Effect of solvent on the homogeneous precipitation of titania by titanium ethoxide hydrolysis

Journal of Non-CrystallineSolids 103 (1988) 49-64 North-Holland, Amsterdam

49

E F F E C T OF S O L V E N T ON T H E H O M O G E N E O U S P R E C I P I T A T I O N OF TITANIA BY TITANIUM E T H O X I D E H Y D R O L Y S I S * Michael T. HARRIS and Charles H. BYERS Chemical Technology Division, Oak Ridge National Laboratory, P.O. Box X, Oak Ridge, TN 37831-6224, USA

Received 5 October 1987 Revised manuscript received12 January 1988

A method has been developedfor studying and controllingthe growth of colloidal titania by titanium ethoxidehydrolysisin ethanol, 1-butanol, and tert-butyl alcohol. Particle growth was followed from approximately 0.02 to 1.0 ~m by dynamic laser-fight scattering. Evaluation of the particle growth kinetics indicated that growth was controlled by surface phenomena and that the type of precipitate formed was affected by the solvent. Electron microscopyshowed that monodispersespherical particles were formed in the solvents ethanol and 1-butanol. The precipitate that was formed in tert-butyl alcohol had no regular shape and was characteristicof uncontrolled homogeneousprecipitation.

1. Introduction

Many new applications for ceramics have been found in high technology industries. These applications include, among others, using ceramics as electrical insulation materials, thermal insulators, humidity sensors, and organic catalysts (enzyme carriers) [1,2]. However, the development of new ceramic materials is sometimes hindered by a poor understanding of the physics and chemistry of forming the starting powders [3]. The phenomena which control the formation, nucleation, and growth, of powders occurs in a size range of 0.005 to 1 micron. In the past, there were limitations in methods of observing submicron particles; therefore, crystal growth was usually observed in the size range above 1 ~m. Invariably, populations of crystals with a wide size distribution were studied, requiring a number of assumptions about population dynamics before any analysis could be made. A better understanding of the fundamentals of nucleation and crystal growth may be obtained if nucleation and growth * Research sponsored by the Office of Basic Energy Sciences, U.S. Department of Energy under contract DE-AC0584OR21400 with Martin Marietta Energy Systems, Inc. 0022-3093/88/$03.50 © ElsevierSciencePublishers B.V. (North-Holland PhysicsPublishing Division)

were followed from the 0.005- to 1-~tm range, and if the growth of monodispersed particles could be observed. The most significant contribution to particle sizing in the past decade has been the development of dynamic laser light scattering, and its applications to the observation of submicron particles in liquids [4]. Laser-light scattering provides an excellent in situ method of nonintrusively observing particles in the size range of interest. Computer algorithms have also been developed to deconvolute laser light scattering data for particle size distribution analysis [5,6]. Metal alkoxide precipitation reactions in liquids are of particular interest in the development of new ceramic materials [3] and are ideal for homogeneous precipitation studies by dynamic laser light scattering. The formation of monodisperse silica particles from the hydrolysis of tetraethylorthosilane in various alcohol solvents has been followed by dynamic laser light scattering and chemical analysis [7]. The kinetics of the hydrolysis and precipitation reactions were given. Titanium ethoxide, an analog of tetraethylorthosilane, hydrolyses to form titania. Barringer and Bowen report the formation of monodisperse titania powders by the hydrolysis of titanium tetraetho-

50

M. T. Harris, C.H. Byers /Homogeneous precipitation of titania

xide in ethanol and have discussed their chemical and physical properties [8,9]. The delay time for the initial observation of turbidity as a function of the initial water and titanium ethoxide concentration was used to establish hydrolysis and condensation reaction kinetics. Presented here is a study of the formation of titania particles by the hydrolysis of titanium ethoxide in ethanol, 1-butanol, and tert-butyl alcohol. The rate of the reaction is retarded so that particle growth may be followed from approximately 0.03- to 0.6-~m by dynamic laser light scattering. The hydrolysis reaction kinetics is determined by monitoring the change in water concentration during the reaction. Kinetic plots of the particle growth data are compared to nucleation and growth theories [10-12].

cohol-alkoxide were prepared to minimized localized reaction zones. The two solutions were rapidly mixed for approximately 5 s. Immediately after mixing, a fraction of the sample was transferred to a clean quartz spectrophotometer cell which was placed in the dynamic fight-scattering spectrometer. Fourier transform infrared absorption spectroscopy was employed to determine if alcoholysis occurred when titanium ethoxide was mixed with alcohol solvents other than ethanol. A Michelson 100 spectrometer (Bomem Inc.) with IBM Personal computer interfacing capabilities was used to obtain these infrared absorption spectra. Liquid samples were contained in a ZnSe flowthrough cell. The characteristic peaks of the metal alkoxide were determined by subtracting absorption due to the solvent. The water concentration (as an impurity) in each solvent was initially determined by the Karl-Fischer method. Water concentrations as an impurity in the "pure" solvents ranged from 0.04 mol/1 in ethanol and 1-butanol to 0.222 mol/1 in tert-butyl alcohol. The cobalt chloride method, a colorimetric technique for determining water concentrations in organic solvents [13], was used to follow the concentration of water during the reaction. The cobalt chloride technique is employed to measure water concentrations from 2 to 10 m g / m L in ethanol and 1-butanol. Solutions containing 400

