From Molecules to Particles: Quantum-chemical View Applied to Fumed Silica

Journal of Nanoparticle Research 1: 71–81, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.

From molecules to particles: Quantum-chemical view applied to fumed silica E. Sheka1 , V. Khavryutchenko2 and E. Nikitina3 Russian Peoples’ Friendship University, Moscow, Russia; 2 Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Kiev, Ukraine; 3 Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, Russia

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Received 17 July 1998; accepted in revised form 15 December 1998

Key words: atomistic simulation, flame-generated nanoparticles, vibrational spectrum, surface passivation

Abstract An extended quantum-chemical study has been performed to examine the flame-generated silica formation at the atomic level. Starting from a set of free molecules, condensation was shown to be a non-barrier and energetically favorable. The coalescence of the formed bare-surface protoparticles can be prevented by particle surface passivation in the course of the hydroxylation reaction. The protoparticle size is determined by a balance of the fusion and hydroxylation/dehydroxylation processes. The main factors responsible for the inherent amorphicity of the fumed silica have been determined.

Introduction Pyrogenic or fumed silica is a product of the reaction between silicon tetrachloride, air, and hydrogen in a premixed flame (e.g., arcs, plasmas, and electrically augmented flames). For years, plant engineers have known that they could vary the size of flamegenerated particles and their aggregates by varying raw material concentration and high-temperature residence time. However, until now, a lack of a full understanding of the processes by which fine particles are formed in flame is a serious restraining factor for broadening the application of flame technology in general, in spite of the fact that the problem has attracted serious attention for years, and a number of fundamental findings have been disclosed. The most elaborated concepts are based on the thermodynamics of combustion (Ulrich, 1971; Ulrich & Milnes, 1976; Ulrich & Subramanian, 1977; Ulrich & Riehl, 1982; Ulrich, 1984). Three microscopic phenomena were suggested to govern particle formation: chemical reaction, nucleation, and

Brownian motion. As confirmed by many experiments, the chemical reaction related to fumed silica starts from converting all of the silicon present to gaseous silica prior to condensation. As a first step in estimating the nucleation rate, the critical radius of particles which are stable, was found to be less than that of a single molecule (Ulrich, 1971). This seemingly absurd result arises from the fact that the condensation driving force in the fluid silica environment is extremely large. Even a hundred times reduced gas phase concentration resulted in merely doubling critical nucleus size. The finding is evidence that any silica particle (bimolecular or larger) is stable under ambient flame conditions. The reaction between silicon tetrachloride, air, and hydrogen is almost thermally neutral (−7 cal/g mol) (Ulrich, 1971), while the production of liquid silica via the same reaction is highly exothermic (−140 kcal/g mol). Therefore, condensation is the source of the overwhelming heat effect in this reaction. Since exothermicity is a necessary characteristic of the combustion process, condensation is an essential step in the flame reaction. Particles thus obtained, called

72 as protoparticles must be multimolecular (Ulrich, 1971). According to experimental observations (Ulrich, 1984), during cooling, the particles continue to collide, because of Brownian motion, thus forming aggregates composed of particles, which, however, are not glued by fusion bonds. Collision among the aggregates stimulates them to be held together as well, although by more weaker inter-aggregate interaction just forming agglomerates. The general picture presented above has been largely accepted by researchers and technologists engaged in the fumed silica production for more than two decades, although a lot of questions still remain unanswered. Among them are the following: 1. What is a protoparticle in reality and what are its main atomic characteristics? 2. What extra factors and /or processes influence the protoparticle size? 3. Is Brownian motion the only factor governing the particle collision /interaction? An attempt to answer these questions from the viewpoint of modern computational chemistry is given in the current paper which is organised in the following way. Section 1 presents general grounds of the computational study performed. Section 2 is devoted to the reaction of a protoparticle formation involving a quantitative description of the object at atomic level as well as the verification of models used by comparative study of the calculated and experimental vibrational spectra. Particular attention is given to the valence state of both surface and interior atoms. Hydroxylation reaction occurring on the protoparticle surface is considered in Section 3 as a process both removing the valency deficiency of the protoparticle surface atoms and controlling the particle size. The interaction between protoparticle with bare and OH-terminated surface is considered in Section 4. The Conclusion summarises the essentials discussed in the paper.

