Figure 1

(Color online) A dendrimer bound to a surface. The dark spheres represent folic acid molecules and the light spheres folate binding protein, the folic acid receptor, on the surface [25].Reuse & Permissions

Figure 2

Distributions of dendrimers with $n$ bound ligands, for average ligand number $\overline{n}$ of (a) 0.9, (b) 3.7, (c) 5.8, and (d) 13.9. Note the log scale. The data points are HPLC data from ligation experiments that are chemically similar to the folic acid ligation. The dashed line is the Poisson distribution and the solid line is the result of Monte Carlo simulations of the ligation model below with $E=-3.7\pm 0.1\text{kT}$.Reuse & Permissions

Figure 3

Ligation on the triangular lattice. Each intersection is a lattice site, a potential location for ligation. The filled circles are already attached ligands. The dotted circles labeled A, B, and C are examples of potential ligation sites. A ligand attempting to attach at the site marked $A$ does so with free energy $E_0=0$. A ligand attempting to attach at site B has a 1/6 chance of attaching with free energy $E$, and a 5/6 chance of having free energy $E_0=0$. A ligand may not attach at site C due to the steric hindrance from its two neighboring ligands.Reuse & Permissions

Figure 4

Acetylation and ligation on the triangular lattice. Acetylation of sites occurs as before, with cooperative or free paths, but without steric hindrance. Acetylation occurs at site A with free energy $E_0=0$; at B with 1/6 chance of free energy $E_{aa}$ and a 5/6 chance of free energy $E_0=0$; and at C with a 1/3 chance of having free energy $E_{aa}$ and 2/3 chance of having free energy $E_0=0$. As in the chemical synthesis, ligation begins only after acetylation is complete. Ligation occurs at site D with a 1/6 chance of having free energy $E$ and a 5/6 chance of having $E_0=0$; at site E with a 1/6 chance of having free energy $E$, a 1/6 chance of having $E_a$, and a 2/3 chance of having $E_0=0$; a ligand may not attach at site F due to the steric hindrance between its two ligand neighbors. Note that since the same catayltic chemistry is present in ligand-ligand, ligand-acetyl, and acetyl-acetyl interactions, we use $E_{aa}=E_a=E$.Reuse & Permissions

Figure 5

Distributions of dendrimers with $\approx 68\mathrm{\%}$ of sites acetylated and with $n$ bound ligands, for average ligand number $\overline{n}$ of (a) 1.0, (b) 1.9, (c) 3.4, and (d) 16.0. Note the log scale. The data points are HPLC data. The dashed line is the Poisson distribution and the solid line is the result of best-fit Monte Carlo simulations of the acetylation/ligation model with $E=-5.0\pm 0.2\text{kT}$.Reuse & Permissions

Figure 6

SPR measurement of nanoparticle coverage. During adsorption (rising part of curve), buffer with FA-bound dendrimer flows across the SPR chip. During desorption, clean buffer flows; $k_d$ is obtained by fitting the desorption in the second phase, dashed line.Reuse & Permissions

Figure 7

Dissociation rate $k_d$ versus $\overline{n}$, from exponential fits to the SPR data with a free horizontal asymptote due to the unknown fraction of permanently bound material. The data are consistent with a rate independent of $\overline{n}$, $k_d\approx 3\times {10}^{-3}{\text{s}}^{-1}$, i.e., the rate of singly-bound nanoparticles dissociating from the surface.Reuse & Permissions

Figure 8

(Color online) Fraction of singly-ligated nanoparticles vs $\overline{n}$. The points are the fraction of desorbed material to adsorbed material in the SPR experiment. The crosses are the fraction of singly-ligated nanoparticles as measured by HPLC. The line is the fraction of singly-ligated nanoparticles $F_1$ simulated with the kinetic model with parameters $E=-5.0\text{kT}$, which matched the best fit to the HPLC data. The dashed line is $F_1$ for the Poisson case.Reuse & Permissions