The role of hydrogen bonding in nanocolloidal amorphous silica particles in electrolyte solutions

Journal of Colloid and Interface Science 339 (2009) 351–361

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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis

The role of hydrogen bonding in nanocolloidal amorphous silica particles in electrolyte solutions S. Jenkins a,*, S.R. Kirk a, M. Persson b, J. Carlen b, Z. Abbas c a

Dept. of Technology, Mathematics and CS, University West, P.O. Box 957, SE 461 86 Trollhättan, Sweden R&D Pulp and Paper, Eka Chemicals (Akzo Nobel) AB, SE 445 80 Bohus, Sweden c Department of Chemistry, University of Gothenburg, SE 412 96 Gothenburg, Sweden b

a r t i c l e

i n f o

Article history: Received 5 February 2009 Accepted 29 July 2009 Available online 4 August 2009 Keywords: Molecular dynamics Particle-mesh Ewald Silica nanoparticle Potential of mean force Hydrogen bonding Charged nanoparticles

a b s t r a c t Explicit solvent (water) molecular dynamics simulations were undertaken containing three pairs of amorphous silica nanoparticles, having diameters of 2.0 nm, 2.4 nm and 2.8 nm, respectively. Mean forces acting between the silica nanoparticles were calculated in a background electrolyte, i.e., NaCl at four different concentrations. Dependence of the inter-particle potential of mean force on the center of mass separation, silicon to sodium ratio (Si:Na+), background electrolyte concentration, number of hydrogen bonds directly linking pairs of silica nanoparticles and the density of charged surface sites, are calculated. The pH was indirectly accounted for via the ratio of silicon to sodium used in the simulations. The close relationship between the variation of the number of hydrogen bonds between the pairs of silica nanoparticles and the inter-particle potential of mean force indicates that the degree of inter-particle hydrogen bonding quantifies, for a given size of nanoparticle, the degree of nanoparticle ‘stickiness’. Simulations also show that the number of hydrogen bonds between the charged surface (O) sites and the surrounding water molecules increases with increase in charged sites, in agreement with the interaction behavior of silica nanoparticles usually seen in experiments. Ó 2009 Elsevier Inc. All rights reserved.

1. Introduction In industrial applications [1–9], the ability to control the stability of silica nanocolloids in (usually) aqueous solutions, both in terms of the chemical stability of the nanoparticles themselves and also colloidal stability (through the interactions between the particles, and possibly any other chemical species present), is vital in order to optimize their effectiveness in the desired application. The Derjaguin–Landau–Verwey–Overbeek (DLVO) theory of inter-particle interactions [10–12], containing terms consisting of a balance of attractive van der Waals forces and repulsive electrical double-layer forces, has been widely and successfully used to predict stability in a wide range of colloidal systems. This theory, however, does not account for specific ion effects and, more importantly, provides incorrect predictions of both chemical stability and colloidal aggregation of silica particles up to sub-micrometer sizes in environments with high levels of background salt and/or low pH [13–15]. The DLVO treatment of colloidal forces and stability wrongly predicts that silica nanoparticles in the size range of interest (10 nm diameter or less) are unstable [13,14], and is unsuitable for highly charged particles such as the silica–water systems of interest here. Aggregation processes in silica colloids are strongly * Corresponding author. E-mail address: [email protected] (S. Jenkins). 0021-9797/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2009.07.069

influenced by solution pH [1], and the variety of potential applications spans a wide range of solution pH values (and background electrolyte concentrations), so the effects of pH on these systems must be adequately understood. Considerable efforts have been undertaken over the years in order to study the pH-dependent coagulation/aggregation behavior of silica particles in different background electrolytes [13–20]. Generally, it was observed that the rate of aggregation of silica particles in the pH range of 3–7 is lower than at pH values >8. Different explanations have been put forward in order to explain the experimental data in the context of silica–solution interaction. Allen and Matijevic [13] claimed that silica sols are stable owing to the adsorption of a water layer on the silica surface. Formation of stable surface silanol (–SiOH) groups due to surface hydration as well of hydrogen bonding between surface silanol groups (–SiOH) and water molecules were pointed out to be the reason for the stability of silica. Moreover, coagulation of silica particles in the presence electrolyte, e.g. NaCl was considered to be due to an ion exchange mechanism in which the Na+ ions replace the acidic H from the surface silanol groups. Despasse and coworkers [14,15] showed that at pH values >10 the silica sols coagulate in the presence of LiCl and NaCl but remain stable in the presence of KCl and CsCl even up to very high concentrations. They claim that coagulation seen in LiCl and NaCl is either due to the inter particle bridging of silica particles through hydrogen bonding of water

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molecules on the silica surface and OH ions or because of the bridging of silica particles through the interaction of hydrating water molecules present around the adsorbed Li+ or Na+ ions. In the case of KCl and CsCl the cations are very weakly hydrated thus there is no such inter particle bridging between the silica particles and therefore silica sols remain stable. Furthermore, they also explained that at pH < 6 there are negligible OH ions which are necessary for inter particle bridging and that is the reason of stability of silica sols and very slow coagulation usually seen in experiments [16,17]. For example, Higashitani et al. [17] reported very low coagulation rate of silica particles at pH values <9 as well as for smallest silica particles, i.e., 5 nm in diameter as compared with the larger particles having diameters >90 nm. They rationalized the slow coagulation rate of small silica particles due to the presence of a stable thick hydration layer present on the silica surface. They also postulate that this layer remains intact at pH < 9 but starts to disintegrate at higher pH values. Moreover, zeta potential measurements also indicate that silica particles are very weakly charged in the pH range of 2–6 and thus surface charge has little effect in stabilizing the silica sols in this pH range. On the other hand, Vigil et al. [21] claimed that stability of silica is due to the formation of hairy layer on the particle surface. The hairy layer consists of flexible polymer-like segments of poly(silicilic acid). Kobayashi et al. [20] found very low aggregation rates of silica at pH < 6 as compared with more basic solutions. They found that small particles, i.e., 30 nm in diameter were completely stabilized at pH values less than 6. The authors concluded that the stability in acidic medium is due to the presence of hairy layer around the silica particles. We may conclude that in the acidic region, i.e., at pH < 6 the stability of silica sols seems to be determined by the hydration/hairy layers present at silica particles surfaces. Another important property of silica solution interface is the number of deprotonated sites present at the silica surface and variation of deprotonated sites with solution pH. The zeta potential measurements [18] as well as the surface charge measurements of silica particles [19–22] show that at pH < 6 silica particle surface is weakly charged but at pH values >7 silica surface becomes highly charged. Recent NMR investigation [23] showed that the concentration of –SiOH sites dramatically decreases from 100% of the surface site density at pH 4 to less than 10% of the site density at pH 11. It was pointed out that it is polymerization reaction as shown below, which is the reason of this decrease in the number of silanol groups. 

