Size-Dependent Second Virial Coefficients of Quantum Dots from Quantitative Cryogenic Electron Microscopy

Abstract

Cryogenic transmission electron microscopy (cryo-TEM) is utilized to determine the second virial coefficient of osmotic pressure of PbSe quantum dots (QDs) dispersed in apolar liquid. Cryo-TEM images from vitrified samples provide snapshots of the equilibrium distribution of the particles. These snapshots yield radial distribution functions from which second virial coefficients are calculated, which agree with second virial coefficients determined with analytical centrifugation and small-angle X-ray scattering. The size dependence of the second virial coefficient points to an interparticle interaction that is proportional to the QD surface area. A plausible cause for this attraction is the interaction between the surface ions on adjacent QDs.

Experimental Method to Distinguish between a Solution and a Suspension

“…where d r and d m are the solvent densities at radial position r and meniscus, respectively; κ is the compressibility; r is the radial position; and m is the meniscus position. EOS Curve Plotting: The concentration gradient curves (raw data from SE-AUC experiments) were converted to an EOS plot (osmotic pressure Π vs number density ρ) by using Equations ( 4) and (5) [23,33] where ρ is the number density of the solute species, ω is the angular velocity, m is the buoyant mass of the particles, N A is the Avogadro number, M is the molecular weight, and d s is solvent density. The concentration can ) and d) different angular velocities (45 000, 48 000, and 52 000 rpm); e) ferritin in saline at different angular velocities (4000, 5000, and 7000 rpm) and f) apoferritin (5 mg mL −1 ) in PBS (pH 7.4) at different angular velocities (5000, 6000, and 8000 rpm).…”

“…The concentration gradient curves (raw data from SE‐AUC experiments) were converted to an EOS plot (osmotic pressure Π vs number density ρ) by using Equations () and (5) [ 23,33 ] where ρ is the number density of the solute species, ω is the angular velocity, m is the buoyant mass of the particles, N A is the Avogadro number, M is the molecular weight, and d s is solvent density. The concentration can be either calculated from absorbance data by knowing the extinction coefficients or from interference data by knowing the specific refractive index increment [ 34,35 ] $$\[ \begin{array}{*{20}{c}}{\Delta \Pi = {\omega ^2}m\mathop \smallint \limits_{{r_m}}^{{r_1}} \rho \left( r \right)r\,{d_{\rm{r}}}}\end{array} \]$$and $$\[ \begin{array}{*{20}{c}}{\rho = \frac{{c{d_{\rm{s}}}{N_{\rm{A}}}}}{M}}\end{array} \]$$…”

A thermodynamic gauge for mobile counter-ions from colloids and nanoparticles

“…11 One system under investigation is an aqueous dispersion of charged silica nanoparticles. 11 For apolar uids it would be interesting to investigate PbSe quantum dots that are suspected to carry charge in decalin, 24 though changes in resistivity might be too small here for a reliable gauge of mobile counter-ions.…”

“…This underlines the statement made in Section 2.2 that the low-salt region is distinctive for the large-reservoir limit. Note from (24) that in the low-salt region the salt concentration expelled by the suspension to reservoir asymptotes to L i / Àr s,0 , which in view of the denition of L i in eqn (1) is equivalent to r i À / 0: the limit in which all anions have le the suspension.…”

Cryogenic electron tomography to determine thermodynamic quantities for nanoparticle dispersions

“…To date, most of these studies were conducted on samples dilute enough so that two-dimensional (2D) images of their vitreous films could be studied. [30][31][32][33][34][35][36][37][38] We find this approach truly promising but the 2D nature of the images has the following limitations. First, the assumption that the thermodynamic properties extracted from 2D images apply to a 3D state needs to be validated.…”