The measurement of interparticle forces

Powder Technology, 58 (1989)

75

- 91

75

An Invited Review The Measurement of Interparticle Forces P. F. LUCKHAM

Department of Chemical Engineering London

and Chemical Technology,

Imperial College of Science and Technology,

SW7 2BY (U.K.)

SUMMARY

Over the last decade an experimental technique has been developed which essentially measured the forces between two surfaces as they approach. The technique is capable of measuring small forces (nN) and small distances (< 0.1 nm) between two surfaces. To date the majority of these data have been published in the physics/colloid literature. This review highlights and summarises some of these experiments which have a direct bearing on particle interactions and the behaviour of large assemblies of particles. Interactions between surfaces in dry and humid air, non-polar and polar liquids and between surfaces bearing adsorbed polymer layers have been measured and are presented here, together with other experimental results where these forces may have a role in more practical systems.

INTRODUCTION

The physical properties of all particulates are determined by the strength and nature of the interactions which make up that system. For example, it is well known that the handling properties of powders are crucially dependent on the humidity of the air and hence the strength of the capillary forces between the agglomerated particles. In the field of solid-in-liquid suspensions the rheological behaviour is determined, to some extent, by the interactions between the particles. To date these interactions have generally only been treated in a qualitative way because of the lack of information on the strength and nature of the interparticle forces. There have been considerable advances in the theoretical treatment of the interaction 0032-5910/89/$3.50

between particles. In the 1930s de Boer [l] and Hamaker [2] proposed a theory to account for the Van der Waals forces between particles, and this theory was combined with early electrostatic theories by Derjaguin and Landau [3] in Moscow and Verwey and Overbeek [4] in Holland to describe interactions between charged particles. These theories have been improved upon with the advent of powerful computers. In addition, the role of polymers in modifying interpaticle forces has also been developed [ 5,6]. Falling somewhat behind these theoretical advances are the experimentalists. Until approximately fifteen years ago, there were only indirect experiments performed which measured the effect and not the strength of particle interactions, e.g. colloid stability measurements [ 7,8]. Clearly more insight into particle interactions could be obtained if we could measure them directly. This is a daunting experiment since the forces involved are small. However, two types of experiments have been tried. One type of experiment has been to measure the interactions between a large number of particles and to average their surface separation [9, lo]. Such experiments have measured the osmotic pressure as a function of volume fraction of particles. However, there are two drawbacks to this approach; firstly, the surface separations are averaged and secondly, it is possible to measure only repulsive forces between the particles. Conceptually the way to overcome this problem is to have just two particles, and to be able to measure the forces as the particles are brought together in a controlled manner and to be able to measure the distance of separation between the two particles. This approach will be reviewed here. It has revealed some fine detail about the interactions between particles, although it is necessary to use macroscopic size particles @

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76

(“1 cm radius) because of the small interactions involved. The technique has elucidated the nature of interactions between surfaces, confirmed some of the theories concerning particle interactions [3 - 61 and has produced some surprising results too. To date this type of experiment has been of major interest to the fundamental scientist. This paper aims to review the results obtained’ using this experimental technique and to speculate on their significance to the applied particle technologist. THE EXPERIMENT

The apparatus used to measure intersurface forces is based on a model developed by Tabor and Winter-ton [ 111. It has been designed primarily by Israelachvili and Adams [ 121 in Australia and is shown schematically in Fig. 1. The first obstacle to be overcome in designing an apparatus to measure intermolecular forces between surfaces is the problem of surface roughness. Our aim is to measure the force between two surfaces as a function of their separation down to separations of the molecular scale (i.e. 0.1 nm resolution). Therefore any surface roughness will nullify results obtained at very short distances. Fortunately the oxide mineral, mica, may be cleaved to reveal several square centimetres of molecularly smooth surface. Therefore, mica, or modified mica, has been used exclusively in these experiments. It is important to note that the chemical nature of the Light to spectrometer t

light

Inld

Fig. 1. Diagram of the apparatus used to measure intersurface forces.

surface is of secondary importance in determining the interactions between particles. The extent of charge or the nature of any adsorbed polymer or surfactant layer is more important, although the surfactant, for example, may not adsorb on the particles if the chemical nature of the surface is not ‘correct’. Therefore the results obtained using mica surfaces will be similar to any other surface (particularly hydrophilic surfaces). Apart from its smoothness there is nothing special about mica. The forces measured are those between two thin sheets of mica (about 10 mm X 10 mm X 1 - 3 pm thick) which are partially silvered (i.e. allow about 10% of light to be transmitted). The sheets are glued to two optically polished glass discs with cylindrically curved surfaces, which are positioned mutually perpendicular to each other. The apparatus is machined from stainless steel and Teflon and in some cases (as shown in Fig. 1) the surfaces are surrounded by a bath. Three aspects of the apparatus require description: (i) how the separation between the two mica surfaces is controlled; (ii) how the separation is measured; and (iii) how the forces between the surfaces are measured. Control of separation The separation between the surfaces is controlled via a three-stage mechanism. The upper micrometer driven rod may be moved up and down by a stepper motor coupled to the rod. This movement constitutes a coarse control and allows positioning to an accuracy of about 1 pm with a total range of about 2.0 cm. Springs are used to eliminate backlash, wobble and creep. The lower micrometerdriven rod is moved by a similar motorised mechanism using a two-way synchronous motor. This constitutes the medium control stage. The lower rod pushes against a helical spring which in turn pushes upon a stiff, double-cantilever, stainless steel spring which is about one thousand times stronger than the helical spring. Therefore a l-pm movement of the lower rod is reduced to a 1-nm displacement between the two surfaces. The lower rod is connected to a high-precision linear resistance potentiometer which enables the measurement of the applied displacement. The fine control of surface separation is achieved using a rigid piezoelectric tube

