Temperature and Particle-size Effects on the Formation of Silica Gels from Silica Sols

Silica nanoparticles (silica sols) based gels have increasingly been used as alternative grouting material for sealing the small fractures in the tunnel walls. Gelling of silica nanoparticles at room temperature has been investigated thoroughly but gelling at different temperatures scarcely investigated. At the same time temperature is one of major factor which can affect the long-term stability of grouted silica. In this work we have investigated the gelling of three different types of silica sols (Levasil CS40-213, Levasil CS40-222, and Levasil CS30-236) having different particle sizes, in 0.28 M NaCl at 10, 20 and 30 °C. Aggregation process, starting from the addition of salt to the gelling point, was monitored by measuring the time dependent particle size distribution. Electrospray scanning mobility particle sizer (ES-SMPS) was used to measure the aggregating. These measurements were complemented by rheological measurements in order to get a relationship between changes in aggregate structure and in the viscosity of silica suspension. Data from the temperature dependent gel time measurements were used to calculate the activation energy. At room temperature, silica sols with smallest average particle size showed the shortest gel times whereas the sols with the largest particle size showed the longest gel time. However, at increasing temperature shorter gel times were seen for all the sols. Temperature dependent rheological measurements showed similar trends in viscosity changes as seen for gel times i.e., increased temperature leads to quicker increase in the viscosity and a sharp increase in viscosity near the gelling point. Our calculations of fractal dimensions showed that in the gel network there are still many free particles which continuously incorporated into the gel network. Apparent activation energies calculated for CS40-213, CS40-222, CS30-236 were 13.40, 23.36 and 41.45 kJ/mol, respectively. These values are lower than values reported for silica in the literature. Moreover, temperature dependent zeta potential measurements show that zeta potential get less negative as temperature increase. The above mentioned measurements are at odd what has been reported in literature but we have provided plausible explanation of these results.


