than that of the initial polymorph I (
Figure 2a). Both these patterns do not coincide with diffractogram of channel-type polymorph II [
16] by their characteristic peaks,
Table 1. The indexing of high-temperature polymorph III diffractogram (Figure A5) for the sample prepared by heating polymorph I to 505 K and cooling in air gives a triclinic cell with parameters of a = 17.09 Å, b = 15.12 Å, c = 11.76 Å, α = 109.5°, β = 95.8°, γ = 70.6°,
Table 1, with R
wp = 5.466. The cell volume of this high-temperature polymorph is V = 2704 ų, which is more compact than the initial dried βCD form having V = 2894 ų [
24]. For comparison, polymorph II has a hexagonal cell [
17] with volume V = 3069 ų,
Table 1.
Hydration of polymorph III at water activity a
w = 0.33 and 298 K gives minor changes in its diffraction pattern (
Figure 2d) without change of its main packing type. In saturated water vapors at a
w = 1.0, this polymorph forms a mixture of aqueous βCD solution and its solid hydrate, unlike the initial polymorph I, which remains in a solid state state under these conditions.[
32,
33] The products of such recrystallization in water vapors (
Figure 2e) and recrystallization of the same high-temperature polymorph III from aqueous solution (
Figure 2f) without drying have practically the same packing as the saturated hydrate βCD·11.2H
2O prepared by saturation of the polymorph I at a
w = 1.0 (
Figure 2g). So, no chemical reactions occur in anhydrous βCD upon heating to 508 K, which is 5 K above the peak point of polymorphic I→III transition. The absence of chemical changes is also confirmed by the identity of the IR spectra of both polymorphs (Appendix A).
3.2. Dissolution rate
Being the high-temperature form produced by endothermic transition, polymorph III is expected to have a higher dissolution rate. To study the dissolution rate in water for this polymorph and the other studied anhydrous forms of βCD and dried HPβCD for comparison, the method of solution calorimetry was chosen, which can estimate the time of fast dissolution processes.[
34]
Calorimetric curves were determined,
Figure 3, for dissolution of polymorphs I and III, and amorphous forms of dried ball-milled βCD and dried HPβCD. The corresponding values of dissolution times
tsoln and enthalpies Δ
Hsoln are given in
Table 2.
The dissolution of polymorph I includes two processes: exothermic hydration curve of anhydrous βCD and endothermic dissolution of βCD hydrate. These processes have been separately characterized elsewhere [
35] and can be seen in a complex shape of polymorph I dissolution curve (
Figure 3a). This calorimetric curve demonstrates rather fast exothermic effect in the first 35 s after the start of dissolution with the next prolonged endothermic event for 155 s. The ratio of these thermal effects 3.5:1 corresponds to the values of the determined polymorph I solution enthalpy Δ
Hsoln = –86±1 kJ mol
-1 and literature data [
35] of Δ
Hsoln = –91 kJ mol
-1 for the same anhydrous βCD form and Δ
Hsoln = +35 kJ mol
-1 for saturated hydrate βCD·12H
2O, which gives the ratio 3.6:1 of βCD hydration and βCD·12H
2O hydrate dissolution enthalpies. The composition of saturated βCD hydrate is from the single crystal XRD.[
36] This means that hydration and hydrate dissolution events occur not simultaneously in any significant extent but one after another.
The dissolution curve of polymorph III (
Figure 3b) performs only the exothermic effect with Δ
Hsoln = –94±1 kJ mol
-1 within the first 43 s,
Table 2. So, its hydration and dissolution are simultaneous. The difference in Δ
Hsoln values of polymorphs I and III at 298 K is 8±2 kJ mol
-1 is lower than the enthalpy of polymorphic transition +16.5 kJ mol
-1 with onset at 495 K,
Figure 1, which may be caused by the difference in experimental temperatures. The amorphous βCD with dissolution enthalpy of Δ
Hsoln = –111±1 kJ mol
-1 shows the same dissolution time of 43 s as polymorph III in practically one exothermic step followed by very small but prolonged (
tsoln = 90±10 s) endothermic effect, which is only ~3% of the total dissolution enthalpy. This may be caused by formation of crystalline βCD hydrate from the minor part of the initial amorphous sample having a higher energy by 17 kJ mol
-1 than polymorph III.
The dissolution curve of anhydrous HPβCD with Δ
Hsoln = –144±1 kJ mol
-1 has the same shape as observed for polymorph III but with much higher dissolution time of
tsoln = 100 s (
Figure 3d,
Table 2). Thus, the dissolution rate of polymorph III in water is close to that of amorphous βCD, being 4.4 and 2.3 times higher than that of the initial polymorph I and HPβCD, respectively, despite the latter one is amorphous, and its dissolution is more exothermic. A similar difference in the dissolution rates of these forms was also observed visually.
3.3. Thermodynamic properties
The different properties of βCD polymorphs I and III were also observed in DSC experiment where dependences of their molar heat capacity
Cp,m on temperature
T in the range of 343–463 K were determined. This range was chosen because it excludes the influence of water traces in dried argon used to purge CD samples. The obtained plots of
Cp,m vs.
