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On the behavior of viscosity at the nematic-isotropic transition
Volume
30A. number
PHYSICS
1
LETTERS
field, the crystal distortion reorients itself to lie along H, and the light, now n-polarized with respect to C4, is absorbed by the crystal. The new distortion remains when the magnetic field is removed, and C4 can be rotated back by re-applying H in the original C4-direction. Such a sequence of experiments is shown in fig. 1. The top trace takes the crystal from its original distortion direction to a new C4 axis, and in the bottom trace from this new axis back to the original one. The difference in the critical magnetic field required for the two cases is most likely due to the crystalline anisotropy, whereby the crystal originally chooses the energetically preferred direction for distortion. Sources of such a preference are numerous. We have observed differences due to growth conditions, cooling history, addition of dopants, and external strain. When the crystal is heated above the 1510K phase transition after having had the axis rotated by the field, upon retooling it will distort once again in the original direction. The source of this phenomenon is evidently the extremely small anisotropy in the crystalline free energy for the two possible orientations, which can be overcome by the anisotropy in the paramagnetic free energy. The Pr8+ ion in PrA108 has three singlets lowest in the ground manifold [ 11, and therefore at low temperature there is only a second-order Van Vleck temperature independent magnetization, and thus an exceedingly small magnetic free energy is involved. Magnetic susceptibility measurements have indicated an anisotropy in this induced
8 September
1969
magnetization. With respect to the pseudo-C4 axis, x,, is approximately 4 times greater than x1 [ 51, with a resultant anisotropy in the magnetic free energy. This small energy barrier is also manifested in the sensitivity of the crystalline distortion to external strain. We have observed that less than $-atmosphere of stress applied along one of the pseudocubic axes was sufficient to rotate the C4direction. The magnetically induced reorientation is observed at all temperatures below 800K. Above this temperature, structural domains are observed [ 11, indicating a change in the crystalline anisotropy energy. Furthermore, the magnetization energy is decreasing with increasing temperature, and the combination of these factors may explain the absence of this phenomenon above 8OoK. We gratefully acknowledge helpful discussions with J. K. Galt, C. G. B. Garrett, R. C. Miller and M. D. Sturge.
References 1. E. Cohen, L. A. Riseberg, W. A. Nordland, R. D. Burbank, R. C. Sherwood and L. G. Van Uitert. Phys. Rev., to be published. 2. E. J. Ryder, to be published. 3. R. D. Burbank, presented at the International Union of Crystallography, Stony Brook, August 1969. 4. L. A. Riseberg, E. Cohen and W. A. Nordland, to be published. 5. E. Cohen, L. A. Riseberg, W. A. Nordland, E. J. Ryder and R. C. Sherwood, to be published.
ON THE BEHAVIOR OF VISCOSITY A-T THE NEMATIC -ISOTROPIC TRANSITION
Laboratoire
de Physique
M. des Soltdes
PAPOULAR * . Faculte
Received The X shaped T-dependence of viscosity theory for the nematic state.
is discussed
In a nematic liquid near the clarification point T,, the temperature dependence of the viscosity 17is known to assume the shape of fig. 1 of * Laboratoire associe! au Centre National de la Recherche Scientifique.
des Sciences,
91- Orsay.
France
4 July 1969 and interpreted
in terms
of Leslie’s
hydrodynamic
ref. 1, if the molecules are oriented &ryalleI to the flow, The negative-sloped wings of this h curve clearly reflect the ordinary exponential law: 17 - exp (-W/kg T) , W being an activation energy for diffusion. 5
Volume
30A. number
PHYSICS
1
On the other hand, the vertical jump and the pretransitional curvature may naturally be thought of as reflecting the well known firstorder transition behavior of the nematic order parameter. This is in fact the case as will be shown below, using Leslie’s hydrodynamic theory
PI.
Let us assume
parallel
that the liquid
to the y axis with a shear Axy
= i $!,
(1)
nx7 ny 2nz are the components unit vector, the bars indicate and the oi are the six friction Leslie among which stand the cY5-o!5=o!2+cY3;
of the director thermal averaging, coefficients of relations [3]:
a!6 - CYij= “2 - cY3 (2)
(the first relation expresses the action-reaction principle, while the second stems from the elongated shape of the molecules). Moreover: (Y4,>0;
“3
- “2
10
;
(3)
because of the dissipative character of the motion. Note that (2) and (3) give immediately: /o3j
<< - o2 > 0 ;
aSZo5+e’2<05.
(4)
Now, consider three (rigid) geometries: 1) molecules parallel to the flow (nX = n, = 0, nY = 1; this is the case correspondig to fig. 1 of ref. 1; 2) molecules parallel to the shear gradient (nX = = 1); 3) molecules perpendicular to both flow and gradient (n, = 1). Relation (1) then gives, respectively: 27/1=CY4++6++3;
cular,
motion is averaged
in the isotropic
2772 =Cr4 f(Y5
-ff2
phase,
out. In particu-
2_ 2-I n,2_- ny-%-I
9
and: 2no = cu4 + ;LY1 + +(o5-o2+CYS+o3)
N (6)
Comparing with the first relation (5) and using (2) and (4), one can see that ~0 > ~1 provided
2 2 + 2c!lnXnY;
((Y6+a3)n;
al) thermal
1969
= o!4 + $Yl + +5.
