Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 147–153

Measurement of Dielectric Polarizations for Analyzing the OrientationalOrder of Langmuir Monolayers

Robert Wagner, Tetsuya Yamamoto, Takaaki Manaka, Mitsumasa Iwamoto∗Department of Physical Electronics, Tokyo Institute of Technology, 2-12-1 S3-33 O-okayama, Meguro-ku, Tokyo 152-8552, Japan

Received 25 June 2005; received in revised form 7 October 2005; accepted 28 October 2005Available online 9 December 2005

Abstract

The dielectric polarizations, i.e. spontaneous, linear, and second order non-linear polarizations, generated from Langmuir monolayers comprisedof rod-shaped molecules were analyzed, and represented as functions of the orientational order parameters S1, S2, and S3 (Sn = 〈Pn(cos θ)〉, θ:molecular tilt angle, 〈〉: thermodynamic average, Pn(cos θ): Legendre polynomial of nth order). It has been shown that the Maxwell displacementcurrent (MDC), Brewster angle reflectometry (BAR), and optical second harmonic generation (SHG), which are attributed to the spontaneous,linear, and non-linear polarization, respectively, are capable of detecting the orientational order parameter S1, S2, and S3 of Langmuir monolayers.A ′

I©

K

1

ctsdoacctmastddOtT

0d

n experiment using the MDC-BAR-SHG was conducted on Langmuir monolayers comprised of 4-octyl-4 -cyanobiphenyl rod-shaped molecules.t is shown that the MDC-BAR-SHG measurements are useful to investigate the orientational structure of Langmuir monolayers. 2005 Elsevier B.V. All rights reserved.

eywords: Dielectric polarization measurement; Orientational order parameter; Langmuir monolayer

. Introduction

The physicochemical properties of Langmuir monolayersomprised of amphiphiles have attracted much attention sincehe discovery of preparation technique by Langmuir [1]. Thetructures of monolayers are determined by the positionalistribution of molecular heads on the water surface andrientational distribution of molecular tails pointing toward their. The structures of various condensed phases of monolayersomprised of rod-shaped molecules, e.g. fatty acids, were elu-idated by means of X-ray diffraction technique coupled withhe conventional surface pressure-area (�-A) isotherm measure-

ent [2]. Microscopic techniques, e.g. fluorescent microscopynd Brewster angle microscopy, were developed to visualize thehapes and orientational patterns of domains [3]. Theoretically,he positional distribution of molecular heads and orientationalistribution of molecular tails are expressed by the positional or-er parameters and orientational order parameters, respectively.f the two order parameters, the orientational order parame-

ers provide basic insight into specific properties of monolayers.he orientational order parameters Sn(≡ 〈Pn(cos θ)〉) were in-

∗ Corresponding author. Tel.: +81 3 5734 2191; fax: +81 3 5734 2191.

troduced as an extension of the orientational order parameter S2of nematic liquid crystal [6,7], where Pn(cos θ) is the Legendrepolynomial of n-th order (θ: molecular tilt angle, 〈〉: thermody-namic average). The symmetry breaking of Langmuir monolay-ers at an air-water interface is characterized by the orientationalorder parameters of odd-number-th order, e.g. S1 and S3. Fromthe view point of dielectric physics, the dielectric polarizationsgenerated from Langmuir monolayers, i.e. spontaneous, linear,and non-linear polarizations, are dependent on the orientationalorder parameters Sn [8]. Thus, we have developed a system tomeasure the dielectric polarizations generated from Langmuirmonolayers in order to gain information on the orientational or-der parameters Sn [9–11]. In our previous study, the spontaneousand second order non-linear polarizations were measured bymeans of the Maxwell displacement current (MDC) [9] and op-tical second harmonic generation (SHG) [10], respectively, andS1 and S3 of monolayers comprised of rod-shaped molecules,e.g. alkyl-cyanobiphenyl homologues (nCB), were investigated[12]. Recently, Brewster angle reflectometry (BAR) was con-structed to measure the linear polarization generated from mono-layers, and to determine the orientational order parameter S2[11], where S2 is responsible for the liquid-crystal-like behaviorsof monolayers in condensed phase, e.g. flow induced reorienta-tion [13,14] and flexoelectric effect [15]. In the present study, the

E-mail address: iwamoto@pe.titech.ac.jp (M. Iwamoto).

