The effect of temperature on the frictional, cohesive and electrical conducting properties of powders

Materials Science and Engineering American Society for Metals, Metals Park, Ohio, and Elsevier Sequoia S.A., Lausanne

281 Printed in the Netherlands

The Effect of Temperature on the Frictional, Cohesive and Electrical Conducting Properties of Powders P. YORK and N. PILPEL Department of Pharmacy, Chelsea College of Science, University of London, London, S. W.3, 6LX ( Gt. Britain) (Received November 1, 1971)

Summary t A study has been made of the mechanical and electrical conducting properties of a variety of powders as the temperature and pressure are raised. The effects of temperature and pressure are explained as due to the melting of asperities at the points where the powder particles are in contact. Some practical consequences of the findings are considered.

INTRODUCTION

Recent work has shown that considerable changes occur in the flow and cohesive properties of certain powders when they are subjected to elevated temperatures up to their melting points 1-4. The results obtained on materials such as coal, lactose and griseofulvin have been explained by postulating that, under the influence of an applied pressure, the melting point of the powder is lowered by an amount d0m given by the Skotnicky thermodynamic equation 5. If it is assumed that when a pressure is applied to a powder bed, it is transmitted via the surface asperities at their actual points of contact, then high pressures will exist at these points and melting may occur. A film of liquid could be formed which would solidify on cooling to form solid bonds. Also, the particles would be enabled to approach one another closely, which would cause an increase in the molecular attractive forces between them 6. Rankell and Higuchi v have previously considered this possibility of melting of asperities in connection

t For French and German translations of the Summary, see p. 291.

Mater. Sci. Eng., 9 (1972)

with the production of pharmaceutical tablets by compressing powders in dies. The purpose of the present investigation has been to develop an improved experimental and interpretive technique and obtain new data on various other powders to those mentioned above in order to test the more general applicability of the hypothesis of asperity melting. On account of considerations of space, data 8 are only presented for two of the powders now investigated---i.e, e-lactose and stearic acid--thotigh similar data are also available for other size fractions of these two powders and for different size fractions of chloroquine diphosphate and calcium carbonate. The data have been combined with the values of electrical conductance of the powders over the same temperature range as a further check on the hypothesis of asperity melting. This hypothesis appears to be relevant to the processes of tabletting and briquetting where high pressure and/or temperature are applied to powder beds. It can be used to explain the bonding of particles that occurs in practice.

EXPERIMENTAL

Materials The powders used were e-lactose monohydrate (Whey Products) and stearic acid (not less than 99 purity from B.D.H. Chemicals Limited). The elactose was dried at 90° C and the stearic acid at 45°C in a hot air oven to < 0 . 1 ~ w/w moisture content. The relevant physicochemical properties of the materials are listed in Table 1. The experimental work involved using a heated shear cell and a heated tensile tester, similar to the design of Ashton et al. 9.

P. YORK, N. PILPEL

282 TABLE 1 Some physicochemical properties of the powders Property

or-Lactose

Stearic acid

Molecular weight Melting point (°C) Average particle size (microns) Latent heat of fusion (cal/g) Effective particle density (g/ml) Moisture content after drying (wt. %)

360.3 200-204 10.1 34.0 1.55 0.05

284.5 68-71 23.3 47.6 0.941 0.08

p__

0

Apparatus and procedure The heated shear cell is shown in Fig. 1, set up for electrical conductance measurements. It consists of a cell in three sections with a top chamber and is mounted on two ball bearing tracks. The cell is 6.98 cm in diameter, 2.85 cm in height (to the top of the middle section) and is designed for use at elevated temperatures in that when the cell is correctly filled, it is unnecessary to remove the top chamber and upper section. Removal would cause cooling and disturbance of the powder bed. Correct filling of the cell is indicated by marks on the stem of the loading lid and shear measurements are only made when the cell is correctly filled. Powder was introduced in layers to fill the cell, which had been maintained at the required tempera-

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Mater. Sci. Eng., 9 (1972)

