Atorvastatin as a Promising Crystallization Inhibitor of Amorphous Probucol: Dielectric Studies at Ambient and Elevated Pressure

Tuning the Physical State of Aripiprazole by Mesoporous Silica

The main purpose of our studies is to demonstrate that commercially available mesoporous silica (MS) can be used to control the physical state of aripiprazole (ARP). The investigations performed utilizing differential scanning calorimetry and broadband dielectric spectroscopy reveal that silica can play different roles depending on its concentration in the system with amorphous ARP. At low MS content, it activates recrystallization of the active pharmaceutical ingredient and supports forming the III polymorphic form of ARP. At intermediate MS content (between ca. 27 and 65 wt %), MS works as a recrystallization inhibitor of ARP. At these concentrations, the formation of III polymorphic form is no longer favorable; therefore, it is possible to use this additive to obtain ARP in either IV or X polymorphic form. At the same time, employing MS in concentrations >65 wt % amorphous form of ARP with high physical stability can be obtained. Finally, regardless of the polymorphic form it crystallizes into, each composite is characterized by the same temperature dependence of relaxation times in the supercooled and glassy states.

Improved Dissolution Properties of Co-amorphous Probucol with Atorvastatin Calcium Trihydrate Prepared by Spray-Drying

A co-amorphous model drug was prepared by the spray-drying (SD) of probucol (PC) and atorvastatin calcium trihydrate salt (ATO) as low water solubility and co-former components, respectively. The physicochemical properties of the prepared samples were characterized by powder X-ray diffraction (PXRD) analysis, thermal analysis, Fourier transform infrared spectroscopy (FTIR), and dissolution tests. Stability tests were also conducted under a stress environment of 40 °C and 75% relative humidity. The results of PXRD measurements and thermal analysis suggested that PC and ATO form a co-amorphous system by SD. Thermal analysis also indicated an endothermic peak that followed an exotherm in amorphous PC and a physical mixture (PM) of amorphous PC and ATO; however, no endothermic peak was detected in the co-amorphous system. The dissolution profiles for PC in the co-amorphous sample composed of PC and ATO were improved compared to those for raw PC crystals or the PM. Stability tests indicated that the co-amorphous material formed by PC and ATO can be stored for 35 d without crystallization, whereas amorphous PC became crystallized within a day. Therefore, co-amorphization of PC and ATO prepared by SD is considered to be a useful method to improve the solubility of PC in water.

Effect of Shear Strain on the Supercooled Itraconazole

This article investigated the effect of shear strain on the nematic itraconazole (ITR) from both elastic and plastic deformation regions. The rheo-dielectric technique was used for this purpose. It has been demonstrated that shear strain can change the sample color, liquid crystal alignment as well as its dielectric and thermal properties. The observed modifications depend on the shear strain value. One can distinguish four regions regarding the slope of ITR stress-strain dependence and caused changes. Proper alignment changes (obtained after the shearing procedure) can additionally affect the further recrystallization of ITR to other than the initial, i.e., second polymorphic form.

Solid-state properties of Nifurtimox. Preparation, analytical characterization, and stability of an amorphous phase

Nifurtimox (NFX) is a nitrofuran derivative used to treat Chagas disease, a neglected disease caused by the protozoan Trypanosoma cruzi. The drug is very sparingly soluble in aqueous media and no other solid phases of NFX have been reported to date. The preparation of the amorphous mode of NFX is reported, as well as its characterization by hot stage microscopy, thermal (differential scanning calorimetry and thermogravimetric analysis), spectroscopic (solid state nuclear magnetic resonance, mid-infrared, and near-infrared), diffractometric and functional (powder dissolution rate) means. The stability of the new phase was investigated. This was characterized using thermal, spectroscopic, and diffractometric methods, finding out its spontaneous reversion to the crystalline state, as sign of instability. In addition, the amorphous material proved to be sensitive to temperature, pressure, and mechanical stress, all of which accelerated phase conversion. However, it was able to remain stable in a model polymeric amorphous solid dispersion with PEG 4000 for more than one month. An approach for monitoring the conversion of the amorphous phase to its crystalline counterpart under thermal stress by chemometric analysis of mid-infrared spectra at different temperatures is also disclosed.

