Probing the electrostatic aggregation of nanoparticles with oppositely charged molecular ions

The co‐assembly of charged nanoparticles with oppositely charged molecular ions has emerged as a promising technique in the fabrication of nanoparticle superstructures. However, the underlying mechanism behind these molecular ions in mediating the repulsion between these charged nanoparticles remains elusive. Herein, coarse‐grained molecular dynamics simulations are used to elucidate the effects of valency, shape, and size of molecular anions on their co‐assembly with gold nanoparticles coated with positively charged ligands. The findings suggest that the valency, shape, and size of molecular anions significantly influence the repulsion and aggregating dynamics among these positively charged nanoparticles. Moreover, the free energy calculations reveal that ring‐shaped molecular anions with higher valences and larger sizes are more effective at reducing the repulsion between these gold nanoparticles and thus enhance the stability of the aggregate. This study contributes to a better understanding of the critical roles of valence, shape, and size of ions in mediating the electrostatic co‐assembly of nanoparticles with oppositely charged ions, and it also guides the future design of DNA templates and DNA origami in co‐assembly with oppositely charged nanoparticles.


INTRODUCTION
The dynamic nature of the self-assembly of charged nanoparticles mediated by crucial interactions with co-assembly partners affects a wide range of physical, chemical, and biological properties, which leads to the formation of both ordered and disordered superstructures. [1] For instance, spherical nanoparticles functionalized with multiple charged ligands (also called superions), and nanoscale analogs of simple ions exhibit similar behaviors in several ways. [2] These oppositely charged "superions" can co-assemble into binary nanoparticle crystals due to the electrostatic attractions and resemble the formation of salt crystals by oppositely charged ions. [2a,3] Despite the extensive studies of the self-assembly of nanoparticles, [4] there is still critical information missing on the co-assembly of charged nanoparticles with oppositely charged ions, such as the effects of valency, shape, and size of these superions.
Garzoni et al. [5] reported that acetate anions can induce the assembly of amino-terminated poly(propylene imine)dendrimer nanofibers through hydrophobic modification of the dendrimer's surface. Subsequently, these nanofibers were reported to be further functionalized with semiconductive cadmium sulfide quantum dots and the fabrication was conducted at room temperature through ionic substitution approaches. [6] Recently, Bian et al. [2c] reported that molecular ions with as few as three electric charges can co-assemble with oppositely charged nanoparticles and effectively induce attractions between charged nanoparticles in water. They experimentally verified that trimetaphosphate, pyrophosphate, and hexametaphosphate are effective candidates in mediating attractions between nanoparticles. These interactions between molecular ions and nanoparticles can remarkably modulate the formation of colloidal crystals. The Classical Derjaguin-Landau-Verwey-Overbeek theory [7] divides the interactions between colloidal particles in solution into van der Waals (attractive) and the electrostatic (repulsive) as a function of separation distance. [8] The theory has been widely adopted for the explanations of colloidal stability and rationalization of the forces acting on colloidal particles. However, this theory is not readily applicable to charged nanoparticles due to the nonadditivity of F I G U R E 1 Representation of the all-atom models and mapped CG models for the main system components (Au-trimethyl (mercaptoundecyl) ammonium (TMA) nanoparticle and six molecular anions). (A) All-atom (AA) model of the Au-TMA nanoparticle with 468 TMA ligands (left), the mapping of the TMA ligand to four CG beads (middle), and a snapshot of the Martini CG model of the Au-TMA nanoparticle (right). In the AA model of the Au-TMA nanoparticle, gold atoms are shown as yellow spheres, and the TMA ligands are shown as sticks. Carbon, nitrogen, and sulfur atoms are shown in cyan, blue and brown, respectively. Hydrogen atoms are omitted for clarity. In the CG model of the Au-TMA nanoparticle, the TMA ligands are represented by one positively charged bead and three neutral beads (also see Figure S5A), and the CG TMA ligands are shown as sticks. The positively charged bead is shown in blue while the other three neutral beads are shown in cyan. (B) Martini mapping of P1 − , P1 2− , P3 