HAL Id: jpa-00215898
https://hal.archives-ouvertes.fr/jpa-00215898
Submitted on 1 Jan 1975
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
MEASUREMENTS OF γ1 IN NEMATIC CBOOA AND (40-7) BY NMR
R. Wise, A. Olah, J. Doane
To cite this version:
R. Wise, A. Olah, J. Doane. MEASUREMENTS OF γ1 IN NEMATIC CBOOA AND (40-7) BY NMR. Journal de Physique Colloques, 1975, 36 (C1), pp.C1-117-C1-120. �10.1051/jphyscol:1975121�.
�jpa-00215898�
Classification Physics Abstracts
7.130 — 8.660
MEASUREMENTS OF 7l I NJ LN E M A T I C CBOOA AND (40-7) BY NMR (*)
R. A. WISE(**), A. OLAH and J. W. DOANE
Department of Physics and Liquid Crystal Institute, Kent State University Kent, Ohio 44242, USA
Abstract. — Nuclear magnetic resonance is used to measure the temperature dependence of the rotational viscosity coefficient, yi, in the nematic phase of the compounds «-p-cyanobenzilidene-p-n- octyloxyaniline (CBOOA.) and in 4-»-butoxybenzylidene-4'-n-heptylaniline (40-7). In this method pulsed NMR is used to observe the recovery of the nematic director following a sudden shift in the direction of an applied magnetic field. At temperatures far removed from the smectic A transition, the temperature dependence of the viscosity is compared to the microscopic theory of Martins with favorable agreement. Near the smectic A transition the divergence of y 1 is fitted to {T— T'o)_v. Using Martins theory for the background viscosity in this region the exponent v was determined to be 0.4 ± 0.1.
1. Introduction. — Recently there has been a theo- heptylaniline. Both of these compounds exhibit a retical interest in the rotational viscosity coefficient, nematic-smectic A phase transition which is « near » yu and its temperature dependence in the nematic second order in character [10, 11] and have been used phase. This interest has been divided into two cate- in studies of the deformation constant [12].
gories. One has been on the effect of fluctuations of
smectic order above a second order nematic-smectic A 2- T h e N M R measurement. — The use of NMR as phase transition. The theory in this region of interest a to°l t o measure viscosity is somewhat unusual.
has been written by Brochard [1], Jahnig and Bro- Normally NMR is thought of as a microscopic measu- chard [2] and by McMillan [3]. These authors have rement used to determine microscopic parameters predicted the value of yt to become enhanced near the instead of macroscopic quantities such as viscosity smectic A transition diverging as (T - Tz)~m- The coefficients. In the case ofyl5 however, we are interested other category of interest has been in the so-called i n observing molecular reorientation. In the presence background viscosity which is that viscosity where o f a magnetic field, H, there will be a torque pretransition phenomena do not contribute. The Mn = h &xH2 sin 2 a on the molecular director temperature dependence of y t in this regime has been w h e r e AX is the anisotropy in the diamagnetic suscepti- studied by several workers [4-9]. The most recent bility> a n d a i s t h e a nSl e between the field direction study, however, has been by Martins [9]. The approach a n d t h e director L. In the nematic liquid crystal there by Martins has been molecular-statistical in nature. w i U b e a n opposing torque Mv = - yt da/d*. The His theory gives yt oc S2 e-sS,kT where S is the degree equation of motion can be found by neglecting the of order and eS is the activation energy. This theory inertial term and equating the two torques giving gives some interesting variants which are not encoun- a differential equation in a. If the field direction is tered in the viscosity of normal liquids. First of all, suddenly switched the director will then relax to the the activation energy is temperature dependent since direction of the field according to the expression :
S varies with temperature. Secondly, eS is independent t a n a _ e-*/t Q \ of the compound in the mean field approximation.
In this paper we show measurements of yx in the w h e r e T _ 1 = (Az/Vi) H2. A measure of x therefore compound (CBOOA), «-p-cyanobenzilidene-p-«-octy- 8i v e s t he ratio yJAx-
loxyaniline and in (40-7) 4-«-butoxybenzylidene-4'-w- W e measure T using pulsed nuclear magnetic reso- nance to observe the return of the director following a sudden shift in the magnetic field direction. The expe- (*) Research supported in part by a National Science Founda- riment is to observe the free induction decay with a tion grant # GH 34164 X. b o x c a r in t e grator following a nil pulse.
(**) Permanent address : Department of Physics, Heidelberg T. . „ , ,, . ,, .,,. f i. . . , College, Tiffin, Ohio. Research supported by the Small College lt l s w e l 1 k n o w n t h a t t h e w l d t h o f t h e f r e e ""taction Research Participation program of the National Science Founda- decay changes drastically as the director is oriented tion. away from the direction of the applied field [13]. In
9 Résumé. — On mesure, par résonance magnétique nucléaire, le coefficient de viscosité rotationnelle yi dans les phases nématiques des composés «-p-cyanobenzilidène-p-w-octyloxyani- line (CBOOA) et 4-«-butoxybenzilidène-4'-«-heptylaniline (40-7). L'étude du signal de précession libre permet de suivre le réalignement du directeur après déplacement angulaire soudain du champ magnétique extérieur. Loin de la transition smectique A-nématique, la variation thermique de yi est en bon accord avec celle prévue par la théorie microscopique de F. Martins. On peut donc extraire, au voisinage de la transition, la contribution des effets prétransitionnels. yi diverge suivant (T — T0)-v avec v = 0,4 ± 0,1.
