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The physical chemistry of dispersion A Doroszkowski

6.1 Introduction The physical chemistry of dispersion may range from producing a polymer dispersion, such as latex, where the particle dispersion is formed in situ, to pigment suspension.

In preparing a latex, there is a strong element of polymerization kinetics which does not apply to pigment dispersion. On the other hand, in pigment dispersion there may be certain interfacial considerations which do not apply to latex formation. However, from a colloidal point of view, once the dispersion is produced, the physical chemistry of the dispersion is the same, whether polymer or pigment.

In this chapter the emphasis is on examining the physical chemistry of the dispersion where the disperse phase is preformed, Le. from a pigment standpoint, although the same considerations apply to polymer particles if they constitute the disperse phase.

Our objective is therefore to look at the physical chemistry involved in forming a dispersion; to examine the factors influencing dispersion stability; and to consider how they can be measured or assessed.

For simplicity, we can define a paint as a colloidal dispersion of a pigment (the ‘disperse’ phase) in a polymer solution (the ‘continuous’ phase). Emulsion paints have both the polymer and pigment as the disperse phase. While the chemical structure of the polymer is important in determining the properties of a paint, the state of dispersion of the pigment in the polymer is no less important.

In practice it is fair to say that most of the problems that arise in a paint come back to the state of the pigment dispersion. The state of pigment dispersion can affect the:

flow properties [2]; durability [3]; opacity [4]; gloss [5]; storage stability [6].

optical properties, e.g. colour [l];

The physical chemistry of dispersion 199

To produce a ‘good’ dispersion of colloidal particles from a dry powder we have to go through a number of processes which can be subdivided, arbitrarily, as separate operations, since in practice they may occur simultaneously. They are:

These simple titles may mask many complex processes but are well worth consideration, as is the ‘simple’ practical question ‘Is it better to disperse TiOz pigment in an alkyd solution using an aromatic or aliphatic solvent?’

immersion and wetting of the pigment; distribution and colloidal stabilization of the pigment.

6.2 Suppose we consider a single solid particle of pigment which will become immersed in a liquid. This can be represented schematically as a three-stage process:

Immersion and wetting of the pigment

If the particle has an area A, and ysysv is the free energy per unit area, then the total energy of the three stages can be written as:

Stage 1: The surface energy of the particle is simply A ysv. Stage 2: The energy of the particle in the vapour plus the work done to create

a hole in the liquid identical to the volume and area of the pigment is A YSV + A YLV.

Stage 3: The work done to plug the hole in the liquid with the particle is A YLS ~ A YSV - A YLV.

Then the total energy change on immersing a particle is the sum of stages 2 + 3-1:

i.e. A YLS - A Ysv (6.1 1

From Young’s equation we have ysv = Y , , ~ + yLv cos 0: The energy change on substitution in equation (6.1) is

-A YLV COS 0 (6.2)

200 Paint and surface coatings

If we examine Young's equation in terms of wetting, or contact angle (e), that is:

(6.3) Ysv -YsL

Y LV COS e =

then, provided that 8 < 90°, a decrease in yLv will reduce 8 and improve wetting, hence an aliphatic hydrocarbon is preferable to an aromatic solvent, since yLv(aliphatic) < yLv(aromatic).

If, however, we add a surface active agent, and it adsorbs at the air interface it will reduce yLv, and if it adsorbs on the particle surface it will decrease ysL. Both these effects will lead to better wetting.

However, if 8 = 0, as in a high-energy surface such as one might expect of a TiOz surface, it would be better to have yLv maximized, i.e. the aromatic solvent should be preferable to the aliphatic solvent as the dispersion medium.

6.2.1 Penetration of agglomerates If we consider the spaces between the powder particles as simple capillaries of apparent radius r, then the surface pressure ( P ) required to force a liquid into a capillary is:

(6-4) -2y,, COS e

P = r

Force = -2xr yLv cos 8 Area = x?

Hence penetration will occur spontaneously (ignoring gravitational effects) only if 8 < 90" and if the pressure within the capillaries does not build up to counter the ingress of liquid.

Thus, to enhance liquid penetration of agglomerates it is desirable to maximize yLv and decrease 8. But since changes in yLv go hand in hand with 8 this is difficult to realize. The addition of surface active agents will tend to decrease both yLv and 8, especially in aqueous media, hence the assessment of which is the dominant effect is best obtained by trial.

The argument used above is rather a simplistic one which uses the surface energy of a solid in equilibrium with the vapour of the liquid. Heertjes & Witvoet [7] have examined the wetting of agglomerates and have shown that only when 8 = 0 can complete wetting of the powder aglomerate be obtained.

The rate of liquid penetration into an agglomerate was derived by Washburn [SI as:

(6.5) dl ry,, cos8 dt 4rl _ - -


where dlldt is the rate of penetration of the liquid of viscosity (q) in a capillary of radius r and length 1.

In a packed bed of powder it is customary to employ an ‘effective pore radius’ or a ‘tortuosity factor’. Thus r/4 can be replaced by a factor K , which is assumed to be constant for a particular packing of particles. Then equation (6.5) becomes

(6.5a)

Thus by inspection of equation (6.5a) we can see that to facilitate penetration of the powder we want to:

maximize yLvcosO; minimize the viscosity (q);

The Washburn equation describes a system in which the walls of the tube are covered with a duplex film (i.e. one where the surface energy of the film is the same as that of the surface of the bulk material). Good [9] generalized the Washburn equation to cover the case where the surface is free from adsorbed vapour. That is,

have K as large as possible, e.g. loosely packed agglomerates of pigment.

(6.5 b)

where ne is the spreading pressure of the adsorbed film that is in equilibrium with the saturated vapour, and II,,,, is the spreading pressure for the film that exists at zero time.

If we consider the question of whether it is better to disperse TiOz in aliphatic or aromatic hydrocarbon, then while it is difficult to assign a specific surface energy to the TiOz, because of its varied surface coating, which consists of mixed hydroxides of alumina, silica and titania, it is nevertheless a high surface energy material and can be likened to a water surface for simplicity [lo], therefore cos0 = 1 for both the aromatic and aliphatic hydrocarbons, unless one of the liquids is auto- phobic [ll]. Hence, in order to maximize yLvcosO it is better to use the aromatic hydrocarbon.

Crow1 [12] has demonstrated the effect of y,,cos0 on grind time, as shown in Table 6.1.

Table 6.1 - Adhesion tension (yLv cose) and rate of milling: laboratory ballmilling of rutile titanium dioxide

Medium Adhesion tension (yLV COS e) Hegman 3” Hegman 5“

Time (hr) to reach

5% isomerized rubber 21.9 5% alkyd 16.3 10% alkyd 14.4 10% isomerized rubber 12.3

0.9 2.0 1 .o 1.7 1.7 2.5 2.0 4.0

~ ~ ~~

” Hegman readings on the 0-8 scale, where 0 = coarse or poor dispersion, 8 = fine or best dispersion.


6.2.2 Solid surface characterization The surface and interfacial tension forces can be subdivided into polar interactions (yAB) which are the (Lewis) acid parameter of surface tension, y+, and (Lewis) base parameter, y- (for hydrogen bonding y+ is the contribution of the proton donor (Brgjnsted acid) and y-, that of electron acceptor (Bronsted base). Thus H-bonding is a special case of Lewis acid-base interactions) and apolar Lifshitz-van der Waals interactions, y W (comprising the London-van der Waals, or dispersion forces; van der Waals-Keesom, orientation; and van der Waals-Debye, induction, forces) as described by van Oss and co-workers) [13]. Hence the total surface tension of a material (i) is

y, = rl"" + rP" The total acid-base free energy of interaction between two materials i and j is

not additive, unlike the apolar components because of the nature of the independent (asymmetric) interactions, hence the total interfacial free energy between substances i and j is:

+2[(y:y;)i + (y;y;)' -

Young's equation, i.e. (1 + cos0)y~"' = -(ysI - ys - y,) can be written in the form:

(1 + cos0)yy = 2(y;"yy): + 2(y3#$ + 2(y;y;):

where i = s (solid) and j = 1 (liquid). By measuring the contact angle at the solid-liquid interface, using at least three

different test liquids of known polar and apolar components (seeTable 6.2) it is possible to obtain three simple equations in three unknowns. Hence the solid surface's polar and apolar surface tension (surface free energy) components can be determined, thereby characterizing the solid surface in energy terms (mJm-*) (or in mN m-' as tension). For example poly(methy1 methacrylate) was found to have surface free energy components of [14]

yLw = 43.1; y+ = 0; y- = 11.3 (in mJrn-').

Table 6.2 - Test liquids [13]

Test liquid

Decane 23.8 23.8 0.0 0.0 0.00092 a-Bromonaphthaline 44.4 44.4 0.0 0.0 0.00489 Diiodomethane 50.8 50.8 0.0 0.0 0.0028 Water 72.8 21.8 25.5 25.5 0.0010 Formamide 58.0 39.0 2.28 39.6 0.00455 Ethylene glycol 48.0 29.0 1.92 47.0 0.0199 Glycerol 64.0 34.0 3.92 57.4 1.490

Surface free energies in mJ m-'; viscosity (q) in Pa s.


The measurement of the contact angle between a powder and a liquid frequently presents problems, when the capillary rise technique is used. This is frequently due the difficulty in obtaining a reproducible powder-packing in a capillary tube, especially when pigments constitute the powder. To overcome the problems associated with the capillary rise in a column of fine powder, van Oss and co-workers used a ‘thin-layer wicking’ (TLW) technique [13, 151. The technique essentially consists of making reproducible, thin-layer chromatography substrates on suitable microscope glass slides; measuring the liquid (solvent) rise as one would in standard thin layer chromatography (TLC), to determine the apparent pore radius ( r ) of the substrate, using an alkane (cos0 = 1); then repeating the process with other test liquids on similar plates. using the experimentaly determined value of r.