—SiO þ —SiOH $ SiOSi þ OH However, the number of deprotonated sites determined from the surface charge density differed considerably from that obtained from the NMR measurements. It is important to bear in mind that the determination of deprotonated sites from surface charge measurements is complicated because silica has very porous structure and variation of the deprotonated sites inside the pores compared to the surface is not known. Theoretical models for property prediction in nanocolloidal systems have been developed covering a wide range of length and time scales at different levels of theory [24,25]. Of particular interest in this paper is the use of molecular dynamics (MD) simulations to probe the detailed interactions of nanocolloidal particles with each other, solvent molecules and counter ions in solution. It is already well known that pH is a significant factor influencing both the growth [1,26] and colloidal stability [1,14] of colloidal nanosilica and, indeed, colloids in general. The pH of a system has, until recent years, been difficult to account for directly in MD simulations. Several approaches to the problem have recently been made for implicit solvent [27] and explicit solvent [28–30] approaches, culminating in the latter case in so-called ‘acidostat’ methods [31,32]. In our case, we have investigated silica nanoparticles

produced by cation exchange of a sodium silicate solution, and the pH has been indirectly accounted for via the ratio of silicon to sodium present in the simulations [1]. The number of deprotonated silanol sites on the surface of the modeled silica nanoparticles has therefore been set equal in all cases to the number of associated sodium cations (related via the fixed Si:Na+ ratio to the number of silicon atoms in the simulation), to ensure overall electro-neutrality. We have performed our simulations for a number of industrially-relevant ranges of the silicon to sodium (Si:Na+) ratios (see Sections 2 and 6 for more details and the companion paper [33] to this current work, where the details of the modeling of amorphous silica particle structure and allocation of surface charge on silica test particles are provided). The purpose of this work is to probe the ‘stickiness’ of pairs of silica particles at close range, i.e., less than 0.5 nm, by examining the relationship between hydrogen bonding linking the silica nanoparticles and the shape of the resultant potential of mean forces as the inter-particle separation is increased. 2. Methods An amorphous silica ‘starting’ particle (approximately spherical, diameter 84 Å, containing 3784 atoms) was created by melting, then quenching a sample of a-quartz in a separate simulation. A set of progressively smaller test particles were generated from this initial configuration, and were equilibrated at 300 K before later use. Further details of the methods used to create the amorphous silica nanoparticle structure and the algorithm used for the allocation of surface charge on the particles can be found in our previous papers [33]. Four different Si:Na+ ratios, i.e., 5:1, 10:1 15:1 and 20:1 were chosen in this work, corresponding to realistic values used in the industrial process for the silica nanoparticles. 3. Molecular dynamics MD calculations were carried out in the NVT ensemble using the GROMACS [34–36] code (version 3.3.1), using OPLS-AA [37] force fields, with additional parameters for silica from literature [38]. The water model used was a flexible variant of the TIP4P 4-site model [39,40]. During actual MD runs, the simulation temperature of all species was set to 300 K, particle velocities being chosen from a Maxwell distribution, using a Berendsen [41] thermostat with a coupling time constant of 0.1 ps. Neighbor list, Coulomb and van der Waals cutoffs were all set to 1 nm. Center of mass motion was removed after every timestep. Long-range electrostatic forces were treated using a particle-mesh Ewald [42] treatment, with long-range dispersion corrections applied. The FFT grid spacing was in all cases around 0.118 nm, varying slightly with simulation box size, and cubic (order 4) spline interpolation was used on the FFT grid. In all cases, a 3-stage MD protocol was used – energy minimization, followed by 100 ps (0.002 ps timestep) of positionrestrained MD, followed by the ‘production’ run (performed with 0.001 ps timestep). In cases where a non-zero background salt concentration was modeled, an appropriate number of water molecules in the simulation box were randomly substituted with equal numbers of Na+ and Cl ions to reach the desired concentration. It should also be noted that our method for modeling pH has a number of consequences, e.g. it does not take account of environmental effects of other particles. 4. Single-particle MD runs The test nanoparticles were centered in cubic simulation boxes with periodic boundary conditions; the boxes were then filled with water, the box size being chosen so that there was at least 1 nm of

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S. Jenkins et al. / Journal of Colloid and Interface Science 339 (2009) 351–361 Table 1 The variation of the number of charged surface sites and charge surface site density with particle size and Si:Na+ ratio. Diameter (nm)

Si:Na+ ratio Surface site density (nm2)

Number of surface sites 5:1 2.0 2.4 2.8

10:1

20 34 56

1.6 1.9 2.3

15:1

10 17 28

0.8 0.94 1.13

water between any side of the box and the nanoparticle, in order to avoid potential spurious water structuring effects caused by the periodicity of the simulation box [43]. Sodium ions were substituted in randomly for water molecules until the contents of the simulation box was overall electrically neutral. The production run in these cases consisted of a 500 ps unconstrained MD run, all other parameters being as previously stated. 5. Double-particle MD runs – PMF calculations The fully equilibrated test nanoparticles from the single-particle MD runs were used as building blocks to investigate inter-particle interactions. Pairs of nanoparticles (along with their accompanying cloud of neutralizing Na+ ions) were placed relative to each other in such a way that the distance between their centers of mass (COM distance) took a number of specified values. The resulting nanoparticle pairs were then centered in large simulation boxes with periodic boundary conditions applied. The dimensions of these large simulation boxes were chosen such that any part of one nanoparticle was closer to all parts of the other member of the pair than to any periodic copies of either particle. The remaining space in the simulation boxes was filled with flexible TIP4P water. In these runs the production phase consisted of a 500 ps (0.001 ps timestep) potential of mean force (PMF) calculation, using the constraints method built into the pull code within GROMACS. The COM distance between the nanoparticle pair at the end of the position-restrained MD run was used as a constraint distance. An additional constraint force was applied by the GROMACS code during the PMF production run to maintain this original COM distance, and the value of the constraint force needed to maintain this distance was monitored and recorded at every timestep of the production run. It should be noted that during the production run, all of the inter-atomic bond angles and lengths in the silica nanoparticles are free to change, in contrast to the preliminary equilibration run

