Surface Technology, 7 (1978) 413 - 425 413 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

MECHANICS OF R E M O V I N G GLASS P A R T I C U L A T E S FROM A SOLID SU RFAC E

S. BHATTACHARYA and K. L. MITTAL

IBM System Products Division, East Fishkill, Hopewell Junction, N. Y. 12533 (U.S.A.)

(Received May 2, 1978)

S u m m a r y

A series o f exper iments underscores the impor t ance o f the capil lary force in the adhesion o f a par t icula te to a surface. The capil lary force result ing f rom a liquid film be tween a par t icula te and a surface remains even af ter the par t icula te~surface combina t ion is baked above the boil ing poin t o f the liquid for 24 h. A mechanical scrubbing force is required to remove the par t icu la te held to a surface by a capil lary force. The force on a parti- culate appl ied by an air je t is calculated using Stokes 's law modi f ied by Cunningham's cor rec t ion factor . Fu r the rmore , the force required to roll a par t icula te o f f a surface is calculated f rom the theore t ica l adhesion force be tween a par t icula te and a surface and par t icula te d e fo rm a t io n character- istics. The appl ied force is in good agreeement wi th the theore t ica l force requi red to roll o f f a par t icula te .

1. I n t r o d u c t i o n

The adhesion o f small particles -- metall ic, non-metal l ic , po lymer ic , e tc . -- on a var ie ty o f solid surfaces is o f great impor t ance in m an y industrial , b iomedical , nuclear , space, au tomot ive and o the r applicat ions. For example , adherence o f a few particles to e lec t ronic or s emico n d u c to r devices can play havoc with the i r pe r fo rmance , and par t icula te con t amina t ion is a major de t r ac to r in device yield.

The depos i t ed particles may be dry or t hey m ay be dispersed in aqueous or nona que ous media. There are many instances where the deposi- t ion o f part icles f rom suspension to solid bodies is significant, e.g. redeposi- t ion o f par t icu la te solid dir t in de te rgency , depos i t ion of wear f ragments in engines, and adhesion o f dust to buildings. I f one considers w h y these sus- pended part icles adhere to solid surfaces on contac t , and what keeps t h em depos i ted , the principles o f col loid chemis t ry relative to the stabil i ty of dis- persions b e c o m e impor tan t . K i t chener [ 1 ] has reviewed the various forces or

414

mechanisms that control the deposition of suspended particles onto solid surfaces. The work of Uno and Tanaka [2] describes the factors affecting the deposition of particles from various media.

Techniques for measuring adhesion of particles are described in a paper by Kettler and Keller [3] . Also, an interesting study of particle adhesion, using a variety of particles and an assortment of solid surfaces, was made by Kordecki and Orr [4] .

A great number of studies, carried out to unravel the interactions that occur in particulate adhesion, are reviewed by Krupp [5] . These inter- actions are van der Waals' forces, which are ubiquitous and are attractive in nature; electrostatic interactions - - d u e to charges already present, or due to electrical double layer formation; and, in the case of particles deposited from suspension, capillary forces. When dry particles are deposited on dry substrates, the increase in relative humidi ty provides a liquid layer that results in the capillary force. The relative magnitudes of these forces as a funct ion of particle size are discussed in this paper. There is a great deal of literature in which the air jet has been used to remove or dislodge particles from various substrates, and Larsen [6] , Orr and Dalla Valle [7] , and Corn and Stein [8 - 10] have found a reasonable agreement (within an order of magnitude) between the air drag forces calculated from a theoretical model of the velocity field adjacent to the surface and the forces of adhesion as determined by centrifugation.

In the present study we compare the air drag force required to remove particles with that predicted on the basis of theoretical calculations, and find a good correlation. Earlier workers [6 - 10] compared the air drag forces required with that of adhesion forces as determined by the ultracentrifugal methods. We discuss the shearing versus rolling mechanism for particle removal and the relative forces required for each mechanism, and compare these forces with air drag forces so as to elucidate the mechanism of particle removal. We show that a relatively simple model predicts reasonably well the forces required to remove particles; the prediction from this model agrees very well with that due to air drag forces.

2. Experimental

2.1. Materials

Eighty per cent of the glass microbeads used in these experiments were within a size range of 0 - 5 pm (Table 1). Extremely small beads which were not measurable were designated 0. The size distribution of particles was unknown. The substrate used was a clean Monsanto p-type silicon wafer 55 mm in diameter with [100] orientation and a resistivity of 10 ~2 cm. The top surface of the wafer was highly polished to an average roughness of 0.063 ~m.

