Reexpansion of charged nanoparticle assemblies in concentrated electrolytes

Significance

In electrolytes, mobile ions surround charged colloids, screening their electric fields. Such electrolyte–macroion interactions modulate the structure, function, and assembly of biological macromolecules. Classical theories predict increasingly screened electrostatic interactions with elevated salinity, enabling more compact arrangements of like-charged components. Here, X-ray scattering measurements and molecular dynamics simulations demonstrate that this principle breaks down at high salt concentrations. Assemblies of DNA-coated nanoparticles switch from contraction with added salt at low salinities, to expansion at high salinities. Interactions between electrolyte ions drive this contraction-to-expansion transition. These results demonstrate the significance of ionic correlations in concentrated electrolytes and should prove useful in the development of theories and electrolyte-based technologies.

Abstract

Electrostatic forces in solutions are highly relevant to a variety of fields, ranging from electrochemical energy storage to biology. However, their manifestation in concentrated electrolytes is not fully understood, as exemplified by counterintuitive observations of colloidal stability and long-ranged repulsions in molten salts. Highly charged biomolecules, such as DNA, respond sensitively to ions in dilute solutions. Here, we use non-base-pairing DNA-coated nanoparticles (DNA-NP) to analyze electrostatic interactions in concentrated salt solutions. Despite their negative charge, these conjugates form colloidal crystals in solutions of sufficient divalent cation concentration. We utilize small-angle X-ray scattering (SAXS) to study such DNA-NP assemblies across the full accessible concentration ranges of aqueous CaCl₂, MgCl₂, and SrCl₂ solutions. SAXS shows that the crystallinity and phases of the assembled structures vary with cation type. For all tested salts, the aggregates contract with added ions at low salinities and then begin expanding above a cation-dependent threshold salt concentration. Wide-angle X-ray scattering (WAXS) reveals enhanced positional correlations between ions in the solution at high salt concentrations. Complementary molecular dynamics simulations show that these ion–ion interactions reduce the favorability of dense ion configurations within the DNA brushes below that of the bulk solution. Measurements in solutions with lowered permittivity demonstrate a simultaneous increase in ion coupling and decrease in the concentration at which aggregate expansion begins, thus confirming the connection between these phenomena. Our work demonstrates that interactions between charged objects continue to evolve considerably into the high-concentration regime, where classical theories project electrostatics to be of negligible consequence.

Concentrated electrolytes are relevant to a wide variety of fields, ranging from the development of electrochemical devices, such as supercapacitors (1), to extremophile biology (2). Electrostatics in dilute solutions of salts have been extensively described by mean-field theories such as the Debye–Hückel theory (3). In such theories, mobile salt ions reorganize in response to the electrostatic potential of the charged macroions (e.g., colloids and membranes). In particular, salt ions concentrate near oppositely charged surfaces and screen their electrostatic field. The effective range of electrostatic interactions (screening length) is expected to decay with salt concentration C as ${\lambda }_D\propto C^{\frac{-1}{2}}.$ Therefore, a direct extension of this theory to high salinity would imply that the range of charge-driven effects decreases to negligible distances. In reality, interactions between the dissolved ions, which are ignored in the Debye–Hückel theory, become increasingly important at high salt concentrations, resulting in ionic correlations that are influenced by ion size and valency (4–6) and strongly regulate ion distributions in confinement by dielectric surfaces (7). These ionic correlations in concentrated monovalent and multivalent electrolytes drive overscreening of charged surfaces (8) and stabilize colloidal nanoparticles against aggregation in molten salts (9). Furthermore, high degrees of ionic organization are theorized to underlie the unexpectedly long electrostatic screening lengths measured via surface force apparatus in highly saline solutions (10–12). Interest in the generality of such findings has motivated additional research (13–19), which has revealed the need for further investigations through experimental studies probing electrostatic interactions in concentrated salt solutions.