Complementarity of mDSC, DMA, and DRS Techniques in the Study of Tg and Sub-Tg Transitions in Amorphous Solids: PVPVA, Indomethacin, and Amorphous Solid Dispersions Based on Indomethacin/PVPVA

Recently, glasses, a subset of amorphous solids, have gained attention in various fields, such as polymer chemistry, optical fibers, and pharmaceuticals. One of their characteristic features, the glass transition temperature (T_g) which is absent in 100% crystalline materials, influences several material properties, such as free volume, enthalpy, viscosity, thermodynamic transitions, molecular motions, physical stability, mechanical properties, etc. In addition to T_g, there may be several other temperature-dependent transitions known as sub-T_g transitions (or β-, γ-, and δ-relaxations) which are identified by specific analytical techniques. The study of T_g and sub-T_g transitions occurring in amorphous solids has gained much attention because of its importance in understanding molecular kinetics, and it requires the combination of conventional and novel characterization techniques. In the present study, three different analytical techniques [modulated differential scanning calorimetry (mDSC), dynamic mechanical analysis (DMA), and dielectric relaxation spectroscopy (DRS)] were used to perform comprehensive qualitative/quantitative characterization of molecular relaxations, miscibility, and molecular interactions present in an amorphous polymer (PVPVA), a model drug (indomethacin, IND), and IND/PVPVA-based amorphous solid dispersions (ASDs). This is the first ever reported DMA study on PVPVA in its powder form, which avoids the contribution of solvent to the mechanical properties when a self-standing polymer film is used. A good correlation between the techniques in determining the T_g value of PVPVA, IND, and IND/PVPVA-based ASDs is established, and the negligible difference (within 10 °C) is attributed to the different material properties assessed in each technique. However, the overall T_g behavior, the decrease in T_g with increase in drug loading in ASDs, is universally observed in all the above-mentioned techniques, which reveals their complementarity. DMA and DRS techniques are used to study the different sub-T_g transitions present in PVPVA, amorphous IND, and IND/PVPVA-based ASDs because these transitions are normally too weak or too broad for mDSC to detect. For IND/PVPVA-based ASDs, both techniques show a shift of sub-T_g transitions (or secondary relaxation peaks) toward the high-temperature region from -140 to -45 °C. Thus, this paper outlines the usage of different solid-state characterization techniques in understanding the different molecular dynamics present in the polymer, drug, and their interactions in ASDs with the integrated information obtained from individual techniques.

Ternary Eutectic Ezetimibe-Simvastatin-Fenofibrate System and the Physical Stability of Its Amorphous Form

In this study, the phase diagram of the ternary system of ezetimibe–simvastatin–fenofibrate was established. It has been proven that the ternary composition recommended for the treatment of mixed hyperlipidemia forms a eutectic system. Since eutectic mixtures are characterized by greater solubility and dissolution rate, the obtained result can explain the marvelous medical effectiveness of combined therapy. Considering that another well-known method for improving the aqueous solubility is amorphization, the ternary system with eutectic concentration was converted into an amorphous form. Thermal properties, molecular dynamics, and physical stability of the obtained amorphous system were thoroughly investigated through various experimental techniques compared to both: neat amorphous active pharmaceutical ingredients (considered separately) and other representative concentrations of ternary mixture. The obtained results open up a new way of selecting the therapeutic concentrations for combined therapies, a path that considers one additional variable: eutecticity.

High-Pressure Dielectric Studies-a Way to Experimentally Determine the Solubility of a Drug in the Polymer Matrix at Low Temperatures

In this work, we employed broad-band dielectric spectroscopy to determine the solubility limits of nimesulide in the Kollidon VA64 matrix at ambient and elevated pressure conditions. Our studies confirmed that the solubility of the drug in the polymer matrix decreases with increasing pressure, and molecular dynamics controls the process of recrystallization of the excess of amorphous nimesulide from the supersaturated drug–polymer solution. More precisely, recrystallization initiated at a certain structural relaxation time of the sample stops when a molecular mobility different from the initial one is reached, regardless of the temperature and pressure conditions. Finally, based on the presented results, one can conclude that by transposing vertically the results obtained at elevated pressures, one can obtain the solubility limit values corresponding to low temperatures. This approach was validated by the comparison of the experimentally determined points with the theoretically obtained values based on the Flory–Huggins theory.