Introduction
Silica nanoparticles have a wide field of applications, ranging from electronic devices [1] to pulp and papermaking [2]. In the recent two decades silica nanoparticles have been introduced as a grouting material [3][4][5][6][7], which due to the abundance of silicon in the earth's crust is considered environmentally friendly. Suspension of silica nanoparticles so called silica sols are due to their low viscosity able to penetrate narrow fractures compared to common grouting materials such as cement. The sols can contain a variety of silica nanoparticles and sols with narrow as well broad particle size distributions are produced at an industrial scale. Typically silica sols contain silica nanoparticles with an average particle size of approximately 4-30 nm [8]. Furthermore, silica sols may contain particles up to 100 nm in size, depending on the size distribution.
When used for grouting purposes silica sols are mixed with a salt solution usually (10 wt% ≈ 2 M) NaCl [4,6,9]. This destabilizes the silica sol causing the nanoparticles to aggregate so that a hydro/particle-gel is formed. The time it takes to form a gel can be varied depending on the concentration of NaCl that the sol is mixed with. This allows the gel time to be set so that there is time enough to transfer the sol into rock fractures. At present a common practice is that the concentration of NaCl introduced to a sol is determined on site to produce the required gel time and it can vary significantly depending on which sol is used and the temperature. Therefore, it is vital to have a clear understanding of the factors which control the gel time such as particle size distribution, effect of salt type, concentration and temperature.
The formations of a gel structure from particles is generally considered to follow the fractal gel model [10,11]. Fractal dimension can be described using Eq. 1 where N d is the number of particles of radius a in the fractal of radius R, and d f is a fractal scaling parameter [11][12][13].
As aggregation commences the particles will form ever increasing fractals which will eventually combine to form a continuous gel network.
Two aggregation procedures have been observed called reaction limited cluster aggregation (RLCA) and diffusion limited cluster aggregation (DLCA) [14][15][16]. In DLCA (/ fast aggregation) every collision between silica particles or fractals/clusters results in the formation of a bigger fractal/ cluster while in RLCA (/slow aggregation) this is not the case. For particles the d f values of Eq. 1 will vary between 1.8-2.1 depending on the aggregation procedure being DLCA or RLCA, respectively [13]. A. Amiri et al. found through rheological measurements that very dilute, 1 vol%, solutions of fumed silica particles follow the DLCA mechanism [17]. However, in a follow-up study the same authors found that for 9 wt% solutions of fumed silica the aggregation mechanism, when the sample was exposed to a shear, followed the RLCA for temperatures ranging from 18 °C to 35 °C [18]. For silica sols containing particles of nanometre size and high particle concentrations (30-40 wt%) it is our experience that the DLCA will result in immediate formation of a gel. Therefore for grouting applications the aggregation procedure will be RLCA since this allows for longer gel times as well as control over gel times.
In recent years much focus has been put on the specific ion effects on the stability and aggregation of silica nanoparticles [14,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. A recent study by L. Zhang et al. concluded that while the choice of cation may influence the kinetics of aggregation but the final structure of the silica gel is not affected [34]. While the direct Hofmeister series for monovalent ions (Li + < Na + < K + < Rb + < Cs + ) is well established for silica particles and the ions ability to induce aggregation, little work has been done on the effect of particle size and temperature on the formation of silica gels. Kobayashi et al. used the Derjaguin, Landau, Verwey, Overbeek (DLVO) theory to make predictions of particle aggregation for different particle sizes but observed that only aggregation of particles 80 nm or bigger could successfully be predicted [35]. Smaller particles were found to aggregate slower than expected, probably due to the presence of non-electrostatic forces. A. Ponton et al. investigated the effect of temperature on the aggregation of titanium butoxide in the presence of complexing ligands and observed faster kinetics of crosslinking at increased temperatures [36]. Similar increase in the speed of gel formation was observed by X. Wang and L. Guo for ZrO 2 particles [37]. However, addition of polyelectrolytes could prevent this aggregation at all temperatures, probably due to steric stabilization. A. Amiri et al. observed faster aggregation at higher temperatures for fumed silica due to an increased Brownian motion of the silica particles and more densely packed aggregates at lower temperatures leading to a more rigid gel [18]. K. Okazaki and M. Kawaguchi concluded that slower aggregation induced by LiCl leads to a more open gel network which has a higher critical strain compared to gels formed by KCl [10]. The above mentioned studies highlight the intricate relationship between, particle size distribution, surface chemistry, nature of ionic solution, temperature and the structure of gel. At the same time it is very important to further investigate this matter in order to understand the stability of silica gels. In this paper we follow the formation of silica gels from silica sols using simple gel time tests as well as rheological measurements. We follow the gel formation at three different temperatures; 283.15 K, 293.15 K, and 303.15 K (10 °C, 20 °C, and 30 °C). The three silica sols used in this work have different particle size distribution. We follow the development of particle fractals/aggregates for the three sols and at three different temperatures using Electrospray-Scanning Mobility Particle Sizer (ES-SMPS). From the data generated from these methods we have evaluated the effect that temperature and particle size have on gel formation. We also construct an empirical equation that can possibly be used to predict gel times of silica sols.

Experimental
The three silica sols used were Levasil CS40-213, Levasil CS40-222, and Levasil CS30-236, kindly provided by Nouryon. The CS40 sols have a 40 wt% particle concentration while the CS30 sol has 30 wt%. The last number of the sols names refers to the particles surface area in g/m 2 . Large surface area means small average particle size therefore sols particle size follows CS30-236 < CS40-222 < CS40-213. Levasil silica sols are provided as stable suspensions of particles which have alkaline pH approximately 9. In alkaline pH silica nanoparticles have negative surface charge which is neutralized by Na + as counter ions. The amount of 1 3 Na + ions present in the suspension is carefully optimized such that stable suspensions can be achieved. To avoid the particle concentration effect on the aggregation and gelling the CS40 sols were diluted using Milli-Q water to obtain a particle concentration of 30 wt%. Such dilution of the sols does not lead to any decrease in the stability of the sols since the diluted sols can be stored without gelation. A very small amount of silica may dissolve upon dilution but this will not have a major impact on the particle sizes. To induce aggregation a 2 M NaCl (Sodium choride for analysis (EMSURE®), Merck KGaA) was prepared using Milli-Q water.

Gel Time Tests
Gel time tests were conducted to map the speed of aggregation of the silica particles. To induce aggregation 2.48 mL of the 2 M NaCl solution was introduced into 15 mL of silica sol. The sample was then shaken vigorously and a timer was started. The sols were placed in a water bath for at least 10 min before aggregation was induced and the samples were placed back into the water bath as aggregation progressed. The gel time was taken as the time at which the sample no longer flowed when the container was tipped 90°. Results from this method have been shown to agree reasonably with gel times determined by rheometer measurements [38]. Three samples were started simultaneously in order to be able to calculate the standard deviations. The temperatures tested were 10, 20 and 30 °C.