which expands by approximately 1.0 nm per volt. This non-mechanical fine control is used to position the two surfaces to an accuracy greater than 0.1 nm and has a total range of about 500 nm. These three mechanisms allow the separation between the surfaces to be varied easily during an experiment. Only the two finest controls are used for measurements, the upper rod is used simply to position the surfaces several micrometres apart before commencing the experiment. Measurement of separation The mica substrates are partially silvered on the reverse side (i.e. the side which is glued to the cylindrical glass formers) such that only 10% of light is transmitted, the remainder being reflected. Therefore, if monochromatic light is passed normally through the silvered mica sheets, interference between the fully transmitted beam and reflected beam occurs, such that constructive interference only occurs when the optical path length between the two silver layers is an integer of the wavelength of light; at all other separations destructive interference occurs. When the cylindrical mica substrates are viewed through a microscope, a series of Newton’s rings are observed. (We note that a crossed cylindrical configuration is geometrically equivalent to a sphere on a flat plate.)

(a)

If, instead of using monochromatic light, white light is used, a series of superimposed Newton’s rings are observed, and appear simply as a bright spot when viewed through a microscope. However, if this light is passed through a monochrometer which resolves the wavelengths of the light, fringes of equal chromatic order (FECO) are observed (see Fig. 2). When the surfaces move relative to each other, the wavelength of the FECO change (i.e. if the surfaces move apart, the optical path length increases, and so the FECO shift to longer wavelengths). Therefore by recording the FECO wavelength when the surfaces are in contact and when the surfaces are separated, the surface separation may be estimated [13,143. Figure 2 shows a typical set of interference fringes: (a) when the mica surfaces are in contact, note that the mica fringes are ‘flat’ at their shortest wavelength position, due to the surfaces being in molecular contact and the strong adhesive force between the surfaces results in deformation of the glue used to attach the mica to the glass formers; (b) when the surfaces are separated by approximately 3 nm, note the shift of the wavelength of the fringes with respect to the calibration mercury line. In addition, the fringes may also be used to measure the refractive index of the medium between the

(b)

Fig. 2. Typical set of fringes of equal chromatic order (FECO). (a), The mica surfaces are in contact; the strong attractive force distorts the shape of the mica such that the contact is flat; this results in a perpendicular region in the fringes; the shape of the fringes reproduces the shape of the cylindrical formers used to mount the mica in these experiments. (b), The surfaces are approximately 3 nm apart.

78

two mica surfaces and the radius of curvature of the mica cylinders. Tolanski [13] and Israelachvili and Tabor [15] have developed equations which enable the surface separation D to be calculated from these wavelength shifts. Typically, surface separations may be measured to an accuracy of 0.2 nm and with care, higher accuracy is possible. Measurement of force The force F(D) betwen the two surfaces is measured by applying a known relative displacement M, to the two surfaces, for example, by applying a known voltage to the piezoelectric tube and subsequently measuring the actual motion, M, of the surfaces relative to each other using the optical technique. If there is no force between the surfaces then the applied motion is the same as the measured motion, i.e. M = AD,; if they attract, AD is greater than M, and if they repel M is less than M,, the difference in both cases being taken up by the bending of the single cantilever spring (see Fig. 1). In general F(D) = k(M,

- M)

(1)

where Fz is the constant of the leaf spring, which is approximately 100 N m-l. Since (M, - M) may be as small as 1.0 nm, forces as small as lo-’ N may be measured. By starting measurements with the surfaces far apart, where F(D) * 0, force-distance profiles may be measured.

EXPERLMENTAL

PROCEDURE

Preparation The precise experimental procedure used obviously depends upon the particular experiment being performed, and therefore only an outline will be given here. Cleanliness is important in this form of experiment. Therefore, scrupulous cleansing of the apparatus is essential prior to any experiment; this involves exhaustive washing of all components in an organic solvent, e.g. toluene or alcohol, to remove organic impurities and acids to remove mineral salts and water. It is important also to prevent any dust or bacterial contamination of the mica surfaces which will prevent the surfaces coming together into molecular contact, and

therefore all assembly stages of the experiment are performed in a laminar flow dustfree cabinet (or room if available) and all solvents and solutions are filtered through fine membrane filters before being introduced into the apparatus. Following assembly of the apparatus, it is necessary to isolate the mica surfaces from any external vibrations of the laboratory and this may be achieved by suspending the apparatus on long springs, or placing it on an antivibration table. Experimentation The mica surfaces are brought to within -1.0 pm from molecular contact using the upper motor. The lower motor, coupled to the mica surfaces via a differential spring mechanism, is then used to bring the surfaces together. (For fine measurements, the piezoelectric ceramic may be used as an alternative to the lower motor.) At large surface separations, where F(D) is negligible, the displacement M, equals the applied motion M and this enables calibration of the lower motor (or piezoelectric ceramic). At close surface separations M # M, and a force is measured (see eqn. (1)). In air, if the mica surfaces are clean, the surfaces come into molecular contact and flatten (see Fig. 2(a)), and the wavelengths of these FECO are measured. In some experiments only forces in air are measured (e.g. van der Waals forces) and the above procedure is followed. Other experiments require the addition of a solvent, so the surfaces are separated to -2.0 mm and the solvent introduced. After allowing time for thermal equilibration to be set up, forcedistance profiles in the solvent are measured in an analogous manner to that described above. In experiments where a solute is added, a portion of solvent is removed to be replaced by a solution of the solute. After allowing time for equilibration in the solute (12 - 20 h), the force profiles are determined.

