Anisotropic Shear Viscosity of Photoaligned Liquid Crystal Confined in

Sep 24, 2015 - In the context of the use of liquid crystals (LCs) as lubricants and lubricant additives, this study investigates the anisotropic shear...
0 downloads 7 Views 2MB Size
Download PDF
Article pubs.acs.org/Langmuir

Anisotropic Shear Viscosity of Photoaligned Liquid Crystal Confined in Submicrometer-to-Nanometer-Scale Gap Widths Revealed with Simultaneously Measured Molecular Orientation Shintaro Itoh,*,† Yuuichi Imura,† Kenji Fukuzawa,† and Hedong Zhang‡ †

Department of Micro-Nano Systems Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan Department of Complex Systems Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan

‡

ABSTRACT: In the context of the use of liquid crystals (LCs) as lubricants and lubricant additives, this study investigates the anisotropic shear viscosity of LCs confined in nanometer-sized gap widths subject to both shearing and photoalignment. The photoalignment is achieved using anisotropically dimerized polyvinyl cinnamate (PVCi) films coated on substrates. We simultaneously measure the viscosity and order parameter of a liquid crystal (4-cyano-4′-pentylbiphenyl) confined and sheared in the gap range of 500 nm down to a few nm. We achieve this simultaneous measurement using an original method that combines a highly sensitive viscosity measurement and a sensitive birefringence measurement. When the LC is sheared in the same direction as the photoalignment (parallel shearing), the order parameter, which is around 0.3 in the bulk state, increases up to around 0.4 at a gap width of less than 50 nm and the viscosity is smaller than half the bulk viscosity. We consider that this increase in the order parameter is due to the highly ordered photoaligned LC layer near the PVCi film, and the viscosity decrease is due to shear thinning of this layer enhanced by both confinement and molecular ordering. In addition, we observe a gradual decrease in viscosity starting at a gap of less than around 300 nm in the parallel shearing. Based on the apparent slip model, we show that the LC layer near the PVCi film can also cause this gradual viscosity decrease. In contrast, when the LC is sheared in the direction perpendicular to the photoalignment direction (perpendicular shearing), the viscosity increases as the gap decreases. We speculate that this is due to the rotational motion of the LC molecules caused by the competing effect of shear alignment and photoalignment. We believe our findings can significantly contribute to a better understanding of the confined LCs utilized for lubrication.

1. INTRODUCTION Liquid crystals (LCs) are unique materials that exhibit both the fluidity and long-range ordered structure of molecules, as in a crystal.1−4 The same LC can have different viscosities due to differences in the ordered structures. The shear viscosity of a nematic LC is characterized by three different viscosities depending on the relationship between the director of the LC molecule and the direction of shear, and these viscosities are known as Miesowicz viscosities.5,6 The other unique property of LCs is that electric and magnetic fields and alignment films on the solid surface can be used to control the ordered structure. Liquid-crystal displays are the most successful application that utilizes this feature in combination with the LC’s optical properties. In the context of LC application, several attempts have been made to use LCs as a lubricant or a lubricant additive in mechanical systems.7 Macroscopic friction measurements using instruments such as the pin-on-disk (POD) tribometer have revealed that LC molecules adsorbed onto the surface work as a lubricious boundary layer and reduce the friction coefficient down to the order of 0.01 in the boundary lubrication regime. LCs can also be potentially utilized for the active control of lubrication performance, since the viscosity can be controlled externally.7,8 The low friction of © 2015 American Chemical Society

the LC boundary layer is considered to be due to viscosity lowering caused by molecular alignment along the sliding direction. However, the detailed mechanisms underlying this phenomenon have not thus far been clarified. The major difficulty in such investigations is the small thickness of the LC boundary layer. The boundary layer is confined and sheared between two sliding surfaces and the confining gap widths can have sizes of the order of submicrometers to nanometers. Therefore, nanometric measurements are essential, and the surface force apparatus (SFA) is one of the most successful methods for nanotribological and nanorheological investigations of thin liquid films.9 SFA measurements have revealed that the mechanical properties of LCs confined in molecularsized narrow gaps are quite different from those in the bulk state depending on the ordered structure.10−16 However, in these studies, the shear viscosity of the confined LCs was not sufficiently low to explain the low friction coefficients measured in macroscopic friction tests. Further investigations are required for a better understanding of these phenomena and for Received: July 23, 2015 Revised: September 7, 2015 Published: September 24, 2015 11360

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir

Figure 1. (a) Schematic of the fiber wobbling method (FWM) apparatus. (b) Block diagram of equipment for the signal processing of photocurrents obtained from the position sensitive detector (PSD). The abbreviations used in the block diagram are as follows: Amp, amplifier; FG, function generator; I−V cnv, current−voltage convertor; Def amp, differential amplifier; LA1, lock-in amplifier #1; LA2, lock-in amplifier #2; PC, personal computer. spot moves at the boundary of the two elements, and the differential signal represents the amount of deflection. This technique has a deflection sensitivity of around 0.01 nm. Since the spring constant of the fiber is 10−50 N/m, the shear force sensitivity is of the order of 0.1 nN. In the viscosity measurement, we oscillated the probe sinusoidally and measured the amplitude and phase shift of the probe tip oscillation. The mechanical model of the viscosity measurement is represented by the following equation of motion (1).

expanding the application of LCs as lubricants or lubricant additives. In this study, we attempt to clarify the effect of alignment films on the apparent viscosity of LCs confined and sheared in submicrometer-to-nanometer-sized gap widths. For the viscosity measurements, we use the fiber wobbling method (FWM), which we developed in our previous study,17 combined with birefringence measurements. This new setup enables us to measure the viscosity and molecular ordering simultaneously. Alignment films, which are commonly used in LC displays, are usually made of polymer and are coated on the solid substrate. For lubrication purposes, we expect that the use of alignment films can be one of the techniques to control the orientation of LCs at the boundary. The preparation of the alignment film can be achieved via two main approaches. One approach involves rubbing the polymer film with a flexible cloth, wherein LC molecules orient along the rubbing direction. The other method involves the irradiation of the film by polarized ultraviolet (UV) light.18 The latter technique is called photoalignment, and we employed this technique in this study, since rubbing leads to the formation of wear debris and surface roughening, which can adversely affect viscosity measurements. Viscosity measurements were conducted under three classifications: without photoalignment, with photoalignment parallel to the shearing direction, and with photoalignment perpendicular to the shearing direction.

