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Thermodynamics of the Antiviral and Antiparkinsonian Drug Amantadine Hydrochloride: Condensed State Properties and Decomposition Ala Bazyleva,*,† Andrey V. Blokhin,‡ Dzmitry H. Zaitsau,§,∥ Gennady J. Kabo,‡ Eugene Paulechka,† Andrei Kazakov,† and John M. Shaw⊥ †

Applied Chemicals and Materials Division, National Institute of Standards and Technology, Boulder, Colorado 80305-3337, United States ‡ Chemistry Faculty, Belarusian State University, Leningradskaya 14, Minsk 220030, Belarus § Competence Center CALOR, Department Life Light and Matter, University of Rostock, Albert-Einstein-Straße 25, 18059 Rostock, Germany ∥ Department of Physical Chemistry, Kazan Federal University, Kremlevskaya street 18, 420008 Kazan, Russia ⊥ Department of Chemical and Materials Engineering, University of Alberta, Edmonton, T6G 1H9 Alberta, Canada S Supporting Information *

ABSTRACT: Heat capacities of the antiviral and antiparkinsonian drug amantadine hydrochloride in the crystalline state were measured by adiabatic and differential scanning calorimetry in the temperature range from 5 K to 470 K. Two unresolved low-enthalpy solid-to-solid phase transitions with peak maxima at 120.0 K and 123.1 K were detected. Thermodynamic functions for crystalline amantadine hydrochloride were derived from the data obtained. Decomposition of amantadine hydrochloride was studied by the Knudsen effusion method. Quantum chemical calculations supported completeness of the amantadine hydrochloride ionic pair disintegration under the effusion conditions. A data treatment model considering the difference in effusion rates of the decomposition products, anisotropy failure in the vicinity of the orifice, and vapor undersaturation in the effusion cell was developed. Thermodynamic parameters for the decomposition were thus derived and shown to be consistent with available literature data on decomposition of similar organic hydrochlorides and with the entropy of reaction calculated directly from the entropies of the decomposition reaction participants. The obtained set of thermodynamic properties of the medication is expected to provide new key information necessary for optimization of production and storage conditions.

1. INTRODUCTION Adamantane derivatives possess pronounced biological activity, which is likely due to their dual molecular structure combining a hydrophobic tricyclic adamantane moiety (lipophilicity) and specific hydrophilic functional groups. 1 A number of adamantane-based medications have been developed to treat viral and inflammatory diseases, brain disorders (Parkinson’s and Alzheimer’s diseases, neuro infections), and alcohol and drug addiction, etc.2,3 One of the first adamantane derivatives introduced into medical practice was 1-aminoadamantane hydrochloride, or amantadine hydrochloride (Figure 1). It is an antiviral agent for the treatment and prevention of influenza A.3,4 It was later shown that the medication has a dopaminergic effect, which widened the range of applications to include treatment of dementia, Parkinson’s and Alzheimer’s disease, anoxic brain injury, and neuro infections.2,5 It was also shown to have some antihyperalgesic activity.6 © XXXX American Chemical Society

Figure 1. Chemical structure of amantadine hydrochloride.

Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 30, 2017 Accepted: April 11, 2017

A

DOI: 10.1021/acs.jced.7b00107 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Sample Description chemical name 1-aminoadamantane hydrochloride (amantadine hydrochloride) sapphire a

initial massfraction purity

source BORIMED: Borisovskiy Zavod Medicinskikh Preparatov, JSC (Borisov, Belarus) NIST, SRM 720

0.99a >0.9995a

purification vacuum treatment at T ≈ 293 K and p ≈ 0.4 kPa for 2 h none

Stated by the supplier. No additional purity analysis was performed.

determined in a vacuum adiabatic calorimeter TAU-10 (“Termis”, Moscow, Russia), described in detail previously.14 The relative expanded uncertainty (0.95 level of confidence) of the Cs,m measurements was estimated to be 0.4% between T = (20 and 370) K, then increasing below 20 K to not more than 2% at 5 K.14 The repeatability for the heat-capacity measurements was observed to be better than ±0.1%. Temperature was measured with a Fe−Rh resistance thermometer (R0 = 50 Ω) calibrated on ITS-90 at VNIIFTRI (Mendeleyevo, Moscow Region, Russia), with the standard uncertainty of 0.01 K. A calorimetric cell made of titanium (V ≈ 1.13 cm3) was loaded with a solid sample of 0.6440 g for measurement in the liquid helium range (5 to 84) K and 0.7308 g for measurement in the liquid nitrogen range (above 77 K). The masses were corrected for buoyancy. After loading, the container was degassed under vacuum (residual pressure of ∼10 Pa) for 0.5 h. Helium gas, at p ≈ 10 kPa and T = 290 K, was introduced into the cell to facilitate heat transfer during measurements. The container was sealed using an indium ring and a titanium head fixed with a bronze screw cap. The ratio of the sample heat capacity to the total (sample + cell) heat capacity was not less than 0.5 in the range of (5 to 30) K and (0.3 to 0.5) at higher temperatures. The heat capacity of helium gas sealed in the calorimetric cell was accounted for in the treatment of the experimental data. Heating periods were (60 to 150) s below 40 K, (200 to 250) s for T = (40 to 80) K, and 400 s above 80 K. The thermal relaxation time was (25 to 100) s at T < 80 K and 150 s at higher temperatures. The periods for the temperature-drift measurements were (200 to 250) s at T < 80 K and (300 to 400) s at T > 80 K. The temperature step for the Cs,m measurements was approximately equal to T/20 at T < 40 K and (1.5 to 2.5) K above 40 K; two additional series with smaller temperature steps (1.0 and 0.5) K were done in the phase transition region between (110 and 130) K. To obtain the overall enthalpy of phase transitions, a series of experiments with continuous energy input was conducted, that is, one-step heating of the sample from a temperature below the beginning of the phase transition region to a temperature above it (more details are given in Section 4.1). As the vapor pressure of the sample is negligible in the temperature interval studied, adjustment of Cs,m to Cop,m was unnecessary (Cs,m ≈ Cop,m). 2.3. Differential Scanning Calorimetry. The isobaric heat capacity of crystalline amantadine hydrochloride was measured in a differential scanning calorimeter TG-DSC 111 (Setaram, France) in the temperature range (310 to 470) K at a scanning rate of 5 K·min−1. A continuous three-step method was applied in this work with NIST SRM-720 sapphire15 used as a reference material. A sample of 58.64 mg (weighed with standard uncertainty of 0.05 mg) was loaded into a stainlesssteel cell, which was then hermetically sealed. The temperature calibration of the calorimeter was done according to the recommendations developed by GEFTA.16,17 The standard

