Liquid–Liquid Miscibility Gaps in Drug–Water Binary Systems: Crystal Structure and Thermodynamic Properties of Prilocaine and the Temperature–Composition Phase Diagram of the Prilocaine–Water System
- Ivo B. Rietveld
- ,
- Marc-Antoine Perrin
- ,
- Siro Toscani
- ,
- Maria Barrio
- ,
- Beatrice Nicolai
- ,
- Josep-Lluis Tamarit
- , and
- René Ceolin
View Author Information
† EAD Physico-chimie Industrielle du Médicament (EA 4066), Faculté de Pharmacie, Université Paris Descartes, 4, Avenue de l’Observatoire, 75006 Paris, France
‡ Sanofi R&D, Lead Generation & Compound Realization/Analytical Sciences/Solid State group, 13, Quai Jules Guesde, 94400 Vitry sur Seine, France
§ Département de Chimie—UMR 6226, Faculté des Sciences, Université de Rennes 1, Bâtiment 10B, 263, Avenue du Général Leclerc, 35042 Rennes Cedex, France
∥ Grup de Caracterització de Materials (GCM), Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, ETSEIB, Diagonal 647, 08028 Barcelona, Spain
*E-mail: [email protected]. Tel: +33 1 53 73 96 75.
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Abstract
EMLA cream, a “eutectic mixture of local anesthetics”, was developed in the early 1980s by Astra Pharmaceutical Production. The mixture of anesthetics containing lidocaine, prilocaine, and water is liquid at room temperature, which is partly due to the eutectic equilibrium between prilocaine and lidocaine at 293 K, as was clear from the start. However, the full thermodynamic background for the stability of the liquid and its emulsion-like appearance has never been elucidated. In the present study of the binary system prilocaine–water, a region of liquid–liquid demixing has been observed, linked to a monotectic equilibrium at 302.4 K. It results in a prilocaine-rich liquid containing approximately 0.7 mol fraction of anesthetic. Similar behavior has been reported for the binary system lidocaine–water (Céolin, R.; et al. J. Pharm. Sci.2010, 99 (6), 2756–2765). In the ternary mixture, the combination of the monotectic equilibrium and the above-mentioned eutectic equilibrium between prilocaine and lidocaine results in an anesthetic-rich liquid that remains stable below room temperature. This liquid forms an emulsion-like mixture in the presence of an aqueous solution saturated with anesthetics. Physical properties and the crystal structure of prilocaine are also reported.
1 Introduction
ARTICLE SECTIONS
EMLA cream (EMLA stands for “eutectic mixture of local anesthetics“) was developed in the early 1980s by Astra Pharmaceutical Production AB, Sweden, presently known by the name AstraZeneca. (1-3) The cream is described as a “nonconventional emulsion” based on a eutectic mixture of lidocaine and prilocaine with a 1:1 molar ratio. The addition of water leads to a “melting” temperature below room temperature; therefore, under ambient conditions, the mixture is an oily “emulsion system [that] does not contain any lipophilic solvent”. (3) However, what is the cause behind the stability of the emulsion? In the absence of any stabilizing agents, the stability must be caused by the inherent thermodynamics of the system. A first clue to the answer is given by the behavior of the lidocaine–water system, which has been described recently. (4) It was found that a liquid–liquid miscibility gap, i.e., an invariant equilibrium involving a water-rich liquid and a lidocaine-rich liquid, forms at 321 K. A miscibility gap occurs if the interaction enthalpy between two different molecules (A and B) in the liquid state is less favorable than the interaction enthalpy between molecules of the same kind (A–A and B–B). Miscibility gaps provide access to liquids much richer in active pharmaceutical ingredients (APIs) than saturated aqueous solutions. Using miscibility gaps to increase drug content in solutions has been suggested previously in reports on other drug–water systems (barbital and phenobarbital). (5, 6) Nonetheless, the miscibility gap in the lidocaine–water system can only be part of the answer to the stability of the stable emulsion, because the monotectic equilibrium is found at 321 K, well above room temperature and above the temperature of the human epidermis.
The prilocaine–water system has been investigated as the third part of the ternary system lidocaine–prilocaine–water constituting the main EMLA ingredients. In the process, the crystal structure of prilocaine has been solved. This paper consists, therefore, of two parts: the first reports on the crystal structure of prilocaine and its main thermodynamic properties (see Figure 1 for the chemical structure of prilocaine). The second part reports on the temperature–composition phase diagram of the prilocaine–water system and discusses its phase behavior in relation to the lidocaine–water system and the EMLA mixture.
Figure 1
Figure 1. Chemical structure of prilocaine.
2 Experimental Section
ARTICLE SECTIONS
Prilocaine of medicinal grade had been provided by former Roger Bellon laboratory (now Sanofi, France) and had been left at room temperature since 1988 in a sealed brown flask protected from light. Prilocaine (N-(2-methylphenyl)-2-(propylamino)propanamide, C13H20N2O, M = 220.31) contains an asymmetric carbon atom (see Figure 1); however, no information had been provided as to whether the sample was a racemic mixture of enantiomers (conglomerate), a racemic compound (true racemate), or even either one of the pure enantiomers. A second batch of (RS)-prilocaine was purchased from SIGMA France for verification of the thermal analysis and density measurements obtained with the 20-year-old batch.
