Determination of micelle formation of ketorolac tromethamine in aqueous media by acoustic measurements

Thermochimica Acta 552 (2013) 5–9

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Determination of micelle formation of ketorolac tromethamine in aqueous media by acoustic measurements Gokhan Savaroglu a,∗ , Lütfi Genc b a b

Eskisehir Osmangazi University, Department of Physics, 26480 Eskisehir, Turkey Anadolu University, Faculty of Pharmacy, Department of Pharmaceutical Technology, 26470 Eskisehir, Turkey

a r t i c l e

i n f o

Article history: Received 27 June 2012 Received in revised form 8 November 2012 Accepted 9 November 2012 Available online 20 November 2012 Keywords: Isentropic compressibilities Speeds of sound Micellization Ketorolac tromethamine Critical micelle concentration

a b s t r a c t Density and speed of sound of ketorolac tromethamine in aqueous solutions have been measured as a function of concentration at atmospheric pressure and in the temperature range from 293.15 to 313.15 K. Apparent molar volumes, apparent isentropic compressibility and isentropic compressibility values have also been calculated from the experimental density and speed of sound data. Partial molar volume and partial molar isentropic compressibility are obtained from fitting procedures the data on apparent molar volume, V , and apparent isentropic compressibility, K(S) . Partial molar volume, V0 , and partial molar 0 isentropic compressibility, k(S) , are informative thermodynamic characteristics that reflect solute hydration. The critical micelle concentration (CMC) was determined from speed of sound data by an analytical method based on the Phillips definition of the CMC. Using these results, it was possible to establish the solvent–drug interactions. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The thermodynamic behaviour of surface active drugs in aqueous solutions is important from standpoint. In last year’s an interest in properties of these drugs has been greatly renewed, particularly for penicillin and phenothiazine drugs. Above a critical micelle concentration (CMC) these drugs form aggregates may be useful in a number of therapeutic applications [1–3]. The thermodynamic parameters governing the aggregate formation are the key to effective physical processing. Furthermore, from an understanding of aggregation one can gain better insights into the influence of the hydrophobe structure on the association mode of amphiphiles. The colloidal properties of these amphiphilic compounds are largely determined by the nature of the aromatic ring systems of their hydrophobic moieties, and such compounds are useful in probing the relationship between molecular architecture and physicochemical properties. The investigating the possibility of aggregation of bioactive molecules is important for drugs formulations, their bactericidal activity and chemical stability [4]. Ketorolac tromethamine (KT) is a member of the pyrrolopyrrole group of nonsteroidal anti-inflammatory drugs (NSAIDs). The chemical name for KT is (±)-5-benzoyl-2,3-dihydro-1Hpyrrolizine-1-carboxylic acid, compound with

∗ Corresponding author. Tel.: +90 2222393750/2809; fax: +90 2222393578. E-mail address: [email protected] (G. Savaroglu). 0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2012.11.008

2-amino-2-(hydroxymethyl)-1,3-propanediol chemical structure is:

(1:1),

and

the

KT is a racemic mixture of [−]S and [+]R KT. KT may exist in three crystal forms. All forms are equally soluble in water. KT has a pKa of 3.5 and an n-octanol/water partition coefficient of 0.26. The molecular weight of KT is 376.41. Its molecular formula is C19 H24 N2 O6 [5,6]. UV spectra-photometric method was used for the assay of KT. The understanding of aqueous solutions needs to be taken into account the volumetric and acoustic properties. In the present study, speed of sound measurements are used to determinate for the CMC of KT aqueous solution at the temperature range 293.15–313.15 K. The data are analyzed using the Phillips definition of the CMC combined with a recently developed numerical algorithm [7]. We has also been reported partial molar volume, isentropic compressibility in the different concentrations of KT aqueous solution. Volumetric and isentropic compressibility results have been interpreted in terms of electrostriction of solvent, solvation of surfactant and the compressibility of micellar aggregates.