In the present study, we investigate the assembly of highly negatively charged DNA-functionalized Au nanoparticles (DNA-NP) in concentrated aqueous solutions of alkaline earth chlorides: CaCl₂, MgCl₂, and SrCl₂. The grafted DNA sequences are designed to exclude interparticle attractions via DNA base-pairing. Even then, these dissolved salts at moderate concentrations (≲1 M) induce attractive interactions between the like-charged particles, driving their assembly into crystalline and noncrystalline aggregates (13, 20). We utilize a combination of small-and-wide-angle X-ray scattering (SAXS/WAXS) to analyze the structures formed by these nanoparticles over the whole accessible range of electrolyte concentrations (via SAXS), while also assessing the ion–ion correlations present in the bulk electrolyte (via WAXS). As would be expected from Debye–Hückel theory, SAXS measurements show that the observed structures contract with added salt. However, this trend holds only until a threshold concentration, above which the structures expand as salt concentration increases. This lattice reexpansion is connected to enhanced cation–anion ordering in the bulk solutions resolved by WAXS measurements and is explained through molecular dynamics (MD) simulations, which reproduce the nonmonotonic swelling of the nanoparticle aggregates. Overall, the combined experimental and computational results demonstrate how interactions mediated by dissolved ions continue to evolve at high salt concentrations, and provide insight into how ion–ion correlations manifest in interactions between charged nanoscale objects dispersed in concentrated electrolytes.

The nanoparticles utilized in this study were prepared by grafting thiolated single-stranded DNA molecules consisting of 35 thymine bases (T₃₅) onto Au cores (nominal radius, R_Au = 4.5 nm). The grafting density was ~ 60 to 80 DNA/Au nanoparticle, with loading varying between synthesis batches (SI Appendix, Table S1). Unless specified otherwise, samples for measurements were prepared with DNA-NP concentration of 50 nM, corresponding to a dilute suspension (volume fraction ~ 10⁻³). Additional sample preparation details are provided in SI Appendix. Despite the exclusion of canonical base pairing between neighboring DNA-NP, such particles assemble into colloidal crystals in solutions containing sufficient amounts of divalent cations. In such a condensed state, the proximity of the AuNP cores causes redshifting of the absorbance corresponding to the surface plasmon resonance, resulting in the suspensions changing color from red to purple (21) (Fig. 1A). Given sufficient time, the nanoparticle aggregates precipitate from the solution. Lowering the salt concentration results in the “melting” of the aggregates and redispersion of the particles, as visualized by the restoration of the suspension’s red color (Fig. 1A). This reversibility implies that the assemblies are equilibrium phases, with salt-concentration-determined structures.

Fig. 1.

Assembly of DNA-NPs in CaCl₂ solutions. (A) Schematic (Top) and photographs (Bottom) of CaCl₂-induced reversible crystallization of DNA-functionalized nanoparticles (DNA-NP). Increasing the salt concentration results in nanoparticle aggregation, which is reflected in the suspension color changing from red to purple (Middle). Decreasing the salt concentration restores the red color, showing that the aggregation of the nanoparticles is reversibly controlled by salt concentration. Note that while the salt concentration is varied, the DNA-NP concentration is held fixed at 50 nM. (B) DNA-NP structural phase diagram and center-to-center interparticle separations, D_nn, as a function of CaCl₂ concentration. Note that the effective volume per particle, calculated after correcting for the packing fractions in different assembly structures, shows the same trend as D_nn (SI Appendix, Fig. S6). (C and D) Representative structure factors with corresponding model fits for DNA-NP face-centered cubic [FCC, (C)] and body-centered cubic [BCC, (D)] lattices. (E) Structure factors for the assemblies formed at high CaCl₂ concentration, which display no long-range order. The position of the primary diffraction peak initially shifts to higher q with added CaCl₂, consistent with a contracting structure; this trend reverses at high CaCl₂ concentrations (>3.3 M). In C−E, the structure factors are offset vertically for clarity.