1. Basic methodology Computational tools. A computational study has been performed by using a standard quantum-chemical approach based on the PM3 (Stewart, 1989) semiempirical technique. The approach makes allowance for determining space and electronic structure of the

object under study, establishing bonding between atoms, exhibiting chemical activity of the atoms via their valence state. The calculation have been carried out on two-processor PentiumPRO PC by using a software package DYQUAMOD (Khavryutchenko & Khavryutchenko Jr., 1993) incorporating both a quantum-chemical (QCh) software enabling computations of superclusters with up to 1000 atoms, and a COSPECO software (Khavryutchenko, 1990) particularly designed for vibrational spectra calculations of large systems. Model of a protoparticle. As follows from the Introduction, a supersaturated liquid consisting of silica molecules forms the starting point for the silica protoparticle formation. Therefore, a set of molecules dispersed in space seems to be an appropriate model for the study. To arrange the starting configuration, silica molecules were placed forming a piece of a ‘cubic lattice’ with intermolecular distance of 7 Å. Two sets were studied consisting of 27 and 64 molecules, respectively. How a combustion reaction is considered. As known, a standard QCh computation consists in seeking total energy minimum of a model under study, thus optimising its atomic structure, while simulation of chemical reactions requires particular techniques. However, as said in the Introduction, a peculiarity of the combustion reaction considered is that it consists of two inseparable parts, one of which concerns the conversion of silicon atoms into silica molecules while the other, which is the main topic of interest, is related to the condensation of the molecules. According to the kinetic approach explored for the reaction description from the thermodynamic viewpoint (Ulrich, 1971; Ulrich & Milnes, 1976; Ulrich & Subramanian, 1977; Ulrich & Riehl, 1982; Ulrich, 1984), the condensation was stimulated by the molecular collisions due to Brownian motion. Obviously, not the motion itself but intermolecular interaction is responsible for the condensation. The collisions just provide conditions when the interaction is the most active. In its turn, QCh calculations are the exact tool to investigate a transformation of a system subjected to any kind of interaction, including intermolecular one. Therefore, a final result of a QCh seeking of the energy minimum for a set of silica molecules subjected to intermolecular interaction would well simulate the condensation constituent of the combustion reaction considered.

73 2. What a silica protoparticle looks like

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2.1. Structure and atomic properties Figure 1 presents the result of the first simulation related to a set of 27 silica molecules. Freely spaced in starting position, the units form a densely packed body when the structure optimisation is over. To characterise the structure, a distribution of interatomic distances, R, is shown in Figure 2a. When plotting, the data were broadened by a Gaussian exp(−R 2 /2λ2 ) with a broadening parameter λ = 0.05 Å which is accepted accuracy in amorphous solid structure determination. Chemical behaviour of the system is presented by the distribution of atomic coordination numbers (ACN) in Figure 3a. The latter is determined as the number of the nearest neighbouring atoms chemically connected with the studied one. As seen from Figure 2a, the final structure is quite disordered compared with the distribution functions in Figure 2c characteristic for the regular cristobalite-like structure. The structural disorder is complemented by a peculiar ‘electronic disorder’, or by a ‘heterogeneity’ in the valence state of both silicon and oxygen atoms as seen from Figures 3a and c. In the case of the regular crystalline structure, only one valence state of each atom is observed, corresponding to the standard

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Figure 1. A set of 27 silica molecules subjected to the energy minimization. a. Starting configuration. b. Final configuration.

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Figure 2. Distribution of interatomic distances. a. Set of 27 silica molecules. b. Set of 64 silica molecules. c. Fragment of cristobalite-like crystal containing 48 SiO2 units.

coordination number equal to either 2 or 4 for oxygen and silicon atom, respectively. Contrary to this, three valence states for the same atoms are exhibited in the conglomerates formed which are characterised by a set of coordination number (1, 2, and 3 for oxygen atom as well as 3, 4, and 5 for silicon one). Atom-by-atom analysis has revealed that standard saturated oxygen and silicon atoms with the coordination number 2 and 4, respectively, are the part of the inner structure of the body. On the other hand, undersaturated O atoms with the coordination number 1 and Si atoms with coordination number 3 are predominantly spread over the particle surface. The remainder oversaturated O and Si atoms with the ACNs 3 and 5, respectively, can be regarded as inner ‘structural defects’. Similar results have been obtained for the second system consisting of 64 silica molecules, as shown in

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Figure 3. Distribution of atomic coordination numbers. a. Set of 27 silica molecules. b. Set of 64 silica molecules. c. Fragment of cristobalite-like crystal containing 48 SiO2 units.

