The variation in, and correlation of, the energetic potential and surface areas of powders with degree of uniaxial compaction stress

Powder Technology,

60 (1990)

15

15 - 26

The Variation in, and Correlation of, the Energetic Potential and Surface Areas of Powders with Degree of Uniaxial Compaction Stress N. G. STANLEY-WOOD,

Department (Received

A. ABDELKARIM*,

of Chemical Engineering,

September

1, 1988;

M.-E.

JOHANSSON

in revised form January

Particulate

solids of different sizes, shapes, were characterized in terms of surface area, surface energy and intraparticulate porosity before and after uniaxial compaction over the stress range 0 - 250 MPa using low temperature (77K) nitrogen adsorption. Prepared compacts of microfine cellulose (Elcema PO50), microcrystalline cellulose (Avicel PHl Ol), dicalcium phosphate dihydrate, magnesium trisilicate and titanium dioxide were diametrally fractured to elucidate the physico-mechanical behaviour of the coherent compacts and to assess the nature of the particle-particle bond. Surface adsorption potentials and a dimensionless bonding factor were correlated with the unaxial compact stress to form coherent compacts for a range of plastic, elastic and fragmentary materials. There is, with the above materials, a linear relationship between the natural logarithm of the diametrally fracture stress and compact voidage. area and hardness

INTRODUCTION

In the compaction of powdered material, a reduction of the surface area of compacts at compaction stresses in the range 10 - 300 MPa is seen with many metallic, inorganic and ceramic powders [l - 61. The variation of compact surface area, usually measured by nitrogen adsorption at low temperature and application of the Brunauer Emmett and Teller (BET) equation, is a complex phenom*Present address: Industrial Research and Consultancy Institute, P.O. Box 258, Khartoum (Sudan) **Present address: Cederroths AB, Box 715, S-194.27 Upplands-VCsby (Sweden) 0032-5910/90/$3.50

G. SADEGHNEJAD

and N. OSBORNE

University of Bradford, Bradford BD7 1DP (U.K.)

SUMMARY

surface

**,

18, 1989)

enon which is related not only to the elastic/ plastic deformation, physical shape and mechanical strength of particles [7 - 91, but also to the changes in the intra- and interparticle respectively, spaces, pores and voids, within compacts [lo, 111, The measurement of surface area and interparticle voidage by permeability [ 12 - 151 or mercury penetration [5,16,17] of compacts produced from granulated and non-granulated materials also shows complex non-linear and non-logarithmic relationships between pore/ void size or surface area and compaction stress. In attempts to resolve the ambiguities seen in the measurement of the topological nature of uncompacted solids, the DubininRadushkevich equation [ 181, which emphasises the energetic nature of solids in conjunction with the porosity of materials, has recently been used to characterise hetero- and homogeneous surfaces [ 19,201. The basis of the Dubinin-Radushkevich equation is the incorporation of the Polanyi phenomenological concept of equipotential surfaces and adsorption potential of vapours onto solids. In any solid-fluid or solid-solid interfacial contact, an energetic interchange occurs at the interface. Measurement of the surface energy or any adjunct to surface energy is thus important to indicate the bonding or disintegration forces within such a system and could possibly be used as a criterion to classify materials which are chemically similar. Buckton and Newton [21] have shown that measurement of contact angles on compressed powder discs because of surface heterogeneity and crystal deformation within microcrystalline material, do not necessarily characterise thermodynamically uncompacted powders. The physical adsorption properties of nonporous solids are often markedly different 0