To investigate the assembly structures, we analyzed DNA-NP dispersions over the whole accessible range of CaCl₂ concentrations (0 to 5.3 M) via in situ SAXS. All dispersions were allowed to equilibrate in epoxy-sealed quartz capillaries for 24 to 36 h prior to measurements. For details of SAXS measurements and data processing, see SI Appendix. Fig. 1 C−E, show examples of SAXS-derived structure factors S(q) at varied salt concentrations. Here, q = 4π sin θ/λ is the scattering vector magnitude, 2θ is the scattering angle, and λ is the X-ray wavelength (here, λ = 0.729 Å). S(q) results from the interference of X-rays scattered from distinct particles in the assemblies and yields assembly phases and interparticle distances. DNA-NP dispersed in [CaCl₂] ≲0.25 M remain suspended, with the suspension retaining its red color. However, very weak diffraction peaks are discernible in S(q) for [CaCl₂] ≳ 0.2 M (SI Appendix, Fig. S1), likely corresponding to fluid-like correlations between small numbers of particles. Such dispersed phases are referred to as precrystalline. By contrast, Fig. 1 C and D show sharp diffraction peaks corresponding to DNA-NP organization into crystal lattices over [CaCl₂] ~ 0.3 to 1.7 M. For [CaCl₂] ≳ 1.7 M, much broader intensity modulations corresponding to short-ranged positional correlations between DNA-NP are observed (Fig. 1E). Detailed analysis of these structure factors reveals that the DNA-NP assemble into face-centered cubic lattices (FCC) for [CaCl₂] ~ 0.3 to 0.8 M (Fig. 1C), as observed in our previous work (20). Furthermore, here we find that for [CaCl₂] ~ 0.8 to 1.7 M, DNA-NP assemblies convert from FCC to body-centered cubic (BCC) (Fig. 1D). Above [CaCl₂] ~ 1.7 M, the intensity profiles exhibit broad peaks with a ratio $\frac{q_1}{q_2}\sim \sqrt{3}$ between the positions of the first 2 intensity maxima. This is consistent with random close packing (RCP) (22, 23). These results were reproduced using multiple batches of DNA-NPs (SI Appendix, Fig. S2) and were influenced minimally by decreasing the DNA-NP concentration from 50 to 20 nM. (SI Appendix, Fig. S3).

Apart from the salt-concentration-induced structural transformations, analysis of S(q) (Fig. 1 C−E) also demonstrates that the distances between the nanoparticles vary with CaCl₂ concentration. We note that for both FCC and BCC structures, the nearest neighbor distance (D_nn) is related to the position of the principal diffraction peak (q₁) as $D_{\mathit{nn}}=\frac{\sqrt{6}\pi }{q_1}$ (SI Appendix, Table S2). This relationship also extends to RCP, which lacks long-range ordering, as demonstrated by nearly identical $D_{\mathit{nn}}$ values extracted through this formulation and via Fourier analysis of the S(q) (SI Appendix, Fig. S4 and Table S3). Fig. 1 C−E show that q₁ increases (D_nn decreases) with added salt up to [CaCl₂] ~ 3.3 M. Over this range, D_nn decreases from ~ 24 to ~16 nm. Assuming that there is minimal interdigitation between the DNA shells from neighboring particles, this corresponds to a contraction of DNA shell $\left[t_{DNA}=\frac{\left(D_{nn}-2R_{Au}\right)}{2}\right]$ from 7.5 to 3.5 nm. These lengths are much smaller than the T₃₅ contour length of ~0.65 × 34 ~ 22 nm (24), implying that DNA acts as a flexible oligomer in compact conformations in the ionic conditions used here. Above the threshold of [CaCl₂] ~ 3.3 M, the trend in q₁ (and thus D_nn) reverses, signifying that the aggregates expand. The phase transformations of DNA-NP assemblies and the variation of the interparticle separation with CaCl₂ concentration are summarized in Fig. 1B.

At first glance, the observed structural transformations, particularly the FCC to BCC transition, are surprising. This is because long-ranged, softer electrostatic interactions expected in the low salt concentration regime favor BCC, as observed in the assembly of like-charged colloids interacting via screened Coulomb potential (23). In that work, the assemblies transformed from BCC to FCC with increasing salt concentration. This is also consistent with observations on colloids and nanoparticles with hard cores and soft polymer shells, for which the BCC phase is favored in systems with longer and more flexible shells, which lead to “softer” interparticle interactions (25, 26). We have analyzed the observed FCC to BCC transformation elsewhere (27) and have shown that interparticle attractive interactions coupled with the dehydration of the DNA shell at elevated salt concentrations lead to the observed FCC to BCC transitions. In this work, we will focus on the surprising contraction and reexpansion of the assemblies at high salinity.

The observed lattice contraction is consistent with a picture where increasing the divalent cation concentration (1) increases attractive interactions between the DNA in the overlap region of the neighboring DNA-NP and (2) screens the repulsions between charged phosphate groups along the DNA strands, allowing more compact DNA conformations. Similar contraction of nanoparticle lattices in a moderate salt concentration regime (<2 M) has also been observed for DNA-NP assembled via Watson–Crick hybridization (28, 29). Therefore, the reexpansion of aggregates above a threshold concentration is nonintuitive. To test whether aggregate reexpansion is an effect of specific Ca²⁺–DNA interactions or a more general phenomenon, we repeated SAXS measurements in MgCl₂ (0 to 4.5 M) and SrCl₂ solutions (0 to 3 M), as shown in Fig. 2.