20:1

7 11 19

0.6 0.6 0.8

5 9 14

0.4 0.5 0.6

where only the inter-atomic bond angles in the silica nanoparticles are allowed to vary. After the end of the production run, the 500,000 values of these constraint forces were averaged, representing the average inter-particle attractive or repulsive force caused by interactions between the particles [44]. Variants of these basic PMF runs were generated and carried out for various different background concentrations of NaCl in the solvent (the additional ions having been present from the beginning of the protocol), in the form of additional Na+ and Cl ions randomly substituted for solvent (water) molecules. Numbers of additional ions were chosen to replicate molecular background salt concentrations of 0.00 M, 0.01 M, 0.10 M and 1.00 M, encompassing the range of background salt levels used in industrial production of these nanoparticles, and found in their common applications. There is currently a limitation in the GROMACS code such that PMF constraints are not possible between groups of atoms that are themselves constrained (as is the case in the position-restrained equilibration phase) by the implemented SHAKE or LINCS constraints algorithms. We see no significant problems with allowing the nanoparticles to drift slightly during this (position-restraints) phase of the simulation, given that our initial fine sampling of possible COM distances (0.05 nm spacing) yielded a sufficiently fine (though irregular) set of PMF constraint distances for the production part of the simulations. Integration of forces was performed using trapezoidal integration which handles irregular intervals transparently. Errors in the calculated PMF forces were evaluated using block averaging [45]. Additionally, plots of PMF force vs. simulation time were examined, showing no significant systematic drift over the 500 ps PMF runs, indicating that the PMF forces had reached a stationary value. This lack of systematic drift was further verified using a small number of trajectories extended to a total simulation time of 1 ns, justifying the use of 500 ps for the duration of the PMF phase of the simulation protocol.

Table 2 The variation of the mean of the time-averaged number of the total number of hydrogen bonds between silica nanoparticles and the surrounding water molecules with background Na+ concentration. The contribution to this total provided by the number of hydrogen bonds between the O sites and the water molecules is given in brackets. Si:Na+ ratio

Background Na+ ion molarity 0.00

0.01

0.10

1.00

2.0 nm nanoparticle 5:1 10:1 15:1 20:1

326.99 242.95 219.84 199.84

(180.69) (91.85) (67.97) (48.02)

328.17 242.05 219.27 199.05

(180.91) (91.19) (66.46) (48.01)

324.91 241.65 217.81 198.13

(179.16) (91.00) (67.04) (47.78)

313.85 236.22 212.08 190.73

(172.17) (89.37) (65.94) (46.61)

2.4 nm nanoparticle 5:1 10:1 15:1 20:1

507.38 377.10 324.04 301.96

(278.42) (152.36) (97.87) (83.92)

507.63 377.78 324.02 302.78

(277.88) (152.57) (98.35) (83.98)

506.85 376.79 322.31 299.66

(278.22) (152.40) (97.88) (83.92)

489.89 364.53 311.22 291.35

(268.06) (147.28) (95.24) (81.13)

2.8 nm nanoparticle 5:1 10:1 15:1 20:1

766.23 541.47 446.78 430.91

(455.96) (227.53) (152.36) (119.82)

767.06 539.26 445.73 430.43

(457.26) (227.45) (153.92) (119.35)

763.35 538.65 444.20 426.56

(455.07) (225.96) (152.49) (118.98)

736.48 522.01 427.59 410.52

(435.87) (220.29) (147.82) (115.21)

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Interparticle pair potential of mean force (kJ mol-1)

Interparticle pair potential of mean force (kJ mol-1)

Fig. 1. A snapshot of the pair of nanoparticles with diameter 2.0 nm and 1.00 M Na+ counter ion concentration is shown with hydrogen bonding (represented by the dashed lines) linking the ‘stickiest’ nanoparticle pair, see also Figs. 2c and 5c and the corresponding figure captions. The isolated dots and spheres represent the sodium counter ions of the two nanoparticles; the surrounding water molecules and background Na+ and Cl ions are removed for clarity.

40.00 20.00 0.00 -20.00 -40.00 0.00M Si:Na ratio 5:1 0.01M Si:Na ratio 5:1 0.10M Si:Na ratio 5:1 1.00M Si:Na ratio 5:1

-60.00 -80.00

2.50

3.00 3.50 4.00 4.50 Interparticle separation (nm)

5.00

40.00 20.00 0.00 -20.00 -40.00 0.01M Si:Na ratio 10:1 0.00M Si:Na ratio 10:1 1.00M Si:Na ratio 10:1 0.10M Si:Na ratio 10:1 Hydrogen bonding contribution to PMF

-60.00 -80.00

2.00

2.50 3.00 3.50 4.00 Interparticle separation (nm)

(b) Interparticle pair potential of mean force (kJ mol-1)

Interparticle pair potential of mean force (kJ mol-1)

(a) 40.00 20.00 0.00 -20.00 -40.00 -60.00 -80.00

2.00

0.00M Si:Na ratio 15:1 0.01M Si:Na ratio 15:1 0.10M Si:Na ratio 15:1 1.00M Si:Na ratio 15:1 Hydrogen bonding contribution to PMF

2.50 3.00 3.50 4.00 Interparticle separation (nm)

(c)

4.50

4.50

5.00

40.00 20.00 0.00 -20.00 -40.00 -60.00

0.00M Si:Na ratio 20:1 0.01M Si:Na ratio 20:1 0.10M Si:Na ratio 20:1 1.00M Si:Na ratio 20:1 Hydrogen bonding contribution to PMF

-80.00

2.00

2.50

3.00

3.50

4.00

4.50

Interparticle separation (nm)

(d)

Fig. 2. The inter-particle potential of mean force vs. inter-particle separation for a pair of nanoparticles with diameter of 2.0 nm and Si:Na+ ratios of 5:1, 10:1, 15:1 and 20:1 are shown in (a–d), respectively for the four background NaCl concentrations of 0.00, 0.01, 0.10 and 1.00 M. The estimated contribution to the PMF from the bridging interparticle hydrogen bonds is shown by the undecorated thicker black plot.

