A new model of reorientational dynamics in nematic liquid crystals, based on a linear generalized... more A new model of reorientational dynamics in nematic liquid crystals, based on a linear generalized Langevin equation (GLE) representation of the dynamics of a probe molecule, is developed. Derived in the limit of high order, the linearized angular motion of a probe molecule under the influence of director fluctuations is analyzed when the time scale of rotational relaxation is comparable to that of the cooperative modes of the liquid crystal solvent. This model allows negative total solvent contributions (director fluctuations plus a negative cross term) to the spectral density J1(ω) relative to the rotational diffusion contribution, a result predicted experimentally by least-squares data fits. This result cannot be justified in terms of existing theories that assume a separation of time scales between the probe molecule motion and relaxation of the cooperative modes of the solvent. Results from the GLE-based model (and the standard model) are compared to measured spectral densities of a highly ordered spin probe dissolved in a nematic liquid crystal [W. H. Dickerson, R. R. Vold, and R. L. Vold, J. Phys. Chem. 87, 166 (1983)]. Because the frequencies involved are low, the model predictions are very similar and excellent numerical agreement is found with both models. However, because the total solvent contribution is observed to involve inhibition of relaxation relative to the rotational diffusion, the standard model must be rejected on the basis of being physically unreasonable. The GLE model, on the other hand, is on firm physical ground and completely reasonable. The observed negative total solvent contribution to the spectral density can be explained in terms of a coupling of cooperative solvent modes with the molecular reorientation of the probe molecule that interferes with relaxation.
The title of this article is a paraphrase of another by the high-energy physicist Sidney Drell [2... more The title of this article is a paraphrase of another by the high-energy physicist Sidney Drell [2]. The latter article asks the question “When is a particle?” and deals with the changing standards of proof which lead us today to accept as “real” some fundamental particles (quarks) which we may never observe. Our situation is somewhat similar in that “hard evidence” of the existence of Davydov solitons remains elusive despite many years of effort expended in their study. As has been revealed during the discussions at this meeting, a part of this elusiveness does not arise from genuine problems of physics but from problems of communication between workers in the field. Among the latter is a considerable variance in the accepted meanings of the central terms “soliton” and “Davydov soliton” themselves. While most of us have a working knowledge of what the latter term means, the lack of a precise definition has been a root cause of some of the softness in the concept of the Davydov soliton. The physics of the underlying physical problem is, of course, completely indifferent to such linguistic difficulties which are purely of human origin; it is well, therefore, not to imbue them with undue importance. However, as the technical portion of this paper addresses a rather broad spectrum of behaviors open to an exciton in a deformable solid, we shall find it necessary to impose some precision on the terms to be used. In our general discussion, we will try use more general terms; when we encounter more distinct and special structures, we will try to preserve the distinctions in our language. It is inevitable that our terminology will conflict with that accepted by some segments of our audience; however, we hope that that will not prevent our message from being understood.
A new model of reorientational dynamics in nematic liquid crystals, based on a linear generalized... more A new model of reorientational dynamics in nematic liquid crystals, based on a linear generalized Langevin equation (GLE) representation of the dynamics of a probe molecule, is developed. Derived in the limit of high order, the linearized angular motion of a probe molecule under the influence of director fluctuations is analyzed when the time scale of rotational relaxation is comparable to that of the cooperative modes of the liquid crystal solvent. This model allows negative total solvent contributions (director fluctuations plus a negative cross term) to the spectral density J1(ω) relative to the rotational diffusion contribution, a result predicted experimentally by least-squares data fits. This result cannot be justified in terms of existing theories that assume a separation of time scales between the probe molecule motion and relaxation of the cooperative modes of the solvent. Results from the GLE-based model (and the standard model) are compared to measured spectral densities of a highly ordered spin probe dissolved in a nematic liquid crystal [W. H. Dickerson, R. R. Vold, and R. L. Vold, J. Phys. Chem. 87, 166 (1983)]. Because the frequencies involved are low, the model predictions are very similar and excellent numerical agreement is found with both models. However, because the total solvent contribution is observed to involve inhibition of relaxation relative to the rotational diffusion, the standard model must be rejected on the basis of being physically unreasonable. The GLE model, on the other hand, is on firm physical ground and completely reasonable. The observed negative total solvent contribution to the spectral density can be explained in terms of a coupling of cooperative solvent modes with the molecular reorientation of the probe molecule that interferes with relaxation.
The title of this article is a paraphrase of another by the high-energy physicist Sidney Drell [2... more The title of this article is a paraphrase of another by the high-energy physicist Sidney Drell [2]. The latter article asks the question “When is a particle?” and deals with the changing standards of proof which lead us today to accept as “real” some fundamental particles (quarks) which we may never observe. Our situation is somewhat similar in that “hard evidence” of the existence of Davydov solitons remains elusive despite many years of effort expended in their study. As has been revealed during the discussions at this meeting, a part of this elusiveness does not arise from genuine problems of physics but from problems of communication between workers in the field. Among the latter is a considerable variance in the accepted meanings of the central terms “soliton” and “Davydov soliton” themselves. While most of us have a working knowledge of what the latter term means, the lack of a precise definition has been a root cause of some of the softness in the concept of the Davydov soliton. The physics of the underlying physical problem is, of course, completely indifferent to such linguistic difficulties which are purely of human origin; it is well, therefore, not to imbue them with undue importance. However, as the technical portion of this paper addresses a rather broad spectrum of behaviors open to an exciton in a deformable solid, we shall find it necessary to impose some precision on the terms to be used. In our general discussion, we will try use more general terms; when we encounter more distinct and special structures, we will try to preserve the distinctions in our language. It is inevitable that our terminology will conflict with that accepted by some segments of our audience; however, we hope that that will not prevent our message from being understood.
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