Thermodynamic properties have recently been studied for 1aminoadamantanethe amine form of the drug.7,8 However, little information on physical and thermodynamic properties of amantadine hydrochloride is available in the literature, despite its long history of medical use. Nonmedical studies are typically focused on molecular/ion mobility in the solid phase,9,10 because many adamantane derivatives form orientationally disordered, or plastic, crystals exhibiting extensive molecular rotations in their lattice sites,11 and regular changes in their molecular structures can shed light on the interconnection between molecular structure peculiarities and plastic crystal formation. For example, a DSC study over the temperature range of (100 to 400) K9 showed that amantadine hydrochloride has a low-enthalpy solid-to-solid phase transition at 124 K with an entropy of transition of 2.5 J·K−1·mol−1, which is too small to correspond to any noticeable molecular disordering. IR, Raman, and XRD studies showed that both low- and high-temperature crystalline phases are ordered with a large barrier of rotation of adamantane moiety about its C3 axis.9,10 The absence of an order−disorder phase transition, typical for many adamantane derivatives, was expected for amantadine hydrochloride because of its chemical nature. It has strong intermolecular interactions including ionic and hydrogen bonding in the condensed phase.10 The crystallographic densities of crystalline amantadine hydrochloride from XRD results at 143 K and “room temperature” were calculated to be 1.192 g·cm−3 and 1.167 g·cm−3, respectively.10,12 The current study addresses data and knowledge gaps in thermodynamic properties of amantadine hydrochloride. High precision solid-state heat capacity, phase change, and decomposition data are reported. Quantum chemical computations are additionally involved to get insight into the amantadine hydrochloride structure and stability in the gaseous phase.

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. A sample of amantadine hydrochloride (C10H18NCl) was provided by the pharmaceutical factory “BORIMED: Borisovskiy Zavod Medicinskikh Preparatov”, JSC (Borisov, Belarus). The initial mass-fraction purity was better than 0.99 according to the manufacturer’s certificate of analysis. The sample was exposed to vacuum at room temperature (T ≈ 293 K) and p ≈ 0.4 kPa for 2 h to remove volatile impurities and moisture if present prior to calorimetry and effusion experiments. No in-house purity analysis was performed. The sample description is summarized in Table 1. The atomic masses of elements recommended by IUPAC (conventional weights reported in Table 3 in Meija et al.13) were used to derive the molar mass of amantadine hydrochloride (0.18771 kg·mol−1). 2.2. Adiabatic Calorimetry. Heat capacities at the saturated-vapor pressure (Cs,m) for crystalline amantadine hydrochloride in the temperature range (5 to 370) K and the temperatures and enthalpies of its solid-phase transitions were B



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uncertainty of temperature values was found to be 0.2 K. The relative expanded uncertainty (0.95 level of confidence) of the heat-capacity measurements was estimated to be 4%. More details about the DSC experiments and uncertainty analysis can be found elsewhere.18 During the DSC experiments, the pressure in the sealed crucible increases by less than a factor of 2, and the vapor pressure of the sample is well below 100 kPa. Therefore, the difference between the measured heat capacity and Cop,m was negligible. 2.4. Knudsen Effusion Method. Effusion measurements for crystalline amantadine hydrochloride in the temperature range (383 to 463) K were carried out in an experimental setup19,20 with a high-temperature copper block thermostat described previously.21 Temperature was measured with a platinum resistance thermometer (R0 = 10 Ω). The standard uncertainty for temperature determination was estimated to be 0.05 K. Residual pressure in the system was maintained below 10−3 Pa with a diffusion vacuum pump. The relative expanded uncertainty (0.95 level of confidence) of the vapor pressure measurements was estimated to be 10%. Crystalline samples were loaded into a cylindrical stainlesssteel cell with 10.0 mm height and 10.0 mm internal diameter. To facilitate heat transfer, the sample was pressed against the whole inner surface of the cell with a stainless-steel rod. Three nickel membranes with different foil thickness (l) and orifice diameters (dor) were used to check for vapor undersaturation. Detailed analysis of the effusion measurement results is presented in section 4.2.

