Brownian diffusion of fibers

Figures & data

Figure 1. Dispersion of nano-fibers originally located at (0.2, 0.2, 0.0) m after 5 s.

Figure 2. PDFs of fiber translational and rotational Brownian displacements at times 0.001, 0.01, and 0.05 s in three-dimensional space (fiber diameter = 1 nm, β = 100).

Figure 3. Time evolving fiber diffusion coefficients: (a) diameter = 1 nm, β = 100; (b) diameter = 1000 nm, β = 100.

Figure 4. Prediction of (a) fiber rotational relaxation time τ_r (Equation (34)[34] ); (b) fiber macroscopic translational diffusion coefficient D_t (Equation (36)[36] ).

Table 1. Equivalent diffusion diameter of nanorods—comparison with the experiment.

			deq(nm)
d (nm)	Length (nm)	β	Experiment	Equation (38)[38] , Cc^1	Equation (38)[38] , Cc^2	Equation (39)[39]
17.3	257.0	14.9	68.1	72.5	69.5	75.8
20.9	232.0	11.3	70.9	72.4	70.1	75.5
11.2	47.4	4.3	30.9	21.2	20.8	21.9
43.3	94.9	2.2	64.6	58.8	58.1	59.5

C_c¹: average of ; C_c²: Cunningham correction for the equivalent volume diameter sphere.

Figure 5. Density effect on fiber diffusion coefficients: (a) diameter = 1 nm, β = 100; (b) diameter = 1000 nm, β = 100.

Figure 6. Comparison of predicted fiber diffusion coefficients with experiments: (a) simulation; (b) experiment (averaged over four experiments).

Figure 7. Fiber diffusion coefficients in the limiting case of a sphere: (a) translational diffusion coefficient; (b) rotation diffusion coefficient.