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Dihedral Angle of Lens and Interfacial Tension of Air/Long Chain Alcohol/Water Systems Makoto Aratono,* Takayuki Toyomasu, Takeo Shinoda, Norihiro Ikeda,† and Takanori Takiue Department of Chemistry, Faculty of Science, Kyushu University 33, Fukuoka 812-81, Japan Received June 17, 1996. In Final Form: January 17, 1997X The dihedral angle of an alcohol lens at the air/water interface and the three kinds of interfacial tensions of air/1-octanol/water and air/1-decanol/water systems have been measured as a function of temperature from 288.15 to 313.15 K at 2.5 K intervals under atmospheric pressure. In order to measure a dihedral angle, the new experimental apparatus was constructed and the new procedure was adopted. By comparing the dihedral angles measured with those calculated by applying Neumann’s relations to the interfacial tension values, it was concluded that the dihedral angle measurement was performed with a satisfactory accuracy. The properties of the interfacial film and also the occurrence of the intruding of water phase on the air/alcohol interface were discussed.

Introduction The shape of a liquid lens resting at a liquid-fluid interface depends on the properties of three kinds of interfaces and the three-phase contact line in the system. It has been shown that the shape of a lens is highly useful to shed light on the wetting and nonwetting phenomena of not only the simple systems1-7 but also the complex systems such as water/oil/nonionic amphiphile mixtures.8-19 However, accurate measurements of dihedral angles are not easy because the contact of a lens with a glass wall of a cell distorts the shape of the lens and also the meniscus at the glass wall distorts the image of a lens. Therefore it is very desirable to measure the dihedral angles of a lens as accurate as possible. In this study, the new apparatus was constructed and the drop shape analysis based upon Young-Laplace equation was adopted to estimate the angles. These experimental improvements diminished greatly the error * To whom correspondence should be addressed at Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki 6-10-1, Higashiku, Fukuoka 812-81, Japan. E-mail address: [email protected]. †Present address: Department of Environmental Science, Faculty of Human Environmental Science, Fukuoka Women’s University, Fukuoka 813, Japan. X Abstract published in Advance ACS Abstracts, March 15, 1997. (1) Moldover, M. R.; Cahn, J. W. Science 1980, 207, 1073. (2) Pohl, D. W.; Goldburg, W. I. Phys. Rev. Lett. 1982, 48, 1111. (3) Seeto, Y.; Puig, J. E.; Scriven, L. E.; Davis, H. T. J. Colloid Interface Sci. 1983, 96, 360. (4) Schmidt, J. W. J. Chem. Phys. 1986, 85, 3631. (5) Kahlweit, M.; Busse, G.; Haase, D.; Jen, J. Phys. Rev. A 1988, 38, 1395. (6) Estrade-Alexanders, A.; Garcı´a-Valenzuela, A.; Guzma´n, F. J. Phys. Chem. 1991, 98, 5028. (7) Amara, M.; Privat, M.; Bennes, R.; Tronel-Peyroz, E. J. Chem. Phys. 1993, 98, 5028. (8) Widom, B. Langmuir 1987, 3, 12. (9) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D.; Jen, J.; Schoma¨cker, R. Langmuir 1988, 4, 499. (10) Robert, M.; Jeng, J. F. J. Phys. (Paris) 1988, 49, 1821. (11) Kahlweit, M.; Busse, G. J. Chem. Phys. 1989, 91, 1339. (12) Chen, L.-J.; Jeng, J. -F.; Robert, M.; Shukla, K. P. Phys. Rev. A 1990, 42, 4716. (13) Smith, D. H.; Covatch, G. L. J. Chem. Phys. 1990, 93, 6870. (14) Aratono, M.; Kahlweit, M. J. Chem. Phys. 1991, 95, 8578; 1992, 97, 5932(E). (15) Chen, L.-J.; Hsu, M.-C. J. Chem. Phys. 1992, 97, 690. (16) Kahlweit, M.; Strey, R.; Busse, G. Phys. Rev. E 1992, 47, 4197. (17) Chen, L.-J.; Yan, W.-J. J. Chem. Phys. 1993, 98, 4830. (18) Chen, L.-J.; Yan, W.-J.; Hsu, M.-C.; Tyan, D.-L. J. Phys. Chem. 1994, 98, 1910. (19) Chen, L.-J.; Hsu, M.-C.; Lin, S.-T.; Yang, S.-Y. J. Phys. Chem. 1995, 99, 4687.

