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Investigation of dielectric relaxation phenomena in liquid crystal monolayer at the air–water interface
Thin Solid Films 327–329 (1998) 232–235
Investigation of dielectric relaxation phenomena in liquid crystal monolayer at the air–water interface Yutaka Majima*, Yoko Sato, Chen-Xu Wu, Mitsumasa Iwamoto Department of Physical Electronics, Tokyo Institute of Technology, 2-12-1 Okayama, Meguro-ku, Tokyo 152-8552, Japan
Abstract Dielectric relaxation phenomena of 4-cyano-4′-n-alkyl-biphenyl (nCB; n = 5 or 10) monolayers at the air–water interface have been investigated by measuring Maxwell displacement current (MDC; I)-area per molecule (A) isotherms and surface pressure (p)–A isotherms at several monolayer compression rates. It is found that I–A isotherms of 5CB monolayer clearly depend on molecular compression rates (a) in the range (range 2) where the surface pressure is almost zero, and that in contrast, I–A isotherms of 10CB monolayer fluctuate in range 2. These results indicate that the monolayer compression of 5CB in range 2 is a non-equilibrium process. 1998 Elsevier Science S.A. All rights reserved Keywords: Relaxation phenomena; Monolayer at the air–water interface; Maxwell displacement current; Relaxation time; Monolayer compression; Liquid crystal
1. Introduction Dielectric relaxation phenomena of monolayers at the air–water interface carry one of the basic physical properties of monolayers. In 1913, Debye [1] developed a method of rotational Brownian motion to analyze the dielectric relaxation phenomena of molecules with permanent electric dipoles in liquid [1,2]. On the basis of the Debye philosophy, many studies have been carried out in order to clarify the dielectric phenomena of organic materials [3–5]. Many measuring techniques, e.g. surface pressure measurement, fluorescence microscopy [6], surface potential measurements [7,8], viscosity measurements [7,9], and Brewster angle microscopy [10], have been applied to investigate the physical properties of monolayers at the air-water interface. The relaxation phenomena of monolayers have been reported by measuring the surface shear mechanical force through application of viscosity measurements [7,9]. However, the dielectric relaxation phenomena of monolayers have not been clarified. Recently, we have developed a Maxwell displacement current (MDC) measuring system [11–13], in which the monolayer at the air–
* Corresponding author. Tel.\fax: +81 3 57342673; e-mail: [email protected]
0040-6090/98/$ - see front matter PII S0040-6090 (98 )0 0636-1
water interface is positioned between electrodes in the air and below the water, and both electrodes are shorted through a sensitive ammeter. MDC flows across monolayer films when the vertical component of the dipole moment of the molecule at the air–water interface and the number of molecules change. For this reason, the MDC measuring system is appropriate for detecting the dielectric relaxation phenomena of a monolayer at the air–water interface. In this paper, we discuss the dielectric relaxation phenomena of a 4-cyano-4′-n-alkyl-biphenyl (nCB, n = 5 and 10) monolayer at the air–water interface. The Maxwell displacement current (MDC; I)-area per molecule (A) isotherms and surface pressure (p)–A isotherms are measured by applying lateral monolayer compression at several compression rates.