2. Experimental 2.1. Reagents and chemical analyses Titania particles were synthesized by the hydrolysis of titanium ethoxide (Alfa Products) in ethanol-water, 1-butanol-water, and tert-butyl alcohol-water mixtures. All reagents and solvents, except for the ethoxide, were passed through a 0.22-~tm filter to minimize heterogeneous nucleation. Separate solutions of alcohol-water and al-

/,

LASER

/

HIGH-TEMPERATURE FOCUSING ENCLOSURE\ LE~NS'~ /~AAMPLE CELL ; ~ POWERDETECTOR

--~.~ APERTURE COLLECTINGLENS~ LIMITING APERTURE I

I

PAD

AUTO CORRELATOR

PHOTOMULTIPLIER

Fig.1.Dynamiclight-scatteringspectrometer.

LAB

M.T. Harris, C.H. Byers / Homogeneous precipitation of titania

m g / m L of Co 2+ in each solvent are combined with the respective reacting solution, and the absorbance is measured at X = 671 nm. The final concentration of soluble titania was determined by centrifuging a portion of the sample at 4000 to 15000 rpm for 10 to 20 min and subsequently adding a portion of the supernatant to 4% hydrogen peroxide for the colorimetric determination of soluble titania [14].

51

which can accurately approximately the ideal autocorrelation function. Details of the electronic and mathematical operation are given in the literature [4]. The time scale that can be probed ranges from decay times of 0.1 ~ts to 10 s. An RS-232 communication connection between the autocorrelator and microcomputer (Apple IIe) permits automated operation, off-line analysis, and convenient data logging. Data and calculated results are stored on a magnetic disk.

2.2. Particle sizing

A custom-built dynamic light-scattering spectrometer was used to determine submicron particle diameters (fig. 1). The apparatus consists of a laser, a focusing lens, a sample cell, collection optics, a detector, and signal processing equipment [151. A 2-W argon-ion laser (Spectra Physics model 165-06) generates a vertically polarized beam (X = 488 nm) that is focused by a 150-ram planoconvex lens onto the center of the sample cell. This beam is then focused to a narrow width (0.2 nun) in order to maximize the modulation of the scattered light. Typically, only low power operation ( < 50 mW) is necessary. The detector is an end-window photomultiplier mounted in a housing that provides radio frequency and magnetic shielding (Pacific model 3262 RF). Voltage requirements (2000 V, dc) were supplied by a stable power supply (Pacific model 204-03). Light reaching the detector passes through a small iris diaphragm (0.68 ram, Ealing No. 22-3305) and a precision adjustable slit (Oriel No. 7250, O- to 3.2-mm opening), which is mounted vertically just in front of the photomultiplier. The collection optics and detector are mounted on an arm that rotates in a plane normal to the plane of polarization. A goniometer accurately positions the arm at various angles. In the present study, only light scattered at 90 ° was used to determine particle diameter. The pulse amplifier discriminator (PAD, Langley Ford model PD-01) converts signals from the photomultiplier tube to TTL pulses (0-5 V; dc) for use in the autocorrelator. Pulses due to spurious effects in the PMT are also eliminated by the PAD. The autocorrelator (Langley Ford model 1096) is a sophisticated digital signal processor

3. Theory 3.1. Dynamic laser light scattering

The scattered light from a dilute colloidal suspension in a transparent liquid is related to the physical properties that cause the fluctuations of the solution and the scattering disposition. The physical phenomenon governing the behavior of dilute colloidal suspensions is Brownian motion. Brownian motion can be observed in particles that are relatively large (diameter = 1 ~m) on the molecular scale [16-19]. Brownian motion of a free particle (i.e., no applied force field) is described by the Langevin equation [17]: dfi dt

+Y(t),

(1)

where fi = t = fl = ~,T(t) =

particle velocity vector, time coefficient of dynamic friction, fluctuating influence of molecular collision process.

For a spherical particle, the coefficient of dynamic friction is given by Stokes' Law: fl = 67raTI/rn ,

(2)

where a --- particle radius, ,/ = fluid viscosity, m = mass of particle. A detailed theoretical formulation of the solution to the Langevin equation and how it is used

52

M.T. Harris, C H. Byers / Homogeneousprecipitation of titania

in relating the particle motion to light signal fluctuations is given elsewhere [16]. This derivation yields the following equation for the autocorrelation of the random light signal fluctuations that are generated by the Brownian motion of a system of monodispersed colloidal particles: AS* --- exp( - q2Dt) = exp( - t/%),

(3)

where A S*= normalized autocorrelation function,

q = Iql = 41rn sin(O/2)/Xi, n 0 X D

= = = =

refractive index of medium, scattering angle, wavelength of incident light, diffusion coefficient = kT/65~ra~, k = Boltzmann constant, T = absolute temperature, K, rc = characteristic decay time = (q2D)- 1. For polydispersed systems, the following equation is given (4):

AS* = Kff--a°°[f(r)P(q, r)r 6 exp(-t/ri)] dr,

(4) where r f(r)

= = P(q, r) = ri =

particle radius, normalized distribution of particle size, Mie scattering factor, P = 1 for r << X, decay time for r = r i.

