Figure 1

Force-distance profile of the particles grafted with streptavidin, $C_p=0.05\%$ volume in $p\mathrm{H}$ 7.2 phosphate buffer as a function of the ionic strength. ○: 1 mM (${\kappa }^{-1}=9.5\mathrm{nm}$), □: 2 mM (${\kappa }^{-1}=6.7\mathrm{nm}$), △: 5 mM (${\kappa }^{-1}=4.2\mathrm{nm}$), +: 10 mM (${\kappa }^{-1}=3\mathrm{nm}$), ◇: 20 mM (${\kappa }^{-1}=2.1\mathrm{nm}$). The surface to surface separation $h$ is deduced from: $h=d-2R$. The distance $d$ is measured from Bragg scattering and $2R$ is the hard core diameter. Plain lines give the confidence interval for the calculated profiles, taking into account an error of 1 nm on the distance measured. To measure $R$, the particles were pushed to contact in a solution of 10 mM chlorhydric acid for which the COOH functions present at the surface of the particles are completely protonated. The evolution of the repulsive profiles with ionic strength shows that both electrostatic and steric forces help to stabilize the particles.Reuse & Permissions

Figure 2

Formation of permanent chains under optical microscope. (a) Under magnetic field (80 mT), the particles align in the direction of the field due to dipolar interactions; (b) 2 min after removing the magnetic field, the chains remain permanent due to bridging by ds-DNA. The filaments have lost their orientation as a result of Brownian motion and flexibility [22]. $C_p=1.3\times {10}^{11}\mathrm{\text{particles}}/\mathrm{mL}$ and $C_{\mathrm{DNA}}=7.3\times {10}^{12}\mathrm{\text{molecules}}/\mathrm{mL}$.Reuse & Permissions

Figure 3

Force-distance profiles in the presence of 1.9 DNA on average between adjacent particles, in phosphate buffer 10 mM $p\mathrm{H}$ 7.2. +: increasing field ramps, ×: decreasing field ramps, ▲: average force-distance profile. Dashed lines are guides to the eye.Reuse & Permissions

Figure 4

Comparison between average force-distance profiles in the absence and in the presence of 1.9 DNA on average between adjacent particles, in phosphate buffer 10 mM $p\mathrm{H}$ 7.2: ●: $F_{\mathrm{Bg}}$, ■: $F_{\mathrm{irr}}$, ▲: $F_l=F_{\mathrm{irr}}-F_{\mathrm{Bg}}$. Dashed lines correspond to the error on force-distance profiles, calculated from the standard deviation of the measured profiles. Inset: contribution of the linker $F_l$ and fit of the data for various numbers of DNA between the particles. ▲: 1.9 DNA, +: 3 DNA, □: 4.7 DNA, ×: 5.5 DNA. Plain lines: fit of the data with $F_{\mathrm{tot}}=N⟨F{⟩}_{\phi }$, with $N=1.9$ and $⟨F{⟩}_{\phi }$ given by Eq. (3).Reuse & Permissions

Figure 5

Definition of the different geometrical parameters appearing in the model. The angle ${\theta }_{\max }$ defines the reactive portion of sphere and the distance $h_f$ is the distance between the particles during the linking process (formation of permanent chains): $\cos {\theta }_{\max }=(h_f+2R-L_c)/2R$. $L_c=51\mathrm{nm}$ is the contour length of the DNA and $R=88\mathrm{nm}$ is the radius of the particles. $\delta$ is the distance between the planes ($P_1$) and ($P_2$) that are used for approximation. ${\phi }_{\max }$ defines the maximal orientation that can take a DNA molecule when linking the beads. The figure is invariant by rotation around (△), the axis of the chain.Reuse & Permissions