S0743-7463(96)00595-1 CCC: $14.00

of angle values. We chose the ternary three-phase systems of air/long chain alcohol/water because the long chain alcohol/water interfaces have been studied in our previous papers20,21 and the experiments on ternary systems were relatively simple. Furthermore, in order to examine how accurately the values of dihedral angles are measured and to clarify the state of the interfacial films coexisting in equilibrium, the interfacial tension of the system was measured accurately by the pendant drop technique. Experimental Section 1. Materials. 1-Octanol (C8OH) and 1-decanol (C10OH) were the highest grade (Tokyo Kasei Kogyo Co., Ltd.) and distilled fractionally under reduced pressure. Their boiling points were 99-100 °C at 20 mmHg and 87-88 °C at 3 mmHg, respectively, and their purities were estimated to be more than 99.9% by a gas-solid chromatography. Water was distilled three times; the second and the third distillations were done from alkaline permanganate solution. 2. Interfacial Tension. Let the symbols γAO, γAW, and γOW represent the interfacial tensions of the air/alcohol (A/O), air/ water (A/W), and alcohol/water (O/W) interfaces, respectively. The interfacial tension was measured by the pendant drop technique22 within (0.05 mN m-1 as a function of temperature from 288.15 to 313.15 ((0.01) K at 2.5 K intervals under atmospheric pressure. In order to obtain the complete equilibrium and phase separation at a desired temperature, an appropriate amount of the mixture of water and alcohol was stirred by a magnetic rotor for about 40 min in the measurement glass cell and then left alone for about 20 min before making the pendant drop. Since even feeble vibration caused a serious error of the interfacial tension, the apparatus for the measurement was settled onto vibration absorbers. 3. Dihedral Angle. The dihedral angle θO interposing the alcohol phase was measured as a function of temperature from 288.15 to 313.15 ((0.01) K at 2.5 K intervals under atmospheric pressure. 3.1. Apparatus. A block diagram of the apparatus for the dihedral angle measurement is given in Figure 1: a liquid lens in the optical cell is illuminated by the light and its silhouette is introduced into the video camera through the objective lens and the bellows. The image from the camera is further digitized by the computer. The details of the experimental setup are as follows: the light source (a tungsten lamp for a microscope, (20) Aratono, M.; Takiue, T.; Ikeda, N.; Nakamura, A.; Motomura, K. J. Phys. Chem. 1992, 96, 9422. (21) Aratono, M.; Takiue, T.; Ikeda, N.; Nakamura, A.; Motomura, K. J. Phys. Chem. 1993, 97, 5141. (22) Matubayasi, N.; Motomura, K.; Kaneshina, S.; Nakamura, M.; Matuura, R. Bull. Chem. Soc. Jpn. 1977, 50, 523.

© 1997 American Chemical Society

Dihedral Angle of an Alcohol Lens

Langmuir, Vol. 13, No. 7, 1997 2159 Table 1. The Values of Angles at Different Temperatures C8OH

Figure 1. A diagram of the experimental setup: (1) light source; (2) thermostat; (3) optical glass cell; (4) objective lens; (5) bellows; (6) CCD camera; (7) camera control unit; (8) monitor; (9) image analysis processor; (10) computer.