Figure 2. Temperature dependence of isobaric heat capacities of crystalline amantadine hydrochloride from this work (black empty circles, adiabatic calorimetry; solid line, DSC) and 1-aminoadamantane (gray filled circles, adiabatic calorimetry7).

the overlap region, that is, within the uncertainty claimed for DSC, and both sets of measurements show the same temperature dependence (slope). Small parallel shifts of heat capacity values without changing heat capacity profiles (within the stated uncertainty) are typical for the DSC instrument due to minute irreproducibilities in the position of a sample cell inside the DSC cylinder tubes from one experiment to another. Adiabatic calorimetry results are not subject to this artifact. Hence, the latter data were used as a benchmark for calculating thermodynamic functions above 370 K along with the temperature dependence from the DSC measurements to avoid a nonphysical heat-capacity profile, which could arise, if simpler joint data treatments are applied. Technically, this is equivalent to using a slope from the DSC results (first derivative with respect to temperature) in the regression. Crystalline amantadine hydrochloride exhibits two unresolved solid-to-solid phase transitions (Figure 3), with maxima

3. COMPUTATIONS Thermodynamic parameters of the amantadine hydrochloride decomposition reaction in the gaseous phase, eq 1: C10H18NCl(gas) ⇄ C10H17N(gas) + HCl(gas)

(1) 22

were computed using a procedure described elsewhere. The ORCA v3.0.3 package23 was used for geometry optimization and single-point energy calculations, and the Gaussian 09 package24 was applied for vibrational frequency computations. Molecular geometries were optimized using RI-MP2/def2TZVP (the density-fitted, or also called “Resolution-of-Identity” RI approximation of the second-order Møller−Plesset perturbation theory25−27 and the def2-TZVP basis set28). The RI-MP2 geometries were used for high-level single-point energy calculations with the DLPNO-CCSD(T) approach29−31 augmented with “TightPNO” settings30 and using the def2QZVP basis set. Vibrational frequencies were computed with the hybrid Density Functional Theory (DFT) B3LYP-D3(BJ) method32 and the def2-TZVP basis set. The computed frequencies were then scaled using scaling factors consistent with those recommended in the literature33 (0.96 for Hstretches and 0.985 for all other vibrations).

4. RESULTS AND DISCUSSION 4.1. Thermodynamic Properties of Crystalline Amantadine Hydrochloride. Experimental molar heat capacities of crystalline amantadine hydrochloride measured in the adiabatic calorimeter and differential scanning calorimeter are presented in Tables S1 and S2 (Supporting Information), respectively, and are shown graphically in Figure 2 together with the heat capacity 1-aminoadamantane (molecular form of the medication) measured previously in Bazyleva et al.7 The Cp,m results for both types of calorimetry (Figure 2) agree within 1.6% in

Figure 3. Temperature dependence of isobaric heat capacities of crystalline amantadine in the vicinity of solid-to-solid phase transitions: black empty circles, experimental data; dashed line, heat capacity baselines used in Table 2; vertical dotted line, crIII−crII/crII−crI phase transition boundary; dash-dotted line in the inset is used only to make a heat capacity anomaly after the solid-to-solid phase transitions more visible. C



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Table 2. Results of the Experiments on Continuous Energy Input for the crIII-to-crI Transition of Amantadine Hydrochloridea Tstart

Tend

qexp

qcont

Qsample −1

K

K

J

J

100.94 100.94 101.16 109.32 Average:

131.02 130.97 131.22 131.27

37.658 37.596 37.688 28.504

26.220 26.176 26.237 19.683

ΔtrsHom

Qbase −1

J·mol

J·mol

2938.0 2933.4 2941.3 2265.8

2740.3 2735.6 2742.8 2067.6

J·mol−1 197.7 197.8 198.5 198.2 198.1 ± 1.0b

a qexp is the energy applied to heat the container with the sample from Tstart to Tend; qcont is the heat needed to increase temperature of the container from Tstart to Tend; Qsample is the energy necessary for heating 1 mol of amantadine hydrochloride from Tstart to Tend; ΔtrsHom is the total enthalpy change for the crIII-to-crI transition calculated as follows:

ΔtrsHmo = Q sample − Q base = Q sample −

∫T

Tend

Cp ,m(baseline) dT

start

with the following joint baseline derived from the heat capacity values from (92.1 to 111.3) K for crIII and from (129.1 to 139.8) K for crI: Cp,m/(J· K−1·mol−1) = 264.29 − 7.5637·(T/K) + 9.9411 × 10−2·(T/K)2 − 5.2477 × 10−4·(T/K)3 + 1.0255 × 10−6·(T/K)4. bThe average value with the expanded uncertainty with 0.95 confidence level, including repeatability and uncertainty of the method.

at (120.0 ± 0.4) K and (123.1 ± 0.4) K obtained from measurements with a temperature increment of (0.4 to 0.5) K, that is, from series 5. The total enthalpy of these two phase transitions obtained in a series of experiments with continuous energy input (Table 2) is (198.1 ± 1.0) J·mol−1. A similar sharp phase transition in the salt was measured by DSC9 at 124 K, with a larger enthalpy change reported (310 J·mol−1). No information about temperature and energy calibration of the instrument as well as uncertainty was provided, so it is not possible to judge the reliability of the results by Harvey et al.9 The enthalpy of the crIII−crII transition of (45 ± 3) J·mol−1 was obtained by direct integration of heat capacity between the experimental points and the baseline from 111.3 K to 121.0 K (saddle point between two peaks), as shown in Figure 3. The enthalpy of the crII−crI transitions of (153 ± 3) J·mol−1 was o obtained by subtraction of the ΔcrII crIIIHm value from the total transition enthalpy from Table 2. This choice of separation method for the two peaks does not impact values of derived thermodynamic functions due to the temperature proximity of the peaks. There are two small peculiarities in the amantadine hydrochloride heat capacity temperature profile. One is a step-like anomaly observed immediately after the crIII−crII and crII−crI phase transitions (Figure 3, inset). The nature of the anomaly is not known. The second reproducible peculiarity is heat capacities at approximately (239 to 242) K by up to 0.6% above the smoothing curve. This may be an indication of a minor impurity exhibiting a phase transition in that temperature range. 1-Aminoadamantane is a likely impurity, since it undergoes high-enthalpy phase transformations in that temperature interval (Figure 2). If the assumption on impurity is correct, its content is less than 0.1 mol %, which does not impact the derived thermodynamic functions significantly. Thermal behaviors of amantadine hydrochloride and 1aminoadamantane (molecular form of the drug) are compared in Figure 2. As expected, the heat capacity of the salt is higher than that of 1-aminoadamantane at very low temperatures. However, this changes dramatically above 200 K. As it was shown previously,7 1-aminoadamantane forms a plastic crystal phase through two phase transitions, which start at approximately 170 K and end at approximately 300 K. Formation of plastic crystals is typically associated with a large heat capacity jump, as observed for 1-aminoadamantane.

