From Fresh to Salty: How Ions Modulate Solvent-Mediated Interactions between Grafted Silica Nanoparticles in Water

TL;DR

This work investigates how salt modulates solvent-mediated interparticle interactions between silica nanoparticles in water, comparing bare surfaces with PE- and PEG-grafted grafts. Using all-atom molecular dynamics and umbrella-sampling PMF calculations, the authors show that salt amplifies attractions most strongly for PE grafts, with PEG grafts showing an intermediate response, and bare NPs remaining largely salt-insensitive. The mechanism links salt-induced solvent depletion and partial cavitation in the interparticle cavity to polymer–ion interactions and solvent structuring, with effects largely transferable across the explored ($T$,$P$) conditions. These findings provide actionable design rules for tuning NP self-assembly through surface chemistry and salt content, advancing inverse design of soft materials.

Abstract

Nanoparticles (NPs) are fundamental building blocks for engineering functional soft materials, where precise control over the solvent-mediated inter-particle effective interaction (Ueff) is essential for tailoring bulk structure and properties. These solvent-mediated interactions are strongly influenced by NP's surface chemistry, solvent properties, and thermodynamic conditions such as temperature (T) and pressure (P). However, despite considerable progress, a general predictive framework for tuning Ueff and guiding self-assembly remains lacking. In this work, using all-atom molecular dynamics simulations, we investigated the alteration of Ueff between silica nanoparticles (Si-NPs) functionalized with polyethylene (PE) and polyethylene glycol (PEG) by salt (sodium chloride) across a range of thermodynamic conditions. At ambient thermodynamic conditions, bare (not functionalized) Si-NPs exhibit minimal variation in Ueff even at high salt concentrations. In contrast, PE-grafted Si-NPs display strong salt-induced attractions, while PEG-grafted Si-NPs show an intermediate, more gradual response. To asses the transferability of these salt-induced effects on effective interactions, we further examined the effects of salt on Ueff under different (T,P) conditions. Our results indicate that the salt-induced modulation of Ueff between both bare and grafted Si-NPs is largely invariant across the explored (T,P) conditions. Molecular-level analysis reveals that salt promotes solvent depletion within the interparticle cavity for both hydrophobic PE and hydrophilic PEG grafts, with the strongest effect observed in the PE case. In general, this study highlights the coupled roles of surface chemistry, ion-polymer interactions, and solvent structuring in the regulation of Ueff, and provides important insights into the predictable control of interparticle interactions for soft material engineering.

Figures (9)

• Figure 1: The salt-dependent behavior of $U_{\rm eff}$ as a function of $r_{\rm com}$ for bare (a), PE-grafted (b), and PEG-grafted (c) systems at $1$ bar and $300$ K is shown. For bare Si-NP case, the absolute change in the depth of $U_{\rm eff}$ with increasing salt concentration is minimal with an increase of $\sim 3$ kJ/mol at $5$ m concentration of NaCl. In contrast, the PE-grafted system exhibits a pronounced increase in the depth of $U_{\rm eff}$. For the PEG-grafted case, the depth of the attractive basin increases to an intermediate extent compared to the bare and PE-grafted cases. Additionally, the hard repulsive core (a measure of the effective Si-NP diameter) shifts towards smaller $r_{\rm com}$ value.
• Figure 2: The effects of salt on $U_{\rm eff}$ profile at elevated (with respect to ambient) pressure and temperature conditions is shown for the bare Si-NP (a) and PE-grafted Si-NP (b) systems. Here we have reported the $U_{\rm eff}$ profile at two thermodynamic conditions: $T = 350$ K, $P = 1$ bar and $T = 300$ K, $P = 1000$ bar; shown in (i) and (ii), respectively. For the bare Si-NP system, $U_{\rm eff}$ remains largely unaffected on salt addition by increase of temperature from $300$ K to $350$ K and pressure to $1000$ bar. In contrast, the PE-grafted system shows a marked increase in the strength of attractive interaction on salt addition at elevated conditions as well.
• Figure 3: Scaled average solvent number density $\langle \rho_{\rm cav}^{\rm s} \rangle$ (top, a-c) and scaled average tetrahedral order parameter $\langle q_{\rm t/cav}^{\rm s} \rangle$ (bottom, d-f) within the icavity as functions of inter-Si-NP center-of-mass separation $r_{\rm com}$ for bare, PE-grafted, and PEG-grafted Si-NPs at various salt concentrations. For PEG-grafted systems, $\langle \rho_{\rm cav}^{\rm s} \rangle$ decreases monotonically with increasing salt concentration, indicating enhanced solvent depletion. In the PEG-grafted case, a sharp decrease near $r_{\rm com} = 4$ nm at $2$ m salt suggests partial cavitation. The tetrahedral order parameter $\langle q_{\rm t/cav}^{\rm s} \rangle$ follows a similar trend to $\langle \rho_{\rm cav}^{\rm s} \rangle$, with water in the bare system largely retaining bulk-like structure.
• Figure 4: Average scaled ion and water number density ($\langle \rho^{\rm s} \rangle$) profile as a function of distance $d$ from the centre of a Si-NP along the axis connecting the centre-of-mass of two Si-NPs (see Fig. S2 in the Supplementary Material) for $r_{\rm com} = 3.0$ nm (i) and $4.0$ nm (ii) and at $2$ m salt concentration. Here, we have reported the results for bare (a), PE-grafted (b), and PEG-grafted (c) Si-NPs at temperature $300$ K and pressure $1$ bar. The bare and PEG-grafted Si-NP systems show enhanced Na$^+$ density in the vicinity of the NP --- more pronounced for the PEG-grafted Si-NP indicating preferential Na$^+$ attraction with the PEG chains. The PE-grafted system exhibits relative lesser ion presence inside the cavity region for $r_{\rm com} = 4.0$ nm and negligibly small for $r_{\rm com} = 3.0$. Also, we report the absence of any preferential ion adsorption on the Si-NP surface for this case.
• Figure 5: Scaled mean end-to-end distance ($\langle r_{\rm ee}^{\rm s} \rangle$) of the grafting PE (a) and PEG (b) polymers as a function of inter-Si-NP center-of-mass separation ($r_{\rm com}$) at temperature $300$ K and $1$ bar pressure. We have reported here the results for $0$ m (pure water) and $2$ m salt concentrations. Error bars represent standard deviations across $5$ independent simulation trajectories. The dashed lines represent the average values of $\langle r_{\rm ee}^{\rm s} \rangle$ calculated over the specified ranges of $r_{\rm com}$. For the PE-grafted case, the short PE chains undergo a transition to relatively elongated conformational states on the onset of the cavitation transition (see Fig. \ref{['fig5']}b). This transition gets more pronounced on adding salt to water. The PEG chains, however, show enhanced conformational fluctuations but no significant conformational change on adding salt.