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(c) Circuit diagram: G: galvanometer; L: heat resistant wires.

ture for 30 minutes, the temperature being recorded by a thermocouple having an accuracy of _+3 deg C. The powder was maintained at this temperature for a further 30 minutes and then critically consolidated under an applied normal load by twisting the lid a predetermined number of times through an angle of _+10 ° 1% The retaining pins were removed, and the bottom section of the cell was sheared with the same consolidating load being applied to the sample at 0.127 cm/minute via a coupling rod connected to the constant speed motor. The shear stress at failure was calculated from the maximum force being exerted by the middle section of the cell against the calibrated proving ring and from a knowledge of the cell's cross sectional area. The weight of powder in the cell was measured and

FRICTIONAL, COHESIVE A N D ELECTRICAL C O N D U C T I N G PROPERTIES OF P O W D E R S

283

the packing fraction calculated. Only when this was within + 1 ~o of the required value were the results used. Yield loci for the samples were obtained at different packing fractions by varying the consolidating load, after carrying out preliminary experiments to establish the relationship between packing fraction and consolidating load at each temperature. The cell was refilled with powder, consolidated under the same conditions and sheared with a lower normal load. This procedure was repeated with progressively decreasing normal load, and also with different consolidating loads, to obtain families of loci at different packing fractions.

extended at a constant rate of 0.127 cm/min. The time taken to split the powder bed was recorded and the weight of powder in the cell measured. The tensile stress was calculated from the weight of powder, the extension of the spring C and the cross sectional area of the fractured surface. The procedure was repeated using different normal loads to obtain results at different packing fractions. The arrangement using the shear cell for measuring the electrical conductance of the powder is illustrated in Figs. 1 (a) and 1 (b) with the circuit diagram shown in Fig. 1 (c). (The circuit consists of a Wheatstone bridge arrangement, with the powder bed as resistance R 1.) Steel pin electrodes are used of length 1.25 cm and diameter 0.15 cm with rubber insulating discs. Marks on the bottom of the shear cell ensure ~//,~?,/"-, \ 1 k \ \ \ \ correct location of the electrodes for the measure®. ,, ®/// ments. The cell was maintained at the required temperature for 30 minutes, then the powder was carefully introduced in layers. The top chamber and lid were ® ® carefully lowered with the high temperature wire B F @ E 7 E (~ C leads from the electrodes passing through the holes l ~'//.,I I ' 1 I / / / /F I in it. After the powder had been maintained at the (~q~'required temperature for 30 minutes, the bed was F / / A ®. . . . . . . . . . . . . . . . . . consolidated with a normal load and slight twisting of the lid. Measurements were taken only when the cell was Fig. 2. Heated tensile tester (powder bed prepared for testing). A: beating coils; B: zero adjustment spring; C: load applying correctly filled and 90 minutes after consolidation, calibrated spring; D: cylindrical split cell; E: horizontal wire this time interval being required for the electrical loop ; F : extension rods; G : ball bearing track; H : beat insulated conductance to attain a constant value. chamber (cover not illustrated).

K///

The heated tensile tester is shown in Fig. 2. It consists of a split shallow cylindrical cell, 6.98 cm in diameter and 0.95 cm in depth. One half of the cell is moveable on two ball bearing tracks, and this half cell is attached to a wire loop. The whole apparatus is enclosed in a heat insulated chamber. Extension rods are attached at two ends of the wire loop and these connect with two calibrated springs. The cell was heated to the required temperature, then the calibrated springs were adjusted so that the two halves of the cell were just touching, and the retaining screws and collar attached. After 30 minutes at the correct temperature, powder was introduced in layers to fill the cell. The top chamber and thermocouple were attached and after a further 30 minutes at the required temperature, the bed was consolidated so that the powder was level with the top of the cell. The collar and retaining screws were removed, and the calibrated spring C (see Fig. 2) was Mater. Sci. En,q., 9 (1972)