mx ̈ + k(x − x0) + c(x ̇ − x0̇ ) + c f x ̇ = 0

(1)

We modeled the probe as a single-degree-of-freedom system composed of a spring (spring constant k), mass (m), and damper (damping coefficient c). The displacement of the probe tip in the horizontal direction is denoted as x and damping coefficient of liquid sample is represented as cf in the above equation. Further, the horizontal displacement of the forced oscillation by the piezo actuator is denoted as x0, and it is written as

x0 = a0 sin ωt

(2)

Here, a0, ω, and t denote the amplitude, frequency, and time, respectively. The mechanical properties of the probe, which are represented as k, m, and c, are determined by fitting an analytical equation to the probe’s resonance curve, which is obtained experimentally. By solving eqs 1 and 2, we can write the damping coefficient of the liquid cf as follows:

cf =

a 0k sin Δδ Aω

(3)

Here, A and Δδ represent the amplitude and phase shift of the oscillation at the probe tip, respectively. Δδ is expressed as

2. EXPERIMENTAL SECTION

Δδ = δ0 − δ

Viscosity Measurement Using FWM. An optical fiber with a spherical tip is used as the shear-force detecting probe in the FWM (Figure 1a). The curvature radius of the spherical tip is typically around 100 μm, and the length of the fiber is 2−3 mm. The probe is placed perpendicular to a flat solid substrate on which the LC sample is placed. With the use of a piezo stage that moves the substrate in the perpendicular direction, the LC sample is confined in the gap between the probe tip and the substrate. In this study, the resolution of the piezo stage was 0.1 nm. A piezo actuator is attached to the fixed end of the probe, and it moves the probe along the horizontal direction. The probe tip shears the LC sample, and the shear forces acting on the tip are measured by detecting the fiber deflections. For the deflection measurement, we developed an original optical technique that uses a laser diode with a focusing unit and a position sensitive detector (PSD). The laser beam is focused onto the PSD by using the fiber as a cylindrical lens. The PSD is a dual-element photodiode. When the fiber undergoes deflections, the focused laser

(4)

where δ and δ0 represent the phase of the probe tip oscillation with and without the LC sample, respectively. The viscosity η of the liquid sample is obtained by means of the following equation with the use of the damping coefficient. cf η= (5) Ω Here, Ω denotes the geometrical parameter that represents the shape of two sliding surfaces. In our measurement, the two shapes involved are the spherical tip and flat plate, and consequently, Ω is written as

⎡ 8 ⎛r ⎞ ⎤ Ω = 6πr ⎢ ln⎜ ⎟ + E ⎥ ⎣ 15 ⎝ h ⎠ ⎦

(6)

Here, r represents the curvature radius of the probe tip, h the minimum gap between the two surfaces, and E the correction term 11361

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir

between the probe tip and the glass substrate. Measurement of d is achieved via a crossed polarizer system with a photoelastic modulator (PEM). In the crossed polarizer system, the sample is placed in between two polarizers with orthogonal directions of polarization. The second polarizer placed in front of the detector (photodiode) is called the analyzer. The PEM is used to modulate the polarization state via the photoelastic effect, and it enables the measurement of low-level birefringence. If we define the direction of the fast axis of the PEM as the origin of the polarization direction, that of the first polarizer is −45° and that of the analyzer is 45°. A half-wave plate is used to adjust the direction of polarization of the beam. A quarter-wave plate is used to compensate for the phase shift that occurs when the light passes through the optical fiber probe and the alignment film. The optical fiber probe is made from silicate glass, which is usually an isotropic material. However, it has slight birefringence under mechanical stress that is assumed to form in the bent part of the fiber. As a light source, we used a helium−neon laser with a wavelength of 632.8 nm. The polarizers used were Glan−Thompson prisms. The light intensity at the detector as derived from Mueller calculus is written as follows.21

that assures quantitative agreement between the analytical and numerical solutions. The parameter E was reported as 0.9588 according to the work of Goldman et al.19 The viscosity of the LC sample, which is denoted as η, was determined by the measured A and Δδ using eqs 3−6. Figure 1b shows a block diagram of the signal processing apparatus used to obtain A and Δδ. The photocurrent signals from each element of the PSD are converted into voltage signals, and their difference is obtained with a differential amplifier circuit. The differential signal represents the displacement of the probe tip oscillation, and its A and Δδ are measured by a lock-in amplifier (LA1). The reference signal of LA1 is the driving signal for the piezo actuator that oscillates the probe. We use another lock-in amplifier (LA2) to detect the contact between the probe tip and the solid substrate. In the FWM, the shearing gap between the probe tip and substrate, which is h, cannot be measured directly. Therefore, we detect solid contact (between the probe and the substrate) and define it as the origin of the gap (gap h of 0 nm). The gap width can be determined by the displacement of the piezo stage from the origin. The amplifier LA2 is used to detect the resonant frequency component included in the probe tip oscillation. At the beginning of the solid contact, intermittent contacts between asperities initiate resonant oscillation of the probe tip. Therefore, by monitoring the increase in the resonant frequency component, we can detect the solid contact point with an accuracy of around 0.1 nm.20 The optical fiber probe used in this study was 3.8 mm long with a tip radius of 115 μm, and the spring constant was 21.51 N/m. Birefringence Measurement. Nematic LCs aligned in a single direction show birefringence, which means that they have two different indexes of refraction, that is, the ordinary index no and the extraordinary index ne. The difference in the optical path between the ordinary and the extraordinary light beams is called the retardation R, and it is written as R = hs(ne − no) = hsΔn

I=

(9) Here, I0 and ρ represent the light intensity after the first polarizer and the angle of the fast axis of the sample with respect to the PEM, respectively. The modulated retardance due to the PEM is dM, and it is expressed as dM = B sin φt, where B denotes the retardance amplitude and φ the modulation frequency. The functions of sin dM and cos dM can be expanded with the Bessel functions of the first kind as follows: ∞

sin dM = J0 (B) + 2 ∑ J2n (B)sin 2nφt

(7)

2πR λ

(10)

n=1

∞

Here, hs denotes the thickness of the sample. The retardation R can be converted to the phase difference, which is called the retardance d, using the wavelength of the light source λ. d=

I0 {1 + (1 − cos d)sin 2ρ cos dM + sin d sin 2ρ sin dM} 2

cos dM = 2 ∑ J2n + 1(B)cos(2n + 1)φt

(11)

n=0

Here, J0, J2n, J2n+1 denote the zeroth, 2nth, and (2n + 1)th orders, respectively, of the Bessel function. From eqs 9−11, we obtain the direct-current component IDC, the modulation frequency component If, and the component equal to twice the frequency of modulation I2f, as follows.

