The internal field in dipole lattices

Nijboer, B.R.A.; Wette, F. W. de

doi:10.1016/s0031-8914(58)95803-8

Cited by 193 publications

(60 citation statements)

References 7 publications

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“…The lattice sums S 2m are conditionally convergent, and can be determined by either using the method of Nijboer and de Wette 36 or following the approach of McPhedran and McKenzie ͑for cubic arrays͒. 37 The internal field in dipole lattices and the related conditionally convergent lattice sums are also discussed in another paper by Nijboer and de Wette, 38 and our method is consistent with theirs.…”

Section: ͑210͒mentioning

confidence: 60%

Static yield stresses and shear moduli in electrorheological fluids

Clercx

Bossis

1995

The Journal of Chemical Physics

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A previously introduced method to study many-body electrostatic interactions among spherical particles ͓H. J. H. Clercx and G. Bossis, Phys. Rev. E 48, 2721 ͑1993͔͒ has been used to study yield stresses and shear moduli for simple cubic ͑SC͒, simple hexagonal ͑SH͒, and body-centered tetragonal ͑BCT͒ structures, with polarizable spheres on the lattice sites, to gain insight in the electrostatic response of these structures to externally applied stresses. The shear modulus G and the static yield stress s have been calculated for several ratios of particle to fluid dielectric constant. It turned out that interchain interactions are very weak in SC and SH structures which is confirmed by the nearly linear dependence of G and s ͑even no weak maximum appears in these curves͒. The results reported for the BCT structure are rather unexpected, because both G and s suddenly decrease to zero at large volume fractions. We discuss the data for G and s and compare some of these results with data obtained by employing the dipolar approximation and the Laplacian relaxation technique to calculate the electrostatics. This comparison shows that in general a multipolar approach is indispensable in obtaining correct values for G and ; especially the dipolar approximation underestimates these quantities. As an example the strength of single vs double chains has been compared for both the dipolar approach and a multipolar calculation. In the dipolar approximation the double chain structure seems strongest. However, multipolar calculations show that the single chain structure is stronger than the double chain structure.

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Section: ͑210͒mentioning

confidence: 60%

Static yield stresses and shear moduli in electrorheological fluids

Clercx

Bossis

1995

The Journal of Chemical Physics

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“…A direct double summation including all lattice vectors within a specified radius, or within a cube of a specified dimension, yields a result of zero. It has been shown [31], however, that the summation may be executed by, first, summing the lattice vectors ρ j in the x − y plane only (so that ρ z,j = 0) for a particular ρ i (convergence is slow). The process is then repeated for different values of ρ i .…”

Section: D Spin Systemsmentioning

confidence: 99%

“…The process is then repeated for different values of ρ i . The full solution, however, is accessible to analytic treatment for a spin fluid and is given by [31] as…”

Section: D Spin Systemsmentioning

confidence: 99%

Nuclear magnetic resonance relaxometry of water in two and quasi-two dimensions

et al. 2013

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Molecular dynamics (MD) and Monte Carlo (MC) methods are used to determine the spin-pair correlation function, G * (t), for the diffusion of bulk water in three-dimensions (3D) and pore water in two-dimensions (2D) and quasi-two-dimensions (Q2D). The correlation function is required for the determination of the nuclear magnetic resonance (NMR) spin-lattice and spin-spin relaxation times T 1 and T 2 . It is shown that the analytic form of the powder-average correlation function, introduced by Sholl [C. A. Sholl, J. Phys. C: Solid State Phys. 7, 3378 (1974)] for the diffusion of spins on a 3D lattice, is of general validity. An analytic expression for G * (t) for a uniform spin fluid is derived in 2D. An analytic expression for the long-time behaviour of G * (t) is derived for spins diffusing on 3D, 2D and Q2D lattices. An analytic correction term, which accounts for spin-pairs outside the scope of the numerical simulations, is derived for 3D and 2D and shown to improve the accuracy of the simulations. The contributions to T 1 due to translational and rotational motion obtained from the MD simulation of bulk water at 300 K are 7.4 s and 10±1 s respectively, at 150MHz leading to an overall time of 4.3 ± 0.4 s compared the experimental value of 3.8 s. In Q2D systems, in which water is confined by alpha-quartz surfaces to thicknesses of 1-5 nm, T 1 for both translational and rotational relaxation is reduced due to the orientation and adsorption of spins at the surfaces. A novel method of parameterising the MC lattice-diffusion simulations in 3D, 2D and Q2D systems is presented. MC results for G * (t) for 3D and 2D systems are found to be consistent with an analytic uniform fluid model for t 40 ps. The value of T 1 for translational diffusion obtained from the MC simulation of bulk water is found to be 4.8 s at 15 MHz. G * (t) obtained from MC simulations of Q2D systems, where water is confined by hard walls, is found to execute a distinct transition from 3D to 2D behaviour. The T 1 is found to be similar to the 3D bulk water result at all pore thicknesses.

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“…The vector g is a two-dimensional reciprocal lattice vector perpendicular to k, g is the length of this vector, cpg its direction and ac the area of the two-dimensional unit cell. The function B equals -1 in the special case treated by Nijboer and De Wette (1958). In general, it depends on the polar angles (tf, cp) and (#', cp'), which describe the orientations of the dipole moments in the two sublattices, relative to a frame which has its z axis parallel to the wavevector k:…”

Section: T H M Van Den Berg and A Van Der A Voirdmentioning

confidence: 99%

On the anomalous vibron-phonon dispersion in solid tetracyanoethene, C₂(CN)₄

Berg

Avoird

1989

J. Phys.: Condens. Matter

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Abstract. The anomalous dispersion found by inelastic neutron scattering in one of the vibron bands in solid tetracyanoethene appears to be due to the electrostatic interactions that couple the infrared-active intramolecular vibrations via the transition dipole resonance mechanism. This is demonstrated by way of both numerical lattice dynamics calculationsand a simple mathematical analysis, which relates the Fourier components of the dispersion curves in specific directions of the wavevector k to two-dimensional lattice sums over the dipole-dipole interactions between layers perpendicular to k. Only for specific orientations of the molecular transition dipole moments in a solid and for specific directions of k will this lead to a dispersion curve of irregular shape.

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The internal field in dipole lattices

Cited by 193 publications

References 7 publications

Static yield stresses and shear moduli in electrorheological fluids

Static yield stresses and shear moduli in electrorheological fluids

Nuclear magnetic resonance relaxometry of water in two and quasi-two dimensions

On the anomalous vibron-phonon dispersion in solid tetracyanoethene, C₂(CN)₄

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The internal field in dipole lattices

Cited by 193 publications

References 7 publications

Static yield stresses and shear moduli in electrorheological fluids

Static yield stresses and shear moduli in electrorheological fluids

Nuclear magnetic resonance relaxometry of water in two and quasi-two dimensions

On the anomalous vibron-phonon dispersion in solid tetracyanoethene, C2(CN)4

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On the anomalous vibron-phonon dispersion in solid tetracyanoethene, C₂(CN)₄