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The order-disorder transition parameter scales as λ ∼ E2 C2 a3. The critical frequency ωCD dictates the particle size dependence of the polarizability, and thus, assuming a power-law dependence on frequency gives C∼ (ω/ ωCD) -n. Substituting this power-law scaling, we obtain, λ ∼ E2 [(ω/ ωCD) -n] 2 a3 ∼ E2 a-4n+3. Analyzing the data of Lumsdon (Ref.) we find that n≈0.22. This leads to λ ∼ E2 a2.1, in close agreement with the previously observed scaling of λ ∼ (Ea) 2. The apparent particle size dependence can be understood as an interplay between the functional form of C (in a narrow range of frequencies) and a shift relative to the critical frequency ωCD.
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The order-disorder transition parameter scales as λ ∼ E2 C2 a3. The critical frequency ωCD dictates the particle size dependence of the polarizability, and thus, assuming a power-law dependence on frequency gives C∼ (ω/ ωCD) -n. Substituting this power-law scaling, we obtain, λ ∼ E2 [(ω/ ωCD) -n] 2 a3 ∼ E2 a-4n+3. Analyzing the data of Lumsdon, (Ref.) we find that n≈0.22. This leads to λ ∼ E2 a2.1, in close agreement with the previously observed scaling of λ ∼ (Ea) 2. The apparent particle size dependence can be understood as an interplay between the functional form of C (in a narrow range of frequencies) and a shift relative to the critical frequency ωCD.
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