RESULTS

The values of cohesion and tensile stress at selected packing fractions and the change of angle of internal friction (A) as the temperature was raised above room temperature (i.e. 23 ° C) are listed in Table 2. For practical reasons the values of packing fraction selected for comparing the values of cohesion and tensile stress were 0.524 for a-lactose and 0.661 for stearic acid. These values correspond approximately to the theoretical packing fraction for a bed of equisized spheres with coordination numbers of six and ten respectively 11. Graphsoflogarithmoftensilestressversuspacking fraction at different temperature are shown in Figs. 3(a) and 3(b) for a-lactose and stearic acid. It is observed that the results can be plotted as a series of straight lines. The results show some scatter and regression lines have been calculated and fitted

284

P. Y O R K , N. PILPEI.

TABLE 2 Values of cohesion, tensile stress and change of angle of internal friction (compared with value at 23°C)

Powder

Temperature C C)

Ratio of temperature melting pt.

Cohesion (g/cm2)

Tensile stress (g/cm2)

Changeof angle of internal friction

or-Lactose

23 60 90 115 135 160 180

0.114 0.297 0.446 0.543 0.668 0.792 0.891

2.31 4.14 4.68 14.45 __ 45.8 15.94

1.89 1.89 3.60 10.45 I 17.99 3.80

0° 0' + 0 ° 12' + 0 ° 25' + 2 ° 32' + 7° 39' + 7° 48' + 5° 57'

Stearic acid

23 35 47.5 55

0.328 0.500 0.679 0.786

5.47 13.74 14.57 12.30

3.76 7.94 7.94 5.18

0 ° 0' + 1° 46' - 0 ° 32' + 1° 19'

~t-Lactose: cohesion and tensile stress values calculated at packing fraction 0.524. Stearic acid: cohesion and tensile stress values calculated at packing fraction 0.661.

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V = 135~ C V = 160°C

1.0

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0.8

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(b) Stearic acid 0 =23°C O=35°C A =47.5°C • = 55°C

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0.46

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0.50

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Packing fraction (p) Fig. 3. Logarithm of tensile strength vs. packing fraction. TABLE 3 Relationshipbetweenlogarithm oftensilestressandpackingfraction ~rthepowdersatdi~renttemperatures

Powder

Temperature (oC)

Equationof best fitting line

Standard deviation of estimate

~-Lactose

23, 60 90 115, 135 160 180

Log Log Log Log Log

0.080 0.094 0.116 0.045 0.039

Stearic acid

23 35, 47.5 55

(p = packing fraction)

Mater. ScL Eng., 9 (1972)

T=4.51p-2.083 T = 18.67p - 9.227 T = 3.54p - 0.863 T = 2.78p - 0.204 T = 1 . 3 1 p - 0.107

Log T = 2.000p - 0.746 Log T = 11.723p - 6.849 Log T = 8.333p-4.791

0.039 0.068 0.055

285

FRICTIONAL, COHESIVE AND ELECTRICAL CONDUCTING PROPERTIES OF POWDERS

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Normal stress (g/cm g)

Tensile stress

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Normal stress (g/era 2)

Fig. 4. Representative yield loci.

through the points. In Table 3, equations for the lines of best fit with values of standard deviation are listed. The scatter of results could be due to several factors. Errors can arise from filling, packing and operation of the instrument and minor variations of packing fraction may occur. In addition, small amounts of powder in the ball bearing track may give rise to additional friction during testing. The use of regression lines permits good estimates to be made of the tensile stresses at selected packing fractions. The values of standard deviation listed are considered acceptable. Representative yield loci for both powders at two of the temperatures studied are shown in Figs. 4(a)-q(d), with the appropriate values of tensile stress calculated and fitted on the loci. The method used for plotting the loci was to convert the Warren Spring equation for powder yield loci 12

(C) "

-

a+T

r

'

where ~ = shear stress at failure C = cohesion n = index of flow a = normal stress T = tensile stress, Mater. ScL Eng., 9 (1972)