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Significant nanoparticle rotation was observed during the simulation runs in agreement with previous work [32]; nanoparticle rotation during simulations were tracked in each case by calculating an initial surface normal vector to a plane defined by the positions of three O sites on the surface of the nanoparticle, then following the angular deviation of this normal vector from its starting direction through the entire simulation trajectory. Hydrogen bonds connecting or bridging the pairs of silica particles were counted using the ‘g_hbond’ utility within the GROMACS suite, with a hydrogen–acceptor (oxygen) cut-off radius of 0.35 nm and a cut-off angle of 30°, averaged over the entire PMF trajectory.

6. Results and discussion

Interparticle pair potential of mean force (kJ mol-1)

Interparticle pair potential of mean force (kJ mol-1)

The amorphous silica nanoparticles consist mainly of tetrahedrally coordinated silicon atoms, including silanol bridges, surface hydroxyl groups and deprotonated oxygen surface (O) sites. For the three particle sizes, i.e., 2.0 nm, 2.4 nm and 2.8 nm, the number of deprotonated surface sites is determined by the Si:Na+ ratio. Four ratios were chosen in this study, i.e., 5:1, 10:1, 15:1 and 20:1. In the case of smallest nanoparticle (2.0 nm in diameter) the number of charged oxygen surface sites (also equal to the number of sodium counter ions) is 20, 10, 7 and 5 per nanoparticle for the 5:1, 10:1, 15:1 and 20:1 Si:Na+ ratios, respectively. If we consider the silica particle as a perfect sphere then by calculating the surface area of a sphere we can estimate the density

40.00 20.00 0.00 -20.00 -40.00 -60.00

0.00M Si:Na ratio 5:1 0.01M Si:Na ratio 5:1

-80.00

0.10M Si:Na ratio 5:1 1.00M Si:Na ratio 5:1

2.80

3.20

3.60 4.00 4.40 4.80 Interparticle separation (nm)

of charged surface sites. Assuming the silica particles as spheres is an approximation because simulated silica particles are not perfect spheres as shown in our previous work [33]. Moreover, the surface area of simulated silica particles is also unknown due to its porosity. However, the estimation of surface site density will facilitate the interpretation of simulation results in the context of experimental findings. Total number of deprotonated sites along with the surface site densities for silica nanoparticles of different sizes and for four Si:Na+ ratios are given in Table 1. In Table 2 variation of the number of hydrogen bonds between silica surface and the surrounding water molecules are given for three different particle sizes and four Si:Na+ ratios (5:1, 10:1, 15:1 and 20:1). In Fig. 1 a snapshot of the hydrogen bonding between the two silica particles is shown. In Figs. 2–4 the potential of mean force plots for the four Si:Na+ ratios for the three sizes of silica particle pairs are presented, note the vertical scale in Fig. 4 is larger than for Figs. 2 and 3. The variation of the number of inter-nanoparticle hydrogen bonds with inter-particle separation for the 2.0 nm, 2.4 nm and 2.8 nm are given in Figs. 5–7, respectively. Superimposed on the PMFs in Figs. 2–4 for the 10:1, 15:1 and 20:1 Si:Na+ ratios is a thick undecorated plot line representing the estimated contributions to PMF made by the inter-silica particle or bridging hydrogen bonds, for clarity shown only for the 0.00 M Na+ background concentration. This estimation of the contribution made by the bridging hydrogen to the PMF is arrived at by combing the calculated values of the time-averaged numbers of bridging hydrogen bonds with the estimation of the individual hydrogen

40.00 20.00 0.00 -20.00 -40.00 0.00M Si:Na ratio 10:1 0.01M Si:Na ratio 10:1 0.10M Si:Na ratio 10:1 1.00M Si:Na ratio 10:1 Hydrogen bonding contribution to PMF

-60.00 -80.00

2.80

5.20

3.20 3.60 4.00 4.40 Interparticle separation (nm)

40.00 20.00 0.00 -20.00 -40.00 0.00M Si:Na ratio 15:1 0.01M Si:Na ratio 15:1 0.10M Si:Na ratio 15:1 1.00M Si:Na ratio 15:1 Hydrogen bonding contribution to PMF

-60.00 -80.00

2.80

3.20

3.60 4.00 4.40 4.80 Interparticle separation (nm)

(c)

(b) Interparticle pair potential of mean force (kJ mol-1)

Interparticle pair potential of mean force (kJ mol-1)

(a)

4.80

40.00 20.00 0.00 -20.00 -40.00 0.00M Si:Na ratio 20:1 0.01M Si:Na ratio 20:1 0.10M Si:Na ratio 20:1 1.00M Si:Na ratio 20:1 Hydrogen bonding contribution to PMF

-60.00 -80.00

2.80

3.20

3.60 4.00 4.40 4.80 Interparticle separation (nm)

(d)

Fig. 3. The inter-particle potential of mean force vs. inter-particle separation for a pair of nanoparticles with diameter of 2.4 nm, see also the figure caption of Fig. 2.

