The effect of particle solubility on the strength of nanocrystalline agglomerates: Boehmite

NanoSbucturedMmials. Vol. 8, No. 4. pp. 399418.1997 Elsevier Science Ltd Q 1997 Acta Mdsllurgica Inc. Printedin the USA. All tights resen’ed 096%9773/97 $17.00 + .OO

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PII SO9659773(97)00180-3

THE EFFECT OF PARTICLE SOLUBILITY ON THESTRENGTH OF NANOCRYSTALLINE AGGLOMERATES: BOEHMITE Seongtae Kwon and G.L. Messing Department of Materials Science and Engineering, The Particulate Materials Center, Pennsylvania State University, University Park, PA 16802, USA {Accepted April 9,1997) Abstract-Nanosizedpowders readily agglomerate during processing and handling. The strength of the interparticle bonds can dramatically affect the strength of the agglomerates and subsequent consolidation. This paperfocuses on the origin of agglomerate strength for
INTRODUCTION Homogeneous mixing, higher strength, and low temperature superplasticity are advantages of nanocrystallline materials. Unfortunately, problems such as increased health risks, difficulty in powder storage and handling, and the increased tendency foragglomeration are often encountered in processing nanosized powder. Among the above mentioned problems, agglomeration, if properly controlled, can relieve the other problems by increasing the effective ‘particle size’. Agglomleration is generally divided into two types. Systematic agglomeration, which often uses a polymeric binder, is called granulation. Granulation is favorable for powder processing because it increases the powder flowability and bulk density. Particle agglomeration is a natural result of the dominant effect of interparticle forces when the particle size is < 1 pm. When weak forces like van der Waals, electrostatic, and liquid films hold the particles together, the agglomerates are referred to as soft agglomerates, in recognition of the ease with which they can be deformed in the dry state or redispersed in liquids. In contrast, strong forces due to sintering, chemical react.ion or precipitation of dissolved species result in hard agglomerates or aggregates. The influence of interparticlebonding forces increases dramatically as particle size decreases. For this reason, nalnosized powders readily agglomerate during processing and handling. Once the nanosized powder is agglomerated, the strength of the dried agglomerate is usually too high to realize the benefits of the small particles. 399

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In an earlier paper we reported that ethanol-dispersedboehmite gel agglomerates comprised of 8 nm boehmite crystallites are readily deformable during compaction and result in homogeneous green and sintered microstructures in contrast to aqueous-dispersed gel agglomerates (1). In this paper, the consolidation behavior of boehmite gel agglomerates prepared in different dispersion media has been investigated to understand how the dispersion medium affects particle adhesion. (More accurately, the material studied was pseudoboehmite; however, we use boehmite for the sake of convenience.) It is shown that boehmite dissolution in Hz0 and precipitation at particle contacts during drying is the primary mechanism for neck growth in boehmite agglomerates. Based on these results, a model is proposed to explain the changes in agglomerate strength as a function of particle solubility. BACKGROUND The tensile strength (0) of agglomerates can be calculated from (2):

VI where Eis the void fraction, F is the bonding force between primary particles, and d is the diameter of the primary particles. The influence of the void fraction (i.e., the relative agglomeratedensity) on strength is much smaller than the contribution of the bonding force. For example, an agglomerate of 60% relative density has approximately 3 times the strength of an agglomerate with 30% relative density if other factors remain constant, whereas the bonding force varies orders of magnitude, depending on the nature of the interparticle force (2-5). For van der Waals forces, the attractive force between two sphericalparticles is proportional to particle size d, and as predicted from this relation and equation [ 11, agglomerate strength is inversely proportional to the primaryparticle size. Agglomerate strengths, calculated by assuming the maximum van der Waals force and a minimum particle separation of 0.4 nm (3). for particle diameters of 10 nm and 100 nm are estimated to be 3.3 MPa and 0.3 MPa, respectively_ Clearly, the van der Waals attraction results in a considerable increase in agglomerate strength for nanosizedparticles, but, these agglomerate strengths are still low compared to hard agglomerates. Electrostatic forces between electrically conducting particles are an order of magnitude smaller than van der Waals attractive forces, and the electrostatic forces between non-conducting are smaller still (4). Therefore, neither electrostatic forces nor van der Waals forces are considered to be responsible for the formation of hard agglomerates. Moisture also plays an important role in particle adhesion. A monolayer of adsorbed liquid is assumed to explain the agglomeration tendency of fine particles in the presence of a small amount of moisture or high humidity (2). Particle adhesion by capillary necks is greatly dependent on the degree of saturation, i.e., the fraction of liquid volume with respect to the void volume. When the degree of saturation equals 1, the agglomerate strength is zero, but it increases rapidly until the agglomerate strength reaches its maximum and the first pore forms in the liquid when the degree of saturation equals = 0.9 (6,7). The agglomerate strength is inversely proportional to the primary particle size when liquid capillary bridges are the predominant mechanism of particle adhesion. Practically, liquid bridge forces are about four times stronger than van der Waals forces (3), but are nonexistent in dried agglomerates.