TABLE 1

Approximate properties of glass microbeads

Size range 0 - 5 pm Dielectric constant 12 at 1 kHz and 23 °C Power factor 0.0003 Volume resistivity 2 × 1015 ~ m at 17 °C Density 2.5 g cm -3 Hardness 5.5 (Moh scale)

415

TABLE 2

Some properties of solvents used in preparing particulate dispersions

Water Acetone Freon Benzene

B.p. (°C) 100 56 48 80 Density 1 0.8 1.57 0.88 Surface tension 73 28.8 17.3 23.7 (dyn cm -1) Dipole moment 1.87 2.88 0.5 0 (D) Viscosity 1 0.32 0.68 0.65 (cP)

Flowmeter

Air Gate valve ~ Filter Air gun m

50 psi ~/Wa fer

~ Microscope stage

Fig. 1. Schematic of experimental setup.

2.2. Deposition of glass beads Two me thods were used to deposi t the glass microbeads under a clean

h o o d o n t o the wafer surface. The dry microbeads were gent ly dus ted on the surface by tapping t h e m f rom a piece o f paper on which t h e y were first deposi ted. Alternat ively, the microbeads were dispersed on the surface f rom various liquid suspensions using a nebulizer. The suspensions were prepared by adding microbeads to the liquid and vigorously shaking the mix- ture by hand. Some of the proper t ies o f the liquids used are listed in Table 2. The liquids used were spect roscopic grade and doubly-dis t i l led deionized water was used. The average a m o u n t o f microbeads used was abou t 1 pg cm -2 for b o t h dry depos i t ion and depos i t ion f rom suspensions.

416

c~

o o

m

cq

Cq

O~

n ~

09 0

LQ

0

~ , ~ . ~ ~ ~ . . ~ - ~ :hE " 0 0

~ ~ - ~

~ ~ ~, ~ o ~ = . . ~ ~ ~

• - ~ . ~ o

o LO •

417

2.3. Removal of particulates Figure I shows a schematic of the experimental setup. Air at about

50 lb in -2 (345 kPa) passes through a gate valve, flow meter and a filter to an air gun. The air gun with a nozzle 2.5 mm in diameter was clamped on a stand which was at a 10 ° angle with the wafer surface. All tubing was 3/8 in plastic. The air velocity was measured by a TSI (Thermo Systems Inc., Minneapolis, Minn.) model 4100 air flowmeter.

The wafer containing the particulates was placed on a microscope stage and the air jet was applied to blow off the particles as they were being observed under the microscope. The particulate diameter was measured with a filar eyepiece at 375X. Single particles as small as 0.3 pm in diameter could be detected and measured with about 50% accuracy. This does not mean that we can measure 0.3 + 0.15 pm, rather that we can measure a dimension which is 0.3 pm (sensitivity of measurement) and the uncertainty of measurement is (accuracy) + 0.15 pm. The accuracy increased with particle size.

3. Results

Results of the initial experiments are shown in Table 3. The code number 1 indicates the removal of many particulates by the air jet. A progressive decrease in particulate removal is indicated by 2 and 3; 4 means that none were removed.

Table 3 also shows that the dry particulates are dislodged more easily than the particulates deposited from a liquid suspension. Baking the liquid- deposited particulates at 180 °C for 24 h did not cause any extra particulate to be blown off by the air jet. This is in agreement with a theoretical predic- tion [11, 12] , where it is shown that incomplete particulate drying will cause the adhesive force between a spherical particulate and a surface to actually increase to a limiting value of 4nr~,, where r is the particulate radius and ~/is the surface tension of the liquid film.

Why a particulate is not completely dry after 24 h can be answered if one applies the Kelvin equation to the case of the submicron size pores, since the liquid under a particulate, in the limiting case, can be likened to the liquid in a small pore [13] . The Kelvin equation for desorption from pores is given by [11] :

27V r -

(R T In P/Po)

where P0 is the normal vapor pressure of the liquid and P is that obtained over a curved surface, ~ is the surface tension, V is the molar volume, r is the equilibrium radius of curvature of the meniscus, R is the gas constant and T is the temperature in kelvins. It follows, therefore, that at a certain drying temperature and vapor pressure of the liquid there exists a limiting pore radius r below which the liquid inside the pore will not escape. A similar situation may be envisioned for the liquid film under a particulate.