(1)

into its logarithmic form, i.e. 1

log z = k + - l o g ( a + T), n

(2)

where C k = log T 1 / , ,

(3)

and plot the logarithm of shear stress at failure v e r s u s the logarithm of the compound normal stress (log (a + T)), fitting the best straight line through the points by regression analysis. The value of the cohesion is calculated from the intercept using eqn. (3). The observed scatter of results is attributed to minor density variations within the cell from experiment to experiment, its mode of operation and to minor temperature variations. It is considered that this technique of calculating cohesion is superior to drawing the loci manually and measuring the intercepts. However, it should be noted that errors involved in the estimation of the tensile strength at a selected packing fraction are included in this method of determining the cohesion. The angle of internal friction (A) is obtained by drawing a straight line from the origin through the end points of the yield loci, when these are plotted on axes of compound normal stress ( a + T) and

286

P. YORK, N. PILPEL

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Ratio temperature/melting point

Ratio t e m p e r a t u r e / m e l t i n g point

Fig. 5. Change in angle of internal friction vs. ratio of temperature to melting point of powder; [] = or-lactose, O = stearic acid.

Fig. 7. Cohesion vs. ratio of temperature to melting point of powder; [] = a-lactose (p = 0.524), O = stearic acid (p = 0.661). (a) or-Lactose © =23°C • = 60° C

A=90°C • = 115°C V = 135°C • = 160°C []=180°C

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20

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Ratio tempePature/melting point

Fig. 6. Tensile stress vs. ratio of temperature to melting point of powder; [] =or-lactose (p=0.524), O = s t e a r i c acid (p=0.661).

21

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Temperature °C Absolute

1~Absolute temp.

x 103

Electrical conductance* (mhos)

23 60 90 115 135 160 180

296 333 363 388 408 433 455

3.38 3,00 2.76 2.58 2,44 2.31 2.20

3.2 × 10-lo 3.9 4.6 4.7 8.9 9.1 38.8

289 296 308 320.5 328

3.48 3.38 3.25 3.12 3.05

2.7 × 10 -~1 3.0 3.3 4.0 5.8

Stearic acid (at packing fraction 0.661)

16 23 35 47.5 55

* Estimated at selected packing fraction from graphs in Fig. 8.

Mater. Sci. Eng., 9 (1972)

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0.64 o.& o.& o.~o

Packing fraction (p)

Values of electrical conductance for the powders at elevated temperatures

~t-Lactose (at packing fraction 0.524)

I

Fig. 8. Electrical conductance vs. packing fraction.

TABLE 4

Powder

I

0.48 0.52 0.56 0.60

287

FRICTIONAL, COHESIVE A N D ELECTRICAL C O N D U C T I N G PROPERTIES OF P O W D E R S

shear stress (r) 8. The changes in angle of internal friction compared with its value at 23°C are listed in Table 2. It has been suggested8 that the angle of internal friction provides a better parameter for assessing the dynamic frictional'properties of powders than the effective angle of friction, 6' ~3, since the former does not include a factor for the expansion of the powder bed which occurs during shearing. Figures 5, 6 and 7 show respectively the changes in angle of internal friction, tensile stress and cohesion as functions of the ratio of the temperature of measurement in degrees Celsius to the melting point of the material concerned. All the curves are similar with maxima in the region 0.6-0.8 on the abscissa, followed by decreases at higher temperatures. The lower curve in Fig. 5 also exhibits a minimum. In Figs. 6 and 7 the values of tensile stress and cohesion have been calculated for equivalent packing densities at all temperatures. Graphs of the electrical conductance (mhos) of e-lactose and stearic acid v e r s u s packing fraction at elevated temperatures are shown in Figs. 8(a) and 8(b) respectively, and the values at the selected packing fractions at different temperatures are listed in Table 4. Figure 9 shows graphs of the logarithm of the electrical conductance v e r s u s the

400

200

100 8c 6c o × 0 v

4c

2c

8;

reciprocal of the absolute temperature at the selected packing fractions. For e-lactose there is a straight line relationship up to 120°C and for stearic acid up to 40°C. Sharp increases of conductance are observed above these temperatures.

