Ind. Eng. Chem. Res. 2000, 39, 349-361
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Structural Investigation of Hydrous Titanium Dioxide Precipitates and Their Formation by Small-Angle X-ray Scattering† Juho-Pertti Jalava,*,‡ Erkki Hiltunen,§ Heikki Ka1 hko1 nen,| Heli Erkkila1 ,⊥ Harri Ha1 rma1 ,#,[ and Veli-Matti Taavitsainen3 Kemira Pigments Oy, FIN-28840 Pori, Finland, Department of Medical Physics and Chemistry, University of Turku, FIN-20500 Turku, Finland, Departments of Applied Physics, Physics, and Chemistry, University of Turku, FIN-20014 Turku, Finland, and Espoo-Vantaa Institute of Technology, Leiritie 1, FIN-01600 Vantaa, Finland
The mechanisms of formation and structure of precipitates hydrolyzed from aqueous solutions of titanium tetrachloride and titanium sulfate were studied by small-angle X-ray scattering (SAXS). SAXS was found a powerful method for that purpose. The small colloidal primary particles that were present in the solutions at room temperature started to aggregate when thermal precipitation started. The aggregated particles coalesced until their radius was approximately 1 nm depending of the precipitation conditions to some extent. After that, the aggregation continued producing either mass fractal or surface fractal structures. The structure was mass fractal when primary particle concentration was high enough and surface fractal when concentrations were closer to the equilibrium state. With a delay ionic titanium started to precipitate. Because of its rather slow precipitation rate in the conditions of this study, only surface fractal aggregates were formed. The mass fractal structure was found X-ray amorphous and the surface fractal aggregates nano crystalline. The mass and surface fractal dimensions of these aggregates were 2.2 (1 s ( 0.1) and 2.7 (1 s ( 0.2), respectively. The “titanic acids” were found to be aggregates of small titanium dioxide particles that have mass fractal structure in ortotitanic acid and surface fractal structure in metatitanic acid. The loose structure of the mass fractal aggregates causes the relatively easy solubility and the X-ray amorphous state found in ortotitanic acid. On the contrary, the more compact structure of metatitanic acid explains its nano crystallinity and insolubility. The changing of ortotitanic acid to metatitanic acid upon aging is obviously a consequence of the restructuring of the primary titanium dioxide particles toward the close-packed porous structure. 1. Introduction The hydrolysis of titanium(IV) solutions and especially the structure of the precipitates are of importance in manufacturing of TiO2 pigments by the sulfate process.1 The precipitation from both the sulfate and the chloride solutions is a part of the process. The latter is used to prepare nuclei2 for the thermal precipitation of the sulfate solutions. In sulfate-containing solutions particles of only the anatase structure are formed. The nuclei are important because they speed up and regulate the precipitation in sulfate solutions. In producing rutile TiO2 pigments these nuclei are also the agents needed in the calcination to regulate the transformation of anatase crystallites to rutile and to participate in the final formation of the pigment particles. The structure of the precipitate depends significantly on the precipitation concentration, temperature, and time.3 The addition * To whom correspondence should be addressed. E-mail:
[email protected]. † Dedicated to the memory of Heikki Ka ¨ hko¨nen. ‡ Kemira Pigments Oy. § Department of Medical Physics and Chemistry, University of Turku. | Department of Applied Physics, University of Turku. ⊥ Department of Physics, University of Turku. # Department of Chemistry, University of Turku. 3 Espoo-Vantaa Institute of Technology. [ Present address: Department of Biotechnology, University of Turku, Tykisto¨nkatu 6A, FIN-20520 Turku, Finland.