927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.colsurfa.2005.10.084

148 R. Wagner et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 147–153

spontaneous, linear, and second order non-linear polarizationsgenerated from monolayers comprised of rod-shaped moleculeswere analyzed, and represented as functions of the orientationalorder parameters S1, S2, and S3, on the purpose for establish-ing the method to probe the orientational structure of Langmuirmonolayers through the dielectric polarizational phenomena.We also discuss the equation of the MDC, BAR, and SHG interms of the orientational order parameters S1, S2, and S3. In or-der to experimentally demonstrate that MDC-BAR-SHG systemis capable of detecting the orientational order parameters S1, S2,and S3, an experiment was carried out on a monolayer comprisedof 4-octyl-4′-cyanobiphenyl (8CB) rod-shaped molecules usingMDC-BAR-SHG system.

2. Analysis

2.1. Polarization Generated From Langmuir Monolayers

The dielectric polarizations generated from Langmuir mono-layers are represented as

P = P0 + χ(1) · E + χ(2) : EE · · · , (1)

where the first, second, and third terms represent spontaneous,linear, and second order non-linear polarization, respectively.χ(1) is the linear susceptibility tensor and χ(2) are the secondoetvpdatranfmibswori

CdfiiFs

Fig. 1. A model of Langmuir monolayers comprised of rod-shaped molecules.(a) The relationship between director coordinate (u, v, w) and laboratory cood-inate (x, y, z). m is the director of the monolayer and n is the water surfacenormal. (b) Definition of the tilt angle θ and tilt azimuth φ on the orientation ofconstituent molecules. (c) the permanent dipole moment and electronic polariz-ability of constituent rod-shaped molecules.

polarization P generated from monolayers is calculated as [17]

P = Ns

∫µf (θ) sin θdθ, (2)

where f (θ) is the molecular orientational distribution functionand is represented as

f (θ) =∞∑

k=0

2k + 1

2SkPk(cos θ). (3)

In this way, the dielectric polarization generated from monolay-ers comprised of rod-shaped molecules are related to the ori-entational order parameters Sn. In order to keep the descriptionsimple, we express the components of polarizations and suscep-tibility tensors in the director coordinate in this section. Notethat in the derivation of the equation of MDC, BAR, and SHG,the transformation using the Euler matrix (see Fig. 1(a))

α sin γ − sin γ cos α cos ϑ − sin α cos γ cos α sin ϑ

γ cos α − sin γ sin α cos ϑ + cos γ cos α sin α sin ϑ

sin ϑ sin γ cos ϑ

⎞⎟⎠ (4)

to the laboratry system is necessary as we discuss in Section 2.2.The spontaneous polarization P0 is generated from mono-

layers even when the external electric field is absent. On ac-count of the thermally induced rapid molecular rotation ofconstituent rod-shaped molecules around molecular long axis,ot

rder non-linear susceptibility (SOS) tensor. E is an externallectric field. The higher rank terms are usually neglected sincehey are small in comparison with the first three terms. In ad-ance of the analysis on the relationship between these dielectricolarizations and orientational structure of monolayers, here, weiscuss a model of Langmuir monolayers used in this paper. Inmanner similar to our previous study [16], we define a direc-

or m as an average orientation of the long-axes of constituentod-shaped molecules with C∞ symmetry, where it is expresseds m = (cos α sin ϑ, sin α sin ϑ, cos ϑ) in the laboratory coordi-ate (see Fig. 1(a)). ϑ is the tilt angle of the monolayer directorrom the water surface normal n, and α is the tilt azimuth ofonolayer director from the plane of light incidence (x-z plane