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Reciprocal temperature x 103 (K-~) Fig. 10. Logarithm of tensile stress vs. reciprocal of absolute temperature × 103 for s-lactose at p =0.524.

Some scatter of results has occurred (see Fig. 8) owing presumably to the extreme sensitivity of the measurements to minor temperature changes, to trace impurities, to point to point contact between particles and to the conditions in the measuring cell. The control resistance measurements varied by 4 % over the temperature range investigated and the variations between replicate determinations were 4 ~ for e-lactose and 8 % for stearic acid. This level of discrepancy was considered acceptable in the present investigation. A graph of the logarithm of the tensile stress v e r s u s the reciprocal of the absolute temperature is shown for e-lactose in Fig. 10, and is seen to be linear between 60°C and 140°C. It was not possible to plot a similar graph for stearic acid in view of its low melting point. DISCUSSION

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Reciprocal temperature 103 ( K - 1) Fig. 9. Logarithm of electrical conductance vs. reciprocal of absolute temperature x103; Vl=~-lactose (p=0.524), O = stearic acid (p = 0.661).

Mater. Sci. Eng., 9 (1972)

It is essential that the values of cohesion and tensile stress, when compared at different temperatures, are calculated at equivalent packing fractions. This has been achieved by using the regression line equations for tensile stress (Table 3) and by obtaining yield loci at the particular packing fractions. The angle of internal friction was found

288

P. YORK, N. PILPEL

to be independent of packing fraction for both powders at all temperatures. The calculations of packing fraction have been made on the assumption that the effective particle density does not change over the temperature range investigated. Also as the powders had been carefully dried, the effects of loss of moisture on the measured parameters were minimised. Figures 5, 6 and 7 show that the angle of internal friction, tensile stress and cohesion all increase to maxima between 0.6 and 0.8 on the abscissa and then decrease at higher temperatures. Similar results have been obtained using other sized fractions of ~-lactose and stearic acid, and also on fractions of chloroquine diphosphate and calcium carbonate powders, though for reasons of space they are not included here. The results can be explained by the hypothesis of melting of surface asperities 4. It is assumed that particles of a powder are only in contact at the tips of their asperities. Consequently, when pressure is applied to a powder bed, it will act initially at these points and very high pressures will develop locally. Estimates for the ratio of true area of contact to apparent area of contact for touching metallic surfaces are in the range of 1/1000-1/10,00014. Bowden and Tabor 15 and McFarlane and Tabor 16 suggest that as solid surfaces are pressed together under a compressive force, plastic deformations occur. This increases the true area of contact and accounts for the increased friction. However, an equally valid hypothesis is that the asperities actually melt. Skotnicky5 derived an equation from thermodynamic considerations which predicts that under an applied pressure the melting point of a solid (0m) is lowered by an amount d0m, when the liquid phase in contact with it is not subjected to the same pressure. This is the condition in a bed of powder subjected to a normal load, and one can therefore write: d0rn

-

V0 m

d-if- = T

(4)

d0m where -d-ff = change in melting point with pressure 0m = melting point (absolute temperature) V = volume per gram of solid L = latent heat of fusion (cal/g). Clearly the amount of asperity melting that occurs under pressure will also depend upon the ambient temperature. Mater. Sci. Eng., 9 (1972)

If it is assumed that in the shear cell and tensile tester the applied normal stress is being transmitted via the asperities, then very high pressures will exist at these points. Taking the ratio of true area of contact to apparent area of contact as between 1/1000 and 1/10,000, then the pressures could be of the order of hundreds of atmospheres. Such pressures would reduce the melting point of the material in the cell by one or two hundred degrees Celsius, as shown by eqn. (4). As a result of melting, the area of contact between the powder particles will increase causing a restoration of the melting point to a new equilibrium value. The previously melted material will solidify to form solid bridges causing an increase in the strength of the powder bed. Also as a result of asperity melting. the particles will tend to approach one another more closely, leading to an increase in the Van der Waals attractive forces between them. Rumpf6 proposed that for equisized spherical particles less than 1000 A apart, the attractive binding force (H) is given by the equation

where d = diameter of particles (cm) a = distance apart (cm) A = constant (assumed equal to 10-12 dynecm) and that for a bed of these particles, the tensile strength (T) is T ~ 8 . 3 x 10-2° (a2-~)kg/cm 2.

