Mechanism of formation and nanostructure of Stober

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Mechanism of formation and nanostructure of Stöber silica particles

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 Nanotechnology 22 275718 (http://iopscience.iop.org/0957-4484/22/27/275718) View the table of contents for this issue, or go to the journal homepage for more

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IOP PUBLISHING

NANOTECHNOLOGY

Nanotechnology 22 (2011) 275718 (9pp)

doi:10.1088/0957-4484/22/27/275718

Mechanism of formation and nanostructure of Stöber silica particles V M Masalov, N S Sukhinina, E A Kudrenko and G A Emelchenko Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow district, Russia E-mail: [email protected]

Received 22 December 2010, in final form 21 March 2011 Published 26 May 2011 Online at stacks.iop.org/Nano/22/275718 Abstract The formation of silica nano- and microparticles has been studied during growth by the modified Stöber–Fink–Bohn (SFB) method. It has been experimentally found that the density and fractal structure of particles vary with size as they grow from 70 to 2200 nm. We propose a model of particle structure which is a dense primary particle core and is composed of concentric secondary particle shells terminating in dense primary particle layers.

Spherical silicon dioxide particles are finding ever increasing applications in different fields of technology including information and communication technologies, medicine and biology, and environmental monitoring [1–3]. Such microspheres can serve as high Q optical resonators [4]. For instance, a Raman laser with an ultra-low excitation threshold [5] and a 1.5 μm fiber laser [6] using silicon dioxide particles have been demonstrated. SiO2 spheres with a closely packed structure (photon crystals) can be used as passive optical devices such as filters, mirrors, switches, and superprisms [7]. Rare earth ion-activated (for instance, Er+3 and Eu+3 ) SiO2 spheres can be used as active elements in nanosensors, microlasers [8–10], and luminescent markers [11]. Mesoporous silicon dioxide spheres infiltrated with magnetic nanoparticles can efficiently absorb DNA particles [12]. Particular attention has been attracted by the investigations of the ‘whispering mode gallery’ of SiO2 spheres owing to their ultra-high Q -factor [5, 13]. In these works it is stated that of all types of resonator, the dielectric spherical resonator is most efficient from the viewpoint of its capacity to confine optical energy inside small volumes over a long period of time. Equatorial light orbits nearby the sphere surface with the longest confinement time (high Q ) cover long distances where interactions occur in fine volume. This sphere feature makes such a resonator most convenient for research into the nonlinear light–matter interaction [5]. Microspheres for such resonators are commonly obtained by laser heat melting of an optical fiber tip [14]. The technique can be used for fabrication of large spheres tens of microns in diameter. Submicron and nanoscale silicon dioxide spheres are grown, as a rule, by tetraethyl orthosilicate (TEOS) hydrolysis 0957-4484/11/275718+09$33.00

using the SFB method [15]. Monodisperse spherical particles of amorphous silica grown by the sol–gel method have a complicated interior fractal-type structure [16–18]. Qualitative data on the density and porosity of matrices from spherical silica particles and their close packing (opal matrices), their structure and related specific surface, characteristic nano- and micropore sizes, and the adsorption capacity of the system are of fundamental importance for modeling various composite materials based on opal matrices. For the closest packing model of rigid contacting balls, their volume fraction makes up 0.7405 of the filled space volume. The apparent density of the opal matrix made up by nonporous spherical particles of amorphous silicon dioxide, the density of which ρp = 2.220 g cm−3 , ρmI = 0.7405ρp = 1.644 g cm−3 , where in the lower indices at ρ ‘p’ stands for particle, ‘m’ for matrix and the superscript indicates the particle structure model number. In this case the opal matrix has a one-level pore system between the particles. The pores can be either tetrahedral or octahedral, their sizes being 0.225 D and 0.414 D , respectively ( D is the sphere diameter). The number of octahedral voids in the opal matrix is equal to and the number of tetrahedral ones is twice the number of the component spheres. The total volume of the tetrahedral or octahedral voids (open matrix porosity) is PmI ∼ 26%. If the structure-forming particles (silicon dioxide spheres) themselves consist of smaller close-packed spheres, their apparent density is ρpII = 1.644 g cm−3 , and that of the opal matrix ρmII = 0.7405ρpII = 1.217 g cm−3 . In this case the opal matrix has a two-level pore system, its theoretical open porosity PmII ∼ 45%. If the secondary particles, in turn, consist of smaller close-packed (primary) particles, the theoretical 1

