644
Langmuir 1987, 3, 644-647
the maximum (pH 5.5-6.0) on the diagram of dependence of coagulation and gelation rates in silica hydrosols on pH. The above conclusions are confirmed by calculations based on the DLVO modified theory in which the structural component of disjoining pressure is taken into consideration.
Acknowledgment. The authors express their gratitude to Dr.N. B. Churaev who generously helped them with his knowledge and expertise for which they feel deeply indebted. Registry No. Silica, 7631-86-9.
Investigation of the Liquid-Crystal Boundary Layers near the Solid Substrate? A. N. Somov, V. D. Sobolev, and N. V. Churaev* The Institute of Physical Chemistry, USSR Academy of Sciences, Moscow 117915, USSR Received December 3, 1986 In thin cylindrical quartz capillaries having r < 10 pm the molecules of N-(p-methoxybenzy1idene)-pbutylaniline liquid crystal (LC) are oriented parallel to the surface due to the effect of short-range forces. In capillaries having r > 10 prn the LC molecules are preferably oriented normal to the surface under the effect of long-range surface forces. The effect of homotropic orientation can be enhanced by the treatment of quartz with a cationic surfactant. The flow of the LC destroys the homotropic orientation, which tends to the planar one when the flow rate grows. Properties of boundary layers of liquids are now under intensive investigation due to their great importance for lyophilic disperse systems and liquid films.' Polar liquids demonstrate the clearest appearance of boundary properties because their molecules are capable q,-the orientation to give ordering structures. The effects of the boundary structure organization were expected to be especially noticeable in the case of liquid crystals (LC). Interface-induced changes of LC properties can occur in the wide boundary layers and this facilitates their investigation. T h e nematic liquid-crystal N-(p-methoxybenzylidene)-p-butylaniline(MBBA) was chosen for these experiments because of the good exploration of its bulk rheological properties.2 A pure grade MBBA sample can be characterized by the transition temperature toto isotrope phase, which was in our case +45.2 "C, close to the +47 OC literature value for the maximal pure substance. The MBBA flow induced by hydrostatic pressure in thin-quartz capillaries with radii r of 1-20 pm and a molecularly smooth juvenile surface was under investigation. The method and the equipment elaborated earlier were used."* I t consists of the measuring the flow rate 13of a liquid in the capillary channel by measuring the rate of meniscus displacement and calculating the mean viscosity 9 by using Poiseuille's equation
Here t is the length of the liquid column in the capillary. In this case the pressure drop is AP = P - P,, where P is the gas pressure near the meniscus and P, is capillary pressure which is equal to 2a cos 0 P, = r 'Presented at the "VIIIth Conference on Surface Forces", Dec 3-5, 1985, Moscow; Professor B. V. Derjaguin, Chairman.
0743-7463/87/2403-0644$01.50/0
where u is the surface tension and 0 is the contact angle. The dependence of u on AP for newtonian liquids is linear if the complete wetting condition is realized. Such liquids (usually nonpolar, such as CC14or CI6HM)were used for capillary calibration, i.e., the mean radius of capillary determination on the basis of eq 1. The constant K was calculated by using the slope of linear u(P) dependence. The condition of complete wetting was simultaneously controlled by measuring P, values cut off on the pressure axis at u = 0. Pseudoplastic systems such as LCs are characterized by a more complicated dependence
v= = a(AP)b
(3)
where a and b are constants. Such a dependence can be directed to the double-logarithmic coordinates and this makes possible the determination of the constants a and b, using the experimental graphs u(AP). One can imagine such the flow being newtonian, having some effective viscosity coefficient q according to any velocity value u. So eq 1 and 3 used together let the capillary constant K = u ( A P ) ~be ' determined and calculate viscosity coefficients for various flow rates q = q(u). Figure 1shows the log u-log AP dependences obtained from experiment. One can see that this graph is really linear within a wide range of flow rates, from 1 to 300 pm-s-'. The nonlinear character of u ( A P ) dependences can, however, be connected with a number of other factors: the MBBA meniscus contact angle dependence on flow rate and generation of a wetting film of variable thickness h (1) Derjaguin, B. V.; Churaev, N. V.; Muller, V. M. Surface Forces; Nauka: Moscow, 1985. (2) Chandrasekhar, S. Liquid Crystls; Cambridge University Press: Cambridge, 1977. (3) Churaev, N. V.; Sobolev, V. D.; Zorin, 2. M. In T h i n L i p i d Films and Boundary Layers; Academic: London, New York, 1971; p 213. (4) Derjaguin, B. V.; Zhelezny, B. V.; Zorin, Z. M.; Sobolev, V. D.; Churaev, N. V. In Surface Forces in Thin Films and Colloid Stability; Nauka: Moscow, 1974; p 90.