How can we improve the physical stability of co-amorphous system containing flutamide and bicalutamide? The case of ternary amorphous solid dispersions

The article describes the preparation and characterization of binary mixtures of two antiandrogens used in prostate cancer treatment, i.e. flutamide (FL) and bicalutamide (BIC), as well as their ternary mixtures with either poly(methyl methacrylate-co-ethyl acrylate) (MMA/EA) or polyvinylpyrrolidone (PVP). The samples were converted into amorphous form to improve their water solubility and dissolution rate. Broadband dielectric spectroscopy and differential scanning calorimetry revealed that FL-BIC (65%) (w/w) does not tend to crystallize from the supercooled liquid state. We made the assumption that the drug-to-drug weight ratio should be maintained as in the case of monotherapy so we decided to investigate the system containing FL and BIC in 15:1 (w/w) ratio with 30% additive of polymers as stabilizers. Our research has shown that only in the case of the FL-BIC-PVP mixture the crystallization has been completely inhibited, both in glassy and supercooled liquid state, which was confirmed by X-ray diffraction studies. In addition, we performed solubility and dissolution rate tests, which showed a significant improvement in solubility of ternary system as compared to its crystalline counterpart. Enhanced physical stability and water solubility of the amorphous ternary system makes it promising for further studies.

Isochronal Conditions-The Key To Maintain the Given Solubility Limit, of a Small Molecule within the Polymer Matrix, at Elevated Pressure

In this work, we proposed the method to maintain the desired level of drug's solubility within the polymer matrix by adjusting conditions to uphold the same molecular dynamics of the system (e.g., temperature for set elevated pressure or vice versa). Namely, we observed, that recrystallization of the drug from the supersaturated drug-polymer system, initiated for the same structural relaxation time of the sample (τα-1) ceases when certain, different than the initial, molecular mobility of the systems is reached (τα-2)-regardless of a given combination of temperature and pressure conditions. Based on the presented results, one can conclude that the molecular dynamics seem to control the process of recrystallization of the excess amount of solute from the supersaturated solution (e.g., small molecules dissolved within the polymer). Therefore, it appears that the elevated pressure compensates the effect of solubility enhancement caused by the elevated temperature. Such information not only is of fundamental relevance in science but also, from a much broader perspective, could be potentially very useful considering extrusion-based manufacturing methods.

Influence of the Internal Structure and Intermolecular Interactions on the Correlation between Structural (α) and Secondary (β-JG) Relaxation below the Glass Transition Temperature in Neat Probucol and Its Binary Mixtures with Modified Saccharides

Broadband dielectric spectroscopy (BDS) has been used to study the molecular dynamics and aging process in neat probucol (PRO) as well as its binary mixtures with selected acetylated saccharides. In particular, we applied the Casalini and Roland approach to determine structural relaxation times in the glassy state of the examined systems (so-called isostructural times, τ_iso). Next, using the calculated τ_iso, primitive relaxation times of the coupling model were obtained and compared to the experimental secondary β (Johari-Goldstein (JG) type) relaxation times. Interestingly, it turned out that there is a correlation between the β-JG and the structural (α)-relaxation processes below the glass transition temperature (T < T_g) in each investigated sample. This is a new observation compared to previous studies demonstrating that such a relationship exists only in the supercooled liquid state of neat PRO. Moreover, it was revealed that the stretching parameters obtained from the aging procedure are very close to the ones determined by fitting the dielectric data above the T_g with the use of the Kohlrausch-Williams-Watts function, indicating that the aging process is governed by the α-relaxation. Complementary Fourier transform infrared and X-ray diffraction measurements allowed us to find a possible reason for these findings. It was demonstrated that although there are very weak intermolecular interactions between PRO and modified saccharides, the intra- and intermolecular structure of PRO is practically unaffected by the presence of modified saccharides.