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Nanotechnology 22 (2011) 275718

V M Masalov et al

Figure 1. Three models of the interior structure of silicon dioxide spherical particles constituting the opal matrix.

apparent density of particles is ρpIII = 1.217 g cm−3 , and the apparent density of the opal matrix is ρmIII = 0.7405ρpIII = 0.901 g cm−3 , respectively. In the three-tier opal matrix the theoretical porosity reaches PmIII ∼ 59%. It was established that the density of silicon dioxide particles in the diameter range of 80–900 nm varies from 1.78 to 1.86 g cm−3 , their porosity 11–15% [19]. Opal matrices obtained by closest packing of particles into a face-centered cubic lattice would have a density of 1.32–1.38 g cm−3 . For spherical silicon dioxide particles in the diameter range of 33–160 nm van Helden and co-workers [20] obtained the density values from 1.6 g cm−3 for smaller and up to 1.8 g cm−3 for larger particles. The density of opal matrices determined by x-ray adsorption [21] was 1.27–1.28 g cm−3 (1.72–1.73 g cm−3 calculated in terms of particle density). In previous studies [22] we obtained different values of opal matrix density: 1.18 g cm−3 for 315 nm particles and 1.07 g cm−3 for 1000 nm particles (1.59 and 1.44 g cm−3 calculated in terms of particle density, respectively). Thus, the literature data on particle density vary significantly and the numerical values do not correspond to the suggested interior structure models (figure 1). Moreover, Garc´ıa-Santamar´ıa et al [23] experimentally found that artificial opals could have an interior pore volume by 4–15% larger than could be expected for closely packed spherical particles. This raised the question of the correctness of considering artificial opals as close-packed fcc structures. In [20] the density of only small (less than 160 nm in diameter) particles was measured and the values obtained appeared to be close to the predictions for the existing models. In [21] the densities of only 250 nm opal particles were measured. The densities (1.27–1.28 g cm−3 ) were somewhat overestimated since the samples were saturated with primary particle suspension in order to correct the contrast of the sample’s refraction index. In [19] the density of large particles (up to 900 nm) was measured and nanopores inside the particles revealed. However, no data have been found on the diameter dependence of particle density. The overestimated density, as compared to the model, could be due to the difficultto-verify assumption about complete C18 -chain filling upon hydrophobization of particles. Based on that assumption, the authors of [19] made the final calculations of the density values. In [22] the densities were changed only for two particle

sizes. For 315 nm particles the density was close to the model predictions (1.18 g cm−3 ), and for 1000 nm particles the density turned out to be underestimated (1.07 g cm−3 ). Therefore, analysis of the literature data revealed that no systematic studies have been made of the density (and porosity) of the colloid SiO2 particles synthesized in identical conditions over a wide size range. We have measured the density and porosity of the opal samples synthesized in identical conditions over a wide size range and calculated the density and porosity of individual particles. There are two major models explaining the particle SiO2 formation process by the SFB method. The first is the monomer addition growth model, which involves nucleation upon exceeding the supersaturation limit and nucleus growth by condensation of monomeric silicic acid on the surface of the existing particles (nuclei) [24, 25]. This growth mechanism results in the formation of internal structure of particles corresponding to model I shown in figure 1. The second model implies the mechanism of controlled aggregation of sub-particles, several nanometers in size (aggregation growth model) [26, 27]. This growth mechanism corresponds to models I and II of the internal structure of the particles shown in figure 1. The particle growth mechanism changes at a later stage during the TEOS hydrolysis reaction, and, hence, particles grow solely by condensation of monomeric and dimeric silicate units on the particle surface. The point at which the growth mechanism changes is determined by the overall reaction conditions [28, 29], and hence the particles can exhibit a diverse microstructure depending on the method of their fabrication. Such a change in the growth mechanism leads to the formation of a dense silica layer on the particles’ surface. As a result, the particles have a smooth surface. The micrograph of a dense layer on the particle surface is presented in the paper by Rybin et al [30]. SiO2 particles can have different structure and density depending on their size [22]. In our previous paper [31] we suggested a structural model of ‘large’ ( D 1000 nm) opal particles consisting of a central core made up of primary particles (model II, figure 1) and an external shell made up of secondary particles (d < 100 nm) which, in their turn, consist of primary particles (model III, figure 1). The central core and secondary particles are identical in density, yet, in the external shell there occurs an additional system of pores 2