Figure 2. A schematic diagram of the optical cell unit and the definitions of θL and θU. Nikon), the optical cell enclosed in a thermostatic water chamber, the objective lens (F2 50 mm, NIKKOR-H‚C, Nikon), the bellows (PB-6, Nikon), the black-and-white CCD camera with the control unit (FCD-10, Ikegami), and the image analysis processor TVIP4100 (XL500, Olympus-Avio) controlled by a software of Image Command 4198 (Ratoc System Engineering Co., Ltd.) installed into a personal computer (PC-9801FA, NEC). 3.2. Image Producing. Figure 2 shows schematically a diagram of the measurement cell. After the thermal and solubility equilibrium are attained, a small quantity of liquid alcohol in the right compartment is transferred by using a pipet onto the water surface in the glass square tube of 3 cm × 3 cm in the left compartment. When the lens was formed on a usual concave-shaped water surface, it was not possible to produce the complete image of a whole lens because part of the silhouette near the three-phase contact line was hidden or distorted by the meniscus of water surface. Therefore the image was produced by the two steps as follows. First the convex-shaped water surface was formed in the left compartment and then the lens of about 4-6 mm in diameter was placed on it as shown in Figure 2. After the water phase was stirred again very mildly for about 40-60 min without breaking the lens for the system to reach the complete equilibrium, an image of the lens being quite stationary was observed from a horizontal direction by using the CCD camera. At this stage, it was possible to produce clearly the image of the upper part of the lens above the plane containing the threephase contact line. Next a proper amount of the water phase was sucked out from the left compartment by the syringe to make the concave-shaped surface, with the lens left as it was. Then the image of the lower part was clearly produced. Therefore the dihedral angle θO was calculated as the sum of the angles θU and θL: the former is the angle between the A/O interface and the plane containing the three-phase contact line and the latter the one between the O/W interface and the plane, respectively. It has been pointed out that an image through a camera and an optical lens is sometimes slightly distorted.23 To check this point, we compared the sizes of image of a stainless steel ball (23) Cheng, P.; Li, D.; Boruvka, L.; Rotenberg, Y.; Neumann, A. W. Colloids Surf. 1990, 43, 151.

C10OH

T/K

θU/deg

θL/deg

θU/deg

θL/deg

288.15 290.65 293.15 295.65 298.15 300.65 303.15 305.65 308.15 310.65 313.15

16.59 ( 0.35 16.28 ( 0.24 16.41 ( 0.12 16.62 ( 0.27 16.44 ( 0.14 16.07 ( 0.36 17.17 ( 0.15 16.33 ( 0.20 17.74 ( 0.23 16.56 ( 0.43 17.51 ( 0.21

71.76 ( 1.15 70.81 ( 0.32 69.17 ( 0.84 67.18 ( 1.07 66.85 ( 0.30 66.38 ( 0.66 65.01 ( 0.16 64.46 ( 0.72 63.70 ( 0.32 62.24 ( 0.52 61.79 ( 0.27

17.21 ( 0.36 17.81 ( 0.12 17.92 ( 0.28 18.24 ( 0.09 18.38 ( 0.30 18.61 ( 0.40 18.46 ( 0.55 18.79 ( 0.42 18.97 ( 0.35 19.25 ( 0.64 19.17 ( 0.12

88.81 ( 1.11 84.86 ( 0.83 83.07 ( 0.27 79.61 ( 0.33 77.62 ( 0.40 75.62 ( 0.80 73.56 ( 0.24 72.26 ( 0.42 70.16 ( 0.43 68.49 ( 0.30 67.47 ( 0.12

Figure 3. Definitions of the coordinate system of the upper part of a lens. with the real sizes, which was 4.752 mm by using a digital micrometer, in both vertical and horizontal directions. Since no distortion was observed, the magnification of image was determined only by using horizontal distance of the image of a precise ruler at image producing processes, although a more precise correction process is required for a more accurate determination of dihedral angles and interfacial tension.23 Furthermore, the CCD camera was mounted with great care so that the vertical and horizontal axes of the real lens were coincident correctly with those of the image. TVIP4100 digitizes a picture of about 5 mm × 5 mm into 512 × 512 pixels with 256 gray levels each. The digitized image of a lens was processed to obtain the threshold image by adopting the automatic procedure installed into the image processor.24 The threshold value k is an important factor affecting the values of angles. In our experiments, the change of (3 levels in the k value alters the dihedral angle by (0.02°, which is very small compared with the reproducibility given in Table 1. The profile of a lens was obtained from the threshold image by using a manual command of edge emphasis. 3.3. Profile Description. The angles θU and θL were estimated by applying the drop shape analysis based on the Young-Laplace equation of capillarity25 to an axisymmetric sessile drop lens as shown in Figure 3.26-28 The equation

b/R1 + b/R2 ) 2 + βz/b

(1)

describes the profile, where b is the radius of curvature at the drop apex, R1 and R2 ) x/sin φ the principal radii of curvature of the profile at the point (x,z), and φ the angle made by the radius of curvature and z-axis, respectively. Here β is the drop shape parameter defined as the positive quantity by (24) Instruction Manual of Image Command 4198; Ratoc System Engineering Co., Ltd., Tokyo, 1992; p 4.25. (25) For example: Padday, J. F. Surf. Colloid Sci. 1968, 1, 101. (26) Butler, J. N.; Bloom, B. H. Surf. Sci. 1966, 4, 1. (27) Maze, C.; Burnet, G. Surf. Sci. 1969, 13, 451. (28) Rotenburg, Y.; Boruvka, L.; Neumann, A. W. J. Colloid Interface Sci. 1983, 93, 169.