2. Experimental details Fig. 1 shows the experimental setup used in this investigation [11]. The Langmuir trough has a rectangular shape with an area of 1050 cm2. Above the deionized water surface at the center of the trough, electrode 1 is suspended parallel to the water surface. The working area (B) of the electrode is 45.6 cm2, and the distance between electrode 1 and the water surface (d1) is 1.00 ± 0.05 mm. The tempera-
1998 Elsevier Science S.A. All rights reserved
Y. Majima et al. / Thin Solid Films 327–329 (1998) 232–235
ture of the water is maintained at 20ºC. An nCB molecule is composed of a hydrophilic polar (cyano) head group and a hydrophobic alkyl tail group. The nCB monolayers are spread from a 1 mM chloroform solution onto the surface of the water in the Langmuir trough. The monolayers on the water surface are compressed from both sides of the trough with the aid of two barriers moving simultaneously at the same speed in opposite directions. The constant barrier velocity used in this study was controlled in a range between 80 and 5 mm/min. Under these experimental conditions, the adopted constant barrier velocities of 80, 40, 20, 10 and 5 mm/min correspond to constant compression rates of molecular area (a) of −0.61, −0.30, −0.15, −0.079, and −0.044 ˚ 2/(s molecule), respectively. A During the compression of monolayers, the Maxwell displacement current (MDC) I is given by [13]: I=
mZ dN N dmZ df + +C S d1 dt d1 dt dt
(1)
Here, mZ is the average vertical component of the dipole moment of a molecule, C and d1 are the capacitance and the distance between electrode 1 and the water surface, respectively, N is the number of molecules under electrode 1, and fS is the surface potential of the water. There are many extrinsic factors such as configuration changes of counterions that vary the potential fS. However, the change in the potential fS does not contribute significantly to the MDC of monolayers on a pure water surface [14]. Therefore, for monolayer compression with a constant compression rate of molecular area a( = dA/dt), MDC I is approximately given by [15]:
Bam S dS − I= d1 A A dA
(2)
under the assumption that nCB molecules are distributed at a density of 1/A (A, area per nCB molecule) on the water surface. Here m is the electric permanent dipole moment along the nCB-molecular axis, S is the polar order parameter defined by S = ,cos v., where , . denotes the
233
thermodynamics average (mZ = Sm), and B is the working area of electrode 1 (N = B/A). It should be noted that mZ is the apparent vertical component of the dipole moment of a molecule under compression when the monolayer is in a non-equilibrium state, which is different from the vertical component of the dipole moment in an equilibrium state (mZeq). If we denote a normalized MDC as −I/a, Eq. (2) indicates that the normalized MDC (−I/a) does not depend on a, but does depend on A, when the monolayer is compressed under the equilibrium condition. The charge (DQ1) flowing through the circuit during the monolayer compression is obtained by the integration of MDC with respect to time, and is given by [13]: DQ1 =
NmZ d1
(3)
under the assumption that the average vertical component of the molecular dipole moment mZ = 0 at t = 0, and the change in fS equals zero.
3. Results Fig. 2a,b shows typical examples of the normalized MDC-I/a generated across 5CB and 10CB monolayers, respectively. Surface pressure (p)–A isotherms and the vertical component of the dipole moment (mZ)–A isotherms are also plotted in the figures. In the case of 5CB, −I/a–A iso˚ 2 with a of therms are initiated around A = 60, 65, and 100 A 2 ˚ −0.61, −0.15, and −0.044 A /(s molecule), respectively, in ˚ 2 (range 2). The value of the MDC peak the range A ≥ 43 A 2 ˚ around 45 A is found to increase significantly as the barrier velocity increased. In range 2, mZ tends to increase at wider ˚ 2 (range 3), A as a decreases. In the range 43 ≥ A ≥ 34 A mZ –A isotherms do not depend on the constant compression rate of molecular area, but correspond well to the trace of surface pressure-area isotherms. These results indicate that the 5CB monolayer compression under a of −0.61, −0.15, or ˚ 2/(s molecule) is a non-equilibrium and an equili−0.044 A brium process in ranges 2 and 3, respectively. In the case of 10CB, in contrast, −I/a–A isotherms are initiated around ˚ 2, and it does not depend on a. We tried to meaA = 100 A sure a dependence of 10CB mZ –A isotherms over 20 times. As shown in Fig. 2b, mZ of 10CB does not depend on a and mZ values coincided well with each other at the end of range 3 and values coincided well with each other. In contrast, in range 2, 10CB mZ –A isotherms tend to fluctuate. It should be noted here that the fluctuation among mZ –A isotherms under several a values in range 2 comes from fluctuation of alignment of the 10CB molecule rather than from experimental error.
4. Discussion Fig. 1. Schematic diagram of the Maxwell displacement current (MDC) measuring apparatus.
In the following, we discuss the dielectric relaxation phe-
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Fig. 2. (a,b) Typical experimental results of p–A isotherms, normalized MDC (I/a, I; Maxwell displacement current, a; a constant compression rate of molecular area)–A isotherms, and mZ –A isotherms of 5CB and 10CB monolayers, respectively.