n Fig. 1(a)). The molecular tilt angle θ is defined as the angleetween the direction of molecular long axis of constituent rod-haped molecules and director m (see Fig. 1(b)). In accordanceith our previous treatment [16], we assumed that orientationf constituent rod-shaped molecules distribute uniformly withespect to the tilt azimuth φ (Fig. 1(b)) around m (uniaxial-ty). This assumption is analogous to the expression of smectic

liquid crystals [6,7]. The constituent molecules possess theipole moment µ = µp + α · Ei + β : EiEi in external electriceld, where Ei is local electric field, α is the linear polarizabil-

ty tensor, and β is second order non-linear polarizability tensor.or simplicity, without loss of physics underlying here, we as-ume Ei ∼ E in this paper. According to dielectric physics, the

R(α, ϑ, γ) =

⎛⎜⎝

cos α cos ϑ cos γ − sin

sin α cos ϑ cos γ + sin

− sin ϑ cos γ

nly the component of permanent dipole moment parallel tohe molecular long axis contribute to generate spontaneous

R. Wagner et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 147–153 149

polarization (see Fig. 1(c)). The permanent dipole momentof a constituent rod-shaped molecule is expressed as µp =µ0(cos φ sin θ, sin φ sin θ, cos θ)D (see Fig. 1(b)), where the suf-fix D represents the director coordinate. As the monolayers pos-sess uniform orientational distribution of rod-shaped moleculeswith respect to φ, the spontaneous polarization generated froma monolayer is described as [12,16]

P0 = Nsµ0S1m, (5)

where Ns is the surface molecular density. Thus, the sponta-neous polarization generated from monolayers is dependent onthe orientational order parameter S1.

The linear polarization P1(= χ(1) · E) is induced by the ap-plication of external electric field. When we use laser light asa source of external electric field, the electronic polarization,which is ascribed to the induced dipole of constituent molecules,is the main origin of the linear polarization generated frommonolayers. Due to the rod-shape of constituent molecules (C∞symmetry), the electronic polarizability α‖ in the molecularlong-axis is different from the electronic polarizability α⊥ in themolecular short-axis. Taking into account the uniform distribu-tion of molecular long axes around m, the linear susceptibilitytensor is represented as [11]

χ(1) =

⎛⎜⎝

χDu 0 0

0 χD 0

⎞⎟⎠

D

(6)

w

χ

χ

χ

woa

ima

P

ws

s

χ

ott

the chiral component of SOS tensor, and when the monolayersare achiral (C∞v symmerty), sD14 = 0. The components of SOStensor are related to the orientational order parameters S1 andS3 as:

sD14 = Ns

2S2β14 (12)

sD15 = Ns

5(S1 − S3)(β33 − β31) + Ns

10(3S1 + 2S3)β15 (13)

sD31 = Ns

5(S1 − S3)(β33 − β15) + Ns

5(4S1 + S3)β31 (14)

sD33 = 2

5Ns(S1 − S3)β31 + Ns

5(3S1 + 2S3)β33, (15)

where β14, β15, β31, and β33 are the non-zero components ofsecond order non-linear polarizability tensor

β(2) =

⎛⎜⎝

0 0 0 β14 β15 0

0 0 0 β15 −β14 0

β31 β31 β33 0 0 0

⎞⎟⎠ (16)

of rod-shaped molecules with C∞ symmetry. Therefore, the sec-ond order non-linear polarization P2 generated from monolayerscomprised of rod-shaped molecules is dependent on S1 and S3.