The ionic crystal of amantadine hydrochloride remains ordered,9,10 despite the two-phase transitions (these transitions are not accompanied by significant heat capacity jumps). Hence, it is not surprising that the heat capacity of the amine form is larger than that of the salt above 200 K due to significant differences in the temperature dependence of molecular mobility in the crystalline phases. The thermodynamic functions for amantadine hydrochloride in the condensed state from (5 to 470) K were derived from the smoothed heat capacities and the parameters of its solid-tosolid phase transitions. The smoothing of heat capacities above 5 K was carried out using overlapping polynomials. Heat capacities below 5 K were extrapolated: it appeared that the low-temperature heat capacity of crIII of amantadine hydrochloride was adequately represented by one Debye function with three degrees of freedom and one Einstein function with one degree of freedom: Cp,m = D3(⟨ΘD⟩/T ) + E(⟨ΘE⟩/T )

(2)

where the average Debye and Einstein characteristic temperatures were derived to be ⟨ΘD⟩ = 75.1 K and ⟨ΘE⟩ = 56.9 K, respectively, from the experimental heat capacities between (5.0 to 6.6) K. Table 3 summarizes the thermodynamic functions. 4.2. Decomposition of Amantadine Hydrochloride from Effusion Measurements. Mass loss data obtained in the effusion experiments for crystalline amantadine hydrochloride are summarized in Table 4. A pH analysis of aqueous solutions containing effusion products condensed on a cold trap shows the presence of an amine form, which indicates that amantadine hydrochloride decomposes upon sublimation to form hydrogen chloride and 1-aminoadamantane. The amine form was not detected by pH measurements for the residue left in the cell after effusion, showing that 1-aminoadamantane does not accumulate in the cell during the effusion experiments. To analyze the effusion results, it is crucial to know the equilibrium degree of amantadine hydrochloride decomposition. The quantum chemistry methods described in section 3 were applied to the analysis of reaction 1. The optimized structure of amantadine hydrochloride already provides important clues. Before the calculations, it was expected that amantadine hydrochloride existed as an ionic pair with chlorine anion symmetrically above the positively charged NH3-group (i.e., equal H−Cl distances), which was D



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Table 3. Standard Molar Thermodynamic Functions of Amantadine Hydrochloride (M = 0.18771 kg·mol−1) in the Crystalline State at a Standard Pressure of 105 Paa ΔT0 Hom/T

Cop,m T/K

−1

−1

J·K ·mol ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.012 0.064 0.10 0.07 0.10 0.12 0.14 0.16 0.17 0.19 0.22 0.24 0.27 0.29 0.32 0.35 0.38

−1

J·K ·mol

5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120.0

0.585 4.396 10.64 17.48 24.00 29.84 34.98 39.56 43.74 47.63 54.53 60.92 67.11 73.32 79.81 86.83 94.01

120.0 123.1

94.01 ± 0.38 96.21 ± 0.38

51.02 52.13

123.1 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460

96.21 101.0 107.9 112.2 117.7 123.8 130.1 136.6 143.3 150.2 157.3 164.5 171.8 179.3 186.8 194.3 202.1 209.9 216.2 217.6 225.3 233.0 240.7 248.6 256.5 264.5 272.5 280 288 296 304 312 319 327 334 342

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

53.37 55.78 59.25 62.64 65.91 69.13 72.35 75.56 78.78 82.02 85.28 88.56 91.88 95.22 98.60 102.0 105.4 108.9 111.8 112.4 115.9 119.5 123.0 126.6 130.2 133.8 137.5 141.1 144.8 148.5 152.2 155.9 159.6 163.3 167.0 170.7

0.38 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.1 1.1 11 12 12 12 12 13 13 13 14

ΔT0 Som

−1

0.1445 1.170 3.244 5.953 8.917 11.93 14.86 17.67 20.34 22.87 27.59 31.90 35.91 39.72 43.40 47.03 50.65

Crystal III 0.0029 0.020 0.042 0.054 0.060 0.07 0.08 0.09 0.09 0.10 0.12 0.14 0.15 0.17 0.18 0.19 0.21 Crystal II ± 0.23 ± 0.24 Crystal I ± 0.26 ± 0.27 ± 0.28 ± 0.29 ± 0.30 ± 0.31 ± 0.32 ± 0.33 ± 0.34 ± 0.36 ± 0.37 ± 0.38 ± 0.39 ± 0.40 ± 0.42 ± 0.4 ± 0.4 ± 0.5 ± 0.5 ± 0.5 ± 0.5 ± 0.5 ± 0.5 ± 0.5 ± 0.5 ± 0.6 ± 0.6 ± 0.8 ± 1.1 ± 1.4 ± 1.6 ± 1.9 ± 2.1 ± 2.4 ± 2.6 ± 2.9 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

E

−1

Φomb −1

J·K ·mol 0.1924 1.564 4.477 8.480 13.09 17.99 22.99 27.96 32.87 37.68 46.99 55.88 64.42 72.68 80.74 88.67 96.53

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0038 0.027 0.061 0.087 0.11 0.13 0.15 0.17 0.18 0.20 0.24 0.28 0.31 0.34 0.38 0.41 0.44