nomena of 5CB and 10CB monolayers at the air–water interface. As discussed in our previous paper [5], the dielectric relaxation process of monolayers can be expressed as: d(S − Seq ) S − Seq =− t dt
(4)
in the first order approximation, assuming a single relaxation process of monolayers. Here, Seq is the polar order parameter in an equilibrium state, and t is the relaxation time of monolayers. As shown in Fig. 2a,b, the value of S is determined from a mZ –A isotherm by utilizing the equation S = mZ/m. The differential vertical component of the dipole moment (dmZ/dt) was evaluated from the mZ –t isotherm by means of a least square method, and the value of d(S − Seq)/dt was determined from dmZ/dt–A isotherms. It should be noted that d(S − Seq)/dt evaluated from mZ –t isotherms which is measured under the constant molecular compression rates should be different from what is measured under the constant A. It was found, however, that the value of d(S − Seq)/ dt did not depend on the range of time for the least square method between 1 and 20 s. For this reason, the evaluated value of d(S − Seq)/dt is thought to be equal to what is measured under the constant A. As indicated in the above session, in range 2, since a deviation from reproducibility of a 10CB monolayer was larger than that of a 5CB monolayer, a dependence of mZ –A isotherms of a 10CB monolayer was not observed clearly in range 2. In the following, we try to evaluate t and Seq of a single 5CB monolayer by applying the experimental results to Eq. (4). Fig. 3 shows a typical d(mZ − mZeq)/ ˚ 2. If dt − mZ characteristic of a 5CB monolayer at A = 50A Eq. (4) describes the relaxation phenomena of 5CB mono-
layer, a linear relationship between d(mZ − mZeq)/dt and mZ should be observed. As shown in Fig. 3, d(mZ − mZeq)/dt tends to decrease as mZ increases, however, the linear relationship is not observed. From Eq. (4), the slope of plotted results in Fig. 3 is inversely proportional to relaxation time. The d(mZ − mZeq)/dt − mZ characteristic indicates that relaxation time increases as the deviation of mZ from mZeq decreases. It should be noted that this tendency of increasing ˚ 2. relaxation time is observed in range 2 at 60 ≥ A ≥ 43 A These results do not suggest that the relaxation phenomena of a 5CB monolayer are explicated as a single relaxation process of monolayers. Fig. 4a shows the mZeq –A isotherm using the evaluated Seq(A). In range 2, mZeq increases as the area per molecule decreases, and mZeq is greater than mZ obtained by a of ˚ 2/(s molecule). This result does −0.61, −0.15, and −0.044 A not indicate that the 5CB monolayer was in an equilibrium
Fig. 3. Typical d(mZ − mZeq)/dt − mZ characteristic of 5CB monolayer at ˚ 2. Solid line is given by the evaluated values of the relaxation A = 50 A time and the polar ordering parameter in the equilibrium state by using Eq. (4). X, experimental results; W, mZeq evaluated using the experimental results.
Y. Majima et al. / Thin Solid Films 327–329 (1998) 232–235
235
10CB monolayer was larger than that in a 5CB monolayer, which seems to reflect the difference in the molecular structure between 10CB and 5CB molecules. Since 10CB molecule possesses longer alkyl chains than 5CB molecules, molecular interactions of 10CB monolayer e.g. van der Waals force should be larger than that of 5CB. Further investigation is now proceeding.
5. Conclusions
Fig. 4. (a) Vertical component of dipole moment in equilibrium state (mZeq)–A isotherm (solid line) obtained from the experimental results. ˚ 2/s are also shown. mZ –A isotherms at a of −0.61, −0.15, and −0.044 A (b) Relaxation time (t)–A isotherm (solid line) evaluated from Eq. (4) by introducing the experimental results.