(8)

Using eqs 7 and 8, we can determine the difference between the two indexes Δn = ne − no by measuring d with known values of hs and λ. The values of Δn represent the degree of molecular alignment. To examine the effect of the ordering structure of LCs in a confined geometry on the shear viscosity, we established a system for the simultaneous measurement of viscosity and Δn (Figure 2). In the setup, a polarized laser beam is introduced into the optical fiber probe, and it passes through the LC sample confined and sheared

IDC =

⎧ ⎛d⎞ ⎛ d ⎞⎫⎤ I0 ⎡ ⎢1 + J0 (B)⎨cos(4ρ)sin 2⎜ ⎟ − cos2⎜ ⎟⎬⎥ ⎝ ⎠ ⎝ 2 ⎠⎭⎦ ⎩ 2⎣ 2

I f = I0J1(B)cos(2ρ)sin d sin φt

(12) (13)

⎧ ⎛d⎞ ⎛ d ⎞⎫ I2f = I0J2 (B)cos(4ρ)⎨cos(4ρ)sin 2⎜ ⎟ − cos2⎜ ⎟⎬cos 2φt ⎝ ⎠ ⎝ 2 ⎠⎭ ⎩ 2 (14) In this study, the samples are nematic LCs confined in nanometersized gap widths, and their retardance d is quite small. Since If includes the term sin d, in our study, its signal level was very low and severely affected by noise. Therefore, we only used IDC and I2f to obtain d. The modulation amplitude B was adjusted to ensure that J0(B) was zero. The LC sample’s angle of the fast axis ρ was set to zero by the proper alignment of the half-wave plate. In this study, we assumed the LC’s fast axis was parallel to the shearing direction. Under these conditions, IDC and I2f are simplified as follows.

IDC =

I0 2

I2f = I0J2 (B)cos d cos 2φt

(15) (16)

As shown in Figure 2, IDC is obtained by the low-pass filtering. The amplitude of I2f is measured by using the lock-in amplifier, and it is written as

Figure 2. Optical setup for birefringence measurements combined with the fiber wobbling method (FWM) system. 11362

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir A 2f = I0J2 (B)cos d

(17)

S=

From eqs 15 and 17, the retardance d is obtained as ⎛ A 2f ⎞ ⎟⎟ d = cos−1⎜⎜ ⎝ 2IDCJ2 (B) ⎠

(18)

⎛ A 2f ⎞ λ ⎟⎟ cos−1⎜⎜ 2π ⎝ 2IDCJ2 (B) ⎠

(19)

To verify the functioning of the birefringence measurement system, we used a Babinet−Soleil (BS) compensator as a standard sample instead of the LC samples and measured the retardation R (Figure 3). The BS

Figure 3. Retardation measured with Babinet−Soleil compensator to verify the accuracy of birefringence measurements conducted in this study. The straight line is obtained by curve fitting to the experimental data using the least-squares method.

Figure 4. Chemical structures of (a) 4-cyano-4′-pentylbiphenyl (5CB) and (b) polyvinyl cinnamate (PVCi). Table 1, η1, η2, and η3 represent the viscosities when the director of the LC molecule is parallel to the direction of the velocity gradient of shear flow, parallel to the direction of the shear flow, and perpendicular to both these directions, respectively (Miesowicz viscosity). The parameter γ1 represents the rotational viscosity. In this study, all measurements were conducted at the room temperature of 24 ± 1 °C. The viscosities and refractive indexes at 24 °C were estimated by curve fitting of the exponential function,23 and these values are also listed in Table 1. The substrate used was a fused silica glass plate. The root-mean-square roughness of the substrate was around 0.3 nm. For the purpose of photoalignment of 5CB, a thin film of polyvinyl cinnamate (PVCi) was coated on the glass substrate by spin coating. Chemical structure of PVCi is shown in Figure 4b. In the spin coating process, we used a 1 wt % PVCi solution diluted with chloroform. The thickness of the film was in the range of 50−70 nm, and the surface roughness was equivalent to that of the glass substrate. PVCi exhibits a photodimerization reaction upon exposure to ultraviolet (UV) light. The anisotropic surface required for the LC alignment was prepared by PVCi exposure to linearly polarized UV

compensator is an optical device whose R can be changed continuously by a micrometer. As shown in Figure 3, our system successfully measured linearly varying retardation with an accuracy of 0.31 nm. We evaluated the accuracy as thrice the standard deviation calculated from the difference between the measured values of R and the straight line fitted to it. In the measurement with LC samples, we determined Δn from the measured R value by dividing it by the sample thickness hs. We assumed that the sample thickness was equal to the gap between the probe tip and substrate, that is, hs = h. From Δn, we calculated the molecular order parameter S, which is defined as follows:

S=

3cos2 θ − 1 2

(21)

Here, n̅ and Δnmax represent the average and difference of no and ne, respectively, in the case when perfect alignment (S = 1) is achieved. We used the values of n̅ = 1.7601 and Δnmax = 0.3389 determined by Li et al.23 to calculate S from Δn. We must note that, in our experiments, the fast axis of the PEM was set parallel to the shearing direction, which means the LC’s fast axis should also have been parallel to the shearing direction. Therefore, the S determined in this study indicates the degree of molecular alignment in the direction of shearing. Although this is not sufficient to reveal the detailed dynamics of the molecular orientation, it allows us to discuss the relationship between the shear viscosity and the molecular orientation parallel to the shearing direction. Sample Preparation and Experimental Procedure. The LC used in this study was 4-cyano-4′-pentylbiphenyl (5CB). The literature values of the viscosities and refractive indexes of 5CB are summarized in Table 1.24−27 Chemical structure of 5CB is shown in Figure 4a. In

The retardance d can be converted to the retardation R via eq 8, and thus, we have

R=

Δn(6n ̅ + Δn) Δnmax (6n ̅ + Δnmax )

(20)

Here, θ represents the angle between the LC’s molecular axis and the local director. The brackets represent both the temporal and spatial averages. Upon assuming Vuks’ model, S is derived from Δn as follows.22

Table 1. Viscosities and Refractive Indexes of 5CB viscositiesb

refractive indexes T [°C]

ne

no

T [°C]

η1 [Pa s]

η2 [Pa s]

η3 [Pa s]

γ1 [Pa s]

23.1 26.4 29.7 32.2 34.1 24a

1.713 1.703 1.693 1.682 1.669 1.711

1.529 1.53 1.532 1.536 1.542 1.528

23 26 29 32 34 24a

0.1296 0.1052 0.0869 0.0685 0.0581 0.1209

0.0229 0.0204 0.01855 0.0172 0.01667 0.0218

0.0374 0.0326 0.0287 0.0256 0.024 0.0356

0.0968 0.0777 0.0607 0.045 0.0334 0.0898

a Estimated values at 24 °C by curve fitting to literature values. bη1, η2, η3, and γ1 denote viscosities when the director of the LC molecule was parallel to the direction of the velocity gradient, parallel to the direction of shear flow, perpendicular to both these directions, and the rotational viscosity, respectively.