Enhancement of the Physical Stability of Amorphous Sildenafil in a Binary Mixture, with either a Plasticizing or Antiplasticizing Compound

The main purpose of this paper was to evaluate the impact of both high- and low-T_g polymer additives on the physical stability of an amorphous drug, sildenafil (SIL). The molecular mobility of neat amorphous SIL was strongly affected by the polymeric excipients used (Kollidon VA64 (KVA) and poly(vinylacetate) (PVAc)). The addition of KVA slowed down the molecular dynamics of amorphous SIL (antiplasticizing effect), however, the addition of PVAc accelerated the molecular motions of the neat drug (plasticizing effect). Therefore, in order to properly assess the effect of the polymer on the physical stability of SIL, the amorphous samples at both: isothermal (at constant temperature—353 K) and isochronal (at constant relaxation time—τ_α = 1.5 ms) conditions were compared. Our studies showed that KVA suppressed the recrystallization of amorphous SIL more efficiently than PVAc. KVA improved the physical stability of the amorphous drug, regardless of the chosen concentration. On the other hand, in the case of PVAc, a low polymer content (i.e., 25 wt.%) destabilized amorphous SIL, when stored at 353 K. Nevertheless, at high concentrations of this excipient (i.e., 75 wt.%), its effect on the amorphous pharmaceutical seemed to be the opposite. Therefore, above a certain concentration, the PVAc presence no longer accelerates the SIL recrystallization process, but inhibits it.

Importance of Mesoporous Silica Particle Size in the Stabilization of Amorphous Pharmaceuticals-The Case of Simvastatin

In this paper, the role of mesoporous silica (MS) particle size in the stabilization of amorphous simvastatin (SVT) is revealed. For inhibiting recrystallization of the supercooled drug, the two MS materials (Syloid® XDP 3050 and Syloid® 244 FP) were employed. The crystallization tendency of SVT alone and in mixture with the MS materials was investigated by Differential Scanning Calorimetry (DSC) and Broadband Dielectric Spectroscopy (BDS). Neither confinement of the SVT molecules inside the MS pores nor molecular interactions between functional groups of the SVT molecules and the surface of the stabilizing excipient could explain the observed stabilization effect. The stabilization effect might be correlated with diffusion length of the SVT molecules in the MS materials that depended on the particle size. Moreover, MS materials possessing different particle sizes could offer free spaces with different sizes, which might influence crystal growth of SVT. All of these factors must be considered when mesoporous materials are used for stabilizing pharmaceutical glasses.

How does the high pressure affects the solubility of the drug within the polymer matrix in solid dispersion systems

In this paper, we employed Broadband Dielectric Spectroscopy (BDS) in order to determine the effect of the high pressure on the solubility limits of the amorphous flutamide within Kollidon VA64 matrix. In order to achieve this goal, drug-polymer systems have been examined: (i) at ambient pressure and both isothermal and nonisothermal conditions by means of BDS as well as Differential Scanning Calorimetry (DSC), to validate proposed method; (ii) at high pressure conditions (20 and 50 MPa) and elevated temperatures (343 K, 353 K and 363 K) by means of dielectric spectroscopy. Our studies revealed that regardless of applied pressure the solubility of the flutamide within the co-polymer matrix increases with increasing temperature at isobar conditions. Moreover, our results clearly indicate that with increasing pressure the solubility of the drug within the polymer matrix is decreasing at isothermal conditions. Therefore, during the solubility limit studies one should consider the situation in which by increasing the pressure (at constant temperature) would achieve an effect similar to the lowering of the temperature (at constant pressure).

How can we improve the physical stability of co-amorphous system containing flutamide and bicalutamide? The case of ternary amorphous solid dispersions

The article describes the preparation and characterization of binary mixtures of two antiandrogens used in prostate cancer treatment, i.e. flutamide (FL) and bicalutamide (BIC), as well as their ternary mixtures with either poly(methyl methacrylate-co-ethyl acrylate) (MMA/EA) or polyvinylpyrrolidone (PVP). The samples were converted into amorphous form to improve their water solubility and dissolution rate. Broadband dielectric spectroscopy and differential scanning calorimetry revealed that FL-BIC (65%) (w/w) does not tend to crystallize from the supercooled liquid state. We made the assumption that the drug-to-drug weight ratio should be maintained as in the case of monotherapy so we decided to investigate the system containing FL and BIC in 15:1 (w/w) ratio with 30% additive of polymers as stabilizers. Our research has shown that only in the case of the FL-BIC-PVP mixture the crystallization has been completely inhibited, both in glassy and supercooled liquid state, which was confirmed by X-ray diffraction studies. In addition, we performed solubility and dissolution rate tests, which showed a significant improvement in solubility of ternary system as compared to its crystalline counterpart. Enhanced physical stability and water solubility of the amorphous ternary system makes it promising for further studies.