The exact solution requires inversion of this equation to yield f(r) directly. This is very difficult to do accurately for complex signals; however, significant improvement has been made in the development of computer algorithms to deconvolute this integral [6]. The r 6 dependence of the scattering power indicates that large particles are more easily detected than small ones. The cumulants method is a widely used technique for detecting polydispersity [20-22]. This analysis leads to the following approximation for the autocorrelation function: In(A*) = - T ' t + /'t2/2 2!

g3t3 3---~--+ "'"

I ~t2 (~t)2

= - Ft + ~

+ ....

~

-

1 I% (~,t)3

3-~ ~,---S

(5)

The form of In(As*) is a polynomial in t with the coefficients representing different properties of the line-width distribution. The linear and quadratic terms, which are the most significant, are readily measured in most experiments. The linear term is the average line-width, F, as defined in eq. (5). Since the scattering power of individual particles is skewed heavy towards large particle [eq. (3)], this 'average" F will result in "average' diameters weighted toward the largest species. The second moment (/,2) normalized by the square of the average linewidth ( # 2 / F 2) is termed the polydispersity parameter. For a perfect monodisperse suspension, /L2/T"2= 0. In practice, valties of # 2 / F 2 less than 0.1 are taken as an indication of a narrow distribution. It is readily apparent that a quadratic regression analysis of ln[A*(t)] vs. t will provide estimates of F and g 2 / F 2. Using the following equation [eq. (6)] which related the diffusion coefficient to the average line-width and the StokesEinstein relation [eq. (7)], we obtain the particle diameter directly:

D = I'/q 2

(6)

and d p = kt/3~r~D.

(7)

This relationship, which is widely used, forms the basis for the size analysis in our current work. In particular, it permits measurements of crystal size and allows estimation of polydispersity.

3. 2. Controlled homogeneous precipitation The preparation of monodisperse sols requires conditions in which nucleation occurs in a very short period at the start of the sol formation (homogeneous precipitation) or by seeding a supersaturated solution with small particles (heterogeneous precipitation). Matijevic and his coworkers have developed homogeneous precipitation as means of producing monodispersed sols [23,24]. The theory of controlled homogeneous precipitation involves slowly increasing the concentration of the disperse-phase material to attain a degree of supersaturation at which nucleation becomes ap-

M.T. Harris, C.H. Byers /Homogeneous precipitation of titania

Z

C ~

--/'~-ffAP, D

/

o

/

F-

koxide and condensation of the dispersed phase material. The following general equations are given: hydrolysis M(OR)x + xH20

n" F-

z Iii 0 Z o o

53

M ( O H ) . + xROH, Cs

(8)

condensation M(OH) x ~ MOy (s) + (x - y ) H 2 0 , A

(9)

B

TIME Fig. 2. Homogeneousprecipitation is achieved by carefully heating aqueoussolutionsof metalsalts. preciable. Since the generation of disperse-phase material is slow, the formation of nuclei accompanied by the relief of supersaturation is restricted to a relatively short period, and few new nuclei are formed after this initial outburst. Fig. 2 qualitatively depicts the path of controlled homogeneous precipitation for the formation of metal oxides from the controlled hydrolysis of metal salt solutions in aqueous solutions. Matijevic used this method to produce fairly monodisperse titanium dioxide hydrosols [24]. Monodisperse metal oxide alcosols are formed from controlled homogeneous precipitation processes which are analogous to the formation of metal oxides from the controlled hydrolysis of metal salt solutions in aqueous solutions. The rate of hydrolysis is slower in the metal oxide alcosol system than in the subsequent condensation reaction. Thus, as the disperse-phase material is produced by the hydrolysis reaction, a critical concentration is achieved at which nucleation occurs and the faster condensation reaction maintains a concentration of disperse-phase material which is lower than the critical concentration. Therefore, no further nuclei are formed, and the growth of monodisperse particles ensues. This is the proposed mechanism for the formation fo monodisperse silica particles from tetraethylorthosilicate hydrolysis by the Stober-Fink method [25]. Monodisperse silica particles have been produced in a number of alcohol solvents by this method [26]. The overall reaction of the synthesis of TiO 2 particles consists of hydrolysis of the metal al-

where M and R represent the metal and the alkyl group, respectively. It should be noted that alcoholysis a n d / o r partial hydrolysis may occur; thus, resulting in the following reactions: M - OR + HOR' ~ M - OR' + HO M - OR + HO - M ---, M - O - M + ROH. (10) In the case of titanium ethoxide, Barringer and Bowen [8] have reported that the removal of the fourth alkoxy group is difficult and therefore, give the following hydrolysis and condensation reaction scheme: Ti(OR)4 + 3H20~Ti(OR)(OH)3 + 3ROH,

(11)

and Ti(OR)(OH)3--TiO2- xH20 + (1 - x)H20 +ROH.