40.00 0.00 -40.00 -80.00 -120.00 0.00M Si:Na ratio 5:1 0.01M Si:Na ratio 5:1

-160.00

0.10M Si:Na ratio 5:1 1.00M Si:Na ratio 5:1

3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00 Interparticle separation (nm)

Interparticle pair potential of mean force (kJ mol-1)

S. Jenkins et al. / Journal of Colloid and Interface Science 339 (2009) 351–361

Interparticle pair potential of mean force (kJ mol-1)

356

40.00 0.00 -40.00 -80.00 0.00M Si:Na ratio 10:1 0.01M Si:Na ratio 10:1 0.10M Si:Na ratio 10:1 1.00M Si:Na ratio 10:1 Hydrogen bonding contribution to PMF

-120.00 -160.00

3.20

40.00 0.00 -40.00 -80.00 -120.00

0.00M Si:Na ratio 15:1 0.01M Si:Na ratio 15:1 0.10M Si:Na ratio 15:1 1.00M Si:Na ratio 15:1 Hydrogen bonding contribution to PMF

-160.00

3.20

3.60 4.00 4.40 Interparticle separation (nm)

4.80

(b)

4.80

(c)

Interparticle pair potential of mean force (kJ mol-1)

Interparticle pair potential of mean force (kJ mol-1)

(a)

3.60 4.00 4.40 Interparticle separation (nm)

40.00 0.00 -40.00 -80.00 -120.00

0.00M Si:Na ratio 20:1 0.01M Si:Na ratio 20:1 0.10M Si:Na ratio 20:1 1.00M Si:Na ratio 20:1 Hydrogen bonding contribution to PMF

-160.00

3.20

3.60 4.00 4.40 Interparticle separation (nm)

4.80

(d)

Fig. 4. The inter-particle potential of mean force vs. inter-particle separation for a pair of nanoparticles with diameter of 2.8 nm, see also the figure caption of Fig. 2.

bond strength. The average hydrogen bond length (–O–H–O–) being of the order of 0.27 nm and the strength is estimated to be 16 kJ mol1. It was difficult to get a consistent estimate from the literature [46–47] of the hydrogen bond strength, other than estimations ranging from 5–25 kJ mol1. The Si:Na+ ratios are much more important than the background Na+ concentrations for determining the distribution of hydrogen bonding (Figs. 5–7). A comparison of the inter-particle potentials given in Figs. 2–4 and the graphs of the variation of the number of hydrogen bonds in Figs. 5–7 shows that the shape of the inter-particle potentials is strongly dependent on the hydrogen bonding and on the Si:Na+ ratios. In Figs. 2–4 the superimposed contributions to the PMF plots from the estimated value for the strength of each the bridging hydrogen bonds (estimated to be 16 kJ mol1) for the background Na+ concentration of 0.00 M, is in good agreement with the form of the PMF plots. Note that beyond the range of the bridging hydrogen bonds the PMF plots tend to be repulsive, this suggests that the silica nanoparticles could be stable in suspension. Thus, differences in the shapes of the potentials may lead to different aggregation behaviors of the nanoparticles [48]. This trend is more clearly depicted for 5:1 case than rest of the Si:Na+ ratios investigated. The inter-particle potentials that are attractive are associated with higher numbers of hydrogen bonds as can be seen by the examination of Figs. 5–7. The range of the attractive potential also appears to be correlated to the number of hydrogen bonds at each separation, e.g.

compare Figs. 4b–d and 7b–d at separations of 3.3 nm, where the number of hydrogen bonds has reduced effectively to zero. When the sum of the time-averaged number of hydrogen bonds (for a given inter-particle separation) drops below one this indicates that the hydrogen bonds are too short lived relative to the length of the trajectory to be considered to be stable. In the case of 5:1 Si:Na+ ratios the variation of the time-averaged number of hydrogen bonds with inter-particle potential shown in Figs. 5a, 6a and 7a, there are very few or no stable hydrogen bonds. The magnitude of PMF obtained by MD simulations at large distances where hydrogen bonding between the two silica particles is absent might be less repulsive compared with the prediction of continuum theories such as by screened Coulomb potential. For example in the case of 2.0 nm particles with 5:1 Si:Na+ ratio (Fig. 2a) the PMF at 0.00 M concentration and at COM (center of mass) distances >3 nm is roughly 5 kJ mol1 while PMF calculated by screened Coulomb potential in water would be around 230 kJ mol1. This reduction in the magnitude of PMF is most likely due to the presence of explicit water molecules which effectively screen the charge due to their dipole orientation. In Fig. 8a and b (refer also to the explanations in the figure caption) the dipole orientation of water molecules between 2.0 nm diameter silica particles having 20:1 Si:Na+ ratio in 0.00 M electrolyte concentration is indicated at two COM distances. Its clear that water dipoles between the two charged silica are highly oriented and the water behavior approaches that of the bulk (random dipole

357

10.00

10.00

9.00

9.00 Number of hydrogen bonds

Number of hydrogen bonds

S. Jenkins et al. / Journal of Colloid and Interface Science 339 (2009) 351–361

8.00 0.00M Si:Na ratio 5:1

7.00

0.01M Si:Na ratio 5:1

6.00

0.10M Si:Na ratio 5:1 1.00M Si:Na ratio 5:1

5.00 4.00 3.00

8.00 0.00M Si:Na ratio 10:1

7.00

3.00 2.00 1.00

2.30

2.40

2.50

2.60

2.70

1.00M Si:Na ratio 10:1

4.00

1.00 2.20

0.10M Si:Na ratio 10:1

5.00

2.00

2.10

0.01M Si:Na ratio 10:1

6.00

2.80

2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80

Interparticle separation (nm)

Interparticle separation (nm)

(b)

10.00

10.00

9.00

9.00

8.00 0.00M Si:Na ratio 15:1

7.00 0.01M Si:Na ratio 15:1

6.00

0.10M Si:Na ratio 15:1

5.00

1.00M Si:Na ratio 15:1

4.00 3.00

Number of hydrogen bonds

Number of hydrogen bonds

(a)

0.00M Si:Na ratio 20:1

8.00

4.00 3.00 2.00 1.00

(c)

1.00M Si:Na ratio 20:1

5.00

1.00

Interparticle separation (nm)

0.10M Si:Na ratio 20:1

6.00

2.00

2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70

0.01M Si:Na ratio 20:1

7.00

1.90

2.00

2.10

2.20

2.30

2.40

2.50

2.60

Interparticle separation (nm)