EFFECTOF PAmu

SOLUBILITV ONTHESTRENGTH OF NAWCRYSTALUNE AOGLOMERATES: B~EHMTE

401

Solid bridges formed by sintering, partial melting, inorganic binders, chemical reaction, and precipitation of dissolved substances result in a wide range of adhesive strengths. At elevated temperature during calcination, solid bridges may develop by diffusion. Aggregates formedin this manner are resistant to consolidation and, thus, powders formed this way require milling. Precipitation of dissolved salts at particle contacts has been investigated as a bonding mechanism (8,9). The agglomerate strength is dependent on the drying condition and the degree of crystallization of the precipitated salt. This bonding mechanism contributes little to agglomerate strength compared tootberbonding mechanismsforparticles< 1 pm (2). Other mechanisms, such as chemical reaction and partial melting, have been listed as mechanisms of particle adhesion, but no models concerning how these processes affect agglomerate strength exist. Most metal oxide powders are assumed to be negligibly soluble during ceramic processing. Consequently, the particle bridging mechanism of precipitation at particle-particle contacts has received little attention. The use of increasingly smaller particles during nanocrystalline and sol gel processing means that increased solubility as a result of the increased curvature (i.e., Kelvin effect) can become an important mechanism for agglomeration. The solubility, S, of a particle is related to its radius, r, by the Ostwald-Freundlich equation:

S =S,exp

(

g

)

[mol/I]

where So is the solubility of a flat plate (equilibrium solubility), ~~1is the solid-liquid interfacial energy, V is the molecular volume of the solid phase, R is the ideal gas constant, and T is the temperature. Bquation [2] shows that particle solubility increases significantly as the particle size decreases: for nanoscale particles, the solubility is 102-lo4 times greater than the equilibrium solubility, depending on the solid-liquid interfacial energy, ysr. If solid lbridges are formed between particles by precipitation of the dissolved species from solution, the bonding between particles will be much more coherent and stronger than if bonded by precipitated salts. Kitayama et al. reported that a small amount of transition alumina in commercial A1203 powder reacts in an acid solution to form a gel and consequently hard agglomerates form, but the effect of the particle solubility was not clearly discussed in their work (10). Maskara et al. investigated the silica agglomerate strength as a function of pH and attributed the formation of hard silica agglomerates to solution-precipitation depending on dissolution rate and solid content in the slurry (11). In this paper we report on a series of experiments that show that particle solubility is the primary reason for the formation of hard, brittle boehmite gel agglomerates. A model is then presented to explain how agglomerate strength depends on the enhanced solubility of nanosize particles. EXPERIMENTAL

PROCEDURE

A flow diagram of the experimental procedure is shown in Figure 1. All samples were prepared from a commercial boehmite powder (CatapaI D, Vista Chemical Co., Houston, TX) having a BET surface area of 250 m2/g. The equivalent particle diameter calculated from the surface area is = 8 nm. Based on inductively coupled plasma (ICP) analysis, the boehmite yields 99.8% Al203 and 0.2% Tie when completely dehydrated An hydrosol was prepared by

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Stabilized for 2 days @pH3

Stabilized for 2 days SpH3

a -Alumina Suspension

Boehmite Sol

I

Centrifuge

2000 rpm, 40 min.

Supematant Seed Sol Mix

Wet Milling in Plastic Bottle for 10 hr

I

In water, ethanol, toluene, and water+butanol solution

and CIP 280 MPa

Figure 1. Flow chart of boehmite powder processing.

dispersing 15 wt.% boehmite powder in distilled water and adjusting the dispersion pH to 3 with nitric acid. Seed particles were obtained by dispersing 10 wt.% a-Al203 powder (AKPJO, Sumitomo Chemical America, Inc., New York, NY) in distilled water after adjusting the pH to 3 with nitric acid. The dispersion was stirred for 2 days, sonicated to break up agglomerates and then centrifuged. The stabilized boehmite hydrosol was mixed with 1.5 wt.% dispersed a-AlzOs, on a dry-weight basis. The seeding process is not critical to this study, but these samples were later sintered, in which case seeding is necessary to achieve high density (12,13). The sol was gelled by heating on a hot plate and the gel fragments were dried at 85°C. The dried gel fragments were ground to c 90 pm (-170 mesh) and dispersed in various media such as water, ethanol, toluene, and a solution of water+butanol. Dispersion was carried out by milling gel fragments in the liquid medium for ten hours in a NalgenerM plastic bottle using high purity alumina balls. Although water-dispersion was not expected to make a difference from the original

