In this chapter the results of the experimental diffusion coefficients, volumetric and viscosimetric techniques for some transport and thermodynamic properties of l-dopa in presence of cyclodextrins are presented. To a better understanding of the behaviour of l-dopa in presence of the cyclodextrins, the results obtained for binary aqueous solutions of l-dopa and these values are also presented and compared with the ternary systems.
4.1. Binary Aqueous Systems
The experimental mutual diffusion coefficients of binary aqueous solutions of
l-dopa at 298.15 K and 310.15 K are already published by Barros et al. [
47].
Looking at the obtained results for the l-dopa, it is possible to observe that, at the lowest studied concentrations, the aqueous diffusion coefficient average presents a decrease with the solution’s concentration increase, in both studied temperatures. However, from the concentration (0.00375 mol dm−3) ahead, the diffusion coefficient presents a rise of approximately 6%, regardless the temperature. From the diffusion coefficient’s data, it was possible to calculate values of the activity coefficients. These values decrease as the solute concentration increases, although there is no significant variation with the temperature. This decrease might be related to a major increase of the solute-solvent interactions with the concentration’s increase, relatively to the solute-solute ones.
The hydrodynamic radius of the l-dopa molecule was calculated from the obtained values of the diffusion coefficient. It was found that the hydrodynamic radius of the l-dopa molecule reaches a maximum value of concentration rounding c = 2.50 × 10−3 (mol dm−3), in both temperatures, which leads to the conclusion that at higher concentrations, the viscosity effect upon the diffusion coefficient value is not significant. From the values of the hydrodynamic radius at infinitesimal concentration, at different concentrations of l-dopa, it was possible to determine the molar hydrodynamic volume that presents the values of 144 cm3 mol−1 at 298.15 K and 145 cm3 mol−1 at 310.15 K.
The density values of binary aqueous solutions of
l-dopa determined in the temperature range of 294.15–312.15 K, as well as the partial molar volumes determined from the obtained values of the density, are presented in
Table S1. They show a linear increase with the concentration’s increase for all studied temperatures. The density values at infinite dilution decrease as the temperature increases. This decrease might be a consequence of a volume increase caused by the thermal effect.
The partial molar volumes will be established from the obtained values of the density, which present an increase with the increasing concentration of the solute in the solution, at all temperatures. This might be related to the rise of the attractive solute-solvent interactions originated by the increase in solute concentration. This behaviour is very similar for all the studied temperatures, which indicates that temperature has no influence on the partial molar volume behaviour. The obtained values for the partial molar volumes, at infinitesimal concentration, point out that in l-dopa aqueous solutions, the interactions solute-solvent type should be predominant. These interactions increase with the temperature increase, which indicates that the solution is more structured at higher temperatures.
From the dependence of the l-dopa partial molar volumes, at infinitesimal concentration, on the temperature, it is possible to attain the value of the molar expansibility at infinite dilution, . This presents a positive value, indicating the existence of strong solute-solvent interactions, which suggests that this solute has a structure-making behaviour.
The results of the viscosity of binary aqueous solutions of
l-dopa at 298.15 K and 310.15 K are already published by Barros et al. [
47]. It was observed that the viscosity values of the
l-dopa aqueous solutions increase with the solute concentration and decrease with the temperature increasing. From this analysis, according to Jones-Dole equation, it is observed that the
A coefficient value is very small and negative, for both studied temperatures, from which it is deduced the existence of very weak interactions of the solute-solute type, being them more significant at the temperature of 298.15 K. On the other hand, once the viscosity
B coefficient value is positive, we may conclude the existence of strong solute-solvent interactions and also that
l-dopa is a structure-making solute type, which is in accordance with the obtained results for the other studied properties.
The study of β-cyclodextrin and HP-β-cyclodextrin properties in aqueous solutions allowed verifying that these cyclodextrins present aspects of their behaviour quite similar between each other when they are in aqueous solutions.