(12)

Bradley et al. have reported that the hydrolysis reaction of titanium ethoxide in boiling ethanol is instantaneous [27]. Ishino and Minami also concluded that the hydrolysis step of titanium 1butoxide was fast and the condensation reaction was the controlling step for precipitation [27]. Monodisperse particles should, therefore, be more difficult to produce from alkoxide reactions than alkoxides with slower rates of hydrolysis (i.e., tetraethylothosilicate). 3.3. Size of critical nucleus and particle growth kinetics The precipitation of a substance from solution requires the formation of nuclei. These nuclei must be in equilibrium with the dissolved substance. The equilibrium condition of a single nucleus of any geometry that has a number of surfaces in equilibrium with the dissolved entity is governed by the following thermodynamic expression [28]: dG = I~o dn + ~_,7i dsi, i

(13)

M. T. Harris, C.H. Byers /Homogeneousprecipitation of titania

54

where

where G /x0 n "t~ s~

= = = = =

Gibbs free energy, bulk chemical potential of the nucleus, number of moles the nucleus contains, interfacial tension associated with surface i, area of surface i.

The overall chemical potential, #, is obtained by dividing eq. (13) by dn:

ct = characteristic geometric shape factor of the nucleus, = Eiki/l.

The chemical potential #' of the substance in solution is given by i~' = ito + R T

In a,

(22)

where I~ = IXo + Y ~ i d s i / d n ,

(14)

i or

t~ = #o + M/p~_,,/~ d s , / d v ,

(15)

i

M = molecular weight of precipitated nucleus, p = density of nucleus, v = volume of nucleus. Assuming that z is a characteristic dimension of the nucleus, the following expression is proposed: (16)

for each surface, and (17)

v = lz 3,

= = = =

where ki = geometric constant, l = geometric constant.

in a = 2Mtx~ ao 3RTpz "

= 2si/3v.

(18)

Defining a " m e a n interfacial tension", ~7, as ~=~,i ,tisi/~,isi,

(19)

the following equation is derived: I~ = #o + 2 M $ ~ . , s i / 3 p v .

(20)

i

Using eqs. (4) and (5), the following equation is obtained: I~ = I~o + 2 M a r / / 3 p z ,

(21)

(23)

This equation suggests that the interfacial tension for a solid-liquid system may be obtained if the supersaturation ratio (S = a / a o ) , z, p, and a are known. For a sphere, the characteristic dimension is r, the radius of the sphere. The shape factor, a, is six for a sphere. Therefore, the interfacial tension is related to the critical radius of a spherical nucleus in equilibrium with the solution by the expression r*=

Subsequently, dsi/dv

standard chemical potential, gas constant, absolute temperature, mean activity of the substance in solution.

Equating/x to/~', as required by the condition of equilibrium between the nucleus and the solution, and assuming that /t o = / ~ + R T In a 0, where a 0 is the saturation activity, the following expression is obtained:

where

S i = ki Z2,

t

#0 R T a

aMy RTp ln(a/ao)"

(24)

After nuclei are formed, the particle growth will be controlled by either surface-controlled phenomena or diffusion of the disperse-phase material through the bulk solution to the surface [29]. Surface-controlled growth and diffusion-controlled growth may occur by either m o n o m e r duster or cluster-cluster interactions [30]. In the case of surface-controlled growth, very small partides of narrow size distribution probably grow by the deposition of molecules or ions (monomers) on the particle surface [10,30]. In most systems where very small particles grow by the surface-controlled deposition of monomers

M.T. Harris, C.H. Byers / Homogeneous precipitation of titania

on the particle surface, the rate of particle growth is given by the following expression:

55

4. Results and discussion 4.1. Hydrolysis reaction

dr d'-t = k l s n = kp (for constant s),

(25)

where particle radius, cm; k 1 = rate constant; cm/s S = supersaturation ratio = (coo - Cs)/Cs; concentration of disperse phase material in Coo bulk fluid, ions/cm3; solubility of disperse phase material in bulk CS solution, ions/cm3;. n 1 if s is high or 2 if s is _<0.01 [11]; k p = linear growth constant, cm/s. r

For constant supersaturation and temperature, eq. (25) shows that particle growth is independent of particle size. Linear growth has been observed for the growth of crystals from solution [11,12]. This model represents the case where surface reactions occur so rapidly that the amount of material precipitating is proportional to the surface area of the particles. Nielsen [10] defines a polynuclear growth mechanism where the rate of particle growth is constant for constant supersaturation and temperature. As indicated by Levenspiel, linear growth represents a number of deposition and condensation processes [31]. In the case where diffusion from the bulk fluid to the particle surface is controlling particle growth, the velocity of growth is given by [10]: dr

v D ( c ~ - Cs)

dt

r

,

(26)

where v = molecular volume, cm3; D = diffusion coefficient, cm2/s; coo = concentration of disperse-phase material in bulk fluid, ions/cm3; cs = solubility of disperse-phase material in bulk solution, ions/cm3. This equation is applicable when particle growth is slow and when steady state concentration fields are set up faster than the particle grows, [i.e. v(coo - cs) < 0.00005)].