Elsevier

Sequoia/Printed

in The Netherlands

16

from micro-, meso- or macroporous solids. The differences seen with porous materials can be due to the restriction in the formation of a multi-layer adsorbed film or the overlap of the potential fields experienced by closely adjacent surfaces within pores. Derjaguin et al. [ 121, who employed permeametric and Knudsen diffusional flow methods for the measurement of powder bed surfaces, divided the particle surface into the voidal surface between particles used for gaseous transport and the adsorption surface of pores within particles. Irradiation of a number of solid surfaces to alter the solid surface energetic state caused an increase in the measured BET adsorption surface area but not the Knudsen diffusional surface area values. The energetic or thermodynamic state of the powder or compacted surface is therefore of decisive importance in the determination of BET surface areas. Although the thermodynamic characterisation of solid-liquid and liquid-liquid systems in terms of solubility, reaction potential and dissociation coefficients has been extensively used to predict the behavioural effects of multiphasic systems, the thermodynamic properties of solids and multiparticulate systems have received scant attention. Analysis and interpretation of adsorptiondesorption isotherms has been attempted, however, by Rand [22] using the generalised Dubinin-Astakov equation to determine the energetic heterogeneity of surfaces. The Freundlich and Dubinin-Radushkevich equations have also been used to determine not only the surface areas of porous solids but also energy distribution functions occurring at solid surface adsorbate interfaces. StanleyWood et al. [23, 241 have, however, used the Polanyi equation to determine the adsorption energy potential on a number of compacted and uncompacted powders. Schubert [25] reviewed the numerous equations deduced, in terms of particle size, shape, surface area, surface bonding, surface energy and voidage, to ascertain and predict the strengths of either agglomerates or compacts. In all the equations appraised, the compact or granulate strength was seen to be dependent upon the voidage V, particle size d, surface area S and a function of particle attraction A.

In this investigation, various microporous and non-porous solids have been compressed over a relatively large uniaxial compaction stress range. The surface energies, determined by the Polanyi potential from low-temperature nitrogen adsorption isotherms, were assessed for each compaction. The diametral strengths of the compacts, expressed in terms of a dimensionless bonding factor which incorporates compact surface area, compact surface energy and compact voidage was then related to the compaction stress required to cause densification and compact coherency of porous and non-porous particles.

EXPERIMENTAL

Powdered materials investigated Cellulose

Two different types of high-grade pharmaceutical cellulose were examined [ 261: (i) microfine cellulose, MFC, (Elcema PO50), which is a product obtained by a milling process, and (ii) microcrystalline cellulose, MCC, (Avicel PH lOl), which was obtained by a spray drying process. Particle density by air pyknometry was 1.56 X lo3 and 1.52 X lo3 kg mV3 with a median size by a sedimentation of 25.0 and 50 pm for MFC and MCC respectively. Dicalcium

phosphate

dihydrate

Dicalcium phosphate dihydrate (DCP) is a white crystalline water-insoluble powder with a median particle size by photosedimenation of 12.8 pm and a size range of 5.3 - 27.5 I.tm. The density of uncompacted particles measured by an air compression pyknometer was 2.40 X lo3 kg rnp3. Magnesium

trisilicate

Photomicrographs of magnesium trisilicate revealed that the particles were irregular in shape and of a crystalline appearance [ 181. Photosedimentation using a wide-angle scanning photosedimentometer gave a median particle size of 14.8 f 12 pm and contained 8% less than 2.0 I.trnwhen dispersed in 0.1% sodium hexametaphosphate in distilled water. The particle density by air pyknometry was 2.21 X lo3 kg rnp3.

17

Titanium dioxide Titanium dioxide, a r-utile pigment produced by Tioxide Ltd, U.K., had a mean particle size determined by centrifugal sedimentation of 0.18 pm [26]. The particle density, by air pyknometry, was 2.40 X lo3 kg me3 with a surface area by nitrogen adsorption of 6.22 mz g-l. Nitrogen characterisation Low-temperature nitrogen adsorption Samples of all powders and uniaxial compressed compacts were degassed at room temperature (23 f 1 “C!)for 48 h at a vacuum of less than lOA Torr to remove any physically adsorbed vapours, before nitrogen adsorption measurements. The adsorption of nitrogen at 77.5 K onto the surfaces of the powders and compacts over the relative pressure range 0.025 - 0.96 was measured by a volumetric low-temperature gas adsorption apparatus similar to that described in British Standard BS 4359 Part 1. The nitrogen used was research grade XX obtained from British Oxygen Company, U.K. The nitrogen surface area of the celluloses was calculated from the relationship S&,(m*