The diffusion of these two cyclodextrins was previously studied by Santos et al. [
51]. This author found that the diffusion coefficient values from β-CD and from HP-β-CD “
are small and little influenced by the increase in the concentration of the solution, regardless of what temperature is considered.” It must be taken into account that cyclodextrins are very large molecules, with a high molar mass, so they present a high resistance to movement and, consequently, it is expected that they have a low diffusion coefficient.
Density values have been determined and, from them, the values of partial molar volumes of the solutions of the CDs under study, at different concentrations and in the temperature range between 294.15 K and 312.15 K. The obtained values for β-CD and for HP-β-CD are presented, in
Tables S2 and S3, respectively.
From the obtained results it is possible to observe that the HP-β-CD presents higher values for density and apparent molar volumes, while the β-CD presents the smallest values. Looking at the studied cyclodextrins, the results suggest that the HP-β-CD is the one that most interacts with the water molecules, incorporating a relatively high number of them into its hydration sphere (simultaneously two phenomena occur: hydrophobic hydration—water molecules more or less immobilized in the surrounding area of the hydrophobic areas of the molecule—and hydrophilic hydration -water molecules anchored around the OH of the hydroxy-propyl- groups).
Regarding the behaviour of the ϕV vs. the molality of the solutions, we can see that these slopes are quite close to each other, presenting values that are always higher than those of , which suggests that in these aqueous solutions there is a predominance of solute-solute type interactions over the ones of the solute-solvent type.
The apparent partial molar volumes of β-CD and HP-β-CD present a linear adjustment as a function of the molality of the solution.
From the dependence of the partial molar volumes of β-CD and HP-β-CD, at infinitesimal concentration, on the temperature, it is possible to attain the value of the molar expansibility at infinite dilution, . For the studied cyclodextrins, the values of the molar expansibility at infinitesimal concentration were determined. They are positive values, which suggests that in aqueous solution these CDs present a structure-making behaviour.
The viscosity values of the aqueous solutions of β-CD and HP-β-CD were previously determined by Santos et al. [
51]. Those studies were made at different concentrations of the CD and at the temperatures of 298.15 K and 310.15 K, and they support the conclusion that both the cyclodextrins have a structure-making behaviour
, in agreement with the behaviour observed by other authors, as well as in this work from other physicochemical properties analysed.
4.2. Ternary Aqueous Systems
It is very likely that interactions between molecules of
l-dopa and CD molecule may occur. Assuming that, a 1:1 type complex can be formed between a molecule of
l-dopa and a molecule of cyclodextrin, as drew in
Figure 1.
The association process can be described by the equilibrium:
whose association constant,
K, is:
Using theoretical models to adjust the experimental data obtained for the main and cross diffusion coefficients, it was possible to estimate values for the association constant K, of l-Dopa-cyclodextrin, considering the mixture water + cyclodextrin as a mixed solvent and the kind of complexes formed are always of the type 1:1.
The diffusion coefficients values of
l-dopa in presence of cyclodextrins have already been published by the Barros et al. [
48,
49,
50].
From the published experimental data values of the diffusion coefficients it was possible to estimate values for the constant K, as well as for the diffusion coefficients of the species in equilibrium,
D11*,
D22* and
D33*, estimated for the aqueous solutions of levodopa in the presence of β-CD and HP-β-CD, at 298.15 K and 310.15 K. These values are presented in
Tables S4 and S5, respectively.
Taking into account that the values for the association constants of
Tables S4 and S5 were estimated by applying the Paduano et al. [
22,
23,
24,
25,
26] theoretical model, in an attempt to understand what occurs in the solutions, from the comparison of the obtained results for the different cyclodextrins under study, it can be deduced that between the
l-dopa and the corresponding cyclodextrin (β-CD and the HP-β-CD) complexation may occur. Moreover, for the β-CD the values suggest that this complexation is strongest at the lowest temperature, 298.15 K, while for the HP-β-CD this interaction increases drastically when the temperature increases to 310.15 K.