2.2. The Maxwell displacement current, Brewster anglereflectometry, and optical second harmonic generation

slSopptS

mi

tmoM

I

wbogamil

5e

v

0 0 χDw

ith

Du = εx − 1 = Ns

(−α‖ − α⊥

3S2 + 2α⊥ + α‖

3

)(7)

Dv = χx (8)

Dw = εz − 1 = Ns

(2

3(α‖ − α⊥)S2 + 2α⊥ + α‖

3

), (9)

here S2(= 〈3 cos2 θ − 1〉/2) is the second order orientationalrder parameter. In this way, the linear polarization is written asfunction of S2.

The second order non-linear polarization P2(= χ(2) : EE) isnduced by the laser irradiation on monolayers due to the sym-

etry breaking [18]. P2 is expressed by the vector representations [12,16,19]

2 = [(sD33 − sD15 − sD31)(E · m)2 + sD31E · E]m + sD15(E · m)E

+ sD14(E · m)(E × m), (10)

here sD14(= (χDuvw + χD

uwv)/2), sD15(= (χDuwu + χD

uuw)/2),D31(= χD

wuu), and sD33(= χDwww) are the non-zero components of

econd order susceptibility (SOS) tensor

(2) =

⎛⎜⎝

0 0 0 sD14 sD15 0

0 0 0 sD15 −sD14 0

sD31 sD31 sD33 0 0 0

⎞⎟⎠

D

(11)

f monolayers with C∞ symmetry. The representation of SOSensor in laboratory coordinate is derived by the Euler matrixransformation using R(ϑ, α, 0) (see ref. [16]). Note that sD14 is

The MDC, BAR, and SHG have been developed to mea-ure the spontaneous, linear, and second order non-linear po-arizations generated from Langmuir monolayers, respectively.ince these polarizations generated from monolayers comprisedf rod-shaped molecules are functions of the orientational orderarameters S1, S2, and S3, the MDC–BAR–SHG system is ca-able of collecting the information of the orientational distribu-ion of constituent rod-shaped molecules. Here, we discuss how1, S2, and S3 are measured by the MDC–BAR–SHG measure-ent. The experimental setup of MDC–BAR and MDC–SHG

s depicted in Fig. 2(a) and (b), respectively.The MDC is measured as a transient current flowing between

he two electrodes (electrodes 1 and 2 in Fig. 2(a) and (b)). Theain contribution to the generation of MDC is reorientation

f spontaneous polarization P0 induced in monolayers, and theDC I is represented as:

= d

dt

(B

dP0 · n

)= d

dt

(Bµ0Ns

dS1 cos ϑ

), (17)

here B is the effective area of electrode 1 and d is the distanceetween electrode 1 and water surface. In LE phase (ϑ = 0), therientational order parameter S1 is derived by the direct inte-ration of I over t. MDC flows during monolayer compressions long as S1 is non-zero due to the condensation of constituentolecules. Thus, the integration constant of S1 is zero if MDC is

ntegrated from the molecular area, where I = 0 during mono-ayer compression.

When p-polarized light incidents at Brewster angle B(∼3.1◦) to an air–water interface without Langmuir monolay-rs, all reflected light vanishes. On the other hand, when there

150 R. Wagner et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 147–153

Fig. 2. (a) The experimental setup of MDC–BAR measurement. He–Ne laserwas used as a light source, and the reflected light is collected by CCD camera.P1: polarizer; P2: analyzer; TL: tube lens; PH: pin hole; Ob: objective. (b) Theexperimental setup of MDC–SHG measurement. The SHG detection system issetup so that the electric field of s-polarized incident, reflected, and transmittedlight is parallel to the barrier compression direction.