96.90 ± 0.46 99.33 ± 0.47 100.6 106.0 113.7 121.3 128.7 136.0 143.3 150.5 157.7 164.8 172.0 179.1 186.3 193.4 200.6 207.8 215.0 222.2 228.1 229.5 236.7 244.0 251.3 258.6 265.9 273.3 280.6 288.0 295.4 302.8 310.2 317.6 325.0 332.5 339.9 347.3

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.5 0.5 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.2 1.2 1.2 1.5 1.8 2.1 2.4 2.7 3.0 3.3 3.6 3.9

−1

J·K ·mol−1 0.0479 0.3948 1.233 2.527 4.171 6.064 8.124 10.29 12.53 14.80 19.40 23.98 28.50 32.95 37.33 41.64 45.89

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0010 0.0067 0.016 0.024 0.031 0.038 0.047 0.06 0.06 0.07 0.09 0.11 0.13 0.15 0.16 0.18 0.20

45.89 ± 0.21 47.20 ± 0.22 47.20 50.18 54.44 58.64 62.79 66.88 70.92 74.92 78.88 82.80 86.69 90.56 94.39 98.21 102.0 105.8 109.6 113.3 116.4 117.1 120.8 124.6 128.3 132.0 135.7 139.5 143.2 146.9 150.6 154.3 158.0 161.7 165.4 169.2 172.9 176.6

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.23 0.24 0.26 0.28 0.29 0.31 0.32 0.34 0.35 0.37 0.38 0.40 0.41 0.43 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.8 1.0 1.3 1.5 1.7 1.9 2.1 2.3 2.5



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Table 3. continued T/K

ΔT0 Hom/T

ΔT0 Som

Φomb

J·K−1·mol−1

J·K−1·mol−1

J·K−1·mol−1

J·K−1·mol−1

Crystal I 174.5 ± 3.1

349 ± 14

470 a

Cop,m

354.8 ± 4.2 b

Expanded uncertainties with 0.95 confidence level are reported inside the table. Function

Φom

=

ΔT0 Som

180.3 ± 2.7

−

ΔT0 Hom/T.

Table 4. Mass Loss Data for Effusion Experiments on Crystalline Amantadine Hydrochloridea dor

l

point no.

mm

μm

1 2 3 4 5 6 7 8 9 10 11

0.4467 0.4467 0.4467 0.4467 0.1833 0.1833 0.1833 0.1833 0.8370 0.8370 0.8370

72 72 72 72 50 50 50 50 50 50 50

τ

Δm

K

s

mg

413.09 423.02 433.04 403.03 442.99 433.04 453.04 463.06 403.06 393.03 383.03

10800 7200 3600 20100 10800 19800 5400 3600 10800 19800 21600

7.84 10.92 10.56 7.03 10.59 9.78 9.94 12.15 10.92 9.01 4.25

T

Δm is the experimental sample mass loss from effusion cell into the vacuum during time τ at temperature T; l is the membrane thickness, and dor is the effusion orifice diameter. Standard uncertainties u are u(T) = 0.05 K, u(dor) = 0.0005 mm, u(l) = 1 μm, u(Δm) = 0.05 mg, u(τ) = 5 s. a

used as a starting-point approximation. However, quantumchemical calculations at various levels of theory (DFT, MP2) consistently give similar representations of the amantadine hydrochloride structure in the gaseous phase: no true ionic pair is seen. The chlorine atom is, in fact, shifted to one of the hydrogen atoms of the NH3-group in such a way that a readyto-go fragment of HCl is formed (Figure 4). For example, according to RI-MP2/def2-TZVP calculations, the bond length in the HCl fragment is 0.141 nm (for comparison, the bond length in a free HCl molecule is 0.128 nm at the same level of theory); the N−H distance is 0.149 nm for the hydrogen located near chlorine, while it comprises only 0.102 nm for two other hydrogen atoms. The computed thermodynamic parameters of reaction 1 are summarized in Table 5. The enthalpy of reaction 1 at 0 K was calculated from the total energies of reaction participants and their zero-point vibrational energies (ZPVE) derived from computed scaled frequencies: Δr Hmo(0

K) = Δr Etot + Δr ZPVE

(Som(T))

Figure 4. RI-MP2/def2-TZVP optimized structure of amantadine hydrochloride (dotted line−hydrogen bonding).

Table 5. Calculated Thermodynamic Parameters of Amantadine Hydrochloride Dissociation According to GasPhase Reaction 1 (po = 105 Pa)a ΔrHom(0 K) kJ·mol 35.4

−1

T K 298.15 400 500

ΔrHom(T) −1

kJ·mol 38.1 38.1 37.8

ΔrSom(T) −1

−1

J·K ·mol 122.7 122.9 122.2

ΔrGom(T) kJ·mol−1

Ko(T)

1.5 −11.0 −23.3

0.55 28 2.7 × 102

Symbols: ΔrHom(0 K) and ΔrHom(T) are the enthalpies of reaction at 0 K and selected temperature T; ΔrSom(T) and ΔrGom(T) are the entropy and Gibbs energy of reaction at selected temperature T; Ko(T) is the equilibrium constant of reaction at selected temperature T. The value ΔrHom(0 K) was calculated by eq 3 with computed values ΔrEtot = 43.09 kJ·mol−1 and ΔrZPVE = −7.67 kJ·mol−1. The uncertainty estimation is presented is section 4.2 a

(3)

(ΔT0 Hom)

