Nanostructures of Aggregates and Gels Formed by Fully Atomistic Molecular Dynamics Simulations

Table of Contents:

In the previous chapter, the spontaneous formation of the gel from complex systems consisting of the nanocolloidal-silica- water-NaCl was examined by molecular dynamics simulations using a fully atomistic model. In this chapter, details of the structure of the gel thus formed are examined and some physical properties such as pair correlation functions and fractal dimensions are discussed [1]. The calculated fractal dimension is comparable to the experimental ones for the aggregation of silica colloids explained in Section 3.2 of Chapter 3, if the differences in the dimensionality of the methods of observations are correctly considered. At longer length scales, super-aggregation was evident in the gelation process.

Multiple Network Structures Found in Gels

The gel discussed here was formed without any prior assumption of the underlying mechanism of the formation in classical

Molecular Dynamics of Nanostructures and Nanoionics: Simulations in Complex Systems Junko Habasaki

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MD simulations as mentioned in ref. [1] and in Chapter 8 from nanocolloidal silica-water-salt system. The detail of MD simulations is also found in Chapter 8. As shown in Fig. 9.1, the silica gel thus spontaneously formed has multiple-networks (a network of silica (composed of Si0₄ units), that of water and that of ions) and therefore we focus on the structures of networks. These substructures with different characteristics have mixed each other to form complex structures of the gel. Here these structures are characterized by several methods such as fractal dimension analyses, dendrograms, and distribution of Q_n (here n means the number of bridging oxygen in Si0₄ units) structures.

Figure 9.1 (Top) Example of nanoporous structures of silica gel spontaneously obtained from nanocolloidal-silica—water-NaCl system. Structures are for a silica part. That is, water and NaCl are not shown in this figure. Red and blue particles are for oxygen and silicon, respectively. (Bottom) A water part of the same system as the upper one. The three- dimensional connections of porous structures are clear from this view. This structure corresponds to holes in gels. As shown in these figures, the structure of gel is formed by multiple networks including the salt part, which will be shown later.

As a first step to learn the characteristics of the coagulation process, a systematic examination of structures of systems with different magnitude of coagulations is done. In this section, several kinds of functions and analyses are used for characterizing structures of silica gels comparing with clusters and aggregates.

In Table 9.1, some characteristics of systems examined are listed with the images of networks (silica part) obtained by MD simulations. An image for I-C is after gelation. As summarized in Table 9.1, systems of series I have larger contents of silica compared with series II, where II-A is a reference system without salt. Of course, with the addition of NaCl, stronger coagulation is produced as shown in series I. Almost all of simulations were performed at 300 K, while higher temperature (400 K) was set in the system I-C. During the long run in that system, a spontaneous formation of the gel with volume reduction (~19%) was observed.

Table 9.1 Characteristics of systems examined in Chapters 8 and 9

System	Ratio of numbers of NaCl pairs and water molecules	Concentration of NaCl in water (mol%)	Temperature (K)	Status and network structures
I-A	128:8192	1.56	300
I-B	320:8192	3.9	300
I-C	320:8192	3.9	400

(Continued)

Table 9.1 {Continued)

System	Ratio of numbers of NaCl pairs and water molecules	Concentration of NaCl in water (mol%)	Temperature (K)	Status and network structures
II-A	0:15872	0	300
II-B	160:15872	1.01	300
II-C	320:15872	2.02	300

Structure of the Silica Part

For the examination of networks formed by Si0₄ units, pair correlation functions, fractal dimension analyses, Q_n structures and dendrogram are used here. Fundamentals of these methods are discussed in Chapter 4. Before showing new data, some of the results discussed in Chapter 8 are briefly summarized here.

Pair correlation functions of Si–Si pairs: characteristics of silica part in clusters, aggregates, and gels

First, the structures of the networks of the silica part will be characterized by pair correlation functions, £f(r)s, for the Si-Si pairs.

In Fig. 9.2, systematic changes of the pair correlation functions for the Si-Si pairs of systems I-A, I-C, II-A, and II-C are shown using a log-log scale. The series of water-rich systems (series II) exhibit higher peaks than the series of silica-rich systems (series I). The former indicates more isolated clusters.

Figure 9.2 Comparison of pair correlation functions, д(г) of Si-Si pairs. From upper to lower in the second peaks are for II-A, II-C, I-A and I-C (gel), respectively. The upper two curves (water-rich systems) have clearer minima at a longer length scale meaning the separation among clusters or aggregates. In the system with the formation of gel, the network is spreading, and the minimum becoming small and shifting to the lower r region. Reproduced from Habasaki, J., Ishikawa, M. (2014), Molecular dynamics study of coagulation in silica-nanocolloid-water-NaCl systems based on the atomistic model, Phys. Chem. Chem. Phys., 16, pp. 24000-24017. With permission from the PCCP Owner Societies.

