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Methyl group rotation, 1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation
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10.1063/1.3677183
/content/aip/journal/jcp/136/5/10.1063/1.3677183
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/5/10.1063/1.3677183
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Figures

Image of FIG. 1.
FIG. 1.

The stretched-exponential characteristic 1H relaxation rate, R*, versus inverse temperature, T −1, in polycrystalline 4,4-dimethoxybiphenyl at NMR frequencies ω 0/2π = 8.50 (■), 22.5 (▲, ▼, ●), and 53.0 MHz (, ◆, ). The inset shows the molecule. The different symbols for 22.5 and 53.0 MHz indicate different groupings of experiment days indicating (at lower temperatures) slightly different structures on different groups of days. At temperatures below (i.e., to the right of) the approximate positions of the vertical lines, the stretching parameter β > 0.95 (see Fig. 4). At these temperatures, the stretched-exponential relaxation fit and a single-exponential relaxation fit, characterized by R, are indistinguishable (R* = R). The experimental uncertainties are within the sizes of the symbols. The solid lines correspond to a single fit as discussed in the text. The dashed line indicates the high-temperature R S values in Fig. 2. The data to the right of the vertical lines are the same in Figs. 1 and 2 and are shown on an expanded scale in Fig. 3.

Image of FIG. 2.
FIG. 2.

The 1H short-time (initial recovery) exponential relaxation rate, R S , versus inverse temperature, T −1, in polycrystalline 4,4-dimethoxybiphenyl at NMR frequencies ω 0/2π = 8.50 (■), 22.5 (▲, ▼), and 53.0 MHz (, ◆, ). The different symbols for 22.5 and 53.0 MHz indicate different groupings of experiment days indicating (at lower temperatures) slightly different structures on different groups of days. At temperatures below (i.e., to the right of) the approximate positions of the vertical lines, R S and a single-exponential relaxation fit characterized by R are indistinguishable (R S = R). Where error flags are not shown, the experimental uncertainties are within the sizes of the symbols. The solid lines correspond to a single fit as discussed in the text. The dashed line indicates the high-temperature R* values in Fig. 1. The data to the right of the vertical lines are the same in Figs. 1 and 2 and are shown on an expanded scale in Fig. 3.

Image of FIG. 3.
FIG. 3.

The single-exponential 1H relaxation rate, R, versus inverse temperature, T −1, in polycrystalline 4,4-dimethoxybiphenyl at NMR frequencies ω 0/2π = 8.5 (■), 22.5 (▲, ▼), and 53.0 MHz (, ◆, ) for temperatures below the vertical lines in Figs. 1 and 2. The relaxation is exponential in this regime. The different symbols for 22.5 and 53.0 MHz indicate different groupings of experiment days, indicating slightly different structures on different groups of days. The six lines are guides for the eye and all have the same slope of lnR versus T −1. All groups except the bottom line for 53.0 MHz involve two or more days of experiments. The experimental uncertainties are within the sizes of the symbols.

Image of FIG. 4.
FIG. 4.

The stretching parameter, β, versus inverse temperature, T −1, for the 1H spin-lattice relaxation measurements in polycrystalline 4,4-dimethoxy-biphenyl. β = 1 corresponds to exponential relaxation. To within experimental uncertainty, single-exponential relaxation is indistinguishable from stretched-exponential relaxation for β > 0.95, indicated by the horizontal lines. The vertical arrows indicate the values of the R* maxima in Fig. 1. (a) Measurements at NMR frequencies ω 0/2π = 8.50 (■), 22.5 (●), and 53.0 MHz (▲). (b) Just the ω 0/2π = 22.5 MHz data.

Image of FIG. 5.
FIG. 5.

An inversion recovery 1H nuclear spin-lattice relaxation experiment in polycrystalline 4,4-dimethoxybiphenyl at an NMR frequency ω 0/2π = 22.5 MHz and at a temperature T = 155 K (103 T −1 = 6.46 K−1). (a) and (b) The nuclear magnetization M versus time t between the perturbation π pulse and the measurement π/2 pulse in an inversion recovery experiment. A stretched-exponential fit (solid line) gives R* = 14.0 ± 0.2 s−1 (see Fig. 1) and β = 0.79 ± 0.01 (see Fig. 4). A single exponential (dashed line) is a poor fit to the relaxation curve. The inset in (a) shows the first 60 ms. (b) The first 9 ms. The uncertainties for both the main plot and the inset in (a) are within the size of the symbols. The uncertainties can be seen in (b). (c) The difference between the observed and fitted M(t) values for the stretched-exponential (●) and single exponential (■) fits in (a) and (b). The logarithmic time scale is used solely to spread the data out. The lines joining the values are guides for the eye. The data in parts (a), (b), and (c) have the same uncertainties. (d) The single-exponential relaxation rate, R S , that characterizes the short-time magnetization recovery versus the maximum time, t max , used in the determination of R S . The R S value (used in Fig. 2) for this experiment is taken to be R S = 35.4 ± 2.8 s−1 as indicated by the datum going through the horizontal line.

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/content/aip/journal/jcp/136/5/10.1063/1.3677183
2012-02-06
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Methyl group rotation, 1H spin-lattice relaxation in an organic solid, and the analysis of nonexponential relaxation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/5/10.1063/1.3677183
10.1063/1.3677183
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