where RT has the value of 640.33 J mol-* at 77.4 K and (P,/P) is the reciprocal of the relative pressure on the low-temperature adsorption isotherms. The Polanyi adsorption potential at zero coverage, e,, was obtained by extrapolation of the relationship e = RT ln(P,/P) with either various degrees of surface coverage or the quantity of adsorbed vapour on the solid surfaces (Fig. 1). Surface coverage 19was obtained from the ratio of the quantity of nitrogen adsorbed at specific relative pressures (V, or X at P/P,) to the monolayer capacity (V,,, or X,) (0 = VJV, or X/X,) obtained from the BET equation where V and X are the volume and weight of adsorbed vapour V,, respectively.

. PHlOl . PO50

g-l) = 4.37V,

where V, is the monolayer capacity (cm3 g-‘) calculated from the adsorption isotherm using the Brunauer Emmett and Teller (BET) equation (eqn. (1)). P 1 -_=-+-P,--P v

1 v,c

c-1

P

VznC P.5

(1)

From the BET equation and the Polanyi adsorption potential relationship, the surface area S and surface energies of both powders and compacts were calculated respectively. Nitrogen adsorption energies The adsorption coefficient C (eqn. (l)), which relates the difference between the energy of adsorption of a vapour onto a bare surface, E,, and the energy of liquefaction, EL, where C - exp(E, - E,)/(RT), was also evaluated from the BET equation to give the thermodynamic property RT In C. The Polanyi adsorption potential e was calculated from eqn. (2).

(ps1

e=RT1n 7

0.0

1

01

02

03 Volume

OL o-5 adaorbed

06 07 V, cm3~’

Fig. 1. Adsorption potential energy (PO50) and microcrystalline (PHlOl)

08

09

10

on microfine celluloses.

Micro- and mesoporosity of solids When mono- and multi-layers of adsorbed nitrogen are formed on the surface of nonporous solids, the thickness of the freely adsorbed layers can be expressed as a ‘t-curve’ [27, 281. Comparison of the quantity of adsorbate adsorbed (V,) on to a porous (intraparticle space) solid or into a compact matrix with voids (interparticle space) with the thickness of an unimpeded adsorbed layer t obtained on a non-porous, non-void material

18

can indicate from the Va-t curve the micro-, meso- or macroporosity and voidage of a solid or compact respectively. Figures 2 and 3 show the Va-t curves for magnesium trisilicate, dicalcium phosphate, titanium dioxide, microcrystalline cellulose (PHlOl) and microfine cellulose (PO50). Uncompacted magnesium trisilicate is microporous in nature with pore sizes <1.6 nm, while dicalcium phosphate is virtually non-porous with the possibility of a small

1 20

Thiekneas

of

Adsorbed

layer

t ,nm1

Fig. 2. V,-t curve of dicalcium phosphate, sium trisilicate and titanium dioxide.

Thlckmem

of adsorbed

layer

t

magne.

[urn]

Fig. 3. V,-t curve for microcrystalline fine (0) cellulose.