Electrospray-Scanning Mobility Particle Sizer
The aggregation of silica nanoparticles has previously successfully been followed using electrospray-scanning mobility particle sizer (ES-SMPS) [22,32,39]. The method gives the particle size distribution for the aerodynamic diameter. It has the advantage over the more classical dynamic light scattering in that the method is not affected by the difference in scattering intensity between particle sizes (I ∝ d 6 ). The ES-SMPS method is thereby not affected by the presence of large particles which tend to skew the particle distribution of DLS results towards the larger particles.
The ES-SMPS system contained a TSI 3482 electrospray aerosol generator coupled to a TSI 3082 electrostatic classifier equipped with a TSI 3085A nano DMA, which in turn was coupled to a TSI 3788 condensation particle counter. The samples were fed into the ES-SMPS system via a Shimadzu SIL-20A Autosampler. The system was controlled and data gathered by TSI 3982 MacrolMS Software v.5.0.5.098. Aggregation of silica sols was initiated in a similar manner as for the gel time tests. At 25, 50, and 75% of the gel times a small amount of sample was diluted to 150 ppm particle concentration in acetate buffer (pH ≈ 8) and fed into the ES-SMPS. Measurements were also conducted for the un-aggregated silica sols to give the initial particle distribution. From the distributions generated by the ES-SMPS the number average diameter for the samples were calculated.

Rheological Measurements
The gelling procedure was followed using an MCR-500 (Anton-Paar) rheometer running oscillatory measurements using a CP25-1 cone with a 1° angle and a plate gap of 0.05 mm. The oscillatory measurement setting was set at an amplitude tau of 5 Pa with a frequency of 1 Hz. To try and prevent evaporation of the water in the sample for the prolonged measurements, all measurements were conducted in a semi-closed chamber.

Zeta Potential Measurements
Zeta potential measurements were conducted using a MAL-VERN Zetasizer Nano ZS (ZEN 3600) instrument. The sample chamber in the instrument can be temperature regulated. DTS 1070 capillaries were used with samples being diluted to 2 wt% prior to measuring. The Smoluchowski approximation was used to acquire the zeta potential.

Gel Times
In Fig. 1 the gel times for the 3 different sols are shown. A clear trend is that as the temperature increases the gel time decreases. This is an effect of increased particle diffusion with increased temperature which results in higher kinetic energy of the particles and more collisions between particles. The increased collision rate will results in faster formation of fractals and thus a faster formation of gel. Regarding particle size we note that the smaller particles, see Fig. 2, of CS30-236 show the fastest gel times and also the least spread in gel times with respect to temperature. The trend follows that increased particle size lead to longer gel times with CS40-213 showing the longest gel times and largest variation of gel times with varying temperature. This, again, can be explained by the number of collisions occurring in each gel. Since the wt% of particles of three sols is the same i.e., is ≈ 30 wt% which means that 30 wt% suspension of CS40-213 overall contain less particles compared with the 30% suspensions of other two sols having smaller particles. This in combination with the slower Brownian motion of larger particles will lead to a smaller collision rate in the CS40-213 sol and thus slower formation of fractals and gel. The overall gel time can thus be explained by the collision rate following CS40-213 < CS40-222 < CS30-236 and with temperature 10 °C < 20 °C < 30 °C.
Using the gel times at different temperatures it is possible to calculate the activation energy for the different sols. By plotting the log of gel time vs 1/temperature, where the gel time is in seconds and the temperature in kelvin the activation energy can be calculated from the slope of the curve [18,36]. An example of such a graph can be seen in Fig. S1 in the supporting material. In accordance with the Arrhenius equation the slope of the curve s E a /R where E a is the activation energy in J/mol and R is the gas constant (8.3145 J/ (K*mol). For the CS30-236 particles the calculated apparent activation energy is13.40 kJ/mol, for the CS40-222 sol 23.36 kJ/mol, and for the CS40-213 sol 41.45 kJ/mol. These activation energies are lower than what were reported by A. Amiri et al. [18] for fumed silica and much lower than that observed by A. Ponton et al. [36] for titanium butoxide mainly due to the much higher particle concentrations of silica sols used in this study leading to faster aggregation. Another important difference between colloidal silica and fumed silica can be the number of silanol (Si-OH) groups per unit area and the ratio between silanol and siloxane (Si-O-Si) groups present on the particle surface. It is well known from the studies of pH dependent stability of silica nanoparticles that at certain salt concentration silica sols are least stable at pH 7 but more stable between pH values 4-6 as well as between pH values 8-10 [40]. The predominant view obout the stability at pH < 7 is due to the dominance of so called hairy layer composed of hydrated silanol groups and low number of charged groups. Att pH > 7 there are enough charged groups on silica surface which provide electrostatic stability to the suspension. Although, at pH 7 there are enough charged groups which give electrostatic stability to silica sol but they are fully screened by the counter-ions for example Na + therefore silica sol becomes less stable in the presence of salt. In fumed silica if the less reactive siloxane groups are more than the silanol groups then it will show more stability than the colloidal silica and therefore the activation energy will be higher.