The following characteristics with the development of coagulations are found:

1. The small minimum (negative deviation from g[r) = 1) is observed in the long-length-scale regions (r > 12~35 A) of the dilute systems before g(r) = 1 is attained. The largest deviation from the line for g[r) = 1 is observed in the system without salt (II-A) at approximately r = 30 A. The positions of the minima are located at approximately half of the mean distance between clusters or aggregates and it means that these structures are separated by solvent (and salt). The size of these clusters is several times larger than that of the original Si0₂ colloidal units in our systems.
2. With the development of the coagulation, both the position and depth of the minimum tend to decrease and finally, gels are formed as found in system I-C.

A comparable existence of the minimum is found by off- lattice diffusion limited cluster aggregation (DCLA) calculations performed by Hasmy et al. [2].

The change of the minimum can characterize the magnitude of the coagulation processes because it corresponds to the maximum of the potential of the mean force (PMF) [3] as discussed in Chapter 8. That is, a deeper minimum corresponds to a higher barrier height for the coagulation process.

Coexistence of two length scale regions

Another important finding in g(r) of Si-Si pair is the coexistence of two length scale regions, especially in the gel.

A decrease in the peak heights of g(r) in the short-length- scale region can be observed with increasing NaCl concentration; hence, changes occur with coagulation. The system I-C can be well characterized by the existence of super-aggregates. In I-C after gelation, the power-law region below r~ 12 A represents the spreading of the network of clusters, and the longer-length-scale region represents the development of connections among these structures to form a gel.

To characterize the networks of the silica part, Q„ distribution (n is the number of bridging oxygens for Si0₄ units) has been widely used in glasses and crystals both in experiments [4-8] and in MD simulations [9] including silicates. The Q„ (notation Q” is also used) structure means the Si0₄ unit with n bridging oxygens.

Some figures for distributions are shown in Chapter 8, while in Table 9.2, the results of Q„ distributions are shown with mean numbers of bridging oxygens and equilibration constant, K.

Both distribution and the mean number of bridging oxygens do not show remarkable changes by systems having a different magnitude of coagulation.

These results mean that the coagulation process proceeds by the rearrangement of Si-0 bonds with keeping a total number of bonds with small changes in Q_n distributions as a first approximation. In aggregates and gels, Some Q_s structures (for Si0₅units) are observed, while the contribution of Q₂ structure tends to decrease. Non-tetrahedral coordinated Si has been observed experimentally in several systems. For example, Stebbins and McMillan [10] observed five and six-coordinated Si by using ²⁹SiMASNMR.

Table 9.2 Q_n distribution (in %) for systems shown in Table 9.1 with the mean number of bridging oxygens for the network of silica part

System	Solvated-unit	System I-A	System I-В	System I-C	System II-A	System 1I-B	System П-С
Status		Aggregate	Aggregate	Gel	Clusters	Aggregate	Aggregate
	—	—	0.24	—	—		—
	3.18	—	3.17	1.14	0.32	0.37	—
	18.94	15.58	25.98	21.93	15.63	13.74	13.81
	75.76	78.64	68.84	75.19	79.76	80.44	80.55
	0	5.62	1.77	1.74	4.29	5.45	5.58
Mean number ofbridging oxygens	3.7	3.9	3.7	3.8	3.9	3.9	3.9
		70.63	103.06	148.16	94.88	86.41	84.20

Source: Reproduced with a small modification from Habasaki, ]., Ishikawa, M. (2014), Molecular dynamics study of coagulation in silica- nanocolloid—water—NaCl systems based on the atomistic model, Phys. Chem. Chem. Phys., 16, pp. 24000-24017, with permission from the PCCP Owner Societies.

Only small changes were observed in series I as shown in Chapter 8. However, the difference becomes clearer if we use the equilibrium (or quotient) constant, К of the reaction among Q_n structures.

In the bottom of Table 9.2, equilibrium (or quotient) constant, К of the reaction,

is shown, with tentatively neglecting Q₁ and Q₂ structures. For the gel, К the value is found to be larger than other systems. Some difference is observed in K. The larger value of К in the gel means the development of homogeneous networks concerning the structural units. As found in these values, К can be a sensitive index to represent the small changes in the distribution and resultant networks. This suggests that the gel is rather homogeneous than other systems with aggregates or clusters, although further investigation may be required to establish the differences among distributions.

It is interesting to note that the distribution of Q_n structures is closely related to the density of the system through the partial volume of the units [8, 9]. This is because the volume of the bridging oxygen is shared between two units. Namely, partial volume with larger n value tends to be smaller. Due to these characteristics of different partial volumes, Q_n distributions are also closely related to the polyamorphism [11] of the system in silicate glasses [9]. Because of the similarity of the shape of the structural units for silica (or silicates) and water including its phase-diagrams [11-13], it is interesting to compare polyamorphism in silica, silicates, and related systems with that of water based on the similar concepts of distribution of Q_n structures [14] and its relationship with the heterogeneity of networks.