of ammonia or alkali hydroxide into the solution of tetravalent titanium salt yields a X-ray amorphous product commonly called ortotitanic acid or alpha titanic acid. It is a white gelatinous and highly hydrous precipitate, which is readily soluble in dilute acids and easily peptized by dilute alkalis and suitable salts to give stable sols. Opposite to this is the thermal precipitation or aging ortotitanic acid to give a product referred to as metatitanic acid, or beta titanic acid. The X-ray diffraction studies of it reveal some anatase lines. It is a granular, relatively insoluble, but slightly peptizable substance.4 It is thought that the titanic acids, like stannic acids, are hydrous oxides whose properties are essentially determined by the differing sizes of the primary particles of which they are made.4 The size of the crystallite particles in metatitanic acid is about 5-10 nm.5 There is very little evidence concerning the possible particle or crystallite size of the X-ray amorphous ortotitanic acid prepared from aqueous solutions of titanium tetrachloride. Kormann et al.6 prepared, by adding cold (-20 °C) TiCl4 to water, ≈2.0-nm anatase TiO2 crystallites determined by TEM. They did not report the X-ray diffraction diagram of the crystallites, but these are likely to be X-ray amorphous according to the studies of Wright et al.7 In their studies by smallangle neutron scattering (SANS) the amorphous solid prepared by hydrolytic polycondensation of titanium isopropoxide with water reveals a texture on a length scale of 3 nm. In thermal treatment, the structure can
10.1021/ie990386q CCC: $19.00 © 2000 American Chemical Society Published on Web 01/19/2000
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be recognized as anatase once the particle size reaches 5-8 nm. Usually, the primary particles are organized to larger aggregates during the precipitation. Many SANS and SAXS studies have been made on silica precipitated with water already in the 1980s.8-10 Generally, the structure of the silica precipitates consists of primary particles, about 10 nm in diameter, and are fractal with different aggregate sizes and fractal dimensions, both depending on the precipitation conditions. Very little data exist on fractality and aggregation formation of precipitates prepared from titaniumcontaining solutions, none of them treating aqueous solutions of TiCl4 or H2SO4. The published studies are very similar to those done with silica. Some examples are referred to here. According to SANS and SAXS experiments of Marignan et al.,11 the aggregate network backbone of the hydrolysis product of tetraisopropyl orthotitanate in nonaqueous solvent consisted of polydisperse cylinders having a radius of gyration of about 0.7 nm. At scales larger than 3 nm, the structure seemed to become fractal, with an effective fractal dimension of 2.08. Rajh et al.12 found rodlike structures of TiO2 particles with a diameter of 4 nm studied with SANS. Kamiyama et al.13 studied, with SAXS, the gelation process of titanium isopropoxide solutions. The process yielded aggregates with mass fractal structure. Our aim was to study the mechanisms of formation and structure of precipitates hydrolyzed from aqueous solutions of TiCl4 and TiOSO4‚2H2O and the structure of precipitates from the sulfate process. Especially the fractal behavior of the structure depending on the method of preparation and aging was emphasized. The SAXS method, supported with some other methods, was used.
where n is the concentration, t is the time, and Kij is the reaction rate also called the collision matrix or the kernel. Smooth and dense particles are formed when a molecule sticks onto a particle. On the contrary, the particles with a looser and often fractal structure grow through aggregation. Fractals and fractal geometry generally provide a quantitative measure and characterization of random systems such as colloidal aggregates, rough surfaces, and porous materials. Qualitatively, fractal objects show self-similarity or dilation symmetry, meaning that the essential geometric features are invariant to scale changes such as magnification in a microscope.8,10 2.2. Theory of SAXS for Small Particles and Their Aggregates. Approximate Survey. It can be shown16 that light-scattering measurements are able to provide a direct estimate of the fractal dimension of a growing aggregate. The intensity of scattering is determined by the probability of finding a particle within a certain distance of another particle; hence, the intensity depends on the density of the aggregate. It turns out that the intensity, I, of the scattered light is related to the magnitude of the scattering vector, h, by the relation