Aggregation Process of Silica Nanoparticles
In Fig. 2 the particle size distributions before aggregation for the three sols are given. Clearly the average particle size distributions for the sols follow CS30-236 < CS40-222 < CS40-213. The size distributions for all the sols are wide stretching over 20-30 nm in difference from smallest to largest particle. In order to be able to analyse the results of the ES-SMPS measurements using Eq. 1 we have calculated the number average size of each distribution as described in detail in ref [41]. For the distributions shown in Fig. 2 we find that the number average particle size for CS30-236, CS40-222, and CS40-213 is 16.82, 21.67, and 33.78, respectively. These values will be used as the starting point or the "zero" values when comparing number averages generated at different times and temperatures during the aggregation. As aggregation proceeds the particle size distributions shift towards larger particles due to the formation of fractals which is exhibited as an increased average particle size.
In Fig. 3 the number averages of particle size for the three different gels at three different temperatures for samples taken at 0, 25, 50, and 75% of the gel times are shown (the time scale of the x axis corresponds to the mentioned percentages and show the time at which the sample was taken after gelling had been initiated). The particle size distributions for the above mentioned measurements are given in supporting material (Figs. S2-S10). The N d from Eq. 1 has been calculated using these number averages of particle size and a d f value of 2.1 assuming DLCA. A collection of the average particle sizes and calculated N d values can be found in the supporting material (Tables S1-S3). The N d value gives the average number of particles in an average size fractal as the gelling proceeds. It has to be pointed out that this method of calculating N d from the ES-SMPS also includes the fraction of un-aggregated particles present in the aggregates as well as in gelled samples. This means that the N d will be smaller than the true N d of the fractals in the sols and this explains the small N d values presented in Fig. 3.
As can be seen in Fig. 3 the fastest formation of aggregates occur at 30 °C followed by 20 °C and 10 °C, respectively. Furthermore, as can be seen by the range on the corresponding x-axis's for plot a-c the smaller particles of CS30-236 (Fig. 3a) show the fastest aggregate formation followed by middle sized CS40-222 (Fig. 3b) and largest sized CS40-213 (Fig. 3c), which is in line with the results of gel time tests.
It is not possible to measure the size distribution at the gel point using ES-SMPS, since this method requires the sample to be liquid. However, using the N d and percentages of gelling as given in Tables S1-S3, it is possible, using linear regression and extrapolation, to calculate the N d value at 100% gelling. These calculated N d values are given in Fig. 4.
There are no clear trends in Fig. 4 with respect to temperature and particle size. It seems that the N d values fluctuate around an average value of 3.01 ± 0.33 for all three sols and all three temperatures. This means that on average the particles in the sols form a fractal of 3 particles at the gel point. Each particle thus impacts on average 2 times before a gel is formed, first to form a fractal of 2 particles and then to form the final fractal of 3. Again it must be stated that the N d value is an average of all particles, including particles that are not part of any fractals and those particles that are part of fractals may contain more than 3 particles. However, the shift in particle size distribution is not massive as can be seen in Figs. S2-S10. The largest particles observed are for the CS40-213 sol and are 120 nm in diameter which, according to Eq. 1, contains 14 particles of an average particle size.
These results agree with that of L. Zhang et al. in that regardless of temperature or particle size the gels seem to follow the same procedure to form a gel [34]. Basically the same types of fractals seem to be formed during the gel formation for all sols. The particle size and the temperature thus only affect the kinetics of gel formation but not the fundamental processes leading to the gel network.
The process of gel formation was also investigated by oscillatory rheology tests and results are presented in Fig. 5.
An increase in the complex viscosity for different sols is in line with our gel time tests, i.e., the largest particles show the slowest increase and the smallest particles show the fastest at all investigated temperatures. Indeed the complex viscosity increase also follows the temperature increase such that faster increase at higher temperatures. An interesting point to note from the rheology data is that a sharp increase in complex viscosity occurs near the gel time. It is highly probable that this sharp increase in viscosity is at the point where a continuous gel network is starting to form. Indeed as we noted in Fig. 4 the critical point at which a gel network starts to forms is reached once an average fractal size of 3 particles has been reached. The temperature and particle size can govern the speed at which these fractals are formed but as it would seem not their size at the gel point. With time the complex viscosity continues to grow as more particles are incorporated into the gel network adding to its rigidity.
It should be noted that the sharp increase of complex viscosity coincide well with the measured gel times for 10 °C and 20 °C. However, for 30 °C the increase in complex viscosity occurs earlier than the corresponding gel times. We expect this to be an effect of sample drying at the edges for this elevated temperature.