11363

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir light. We used a UV light source of a wavelength of 313 nm and power of 2 mW. The exposure time was 500 s. To confirm that the PVCi films prepared via the above-mentioned procedure had the ability to align 5CB, we constructed a parallelaligned LC cell and measured the order parameter. The LC cell consisted of two glass substrates facing each other with their sides covered with the PVCi film, and the gap between them was around 10 μm. We doped 1 wt % of a dichroic dye (LCD-118) in 5CB to measure the order parameter based on the guest−host effect. We measured the sample’s dichroic absorption by using a spectrometer with a polarizer, and estimated the order parameter SGH using the equation28 SGH = (A∥ − A⊥)/(A∥ + 2A⊥). Here, A∥ and A⊥ represent the maximum absorbance of the dye when the electric vector of the polarization direction of incident light is parallel and perpendicular, respectively, to the alignment direction of the LC. The wavelength of maximum absorption was 636 nm. SGH calculated from the absorbance was 0.64, and we confirmed that the PVCi film successfully aligned the LC. In the simultaneous measurement, we obtained the shear viscosity η and order parameter S while reducing the gap from submicrometers to a few nanometers. The details of the experimental procedure are as follows. First, a drop of 5CB was placed on the glass substrate covered with PVCi film with the use of a microsyringe. This sample was heated to 40 °C to eliminate the effect of alignment by injection flow, and subsequently, it was placed on the piezo stage of the FWM setup. The spherical tip of the probe was immersed into the LC droplet. We started the oscillation of the probe with an amplitude of 50 nm and a frequency of 1 kHz. The gap between the probe tip and the substrate surface, which was initially set to around 1 μm, was decreased at a constant rate of 10 nm/s by means of the piezo stage. During this period, we measured the amplitude A and the phase shift Δδ of the probe tip oscillation to determine η, and we simultaneously measured IDC and A2f to determine S. The measurement was conducted under three different conditions. The first case involved measurement with PVCi film that was not exposed to polarized UV light, which means that the film did not have the ability to align the LC molecules. This measurement was for the purpose of comparison with the two following conditions. The second was the case when the shearing direction was parallel to the alignment direction induced by the PVCi film (Figure 5a). The third case was when the shearing direction was

and perpendicular shearing in the above-mentioned order. In the case of perpendicular shearing, the mean direction of the LC molecules in the gap may not be parallel to the shear direction, and the tensor order parameter should be used to indicate the specific molecular orientation. However, we must note that the S determined in this study represents the degree of molecular alignment to the shearing direction only, as mentioned in the previous section.

3. RESULTS Figures 6−8 show the experimental results for η and S measured in the cases of shearing without photoalignment, parallel shearing, and perpendicular shearing, respectively. The order parameter S is calculated only when the measured retardation is larger than the measurement accuracy of 0.31 nm. The transverse axis shows the gap between the probe tip and the substrate, which corresponds to a distance of h. Each plot shows the averaged value of about ten measurements for every 5 nm gap width. Error bars denote the standard deviation of the measured values. We note here that some error bars are hidden behind the plots. The triangles in Figures 7a and 8a represent the results measured in the case of shearing without photoalignment shown in Figure 6a for comparison. In the shearing without photoalignment case, the order parameter was around 0.3. This is considered to be the result of flow alignment induced by probe shearing. The viscosity at a gap of around 500 nm was about 0.025 Pas, and this value is slightly higher than the η2 value expected at a room temperature of 24 °C (see Table 1). The higher viscosity was considered to be caused by the lower degree of flow alignment when compared with the case of alignment realized with the use of an external electric or magnetic field in the measurement of η2. If no external orienting field is applied, the viscosity of a nematic liquid crystal aligned only by flow is expressed as follows.29 η=

⎛ ⎛ γ ⎞2 ⎞ 1 1 1 ⎟⎟ ⎟ (η1 + η2 − γ1) + η12⎜⎜1 − ⎜⎜ ⎟ 2 4 ⎝ η − η ⎝ 2 1⎠ ⎠

(22)

Here, η12 is the Helfrich viscosity and is equal to α1, which is one of the Leslie coefficients. α1 measured by Herba et al. was around 7.32 mPas at 24 °C.30 By substituting this value of α1 and η1, η2, and γ1 at 24 °C listed in Table 1, we obtained η estimated based on the bulk state theory. The results are plotted using filled circles in Figure 6a. The viscosities measured at gaps from 200 to 500 nm agree well with the estimated values. This result indicates the validity of our measurement. At gaps less than 200 nm, the measured viscosity was greater than the estimated values. We considered that the viscosity increase was caused by confinement in the nanometersized gap. As a result of the intermolecular interactions with the surface, the mobility of the LC molecules confined in the

Figure 5. Graphical explanation of (a) parallel shearing and (b) perpendicular shearing. perpendicular to the alignment direction (Figure 5b). We refer to these conditions as shearing without photoalignment, parallel shearing,

Figure 6. Results of simultaneous measurement of (a) viscosity and (b) order parameter in the case of shearing without photoalignment. Filled circles in (a) represent the viscosity estimated based on bulk theory. Dashed line in (a) represents the viscosity η2. 11364

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir

Figure 7. Results of simultaneous measurement of (a) viscosity and (b) order parameter in the case of parallel shearing. Filled triangles in (a) represent the viscosity measured in the shearing without photoalignment case, depicted here for comparison. Dashed line in (a) represents the viscosity η2.

