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 Two-particle random walk simulation of outer-sphere nuclear relaxation
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10.1063/1.3429221
/content/aip/journal/jcp/132/22/10.1063/1.3429221
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/22/10.1063/1.3429221
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Change of the random trajectory of a hard point molecule of center due to the anisotropic plates of a stegosaurus molecule of center defined by Eqs. (6) and (7) and made of a central hard sphere of radius , a green equatorial hard plate, and three blue meridian hard plates of extension . Here, the stegosaurus has a fixed orientation in the course of time, practically, a very slow rotation of correlation time . Starting from the same initial position in a molecular frame rigidly bound to , the green and red dots are the successive positions of for typical random trajectories generated without (green) and with (red) the geometrical restraints of the plates. The lengths of the vertical bars are proportional to the distances written below between and traveling along the trajectories. The black bar represents the initial distance. The random displacements of with time can be viewed by playing movies_Fig1.gif (Ref. 58).

Image of FIG. 2.
FIG. 2.

Effects of the anisotropic plates of the stegosaurus of Fig. 1 on the (a) MC OS-DTCF and (b) associated spectral density of the relative translational motion of centered spins and on and . These functions reflect the changes of the relative Brownian trajectories of due to three different kinds of plates of , which are assumed to be the following: (k1) the reference hard sphere of radius without plates, (k2) the stegosaurus of Fig. 1 with meridian plates, and (k3) a stegosaurus with meridian plates. For the hard sphere, the values of from the MC simulation superimpose with their analytical ABHF counterparts.

Image of FIG. 3.
FIG. 3.

Change of the random trajectory of the molecule by rotational (r) driving of the stegosaurus having the initial orientation as defined in Fig. 1. Here, the stegosaurus drives in its tumbling (rotational effects RE2 of Sec. V B). (a) Moderately fast tumbling rate with . (b) Fast tumbling rate with . The green random trajectory of already shown in Fig. 1 is transformed into the red ones by the geometrical restraints of the plates and the rotational driving. The meaning of the other symbols is as in Fig. 1. The random displacements of with time can be viewed by playing movies_Fig3(a).gif and movies_Fig3(b).gif (Ref. 58).

Image of FIG. 4.
FIG. 4.

Effects of the rotational (r) driving of a molecule by the stegosaurus of Fig. 1 on the (a) MC OS-DTCF and (b) associated spectral density of the relative translational motion of centered spins and on and . The stegosaurus drives in its tumbling (rotational effects RE2 of Sec. V B) at the tumbling rates of Fig. 3.

Image of FIG. 5.
FIG. 5.

Change of the random trajectory of the molecule due to retarding solvation layers in the holes of the tumbling stegosaurus of Fig. 1. The stegosaurus starts tumbling with the same initial orientation as in Fig. 1. Here, the slow rotation of the stegosaurus with does not change the position of (indirect rotational effects RE1 of Sec. V B). The green random trajectory of already shown in Fig. 1 is transformed into the red ones by (a) the sole geometrical restraints of the plates (reference situation), (b) the same plate restraints and a rather modest local slowdown in the stegosaurus holes with , (c) the same plate restraints and a stronger local slowdown with The meaning of the other symbols is as in Fig. 1. The random displacements of with time can be viewed by playing movies_Fig5(a).gif, movies_Fig5(b).gif, and movies_Fig5(c).gif (Ref. 58).

Image of FIG. 6.
FIG. 6.
Image of FIG. 7.
FIG. 7.

(a) MC hat OS-DTCF and (b) associated star relaxivity of the relative translational motion of a centered spin on the molecule with respect to centered (c) and eccentric (e) spins of on a molecule assumed to be the HS of radius without plates and without retarding solvation layers, the stegosaurus s5A of Fig. 5(a) without retarding layers, the stegosaurus s5C of Fig. 5(c) with retarding layers in its holes where has a slower relative translational diffusion such as . The slow rotation of with does not change the position of (indirect rotational effects RE1 of Sec. V B). The position of the eccentric spin is in the molecular frame . Note that the statistical errors on are larger for the eccentric spin because of the wider scattering of the values of in Eq. (18).

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/content/aip/journal/jcp/132/22/10.1063/1.3429221
2010-06-09
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation:  Two-particle random walk simulation of outer-sphere nuclear relaxation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/132/22/10.1063/1.3429221
10.1063/1.3429221
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