is a monolayer at the air-water interface, the reflected light nolonger vanishes and can be collected. Since the background sig-nals from the bulk mediums (the air and water) are minimizedat the Brewster angle, the collected signals are only dependenton the refractive index of monolayers, which represents the ef-fect of the linear polarization generated from the monolayers.Brewster angle microscopy (BAM) had been developed to vi-sualize domain shapes and orientational patterns in monolay-ers without fluorescent probe as an in-plane contrast of reflec-tive index due to the optical anisotropy or phase coexistence ofmonolayers [4,5]. Therefore, reflectometry at the Brewster angle(BAR) allows us to collect quantitative information of linear po-larization generated from monolayers in the same experimentalsetup [11]. The reflectivity r of monolayers comprised of rod-shaped molecules (p-polarized reflected light) is derived usingthe Berreman’s 4 × 4 matrix formalism as (see Fig. 2(a)) [20]:

r = A cos2 α + B (18)

with

A = k�z 2n1 cos B cos2 t(n2 cos B+n1 cos t)2

εx(εz−εx) sin2 ϑ

εx sin2 ϑ+εz cos2 ϑ

B = k�z 2n1 cos B cos2 t(n2 cos B+n1 cos t)2

× [(n21(1+tan2 B)−εx)(εz−εx) cos2 ϑ+(n2

1−εx)(εx−n21 tan2 B)]

εx sin2 ϑ+εz cos2 ϑ,

where n1(∼ 1.00) and n2(∼ 1.33) are reflective indices of theair and water, and t is the transmitted angle of the incidentlight passing through the water. �z is the monolayer thickness,and k is the wave number of incident light (k�z � 1). When theinteraction between domains is not strong, the in-plane orien-tation of domains consisting a monolayer is random. Thus, thereflected light intensity collected by BAR is proportional to theaverage of r2 with respect to α, i.e.

r2 = 3

8A2 + AB + B2. (19)

Here, we assumed that the director tilt angle ϑ is constantin the plane of monolayers, where ϑ is estimated by SHGmeasurements [22,23]. The constants �ξ(= Ns(α‖ − α⊥)) andε(= 1 + Ns(2α⊥ + α‖)/3) (see Eqs. (7)–(9)) are extrapolatedfrom refraction index of bulk liquid crystal [21]. In accordancewith the algorithm we used in our previous study [11], the orien-tational order parameter S2 is determined by the measurementof the intensity of reflected light using BAR.

banjrptpmsbns

P

P

acra(amwgms

The second harmonics are generated (SHG) from monolayersy the irradiation of laser light due to the symmetry breaking atn air–water interface [18]. The source of SHG is second orderon-linear polarization P2. The SH measurement system is ad-usted so that the electric fields of s-polarized signal of incident,eflected, and transmitted light are parallel to the barrier com-ression direction. The intensities of SH signals are proportionalo |P2 · aanalyzer|2 (|P2|: the absolute value of P2, aanalyzer: theolarization of analyzer). The symmetry of monolayers is deter-ined by the SHG measurement at 4 fundamental polarization

ets (p–p, p–s, s–p, and s–s). We denote the s-polarized SH lighty p-polarized incidence as p–s in this paper. The second orderon-linear polarizations generated from monolayers at p–s and–s geometries are written as:

2 p · aouts = E2

0[(sD33 − sD15 − sD31)(ainp · m)2aout

s · m

+ sD31aouts · m + sD14(ain

p · m)(aouts ×ain

p ) · m] (20)

2 s · aouts = E2

0[(sD33 − sD31)(ains · m)2 + sD31](aout

s · m), (21)

inp and ain

s are polarizations of p-polarized and s-polarized in-ident light, respectively. aout

s is the polarization of s-polarizedeflected or transmitted light. Thus, neither p–s nor s–s signalsre detected from the achiral monolayers with C∞v symmetrym = n and sD14 = 0). Information on the average of Eqs. (20)nd (21) over the domains in irradiated area is collected by SHGeasurement. When the inter-domain interaction is sufficientlyeak, the orientational distribution of the director m is homo-eneous with respect to the tilt azimuth α (m = cos ϑn). If suchonolayers are comprised of achiral molecules, neither p–s nor