0 1987 American Chemical Society
Langmuir, Vol. 3, No. 5, 1987 645
Liquid-Crystal Boundary Layers
.eb.dV 2.5
50 /
Z,?
t
0
-50.
1,5
-100
I,@
t
0,5
’
@,@
I
I
1
1
-1,s
-1,o
-0,5
0,o
-
&“6p
Figure I. Dependences log log AP for MBBA samples oriented in a homotropic manner in quartz capillaries of different radii: (1)r = 3.0 f 0.2 pm, CTAB treated; (2) r = 7.0 0.4 pm, CTAB treated; (3) r = 8.3 i 0.1 pm; (4) r = 11.7 i 0.1 pm; (5) r = 20.1 i 0.2 pm; (6) r = 20.1 f 0.2 pm, CTAB treated.
*
v .IO‘
m.s-’
Figure 3. Dependence of flow rate u on the pressure drop hp for planar MBBA in the quartz microcapillary r = 0.86 pm. In order to clear the wetting films influence, the film thickness measurements were carried out by using a spreading up method.6 The MBBA column l1 N 1 mm has been shifting along the capillary to a distance x N 1 cm and returning back again. Decrease of the MBBA column A1 = Zl - l2 (where l2 is the column length after its return to the initial position) was used for calculation of the wetting film thickness
h = r [ 1 - (1 -
50
\ I Figure 2. Dependence of MBBA meniscus displacementvelocity v on the gas pressure P in the capillary r = 7.0 pm, CTAB treated. = h ( v ) by the receding meniscus.
Figure 2 shows one of the experimental dependences v(AP) (curve 1)for MBBA flow in the capillary with radius r = 7.0 pm that was CTAB treated. The receding meniscus was used for the measurement (v < 0). The effective values of viscosity coefficients corresponding to given values of flow rate can be easily calculated by using a tangent drawn by dashed lines 2-5 for a number of points of curve 1. Intersections of these lines and the pressure axis accordingly give effective values of the capillary pressure Pc(6), but the last corresponds to the physically unreal situtation 6 < Oo. This is evidence the the lack of connection of u ( h p ) graph nonlinearity with contact angle dynamics. Besides, contact angle variations of the receding meniscus are usually small. There is another fact in favor of small significance of this effect. Namely, when MBBA becomes isotropic at a temperature above to,v(AP) dependences become linear according to Poiseuille’s equation for newtonian liquids.
$)]
(4)
The measurements carried out for various returning rates v show that in accordance with Derjaguin’s theory: the h values increase with flow rate. However, the film thickness didnot exceed 140 nm even in the case of maximal flow rate up to 0.1 c m d . The meniscus displacement rate corrections due to wetting film formation didnot exceed 1%. Therefore, nonlinear dependencies v(AP) which are shown in Figures 1and 2 reflect the functional connection of MBBA effective viscosity with the LC mean flow rate in the capillary. The cause is alteration of the LC molecules orientation by flow rate gradient. However, the nonlinear character of v(AP) dependences was found to be inherent only to sufficiently wide capillaries. In contrast, the v(AP) dependences were linear for the narrow capillaries having juvenile surfaces (r = 0.86-7.0 pm). The MBBA in these capillaries can be characterized by a constant viscosity coefficient q = 24 f 0.5 m P a d like the newtonian liquid flow (Figure 3). This viscosity value coincides with Miesowitz’ viscosity coefficient q2 in the case of planar orientation of MBBA molecules? It is clear that for this orientation pattern with long molecular axes parallel to channel walls there shouldnot be dependence of viscosity on flow rate. The orientation of LC molecules coincides in this case with the field of tangent shear stresses created by stream. The experimental results for the group wider capillaries are shown on Figure 4. The increase in the flow rate is accompanied with viscosity lowering down to almost v2the Miescowitz viscosity coefficient for the planar structure. On the other hand, q values approach the Miescowitz coefficient ql = 136 m P a d for homotropic orientation in ( 5 ) Deriamin. - - B. V.: Churaev, N. V. Wetting Films: Nauka: Moscow, 1984. (6) Derjaguin, B. V. Zh.Fiz. Khim. 1940,14,137; Dokl. Akad. N a u k USSR 1943,39,11. (7) Kneppe, H.; Schneider, F. Mol. Cryst. Liquid Cryst. 1982,65,23.