RESULTS

AND IMPLICATIONS

IN PARTICLE

TECHNOLOGY

Experiments in air The apparatus described above was originally used to measure the strength of van der Waals forces between mica surfaces in air. These pioneering studies were undertaken by

79

Tabor and Winterton [ll] in the late 1960s. They observed that as the two mica surfaces approached each other at a certain separation the two mica sheets spontaneously ‘jumped’ into contact. The reason for this jump is that as the surfaces approach they start to experience Van der Waals attractive forces. When the attraction is greater than the spring constant (i.e. dF/dF > k) the surfaces undergo a spontaneous movement until the rate of change of attraction is less than the spring constant. Thus, by measuring the distance of this jump for springs of different strengths, the attraction between the surfaces as a function of surface separation was measured. Measurements using a similar method were also performed by Israelachvili and Tabor [ 151. Their results are given in Fig. 3. Theoretically the van der Waals energy E, is given by [2,4,161

4”

Ea=-3

where A, is the Hamaker constant between the mica surface and air (vapour). Thus the force should decay with De2. However, at larger surface separations the force law has a lower dependence due to the time taken for the transient dipole/induced dipole to develop. This interaction is known as the retarded van der Waals interaction [17 ] and is of the form

llf

10'

FORCE d/m 10"

10'

1111

1

I

2

I

5

I

10

20

50

100

OISTANCE,nrn

Fig. 3. The strength of the van der Waals attractive energy between two mica surfaces across a vacuum as a function of the surface separation D.

TRANSITION REUON

Ad

Ea=-03

The results of these workers show a distinct change in the force laws from a Dw2relationship over surface separations of 12 to 50 nm (see Fig. 4).:In air, then, these experiments have shown that the theoretical equations for Van der Waals forces do hold and that retardation effects are present. It has also been possible to calculate the constants A, and AL for mica in air (A, = 1.35 X lo-l9 J and Ad = 0.97X 10F2s J). From an experimental viewpoint these experiments were a tremendous breakthrough in the field of surface interactions; from the viewpoint of the particle technologists the experiments confirm conventional wisdom. All the forces measured above were forces measured as the two surfaces approach. Of considerable interest to the technologist is the strength of the adhesive forces. These

NONRETAROEO

/

lo DISTANCE.0

nm

100

Fig. 4. Variation of the power law n of the van der Waals force between crossed mica cylinders with distance 0

experiments were performed by Fisher and Israelachvili [ 18,191. The adhesion of particles to solid surfaces and to each other is fundamental to many industrial processes, e.g. spray drying, xerography, crop spraying and the pneumatic transport of powders. Condensable vapours, such as water, can increase the force of adhesion because the surface tension of the capillary condensate formed around solid-solid contact regions is often dominant.

80

The ‘surface forces’ technique was applied to this problem. The experiment was as follows. The two mica surfaces were brought together and allowed to ‘jump’ into adhesive contact under the influence of the attractive van der Waals forces. Vapour (if present) condensed at the annulus of the two surfaces, which took up to 10 s and the surfaces were then separated. Initially, although the clamped end of the spring was lowered, no surface motion was observed. A critical point was eventually reached where the adhesion and spring deflection forces were equal and the mica surfaces then jumped apart to a very large separation (>lO pm) depending on the force. The adhesion force was calculated by measuring the jump distance and multiplying by the spring constant k (eqn. (1)). The surface geometry in these experiments is equivalent to a sphere on a flat plate. Thus, if an annulus of liquid is present, the general formula for the adhesive force F is F = F(M)

+ F(S-S)

+ F(T~~)

(4)

For such cases, sin C$sin(0 + 4) Q 1 so F(T~~) is negligible. Thus F = 41~Ryr.v

COS 8 + 4dTSL

(8)

This equation was not tested experimentally until these experiments were performed. Their experiments were performed for five liquids of different surface tensions, water, benzene, cyclohexane, hexane and 2-methyl butane and in Fig. 6 F/(4mR cos 0) is plotted against yLv . Figure 7 shows the adhesive force between dry mica surfaces (where yLv = 4) i.e. the F(S-S) contribution. This means that the solid-solid interaction is small. For liquids where yLv < yLs, e.g. 2-methyl butane, the force is given by 47rRysL regardless of

60-

F LnRcos8

where F(D) is the force due to the Laplace pressure AP [20], F(S-S) is the force due to direct solid-solid interactions and F(Y~,,) is the resolved force due to the liquid/vapour surface tension yLv. For a large volume of liquid where bulk thermodynamics apply, theory gives [ 21,221

lmN/m)

F(o)

Fig. 6. Plot of F(4nR cos 8) uersus ~~~ for various liquids adsorbed on mica: 4, water; 0, benzene; A, cyclohexane; n, n-hexane; V, 2-methyl butane; 0, nitrogen at atmospheric pressure.

F(S-S)

= 4xRy~v

COS 8

= 47rRysL

F(yLV) = 27rRyLv sin $ sin(8 + 4)

(5) (6) (7)

where R is the radius of the sphere, &Jis the solid/liquid contact angle, -ysL is the solid/ liquid interfacial free energy and 4 is shown in Fig. 5. In most cases (and in Israelachvili and Fischer’s paper [ 181) 0 is small and the neck radius r is much less than R, so C#J is small.

‘d:y ImN/m)

. 0.’ .

50 F LnRcosE 10t mNlm 30

:

.

I

.-*

: I

20 10 1

00 Fig. 5. Capillary condensed liquid between a rigid sphere of radius R and a rigid flat surface. The geometry is equivalent to two crossed cylinders.