(6)

The hypothesis of the melting of asperities under pressure and the predictions of eqns. (4), (5) and (6) are in agreement with the results shown in Figs. 5, 6 and 7. It is seen from the positions of the maxima in these Figures that the asperity melting commences at about 120°C for e-lactose and at about 40°C for stearic acid. However, with e-lactose the results are slightly complicated by the fact that the monohydrate loses its water of crystallisation at 130°C and is converted into the anhydrous form. Some additional solid bridges may thus be formed between the particles. But this effect is probably small since the values of tensile stress and cohesion for the monohydrate at temperatures of up to 130°C are found to be only slightly lower than those of the anhydrous form at the same temperatures. If melting of the asperities continues as the temperature is raised and as the pressure is applied,

FRICTIONAL, C O H E S I V E A N D ELECTRICAL C O N D U C T I N G PROPERTIES OF P O W D E R S

then complete melting of the asperities may occur and a liquid meniscus or film will form around the particles. Derjaguin's equation ~v may then be used to obtain the change in adhesion between particles. This is dH _nd (a-Zh) d (lnp) 2M

(7)

dH variation of particles adhesion with where -d(lnp) - change in vapour pressure d = diameter of particles M = molar volume of liquid a -- distance apart h = thickness of adsorption layer. It is seen that when a ~< 2h, the adhesion force, and hence also the friction between particles, decreases and this could account for the rapid decreases in angle of internal friction, tensile stress and cohesion after the maxima in Figs. 5, 6 and 7 have been passed. In the case of stearic acid, a second increase in the angle of internal friction is observed above 55°C (see Fig. 5). This may be caused by softening and deformation of the "waxy" textured stearic acid particles as the melting point is approached. It would produce an increase in area of contact and hence in the angle of internal friction of the particles. The straight line sections of the graphs in Fig. 9 for c~-lactose between 23°C and 120°C and for stearic acid between 16°C and 40°C show that, in these temperature ranges, the powders are behaving as ideal semiconductors or insulators for which the following equation holds 18,19 :

e where

3o =

(8)

conductivity at OK 3o = conductivity at 273 K Eo = activation energy 0 = absolute temperature (OK) K 1 = constant whose value depends on the nature of the insulator or semiconductor The orders of magnitude of E o and K~ are different for semiconductors, where the charge is carried by electrons, and insulators, where it is carried by ions. This is due essentially to the greater mobility of the electrons and their ability to surmount higher energy barriers. At temperatures above 120°C for a-lactose and 40°C for stearic acid, the electrical behaviour changes. At 130°C the a-lactose monohydrate loses its water of crystallisation and the area of contact Mater. Sci. Eno., 9 (1972)

289

between the particles increases, probably as a result of the formation of crystal bridges. This accounts for part of the sudden increase in conductance, since the primary cause of electrical resistance in powder beds is the small area of contact between the particles 2°. Also, at temperatures above 130°C for e-lactose and 40°C for stearic acid, the melting of asperities commences (are previously discussed) and this also causes an increase in contact area, ~and hence conductance. The increases become very marked above 180°C and 55°C for e-lactose and stearic acid respectively, when it is postulated that molten material is present forming menisci and liquid films around the particles. It is possible that the charge carriers now operate in the liquid phase, which provides less resistance to movement than the solid phase. To explain the sintering of particles to substrates at elevated temperatures and the relationship between temperature and adhesion force, Polke 21 has used the Kuczynski equation 22 which can be written Zg r~ - e -E°/K2°

(9)

where Z = radius of sinter neck r = radius of particle E o = activation energy g, j = integers 0 = absolute temperature K 2 = constant. This applies to the situation as illustrated in Fig. 11. If "r" is constant, then eqn. (9) becomes Z g = K 3 e -E°/K20

(10)

By assuming that the adhesion is exclusively due to the tensile stress (S) of the sinter neck F n = 7~2S

(11)

Fig. 11. Cross-section of a spherical particle sintered to a substrate F, = normal adhesion force, X= radius of sinter neck, r = radius of particle.