2$=_= AXY + (‘y5-02);:+
8 September
is flowi;;
and the molecules are (e.g., magnetically) oriented. Then, the corresponding stress uXY and effective viscosity 77are given by [2]:
=o4
LETTERS
; (5)
that: oy6 < 2 ( :A - 02). This is a rather loose condition since in most cases we expect o I to be small and ff 6 negative, while cu2 is always negative. Thus, at the transition, the viscosity nl increases abruptly, in agreement with fig. 1 of ref. 1. The jump for 772and 773could be discussed in the same way. (Note that, in general, we expect 712 to decrease at T,.) Below pressed
the transition, in terms
the rzf may be ex-
of cos2 0, or of the order pa-
rameter S = -$[3 cos2 0 - 11, where 0 is the local angular deviation from the preferred orientation. Substituting, then, the familiar S(T) dependence in eq. (l), we obtain, e.g., for ~1, the other characteristic features of fig. 1 of ref. 1: pretransitional curvature and reduced slope below T,. (Note that tile slope in the ordered phase is further reduced due to the smaller value of the activation energy IV.) The curvature just below T, is known to decrease in a strong magnetic field [ 11: this reflects the more pronounced steplike shape of S(T). Finally let us note that: a) the small density discontinuity at T, (typically: 0.30/o), though itself related to the jump in the order parameter, does not significantly affect the viscosity behavior which is essentially a structural effect; b) we have not considered short-range order effects here: these may act to reduce the viscosity discontinuity.
2~73 =o4. From relations (4) we see that: ~1 < r]2 and, if 2 o2 < (Y6 < 0 : ?,11< q3 < 71~. This double inequality was first demonstrated experimentally by Miezowicz [4] for p-azoxyanisol (and -phenetol); for pAA, in cp, he found: ~1 = 2.4; 773 = 3.4; 772 = 9.2. Relation (1) remains valid near and above the transition T, since the internal (orientation-
References R.S. Porter, J. F. Johnson and E. M. Barrall, J. Appl. Phys. 34 (1963) 51; J. Chem. Phys. 45 (1966) 1452. F. M. Leslie, Quart. J. Mech. Appl. Math. 19 (1966) 357. 0. Parodi, to be published. M. Miezowicz, Nature 158 (1946) 27.
30A. number
PHYSICS
1
LETTERS
field, the crystal distortion reorients itself to lie along H, and the light, now n-polarized with respect to C4, is absorbed by the crystal. The new distortion remains when the magnetic field is removed, and C4 can be rotated back by re-applying H in the original C4-direction. Such a sequence of experiments is shown in fig. 1. The top trace takes the crystal from its original distortion direction to a new C4 axis, and in the bottom trace from this new axis back to the original one. The difference in the critical magnetic field required for the two cases is most likely due to the crystalline anisotropy, whereby the crystal originally chooses the energetically preferred direction for distortion. Sources of such a preference are numerous. We have observed differences due to growth conditions, cooling history, addition of dopants, and external strain. When the crystal is heated above the 1510K phase transition after having had the axis rotated by the field, upon retooling it will distort once again in the original direction. The source of this phenomenon is evidently the extremely small anisotropy in the crystalline free energy for the two possible orientations, which can be overcome by the anisotropy in the paramagnetic free energy. The Pr8+ ion in PrA108 has three singlets lowest in the ground manifold [ 11, and therefore at low temperature there is only a second-order Van Vleck temperature independent magnetization, and thus an exceedingly small magnetic free energy is involved. Magnetic susceptibility measurements have indicated an anisotropy in this induced
8 September
1969
magnetization. With respect to the pseudo-C4 axis, x,, is approximately 4 times greater than x1 [ 51, with a resultant anisotropy in the magnetic free energy. This small energy barrier is also manifested in the sensitivity of the crystalline distortion to external strain. We have observed that less than $-atmosphere of stress applied along one of the pseudocubic axes was sufficient to rotate the C4direction. The magnetically induced reorientation is observed at all temperatures below 800K. Above this temperature, structural domains are observed [ 11, indicating a change in the crystalline anisotropy energy. Furthermore, the magnetization energy is decreasing with increasing temperature, and the combination of these factors may explain the absence of this phenomenon above 8OoK. We gratefully acknowledge helpful discussions with J. K. Galt, C. G. B. Garrett, R. C. Miller and M. D. Sturge.
References 1. E. Cohen, L. A. Riseberg, W. A. Nordland, R. D. Burbank, R. C. Sherwood and L. G. Van Uitert. Phys. Rev., to be published. 2. E. J. Ryder, to be published. 3. R. D. Burbank, presented at the International Union of Crystallography, Stony Brook, August 1969. 4. L. A. Riseberg, E. Cohen and W. A. Nordland, to be published. 5. E. Cohen, L. A. Riseberg, W. A. Nordland, E. J. Ryder and R. C. Sherwood, to be published.