I ∝ h-x
(2)
where x is related to the fractal dimension of the aggregate or particle and h is related to the wavelength, λ, and the scattering angle, θ, by
h)
4π sin(θ/2) λ
(3)
The exponent x can be written in the form 2. Theoretical
x ) 2Dm - Ds
2.1. Particle Nucleation and Growth. With many compounds, the super saturation in liquid has to be high enough to permit nucleation. The nuclei have to reach a certain critical size to allow a spontaneous growth of particles. When, due to nucleation and growth, the concentration decreases below the level needed for nucleation, only the growth of particles occurs and the number of particles remains constant. The critical size for anatase, estimated from the Gibbs free energies for the surface and bulk, is even as small as the molecule size.14 Thus, in the case of anatase, the size of the critical nucleus does not prevent the formation of new nuclei, but they are formed spontaneously, dependent on the degree of the super saturation. Thus, the growth of particles through aggregation becomes prominent because the number of small particles increases readily. The growth of a particle is possible through molecular sticking or aggregation of small particles. The sticking probability depends on the electrical double layer on them, and it can be approached, for example, by the DLVO theory.15 The kinetics of the growth depends also, for example, on the size, diffusivity in the solution, and concentration. The kinetics of the aggregation has been studied by Smoluchowski.8 The rate equation for aggregation of two particles with masses i and j producing an aggregate with mass s is given
dns(t) dt
)
1
∞
Ksjnsj(t) ∑ Kijni(t)nj(t) - ns(t)∑ 2 i+j)s j)1
(1)
(4)
where Dm and Ds are structural parameters. For mass fractals Dm < 3 and Dm ) Ds, so that x ) Dm, which means that the fractal dimension can be measured directly from the scattering curve in the power-law area.9 If x > 3, the structure is surface fractal, which means that the particle itself is compact but its surface is rough. Thus, Dm ) 3 and the surface fractal dimension Ds ) 6 - x. If the surface of the particle is coarse, then 2 e Ds e 3. For smooth compact particles Dm ) 3 and Ds ) 2 so that x ) 4. Equation 1 is valid only for values of h which satisfy the relation
r , h-1 , ξ where r is the smallest unit of aggregate, for example, the primary particles, and ξ is the diameter of the aggregate. In our study, it turned out that these approximate equations were not satisfactory because there were many different kinds of particles at the same time in the solutions. Thus, more rigorous equations to give a satisfactory model for the measured intensities were needed. More Rigorous Survey. In the case of individual scatterers which are relatively monodisperse spheres the scattered intensity, Ip(h), is17,18
Ip(h) ) cpP(h,r0)
(5)
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where cp is the number concentration of spheres and P(h,r0) is a function of the form factor of spheres. For uniform spheres,
[
]
sin(hr0) - hr0 cos(hr0)
P(h,r0) ) V2∆F2 3
(hr0)3
2
(6)
Im(h) ) cmP(h,r0m)S(h,r0m,ξm,Dm)
(1 + 1/ξs2 h2)2ξsh4 Γ(5 - Ds) N0 sin[(5 - Ds) × φ1(1 - φ1)V (1 + 1/ξs2h2)(5-Ds)/2h6-Ds
V)
where Dm is the mass fractal dimension and ξm represents the size of the aggregate. At large h values, S(h) = 1, and therefore the measured intensity, describes mainly the individual particles. At small h values, P(h) = 1, and the measured intensity is related to S(h) and the number density of particles cm. When mass fractal aggregates coalesce, they form porous particles whose scattering behave essentially similar to fractal surfaces.21 Therefore, later in the text the term surface fractal refers to porous particles whose scattering properties are identical to those of fractal particles. For the scattering intensity of surface fractal objects, Reich et al.22 give the following equation,
I(h) ) 4πIe∆F2csφ1(1 - φ1)Vh-1 × Γ(2)
sin[2 tan-1(ξsh)] [(1/ξs)2 + h2] N0Γ(5 - Ds) sin[(5 - Ds) × 4φ1(1 - φ1)V[(1/ξs)2 + h2](5-Ds)/2
}
(9)
where Ie is the intensity scattered by one electron, ξs represents the size of the surface fractal particle, cs is the number concentration of particles in the sample, φ1 is the volume fraction of solid material, Ds is the surface fractal dimension (2 e Ds < 3), and N0 is the interface area between pores and solids. By using the following expression,