Empirical Aggregation Model
By using the data from the gel time tests we have derived an empirical equation (Eq. 2) with the aim of predicting the gel time with respect to temperature and average particle size. The derivation procedure is described as follows. To start with we assume that the gel time follows a linear equation with respect to temperature: GT = kT + m where GT is the gel time in minutes, T is the temperature in kelvin, m and k are constants. The m and k constants will vary with the As can be seen the complex viscosity development is sudden and rapid once the gel point is reached average particle size. To extract k and m we plot the GT vs T for all three sols, see Fig. 6. The linear fits in Fig. 6 is reasonably well for CS40-222 and CS40-213 while for CS30-236 it is not as good due to the similarity in gel time at 283.15 and 293.15 K. When the k and m values for the linear lines are known we plot these vs the average number size of the corresponding silica sol and make a second degree polynomial regression, see Fig. 7.
The polynomial fits for the k and m-values are excellent. When the corresponding equations for the polynomial fit for the k and m-values are inserted in the GT = kT + m we get Eq. 2, where S is the average number size of the sol, T is temperature in kelvin, and GT is the gel time in minutes.

Equation 2
can be used to predict the gel time of silica sols but being empirical in nature it has several limitations. It does not take into account the particle size distribution, the salt concentration, and it does not take into account the effect of differences in surface chemistry of silica sols. All of these are connected to the so called sticking factor i.e. how many collissions between particles lead to the formation of a aggregate. The temperature and size of the particles which has been investigated here are coupled to the spread in Brownian diffusion and thus increases or decreases the number of collisions between particles per time unit. Equation 2 is thus sensitive to the speed of Brownian motion but not on the extent of attraction between the particles during collisions. In order to include the above mentioned processes we need to develop a complex theory which will require a separate thorough theoretical work.
We constructed a 3D graph using Eq. 2 to predict the gel times of sols with similar characteristics as the Levasil sols used in this study, see Fig. 8. Not surprisingly Fig. 8 shows that as temperature decreases the gel time increases. For particle size the trend is the oposite since smaller particles difuse faster and we see faster gel times. Overall it seems that the size of the particles has the larger effect on the gel time while temperature has only a minor effect. However, the effect of temperature increase with particle size.
To test the accuracy of Eq. 2 we have tested the gel time of two sols which were not used to generate Eq. 2. These sols were TM40 and Levasil Cembinder 17 (CB17). The TM40 sol is produced by Grace and has an average particle size of 33.20 nm which is very close to the average particle size of CS40-213, see Table 1. The particle size of TM40 is similar to that of CS40-213 but the particle size distribution is narrower centering around 33 nm, see Fig. S11. The second sol used to test the Eq. 2, CB17, has a much broader particle size distribution compared to TM40 and CS40-213, but the average particle size is smaller than the TM40 sol with particles around 29.87 nm in diameter. The original suspensions of  The colour bar to the right helps with the interpretation of gel times and shows colours corresponding to gel time in minutes TM40 and Cembinder 17 were 40 wt% which were diluted with MilliQ water to achieve 30% suspensions. The diluted suspensions were used for gelling experiments.
In Table 1 predicted gel times by using the Eq. 2 are given. It is not surprizing that the the predicted gel time for CS40-213 agrees very well with the experimentally determined gel time because that data is used to derive Eq. 2. Predictions of gel times of all the original sols are within a few minutes difference than measured gel times and within the temperature range. However, limitation in the ability of of Eq. 2 to predict the gel time becomes clear for sols that were not included in the derivation. TM40 is one of these sols and although it has a particle size distribution close to CS40-213 its experimental gel time is twice than predicted by Eq. 2. The reason for this might be the fact that TM40 is produced by a different company compared to CS40-213, Grace and Nouryon respectively, and differences in the synthesis procedure may have affected the surface chemistry of the nanoparticles. For example any difference in the use of stabilizer (Na 2 O) might affect the effective surface charge which will result in different gel times or as discussed above the number of silanol groups plays role. Furthermore, any presence of organic molecules may have a stabilizing effect on the particles. Therefore, It is difficult to know the exact reasons for the difference in gel time without knowing the exact synthesis methods used in producing these sols.
For CB17 Eq. 2 is more accurate than for TM40 but somewhat underestimates the gel time. It is highly improbable that surface chemistry difference is the reason for this underestimation since CB17 and the CS40/30 sols have the same producer and presumably the particles have been synthesized by using similar protocols. Instead the underestimation most probably is due to the very broad particle size distribution of CB17. The presence of large particles in CB17 increases the gel times in accordance with the effect of particle size that can be seen in Fig. 7. As we have shown here Eq. 2 has its limitations when predicitng gel times of different sols. However, it may still offer information about the general magnitude of the gel time and may thus be of use when these gels are used in industrial applications.