Although the TLW technique appears to work reasonably well in characterizing pigment and other powder surfaces, it should be noted that when applied to titanium dioxide pigment characterization, the ‘solvent front’ moves very slowly (about 1 cm in an hour, at the most) and great care has to be taken to prevent solvent evaporation, so as not to make the measurements meaningless. However, it is possible to differentiate between various grades of commercial titanium dioxide pigments using this approach.

There are some criticisms associated with the TLW technique as discussed by Chibowski and Gonzalez-Caballero [14]. The original form of the Washburn equation describes the process correctly only if the liquid completely wets the powder (zero contact angle) and a duplex film of the liquid has been formed well ahead of the penetrating front, hence the solid surface free energy has no influence on the rate of wicking. Chibowski and co-workers, however, have shown that by using equations based on Good’s derivation of the ‘Washburn’ equation, this argument can be negated and that the TLW technique is a useful tool in characterizing solid surface free energies, provided care is exercised to ensure that there is no solvent loss from the moving front, and preferably horizontal sandwich plates are used [16-181.

6.3 Deagglomeration (mechanical breakdown of agglomerates) Pigmentary titanium dioxide exists in powder form as loose agglomerates of about 30-50ym in diameter. The surface coating of the pigment, by the manufacturer, has a large effect on reducing the cohesive forces of the powder and thus assists in the disintegration (or deaggregation) process [19]. It is difficult to define the ‘grind’ or dispersion stage where the loose agglomerates are broken down into finer particles after all the available surface has been wetted out, and the process is generally treated empirically, as described in Chapter 8.

The surface coating applied by the pigment manufacturer, for example onto TiOz. is proprietary information and probably not completely understood, though there are many publications attempting to describe it [20, 211. The chemical analysis of the pigment and surface coating is generally in terms of ‘equivalent to’ Al2O3, SiO?. ZnO.Ti0, etc. even though the coating consists of mixed hydroxides which are probably more correctly described by M,(OH),. where M can be a mixture of Al, Si, Ti, Zr, etc. (as well as organic treatments with polyols, to facilitate stages of paint manufacture). The main purpose of the surface coating is to deactivate the surface of


Fig. 6.1 - Particle size analysis of Ti02 (log-probability plots).


the rutile pigment, which would otherwise accelerate the degradation of the resin on weathering. The pigment coating is also there to aid pigment dispersion by the paint manufacturer. The ‘grinding stage’ in millbase manufacture is not a com- minution stage but a dispersion stage of the pigment to the primary particle size as made by the pigment manufacturer. Some of the ‘primary’ particles consist of sinters of TiO, crystals produced during the ‘surface coating’ stage in pigment manufacture and remain intact per se on completion of the ‘grind stage’, as can be shown by particle size analysis before and after incorporation of the pigment in a paint (see Fig. 6.1); that is, the median particle size by count (dgc = 0.16pm) and distribution (o = 1.52) of the TiOz before ‘grinding’ was found to be the same as that obtained by sedimentation analysis after ‘grinding’ in a ballmill (using the appropriate Hatch-Choate equation to convert particle size by mass to that of size by count; d,, = 0.16pm = d,, = 0.3pm when o = 1.52 which is in good agreement with the measured size d,, = 0.36pm, o = 1.5).

6.4 Dispersion - colloid stabilization It is not enough to ‘wet out’ particles by the continuous phase to produce a stable colloidal dispersion. It is important to realize that attractive, interparticle forces are always present in pigment dispersions. These are the London, van der Waals (or surface) forces. These attraction forces are a consequence of the attractive inter- atomic forces amongst the atoms which constitute all particles.

Polar materials exert electrostatic forces on other dipoles (Keesom forces [22]), and polar molecules can attract nonpolar molecules by inducing dipoles (Debye forces [23]). The attraction between nonpolar atoms or molecules was not understood until it was realized that the electron cloud surrounding the nucleus could show local fluctuations of charge density. This produces a dipole moment, the direction of the dipole fluctuating with the frequency of the charge fluctuations. If there is another atom in the vicinity, then it becomes polarized and it interacts with the first atom.

London [24] showed how this treatment could be used to calculate the interaction between two similar atoms, and he extended it to dissimilar atoms. London’s analysis is based on instantaneous dipoles which fluctuate over periods of lo-’’ to 10-“s. If two atoms are further apart than a certain distance, by the time the electric field from one dipole has reached and polarized another, the first atom will have changed. There will be poor correlation between the two dipoles, and the two atoms will experience what are known as ‘retarded’ van der Waals forces.

In general, we can expect strong non-retarded forces at distances less than lOOA (10nm) and retarded forces at distances greater than this.

6.4.1 Forces between macroscopic bodies The forces between two bodies, due to dispersion effects, are usually referred to as surface forces. They are not only due to the atoms on the surface, but also to the atoms within the bulk of the material. Hamaker [25] computed these forces by pair- wise addition. They may be summarized as:


r v 1 2

(d+:r

if

-Zi2A d >> 6 then VA = ~

32xd4 (6.6a)

(6.6b)

(6 .6~)

where VA is the attraction energy for two plates of thickness 6 at a distance of separation of 2d from each other, and A is the Hamaker constant for the substance comprising the plates.

Hamaker [26] also showed that the attraction energy (V,) between two like spheres of radius a separated by a surface to surface distance d is:

where

d s=2+- a

-Aa If d 4 a then VA 2- __

12d

and for spheres of radii a, , a2:

-Aala2 v, = 6 4 a l + a21

(6.7a)

(6.7b)

We can compute these attraction forces in terms of particle size, medium, and distance of separation, and express the result as an energy of attraction (V,). However, the Hamaker constant A is the value in vacuo, and if one is considering the attraction energy between two particles in a fluid, it has to be modified according to the environment. Hamaker showed that particles of substance AI in a medium of substance A2 had a net Hamaker constant of A = AI + AZ - 2d(A1A2). Thus if we have two different materials - material 1 and material 2 in medium 3 - the net Hamaker A 132 is modified according to

For a list of Hamaker constant values for common substances see Visser 1271. Gregory [28] showed how the Hamaker constant could be estimated from simple experimental measurements.


The point to note is that these forces are always attractive; they may be modified to varying extents depending on one’s wish for accuracy, e.g. Vold’s correction due to adsorbed layers [29] or Casimir and Polders’ correction due to retardation of the attraction forces [30,31]. However, simple examination of the published values of the Hamaker constants reveals that they may vary by an order of magnitude and therefore rarely justify laborious correction for varying subtle effects such as that of Vold [29] and Vincent and co-workers [32].

Although there is always an attraction force between two like particles, Visser [33] points out that in certain circumstances it is possible to have a negative Hamaker constant in a three-component system such as when A l l < A33 < Az2 or A l l > A33 > AZ2 where A33 is the individual Hamaker constant of the medium. It is important to note that there is still an attractive potential between like particles of A l l in A33 as well as Az2 particles attracting each other in medium A33, but there will be a repulsion between A , , particles with AZ2 particles. A suggested example of this type of non-association is thought to be exemplified by poly(tetra fluoroethane) (PTFE) and graphite particles in water.

To obtain a ‘colloidal dispersion’ one must somehow overcome the omnipresent attraction energy by generating some kind of repulsion energy (V,) between the particles, such that when the repulsion energy and attraction energy are added, there is still a significant net repulsion energy. Since the attraction and repulsion energies are dependent on interparticle distance, i t is important to know something of particle spacing, especially in paint systems which, in conventional colloidal terms, are considered to be ‘concentrated’. It can be shown that in a hexagonally close-packed array of spheres, the ratio of surface-to-surface separation (S) to centre-to-centre separation (C) is related to total volume by

1

- = I - C S [:3 ~ (6.9)

where PVC is pigment volume concentration (%). The surface-to-surface distance in relation to pigment volume concentration

is given in Table 6.3, where the distance S is expressed in terms of sphere diameter. Thus for any particle size of mono-disperse spheres the average separation is equal to one particle diameter at a PVC of 9.25%. Therefore the average

Table 6.3 ~ Relationship between pigment volume concentration (PVC) and surface-to-surface spacing (S)


Fig. 6.2 -Typical energy V . S . particle separation curves for the approach of two like particles: VR = repulsion energy; V , = attraction energy, where the total

interaction energy (V,,,) is V,,, = V R + V,. Note that weak flocculation, or secondary minimum flocculation (Vmin>, occurs if VA > V , at large particle separations, even though there is strong repulsion (VmaX) on closer approach; on very close approach there is very

strong primary flocculation due to VA D V,.

interparticle distance for TiO, at this concentration is about 2000A (200nm), and for smaller particles at the same volume concentration the distance is propor- tionally smaller.

If we compare repulsion energies and attraction energies, and remember that if particles are in Brownian motion, which at room temperature have an average translational energy of $kT, then to stabilize them we must have an energy barrier (Vmax) which is significantly greater than this (see Fig. 6.2).

Depending on the nature of the net energy curve we can have a ‘secondary minimum’ or an energy trough which may bring about flocculation which is weak. This is called ‘weak flocculation’ (V,,,,,) or ‘secondary minimum flocculation’ and is used to differentiate it from the stronger flocculation which occurs on closer approach of particles, sometimes called ‘primary flocculation’. It is worth noting that sometimes in the literature [34] the terminology is different from that used in the paint industry, e.g. the term ‘coagulation’ in the literature is used to mean flocculation, when normally that term is reserved by industrial chemists for the irreversible association of latex or emulsion particles.