2.1 High-Resolution X-ray Powder Diffraction (XRPD) as a Function of Temperature
XRPD measurements using the Debye–Scherrer geometry and transmission mode were carried out with a vertically mounted INEL cylindrical position-sensitive detector (CPS-120). (7) Monochromatic Cu Kα1 (λ = 1.54056 Å) radiation was selected by an asymmetrically focusing incident-beam curved quartz monochromator. Low-temperature measurements were carried out with a liquid nitrogen 700 series Cryostream Cooler from Oxford Cryosystems. Cubic phase Na2Ca3Al2F4 was used for external calibration. (8) The PEAKOC application from the DIFFRACTINEL program was used for calibration as well as for the determination of the peak positions. After indexing, lattice parameters were refined by least-squares minimization with the FullProf suite. (9)
The specimen rotated perpendicularly to the X-ray beam during the experiments to improve the averaging over the crystallite orientations. Before each isothermal data acquisition, the specimen was allowed to equilibrate for approximately 10 min, and each acquisition time was no less than 1 h. The heating rate in between data collection was 1.33 K min–1. Patterns were recorded on heating in the temperature range from 100 K up to the melting point.
2.2 Crystal Structure Determination from High-Resolution X-ray Powder Diffraction Data at Room Temperature
A sample was introduced in a Lindemann capillary (0.5 mm diameter) and analyzed at room temperature on a high angular resolution X-ray diffractometer (PANalytical X’Pert Pro MPD, Debye–Scherrer transmission geometry, equipped with a hybrid monochromator offering a parallel beam of pure Cu Kα1 radiation). The obtained powder pattern was used for indexing. Taking 20 positions of well separated single peaks, the X-CELL indexing program (10) found a monoclinic unit cell and suggested the space group P21/c, based on systematic absences. This assignment was confirmed by a modified Pawley refinement. (11)
Based on the molecular geometry obtained from lidocaine single-crystal XRD data (12) the prilocaine molecular model was sketched using Material Studio software (Accelrys, Inc., 2003 San Diego). Trial crystal structures were generated by stochastic movements of the prilocaine molecule within the previously indexed crystal cell. (11) Intermolecular torsion angles were allowed to vary in combination with different orientations and positions of the molecule within the asymmetric unit. For each trial structure, a powder pattern was simulated and compared to the experimental data. The acceptance criterion for each successive structural model was a lower Rwp profile factor. An acceptance probability was used for trial structures with an unfavorable Rwp profile factor. Finally, to optimize the crystal structure with the lowest Rwp, Rietveld refinement was used.
For the Rietveld refinement, data out to 60° 2θ were used, which corresponds to 1.54 Å real-space resolution. The Rietveld refinement was carried out with TOPAS-Academic. (13) Restraints were included for all bond lengths and bond angles and for the planarity of the aromatic ring; the values for the restraints were taken from the DFT-D calculations (see below). A global Biso was refined for all non-hydrogen atoms, with the Biso of the hydrogen atoms constrained at 1.2 times the value of the global Biso. The inclusion of a preferred-orientation correction with the March–Dollase formula (14) was tried for directions (100), (010), and (001). The preferred-orientation correction for the (100) and (001) directions made a significant difference to the Rwp value, with opposite deviations of the March–Dollase parameter from 1. The directions (−101), (−102), and (−103) were tried, with (−102) giving slightly better results, and it was this direction that was used.
The molecular geometry was checked with Mogul, (15) which compares each bond length and bond angle to corresponding distributions from single-crystal data.
2.3 Proof of Structure Using Density Functional Theory (DFT) Calculations
The crystal structure determined from powder data was energy-optimized with the program GRACE, (16) which uses VASP (17-19) for single-point pure density functional theory (DFT) calculations. The generalized gradient approximation (GGA) with the Perdew–Wang 91 (20) exchange-correlation functional was used, with standard projector-augmented wave (PAW) potentials. The plane-wave cutoff energy was 520 eV, and the k-point spacing was approximately 0.7 Å–1. The DFT calculations were augmented with a dispersion correction to give a dispersion-corrected DFT potential, or DFT-D potential. The settings for the DFT calculations as well as a full description of the dispersion correction are given in Neumann and Perrin. (21) The root mean square (RMS) Cartesian displacement of the non-hydrogen atoms of the energy-minimized crystal structure with respect to the experimental structure was calculated as described in ref 22. (22-24) From calculations on a validation set of 225 organic single-crystal structures, it is known that RMS Cartesian displacement values up to 0.25 Å indicate that the structure is correct, whereas values greater than 0.30 Å point to an incorrect structure.
Hydrogen atoms are poor X-ray scatterers, and their positions cannot be determined reliably from X-ray powder diffraction data. Usually, all hydrogen atoms can be located based on chemical considerations, but in the structure of prilocaine, the position of one of the two N–H hydrogen atoms is ambiguous. Assigning a position to the N–H hydrogen atom in the amide group is trivial: it must lie in the plane of the amide group because the nitrogen atom is sp2 hybridized and because otherwise no hydrogen bond can be formed. The second N–H hydrogen atom, however, has two possible positions, because the second nitrogen is sp3 hybridized. Both positions were tried, and for both possibilities a DFT-D calculation was run with variable lattice parameters with the experimental space-group symmetry imposed.
2.4 Differential Scanning Calorimetry
Calorimetric data were obtained with a Q100 thermal analyzer from TA Instruments with heating rates of 5 and 10 K·min–1. The analyzer was calibrated with indium (Tfus = 429.75 K and ΔfusH = 3.267 kJ mol–1). Prilocaine was weighed using a microbalance sensitive to 0.01 mg and sealed in aluminum pans.