Before examining the nature of particle growth kinetics, it is necessary to understand the alcoholysis and hydrolysis reactions. Since the titanium ethoxide and water are mixed in separate portions of alcohol, it is possible that alcoholysis will occur in the "water-free" titanium ethoxide solution. Fourier transform infrared spectroscopy (FTIR) with solvent subtraction is, therefore, used to determine the chemical species in this solution. This analysis is performed in less than two minutes after adding the titanium ethoxide to the solvent. The major characteristic peaks at 1369, 1130, 613, 600 and 574 cm -a are observed when titanium ethoxide is added to ethanol and 1-butanol. However, characteristic peaks at 1011, 793, and 599 cm-1 are observed when tert-butyl alcohol is the solvent. Infrared spectra reported by other investigators show strong characteristic absorption at 1136, 1101, 1064, 916, and 625-500 cm -1 for titanium ethoxide in a two-solvent system of carbon disulfide and carbon tetrachloride [32] and 1190, 1008, 909, 797, and 597 cm -1 for tert-butyl alcohol in carbon disulfide [33]. Spectra in the former study [32] were recorded over the range 500-1300 cm -1. Comparison of the characteristic peaks that are observed in the present study with those given in the literature for titanium ethoxide and titanium tert-butoxide, it is seen that alcoholysis occurs very rapidly (in less than 2 minutes) between titanium ethoxide and the tert-butyl alcohol. Complete alcoholysis does not occur since it is rather difficult to replace the last ethoxy group with a t e r t - b u t o x y group [27]. It is also postulated that alcoholysis also occurs between titanium ethoxide and the 1-butanol solvent since alcoholysis occurs more readily with unbranched moieties than branched ones. Several investigators [8,27] suggest that hydrolysis is fast and that the condensation reaction is slow for titanium alkoxides. In this study, the rate of hydrolysis is evaluated by using the cobalt chloride method to follow concentration in ethanol and 1-butanol solvent systems. Water concentrations in ethanol and tert-butyl alcohol are also

56

M.T. Harris, C.H. Byers / Homogeneous precipitation of titania

Table 1 Effect of initial titanium ethoxide and water concentration on the induction period [Ti(OC2Hs) 4] (mol/L)

[H20 ] (mol/L)

Solvent

Induction period (rain)

0.0078 0.016 0.023 0.032 0.016 0.016 0.016 0.032 0.062 0.032 0.047 0.071

0.36 0.36 0.36 0.36 0.71 1.06 0.38 0.38 0.38 0.80 0.80 0.80

ethanol 188 ethanol 15 ethanol 7.25 ethanol 5 ethanol 6.5 ethanol 3.3 1-butanol 120 1-butanol 51.8 1-butanol 33.8 tert-butanol 10.3 tert-butanol 4 tert-butanol 4

determined by the Karl-Fischer method. In all cases, the moles of water consumed achieved a level of approximately 3 times the initial moles of titanium ethoxide within the first minute of the reaction. During the induction period, the time between the mixing of the reagents and the first observation of particles in the mixture, the water consumption does not proceed beyond the value achieved in the first rapid period of the reaction. Table 1 gives the induction time, t i, which is greater than the approximately I minute period during which hydrolysis reaction occurs. Therefore, it is concluded that the hydrolysis reaction is fast and that the condensation reaction is slow for the hydrolysis of titanium alkoxides in ethanol, 1-butanol, and tert-butyl alcohol. Furthermore, the observation that approximately 3 moles of water per mole alkoxide was consumed during this 1-min hydrolysis period suggests that eq. (11) is correct and that the precipitation reaction proceeds from the condensation of the titanium hydroxide alkoxide species, Ti(OCEH5)(OH)3 or Ti(OC4H9)(OH)3. Barringer and Bowen used t i as a function of [ H 2 0 ] and [Ti(OC2Hs)4] to determine the reaction kinetics of the hydrolysis reaction [8]; however, our data (table 1) show that, for reactant concentrations much less than those used in Barringer and Bowen's study, most of the induction time is due to the delay period between the completion of the initial-phase hydrolysis reaction and

the subsequent precipitation reaction. In this case, the variation of t i with water and [ T i ( O C E H s ) 4 ] concentrations will not yield the correct information about the hydrolysis reaction kinetics. The data in table 1 suggest that t i varies inversely with [H20 ] a n d [ Z i ( O C 2 n s ) 4 ] 2, where these concentrations represent the initial values.

4.2. Condensation reaction and particle growth The slower condensation reaction that succeeds the fast hydrolysis reaction ultimately results in the precipitation of "titania" particles. The quotation marks are used to indicate that the precipitate is hydrated and that it also possibly contains unhydrolyzed ethoxy groups [34]. Particle growth is followed by dynamic laser-light scattering during the very early stages of the condensation reaction such that the concentration of the disperse-phase material, Ti(OC2Hs)(H20)3 or Ti(OC4H9)(OH)3, is essentially constant. Due to the fast hydrolysis reaction, the concentration of the disperse-phase material is equal to the initial concentration of T i ( O C E H 5 ) 4. The sample is also mildly turbid during the dynamic laser-light scattering measurements. As the turbidity of the sample increases, analysis of the light scattering signal becomes complicated by multiple scattering and particle-to-particle interactions [4]. Typical plots of the particle growth kinetics in ethanol are presented in fig. 3. Linear growth (eq. 25) is observed for precipitation reactions in ethanol. Furthermore, the polydispersity parameter, # / F 2 (eq. 5), that is obtained from dynamic laser-light-scattering indicates that the particles in solution are fairly monodisperse. It is interesting to note that the first observed particle size by dynamic laser light scattering was approximately 0.2 ~m. It is easily within the analytical capability of the laser-light scattering equipment to observe particles in the 0.02 ~tm size range; therefore, it may be concluded that no coherent mass of partides occurs until a 0.2 ~m particle is "assembled". Since particle size measurements by laser-light scattering requires approximately 1 rain for data collection and analyses, the assembling of mass to form the 0.2 ~m particles must occur rapidly once