Fig. 2.

Assembly of DNA-NPs in SrCl₂ and MgCl₂ solutions. (A) Structure factors for DNA-NP assemblies at varied SrCl₂ concentrations. The dotted line is a guide to the eye and indicates the variation in the position of the principal peak. The corresponding inter-DNA-NP distances as a function of [SrCl₂] are shown in (B). (C and D) Structure factors observed at various MgCl₂ concentrations. Note that the position of the principal peak shifts to higher q up to 2 M (lattice contracts with added MgCl₂). Above this concentration, added salt leads to lattice expansion. (E) Summary of structural phases and interparticle separations observed as a function of MgCl₂ concentration. No detectable scattering peaks were observed in solutions below ~1 M. In A, C, and D, the structure factors are offset vertically for clarity.

There are clear distinctions between the assembly structures observed in CaCl₂ (Fig. 1B), SrCl₂ (Fig. 2B), and MgCl₂ (Fig. 2E). For example, DNA-NP dispersed in SrCl₂ solutions do not form precipitates. The suspensions at all concentrations retain their red color. The SAXS-derived structure factors for these dispersions (Fig. 2A) display a weak, broad diffraction peak, indicative of a fluid-like ordering (30), here defined as precrystalline. In MgCl₂ solutions, DNA-NP assemble into FCC for [MgCl₂] ~ 1 to 2.5 M (Fig. 2C) and convert to structures with short-ranged ordering above 2.5 M (Fig. 2D). This behavior is comparable to that observed in CaCl₂ solutions (Fig. 1B), with the exceptions that 1) no BCC phase is observed in MgCl₂ solutions and 2) the salt concentration for DNA-NP crystallization into FCC is higher (1 M for MgCl₂ vs. 0.3 M for CaCl₂). These contrasting properties of the assemblies reflect specific cation–DNA interactions. For example, the observed assembly behavior is consistent with the established understanding that the smaller Ca²⁺ or Mg²⁺ cations associate more strongly with DNA than larger Sr²⁺ or Ba²⁺ cations (31). Interestingly, the smaller size of Mg²⁺ (as compared to Ca²⁺) would suggest a stronger electrostatic interaction with DNA. However, we observe that higher concentrations of MgCl₂ are required to induce nanoparticle crystallization and that assemblies in MgCl₂ solutions feature larger interparticle separations than those in CaCl₂ solutions (Figs. 1B and 2E). We speculate that this weaker interaction arises due to the tendency of Mg²⁺ to retain its primary hydration shell when interacting with the DNA phosphate backbone (32, 33). Despite these distinctions in the assembly behavior, the SAXS-extracted D_nn values show the same qualitative trend of aggregate contraction followed by reexpansion for assemblies in each of the three salt solutions (Figs. 1B and 2 B and E).

There are some interesting phenomenological observations associated with the observed reexpansion. 1) The reexpansion occurs regardless of whether the structures exhibit crystalline (MgCl₂), short-ranged (CaCl₂), or liquid-like order (SrCl₂). 2) The value of the threshold concentration C_th for the upturn in D_nn is cation-dependent, increasing in the sequence Sr²⁺ (1.5 M) < Mg²⁺ (2.0 M) < Ca²⁺ (3.3 M). A potentially related phenomenon to this reexpansion has been observed in high charge density polyelectrolytes, which precipitate from solution at low concentrations of cationic multivalent ions and polyamines with Z ≥ 3 and redisperse at higher salt concentrations (34, 35). The redissolution was speculated to be due to a charge reversal (36), in which the charge due to adsorbed counterions, at the macro-ion surface, exceeds the charge required to neutralize the macro-ion. However, DNA charge reversal has not been documented in aqueous concentrated electrolytes with Z ≤ 3 cationic proteins or ions, (37). Additionally, this charge reversal model does not consider the association of cations to anions in the bulk (38), which can lead to redissolution without charge reversal (39). Furthermore, if a charge-reversal mechanism were to underlie the presently observed DNA-NP reexpansion, then the C_th would be expected to be lowest for the cation that interacts most strongly with the DNA-NP (Ca²⁺). The observed C_th sequence is, in fact, the reverse of this prediction. Rather, the sequence follows that of the solubility limits of the corresponding chloride salts in water (40). Notably, for each salt, C_th is consistently ~ 40 to 60% of the salt’s solubility limit in water at room temperature (SI Appendix, Fig. S5). Furthermore, our molecular simulations (discussed below) reveal that the effective electric field outside the DNA shells remains weakly negative at all salt concentrations (SI Appendix, Fig. S10). These observations suggest that it is the interactions between electrolyte ions in close proximity, which become prominent at high salinities, that drive the nonmonotonic interparticle separation behavior.