From the application of the theoretical model of Paduano et al. [
22,
23,
24,
25,
26] to the diffusion measurements, it was possible to estimate the diffusion coefficient values of the associated species,
D33*, for the same systems.
For the β-CD case it is observed that D33* presents a value close to that of D22*, mainly at 298.15 K. This result allows to state that the l-dopa molecule can be totally, or partially, included in the cyclodextrin cavity and so, the dimensions of the diffusing species, cyclodextrin or complex l-dopa-cyclodextrin, are very similar, especially for the lowest temperature, 298.15 K, where the inclusion is stronger, which is in accordance with the value determined for the association constant.
For the HP-β-CD case, D33* presents a different value from that of D22*, for the two studied temperatures. This result seems to indicate that the estimated value for K may be mainly due to the existence of external interactions between the molecules of l-dopa and HP-β-CD, than to the inclusion of l-dopa in the cyclodextrin cavity.
The obtained values of the apparent partial molar volumes point to the idea that there is an association between l-Dopa and cyclodextrins β-CD and HP-β-CD. In addition, it is observed that l-dopa in the presence of β-CD presents values of the association constant higher than in the presence of HP-β-CD, which is in line with what has been concluded through the diffusion coefficient values. Finally, it is found that for β-CD the association constant, K, decreases with increasing temperature and that for the HP-β-CD, K, it increases with increasing temperature.
In this work, the experimental values of the density of aqueous solutions of l-dopa in the presence of different cyclodextrins, at different temperatures are presented. From them, the corresponding values of the apparent molar volumes were determined, using Equation (5) and considering the mixture water + cyclodextrin as a solvent. From the obtained values, the interactions between the solute, the solvent and the co-solvent, are discussed.
The experimental values of the density, together with those calculated for the corresponding apparent molar volumes, for aqueous solutions of
l-dopa in presence of β-CD and HP-β-CD, in the temperature range between 294.15 K and 312.15 K, are presented in
Tables S6 and S7, respectively. In all cases, the standard deviations of the density measurements were less than 5.0 × 10
−6, which leads to an uncertainty associated with the calculation of the apparent molar volumes, always lower than 5%. The concentration range selected for the solutions of
l-dopa, between 0.5–7.5 mol kg
−1, was chosen not to exceed the limit of solubility of this drug.
Analysing the density values of these aqueous ternary solutions of l-dopa in the presence of the β-CD and HP-β-CD, it is observed that they present density values higher than those of the corresponding binary aqueous solutions, for all the concentrations and temperatures studied. It is also observed that as the temperature increases, the density of the solutions decreases, although always maintaining a parallel behaviour for the different temperatures studied. In all cases, the results obtained responded to linear adjustment, with values of density of the solvent, ρ0, very close to those of the density of the binary aqueous solutions of the β-CD or HP-β-CD, with the same molal concentration.
In relation to the apparent molar volumes, ϕV, calculated from the values of the density, it should be noted that they are always positive and that, in general, they have higher values than those of the l-dopa in aqueous solution. That is, in general, the presence of cyclodextrins in the medium causes an increase in the value of the apparent molar volume of l-dopa.
The values of the apparent molar volumes at infinitesimal concentration can be determined from the Equation (8), whose values coincide with those of the partial molar volumes),
=
. These values are presented in
Tables S7 and S8.
Comparing these values with those obtained for the binary systems: water + β-CD/water + HP-β-CD and water + l-dopa, at infinitesimal concentration, the values corresponding to their partial molar volumes of transfer are obtained [according to the Equation (9).
Thus,
Tables S8 and S9 present the calculated values for the partial molar volumes of the transfer of the
l-dopa from water to the mixed solvent water + β-CD and water + HP-β-CD at the different concentrations studied, in the range of temperatures between 294.15–312.15 K.