sin[2 tan-1{ξsh)] )
2ξsh 1 + ξs2 h2
the equation may be simplified in the form
4 πr 3n/φ1 3 0s
(12)
N0 ) Ar0sDs-2
(13)
where A is the surface area of the interface. It can also be given as the total surface area of all spheres reduced by a fraction, fs, because of the sintering in the contact points
sin[(Dm - 1)
tan-1{ξsh)]
(11)
where n is the number of spheres in the surface fractal particle, and22
tan-1(hξm)] (8)
{
}
If the surface fractal particle is formed by monodisperse spherical particles with close-packed structure (e.g., Kittel23), then
(7)
where S(h) is an effective structure factor that describes the spatial distribution of the individual scatterer. According to Teixeira,19,20 S(h) can for the mass fractal objects be given in a form
(hr0m)Dm (1 + h-2ξm-2)(Dm-1)/2
8
tan-1(ξsh)]
where V is the volume of the sphere, ∆F is the density difference between the sphere and the medium, and r0 is the radius of the sphere. The scattered intensity, Im (h), of mass fractal aggregated spheres can be decomposed as
S(h,r0m,ξm,Dm) ) 1 + DmΓ(Dm - 1) 1
{
I(h) ) πIe∆F2csφ1(1 - φ1)V
(10)
A ) 4πr0s2n(1 - fs)
(14)
Thus,
I(h,r0s,ξs,Ds,φ1,fs) )
{
8(1 - φ1)r0s3 4 2 π Ie∆F2csn 3 (1 + ξs-2 h-2)2ξsh4 Ds
3(1 - fs)r0s Γ(5 - Ds) -2 -2 (5-Ds)/2 6-Ds
(1 + ξs h )
h
sin[(5 - Ds) tan-1(ξsh)]
) csQ(h,r0s,ξs,Ds,φ1,fs)
}
(15)
3. Experimental Section SAXS intensities of six different series of samples were measured. These series are called EMSU, EMS, TAS, TOS, TISO, and TSA. Their differences are described below. 3.1. Chemicals and Analytical Methods. Determinations of Component Concentrations. All chemicals were of analytical grade except TiCl4, which was of technical grade (contents of trace elements are mentioned elsewhere1). Ti(IV) was reduced to Ti(III) with zinc amalgam and titrated with 0.0625 mol/dm3 ammonium iron(II) sulfate. H2SO4(act.) was titrated with 0.5 mol/dm3 sodium hydroxide and Fe(II) with 0.05 mol/dm3 cerium(IV) sulfate. The concentration of ammonium hydroxide was determined by adding 1.5 g of it to 50 mL of 0.25 mol/ dm3 sulfuric acid and titrating the excess sulfuric acid with 0.5 mol/dm3 sodium hydroxide. 3.2. Preparation of the TiO2 Hydrate from TiCl4. TiCl4 was diluted with distilled water to a concentration (calculated as TiO2) of 215 g/dm3. The diluted TiCl4 amount was 1.5 dm3. Titanium was precipitated as hydrated titanium dioxide by adding 25.4 wt% NH4OH solution to the diluted TiCl4 solution, cooling in an ice bath, and stirring mechanically. The addition rate was slow enough to keep the solution temperature below 30 °C. The addition of the NH4OH solution was continued
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until the pH reached 4.8 for EMS precipitation and 5.8 for the EMSU precipitation. The same precipitates are referred to as C1 and C2 samples, respectively, by Jalava et al.24 The precipitates were filtered and washed by suspension with distilled water until the filtrates did not show any cloudiness with silver nitrate solution. Both precipitates were stored at (24 ( 1) °C. The freshly prepared thick slurries became more fluid upon aging. 3.3. Preparation of the TiO2 Hydrate from TiOSO4‚2H2O. The samples for SAXS measurements were prepared by thermal hydrolysis of titanium sulfate solution. Prior to the hydrolysis, titanium oxide sulfate dihydrate was dissolved in distilled water and the slightly turbid solutions were carefully filtrated. TiO2 concentration was 259 g/dm3 for TAS, 107 g/dm3 for TOS, and 258 g/dm3 for TISO solution. Precipitation was carried out by heating the solutions at (70 ( 4) °C for TISO and (90 ( 4) °C for TAS and TOS solution. Samples were taken from different stages of the precipitation and cooled immediately to 20 °C. TSA samples were taken from the different stages of the sulfate process1 and were immediately cooled to 20 °C. They were then diluted with 10% H2SO4 (1:1) to prevent the iron(II) sulfate crystallization. 