M.T. Harris, C.H. Byers /Homogeneous precipitation of titania 1.6

I

I

}

I

57

I

[TIE], mol/L

1.1

• •

0.031 0.023

• •

0.016 0.0078

[H2o]:

/

0.36 mo.L

~L v muJ < r~

,/

0.6

& /

A=" *i=

•

,(

d

,i

/d,

0.1

./ I

~b

I

20

10

I

160

240

320

TIME (min)

F i g . 3. " T i t a n i a "

growth kinetics: hydrolysis of titanium ethoxide in ethanol.

the precipitation process has begun. Barringer and Bowen reports that one of the requirements for synthesizing monodisperse TiO2 particles is the rapid growth of particles to a size of > 0.1 ~m [8]. 0.15

A c

E

I

This would minimize the presence of very small particles (i.e., < 0.1 t~m) which have a tendency to flocculate, thus, resulting in uncontrolled precipitation. Under the experimental conditions of the 1

I

0.10

E

I k0 m

0.05

I 0

0.01

I

I

0.02

0.03

0.04

TIE CONCENTRATION (mollL)

F i g . 4.

Effect of i n i t i a l t i t a n i u m ethoxide concentration on " d t a n l a "

growth rate: hydrolysis of titanium ethoxide in ethanol.

M.T. Harris, C.H. Byers / Homogeneous precipitation of titania

58 0.5

I [TIE], mmol/L •

62

•

31

•

16

HYDROLYSIS

O F T I E IN 1 - B U T A N O L

['H20 ] = 360 mmol/L 0.4 :t.

/

re u.I Iu.I

I

/

/ 0.3

m

7

•

/

/ Z

r

g

1

/

/

I

!

I

I

I

I

50.0

75.0

100.0

125.0

0.2 25.0

/

150.0

T I M E (rain)

Fig. 5. "Titania" growth kinetics: hydrolysis of titanium ethoxide in 1-butanol.

reaction, the desired conditions for minimizing uncontrolled precipitation are achieved. Fig. 3 shows the effect of the initial concentra-

tion of titanium ethoxide and the concentration of water in ethanol on the rate of particle growth and induction time, t i. Fig. 4 shows a linear relation-

0.05

/ 0.04

"E v

:L

0.03

I.
0.02

--

0.01

--

O nO

/° I

O.0 0.0

0.05 TIE C O N C E N T R A T I O N (tool/L)

o.1

Fig. 6. Effect of initial titanium ethoxide concentration on "titania" growth rate: hydrolysis of titanium ethoxide in 1-butanol.

M.T. Harris, C.H. Byers /Homogeneous precipitation of titania

Fig. 7. Scanning electron micrographs of "titania" particles synthesized in ethanol and 1-butanol.

Fig. 8. Transmission electron micrograph of "titania" particles produced in ethanol.

59

60

3t. T. Harris, C.H. Byers /Homogeneous precipitation of titania

ship between the linear growth constant, kp, and the initial concentration of titanium ethoxide [or due to rapid hydrolysis, the concentration of Ti(OC2Hs)(Oh03 ] or Ti(OC4H9)(OH)3. As discussed by Levenspiel [31] (eq. 25), kp is expected to increase linearly with the supersaturation ratio of the supersaturation ratio is greater than 0.01. In the experiments performed during this study, the solubility of Ti(OC2Hs)(H20)3 or Ti(OC4H9) (OH)3 is approximately 0.004 mol/L. Therefore, applying the initial titania ethoxide concentrations given in table 1, all of the experiments have supersaturation ratios that are greater than 0.01. Fig. 5 shows the linear growth behavior of the "titania" particles from about 0.2 to 0.4 ~m in 1-butanol. It is interesting to note that as with ethanol, the first observed particle size by dynamic laser-light scattering was approximately 0.2 ~m. Similar to reactions in ethanol, dynamic laser-light-scattering measurements indicate that the particles are fairly monodisperse in solution.

The effect of the initial concentration of titanium ethoxide in 1-butanol on the rate of particle growth and induction time, ti, is also shown on this plot. The induction time decreases as the initial concentration of titanium ethoxide increases. Fig. 6 shows that the particle growth constant for the reaction in 1-butanol also increases linearly with the initial concentration of titanium ethoxide. The supersaturation ratios are also greater than 0.01. Scanning electron micrographs of dried titania particles in ethanol and 1-butanol are shown in fig. 7. The powders were dried directly from the alcohol-water solutions without further preparation to minimize agglomeration upon drying; therefore, the observed particle agglomeration was probably due to precipitation of the unreacted "titania" and the drying process. Looking beyond the agglomeration, the particles are spherical and monodisperse. The sizes of the particles range from 0.5 to 1.5 ~m for reactions in ethanol and 1-butanol, and the particles are quite monodis-

Fig. 9. Transmission electronmicrograph of "titania" producedin 1-butanol.