EFFECT01: Pmncti

S~LIJSILITV ONTHESTRENGTH OF NANOCRYSTALLINE AGGLOMERATES: B~EHMITE

403

sol, the gel fragments were dispersed in water in the same manner as in the other media to avoid differences due to the dispersion procedure. Dried gel fragments were sievedintoagglomerate size fractions of > 53 l.un, < 90 l.trn(hereafter referred to as 75 pm) and c 45 l.tm. Tap densities of the agglomerates were measured after drying at 100°C for 5h. Classified agglomerates were uniaxially pressed into pellets in a 12.7 mm diameter steel die at 5 MPa and pellets were cold isostatically pressed (CIP) at 280 MPa. Pore size distributions of green bodies were measured by mercury porosimetry. The agglomerate strength was directly measured using a thermomechanical analyzer. Gel agglomerates were crushed and sieved between 250 and 600 ~rrrtand slightly ground using abrasive paper to obtain agglomerates between 198 and 250 pm. The agglomerates were not exactly spherical, but the more spherical agglomerates were selected for testing. Pressed pellets were heated in air from room temperature to 600°C at 5”Cfmin and from 600°C to 1250°C at lS’C/min. The samples were sintered at 1250°C from 6.2 min to 200 min. Sintered densities were measured by the Archimedes technique. Polished samples for SEM were thermally etched at 1200°C for 30 min to reveal the grain structure,

RESULTS AND DISCUSSION 4.1 Effect of Ethanol-dispersion Tap densities of the ethanol-dispersed agglomerates were always less than those of the water-dispersed agglomerates. We approximated the agglomerate density by assuming they occupy 55% of space, or slightly less than dense random packing of spherical particles. Based on this calculation, the water-dispersed 75 pm agglomerates are = 53% dense and the ethanoldispersed aggl’omerates are = 40% dense. The cumulative pore size distributions in green bodies isostatically pressed at 280 MPa are compared in Figure 2. The green body formed from 75 ym water-dispersed agglomerates has a wide, bimodal pore size distribution and a maximum pore diameter of = 1.5 l.tm. The coarse pores range from 0.5 pm to 1.5 I.trnand comprise = 10% of the total pore volume. In contrast, the ethanoldispersed samlple does not have any pores > 0.1 ltm diameter. The same trend is observed when the pressed c 45 vrn powders are compared. It is interesting that there does not appear to be a size effect on agglomerate consolidation for ethanol-dispersed agglomerates. Furthermore, the coarser, ethanol-dispersed powder has a smaller pore size distribution than the < 45 pm waterdispersed sample. The green densities of all samples after CIP at 280 MPa were approximately 5 1% of theoretical density. Water-dispersed powder samples had 1% higher green densities in most cases. Sintered. density is presented in Figure 3 as a function of sintering time for samples fabricated from water-dispersed and ethanol-dispersed 75 pm agglomerates. For a sintering time less than = 30 min, both systems are less than 9 1% of theoretical density. The water-dispersed samples have higher densities than ethanol-dispersed samples. There is a crossover point in sintering behavior around 9 1% of theoretical density and the density of the water-dispersed samples reaches a plateau at about 95%. The higher sintered densities of the water-dispersed samples in the low density region (i.e., shlortsintering time) is due to a higher agglomerate density and consequently, the faster kinetics of intra-agglomerate densification than the ethanol-dispersed agglomerates.

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water-dispersed 75 pm ___-_ water-dispersed c45 pm ____.____ethanol-dispersed 75 pm ..*............... ethanol-dispersed ~45 pm

Pore Diameter

(pm)

Figure 2. Cumulative pore volume in green samples fabricated from water-dispersed and ethanol-dispersed boehmite gel agglomerates.

n 8 l

8

0

l

I

. n

n

l

80 ’ 1

ethanol-dispersed water-dispersed

I

I

10

100

Sintering

Time

1000

(min)

Figure 3. Sintered density of samples fabricated from 75 pm boehmite gel agglomerates as a function of time at 1250°C.