Figure 4. The above-discussed characteristic distributions are presented in Figures 2b and 3b. A clearly seen qualitative similarity of both systems is observed. Since the studied sets differ more than twice in the atom numbers, the similarity found may indicate that the observed structural and electronic disordering should be attributed to fundamental characteristics of the systems studied and should be expected in a real case as well. The study of both systems convincingly revealed that the condensation of silica molecules was a nonbarrier, energetically favourable process. The finding well supports the suggestion brought forward previously (Ulrich, 1984) that the condensation is an essential step of the combustion reaction. Therefore, the condensed structures presented in Figures 1b and 4b may be surely attributed to model protoparticles (27-Si and 64-Si particles below) formed during the

Figure 4. A set of 64 silica molecules subjected to the energy minimisation. a. Starting configuration. b. Final configuration.

reaction. Hereinafter they will be referred to as baresurface protoparticles. 2.2. Vibrational spectrum A convincing argument in favour of the above suggestion can be obtained from a comparative study of experimental and calculated vibrational spectra. Curve 1 in Figure 5 presents the spectrum, obtained by a comprehensive study by inelastic neutron scattering (Markichev et al., 1993; Sheka et al., 1995), of the siloxane core vibrations of a fumed silica (A380). Curve 2 in the figure represents the all-vibrations spectrum calculated for the 27-Si protoparticle.1 The spectrum 1 The spectrum has been obtained by calculating the particle force field quantum-chemically then corrected during the solution of the inverse spectral problem (Khavryutchenko, 1998).

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Figure 5. One-phonon amplitude-weighted-density-of-states spectra. 1. Experimental spectrum of A380 fumed silica particles core (Markichev et al. 1993). 2. All-vibrations spectrum. 3. Spectrum of surface atom vibrations. 4. Spectrum of inner atom vibrations.

has been partitioned (Khavryutchenko & Sheka, 1995) over inner and surface oxygen and silicon atoms in full respect with their coordination number, and, in consequence, a ‘bulk’ (curve 3) and ‘surface’ (curve 4) spectra were obtained. As seen from the figure, the bulk spectrum thus calculated is well consistent with the experimental one, convincingly justifying a suiting of the 27-Si particle core to that one of real fumed silica. 3. The function of water in the fumed silica production

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3.1. Passivation of the bare-surface protoparticle As mentioned, the particles described above are baresurface. A large number of atoms with the undersaturated valency, or, as more accepted in surface science, with dangling bonds, is their characteristic peculiarity. The latter dictates a high chemical activity of particulate products, which conventionally is suppressed largely by applying passivation of their surfaces. In the majority of cases, the passivating agents accompany the main process. This is the case of the fumed silica production, where, as known for years, water plays the role of such agent (Iler, 1979). However, a particular function of water still remains rather obscure. We have considered the problem, aiming at highlighting the very process of the bare surface passivation. Two possibilities for the water involvement into the protoparticle formation have been considered. The first concerned the case when water molecules participate in the protoparticle formation from the very beginning. Figure 6 shows the results obtained for the set of 27 silica molecules complemented by 21 water molecules.

Figure 6. A set of 27 silica and of 21 water molecules subjected to the energy minimisation (Khavryutchenko, 1998). a. Starting configuration. b. An intermediate configuration. c. Final configuration.