2.5 High-Pressure Differential Thermal Analysis
HP-DTA measurements were carried out at a 2 K min–1 heating rate using an in-house built high-pressure differential thermal analyzer similar to Würflinger’s apparatus (25) that operates between 298 and 473 K and 0 and 250 MPa. To ascertain that in-pan volumes were free from residual air, specimens were mixed with an inert perfluorinated liquid (Galden, from Bioblock Scientifics, Illkirch, France) as a pressure-transmitting medium, and the mixtures were sealed into cylindrical tin pans. To verify that the perfluorinated liquid was chemically inactive and that it would not affect the melting temperature of prilocaine, DSC measurements were carried out on a Galden–prilocaine mixture with the TA Instruments Q100 under ordinary conditions.
2.6 Liquid Density Measurements as a Function of Temperature
Liquid density as a function of temperature was determined with a DMA-5000 density meter from Anton-Paar. Data were obtained at isothermal intervals while slowly and stepwise cooling from 360 to 300 K. Dry air and bidistilled water were used as calibration standards in the temperature range. Once the temperature inside the apparatus had equilibrated above the temperature of fusion, the specimen was introduced with an in-house built filling device. The temperature was controlled with a precision of ±1 mK.
3 Results
ARTICLE SECTIONS
3.1 Crystal Structure of Racemic Prilocaine
Single crystals of prilocaine had spontaneously grown by sublimation-condensation in its container over a 20 year period. The crystals consisted of thin needles (Figure 2) too thin for single crystal X-ray diffraction structure determination; therefore, the needles were analyzed by high-resolution X-ray powder diffraction.
Figure 2
Figure 2. Crystal needles as obtained from the sample container by sublimation-condensation over 20 years.
The Rietveld refinement progressed smoothly and produced a good fit with χ2 = 1.273, R′p = 9.420, and R′wp = 8.388 (values after background correction) and Rp = 2.650 and Rwp = 3.406 (values before background subtraction). The March–Dollase parameter (14) for the (−102) direction refined to a value of 0.968(2); Biso refined to 2.78(13) Å2. The resulting fit of the powder diffraction pattern can be found in Figure 3, and the crystal structure and refinement data can be found in Table 1.
Figure 3
Figure 3. Powder diffraction pattern of prilocaine with Rietveld refinement and underneath the difference curve.
Table 1. Crystal Data and Structure Refinement of Prilocaine
| Crystal Data |
| C13H20ON2 |
| Mr = 220.31 |
| monoclinic, P21/c |
| a = 12.68570(16) Å |
| b = 12.42470(16) Å |
| c = 8.33776(7) Å |
| β = 101.5266(6)° |
| V = 1287.66(3) Å3 |
| Z = 4 |
| Dx = 1.136 g cm–3 |
| Cu Kα1 radiation |
| μ = 0.095 mm–1 |
| T = 293 K |
| specimen shape: cylinder 10 × 0.5 mm |
| Data Collection |
| diffractometer: Panalytical X’pert pro MRD |
| specimen mounting: Lindemann glass capillary 0.5 mm |
| specimen mounted in transmission mode |
| detector: X’celerator (Real Time Multiple Strip) |
| absorption correction: none |
| 2θ min = 5.0°, 2θ max = 60.0° |
| increment in 2θ = 0.0167° |
| Refinement |
| refinement on Inet |
| Rwp = 3.406 |
| Rp = 2.650 |
| Rexp = 2.676 |
| χ2 = 1.273 |
| profile function: modified Thompson–Cox–Hastings pseudo-Voigt |
| 379 reflections |
| 159 parameters |
| 100 restraints |
| H-atom parameters restrained |
| weighting scheme based on measured s.u.’s w = 1/σ(Yobs)2 |
| (Δ/σ)max = 0.001 |
| preferred orientation correction: March–Dollase with direction (−102) and a March–Dollase parameter of 0.968(2) |
As mentioned in the Experimental Section, the position of an N–H hydrogen atom was ambiguous. Two models were prepared, in which the hydrogen atom was manually placed in one of the two possible positions. The two models were energy-minimized with the DFT-D method, and then the RMSD value of each model was calculated. The energy minimizations took 12 h each on four 1 GHz 64-bit quad-core Opteron processors. For one of the models, the RMSD value was 0.42 Å, a strong indication that the structure is incorrect. The lattice energy for the other crystal structure was 4.8 kcal mol–1 more favorable, and the RMS Cartesian displacement was only 0.11 Å. This proves beyond reasonable doubt that this is the correct position for the N–H hydrogen; moreover, this is a strong indication that the crystal structure as a whole is correct. All results given in this paper refer to the structure with the latter position for the N–H hydrogen atom, which from here on is considered as the correct position.
According to the geometry check with Mogul of the crystal structure of prilocaine from powder diffraction data, all bond lengths are within at most 0.78 standard deviation from their mean single-crystal values and all bond angles are within at most 2.06 standard deviations from their mean single-crystal values. It can be concluded that the crystals are a racemic compound with both (R)- and (S)-prilocaine forming part of the structure. The molecular structure can be seen in Figure 4. Supplementary crystallographic data can be found in the CCDC, deposit number 902387, and obtained free of charge from the Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif/.
Figure 4
Figure 4. Molecular structure of prilocaine as determined by X-ray diffraction.