0.3 ot

05 0.6 0.7 03 P/p,

09

Fig. 7. Measured force of adhesion F, scaled by 4zR cos 8, between cylindrical mica surfaces as a function of relative vapour pressure (P/P,) of water (YLV = 72.6 mN m-r).

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the presence or absence of capillary condensed liquid. The question of the limit of the applicability of bulk thermodynamics to menisci was established by measuring the Laplace pressure AR = T&r as r + 0. This was achieved experimentally by noting at which partial pressure of liquid and hence r the adhesion force was not described by 47rRy, cos 0 but by 47rR~~~. Results show that for cyclohexane bulk thermodynamics applies to menisci as small as 1 nm representing only one or two molecules (see Fig. 6) whilst for water bulk thermodynamics only applies for r > 5.0 nm which is -20 water molecules. Fisher and Israelachvili [18] attributed this to the presence of hydrogen bonding in water although trace organic impurities would drastically alter yLv and hence the adhesion. Israelachvili [14] also concluded that surface deformations do not drastically affect the strength of adhesive forces. Using this approach these authors also confirmed the validity of the Kelvin [23] equation for radii as small as 4.0 nm. The results obtained for the interactions between solid surfaces in air has shown that for dry surfaces the interactions are well described by van der Waals forces. By simply knowing the Hamaker constants of the solid surface (see ref. 24 for a listing of Hamaker constants of many materials) the form of the force profile between the surfaces may be calculated. In the presence of a vapour of condensable liquid the adhesion between the surfaces increases. These experiments have shown that thermodynamic treatment frequently used to predict particle adhesion forces [20 - 231 are valid for very thin liquid films frequently enktered in powder handling problems and soil mechanics [25]. Having considered the implications of these experiments for particle handling in air we now consider the impact of this method on particles dispersed in a liquid. Experiments in non-polar liquids When immersing mica surfaces in nonpolar liquids one may expect the forces to be explainable simply in terms of van der Waals forces, i.e. to be predicted by eqns. (2) and (3) with suitably modified Hamaker constants. From an experimental viewpoint, however, we may note that it has long been

known that the lubricating efficacy of oils is often much better than theoretically expected [26] and that particles are often stable in non-polar organic solvents [27]. Does this indicate the existence of a strong additional repulsion at short separations, strong enough to outweigh the van der Waals attraction? To pursue this Israelachvili and Horn [28] carried out experiments using the apparatus described above. They chose to study initially carefully dried octamethylcyclotetrasiloxane (OMCTS) which is a nearly spherical molecule - 1 .O nm in diameter. The results obtained are presented in Fig. 8. The main feature of the force profile is that an oscillatory force is observed which decays rapidly with increasing distance and merges with the conventional van der Waals continuum force only at large separations. The periodicity of these spatial oscillations is the same as the molecular diameter of the molecule (other solvents with different molecular diameters, e.g. cyclohexane, octane, etc., have also been studied) indicating that near the surfaces the molecules lie in layers. The decrease in the amplitude of these force oscillations with increasing separation shows that the layering becomes more diffuse further out as the liquid takes on its bulk properties. The idea that forces may oscillate as a function of distance is foreign to the 3

2 F/R

[mUmI

Distance,0

(nml

Fig. 8. Forces between two mica sheets immersed in dried octamethylcyclotetrasiloxane (OMCTS) as a function of the surface separation D.

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colloid and particle technologists and it is therefore worth considering the origin of these forces. The van der Waals energy between two planar surfaces immersed in a continuum liquid is given by [2]

E,=---

A 12x0=

to the condensation of vapours into mica in air. Recently this study has been extended by Christenson [19] who has shown that the measured adhesion on the separation of the surfaces agrees to within 5% of that predicted by the Young/Laplace equation

[201 (9)

where ASL is the Hamaker constant for the interaction of the solid across the liquid. It is clear though that no liquid molecules can enter between the surfaces until the separation has reached the molecular diameter of the liquid molecules. So that from D = 0 (contact) to D = 6 (6 is the thickness of one molecule) the van der Waals interaction between the surfaces is actually across a vacuum, i.e. j&z---

&v 121rD=

(10)

for 0 < D < 6, where Asv is the Hamaker constant for the interaction across a vacuum, and generally Am > ASL (typically Am lo-l9 J while A - 10s20 J). Thus, as the surfaces separatEthe force rises. At D = 6, the gap will fill with a fairly close packed monolayer of liquid molecules and the van der Waals energy will decrease. Between D = 6 and D = 26 the liquid molecules cannot close pack between the surfaces, resulting in the van der Waals energy rising again. At D = 28 the energy will once more fall to that across quasi-close packed fluid molecules and so on. In addition to the oscillatory nature of the Hamaker constant at close surface separation, there is the additional repulsive force due to the physical expulsion of the fluid from the gap between the surfaces which will have to be overcome as the surfaces approach and an entropic attraction due to the development of the order of the solvent molecules. Therefore it is not too surprising that such forces exist. The results obtained on addition of trace amounts of water (100 ppm or less) to mica surfaces immersed in OCTS were entirely different. The structural forces disappeared to be replaced by a strong attraction at surface separations of around 10 nm. This was accompanied by the appearance of a thin fihn of condensed water around the contact zone of the mica surface. This case is analogous