M.T. Harris, C H. Byers / Homogeneous precipitation of titania

perse. Transmission electron micrographs of titania particles synthesized in ethanol 1-butanol are shown in figs. 8 and 9. Once again, the particle produced in ethanol and 1-butanol appear spherical and, although agglomerated upon drying, are monodisperse. The particle growth behavior in tert-butyl alcohol yield kinetic plots that are quite different from those obtained for growth in ethanol or 1-butanol. This is probably due to the fact that the particles are formed from a titanium-hydroxytert-butoxy compound, and that the solvent molecules interact with this compound by short-range bonding. These graphs show an increase in the rate of growth with time (fig. 10). It is postulated that the slow growth regime represents the situation in which most of the disperse-phase material is used to form new nuclei and the subsequent particle growth is very slow. Therefore, the initially observed particle sizes during this slowgrowth regime represent the diameter of the critical nuclei. The particles that are produced in tert-butyl alcohol during this period are very small (i.e., diameter=0.02 I~m). Approximating the nuclei as spheres and according to eq. (24), an interracial tension of approximately 480 erg/cm 2 0.10

I

61

is obtained when experimentally determined values of RT = 2.408 × 101° erg/mol, In S = 8, r* (critical radius f nucleus) = 1 × 10 -6 cm, M(TiO2) = 79.9 g/mol, and P = 3.1 g / c m 3 are used [8]. Due to the uncertainty in the true molecular formula of the precipitating species and the shapes of the nuclei, this interfacial tension represents only a rough estimate of the value. The interracial tension estimate is, however, of the correct order of magnitude for liquid-solid surfaces which have been reported as having interfacial tensions ranging from less then a hundred to approximately 1000 erg/cm 2 [10,28]. In evaluating the particle growth rate behavior that is observed in tert-butyl alcohol, it is known that very small particles, < 0.1 ~m, are susceptible to flocculation on collision due to Brownian motion of these particles [8]. Therefore, it is likely that, as the concentration of nuclei in the solution increases, the collision frequency between these nuclei increases; thus, flocculation occurs. This is depicted by the rapid increase in growth rate at later times. Furthermore, smaller nuclei will also attach to the surface of larger particles, and the consequence is a rapid growth in particle size. The result of this uncontrolled nucleation and growth

I

I

l

0.08

0.06

0.04

//

j

&-&/&

i,s,:

.' ". l / ~

/ •

~.TIET_ ~

mmo

ii L

0.02 EH20"]=800 mmol/L I

I

I

I

10

20

30

40

TIME (min}

Fig. 10. "Titania" growth kinetics in tert-butyl alcohol.

50

M.T. Harris, C.H. Byers /Homogeneous precipitation of titania

62

Fig. 11. Transmission electron micrographs of " t i t a n i a " particles synthesized in 5.0

I

I

I

tert-butyl alcohol.

1 /

4.0

E

3.0

E

/

tt/ Irr

"r I-

2.0

0tw 0 1.0

I 0.00

0.02

I

I

0.04 0.06 TIE CONCENTRATION (mol/L)

I 0.08

0.10

Fig. 12. Effect of initial titanium ethoxide concentration on " t i t a n i a " growth rate: hydrolysis of titanium ethoxide in alcohol.

tert-buty]

M.T. Harris, C.H. Byers / Homogeneous precipitation of titania

is the production of an agglomerated mass with no definite shape. This is shown by fig. 11, an electron micrograph of "dried titania" particles that are synthesized in tert-butyl alcohol. Although the precipitate does not have a definite shape, the stringy nature of the precipitate is possibly suitable for sol-gel processing, which is another method that is being studied for ceramic powder synthesis. The following empirical expression models particle growth in tert-butyl alcohol:

r = ( rol - krt ) -1,

(27)

where r = r0 = kr= t =

particle radius, cm; particle radius at time zero, cm; rate constant, cm -1 s -1 time, s.

Although this equation is empirical, it is interesting to note that the rate constant, kr, increases linearly with the initial concentration of titanium ethoxide (fig. 12). Further theoretical studies are needed to broaden our understanding of the growth behavior in tert-butyl alcohol. Therefore, mathematical models are being investigated that will incorporate the theory of Brownian coagulation in colloids with simultaneous nuclei formation. To enhance our understanding of the effect of solvent on particle growth, the models will also need to incorporate the effect of short-range forces between the solvent molecules and the particles (and/or the disperse-phase material). The preceding particle growth data for reactions in ethanol, 1-butanol, and tert-butyl alcohol can also be tested for diffusion-controlled growth by applying eq. (26). This evaluation suggests that for diffusion controlled growth (i.e., diffusion from the bulk phase to the particle surface), the particles should have grown several orders of magnitude faster than they did under observation. Therefore, the particle growth in the solvents tested is probably controlled by surface phenomena.