The racemic crystal of (RS)-prilocaine contains an infinite hydrogen chain interconnecting alternatingly (R)- and (S)-prilocaine as can be seen in Figure 5. This chain runs along the c axis of the unit cell and is made up of hydrogen bonds with a donor–acceptor distance of 3.025 Å. A much weaker hydrogen bond (Figure 5c) can be found running along the b axis between the amine group with the hydrogen atom placed by the DFT calculations and the oxygen of the amide group with a donor–acceptor distance of 3.404 Å. The corresponding molecule reciprocates this hydrogen bond with its own amine group; thus, each pair of (R)- and (S)-prilocaine molecules is interconnected by two weak hydrogen bonds. In the direction of the a axis the interactions are mainly van der Waals in nature.
Figure 5
Figure 5. Details of the structure of Prilocaine. (a) Hydrogen-bond chain along the c axis with interchanging (R)- and (S)-prilocaine. (b) The infinite hydrogen-bond chain runs along the c axis of the unit cell. The rings and the aliphatic chains form planes parallel to b. (c) Weaker hydrogen-bond chains along the b axis form (R)–(S) dimers.
Both the aromatic rings as well as the aliphatic chains of the prilocaine molecules are aligned in their respective planes that run along the b axis. The angle between the two planes is approximately 49°.
3.2 Calorimetric Data for Racemic Prilocaine
The temperature of fusion of (RS)-prilocaine has been determined by DSC (onset value) and was found to be Tfus = 311.5 ± 1.0 K. The specific enthalpy of melting is Δfush = 147 ± 5 J g–1 (32.4 kJ mol–1). The temperature and enthalpy of melting had not changed after 20 years of storage, a strong indication that the prilocaine sample did not degrade. Quenching the melt resulted in a glass, and on reheating a glass transition was observed between 218 and 219 K (midpoint).
3.3 Specific Volume as a Function of Temperature
The specific volume of racemic prilocaine was measured in the solid and liquid phases. The results can be seen in Figure 6. The specific volume of molten racemic prilocaine was found to increase linearly as the temperature increases, and it was fitted to (r2 = 0.9999)
(1)X-ray powder diffraction as a function of temperature resulted in the following equation for the specific volume of solid prilocaine (r2 = 0.9998):
(2)At fusion, 311.5 K, the specific volume of solid racemic prilocaine equals 0.884 ± 0.001 cm3 g–1 and the specific volume of the melt is 1.000 ± 0.002 cm3 g–1. These two values lead to a volume change on melting of Δfusv = 0.116 ± 0.003 cm3 g–1.
(1)X-ray powder diffraction as a function of temperature resulted in the following equation for the specific volume of solid prilocaine (r2 = 0.9998):(2)At fusion, 311.5 K, the specific volume of solid racemic prilocaine equals 0.884 ± 0.001 cm3 g–1 and the specific volume of the melt is 1.000 ± 0.002 cm3 g–1. These two values lead to a volume change on melting of Δfusv = 0.116 ± 0.003 cm3 g–1.Figure 6
Figure 6. Specific volume of solid and liquid prilocaine as a function of temperature. The specific volume difference between the liquid and the solid state is indicated as Δvs→l.
Extrapolating the thermal expansion of the liquid to low temperature, the specific volume of the liquid will cross the specific volume of the solid at the so-called Kauzmann temperature; for the present system that happens at 112 K. Here, the specific volume of the liquid becomes smaller than that of the solid. This is impossible considering that the liquid is a disordered system, and it is known as the Kauzmann paradox. However, generally well above the Kauzmann temperature, the liquid turns into a glassy solid, with a different, solid-like thermal expansion. In the case of prilocaine, this happens around 218–219 K. The difference between the specific volumes of the glassy solid and that of the crystalline solid (at 219 K) is 0.0653 cm3 g–1; the specific volume of the crystalline solid is smaller than that of the glass, as expected.
3.4 Pressure–Temperature Melting Curve for Racemic Prilocaine
HP-DTA experiments demonstrate that the temperature of fusion of racemic prilocaine increases as a function of pressure in the range of 0–250 MPa as can be seen in Figure 7. The data were fitted to (r2 = 0.9992)
(3)The initial slope of the pressure–temperature curve can also be calculated with the Clapeyron equation:
(4)Δfuss is the specific entropy change of fusion, and the other variables have been introduced above together with their values for prilocaine. They give rise to a value for the initial slope dP/dT at the melting point under ordinary conditions of 4.1 ± 0.4 MPa K–1, which is comparable to the slope of the linear fit to the direct measurements (eq 3).
(3)The initial slope of the pressure–temperature curve can also be calculated with the Clapeyron equation:(4)Δfuss is the specific entropy change of fusion, and the other variables have been introduced above together with their values for prilocaine. They give rise to a value for the initial slope dP/dT at the melting point under ordinary conditions of 4.1 ± 0.4 MPa K–1, which is comparable to the slope of the linear fit to the direct measurements (eq 3).Figure 7
Figure 7. (a) Prilocaine melting curves measured by high-pressure differential thermal analysis. (b) Measurement pressure as a function of the measured prilocaine melting temperatures (peak onset).
3.5 Demixing in the Binary System Prilocaine–Water
DSC curves for the prilocaine–water system are presented in Figure 8. The temperature (T) (onset, unless stated otherwise) of the peaks has been plotted against the mole fraction (x) in Figure 9a, and the enthalpy of the transition peaks has been plotted as a function of x in Figure 9b. At 273.1 K (0.0 °C), a peak can be observed increasing in enthalpy with increasing water concentration, indicating the presence of a degenerate eutectic equilibrium between three phases: pure solid water, a water-rich solution saturated with prilocaine, and pure solid prilocaine. The recorded temperature demonstrates that there is virtually no decrease in the melting temperature of solid prilocaine–ice mixtures with respect to the melting point of ice.