To gain insights into the electrolyte ion–DNA-NP and interelectrolyte interactions, we performed MD simulations using a coarse-grained model to analyze a dense phase of DNA-NP in equilibrium with MX₂ reservoirs (Fig. 3 A and B). The model used implicit solvent, but explicit ions. Due to computational constraints, the simulations utilized smaller nanoparticles, (R_{Au, MD} = 2.25 nm) coated by 18 DNA, each represented by 16 charged (−e) beads with monovalent counterions, here labeled M⁺ (for more details, see SI Appendix). MD results of the equilibrium ion concentration distributions ([M²⁺], [X⁻], [M⁺]) and D_nn as a function of reservoir concentration are shown in Fig. 3 C and E, respectively. Fig. 3D. illustrates the method for extracting D_nn at a given concentration. Fig. 3E corroborates the experimentally observed (Fig. 1B) D_nn nonmonotonic behavior. The transition molar concentration C_{th, MD} ~ 2.0 M for the upturn in D_nn is lower than the experimentally observed C_th for Ca²⁺(~3.3 M) but close to C_th for Mg²⁺. We note that the implicit solvent utilized in the MD simulations does not consider ion hydration effects. Furthermore, below 2.0 M, in the regime where D_nn decreases with increasing salt concentration, MD simulations (Fig. 3F) reveal that the divalent ions’ molar concentration in the dense DNA-NP phase is higher than in the reservoir $\left({\left[M^{2+}\right]}_{\mathit{DNA}}>{\left[M^{2+}\right]}_{\mathit{Bulk}}\right)$ Interestingly, in the expansion regime, the concentration of the divalent cations in the DNA-NP phase is slightly lower than in the reservoir $\left({\left[M^{2+}\right]}_{\mathit{DNA}}>{\left[M^{2+}\right]}_{\mathit{Bulk}}\right)$. It should be noted that, across the whole salt concentration regime for DNA-NP assembly, the DNA brush contains high concentrations of both cations and anions. Details of the radial ion distribution profiles are provided in the SI Appendix, Fig. S9. In the aggregate contraction regime, these results suggest that the system’s equilibrium is driven by the internal energy decrease due to DNA-M²⁺ interactions. In contrast, in the aggregate expansion regime, the system’s equilibrium is dictated by 1) the entropy gained through DNA adapting more extended conformations, enabling ions redistribution in a larger volume of the DNA shell, and 2) favorable electrostatic interactions between salt ions.

Fig. 3.

MD simulations on DNA-NP assemblies at different salt concentrations. (A) Coarse-grained model for a DNA-NP. The 16 DNA beads, representing a single DNA, bear a negative elementary charge (−e) and are connected using a harmonic potential. (B) To form the dense phase, 108 nanoparticles are initially arranged in an FCC lattice and surrounded by monovalent counterions. An ion solution containing divalent cations and monovalent anions is in contact with the dense phase. (C) The ionic concentration profiles in the z-direction, after equilibration, for divalent cations, and monovalent cations and anions. (D) Radial distribution functions g_NP(r) for DNA-NP are calculated using the equilibrium configurations. (E) The nearest-neighbor separation distance D_nn [defined as the position of the maxima of the radial distribution functions (D)] shows a nonmonotonic behavior as a function of the divalent ion concentration in the reservoir. Note that the shorter contour length of the DNA (~7.6 nm vs. ~22 nm in experiments) and smaller core (4.5 nm vs. 9 nm in experiments) in the simulations lead to notably smaller D_nn values. (F) The mean ionic concentrations in the dense phase as a function of the divalent ion concentration in the reservoir. Note that in the DNA-NP aggregate expansion regime (>2.0 M), the divalent ion concentration in the reservoir exceeds that in the DNA-NP dense phase. The dashed line signifies where the concentration in the dense phase is equal to that of the reservoir. These results were corroborated via chemical potential calculations (SI Appendix, Table S6).