5. Conclusions

The solvent system used in the preparation process and alcoholysis have a profound effect on

63

the nature of "titania" precipitates that are synthesized by the hydrolysis of titanium ethoxide in ethanol, 1-butanol, and tert-butyl alcohol. Monodisperse and spherical "titania" particles grow at constant rates when produced in ethanol and 1-butanol. However, the rate of growth in tert-butyl alcohol increases with time. The particles that are formed in tert-butyl alcohol are agglomerated and have irregular shapes. Although not monodisperse or spherical, the precipitate that is produced in tert-butyl alcohol could possibly form a sol-gel system. This system could subsequently be used to produce ceramic powders. Theoretical treatment of these systems is greatly needed and would provide an understanding of the physical and chemical phenomena tha t govern precipitation in the different solvent systems. Brownian coagulation with nucleation could possibly explain the growth behavior that is observed in tert-butyl alcohol. The contribution of the short-range bonding between solvent molecules and the precipitate should also be incorporated into the model to assess the effect of solvent on precipitation. The authors express their gratitude to Ronald Brunson for his careful efforts in performing the experiments in this program.

References [1] H.K. Bowen, Mat. Res. Soc. Symp. Proc. 24 (1984) 1. [2] B.P. Sharma, L.F. Bailey and R.A. Messing, Angew. Chem. Int. Ed. Engl. 21 (1982) 837. [3] H.K. Bowen, Mater. Sci. Eng. 44 (1980) 1. [4] B. Dahneke, Measurement of Suspended Particles Using Quasi-Elastic Light Scattering (John Wiley and Sons, New York, 1982). [5] S.W. Provencher, Comput. Phys. Commun. 27 (1982) 229. [6] S.W. Provencher, Makromol. Chem. 180 (1979) 201. [7] C.H. Byers, M.T. Harris and D.F. Williams, Ing. Eng. Chem. Res. 26 (9) (1987) 1916. [8] E.A. Barringer and H.K. Bowen, Langmuir 1 (1985) 414. [9] E.A. Barringer and H.K. Bowen, Commun. Am. Ceram. Soc. (December 1982) C-199. [10] A.E. Nielsen, Kinetics of Precipitation (Pergamon Press, new York, 1964). [11] G.D. Botsaris and E.G. Denk, Jr., Ind. Eng. Chem. Fundam. 9 (1970) 276. [12] C.Y. Tai, W.L. McCabe, and R.W. Rousseau, AICHE J. 21 (1975) 351.

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M.T. Harris, CH. Byers /Homogeneous precipitation of titania

[13] B.J. Berne and R. Pecora, Dynamic Light Scattering (John Wiley and Sons, New York, 1976). [14] S. Chandrasekar, Rev. Mod. Phys. 15 (1943) 1. [15] D.F. Boltz and J.A. Howell, Colorimetric Determination of Nonmetals (John Wiley and Sons, New York, 1978) p. 316. [16] E.B. Sandell, Colorimetric Determination of Trace Metals (Interscience Publishers, Inc., New York, 1959) p. 868. [17] C.H. Byers, R.R. Brunson, M.T. Harris, and D.F. Wilhams, Controlled Nucleation and Growth Studies in Metal Oxide and Alkoxide Systems by Dynamic Laser-LightScattering Methods, ORNL/TM-10285 (Oak Ridge National Laboratory, Oak Ridge, Tenn., April 1987). [18] B. Crosignoni, P. Di Porto, and M. Bertolotti, Statistical Properties of Scattered Light (Academic Press, New York, 1974). [19] B. Chu, Laser Light Scattering (Academic Press, New York, 1974). [20] J.C. Brown and P.N. Pusey, J. Chem. Phys. 62 (1975) 1136. [21] C.B. Bargeron, J. Chem. Phys. 61 (1974) 2134. [22] D.E. Koppel, J. Chem. Phys. 57 (1972) 4184. [23] E. Matijevic, Acc. Chem. Res. 14 (1981) 22. [24] E. Matijevic, Prog. Colloid Polym. Sci. 61 (1976) 24. [25] W. Stober, A. Fink, and E. Bohn, J. Colloid Inter. Sci. 25 (1968) 62.

[26] M.T. Harris, C.H. Byers and R.R. Brunson, Hydrolysis and Condensation Kinetics for Liquid-Phase Tetraethylorthosilicate Reactions in Alkaline-Alcohol Solvents, accepted for presentation at the AICHE Annual Meeting in New York (November 15-20, 1987). [27] D.C. Bradley, R. Mehrotra and D.P. Gaur, Metal Alkoxides (Academic Press, New York, 1978) p. 152. [28] B.V. Enustun and J. Turkevich, J. Am. Chem. Soc. 82 (1960) 4502. [29] D.J. Shaw, Introduction to Colloid and Surface Chemistry (Butterworths, Boston, 1980). [30] D.W. Schaefer and K.D. Keefer, Growth and Structure of Silica polymers, presented at the DOE/BES/Materials Science Information Meeting, Sandia National Laboratory (1986). [31] O. Levenspiel, Chemical Reaction Engineering (John Wiley and Sons, new York, 1972). [32] C.G. Barraclough, D.C. Bradley, J. Lewis and I.M. Thomas, J. Chem. Soc. (1961) 2601. [33] C.T. Lynch, K.S. Kazdiyasni, J.S. Smith and W.J. Crawford, Analytical Chemistry 36 (1964) 2333. [34] K.A. Berglund, D.R. Tallant, and R.G. Dosch, Ceramic Chemical Processing, eds. L.L. Hench and Donald R. Ulrich (John Wiley and Sons, New York, 1986) p. 94.