The different behaviour of
l-dopa in relation to the complexation processes with the studied cyclodextrins, can be analysed through the changes of the transfer volumes. As can be observed at
Table S8, in the presence of β-CD the
l-dopa shows, for almost all concentrations and temperatures studied, positive volumes of transfer increasing with the concentration and the temperature. This indicates that the interaction
l-dopa-β-CD decreases as both the variables get higher. Therefore, it is highly probable that the release of the
l-dopa molecules, which may be initially included in the cavity of the β-CD, occurs in parallel with the conformational changes that take place with the increase in temperature. By applying the Friedman and Krishnan model to this system [
31], we can conclude that the hydrophilic-ionic type and/or of the hydrophilic-hydrophilic type are the predominant interactions.
Looking at the volumes of transfer of
l-dopa in the presence of HP-β-CD we checked that they have negative values for almost all temperatures and concentrations. In addition, in this system the partial molar volumes of transfer decrease with the increase in concentration, which can be interpreted, mainly, as a sign of the formation of inclusion complexes
l-dopa-HP-β-CD. Thus, applying the model of Friedman and Krishnan [
31], it can be stated that the predominant interactions that take place in this system could be either hydrophilic-hydrophobic or between hydrophobic groups.
Taking into account the analogy between the structures of the cited two cyclodextrins to explain the volume changes that accompany the transfer of l-dopa from water to water + cyclodextrin, it is evident that the volume variations determined for each different media are totally different, verifying that the inclusion is favoured by the presence of the hydroxypropyl groups, instead of the hydroxyl groups.
To examine how the addition of l-dopa affects the structure of the mixed solvents, the partial molar expansibility at infinite dilution can also be used and, from this, it is possible to determine the Hepler constant for the systems under study.
The values of partial molar expansibility at infinite dilution for the
l-dopa in presence of different concentrations of β-CD and HP-β-CD are presented in
Tables S10 and S11.
Since a positive value of indicates the existence of strong solute-solvent interactions and that a negative value of shows that the solute-solvent interactions are very weak, l-dopa acts as a structure-breaking solute of the mixed solvents water-β-CD and water-HP-β-CD, once the partial molar expansibility at infinitesimal concentration always presents positive values.
The second derivative of the partial molar volume at infinite dilution was a criterion of hydrophobicity proposed by Hepler [
33], according to:
if | | y | | , |
the solute is considered hydrophilic |
if | | y | | , |
the solute is considered hydrophobic |
Through the obtained results for these systems it can be deduced that the l-dopa, in the presence of the mixed solvents water + β-CD and water + HP-β-CD, presents hydrophilic characteristics. On the contrary, for the mixed solvent water + NaSO3-β-CD, the l-dopa presents negative values of , demonstrating the presence of very weak, or almost non-existent, solute-solvent interactions.
It is possible to estimate the values of the constant
K from the values of
for each of the components of the system and from the dependence of
K on the temperature, to determine the thermodynamic functions ∆
H0, ∆
S0 and ∆
G0 for the balance between the cyclodextrin and a drug. These values are presented in
Tables S13 and S14.
The calculated values of ∆G0 for the systems under study show that the process of complexation between l-dopa and β-CD and l-dopa and HP-β-CD is spontaneous (∆G0 < 0).
Usually, the inclusion of a drug in the cyclodextrin cavity is associated to negative values of ∆
H0 and negative or slightly positive values of ∆
S0, showing that the inclusion process is not accompanied by desolvation but it is a process governed mainly by the enthalpy [
24]. The present estimation shows that only the complex formed between
l-dopa and β-CD presents this behaviour, with an enthalpy term predominating in the formation of the inclusion complex.
The inclusion of l-dopa in HP-β-CD presents a different result. In fact, when the l-dopa is dissolved in the solution, it seems to have strong interactions with the solvent. Once the inclusion complex is formed, an unfavourable entropy change occurs due to the rupture of the solvation sphere, which explains a positive value of ∆S0, indicating that the formation of the inclusion complex with HP-β-CD is governed by the entropy term.