JOURNAL DE PHYSIQUE Colloque Cl, supplément au n° 3, Tome 36, Mars 1975, page Cl-117
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975121
Cl-118 R. A. WISE. A. OLAH AND J. W. DOANE the nematic as well as in the smectic A phases where
the molecule is rotating about its long molecular axis the nuclear spin-spin interactions are motionally ave- raged to give a free induction decay which has a width, T,, say at 3 maximum amplitude, where
Instead of measuring the width, however, it is more convenient to measure the decay amplitude at some fixed time, z,, following the n/2 pulse. This can be done with a box car integrator. The amplitude of the decay (or the output of the box car) will not be the simple function of cc given above but will depend upon the shape of the free induction decay and the time 7,.
This functional dependence can easily be determined experimentally with the sample in the smectic A phase.
In this phase an aligned sample will not distort upon reorientation of the sample container in the applied magnetic field and one can reorient the director without it relaxing back to the field direction thereby obtaining the calibration of the decay amplitude to the angle cc. Such a calibration curve is seen in figure 1.
The curve has a minimum as well as a maximum because phase sensitive detection was used in observing the free induction decay. The inset to figure 1 shows
I
A N G L E ides1
FIG. 1. - Calibration CUNe illustrating the amplitude of the free induction decay (FID) at a fhed time zo, following a w/2 pulse as a function of the angle between the molecular director L and magnetic field H. The data were obtained by ordering the sample in the nematic phase then lowering the temperature into the smectic A region and then recording the amplitude for selected angles of sample orientation. The inset illustrates the typical behavior of the amplitude of the FID in the nematic phase at a fixed time zo following a n/2 pulse. The curve was obtained by quickly rotating the magnet through an angle of about 750. This rotation took place between about 0.8 and 2 S.
One observes the director to relax to a direction parallel to the field between the time of 2.0 to 10 S.
seen in figure 2 where it is seen to obey eq. (1). The slope of the straight line gives ( A ~ l y , ) H'. In the actual analysis of the data it was more convenient to obtain the ratio above from the times where the relaxation curve goes through its maxima and minima.
m
FIG. 2. - Evidence that the molecular realignment is given by tan a = e-tlz where a is the angle between the molecular director L, and magnetic field H and 7-1 is AxH2ly I. The curve is obtained from data shown in figure 1. The squares represent the maximum
and minimum amplitudes of the FID.
Since the width of the free induction decay changes with temperature (cc 11s) the calibration curve would change if z, were held constant. This problem is easily avoided by positioning the box car integrator at a time z,/S instead of at a fixed time 7,.
a relaxation curve which follows a sudden shift in the direction of the 'magnetic field when the sample is in the nematic phase. The relaxation curve, of course, has the same shape as the calibration curve and gives the time dependence of a. This time dependence is
TEMPERATURE PC)
FIG. 3. - Temperature dependence of transverse relaxation time for (40-7). The order parameter as a function of temperature is obtained by recognizing that S cc 1/Tz and assigning a value of S = 0.65 at 55 OC. The latter value was obtained from the
absorption line splittings.
MEASUREMENTS O F 71 IN NEMATIC CBOOA AND (40-7) BY NMR Cl-119 The order parameter, S, is a common and straight
forward NMR measurement [14]. Relative values of S for (40-7) and CBOOA are shown in figures 3 and 4.
h. 4. - Temperature dependence of transverse relaxation time for CBOOA. The order parameter as a function of tempe- rature is obtained by recognizing that S CK 1/T2 and assigning a value of S = 0.60 at 84 OC. The latter value was obtained from
the absorption line splittings.
These values were obtained from the free induction decay time. Under phase sensitive detection the free induction decay has the appearance of a damped cosine wave. The time for one period gives a relative value of S-'. The absolute value can be obtained from a recording of the absorption line shape at some tem- perature [14]. Figures 3 and 4 show the characteristic curve [l51 of a second order nematic-smectic A phase transition.
3. The data. - In order to examine the tempera- ture dependence of y, it is most convenient to plot In (y ,/AxS) vs SIT. In Martins theory this would be a straight line since y,/AxS cc y,/S2. Figures 5 and 6 show the data of CBOOA and (40-7) plotted in this fashion. In the high temperature region of CBOOA, figure 5, the plot certainly gives a straight line. The slope of the line gives a value of E = 0.87 kcal/mole which is that predicted by Martins.