Somov et al.
646 Langmuir, Vol. 3, No. 5, 1987
t-
i
5
1
-13,c
I
I
-9.0
I
1,
I
I
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-8,O
4TR ,n+1
Figure 4. Effective viscosity of MBBA dependence on the flow rate in the capillaries [(l)r = 20.1 wm; (2) r = 11.7 pm; (3) r = 8,3 pm] and in the capillaries having CTAB treated surfaces [ (4) r = 7.0 pm; (5) r = 13.4 pm; (6) r = 20.1 pm]. the range of lowest flow rates. Hence one can assume that there is destruction of homotropic orientation induced by flow and gradual destruction of this structure to the mainly planar one. Treatment of surfaces of the capillaries by cation-active surfactant cetyltrimethylammonium bromide (CTAB) is known to facilitate the organization of MBBA homotropic orientation.s Figure 4 shows that such treatment (curve 4-6) leads to viscosity increase which is connected with the more perfect homotropic orientation of LC molecules. Thus, MBBA orientation in the narrow capillaries is mainly planar and that in the wide ones is mainly homotropic. Similar transition from a planar orientation to a homotropic one was observed by Ter-Minassian-Saraga and othersg for a 5-CB nematic film of increasing thickness on a water surface. The possibility of orientation change from planar to homotropic was theoretically grounded by Katzlo on the basis of the macroscopic theory of dispersion forces. According to Katz’s theory, structural reorganization of that kind is due to the effect of long-range forces and occurs in film of critical thickness equal to aproximately 1 pm. In the cylindrical capillaries such a structural transition was found for r values of 8-13 pm. In the transition range of the capillary radii (8-13 pm) LC molecule orientation is determined not only by channel width but also by short-range surface forces. The last ones can be characterized by the energy of adhesion of MBBA to the capillary surface. The energy of adhesion can easily be calculated by using the Young-Duprent equation = a(l + cos 0) (5) where c = 38 mJ.m-2 is the MBBA surface tension. Contact angle values were determined by using measured values of the capillary pressure of the MBBA meniscus and eq 2. In all cases the homotropic orientation corresponds to the lower values of W,. Thus, for instance in one of the capillaries of close radii, the MBBA sample was oriented in a planar manner (r = 13.4 pm) but in another one, in a homotropic manner (r = 11.7 pm). The fact of planar MBBA orientation in the wider capillary seems to contradict the above mentioned. But the chem-
w,
(8) Proust, J. E.; Ter-Minassian-Saraaa, L.; Guyon, E. Solid State Commun. 1972, 11, 1221. (9) Perez. E.;Proust, J. E.: Ter-Minassian-Sarana, - L. Colloid Polvm. Sci. 1978, 256, 184. (10) Katz, E.I. Zh. Eksp. Teor. Fiz. 1976, 70, 1394.
1
I
0,001
I
0,CI
I
t
@,I 4TR
.IOT$a-l
Figure 5. Dependence of relative thickness h / r of homotropic oriented MBBA boundary layers on the flow parameter 4or in the capillaries: (1)r = 3.0 pm, CTAB treated; (2) r = 8.3 pm; (3) r = 11.7 pm; ( 4 ) r = 20.1 pm; (5) r = 7.0 pm, CTAB treated; (6) r = 13.4 pm, CTAB treated; (7) r = 20.1 pm, CTAB treated. istry of capillary surface expressed in W , values is of great importance for the orientation pattern in the transition range. The value W, = 72.6 mJ.m-2 for the capillary r = 13.4 pm is more than W, = 66.7 m J.m-2 for the r = 11.7 pm capillary, and the explanation follows. Treatment of surfaces in the capillaries with CTAB results in lowering of the W , value by 2-3 mJ.m-2 for narrow capillaries and by 11-13 mJ-m-2 in wide ones. The continual theory of nematic state2gives a universal dependence of viscosity on the parameter 4vr for capillaries of any radius in the case of perfect homotropic orientation of LC molecules, for instance, by a magnetic field. As follows from Figure 4, this conclusion of the theory is not fulfilled in the case of fine capillaries. The lack of perfect orientation which changes from mainly homotropic to mainly planar as capillary radii decrease may be main cause of the discrepancy. The mean viscosity lowering seem to be confirmation of the proposal. Really, the highest viscosity values near q1 = 136 mPa.s-’ for u 0 were obtained in wide capillaries treated with CTAB (curves 5 and 6 on Figure 4). The STAB treatment creates the most perfect LC homotropic orientation. The hydrodynamic solution of the problem of the flow of a nematic LC oriented in a homotropic manner shows the orientation change induced by the stream from perfectly homotropic near the capillary wall to perfectly planar in the center of the channel.2 For the first approximation, the capillary space can be divided into two zones: a boundary zone having thickness h and homotropic orientation and the central core with a planar orientation pattern. Then one can consider ql = 136 mPa-s-l for the first zone and q2 = 24 m P a d for the second one. On the basis of this model, the mean viscosity q changes during the flow (Figure 4) can be characterized by accordant changes of the thickness of the boundary layer h, oriented
-
Langmuir, Vol. 3, No. 5, 1987 647
Liquid-Crystal Boundary Layers
h,
b7 5,O
t
A
t
IO IUU
600 500 4CO
30c
200 IC0 U
I
I
I
I
31
32
33
.c
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Figure 6. Dependence of MBBA effective viscosity on temperature in the capillary r = 20.1 pm, CTAB treated. Curves 2-9 represent experimental data for different flow rates (curve 2, the maximal rate-curve 9, the minimal rate). Curve 1 corresponds to the Miescowitz viscosity coefficient q2, curve 10 to the Miescowitz coefficient ql.'