EFFECTOF PAmmE SOLUBILI~ ONTHESTRENGTH OF NANOCRYSTALLINE AGGLOMEFMES: B~EHMTE

(a)

405

(b)

Figure 4. Optical micrograph of polished surface of samples fabricated from (a) 75 p water-dispersed (b) 75 pm ethanol-dispersed boehmite gel agglomerates. Samples were sintered at 125OOCfor 100 min.

Polished surfaces of samples sintered for 100 min are compared in Figure 4. The microstructures clearly show that the water-dispersed agglomerates are not suffkiently deformed during compaction to form a homogeneous green body, and that ethanol-dispersed agglomerates achieve a more homogeneous microstructure. 4.2 Agglomerate Deformation Characteristics and Bonding Mechanism Based on the above results, it is clear that ethanol dispersion significantly improves the deformability of the dried, agglomerated boehmite powder. Obviously, particle size differences cannot account for the apparent agglomerate strength differences between water-dispersed and ethanol-dispersed agglomerates. The agglomerate strength is thus dependent on the interparticle bonding forces and the void fraction. Based on the density difference, the calculated relative strength of the ethanol-dispersed agglomerates is = 60% of the water-dispersed agglomerates. This small difference does not seem sufficient to affect the compaction differences reported above. The most likely reason for the difference is the bonding within the agglomerates. As discussed earlier, the strength of interpartitle bonds can range orders of magnitude depending on the nature of the interparticle force. Of these bonding mechanisms, we believe that chemical bonding is the reason for the higher strength of the water-dlispersed boehmite agglomerates.

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Kaliszewski et al. (14) reported that the formation of surface ethoxy groups during dispersion of zirconium hydroxide in ethanol prevents chemical bonding between the primary particles upon dehydration and thus soft agglomerates form. To investigate whether such reactions occur in boehmite, the water-dispersed and ethanol-dispersed gel agglomerates were examined by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). After drying, the gel agglomerates were stored at 80°C. Unlike Zr(OH)4 powder, the DRIFI’S spectra were identical for the boehmite powders. This result suggests that other factors ate responsible for the different pressing character of the agglomerates. To further examine the effect of surface reaction, agglomerates were dispersed in toluene. Toluene has a ring type molecular structure and thus nosurfacereaction with boehmite is expected. After toluene dispersion, no gel formed and only a very soft cake was obtained because aprotic solvents, like toluene, do not cause reestrification or hydrolysis reactions (15). The powder cake was sieved to obtain <9Opm size agglomerates. When pressed at 280 MPa, the green density was 51%. The densification kinetics of the toluene-dispersed and ethanol-dispersed powders are compared in Figure 5. It is obvious that dispersing the nanocrystalline boehmite in toluene is as effective for obtaining soft agglomerates and high sir&red density as ethanol dispersion. From the above examples, it is evident that surface reactions with the organic solvent are not responsible for agglomerate softening. The agglomerate strengths of individual agglomerates determined with a thermomechanical analyzer are shown in Table 1. With an average strength of = 23 MI?a, the water-dispersed agglomerates are more than three times stronger than the ethanol-dispersed agglomerate.

Sintering

Time (min)

Figure 5. Sintered density of samples fabricated from ethanol-dispersed and toluenedispersed agglomerates (<90 I.trn)as a function of time at 125O’C.

EFFECTCIF PAR~CLESOLUBJLIN

ON THE

STRENGTH OF NANOCRYSTAUNE AGGLOMERATES: B~EHMITE

407

TABLE 1 Strength of Water-dispersed and Ethanol-dispersed Boehmite Measured by Thermomechanical Analyzer Dispersion medium

Agglomerate size (pm)

Number of samples

Strength (Mpa)

Standard Deviation (MPa)

Water Ethanol

198-250 198-250

8 8

22.9 6.3

4.2 1.3

A comparison of the measured strength with the theoretically calculated value for van der Waals adhesion gives some insight about the relevant mechanism of boehmite gel agglomerate strengthening. The maximum van der Waals force can be approximated by assuming an interparticle separation of 0.4 nm and a Hamaker constant of lo-l9 J. Using the calculated force as F in equation [l] gives an agglomerate strength of = 4 MPa for 8 nm particles. This calculation makes many assumptions but, it is apparent that for water-dispersed agglomerates, the van der Waals force is not the predominant bonding mechanism. 4.3 Agglomerate Density The diffemnce in agglomerate density may be due to the difference in capillary stress during gel drying. During drying the liquid causes acompressivestress on the drying gel when it reaches the critical point or the pendular state At this condition, the liquid forms a surface film around the drying@ and the partcannot shrink without the liquid-vapor interface receding into the part. The capillargr pressure is a maximum at this point (16). The capillary stress (PC) during drying is proportkmal to the surface tension y/Yof the solvent as follows: pc = _