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(between secondary particles). Hence, the core has a one-level system of pores ρcore = ρpII = 1.644 g cm−3 , and the shell is a two-level pore system consisting of pores between primary particles and those between secondary particles ρshell = ρpIII = 1.217 g cm−3 . According to the aggregation growth model, formation of silicon dioxide particles in the Stöber process is due to aggregation of primary particles of molecule bound silica, its diameter d = 5–10 nm, formed as a result of TEOS hydrolysis. However, upon multistage particle growth there is a diameter limit ( D ∼ 350 nm) above which growth by aggregation of primary particles is terminated [32]. When reaching a certain critical ratio d/D , primary particles cannot overcome the barrier of electrostatic repulsion of the ion atmosphere around the growing particle and they start forming new smaller diameter particles [33]. On reaching some critical diameter, the secondary particles can join the growing ‘seed’ particle. We have studied the interior nanostructure of SiO2 particles forming the opal matrix, determined their size-related density and porosity, investigated the mechanism of particle formation during multistage TEOS hydrolysis in the presence of ammonia and developed a structural model of such particles. Silicon dioxide particles were obtained using the modified SFB method by TEOS hydrolysis in alcohol–water solution in the presence of ammonia hydroxide (50 vol.% ethanol; 1.0 M ammonia). Particles from 70 nm to 2.2 μm in diameter were obtained by multistage growth to specified sizes using particles obtained at the previous synthesis stage as seeds for further growth. To this end, part of the suspension obtained at the previous stage was dissolved in an appropriate volume of alcohol–water–ammonium mixture of the same composition and new added portions of TEOS. The added amount of TEOS ensured an increase of particle diameter by 5–25%. Silicon dioxide particles of different diameter from 70 nm to 2.2 μm were used to form opal matrices by the following sequential operations: particle sedimentation, precipitation drying at room temperature, at 150 ◦ C (120 h) and, for some samples, annealing at 600 ◦ C (4 h). Drying at 150 ◦ C ensures removal of physical water from the opal matrix structure whereas annealing at 600 ◦ C allows removing chemically bound water (in the form of hydroxyl groups) and the remains of organic matter from the matrix without significant changes of the porosity of the structure which results in its relative strengthening. The density and porosity of the samples were studied by hydrostatic weighing which involved determination of the specific weight of the dry sample (m), the specific weight of the air-weighed liquid-saturated sample (m 1 ), and the specific weight of the liquid-saturated sample weighed in the same liquid (m 2 ). The effective density (ρef ), apparent density (ρap ) and open porosity (Po ) of the opal matrices were calculated by the formula:

ρef =

Water, methanol, ethanol, propanol, toluene, benzene, and carbon tetrachloride were used as pycnometric liquids. Liquid filling of the opal matrix was controlled by the changing weight of the filled matrix depending on saturation time and the value ρef calculated by the above formula. Attainment of a constant weight value and approximation of the value ρef ∼ 2.22 g cm−3 (the value of true amorphous silica density) was the criterion of completeness of liquid filling of the opal matrix. As the initial (on drying at ∼150 ◦ C) opal matrices were saturated with relatively large molecule liquids (ethanol, propanol, toluene, benzene, and carbon tetrachloride), the increase of the ρef value reached its maximum in the interval 1.71 ± 0.06 g cm−3 over the whole matrix particle size range (70–2200 nm). Such underestimated values of the effective matrix density compared to the true amorphous silica density (2.22 g cm−3 ) indicate that the opal matrix pore space (interglobular pores) is inaccessible for such liquids. The matrix porosity values calculated by the experiments with large molecular liquids data were ∼35% and the same over the whole matrix particle size range. The value of numerical porosity exceeds significantly that of theoretical porosity for the model of closely packed nonporous spheres (26%). This is explained by the presence of stacking faults of silicon dioxide particles in the real matrix and partial penetration of large molecule liquids into the surface layer of the spherical matrix particles. Figure 2 shows the dependence of apparent density of opal matrices on silicon dioxide sphere diameter. Since the matrices were not subjected to high temperature treatment (rather dried at ∼150 ◦ C), their structure and the micro- and nanostructure of their forming particles did not suffer any changes compared to the initial ones. As the matrices dried at ∼150 ◦ C were saturated with water, the increase of the ρef value reached its maximum values of 2.17±0.02 g cm−3 during 7–8 h. The deviation of the effective density from 2.22 g cm−3 is accounted for by the presence of organic matter and an insignificant amount of water remained upon drying of the pore space volume. Complete water saturation of the matrices was achieved for approximately the same time irrespective of the size of the matrix-forming silicon dioxide globules. From figure 2 it is seen that the opal matrices made up by small particles have approximately the same density (1.17– 1.19 g cm−3 ). This density is close to its theoretical value for closest packing of spheres for model II of the interior particle structure (1.217 g cm−3 ). However, as soon as the particle diameter has reached its critical value (between 300 and 400 nm), the opal matrix density decreases and reaches its constant value (∼1.05 g cm−3 ) at a particle diameter of ∼1200 nm. The total decrease in density was about 11%. Such systematic decrease in particle density with increasing diameter cannot be explained by the disordering process caused by dispersion of sphere sizes and other defects. To determine the effect of the degree of disorder of packed silicon dioxide particles on the density of the opal matrix, opal samples were prepared by a special technique. In the upper part of the opal matrix (a) the deviation of the particle diameter from the mean value is ±3%, and at the bottom part

mρL mρL ; ρap = ; m − m2 m1 − m2 m1 − m Po = × 100% m1 − m2

where ρL is the density of the pycnometric liquid. 3


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Figure 2. Experimental dependence of opal matrix apparent density on the size of the constituent particles of silicon dioxide (curve 1). The dotted line (curve 2) shows the same dependence calculated for particles of diameters exceeding 370 nm, provided the ratio of secondary and primary particles sharing the shell is constant. The additional axis (right) shows the densities of silica particles, corresponding to the values of opal matrix densities calculated for fcc particle packing.

diameter from ∼70 to ∼2200 nm. The experimental data of opal matrix density measurement (figure 2) are well described by the sigmoid logistic function

y=

A1 − A2 + A2 1 + ( xx0 ) p

(1)

where y = ρm , A1 = 1.185 g cm−3 , A2 = 1.051 g cm−3 , x 0 = 470 nm, p = 3. The values A1 and A2 in equation (1) are the maximum and minimum values of the experimental densities of the opal matrices made up by the smallest and largest particles, respectively, in the diameter range in question. The density value A1 (∼1.185 g cm−3 ) is close to the theoretical density of opal matrices provided matrix particles have a one-level pore system (and opals themselves have a two-level pore system, accordingly). The density ∼1.6 g cm−3 of small (d 200 nm) particles, calculated from the density of opal matrices is close to the theoretical particle density (ρ = 1.644 g cm−3 ) of particles with a one-level pore system (model II, figure 1). The deviation from the theoretical value of density (model II) for such particle can be attributed to the total disordering value of packages of both particles in the opal matrix, and the primary particles as well as their constituents. Figure 4 shows the selfassembled packing of 400 nm diameter particles in a large particle, which exhibits a deviation of the particle packing density from closest packing. Apparent opal matrix density A2 (∼1.05 g cm−3 ) composed of ‘large’ particles (over 1200 nm) is essentially different from both the theoretical density value of model II (1.217 g cm−3 ) and that of model III (0.901 g cm−3 ). The particle shell appears to be denser than follows from the closest packing model for secondary spherical particles. The density of opal matrices composed of particles whose diameter exceeds

Figure 3. Opal matrix with almost completely ordered sphere packing (sector (a)) and disordered packing (sector (b)). (This figure is in colour only in the electronic version)

it is ±17%. Sector (b) exhibits a highly disordered packing of particles, and sector (a) a highly ordered packing with a minimum number of defects. This is confirmed by electron microscopy studies and visual observations. The top of the opal matrix shows unusually large colored columns (pseudosingle crystals) ranging in size from 3 to 8 mm. The density of samples cut out from sector (a) was ρap = 1.17 g cm−3 , and that of samples from sector (b) ρap = 1.15 g cm−3 , the average particle size was 280 nm. The density of maximum disordered samples (figure 3, sector (b)) decreases by only ∼2% compared to almost completely ordered sphere packing (figure 3, sector (a)). Hence, the decrease in density by 11% with increasing diameter of particles is due to decreasing density of opal particles during their multistage growth. From the experimental data shown in figure 2 it follows that in the course of multistage growth the particle density changes from ∼1.6 to ∼1.4 g cm−3 with increasing particle 4


