- Email: [email protected]
Periodic structure at the free surface of smectics A
Volume 56A, number 1
PHYSICS LETTERS
23 February 1976
PERIODIC STRUCTURE AT THE FREE SURFACE OF SMECTICS A D. LANGEVIN Laboratoire de Spectroscopie Hertzienne, Paris, France Received 9 December 1975 We observe at the free surface of several smectics A in a horizontal magnetic field H a periodic focal conic texture. The period varies roughly as 1/H.
We have studied the properties of the free surface of several smectics A liquid crystals: the cyanobenzilidene octyloxyaniline (CBOOA), the octyloxycyanobiphenyl (M 24) and the octylcyanobiphenyl (K 24). These compounds present a second order (or quasi second order) nematic to smectic A phase transition. We used a He-Ne laser beam at an incident angle of 3 ° . The beam reflected at the free surface is focused into a point of a horizontal plane where the observations are made. The samples are cooled from the nematic phase into the smectic A phase once the horizontal magnetic field//is turned on. We then observe two diffracted light spots along the direction perpendicular to the magnetic field and symmetric with respect to the reflected dot. These dots are characteristic of a periodic structure at the free surface. The corresponding wave vectors q depend on the H value as shown in fig. 1: q - qo ~ H(1-+0'25)*" In zero magnetic field, the spots are very close to the reflected dot and their direction is arbitrary; qo is of the order of 21rid where d is the sample thickness. From intensity and polarization measurements of the diffracted light, we found that the periodic structure is characterized by: small planeity defects of the free surface of the order of 100h distorsion of the orientation of the molecules in the surface plane. The observation of the free surface under a microscope shows the existence of a focal conic structure (fig. 2). The ellipses are organized along the field direction and the projections of their long axes onto a -
T /
24
cm"1
/ error bar
/
H I
200(3
3000
4000
G~Ju
Fig. 1. Characteristic wave vectors of the diffracted spots as a function of the magnetic field for the three studied liquid crystals.
horizontal plane are parallel to H. In zero magnetic field, or in a vertical magnetic field, we observe the same type of pattern, but without any preferential direction. To a good approximation, the mean size of the ellipses is given by:
-
* q seems temperature independent, at least close to the nematic to smectic transition, where the measurements are the most accurate.
L(H) = 21r/q(I-l). All these observations suggest that the molecules are tilted at the free surface. If they were exactly parallel (respectively normal) to the surface, when applying a horizontal (respectively vertical) magnetic field, one should obtain a uniform orientation of the molecules along the field direction. As we have seen, this is not the case, and the observed structures probably result from a conflict between the anchoring con61
Volume 56A, number 1
PttYSICS LETTFRS
23 February 1976
nitude, that is ~H ~ %/K1/Xa/H(K1 elastic constant, Xa diamagnetic anisotropy). The elementary volume of the texture associated with each ellipse is a cone. The set of cones relative to the largest ellipses cannot fill all the space in the distorted region. The inserstices between the cones can be filled by other cones associated to smaller ellipses, following an iterative process [2]. This model leads to a magnetic field dependent size of the largest ellipses:
L ~ (~it) 6/5 (p*)- 1/5, p* being a molecular length. This model is consistent with our results. But in view of the uncertainty on the exponent of H, we cannot disregard the possibility of a non iterative process where the insertices between the largest ellipses are filled by dislocations. A more complete account of this work is in preparation At the origin, we wanted to study the spectrum of waves thermally excited at the free surface of smectics A. This is obviously impossible in the presence of the distorted structure. We plan to use an oblique magnetic field parallel to the preferential molecular orientation at the free surface, to see if we then obtain a perfectly plane surface. This will also constitute a determination of the tilt angle of the molecules at the surface.
Fig. 2. K 24 free surface aspect under a microscope. The magnetic field is parallel to the largest side of the photograph. ditions at the surface and the effect of the field. In a focal conic structure [1], the distortion energies are of the same order of magnitude than for a distorted structure in a nematic phase. One can thus expect that the thickness of the distorted region below the free surface will also be of the same order of mag-
62
We are indebted to P.G. De Gennes, L. Leger, Y. Bouligand and M. Kleman for stimulating and fruitful discussions.
References [ 1] P.G. De Gennes, The physics of liquid crystals, Chapt.VII (Oxford Un. Press, 1974). [2] R. Bidaux, N. Boccara, G. Sarma, L. De Seze, P.G. De Gennes and O. Parodi, J. Phys. 34 (1973) 661.