6.4.2 Dispersion stabilization by charge To produce a stable colloid dispersion, a source of repulsion energy must be induced onto particles so that within the interparticle distances (at the desired particle concentration, Le. PVC) there is sufficient net energy to prevent flocculation.

This repulsion energy may arise from coulombic forces as described by the DLVO theory (see below) or from ‘steric stabilization’. Charge may be generated at a surface in different ways:

preferential adsorption of ions; dissociation of surface groups; isomorphic substitution; adsorption of polyelectrolytes; accumulation of electrons.

Preferential adsorption of ions is the most common way of obtaining a charged particle surface, e.g. the adsorption of Ag’ or I- ion on Ag halide sols, or ionic surfactants on pigments. The dissociation of surface groups is a common feature with latexes which become charged by the dissociation of sulphate or carboxyl groups. The theory of stabilization of colloidal particles by charge has evolved over the years. It culminated in what is known as the DLVO theory, and is expounded by Verwey and Overbeek (the VO of DLVO) in their book [35]. There are many excellent reviews [36,37] and papers on the subject, and the present author does not intend to go into the theory. In outline the double layer theory at a flat surface consists of an innermost adsorbed layer of ions, called the ‘Stern layer’. The plane (in the Stern layer) going through the centre of the hydrated ions (when no specific adsorption takes place) is known as the ‘outer Helmholtz plane’ (or Stern plane), OHP, and is directly related to the hydration radius of the adsorbed ions.

If some specific adsorption takes place (usually the dehydration of the ion is a prerequisite) then the plane going through the centre of these ions is known as the ‘inner Helmholtz plane’, IHP. The distinction between the OHP and IHP is generally necessary since the specifically adsorbed ions allow a closer approach to the surface than the hydrated ions at the OHP and thus increase the potential decay.

Beyond the Stern (or compact) layer there is a diffuse layer, known as the ‘Gouy’ (or Gouy-Chapman) layer.

When the charge in the Stern layer, diffuse layer, and the surface is summed the total = 0 because of electroneutrality. The potentials just at the solid surface (v,,), at the IHP (v\) and OHP (vd) are, as Lyklema [36] points out, abstractions of reality, and are not the zeta potential, which is the experimentally measureable potential defined as that occurring at the ‘slipping plane’ in the ionic atmosphere around the particle.

However, while the zeta potential and the potential at the Helmholtz plane are not the same, for simple systems such as micelles, surfactant monolayers on particles, etc., there is considerable evidence to equate them [38].

6.4.3 Zeta potentials Zeta potentials can be estimated from experimentally determined electrophoretic mobilities of particles. The equation used to convert observed mobilities into zeta potentials depends on the ratio of particle radius ( a ) to the thickness of the


double layer (UK), e.g. for M aqueous solution at 25 "C with a 1 : 1 electrolyte, I/K = 1.10Pcm.

Values for other electrolyte types or other concentrations modify K on a simple proportionality basis, since for an aqueous solution of a symmetrical electrolyte the double layer thickness is

I cm 1 3x10-'

K z c i _ - -

where z is the valency, and c is expressed as molarity.

zeta potential (5) by If ~a > 200 then the mobility (p) is related by the Smoluchowski equation to the

where E is the permittivity of the medium and q = viscosity.

aqueous solutions. If the mobility is measured in pm s-'Ncm-' then

When Ka < 0.1 then the Huckel equation

= 12.8pmVper mob,l,ty for

p=- e5 6m

applies. For 200 < m < 0.1 it is necessary to use the computations of O'Brien and White

[39] which are an update of the earlier Wiersema el al. [40] computations relating mobility to zeta potential.

The conversion of electrophoretic mobility to zeta potential is based on the assumption that the particles are approximately spherical. If they are not, then unless ~a is large everywhere, there is obviously doubt as to the value of the zeta potential obtained from the mobility calculation.

If the particle consists of a floccule comprising small spheres and if ~ca (for a small sphere) is large, the Smoluchowski equation applies.

Hence the zeta potential has frequently a small uncertainty attached to its value, and many workers prefer to quote just the experimentally determined electrophoretic mobility.

6.4.4 Measurement of electrophoretic mobility The electrophoretic mobility of small particles can be measured by microelectrophoresis, where the time taken for small particles to traverse a known distance is measured, or alternatively by a moving-boundary method. The microelectrophoresis method has many advantages over the moving-boundary method, and it is the more frequently adopted method, although there are some circumstances which favour the moving-boundary method [41].

An alternative method based on the electrodeposition of particles has been devised by Franklin [42]. While the quoted values appear to be in good agreement with microelectrophoresis measurements, the method is fundamentally unsound because electrodeposition of a dispersion is based on electrocoagulation and does not depend on electrophoresis [43].

The physical chemistry of dispersion 21 1

If the mobility of charged particles is examined in a microelectrophoresis cell then it will be noticed that there is a whole range of velocities, with some particles even moving in the opposite direction. This effect is due to electro- osmotic flow within the cell. The true electrophoretic mobility can only be determined at the ‘stationary levels’ where the electro-osmotic flow is balanced by the hydrodynamic flow. The position of the stationary levels depends on the shape of the microelectrophoresis cell, i.e. whether it is circular or rectangular. There are many varieties of microelectrophoretic cell [44], and there are many refinements to enable rapid and accurate measurements to be made, such as Rank Bros’s microelectrophoresis apparatus [45] equipped with laser illumination, rotating prism, and video camera and monitor. For details on how to measure electrophoretic mobilities the reader is referred to Smith [38], James [46], and Hunter [47].

In extremis one can construct a simple ‘flat cell’ suitable for viewing under an ordinary microscope, just using a microscope glass slide and two sizes of glass cover slips, as shown in Fig. 6.3.

6.4.5 Application to colloid stability When two charged surfaces approach each other they start to influence each other electrostatically as soon as the double layers overlap. For surfaces of the same sign the ensuing interaction is repulsion. In a qualitative interpretation a number of points have to be taken into account.

The essence of DLVO theory is that interparticle attraction falls off as an inverse power of interparticle distance and is independent of the electrolyte content of the continuous phase, while the coulombic (or electrostatic) repulsion falls off exponentially with a range equal to the Debye-Hiickel thickness 1 / ~ of the ionic atmosphere.

The Stern layer does not take a direct role in the interaction, but its indirect role in dictating the value of vd is enormous. In the DLVO theory, the double layers are considered as if they were purely diffuse, but in reality the theory applies to the two diffuse parts of the two interacting double layers. The surface potential v(i should be replaced by Stern potential vdr which in turn is replaced by the zeta potential for non-porous substances.

Typical double-layer thicknesses at varying electrolyte concentrations are given in Table 6.4, illustrated in Fig. 6.4 and calculated from

(6.10)

where F = Faraday constant, RT = 2.5 x 10”’ ergs at 298K, &,Eo are relative permittivity and permittivity in a vacuum and, 2,; e, are the charge and number of all ions in solution.

For an aqueous solution of a symmetrical electrolyte the double-layer thickness is

1 3x10-’ I cm _ - -

K zcT

where z is the valency and c is expressed as molarity.

ma,

55

2

%

.a 0

k .5 2

3

23 e 2

%

- :8

gm

;.

.- t .? g zp E

x=

2

98

a m

5

25

.-

+a,

m- G

-4

- OD

m

>D

OM

a.2

o

a

D%

*a,

a,= a

- -00

8 2

.2

E%

g

qs

$4 %

Q,G

.i! E

a, 4

-4

2

0 aa,

2 0

%

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s

;zv

m

2 .z

FO

4-

4-z

s; 2

.E ~

2

E2

2

2

2: m”

2m

m

’S a

+a

,c

os a,

sa, t;s

3 .z

23

2%

cc

o

m

.- 69 1s M

-a

&lE!

DO

EM


Table 6.4 - Effect of electrolyte on double layer thickness Concentration of 1 : 1 electrolyte in water at 25 "C

Double layer thickness t i n cm x IO-* Molar concentration

10-5 1000 1o-4 300 1 o-? 100 10-2 30 10-1 10

Fig. 6.4 - Schematic effect of electrolyte concentration on double layer thickness 1 / ~ .

6.4.5.1 The dynamics of interaction Much depends on the timescale of particle interaction, e.g. diffusion relative to adjustments of the double layers on overlap. If the rate of approach is fast, the double layers have little or no time to adjust.

If there is slow approach, then the double layers are continually at equilibrium. The DLVO approach, in this latter case, is that the energy of repulsion, V,, can be


calculated by reversible thermodynamics as the isothermal reversible work to bring the particle from infinity to distance H .

The underlying idea is that in an equilibrium encounter the potential should remain constant, since it is determined by adsorption of the charge-determining ion, the chemical potentials being fixed by their values in the bulk. This is what is known as ‘constant potential’ interaction.

‘Constant charge’ interaction is expected to occur if the interaction proceeds so fast that there is no readjustment of ionic adsorption/desorption, and hence the surface potential, wo, is not constant but rises during overlap.

When all is said and done, there is not a great difference in VR for the two types of interaction, but the constant charge case tends to give larger VR than constant potential.

For two small spherical particles of radius a at constant charge the energy of repulsion is given by Verwey and Overbeek [35] as

while for constant potential

e-T(s-2)

VR = Eavi( J)P

where

I - ( T - 1 +

+ e-2r I-- ~

2sr T + l

and

(6.11)

(6.12)

s = Rla; R is the centre-to-centre distance between two particles of radius a. Since y and P are always between 0.6 and 1.0 we may neglect their influence in many cases [35, p. 1521. Hence equation (6.13) is a good approximation for the free energy of electrostatic repulsion. (Overbeek points out that there is no exact equation [36].)