–s SH signals are detected from the monolayers since symmetry

R. Wagner et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 147–153 151

of the monolayers is C∞v on the scale of irradiated area. Notethat when the tilt direction of directors m is arranged to be par-allel (Cs symmetry), e.g. by anisotropic shear stress, both p–sand s–s signals are detected [13,14]. The SH intensities detectedfrom the monolayers with C∞v symmetry (sD14 = 0) are repre-sented as (see Appendix A):

Ir = |R1S1 + R3S3|2 (22)

It = |T1S1 + T3S3|2 (23)

for the reflected and transmitted geometry, respectively. The po-larizations of incident, reflected, and transmitted lights are ad-justed so that either of R1, R2, T1, and T2 (given in AppendixA) becomes zero. When R3 and T3 = 0, the detected intensitiesof SH signals are proportional to |S1|2, whereas when R1 andT1 = 0, the detected intensities of SH signals are proportionalto |S3|2. In this way, S1 and S3 are derived by SHG measure-ment. Thus, taking advantage of the symbiotic relationship ofMDC, BAR, and SHG systems, we are now able to measure thespontaneous, linear, and second order non-linear polarizationsgenerated from monolayers, and to obtain the orientational orderparameters S1, S2, and S3.

3. Experiment

The experimental setups of MDC–SHG and MDC–BARmeasurements are the same as in refs. [10] and [11], respec-tively (see Fig. 2(a) and (b)). The MDC–SHG and MDC–BARmeasurement systems are mounted to two rectangular troughsin the same size (730 mm × 150 mm). 8CB monolayers are pre-pared by spreading 8CB molecules in a chloroform solution(1.0 mM) on the surface of water filled in the rectangular Lang-muir troughs. The volume of solutions spread on the water sur-faces is 130 �l in MDC–SHG measurement and 180 �l in MDC–BAR measurement. The MDC–SHG and MDC–BAR measure-ments are performed during the compression of monolayers bytwo barriers installed on the troughs. The barrier compressionspeed is adjusted to 10 mm/min (compression rate: 4.2 A2/min)in MDC–SHG measurement and 20 mm/min (compression rate:5.6 A2/min) in MDC-BAR measurement for the purpose to com-press the monolayers at the similar rates.

4. Results and discussion

Typical examples of the results of MDC–SHG measurementson 8CB monolayers is shown in Fig. 3(a) and (b). p–p and s–p

Fllm

ig. 3. Typical examples of the result of MDC–SHG measurements on 8CB monolayines. (a) SHG measurement was performed in four-fundamental polarization setup.ine, s–p: solid line), and p–s and s–s SH signals were detected at reflected geometery

easured selectively in the SHG measurement. The polarization of incident δi, reflec

ers. SHG measurements. Each result was divided into three region by the grayp–p and s–p SH signals were detected at transmitted geometry (p–p: broken(p–s: broken line, s–s: solid line). (b) S1 (reflected) and S3 (transmitted) were

ted δr, and transmitted δt are adjusted to 34◦, 41◦, and −68◦, respectively.

152 R. Wagner et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 147–153

Fig. 4. A typical example of the result of MDC–BAR measurements. The resultwas divided into three regions by gray lines.

signals were detected at transmitted geometry, and p–s and s–ssignals were detected at reflected geometry (Fig. 3(a)). S1 andS3 were selectively collected using the method described in Sec-tion 2.2, and plotted in Fig. 3(b). The transmitted and reflectedSH signals in Fig. 3(b) are proportional to |S1|2 and |S3|2, re-spectively. The z-component of dipole moment is calculated byintegrating the MDC I over time during the monolayer compres-sion (the third graph from the bottom in Fig. 3(a) and (b)), and isproportional to S1. A typical result of MDC–BAR experimentsis shown in Fig. 4. S2 was calculated by the algorithm used in[16], and plotted in Fig. 4 (second graph). The experimental re-sults in Figs. 3 and 4 were divided into three regions accordingto the surface pressure measurement (�–A isotherm). Region1 was further divided into A and B on the basis of MDC data.There is a small difference of MDC curve between Figs. 3 and4, e.g. the partition between region 1A and 1B. This is becauseMDC is very sensitive to the humidity of atmosphere. In spiteof the difference, the region by region characteristics of surfacepressure and MDC data in Fig. 4 are quite similar to that in Fig.3.