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β ) g∆db2/γ

(2)

where g is the acceleration of gravity, ∆d the density difference between the outside and inside phases of the interface, and γ interfacial tension, respectively. A geometrical consideration on Figure 3 yields the two differential equations

dx ) R1 cos φ dφ

(3)

dz ) R1 sin φ dφ

(4)

and

where the boundary conditions are given by

(x,z) ) (0,0),

R1 ) b

at

φ)0

(5)

The solution of the three equations 1, 3, and 4 gives the expressions for the drop coordinates in terms of x, z, φ, and the two parameters β and γ . Since it has been known that the equations cannot be solved in terms of conventional analytical functions, we used the numerical integration of the fourth-order Runge-Kutta method. In order to obtain the optimum values of β and γ by using the nonlinear regression method, the objective function S was chosen as the sum of squares of the residual between the calculated and measured coordinates in x direction and then the values of β and γ producing the minimum of S were selected as their optimum ones. Let us refer to this as the β-γ method. However, as Maze and Burnet29 have reported, a small error in the apex location caused a large variation of interfacial tension and contact angles. Therefore, in another method, an error of the apex coordinate in the z direction  was introduced as a new parameter and the γ value was fixed at the one obtained independently and accurately by the pendant drop technique in our experiments. Then the values of β and  producing the minimum of S were selected as their optimum ones. This is referred to as the β- method. In the practical procedure of the drop shape analysis, the 20 points were selected on the upper or lower half of the profile of the image and the computer program proposed by Maze and Burnet27 was rewritten to be applicable to our methods. Then the angles θU and θL were obtained as the value of φ calculated by using the optimum values of β and γ or β and  at the coordinate on the three-phase contact line. Now we should point out that the magnitude of the step size of φ in the numerical integration process influences greatly on the values of γ, , and θ. In Figure 4 are shown the results of the effect of step size ∆φ on the lower part of a lens. It is clear that a step size smaller than about π/1000 is required for the quantities to arrive at constant values in both β-γ and β- methods. The parallel examination for the upper part showed that a step size smaller than about π/2000 was required. Therefore, we adopted π/1000 and π/2000 as the step sizes for the lower and upper parts, respectively. Furthermore an appropriate estimate of the initial values of β, γ, and  is essential for the numerical integration to converge. The values used were as follows: β ) 20 for the upper part and β ) 2 for the lower one for both methods, γ was the value obtained by pendant drop technique for the β-γ method, and  ) 0.2 pixels for the β- method, respectively. 3.4. Comparison between the β-γ and β-E Methods. In Figure 4, it is noted that the residual of the β- method is smaller by 1 order than that of the β-γ method. Furthermore, as is shown in Figure 5, the scattering of the estimated values of the angles θU and θL in several runs is small in the case of the β- method. These findings show that the β- method is more trustworthy than the β-γ method. Therefore the angle values obtained by the β- method are employed in the following.

Results and Discussion According to the Gibbs phase rule, the degree of freedom is two for the three-component and three-phase systems. Therefore, we adopted temperature T and pressure p as the independent variables and measured the interfacial (29) Maze, C.; Burnet, G. Surf. Sci. 1971, 24, 335.

Figure 4. Effect of the step size on some quantities of the C8OH system: (a) error of the apex coordinate in z direction and interfacial tension of the O/W interface; (b) angle of the lower part; (c) sum of squares of the residual between the measured and calculated coordinate in x direction; (0) β-γ method; (9)β- method. i is defined by ∆φ ) π/i.