3− , P2 4− , P4 6− , and P6 6− anions is also presented. Whereas, the CG beads of P1 − , P1 2− , P3 3− , P2 4− , P4 6− , and P6 6− anions are shown as semi-transparent grey, pink, red, purple, magenta, and orange spheres, respectively. nanoparticle interactions at the nanoscale. [1a,1b] In the same work, Bian et al. [2c] reported the molecular dynamics simulations (MD) of positively charged trimethyl (mercaptoundecyl) ammonium (TMA)-coated gold nanoparticles (denoted as Au-TMA nanoparticles) and citrate anions with three electric charges using coarse-grained (CG) Martini 2 force field. [9] Compared with the Martini 2 model, the newly refined Martini 3 shows significant improvements in the modeling of biomolecular systems, as well as material science applications such as nanoparticles and molecular ions. [10] One notable example is the water bead in the Martini 3 model, which has its own bead type and interaction levels, which enable significant improvements for the description of water. Moreover, accurate Martini 3 beads are also available for the divalent and monovalent ions. [11] Although it is known that electrostatic interactions play a major role in the co-assembly of molecular ions and nanoparticles, the detailed co-assembly mechanism of charged nanoparticles and oppositely charged molecular ions remains to be elucidated. Herein, we focused on probing the electrostatic co-assembly mechanisms of charged nanoparticles and phosphate anions with special attention to the effects of valency, shape, and size of molecular ions on this co-assembly. We used a series of phosphate anions with different valences for the depiction of co-assembly with Au-TMA nanoparticles. The anions used in the study included dihydrogen phosphate (P1 − ), hydrogen phosphate (P1 2− ), trimetaphosphate (P3 3− ), pyrophosphate (P2 4− ), tetraphosphate (P4 6− ), and hexametaphosphate (P6 6− ). These anions are denoted as Pn m , where n is the number of phosphates, and m is the net electrical charge. We speculated that P3 3and P2 4− anions are comparable, with the P3 3− anion having a slightly larger molecular size and lower charge density than the P2 4anion. Moreover, the P4 6− anion was used as a reference to P6 6− due to its equal charge despite having a smaller molecular size. Similarly, P2 4− and P4 6− anions act as linear molecular anions while P3 3− and P6 6− anions as ring-shaped. Our results confirm that anions with electric charges less than three may not mediate sufficient attractions between Au-TMA nanoparticles [2c] and reveal that the size and shape of anions have great influences on the distribution and dynamics of adsorbed anions as well as the dynamics of positively charged nanoparticles. Moreover, the selected phosphate anions are particularly interesting as they are related to the phosphate diesters of the DNA backbone. Therefore, the co-assembly of phosphate anions and gold nanoparticles in this study may serve as a motivation for designing the DNA-based nanostructures, such as DNA templates and DNA origami, for their co-assembly with the positively charged gold nanoparticles into highly ordered superstructures, as reported by previous experimental studies. [12] 2 RESULTS AND DISCUSSION

Interactions between positively charged Au-TMA nanoparticles and molecular anions
Detailed models of Au-TMA nanoparticle and phosphate anions are shown in Figure 1A,B, respectively. The chemical structures of the TMA ligand and phosphate anions are shown in Figure S1. The model-building methodology of the coarse grained Au-TMA nanoparticle and phosphate anions using the Martini 3 force field are provided in the Supplementary Information. It is worth noting that each TMA ligand carries one positive charge ( Figure S1), and the gold core of the Au-TMA nanoparticles has a diameter of 4.9 nm ( Figure S2). To evaluate the potential interactions, we performed MD simulations of Au-TMA nanoparticles and a series of phosphate anions. Initially, two Au-TMA nanoparticles were randomly distributed in the simulation box; then phosphate anions were inserted randomly into the simulation box with a total of negative charges twice the positive charges of the two Au-TMA nanoparticles. Finally, systems were solvated with Martini water beads and sodium ions were added to neutralize the overall system (see Supporting Information for the details of the simulated systems). Figure 2A shows the final structures of Au-TMA nanoparticles in the P1 − , P1 2− , P3 3− , and P2 4− systems after the MD simulations. The results show that the two Au-TMA nanoparticles stay separated from each other in the P1 − and P1 2− systems while clustered in the P3 3− and P2 4− systems ( Figure 2A).