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shell’ model can be calculated by the formula

ρm = 0.74[nρcore + (1 − n)ρshell ], where n is the fraction of the particle volume occupied by the core, ρcore , the core density, and ρshell the shell density. Since core fraction volume n is the ratio between the core volume (Vcore ) to the whole particle volume (V p ): n = Vcore /V p = (Dcore /D p )3 . Upon substitution and transformations equation (1) can be written as

ρm =

0.74(ρcore − ρshell ) D

p ( Dcore )3

+ 0.74ρshell .

(2)

‘Small’ size particles have no external sphere made up by secondary particles (n = 1). The density of such particles is equal to that of the core, and the apparent density of the opals obtained as a result of their closest packing is equal to 0.74ρcore . Since the increase of particle volume is proportional to the increase of cubed particle diameter, the core volume fraction in the particle decreases rapidly with increasing diameter. For instance, the core volume of 350 nm diameter particles is only 1.75% of the volume of the particle 1350 nm in diameter. Thus, with increasing diameter (n → 0), the density of ‘large’ particles approaches that of the shell (ρshell ). In figure 2 the dashed line represents the theoretical curve of variation of the apparent density of opal matrices as a function of the size of constituent particles (at D p > 370 nm). The curve calculated by equation (2) with allowance made for the experimental values ρcore = 1.185 g cm−3 and ρshell = 1.051 g cm−3 is an exponent with its origin in the point corresponding to the apparent density of the opal matrix made up by ‘nuclei’ (particles with a one-level pore system, model II) and exponentially approaching the density of the opal matrices made up by particles with densities close to (approaching) the density of the shell (with a two-level pore system, model III). Figure 2 shows the theoretical curve built for the particle core diameter Dcore = 370 nm obtained on the basis of the sigma dependence describing the experimental points. As it is seen from figure 2, for constant shell density, the experimental particle density data are well described by the theoretical curve of variation of opal matrix density with increasing number of constituent shelled particles (at D p > 370 nm), i.e. for the case when the shell density is independent of the number of particles. The shell density, however, can depend on the amount of TEOS added to the system during particle growth. Thus, stepwise addition of TEOS to the solution during synthesis of silicon dioxide colloid particles gives rise to a sphere-like structure in the form of spherical concentric shells. Each growth stage (cycle) results in the formation of a grown shell with a one-or two-level system of pores, their thickness determined by the TEOS mass, which terminates in a thin dense layer of SiO2 primary particles. This layer smoothes the two-level shell surface so that at the end of each cycle the sphere surface looks smooth with a roughness of several nanometers.

Figure 4. Micrograph of a coupled (twin) silicon dioxide microparticle of size ∼10 μm × 20 μm composed of ∼400 nm particles. One can see a deviation of particles’ packing density from closest packing.

1200 nm remains constant. This implies a constant density of each new layer formed at a subsequent particle growth stage. The opal matrix density value for large particles (1.05 g cm−3 ) suggests that the particle shell density (and each additional layer) is ρshell = 1.05/0.74 = 1.42 g cm−3 . However, for the secondary particle shell model the shell density must be significantly less (ρmII = 1.217 g cm−3 ). Hence, each additional shell layer has an additional amount of dense matter. It would be logical to assume that this holds for primary particles which, along with secondary particles, form each new growing layer. This is confirmed by the experimental observation of the specific morphology of the shape of silicon dioxide particles during multistage growth: SiO2 particles always had a ‘smooth surface’ at the onset as well as the end of the process. The term ‘smooth surface’ implies roughness corresponding to primary particle size (5–10 nm). Roughness corresponding to secondary particle size was observed only upon interruption of the growth process (see figure 6 below). Besides, this suggests that primary particles always participate in the formation of final shell layers. The sigmoid logistic function describing the experimental data (figure 2) has an inflection point of the S-shaped curve, its second derivative function being equal to zero. The value of the abscissa in this point corresponds to the particle core size and is about 370 nm. Point x 0 stands for the argument corresponding to the average value of the function. The physical meaning of parameter x 0 lies in the fact that x 0 corresponds to the diameter value of particle D0 whose core volume fractions (Vcore ) and spherical shell fractions (Vshell ) equal (Vcore = Vshell = V p – Vcore ), where V p is the particle volume. Hence, Dcore = 1.26 D0 . At D0 ∼ 470 nm the core diameter Dcore ∼ 370 nm which agrees with the theoretical predictions of the onset of particle formation at 350 nm. Given the closest packing of structure-forming particles, the apparent density of the opal matrix for the particle ‘core– 5