The experimental values obtained for the viscosity of the solutions of
l-dopa considering the mixed solvent mixture water + β-CD and mixture water + HP-β-CD were determined and are presented in
Tables S15 and S16. In all cases, the standard deviation of these viscosity measurements was less than 3.5 × 10
−4 units.
To determine the variation of the viscosity of these solutions, the solutions of l-dopa, at different concentrations, were prepared in each of the mixed solvents studied and which were formed by water and the corresponding cyclodextrin, at a constant concentration. This way, changes in the viscosity of these solutions are, consequently, attributed only to the l-dopa dissolved in the mixed solvent and not to the composition of the solvent.
From the analysis of the
Tables S15 and S16 it can be seen that, as expected, the values obtained for the viscosity of the solutions of
l-Dopa in the mixed solvent water + HP-β-CD and water + β-CD, increase with the increase of the concentration of the solute and decrease with temperature.
The analysis of these experimental values was made by adjusting them to the Jones-Dole equation (16) [
37].
The values obtained for the coefficients A and B of the Jones-Dole equation, corresponding to the aqueous solutions of
l-dopa in the presence of β-CD and HP-β-CD, are presented in
Tables S17 and S18, for the studied temperatures of 298.15 K and 312.15 K.
As it can be seen from the observation of the values in
Table S17, obtained for coefficient
A, at 298.15 K and 310.15 K, for
l-dopa in presence of β-CD, are small but they increase with the increase of the amount of β-CD in the dissolution. These data reveal that the solute-solute interactions are very weak but they increase with the increase of the amount of β-CD present in the solution.
For the system
l-dopa in presence of HP-β-CD as it can be appreciated in
Table S18, the values obtained for the coefficient
A at 298.15 K are small and, in general, tend to decrease with increasing the amount of cyclodextrin present in the solution. On the other hand, at 310.15 K, it is seen that the value of
A parameter increases with the increase of the concentration of cyclodextrin in the solution. This behaviour seems to indicate the existence of weak solute-solute interactions and that, in both cases, such interaction becomes more and more important with the increase of the amount of cyclodextrin in solution.
Analysing the viscosity coefficient
B values for the
l-dopa (
Table S17), it is verified that, in general, they are positive but decrease with the increase of the concentration of the β-CD in the solution. From such behaviour it can be concluded that there are strong solute-co-solvent interactions that weaken as the amount of cyclodextrin present in the solution increases. Taking into account that the coefficient
B provides information on the interactions that take place between the molecules of the solute and those of the solvent (in this case, of a mixed solvent), which result in a greater or lesser structuring of the solution (structure effect making or structure effect breaking, of the solute) [
38], it is deduced that the
l-dopa presents a behaviour of the structure breaking type at both temperatures, once the interactions decrease with the amount of β-CD present in the dissolution.
Analysing the values of the coefficient B for the l-dopa in presence of HP-β-CD, it is noticed that these are high and positive, although they do not present a definite variation with the increase of the cyclodextrin concentration in the solution. On the other hand, it is observed that the magnitude of the coefficient B is much superior than that of the coefficient A, suggesting that in this system there are weak solute-solute interactions and strong solute-solvent interactions. From the above, it is possible to conclude that l-dopa presents structure-making characteristics in the of HP-β-CD solutions.
Relatively to the viscosity B-coefficients of transfer, ΔB, for aqueous solutions of l-dopa in the presence of the cyclodextrins, it is possible to observe that the values of ΔB are, in general, positive for almost all the systems and studied temperatures. These results, together with those obtained for the viscosity measurements, show that the l-dopa presents structure maker characteristics in the presence of β-CD and HP-β-CD. This agrees with the results obtained from the partial molar expansibility at infinitesimal concentration and the Hepler constant.