To quantitively monitor the aggregations of Au-TMA nanoparticles, we calculated the center-of-mass (COM) distances between the two gold cores for the four systems. During the MD simulations, the distance between the nanoparticle fluctuated for the P1 − and P1 2− systems, indicating the presence of dominant electrostatic repulsions between the two Au-TMA nanoparticles ( Figure 2B). In contrast, the two equally charged Au-TMA nanoparticles in the P3 3− and P2 4− systems agglomerated at ∼850 and ∼50 ns, respectively. The aggregates formed in both systems remained stable during the rest of the simulations maintaining a COM distance of ∼8.5 nm. This result shows that both P3 3− and P2 4− anions can mediate efficient attractions between Au-TMA nanoparticles and is consistent with previous experimental findings. [2c] Since the attraction between Au-TMA nanoparticles is associated with negative charges in the interfaces, it is essential to compute the negative charge near the contact interface of the Au-TMA nanoparticles. To do so, we adopted a cutoff distance of 2 nm and counted the number of negative charges of the anions within a diameter of 2 nm around the two Au-TMA nanoparticles. The selection of a 2 nm cutoff allows us to efficiently select all the charges in the interface between the Au-TMA nanoparticles (see Figure S9). Consistent with the fluctuations of inter-nanoparticle distance in the P1 − and the P1 2− systems ( Figure 2B), the negative interface charge of the two analyzed systems also fluctuated with the charge number less than 80 ( Figure 2C). Interestingly, the negative interface charges reached ∼140 for both the P3 3− and P2 4− systems after the aggregation of the two Au-TMA nanoparticles. This indicates that interfacial P3 3− and P2 4− anions produce close electrostatic attractions with the Au-TMA nanoparticles. It can be noticed that the negative interface charges of P3 3− increase with a delay compare to P2 4− . This is due to the randomized initial position of the Au-TMA nanoparticles that placed the nanoparticles of the P3 3− at a higher distance ( Figure 2B).
The same analyses have been adopted to study the coassembly of Au-TMA nanoparticles with molecular anions featured with six negative charges (i.e., P4 6− and P6 6− ). Interestingly, the COM distance of the P4 6− system converged rapidly to ∼8.5 nm ( Figure 3A) and was close to the results of the P2 4− and P3 3− systems ( Figure 2B), while the COM distance of the P6 6− system reached ∼9.5 nm and remained steadfast indicating stable aggregations of Au-TMA nanoparticles at a higher distance. Moreover, the final structures at the end of MD simulations showed a close association between Au-TMA nanoparticles in P4 6− and relatively loose contacts of Au-TMA nanoparticles in the P6 6− systems (inset of Figure 3A). We speculate that this is due to the difference in shape and size of P4 6− and P6 6− anions. In fact, despite having the same number of negative charges, P4 6− has a smaller size (only four beads) and a higher charge density compared to P6 6− (having six beads).