2Ylvcos@) a

[31

where a is the Jpore channel radius. The capillary stress for the ethanol and water dispersed gels should only difkr by the surface tension because the other factors determining the capillary stress such as surface: area (258 m2/g for water-dispersed and 239 m2/g for ethanoldispersed agglomerate) and contactangle are nearly the same for both liquids (17). The surface tension of water at 20’C is 72.8 niN/m and ethanol is 23 mN/m (18). Thus, the water-dispersed gel would have three times more capii stress than the ethanol-dispersed powder. To further investigate the effect of surface tension on agglomerate density, agglomerates were redispersed with a solution of water+9.53 wt.% butanol. This solution has a surface tension of 27 mN/m (18), and the solubility of boehmite in this solution is believed to be approximately the same as in water. The gel obtained after dispersion in water+butanol solution was as strong as the water-dispersed gel, and the agglomerate density was only 1% lower than the waterdispersed gel agglomerates. This result indicates that the capillary stress during drying is not the predominant reason for the agglomerate density differences but instead may be due to colloid stability diffemnces.

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The densification of samples fabricated from 75 pm, water+butanol solution-dispersed gel agglomerates at 1250°C is compared in Figure 6 to that of samples fabricated from 75 pm, waterdispersed agglomerates. The water-dispersed sample has a slightly higher sintered density when the sintering time is less than 15 min, but the overall sintered densities are similar for both cases. It is apparent that the deformability of the water+butanol solution-dispersed agglomerates is not improved by lowering the surface tension of the dispersing solvent. Lowering the surface tension of the medium relative to water by using an organic solvent resulted in more porous gel structures (19,20) or lower agglomerate strengths (21). However, changing the surface tension is in most cases, believed to be accompanied by a change in the colloidal stability and the material solubility in the media. Thus, it is difficult to separate the effect of surface tension from the effects of colloidal stability and material solubility. As discussed in section 2, capillary forces are nonexistent in dried agglomerates and the effect of surface tension on agglomerate strength should be limited to its contribution to agglomerate density. In the present work, the surface tension has little effect on even agglomerate density and it can be concluded that lowering the solvent surface tension does not effectively weaken the agglomerates. To examine the effect of sol stability on the density of the dried gel, the pH of the boehmite sols was adjusted with NH40H after initial stabilization at pH 3. The densities of the 75 pm agglomerates obtained from the sols dispersed at various pHs are shown Figure 7. The agglomerate density decreases from 53% at pH 3 to44% atpH9, the isoelectric point of boehmite. Figure 8 shows the pore size distributions for isostatically pressed (at 280 MPa) samples of the above agglomerates. Both the maximum pore size and the fraction of large pores are observed to decrease as the agglomerate density decreases. It should be noted that although the pH 9 sample 9.5 I

El l

90 -

85 -

D l

0 80 -

l q l

water-dispersed water+butanol-dispersed

.I

1

100

10

Sintering

Time

1000

(min)

Figure 6. Sintered density of samples fabricated from water+butanol solution-dispersed and water-dispersed agglomerates (75 pm) as a function of time at 1250°C.

BoEHMTE EFFECT01: PARTICLESOLUBIUWONTHESTRENGTH OF NANOCRYSTALLINE AGGLOMERATES:

409

50 P 48 -

0

8

6

10

PH Figure 7. Dried gel agglomerate density as a function of initial sol pH.

-

pH3 (53%)

----..................

pH4(49%) pH6(46%)

-------.

pH 9 (44%)

-_-_-

ethanol dispersed (40%)

Pore Diameter

(pm)

Figure 8. Cumulative pore volume in samples fabricated from gel agglomerates dispersed at various pHs (numbers in the parenthesis indicate relative agglomerate densities).

S KWONANDGL MESSING

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and ethanol-dispersed sample are fabricated from agglomerates of similar densities, there are still large pores in the pH 9 sample after pressing and the maximum pore size is close to that of the pH 3 sample. Thus, the agglomerate density is not a predominant factor for the strength of the agglomerate. EFFECT