The results of our MD simulations suggest that altered ionic distributions in the DNA shell and in the bulk solutions at high salinity underpin the observed lattice swelling. It is challenging to directly measure the ionic distributions surrounding DNA-NP via X-ray scattering because the scattered intensities are dominated by the electron-dense Au cores (41). However, WAXS can be used to measure Å to nm scale interionic structuring in the bulk solution. Thus, we prepared solutions of CaCl₂, MgCl₂, and SrCl₂ of the same concentrations used in the assembly experiments and conducted in situ WAXS measurements. Background subtracted WAXS intensity profiles for CaCl₂, MgCl₂ and SrCl₂ salt concentration series are shown in Fig. 4 A−C. The scattering peaks for q > 2 Å⁻¹ correspond to water structure and ion hydration (42, 43). The present analysis will focus on q < 2 Å⁻¹, which corresponds to ion ordering beyond local solvation.

Fig. 4.

Electrolyte ion–ion interactions studied with WAXS and varied solvent composition. (A−C) Capillary-subtracted WAXS intensity profiles for aqueous CaCl₂ (A), SrCl₂ (B), and MgCl₂ (C) solutions. Two sets of peaks, which are not apparent in deionized water (blue profiles in A–C), are denoted as “Peak 1” and “Peak 2”. (D) Plot demonstrating the concentration-dependence of the peak positions, and their corresponding real-space separations. The position of Peak 1 scales with the cube root of concentration and is consistent with a repulsive interaction. Peak 2 does not shift appreciably with the salt concentrations but does shift to lower q (larger d spacing) with increasing cation size. Determination of peak positions is detailed in SI Appendix, Fig. S7. (E) Interparticle separation (D_nn) as a function of [CaCl₂] in solutions with 0%, 5%, and 10% ethanol (v/v). Yellow markers denote precrystals, blue FCC, red BCC, and green RCP. Vertical lines mark the estimated salt concentrations corresponding to the minimum spacings observed in each sequence. The transition between contraction and expansion occurs more rapidly with higher ethanol volume fractions. Additionally, higher ethanol volume fractions lead to more contracted structures at low [CaCl₂], and more expanded structures at high [CaCl₂]. Corresponding SAXS patterns can be found in SI Appendix, Fig. S8. (F) A comparison of capillary-subtracted WAXS intensity profiles of CaCl₂ solutions of various concentrations, with and without 10% ethanol. Notably, the peak at q ~ 1.5 Å (“Peak 2”) is enhanced in the presence of ethanol.

For all salt solutions, a low q intensity modulation (labeled “peak 1”) is observed. The corresponding intensity maxima shift monotonically to higher q, with a direct dependence on the cubic root of the salt concentration ($q_{Peak1}\propto C^{\frac{1}{3}}$, Fig. 4D). Based on previous studies on multivalent metal halide salts (44–46), peak 1 can be assigned to arise from repulsions between divalent cations. This is because the separation between the scattering ions decreases with increasing salt concentration ($d\propto C^{\frac{-1}{3}}$) in a manner consistent with the distribution of repulsive objects in confinement in three dimensions. This is also verified by noting that $q_{Peak1}$ depends on the salt concentration, but not on the cation type. In fact, the $q_{Peak1}\propto C^{\frac{1}{3}}$ dependence for all salt solutions follows a “universal” curve (Fig. 4D). At higher salt concentrations ($C\gtrsim C_{\mathit{th}}$), where the DNA-NP structures expand with added salt, an additional modulation (labeled “peak 2”) near q ~1.5 Å⁻¹ (d ~ 4 Å) becomes prominent (Fig. 4 A−C). The positions of this peak are independent of salt concentration but vary with cation type. In fact, the corresponding distance increases with cation size (Fig. 4D). It is concluded that peak 2 arises from attractive interactions between the divalent cations and anions. Previous scattering studies have also observed such intensity modulations (43, 46) and attributed them to positional correlations between hydrated cations and anions. This is further verified by the observations that the intensity of this peak is enhanced in salt solutions with anions of higher atomic number, e.g., CaBr₂ vs. CaCl₂ (45). For the specific case of CaCl₂, additional evidence from dielectric relaxation spectroscopy (47) and Raman spectroscopy (48) support that Ca²⁺ and Cl⁻ form complexes with shared hydration shells, called solvent-separated ion pairs.