Influence of Polymeric Additive on the Physical Stability and Viscoelastic Properties of Aripiprazole

In this article, we investigated aripiprazole + Kollidon VA64 (ARP/KVA) and aripiprazole + Soluplus (ARP/SOP) amorphous solid dispersions. Thermal properties of all prepared systems have been examined by means of differential scanning calorimetry (DSC). Compositions revealing the recrystallization tendency were subsequently investigated by means of broadband dielectric spectroscopy (BDS). On the basis of dielectric data, the physically stable drug-polymer concentrations have been found. Finally, these systems have been investigated by rheology, which enables us to determine the minimal temperature required for dissolving the drug in the polymeric matrix, as well as the temperature dependence of the sample viscosity. Our investigations have shown that the amorphous form of the investigated antipsychotic drug might be effectively stabilized by both employed polymers. However, due to the better stabilization effect and the more favorable rheological properties, KVA proved to be a better polymeric excipient for extrusion of amorphous aripiprazole.

Physical Stability and Viscoelastic Properties of Co-Amorphous Ezetimibe/Simvastatin System

The purpose of this paper is to examine the physical stability as well as viscoelastic properties of the binary amorphous ezetimibe⁻simvastatin system. According to our knowledge, this is the first time that such an amorphous composition is prepared and investigated. The tendency toward re-crystallization of the amorphous ezetimibe⁻simvastatin system, at both standard storage and elevated temperature conditions, have been studied by means of X-ray diffraction (XRD). Our investigations have revealed that simvastatin remarkably improves the physical stability of ezetimibe, despite the fact that it works as a plasticizer. Pure amorphous ezetimibe, when stored at room temperature, begins to re-crystallize after 14 days after amorphization. On the other hand, the ezetimibe-simvastatin binary mixture (at the same storage conditions) is physically stable for at least 1 year. However, the devitrification of the binary amorphous composition was observed at elevated temperature conditions (T = 373 K). Therefore, we used a third compound to hinder the re-crystallization. Finally, both the physical stability as well as viscoelastic properties of the ternary systems containing different concentrations of the latter component have been thoroughly investigated.

Broadband dielectric spectroscopy as an experimental alternative to calorimetric determination of the solubility of drugs into polymer matrix: Case of flutamide and various polymeric matrixes

In this paper we determined the solubility limits of the amorphous flutamide within the two different polymeric matrixes - poly vinylpyrrolidone and poly vinylacetate. In order to achieve this goal, series of broadband dielectric spectroscopy measurements were performed. As a result we found that the maximal amount of the drug that can be successfully dissolved within the PVAc (maintaining the non-supersaturated conditions) is equal to 35 wt% of the amorphous solid dispersion system. Interestingly enough similar results, in terms of solubility limits, were achieved utilizing significantly higher amount of the pharmaceutical - 71 wt% - in the PVP matrix. Accordingly, we established the following relationship in the solubility limits of the amorphous flutamide dispersed within examined polymer matrixes: PVP > PVAc. It is worth highlighting that in order to preserve the thermodynamic stability - one of the two contributors to the physical stability - drug loading in the amorphous solid dispersion system should not exceed its solubility limits. Hence, choosing appropriate amount of the polymer addition will determine if obtained system remains physically stable. Subsequently, we presented the "stability maps" for all investigated FL-based ASD systems from which one might predict the stabilization effect exerted by certain amount of polymer.

Advances in coamorphous drug delivery systems

In recent years, the coamorphous drug delivery system has been established as a promising formulation approach for delivering poorly water-soluble drugs. The coamorphous solid is a single-phase system containing an active pharmaceutical ingredient (API) and other low molecular weight molecules that might be pharmacologically relevant APIs or excipients. These formulations exhibit considerable advantages over neat crystalline or amorphous material, including improved physical stability, dissolution profiles, and potentially enhanced therapeutic efficacy. This review provides a comprehensive overview of coamorphous drug delivery systems from the perspectives of preparation, physicochemical characteristics, physical stability, in vitro and in vivo performance. Furthermore, the challenges and strategies in developing robust coamorphous drug products of high quality and performance are briefly discussed.