Figure 5. Angle vs temperature curves for the C8OH system: (a) angle of the lower part; (b) angle of the upper part; (1) β-γ method; (2) β- method.

tension and dihedral angle as a function of temperature under atmospheric pressure. 1. Interfacial Tension. There are three interfaces when a lens of liquid alcohol is thermodynamically stable at the A/W interface as is shown in Figure 6. The values of the interfacial tensions strongly affect the shape of the lens and are also important for checking if the dihedral angles are correctly measured by our new experimental setup and procedure. Figure 7a shows the γAO, γAW, and γOW vs temperature curves of the C8OH system. It is seen that the γAW value passes through a very shallow maximum at about 300 K, and the γAO and the γOW values decrease and increase monotonously with increasing temperature, respectively. The corresponding curves of

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Figure 6. Definitions of angles and interfacial tensions.

Figure 8. Interfacial tension vs temperature curves: (a) γAO; (b) γAW; (c) γOW; (O) C8OH; (b) C10OH.

Figure 7. Interfacial tension vs temperature curves: (a) C8OH; (b)C10OH; (1) γAW; (2) γAO, (3) γOW.

the C10OH system are shown in Figure 7b. The γAO and γOW vs T curves are similar in their shape to those in Figure 7a while the γAW value increases monotonously with increasing temperature in this case. It should be noted that the γAW and γAO curves intersect at about 295 K. This point will be discussed later in connection with the intruding phenomenon of the water phase into the A/O interface. In Figure 8, the three interfacial tensions for the two systems are compared. Figure 8a shows that the surface tension decreases with increasing temperature and that the γAO value of the C8OH system is lower than that of the C10OH system. These trends are very similar to those observed for the A/O interfaces in the absence of water30 and the hydrocarbon liquid/air interfaces. This may suggest that the longer hydrocarbon chains interact more strongly than the shorter ones in the alcohol phases and, therefore, the transfer of alcohol molecules from the interior of bulk phase to the air/alcohol interface is energetically less favorable for the longer chain. The difference in γAW values in Figure 8b exhibits the difference in surface activity in a usual sense. In Figure 8c, it is seen that γOW increases with increasing temperature. This trend is in striking contrast to the one observed for hydrocarbon/water interfaces and has been discussed in (30) Jasper, J. J. J. Phys. Chem. Ref. Data 1972, 1, 841.

terms of the interaction between hydroxide group and water molecules and the orientation of alcohol molecules enforced at the interface due to their amphiphilicity.20,21 It is also seen that the C10OH system exhibits a higher interfacial tension at a higher temperature and a lower one at a lower temperature than the C8OH system. This may be explained as follows: the interaction between hydroxide group and water becomes gradually weak with increasing temperature and hence the transfer of molecules to the O/W interface at a higher temperature is not so energetically favorable compared with that at a lower temperature. Therefore the relation of γOW(C10OH) > γOW(C8OH) at a higher temperature is expected to be same as the one of γAO(C10OH) > γAO(C8OH) at the A/O interface given in Figure 8a. At a lower temperature, the transfer of alcohol molecules to the O/W interface becomes more energetically favorable and the interaction between hydrocarbon chains plays an important role in determining the property of the interfacial film. Then the relation of γOW(C10OH) < γOW(C8OH) at a lower temperature is same as that of γAW(C10OH) < γAW(C8OH) at the A/W interface given in Figure 8b. 2. Dihedral Angles. Let us now describe the dihedral angles. The values of angles of θU and θL are given together with their reproducibilities in Table 1 and plotted against temperature together with the sum of them, θO , in Figure 9. It is seen that the θU values increase very slightly with increasing temperature and are not so different for the two systems. The θL values and hence the θO values, on the other hand, decrease with increasing temperature and are considerably different for the two systems. Then it is said that the lens of the C10OH system is more contracted at a given temperature and this difference in shape between the two systems stems mainly from the angle of the lower part of the lens. 3. Dihedral Angle and Interfacial Tension. Now let us look more closely at the relation between the interfacial tension and dihedral angle. The typical profile of a lens is shown in Figure 6, where we define the other two dihedral angles θA and θW interposing respectively the air and water phases. Since the mechanical equilibrium condition requires that the resultant force acting at the three-phase contact line is zero and it is probable

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Figure 10. Dihedral angle vs temperature curves: (O) θO for the C8OH system; (b) θO for the C10OH system; (s) θO,C.