@=Z

r

(11)

where AP is the pressure of adhesion, 7 the surface tension and r the radius of curvature of the meniscus formed at the mica/water/oil interface. It was found that down to values of r as small as 2 nm bulk interfacial tensions hold. Oscillatory forces have been measured for many solvents between molecularly smooth mica surfaces. However, it is not clear how surface topography will smooth out these effects. If these forces are representative of a more widespread phenomenon they have obvious significance for lubrication, adhesion and particle technology. For example, the tendency of liquids to form quasi-rigid layers at solid surfaces and therefore give rise to steric force barriers may explain why lubricants are often more effective than theoretically expected [26] and why colloidal dispersions are often stable in pure organic solvents [8,27]. The large adhesive forces observed in the presence of trace amounts of water are of crucial importance to the technologist formulating dispersions in nonaqueous media. One would, for example, expect a large effect on the sediment volume of such suspensions. The sediment volume depends essentially on the magnitude of the adhesive forces at contact; if these are large the particles will stick on contact and settle to form a loose open structure, if they are weak the particles will rearrange themselves during settling and the sediment will be compact. Bloomquist & Shutt [30] have shown the effect of trace amounts of water on the sediment volumes of glass ballatini (5 - 15 pm in diameter) in a range of organic liquids. In carefully dried liquids the volumes were low and similar to the sediment volume in water. However, in the presence of trace amounts of water much higher sediment volumes were noted, consistent with the formation of water bridges between the glass spheres indicating that the results obtained

83

in the apparatus for measuring surface forces are of significance to the technologist. Results obtained in polar liquids Mica is an aluminosilicate which contains a regular array of potassium ions. On immersion in water some potassium ions dissolve leaving the mica surface negatively charged. This charge gives rise to an electrical double layer close to the mica surface. It is known from electrical double-layer theories that the force between two charged surfaces decays exponentially with surface separation D and that the slope of the decay is dependent on electrolyte concentration [ 3,4,31]. One such equation assuming a constant surface potential is F -= 2nR

64nkT tanh2 K

w(--KW

(12)

where n is the number of ions, $, is the surface potential and K is the Debye-Hiickel parameter which is a property of the bulk electrolyte solution and is defined as K=

(13)

where e, is the relative permittivity of free space, e is the relative permittivity and ni and Zi are the number and charge of ions i in the solution. The Van der Waals attractive component to the force is given by eqn. (9). These equations enable us to predict that the force between two charged surfaces decays approximately exponentially with distance and is expected to decrease as the electrolyte concentration increases. Figure 9 shows the measured forces as a function of distance between two mica surfaces in various dilute electrolyte solutions [ 121. Repulsion is observed up to separations of 3 - 5 nm, below which the forces becomes rapidly attractive and the surfaces come into a strong adhesive contact at D = 0. These results are remarkable in that they vindicate the DLVO [3,4] theory even at close separations where the theory may not be expected to hold. Mica surfaces bearing adsorbed films of ionic surfactants [ 321 and polyelectrolytes [33 - 351 can also be well described by DLVO theory. This strong correlation between theory and experiment presents some problems though as there are many colloidal and particulate systems where DLVO theory fails.

10' Force FIR IpNiri’l

10’

10

l(

25

50 01stance

75

100

0 Inml

Fig. 9. Electrolyte forces as a function of the surface separation for two cylindrical mica surfaces immersed in aqueous potassium nitrate solutions.

For example, some clays are known to swell spontaneously in aqueous solution and some particulate materials are known to be stable at high ionic concentrations [ 361. These anomalous effects have been attributed to a repulsive ‘hydration’ force which is in addition to the expected DLVO interaction. Can this effect be measured using the method described in this paper? At first glance (e.g. Fig. 9) it appears that there is no hydration force, but we must remember that all the results in Fig. 9 are for dilute electrolyte solution whereas the anomalous effects of hydration have been noted at high electrolyte concentrations. What are the results at high electrolyte concentrations? The results for sodium chloride are given in Fig. 10 [12,37]. They show that above a critical electrolyte concentration the strong adhesive force measured is replaced by a very steep exponentially increasing force. Thus at low ionic strengths no hydration effects are noted whilst at high electrolyte solutions hydration effects are present. The strength of hydration was also found to correlate with the hydration of cation in solution (i.e. following the lyotropic series Na+>, Li+, >K+, >Cs+). Thus hydration is stronger at high electrolyte solutions due to the binding to the surface of hydrated cations [ 37 - 391. Recent, very careful experiments by Israelachvili and Pashley [40] have shown that in 10m3 mol dmS3 KC1 solution the hydration force is not a continuum force but is also oscillatory. The frequency of the oscillations was -2.5 A which agrees closely with the size of a water molecule (see Fig. 11).

84

\ 0

10

I

20 OiStMCe

30 0 Inm)

Fig. 10. Forces measured between mica surfaces in NaCl solutions at pH 5.7. V, 1 x.10m2 mol dmm3; l, 1.4 x 10e3 mol dmm3; =, 1 X 10m4 mol dmm3. No hydration forces were measured in solutions up to -10m3 M, henceforth barriers were observed at 2 - 3 nm, with there still being an attraction. At 10F2 mol drnF3 hydration forces remove the primary minimum.

-losOOistance0 (nml

Fig. 11. Forces measured in 10m3 M KC1 showing the forces measured on approach and separation of the surfaces on a linear scale.