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Figure 5. Silicon dioxide particles subject to ultrasound treatment together with diamond powder. The diameter of secondary particles is 40 nm.

D = κρ D0 (V /V0)1/3 . The maximum value of the correction factor κρ in the particle diameter range from 70 nm to 2 μm is 1.04. Two series of experiments were carried out to confirm the described colloid SiO2 particle model. In the first series, attempts were made to open up the sphere shell by ultrasound bath treatment of a suspension containing a mixture of colloid SiO2 particles and diamond powder. The sizes of SiO2 particles and that of diamond powder were 1800 nm and 2000 nm, respectively. Figure 5 shows scanning electron microscopy (SEM) images of several particles. One can see diamond-cut segments of SiO2 spheres with interior secondary particles and an exterior thin dense layer, where the particle size is in the SEM resolution limit. Using high resolution transmission electron microscopy (HRTEM), the authors demonstrated the presence of a smooth dense amorphous microstructure layer on the SiO2 microsphere (315 nm) surface [30]. The method of interrupted particle growth was used to study the mechanism of formation of ‘large’ spherical SiO2 particle shells in the second series of experiments. To this end, the suspension was sampled at a certain stage of particle growth upon adding a new TEOS portion at time intervals (1, 5, 10, 30, and 60 min). Each sample was placed into a test tube with ethanol and the silicon dioxide particles were precipitated by centrifugation. In this way the particles were separated from the unreacted TEOS and free primary SiO2 particles in the sample of the reaction mixture. Thereafter the precipitation was dispersed in pure ethanol and sampled for SEM investigation. Figure 6 shows SEM images of particles obtained during their growth. It is seen that the growth process starts as the initial particle is joined by secondary particles 30–40 nm in size, the initial and final particles exhibiting a smooth surface with roughness of the order of primary particle size (5–10 nm). This enables us to conclude that at each growing stage a new particle layer is formed in two stages: first a layer (several layers) is formed by secondary SiO2 particles which are then covered by primary particles forming a smooth particle surface. It can be assumed that molecular silica also participates in the formation of the smooth surface. Such cycle growth may be due to discrete addition of TEOS into the solution in the course of synthesis. During hydrolysis there is a regular decrease in

It is also important to establish the share of primary particles in the shell layers and their distribution throughout the sphere volume. There are two extreme options of primary particle distribution in the shell: either all primary particles form the shell surface layer or part of them is inside the pores between secondary particles. Geometric consideration of the second (general) variant leads to the following formula of shell density: 1−m ρpsp , ρshell = mρppp + 1−x where ρshell = 1.42 g cm−3 is the particle shell density, m the volume fraction of packed primary particle layers in the shell, x the volume fraction of primary particles inside pores between secondary particles in the shell, ρppp = 1.6 g cm−3 the densities of packed primary particles, and ρpsp = 1.185 g cm−3 the densities of packed secondary particles, respectively. For the first variant of primary particle distribution (all particles in the surface layer) x = 0, then m ∼ 0.57. If all the primary particles are inside the pores between the secondary particles in the shell (x = 1), then m ∼ 0.15. It can be assumed that the volume fraction and the real distribution of primary particles in the shell are between these extreme variants. The growth of silicon dioxide particles by multistage modification of the SFB method revealed cases of deviation of the finite diameters of balls from those calculated by the formula D = D0 (V /V0 )1/3 , where D is the diameter of the growing ball, D0 the nucleus diameter, V0 the TEOS volume spent for nucleus formation, V the total TEOS volume introduced into the system, including V0 [16], when the diameter of particles exceeding 1000 nm was calculated using particles of diameter 300 nm as those of diameter D0 . For particle sizes from 1 to 2 μm, the deviation was 40–80 nm. This is explained by the fact that the formula does not allow for the difference in density between ‘seed’ and finite particles. In cases where the sizes of the ‘seed’ (D0 ) and finite particle (D) refer to size ranges of less than 300 nm or over 1200 nm, such deviation from the calculated value is negligible or absent. To calculate the value of deviation, the formula should include a correction factor κρ = (ρ0 /ρ)1/3 , where ρ0 is the density of the initial particle and ρ the density of the finite particle. Hence, the formula for calculation of the diameter of the finite particle based on the volume of TEOS, takes the form 6