(d)

Fig. 5. The number of time-averaged inter-nanoparticle ‘bridging’ hydrogen bonds vs. inter-particle separation for a pair of nanoparticles with diameter of 2.0 nm and Si:Na+ ratios of 5:1, 10:1, 15:1 and 20:1 are shown in (a–d) for background NaCl concentrations of 0.00, 0.01, 0.10 and 1.00 M, respectively.

orientation) at large distances, as in shown in Fig. 8b where the two silica particle COM separation is 6.465 nm. The shape of inter-particle potentials also correlates with the time-averaged number of hydrogen bonds; attractive potentials which have a steeper gradient and become zero faster have fewer hydrogen bonds, e.g. the 2.4 nm nanoparticle (for 10:1, 15:1 and 20:1 Si:Na+ ratios) there are fewer hydrogen bonds for any of the Na+ concentrations for the 2.0 nm and 2.8 nm nanoparticles at any Si:Na+ ratios. There are general trends in the potential of mean force profiles; the short-range attraction tends to increase with increasing Si:Na+ ratio or at least become less repulsive. For example in the case of 2 nm particles with 5:1 and 20:1 Si:Na+ ratios there is more attraction for later than for the former (Fig. 2). An explanation for this is that in the case when there are many charged surface sites, i.e., 5:1 Si:Na+ ratio there is enhanced repulsion between the silica particles which results in less hydrogen bonding for the 5:1 ratio than for any of the other Si:Na+ ratios. In the case of the 20:1 Si:Na+ ratio there are more neutral silanol groups present on the surfaces of silica particles (see earlier in this section) which enhances hydrogen bonding relative to the 5:1. However, this increase in hydrogen bonding with increasing Si:Na+ is not seen for all the particle sizes. For example, the potential of mean force for the 2.8 nm particle for a 15:1 Si:Na+ ratio are more attractive than in for the 20:1 silicon to sodium ratio (see Fig. 4), this is also reflected in the greater number of hydrogen bonds for the 15:1 as compared with the 20:1 ratios.

The silica nanoparticles are not behaving as a perfect size dependent sequence in terms of the numbers of inter-particle hydrogen bonds. This has previously been be observed [33] from the form of the solvation forces for a Si:Na+ ratio of 5:1, which obeyed a decaying oscillatory function with particle separation, including both the attractive depletion and repulsive structural energy barrier [49]. A physical explanation may be the variation in the porosities of the individual particles (see Table 3), where the 2.4 nm particles are ‘harder’, i.e., denser than the 2.0 nm and 2.8 nm particles, based on the lower numbers of trapped water molecules in the 2.4 nm particles. If the 2.0 nm and 2.4 nm particles were equally dense then the 2.4 nm particle by scaling up the increase in the volume should contain 1.7 times the number of water molecules than the 2.0 nm particle, which is clearly not the case. The variations in the porosities of the nanoparticles are due to the necessity to recreate the correct deprotonated surfaces from a much larger (5 nm diameter particle) melted silica glass, the reconstruction process then magnifies any differences in the original bulk silica glass porosities. Notice in particular, the large relative drop in the number of trapped water molecules inside the 2.4 nm and 2.8 nm particles (see Table 3) when the Si:Na+ ratios are increased from 5:1 to 20:1, especially for the 2.4 nm particle where there are more than three times fewer trapped water molecules at the 20:1 ratio than for the 5:1 ratio, this is not the case for the 2.0 nm particle. This difference in the decrease of the numbers of trapped water molecules with Si:Na+ ratio (i.e., comparing the

S. Jenkins et al. / Journal of Colloid and Interface Science 339 (2009) 351–361

10.00

10.00

9.00

9.00

8.00

Number of hydrogen bonds

Number of hydrogen bonds

358

0.00M Si:Na ratio 5:1

7.00

0.01M Si:Na ratio 5:1

6.00

0.10M Si:Na ratio 5:1 1.00M Si:Na ratio 5:1

5.00 4.00 3.00 2.00

8.00 0.00M Si:Na ratio 10:1

7.00 0.01M Si:Na ratio 10:1

6.00

0.10M Si:Na ratio 10:1

5.00

1.00M Si:Na ratio 10:1

4.00 3.00 2.00

1.00

1.00 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30 3.40 3.50

2.60

Interparticle separation (nm)

2.80 3.00 3.20 Interparticle separation (nm)

(a)

(b)

10.00

10.00

9.00

9.00

8.00

8.00 0.00M Si:Na ratio 15:1

7.00 0.01M Si:Na ratio 15:1

6.00

0.10M Si:Na ratio 15:1

5.00

1.00M Si:Na ratio 15:1

4.00 3.00

Number of hydrogen bonds

Number of hydrogen bonds

3.40

0.00M Si:Na ratio 20:1

7.00

3.00

1.00

1.00

3.40

(c)

1.00M Si:Na ratio 20:1

4.00

2.00

2.80 3.00 3.20 Interparticle separation (nm)

0.10M Si:Na ratio 20:1

5.00

2.00

2.60

0.01M Si:Na ratio 20:1

6.00

2.50

2.60

2.70

2.80

2.90

3.00

3.10

3.20

Interparticle separation (nm)

(d)

Fig. 6. The number of time-averaged inter-nanoparticle ‘bridging’ hydrogen bonds vs. inter-particle separation for a pair of nanoparticles with diameter of 2.4 nm, see also the figure caption of Fig. 5.