(6.13)

(6.13a)

where y’ = tanh(z@r0/4RT) E, = relative permittivity of medium

R, T, F, z have their usual meanings = permittivity of a vacuum


(6.1 3b)

For the interaction of two particles of different surface potential (w~~,, vo2) and different radii, a, and a2 (provided that KH > 10 and yo < 50mV), is according to Hogg et al. [48],

F2Cc,z, E I &OR T

K 2 =-

VR = &a,az(WoZ, + W i d B (6.14) 4(al + a * )

where

+ In [I - exp( - ~ K H ) ] 1 2W01W02 ln( 1 + 2exp - K H B = (W(:l +w&) 1 - e x p - a

Figures 6.5-6.7 illustrate the evaluation of V,,, (= VR + VA) in terms of surface-to-surface distance ( H ) when the particle size and electrolyte content are kept constant, but the surface potential is varied; the surface potential and electrolyte content are kept constant, but the particle size is varied, and when the particle size and surface potential are kept constant, and the electrolyte content is varied.

6.4.5.2 Flocculation by electrolyte From the evaluation of V,,,, = VR + VA shown in Fig. 6.7 it is seen that the addition of an electrolyte will make a charge-stabilized dispersion flocculate. This property was recognized at the end of the nineteenth century when Schulze found that the

Fig. 6.5 - Net interaction energy (V,,, = VK + V,)-particle separation curves, where particle size and electrolyte content are constant and the surface potential is varied (using

equations (6.13) and (6.7).


Fig. 6.6 - Net interaction energy (V,,, = VR + VA)-particle separation curves, where electrolyte content and surface potential are constant and particle radius is varied (using


Fig. 6.7 - Net interaction energy (V,,, = VR + VA)-particle separation curves, where particle size and surface potential are constant and the electrolyte content is varied (using



flocculating power of a counterion is greater, the higher its valency. It was confirmed by Hardy, and is now known as the Schultz-Hardy rule.

We can define the onset of dispersion instability using Overbeek's approach [37] as the condition when

(6.14a) vn,, = VR + VA = 0

and aV,,,/aH = 0 are satisfied for the same value of H . That is,

using equations (6.13a) and (6.7a), where d = H = surface-to-surface separation distance, we obtain

therefore the critical condition is when KH = 1. Substituting K for H in equation (6.14a), we obtain the critical condition as:

K,,,, = ~ ~ K E , E ~ , ( ~ R T / F ) ' e-'(y')2/Az2

= 2.03 x 10-5(y')2/z2A in c.g.s. units.

where: E, = dielectric constant (78.5) for water at 25 "C. = = 1 1 4 ~ (E, = 1 and dimensionless in c.g.s.-e.s.u. units, but not in SI

units) e = 2.718 R = 8.314 x lo7 erg T-' mol-' T = 298°K F = 2.892 x 10" e.s.u. mol-'.

and for water at 25°C we can (for symmetrical z-z electrolyte) write equation (6.13b) as:

and substituting for K,~,, we obtain the critical flocculation concentration (M,,,,) as

3.7 x 10-*'(y')4 moIes/Iitre

2' A* Mcnt = (6.14b)

If the surface potential (vi,) is high (v,, S 100mV) then y'= tanh (zFiy0/4RT) + 1. Hence the DLVO theory predicts that the flocculation efficiency of indifferent lectrolytes should be inversely proportional to the sixth power of the valency (that is, liz'; hence the relative concentration to bring about flocculation by monova1ent:divalent:trivalent ions is l/l':1/2h:1/3h or 729: 11.4: 1.

For low surface potentials (vo < 25mV) we can equate the surface potential to the zeta potential and simplify equation (6.14b) to

3.31 x moles/litre

A2z2 Men, =


where 6 is in mV since (4RTIF) = 102.8mV at 25 "C and tanh x -L x, for low values of x. Hence the ratio of flocculating concentrations for monovalent : divalent : trivalent ions becomes 1/12:1/22:1/32 or 100:25:11.

In practice there has been found to be good general agreement with the predictions of the DLVO theory, but since flocculation studies are dependent not only on equilibrium conditions, but also on kinetic factors and specific ion effects, care has to be exercised in using this simplified approach, for even ions of the same valency form a series of varying flocculating effectiveness such as the lyotropic (Hofmeister) series where the concentration to induce flocculation of a dispersion decreases with ion hydration according to [Li'] > [Na'] > [K'] > [Rb'] >

In emulsion paints the presence of electrolytes is thus seen to be a very important factor. Pigment millbases formulated on the use of charge alone, e.g. Calgon (sodium hexametaphosphate), are very prone to flocculation; sometimes even by the addition of latex, since the latex may carry a considerable concentration of electrolyte. Such dispersions, once made, are usually further stabilized by the addition of a water-soluble colloid (polymer) such as sodium carboxy methyl cellulose, which may be labelled only as a 'thickener'; nevertheless it increases the dispersion stability to the presence of electrolyte by its 'protective colloid' action.

[ CS'] .

6.4.5.3 Charge stabilization is of great importance in media of high dielectric constant, i.e. aqueous solution, but in non-aqueous and particularly in non-polar, systems (of low dielectric constant) repulsion between particles by charge is usually of minor importance [49].

There have been attempts to use charge to explain colloid stability in media of low dielectric constant such as p-xylene [50].

Osmond [51] points out that the attempted application of double layer theory, with all the corrections necessary to apply it to non-polar, non-aqueous media, reduces the DLVO approach to simple coulombic repulsion between two charged spheres in an inert dielectric (thus ignoring the existence of ions in solution).

Examination of Lyklema's calculation [52] of the total interaction between two spherical particles of radius 100OA (0.1pm) (e.g. TiOz particles) in a low dielectric medium shown in Fig. 6.8, reveals that if the particles had a zeta potential of 45mV and were at 9% PVC - i.e. average spacing of 2000A (0.2pm) - then the maximum energy barrier to prevent close approach is only about 4 kT. While at 20% PVC - average spacing 100OA (0.1 nm) - only 2 kT is available to prevent flocculation, which is clearly insufficient.

Thus, because the repulsion energy-distance profile in non-polar media is very 'flat' (see Fig. 6.8); concentrated dispersions (their definition implying small interparticle distances) cannot be readily stabilized by charge. In very dilute concentration where interparticle distances are very large, charge may be a source of colloidal stabilization. While charge is not considered to be important in stabilizing concentrated non-aqueous dispersions in media of low dielectric constant, however, it can be a source of flocculation in such systems if two dispersions of opposite charge are mixed.

Charge stabilization in media of low dielectric constant


Fig. 6.8 - Net energy-distance plots in non-aqueous medium (from [52]) .

6.5 Steric (or polymer) stabilization An alternative source of repulsion energy to stabilize colloidal particles in both aqueous and non-aqueous (including non-polar) media is what is now known as ‘steric’ or ‘entropic’ stabilization. In 1966 Overbeek said ‘The theory of protective (entropic) action is still in rather a primitive state’ [S3] . Since then great progress in the understanding of steric stabilization has been made with many comprehen- sive reviews on the subject [S4-56].

Napper [S7] presents the latest ‘state-of-knowledge’ in a very readable form. The important feature of steric stabilization is that it is not a steric hindrance as normally considered in organic chemistry terms, where molecular configuration pre- vents a reaction, but a source of energy change due to loss of entropy. I t is sometimes known as ‘polymer stabilization’, but since non-polymeric material can also produce stabilization, this name too is wanting, as are the many alternatives that have been suggested, e.g. non-ionic, entropic.

In its simplest form, steric stabilization can be visualized as that due to a solvated layer of oligomeric or polymeric chains irreversibly attached to a particle surface of uniform concentration producing a ‘solvated’ sheath of thickness 6.

If two such particles approach each other, so that the solvated sheaths overlap, or redistribute their segment density in the overlap zone, there is a localized increase in polymer concentration (see Fig. 6.9). This localized increase in polymer concentration leads to the generation of an osmotic pressure from the solvent in the system. Hence the source of the repulsion energy is equivalent to the non-ideal component of the free energy of dilution.

It is possible to estimate the size of the adsorbed layer of polymer around a particle by measuring the viscosity of the dispersion at varying shear rates [%]. From these measurements it is also possible to obtain some idea of the effectiveness of


Fig. 6.9 - Schematic representation of steric-barrier overlap: (a) Ottewill and Walker [82], (b) Doroszkowski and Lambourne [75] .

the adsorbed layer by examining the slope in a plot of log (dispersion viscosity) against the square root of the reciprocal shear rate, as suggested by Asbeck and Van Loo [59]. The greater the slope, the larger the degree of flocculation. If the viscosity is independent of shear then there is no detectable flocculation under these specific conditions.

A check on the validity of measuring adsorbed layer thickness was made by syn- thesizing a series of oligoesters of known chain length which could be adsorbed only through their terminal carboxyl group onto the basic pigment surface. The measured ‘barrier thicknesses’ were found to be in very good agreement with terminal oli- goester adsorption [60], confirming the effectiveness of the method.

From measurements such as these, it is clear that the size of the adsorbed polymer is not all-important as has been suggested by some [61]. Smaller adsorbed layers can be more effective than larger ones 1621. Chain branching, and where it occurs can have a marked influence on the effectiveness of the stabilizing layer [60]. For example, poly-12-hydroxy stearic acid, which is used as the soluble moeity in a graft copolymer as described in [63], is very effective.

The theory of steric stabilization, like most, has undergone evolution. Its origins are irrelevant, except maybe to historians, whether it is founded in the concept of ‘protective colloids’ as discussed by Zigmondy [64] with his gold sols in 1901, or the early attempts to calculate the effect of entropy loss by adsorbed molecules such as envisaged by Mackor [65]. Nevertheless, steric stabilization was practised by crafts, including paintmakers, before scientists classified the various stages by nomencla- ture and explanation. Fischer [66] probably contributed most to the understanding of steric stabilization, since he envisaged the important influence of the solvent environment on steric stabilization, which was not appreciated even by later workers w71.