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reveal the inner nanostructure of silicon dioxide particles grown by SFB multistage modification. The measured specific surface areas (SBET ) of opals with silicon dioxide ball diameters of 260 and 1800 nm were 14 and 2 m2 g−1 which is appreciably less than could be expected taking into account the porosity of the silicon dioxide particles per se. This can be explained by the presence of dense outer layers on the surface of each concentric shell which prevent nitrogen molecules penetrating into the particle [34]. Based on the analysis of the literature and our research data, we suggest the following mechanism of particle formation by the multistage SFB method (figure 7). The mechanism described is determined by the periodicity of multistage particle growth when particles obtained at the previous growth stage are used as ‘seeds’ for the next stage. Introduction of tetraethoxysilane into the reaction medium and subsequent TEOS hydrolysis and condensation reactions give rise to silicon acid monomers. When the concentration of Si(OH)4 in the solution exceeds 0.02–0.03% (depending on the pH of the medium), there occurs polymerization of monomers. At first the process yields low-molecular polymers and then high-molecular ones which, given subsequent condensation and formation of extra siloxane bonds, collapse [35] to form nuclei of future particles 1–2 nm in size (figure 7). The density of these particles corresponds to that of molecular bound amorphous silica (2.22 g cm−3 ). Next the nuclei increase in size owing to silica monomer and polymer bonding to their surface (LaMer growth pattern) until their diameter reaches a critical value of 5–7 nm (primary particles), following which they start aggregating to form a growing SiO2 particle (aggregation growth pattern). The process of primary particle formation continues uninterruptedly as long as the concentration of silica in the solution exceeds the value of supersaturation for SiO2 nucleation. However, the concentration of TEOS and that of intermediate hydrolysis products decreases in the course of the chemical reaction. As a result, the number of primary particles formed per time unit decreases at the final hydrolysis stages, and silicon oxide monomers and dimers hydrolyzed to various extents start joining the growing particle. Thus, the growth cycle ends in the formation of growing particles of a dense silicon oxide layer on the sample surface which ensures a ‘smooth’ particle surface. Given a new TEOS portion, the

Figure 6. Micrographs of SiO2 particles in the course of growth from 1 to 1.3 μm: (a) initial particles, (b) 1 min, (c) 5 min, (d) 10 min, (e) 30 min, (f) 60 min after the introduction of the next TEOS portion into the reaction system. The scale bar is 500 nm for all images.

TEOS concentration so that at the end of the cycle the TEOS content is insufficient to form secondary particles. At that point there are only primary particles and maybe molecular silica left in the suspension to form the SiO2 particle surface. It has been previously shown [34] that Brunaumer– Emmet–Teller (BET) measurements of opal matrices do not

Figure 7. Particle growth diagram during multistage growth by TEOS hydrolysis in alcohol–water–ammonia medium.