It is well known that addition of electrolyte to particulate dispersions causes aggregation of particles [ 3,4]. This phenomenon is observed, for example, in river water where suspended particulate material is carried by the river at low electrolyte to the sea (high electrolyte). Where aggregation of the material occurs, the particles settle and muddy estuaries and deltas form. There are many

examples where an additional repulsive force appears to be present. Clays, e.g. montmorillontite and vermiculite, are known to swell spontaneously in aqueous solution. For example, sodium monmorillonite [ 361 swells indefinitely due to a combination of hydration and double-layer forces, but caesium montmorillonite [41] will only swell to a separation of 0.25 nm (one water molecule) and calcium montmorillonite does not swell beyond 0.95 nm (four water molecules). If we consider surfaces other than clays we are immediately faced with the question of whether or not these oscillations require the presence of a smooth rigid surface. The evidence to date suggests this is the case. Phospholipid bilayers show a strong monotonically increasing hydration force down to 0.4 nm separations indicating the necessity of a rigid surface [42 - 441, whilst polished silica surfaces also show no oscillatory behaviour [45] in the hydration force. In this case it may be that the solid surface is not sufficiently smooth to detect the oscillatory forces. It is worth pointing out here that oscillatory forces have also been measured in other polar liquids such as ethylene glycol and methanol between mica sheets [ 461. Another example of an apparent additional repulsive force is when a surface has an adsorbed polymer layer. Surfaces bearing an adsorbed polymer layer The experimental results which will be described in this section are those obtained when a soluble polymer is adsorbed onto a surface of mica from solution and the modification of the forces between the surfaces measured. In order for the effect of the polymer to be seen clearly these experiments have been performed either in non-aqueous media where the range of forces between the surfaces is
85

Fig. 12. Force F(D) between curved mica surfaces as a function of separation in 0.1 mol dmB3 KNOsPEO solution. Three molar mass polymers were studied, namely, 1120 000, 160 000 and 40 000. For clarity, data points for only PE04 of molecular weight 1120 000 are shown: l, (and solid lines) indicate the ‘equilibrium’ compression profile; 0, (and broken lines) indicate profiles following a rapid decompression of the surfaces (see text).

CH,O),) of molecular weights 40000,160000 and 1120 000 from an aqueous electrolyte solution [47,48] which corresponds to good solvency conditions for the polymer. For all molecular weights, as the polymer layer overlaps a repulsive force is measured. The repulsion is due essentially to osmotic forces arising from the increase in polymer concentrations as the surfaces come close together. There are time-dependent effects, however, which complicate the behaviour, though the behaviour for all the molecular weight polymers studied are similar. We shall describe, therefore, the behaviour of only the highest molecular weight polymer in detail. During the initial approach of the surfaces, no interaction was measurable until the surfaces were -200 nm apart when a monotonically increasing repulsion was observed (solid line), down to -5 nm when compression of the surfaces was stopped. Subsequent behaviour on decompression (i.e. increasing surface separation D) depends upon the rate at which it is carried out. For a slow decompression, i.e. taking about 1 h in moving outward from 5 nm, the force followed the compressionforce profile. For a rapid decompression, however, i.e. about 5 min in moving out from 5 nm, the force followed the curves (broken lines), which for the case of PEO of molecular weight 1120 000 became zero at about D N 120 nm. For the higher molecular weight polymers, on an immediate recompression of the surfaces the rapid

decompression profile was followed. It was necessary to allow the surfaces to ‘relax’ for an hour or so before the initial compression curve was followed. For PEO of molecular weight 40000, however, on immediate recompression following a rapid decompression the initial compression curve was always followed. These time-dependent hysteretic effects were unexpected and their origin is still speculative; the most plausible explanation is that the polymer is forced onto the surface of the mica during the compression. As the surfaces are separated, the time for the polymer to desorb and adopt its initial, equilibrium configuration is many minutes (up to 1 h) [ 47,481 and hence the force at a given surface separation is greater on decompression than on compression. Experiments performed on AB block copolymers [49,50] where one part of the polymer (the A block) adsorbs very strongly and another part is non-adsorbing show no such hysteresis effects. This eliminates the possibility that the hysteresis is due to any entanglements of the adsorbed polymers. Since in all cases following decompression of the surfaces the forces eventually relaxed to that of the initial compression, the equilibrium force profile is the first compression of the surfaces. It is possible that this timedependent nature of the interaction force profile may be responsible for some of the time-dependent effects noted in rheological measurements such as thixotropy where

86

following the viscosity takes time to relax to its 'initial' viscosity. The force-distance profiles represented b y the solid curves in Fig. 12 show the relaxed limit for the interaction between mica surfaces bearing adsorbed P r o in aqueous electrolyte. From these graphs we can estimate the adsorbed layer thickness of the PEO on mica to be half the value of D at which repulsion commences. In terms of the dimensions of the polymer in solution (radius of gyration, Rg), this corresponds to a b o u t 2-3Rg. These results clearly show that repulsive forces exist between surfaces bearing adsorbed polymers from a good solvent. This implies that particles bearing adsorbed polymer layers should be stable under conditions where particle aggregation would normally occur, e.g. at high electrolyte concentrations and in non-polar solvents as is well documented [ 7, 8 ]. In order for a polymer to act as a good stabfliser it must adsorb strongly to the surface y e t extend sufficiently far from the surface to prevent aggregation due to Van der Waals forces. Such conditions are mutually exclusive for homopolymers, b u t block and graft copolymers may be synthesised such that one part of the polymer will adsorb strongly to the surface whilst the other part of the polymer will extend away from the surface. It is well known that such polymers are effective stabilisers of suspensions [7] and recently [49, 50] it has been shown that for a given molecular weight polymer a much stronger and longer ranged repulsive force is measured for a block copolymer than for a h o m o p o l y m e r (Fig. 13). For block copolymers the hysteresis observed on decompression of the surface did not occur, establishing that the origin o f the hysteresis is due to the h o m o p o l y m e r being forced onto the mica surface and subsequently desorbing rather than being due to the adsorbed polymers entangling. Under certain conditions, however, attractive forces b e t w e e n polymers adsorbed onto mica sheets from a good solvent have been measured. In this case, the surfaces were only partially coated with polymers [48]. The procedure adopted in these studies was somewhat different to that used in the previous experiments and will, therefore, be