Zeta Potential
To understand how the surface charge of the different silica sols may have affected the gelling we have measured zeta potentials at the different temperatures (Fig. 9). Note that these measurements were conducted without introducing any salt. A clear trend is the decrease i.e., less negative in zeta potential as temperature increase for all silica sols. This is contrary to trends previously reported for zeta potential by A. Amiri et al. where the zeta potential for silica suspensions was unchanged at increasing temperature [18]. This is also contrary to the potentiometric determined surface charge densities [42] as well surface charge determination by second harmonic generation spectroscopy (SHGs) [43]. Both these studies show that surface charge of silica particles becomes more negative at increasing temperature due to increased deprotonation. In a recent study [44] an increased deprotonation of silica at increasing salt concentration but a decrease in the zeta potential was explained by XPS measurements. It was shown that at increasing salt concentration (NaCl) the thickness of Stern layer decreases. Since Zeta potential is a potential at slip plane which often coincide with the Stern layer therefore an increased salt concentration leads to thinner Stern layer and consequently less negative potential. On the other hand the surface charge density in potentiometric titrations is based on protonation/ deprotonation of surface sites. Moreover in potentiometric titration method based on equilibrium between the surface groups and ions in solution whereas zeta potential is calculated from the electrophoretic mobility of charged particles under applied electric field. Equilibrium based processes and mobility under the electric field driven processes are different in their nature. Considering these points we propose the decrease in zeta potential seen at increased temperature is due to the increased accumulation of counterions near a negatively charged surface. The counter-ions in this case will be Na + because Na 2 O is used to stabilize the suspensions at pH 9.5.
Generally it is very difficult to find clear correlation between gel time and zeta potential. For some sols we can make such a correlation. For example in case of CS-40-222 and CS30-236 which show less negative zeta potentials and faster gel times. The larger particles of CB17, TM40, and CS40-213 show higher magnitude of zeta potentials but the differences in gel times cannot be explained by differences in their zeta potentials. For example CB17 show the shortest experimental gel time but have the most negative zeta potential. Although zeta potentials cannot be correlated with the gel times measured for different sols they point toward the important factor that Brownian motion of particles and increased collision frequency at increasing temperature is the dominant factor for gelling of silica nanoparticles.

Conclusions
Gel time measurements of three different silica sols with respect to particle size have revealed that the gel time varies greatly with particle size i.e., larger particles showing much longer gel times than smaller particles. Temperature also has profound effect on the gel time such that higher temperature leading to faster gelling. However, the effect of temperature on gelling was not as pronounced as the effect of particle size.
Using ES-SMPS we could follow the fractal/aggregate formation during gelling. The silica nanoparticles seem to follow the same aggregation procedure regardless of temperature and particle size, which is in agreement with previous research. The average particle fractal was found to contain around 3 particles at the gel point. This low number is due to a large number of particles not being incorporated into the much larger gel network at the gel point.
Using the gel time data we derived an empirical equation to predict gel times of silica sols. Despite the fact the equation is based on polynomial fit to certain gel time data it the gel time of sols produced by Nouryon could be predicted reasonably well. The prediction for a sol produced by Grace showed major discrepancy which we believe to be an effect of the surface chemistry resulting from the synthesis method. Further work is needed in order to incorporate more effects in the model such as salt type, salt concentration, and particle size distribution.