3.4. SAXS. The small-angle X-ray scattering data were obtained using the Kratky X-ray small-angle scattering camera and a proportional counter. The wavelength of the incident beam was 0.0711 nm (characteristic MoKR radiation). For each spectrum, 70 steps at different angles were measured. The measuring time for each step was 600 or 1200 s, and they were all reduced to 1200 s. The samples were placed between two Mylard tapes, which did not cause any significant scattering. To avoid the settling of the particles in the slurry sample, a sample cell was constructed to the sample holder and a pump was used to keep a constant flow. The path length of the X-ray beam through the sample was 2 mm. 3.5. Modeling of Time Series. Unique estimation can be possible from a time series of different curves where several unknowns are constant in time, even though all parameters cannot be uniquely estimated from a single intensity curve. This is intuitively clear since there are fewer degrees of freedom for those parameters that are common or otherwise restricted (e.g., by mass balance) within the series. This fact is often used, for example, in estimating chemical kinetic parameters (see, for example, Bard25). The mass-balance restriction is that at each time within the same series the concentrations should satisfy the equation m
cj(t) ) const. ∑ j)1
(16)
where m is the number of different kinds of particles or aggregates. 3.6. Modeling of SAXS Measurements. The theory for SAXS has been expressed for the pinhole geometry, but to receive larger scattering intensities the measurements are made using a slit. In the case when the scattering curve in pinhole geometry obeys the h-x law, the same scattering curve measured in slit geometry with a Kratky camera and infinite slit height can be written in the form h-(x-1). Thus, in modeling the intensities must be corrected. The slit correction is made to the calculated intensities by numerical integration
over the used slit length, L, presented by eq 3.
∫00.5LIcalc,uncorr(xh2 + y2) dy
Icalc(h) ) 2
(17)
where Icalc,uncorr and Icalc are the calculated intensities before and after the slit correction, respectively, and the value for L was 42. The final estimation was done using all intensities forming one time series. The other principles in modeling were as follows: (1) The primary particles were assumed spherical. (2) The measured SAXS intensities are superpositions of intensities of (a) base scattering having constant level within precipitation or aging series, (b) two kinds of primary particles both having constant monodisperse sizes within the series, (c) mass fractal aggregates, and (d) surface fractal aggregates. (3) The concentration of particles change monotonically as a function of time. (4) Mass-balance equation (16) was used. Because the measured intensity curves are linear combinations of intensity curves of different species, these parameters are related to the intensity functions (5), (7), and (15) by the equation
Icalc(t,h) ) Ip1(t,h) + Ip2(t,h) + Im(t,h) + Is(t,h) + base ) cp1(t)P(h,r01) + cp2(t)P(h,r02) + cm(t)P(h,r0m)S(h,r0m,ξm,Dm) + cs(t)Q(h,r0s,ξs,Ds,φ1,fs) + base
(18)
where r01 and r02 are the radii of two free spherical particles with different sizes and c01(t) and c02(t) the time-dependent concentrations of them; r0m is the radius of the mass-fractal-aggregated spherical particles; cm(t), ξm, and Dm are the time-dependent concentration, the size, and the mass fractal dimension of the mass fractal aggregates, respectively; r0s is the radius of surfacefractal-aggregated spherical particles; cs(t), ξs, Ds, φ1, and fs are the time-dependent concentration, the size, the surface fractal dimension, the volume fraction of the solid material, and the fraction of the diminishing surface area of the surface fractal aggregates, respectively. Constant, linear, simple exponential (corresponding to a first-order chemical reaction), or Gaussian functions were used to describe the time behavior of particle concentrations. The principle for choosing these functions was to achieve an as parsimonious model as possible. In addition, a multiplicative parameter was used to correct the small differences in the levels of intensity curves in a time series. The values of these parameters were mostly between 0.9 and 1.1. All estimations were performed using least-squares estimation. Because of the nature of the measurement errors, logarithms of the measured and theoretically calculated intensities were used instead of the original ones. Thus, the problem was to minimize the sum of squares, SS, with respect to the unknown parameters: p
SS )
n
∑∑ k)1i)1
m
Icalc,j(tk,hi)]2 ∑ j)1
[log Imeas(tk,hi) - log
(19)
where “meas” and “calc” mean the measured and calculated values respectively, p and n are the number
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Figure 1. EMSU aging series. Precipitation and aging temperature,