Figure 9. Angle vs temperature curves: (1) θU; (2) θL; (3) θO; (O) C8OH; (b) C10OH.

that the effect of line tension is negligibly small31 for a large lens studied here, there exist the three relations between the dihedral angles and interfacial tensions called Neumann’s equations32,33 as follows:

cos θA ) (γOW2 - γAO2 - γAW2)/2γAOγAW

(6)

cos θW ) (γAO2 - γAW2 - γOW2)/2γAWγOW

(7)

cos θO ) (γAW2 - γOW2 - γAO2)/2γOWγAO

(8)

Here it is noted that the gravity has no influence on the magnitude of a dihedral angle.34 It is apparent from a geometrical point of view that these equations hold in a triangle of the interfacial tensions as its three sides and the supplements of the dihedral angles as its three angles, where three interfacial tensions satisfy the inequalities given by33

γAO < γAW + γOW, γAW < γOW + γAO, γOW < γAO + γAW (9) As will be shown in the following, since these conditions are undoubtedly satisfied at all the temperatures examined, the lenses are all thermodynamically and mechanically stable ones. By using the Neumann’s relations and the γ values given in Figure 7, the three kinds of dihedral angles can be calculated. The angle calculated from eq 8 is denoted by θO,C and drawn by full lines in Figure 10, where the dihedral angle measured is also plotted against temperature. It is seen that the θO values of the C10OH system are sufficiently close to the θO,C values and those of the C8OH system are scattered with no more (2°. Since the interfacial tension has been measured separately with a high accuracy, this finding proves that the dihedral angle has been measured accurately. (31) Li, D.; Neumann, A. W. Colloids Surf. 1990, 43, 195. (32) Princen, H. M. Surf. Colloid Sci. 1968, 2, 1. (33) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillality; Oxford University Press: Oxford, 1982. (34) Ivanov, I. B.; Kralchevsky, P. A.; Nikolov, A. D. J. Colloid Interface Sci. 1986, 112, 97.

Figure 11. Sum of the two interfacial tensions vs temperature curves: (a) C8OH; (b) C10OH; (1) γAO + γAW; (2) γAW + γOW; (3) γOW + γAO.

Interfacial behavior such as the wetting and nonwetting of a middle phase between the two phases and the intruding of a heavy phase into a light phase is directly related to the interfacial tensions among the three coexisting phases. When the condition given by eq 9 is fulfilled and the drop of the alcohol is small enough to form a lens, the geometrical shape of the lens changes with the balance of the interfacial tensions. Then let us consider the situation of the present systems on the basis of the interfacial tensions and with reference to the scheme reported previously.17 In Figure 11 are plotted the sum of the two of interfacial tensions against temperature. First we note that, by comparing the results given in Figure 7 with those in Figure 11, all the inequalities given by eq 9 are satisfied and, therefore, the lens of alcohol phase is thermodynamically stable and floating on the A/W interface at all the temperatures. Second it should be noted that the γAW and γAO vs T curves in Figure 7b and therefore the curves 2 and 3 of the C10OH system in Figure 11b cross each other at about 295 K and the value of γAW is lower than that of γAO below about 295 K. This suggests that the water phase may intrude into the A/O interface

Dihedral Angle of an Alcohol Lens

at a temperature below about 295 K and the intruding phase is contracted again to a small lens because the three inequalities still hold. Furthermore the value of θO should be larger than 90° from eq 8 and the experimental value of θO is about 98°. Although a stable intruding lens was not observed and the dihedral angle interposing the water phase of a lens could not be measured, the value was estimated to be around 100° by applying eq 7 to the interfacial tension given in Figure 7. Actually a small lens of the water phase was sometimes incidentally observed. With respect to the C8OH systems, the intruding does not take place; indeed the interfacial tension of the A/W interface is higher than that of the A/O interface at all the temperatures as is shown in Figure 7. We have shown previously that the O/W interfacial films of the longer chain alcohol such as 1-undecanol and

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1-dodecanol exhibit the phase transition between the expanded and condensed states.20,21 The dihedral angle and the three kinds of interfacial tension of these systems have been measured recently: the preliminary results demonstrate the phase transition of interfacial film, the nonwetting oil lens, and the intruding of the water phase. The complete sets of the experimental data and the close examination of the phenomena will be published in our forthcoming paper. Acknowledgment. The present paper was supported by Grant-in-Aid for Scientific Research (B) No. 06453057 from The Ministry of Education of Science and Culture. LA9605955