5:1 and 20:1) may explain why the 20:1 Si:Na+ ratio has the highest number of inter-particle hydrogen bonds for all three sets of particles and four Si:Na+ ratios. To summarize, there are some generalizations that can be made about the number water molecules trapped inside the silica particles; firstly for a given Si:Na+ ratio the 1.00 M concentration of Na+ background ions has the fewest number of trapped molecules, the dipole moment follows this same trend, i.e., decreases with increasing Si:Na ratio (see Table 4). Secondly, for a given particle the 5:1 Si:Na+ ratio always has more trapped molecules than does the 20:1, for all Na+ background concentrations. Thirdly, there appears to be a correlation between the trends in the number of trapped water molecules and the number of inter-particle hydrogen bonds. From the experimental perspective, the increase in Si:Na+ ratio corresponds with approaching the pH at the point of zero charge of the silica particles. We have discussed in the Introduction that in the pH range of 3–6 there are only a few charged sites present at the surface, but at pH > 7 the surface silanol groups become increasingly deprotonated. Recent XPS measurements [50] have also shown that there are very few Na+ ions near the silica particles surface in the pH range of 2–6. However, the number of Na+ ions crowded around the silica surface increases dramatically at pH values >7. Zhuravlev [51] found the silanol groups surface site densities of some 100 amorphous silicas to be constant with values between 4 and 6 sites/nm2. Hiemstra et al. [52] successfully modeled the experimentally-determined surface charge density of silica

particles by using the Multisite Surface Complexation (MUSIC) model. It was found that a surface site (Si–OH) density of 8 sites/ nm2 was good enough to predict the experimental data correctly. However, one should be aware of the fact that in the surface complexation modeling the site density is a fitting parameter and may change depending upon the type of silica and model of the interpretation. For example, Sahai and Sverjensky [53] successfully predicted the surface charging of six different silica particles by using a site density of 4.6 sites/nm2. If we compare the site density used in our MD simulations with the values extracted from experiments (approximately 4 sites/nm2), it is more likely that we are modeling the acid side of the titration curve. For example, if we consider the lowest experimentally determined values (4 sites/nm2) then the maximum density of charged sites used in our MD simulations is just half of this value (see Table 1). This means that in our modeling approach we are considering only half of the surface sites as deprotonated, which can only be true in the acidic region. In this context our findings from the MD simulations that hydrogen bonding between the silica surface and surrounding water molecules decreases as the Si:Na+ ratio increases is plausible because as the number of charged sites on the silica surface increases more water molecules will be present near the silica surface due to the solvation of charged sites as well as attraction of solvated counter ions (see Table 2). Moreover, Song et al. [54] have stated (based on their viscosity measurements) that an increased hydration of nanosilica in NaCl can be due to the

359

10.00

10.00

9.00

9.00 Number of hydrogen bonds

Number of hydrogen bonds

S. Jenkins et al. / Journal of Colloid and Interface Science 339 (2009) 351–361

8.00 0.00M Si:Na ratio 5:1

7.00

0.01M Si:Na ratio 5:1

6.00

0.10M Si:Na ratio 5:1 1.00M Si:Na ratio 5:1

5.00 4.00 3.00

8.00 0.00M Si:Na ratio 10:1

7.00

3.00

1.00

1.00

3.10 3.20 3.30 3.40 Interparticle separation (nm)

1.00M Si:Na ratio 10:1

4.00

2.00

3.00

0.10M Si:Na ratio 10:1

5.00

2.00

2.90

0.01M Si:Na ratio 10:1

6.00

3.00

3.50

3.10 3.20 3.30 3.40 Interparticle separation (nm)

(b)

10.00

10.00

9.00

9.00 Number of hydrogen bonds

Number of hydrogen bonds

(a)

8.00 0.00M Si:Na ratio 15:1

7.00 0.01M Si:Na ratio 15:1

6.00

0.10M Si:Na ratio 15:1

5.00

1.00M Si:Na ratio 15:1

4.00 3.00

8.00 0.00M Si:Na ratio 20:1

7.00

0.01M Si:Na ratio 20:1

6.00

0.10M Si:Na ratio 20:1

4.00 3.00 2.00

1.00

1.00 3.00

3.10

3.20

3.30

3.40

3.50

1.00M Si:Na ratio 20:1

5.00

2.00

2.90

3.50

2.90

Interparticle separation (nm)

3.00

3.10

3.20

3.30

3.40

3.50

Interparticle separation (nm)

(c)

(d)

Fig. 7. The number of time-averaged inter-nanoparticle ‘bridging’ hydrogen bonds vs. inter-particle separation for a pair of nanoparticles with diameter of 2.8 nm, see also the figure caption of Fig. 5.

accumulation of hydrated Na+ ions near the negatively charged silica surface. In the present MD simulations an ion exchange mechanism responsible for increased particle attraction which leads to coagulation as proposed by the Allen and Matijevic [13], could not be modeled. On the other hand we do see an increase in the hydrogen bonding between the two silica particles (Figs. 5–7) and enhanced attraction of two silica particles as Si:Na+ ratio is increased (see Figs. 2–4). As discussed in the introduction bridging of two silica particles due to the hydrogen bonding has been pointed out by the Despasse et al. [14,15] in order to explain the coagulation behavior of silica particles in the presence of LiCl and NaCl at pH > 9. Our findings may at first sight seems at odds regarding the stability of silica at low pH values because our simulations show an enhanced attraction for weakly charged silica. It has been previously demonstrated [32] that there is an increase in water ordering around the silica nanoparticles with increase in Si:Na+ ratio that may be related to the gel type of layer that has been observed to surround such silica particles. As discussed in the introduction hydration/hairy layer has been pointed out to be the main cause of silica stability at pH < 6. The hydrogen bonding between two silica particles shown by MD simulations may be present in the real systems but its effect in destabilizing the silica particles is probably masked by the presence of hydration/hairy layer. Due to very short time of hydrogen bonding interactions as well as a low total number of hydrogen bonds between the silica particles seen in MD simulations (Figs. 5–7) it is most probable that

hydrogen bonding will play a minor role in the overall stability of silica sols at low pH values. Vigil et al. [23] have shown by adhesion measurements that growth of hairy layer on silica films generated at mica surfaces is a slow process. For example, even after 30 min the layer was still growing on the silica particles. It might be possible that the growth of hydration/hairy layer on silica nanoparticles suspended in solution is much faster because it is shown experimentally that small (7.12 nm) silica particles are strongly hydrated compared to the large (16.5 nm) silica particles [55,56]. This increased hydration of small particles is due to the increased curvature at the particle solution interface.