Figure 8
Figure 8. Typical DSC curves for prilocaine–water mixtures. The monotectic peak at 302.4 K can be observed for the 0.967 mol fraction. For the other mixtures down to 0.754 mol fraction the liquidus and the monotectic peaks have been convoluted. The last three peaks (0.660–0.398) represent the monotectic equilibrium underneath the miscibility gap. The peak at 273.1 K is the degenerate eutectic equilibrium between ice, prilocaine, and the saturated aqueous solution.
Figure 9
Figure 9. (a) Temperature–composition (mol fraction) phase diagram of the binary system prilocaine–water exhibiting a miscibility gap in the liquid phase. L1 is the prilocaine-rich liquid, L2 the water-rich liquid. Solid squares: eutectic equilibrium. Solid circles: monotectic equilibrium. Solid diamonds: liquidus related to the fusion of prilocaine. (b) Tammann plot (transition enthalpy change as a function of the mol fraction of the mixture) for the eutectic and monotectic equilibria.
A second set of peaks can be found at 302.4 K (29.2 °C) (see Figure 8). They convolute very rapidly starting from the prilocaine-rich side. Analogous to the system of lidocaine–water, (4) the peaks at 302.4 K represent a monotectic equilibrium between two immiscible liquid phases and solid prilocaine. The liquids are a water-based solution saturated with prilocaine (L2) and a prilocaine-based solution saturated with water (L1) (see Figure 9). The demixing of the two liquids can be observed in Figure 10. The liquids remain stable for a minimum of two years at room temperature. Thus demixing even persists in the metastable domain below the temperature for the monotectic equilibrium as measured by DSC.
Figure 10
Figure 10. Evolution of the prilocaine–water system at room temperature. From left to right: 0, 8, 12, and 24 months after mixing. The liquid on top is oily and viscous in appearance and must therefore be the lidocaine-rich liquid (in addition, after two years this layer has turned slightly yellow). Its initial milky aspect is due to droplets of water-rich liquid that form a persistent emulsion “with no lipophilic solvent”, a clear indication that the densities of both liquids do not differ much.
The interpretation of the peaks resulting from the monotectic equilibrium shift is aided by the T–x phase diagram in Figure 9a. For pure prilocaine, fusion takes place at 311.5 K. Once water is added, the peak of fusion turns into a liquidus peak, which can be observed in the DSC curve of 0.967 mol fraction with a maximum at about 310 K (Figure 8). The small peak with an onset at 302.4 K belongs to the monotectic equilibrium. For lower concentrations of prilocaine, the monotectic peak and the liquidus peak are convoluted as mentioned above (Figure 8). This affects the precision of the determination of the concentration of L1 (prilocaine-rich liquid) by extrapolation of the Tammann plot (enthalpy change versus composition); the plot can be seen in Figure 9b. Nevertheless, the Tammann plot leads to an estimate for the concentration of L1 between 0.65 and 0.7 mol fraction.
To determine the concentration of L1, it is also possible to use the maximum temperatures of the liquidus peaks, which can be extrapolated to the monotectic temperature with the Schröder equation; this leads to a composition for L1 between 0.69 and 0.67 mol fraction.
The value of 0.69 is the estimate for ideal behavior and is obtained from the data for prilocaine fusion (311.5 K and 147 J/g) by direct application of the Schröder equation; the resulting curve follows the liquidus values reasonably well and reaches 0.687 at the monotectic temperature of 302.4 K. As a verification, the first term of the Redlich–Kister expansion was added as a simple excess function to the Schröder equation: Hexc(1 – x)2. The excess enthalpy term, Hexc, was optimized against the measured liquidus maxima using the least-squares method leading to a value of 582 J mol–1. This small value essentially indicates that the liquidus related to the fusion of prilocaine can be considered ideal between the melting point and the monotectic equilibrium. The Schröder equation with the excess enthalpy leads to an intersection of the liquidus with the monotectic equilibrium at 0.669 mol fraction.
It can be observed that the three peaks at 302.4 K from 0.660 mol fraction downward (Figure 8) have the same onset and maximum, indicating that they represent the pure monotectic transition without any liquidus contribution resulting from the miscibility gap. It corroborates the concentration interval found for the monotectic equilibrium as the peak for 0.660 mol fraction must be located approximately at or just below the concentration of the prilocaine-rich liquid. The liquidus of the miscibility gap must increase quite rapidly with temperature, as no maximum critical temperature could be determined.
4 Discussion
ARTICLE SECTIONS
The crystal structure clearly indicates that the studied prilocaine sample is a racemic compound and not a conglomerate, because both (R)- and (S)-prilocaine are present in the crystal structure. The two enantiomers alternate along an infinite hydrogen-bond chain along the c axis of the unit cell (Figure 5). Furthermore, a weaker hydrogen bond gives rise to (R)- and (S)-enantiomer pairs interconnecting the infinite hydrogen-bond chains.
The change of specific volume as a function of temperature of molten racemic prilocaine, dv/dT, is 7.66 × 10–4 cm3 g–1 K–1 (0.169 cm3 mol–1 K–1, eq 1), which is smaller than the value 9.33 × 10–4 cm3 g–1 K–1 (0.219 cm3 mol–1 K–1) found for molten lidocaine. (4) This indicates that intermolecular interactions in molten prilocaine should be somewhat stronger than those in lidocaine. Ternidazole, a 2-methyl-5-nitroimidazole with antiprotozoal and antibiotic properties, has a liquid volume change with temperature of 5.09 × 10–4 cm3 g–1 K–1 (185.19 g/mol). (26) These three values lead to an average specific volume change with temperature in the liquid for these small organic molecules of 7.36 × 10–4 cm3 g–1 K–1. This value is of importance for the estimation of thermal expansion in the liquid phase for APIs, if such data cannot be obtained experimentally, for example due to decomposition in the melt.