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increasing diameter. Three different sections were found on the density–diameter curve. For particle diameters in the range of 70–370 nm the density changes only slightly, its average value being 1.58 g cm−3 . In the diameter range of 370–1200 nm the particle density decreases almost exponentially down to 1.42 g cm−3 . In the third section (particle diameters over 1200 nm) the particle density changes slightly, approaching the asymptote 1.43 g cm−3 . In the inflection point of the S-shaped curve the sigmoid logistic function describing the experimental data determines the particle core size of approximately 370 nm which is in agreement with the theoretical predictions. It is shown that stepwise addition of TEOS to the solution during synthesis of silicon dioxide colloid particles gives rise to a sphere-like structure in the form of spherical concentric shells (sphere shell model). Each growth stage (cycle) results in the formation of a grown shell with a two-level system of pores, their thickness determined by the TEOS mass, which terminates in a thin dense layer of SiO2 primary particles. This layer smoothes the two-level shell surface so that at the end of each cycle the sphere surface looks smooth with a roughness of several nanometers. The developed model of sphere structure as spherical concentric shells was confirmed by the investigation of the formation mechanism of ‘large’ spherical SiO2 particles during their multistage interrupted growth. It is shown that the growth process starts as the initial particle is joined by secondary particles 30–40 nm in size and proceeds in two stages: first a layer (several layers) is formed by secondary SiO2 particles which are then covered by primary particles forming a smooth microparticle surface. Opening the sphere shell by ultrasound bath treatment with the use of diamond powder confirmed the presence of secondary particles under the dense exterior layer. Therefore, the experiments performed have proved the ‘three-level hierarchical’ interior structure of submicron spherical silicon dioxide particles obtained by hydrolysis of TEOS. The presence of a central core was established and the mechanism of formation of ‘tertiary’ particles during their multistage growth determined. It has been shown that particle nanopores are accessible for water (kinetic diameter 0.264 nm) and inaccessible for large molecule liquids. The ‘sorption capacity’ of opal matrices is determined by voids between structure-forming silicon dioxide particles. The open matrix porosity for large molecules (over 0.45 nm) liquids is 35–36%. Implantation of active elements, whose size exceeds that of the water molecule, into the particle is possible only at the stage of particle synthesis as a result of their capture during particle growth. Analysis of the literature data showed that despite the significant spread of the particle density values obtained in different studies, some of the data agree with the predictions for the model suggested, and the deviations in other works could be due to the differences in the preparation of the samples. Thus, the systematic investigations of the density and porosity of the SiO2 particles synthesized in identical conditions enabled us to gain a more penetrating insight into the internal structure of particles and suggest a general model of particle formation under the conditions of multistage Stöber particle growth.

Figure 8. Schematic representation of the shell-like model of the internal structure of silicon dioxide particles grown by the multistage SFB method.

particles continue their growth by the above mechanism. All the growth processes are repeated. The number of primary particle layers terminating in a thick silicon dioxide layer is equal to the number of growth stages. This continues until the growing particle reaches a critical diameter of 350– 370 nm. As particles reach their critical diameter, they generate a double electrical layer with sufficient potential to counteract the penetration of primary particles from the reaction medium to the growing particle surface. From this point on, for primary particles it becomes more thermodynamically efficient to aggregate into newly formed (secondary) particles than join the surface of the growing particle. Reaching 30–40 nm, secondary particles become capable of overcoming the energy barrier and joining the growing silicon dioxide particle. This initiates the formation of the growing particle shell, the density of which is less than that of the ‘nucleus’ (particles 350– 370 nm in diameter) owing to the additional system of pores between the secondary particles. However, at the final stages of TEOS hydrolysis, the number of newly formed secondary particles decreases at each growing stage as a result of the decreasing concentration of the primary particles. The remains of TEOS hydrolysis and the rest of the non-aggregated primary particles complete formation of the growing particle surface overcoming its energy barrier. As a result, upon completion of the growing cycle, the silicon dioxide particles exhibit a regular spherical form and a ‘smooth’ surface due to the dense surface silica layer. Figure 8 shows a schematic representation of the shell-like model of silicon dioxide particles grown by the multistage SFB method. The dense surface layer is not solid: it has pores and channels, yet, their sizes are sufficient for penetration of molecules small compared to those of water (kinetic diameter dk = 0.264 nm) though they prevent penetration of larger molecules, the smallest of them being methanol molecules (dk = 0.363 nm). On thermal treatment these voids and channels are the first to collapse, isolating the internal pore space of the particles. The investigation of the porosity of the opal matrices composed of spherical silicon dioxide particles of different diameter (from 70 to 2200 nm) has revealed that the density of silicon dioxide particles obtained by multistage growth depends on their diameter and decreases regularly with 8


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Acknowledgments

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This work was supported by the Fundamental Research Program of Presidium RAS No. 21 ‘Basics of Fundamental Nanotechnology and Nanomaterial Research’.

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