Figure 8. Results of simultaneous measurement of (a) viscosity and (b) order parameter in the case of perpendicular shearing. Filled triangles in (a) represent the viscosity measured in the shearing without photoalignment case, depicted here for comparison. Dashed lines in (a) represent the viscosities η2 and η3.

the viscosity increase and order parameter decrease was considerably larger in the case of perpendicular shearing. In addition, the viscosities at a gap of around 500 nm were about half those in the case of shearing without photoalignment. In the Discussion section, we discuss the reasons for these various dependences of the viscosity and order parameter on the narrowing gap width, which were uniquely observed with photoalignment.

molecularly narrow gap was suppressed, which led to the viscosity increase.15,16 Although the gap of 200 nm is considerably larger than the molecular size, we speculate that the retarded mobility of LC molecules proximate to the surface affects the viscosities measured at this relatively wide gap, since the LC molecules are assumed to have an ordered structure in the direction of the gap width even without photoalignment. The enhanced viscosity of LC near surface is known as surface viscosity and some experimental approaches to measuring it directly have been developed. Representative studies have utilized SFA,15,16 as mentioned in the Introduction. Further, Tsvetkov has estimated the surface viscosity by measuring the flow rate of LCs passing through nanometer-sized capillary tubes based on Poiseuille’s law.31 He reported that 5CB confined in a gap of 74 ± 10 nm showed about 10 times larger viscosity than η2 and, also, the η dependence on the tube radius was expressed by the exponential relationship. These results were qualitatively consistent with our findings for the case of shearing without photoalignment. The proposed exponential relationship was expressed as η = X + Y exp(−h/Z), where X, Y, and Z are the fitting parameters. When this equation was fitted to the measured viscosity shown in Figure 6a, we obtained X = 0.025152, Y = 0.012624, and Z = 95.347, and the curve agreed well with the experimental result. Completely different results were obtained with photoalignment. In the parallel shearing case (Figure 7), although the viscosity and the order parameter were similar to the corresponding values in the shearing without photoalignment case at around the widest gap of 500 nm, the viscosity gradually decreased and the order parameter increased when the gap decreased. In particular, the order parameter curve exhibited a plateau in the gap range between 25 and 50 nm, as shown in the inset of Figure 7. The gap dependence of the viscosity and order parameter in the case of perpendicular shearing (Figure 8) was qualitatively similar to that of the measurements of the shearing without photoalignment case. However, the extent of

4. DISCUSSION As mentioned previously, for a gap of around 500 nm, the viscosity and order parameter measured with parallel shearing were nearly identical to the corresponding values measured in the case of shearing without photoalignment. However, the gap dependences in both cases were completely different. In the parallel shearing case, the viscosity decreased along with the decrease in the gap. Further, the order parameter exhibited a rapid increase at a gap of less than around 100 nm. This result suggests that there was a photoaligned LC layer near the PVCi surface that had a higher order parameter. In particular, the order parameter curve exhibited a high plateau of 0.4 in the gap range from 50 nm down to 25 nm. The filled circles in Figure 9 illustrate the viscosity measured over this gap range as a function of the shear rate in a double logarithmic chart. The shear rate was determined by dividing the shear velocity by the gap width. The curve of the filled circles shows an exponential decrease in viscosity with increasing shear rate. This phenomenon is known as shear thinning and is caused by a “slip” between molecules when the shear rate exceeds the rate of molecular rearrangement. In a bulk-state liquid, shear thinning occurs when the liquid is highly viscous or the shear rate is fairly large. In contrast, liquids that are relatively less viscous can exhibit shear thinning when they are confined within molecularly sized narrow gaps.32 This is because the molecular mobility is highly restricted in the confined state, and 11365

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir

Figure 10. Apparent slip model.

ηapp = τ Figure 9. Relationship between the shear rate and estimated (open circles) and measured (filled circles) viscosities of the photoaligned LC layer near the PVCi surface (h < 50 nm).

h U

Upon substituting eq 23 into eq 24, we can write ηapp as ηapp = ηbulk

the viscosity is enhanced by a value that is considerably more than that in the bulk state. When the shear rate exceeds a certain yielding point, the viscosity decreases exponentially with further increases in the shear rate. In our previous study, we showed that the enhanced viscosity of nanometer-thick liquid films could be lower than the bulk viscosity because of shear thinning.33 We considered that this is the case with the LC’s viscosity in the gap range of 25−50 nm with parallel shearing. We remark here that the viscosity for the same gap range without photoalignment (shearing without photoalignment case) only exhibited an enhancement and no shear thinning (Figure 6a). Therefore, we speculate that the highly ordered photoaligned LC molecules near the surface contributed to the lowering of the yielding point and led to shear thinning. The gap range of 100−50 nm might be the transition region. For gaps less than 25 nm, although an increase in S was observed, the viscosity behavior was opposite to the shear thinning trend and showed a slight increase. We attribute this result to the viscosity increase due to confinement overcoming the decrease caused by shear thinning. When we focus on the gaps larger than 50 nm in Figure 7, we observe that the viscosity gradually starts to decrease at a gap of less than around 300 nm, even though the order parameter values are almost the same as those measured for shearing without photoalignment. Therefore, we speculate that the mechanism of viscosity decrease in this wider gap range is different from that for gaps of less than 50 nm. We attribute this result to the apparent slip34 caused by a low-viscosity layer near the surface. We hypothesized that the photoaligned LC layer near the surface (h < 50 nm) that exhibited a higher molecular order could be the low-viscosity layer. The open circles in Figure 9 indicate the viscosity values of the presumed lowviscosity layer estimated from the viscosity measured at gaps larger than 50 nm based on the apparent slip model shown in Figure 10. We modeled the low-viscosity layer that has a thickness of hb and a viscosity of ηb. Due to the presence of this layer, a slip length b was introduced. Assuming that the LC above the low-viscosity layer has a viscosity of ηbulk (ηbulk > ηb) and is a Newtonian fluid, the shear stress acting on the shearing surface is written as follows: τ = ηbulk

U h+b

(24)

h h+b

(25)

This relation indicates that the measured viscosity appears to be lower than the actual value when an apparent slip exists (b ≠ 0). The shear stress τb at the boundary between the lowviscosity layer and the above-mentioned Newtonian layer can be expressed in two ways, using ηbulk and ηb, as follows τb = ηbulk

Ub U = ηb b hb + b hb

(26)