As seen in Figure 6a, the starting configuration of the silica molecules repeats that one for the 27-Si particle in Figure 1, while water molecules are quite arbitrarily spread outside of the former molecular massive. Intermediate iterations have revealed that intermolecular interaction in the system greatly mixes up the molecules of both types (see Figure 6b), while the final result is quite surprising. As seen in Figure 6c, the main body of the particle is formed by silica molecules, while

76 all water molecules are squeezed out to the periphery, forming an outer water shell around the silica body. The molecules remain non-dissociated and are bound to both the silica core and each other by numerous Hbonds. As for the core, its structure is obviously looser than that one shown in Figure 1b. The outer silicon and oxygen atoms still remain very active, since the deficiency in their valency has not been removed. The other case shown in Figure 7 presents the final result of the interaction of the 27-Si particle previously formed with one water molecule. The molecule is attached to one of the one-coordinated surface oxygen atoms by an H-bond. Therefore, the findings obviously manifest that water molecules willingly coat the siloxane core, remaining non-dissociated so that the hydroxylation of the surface does not occur even with high chemical activity of the surface atoms. This means that the hydroxylation is a barrier reaction, and its (a)

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Figure 7. The 27-Si protoparticle interacting with one water molecule subjected to the coordinate-of-reaction approach. a. Starting configuration. b. Final configuration (Khavryutchenko, 1998).

proceeding requires overcoming a barrier. To estimate the reaction barrier, the reaction pathway has been investigated using a coordinate-of-reaction approach (Dewar, 1971). The H . . . O bond connecting the hydrogen atom of water molecule with the surface oxygen atom of the 27-Si particle in Figure 7a has been taken as the reaction coordinate. A series of calculations seeking the total energy minimum have been performed under a constant-pitch contraction of the coordinate, which was the only one excluded from the structure optimisation (Khavryutchenko, 1998). Figure 8 presents a dependence of the system heat of formation from the reaction coordinate. As seen from the figure, the energy increases when the coordinate shortens until its length achieves 0.97 Å, which is the characteristic value of a standard O–H chemical bond. At this point one stable hydroxyl is formed on the surface, and, simultaneously, the other one is attached to one of the three-coordinated silicon atoms, so that two hydroxyl units appear on the surface. The energy abruptly drops, therewith, indicating that the formation of two hydroxyl units on the particle surface is energetically favorable. The reaction energy is 98 kcal /mol, 20 percent of which (∼ 20 kcal /mol) is related to the energy barrier. The barrier is not very high, and it can be easily overcome thermally when the particle resides in the hightemperature zone. The characteristics obtained for an individual water molecule remain almost unchanged when the number of the molecules is enlarged. A continuous set of configurations, involving from one to twelve water molecules interacting with the 27-Si particle, has been considered. All kinds of possible arrangements of the hydroxyls on the surface have been observed, including configurations known as silanol and silanediol groups, as well as a peculiar bridge Si–O(H)–Si. The final results were rather insensitive to whether the molecules were considered successively one after the other, or by two or three together. The only constraint has been to prevent them from interacting between themselves. Figure 9 presents the final structure of the 27-Si particle passivated by 24 hydroxyls due to interaction with 12 water molecules. The particle surface is almost entirely terminated by the hydroxyl units, and the related particle can exemplify an OH-terminated protoparticle. 3.2. Vibrational spectrum A correlation between the suggested OH-terminated protoparticle model and that of the fumed silica may

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Figure 8. Heat of formation of the 27-Si particle interacting with one water molecule versus O · · · H coordinate (Khavryutchenko, 1998).

Figure 9. Final configuration of the 27-Si protoparticle interacting with 12 water molecules.

be traced by comparing calculated and experimental vibrational spectra. Figure 10 presents a set of spectra obtained by different techniques exhibiting different facets of the spectrum of silica particle vibrations. The calculated spectra were obtained for a fully OHterminated particle 28Si–OH containing 28 silica units. As previously, the calculated spectra were obtained in the harmonic approximation based on the force constants initially derived in the course of the QCh calculations performed, and then corrected by solving the inverse spectral problem. Figure 10a shows the IR transmission spectra, which are provided by the vibrations of the particle bulk (core). As seen from the figure, the calculated spectrum well reproduces the main three-band pattern of the experimental spectrum related to the symmetrical (the band peaked at ∼800 cm−1 ) and antisymmetrical