Ideal-gas entropies and thermal enthalpies of reactants and products in reaction 1 at selected temperatures were calculated by a statistical thermodynamic method with the use of molecular and spectral parameters obtained in this work as described in section 3 (see Table S3 in the Supporting Information for the numerical values of the parameters). The conventional rigid-rotor harmonic-oscillator approximation was used without special treatment of the NH2 and NH3Cl torsions, since the arising systematic errors in both 1-aminoadamantane and amantadine hydrochloride are expected to cancel out on subtraction. The total pressure in the effusion cell did not exceed 100 Pa during effusion experiments, so the mole fraction of amantadine

hydrochloride calculated from the equilibrium constants from Table 5 did not exceed 10−5. Even assuming the expanded uncertainty (0.95 level of confidence) in calculated enthalpy and entropy of reaction to be, respectively, 4 kJ·mol−1 (typical uncertainty of quantum chemical energy calculations) and 20 J· K−1·mol−1 (roughly estimated from the possible contribution from low vibrational frequencies of the amantadine hydrochloride adduct), the equilibrium mole fraction of amantadine F



Article

hydrochloride should not be more than 2 × 10−4. Thus, there is essentially no amantadine hydrochloride adduct in the gas phase. For further calculations, it was assumed that decomposition of amantadine hydrochloride occurs on the surface of the crystalline salt according to the reaction: C10H18NCl(cr) ⇄ C10H17N(gas) + HCl(gas)

* = pamine

(4)

The equilibrium constant for this reaction (K ) can be expressed as peq,amine ·peq,HCl Ko = (po )2 (5) where po is the standard pressure (105 Pa); peq,amine and peq,HCl are the equilibrium partial pressures of 1-aminoadamantane and hydrogen chloride, respectively. The total mass loss rate upon effusion into vacuum is a sum of the mass loss rates of 1-aminoadamantane and HCl: (6)

where Δmi is the integral mass loss of a component or the sample in total from the effusion cell during exposition to vacuum during τ period. For each component i of the gas mixture, the mass loss can be expressed through the Knudsen equation for effusion of vapors with pressure pi* into vacuum: Δmi Mi = pi* kiSor τ 2πRT

kamineSor(Mamine

(11)

The total pressure in the cell is obtained from eqs 10 and 11) as a sum of partial pressures. The challenge in treating the effusion results is to obtain transmission coefficients ki for each component. As shown earlier,19,20,34 the mean free paths of a molecule inside an effusion cell and in the vicinity of an effusion orifice differ (gas isotropy failure), which affects the transmission probability coefficient in the Knudsen equation. Transmission probabilities of gas components were calculated in terms of the Wahlbeck theory for gas mixtures35 and by extending the iteration procedure developed elsewhere19,20 to gas mixtures. The effective diameters of 1-aminoadamantane (0.682 nm) and hydrogen chloride (0.359 nm) molecules were evaluated from their van der Waals volumes in Tinker 3.636 based on atomic van der Waals radii37 and molecular geometric parameters calculated with the RI-MP2/def2-TZVP level of theory. Figure 5a shows the temperature dependence of the total pressure (sum of p*amine and p*HCl) obtained from the effusion measurements for crystalline amantadine hydrochloride with

o

⎛ Δmtot ⎞ ⎛ Δmamine ⎞ ⎛ ΔmHCl ⎞ ⎜ ⎟ ⎟=⎜ ⎟+⎜ ⎝ τ ⎠ ⎝ τ ⎠ ⎝ τ ⎠

⎛ Δmtot ⎞ ⎜ ⎟ + MHCl) ⎝ τ ⎠

2πRTMamine

(7)

giving ⎛ Δmtot ⎞ 1 * MHCl ⎜ ⎟ = Sor (kHClpHCl ⎝ τ ⎠ 2πRT * + kaminepamine Mamine )

(8)

where pamine * and pHCl * are the partial pressures of 1aminoadamantane and HCl in the cell; Sor is the effusion orifice area; kamine and kHCl are the transmission probabilities for the molecules of 1-aminoadamantane and HCl through the orifice, respectively; T is the average temperature in the effusion experiment; Mamine and MHCl are the molar masses of the effusing vapors of 1-aminoadamantane and HCl (M = (0.15125 and 0.03646) kg·mol−1, respectively); R is the gas constant (R = 8.3144598 J·K−1·mol−1). The initial molar rate of effusion of HCl is higher than that of 1-aminoadamantane due to the difference in their molar masses (see eq 7). The rates are expected to become the same very quickly. Since the initial rate difference should not have any noticeable effect on the effusion results due to the small volume of the cell, only steady state effusion is considered: ⎛ Δnamine ⎞ ⎛ ΔnHCl ⎞ ⎜ ⎟=⎜ ⎟ ⎝ τ ⎠ ⎝ τ ⎠

(9)

where Δni is the integral molar loss of a component from the effusion cell during exposition to vacuum during τ period. If eq 9 is combined with eq 7 for each gas component: * = pHCl

kamine kHCl

MHCl p* Mamine amine

Figure 5. Temperature dependence of (a) apparent total pressure (sum of p*amine and p*HCl from Table 6) and (b) equilibrium total pressures (sum of peq,amine and peq,HCl from Table 6) obtained with the use of membranes with different orifice diameters: □, dor = 0.1833 mm; ●, dor = 0.4467 mm; △, dor = 0.8370 mm.

(10)

eq 8 becomes G



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Table 6. Apparent (pi*) and Equilibrium (peq,i) Partial Pressures (in Pa) together with Transmission Probabilities for 1Aminoadamantane and HCl as Well as Equilibrium Constant for Reaction 4 Calculated from the Effusion Results (po = 105 Pa)a point no.

