Microscopic Perspective on the Adsorption Isotherm of a Heterogeneous Surface

Abstract

Adsorption of dissolved molecules onto solid surfaces can be extremely sensitive to the atomic-scale properties of the solute and surface, causing difficulties for the design of fluidic systems in industrial, medical and technological applications. In this communication, we show that the Langmuir isotherm for adsorption of a small molecule to a realistic, heterogeneous surface can be predicted from atomic structures of the molecule and surface through molecular dynamics (MD) simulations. We highlight the method by studying the adsorption of dimethyl-methylphosphonate (DMMP) to amorphous silica substrates and show that subtle differences in the atomic-scale surface properties can have drastic effects on the Langmuir isotherm. The sensitivity of the method presented is sufficient to permit the optimization of fluidic devices and to determine fundamental design rules for controlling adsorption at the nanoscale.

Figure 1

Molecular dynamics simulations of adsorption. (Top) Typical starting configuration containing randomly placed DMMP solute (shown as vdW spheres), two silica slabs (shown as gray molecular surfaces) and water (not shown). The plot specifies the average concentration of the solute along the z axis. (Bottom) The same system at the end of a 100-ns MD trajectory.

Figure 2

Adsorption isotherm. Black squares indicate the data directly obtained from all-atom MD simulations. The solid line shows the fit of the Langmuir isotherm to the MD data; the expected error of the fit is shown in light blue. Blue circles show the predictions of the theoretical model based on the 3-dimensional potential of mean force (see text).

Figure 3

Potential of mean force (PMF) of a DMMP solute in proximity to a heterogeneous surface. The silica slab is shown as a molecular surface colored by the local minimum value of the PMF in the direction normal to the slab (see text). Inset shows the PMF averaged over the x–y plane as a function of the distance from the surface.

Figure 4

Test of the 3D-PMF model of adsorption using different heterogeneous surfaces. (a–d) Atomic model of the surface of silica slabs A–D, respectively. Oxygen and silicon atoms are shown as red and yellow vdW spheres, respectively. (e) Test of the model. Black squares indicate data directly obtained from MD simulations, other symbols show predictions of the 3D-PMF model. Labels A, B, C, and D indicate the surfaces the data were obtained for (also shown as panels a–d); AB labels the system that combined two different surfaces (A and B, labeled A_AB and B_AB), and Ph indicates a phantom surface, a smooth surface that lacks atomic-scale features (see text).

Figure 5

Atomic features affect adsorption. For the four silica surfaces, the Langmuir constant is plotted as a function of (a) the root mean square (RMS) surface charge density and (b) the conformation of the adsorbed solutes. The latter is characterized by the average projection of the P–O bond unit vector onto the normal of the slab. Colors and symbols are the same as in Figure 4 e. Inset to (a) shows a DMMP molecule bound to a small pocket (surface D).