(the band peaked at ∼1100 cm−1 ) Si-O stretchings, as well as to the deformational vibrations of the Si–O–Si type (the band at ∼400 cm−1 ). Therefore, the core structure of the OH-terminated protoparticle is well consistent with that of fumed silica. As evidenced by the interatomic distance distribution, the core structure of the OH-terminated particle is quite similar to that of the bare-surface one, although, somewhat less compact (Khavryutchenko et al., 1998). Optical IR spectra are shown in Figure 10b as well. The calculated spectrum is the spectrum of the IR transmission as in the previous case while the experimental spectrum is obtained by the diffuse reflection infrared Fourier transform spectroscopy (DRIFTS) (Griffiths, de Haseth, 1986)2 . Contrary to that shown in Figure 10a, the spectra considered are related to the surface vibrations connected with the O-H stretchings of the terminating hydroxyl units, both free (a sharp peak at 3750 cm−1 ) and H-bonded (a broad low-frequency sideband) (Khavryutchenko et al., 1998; Morrow, 1990). As seen from the figure, the calculated spectrum reproduces exactly both features of the experimental one. As might be seen in Figure 9, the calculations actually simulate the H-bonding between neighbouring hydroxyls. Figure 10c shows the spectrum of the doubleamplitude-weighted density of vibrational states (AWDS) obtained by inelastic neutron scattering. The experimental spectrum represents the spectrum of the surface vibrations mainly consisting of the deformational and torsional vibrations of the OH-units (Markichev et al., 1993; Sheka et al., 1995). As seen from the figure, the calculated and experimental 2 Authors are thankful to Dr. Barthel for supplying the DRIFT spectrum of fumed silica.

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Figure 10. Vibrational spectrum of the OH- terminated silica particle. a. IR spectrum of the bulk vibrations. b. IR (calculated) and DRIFT (experimental) spectrum of the O-H stretchings (Morrow, 1990). c. Amplitude-weighted density-of-states spectrum for the surface atom vibrations (see Markichev, Natkaniec & Sheka, 1993 for experimental INS spectrum).

spectra are well consistent, evidencing an undoubted possibility for the 28Si–OH particle to simulate a real particle of fumed silica. 4. Interaction between protoparticles Obviously, interparticle interaction should greatly depend on whether the partners are bare-surface or OHterminated-one. Both limit cases have been considered in the study and Figure 11 presents the final results for two-particle interaction. Figure 11a is related to the case when both interacting partners (27-Si particles each) are bare-surface. The interaction causes the partner non-barrier bonding accompanied by the formation of the stable Si–O–Si bonds. The process will continue if the number of protoparticle increases, unless all particles are bonded, forming a bulk glass. Actually, the sintering of fumed silica can be observed under particular conditions long after all the silica has precipitated (Ulrich, 1984). Therefore, bare-surface particles do not seem to posses a factor terminating the particle growth.

Contrary to this, the partners presented in Figure 11b (fully OH-terminated particles Si18 consisting of 18 SiO2 units each) being also tightly stuck together, are not glued by formation of chemical bonds but are bonded by rather weak H-bonds. As a consequence, the configuration in Figure 11b is not a unit, but is an aggregate of previously formed protoparticles. The findings make allowance for an important conclusion that the OH-termination of the surface prevents particle from the coalescence. Therefore, the hydroxylation process must be responsible for the particle size termination. In the real technological process, the hydroxylation is always accompanied by the dehydroxylation, which will stimulate the gluing and, thus, growing in size of the sticking particles. Hence, the particle size is determined by a balance between the above-mentioned three processes. The balance can be shifted towards the small or large sizing by regulation of the residence high-temperature time and the flux density of incoming gases that is the case of a conventional technological process indeed.