418

Table 3 also shows that a mechanical method, such as scraping with the edge of a dry piece of paper, can be used to disturb the contact and the liquid film between a particulate and a solid surface. With the disruption of the liquid film the particulate is removed as effectively as the dry-deposited particulate, except when the particulates were damaged in deposition.

The damage to the particulates was extensive when acetone and benzene were used as the liquids for the suspension and sprayed using the nebulizer. A possible explanation for this is the well-known phenomenon of charge generation in the production of a mist of liquid particulates [14]. The more insulating a liquid droplet is, the greater is the double layer thick- ness and the longer is its charge relaxation time. Consequently, insulating droplets of acetone and benzene will be easily charged and will carry their charges longer. A particulate being carried by such a droplet will hit the wafer surface with a greater force, owing to the additional electrostatic force, than an uncharged particulate in a similar situation.

Table 2 indicates that aerosol particulates deposited from liquids of lower density are more damaged than particulates deposited from liquids of higher density. However, no physical reason for this behavior is apparent. The damaged particulates adhere to a surface very strongly since all of the adhesion forces increase with increase in the contact area. Also it becomes extremely difficult to exert a removal force on a submicron-thick damaged particulate. This is why damaged particulates in Table 3 could not be removed even when the particulates were mechanically scraped with a dry piece of paper.

Table 3 also shows that particulates deposited from a liquid having a lower surface tension 7, such as acetone and Freon, have a better chance of coming off than a particulate deposited from a liquid having a higher surface tension (since F = 4 urT) such as water unless the particulate is damaged during deposition. The damage occurred with benzene and so the particulate could not be blown off even though the surface tension of benzene is low.

4. Discussion

4.1. Mechanics o f particulate removal by an air jet A particulate may be removed from a surface by either shearing or

rolling when an air jet is used to blow it off. The forces necessary for each of the two mechanisms, i.e. shearing and rolling of the spherical particu- lates, were calculated and compared with the forces exerted by the air jet. The calculated and the experimental forces correlated well. The cal- culations are for spherical particulates only. However, since all particulates less than about 10 pm in diameter approach a spherical shape, the calcula- tions are applicable for most particulates within the size range.

419

~ Fai r Cos0 / A

Fad + Fai r Sin~

Fig. 2. Forces on a particulate.

100

50 I Jr.--to SCFH

/ A i25 cm/sec

Applied ~" 4 / 250 cm/sec drag e ~ / / / / ~ 40 SCFH for 40 cm/sec

, 0 2 y%2 (i) Calculated drag force imum i 5 required to roll off / ~ ~ / / 65 SCFH

_~ (ii} Particulates deposited__ /~/ /~. ~/'

0.5 tes deposited / / %41 . :i°::: TM ,

~ / / ~ i (iv) Particulates deposited

10-7 10-6 10 -5 10-4 10-3 10-2

Drag force (dyne)

Fig. 3. Drag force on a part iculate due to an air jet and its comparison w i th the force required to rol l o f f a part iculate.

4.2. Removal of dry deposited particles 4.2.1. Shearing Referr ing to Fig. 2, F ~ is the appl ied force on the par t icula te due to the

drag force o f the air jet , which can be calculated f rom Stokes 's law [15]

3~r#vd Fa~ - (1)

C

where p is the kinematic viscosity of air, d is the particulate diameter, v is the velocity of air, and C is the Cunningham correction factor which appears when the particulate size is of the order of the mean free path of the gas molecules surrounding it (0.5 pm in air). The calculated drag force as a function of particulate diameter and flow rate is illustrated in Fig. 3.

Zimon [15] and Corn and Stein [8] also describe another model where the air drag force is given by

F - Cxpu2Ap (1) 2

420

100

A 10 E :x v 5

t : 1

0,5

0.1

10-4

u le

10 .3 10 "2 0.1 1

Force/part iculate (dyne)

Fig. 4. Summary of adhesion forces.