(m) and micro-

3 w

Y_+

amount of mesoporosity (pore sizes 1.6 - 100 nm). Microcrystalline and microfine ceiluloses are mesoporous in the uncompacted state, while uncompacted titanium dioxide gives the impression that there is a small degree of microporosity present when the isotherms are analysed. Electromicroscopy shows, however, that titanium dioxide consists of a collection of almost spherical submicrometre particles. Particle packing could thus produce an interparticle voidage within the uncompacted powdered sample. The slope of the Va-t curve passing through the origin can be used to evaluate the surface area freely accessible for mono- and multilayer adsorption. The surface area S, being regarded as the nonporous surface area of the solid. Deviations of the V,-t curve from linearity can also be analysed to obtain micro- or mesopore distributions [ 27, 281. Uniaxial direct compaction The compaction of DCP, magnesium trisilicate and titanium dioxide in the range 15 to a maximum stress of 250 MPa were individually carried out in an instrumented punch and die assembly by placing double the powder density weight into a lubricated stainless steel 20.0-mm internal diameter die (DCP, magnesium trisilicate) or a 13-mm internal diameter die (TiO,). Lubrication prior to each compaction was with a 0.1 wt.% solution of magnesium stearate. Time was allowed for the solvent to evaporate from the die surfaces before hand filling and compaction. As uniaxial force was applied to the upper punch, force transducers (Kistler Ltd. Type 906B and 903A) located on the upper and lower punches and on a radial collar around the die recorded the variation of force with time. Simultaneously, the height of the upper punch and therefore compact thickness was measured with a linear variable displacement transducer. All electrical output was recorded on cassette tape by a data logger. MCC and MFC powders were uniaxially compacted in an instrumented single-punch machine (Type E2, Manesty Machines Ltd., Liverpool, U.K.) over the stress range 15 - 120 MPa using 4 g of powder in a 12.2-mm internal diameter die. All prepared compacts were aged by storing in a screw-capped jar at 20 “C in a controlled

19

temperature and humidity room (40% R.H.) prior to a physico-mechanical crushing strength test.

at=

Diametral

where F is the recorded fracture force (N), D is the compact diameter (mm) and t is the compact thickness (mm).

fracture

test

The measured compact was placed diametrally between the upper and lower platen of a hydraulic press (Model T42U Denison Ltd., Leeds, UK) which moved at a constant strain rate of 10.2 mm min- l to increase the applied force on the circumference of the compact. The fracture force was recorded when the compact underwent catastrophic cleavage. The fracture stress cTfwas calculated in accordance with BS 1881 Part 4 (1970) (eqn. (3)):

2F ?rDt

(3)

RESULTS AND DISCUSSION

Low-temperature

nitrogen

adsorption

Tables 1 -4 show the BET surface area, the BET adsorption coefficient, the energy from the overall coefficient (RT In C), and the Polanyi adsorption potential at zero coverage

TABLE 1 Mechanical, physical and physico-chemical Compaction stress T&Pa)

Surface area S (mZ g-l)

Adsorption potential at zero coverage

characteristics of compacted and uncompacted

Ratio e0/S

(kJ g

Compact mean voidage

Compact diametral strength

e0

mole1 mp2)

(“-)

y&Pa)

(kJ mol-‘)

Dimensionless bonding factor DBF 10-z

Range of diametral strengths (MPa)

0 15

2.20 2.05

5.75 5.46

2.61 2.66

1.0 0.89

-

-

32 47 77 120 155 248

1.97 2.11 2.16 2.17 2.20 2.19

5.53 5.55 5.17 5.20 5.30 5.19

2.81 2.63 2.39 2.39 2.41 3.27

0.71 0.524 0.454 0.260 0.387 0.257

0.203 0.331 0.683 1.22 1.42 2.75

0.189 0.311 0.661 1.128 1.388 2.420

dicalcium phosphate

0 0

- 0.218 - 0.35 - 0.705 - 1.33 - 1.456 - 3.07

Energy from BET adsorption RTlnC (kJ mol-‘)

3.76 -

3.75 3.46 6.54 8.53 11.6 19.0

2.90 2.14 3.30 2.38 2.82 -

TABLE 2 Mechanical, physical and physico-chemical microcrystalline (MCC PHlOl) celluloses Powder

Compaction stress

Surface area S (m2 g-l)

T&Pa)

Adsorption potential at zero coverage

properties of uncompacted

Ratio e0lS

(kJ mol-’ mW2)

e0

(kJ mol-‘)

and compacted microfine (MFC PO50) and

Compact mean voidage

Compact diametral strength

L

T&Pa)