state in range 2 when the monolayer was compressed at rates ˚ 2/(s molecule). The difference of −0.61, −0.15, and −0.044 A between mZeq and mZ is reduced as the constant barrier speed decreases. This result agrees with the fact that the relaxation tends to proceed when the compression ratio becomes small. In ranges 3 and 4, the mZeq –A isotherm is in good agreement with the experimental results. These results indicate that in range 2 where p is too small to measure, the 5CB monolayer does not reach the equilibrium states. In contrast, in range 3 where p is increased with the compression, the 5CB-monolayer reaches the equilibrium states under the same measuring condition as in range 2. Fig. 4b shows the t–A isotherm with t(A) evaluated from Eq. (4). t decreased as A decreased by monolayer compression. The relaxation time t at A = 60 ˚ 2 is about 180 s. It should be noted that the evaluated A ˚ 2 is comparable to or relaxation time (180 s) at A = 60 A longer than the compression time in this work. As discussed above, the fluctuation of mZ –A isotherm in a
In this paper, we studied the dielectric relaxation phenomena of 5CB and 10CB monolayers at the air–water interface by means of the MDC-measuring system. It was found that in range 2, mZ of 5CB molecule tends to increase in large A region as the compression rate becomes small, while in range 3, the mZ –A isotherms with various compression rates become identical. These results indicate that the compression processes of a 5CB monolayer in range 2 and range 3 are non-equilibrium and equilibrium processes, respectively. In contrast to mZ –A isotherms of 5CB monolayer, the relaxation process of 10CB monolayer is not clearly observed due to the difference in molecular structure between 10CB and 5CB. References [1] P. Debye, Ber. Dt. Phys. Ges. 15 (1913) 777. [2] P. Debye, Polar Molecules, Dover, New York, 1929. [3] H. Fro¨hlich, Theory of Dielectrics, Oxford University Press, New York, 1958. [4] R. Chen, Y. Kirsh, Analysis to Thermally Stimulated Process, Pergamon, Oxford, 1981. [5] M. Iwamoto, C.X. Wu, Phys. Rev. E 54 (1996) 6603. [6] V. Tscharner, H.M. McConnell, Biophys. J. 36 (1981) 409. [7] G.L. Gaines, Jr., Insoluble Monolayers at Liquid Gas Interfaces, Interscience, New York, 1965. [8] H. Mo¨hwald, Thin Solid Films 159 (1988) 1. [9] K. Miyano, M. Veyssie, J. Chem. Phys. 87 (1987) 3153. [10] S. He´non, J. Meunier, Rev. Sci. Instrum. 62 (1991) 936. [11] Y. Majima, M. Iwamoto, Rev. Sci. Instrum. 62 (1991) 2228. [12] M. Iwamoto, Y. Majima, H. Naruse, T. Noguchi, H. Fuwa, Nature 353 (1991) 645. [13] Y. Majima, M. Iwamoto, Jpn. J. Appl. Phys. 29 (1990) 564. [14] Y. Majima, H. Naruse, M. Iwamoto, Jpn. J. Appl. Phys. 31 (1992) 864. [15] M. Iwamoto, T. Kubota, O.Y. Zhong-can, J. Chem. Phys. 104 (1996) 736.
Investigation of dielectric relaxation phenomena in liquid crystal monolayer at the air–water interface Yutaka Majima*, Yoko Sato, Chen-Xu Wu, Mitsumasa Iwamoto Department of Physical Electronics, Tokyo Institute of Technology, 2-12-1 Okayama, Meguro-ku, Tokyo 152-8552, Japan
Abstract Dielectric relaxation phenomena of 4-cyano-4′-n-alkyl-biphenyl (nCB; n = 5 or 10) monolayers at the air–water interface have been investigated by measuring Maxwell displacement current (MDC; I)-area per molecule (A) isotherms and surface pressure (p)–A isotherms at several monolayer compression rates. It is found that I–A isotherms of 5CB monolayer clearly depend on molecular compression rates (a) in the range (range 2) where the surface pressure is almost zero, and that in contrast, I–A isotherms of 10CB monolayer fluctuate in range 2. These results indicate that the monolayer compression of 5CB in range 2 is a non-equilibrium process. 1998 Elsevier Science S.A. All rights reserved Keywords: Relaxation phenomena; Monolayer at the air–water interface; Maxwell displacement current; Relaxation time; Monolayer compression; Liquid crystal
1. Introduction Dielectric relaxation phenomena of monolayers at the air–water interface carry one of the basic physical properties of monolayers. In 1913, Debye [1] developed a method of rotational Brownian motion to analyze the dielectric relaxation phenomena of molecules with permanent electric dipoles in liquid [1,2]. On the basis of the Debye philosophy, many studies have been carried out in order to clarify the dielectric phenomena of organic materials [3–5]. Many measuring techniques, e.g. surface pressure measurement, fluorescence microscopy [6], surface potential measurements [7,8], viscosity measurements [7,9], and Brewster angle microscopy [10], have been applied to investigate the physical properties of monolayers at the air-water interface. The relaxation phenomena of monolayers have been reported by measuring the surface shear mechanical force through application of viscosity measurements [7,9]. However, the dielectric relaxation phenomena of monolayers have not been clarified. Recently, we have developed a Maxwell displacement current (MDC) measuring system [11–13], in which the monolayer at the air–
* Corresponding author. Tel.\fax: +81 3 57342673; e-mail: [email protected]
0040-6090/98/$ - see front matter PII S0040-6090 (98 )0 0636-1
water interface is positioned between electrodes in the air and below the water, and both electrodes are shorted through a sensitive ammeter. MDC flows across monolayer films when the vertical component of the dipole moment of the molecule at the air–water interface and the number of molecules change. For this reason, the MDC measuring system is appropriate for detecting the dielectric relaxation phenomena of a monolayer at the air–water interface. In this paper, we discuss the dielectric relaxation phenomena of a 4-cyano-4′-n-alkyl-biphenyl (nCB, n = 5 and 10) monolayer at the air–water interface. The Maxwell displacement current (MDC; I)-area per molecule (A) isotherms and surface pressure (p)–A isotherms are measured by applying lateral monolayer compression at several compression rates.
