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Electron‐spin relaxation and ordering in smectic and supercooled nematic liquid crystals
1.(a) C. F. Polnaszek and J. H. Freed, J. Phys. Chem. 79, 2283 (1975);
1.(b) W. J. Lin and J. H. Freed, J. Phys. Chem. 83, 379 (1979)., J. Phys. Chem.
2.(a) K. V. S. Bao, C. F. Polnaszek, and J. H. Freed, J. Phys. Chem. 81, 449 (1977);
2.(b) C. F. Polnaszek, G. V. Bruno, and J. H. Freed, J. Chem. Phys. 58, 3185 (1973);
2.(e) J. H. Freed, J. Chem. Phys. 66, 4183 (1977)., J. Chem. Phys.
3.(a) E. Meiroviteh and J. H. Freed, J. Phys. Chem. 84, 2459 (1980);
3.(b) 84, 3281 (1980); , J. Phys. Chem.
3.(c) E. Meiroviteh and J. H. Freed, 84, 3295 (1980); , J. Phys. Chem.
3.(d) More recent work, however, [L. Kar, E. Igner, and J. H. Freed (unpublished)] has indicated that the matter may be more complex and may involve precise details of the preparation and annealing of the multibilayers of this lyotropic material .
4.(a) G. H. Luckhurst and M. Setaka, Mol. Cryst. Liq. Cryst. 19, 179 (1972);
4.(b) G. R. Luckhurst, M. Setaka, and C. Zannoni, Mol. Phys. 28, 49 (1974).
5.(a) F. Pusnick, M. Schara, and M. Sentjurc, J. Phys. (Paris) 36, 665 (1975);
5.(b) F. Pusnick and M. Schara, Chem. Phys. Lett. 37, 106 (1976).
6.(a) G. R. Luckhurst and A. Sanson, Mol. Phys. 24, 1297 (1972);
6.(b) G. R. Luckhurst, M. Ptak, and A. Sanson, J. Chem. Soc. Faraday Trans. 2 69, 1752 (1973);
6.(c) D. Sy and M. Ptak, Mol. Cryst. Liq. Cryst. 39, 53 (1977);
6.(d) M. A. Hemminga, J. Magn. Reson. 26, 25 (1977).
7.G. R. Luckhurst et al., J. Magn. Reson. 42, 351 (1981).
8.A. E. Stillman and J. H. Freed, J. Chem. Phys. 72, 550 (1980).
9.L. P. Hwang and Freed, J. Chem. Phys. 63, 118 (1975).
10.(a) F. Barbarin, D. Cabaret, B. Chevarin, C. Fabre, and J. P. Germain, Mol. Cryst. Liq. Cryst. 46, 181, 195 (1978);
10.(b) F. Barbarin, B. Chevarin, and J. Germain, J. Phys. 40, C3, 153 (1979);
10.(c) F. Barbarin, J. P. Chausse, C. Fabre, and J. P. Germain, J. Phys. 42, 1183 (1981). Barbarin et al. used the longer chain in (a) and (b) and the shorter chain in (c) compared to our use of C4H90, of. Fig. 1. In the recent work of part (c) these authors study the motional dynamics of their probe in 40, 8 but use a simple motional narrowing approach with a “strong‐collision” model without the benefit of angular‐dependent line‐shape measurements, so it is not surprising there are differences in details of analysis vs our study of P in 40, 6, which employs a full line shape (and slow‐motional) analysis and a Brownian motion model.
11.Good summaries of the properties of these types of liquid crystals may be found in The Molecular Physics of Liquid Crystals, edited by G. R. Luckhurst and G. W. Gray (Academic, New York, 1979);
11.Chap. 12 by G. W. Gray, Chap. 13 by A. J. Leadbetter, Chap. 14 by J. Doucet.
12.(a) G. Moro, TRIDG (unpublished report, Cornell University, 1980);
12.(b) G. Moro and J. H. Freed, J. Phys. Chem. 84, 2837 (1980);
12.(c) G. Moro and J. H. Freed, J. Chem. Phys. 74, 3757 (1981).