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G. Savaroglu, L. Genc / Thermochimica Acta 552 (2013) 5–9

Table 1 Density, , of KT aqueous solutions at different temperatures.  (kg m−3 ) m (mol kg−1 )

0 0.010 0.020 0.030 0.040 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.250

T (K) 293.15

298.15

303.15

308.15

313.15

998.19 999.38 1000.35 1001.41 1002.57 1003.30 1006.13 1008.75 1011.43 1014.02 1016.56 1019.22 1024.63

997.03 998.20 999.17 1000.21 1001.23 1002.07 1004.88 1007.46 1010.10 1012.67 1015.19 1017.80 1023.16

995.64 996.79 997.75 998.78 999.83 1000.62 1003.40 1005.95 1008.54 1011.11 1013.63 1016.15 1021.49

994.02 995.17 996.11 997.13 998.13 998.96 1001.71 1004.24 1006.74 1009.34 1011.84 1014.32 1019.63

992.21 993.34 994.28 995.29 996.22 997.10 999.82 1002.31 1004.79 1007.39 1009.86 1012.32 1017.59

2. Experimental KT was obtained from Dr. Reddy’s laboratories LTD (high quality USP version, purity: 99%). Solution was prepared by completely dissolving in degassed deionised water at room temperature. The solutions in this study were also prepared by mass using an electronic balance (Scaltec, SBC22) accurate to 0.01 mg. Concentrations (noted mi ) are expressed in terms of molality (mol kg−1 ). The density and speed of sound values were measured using an Anton Paar DSA-5000, the temperature was automatically kept constant within ±0.01 K. Measurements of densities and speed of sound of the aqueous solutions of KT in the range of temperature T = 293.15–313.15 K were taken as a function of those of concentration. The calibration of the apparatus was carried out with air and double-distilled water. The uncertainties in density and speed of sound measurements were within ±1.10−2 kg m−3 and ±0.5 m s−1 , respectively. The reproducibility of the density and speed of sound values were found to be within 1.10−3 kg m−3 and 0.1 m s−1 respectively. 3. Calculations The apparent molar volumes V of KT in water with different concentrations were calculated by means of the following relations, V =

∗ −  M + m ·  · ∗ 

(1)

where M is the molar mass of the solute, m (mol kg−1 ) is molality of KT in solution, * and  are density of solvent and solution, respectively. Isentropic compressibilities, S , was calculated from the density and speed of sound values, using the Laplace equation S =

1 u2

(2)

where u is speed of sound and  is the density of solution. Apparent molar isentropic compressibities, K(S) , were calculated by means of the following equation K(S) =

S − S∗ m∗

+ V,2 S

(3)

The respective values of S and S∗ denote the isentropic compressibilities of the solution and of the solvent. 4. Results and discussion Tables 1–3 present the values of the density, , speed of sound, u, and isentropic compressibilities, S , for KT aqueous solution in a temperature range of 293.15–313.15 K at atmospheric pressure. Fig. 1 shows the speeds of sound, u, as a functions of molality, m, for KT aqueous solution in temperature range from 293.15 to 313.15 K. Rassing and Attwood [8] have shown that the speed of sound is very sensitive to the onset of association processes induced by increasing temperature or concentration. The speed of sound, u, is smaller in solutions containing aggregates and monomeric species than those containing monomeric species only. Value of

Table 2 Speed of sound, u, of KT aqueous solutions at different temperatures. u (m s−1 ) m (mol kg−1 )

0 0.010 0.020 0.030 0.040 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.250

T (K) 293.15

298.15

303.15

308.15

313.15

1482.6 1485.6 1486.8 1488.7 1491.0 1492.1 1497.4 1501.5 1506.0 1509.9 1514.6 1518.9 1525.6

1496.8 1499.7 1500.7 1502.5 1504.7 1505.7 1510.7 1514.5 1518.8 1522.5 1527.1 1531.4 1537.4

1509.2 1512.0 1512.9 1514.6 1516.7 1517.6 1522.3 1525.8 1530.0 1533.4 1538.0 1542.3 1547.6

1520.0 1522.5 1523.3 1524.9 1527.0 1527.7 1532.2 1535.5 1539.4 1542.7 1547.2 1550.8 1556.0