At present steric stabilization is generally considered to arise from two factors

A volume restriction term (i.e. the configuration of the adsorbed molecules is reduced by the presence of a restrictive plane VVR). A mixing or osmotic term (i.e. an interpenetration or compression of adsorbed layers resulting in an increase in polymer concentration V,).

These two contributions are regarded as being additive. That is, VI,,, = VVK + V,. It is difficult to evaluate the contribution of these two terms since it entails a

knowledge of the polymer configuration of the adsorbed polymer, and more impor- tantly the segment density distribution normal to the surface of the particle.

Meier [68] and Hesselink [69,70] have attempted to calculate this segment distribution and hence the relative contribution of the two sources of repulsion energy. However, there is dispute in that by subdividing the repulsion energy in this way, there is double counting [71].

There have been, unfortunately. only a few attempts to measure the energy of repulsion by direct experiment [72-771, and it would appear that the theoretical and mathematically complex calculations of Meier and Hesselink grossly overestimate the repulsion energy measured by experiment 1751. The more simple estimates of energy of repulsion (derived from purely the ‘osmotic’ term VKM) appear to be in better accord with practice. Napper, in many investigations [78-801, has shown the importance of the solvent environment in contributing to steric stabilization, and for all intents and purposes the osmotic contribution to steric stabilization is all that needs to be considered. Therefore the repulsion energy on the interaction of two solvated sheaths of stabilizing molecules may be simply written as:

(which are not necessarily equal):

c’RT

“I P VK - K I ) v > (6.15)

where c p = polymer density, v, w,, K, = Flory’s entropy and enthalpy parameters [81], V a

= polymer concentration in solvated barrier,

= partial molar volume of solvent,

= increase in segment concentration in terms of barrier thickness 6, = particle size and surface-to-surface separation (h) .

Which in the Ottewill and Walker model [82] is

V = ( 6 - :) (30 + 26 + $) and the Doroszkowski and Lambourne model [75]

~x’Rl(3K1 -x)(2R1 -x)4(R,’ - r 3 ) + x R , ( x - 3 R 1 ) 2(R? - r ’ ) + xR1 (x - 3 R l )

V =

where R , = a + 6; r = a; and x = 6 - hl2. One has a more useful relationship if one rewrites equation (6.15) and substi-

tutes (w, - K,) by yl(l - 0iT) where 0 is the theta temperature as defined by Flory [81], i.e. where the second virial coefficient is zero, meaning that the molecules behave in their ideal state and do not ‘see or influence each other’.


Thus one can immediately realize that at the theta temperature, [1 - (0/T)] reduces to zero (0 = T ) , and the repulsion energy disappears, allowing the attractive energy to cause flocculation, as shown by Napper. Furthermore, if T < 8, the repulsion energy not only does not contribute to the repulsion, but it actually becomes an attraction energy.

An important point to bear in mind is the c2 term, which is the polymer concentration term in the ‘steric barrier’. If this is small then flocculation can occur, even when the solvency is better than ‘theta’, which has been observed in a few instances.

Napper [83] has subdivided steric stabilization into ‘entropic stabilization’ and ‘enthalpic stabilization’. Depending on whether the entropy parameter is positive or negative, e.g. in the case of steric stabilization by polyhydroxy stearic chains in aliphatic hydrocarbon, flocculation is obtained by cooling; and in enthalpic stabilization, flocculation is achieved by heating (as with polyethyleneglycol chains in water). A purist [84] might correctly insist that this is entropic or enthalpic flocculation, and not stabilization. Nevertheless, in simple practice it is a useful distinction.

Another simple way of achieving the theta point is by changing the degree of solvency of the continuous phase, Le. by the addition of a non-solvent. Napper [85] has illustrated the utility of varying the solvency to achieve incipient flocculation at constant temperature, and has thus again demonstrated the overall importance of the ‘osmotic’ term in steric stabilization.

If we examine the requirement for steric stabilization by an adsorbed layer of molecules, then we can intuitively see that the effectiveness of the stabilization is dependent on the strength of the attachment of the ‘polymeric’ (or oligomeric) sheath to the particle surface. One can envisage three degrees of effectiveness of steric stabilization by the same molecule:

Suppose the stabilizing layer comprises an adsorbed layer of molecules (e.g. and oligomer of 12-hydroxy-stearic acid as shown in Fig. 6.10. Let us suppose that the molecules are covalently attached to the surface of a particle. Then if two such layers overlap to give an overlap zone of increased segment density, then the free energy of dilution (due to increased localized segment density) can only be relieved by separation of the two particles. Suppose the stabilizing layer of the oligomer is strongly adsorbed on the surface of the particle, but not anchored to a specific site on the surface, Le. the oligomer is free to move over the particle surface but cannot be desorbed. On overlap of the stabilizing sheaths (as two particles approach), the increase in segmental concentration can be redistributed over the whole of the surface layer by lateral compression of the molecules and thus the increase in surface concentration of the attached molecules is reduced, hence a lower free energy of dilution to repel (separate) the two particles. This situation is clearly less effective than case 1. Suppose the oligomer molecules are weakly adsorbed on the particle surface. i.e. they are free to move over the particle surface, as in case 2, but they are also free to ‘pop-off (desorb from) the particle surface if the compression forces become too great. This clearly will give rise to the weakest form of steric stabilization, for on overlap of the solvated sheaths, the surface molecules can relieve the increase in surface concentration by a combination of redistribution, desorption and particle separation.


Fig. 6.10 - Degrees of effectiveness in stabilisation by steric barriers on close approach of like particles: (1) stabilishing molecules bound to site on particle surface (large localised increase in segmental concentration); (2) molecules free to move over particle surface (no desorption), hence reduced increase in segmental concentration, leading to weaker particle-particle repulsion; (3) molecules free to move over surface and desorb, hence

increase in segmental concentration reduced by partial desorption, ie, steric stabilisation effectiveness is a > b > c.

Thus the effectiveness of steric stabilization is (1) > (2) > (3) because of the depen- dence on the nature of the molecules’ attachment to the surface of the particles, as well as, the nature of the continuous phase, etc.

The molecular weight of the adsorbed polymer, which determines the size of the steric barrier, is not an overriding criterion. For example it has been suggested [86] that if one uses the best estimate of the Hamakar constant for TiO, in aliphatic hydrocarbon media as A12 = 5 x lO-*OJ [27] then one is left with a value of 51nm for the thickness of the solvated polymer sheath around the TiO, pigment to produce effective steric stabilization. This in turn must mean that the molecular weight of the polymer molecules (adsorbed in chains and loops) must be at least many tens of thousands, if not more! Yet pigment dispersion experience has shown that small molecules, about 500 in molecular weight, can give effective colloid stability 187-891.

There are many variations of the theory of steric stabilization. Napper (57, Ch. 11,121, for example divides them into pragmatic’ and ‘ab initio’ theories, Pragmatic theories assume some form of segment distribution in the adsorbed layer, e.g. a uniform segment distribution, or an exponential segment density distribution. Ah


initio theories attempt to calculate segment distributions from first principles: these can be further subdivided into classical theories which use Flory’s mixing and elastic (entropic) contributions to the steric repulsion energy, and the mean-field theories, which effectively combine these effects, treating the segments as having a real volume. While the latter may be more sophisticated in their approach, they are more difficult to use. Dividing the repulsion energy into separate mixing and elastic terms might be more ‘synthetic’ it is, however, conceptually more useful. While many theories on steric stabilization differ in complexity, and the simplifying assumptions made, their qualitative description of steric stabilization is similar. For a discussion of various attempts to estimate the steric repulsion energy the reader is referred to the review by Vincent and Whittington [90].

The study of the nature of colloid stability in the absence of solvent in a fluid-polymer matrix (polymer-melt condition) has somehow been neglected in the scientific literature, yet it is of the utmost importance in paint technology. This situation occurs during the final stages of solvent evaporation in air-drying films, re- flow in stoving (baking) finishes and in the dispersion stage, as well as ‘cure’ of powder coatings to mention but a few. The mechanism of colloid stabilization in the ‘polymer-melt’ condition is ascribed to the ‘volume restriction’ component of steric stabilization. For the total steric repulsion free energy ( V,,,) comprises the mixing (V,) and the volume restriction ( VVR) terms, i.e. V,,, = VM + VVR; which for spherical particles is [89,91]:

where SM and SE are geometric functions of barrier thickness and particle separation; VI and V, are the solvent and polymer segment volumes respectively, Q2 is the average volume fraction of segments in the barrier; X is Flory’s interaction parameter, and a, k , and T have their usual meaning.

Under ‘melt’ conditions the solvent can be regarded as a polymer, hence V , is very large. The above equation shows that the consequence of making VI large is that VM becomes very small, leaving V,, to be the source of free energy change to provide particle stabilization, as for example in making a dispersion of particles in molten polyethylene oxide [92].

6.6 Depletion flocculation and stabilization Steric stabilization arises as a consequence of polymer adsorption onto the surface of particles. The effects of free polymer in solution on colloid stability give rise to what was coined by Napper and Feigin ‘depletion flocculation’ [93] and ‘depletion stabilization’. (For a review on the topic see [57, Ch. 171.)

The concept of depletion flocculation may be traced back to Asakura and Oosawa [94, 951. However, it was Li-in-on et al. [96] who showed that at higher concentration of free polymer in solution, the flocculating effect of added polymer disappeared.

