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The relation (Formula presented) is valid only for one-dimensional motions; for three-dimensional isotropic motions, (Formula presented) should be replaced by (Formula presented) In this paper, we use the above relation to evaluate (Formula presented) because it is not obvious whether the motions observed here are one-, two-, or three-dimensional and the numerical factor (Formula presented) is not essential in the discussion of this paper
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The relation (Formula presented) is valid only for one-dimensional motions; for three-dimensional isotropic motions, (Formula presented) should be replaced by (Formula presented) In this paper, we use the above relation to evaluate (Formula presented) because it is not obvious whether the motions observed here are one-, two-, or three-dimensional and the numerical factor (Formula presented) is not essential in the discussion of this paper.
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J. D. Ferry, Viscoelastic Properties of Polymers (WLF Parameter) (John Wiley & Sons Inc., New York, 1980), p. 277.
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Strictly speaking, the relation of Eq. (11) is valid only for a two-dimensional case. In one-and three-dimensional cases, more complex expressions are obtained [see Eqs. (6) and (7) in Ref. 21], giving a temperature-dependent preexponential factor. However, since the variation of the prefactors with temperature is very small compared with the variation of the exponential term, the deviation due to the prefactors is unobservable
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Strictly speaking, the relation of Eq. (11) is valid only for a two-dimensional case. In one-and three-dimensional cases, more complex expressions are obtained [see Eqs. (6) and (7) in Ref. 21], giving a temperature-dependent preexponential factor. However, since the variation of the prefactors with temperature is very small compared with the variation of the exponential term, the deviation due to the prefactors is unobservable.
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24
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85036141770
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As described in Sec. II, the mean-square displacement observed by LAM-80 and GP-TAS are related to motions in time ranging faster than (Formula presented) and (Formula presented) respectively. The slower motions are observed in the LAM-80 measurements, so that the mean-square displacement observed by LAM-80 is larger and the temperature dependence is stronger than those observed by GP-TAS, respectively. Hence the apparent critical value (Formula presented) evaluated from the LAM-80 data is smaller than that from GP-TAS
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As described in Sec. II, the mean-square displacement observed by LAM-80 and GP-TAS are related to motions in time ranging faster than (Formula presented) and (Formula presented) respectively. The slower motions are observed in the LAM-80 measurements, so that the mean-square displacement observed by LAM-80 is larger and the temperature dependence is stronger than those observed by GP-TAS, respectively. Hence the apparent critical value (Formula presented) evaluated from the LAM-80 data is smaller than that from GP-TAS.
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28
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85036265232
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This assumption corresponds to (Formula presented) at (Formula presented)
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This assumption corresponds to (Formula presented) at (Formula presented)
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