1529.1 1531.5 1532.2 1533.7 1535.7 1536.3 1540.5 1543.6 1547.3 1550.4 1554.6 1558.1 1563.0

G. Savaroglu, L. Genc / Thermochimica Acta 552 (2013) 5–9

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Table 3 Isentropic compressibility, S , of KT aqueous solutions at different temperatures. S (T Pa−1 ) m (mol kg−1 )

T (K)

0 0.010 0.020 0.030 0.040 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.250

293.15

298.15

303.15

308.15

313.15

455.8 453.4 452.2 450.6 448.7 447.7 443.3 439.7 435.9 432.6 428.8 425.3 419.3

447.7 445.4 444.4 442.9 441.1 440.2 436.0 432.7 429.2 426.0 422.4 418.9 413.5

441.0 438.8 437.9 436.4 434.8 433.9 430.1 427.0 423.6 420.6 417.1 413.7 408.7

435.4 433.5 432.6 431.3 429.7 428.9 425.2 422.3 419.2 416.3 412.9 409.9 405.1

431.0 429.2 428.4 427.1 425.6 424.9 421.5 418.7 415.7 413.0 409.7 406.9 402.3

CMCs were detected by speed of sound and determined by an analytical method based on the Phillips definition of the CMC [9]:



=0

(4)

m=CMC

The numerical analysis of the data was made by means of developed algorithm based on the Runge–Kutta numerical integration method and Levenberg–Marquardt least-squares fitting algorithm which allows the determination of precise values (±0.05%) of the CMC’s [7]. Fig. 2 shows the speed of sound data versus molal concentration, m, and a Gaussian fit of its second derivative, at the temperature of 298.15 K. CMC derived in this way from the speed of sound data in the temperatures range of 293.15–313.15 K are shown in Table 4. Fig. 3 shows the apparent molar volumes, V , of KT aqueous solution with different concentrations in temperature range 293.15–313.15 K. This plot gives a general overview of the aggregation behaviour of the KT aqueous solution. The plot of apparent molar volumes, V , against concentration reveals structural changes occurring in KT aqueous solution and shows that the aggregation process is dependent on temperature. The concentration dependence of apparent molar volumes, V , reflects the nature of solute–solute interactions. At concentrations below the CMC, apparent molar volumes, V , increase until the critical concentration of KT; this region is characteristic of

1540 1535 1530 1525 -1

d3 u dm3

u/m.s



the monomeric to micellar state: this last behaviour is characteristic of the aggregate state and indicates that the micelle-only domain has been reached. After the CMC, there is decrease in V that increases with the concentration, may be related with

1520 1515 1510 1505 1500 1495 0.00

0.05

0.10

0.15

0.20

0.25

-1

m/mol.kg

Fig. 2. Speed of sound, u, versus concentration, m, for KT aqueous solutions. 䊉, T = 298.15 K. The dotted indicates the Gaussian fit of the second derivative of the speed of sound against molality. Arrow shows point of the CMC. 280

1565

278

1560 1555

276

1550

274

1545

272 -1

1540

1525 1520 1515 1510

270

3

1530

268

-6

Vφ.10 /m .mol

u/m.s

-1

1535

266 264 262

1505 1500

260

1495

258

1490 0.00

0.05

0.10

0.15

m/mol.kg

0.20

0.25

-1

Fig. 1. Speed of sound, u, versus concentration, m, for KT aqueous solutions. , T = 293.15 K; 䊉, T = 298.15 K; , T = 303.15 K; , T = 308.15; , T = 313.15 K.

256 0.00

0.05

0.10

0.15

0.20

0.25

-1

m/mol. kg

Fig. 3. Apparent molar volumes, V , of KT aqueous solution. , T = 293.15 K; 䊉, T = 298.15 K; , T = 303.15 K; , T = 308.15 K; , T = 313.15 K.