We further calculated the negative charges near the contact interface of the Au-TMA nanoparticles in P4 6− and P6 6− systems. We adopted the same cutoff distance of 2 nm for the calculations of negative interface charges in the previous analysis. The results show a rapid increase in the number of negative interface charges in the P4 6− system while remaining steady at ∼150. This indicates that the equilibrium state is attained quickly after the aggregation of the two Au-TMA nanoparticles ( Figure 3B). On the other hand, we observed that the number of negative interface charges as a function of time in the P6 6− system could be divided into three stages. Stage I corresponds to the sharp increase to ∼150 e during the first ∼300 ns and remaining steady until 700 ns. This first stage indicated the encounter of Au-TMA nanoparticles and the formation of a metastable state. Similarly to the system with P3 3− , we can notice a brief delay in the increase of negative interface charges. This is also due to the randomized initial position of the Au-TMA nanoparticles that placed the nanoparticles of the P6 6− system at a higher distance ( Figure 3A). The number of negative interface charges increased gradually to ∼200 e until ∼1000 ns defining stage II (from ∼700 ns to ∼1000 ns). This second stage is suggesting aggregation of P6 6− anions in the interfacial region. Finally, Stage III is considered the equilibrium stage occurring after ∼1000 ns where the number of negative interface charges remained qualitatively steady. All the representative snapshots of these three stages are shown in Figure S10. Furthermore, higher negative interface charges in the P6 6-system (∼200 e) were observed as compared to the P4 6− system (∼150 e) during the final equilibrium stage. These results suggested the presence of stronger electrostatic attractions in the interfacial P6 6− than those of the interfacial P4 6− anions toward the Au-TMA nanoparticles.
These analyses revealed that the negatively charged phosphate anions are attracted by the positively charged Au-TMA nanoparticles by electrostatic attractions. Meanwhile, anions diffuse more quickly than Au-TMA nanoparticles due to their significantly smaller sizes. The anion density near the Au-TMA nanoparticle surface plays a critical role in mediating the aggregations of Au-TMA nanoparticles and is influenced by the valency of molecular anion.

Structural analysis of aggregates formed by Au-TMA nanoparticles and ions
Our results showed that P2 4− , P3 3− P4 6− , and P6 6− anions can mediate effective aggregations of Au-TMA nanoparticles. We further evaluated the potentially important role of sodium ions in these aggregations by comparing the positive interface charge of sodium ions in our four systems ( Figure 4A). Our results suggested a higher number of interface charges of the P3 3− system (∼32 e) as compared to the positive interface charge of the P2 4− system (∼15 e). Interestingly, this observation with higher charges of P3 3− than the P2 4anion indicated that the number of positive interface charges may correlate with the anion size and shape. Furthermore, we found more cations (∼135 e) in the interfacial regions of the P6 6− system as compared to the P4 6− system (∼42 e) during the equilibrium stage (i.e., after ∼1000 ns). This result further shows that the anion shape and size influence the interfacial ion distributions. Figure 4B shows the representative detailed snapshots of the interfacial regions of the P3 3− , P2 4− , P4 6− , and P6 6− systems.
In the next analysis, we systematically compared the electrostatic interactions in the aggregates by calculating the charge densities of the four tested systems. We first divided the space around the two gold nanoparticles into small volumes at fixed distances (see Figure S11). The charge density distributions were calculated by summing the number of charges inside every volume over the last 1500 ns of MD simulations, and we divided the results by the volume (see Systems and Methods). The results show one positive peak (with max value named Δρ + ) followed by a negative peak (with min value named Δρ − ). It is important to notice that the initial peaks of the charge density at ∼1.5 nm for the four systems correspond to the positive charges of TMA ligands ( Figure 5A). We can observe that Δρ + of the P2 4− system is significantly lower than those of the other systems. This may be attributed to the smaller sizes of the P2 4− anions that enable these anions to partially permeate the coating layer of TMA ligands and cause neutralization of the positive charges in these ligands. On the other hand, the P6 6− system shows the highest Δρ + , and this can be attributed to the bigger size of the P6 6− anions. The Δρ + peaks for the P2 4− and P2 4− systems, instead, are comparable.