There are variations on the theme of depletion flocculation [97-991, but basically the concept arises from consideration of non-adsorbing surfaces and polymer molecules in solution. When surfaces of colloidal particles approach each other to separations less than the diameter of the polymer molecule in solution, the polymer is


then effectively excluded from the interparticle space, leaving only solvent. Ther- modynamically, this is not favourable, leading to osmosis of the solvent into the polymer solution and thereby drawing the two particles even closer together, i.e. the particles flocculate.

Napper and Feigin [93] extend the depletion flocculation mechanism to depletion stabilization by considering what happens under equilibrium conditions to two inert, flat plates immersed in non-adsorbing polymer solution, and by examining the segmental distribution of a polymer molecule adjacent to the surfaces in the bulk solution from a statistical point of view.They showed that the polymer segment concentration adjacent to the flat, non-adsorbing surface was lower than in the bulk. By estimating the ‘depletion-free energy’ as a function of plate separation in terms of polymer molecule diameter, they showed that as the two plates were brought together there was first a repulsion as the polymer molecules began to be con- strained, followed by an attraction on closer approach of the two surfaces (see Fig. 6.11).

They applied Derjaguin’s method of converting flat plate potential energy curves into those for curved surfaces (i.e. sphere-sphere) interactions, by the equivalent of mathematical ‘terracing’ of a curve as shown in Fig. 6.12.

Vincent et al. studied the flocculating effect of added polymer in sterically stabilized latexes [loo] and explained the findings with a semi-quantitative theory that is schematically represented in Fig. 6.13.They showed that the strength of the repulsion energy on overlap of the adsorbed polymer sheaths (GLL) is reduced by the presence of polymer in the continuous phase by G1~’- = G’-L.o - ni2 Gpp where G’,L.o is repulsion energy of the polymer sheaths in the absence of polymer in solution and Gpp is the interaction between two polymer coils in solution: n is the number of polymer coils displaced into solution.

The theory predicts that flocculation by added polymer occurs between the polymer concentration @& when the expanded polymer coils in solution just touch one another (see Fig. 6.14); and a::, the concentration when uniform segment density, occurs as the polymer coils contract to their theta configuration (a::) on the further addition of polymer. That is,

M b * *(S ’):” Np

and a;; = M

@& = b ( ) * s2 312 Np

Fig. 6.1 1 - Schematic representation of depletion flocculation (a) and stabilization (b).


Fig. 6.12 - Derjaguin’s flat plate-sphere conversion.

Fig. 6.13 - Vincent et aZ.’s depletion flocculation mechanism (from [lOO]).

Fig. 6.14 - Schematic representation of polymer molecules in a good solvent (adapted from [102]); (a) the dilute region, where concentration ( c < c*) polymer coils are expanded

and well separated from one another; (b) the intermediate region (semi-dilute) polymer chains start to overlap, but segment density is not large (c* < c < c**);

(c) concentrated region where every segment is in contact with other segments ( c > c**) and polymer coils contracted (effectively in theta condition).


where M is the molecular weight of the polymer of density p; N is Avogadro’s number; (S’); is the radius of gyration; b* and b** are packing factors (8 and 2.52 for cubic close packing, and 5.6 and 1.36 for hexagonal close packing respectively).

When applied, their theory gave a reasonable, broad co-relation with experiment for both aqueous and non-aqueous systems [102].

Scheutjens and Fleer [lo31 proposed a similar depletion flocculation- stabilization mechanism to Napper, also based on theoretical conformations of polymer molecules.

Both Napper and Feigin [93] and Scheutjens and Fleer I1031 predict large depletion stabilization energies available to colloidal particles at suitable free polymer content, but the two theories differ in several respects. For example, Scheutjens and Fleer predict greater stabilization effects in poor solvency conditions (Le. theta conditions), while Napper and Feigin favour good solvency.

One criticism of depletion stabilization theory is that it appears to teach that it is only necessary to have a sufficiently concentrated polymer solution, preferably of high molecular weight, to make a good pigment dispersion. In practice this is clearly found to be an inadequate requirement. It does not necessarily mean that depletion stabilization theory is wrong, but only incomplete, maybe because concentrated polymer solution theories are still poor. Fleer ef al. [104], unlike Napper, have revised their estimates of depletion stabilization energy downwards to be more in line with Vincent et al., who strictly speaking do not have a depletion stabilization energy, but only an absence of depletion flocculation at high polymer concentrations.

The concept of depletion flocculation has an important bearing on paint properties. It teaches, for example, that even if good pigment dispersion is achieved in dilute solution, then the addition of even compatible non-adsorbing polymer may cause flocculation. (Note the care necessary in ‘letting-down’ a ballmill on completion of the pigment dispersion stage.) It also suggests the possibility of pigment flocculation occurring on the addition of solvent, e.g. dilution with thinners prior to spraying.

I t also suggests that different methods of paint application which rely on varying degrees of solvent addition may cause different degrees of pigment flocculation, leading to variation in colour development, even when the dispersion is well deflocculated at low polymer content in the continuous phase. Depletion flocculation may also occur with charge-stabilized systems such as latexes on the addition of an ‘inert’ thickening agent, as shown by Sperry [lo51 which may produce different types of sedimentation phenomena.

6.7 Adsorption To obtain good dispersion stability by steric stabilization it is important to fix the stabilizer molecules to the surface of the particle. The more firmly they are held, provided that they are also well solvated and free to adopt varying configurations, the better; for example, terminally adsorbed polymeric molecules such as polyhy- droxystearic acid, have been found to be excellent stabilizers [63]. If, for example, the adsorbed molecules are attached to the surface of a particle and are able to move about on the surface, then on overlap of the solvated layers the increased concentration could be partly accommodated by a surface redistribution which will


result in a lower repulsion energy than if surface redistribution is not possible. Furthermore, if the adsorption of the stabilizing molecules is weak, then not only could the increase in osmotic pressure be countered by surface redistribution, but also by stabilizer desorption, leaving little, if any, force for approaching particle repulsion, as discussed earlier.

But, if adsorption of the stabilizer molecules is so strong that the stabilizer molecules are ‘nailed flat’ to the surface of the particle, effectively producing a pseudo, non-solvated layer, then on the close approach of another similar layer there would be no entropy loss of the polymer chains, and all that would be achieved would be the extension of the particle surface by some small distance. The attraction potential would then be from the new surface, and the particles would have a composite Hamaker constant producing an attraction potential with no source of repulsion energy.

In the design of dispersion stabilizers it is important to have something with which to attach the solvated stabilizing molecule firmly to the surface, preferably at a point, leaving the rest of the molecule to be freely solvated in its best solvent, e.g. chemically bonding the stabilizer to the particle surface either covalently, as with reactive stabilizers such as those described by Thompson et al. [106], or by acid-base interaction in non-polar media such as reacting carboxyl terminated fatty chains, e.g. poly-12 hydroxy stearic acid with an ‘alumina’ coated pigment.

Sometimes it is not possible to react a stabilizer to the surface of the particle, and the demand for strong anchoring and maximum solvation can be achieved only by physical adsorption using amphipathic copolymers in hemi-solvents, such as block or graft copolymers, where one portion of the molecule is ‘precipitated’ onto the surface of the particle (i.e. the anchor component is non-solvated) leaving the solvated portion to produce the stabilizing barrier as described in [63]. For a compre- hensive discussion on polymers at interfaces the reader is referred to Fleer et al. [107].

6.7.1 Adsorption isotherms Adsorption isotherms are very useful in obtaining an understanding of what may be happening in a pigment dispersion. For example, it may be expected that when TiO, pigment is dispersed in butyl acetate, xylol, and white spirit, using the same dispersant [60], then the attraction energy because of the Hamaker constant values of the respective solvents should be of the order.

where Vk = attraction energy in white spirit, V i = attraction energy in xylol, V i = attraction energy in butyl acetate.

Since the stabilizer is terminally adsorbed (i.e. the barrier thickness is the same), it should give the best stability in butyl acetate solution. However, viscometric measurements indicate that the reverse sequence holds, i.e. the dispersion with the least flocculation was in white spirit, followed by that in xylol, and the worst was in butyl acetate. Inspection of the adsorption isotherms immediately revealed that the surface concentration was the least in butyl acetate (see Fig. 6.15), hence the stabilizing barriers were the weakest in butyl acetate solution.


Fig. 6.15 - Adsorption isotherm of dimer 12-hydroxy-stearic acid in (1) white spirit; (2) xylol; (3)butyl acetate onto TiOz [60].

Adsorption isotherms are most readily measured by placing a fixed amount of pigment in a known amount of polymer solution, in glass jars, along with small (e.g. 8mm) glass beads as a milling aid, and leaving the jars for at least 24 hours on rollers. so that constant agitation is obtained. Centrifugation will then enable the separation of the continuous phase, so that the amount of material adsorbed may be determined, as described in [60].

An alternative method to obtain an adsorption isotherm is to place the pigment in a chromatographic column and to pass a dilute solution of the adsorbate down the pigment column, as described by Crow1 [108].

The advantage of the chromatographic method is that it enables preferential adsorption and adsorption reversibility to be easily determined. The method generally works well with organic pigments; however, with TiO, pigments flow rates through the pigment column are in practice very slow, making the method very much less attractive than might appear at first sight.