290

P. YORK, N. PILPEL

where Fn=normal adhesion force and combining eqns. (10) and (11), Polke 21 derived the equation F = K 4 e - 2Eo/g K20.

(12)

If the mechanism of sintering described by eqn. (12) applies to the present materials, a plot of the logarithm of adhesion versus the reciprocal of the absolute temperature should give a straight line graph from which the activation energy can be calculated from the slope, if the values of 9 and K 2 are known. Although the present experimental conditions for obtaining the values of adhesion differ from those used by Polke 21, nevertheless it is seen from Fig. 10 that a straight line relationship occurs for a-lactose between the logarithm of adhesion (measured by the tensile stress of the powder bed) and the reciprocal of the absolute temperature in the range 75°C135°C. This result indicates that within the range 75°C-135°C for a-lactose the atomic transport and/or diffusion mechanisms which are involved in the first stage of sintering may be causing the increases which have been observed in the adhesion forces between the particles. Departure from linearity outside this range suggests that the other mechanisms previously discussed are also involved. It can be seen from this discussion that the strengths of powder compacts will be affected by the melting of surface asperities. In tabletting of pharmaceuticals, very high pressures are applied to powder beds and temperature rises occur on account of friction during compression. Rises in temperature of between 5 deg and 20 deg C have been reported L7'23, which represent average temperature rises for the whole tablet. However, the temperatures at the contact points will be higher since the frictional heat within the powder bed develops at these points. Also, in the short time of compression (in the region of 0.1 second) there is no time for the heat to be dissipated through the powder particles, and the asperities melt under the combined effect of temperature and pressure. Upon removal of the pressure, solidification occurs with the formation of solid bonds between the particles, which impart strength to the tablet. This mechanism of bond formation also has application in the briquetting of coal and may be involved in the sintering of powders where pressures are applied to powders at elevated temperatures.

CONCLUSIONS

The increases which occur in certain of the mechanical properties and electrical properties of consolidated powders with increase in temperature are explained by the hypothesis of melting of surface asperities. This occurs under the combined influence of temperature and pressure. The explanation is applicable to powders which differ considerably in their chemical and physical properties, and particle size. It is suggested that asperity melting may be relevant in bond formation in the tabletting of pharmaceuticals, in briquetting of coal and in the sintering of powders at elevated temperatures. LIST OF SYMBOLS USED

A a C d Eo F, g H

= constant (assumed to be equal to 10 -lz dyne-cm) =distance apart between two spherical particles (cm) = cohesion (g/era 2) = diameter of spherical particle (cm) = activation energy = normal adhesion force = integer = binding force between two spherical particles (dynes)

dH variation of particle adhesion with change d (lnp) = in vapour pressure h j L M n

= = = = =

thickness of adsorbed layer (cm) integer latent heat of fusion (cal/g) molar volume of liquid index of flow

dP

change of melting point of solid with

d0 m

pressure

r S T flo

flo 6' A a x 0 0m p

= = = = = = = = = = = = =

radius of particle tensile stress of sinter neck tensile stress (g/cm 2) radius of sinter neck electrical conductivity at 0°K electrical conductivity at 273°K effective angle of friction angle of internal friction normal stress (g/cm 2) shear stress at failure (g/cm 2) absolute temperature melting point of solid (K) packing fraction

FRICTIONAL, COHESIVE AND ELECTRICAL C O N D U C T I N G PROPERTIES OF POWDERS ACKNOWLEDGEMENT

P. Y. thanks the Science Research Council for financial assistance, and we are indebted to I.C.I. Pharmaceuticals Division for gifts of apparatus and materials. REFERENCES 1 2 3 4 5 6 7 8 9 10