The P–T melting curve for prilocaine is almost straight in the pressure range of 0 to 250 MPa. In the case of lidocaine, the solid–liquid equilibrium is somewhat more curved. Their initial slopes are respectively 4.7 and 3.56 MPa K–1. (4) This indicates that, relatively speaking, pressure stabilizes the solid state in the case of lidocaine more than in the case of prilocaine and that the solid–liquid equilibrium of prilocaine is slightly less influenced by pressure with respect to temperature.
The volume changes on melting are about 0.110 ± 0.003 cm3 g–1 (24.3 cm3 mol–1) for prilocaine, twice as large as that of lidocaine with 0.057 cm3 g–1 (13.3 cm3 mol–1). (4) A similar difference is found for the entropy changes on melting: 99.3 J mol–1 K–1 for prilocaine and 47.5 J mol–1 K–1 for lidocaine. (4) Prilocaine gains more in entropy and more in volume on melting. These data add some nuance to the analysis of the P–T melting curves above. Pressure favors large (negative) volume changes, which would favor the melting of prilocaine under pressure over the melting of lidocaine. However, the large entropy change of fusion of prilocaine is favored by the temperature, and in this case the increase of entropy offsets the large volume change of prilocaine on melting in comparison to the changes observed for lidocaine (see also eq 4, the Clapeyron equation). Under ordinary conditions, pressure is low for both prilocaine and lidocaine, therefore the lower melting temperature of prilocaine may be an immediate result of its higher entropy change on melting.
A monotectic equilibrium is present at 302.4 K in the prilocaine–water diagram; this implies the presence of a prilocaine-rich liquid, which can be considered as a solution of water in prilocaine. At the monotectic equilibrium composition, 0.3 mol of water dissolves in 0.7 mol of prilocaine (i.e., ≈966 mg prilocaine/mL solution). In comparison with the solubility of prilocaine in water at 302.04 K, 7.0 mg/mL, (1) it is obvious that the prilocaine-rich liquid L1 will be a much more effective anesthetic than the saturated solution in water.
As stated in the Introduction, lidocaine–water mixtures exhibit a monotectic equilibrium at 321 K. (4) The lidocaine-rich liquid contains approximately 0.7 mol fraction in lidocaine like in the case of prilocaine. This is very high compared to the concentration in its saturated aqueous solution (at 302.4 K for comparison with prilocaine) of 3.7 mg/mL. (1) The monotectic equilibrium containing prilocaine and water is even below the temperature of the human epidermis, ensuring that the mixture will be liquid, when applied to the skin.
Both the lidocaine and prilocaine systems exhibit a monotectic equilibrium with water. It is likely that a mixture of the three constituents (lidocaine, prilocaine, and water) will result in a ternary monotectic equilibrium at a temperature that is even lower than the one found for the prilocaine water system. In that case, the two immiscible liquids in the ternary mixture, one rich in lidocaine and prilocaine and one rich in water, will remain in the liquid state at room temperature and form a “nonconventional” stable emulsion. The temperature of the monotectic equilibrium lies even below room temperature, which can be deduced from the lidocaine–prilocaine system, which contains a eutectic equilibrium at 293 K. (1) As the latter temperature effectively represents the “melting temperature” of the prilocaine–lidocaine mixture, it is only reasonable that the monotectic equilibrium with water should be at least a few degrees below the eutectic temperature. This conclusion is confirmed by the observations reported by Brodin and Nyqvist-Mayer et al. (1-3)
5 Conclusion
ARTICLE SECTIONS
Prilocaine does not degrade while stored at room temperature for 20 years in a hermetically closed container in the dark. Its vapor pressure is high enough to cause sublimation and recrystallization. The resulting crystalline powder has been used to obtain the crystal structure of prilocaine from high-resolution powder diffraction.
Physical properties of prilocaine have been determined, such as the melting properties and the expansion of the specific volume with temperature. The slope of the melting transition in the pressure–temperature phase diagram has been obtained by direct measurement and with the Clapeyron equation.
A comparison of the prilocaine–water system and the lidocaine–water system leads to the conclusion that the “emulsion system [that] does not contain any lipophilic solvent” (3) is in fact demixing of two liquids, one rich in prilocaine and lidocaine and one rich in water. The system remains stable, because the underlying monotectic equilibrium for the ternary system is most likely found below ambient temperature. This can be concluded, first, because the monotectic equilibria between water and either prilocaine or lidocaine are found well below their respective melting temperatures and, second, because the eutectic mixture of prilocaine and lidocaine possesses a eutectic temperature of 293 K.
Acknowledgment
ARTICLE SECTIONS
We thank Jacco van de Streek and Marcus Neumann (Avant-Garde Materials Simulation, Freiburg, Germany) for the DFT calculations and discussion. M.B. and J.-L.T. were supported by the Spanish Ministry of Science and Innovation (Grant FIS2011-24439) and the Catalan Government (Grant 2009SGR-1251).
References
ARTICLE SECTIONS
This article references 26 other publications.
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Abstract
Figure 1
Figure 1. Chemical structure of prilocaine.
Figure 2
Figure 2. Crystal needles as obtained from the sample container by sublimation-condensation over 20 years.
Figure 3
Figure 3. Powder diffraction pattern of prilocaine with Rietveld refinement and underneath the difference curve.