10

where C~ is the resistance coefficient of the particle, p is the density of air, Ap is the particle projected area and u is the air speed. Here the indeter- minacy of the resistance coefficient Cx = f(Re) makes calculations based on eqn. (1) difficult. Corn and Stein estimate

18.5 C~ - for Re < 1.0

Re °.6

On the basis of this expression, we calculated the drag force exerted on a particulate 1 pm in diameter by a ii00 cm s I air jet to be 1.28 X 10-4 dyn, which is very close to the force calculated from Stokes's law for a 1 pm particulate at II00 cm s -I (2 X 10 -4 dyn, see Fig. 3).

A particulate is sheared off when

Fai r cos O >_ (Fad + Fai r sin O)Uf (2)

where Fad is the force of adhesion between the particulate and the surface, as depicted in Fig. 2, and pf is the static coefficient of friction.

At equilibrium one obtains from eqn. (2) the force necessary to shear off a particulate

PfFad F~ir = (3 )

cos 0 --pfsin 0

The coefficient of friction pf between an SiO 2 particulate and an SiO2 surface is about unity [16] . If 0 is also close to 0, one obtains the condit ion for the particulates to shear off

Fair ~ F ~ i

Figure 4 depicts the theoretical adhesion forces between a spherical glass particulate and a wafer surface. The forces are an order of magnitude

TABLE 4

Adhesive force be tween a part iculate and a solid surface

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Type of force General force equa t ion Force equat ion reduced Reference for part iculates

Capillary 47rr 7 4.52 × 102d

Electrosta t ic Q2 image force eoed 2 5 × 104d 2

Electric al ne 0 ( A¢ )2d double layer 2z 34.8d force

van der Waals' 4~cod force 16T~z ~2- 1.43 × 102d

5 , 1 1 , 1 3

1 2 , 1 4

5, 14

1 5 , 1 7 , 1 8

d z

Co

= 2r, par t iculate d iameter in cm = 4 A surface tens ion o f the liquid = 73 dyn cm -1 for water d i f ference in work func t ion ~ 1 V van der Waals' cons tan t = 7.2 eV part iculate charge = 10 - 16 C per o n e / / m size par t iculate dielectric cons tan t = I for air permi t t iv i ty of free space = 8.86 pF m -1

calculation for glass particulates. Although calculated for glass, the force values should be similar within an order of magnitude for other insulating particles on a wafer surface. The equations which have been used for calculating theoretical adhesion forces and the assumptions involved are included in Table 4.

For the dry uncharged particulates only the van der Waals' and the double layer forces will be present. Adding these two forces from Fig. 4 (see Table 5) and comparing with the applied drag force from Fig. 3, one can conclude that the particulates are not removed by shearing off, since Fad >>Fair.

Referring to eqn. (3), the force necessary to shear off a particulate may become considerably lower if the coefficient of friction p~ between the particulate and the surface is much less than unity. This may cause parti- culate removal by shearing, depending on the particulate and the surface material and the coefficient of friction between them.

4.2.2. Rolling Referring to Fig. 2, a particulate may be rolled off a surface about the

point A. When the particulate touches the surface, either the particulate or the surface, or both, are deformed. One obtains

422

TABLE 5

Rolling force required to remove a dry part iculate

Part iculate Fad Fad 2F 3/2 dx/-~'-'H 2F 3/2 diameter van der Waals' + (N) (N) 3/2 (N) 1/2 d x / - ~ Fr°ll d (m) double layer force

(dyn) (dyn)

1 x 10 -6 1.75 x 10 -2 1.75 x 10 -7 1.46 × 10 -1° 1.59 × 10 -1 0.918 x 10 -4

10 x 10-6 1.75 x 10 -1 1.75 x 10-6 4.6 × 10 -9 1.59 2.9 × 10 -4

Fad = 7rpo2H (4)

where Fad is the adhesion force between a particulate and a surface, H is the average deformation resistance of the materials at the contact point and ~p02 is the contact area. In order to obtain numerical estimates, we have used Meyer microhardness data for H, like Krupp and Sperling [17], since better values of H are not available.

Taking moments of the two forces about point A one obtains at limit- ing equilibrium

d ~dPO = F~on- (5)

2

where d is the particulate diameter and Fro n is the force required to roll off the particulate. From {4) and (5),

Frou = 2(Fa d)3/2/d(TrH)l /2 (6 )

The micro-deformation resistances H of the particulate and the surface are assumed to be equal. If they are unequal, the hardness of the softer of the two materials should be used in eqn. (6).

The particulate will roll off a surface if the force due to the air drag is greater than From the force necessary to roll off the particulate.