In region 1, surface pressure was immeasurably small. There-fore, monolayers were in the fluid phase (gas and liquid ex-

panded phase) in this region. All SH signals were not detectedin region 1A, i.e. 8CB monolayers were not SH active in thisregion (S1 = 0 and S3 = 0 in Eqs. (12)–(15)). This result is alsosupported in MDC data (I = 0). In region 1B, p-p and s-p signalsincrease gradually, whereas p–s and s–s signals are still immea-surably small (see Fig. 3(a)). As we discussed in Section 2.2, itindicated that monolayers with C∞v symmetry was formed inthis region (see Eqs. (20) and (21)). In Fig. 3(b), |S1| and |S3|increased steadily up to ∼ 70 A2/molecule, and then becomeconstant. The increase of S1 was also detected from MDC datain this region. In Fig. 4, the intensity of reflected light was con-stant in region 1. Thus, S2 was also constant, and was zero inregion 1. Even in region 1B, significant change of the intensity ofreflected light has not been detected (Fig. 4). In region 2, surfacepressure increased steeply, and reached the maximum at the endof this region (see Fig. 3(a) and (b)). Thus, the 8CB monolayerswere in the condensed and solid phases in this region. Whereasp–p and s–p SH signals were detected, p–s and s–s SH signalswere not detected in region 2, i.e. the 8CB monolayers also pos-sess C∞v symmetry in this region. From MDC and SHG (seeFig. 3(b)) measurement, S1 increases a little in region 2, whereas|S3| keeps a constant value during the monolayer compressionin this region. On the other hand, the intensity of reflected lightincreases steeply during monolayer compression. Thus, S2 alsoincreases in this region. In region 3, the surface pressure becameconstant incontinuously. In other words, the 8CB monolayer wascwom

S

aamIlnzsiticS

raS

tacs3tmr(

ollapsed, and multilayer of 8CB was formed [12]. In this way, itas demonstrated that S1, S2, and S3 of monolayers comprisedf rod-shaped moleucles were probed using MDC–BAR–SHGeasurements.Here, we summarize our experimental results. S1, S2, and

3 were zero in region 1A in our experimental results (Figs. 3nd 4). In other words, there were neither polar order (S1 = 0nd S3 = 0) nor nematic order (S2 = 0), i.e. constituent 8CBolecules are lying flat on the water surface in this region.

n region 1B, S1 and S3 increased gradually in the mono-ayer compression. In other words, polar symmetry was begin-ing to break in this region (S1 �= 0 and S3 �= 0). S2 is stillero in region 1B, since no significant change of the inten-ity of reflected light has been detected by BAR measurementn region 1B (Fig. 4). Thus, the nematic order does not es-ablish in this region. Constituent 8CB molecules are stand-ng up to point molecular tail to the air during the monolayerompression, but still distributed randomly. A large jump of2 value from ∼ 0 to ∼ 0.8 was detected at the boundary ofegion 1B and region 2 in Fig. 4. More careful experimentsre needed to confirm the quantity of S2 jump. Anomaly of1 and S3 were not detected at the boundary probably due

o little dependence of S1 and S3 on this phase transitionnd its weakness. In region 2, whereas S2 increases in theourse of monolayer compression, S1 and S3 are almost con-tant in this region from MDC–SHG measurement (see Fig.). Note that liquid-crystal-like behaviors, e.g. flow reorienta-ion [13,14] and flexoelectric effect [15], were detected from

onolayers comprised of alkoxyl-cyanobiphenyls in the sameegion (condensed phase). Thus, the presence of nematic orderS2) is possibly the origin of these liquid-cystal-like behaviors

R. Wagner et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 284–285 (2006) 147–153 153

of Langmuir monolayers in condensed phase. In this way, theMDC–BAR–SHG system is demonstrated to be useful to in-vestigate the relationship between the orientational distributionof constituent molecules and domain patterns of Langmuirmonolayers.