Range of diametral strengths (MPa)

Dimensionless bonding factor DBF 10-z

Energy from BET adsorption coefficient RTlnC (kJ mol-‘)

0 8.42 22.6 30.1 47.1

2.65 1.72 2.29 1.39 1.99

0 8.89 15.3 20.8 29.2

1.61 1.32 1.37

MCC PHlOl

0 17.6 39 60 89

1.21 1.97 1.37 1.50 1.38

4.22 2.26 2.69 2.93 2.84

3.48 1.14 1.96 1.95 2.05

0.44 0.31 0.23 0.15

-

-

2.75 7.45 13.1 20.6

2.68 - 2.87 7.27 - 8.10 12.6 - 13.52 19.9 - 22.8

MFC PO50

0 17.6 21.0 38.5 60 70

1.85 2.96 2.01 2.30 2.14 2.86

2.49 2.23 2.25 2.53 2.95 3.10

1.35 0.75 1.12 1.10 1.38 1.08

0.51 0.48 0.32 0.24 -

-

-

2.64 3.30 7.59 12.89 -

2.47 3.00 7.28 12.45 -

- 2.82 - 3.44 - 7.96 - 13.26

20 TABLE

3

Thermodynamic

physical

Compaction stress

0 17.5 70 140 210 280

s

(m2 g-l)

e0

280 270 260 300 278 226

of magnesium

trisilicate

compacts

Coefficient of adsorption

(kJ mol-‘)

?-)

Adsorption coefficient energy RTlnC (kJ mol-‘)

10.65 9.24 8.47 9.28 8.00 8.03

43.7 54.0 61.6 56.0 45.0 5.5

2.42 2.56 2.64 2.57 2.44 1.09

Ratio e0/S

(kJ g mol-r me2) 10-a 3.80 3.42 3.26 3.09 2.87 3.50

4

Mechanical, Compaction stress YiPa)

properties Potential at zero coverage

Surface area

$Pa)

TABLE

and mechanical

physical

and physico-chemical

Surface area S (m2 g-l)

Adsorption potential at zero coverage e0

properties

Ratio

of compacted

and uncompacted

Compact mean voidage

Compact diametral strength

mol-’ mm2)

Y-)

$Pa)

e0/S

(kJ g

Range of diametral strengths (MPa)

titanium

dioxide

Dimensionless bonding factor DBF 10-a

Energy from BET adsorption RTlnC (kJ mol-t )

(kJ mol-*) 0 54 101 110 201 302 402 503 1007 1510 2013

6.22 7.40 -

4.17 -

0.669 -

1.0 0.429 0.314

0 0 9.2

7.15 7.02 6.92 6.82 6.76 6.43 6.63 6.68

3.96 3.99 3.84 3.66 3.78 4.30 4.72 5.25

0.554 0.569 0.055 0.537 0.559 0.669 0.711 0.786

0.296 0.230 0.190 0.163 0.147 0.099 0.071 0.050

10.2 14.4 22.5 32.6 38.8 47.9 40.5 85.9

for uniaxially compacted and uncompacted dicalcium phosphate, microfine and microcrystalline cellulose, magnesium trisilicate and titanium dioxide respectively. Figure 4 shows the variation of compact surface area with degree of compaction for all powders. In some cases, there is a steady decline in compact surface area as compaction stress increases (titanium dioxide). Reduction in available surface area within compacted material has been found by other workers. Ramsay and Avery [3, 41 compacted ultrafine spherical particles of silica and zirconia over the stress range 0 to 100 ton in2 (0 - 1540 MPa) and found a decrease in surface area with compaction (Table 5). Surface area reduction with compaction was also seen by German [2] and Stefanovic and Ristic [20] when compacting palladium