T/K

pamine *

kamine

pHCl *

kHCl

peq,amine

peq,HCl

Ko·1010

1 2 3 4 5 6 7 8 9 10 11

413.09 423.02 433.04 403.03 442.99 433.04 453.04 463.06 403.06 393.03 383.03

1.51 3.04 5.64 0.744 12.6 6.62 22.9 40.7 0.549 0.252 0.109

0.933 0.981 1.034 0.902 0.927 0.881 0.973 1.012 1.006 0.975 0.958

0.773 1.59 2.99 0.375 6.66 3.43 12.1 21.4 0.279 0.126 0.0542

0.895 0.922 0.958 0.879 0.864 0.834 0.901 0.945 0.971 0.957 0.950

1.74 3.52 6.58 0.852 13.0 6.78 23.5 41.8 0.861 0.390 0.168

0.885 1.82 3.45 0.427 6.81 3.51 12.4 22.0 0.432 0.194 0.0832

1.54 6.41 22.7 0.364 88.2 23.8 291 919 0.372 0.0757 0.0140

a

The direct experimental data are reported in Table 4 with the corresponding numeration. Standard uncertainties u are u(T) = 0.05 K, ur(p) = 0.05, ur(Ko) = 2ur(p) = 0.10.

⎛ ⎛T ⎞ θ⎞ R ln[K o(T )] − Δr C po,m·⎜ln⎜ ⎟ − 1 + ⎟ ⎝ ⎝θ⎠ T⎠ o Δ H (θ ) =− r m + Δr Smo(θ ) T

the use of the above-described approach (Table 6). There is an obvious dependence of the apparent vapor pressure in the cell on the orifice size. This is evidence of vapor undersaturation. Consequently, extrapolation to a zero-size orifice is needed. The extrapolation approach is based on work by Nesmeyanov38 and is similar to that presented previously,39 with the only difference being that components (1-aminoadamantane and hydrogen chloride) are treated separately. The extrapolation equation becomes peq, i = pi* (1 + Ai kiSor)

where Δr C po,m is the average heat-capacity change in reaction 4 for the studied temperature range and θ is the reference temperature. The average Δr C po,m value for reaction 4 for the studied temperature range was determined to be −24 J·K−1· mol−1 based on the heat capacity of crystalline amantadine hydrochloride from Table 3, gaseous 1-aminoadamantane obtained in our previous work by statistical thermodynamics,7 and gaseous HCl from the CODATA tables.41 The average temperature of the studied temperature range (423 K) was taken as the reference temperature θ. The value of A = 1.03 × 106 m−2 in eq 12 was determined by combining eqs 12 and 15 and conducting simultaneous leastsquares fitting of the apparent partial pressures of 1aminodamantane and HCl obtained in the experiments with different orifice sizes (Table 6). The equilibrium partial pressures were thus calculated and presented in Table 6. The resulted total equilibrium pressure (Figure 5b) does not exhibit any effusion orifice size dependence. The obtained equilibrium partial pressures of 1-aminoadamantane over crystalline amantadine hydrochloride are several orders of magnitude lower than the saturated vapor pressure over crystalline 1aminoadamantane measured earlier7 (e.g., peq,amine of 10 Pa exists over crystalline 1-aminoadamantane at 296.5 K and over crystalline amantadine hydrochloride at 439 K). This confirms our initial observation that there is no accumulation of condensed phase 1-aminoadamantane in the cell during the decomposition measurements. The enthalpy and entropy of decomposition reaction 4 at reference temperature θ = 423 K were obtained from eq 15: ΔrHom(θ) = (203.7 ± 7.5) kJ·mol−1 and ΔrSom(θ) = (305 ± 18) J·K−1·mol−1, where the expanded uncertainties with 0.95 level of confidence are reported. To account for possible systematic errors in the partial pressures from the Knudsen effusion method, the changes in slope and intercept in the right side of eq 15 were calculated with values at the temperature extremes with equilibrium constants fractionally shifted with opposite sign by twice the relative standard uncertainty in Ko reported in Table 6, which was evaluated from the partial pressure uncertainties.

(12)

where peq,i is equilibrium partial pressure of component i at temperature T, pi* is the apparent partial pressure of component i measured in the effusion experiments at temperature T (eqs 10 and 11); Ai is the fitting coefficient combining the real sublimation surface (including surface roughness) and the condensation coefficient for component i. This procedure accounts for vapor undersaturation in the effusion cell. Trial application of eq 12 to each mixture component separately gives Aamine similar to AHCl within 0.5%. Since this difference has a minor effect on the calculated equilibrium pressures in comparison to the stated uncertainty, it was assumed that Aamine = AHCl = A in the calculations. The equilibrium constants of reaction 4 at each studied temperature can be calculated from the equilibrium partial pressures by eq 5. Enthalpy and entropy of decomposition reaction 4, ΔrHom(T) and ΔrSom(T), can be obtained from the temperature dependence of Ko(T) according to the following thermodynamic expression: −RT ln[K o(T )] = Δr Hmo(T ) − T Δr Smo(T )

(13)

where the standard pressure po is 105 Pa. Since the temperature range of the effusion study is wide (80 K), the temperature dependence of ΔrHom(T) and ΔrSom(T) should be taken into account by analogy with the Clarke−Glew equation:40 1 R ln[K o(T )] = − {Δr Hmo(θ ) + Δr C po,m·(T − θ )} T + {Δr Smo(θ ) + Δr C po,m·ln(T /θ )}

(15)

(14) H



Article

Table 7. Enthalpies of Decomposition (ΔrHom) of Crystalline Organic Hydrochlorides into Gaseous Amine and HCl at 298.15 K Derived from the Corresponding Literature Valuesa ΔfHom (g) amines 42

methylamine dimethylamine42 trimethylamine42 1-propylamine42 diethylamine42 dipropylamine42 di-isopropylamine42 tripropylamine42 cyclohexylamine43

ΔfHom (cr)