As the positive charges of TMA ligands are further neutralized by the charges of anions, we observe the Δρ − valleys for the charge density of these four systems. It can be described as charge reversal at the interface of Au-TMA nanoparticles. A detailed examination reveal that the Δρ − values are in the order of P2 4− ≈ P3 3− < P4 6− < P6 6− , which can be attributed to the increase in anion sizes and negative charges. It can be inferred that the electrostatic attraction between Au-TMA nanoparticles and surface anions is similar for the P2 4− and P3 3− systems, while increase for the P4 6− and P6 6− systems. The snapshots of systems at the end of the MD simulation are shown in Figure 5B. In comparison with the P2 4− and P3 3− systems, the P4 6− and P6 6− systems showed much fewer anions in the solutions, and this is particularly evident for the P6 6− system. This also implies that the molecular anions absorbed onto the Au-TMA nanoparticles reverse the surface charge from positive to negative and allow sodium ions further toward the surface of Au-TMA nanoparticles.

Distributions and fluctuations of anions on the surface of Au-TMA nanoparticles
To characterize the position of anions on the surface of Au-TMA nanoparticles, we analyzed the distribution of anions on the Au-TMA nanoparticles for the P2 4− , P3 3− , P4 6− , and P6 6− systems. For this analysis, we considered two variables (i.e., DIST and Rmin) similar to previous studies. [2c,13] Herein, the two gold cores are denoted as I and II, respectively. The distribution of each anion on the Au-TMA nanoparticles was calculated by its distance to the COMs of the gold core I and II (denoted ad Dist(I) and Dist(II), respectively). The variables DIST and Rmin are defined as the absolute difference and minimum of Dist(I) and Dist(II), respectively ( Figure 6A). The variable DIST characterizes the anion positions on the two nanoparticles, whereas Rmin indicates the radial distance to the closer Au-TMA nanoparticle.
We calculated the relative probabilities of anions distributions on the Au-TMA nanoparticles in the P2 4− , P3 3− , P4 6− , and P6 6systems as a function of DIST and Rmin over the last 1500 ns of MD simulations. The probability is first normalized by the total number of ions used in each system. This was necessary because of the higher number of anions in the P3 3− ad P2 4− systems than those in the P4 6− and P6 6− systems (see Table S4). In the second step, we rescale the probabilities dividing them by the maximum of the four normalized probabilities. This allowed us to have the max probability equal to 1 (see Systems and Methods). We found that the P3 3− anions were distributed mostly on the nanoparticle with DIST values greater than 2.5 nm, while the P2 4− anions were located mainly on the nanoparticle with DIST values greater than 3.5 nm ( Figure 6B). Meanwhile, as compared to the Rmin distributions of the P3 3− system, the Rmin distribution of the P2 4− system was found wider with an obvious difference at Rmin ∼ 4 nm. This result implies a specific higher ability of the P2 4− anions to permeate the TMA ligands and can be attributed to the smaller size of P2 4− anions. On the other hand, the distributions of P4 6− and P6 6− on the Au-TMA nanoparticles were denser. This is consistent with the previous finding of strong electrostatic interactions between anions with six negative charges and Au-TMA nanoparticles. The distributions of P4 6− and P6 6− on the Au-TMA nanoparticles were found quite similar except for barely seen distributions of P6 6− anions in proximity to the interface of the two nanoparticles (i.e., the DIST close to zero). This may be attributed to the larger COM distance of Au-TMA nanoparticles in the P6 6− system and the assembly of the interface region with sodium ions and P6 6− anions (see Figures 3B and 4B).
Next, we characterized the anions into three classes based on their dynamics on the nanoparticles and in the solution. We first select the anions in the solution as the anions that are more than 1.5 nm away from the Au-TMA aggregate (first class). Then, we adopted a DIST criterion of 2 nm to further classify the two other classes of anions (interface and outer) on the nanoparticles. We decided to use this criterion due to its close definition to the previously defined interfacial region ( Figure S12). The anions on the Au-TMA nanoparticle surfaces with DIST greater than 2.0 nm and DIST equal to or less than 2.0 nm were classified as interface anions (the second class) and outer anions (the third class), respectively ( Figure 6C).