6.7.2

6.7.2.1 Estimation of free energy of adsorption (AGad,) f r o m adsorption isotherms Suppose that we examine a particle immersed in a liquid, e.g. water. and we imagine the surface of the particle to consist of a ‘mosaic’ of adsorption sites where ‘S’ rep- resents such a site occupied by the solvent. If we introduce a solute molecule. X. into the liquid, then if it were to adsorb on the surface, it will displace the water molecule occupying the site. Let SX represent the adsorption of the solute at a site, and S(H20) the water molecule adsorption. We can express this as an equilibrium reaction by:

Free energy of adsorption and adsorption isotherms


Le. K is the partition, or equilibrium, constant for the solute between the surface of the particle and the solvent, and is related to the free energy of adsorption (AG,,,) by

AGads = -RT In K

Using Glasstone’s notation [109], where possible, we can express K as:

(mole fraction solute on surface) (mole fraction solvent in bulk) (mole fraction solvent on surface) (mole fraction solute in bulk)

K =

Suppose the surface has a sites per g adsorbent which are occupied by the solvent molecules in the absence of solute and that x 1 of these are occupied by the solute when dissolved in the solvent, then

(xl / a ) (mole fraction solvent in bulk)

( y) (mole fraction solute in bulk) K =

If we restrict our considerations to low @e. initial) adsorption, i.e. when x1 << a, and have dilute solute concentration, then

hence AGads = -RT In( 7) XI / a

where N is the mole fraction of solute of concentration, c, g moles in solution of a liquid of molecular weight M , and density ‘p’ so that N = McIlO0Op and hence for aqueous solution N = ~155.5.

Let x/m be the number of g moles adsorbed solute per g adsorbent. This is proportional to the fraction of sites occupied by solute, i.e. x/m = p(xl la) where p is a proportionality constant.

If the surface is completely covered by a monolayer of solute, then x,la = 1; and xlm = p = maximum adsorption (or plateau value). Thus for aqueous solution,

(x’z5-5) AGads = -RT In

At low solution concentration, (x/m)/c = initial slope (IS) of an adsorption isotherm, hence

AGads = -RT In (plat:: E e , p ) (6.16)

By plotting an adsorption isotherm in terms of g moles adsorbed per g adsorbate against molar equilibrium concentration it is thus possible to estimate the free energy of adsorption in a monolayer or Langmuir-type adsorption isotherm from the initial slope and saturation value.

The usefulness of equation (6.16) is that it gives a ‘feel’ for the strength of adsorption and especially its ‘converse’ use, Le. in estimating the adsorption of a surfactant


by particle surfaces such as those of pigment or emulsion droplets, and ensuring that sufficient material is added to satisfy the adsorption requirement of the dispersion. For if the free energy of adsorption is known, and for simple physical adsorption it is of the order of 5 Kcal/g mole, the cross-sectional area of a surfactant molecule is known (obtainable in the literature, or it can be estimated using molecular models). It is thus possible to construct the initial slope and plateau portions of the adsorption isotherm. By joining the initial slope to the plateau level, by drawing a gentle curve in the 'near-saturation' zone (as shown by the broken line in Fig. 6.16), the adsorption isotherm can be completed with a little 'artistic licence', hence the minimum surfactant requirement estimated.

The derivation of AGad\ as outlined above is based on a simple model of an adsorption surface composed of adsorption sites which are either occupied by solvent molecules or solute, such as a simple surfactant.

This is useful in giving an insight into the interpretation of an adsorption isotherm and illustrates the importance of the initial slope, as well as the saturation value

Fig. 6.16 - Prediction of surfactant adsorption using equation (6.16). The construction of the isotherm is based qn the physical adsorption of surfactant (aqueous) at 5 Kcal per

mole at the rate of 20OA' per molecule onto a powder of density 1.5g/cm3, with average particle diameter of 0.5 pm. a is the required surfactant concentration which comprises

6.7 x lO-'g moles surfactant per lOOg powder in equilibrium with a minimum surfactant solution concentration of 9.5 x IO-' M.


(which also applies to polymer adsorption); but the calculation of AGads for a polymer molecule, which may occupy a varying number of sites depending on its conformation, should not be made unless refinements, or constraints to polymer chain configurations, are taken into account. A similar proviso is as made by Koral et al. [110] who determined the ‘isosteric’ heats of polymer adsorption from adsorption isotherms. That is, if the adsorption isotherm is measured at different temperatures, then it is possible to estimate the enthalpy of adsorption (AH) using an analogue of the Clausius-Clapeyron equation (Huckel equation):

(6.17)

where H , and HI- are the partial molar enthalpies of the polymer on the adsorbate and in solution: a, and uL are the corresponding activities of the polymer at the surface and in solution. Under very dilute condition aL = c and, if it is assumed that the activity of the polymer at the surface does not change if the amount adsorbed is kept constant, the above equation becomes:

AH d l n c -- - R d(l/T).

(6.17a)

Hence by measuring the adsorption isotherm at different temperatures, taking equal amounts of the adsorbed material at different temperatures, and plotting the corresponding equilibrium solution concentration on a logarithmic scale against the reciprocal of the absolute temperature, a straight line is obtained whose slope is equal to AHIR.

6.7.3 Adsorption and temperature The amount of polymer adsorbed from solution frequently increases with temperature, thus indicating that the process is endothermic. However, there are also cases when the adsorption will decrease with temperature [ l l l ] or it may be unaffected by temperature [112].

Koral et al. [110] point out that the adsorption process could not be endothermic in the case of physical adsorption of simple molecules on a clean surface, since then the entropy lost on adsorption will be negative, necessitating the enthalpy to be also negative (to ensure a decrease in the free energy of adsorption). However, in the case of polymers one must consider the system as a whole. The adsorption of a polymer molecule at several sites on a surface requires that several solvent molecules are released from the surface to the solution. The translational entropy of the polymer molecule, along with some of its rotational and vibrational entropy, is lost on adsorption, because of partial restriction to its segmental mobility. Thus the solvent molecules which are desorbed gain their translational entropy, which cumu- latively is much larger than that of the polymer molecule.The net result is that there is an overall entropy gain in the system on the adsorption of a polymer molecule which displaces solvent molecules, even if the process is endothermic.

The quality of the polymer solvent also has an effect on the amount of polymer adsorbed by the substrate. Generally the poorer the solvent the greater the amount adsorbed [110], and adsorption can be related to the solubility parameter [113]. However, the adsorption of polymer does not depend on polymer-solvent interac-


tion alone, but also on substrate-solvent interaction as well [114]. It is also possible to obtain less polymer adsorption by a substrate on the addition of small amounts of non-solvent to a polymer solution, if the solvent has a strong interaction with the substrate [115].

6.7.4 It is difficult to define how quickly adsorption takes place since it depends on many factors, especially concentration [116], but it is generally considered to be fast [117, 1181. For a review of polymer adsorption see Lipatov and Sergeeva [119]. However, in most practical instances one is more interested in the state of equilibrium adsorption in a mixed component system; and with polymer adsorption from solution, the simple principle of first come, first adsorbed applies, Le. adsorption is diffusion controlled [114, 120, 1211. The smaller molecules arrive at a surface first and are adsorbed only to be displaced on the later arrival of the larger molecules which are preferentially adsorbed [122]. This phenomenon of preferential adsorption of the higher molecular weight analogues frequently gives rise to the observed ‘maxima’ in adsorption isotherms of polymers [62]. In dispersing pigments, e.g. making a millbase, it is important to ensure that the preferentially adsorbed polymer is in sufficient quantity at the very start, since displacement may be very slow.

This is sometimes vividly demonstrated in practice, as for example when pigment is initially dispersed in a polyethylene glycol (PEG) modified alkyd, and the other polymeric constituents are added afterwards: then good pigment flushing into the aqueous phase occurs immediately, as shown when the freshly prepared oil-based paint adhering to a paint brush is washed in detergent solution (Le. when the modified PEG alkyd is adsorbed on the pigment surface). However, if the pigment is milled in the other polymeric constituents first, and then the PEG alkyd is added, it then takes about four weeks for the ‘brush wash’ properties to appear, signalling that the PEG alkyd has displaced the other constituents from the pigment surface [123].

Another example of the slow re-equilibration of adsorbed molecules sometimes manifests itself as a ‘colour drift’ (a gradual shift in colour on storage), for example when the ‘colour‘ is made by blending various (colour stable) pigment dispersions (tinters), especially if the tinters are based on different resins. One way of solving this colour drift problem is simply to pass the finished paint through the dispersion mill (e.g. a Sussmeyer). The shearing in the mill, as well as the temperature rise, accelerate the re-equilibration of the adsorbed species, just as agitation is found to accelerate adsorption of polymer [121] and thereby stops the colour change.

Stereo regularity is also an important factor in polymer adsorption, as shown by Miyamoto et of. [124] who found that isotactic polmethyl methacrylate is more strongly adsorbed from the same solvent than syndiotactic polymer of the same molecular weight. Syndiotactic PMMA (polylmethy (methacrylate)), in turn, is more strongly bound than atactic polymer. as shown by TLC development with ethyl acetate [125].

Rate of adsorption and equilibration

6.7.5 Specific adsorption Adsorption of polymer from solution onto a surface depends on the nature of the solvent and the ‘activity’ of the surface.


While in the simple physical adsorption of polymer it can be seen intuitively that higher molecular weight species might be preferentially adsorbed in a homologous series, to the low molecular weight species, specific adsorption may override molecular weight considerations. A typical example is the preferential adsorption of the low molecular weight, more polar species, such as the phthalic half esters present in long oil alkyds. Walbridge et ai. [126] showed that the adsorption of these materials could be explained in terms of acid-base interactions, where the base was the Ti02 pigment coating and the metal of the ‘driers’. They were able to show that the complex flocculation-deflocculation behaviour depended on the order of addition of drier and dimer fatty acid to a simple white, long oil alkyd-paint. They found that it also depended on the relative acid strength and the formation of irreversible carboxyl-pigment coating bonds, which in turn were a function of the temperature of dispersion. Just as ion exchange resins can bind acids (or bases), so can certain pigment surfaces behave in a similar manner. Solomon et al. [127] studied the effect of surface acid sites on mineral fillers and concluded that they were comparable in strength to, but fewer than, those found in ‘cracking’ catalysts. The presence of these sites, which were developed by heat, profoundly affected chemical reactions in polymer compounds, particularly in non-polar media.