10~ FIR

pK~ •

1#

10' 1

2~

~'o

6'o

e'o

Obstonce 0 (nm)

Fig. 13. Force-distance profiles following a 16 h incubation of mica surfaces in a 100 mg dm -3 solution of block copolymers of poly-2-vinylpyridinepolytertiary butylstyrene of molecular weight: A, 6200; B, 21 400; and C, 33 000, showing the molecular weight dependence of the force profiles.

described in some detail. The forces F(D) between bare mica surfaces immersed in 0.1 mol dm -3 potassium nitrate were determined and then the surfaces separated to D ~ 20 ~m. PEO o f molecular weight 1 112 000 was added to the system at a concentration of 10 pg m1-1 and, after gently stirring, the surfaces were left to incubate in the solution to allow adsorption to occur. At no time during the incubation did the surface separation exceed a b o u t 20 pm. Therefore the polymer molecules from the bulk solution had to diffuse a considerable lateral distance (about 1 mm) through the narrow intersurface gap (20 - 100 ~m wide) before reaching the area of closest approach between the mica sheets and adsorbing onto these 't~st' surfaces. Thus, the rate of adsorption of the polymer onto the mica in the region of interest (where F(D) is measured) was severely reduced, relative to the corresponding rate of adsorption from bulk solution onto a free surface and several hours were required fo the limiting adsorption of polymer to be attained, b e y o n d which no

87

501 0

100 200 Oistonce 0 Inm)

Fig. 14. Force-distance profiles between two curved mica surfaces immersed in aqueous 0.1 mol drne3 KNOB at 23 f 2 “C: (a) before addition of polymer; (b) after addition of poly(ethylene oxide) and incubation of the surfaces at D = 20 pm for 1 h; (c) after incubation for 3 h in the polymer solution at D = 20 pm; (d) 0, after incubation for 5 h at D = 20 pm and l, after 32 - 42 h at D = 20 pm. (Reproduced by permission Nature, Vol. 308, No. 5967, pp. 336 837. Copyright (c) (1984), MacMillan Journals Limited.).

further changes in the force profile were observed. Hence, by measuring F(D) at various times following introduction of the polymer it was possible to measure force-distance profiles as progressively more polymer adsorbed. Figure 14 shows the change in F(D) with time. The force-distance profile between the mica surfaces before the addition of polymer is shown in Fig. 14(a), again a secondary minimum is observed in line with previous observations. Following addition of polymer and incubation for 1 h at D = 20 pm, the secondary minimum disappeared and only a strong repulsion is observed from D < 20 nm. After incubation for 2-3h(atD= 20 pm) a clear attraction between the two surfaces is observed commencing at D = 90 +lO nm with an attractive minimum at D = 45 nm; as the surfaces are brought closer together the attraction decreases and changes to an ultimate strong

repulsion for D < 20 nm), but after 6 - 8 h the attraction disappeared to be replaced by a repulsion commencing at D = 100 nm. On leaving the surfaces to incubate for a further 24 h at D = 180 nm, the form of the force profile was found to be similar to that for the ‘quasi-equilibrium’ force profile shown in Fig. 12. The origin of the attraction between the two surfaces following partial adsorption is probably due to bridging of the intersurface gap by polymer molecules adsorbed simultaneously on both surfaces. This effect is more significant at low (as opposed to full) surface coverages of the polymer for two reasons: (i) At low polymer coverages there are several ‘vacant’ sites for polymer adsorption so that it is easier for a polymer molecule adsorbed on one surface to ‘reach across’ to the second mica surface and find a vacant adsorption site. (ii) At low adsorption the concentration of polymer segments in the gap is also low, so that the repulsive osmotic interactions are weak relative to the strong attractive bridging forces. The question we now have to ask ourselves is has this effect, measured directly here, been observed previously with particulate systems? The answer, of course, is that this bridging flocculation [51,52] has been observed for at least twenty years and indeed high molecular weight polymers (and polyelectrolytes) have been used industrially as flocculants particularly in the removal of particulates and colour from potable water 1531. The other occasion when polymers adsorbed to particles allow flocculation of particles is when the solvent is a poor one for polymer. This phenomenon was studied intently during the 1970s by Napper [54] in Australia and by Vincent [7,55] and Dawkins and Taylor [56] in the U.K. If we measure the forces between ’ adsorbed polymers in a poor solvent we would expect to see an attraction between the surfaces. The interactions between adsorbed polystyrene layers in cyclohexane (which is a poor solvent) at room temperature (21- 25 “C!) have been investigated [ 571. Figure 15 shows the force-distance profile between mica surfaces following incubation

88

-_ 14 FIR mN.m’

I _o_

04

polymer

volume

fraction

4

Fig. 16. Schematic phase-equilibrium diagram for the polystyrene-cyclohexane system.