-

0 0

15.7 31.5 33.4 45.0 51.5 76.5

0 0

4.14

10.7 14.0 22.0 32.9 37.5 40.5 43.4 54.4

2.83 2.91 3.02 2.88 2.96 4.84 2.82 3.55

-

- 29.3 - 33.7 - 42.7 - 49.8 - 67.5 - 112.1

black. Hardman and Lilley [8,9], compacting sodium chloride, sucrose and coal, found a reduction in compact surface area for sodium chloride with increase in compaction stress. Reduction in the compact surface area from uncompacted magnesium oxide was reported by Stanley-Wood and Johanson [ll, 29,471 and also by Stanley-Wood and Abdelkarim [30, 461 for sodium chloride in the stress range below 200 MPa. Figure 1 shows the variation of Polanyi adsorption potential e, calculated from eqn. (2), uersus the volume adsorbed into the surface of either microfine cellulose PO50 or microcrystalline cellulose PHlOl. The extrapolated value e, for all powders and compacts investigated are tabulated in Tables 1 - 4. The ratio of the Polanyi adsorption potential per unit surface area (e,/S) for five

21

pfy___f&l~ so

100

so0

1000

160

lsoo chmpaction streaa

200

260

800

cc

MPa

¶ooo

as00

aooo

q

kPn

Fig. 4. Variation of BET surface area of uncompacted

and compacted powders with compaction stress.

TABLE 5 Surface areas and adsorption potentials from microporous silica compacts [ 3] BET coefficient c (-)

BET adsorption coefficient energy RTlnC (kJ mol-‘)

Monolayer adsorption

y&Pa)

Specific surface area S (m2 g-l)

0 0.77 1.16 1.54

739 346 268 213

73 184 601 > 103

46.7 117.8 384.8 > 640.3

7.59 3.55 2.76 2.19

Compaction pressure

different powers is shown in Fig. 5. For dicalcium phosphate, the initial response is an increase in the Polanyi potential ratio as compaction increases. In the case of the celluloses (cornminuted and spray dried), titanium dioxide and magnesium trisilicate, there is an initial decrease in the Polanyi adsorption potential per unit area ratio. In the case of cellulose and magnesium trisilicate, an approximate constant value of e,/S with only a slight tendency to decrease as compaction stress increases is obtained. With titanium dioxide (Table 4), these submicrometre spherical particles show an increase in the es/S ratio as compaction stress increases toward the material’s gross deformation stress range. This tendency for very small spherical particles to produce an increase in energy per unit surface area with stress increase has also been seen from recalculation of the work of Ramsey

%I (m mol g-l)

Potential energy at monolayer e, (kJ mol-‘)

Ratio of potential per unit surface area e,/S (kJ mol-’ me2) 10-s

1.44 1.80 2.04 2.40

1.95 5.20 7.76 11.26

and Avery [4], who used nanometre-sized silica and zirconium (Table 5). Stanley-Wood [35] has shown that the strength of the particle-particle bond obtained by diametral fracture can be correlated to either the Clausius-Clapeyron nitrogen isosteric heat of adsorption or the Polanyi nitrogen adsorption potential. It has also been found, from nitrogen and water adsorption isotherms at 77.5 K and 293.2 K respectively on spray-dried and comminuted celluloses [ 361, that the variation of interfacial surface Polanyi adsorption energy with adsorbate coverage on the cellulose surfaces is similar in form to the variation of nitrogen isosteric heat of adsorption and water microcalorimetric differential heats of sorption. The surface area values and magnitude of water heats of sorption on various celluloses were, however, much greater than the values obtained using

22 4.0

1

l

PlOl

.