ON THE BEHAVIOR OF VISCOSITY A-T THE NEMATIC -ISOTROPIC TRANSITION
Laboratoire
de Physique
M. des Soltdes
PAPOULAR * . Faculte
Received The X shaped T-dependence of viscosity theory for the nematic state.
is discussed
In a nematic liquid near the clarification point T,, the temperature dependence of the viscosity 17is known to assume the shape of fig. 1 of * Laboratoire associe! au Centre National de la Recherche Scientifique.
des Sciences,
91- Orsay.
France
4 July 1969 and interpreted
in terms
of Leslie’s
hydrodynamic
ref. 1, if the molecules are oriented &ryalleI to the flow, The negative-sloped wings of this h curve clearly reflect the ordinary exponential law: 17 - exp (-W/kg T) , W being an activation energy for diffusion. 5
Volume
30A. number
PHYSICS
1
On the other hand, the vertical jump and the pretransitional curvature may naturally be thought of as reflecting the well known firstorder transition behavior of the nematic order parameter. This is in fact the case as will be shown below, using Leslie’s hydrodynamic theory
PI.
Let us assume
parallel
that the liquid
to the y axis with a shear Axy
= i $!,
(1)
nx7 ny 2nz are the components unit vector, the bars indicate and the oi are the six friction Leslie among which stand the cY5-o!5=o!2+cY3;
of the director thermal averaging, coefficients of relations [3]:
a!6 - CYij= “2 - cY3 (2)
(the first relation expresses the action-reaction principle, while the second stems from the elongated shape of the molecules). Moreover: (Y4,>0;
“3
- “2
10
;
(3)
because of the dissipative character of the motion. Note that (2) and (3) give immediately: /o3j
<< - o2 > 0 ;
aSZo5+e’2<05.
(4)
Now, consider three (rigid) geometries: 1) molecules parallel to the flow (nX = n, = 0, nY = 1; this is the case correspondig to fig. 1 of ref. 1; 2) molecules parallel to the shear gradient (nX = = 1); 3) molecules perpendicular to both flow and gradient (n, = 1). Relation (1) then gives, respectively: 27/1=CY4++6++3;
cular,
motion is averaged
in the isotropic
2772 =Cr4 f(Y5
-ff2
phase,
out. In particu-
2_ 2-I n,2_- ny-%-I
9
and: 2no = cu4 + ;LY1 + +(o5-o2+CYS+o3)
N (6)
Comparing with the first relation (5) and using (2) and (4), one can see that ~0 > ~1 provided
2 2 + 2c!lnXnY;
((Y6+a3)n;
al) thermal
1969
= o!4 + $Yl + +5.
2$=_= AXY + (‘y5-02);:+
8 September
is flowi;;
and the molecules are (e.g., magnetically) oriented. Then, the corresponding stress uXY and effective viscosity 77are given by [2]:
=o4
LETTERS
; (5)
that: oy6 < 2 ( :A - 02). This is a rather loose condition since in most cases we expect o I to be small and ff 6 negative, while cu2 is always negative. Thus, at the transition, the viscosity nl increases abruptly, in agreement with fig. 1 of ref. 1. The jump for 772and 773could be discussed in the same way. (Note that, in general, we expect 712 to decrease at T,.) Below pressed
the transition, in terms
the rzf may be ex-
of cos2 0, or of the order pa-
rameter S = -$[3 cos2 0 - 11, where 0 is the local angular deviation from the preferred orientation. Substituting, then, the familiar S(T) dependence in eq. (l), we obtain, e.g., for ~1, the other characteristic features of fig. 1 of ref. 1: pretransitional curvature and reduced slope below T,. (Note that tile slope in the ordered phase is further reduced due to the smaller value of the activation energy IV.) The curvature just below T, is known to decrease in a strong magnetic field [ 11: this reflects the more pronounced steplike shape of S(T). Finally let us note that: a) the small density discontinuity at T, (typically: 0.30/o), though itself related to the jump in the order parameter, does not significantly affect the viscosity behavior which is essentially a structural effect; b) we have not considered short-range order effects here: these may act to reduce the viscosity discontinuity.
2~73 =o4. From relations (4) we see that: ~1 < r]2 and, if 2 o2 < (Y6 < 0 : ?,11< q3 < 71~. This double inequality was first demonstrated experimentally by Miezowicz [4] for p-azoxyanisol (and -phenetol); for pAA, in cp, he found: ~1 = 2.4; 773 = 3.4; 772 = 9.2. Relation (1) remains valid near and above the transition T, since the internal (orientation-
References R.S. Porter, J. F. Johnson and E. M. Barrall, J. Appl. Phys. 34 (1963) 51; J. Chem. Phys. 45 (1966) 1452. F. M. Leslie, Quart. J. Mech. Appl. Math. 19 (1966) 357. 0. Parodi, to be published. M. Miezowicz, Nature 158 (1946) 27.