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85037185210
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4the quantity (Formula presented) is of order unity, rather than much smaller than this, hence presumably corrections to the expressions for the electrostatic moduli, due to electrostatic coupling, will not be completely negligible
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4the quantity (Formula presented) is of order unity, rather than much smaller than this, hence presumably corrections to the expressions for the electrostatic moduli, due to electrostatic coupling, will not be completely negligible.
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29
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0026851671
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85037230023
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the present theory
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and the present theory.
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33
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85037217427
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That a general harmonic Hamiltonian for charged lamellar phases is indeed obtained by replacing the moduli of the harmonic long-wavelength theory by wave-vector-dependent moduli can also be seen by explicitly calculating the electrostatic free energy of the undulations from the Poisson-Boltzmann equation, in a harmonic approximation. However, instead of considering only even and odd undulation modes of a certain wavelength, as Fogden et al
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That a general harmonic Hamiltonian for charged lamellar phases is indeed obtained by replacing the moduli of the harmonic long-wavelength theory by wave-vector-dependent moduli can also be seen by explicitly calculating the electrostatic free energy of the undulations from the Poisson-Boltzmann equation, in a harmonic approximation. However, instead of considering only even and odd undulation modes of a certain wavelength, as Fogden et al
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34
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4243791610
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The universal wave-vector dependence of the moduli of a smectic-A liquid crystal at extremely long wavelengths, due to anharmonic corrections to the long-wavelength, harmonic continuum model, was first considered by G. Grinstein and R. A. Pelcovits, Phys. Rev. Lett. 47, 856 (1981).PRLTAO
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See also F. C. Larche, J. Appel, G. Porte, P. Bassereau, and J. Marignan, Phys. Rev. Lett. 56, 1700 (1986).PRLTAO
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84956107315
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41
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85037220077
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Following Schomäcker and Strey, the following values for the parameters were used: membrane thickness (Formula presented) headgroup area (Formula presented). The relation between the position of the Bragg peak, (Formula presented), and the repeating distance (Formula presented) was taken to be (Formula presented), as in Schomäcker and Strey, with an index of refraction (Formula presented). The surface charge density (in number of elementary charges per unit area) was calculated from (Formula presented), with concentrations of SDS and (Formula presented) in M. Finally, the Bjerrum length (Formula presented) nm
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Following Schomäcker and Strey, the following values for the parameters were used: membrane thickness (Formula presented) headgroup area (Formula presented). The relation between the position of the Bragg peak, (Formula presented), and the repeating distance (Formula presented) was taken to be (Formula presented), as in Schomäcker and Strey, with an index of refraction (Formula presented). The surface charge density (in number of elementary charges per unit area) was calculated from (Formula presented), with concentrations of SDS and (Formula presented) in M. Finally, the Bjerrum length (Formula presented) nm.
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