PO60

0.4 0, 0.0

9

0

-

60

100

160

loo

!m

60

100

lb0

!mo

250

0.06 _

+-

phenomenological method to assess the internal matrix of compacts. Such a discriminatory assessment is achievable by the measurement of interparticulate void surfaces by either permeametric or Knudsen diffusional flow and comparison of these surfaces with the surface area measured by the adsorption technique as has been shown with packed beds by Derjaquin et al. [ 121 and Stanley-Wood and Chatterjee [ 291. Carless and Sheak [37] used the difference between, and variation of, the surface area of sulpathiazole before and after compaction to postulate a critical surface where the phenomena of particle crushing and bonding inherent in most compaction processes cancel each other out. The concept of breakage by compression originates from Griffiths [ 28, 511. The Griffiths crack relationship (eqn. (4)) of=

9

.J

Ob

A

A0

A

A0

kPa A00

Fig. 5. Variation of Polanyi adsorption potential per unit area with compaction stress.

nitrogen as an adsorbate. The particle-particle bonds between microfine or microcrystalline celluloses were correlated with the thermodynamic properties evaluated from either the isosteric heat of adsorption or the Polanyi adsorption potential [ 501. Compact voidage Numerous attempts have been made to correlate the mechanical properties of compacts with the characteristics of particle size, size distribution, shape and shape distribution [17, 35 - 371. On the application of stress to either plastic deforming or brittle fragmenting materials, the discrete initial particle sizes and shapes are deformed or broken. The final compact integrity then bears little relationship to the initial physical powder dimensions of the original material Measurement of compact surface area can evaluate the changes that a solid surface undergoes together with intraparticle pores as well as interparticle voids and purports to be a more discriminatory

k 0.5 0I;

(4)

where r, is the void size radius within compacts or the crack radius within solids and k a constant, can be used to discriminate between compacts manufactured from fragmentary materials (where linearity between uf and l/r, occurs) and compacts manufactured from plastic deforming materials (where nonlinearity ensues) [ 391. James [ 321 has shown a linear relationship between the strength of compacts prepared at 770 MPa, from eight different particle sized fractions of zinc each having a different surface area, and compact surface area. He concluded that as stress increases, compact strength is probably more dependent upon the bonding forces of attraction than upon the contact surface area between particles. Addition of a second component, such as a binder or lubricant, can, however, have a marked effect on the relationship between compact strength and compaction stress. Lerk [40, 411 has found that pharmaceuticals, such as dextrose monohydrate and extrafine crystalline lactose, decrease in strength as compaction stress increases. It is the compact matrix voidage and interparticulate space which has a more influential and predictive effect on the mechanical strength of uniaxially compacted powders than the micro-characteristics of particle size and shape.

23 6.0

. D.C.P. PHlOl A PO60 o Ti02

l

-La

0

0.1

0.1

0.8

0.4

0.6

0.6

0.7

Compact voldage V. I-1

Fig. 6. Relationship between and compact voidage.

diametral

fracture

stress

Figure 6 shows the relationship between diametral fracture and voidage for the four powders, dicalcium phosphate, microfine and microcrystalline celluloses and titanium dioxide. From the powder compacts investigated, there is a linear logarithmic relationship between diametral fracture strength and voidage. Because compact voidage was related to TABLE

6

Surface

area, surface

Powder

energy

and strength

Correlations between surface area, surface energies, compact voidage and compact fracture strength

Schubert [25, 421 reviewed the variables in equations used, since Newitt and ConwayJones [43], to predict the tensile strength of

of powders Va-t area

BET surface area S

St

(mZ

(m2

g-‘)

fracture strength uf rather than uniaxial stress, the resultant fracture stress is independent of material and compact volumes. There is, however, a fundamental difference between the mechanical strengths of deforming and brittle materials. The spread of fracture strengths obtained from plastically deforming materials is of the order of 5%, while with brittle systems the variability in fracture strength can be a hundredfold. Statistical models should therefore be used to quantify the fracture strength of brittle fragmentary systems. The spread and scatter of the diametral compact strengths for DCP, which is known to be a fragmentary material, is reasonable and comparable to cellulose and titanium dioxide, which are known to be non-brittle materials. The fracture of the DCP compacts can be assumed therefore to occur at a particle-particle bonded surface rather than across a brittle particle crystal. Extrapolation of the fracture strength to zero voidage o. can give an indication of the particle strength, since all voids have been removed. Table 6 shows for DCP and cellulose, o. to be in the megapascal stress range rather than the gigapascal range normally observed in strength tests of many materials, while titanium dioxide at zero porosity has u. in the kilopascal range.