We calculated the transition probabilities of these three regions during the last 1500 ns of MD simulations. The results showed that anions in the solutions and the outer regions were quite stable for all four systems ( Figure 6D). Notably, the anion transition between outer anions and interface anions in the P2 4− system was more dynamic than that of the P3 3− system. Similarly, the transition between outer anions and interface anions was more dynamic in the P4 6− system than that in the P6 6− system. Interestingly, close transition probabilities of outer anions and interface anions were observed for the P3 3− and P4 6− systems. These comparisons briefly summarize that the increase in anion charge mainly reduces the dynamics of anion transitions. Similarly, the detailed analysis also implies that the ring structure and larger size of anions reduce the dynamics of anion transitions in contrast to the linear ones with smaller sizes. This analysis is consistent with previous studies. [2c,13] It is worth noting that the classification criterion for the anion classes adopted in this study is somewhat different from the previous studies. [2c,13] Still, we notice remarkably similar results with high probabilities within clusters (i.e., numbers on the diagonal) and low transaction probability. This suggests that the two clustering methods give similar results and indicate that anions tend to stay in their clusters due to the strong electrostatic attractions with the Au-TMA nanoparticle.

Dynamics of Au-TMA nanoparticles
To understand the influence of the different molecular anions on the dynamics of the aggregated Au-TMA nanoparticles, we estimate the relative rotation of two Au-TMA nanoparticles. The relative rotation of Au-TMA nanoparticles was calculated by using one Au-TMA nanoparticle as the refer-ence and a vector between the COMs of the gold core I and II (see Figure 6A). We define the rotational angle as the relative angle between the vectors of consequent frames. The analysis was performed over the last 1500 ns of MD simulations with a time interval of 4 ns ( Figure 7A). In comparison with the rotation angle of the P2 4− system, the rotation angle of the P3 3− system was significantly smaller, which indicated a more dynamic rotation of Au-TMA nanoparticles in the P2 4− system ( Figure 7B). This may be potentially contributed by the higher charge density and smaller anion size of the P2 4− anion. On the other hand, the dynamics of the P2 4− anions in the interface region were found higher than the interface of anions in the P3 3− system (see Figure 6D). This may be attributed to a lower rotational barrier of Au-TMA nanoparticles in the P2 4− systems than that of the P3 3− system. However, the rotation angle of the P3 3− system is close to that of the P4 6− system. Interestingly, proximity transition probabilities involving anions in the interface region for both P3 3− and P4 6− systems were also observed (see Figure 6D). The data infer that the linear-shaped P4 6− anion with higher charge density matches the dynamics properties of the P3 3− anion because of its stronger interaction with Au-TMA nanoparticles. Moreover, the rotation angle in the P6 6− system was much smaller than that of the P4 6− system and consistent with the transition probability of these two systems. Comparing Figures 4 and 7 we can notice a direct correlation between the interface positive charge and the average rotation angle. Our results suggest that the massive presence of cations (sodium ions) on the interface of P6 6− system generates a significant rotational barrier to the rotation of Au-TMA nanoparticles. We propose this effect to significantly reduce the dynamics of Au-TMA nanoparticles within the aggregate. It is important to note that the relative concentrations of Au-TMA nanoparticles and anions can have strong influences on the dynamics of the Au-TMA nanoparticles. Decreasing the number of anions per Au-TMA nanoparticles, the dynamics of Au-TMA nanoparticles are likely to be enhanced due to the more prominent repulsions among Au-TMA.