Here, Ub represents the shearing speed at the boundary, and it can be written as follows based on the scaling relation Ub = U

hb + b h+b

(27)

From eqs 25 and 26, we can write ηb as ηbulk ηb = 1 + (ηbulk /ηapp − 1)(h/hb)

(28)

From eq 28, we can attribute the gap dependence of ηapp measured at h > 50 nm to the viscosity ηb of the low-viscosity layer. The shear rate at the surface of low-viscosity layer, which is γ = Ub/hb, can be estimated by using eqs 25 and 27 as follows γ=

⎧ ηapp ⎛ 1 Ub 1⎞ 1⎫ = U⎨ ⎜ − ⎟+ ⎬ hb hb ⎠ hb ⎭ ⎩ ηbulk ⎝ h ⎪

⎪

⎪

⎪

(29)

We assumed hb to be 50 nm and ηbulk to be 0.238 Pa s (the average of the measured viscosity at the gap of around 500 nm where the effect of the apparent slip was assumed to be negligible). We plotted the viscosity ηb estimated from ηapp (viscosity measured at h > 50 nm) against shear rate Ub/hb as open circles in Figure 9. From Figure 9, we observe that the shear-rate dependence of ηb (open circles) and that of the viscosity actually measured at gaps less than 50 nm (filled circles) exhibit a close consistency. Further, the shear-rate dependence exhibits typical shear-thinning behavior, which in turn means that the viscosity that is constant at low shear rates decreases exponentially at shear rates higher than a certain yielding point. In addition, we observe a two-stage decrease in the viscosity, as represented by the straight lines of the curve fitting in Figure 9. The shear-rate dependences of these lines were η ∝ γ−0.39 and η ∝ γ−0.90 in that order. This transition occurs at a shear rate of around γ = 3.8, for which case the shearing gap is about 75 nm. From the results of shearing without photoalignment results, we observe that the confinement causes the viscosity enhancement at this gap range.

(23)

Here, τ and U represent the shear stress and shearing speed, respectively. On the other hand, the viscosity measured in the FWM experiments is the apparent viscosity ηapp, which is expressed as follows 11366

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir

the oscillation frequency was 1 kHz in this study. If we compare these shearing conditions with analyses conducted in previous studies,39−41 it can be seen that they correspond to relatively large disturbance of the weakly aligned LC. Thus, we assume that the molecular orientations were primarily dominated by the flow alignment. This speculation does not contradict our results, in which the S values were almost identical for shearing without photoalignment, parallel shearing, and perpendicular shearing at h values of 100−500 nm. However, observation of shear thinning in the case of parallel shearing has not been reported in these previous studies examining oscillatory shear flow.39−41 We believe this is because of the high shear rates of 103 to 104 s−1 expected at the surface layer, which were not achieved in other measurements. For h less than 100 nm, we expected that the LC affected by the surface dominated the dynamics in the gap. Although some experimental approaches to measuring the surface viscosity directly have been developed by using the SFA15,16 or by utilizing capillary tubes,31 as already mentioned in the previous section, to the best of our knowledge, no theoretical studies examining such cases have been conducted. Especially, since the shear thinning behavior is related to fracture mechanics, it is difficult to theoretically predict this phenomenon based on the continuum physics of the LCs. In the case of perpendicular shearing, shear thinning was not observed, even under the same shearing condition as in the parallel shearing case. We expect that there are two possible reasons for this. One is that there is less yielding stress in the case of parallel shearing, because of the higher molecular ordering in the shear direction. The other reason might be that the relaxation rate of the LC’s rotational motion, which is assumed in the case of perpendicular shearing, is sufficiently fast to follow the shearing motion caused by the probe tip. In the parallel shearing case, as the LC molecules have less rotational degrees of freedom, the translational movement of the LC molecules in the shearing direction may dominate the relaxation of the applied shear stress. This rate of relaxation is assumed to be highly retarded as a result of the confinement. To examine the validity of these speculations, more detailed measurements dealing with frequency dependence and temperature dependence must be useful. Especially, if we conduct the same series of measurements in the isotropic phase, we may be able to distinguish the effects of photoalignment clearly from those of confinement and surface anisotropy of the PVCi films. However, this requires further improvement of the measurement system to achieve temperature control of samples. This is a challenge that must be addressed in future study. Finally, based on the results obtained in this study, we discuss the reason as to why using a LC as lubricant or lubricant additive yields low friction coefficients, particularly in the boundary lubrication regime, as reported in previous studies that typically used macroscopic tribology tests such as the POD. The SFA measurement of the confined LC indicated enhanced viscosity, which contradicts low friction. Moreover, in our measurement using FWM, the enhancement of viscosity was measured with shearing without photoalignment. In contrast, when the LC molecules were photoaligned in the shear direction, the viscosity exhibited a gradual decrease at gaps less than around 300 nm. We speculate that this was the result of apparent slip caused by the shear-thinning layer of the photoaligned LC molecules adjacent to the substrate. As already mentioned above, the presence of an apparent slip near the substrate leads to lower friction and higher load capacity,