The ionic ordering induced by attractive electrostatic interactions in our WAXS measurements provides a plausible explanation for the observed ion redistributions in the MD simulations. In particular, at high salt concentrations, cations are no longer independent. Complexation with anions increases the effective volumes occupied by the ions in the DNA-NP condensed phase and restricts the ability of the cations to organize densely in the DNA shells, thereby driving the local cation concentration below that of the bulk solution. Furthermore, the cation–anion pairing/correlations can effectively reduce the number of free cations that can interact with the DNA-NP, thus explaining the observed DNA-NP reexpansion at high salinities. That is, since increasing the number of counterions in the DNA-NP shell at low salt concentrations leads to compression of the assemblies, reducing the effective concentration of free counterions by clustering could lead to a reverse effect. Such a reduction in free ion concentration caused by the formation of electrolyte ion clusters has been recently proposed in theoretical treatments of concentrated electrolytes (49).

To further establish the role of ion–ion interaction in the aggregate reexpansion, we analyzed the DNA-NP assemblies in CaCl₂ solutions with solvents of varied permittivity. Specifically, we utilized ethanol–water mixtures with 5% and 10% v/v ethanol. Ethanol and water are fully miscible and increasing ethanol content decreases the static dielectric constant of the mixture (50), thus increasing the electrostatic coupling within the solution (51). For example, enhanced interactions between DNA and ions in ethanol are known to lower the salt concentrations required to precipitate DNA (52). Therefore, in the low salt concentration regime, the enhanced DNA–ion attractions in ethanol should lower the minimum CaCl₂ concentration required for DNA-NP crystallization. Furthermore, cation–anion interactions are enhanced in ethanol–water mixtures (53); based on our prior observations implicating ionic correlations as driving reexpansion, we hypothesized that increasing ethanol fractions will shift C_th to lower CaCl₂ concentrations.

SAXS/WAXS measurements reveal the effects of enhanced DNA–ion and cation–anion attractive interactions in solutions with ethanol. With regard to DNA–ion interactions at low salt, we find that, as hypothesized, the CaCl₂ concentration required for DNA-NP assembly into crystals decreases with increased ethanol content and that the boundaries for transitions to BCC and RCP structures shift to lower CaCl₂ concentrations. For example, in a 5% ethanol solution, [CaCl₂] ~ 0.175 M (vs. 0.3 M in 0% ethanol) is sufficient for forming DNA-NP FCC structures (Fig. 4E). Below C_th, for a given CaCl₂ concentration, the D_nn is lowest for the 10% ethanol case and highest for the 0% ethanol case. By contrast, at high salinities ([CaCl₂] > 3.5 M), i.e., in the regime where electrolyte cation–anion interactions drive lattice reexpansion, D_nn is found to increase with ethanol content (Fig. 4E). Furthermore, C_th shifts downward with increasing ethanol fraction: C_th ~ 3.3, 2.8, and 2.3 M for 0%, 5%, and 10% ethanol, respectively. This enhanced reexpansion and the above-described lowering of C_th are directly correlated to the enhanced propensity for short-ranged ordering of cations and anions in the solution as verified by WAXS (Fig. 4F). Specifically, WAXS intensity profiles exhibit higher amplitudes for the intensity modulations associated with Ca²⁺–Cl⁻ ion paring (Peak 2) in 10% ethanol solutions, as compared to the 0% ethanol solutions, thus implying a higher degree of ionic clustering in the ethanol-containing solutions. These observations establish an empirical connection between the enhanced ion-pairing in bulk solution and the anomalous expansion of the DNA-NP aggregates in high salinities.