6.8 Rate of flocculation When considering dispersions and flocculation phenomena it is useful to have some idea of the rate of flocculation, at least in order of magnitude terms. Smoluchowski [128] showed that for uniform spheres which have neither attraction nor repulsion forces present and adhere to each other on collision, the rate of decrease in the number of particles can be expressed as: -dNldt = KN2 where N = number of particles, and K is the rate constant. On integration, this becomes

(6.18)

where No is the initial number of particles; i.e. N = No at time to. If we define a ‘half-life’ time tt where the number of particles is one half the original number. i.e. 2N = No at time t i then on substitution in equation (6.18) we have 2/No = l/No + Kt+, that is,

1IN = 1INo + Kt

(6.18a)

If the rate constant is diffusion controlled, then K = KD = 4kTl3q where k = Boltz- man constant; T = temperature, q = viscosity of the medium.

Table 6.5 gives the time taken for different particle sizes at various pigment volumes to reduce their number by one half, according to Smoluchowski’s rapid flocculation kinetics based on Brownian motion when the medium is at room temperature and has a typical paint viscosity (1 poise, 0.1 Pa s). If flocculated, a typical gloss paint (TiO, at 15% PV) will revert to its flocculated state in half a second after having been subjected to disturbance, e.g. by brushing. Even if the vehicle viscosity is very much greater, the time taken for reflocculation to occur after shear is still very short. For a similar reason when Aerosil (fumed silica) is used as a structuring agent, the quantity required is small compared with TiO, volume, and the structure developed through flocculation is almost instantaneous. There have been a number of attempts to verify and improve on Smoluchowski’s rapid flocculation kinetics by


Table 6.5 - The half life of particles of different particle size undergoing rapid flocculation at 25 "C in a medium of 0.1 N s m-'

Half-life time % pigment volume Half-life time % vol (Aerosil) (q) (s) (e.g.Ti02) (-0.2pm diam.) (a) (ps) (-0.014pm diam.)

7.6 1 1.5 5 0.76 10 0.5 15 0.38 20

2400 1 480 5 240 10 160 15 120 20

taking into account interparticular forces and hydrodynamic interactions [129-1331. While these findings suggest that the rate constant should be approximately half of Smoluchowski's value, they do not significantly alter the concept that in practical systems the flocculation of pigment is very fast.

Gedan et al. [134] have measured the rapid flocculation of polystyrene particles. While they are in contention with Smoluchowski's approximation that the rate constant for doublet, triplet, and quadruplet formation is the same, nevertheless Smolu- chowski's theory is still considered to give a good insight as to the rate of dispersion flocculation and has been well confirmed by experiment [129,130].

6.8.1 Sedimentation and flocculation Pigments generally have a density greater than the resin solution constituting the paint, and under the influence of gravity they will tend to settle out, according to Stokes law. This may be expressed as

(6.19)

where a particle of apparent diameter d (Stokes diameter) falls a distance h in a medium of viscosity for a time t under the influence of gravity g when there is a difference in density of Ap between the particle and medium.

If well deflocculated, the particle dispersion will sediment according to the above relationship to give a hard, compact deposit which is difficult to redisperse. However, a sedimentation velocity of up to circa 1OF'cm s-' is generally countered by diffusion and convection, and sedimentation may seem to be absent. If flocculation is present, pigment sedimentation is rapid and the deposited material is soft, voluminous, and readily reincorporated into suspension by stirring.

When sedimentation takes place the volume of the final sediment depends upon the degree of flocculation; the greater the flocculation, the larger the sediment volume. In the extreme, the sedimentation volume may equal the total volume and should not be confused with the deflocculated state when no sedimentation may occur. The sediment volume is not only dependent on the flocculation forces, but i t also depends on particle shape and size distribution [135]. Care should be taken to ensure that sedimentation volumes are used only as a relative measure of the degree of flocculation in similar systems.

Plate 6.1 shows how sedimentation tubes may be used to determine the optimum


Plate 6.1 - Sedimentation tubes used to determine optimum concentration of Calgon to produce TiOz dispersion in water. Tube ‘e’ is marginally the best - note the lower sedimentation volume of tubes ‘g’ and ‘h’, indicating that although flocculated they

are not as intensely flocculated as ‘a’ and ‘b’.

concentration of dispersing agent (Calgon) to produce a well-deflocculated suspension of Ti02 in water.

A simple alternative way of assessing the degree of pigment flocculation is to spot the dispersion onto filter paper and measure the ratio of pigment stain to solvent stain, in an anlogous manner to Rf values in chromatography; the higher the ratio the more deflocculated the dispersion.

Plate 6.2 illustrates the respective ‘spot’ testing of the dispersions shown in the sedimentation test. Note how tube and spot tests both show dispersion ‘e’ to be the best dispersion.

Smith and Pemberton [136] have described a variant of the ‘spot’ method of assessing flocculation which they claim gives better results.

Generally, in order to assess flocculation by observing sedimentation behaviour or measuring the Rf flocculation value, it is necessary to reduce the viscosity of a paint, by the addition of solvent, otherwise sedimentation is too slow to be of experimental value; though on dilution, care must be exercised, since this may introduce a new source of flocculation due to desorption, or depletion flocculation, or both.

Flocculation is more readily assessed in the liquid state where it can be measured by viscometry [%I. For example, if the viscosity of the continuous phase (qo) is New- tonian, then if there is no particle-particle interaction, the dispersion viscosity (q) should also be Newtonian. If the dispersion is not Newtonian, then the degree of deviation from Newtonian behaviour is a measure of particle-particle interaction, Le. of flocculation, provided that the disperse phase volume is <30% +, otherwise inertial effects may be observed 11371. By plotting log q against the reciprocal square


Plate 6.2 - ‘Spot’ tests on filter paper of the dispersions used in Plate 6.1 to determine optimum Calgon concentration for Ti02 dispersion. R, = x/y . The larger the value the better

the dispersion. Spot ‘e’ is the best.

root of the shear rate, straight-line plots are obtained. The steeper the gradient the greater the degree of flocculation, as shown in Fig. 6.17.

This method of assessing flocculation has been found in practice to be very reli- able and applicable to typical pigment concentrations in paint formulations. The comparison of flocculation by this method is strictly for similar volume concentrations, since the slope in the above plot will increase with disperse phase concentration. However, the effect of dissimilar disperse phase volumes can be estimated, and corrections can be applied to enable comparison.

It is worth noting that the rheological assessment of flocculation is a function of the total interaction of the system which is measured. Therefore, if there is a large difference in particle size between two dispersions, even though the two dispersions are compared at the same disperse phase volume, the dispersion with the smaller particle size and weaker interparticle interactions will appear to be more non- Newtonian (i.e. more flocculated). This is due simply to the interparticular forces being proportional to the first order of particle radius, while the number of particles per unit volume is proportional to the cube of the radius; hence the total ‘strength’ of a large number of weak bonds amongst small particles is greater than a few strong bonds between larger particles.

There have been attempts to estimate interparticle forces from rheological measurement by determining a ‘critical shear rate’ [138], but these estimates are very questionable [139].

The degree of pigment flocculation can also be assessed by colour measurement [140], anti-sag properties [126], or by direct visual observation through a microscope, as shown in Plate 6.3. Flocculation in a dry paint is more difficult to assess since microtoming thin sections of paint film for electron micrographs may alter the


Fig. 6.17 - Log (dispersion) viscosity-(shear rate)-; plots as a measure of varying degrees of pigment flocculation [60] (1) most flocculated to (4) least flocculated.

apparent state of pigment dispersion [141]. Freeze fracture, followed by oxygen etching methods [ 1421, has been developed to overcome this shortcoming; but at concentrations around 12% or more, visual interpretation becomes more difficult.

An alternative approach to the assessment of pigment flocculation has been developed by Balfour and Hird [143] who used the measurement of scatter coefficients determined in the IR region which are more sensitive to large particles. However, none of these methods can measure the state of pigment flocculation directly in both the liquid and solid state. Doroszkousk and Armitage 11441 have described a method based on proton straggling which can measure the state of pigment flocculation directly, irrespective of the nature of the phase (i.e. dry or liquid paint).

In conclusion, the apparently simple question asked at the beginning of this chapter, as to whether it is better to disperse a pigment in aliphatic or aromatic hydrocarbon, is in reality extremely complex, for it contains conflicting considerations, viz:

1 It is necessary to maximize y cos0 for the system, and this may depend on the nature of the substrate and the concentration of alkyd. For TiOz, which has a high surface energy, it would probably be better to use the aromatic solvent, since cos0 = 1 for both solvents.

2 From a consideration of attraction energies it would appear that the aromatic solvent might be the better choice when TiO, is the pigment, since this would produce a better match of Hamaker constants. When considering the nature of the adsorbed layer and its contribution to steric 3


6.3a -A well-dispersed TiOz. When viewed through a microscope (x400) the particles appear to shimmer, owing to Brownian motion. Although the particles seem to be visible, in fact they are not resolved, and only their diffraction pattern is seen as a dot.

6.3b - Lightly flocculated TiO2 dispersion. The particles have lost their Brownian motion and are seen as clusters (x400).

6 . 3 ~ - Highly flocculated TiOz dispersion. The particles are flocculated into large clusters and are reminiscent of the mud- flats of a river bed (x400).

Plate 6.3 - Photomicrographs of TiO? pigment dispersion showing varying degress of flocculation.


repulsion it would probably be better to use the aliphatic solvent (white spirit) since a greater concentration of resin might be adsorbed, and this may give a more robust dispersion at only a small trade-off in solubility of the solvated layer than using aromatic solvent (toluene).

Finally, consideration ( 3 ) will probably outweigh considerations (1) and (2) combined.

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