C. F. Harwood, Ph.D. Thesis, London University, 1969. S. S. Jayasinghe, Ph.D. Thesis, London University, 1970. S. S. Jayasinghe and N. Pilpel, J. Inst. Fuel, 43 (1970) 51. S. S. Jayasinghe, N. Pilpel and C. F. Harwood, Mater. Sci. Eng., 5 (1969/70) 287. J. Skotnicky, Czech. J. Phys., 3 (1953) 225. H.Rumpf, inW.A. Knepper(ed.),lntern. Symp.onAgglomeration, Interscience, New York and London, 1962, p. 392. A. S. Rankell and T. Higuchi, J. Pharm. Sci., 57 (1968) 574. J. C. Williams and A. H. Birks, Powder Technol., 1 (1967/68) 199. M. D. Ashton, R. Farley and F. H. H. Valentin, J. Sci. Instr., 41 (1964) 763. J. C. Williams and A. H. Birks, Rheol. Acta, 4 (1965) 170.

Influence de la temperature sur les caract~ristiques de frottement, de cohksion et de conductibilitk ~lectrique des poudres Les auteurs ont 6tudi6 comment 6voluent les propri6t6s m6caniques et les caract6ristiques de conductibilit6 61ectrique d'un grand nombre de poudres, lorsque l'on fait augmenter la temp6rature et la pression. Ils consid6rent que les effets de la temp6rature et de la pression sont dus ~t la fusion des asp6rit6s des grains dans les zones off les particules de poudre sont en contact. Ils examinent quelques cons6quences pratiques de ces r6sultats.

Mater. Sci. Eng., 9 (1972)

291

11 L. C. Graton and H. J. Fraser, J. Geol., 43 (1935) 785. 12 M. D. Ashton, R. Farley, D. C. H. Cheng and F. H. H. Valentin, RheoL Acta, 4 (1965) 206. 13 A. W. Jenike, Bull. 108, Utah Univ. Expt. Engng. Stn., 1961. 14 F. P. Bowden and D. Tabor, Friction and Lubrication, Wiley, New York, 2nd edn., 1967, p. 18. 15 F. P. Bowden and D. Tabor, Mechanism of adhesion between solids, Second Intern. Congr. on Surface Activity, Butterworths, Vol. 3, 1957. 16 J. S. McFarlane and D. Tabor, Proc. Roy. Soc. (London), 202A (1950) 224. 17 B. V. Derjaguin, Powders in industry, Soc. Chem. lnd., Monograph No. 14, London, 1961, p. 102. 18 Y. Okamoto and W. Brenner, Organic Semiconductors, Reinhold, New York, 1964, p. 8. 19 E. I. Parkhomenko, Electrical Properties of Rocks, Plenum, New York, 1967, p. 64. 20 B. Scarlett, R. Hauser and R. E. Buxton, Symp. on Recent Advances in Powders--Electrical and Thermal Conductivity of Powders, Royal Aeronautical Soc., March, 1969. 21 R. P. Polke, paper presented at Conj. on Physics of Adhesion, Karlsruhe Univ., July, 1969. 22 G. C. K. Kuczynski, Metals Trans., Feb. 1949, p. 169. 23 E. J. Hanus and L. D. King, J. Pharm. Sci., 57 (1968) 677.

Der Einflufl der Temperatur auf Reibungs-, Kohiisions- und elektrische Eigenschaften yon Pulvern Die mechanischen und elektrischen Eigenschaften einer Vielzahl von Pulvern wurden als Funktion der Temperatur und des Druckes untersucht. Die Temperatur- und Druckeinflfisse werden dadurch erkl~irt, dab Oberfl~ichenrauhigkeiten an den Beriihrungsstellen der Pulverk6rner schmelzen. Einige praktische Konsequenzen unserer Ergebnisse werden diskutiert.