PHYSICS LETTERS
23 February 1976
PERIODIC STRUCTURE AT THE FREE SURFACE OF SMECTICS A D. LANGEVIN Laboratoire de Spectroscopie Hertzienne, Paris, France Received 9 December 1975 We observe at the free surface of several smectics A in a horizontal magnetic field H a periodic focal conic texture. The period varies roughly as 1/H.
We have studied the properties of the free surface of several smectics A liquid crystals: the cyanobenzilidene octyloxyaniline (CBOOA), the octyloxycyanobiphenyl (M 24) and the octylcyanobiphenyl (K 24). These compounds present a second order (or quasi second order) nematic to smectic A phase transition. We used a He-Ne laser beam at an incident angle of 3 ° . The beam reflected at the free surface is focused into a point of a horizontal plane where the observations are made. The samples are cooled from the nematic phase into the smectic A phase once the horizontal magnetic field//is turned on. We then observe two diffracted light spots along the direction perpendicular to the magnetic field and symmetric with respect to the reflected dot. These dots are characteristic of a periodic structure at the free surface. The corresponding wave vectors q depend on the H value as shown in fig. 1: q - qo ~ H(1-+0'25)*" In zero magnetic field, the spots are very close to the reflected dot and their direction is arbitrary; qo is of the order of 21rid where d is the sample thickness. From intensity and polarization measurements of the diffracted light, we found that the periodic structure is characterized by: small planeity defects of the free surface of the order of 100h distorsion of the orientation of the molecules in the surface plane. The observation of the free surface under a microscope shows the existence of a focal conic structure (fig. 2). The ellipses are organized along the field direction and the projections of their long axes onto a -
T /
24
cm"1
/ error bar
/
H I
200(3
3000
4000
G~Ju
Fig. 1. Characteristic wave vectors of the diffracted spots as a function of the magnetic field for the three studied liquid crystals.
horizontal plane are parallel to H. In zero magnetic field, or in a vertical magnetic field, we observe the same type of pattern, but without any preferential direction. To a good approximation, the mean size of the ellipses is given by:
-
* q seems temperature independent, at least close to the nematic to smectic transition, where the measurements are the most accurate.
L(H) = 21r/q(I-l). All these observations suggest that the molecules are tilted at the free surface. If they were exactly parallel (respectively normal) to the surface, when applying a horizontal (respectively vertical) magnetic field, one should obtain a uniform orientation of the molecules along the field direction. As we have seen, this is not the case, and the observed structures probably result from a conflict between the anchoring con61
Volume 56A, number 1
PttYSICS LETTFRS
23 February 1976
nitude, that is ~H ~ %/K1/Xa/H(K1 elastic constant, Xa diamagnetic anisotropy). The elementary volume of the texture associated with each ellipse is a cone. The set of cones relative to the largest ellipses cannot fill all the space in the distorted region. The inserstices between the cones can be filled by other cones associated to smaller ellipses, following an iterative process [2]. This model leads to a magnetic field dependent size of the largest ellipses:
L ~ (~it) 6/5 (p*)- 1/5, p* being a molecular length. This model is consistent with our results. But in view of the uncertainty on the exponent of H, we cannot disregard the possibility of a non iterative process where the insertices between the largest ellipses are filled by dislocations. A more complete account of this work is in preparation At the origin, we wanted to study the spectrum of waves thermally excited at the free surface of smectics A. This is obviously impossible in the presence of the distorted structure. We plan to use an oblique magnetic field parallel to the preferential molecular orientation at the free surface, to see if we then obtain a perfectly plane surface. This will also constitute a determination of the tilt angle of the molecules at the surface.
Fig. 2. K 24 free surface aspect under a microscope. The magnetic field is parallel to the largest side of the photograph. ditions at the surface and the effect of the field. In a focal conic structure [1], the distortion energies are of the same order of magnitude than for a distorted structure in a nematic phase. One can thus expect that the thickness of the distorted region below the free surface will also be of the same order of mag-
62
We are indebted to P.G. De Gennes, L. Leger, Y. Bouligand and M. Kleman for stimulating and fruitful discussions.
References [ 1] P.G. De Gennes, The physics of liquid crystals, Chapt.VII (Oxford Un. Press, 1974). [2] R. Bidaux, N. Boccara, G. Sarma, L. De Seze, P.G. De Gennes and O. Parodi, J. Phys. 34 (1973) 661.