The low temperature end of the plot diverges as expected. The critical exponent can be obtained by subtracting off the determined background curve CS2 e-"lkT to obtain values of G(Sy,/Ax). Here the enhanced values of y,/Ax are multiplied by S to remove the temperature dependence of Ax. The inset in figure 5 shows a plot of log G(Sy,/Ax) vs log (T,- 7').
The curve is clearly not a straight line in the higher temperature region. The slope of the line as the tran- sition is approached is 0.4 +_ 0.1. The estimated error is conservative.
The data for the (40-7) compound is not quite as clean as can be seen from figure 6. To obtain the background we simply sketched in a straight line for
E = 0.87 kcal/mole which is certainly within the expe-
FIG. 5. - Determination of the activation energy and critical exponent for CBOOA. The slope of the line drawn gives a value of E of 0.87 kcal/mole. The inset shows the enhanced portion of the viscosity coefficient near the nematic-smectic A transition.
The critical exponent obtained is 0.4 f 0.1. A magnetic field of 1 222 G was used anda nematic-smectic transition temperature,
TC = 82.7 OC, was obtained.
RG. 6. - Determination of the activation energy and critical exponent for (40-7). The slope of the line drawn gives a value for e, of 0.87 kcal/mole. The inset shows the enhanced portion of the viscosity coefficient near the nematic-smectic A transition. The critical exponent obtained is 0.4 f 0.1. A magnetic field of 1 316 G was used and a nematic-smectic transition temperature,
Tc = 54.3 f 0.1 OC, was obtained.
rimental error of the data in the high temperature region. Again the enhanced portion is plotted in the inset. The exponent obtained is 0.4 + 0.1.
Using a different method Hardouin, Achard and Gasparoux [l61 have measured y, and its temperature dependence in several compounds which exhibit a nematic-smectic A phase transition. In their work they used different forms for the background viscosity [5-71 than we have used here which, of course, will
Cl-120 R. A. WISE, A. OLAH AND 5. W. DOANE also give different values for the critical exponents.
Our measurements of yJAx in CBOOA are good agreement with those reported by Hardouin et al. at the intermediate temperatures of the nematic range.
Near the nematic-smectic A transition there is a small difference with the data of Hardouin et al. showing somewhat more enhancement than ours which could be related to purity.
There is no direct advantage of the NMR method
of measuring the temperature dependence of yl(yl S/Ax vs T) over other reported techniques. One indirect advantage, however, might be that the sample can be contained in a sealed oven allowing better control over the temperature gradients. In our system the sample was contained in a sealed oven with air at the oven temperature circulated over the sample. Our temperature gradients were measured to be less than 0.05 OC.
References
[l] BROCHARD, F., J. Physique 34 (1973) 411.
[2] JAHNIG, F. and BROCHARD, F., J. Physique 35 (1974) 301.
[3] MCMILLAN, W. L., Phys. Rev. A 9 (1974) 1720.
[4] GASPAROUX, H., PROST, J., J. Physique 32 (1971) 953.
[S] HELFRICH, W., J. Chem. Phys. 56 (1972) 3187.
[6] IMURA, H., OKANO, K., Japan J. Appl. Phys. 11 (1972) 1440.
[7] MEIBOOM, S., HEWITT, R. C., Phys. Rev. Lett. 30 (1973) 261.
[ S ] YUN, C. K., Phys. Lett. A 43 (1973) 369.
[9] ASSIS FARINHA MARTINS, Vth International Liquid Crystal Conference, Stockholm, Sweden (June 1974) also to appear in Portugaliae Physica.
[l01 DJUREK, D., BATURIC-RUBCIC, J. and FRANULOVIC, K., Vth International Liquid Crystal Conference, Stock- holm, Sweden (June 1974).
[l11 SMITH, G. W., GARDLUND, 2. G., J. Chem. Phys. 59 (1973) 3214.
[l21 CLADIS, P. E., Phys. Rev. Lett. 31 (1973) 1200 ;
CHEUNG, L., MEYER, R. B., GRULER, H., Phys. Rev. Lett.
31 (1973) 349 ;
DEBYE, M., RIBOTTA, R. and DURAND, G., Phys. Rev. Lett.
31 (1973) 443 ;
BALOG, P., JOHNSON, D. L., CHRISTENSEN, S. H., Bull. Am.
Phys. Soc. 19 (1973) 173.
[l31 WISE, R. A., SMITH, D. H. and DOANE, J. W., Phys. Rev.
A 7 (1973) 1366.
1141 BROWN, G. H., DOANE, J. W. and NEFF, V. D., Crit. Rev.
Solid State Sci. 1 (1970) 303.
1151 DOANE, J. W., PARKER, R. S., CVIKL, B., JOHNSON, D. L.
and FISHEL, D. L., Phys. Rev. Lett. 28 (1972) 1694.
[l61 HARDOUIN, H., ACHARD, M. F. and GASPAROUX, H., Solid State Commun. 14 (1974) 453.