T are given in
Figure 4, and the values of
Cp,m at each studied temperature are given in Appendix A. The molar heat capacity of the initial polymorph I can be described by the equation
Cp,m = –1219 + 10.36
T – 0.00623
T². This equation extrapolated to the temperature
T = 298 K gives
Cp,m = 1316±13 J mol
-1 K
-1, which is slightly lower than 1342±10 J mol
-1 K
-1 measured earlier at the same temperature.[
37] The molar heat capacity of polymorph III can be described as
Cp,m = –884 + 9.05
T – 0.00478
T². Hence, molar heat capacity of polymorph III is higher, than that of polymorph I in the studied range of temperatures (
Figure 4).
The enthalpy of I→III transition Δ
Htr at 298 K can be estimated using Kirchhoff's law by the value of Δ
Htr(495K) = 16.5 kJ mol
-1 determined in DSC experiment (
Figure 1) and the difference of heat capacities Δ
Cp,m of polymorphs I and III:
The calculated value of Δ
Htr(298 K) coincides with the difference in enthalpies of polymorphs I and III dissolution in water at 298 K, which is equal to 8±2 kJ mol
-1,
Table 2.
Since the endothermic process in anhydrous βCD at 495 K is the transition from polymorph I to polymorph III followed by melting of βCD at 774 K,[
31] this polymorphic transition is enantiotropic with zero value of transition Gibbs energy Δ
Gtr(495 K) = 0 according to the heat-of-transition rule of Burger and Ramberger.[
38] Hence, the value of polymorphic transition entropy at its onset point is equal to Δ
Str(495 K) = 33 J mol
-1 K
-1. So, the entropy of I→III transition at 298 K can be calculated:
This gives the positive value of transition Gibbs energy at standard temperature, ΔGtr(298 K) = 4.7 kJ mol-1, which means that polymorph III has a higher Gibbs energy than polymorph I at 298 K. Such relationship can explain the higher dissolution rate of polymorph III and, respectively, its higher bioavailability.
3.4. Affinity for water
To compare the affinity of polymorph III for water with that of polymorph I and HPβCD, the hydration isotherms were measured for polymorph III and HPβCD using their equilibration with water vapors of fixed humidity at 298 K and gravimetric determination of hydrate composition. Hydration isotherm of polymorph I has been determined elsewhere.[
33] The isotherms were fitted using Hill equation, as described earlier.[
39] The used equation and approximation parameters are given in Appendix A. These are inclusion capacity
S, water activity at 50% saturation extent
a0.5S, which is a hydration threshold, and cooperativity parameter for separate inclusion steps.
Hydration of polymorph III occurs in two steps (
Figure 5b), corresponding to the inclusion capacity
S of 2.5 and 1.6 mol water per mol βCD with hydration threshold
a0.5S at 0.09 and 0.30, respectively. Such steps means that hydration of polymorph III produces a phase transition, which may be induced by inclusion inside βCD cavity because of the uptake of 4 water molecules at
aw = 0.33 does not produce does not show significant changes in polymorph III PXRD pattern (
Figure 2d). For comparison, 4.5 and 7 water molecules have such inclusion type in βCD·9.4H
2O and βCD·12.3H
2O single crystals, respectively.[
35] Hydration of polymorph III at
aw = 0.43 gives a mixture of aqueous solution and crystalline βCD hydrate with a total βCD/water molar ratio of 1:20.5, where the liquid phase is observed visually. Such behavior was not observed under the same conditions for polymorph I, which cannot sorb more water than needed to form its hydrates in two steps (
Figure 5b), corresponding to the inclusion capacity
S of 9.2 and 2.2 mol per mol βCD with hydration threshold
a0.5S at 0.26 and 0.97, respectively.[
33]
The isotherm of HPβCD hydration (
Figure 5c) performs only one step with a lower hydration capacity
S = 2.2 mol mol
-1 and hydration threshold of
a0.5S=0.04. This isotherm also becomes vertical at
aw = 0.43 with HPβCD giving a drop of its liquid aqueous solution. So, this βCD derivative is more water soluble than the earlier studied HPβCD with a lower substitution ratio of 0.6, which does not dissolve in water vapors even at
aw = 1.[
40]
The affinity of the studied CDs for water can be characterized by their hydration Gibbs energy Δ
Gh, which was calculated for each step using equation:
This equation gives Gibbs energy [
39] of water transfer from its pure liquid to stable hydrate with the inclusion capacity
S. The values of Δ
Gh for the first and second hydration step of polymorph III are –5.9 and –3.0 kJ per 1 mol of water, respectively. HPβCD has this value of Δ
Gh = –7.9 kJ mol
-1. For comparison, two steps of polymorph I hydration correspond to Δ
Gh values of –3.3 and –0.1 kJ mol
-1, respectively.[
33] So, the affinity for water changes in order: HPβCD > polymorph III > polymorph I. While as HPβCD is well soluble in water (>600 mg mL
-1),[
41] a similar good solubility could be expected for polymorph III. Still, the equilibrium solubility of polymorph III is restricted by ability of βCD to recrystallize into its saturated hydrate having poor solubility of 18.4 mg mL
-1,[
41] which was observed visually for III in water vapors at activity of
aw = 0.43 as mentioned above. Such dissolution-crystallization behavior can be useful for a preparation of inclusion compounds in pastes using small amount of water or for a quick removal of undesirable compounds from aqueous solution by their complexation with βCD using much faster dissolution of its polymorph III. This property makes polymorph III a promising alternative to the more expensive synthetic derivatives of cyclodextrins.