As mentioned before, when the particulates are uncharged and dry only the electrical double layer and the van der Waals' forces are present. Therefore, in order to estimate the force necessary to roll off a particulate one may substitute the sum of the van der Waals' and the electrical double layer [15, 18] for Fad in eqn. (6). The average Knoop hardness for the particulate-surface combination is taken to be equal to 820 kg mm -2. Hence from eqn. (6), the force Fron necessary to roll off a dry particulate is calculated as a function of particulate diameter. The calculation is shown in Table 5 and the results are shown in Fig. 3. Figure 3 also shows the applied drag force as a function of the flow rate and the particulate diameter. It is clear from the figure that the dry particulates above about 0.5 pm will be removed by the air jet and the particulates below 0.5 um will not be blown off; this is in fact experimentally observed (Table 3).

TABLE 6

Rolling force required to remove part iculates

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Part iculate Fad Fad 2F 3 /2 dx/-~H diameter van der Waals' + (N) (N)3/2 (N)l /2 d (m) electrical double

layer + capillary force (dyn)

F.,7 (dyn)

Particulates deposited from a suspension in Freon (~ = 17.3 dyn cm -1)

1 x 10 -6 2.83 x 10 -2 2.83 x 10 -7 3 x 10 -7 1 . 5 9 x 10 -1

10 x 10 -6 2.83 × 13 -1 2.83 x 10-6 9.52 x 10 -9 1.59

Particulates deposited from water (3' = 73 dyn cm -1)

0.1 x 10-6 6.25 x 10 -3 6.25 x 10 -8 3.12 x 10 -11 1.59 x 10 -2

1.0 x 10-6 6.25 x 10 -2 6.25 x 10 -7 9.8 x 10 - m 1.59 x 10 -1

Particulates deposited from acetone and benzene (~/ ~ 25 dyn cm -1)

0.1 x 10-6 3.32 x 10 -3 3.32 x 10 -8 1.2 x 10 -11 1.59 x 10 2

1 x 10-6 3.32 x 10 -2 3.32 × 10 -7 3.8 x 10 - m 1.59 x 10 -1

1.9 x 10 -4

6× 10 -4

1.96 x 10 -4

6.16 × 10-4

7.5 X 10 -5

2.3 X 10 -4

aFroll = 2F3/2 /d ~x/-~.

~A (a) (b)

Fig. 5. Point A ( fulcrum): (a) con t inuous liquid film be tween the part icle and the surface; (b) b roken liquid film.

4.3. Removal o f particles deposited from a liquid suspension Two cases are described here: case (1) when there is a continuous liquid

film between the particle and the surface, and case (2) when there is a broken liquid film.

Case (1) With liquid film between a particulate and a surface, we can hardly

discuss the rolling of the particle since the liquid will deform and point A (Fig. 5(a)) will be unable to act as a moment point for rolling (lack of rigi- dity).

Thus shearing will be the primary mechanism of particulate removal for a wet particulate with an unbroken film of liquid between it and the sur- face. In such a ca.se r = v(av/az) and the particulate will move, satisfying this equation; the lower the viscosity of the liquid, the higher will be the velocity of the particle for a given applied stress. The exact calculations are beyond the scope of this paper.

424

Case (2) Here the effect of the liquid film will be to increase the adhesion

force (Fig. 5(b)). The particle can roll about the fulcrum point A. The calculation for Fro H is similar to that for the dry particulates

discussed earlier with the difference that, in this case, Fad will contain contributions due to capillary forces. Table 6 shows such calculations and the results are plot ted in Fig. 3 along with those for dry particles.

Figure 3 shows that particulates greater than about 1.5 ~m should be blown off at the maximum air jet velocity of 1100 cm s -1. Experimental results detailed in Table 3 show that all large particulates greater than 3 pm were blown off at 1100 cm s 1. This is a good agreement between the cal- culated and experimental results, considering some of the assumptions made in the force calculations.

Figure 3 also shows that the particulates deposited from water will not be blown off unless they are greater than about 10 pm. The particulates from acetone and benzene were physically damaged when deposited from the nebulizer; hence the actual force necessary to roll these particles off will be greater than the calculated force. This is due to flattening of the damaged particles. The particulates may also have been chemically affected by the solvents, which may be the reason why the smeared-on particulates from acetone were not blown off at 1100 cm s -1.