5. Conclusion

The dielectric polarizations generated from Langmuir mono-layers are dependent on the orientational distribution of con-stituent molecules of the monolayers, which is represented bythe orientational order parameters Sn. In order to gain infor-mation of the orientational order parameters S1, S2, and S3, wedeveloped the MDC–BAR–SHG system, which is ascribed tothe spontaneous, linear, and non-linear polarizations generatedfrom monolayers. In the present study, in order to establish thismethod, the dielectric polarizations were analyzed and repre-sented as functions of S1, S2, and S3. We also discussed the meth-ods to determine S1, S2, and S3. The experiments were carriedout on monolayers comprised of 8CB molecules to demonstratethat the MDC–BAR–SHG system is capable of probing S1, S2,and S3. As we discussed in Section 2.2, it is possible to use BARas Brewster angle microscopy (BAM), and to collect the imagesof domain shape and orientational patterns of monolayers inthe same setup. Thus, the MDC–BAR–SHG system is useful toitm

A

R

A

R

R

T1 = Ns

5{(2β33 − 2β31 + 3β15) sin δi cos δi sin δt sin θi

− (2β33 − 2β31 + 3β15) cos2 δi cos δt cos θi cos θt sin θi

+ (β33−β15 + 4β31)(sin2 δi + cos2 δi cos2 θi) cos δt sin θt

+ (2β31 + 3β33) cos2 δi cos δt sin2 θi sin θt} (A.3)

T3 = −Ns

5{2(β33 − β31 − β15) sin δi cos δi sin δt sin θi

− 2(β33 − β31 − β15) cos2 δi cos δt cos θi cos θt sin θi

+ (β33 − β31 − β15)(sin2 δi + cos2 δi cos2 θi) cos δt sin θt

− 2(β33 − β31) cos2 δi cos δt sin2 θi sin θt}, (A.4)

where δi, δr, and δt are the polarizations of incident, reflected,and transmitted light, respectively. The equations when ϑ �= 0is describe in ref. [16].

References

[1] G.L. Gaines, Insoluble Monolayers at Liquid-Gas Interfaces, Interscience,New York, 1966.

[2] V.M. Kaganer, H. Mohwald, P. Dutta, Rev. Mod. Phys. 71 (1999) 779.[3] R.M. Weis, H.M. McConnell, Nature 310 (1984) 47.[4] S. Henon, J. Meunier, Rev. Sci. Instrum. 62 (4) (1991) 936.

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nvestigate the relationship between the orientational distribu-ion of constituent molecules and domain patterns of Langmuir

onolayers.

cknowledgement

This work was supported by the Grants-in-Aid for Scientificesearch of JSPS.

ppendix A. The Expression of R1, R3, T1, and T3

Here, We summarize R1, R3, T1, and T3 (ϑ = 0):

1 = Ns

5{(2β33 − 2β31 + 3β15) sin δi cos δi sin δr sin θi

− (2β33 − 2β31 + 3β15) cos2 δi cos δr cos θi cos θr sin θi

+ (β33−β15 + 4β31)(sin2 δi + cos2 δi cos2 θi) cos δr sin θr

+ (2β31 + 3β33) cos2 δi cos δr sin2 θi sin θr} (A.1)

3 = −Ns

5{2(β33 − β31 − β15) sin δi cos δi sin δr sin θi

− 2(β33 − β31 − β15) cos2 δi cos δr cos θi cos θr sin θi

+ (β33 − β31 − β15)(sin2 δi + cos2 δi cos2 θi) cos δr sin θr

− 2(β33 − β31) cos2 δi cos δr sin2 θi sin θr} (A.2)

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