J. Phys. Chem. A 2011, 115, 535–539
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Dynamic Characteristic of Amitriptyline in Water by Ultrasonic Relaxation Method and Molecular Orbital Calculation Sadakatsu Nishikawa*,† and Eri Kamimura‡ Nishikyushu UniVersity Junior College, Saga, 840-0806, Japan, and Department of Chemistry and Applied Chemistry, Faculty of Science and Engineering, Saga UniVersity, Saga, 840-8502, Japan ReceiVed: NoVember 11, 2010
Ultrasonic absorption coefficients in the frequency range of 0.8-220 MHz have been measured in aqueous solution of amitriptyline (3-(10,11-dihydro-5H-dibenzo[a,d]cycloheptene-5-ylidene)-N,N-dimethyl-1propanamine) in the concentration range from 0.20 to 0.60 mol dm-3 at 25 °C. A single relaxational phenomenon has been observed, and the relaxation frequency is independent of the concentration. It has been also observed that the amplitude of the relaxational absorption increases linearly with the analytical concentration. From these ultrasonic relaxation data, it has been concluded that the relaxation is associated with a unimolecular reaction due to a conformational change of the solute molecule, such as a structural change due to a rotational motion of a group in the solute molecule. Molecular orbital semiempirical methods using AM1 (Austin model 1) and PM3 (modified neglect of diatomic overlap parametric method 3) have been applied to obtain the standard enthalpy of formation for amitriptyline molecule at various dihedral angles around one of the bonds in alkylamine side chain. The results have shown the two clear minimum standard enthalpies of formation for amitriptyline. From the difference of the two values, the standard enthalpy change between the two stable conformers has been calculated be 2.9 kJ mol-1. On a rough assumption that the standard enthalpy change reflects the standard free energy change, the equilibrium constant for the rotational isomers has been estimated to be 0.31. Combining this value with the experimental ultrasonic relaxation frequency, the backward and forward rate constants have been evaluated. The standard enthalpy change of the reaction has been also estimated from the concentration dependence of the maximum absorption per wavelength, and it has been close to that calculated by the semiempirical methods. The ultrasonic absorption measurements have been also carried out in amitriptyline solution in the presence of β-cyclodextrin. However, the ultrasonic relaxation has not been found in the above frequency range. The result has been discussed in relation to the host-guest complex formation between β-cyclodextrin and amitriptyline. 1. Introduction On the line of our research series for dynamic interaction between host and guest, cyclodextrin as host and various guest molecules as guest have been chosen, and an ultrasonic relaxation method with a wide frequency range has been applied to clarify the dynamical mechanism of complex formation by host and guest.1-4 Chemical relaxation methods, one of which is the ultrasonic relaxation method, have been widely used to investigate such reactions in solutions.5-7 The advantages of the ultrasonic method are that no indicator is necessary for monitoring the reaction process and that a special solvent is not needed. Small perturbation of chemical equilibrium by applying weak sound wave to chemical systems provides useful information occurring in liquids or solutions as a response of the ultrasonic relaxation. To further our research, we have desired to see how well-known drugs can be applicable when the molecular size of drug is taken into account for drug delivery system. Manzo et al.8 have examined the detail properties of amitriptyline (3-(10,11-dihydro-5H-dibenzo[a,d]cycloheptane-5ylidene)-N,N-dimethyl-1-propanamine), which is a tricyclic * To whom correspondence should be addressed. E-mail: nishikawasa@ nisikyu-u.ac.jp. † Nishikyusyu University Junior College. ‡ Saga University.
antidepressant belonging to the first generation of antidepressant drugs. Junquera and et al.9 have reported that the amitriptyline molecule may aggregate and forms a complex with β-cyclodextrin. Din et al.10 have published the interaction between amitriptyline and surfactants. These research results have provided useful and important information in relation to biological activities of drugs. Most of this research has been carried out by static experimental methods. Another point that should be stressed is the clarification of the dynamic characteristics for a drug delivery system. However, much dynamic information has been published previously, and the effect of the size of guest molecules is not so evident kinetically. According to the published kinetic results, the complexation reaction between a host and guest is becoming clarified very rapidly, and the ultrasonic relaxation method is a very effective tool to receive such dynamic information.11,12 The time range associated with the host-guest interaction is just fitted, and the dynamic process is clearly observed. We have considered that an aqueous system with amitriptyline and β-cyclodextrin is appropriate for kinetic investigation by the ultrasonic relaxation method. In this paper, the results of the ultrasonic absorption and velocity in aqueous solution of amitriptyline and in solution along with β-cyclodextrin are reported.
10.1021/jp1107729 2011 American Chemical Society Published on Web 12/27/2010
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J. Phys. Chem. A, Vol. 115, No. 4, 2011
Nishikawa and Kamimura
Figure 1. The structure of amitriptyline. The axis of the bond between 30C and 33C has been rotated, and the heat of formation has been calculated.
2. Experimental Section Chemicals. Amitriptyline and β-cyclodextrin (β-CD) were purchased from Wako Pure Chemical Co. Ltd. Amitriptyline was used without further purification, and β-CD was purified as described elsewhere.12,13 Sample solutions were prepared by weighing and water distilled and filtered by a Milli-Q SP-TOC filter system from Japan Millipore Ltd. was used as a solvent. Flasks with the sample solutions were filled with N2 gas, and then they were kept in a refrigerator until measurements were performed. The structure of amitriptyline molecule is shown in Figure 1. The numbers on carbon, nitrogen and hydrogen atoms are put conveniently. Apparatus. The measurements of the ultrasonic absorption coefficients were carried out by the resonance method in the frequency range from about 0.8 to 9 MHz. The pulse method was used the measurements in the range from 15 to 220 MHz. Dry N2 gas was circulated gently in most of the measurement cells. More details about the absorption apparatus and the procedure for determining the absorption coefficient, R, are described elsewhere.14,15 Sound velocity values were obtained by the resonator at around 3 MHz, and the solution densities were measured by a vibrating density meter (Anton Paar DMA 60/602). All the measurements were performed at 25 °C. Calculation. Semiempirical quantum chemical methods by AM1 (Austin model 1) and PM3 (modified neglect of diatomic overlap parametric method 3) were applied to determine the standard enthalpy of formation for the amitriptyline molecule with the help of the free software “Winmostar”. The calculation was carried out in a vacuum environment because our small computer ability is out of the calculation in aqueous environment, and a rough value of the standard enthalpy change of reaction was desired. It is also possible to calculate the values of the entropy of the target molecule by the program in the same package. However, it is not applied because oversimplifications are used in the entropy calculation. 3. Results and Discussion The adiabatic compressibility of solution, κs, is obtained from the values of the sound velocity, V, and density, F, using the
Figure 2. The concentration dependence of the compressibility in aqueous solution of amitriptyline at 25 °C.
Laplace equation as κs ) 1/(FV2). Figure 2 shows the plots of the compressibility as a function of the concentration. An intersection in the concentration dependence has been found at 0.04 mol dm-3. This break concentration is very close to those observed by the conductivity measurement.9,10,16 It has been said that aggregates exist above this concentration, and the aggregation number has been also predicted to be less than 10. It is not so simple to determine the aggregation number from the compressibility data.17-19 Further theoretical background for the interpretation of the aggregation number in solution seems to be necessary. In the concentration range