curve

g-‘)

Strength modulus In oo/V

Strength at zero voidage

Energy at zero coverage cop

f-J

$Pa)

(kJ mol-‘)

Dicalcium phosphate

2.20

2.65

-8.36

26.1

5.75

Microfine cellulose (PO50)

1.85

2.28

-6.06

55.0

2.67

Microcrystalline cellulose (PHlOl)

1.21

1.02

-6.66

55.8

4.22

6.27

-9.13

Titanium Magnesium trisilicate

dioxide

6.22 280

343.8

-

0.124 -

4.17 10.65

24

bulk materials and agglomerates produced from fine particles with and without binders. In the majority of equations reviewed the variables quoted were - an attractive force between particles, - the voidage (porosity) within the powder matrix, - the surface area or median diameter of the original non-agglomerated particles. In an attempt to correlate the strength of compacts with degree of uniaxial stress from the range of material currently under investigation, a dimensionless bonding factor expressed as ofW8

o,e,S( 1 - LJ)

=

to account for these two linear relationships [49]. There is, however, no unique correlation as seen with agglomerates of sand, silts and limestone [ 451. This may be due in part to the choice of the compact strength at zero voidage, uo, which does not represent the material hardness, ductility, toughness or brittleness and which could thus cause separation of the dimensionless correlation (Fig. 7) into different powder classes. Recent work by Schubert and Wibowo [42] and Tsunakawa and Aoki [44] has shown that even with a system consisting of glass spheres there was a difficulty in the determination of particle assemble strength. Even the Newitt and Conway-Jones approach gave a fourfold deviation between agglomerate strengths. The angle of internal friction, which has been extensively used in the characterisation of bulk powder systems to quantify the flowability of powders, plus the microhardness testing of micrometre-sized particles, used in new technologies of thin film plastics or polyphase materials [ 451, together with the material properties of plasticity and brittleness may soon enable a more universal dimensionless correlation to be found between the characteristics of particles, and compact strength and coherency.

DBF

was calculated. The diametral fracture strength at zero voidage, uO, the Polanyi potential at zero coverage for the uncompacted powder efS and the freely available surface area from the Va-t curves St are tabulated in Table 6. Figure 7 shows that for the celluloses produced by different methods a linear relationship exists between DBF and compaction stress. A linear relationship also exists with the totally different material DCP while titanium dioxide shows two linear regions. Measurement of the internal angle of friction ijE of titanium dioxide by a Jenike shear cell has shown that there is a sudden change in hE from 42” to 36” in the uniaxial compaction stress range 400 to 600 kPa [ 6,481. The change in the bulk property of titanium dioxide could be a contributory factor

CONCLUSION

Characterisation of the physico-chemical nature of particulate solids in terms of surface

z I

? .d

0.6

I

200

20

I

I

600

40

60

I

I

1006

SO

I

1400

I

I

I

1600

I

2260

wa

100 120 140 160 160 200 220 240 260

Compaction stress vc Fig. 7. Bonding factor variation with celluloses and titanium dioxide (0).

Wal

compaction

stress

for dicalcium

phosphate

(O), PHlOl

(*),

and PO50 (A)

25

area, surface energy and intraparticulate porosity before and after compaction is beginning to illuminate and elucidate the physico-mechanical behaviour and nature of the particle-particle bond formed by uniaxial compaction. The complex interaction between particle surfaces and the ability to predict compact behaviour from single or multiple particle characteristics is advancing. There is, however, a need for determination of microparticle hardness, ductility, and brittleness of compacting surfaces to analyse the powder densification process, although the relationship between macrocompact voidage and strength has now been well established.

20 21 22 23 24 25 26 27

28

29 REFERENCES 30

4 5 6 I 8 9 10 11 12 13 14 15 16 17

18 19

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