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G. Savaroglu, L. Genc / Thermochimica Acta 552 (2013) 5–9

Table 4 CMC, apparent molar volumes of the monomer at infinite dilution, V0 , coefficients, AV and BV , with standard deviation, , apparent molar volumes in aggregate, Vm , and

change of apparent molar volume, Vm , of KT at different temperatures. T (K)

293.15 298.15 303.15 308.15 313.15

CMC (mmol kg−1 )

V0 × 10−6

(m3 mol−1 )

AV × 10−6 (kg1/2 m3 mol−3/2 )

BV × 10−6 (kg m3 mol−2 )

 × 10−6 (m3 mol−1 )

(m3 mol−1 )

Vm × 10−6

(m3 mol−1 )

Vm × 10−6

41.6 41.4 42.8 43.2 43.3

231.3 (±28.3) 233.1 (±16.1) 238.6 (±19.2) 233.3 (±16.8) 237.3 (±12.4)

348.7 (±368.1) 344.5 (±209.5) 303.0 (±250.1) 379.1 (±219.4) 352.8 (±161.9)

−771.2 (±1132.9) −734.3 (±644.8) −634.5 (±769.8) −841.4 (±675.4) −765.9 (±498.3)

2.9 1.6 1.9 1.7 1.3

282.7 284.0 284.0 288.5 288.7

51.4 50.9 45.4 55.2 51.4

Parentheses indicate standard errors.

0

-1

-2

3

1/2

+ AV m

+ BV m

(5)

where V0 is the apparent molar volume at infinite dilution, AV is the Debye–Hückel limiting law coefficient, BV is adjustable related to a pair interaction [11] and equivalent to the second virial coefficient which measures the deviation from the limiting law because of non-electrostatic solute–solute interaction. V0 , AV and BV are obtained from the least squares methods by using the V numerical values together with their standard errors. Values of V0 , AV and BV for the KT aqueous solution are summarized in Table 4. BV coefficient is generally negative except for hydrogen-bonding interaction [12]. The values of BV are negative in all temperature range 293.15–313.15 K. In the literature, there are positive values of BV that lead to dimerization in the premicellar region for different amphiphiles [13,14] as well as there are negative values of BV which supports the non-existence of dimers [15,16]. The sign of parameter BV could be associated with the presence of dimers in the premicellar region. The more negative BV values indicates that is not presence of dimer in the premicellar region. According to these results we assumed that the total drug concentration is to be the same as monomer (aqueous phase) drug concentration. Assuming the pseudo phase model of micellization, the apparent molar volume of the amphiphilic solutes can be expressed by the following equations: V = Vm +

CMC 0 [V − Vm ] m

(6)

where Vm is the apparent molar volume of the monomer in the aggregate. The value of V is nearly not concentration-dependent in the concentration range above CMC. The apparent molal volume of the drug in the micelle, Vm , at the points in the CMC/m ≤ 1 region were determined from the least squares methods by using the V numerical values. The change in apparent molar volume associated with the formation of stable aggregate of an amphiphilic drug was taken to be Vm = Vm − V0 . Values obtained for Vm and Vm are shown at different temperature in Table 4. The Vm values of the KT aqueous solution were positive at different temperature under study. This shows that the structure of micelles is looser than that of the monomers at all temperature under study. Fig. 4 shows plots of apparent molar isentropic compressibilities, K(S) , against concentrations in temperature range

-14

V =

V0

-4

-1

Kφ (S).10 /m .Pa .mol

a structural rearrangement of the aggregates previously formed. To approximately 0.05 mol kg−1 , V increases sharply, and from approximately 0.05 mol kg−1 it decreases steadily. V increases with rising temperature. Since it is accepted that a viral expansion is used for partial or apparent molar quantities. In the premicellar region, the values of V can be expressed as [10]

-6 -8 -10 -12 0.00

0.05

0.10

0.15

0.20

0.25

-1

m/mol. kg

Fig. 4. Apparent molar isentropic compressibilities, K(S) , of KT aqueous solution., T = 293.15 K; 䊉, T = 298.15 K; , T = 303.15 K; , T = 308.15 K; , T = 313.15 K.