Therefore, we speculate that the transition of the shear-thinning behavior could be caused by the confinement. The confinement can retard the molecular mobility of the photoaligned LC, which in turn can enhance the shear thinning. From the estimation of ηb, we can conclude that the shear-thinning behavior at the highly aligned and low-viscosity LC layer near the surface can cause the observed gradual decease in the apparent viscosity measured in the gap range of less than 300 to 50 nm, wherein the actual viscosity is Newtonian and the same as that in the bulk state. From the viewpoint of lubrication, the apparent slip induced by the aligned LC layer must effectively reduce the viscous friction and simultaneously increase the flow rate, leading to enhanced load capacity. In the case of perpendicular shearing, it is assumed that LC molecules near the probe surface align in the direction of the shear, although those molecules near the PVCi films align in a direction perpendicular to the shear. Therefore, we considered that the twisted nematic (TN) phase was formed in the gap. Janik et al. have reported that the viscous friction of a confined LC in the TN phase measured using SFA was about half that measured with parallel alignment.16 These authors suggest that reduced intermolecular interactions between LC molecules in the direction of the gap cause the lower viscosity. We assume this is the case in our measurement, since the viscosity measured at around 500 nm was about half that obtained in the case of shearing without photoalignment. However, the order parameter was almost constant at 0.3 in the gap range from 500 to 100 nm and comparable to those obtained in the case of shearing without photoalignment. If the thicknesses of the shear-aligned and photoaligned phases are comparable, the order parameter must be smaller, since the retardations of these phases cancel each other. Therefore, it is believed that either the thickness of the shear-aligned phase or that of the photoaligned phase is dominant in the gap. However, we have not thus far been able to determine which is dominant, since we only measured retardation and the director direction was unknown. At a gap of less than around 100 nm, the order parameter decreased and the viscosity increased with further gap decreases. We speculate that this is the result of the competition between the shear alignment and photoalignment. Since the shearing was sinusoidal, its speed varied periodically between zero and the maximum. When the shear speed was reduced, the shear-aligned LC molecules were able to realign in the direction of photoalignment. Similarly, the photoaligned LC molecules could realign in the direction of the shear when the shear speed was increased. Since the sampling time of the measurement of the order parameter was around 0.1 s and considerably longer than the oscillation period of shearing, which was 1 ms, this dynamic change in alignment was temporally averaged and observed as the decrease in the order parameter. During the realignment, LC molecules exhibited rotational motion. We posit that this rotation led to the increase in viscosity accompanied by the decrease in the order parameter during the confinement. From Table 1, we note that the rotational viscosity γ1 is usually larger than the shear viscosities η2 and η3. It is known that the anchoring effect and surface viscosity must be taken into account in the theoretical expression of the dynamics of LCs confined in a narrow gap.35−37 The anchoring energy of photoalignment using PVCi film was experimentally determined and was found to be of the order of 10−6 J/m2, which corresponds to so-called “weak anchoring”.38 The peakto-peak displacement of the shearing probe tip was 100 nm and 11367

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir

(3) Bisoyi, H. K.; Li, Q. Light-Directing Chiral Liquid Crystal Nanostructures: From 1D to 3D. Acc. Chem. Res. 2014, 47, 3184− 3195. (4) Xue, C.; Xiang, J.; Nemati, H.; Bisoyi, H. K.; Gutierrez-Cuevas, K.; Wang, L.; Gao, M.; Zhou, S.; Yang, D.; Lavrentovich, O. D.; Urbas, A.; Li, Q. Light-Driven Reversible Alignment Switching of Liquid Crystals Enabled by Azo Thiol Grafted Gold Nanoparticles. ChemPhysChem 2015, 16, 1852−1856. (5) Miesowicz, M. Influence of a Magnetic Field on the Viscosity of Para-azoxyanisol. Nature 1935, 136, 261. (6) Miesowicz, M. The Three Coefficients of Viscosity of Anisotropic Liquids. Nature 1946, 158, 27. (7) Carrion, F. J.; Martinez-Nicolas, G.; Iglesias, P.; Sanes, J.; Bermudez, M. D. Liquid Crystals in Tribology. Int. J. Mol. Sci. 2009, 10, 4102−4115. (8) Matsumura, Y.; Shiraishi, T.; Morishita, S. Stiffness and Damping of Liquid Crystal Lubricating Film under Electric Field. Tribol. Int. 2012, 54, 32−37. (9) Israelachvili, J.; Min, Y.; Akbulut, M.; Alig, A.; Carver, G.; Greene, W.; Kristiansen, K.; Meyer, E.; Pesika, N.; Rosenberg, K.; Zeng, H. Recent Advances in the Surface Forces Apparatus (SFA) Technique. Rep. Prog. Phys. 2010, 73, 036601. (10) Horn, R. G.; Israelachvili, J. N.; Perez, E. Forces Due to Structure in a Thin Liquid-Crystal Film. J. Phys. 1981, 42, 39−52. (11) Ruths, M.; Steinberg, S.; Israelachvili, J. N. Effects of Confinement and Shear on the Properties of Thin Films of Thermotropic Liquid Crystal. Langmuir 1996, 12, 6637−6650. (12) Dushkin, C. D.; Kurihara, K. Nanotribology of Thin Liquid Crystal Film Studied by the Shear Force Resonance Method. Colloids Surf., A 1997, 129−130, 131−139. (13) Janik, J.; Tadmor, R.; Klein, J. Shear of Molecularly Confined Liquid Crystals 0.1. Orientation and Transitions under Confinement. Langmuir 1997, 13, 4466−4473. (14) Artsyukhovich, A.; Broekman, L. D.; Salmeron, M. Friction of the Liquid Crystal 8CB as Probed by the Surface Forces Apparatus. Langmuir 1999, 15, 2217−2223. (15) Ruths, M.; Granick, S. Influence of Alignment of Crystalline Confining Surfaces on Static Forces and Shear in a Liquid Crystal, 4′n-Pentyl-4-cyanobiphenyl. Langmuir 2000, 16, 8368−8376. (16) Janik, J.; Tadmor, R.; Klein, J. Shear of Molecularly Confined Liquid Crystals. 2. Stress Anisotropy across a Model Nematogen Compressed between Sliding Solid Surfaces. Langmuir 2001, 17, 5476−5485. (17) Itoh, S.; Fukuzawa, K.; Hamamoto, Y.; Zhang, H. D.; Mitsuya, Y. Fiber Wobbling Method for Dynamic Viscoelastic Measurement of Liquid Lubricant Confined in Molecularly Narrow Gaps. Tribol. Lett. 2008, 30, 177−189. (18) Schadt, M.; Schmitt, K.; Kozinkov, V.; Chigrinov, V. SurfaceInduced Parallel Alignment of Liquid Crystals by Linearly Polymerized Photopolymers. Jpn. J. Appl. Phys. 1992, 31, 2155−2164. (19) Goldman, A. J.; Cox, R. G.; Brenner, H. Slow Viscous Motion of a Sphere Parallel to a Plane Wall.I. Motion through a Quiescent Fluid. Chem. Eng. Sci. 1967, 22, 637−651. (20) Itoh, S.; Hamamoto, Y.; Ishii, K.; Fukuzawa, K.; Zhang, H. D. Detection of Asperity Contact for Precise Gap Determination in ThinFilm Nanorheometry. Tribol. Lett. 2013, 49, 1−10. (21) Fuller, G. Optical Rheometry of Complex Fluids; Oxford University Press: New York, 1995. (22) Hanson, E. G.; Shen, Y. R. Refractive-Indices and Optical Anisotropy of Homologous Liquid-Crystals. Mol. Cryst. Liq. Cryst. 1976, 36, 193−207. (23) Li, J.; Gauza, S.; Wu, S. T. Temperature Effect on Liquid Crystal Refractive Indices. J. Appl. Phys. 2004, 96, 19−24. (24) Skarp, K.; Lagerwall, S. T.; Stebler, B.; Mcqueen, D. Flow Alignment in Cyanobiphenyl Liquid-Crystals. Phys. Scr. 1979, 19, 339−342. (25) Skarp, K.; Lagerwall, S. T.; Stebler, B. Measurements of Hydrodynamic Parameters for Nematic 5CB. Mol. Cryst. Liq. Cryst. 1980, 60, 215−236.