50

100 Oistonce

D

J

lnm)

Fig. 15. Forces between curved mica surfaces following a 10 h incubation in polystyrene of molecular weight 600 000: 0, polystyrene-cyclohexane; l, following replacement of the solution by pure cyclohexane. (Reproduced by permission of the Royal Society of Chemistry.)

in a polystyrene solution (molecular weight 600 000) at 24 “C before (closed symbols) and after (open symbols) replacing the solution by pure solvent. F(D) was measured in the range D < 300 nm. No forces were detected as the mica surfaces approach from large separations down to about 60 nm when an attraction is observed. On further decreasing the surface separation the surfaces jump together by some 20 - 25 nm (this is because the rate of attraction between the surfaces dF/dD is greater than the strength of the spring on which one of the mica surfaces is attached). On further decreasing the separation a repulsion is observed. Upon decompression, the force decreases, becoming attractive again until the surfaces jump apart; further separation shows no detectable interaction between the two surfaces. Further compression/decompression cycles fully reproduced the force profiles described above. The main difference between the interactions of adsorbed polymers in a poor solvent as compared to a good one is the presence of an attraction between the surfaces. The nature of the interaction profile in a poor solvent may be discussed with reference to the phase diagram of the polymer solvent system, which is schematically represented in Fig. 16 and shows the conditions under which the polymer exists as an homogene-

neous solution (one phase) or phase separates into two phases. Broadly speaking the onephase region corresponds to conditions where overlap of segments from two different molecules is energetically unfavourable (i.e. they repel) whilst in the two-phase region such overlap results in a net reduction of free energy (i.e. an attraction). The critical temperature Z’, increases as the molecular weight of the polymer increases, and for an infinite molecular weight polymer the critical temperature corresponds to the 19 temperature, which for polystyrene in cyclohexane corresponds to 34.5 “C. When the two surfaces are compressed we effectively pass along an isotherm as shown in Fig. 16. When the surfaces initially overlap, the polymer concentration in the overlap q&,region increases to $i; in this regime we would expect to see a repulsion, but as no such repulsion is observed, if it is present, it is beyond the detectable limit of the apparatus. Further approach of the surfaces results in more extensive overlap and increase in the volume fraction of the overlapping polymer. Between & and & the overlap region is in the biphasic part of the phase diagram and we expect a net reduction in the free energy and hence an attraction between the plates, as observed. Further compression of the surfaces results in the volume fraction of polymer in the overlap region r$oVincreasing beyond &, i.e. c$ov is now in a one-phase region so that further compression of the surfaces with a corresponding increase in GoV must result in an increasing repulsion. This argument has focused on the ‘osmotic’ aspect of the interaction between the adsorbed polymers. In addition, one expects a contribution (not necessarily independent) due to ‘volume

89

restriction’ effects. As the surface separations become small, the presence of a second impermeable surface must lead to a considerable reduction in the number of configurations available to the adsorbed polymer and hence to an entropic repulsion. This qualitative theory has been semi-quantified by Pincus, Klein and Inkersert [ 57,581 who have used a mean field polymer theory to calculate the force between the surfaces as a function of surface separation. The flocculation of polymer-stabilised particles by changing the solvency of conditions of the polymer has been studied in many particulate systems [ 7,54,55,56]. It has been seen that flocculation occurs very close to the 8 point of stabilising polymer. A listing of critical flocculation temperature and the 8 temperature for many polymerstabilised particulates is given in the Table [ 541. Recently Marra and Hair [59] have measured the forces between terminally attached polystyrene layers adsorbed to mica

surfaces in toluene/heptane mixtures. In pure toluene (a good solvent for polystyrene) the force is entirely repulsive (similar to the results presented in Fig. 13). However, on addition of heptane (a poor solvent for polystyrene), the repulsive force decreases and eventually the surfaces become attractive in worse than 8 conditions. This is the first case where the forces between surfaces bearing adsorbed polymer layers have been changed from repulsive to attractive by passing through the 19point for the adsorbed polymer.

CONCLUSIONS

It can be concluded that by reviewing the current literature the apparatus described in this paper does simulate the interactions between two particles as they approach. Using this technique, new insights into the behaviour of particles in air, in a simple liquid and

TABLE Comparison of the critical flocculation (C.F.T.) Stabiliser

with the 0 temperature [ 541

Molecular weight

Dispersion medium

C.F.T.

6 (E)

339.5 340.1 339.0 340.5 340.5 340.5 338.0

341 341 341 341 341 341 341

PDMS PDMS PDMS PDMS PDMS PDMS PDMS

3200 11200 13700 16100 23800 29800 48000

heptane heptane heptane heptane heptane heptane heptane

PDMS PDMS PDMS PDMS

15000 15000 15000 15000

hexane pentane butane propane

488 449 423 332

491 455 430 350

Polyisobutylene Polyisobutylene Polyisohutylene Polyisobutylene Polyisobutylene Polyisobutylene Polyisohutylene

23000 150000 760000 760000 760000 760000 760000

a-methyl butane a-methyl butane a-methyl butane a-methyl pentane a-methyl hexane 3ethyl pentane cyclopentane

325 325 327 381 423 463 455

325 325 318 376 426 458 461

9400 9400

n-butyl chloride n-butyl chloride

254 403

263 412

110000 110000 6000 6700 22000

cyclopentane cyclopentane n-butyl formate n-butyl formate n-hutyl formate

280 410 264 264 264

293 427 264 264 264

Poly(methy1 styrene) Poly(methy1 styrene) Polystyrene Polystyrene Polystyrene Polystyrene Polystyrene

ethanol ethanol ethenol ethanol ethanol ethanol ethanol

90

in polymer solutions have been obtained. This paper is not a comprehensive review of the subject, but is focused on experiments which have a bearing on particle forces. It is by understanding inter-particle forces that the particle technologist is able to optimise the formulation procedure and design the formulating and transporting apparatus to obtain the desired product. The technique described here does simulate the interactions between two particles as they approach.

ACKNOWLEDGEMENTS

The author would like to thank Mr. L. J. Ford for many useful discussions and Dr. M. A. Ansarifar and Mr. B. A. de1 Costello for many helpful comments on the manuscript. The author is also grateful to the SERC, grant number GR/D/24326 for their support of this work. REFERENCES

4

10 11 12 13 14 15 16

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