Figure 4
Figure 4. Molecular structure of prilocaine as determined by X-ray diffraction.
Figure 5
Figure 5. Details of the structure of Prilocaine. (a) Hydrogen-bond chain along the c axis with interchanging (R)- and (S)-prilocaine. (b) The infinite hydrogen-bond chain runs along the c axis of the unit cell. The rings and the aliphatic chains form planes parallel to b. (c) Weaker hydrogen-bond chains along the b axis form (R)–(S) dimers.
Figure 6
Figure 6. Specific volume of solid and liquid prilocaine as a function of temperature. The specific volume difference between the liquid and the solid state is indicated as Δvs→l.
Figure 7
Figure 7. (a) Prilocaine melting curves measured by high-pressure differential thermal analysis. (b) Measurement pressure as a function of the measured prilocaine melting temperatures (peak onset).
Figure 8
Figure 8. Typical DSC curves for prilocaine–water mixtures. The monotectic peak at 302.4 K can be observed for the 0.967 mol fraction. For the other mixtures down to 0.754 mol fraction the liquidus and the monotectic peaks have been convoluted. The last three peaks (0.660–0.398) represent the monotectic equilibrium underneath the miscibility gap. The peak at 273.1 K is the degenerate eutectic equilibrium between ice, prilocaine, and the saturated aqueous solution.
Figure 9
Figure 9. (a) Temperature–composition (mol fraction) phase diagram of the binary system prilocaine–water exhibiting a miscibility gap in the liquid phase. L1 is the prilocaine-rich liquid, L2 the water-rich liquid. Solid squares: eutectic equilibrium. Solid circles: monotectic equilibrium. Solid diamonds: liquidus related to the fusion of prilocaine. (b) Tammann plot (transition enthalpy change as a function of the mol fraction of the mixture) for the eutectic and monotectic equilibria.
Figure 10
Figure 10. Evolution of the prilocaine–water system at room temperature. From left to right: 0, 8, 12, and 24 months after mixing. The liquid on top is oily and viscous in appearance and must therefore be the lidocaine-rich liquid (in addition, after two years this layer has turned slightly yellow). Its initial milky aspect is due to droplets of water-rich liquid that form a persistent emulsion “with no lipophilic solvent”, a clear indication that the densities of both liquids do not differ much.
References
ARTICLE SECTIONSThis article references 26 other publications.
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- 15Bruno, I. J.; Cole, J. C.; Kessler, M.; Jie, L.; Motherwell, W. D. S.; Purkis, L. H.; Smith, B. R.; Taylor, R.; Cooper, R. I.; Harris, S. E.; Orpen, A. G. Retrieval of crystallographically-derived molecular geometry information J. Chem. Inf. Comput. Sci. 2004, 44, 2133– 2144[ACS Full Text], [CAS], Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXotlalsr8%253D&md5=a7909c257045351d5bff7b78c7fba2d5Retrieval of Crystallographically-Derived Molecular Geometry InformationBruno, Ian J.; Cole, Jason C.; Kessler, Magnus; Luo, Jie; Motherwell, W. D. Sam; Purkis, Lucy H.; Smith, Barry R.; Taylor, Robin; Cooper, Richard I.; Harris, Stephanie E.; Orpen, A. GuyJournal of Chemical Information and Computer Sciences (2004), 44 (6), 2133-2144CODEN: JCISD8; ISSN:0095-2338. (American Chemical Society)The crystallog. detd. bond length, valence angle, and torsion angle information in the Cambridge Structural Database (CSD) has many uses. However, accessing it by conventional substructure searching requires nontrivial user intervention. In consequence, these valuable data were underused and were not directly accessible to client applications. The situation was remedied by development of a new program (Mogul) for automated retrieval of mol. geometry data from the CSD. The program uses a system of keys to encode the chem. environments of fragments (bonds, valence angles, and acyclic torsions) from CSD structures. Fragments with identical keys are deemed to be chem. identical and are grouped together, and the distribution of the appropriate geometrical parameter (bond length, valence angle, or torsion angle) is computed and stored. Use of a search tree indexed on key values, together with a novel similarity calcn., then enables the distribution matching any given query fragment (or the distributions most closely matching, if an adequate exact match is unavailable) to be found easily and with no user intervention. Validation expts. indicate that, with rare exceptions, search results afford precise and unbiased ests. of mol. geometrical preferences. Such ests. may be used, for example, to validate the geometries of libraries of modeled mols. or of newly detd. crystal structures or to assist structure soln. from low-resoln. (e.g. powder diffraction) x-ray data.