2. Experimental details Fig. 1 shows the experimental setup used in this investigation [11]. The Langmuir trough has a rectangular shape with an area of 1050 cm2. Above the deionized water surface at the center of the trough, electrode 1 is suspended parallel to the water surface. The working area (B) of the electrode is 45.6 cm2, and the distance between electrode 1 and the water surface (d1) is 1.00 ± 0.05 mm. The tempera-
1998 Elsevier Science S.A. All rights reserved
Y. Majima et al. / Thin Solid Films 327–329 (1998) 232–235
ture of the water is maintained at 20ºC. An nCB molecule is composed of a hydrophilic polar (cyano) head group and a hydrophobic alkyl tail group. The nCB monolayers are spread from a 1 mM chloroform solution onto the surface of the water in the Langmuir trough. The monolayers on the water surface are compressed from both sides of the trough with the aid of two barriers moving simultaneously at the same speed in opposite directions. The constant barrier velocity used in this study was controlled in a range between 80 and 5 mm/min. Under these experimental conditions, the adopted constant barrier velocities of 80, 40, 20, 10 and 5 mm/min correspond to constant compression rates of molecular area (a) of −0.61, −0.30, −0.15, −0.079, and −0.044 ˚ 2/(s molecule), respectively. A During the compression of monolayers, the Maxwell displacement current (MDC) I is given by [13]: I=
mZ dN N dmZ df + +C S d1 dt d1 dt dt
(1)
Here, mZ is the average vertical component of the dipole moment of a molecule, C and d1 are the capacitance and the distance between electrode 1 and the water surface, respectively, N is the number of molecules under electrode 1, and fS is the surface potential of the water. There are many extrinsic factors such as configuration changes of counterions that vary the potential fS. However, the change in the potential fS does not contribute significantly to the MDC of monolayers on a pure water surface [14]. Therefore, for monolayer compression with a constant compression rate of molecular area a( = dA/dt), MDC I is approximately given by [15]:
Bam S dS − I= d1 A A dA
(2)
under the assumption that nCB molecules are distributed at a density of 1/A (A, area per nCB molecule) on the water surface. Here m is the electric permanent dipole moment along the nCB-molecular axis, S is the polar order parameter defined by S = ,cos v., where , . denotes the
233
thermodynamics average (mZ = Sm), and B is the working area of electrode 1 (N = B/A). It should be noted that mZ is the apparent vertical component of the dipole moment of a molecule under compression when the monolayer is in a non-equilibrium state, which is different from the vertical component of the dipole moment in an equilibrium state (mZeq). If we denote a normalized MDC as −I/a, Eq. (2) indicates that the normalized MDC (−I/a) does not depend on a, but does depend on A, when the monolayer is compressed under the equilibrium condition. The charge (DQ1) flowing through the circuit during the monolayer compression is obtained by the integration of MDC with respect to time, and is given by [13]: DQ1 =
NmZ d1
(3)
under the assumption that the average vertical component of the molecular dipole moment mZ = 0 at t = 0, and the change in fS equals zero.
