dynamic light scattering size distribution by number

#DYNAMIC LIGHT SCATTERING SIZE DISTRIBUTION BY NUMBER VERIFICATION#
#DYNAMIC LIGHT SCATTERING SIZE DISTRIBUTION BY NUMBER FREE#

( A) Mean squared displacement 〈δ x(τ) 2〉 of the membrane cantilever tip as a function of the observation time interval τ. 2A, one can conclude that over intervals up to ~10 −5 s, the cantilever essentially moves ballistically over average distances up to 3 nm. At short time intervals, the near-unity value of the normalized autocorrelation function is again explicit evidence of the ballistic regime. 2B, which evaluates how close the velocity at the end of the observation period is to the velocity at the beginning. This is confirmed by the normalized velocity autocorrelation function 〈 v( t) v( t + τ)〉/( k B T/ m eff) plotted in Fig. This is direct evidence of the ballistic motion regime, as it means that velocity is constant over the observation interval. For small observation intervals τ ≪ θ (where θ = 1.75 × 10 −4 s is the oscillation period of the cantilever), the mean squared displacement 〈δ x(τ) 2〉 grows quadratically with τ. To reveal the detailed nature of nanomembrane cantilever thermal motion, from the experimental data, we evaluate the mean squared displacement 〈δ x(τ) 2〉 as a function of observation time τ ( Fig. The natural oscillation frequency of the cantilever ω 0/2π = 5.7 kHz and the damping time τ b = 1/γ = 14 ms were evaluated from the Fourier spectrum of the displacement autocorrelation function. Position measurements as a function of time reveal Gaussian distributions of the membrane’s position and velocity with root-mean-square values of 〈 x〉 = 8.3 nm and 〈 v〉 = 0.30 mm/s, respectively ( Fig. The secondary electron flux generated by scattering of an electron beam tightly focused on the edge of the membrane is highly sensitive to its position (see Materials and Methods). The cantilever was 30 nm thick and 62 μm long with a width tapered from 0.6 μm at the fixed end to 3 μm at the other, and an effective mass m eff = 47 pg (see the Supplementary Materials). The material and geometry were selected to facilitate observation of the ballistic regime by consideration of the cantilever’s effective mass, the natural frequency and quality factor of its fundamental flexural mode, and the secondary electron yield. We investigated the dynamics of thermal motion in the out-of-plane flexural mode of a cantilever cut from a freestanding gold nanomembrane.

#DYNAMIC LIGHT SCATTERING SIZE DISTRIBUTION BY NUMBER VERIFICATION#

Access to the ballistic regime provides verification of the equipartition theorem and Maxwell-Boltzmann statistics for flexural modes and can be used in fast thermometry and mass sensing during atomic absorption/desorption processes on the membrane. Within intervals <10 μs, the membrane moves ballistically at a constant velocity, typically ~300 μm/s, while Brownian-like dynamics emerge for longer observation periods.

#DYNAMIC LIGHT SCATTERING SIZE DISTRIBUTION BY NUMBER FREE#

Here, we report on the observation of short–time scale ballistic motion in the flexural mode of a nanomembrane cantilever, driven by thermal fluctuation of flexural phonons, including measurements of ballistic velocities and displacements performed with subatomic resolution, using a free electron edge-scattering technique. Flexural oscillations of freestanding films, nanomembranes, and nanowires are attracting growing attention for their importance to the fundamental physical and optical properties and device applications of two-dimensional and nanostructured (meta)materials.

Dynamic light scattering size distribution by number