293.15–313.15 K. The apparent molar isentropic compressibilities 0 ,can be estimated using Eq. (7): at infinite dilution, K(S) 0 K(S) = K(S) + AK m1/2 + BK m

(7)

where AK is the Debye-Hückel limiting law coefficient and BK is adjustable parameters that represent the deviations from the 0 , A and B are obtained from the least limiting law. Parameter K(S) K K 0 , squares methods by using the K(S) numerical values and K(S)

AK and BK values together with their standard errors are given in Table 5. According to our knowledge, there is no similar results for the parameters AK and BK for the same sample under the same condition [17,18]. This is the reason for applying Eq. (7) with AK and 0 BK free parameters. The K(S) values are negative for the KT aqueous solution at all temperatures. The apparent molar isentropic compressibilities, at infinite dilution, supply insight into the compressibility of hydration layer around the solute molecule, since the solute intrinsic compressibility is assumed to be zero [19]. In the solute with more negative compressibility, the occurrence of 0 strong hydration is suggested. The increasing of K(S) with increasing temperature. This behaviour is a consequence of a decrease in the extent of structuring of water at higher temperatures. In the postmicellar region, an equation similar to Eq. (6) for the values of K(S) has been applied. The values of K(S) have been fitted to the function m + K(S) = K(S)

CMC 0 m ] [K(S) − K(S) m

(8)

m where K(S) is the value of the apparent molar isentropic comm pressibilities of monomers at the aggregations concentration. K(S)

values were calculated by using same procedure with the Vm .

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Table 5 0 (with standard deviation, ), AK and BK parameter, apparent molar isentropic compressApparent molar isentropic compressibilities of monomer at infinite dilution, K(S)

m m ibilities of monomers at the aggregations concentration, K(S) , and change of apparent molar isentropic compressibilities, K(S) , of KT at different temperatures.

T (K)

293.15 298.15 303.15 308.15 313.15

0 K(S) × 10−14

(m3 Pa−1 mol−1 )

AK × 10−14 (kg1/2 m3 Pa−1 mol−3/2 )

BK × 10−14 (kg m3 Pa−1 mol−2 )

 × 10−14 (m3 Pa−1 mol−1 )

m K(S) × 10−14

(m3 Pa−1 mol−1 )

(m3 Pa−1 mol−1 )

m × 10−14 K(S)

−33.6 (±10.5) −33.1 (±9.8) −31.3 (±9.8) −27.2 (±9.7) −25.9 (±9.0)

292.0 (±137.2) 301.1 (±127.3) 291.3 (±128.1) 262.1 (±125.7) 256.1 (±256.1)

−730.2 (±422.3) −759.3 (±391.7) −735.1 (±394.2) −668.9 (±386.9) −652.8 (±362.3)

1.1 1.0 1.0 1.0 0.9

9.2 10.2 10.8 10.2 10.6

42.8 43.3 42.1 37.4 36.5

Parentheses indicate standard errors.

The change in the apparent molar isentropic compressibilities of aggregation, K(S) , can be evaluated from m 0 K(S) = K(S) − K(S)

(9)

m for the KT aqueous solution Values obtained for K(S) and K(S)

m at all temperatures are listed in Table 5. K(S) and K(S) values

are positive in the range of temperature studied. The positive valm ues of K(S) are indicated that water molecules surrounding the monomer become bulk water. K(S) values decrease as the temperature increases. This decrease is mainly as a consequence of a 0 m due to dehydration of the higher increase of K(S) than that of K(S) ionic head groups. 5. Conclusions The Phillips definition model was used to investigate the impact of premicellar association on the use of the speed of sound for the determination of critical micelle concentrations. As it is shown in Table 3, the decrease in isentropic compressibility values with an increase in temperature may be due to thermal rupture of water clusters which may cause the formation of a smaller cluster of water molecules leading to the compact clusters at higher temperatures. 0 may be due to the hydration of KT as the hydrated The negative K(S) water molecules appear to be less compressible than the bulk water (Table 5.). The V0 values of KT aqueous solution increase with an increase in temperature suggests the corresponding reduction of electostricted water molecules. Interactions of drugs with their environmental conditions (temperature, solvent) play an important role in their conformational characteristics. The most important of those are between solute (drug) and solvent molecules. The study of these interactions provides important insight into the stability and their behaviour during the formulation. References [1] P. Taboada, M. Gutierrez-Pichel, S. Barbosa, D. Attwood, V. Mosquera, Effect of temperature on the volume and compressibilities of some amphiphilic penicillins in aqueous solution, Phys. Chem. Chem. Phys. 5 (2003) 703–709.