OF BOEHMITE

SOLUBILITY

5.1 Model

As discussed in section 2, the solubility of the material itself may be the reason for agglomerate strengthening (22). During drying, the solute may preferentially precipitate at the particle contacts due to the negative curvature of the geometry. This process is analogous to solution precipitation during sintering except that solute supersaturation is enhanced by drying. In addition, at the end of drying, the liquid is last present at particle-particle contacts due to the small curvature between the particles. As aresult, the solute preferentially condenses at particle contacts to form strong chemical bonds. The effect of neck formation on the gel strength becomes more pronounced when particle size is small (23). Maskara et al. reported that the solid content of the slurry affects the agglomerate strength because the ratio of dissolved material to solid is inversely proportional to the solid content (11). Neck formation by precipitation of dissolved material is, however, possible only when there ate particle contacts. Thus, the initial solid content in a slurry is not as important as the solid content at the point of particle contact during drying. In addition, the effect of precipitation on agglomerate strength is ambiguous unless there is a distinct particle-contacting phenomenon. In the present work, the boehmite sol undergoes gelation at the point where the particles form a threedimensional network, and the solid content at this point has significant meaning. The solubility of aluminum hydroxide is a function of temperature and pH. Aluminum hydroxides are amphoteric; they are soluble in both acidic and basic solutions. In aqueous solutions of pH 6-8, boehmite solubility is very low (24-26). It is known that below 35O“C, the precipitate is gibbsite (y-Al(OH)3) if the pH of the solution is lower than 5.8 and higher than 9. Bayerite forms in the pH range of 5.8 to 9 (24). In the earlier pH dispersion experiment (section 4.3), the phase of precipitates might be different depending on pH. Also, it should be noted that the solubility of boehmite in water in the pH 6-8 range can be as low as in ethanol. The agglomerates from the sols of this pH range, however, do not appear as soft as ethanol-dispersed agglomerates (Figure 7 and 8). The reason for this difference can also be correlated to the precipitation of solutes during drying. When adjusting pH from3, the solsrapidly flocculate above pH 5. However, the solubility decreases simultaneously with the formation of particle contacts. After formation of the flocculated gel, the solubility decrease results in deposition of solute at particle contacts and this still contributes to gel strengthening. The size of the neck formed by precipitation at the particle-particle contacts can be calculated by assuming the particles are spherical. In fact, the primary boehmite particles are needle-like: thus, the solubility and neck shape may be different from spherical particles. However, it is believed that the effect of the solubility on the agglomerate strength based on the spherical model can be also applicable for the particles with irregular shape. The interparticle neck has both positive (r-1in Figure 9) and negative (rz in Figure 9) curvatures. The positive curvature (rl) is indicative of the extent of neck growth. The volume of the neck was calculated from the geometry in Figure 9 by considering the relationship:

EFFECTOF PARTICLESOLIJBILI~ON THESTRENGTHOF NANOCRYSTALLINE AGGLOMERATES: B~EHMITE

(R +c$ =(n

+

411

r$ +R2

and by integration, where R is particle radius. The general equation forfN, the ratio of neck to particle volume, is a complicated function of t-1(or Q). For a given value ofR (4 nm in this work), by using regression, the relationship can be approximated as: f~ = 0.0016r;4.04

PI

The value of fN is plotted in Figure 10 as a function of the neck radius t-1and compared to the value calculated using the equation reported by Endo et al. (9) for the liquid bridge volume of the same geometry. The difference between the two results occurs because Endo et al. approximated the neck volume by using r2
161 where Vzbb, is the molecular volume of the precipitate (gibbsite). The total volume of the necks that form between particles in a dried gel which initially contained one liter of solution at the gel point, Vneck,is Scalculatedas: Vneck

= ~xS.G.fNv%dcm3

/ 11

where Vroeh,is the molecular volume of boehmite, a.ndXs.G.is the particle concentration [mol/fl at the gel point. k is divided by 2 because each neck is shared by two particles. The average number of contacts per primary particle, kcan be approximated by using k+E=rc, where& is the void fraction (28). The void fraction of the water-dispersed gel agglomerates is 0.47 and the calculated k value is 6.68. By equating V,,, and vneck, one can obtain SCas:

sc =fN.i.Xs.~

* ’ Vgibb.