The effects of the ordered structure of electrolyte solution at high salinities have been invoked in other systems where nonmonotonic changes are observed. Most notably, in the aforementioned series of surface force measurements (10–12), an upturn in the range of electrostatic interactions (screening length) was observed (dubbed “underscreening”), which was attributed to strong positional correlations between the electrolyte cations and anions. It is also hypothesized that this underscreening effect is the cause of reentrant swelling and redissolution of polyelectrolytes at high salt concentrations (54). Parsimony suggests a unified explanation for all the nonmonotonic system responses: namely, underscreening, polyelectrolyte redissolution, gel reentrant swelling, and nanoparticle aggregate expansion observed at high salinities. However, some differences must be noted. The underscreening effect in 1:1 electrolytes (e.g., NaCl) was observed for ${\lambda }_D\le a$. Here, a is the average diameters of the unhydrated electrolyte ions and ${\lambda }_D$ is the classical electrostatic screening length. Extending this result to the present study, using the average of the unhydrated diameters of Ca²⁺ (0.20 nm) and Cl^- (0.362 nm) (55), would imply C_th ~ 0.3 to 0.4 M for CaCl₂, which is much smaller than the experimentally observed 3.3 M. Furthermore, the experimentally observed C_th sequence (Sr²⁺ < Mg²⁺ < Ca²⁺) seemingly depends on salt solubility limit, rather than ion size (SI Appendix, Fig. S5). Additional experiments on DNA-NP assembly, such as anomalous X-ray scattering measurements on low electron density cores (e.g., proteins) functionalized with DNA in specific salt solutions (e.g., SrBr₂) could measure the composition and extent of the ionic atmosphere near these particles, thus, resolving ion–ion correlations at DNA-NP interfaces in the assembly contraction and expansion regimes.

To summarize, the present study demonstrates that ionic correlation at interfaces and in bulk solutions modulate interactions between charged macromolecules over the full range of achievable salinities, up to saturation. The assembly behavior of DNA-NP was analyzed concomitantly with the structure of the bulk electrolyte by combining X-ray scattering and MD simulations. Our study identifies two regimes. First, in solutions with salinities below half the solubility limit of the dissolved salts, divalent cations are free to organize around DNA molecules, inducing net attractive forces between DNA-NPs that drive the aggregation of DNA-nanoparticles. In this regime, adding salt strengthens DNA-NP interactions, causing assemblies to become more compact. Second, in the regime of salinities approaching the solubility limit, divalent cations form clusters with neighboring anions in the dense electrolyte solution. In this regime, these clusters partition favorably into the bulk solution away from the DNA-NP aggregates. Adding salt strengthens this electrolyte ordering, with the net effect of reducing the effective counterion concentration that can interact with the nanoparticles. This reverses the trend of aggregate compression with added salt. Strengthening electrolyte ion ordering by lowering solution permittivity shifts the transition between these two regimes to lower concentrations. Overall, our study provides insight on how ion–ion correlations shape interactions of electrolytes with charged materials at the nanoscale, and furthers the discussion on electrostatics in concentrated electrolytes.

Materials and Methods

Experimental Methods.

Thiol-terminated oligonucleotides (5′-T35-C3SH-3′) were synthesized using a MerMade solid-state controlled pore glass DNA synthesizer (BioAutomation) via phosphoramidite chemistry. Following separation from the pore glass, and purification via reverse-phase high-performance liquid chromatography (1260 Infinity II LC System, Agilent Technologies), the thiolated DNA was attached to the Au nanoparticles with a slow salting out procedure, with loading quantified via Quant-iT Oligreen Assay (Invitrogen). For X-ray scattering measurements, DNA-NP were dispersed in concentrated solutions of CaCl₂ or MgCl₂ or SrCl₂ and allowed to equilibrate in sealed quartz capillaries for 1 to 2 d prior to measurements. X-ray scattering data were collected primarily at beamline 5ID-D of the Advanced Photon Source. X-ray energies of 16 and 17 keV were used. The SAXS/WAXS scattered intensities were measured simultaneously using three Rayonix CCD detectors positioned at 0.2 m, 1.0 m, and 7.5 m from the sample. Other details of sample preparation, X-ray measurements, data reduction, and analysis can be found in SI Appendix.

Simulation Methods.

We conducted MD simulations of a dense phase of nanoparticles functionalized with single-stranded DNA chains. The nanoparticles are embedded in an electrolyte solution which is in equilibrium with a reservoir. The chains, ions, and spherical nanoparticles are composed of spherical beads of the same size. The solvent is modeled as a uniform medium of dielectric constant ε_r. The beads interact via a truncated Lennard-Jones potential plus the Coulomb potential between charged beads. The system is equilibrated by performing 10⁷ time-steps of MD simulation. The interparticle distances are calculated from a production run of at least 3 × 10⁷ simulation time-steps. Further simulation details and the system parameters are reported in SI Appendix.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

All data supporting this study are included in the article and/or SI Appendix.