−1

kJ·mol −23.4 −18.8 −23.6 −70.1 −72.2 −116.0 −143.8 −161.0 −104.9

± ± ± ± ± ± ± ± ±

1.0 1.5 1.3 0.4 1.2 0.5 0.5 0.9 1.3

hydrochlorides

kJ·mol 42

methylammonium chloride dimethylammonium chloride42 trimethylammonium chloride42 propylammonium chloride42 diethylammonium chloride42 dipropylammonium chloride42 di-isopropylammonium chloride42 tripropylammonium chloride42 cyclohexylamine hydrochloride43

−298.1 −289.3 −282.9 −354.7 −358.6 −389.5 −417.8 −446.4 −408.2

ΔrHom

−1

± ± ± ± ± ± ± ± ±

kJ·mol−1

4.1 4.2 4.2 0.4 1.4 1.0 0.5 1.0 1.5

182.4 178.2 167.0 192.3 194.1 181.2 181.7 193.1 211.0

± ± ± ± ± ± ± ± ±

4.2 4.5 4.4 0.6 1.8 1.1 0.7 1.3 2.0

a

The enthalpy of formation of gaseous HCl used was taken from the CODATA tables.41 The uncertainty is taken from the cited references, but the uncertainty type (whether standard uncertainty or expanded uncertainty with 0.95 level of confidence) is not identified there.

■

The standard decomposition entropy of amantadine hydrochloride derived in this way agrees satisfactorily with the value (320.5 ± 3.6) J·K−1·mol−1 obtained at 423 K from the entropy of crystalline amantadine hydrochloride (Table 3), gaseous 1aminoadamantane,7 and gaseous HCl.41 The enthalpy of decomposition reaction 4 was adjusted from 423 to 298.15 K with the use of heat-capacity data for the reaction participants: ΔrHom (298.15 K) = (206.0 ± 7.5) kJ·mol−1. This methodology for deriving decomposition enthalpies from effusion results is indirectly supported through comparison with literature values of enthalpies of decomposition of crystalline organic hydrochlorides (similar to reaction 4) as shown in Table 7. The measured enthalpy of decomposition of crystalline amantadine hydrochloride is in a similar range of other organic hydrochlorides. The enthalpy of formation of crystalline amantadine hydrochloride at 298.15 K was obtained from reaction 4 using the derived enthalpy of decomposition at 298.15 K and enthalpies of formation of gaseous 1-aminoadamantane7 (−133.8 ± 2.4) kJ·mol−1 and gaseous hydrogen chloride (−92.31 ± 0.10) kJ·mol−1 from the CODATA Tables.41 The calculated value is ΔfHom(cr, 298.15 K) = (−432.1 ± 7.9) kJ· mol−1.

Corresponding Author

*Tel.: +1-303-497-5981. E-mail: [email protected]. ORCID

Ala Bazyleva: 0000-0003-3018-2020 Eugene Paulechka: 0000-0002-6441-8364 John M. Shaw: 0000-0002-6176-4421 Funding

D.H.Z. is grateful to the Russian Government Program of Competitive Growth of Kazan Federal University for partial financial support of this work. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Bagrii, E. I. Adamantanes: Production, properties, application; Nauka: Moscow, 1989 [in Russian]. (2) Morozov, I. S.; Petrov, V. I.; Sergeeva, S. A. Pharmacology of Adamantanes; Volgograd Medical Academy: Volgograd, 2001 [in Russian]. (3) Oxford, J. S.; Galbraith, A. Antiviral activity of amantadine: a review of laboratory and clinical data. Pharmacol. Ther. 1980, 11, 181− 262. (4) De Clercq, E. Antiviral drugs in current clinical use. J. Clin. Virol. 2004, 30, 115−133. (5) Morozov, I. S.; Ivanova, I. A.; Lukicheva, T. A. Actoprotector and Adaptogen Properties of Adamantane Derivatives (A Review). Pharm. Chem. J. 2001, 35, 235−238. (6) Amantadine hydrochloride: https://www.ncbi.nlm.nih.gov/ medgen/181680 (accessed on December 20, 2016). (7) Bazyleva, A. B.; Blokhin, A. V.; Kabo, A. G.; Kabo, G. J.; Emel’yanenko, V. N.; Verevkin, S. P. Thermodynamic properties of 1aminoadamantane. J. Chem. Thermodyn. 2008, 40, 509−522. (8) Gobble, C.; Rath, N.; Chickos, J. The Vaporization Enthalpies and Vapor Pressures of Some Primary Amines of Pharmaceutical Importance by Correlation Gas Chromatography. J. Chem. Eng. Data 2013, 58, 2600−2609. (9) Harvey, P. D.; Gilson, D. F. R.; Butler, I. S. A study of the phase transition and molecular motion in adamantanamine hydrochloride. J. Phys. Chem. 1987, 91, 1267−1270. (10) Bélanger-Gariépy, F.; Brisse, F.; Harvey, P. D.; Butler, I. S.; Gilson, D. F. R. Structure of adamantanamine hydrochloride at 143 K. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1987, C43, 756−759. (11) Parsonage, N. G.; Staveley, L. A. K. Disorder in Crystals; Clarendon Press: Oxford, 1978.

5. CONCLUSIONS High-precision thermodynamic properties of crystalline amantadine hydrochloride, including condensed-phase heat capacity, thermodynamic parameters of solid-to-solid phase transitions, decomposition, and formation are reported for the first time. These results comprising a combination of careful experimental measurements and molecular simulations have been validated where possible and should be of considerable interest to the pharmaceutical industry, where they can be applied to the optimization of production and storage conditions for this active pharmaceutical ingredient.

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AUTHOR INFORMATION

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00107. Experimental heat capacities of crystalline amantadine hydrochloride measured in the adiabatic calorimeter (Table S1) and differential scanning calorimeter (Table S2) as well as molecular and spectral parameters from quantum chemical calculations (Table S3) (PDF) I



Article

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