which implies a low friction coefficient. In addition, the result in the case of perpendicular shearing indicates that the confined LC had a higher viscosity in the case of flow perpendicular to the photoaligned direction. This could suppress the “side leakage” of the LC during sliding, which could also lead to an increase in load capacity. Therefore, we deduce that the aligned LC layer must be formed near the substrate also in the case of macroscopic friction tests. Other than the photoalignment, we suppose that one of the potential candidates that aligned the LC molecules must be a wear track. It is not surprising that wear tracks are formed during tribological testing in the boundary lubrication regime. The geometrical or chemical anisotropy of the track can also align the LC molecules.

5. SUMMARY We developed an original system that enabled us to simultaneously measure the shear viscosity and order parameter of a confined LC sample. The shearing gap that confined the LC was controlled precisely from 500 nm down to a few nm, and the LC’s viscosity and order parameter were measured while the gap decreased. The LC was photoaligned using anisotropically dimerized PVCi films. The measurement was conducted under three different conditions. The first case involved the measurement of LC without photoalignment, which we called shearing without photoalignment. The other two conditions were shearing along the directions parallel and perpendicular to the photoalignment, which we called parallel and perpendicular shearing, respectively. The results of our study can be summarized as follows: (1) Without photoalignment, the confined LC exhibited enhanced viscosity at gaps less than around 200 nm. (2) In the parallel shearing case, the viscosity decreased as the gap decreased. This decrease began at a gap less than around 300 nm. We attribute this result to the apparent slip and shear thinning caused by the photoaligned LC layer near the surface (gap less than 50 nm) that exhibited a higher order parameter than the bulk state. (3) In the perpendicular shearing case, the viscosity increased with decreases in the gap width. In addition, the order parameter decreased for gaps less than 100 nm. We speculate that these phenomena were caused by the competition between shear alignment and photoalignment that led to the rotational motion of the LC molecules. In conclusion, we believe that our findings can significantly contribute to the development of liquid crystals as lubricants and lubricant additives.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +81-52-789-3130. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS The present research was partially supported by the Asahi Glass Foundation and JSPS KAKENHI Grant Number 15H03911. REFERENCES

(1) Li, Q. Liquid Crystals Beyond Displays: Chemistry, Physics, and Applications; Wiley: New York, 2012. (2) Li, Q. Anisotropic Nanomaterials Preparation, Properties, and Applications; Springer: New York, 2015. 11368

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369

Article

Langmuir (26) Kneppe, H.; Schneider, F.; Sharma, N. K. A Comparative Study of the Viscosity Coefficients of Some Nematic Liquid Crystals. Ber. Bunsen Phys. Chem. 1981, 85, 784−789. (27) Kneppe, H.; Schneider, F.; Sharma, N. K. Rotational Viscosity γ1 of Nematic Liquid Crystals. J. Chem. Phys. 1982, 77, 3203−3208. (28) Kawashima, Y.; Nakagawa, M.; Ichimura, K.; Seki, T. Photoorientation of Mesoporous Silica Materials via Transfer from an Azobenzene-Containing Polymer Monolayer. J. Mater. Chem. 2004, 14, 328−335. (29) Ehrentraut, H.; Hess, S. Viscosity Coefficients of Partially Aligned Nematic and Nematic Discotic Liquid Crystals. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1995, 51, 2203− 2212. (30) Herba, H.; Szymanski, A.; Drzymala, A. Experimental Test of Hydrodynamic Theories for Nematic Liquid Crystals. Mol. Cryst. Liq. Cryst. 1985, 127, 153−158. (31) Tsvetkov, V. A. Attempt of Direct Measuring of Near Surface Shear Viscosity. Mol. Cryst. Liq. Cryst. 2005, 436, 203−216. (32) Yamada, S. General Shear-Thinning Dynamics of Confined Fluids. Tribol. Lett. 2002, 13, 167−171. (33) Itoh, S.; Ishii, K.; Fukuzawa, K.; Zhang, H. Shear Thinning of Nanometer-Thick Liquid Lubricant Films Measured at High Shear Rates. Tribol. Lett. 2014, 53, 555−567. (34) Mate, C. M. Tribology on the Small Scale; Oxford University Press: New York, 2008. (35) Mertelj, A.; Copic, M. Surface-Dominated Orientational Dynamics and Surface Viscosity in Confined Liquid Crystals. Phys. Rev. Lett. 1998, 81, 5844−5847. (36) Durand, G. E.; Virga, E. G. Hydrodynamic Model for Surface nematic viscosity. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1999, 59, 4137−4142. (37) Zhao, W.; Wu, C. X.; Iwamoto, M. Analysis of Weak-Anchoring Effect in Nematic Liquid Crystals. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 62, R1481−R1484. (38) Vilfan, M.; Olenik, I. D.; Mertelj, A.; Copic, M. Aging of Surface Anchoring and Surface Viscosity of a Nematic Liquid Crystal on Photoaligning Poly-(vinyl-cinnamate). Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2001, 63, 061709. (39) Nasibullayev, I.; Krekhov, A. P.; Khazimullin, M. V. Dynamics of Nematic Liquid Crystal under Oscillatory Flow: Influence of Surface Viscosity. Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 2000, 351, 395− 402. (40) Nasibullayev, I.; Tarasov, O. S.; Krekhov, A. P.; Kramer, L. Orientational Instabilities in Nematic Liquid Crystals with Weak Anchoring under Combined Action of Steady Flow and External Fields. Phys. Rev. E 2005, 72, 051706. (41) Pasechnik, S.; Nasibullayev, I.; Shmeliova, D.; Tsvetkov, V.; Zhijian, L.; Chigrinov, V. Oscillating Poiseuille Flow in Photo-aligned Liquid Crystal Cells. Liq. Cryst. 2006, 33, 1153−1165.

11369

DOI: 10.1021/acs.langmuir.5b02713 Langmuir 2015, 31, 11360−11369