It is clear that the molecular anions play a significant role in mediating the aggregations of Au-TMA nanoparticles and influence their dynamics, and are referred to as "ionic glues". [14] We further evaluated the interactions between the two Au-TMA nanoparticles by calculating the potential of mean force (PMF) profile. This was performed using the distance between the COMs of the two gold cores in the Au-TMA nanoparticles as reaction coordinate (see System and Methods). The results suggested a higher disassociation free energy barrier in the P4 6− and P6 6− systems compared to the P3 3− and P2 4− systems. Specifically, the disassociation free energy barrier of P3 3− was found slightly lower than that of the P2 4− system despite a higher electric charge ( Figure 7C). In comparison, the PMF profile of the P6 6− system showed a significantly larger disassociation free energy barrier than the P4 6system. Moreover, a direct comparison between Figures 5A and 7C shows a correlation between Δρ − and the disassociation free energy barriers (Figure 8). This is reasonable since Δρ − is a measure of the negative charges on the Au-TMA nanoparticle surface that can act as "glue" for the aggregate. These observations further emphasized the critical roles of the shape and size of these anions in mediating the aggregation of Au-TMA nanoparticles. F I G U R E 8 Summarized figure on the effects of anion valency, size, and shape on the aggregations of Au-trimethyl (mercaptoundecyl) ammonium (TMA) nanoparticles. The molecular volumes of anions are calculated with MOPAC2016 and PM6 method. [15] Based on the overall results, we speculate two folds effect of anion size and shape on these aggregations. Notably, the effects of anion ring structures (P3 3− and P6 6− ) are associated with their relatively low configuration entropies. It may also serve as a major contributor in altering electrostatic interaction with Au-TMA nanoparticles and sodium ions. This effect resembles the configurational entropy loss, where the ligand is rigidified in the classic ligand-protein binding. This configuration entropy loss of ligand is favorable for its binding to protein. [16] On the other hand, the effects of molecular size can be interpreted as the distributed charges being superior to collected charges in adsorbing onto the Au-TMA nanoparticles. Molecular anions with more distributed charges (P3 3− and P6 6− ) can adsorb efficiently onto Au-TMA nanoparticles. This infers stronger electrostatic interactions with Au-TMA nanoparticles (see Figure 5A) and further promotes the adhesions between Au-TMA nanoparticles.

CONCLUSION
In this work, we studied the effects of valency, shape, and size of molecular anions on their co-assembly with the positively charged Au-TMA nanoparticles. The results of COM distance of gold cores showed that anions with charges greater or equal to three serve as effective "ionic glues" [14] to the Au-TMA nanoparticles in consistence with the previous experimental findings. [2c] Furthermore, the charge density calculations suggest that ring-structured P3 3− anion with a larger size can more efficiently reverse the surface charge density from positive to negative and has a lower transition probability in the interface region as compared to the linear P2 4− anion. Similar observations were evident from the comparison of the linear P4 6− anion and the ring-structured P6 6− anion with a larger size. These findings suggested that ring structures and large sizes of the anions facilitates the interactions with Au-TMA nanoparticles and reduces the electrostatic repulsions between Au-TMA nanoparticles. Consistently, the PMF profiles revealed that the disassociation free energy tends to increase as anion valency increases. In our results, the P6 6− system showed a significantly larger disassociation free energy barrier than the P4 6− system. These findings suggested the critical roles of the shape and size of an anion in mediating the aggregation of Au-TMA nanoparticles. Furthermore, these Au-TMA nanoparticles in the P6 6− system show relatively low rotational dynamics but higher dissociation free energy. However, molecular assemblies of sodium ions and P6 6− anions are formed in the highly curved interface regions of Au-TMA nanoparticles mediated by strong electrostatic attractions between sodium ions and P6 6− anions. These observations mainly attribute to the combination of the high valency, ring structure and large size of P6 6− anions. Our performed study emphasizes that the valency, shape, and size of molecular anions are important factors in mediating attractions between the Au-TMA nanoparticles.
The potential future implication may be based on the P6 6− system with augmented inter-particle distance due to increased ion size. This property may aid as a potential method to fine-tune the lattice parameters of electrostatic coassembly formed by charged nanoparticles and oppositely charge molecular ions. [17] Furthermore, the phosphate anions related to the phosphate diesters of the DNA backbone may also be useful. Previously, DNA and DNA origami have been widely adopted as templates in nanoparticle assembly or co-assembly with nanoparticle. [18] Therefore, designing DNA-based nanostructures, such as DNA templates and DNA origami, for their co-assembly with positively charged gold nanoparticles into highly ordered superstructures may be inspired by the findings of the current study.