3. Results Fig. 2a,b shows typical examples of the normalized MDC-I/a generated across 5CB and 10CB monolayers, respectively. Surface pressure (p)–A isotherms and the vertical component of the dipole moment (mZ)–A isotherms are also plotted in the figures. In the case of 5CB, −I/a–A iso˚ 2 with a of therms are initiated around A = 60, 65, and 100 A 2 ˚ −0.61, −0.15, and −0.044 A /(s molecule), respectively, in ˚ 2 (range 2). The value of the MDC peak the range A ≥ 43 A 2 ˚ around 45 A is found to increase significantly as the barrier velocity increased. In range 2, mZ tends to increase at wider ˚ 2 (range 3), A as a decreases. In the range 43 ≥ A ≥ 34 A mZ –A isotherms do not depend on the constant compression rate of molecular area, but correspond well to the trace of surface pressure-area isotherms. These results indicate that the 5CB monolayer compression under a of −0.61, −0.15, or ˚ 2/(s molecule) is a non-equilibrium and an equili−0.044 A brium process in ranges 2 and 3, respectively. In the case of 10CB, in contrast, −I/a–A isotherms are initiated around ˚ 2, and it does not depend on a. We tried to meaA = 100 A sure a dependence of 10CB mZ –A isotherms over 20 times. As shown in Fig. 2b, mZ of 10CB does not depend on a and mZ values coincided well with each other at the end of range 3 and values coincided well with each other. In contrast, in range 2, 10CB mZ –A isotherms tend to fluctuate. It should be noted here that the fluctuation among mZ –A isotherms under several a values in range 2 comes from fluctuation of alignment of the 10CB molecule rather than from experimental error.
4. Discussion Fig. 1. Schematic diagram of the Maxwell displacement current (MDC) measuring apparatus.
In the following, we discuss the dielectric relaxation phe-
234
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Fig. 2. (a,b) Typical experimental results of p–A isotherms, normalized MDC (I/a, I; Maxwell displacement current, a; a constant compression rate of molecular area)–A isotherms, and mZ –A isotherms of 5CB and 10CB monolayers, respectively.
nomena of 5CB and 10CB monolayers at the air–water interface. As discussed in our previous paper [5], the dielectric relaxation process of monolayers can be expressed as: d(S − Seq ) S − Seq =− t dt
(4)
in the first order approximation, assuming a single relaxation process of monolayers. Here, Seq is the polar order parameter in an equilibrium state, and t is the relaxation time of monolayers. As shown in Fig. 2a,b, the value of S is determined from a mZ –A isotherm by utilizing the equation S = mZ/m. The differential vertical component of the dipole moment (dmZ/dt) was evaluated from the mZ –t isotherm by means of a least square method, and the value of d(S − Seq)/dt was determined from dmZ/dt–A isotherms. It should be noted that d(S − Seq)/dt evaluated from mZ –t isotherms which is measured under the constant molecular compression rates should be different from what is measured under the constant A. It was found, however, that the value of d(S − Seq)/ dt did not depend on the range of time for the least square method between 1 and 20 s. For this reason, the evaluated value of d(S − Seq)/dt is thought to be equal to what is measured under the constant A. As indicated in the above session, in range 2, since a deviation from reproducibility of a 10CB monolayer was larger than that of a 5CB monolayer, a dependence of mZ –A isotherms of a 10CB monolayer was not observed clearly in range 2. In the following, we try to evaluate t and Seq of a single 5CB monolayer by applying the experimental results to Eq. (4). Fig. 3 shows a typical d(mZ − mZeq)/ ˚ 2. If dt − mZ characteristic of a 5CB monolayer at A = 50A Eq. (4) describes the relaxation phenomena of 5CB mono-
layer, a linear relationship between d(mZ − mZeq)/dt and mZ should be observed. As shown in Fig. 3, d(mZ − mZeq)/dt tends to decrease as mZ increases, however, the linear relationship is not observed. From Eq. (4), the slope of plotted results in Fig. 3 is inversely proportional to relaxation time. The d(mZ − mZeq)/dt − mZ characteristic indicates that relaxation time increases as the deviation of mZ from mZeq decreases. It should be noted that this tendency of increasing ˚ 2. relaxation time is observed in range 2 at 60 ≥ A ≥ 43 A These results do not suggest that the relaxation phenomena of a 5CB monolayer are explicated as a single relaxation process of monolayers. Fig. 4a shows the mZeq –A isotherm using the evaluated Seq(A). In range 2, mZeq increases as the area per molecule decreases, and mZeq is greater than mZ obtained by a of ˚ 2/(s molecule). This result does −0.61, −0.15, and −0.044 A not indicate that the 5CB monolayer was in an equilibrium
Fig. 3. Typical d(mZ − mZeq)/dt − mZ characteristic of 5CB monolayer at ˚ 2. Solid line is given by the evaluated values of the relaxation A = 50 A time and the polar ordering parameter in the equilibrium state by using Eq. (4). X, experimental results; W, mZeq evaluated using the experimental results.