79 in the formation of OH-terminated protoparticles with a fixed size in average. The dehydroxylation causes an additional densification of the siloxane core with an energy gain of 2.7 kcal /mol per each SiO2 unit (Khavryutchenko et al., 1998). The reaction output is determined by the rates of fusion, hydroxylation, and dehydroxylation, and may be regulated by temperature and by the input species concentration influencing the rates. Colliding, the OH-terminated protoparticles are stuck together by rather weak H-bonds forming aggregates of different shape. One such aggregate is shown in Figure 12, together with a proposed theoretical

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Figure 11. Final configurations of a pair of interacting protoparticles. a. Two bare-surface 27-Si protoparticles. b. Two OHterminated Si18 protoparticles (Khavryutchenko et al., 1998). (b)

Based on the findings elucidated, the following description of the fumed silica formation can be suggested. The combustion reaction occurring in the flame consists in two stages covering a synthesis of silica molecules from the silicon and oxygen atoms present and a practically instantaneous condensation of the molecules. The condensed drops may collide and adhere to each other. Until now the suggested description is consistent with that previously made (Ulrich, 1984)3 , although differing in details. A new point is that condensed drops are subjected to the reaction of the surface hydroxylation/dehydroxylation, which results 3 A new dynamical view has been suggested recently (Barthel et al., 1998) on the hierarchy of the fumed silica structure: molecules – protoparticles – primary particles-aggregates – agglomerates. The primary particles are the smallest units to be detected.

Figure 12. Electron micrograph (Barthel et al., 1998) (a) and a theoretical model (b) for silica protoparticle aggregates.

80 model. The aggregates, in their turn, colliding can form agglomerates still more weakly bonded within them. The picture suggested well explains the main distinction of the fumed silica from other fine particles that has been noticed years ago: ‘. . . For this compound (silica) . . . single spherical particles do not exist at all. Rather, aggregates or flocks emerge as the true colliding partners from the earliest stages of nucleation and chemical reaction.’ (Gael U. Ulrich (Ulrich, 1984)). 5. Why fumed silica is always amorphous As well known, fumed silica is always amorphous, while other species such as silicon nitride, titanium oxides, zirconium oxide, etc. are crystalline (Ulrich, 1984). The QCh calculations considered seem to be able to throw light onto the problem. The following aspects are seemed to be crucial for the topic: a rapid condensation as an inseparable constituent of the combustion reaction and the hydroxylation /dehydroxylation process. As shown by the calculations, the silica molecule condensation is actually an energetically favorable non-barrier process that might allow the condensation to be practically instantaneous. From condensed matter science it is well known that, if the condensation process is rapid, a disordered phase forms predominantly. Actually, the distribution functions for the interatomic distances for the primarily condensed 27-Si and 64-Si protoparticles are typical of those for the disordered phases. The situation is not improved when the particles are bonded to form larger structures (Khavryutchenko, to be published). As shown by a recent detailed analysis (Khavryutchenko et al., 1999), the disordering is mainly due to the scattering in the values of the bond angles Si–O–Si, as well as torsional angles, while the dispersion of the valence bond is quite small. On the other hand, the hydroxylation and dehydroxylation, being the main processes in the post-reaction existence of the condensate, intensify the disorder still further. As shown (Khavryutchenko et al., 1998; Khavryutchenko et al., 1999), both processes force the above-mentioned angle dispersion to increase, thus supporting the species amorphicity. Conclusion An extended QCh study has been performed to examine the flame-generated silica formation at the atomic level.

Starting from a set of free molecules, their condensation was shown to be non-barrier and energetically favorable. The finding proved a previously made suggestion (Ulrich, 1984) that the molecule condensation is an essential component of the silica combustion reaction in a flame. However, thus formed bare-surface particles willingly coalesce when colliding, forming a continuous glass-like condensate. The coalescence may be prevented by particle surface passivation in the course of the hydroxylation reaction. The latter is low-barrier enough to proceed in the flame without additional activation. The protoparticle size is determined by a balance of the fusion and hydroxylation /dehydroxylation processes. The findings highlighted during the study make allowance for suggesting a rather complete picture of the fumed silica formation in a flame, starting from free molecules condensation and completed by the hydroxylation /dehydroxylation of the particle surface as well as by the formation of the particle aggregates. Additionally, these threw light onto the inherent amorphicity of the fumed silica as well. Both bare-surface and OH-terminated protoparticles are disordered in structure, supporting the fact. Two factors specific for silica explain the phenomenon: practically instantaneous condensation of the silica molecules in the course of the combustion reaction, and the hydroxylation /dehydroxylation reaction followed afterwards.

Acknowledgement The authors are grateful to Dr. H. Barthel for stimulating and fruitful discussions.

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