13.(a) Flexible deuterated probes somewhat related to P have been used previously to study side‐chain motion in polymers [cf. J. Pilar, J. Labsky, J. Kalal, and J. H. Freed, J. Phys. Chem. 83, 1907 (1979)].Rotation about the piperidine axis was typically four to six times faster than about the other axes, and decreases with chain length to the asymptotic value of the free piperidine, but in all cases the
13.(b) G. R. Luckhurst and R. Poupko, Mol. Phys. 29, 1293 (1975), and references therein.
14.(a) J. A. Murphy, Mol. Cryst. Liq. Cryst. 22, 133 (1973);
14.(b) P. G. deGennes, The Physics of Liquid Crystals (Oxford, New York, 1974);
14.(c) S. A. Pikin, Mol. Cryst. Liq. Cryst. 63, 181 (1981);
14.(d) Very small regions near each glass surface, of thickness out of a sample thickness of 200 μ did exhibit some misalignment under the microscope, but this was judged to be an insignificant fraction of the sample, so no effort was made to ensure perpendicular alignment on the plate surfaces.
15.(a) J. S. Hwang, R. P. Mason, L. P. Hwang, and J. H. Freed, J. Phys. Chem. 79, 489 (1975);
15.(b) J. H. Freed, J. Chem. Phys. 41, 2077 (1964).
16.The definition of λ here is a little different than that used by Polnaszek and Freed [Ref. 1(a)]. Thus, Also
17.A. de Vries, Mol. Cryst. Liq. Cryst. 63, 215 (1981), and references therein.
18.(a) P. A. C. Gane, A. J. Leadbetter, and P. G. Wrighton, Mol. Cryst. Liq. Cryst. 66, 247 (1981);
18.(b) P. S. Pershan, G. Aeppli, J. A. Litster, and R. J. Birgeneau, Mol. Cryst. Liq. Cryst. 67, 205 (1981)., Mol. Cryst. Liq. Cryst.
19.Somewhat different behavior has been observed for the large and rigid probe CSL in 40, 6 [cf. Ref. 3(a)]. It exhibits values of that are approximately an order of magnitude longer than for P, as well as significantly larger ordering. Large SRLS effects were postulated in both the and phases for CSL, but the low resolution of the ESR spectra and the lack of an orientation‐dependent study does somewhat reduce the reliability of those studies. Nevertheless, the inferred existence of a SRLS mechanism for CSL does correlate well with the strong cooperativity for reorientation expected especially in the phase.
20.(a) E. Meiroviteh (unpublished results);
20.(b) On the other hand, if PDT were located in the chain region and the cooperative chain distortion mode exists, then rapid enough translational diffusion of PDT could average out such inhomogeneities, but it could not be expected to average out inhomogeneities in macroscopic alignment.
21.(a) This comes about in the following way. The range of values between and which correspond to a particular value of is
21.(b) More generally, we can have a distribution in values of pitch p (corresponding, e.g., to a Fourier decomposition of the chain distortions). Only those Fourier components with p satisfying this inequality would contribute to the static distribution function
21.(c) We have in recent work found that line shapes quite similar to those obtained with the distribution could be obtained with a small admixture of a well aligned spectrum with a nearly random distribution Such a large misalignment is ruled out by our optical observations under a polarizing microscope (Sec. II) and by the well‐aligned results with CSL [cf. Fig. 5(c)] and PDT.
22.(a) The calculated series of line shapes corresponding to the experimental spectra recorded at involved storage requirements which were limiting for the PDP‐11 minicomputer. Since these spectra might be slightly nonconverging we assign a larger error to the point in Fig. 2.
22.(b) Actually, it is possible that as the temperature is lowered the bilayer structure becomes more like a monolayer, cf. G. J. Brownsey and A. J. Leadbetter, Phys. Rev. Lett. 44, 1608 (1980), who have found two mass density fluctuations of incommensurate wavelength.