by substrate in a homotropic manner. The relative thickness of boundary layer can be obtained from the known equation"J2 h r
- 11) (111 - 112)
112 (771
77
Results of calculations of h / r dependence on flow rate for capillaries of different radii are shown on Figure 5. As one can see from the graphs, the relative thickness of LC boundary layers is higher in wider capillaries and in CTAB-treated ones which may have more perfect homotropic orientation. In this case t h e destruction of LC boundary layers during the flow is more pronounced. Figure 6 shows the dependence of the mean (effective) viscosity 11 on temperature for the CTAB-treated capillary. Curves 2-9 are experimentally obtained for different velocity gradients 4v/r, varying in the range 5-50 s-l. Curves 1 and 10 show appropriate dependences of Miescowitz coefficients 712 and The experimental points lie between these latter curves, and it is reasonable enough because the homotropic orientation pattern in this capillary was not perfect. As is clear from the figure, the temperature dependence of 7 varies according to the flow rate value. The calculated boundary layer thickness h / r shows only slow dependence on temperuture. Therefore the small (11)Fisher, J. A.;Frederickson, A. G. Mol. Cryst. Liquid Cryst. 1969, 8,267. (12) Somov, A. N.;Churaev, N. V. Kolloidn. Zh. 1982,44, 614.
2
4
5
8
IO
e.
MM
Figure 7. Profile of the MBBA wetting film on steel substrate (after blowing);1 is the distance from the wetting boundary line.
temperature increase (25 to 43 "C) almost does not change the LC structure in the capillary controlled by the surface force field. The measurements of MBBA viscosity in wetting film carried out by the blowing off method13give another argument for LC constant orientation within boundary layers. The MBBA film has been deposited onto a wellpolished metal plate in the form of a thin layer. The film profile after 15 min of blowing (Figure 7) was obtained with the help of a laser ellipsometer. Figure 7 shows that the profile looks like a wedge. That is, viscosity is not dependent on distance from the substrate and is equal to 46 f 4 mPa.s-'. This value is close to Miescowitz's coefficient = 48.5 f 1.5 mPa.s-l for the planar molecular orientation mth long axes normal to the flow direction. The molecular orientation stays constant within the whole range of thicknesses investigated up to 800 A. These measurements demonstrate simultaneously that MBBA orientation of high adhesive steel substrate is planar. In conclusion, the results of investigations carried out show that MBBA molecules orient in a planar manner parallel to the capillary long axis thanks to short-range forces in narrow cylindrical capillaries. If the capillary radius is more than 10 f 3 pm, mainly homotropic orientation is realized due to long-range dispersion forces. This homotropic orientation can be strengthened by CTAB treatment of the capillary surface. The change of temperature of 15-20 "C exerts weak influence upon molecular orientation because dispersion forces and adhesion forces are slowly dependent on temperature. The flow of mainly homotropic oriented LCs leads to orientation disturbances and finally to planar orientation as the flow rate increases. Registry No. MBBA, 97402-82-9. (13) Karaaev, V.V.;Derjaguin, B. V. Dokl. Akad. Nauk USSR 1948, 62,761; Kolloidn. Zh. 1953, 15, 365.