Y. Majima et al. / Thin Solid Films 327–329 (1998) 232–235
235
10CB monolayer was larger than that in a 5CB monolayer, which seems to reflect the difference in the molecular structure between 10CB and 5CB molecules. Since 10CB molecule possesses longer alkyl chains than 5CB molecules, molecular interactions of 10CB monolayer e.g. van der Waals force should be larger than that of 5CB. Further investigation is now proceeding.
5. Conclusions
Fig. 4. (a) Vertical component of dipole moment in equilibrium state (mZeq)–A isotherm (solid line) obtained from the experimental results. ˚ 2/s are also shown. mZ –A isotherms at a of −0.61, −0.15, and −0.044 A (b) Relaxation time (t)–A isotherm (solid line) evaluated from Eq. (4) by introducing the experimental results.
state in range 2 when the monolayer was compressed at rates ˚ 2/(s molecule). The difference of −0.61, −0.15, and −0.044 A between mZeq and mZ is reduced as the constant barrier speed decreases. This result agrees with the fact that the relaxation tends to proceed when the compression ratio becomes small. In ranges 3 and 4, the mZeq –A isotherm is in good agreement with the experimental results. These results indicate that in range 2 where p is too small to measure, the 5CB monolayer does not reach the equilibrium states. In contrast, in range 3 where p is increased with the compression, the 5CB-monolayer reaches the equilibrium states under the same measuring condition as in range 2. Fig. 4b shows the t–A isotherm with t(A) evaluated from Eq. (4). t decreased as A decreased by monolayer compression. The relaxation time t at A = 60 ˚ 2 is about 180 s. It should be noted that the evaluated A ˚ 2 is comparable to or relaxation time (180 s) at A = 60 A longer than the compression time in this work. As discussed above, the fluctuation of mZ –A isotherm in a
In this paper, we studied the dielectric relaxation phenomena of 5CB and 10CB monolayers at the air–water interface by means of the MDC-measuring system. It was found that in range 2, mZ of 5CB molecule tends to increase in large A region as the compression rate becomes small, while in range 3, the mZ –A isotherms with various compression rates become identical. These results indicate that the compression processes of a 5CB monolayer in range 2 and range 3 are non-equilibrium and equilibrium processes, respectively. In contrast to mZ –A isotherms of 5CB monolayer, the relaxation process of 10CB monolayer is not clearly observed due to the difference in molecular structure between 10CB and 5CB. References [1] P. Debye, Ber. Dt. Phys. Ges. 15 (1913) 777. [2] P. Debye, Polar Molecules, Dover, New York, 1929. [3] H. Fro¨hlich, Theory of Dielectrics, Oxford University Press, New York, 1958. [4] R. Chen, Y. Kirsh, Analysis to Thermally Stimulated Process, Pergamon, Oxford, 1981. [5] M. Iwamoto, C.X. Wu, Phys. Rev. E 54 (1996) 6603. [6] V. Tscharner, H.M. McConnell, Biophys. J. 36 (1981) 409. [7] G.L. Gaines, Jr., Insoluble Monolayers at Liquid Gas Interfaces, Interscience, New York, 1965. [8] H. Mo¨hwald, Thin Solid Films 159 (1988) 1. [9] K. Miyano, M. Veyssie, J. Chem. Phys. 87 (1987) 3153. [10] S. He´non, J. Meunier, Rev. Sci. Instrum. 62 (1991) 936. [11] Y. Majima, M. Iwamoto, Rev. Sci. Instrum. 62 (1991) 2228. [12] M. Iwamoto, Y. Majima, H. Naruse, T. Noguchi, H. Fuwa, Nature 353 (1991) 645. [13] Y. Majima, M. Iwamoto, Jpn. J. Appl. Phys. 29 (1990) 564. [14] Y. Majima, H. Naruse, M. Iwamoto, Jpn. J. Appl. Phys. 31 (1992) 864. [15] M. Iwamoto, T. Kubota, O.Y. Zhong-can, J. Chem. Phys. 104 (1996) 736.