23.(a) One could conceive of the possiblity that different probes exhibit different “solubility” in regions of different alignment. That is, CSL might preferentially seek out well‐aligned regions, while P probe might prefer more disordered regions of the sample. Our observations under the polarizing microscope are, of course, inconsistent with the existence of such regions except if they were submicroscopic in size (and/or relaxing too fast to be seen optically, but slow on ESR time values). One would then require periodic distortion modes in the disordered regions, that need not necessarily involve just the alkyl chains in order to “explain” our P probe ESR results. The pitch of such a mode must be large enough that the P probe diffusion (and/or relaxation of the mode or its propagation relative to the probe location) cannot average out the spectral effects of the distortion mode. This domainlike model seems to us less consistent with the known properties of liquid crystals than the model used in the main text, although the possibility of submicroscopic regions of faults or dislocations into which some probes may segregate could be of importance, but it is likely to lead to exchange narrowing effects on the ESR spectrum. Note added proof: A. M. Levelut and C. Druon, [J. Phys. Lett. 43, 193 (1982)]have recently suggested, from x‐ray and dielectric measurements on another cyanobiphenyl, the existence of tilted monolayer cybotactic groups of molecules inside a partially bilayer smectic A phase, with all linear dimensions of such groups corresponding approximately to eight molecular lengths and with a tilt angle of about 35°, Since the cybotactic clusters are found only at lower temperature, the possibility exists that P probe is preferentially soluble in such clusters. For such small clusters of the size reported, any inhomogeneities in the ordering of the molecules should be averaged out in the ESR by translational diffusion within such a cluster. Thus, one might consider the possibility of, e.g., different degrees of chain tilt (cf. Fig. 7) for the different cybotactic clusters, which is then sensed by the P probe. The CSL, on the other hand, could be almost entirely in the normal smectic A bilayers.
23.(b) S. A. Goldman, G. V. Bruno, C. F. Polnaszek, and J. H. Freed, J. Chem. Phys. 56, 716 (1972).
24.A. J. Leadbetter, J. C. Frost, J. P. Gaughan, G. W. Gray, and A. Mosley, J. Phys. Paris 40, 375 (1979).
25.(a) P. G. de Gennes, Solid State Commun. 6, 163 (1968);
25.G. R. Luckhurst and H. J. Smith, Mol. Cryst. Liq. Cryst. 20, 319 (1973).
25.(b) Another possiblity would be to restrict to be zero for values of greater than some value We found from our simulations that for significantly less than 90° (e.g., 75°–80°), poorer agreement with experiment was found,
25.(c) An even more dramatic discrepancy of this general character was noted in Ref. 3(c) in the study of the stearamide probe in the lipid phase. While in tube samples an G was found, oriented plate samples yielded an apparent G. It was suggested in that work [Ref. 3(c)] that (1) the well‐aligned plate samples had large arrays of uniform bilayers with strong cooperative interbilayer forces prevailing in the headgroup regions (and this was not so for tube samples) and (2) the stearamide could take on an ordered conformation similar to the lipid molecules with its chain aligned with the lipid chains and its piperidine ring aligned perpendicular to the chains and located in the fluid head‐group region. It was further postulated that the piperidine ring would be substantially ordered to exhibit an apparent G even though one usually expects this piperidine ring to be weakly ordered due to its extensive flexibility. If instead, we merely assume that the 90° twist of the piperidine ring significnatly increases by analogy to our above discussion of P probe, then it would no longer by necessary to invoke appreciable ordering of this probe to explain this unusual experimental result.
26.G. Moro, Implementation of the Lanczos Algorithm in the Calculation of Spectral Functions (unpublished report, Cornell University, 1980).
27.M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957).
28.P. L. Nordio, in Spin Labelling: Theory and Applications, edited by L. J. Berliner (Academic, New York, 1976) uses these conventions.
29.J. H. Freed, in Spin Labeling: Theory and Applications, edited by L. J. Berliner (Academic, New York, 1976).
29.Here the Freed‐Franekel conventions [J. Chem. Phys. 39, 326 (1963)]are used.
30.R. F. Campbell, E. Meirovitch, and J. H. Freed, J. Phys. Chem. 83, 525 (1979).
31.S. Alexander, A. Baram, and Z. Luz, Mol. Phys. 27, 441 (1974).
32.M. P. Eastman, R. G. Kooser, M. R. Das, and J. H. Freed, J. Chem. Phys. 51, 2690 (1969);
32.J. H. Freed, J. Phys. Chem. 71, 38 (1967).
33.(a) More generally, one must replace by the magnetization but this is only important for a very anisotropic g tensor [cf. R. F. Campbell and J. H. Freed, J. Phys. Chem. 84, 2668 (1980)];
33.(b) An earlier version is given by Campbell and Freed (ibid.).
34.E. C. Kemble, The Fundamental Principles of Quantum Mechanics with Elementary Applications (Dover, New York, 1958), p. 394.
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