[2] P. Taboada, D. Attwood, M. Garcia, M.N. Jones, J.M. Ruso, V. Mosquera, F. Sarmiento, Thermodynamics of association of structurally related amphiphilic penicillins, J. Colloid Interface Sci. 221 (2000) 242–245. [3] V. Mosquera, J.M. Ruso, D. Attwood, M.N. Jones, G. Prieto, F. Sarmiento, Thermodynamics of micellization of surfactants of low aggregation number: the aggregation of propranolol hydrochloride, J. Colloid Interface Sci. 210 (1999) 97–102. [4] L.M. Varela, C. Rega, M.J. Suarez-Filloy, J.M. Ruso, G. Prieto, D. Attwood, F. Sarmiento, V. Mosquera, Self-association of penicillin V in aqueous solution, Langmuir 15 (1999) 6285–6290. [5] U. Pharmacists’, Pharmacopeia, US Pharmacopeial Convention, Inc., Rockville, MD, 2008. [6] H. Use, T. Side-effects, W. Contra-indications, Martindale: the Complete Drug Reference, 2007. [7] M. Perez-Rodriguez, G. Prieto, C. Rega, L.M. Varela, F. Sarmiento, V. Mosquera, A comparative study of the determination of the critical micelle concentration by conductivity and dielectric constant measurements, Langmuir 14 (1998) 4422–4426. [8] D. Attwood, L. Johansen, J.A. Tolley, J. Rassing, A new ultrasonic method for the measurement of the diffusion-coefficient of drugs within hydrogel matrices, Int. J. Pharm. 9 (1981) 285–294. [9] J.N. Phillips, The energetics of micelle formation, Trans. Faraday Soc. 51 (1955) 561–569. [10] K.L. Mittal, Solution Chemistry of Surfactants, Plenum Publishing Corporation, 1979. [11] T.S. Brun, H. Hoiland, E. Vikingstad, Partial molal volumes and isentropic partial molal compressibilities of surface-active agents in aqueous solution, J. Colloid Interface Sci. 63 (1978) 89–96. [12] G.M. Musbally, G. Perron, J.E. Desnoyers, Apparent molal volumes and heat capacities of ionic surfactants in water at 25 ◦ C, J. Colloid Interface Sci. 48 (1974) 494–501. [13] P. Taboada, D. Attwood, J.M. Ruso, M. Garcia, V. Mosquera, Thermodynamic properties of some antidepressant drugs in acqueous solution, Langmuir 17 (2001) 173–177. [14] D. Attwood, V. Mosquera, M. Garcia, M.J. Suarez, F. Sarimento, Comparison of the micellar properties of structurally related antidepressant drugs, J. Colloid Interface Sci. 175 (1995) 201–206. [15] K. Fukada, J. Li, M. Fujii, T. Kato, T. Seimiya, Adiabatic compressibility of aqueous solutions of amphiphiles with an ammonium group as the hydrophilic domain, J. Oleo Sci. 51 (2002) 103–111. [16] G. González-Gaitano, A. Guerrero-Martínez, F. Ortega, G. Tardajos, Thermodynamic and spectroscopic study of a molecular rotaxane containing a bolaform surfactant and ␤-cyclodextrin, Langmuir 17 (2001) 1392–1398. [17] R. Zana, Micelles and microemulsions – review of recent structural and dynamic results in relation with reactivity, J. Chim. Phys. Phys. Chim. Biol. 83 (1986) 603–612. [18] D.J. Bradley, K.S. Pitzer, Thermodynamics of electrolytes. 12. Dielectric properties of water and Debye–Huckel parameters to 350 degree C and 1 kbar, J. Phys. Chem. 83 (1979) 1599–1603. [19] A. González-Pérez, J.M. Ruso, G. Prieto, F. Sarmiento, The self-aggregation of sodium perfluorooctanoate in aqueous solution at different temperatures, J. Surfactants Deterg. 7 (2004) 387–395.