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Figure 9. Neck formed between two spherical particles.

calculated value

0

4 2 3 Neck Radius (nm) Figure 10. Neck to particle volume ratio as a function of neck size. 1

where V&J,. is 19.55 cm3/mol, Vzbb. is 31.965 cm3/mof (24), and is 2.94 mollf. For boehmite, equation 8 can be simplified as follows: s, = 0 .0097r14.04

191

and the resulting neck size r-1is plotted in Figure 11 as a function of SC. It is shown in Figure 11 that a solubility of 0.01 mol// results in = 1 nm neck for the 8 nm diameter boehmite particle. As shown in Figure 10, the volume of the neck between two particlesis very small relative to the particle volume, and consequently a low solubility can result in a considerable neck size. When one considers that the gel strength is proportional to the cross-sectional area of the neck, i.e.,

BoEHMlE EFFECTOF PARTNXESOLIJ~ILIT~ ONTHESTRENGTH OF NAWXYSTAUNE AGGLOMERATES:

0.01 0.00

0.01

0.02

Solubility

0.03

413

0.04

(moU1)

Figure 11. Neck size as a function of particle solubility. to the square of the neck radius (rl in Figure 9) (29), the solubility is an important issue for the agglomerate gel strength, especially when the particle size is small. In the present model, the precipitated neck is assumed to be fully dense, but in reality, it can range from 30 to 70%, which is a typical relative density range of molecular gels. The particle bonding strengrh from neck formation, however, is believed to be insensitive to the relative neck density when we consider that the load-bearing area and the nature of molecular bonding in the neck do not change as the relative density changes. Another :important effect of particle size on agglomerate strength arises from the fracture mechanics perspective. Equation [l] is valid under the assumption of uniform particle size and homogeneous bonding throughout the agglomerate. If an agglomerate contains defects such as cracks, then the agglomerate strength is strongly dependent on the crack size. Kendall proposed an equation for the agglomerate strength based on this concept (30). A sol-gel derived xerogel, like the present system, is fairly uniform and the critical crack size can be on the order of the particle size. The strength of an agglomerate with a uniform microstructure is thus, dependent on the particle size not only from the bonding mechanism point of view (equation l), but also from the fracture mechanics point of view. 5.2 Effect of Solubility on Gel Integrity The solubility of boehmite in pH 3 water and ethanol was measured in the following manner. The boehmite powder was dispersed in both media for one week before centrifugation at 40,000 rpm (160,000 g) for 12 hours. The aluminum concentration in the supematant was determined by inductively coupled plasma (ICP). The ICP result showed that the total dissolved aluminum was

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437 ppm and 0.76 ppm in the water and ethanol supematants, respectively. The concentration of A13+,which is believed to be the primary solute species in acidic solution below pH 4 (24), is 0.018 mol/l and 2.5~10~~mol/I in water and ethanol, respectively. For the ethanol case, the phase of the precipitate and the solid content at gel point, Q.c., may be different from the water case, but these factors do not significantly influence the neck size as much as the solubility difference. Some typical solubilities including measured values for water and ethanol and corresponding neck sizes are listed in the Table 2. The precipitate phase and the solid content at the gel point, XS.G.,for the ethanol case are assumed to be the same as for the water case. It is evident that the solubility difference between the two media is sufficient to yield water-dispersed agglomerates 25 times stronger than ethanol-dispersed agglomerates. However, in the ethanol case, the bonding between the primary particles cannot be simply predicted from the measured solubility since the agglomerates were initially formed in water, and they cannot be redispersed to primary particles in ethanol as discussed below. The solubility measurement allowed the prediction of the neck size and the subsequent relative strength of agglomerates for different primary particle sizes. Equation 2 gives the solubility of the specific particle size if the solid-liquid interfacial energy, ysr, is known. Unfortunately, the boehmite-water interfacial energy is unknown, so instead, we examined the effect of particle size in the possible range of the interfacial energy. The solubility of boehmite was calculated as a function of particle size using equation 2 and the measured solubility of 8 nm diameter particle for different values of interfacial energy. The calculated solubility is converted to a neck radius (rl) using equation 9 and the agglomerate strength was assumed to be proportional to the square of rt (27). The relative agglomerate strength was normalized to the agglomerate strength of the 8 nm particles (Figure 12). It is evident that the particle size is a critical factor in determining agglomerate strength of nanoscale particles, and that the dependence of strength on the particle size is much more pronounced for large values of interfacial energy. In order to verify the role of solubility on boehmite agglomerate strength agglomerates were prepared by immersing water-dispersed gel fragments in ethanol for 7 days. The long immersion time was used to encourage any possible reaction with ethanol. The only difference between these agglomerates and the ethanol-dispersed agglomerates used above is the absence of mechanical force during the immersion and the immersion time. The extended period of immersion, however, proved to have no effect on the integrity of gel fragments: the gel fragments completely retained TABLE 2 Solubilities of Boehmite and Calculated Neck Radius Solubility (mol/E)

Neck Radius, rt (nm)

Neck to Particle Radius Ratio, f-l/R (%)

8.9~10-~ 2.5x10m5(ethanol) 2.3~10-~ 1.2x10-3 1.8~10~~(water)

0.1 0.23 0.4 0.6 1.16

2.5 5.75 10

15 29

EFFECTOF PmncE

SOLUBILITV ONTHESTRENGTH OF NANOCRYSTALUNE AGGLOMERATES: B~EHMITE

415

interfacial energy (N/m)

&tite-water

..................