If the particulates are charged, Coulomb-type forces should also be considered and this will increase the total adhesion force. Consequently, there is an increase in the force necessary to roll off the particles since F~oll ~ (Fa~) 3/2.

Apart from the force effects, there is another phenomenon, the bound- ary layer effect, which may become important when removing submicron- size particles. The particle size below the boundary layer thickness, which depends on the air jet angle, will be acted on by a considerably smaller force than those outside the layer where the air velocity is equal to the full air jet velocity. However, under the conditions used in our experiments, all dry particulates greater than 0.3 pm were removed by an air jet of 500 cm s q , as shown in Table 3, indicating the negligible effect of the boundary layer for particulates larger than 0.3 pm.

Conclusion

We have shown the importance of the capillary force in the total adhesion between a particulate and a surface. The liquid film and conse- quently the capillary force between a particulate and a surface remains even after the particulate-surface combination is baked above the boiling point of the liquid for 24 h. A mechanical scrubbing force such as scraping with a dry piece of paper is necessary to remove a particulate held to a surface by the capillary force. We have calculated the force on a particulate applied by an air jet using Stokes's law, modified by Cunningham's correction factor

425

A l s o c a l c u l a t e d is t h e f o r c e r e q u i r e d to ro l l a p a r t i c u l a t e o f f a s u r f a c e w h e n t h e p a r t i c u l a t e is h e l d to t h e s u r f a c e b y c a p i l l a r y f o r c e d u e to f o u r d i f f e r e n t l i q u i d f i lms - - w a t e r , a c e t o n e , F r e o n , a n d b e n z e n e . T h e a p p l i e d a i r j e t f o r c e is in g o o d a g r e e m e n t w i t h t h e t h e o r e t i c a l f o r c e r e q u i r e d t o ro l l o f f a pa r t i - c u l a t e .

A c k n o w l e d g m e n t

T h e a u t h o r s wi sh t o t h a n k Mr. A. L a n d z b e r g f o r h e l p f u l d i s c u s s i o n s a n d c r i t i c a l c o m m e n t s .

R e f e r e n c e s

1 J. A. Kitchener, J. Soc. Cosmet. Chem., 24 (1973) 709. 2 H. Uno and S. Tanaka, Kolloid Z. Z. Polym., 250 (1972) 238. 3 A. B. Kettler and D. V. Keller, Jr., J. Adhes., 7 (1975) 235. 4 M. L. Kordecki and C. Orr, Arch. Environ. Health, 1 (1960) 13. 5 H. Krupp, Adv. Colloid Interface Sci., 1 (1960) 13. 6 R. I. Larsen, Am. Ind. Hyg. Assoc. J., 19 (1958) 265. 7 C. Orr and J. M. Dalla Valle, Studies and investigation of agglomeration and deag-

glomeration, Semi Final Report Project A-233, Eng. Expr. Station, Georgia Institute of Technology, Atlanta, June 30, 1956.

8 M. Corn and F. Stein, Am. Ind. Hyg. Assoc. J., 26 (1965) 325. 9 M. Corn and F. Stein, in B. R. Fish (ed.), Symposium on surface contamination,

Pergamon Press, New York, 1966, pp. 45 - 54. 10 M. Corn, in C. N. Davies (ed.), Aerosol Science, Academic Press, New York, 1966,

Chap. 11, pp. 381 - 389. 11 H. M. Princen, in E. Matijevic (ed.), Surface and Collid Science, Vol. 2, Wiley-Inter-

science, New York, 1969, pp. 1 - 84. 12 N. L. Gross and R. G. Picknett, Trans. Faraday Soc., 59 (1963) 846. 13 A. W. Adamson, Physical Chemistry of Surfaces, Interscience, New York, 1967, p.

58, pp. 637 - 639. 14 A. D. Moore, Electrostatics and its applications, Wiley-Interscience, New York, 1967. 15 A. D. Zimon, Adhesion of Dusts and Powder, Plenum Press, New York, 1969, pp.

1 -60. 16 Handbook of Chemistry and Physics, 54th edn., CRC Press, 1973 - 74, p. F15. 17 H. Krupp and C. Sperling, J. Appl. Phys., 37 (1966) 4176. 18 I. E. Dzyaloshinskii, E. M. Lifshitz and L. P. Pitaevskii, Adv. Phys., 10 (1961) 165.