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- 17Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Phys. Rev. B: Condens. Matter 1996, 54, 11169– 11186[Crossref], [PubMed], [CAS], Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xms1Whu7Y%253D&md5=9c8f6f298fe5ffe37c2589d3f970a697Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setKresse, G.; Furthmueller, J.Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
- 18Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals Phys. Rev. B: Condens. Matter 1993, 47, 558– 561[Crossref], [PubMed], [CAS], Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3sXlt1Gnsr0%253D&md5=c9074f6e1afc534b260d29dd1846e350Ab initio molecular dynamics of liquid metalsKresse, G.; Hafner, J.Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
- 19Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method Phys. Rev. B: Condens. Matter 1999, 59, 1758– 1775[Crossref], [CAS], Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXkt12nug%253D%253D&md5=78a73e92a93f995982fc481715729b14From ultrasoft pseudopotentials to the projector augmented-wave methodKresse, G.; Joubert, D.Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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- 21Neumann, M. A.; Perrin, M.-A. Energy ranking of molecular crystals using density functional theory calculations and an empirical van der Waals correction J. Phys. Chem. B 2005, 109, 15531– 15541[ACS Full Text], [CAS], Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXmtlSrtro%253D&md5=8540465f5042258b69e5098dbd040b93Energy Ranking of Molecular Crystals Using Density Functional Theory Calculations and an Empirical van der Waals CorrectionNeumann, Marcus A.; Perrin, Marc-AntoineJournal of Physical Chemistry B (2005), 109 (32), 15531-15541CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)By combination of high level d. functional theory (DFT) calcns. with an empirical van der Waals correction, a hybrid method has been designed and parametrized that provides unprecedented accuracy for the structure optimization and the energy ranking of mol. crystals. All DFT calcns. are carried out using the VASP program. The van der Waals correction is expressed as the sum over atom-atom pair potentials with each pair potential for two atoms A and B being the product of an asymptotic C6,A,B/r6 term and a damping function dA,B(r). Empirical parameters are provided for the elements H, C, N, O, F, Cl, and S. Following Wu and Yang, the C6 coeffs. have been detd. by least-squares fitting to mol. C6 coeffs. derived by Meath and co-workers from dipole oscillator strength distributions. The damping functions dA,B(r) guarantee the crossover from the asymptotic C6,A,B/r6 behavior at large interat. distances to a const. interaction energy at short distances. The careful parametrization of the damping functions is of crucial importance to obtain the correct balance between the DFT part of the lattice energy and the contribution from the empirical van der Waals correction. The damping functions have been adjusted to yield the best possible agreement between the unit cells of a set of exptl. low temp. crystal structures and their counterparts obtained by lattice energy optimization using the hybrid method. On av., the exptl. and the calcd. unit cell lengths deviate by 1%. To assess the performance of the hybrid method with respect to the lattice energy ranking of mol. crystals, various crystal packings of ethane, ethylene, acetylene, methanol, acetic acid, and urea have been generated with Accelrys' Polymorph Predictor in a first step and optimized with the hybrid method in a second step. In five out of six cases, the exptl. obsd. low-temp. crystal structure corresponds to the most stable calcd. structure.
- 22Van de Streek, J.; Neumann, M. A. Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations Acta Crystallogr., B 2010, 66, 544– 558[Crossref], [PubMed], [CAS], Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtFGisr7N&md5=48c5a5c1d8051cecf9155ab993b5528bValidation of experimental molecular crystal structures with dispersion-corrected density functional theory calculationsvan de Streek, Jacco; Neumann, Marcus A.Acta Crystallographica, Section B: Structural Science (2010), 66 (5), 544-558CODEN: ASBSDK; ISSN:0108-7681. (International Union of Crystallography)This paper describes the validation of a dispersion-cor. d. functional theory (d-DFT) method for the purpose of assessing the correctness of exptl. org. crystal structures and enhancing the information content of purely exptl. data. 241 Exptl. org. crystal structures from the August 2008 issue of Acta Cryst. Section E were energy-minimized in full, including unit-cell parameters. The differences between the exptl. and the minimized crystal structures were subjected to statistical anal. The r.m.s. Cartesian displacement excluding H atoms upon energy minimization with flexible unit-cell parameters is selected as a pertinent indicator of the correctness of a crystal structure. All 241 exptl. crystal structures are reproduced very well: the av. r.m.s. Cartesian displacement for the 241 crystal structures, including 16 disordered structures, is only 0.095 Å (0.084 Å for the 225 ordered structures). R.m.s. Cartesian displacements above 0.25 Å either indicate incorrect exptl. crystal structures or reveal interesting structural features such as exceptionally large temp. effects, incorrectly modeled disorder, or symmetry breaking H atoms. After validation, the method is applied to nine examples that are known to be ambiguous or subtly incorrect.
- 23Deringer, V. L.; Hoepfner, V.; Dronskowski, R. Accurate Hydrogen Positions in Organic Crystals: Assessing a Quantum-Chemical Aide Cryst. Growth Des. 2012, 12 (2) 1014– 1021[ACS Full Text], [CAS], Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhs1emsbjM&md5=c5eeb167a8ed5acbb32d29c576df8994Accurate Hydrogen Positions in Organic Crystals: Assessing a Quantum-Chemical AideDeringer, Volker L.; Hoepfner, Veronika; Dronskowski, RichardCrystal Growth & Design (2012), 12 (2), 1014-1021CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)Org. mols. crystallize in manifold structures. The last few decades have seen the rise of high-resoln. X-ray diffraction techniques that make the structures of even the most complex crystals easily accessible. Still, an intrinsic challenge lies in assigning hydrogen atoms' positions from X-ray expts. alone. Quantum chem. plays a fruitful, complementary role here, and so ab initio optimization techniques for org. crystals are on the rise as well. In this context, the authors evaluate a popular ab initio strategy based on plane-wave d.-functional computations, namely, selectively relaxing H positions in an otherwise fixed cell. Our data show that such-optimized C-H, N-H, O-H, and B-H bond lengths coincide well with results from neutron diffraction-the exptl. technique that sets the gold std. for H positions in mol. crystals but which is far less easily available. The authors justified the use of a quantum-chem. aide with a broad variety of possible applications.
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- 26Mahe, N.; Perrin, M.; Barrio, M.; Nicolai, B.; Rietveld, I.; Tamarit, J.; Ceolin, R. Solid-State Studies of the Triclinic (Z ′=2) Antiprotozoal Drug Ternidazole J. Pharm. Sci. 2011, 100 (6) 2258– 2266