Effects of cooling rate on structural relaxation in amorphous drugs: elastically collective nonlinear langevin equation theory and machine learning study

Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs. We describe the structural relaxation of a tagged molecule as a coupled process of cage-scale dynamics and collective molecular rearrangement beyond the first coordination shell. The coupling between local and non-local dynamics behaves distinctly in different substances. Theoretical calculations for the structural relaxation time, glass transition temperature, and dynamic fragility are carried out over twenty-two amorphous drugs and polymers. Numerical results have a quantitatively good accordance with experimental data and the extracted physical quantities using the Vogel–Fulcher–Tammann fit function and machine learning. The machine learning method reveals the linear relation between the glass transition temperature and the melting point, which is a key factor for pharmaceutical solubility. Our predictive approaches are reliable tools for developing drug formulations.

Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs.

Changes in Physical Stability of Supercooled Etoricoxib after Compression

In the case of formulations with amorphous active pharmaceutical ingredients the risk of pressure-induced recrystallization should be carefully considered. We reported here that supercooled etoricoxib (ETB), which was found as a relatively stable system with low crystallization tendency at atmospheric pressure, crystallized quickly after compression. The observed strong pressure-dependence of the induction period suggests that during compression the first step of crystallization that is nucleation may be accelerated. To overcome the experimental challenge associated with studies at elevated temperatures and high pressures we applied broadband dielectric spectroscopy. Dielectric measurements gave us detailed insight into crystallization kinetics of ETB at varying ( T, p) conditions corresponding to the supercooled liquid state of a drug. We found that pressure-induced recrystallization of supercooled ETB, constituting a serious impediment from a technological point of view, can be efficiently inhibited when amorphous solid dispersion containing ETB and polymer polyvinylpyrrolidone PVP (10% w/w) was prepared. Besides, we performed the comprehensive analysis of molecular dynamics of both systems at elevated pressure to address some fundamental issues related to the pressure sensitivity of their supercooled dynamics.

Can Storage Time Improve the Physical Stability of Amorphous Pharmaceuticals with Tautomerization Ability Exposed to Compression? The Case of a Chloramphenicol Drug

In this article we thoroughly investigated the physical stability of the amorphous form of a chloramphenicol drug. The tendency toward recrystallization of this drug has been examined (i) at nonisothermal conditions by means of a DSC technique; (ii) at isothermal conditions and temperature close to T_room by means of dielectric spectroscopy; (iii) at isothermal conditions and elevated temperatures of T = 323 K and 338 K by dielectric spectroscopy; and (iv) at conditions imitating the manufacturing procedure (i.e., elevated temperature and compression procedure). Our investigations have shown that amorphous chloramphenicol, stored at both standard storage and elevated temperature conditions, does not reveal a tendency toward recrystallization. However, compression significantly changes this behavior and destabilizes the examined compound. We found that due to chemical equilibration of the sample, the elongation of the storage time before compression might improve the physical stability of the examined pharmaceutical exposed to compression 34-times.

Investigation of Drug-Excipient Interactions in Biclotymol Amorphous Solid Dispersions

The effect of low molecular weight excipients on drug-excipient interactions, molecular mobility, and propensity to recrystallization of an amorphous active pharmaceutical ingredient is investigated. Two structurally related excipients (α-pentaacetylglucose and β-pentaacetylglucose), five different drug:excipient ratios (1:5, 1:2, 1:1, 2:1, and 5:1, w/w), and three different solid state characterization tools (differential scanning calorimetry, X-ray powder diffraction, and dielectric relaxation spectroscopy) were selected for the present research. Our investigation has shown that the excipient concentration and its molecular structure reveal quasi-identical molecular dynamic behavior of solid dispersions above and below the glass transition temperature. Across to complementary quantum mechanical simulations, we point out a clear indication of a strong interaction between biclotymol and the acetylated saccharides. Moreover, the thermodynamic study on these amorphous solid dispersions highlighted a stabilizing effect of α-pentaacetylglucose regardless of its quantity while an excessive concentration of β-pentaacetylglucose revealed a poor crystallization inhibition. Finally, through long-term stability studies, we also showed the limiting excipient concentration needed to stabilize our amorphous API. Herewith, the developed procedure in this paper appears to be a promising tool for solid-state characterization of complex pharmaceutical formulations.