Adsorption of charged and neutral polymer chains on silica surfaces: The role of electrostatics, volume exclusion, and hydrogen bonding

We develop an off-lattice (continuum) model to describe the adsorption of neutral polymer chains and polyelectrolytes to surfaces. Our continuum description allows taking excluded volume interactions between polymer chains and ions directly into account. To implement those interactions, we use a modified hard-sphere equation of state, adapted for mixtures of connected beads. Our model is applicable to neutral, charged, and ionizable surfaces and polymer chains alike and accounts for polarizability effects of the adsorbed layer and chemical interactions between polymer chains and the surface. We compare our model predictions to data of a classical system for polymer adsorption: neutral poly($N$-vinylpyrrolidone) (PVP) on silica surfaces. The model shows that PVP adsorption on silica is driven by surface hydrogen bonding with an effective maximum binding energy of about $1.3k_{\mathrm{B}}T$ per PVP segment at low $p\mathrm{H}$. As the $p\mathrm{H}$ increases, the Si-OH groups become increasingly dissociated, leading to a lower capacity for H bonding and simultaneous counterion accumulation and volume exclusion close to the surface. Together these effects result in a characteristic adsorption isotherm, with the adsorbed amount dropping sharply at a critical $p\mathrm{H}$. Using this model for adsorption data on silica surfaces cleaned by either a piranha solution or an ${\mathrm{O}}_2$ plasma, we find that the former have a significantly higher density of silanol groups.

Figure 1

Artist's impression of the interface between a silica surface and the solution containing adsorbing polymer chains (PVP) and ions, as implemented in our model.

Figure 2

(a) Adsorption profiles of polyelectrolytes on an oppositely charged surface in the presence of a 1:1 electrolyte, using various models to account for the excluded volume interactions. Profiles I–IV are calculated using the exchange potential definitions in Fig. 1 of Ref. [32] ($v=0.5{\mathrm{nm}}^3/\mathrm{nm}$, $v_{\mathrm{FH}}=0.18{\mathrm{nm}}^3$, $z_{\mathrm{s}}\Lambda =-1{\mathrm{nm}}^{-2}$ (fixed charge), $z_{\mathrm{p}}\lambda =1{\mathrm{nm}}^{-1}$ (fixed charge), $a=1$ nm, ${\epsilon }_{\mathrm{p}}=20$, ${\epsilon }_{\mathrm{w}}=78$, $\chi =0$, $n_{\infty }/N_{\mathrm{Av}}=10$ mM, and ${\varphi }_{\mathrm{p}}^{\mathrm{b}}={10}^{-3}$), profile V includes the volume exclusion term of Eq. (15) for both polymer chains and ions (${\sigma }_{\mathrm{p}}=\sqrt{6v/\pi }=0.98$ nm and ${\sigma }_{\mathrm{ion}}=0.69$ nm), and $x$ denotes the distance from the surface. (b) and (c) Individual contributions to the exchange potential $u$ for profile IV and V, respectively. All potential energy differences approach zero far from the surface. The electrostatic potential difference $\Delta {\mu }^{\mathrm{el}}$ first becomes positive (around $x\approx 2$ nm) before decaying to zero.

Figure 3

(a) Adsorbed amount of PVP on silica as a function of the solution bulk $p\mathrm{H}$. The adsorption strength is assumed proportional to the number of potential H bonds between PVP and silica [Eq. (23), with ${\varepsilon }_{\mathrm{s}}^{\prime }=-3.5k_{\mathrm{B}}T/\mathrm{nm}$, and $\Lambda =3.8{\mathrm{nm}}^{-2}$ for piranha-cleaned surfaces and $1.5{\mathrm{nm}}^{-2}$ for plasma-cleaned surfaces]. The Stern layer capacitance is $C_{\mathrm{St}}=2.4\mathrm{F}/{\mathrm{m}}^2$. (b) Polymer (top) and ion (bottom) volume fraction profiles near silica surfaces with $\Lambda =3.8$ (left) and 1.5 (right) ${\mathrm{nm}}^{-2}$, at varying solution $p\mathrm{H}$ as indicated by the labels.

Figure 4

Alternative models for the adsorbed amount of PVP on silica as a function of the solution bulk $p\mathrm{H}$: (a) fixed adsorption strength of $-4k_{\mathrm{B}}T$ per unit length of polymer, regardless the number of Si-OH groups on the surface (dashed lines), and electrostatic attraction between the ionizable silica surface and the polymer chains ($\lambda =4.0$ ${\mathrm{nm}}^{-1}$, $\mathrm{p}{K}_{\mathrm{a}},\mathrm{p}=6$, dotted lines); (b) H bonding without volume effects, using an adsorption strength ${\varepsilon }_{\mathrm{s}}^{\prime }=-1.2k_{\mathrm{B}}T/\mathrm{nm}$ [Eq. (23)]. In both cases, the density of ionizable groups on the silica surface is $\Lambda =3.8$ (piranha-cleaned) and $1.5{\mathrm{nm}}^{-2}$ (plasma-cleaned).

Figure 5

(a) Adsorbed amount of PVP on plasma-cleaned silica as a function of the bulk ionic strength for two $p\mathrm{H}$ values in experiments: $p\mathrm{H}$ 3.5 (open diamonds) and 7.0 (filled triangles). The predicted salt-dependent adsorption isotherms of our model as described in relation to Fig. 3 are shown for four $p\mathrm{H}$ values (3.5, 7.0, 8.0, and 8.5, as indicated by the labels). (b) Polymer (top) and ion (bottom) volume fraction profiles near plasma-cleaned silica surfaces at $p\mathrm{H}$ 3.5 (left) and 8.5 (right), at ionic strength as indicated by the labels.