7. Conclusions This study has shed light on the role that hydrogen bonding has on the inter-particle potentials of pairs of nanoparticles using realistic molecular dynamics force fields. The form of the interaction potential between two silica particles is found to depend strongly on the number of bridging hydrogen bonds and to a lesser extent the density of charged groups present on the particles surfaces. The assessment that the contribution to the attractive portion of the potentials where there is significant inter-particle hydrogen bonding that is the 10:1,15:1 and 20:1 Si:Na ratios, is arrived at by an estimation for the strength of an average inter-particle hydrogen bond (16 kJ mol1 per bond). This estimated hydrogen

360

S. Jenkins et al. / Journal of Colloid and Interface Science 339 (2009) 351–361 Table 3 The mean of the time-averaged number of water molecules trapped inside nanoparticles ‘snp1’ and ‘snp2’ for the three nanoparticles in this study.

Water molecule orientation as a function of distance 1

Si:Na+ ratio



0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1

0

(a) Water molecule orientation as a function of distance 1



0.8

0.00

0.01

0.10

1.00

2.0 nm nanoparticle 5:1 snp 1 snp 2

9.54 9.27

9.38 9.26

9.32 8.93

7.99 7.83

10:1 snp 1 snp 2

7.01 7.17

7.14 7.19

6.73 7.38

6.44 6.31

15:1 snp 1 snp 2

8.03 7.89

7.81 7.76

7.73 7.53

6.68 6.66

20:1 snp 1 snp 2

7.58 7.86

7.74 8.06

7.86 7.81

5.15 5.46

11.22 11.66

11.85 12.08

11.71 11.67

10.70 10.58

10:1 snp 1 snp 2

5.43 5.89

5.92 6.04

5.65 5.63

4.63 5.08

15:1 snp 1 snp 2

6.47 6.34

6.39 6.19

5.95 6.11

5.45 5.66

20:1 snp 1 snp 2

3.21 3.57

4.05 4.36

3.90 4.25

3.44 3.62

2.8 nm nanoparticle 5:1 snp 1 snp 2

20.56 21.72

20.91 21.45

20.75 21.32

19.04 19.41

10:1 snp 1 snp 2

16.75 17.05

16.32 16.83

16.36 16.18

14.48 14.88

15:1 snp 1 snp 2

14.45 14.44

13.95 13.97

13.62 14.16

12.43 12.38

20:1 snp 1 snp 2

12.64 13.71

12.58 14.46

11.60 13.99

10.81 11.55

2.4 nm nanoparticle 5:1 snp 1 snp 2

1 2 3 0.5 1.5 2.5 Separation of water molecules and nanoparticle (nm)

Background Na+ ion molarity

0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1

0

1 2 3 0.5 1.5 2.5 Separation of water molecules and nanoparticle (nm)

(b) Fig. 8. The time-averaged orientation of water molecules within the defined radius relative to the center of mass of a silica nanoparticle shown for a pair of closely spaced, but not touching, (2.112 nm center of mass separation) 2.0 nm diameter nanoparticles, a Si:Na+ ratio of 20:1 and a background Na+ concentration of 0.00 M in (a). The same quantities are shown in (b) for a pair of widely spaced (6.465 nm center of mass separation) 2.0 nm diameter silica nanoparticles with a Si:Na+ ratio of 20:1 and again a background Na+ concentration of 0.00 M. The outer cut-off radius for the time-averaged water molecule orientation of the nanoparticle is 1.0 nm. A value of +1 or 1 for cos(q1) represents a water molecule oriented so that the bisecting in plane vector (of the water molecule) is parallel or anti-parallel, respectively, to the vector joining the center of mass of the nanoparticle to the oxygen atom of the water molecule.

bond strength shows the possibility that at very short inter-particle separations the hydrogen bonding is a major contributor to the attractive portion of the potential and moreover regardless of the accuracy of the estimation for the hydrogen bond strength the potentials become repulsive in the absence of the inter-particle hydrogen bonds.

As the number of charged groups on two silica particles decreases and so the Si:Na+ ratio increases, the potential of mean force becomes more attractive. This enhanced attraction at decreasing charge density correlates very with the increased hydrogen bonding between the two silica particles and can be regarded as a measure of particle ‘stickiness’, i.e., the greater the number of bridging hydrogen bonds the greater the stickiness of a nanoparticle. Moreover, an increase in the number of hydrogen bonds between the silica surface and solvating water molecules is observed when Si:Na+ ratio decreases. This implies that as the charge on the silica surface increases more water molecules gathered near the silica surface in order to hydrolyse the charged groups as well as due to the attraction of solvated counter ions. These simulation results are also supported by recent experimental data on the hydration of silica in NaCl by viscosity measurements. However, our simulations could not predict the stability of silica at low pH as seen in experiments. The difficulties lie in simulating the slow growing hydration/hairy layers around the silica particles which are present in real systems. In future, the PMF of the interaction of an approximately spherical nanoparticle with a ‘peanut’ shaped nanoparticle formed from a pair of pre-coalesced nanopar-

S. Jenkins et al. / Journal of Colloid and Interface Science 339 (2009) 351–361 Table 4 Variation of the average nanoparticle electric dipole moment with Si:Na+ ratio for the three particle sizes of this study; 2.0 nm, 2.4 nm and 2.8 nm in diameter. Si:Na+ ratio

Average nanoparticle electric dipole moment/Debye

2.0 nm diameter particle 5:1 snp 1 snp 2

5.9  103 7.4  103

10:1 snp 1 snp 2

3.9  103 4.6  103

15:1 snp 1 snp 2

2.5  103 3.1  103

20:1 snp 1 snp 2

1.9  103 2.3  103

2.4 nm diameter particle 5:1 snp 1 snp 2

1.5  104 1.8  104

10:1 snp 1 snp 2

7.2  103 9.2  103

15:1 snp 1 snp 2

4.4  103 5.5  103

20:1 snp 1 snp 2

2.8  103 3.7  103

2.8 nm diameter particle 5:1 snp 1 snp 2

2.0  104 2.5  104

10:1 snp 1 snp 2

1.1  104 1.5  104

15:1 snp 1 snp 2

7.8  103 9.7  103

20:1 snp 1 snp 2

4.7  103 6.2  103

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