1.2 0.9

-------.

0.6

10

Particle

Radius

(nm)

Figure 12. Normalized agglomerate strength as a function of particle size and boehmite-water interfacial energy. their initial shape after 7 day immersion (this same result was obtained when gel fragments were immersed in toluene or cyclohexane). In contrast, if the fragments are immersed in the water, they spontaneously form a stable sol in a few hours. The different behavior of gel fragments in water and ethanol shows that water can redisperse the gel particles whereas ethanol does not. Since both media are protic and can participate in hydrolysis or alcoholysis, the only possible reason for the different behavior of gel fragments when immersed is believed tobe the difference in the solubility. After ethanol-immersion, agglomerates for strength measurement were obtained in the same manner as described in the experimental procedure. The ethanol-immersed agglomerate strength measured directly with a thermomechanical analyzer, was 18.4 MPa, which is much closer to the water-dispersed agglomerate strength than to ethanol-dispersed. This result indicates that unless the gel fragments are crushed during dispersion, the effect of using ethanol is greatly diminished. It is proposed that during water-dispersion, the fragments are dispersed to primary particles because the particle binding necks are dissolved. Upon drying, they form a homogeneous gel network whereas for the ethanol-dispersion, the gel fragments are mechanically crushed and the smaller fragment units can not form as strong a network as the water-dispersed agglomerates. The particle size of the ethanol-dispersed slurry after dispersion was 0.4 pm which is significantly larger than the primary particle size. The proposed schematic structure of water and ethanoldispersed agglomerates are presented in Figure 13. The water-dispersed agglomerates have a uniform structure and strong bonding between primary particles. The ethanol-dispersed agglomerates are believed to consist of = 0.4 pm scale units which have primary interparticle bonding similar to water-dispersed agglomerates, but the loose packing of these units and the lack of a strong bonding mechanism between these units results in soft agglomerates. Assuming the above

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Figure 13. The schematic structure of (A) water-dispersed agglomerates and (B) ethanol-dispersed agglomerates,

structure and a van der Waals force as the bonding mechanism between the units, the calculated ethanol-dispersed agglomerate strength is = 0.05 MPa, which is significantly less than the measured ethanol-dispersed agglomerate strength. The difference between measured and calculated agglomerate strength implies that another bonding mechanism besides van der Waals forces such as hydrogen bonding, may contribute to the bonding of units in ethanol-dispersed agglomerates. CONCLUSIONS Hard boehmite gel agglomerates can be softened by dispersing in ethanol. Because boehmite is significantly more soluble in water than in ethanol, hard boehmite agglomerates form in the aqueous system by condensation of dissolved aluminum species at interparticle contacts during drying. For the condensation of dissolved species to form necks, particle contact must occur prior to the precipitation of dissolved species. A two particle model shows that the neck volume is very small relative to the particle volume and that limited solubility can result in a considerable degree of neck formation. The brittle characteristic of the water-dispersedboehmite agglomerates is mostly attributed to neck formation by solute precipitation. This solubility issue becomes more significant as the particle size decreasesbecause of the increased solubility of finer particles. Other possible softening mechanisms by ethanol dispersion such as low capillary forceduring drying and

B~EHMITE EFFECT OFPmnc~ S~LIJBILIT~ ON THE STRENGTH OFNAWCRYSTALM AGGLOMERATES:

417

the formation of ethoxide by ethanol-dispersion, were shown not to be responsible for agglomerate softening in this system. ACKNOWLEDGMENTS The authors are gratefulto Ssangyong Cement IndustrialCo., Ltd. in Korea for the financial support to Seongtae Kwon. REFERENCES 1.

2. 3. 4.

5. 6. 7.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19. 20. 21. 22. 23. 24. 25.

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May, H.M., Helmke, P.A., and Jackson, ML., Geochimica et Cosmochimica Acta, 1979,43,861. Kousaka, Y., Endo, Y., and Nishie, Y., Kagaku Kogaku Ronbunshu, Japanese Journal of Chemical Engineering, 1992, 18,942. Smith, W.O., Foote, P.D., and Busang, P.F., Physics Review, 1929,34, 1271. Iler, R.K., The Chemistry of Silica, John Wiley & Sons, Inc., New York, ,1979, p. 5 19. Kendall, K., Powder Metallurgy, 1988,31,28.