effect of pigment volume concentration and latex particle size on pigment distribution

E L S E V I E R Progress in Organic Coatings 30 (1997) 185 194

PROGRESS IN ORGANIC COATINGS

Effect of pigment volume concentration and latex particle size on pigment distribution

R o g e r F.G. B r o w n * , C h r i s t o p h e r Carr, Michae l E. T a y l o r

PRA, S Waldegrave Road. Teddington, Middlesex TWI I 8LD, UK

Received 8 July 1996; accepted 26 August 1996

Abstract

Pigment distribution in latex paints has been investigated by experiments using a combination of computer modelling, experimental model systems and pigmented paints. This paper deals with the geometric effects of variables such as pigment volume concentration and latex particle size on the pigment distribution in water-borne coatings. Physico-chemical effects, such as particle surface potentials and ionic strength of the serum, are dealt with in a subsequent paper. Computer modelling and experimental model systems gave a clear picture of the geometric effects of PVC and latex particle size on pigment distribution. Higher PVC leads to a higher density of pigment in the film and consequently more crowding of pigment particles, but has no further effect on the quality of pigment distribution. Computer and physical model systems show that pigment distribution is improved by reducing the latex particle size. From purely geometric considera- tions, the best results should he obtained with infinitely small latex particles. A series of model paints pigmented with titanium dioxide showed that the results were valid for latex/pigment size ratios from 0.75 to 1.5. © 1997 Elsevier Science S.A.

Kevwords: Latex paint: Particle size: Monte Carlo simulation; Pigment distribution: Water-borne coatings; Solvent-borne coatings

1. Introduction

It is important that a paint applied for decorative purposes completely obliterates the substrate. To prevent incident light being reflected by the substrate and returning to the observer, all light must be scattered or absorbed by the paint film. For white paints the main mechanism for imparting opacity is multiple scattering.

Where a gloss finish is not required, paints may contain up to 70% total volume concentration of pigments and extenders in the dry paint film. At such high levels complete opacity is easily achieved. For gloss paints much lower pigment volume concentrations must be used to prevent particles disrupting the surface and hence reducing the gloss of the film. Pigment volume concentrations below 20% are typical for gloss paints. At these concentrations the scattering efficiency of the pigment is crucial in achieving a fully opaque coating.

Titanium dioxide is the favoured pigment for producing opacity in paint films due to its exceptionally high refractive index. Light scattering is maximised when pigment particle size is between 230 and 25{) nm [1] and titanium dioxide

* Corresponding author.

pigments are manufactured close to this particle size. How- ever, if the pigment crystals form clusters the scattering efficiency decreases because each cluster scatters approxi- mately like a single, larger particle. Therefore, scattering efficiency depends on how well the titanium dioxide particles are dispersed in the paint film.

Clusters may be produced because of poor dispersion technique, but it has been shown that most clumps are dispersed in only a short time by' the milling process [2]. There- fore, pigment clustering in emulsion paints must involve other factors [3].

It has been shown that scattering increases linearly as pigment volume concentration (PVC) is increased up to 10c~ [2,41. Beyond this point the increase is limited due to crowding and ultimately clustering of pigment particles. Pigment clustering is much more pronounced in water- borne gloss paints [51 than in solvent-borne paints [6,7] (see Figs. I and 2).

Uneven distribution and clustering of pigment crystals reduce gloss and opacity', and contribute to high water vapour permeability and poor flow in emulsion paints [2,8]. The main causes of pigment clustering were cate- gorised as geometric or chemical in origin. Geometric factors include latex particle size and size distribution as well

0300-9440/97/$17.00 tg 1997 Elsevier Science S A. All righls reserved PII S0300-9440196)(10(r86-8

R.F.G. Brow. et ell. /Progress in Organic Coatings 30 (1997) 185 194 186

Fig. 1. Scanning elecmm micrograph (SEM) showing pigment distribution in commercial water-borne gloss (taken at x 8300).

as the number and size distribution of the pigment particles. Chemical factors are considered in a subsequent paper and include surface charge density of both the latex and pigment particles and the ionic strength of the suspending medium

I91. Geometric effects arise in latex paints due to constraints

on the location of pigment particles as a result of the shape of the volume occupied by latex particles at the point prior to coalescence of the latex. Other geometric factors to be considered are pigment volume concentration (PVC) and the size distribution of the pigment and latex particles. The extent to which each of these contributes to pigment clustering was investigated using computer models of hard sphere packing in binary systems. Mixtures of chemically similar, but distinguishable latexes were developed to test the computer model predictions.

Previous to this study, Monte Carlo simulations of paint film morphology have shown that random packing of pigment particles is able to reproduce the observed state of dispersion in a well dispersed organic solvent-borne coating. Results showed that pigment dispersion was improved in systems containing fine particle extenders but there was an optimum particle size ratio [6]. This paper describes a computer program which models binary and ternary packings of hard spheres. Spherical particles are randomly packed into a periodic cell, then 'shaken' randomly. The walls of the periodic boundary are moved inwards until a state approximating to random close packing is achieved. The effect of latex particle size, size distribution and PVC on the degree of dispersion of the pigment particles can be investigated.

Initial practical work used model systems consisting of binary mixtures of distinguishable latexes. Several ways of achieving this were considered including chlorinated/non- chlorinated particles and heavy metal stainable/non-stainable combinations. The method selected used a combination

Fig. 2. SEM showing pigment distribution in commercial solvent-borne gloss (taken at x 8300).

of soft, film-forming acrylic particles in combination with hard, non-film-forming acrylic particles. The hard latex spheres were synthesised to a particle diameter close to 250 nm and were used to represent pigment particles in a real paint. The volume concentration of the hard spheres was termed Hard Sphere Volume Concentration (HSVC) which is analogous to PVC in a pigmented system. The effects of latex particle size and HSVC on the quality of dispersion of the hard latex particles were investigated.

Later practical work studied systems containing real pigments and compared measurements and images with those from the model systems and computer studies.

O Random Parking

~ Monte Carlo

~ Remove Overlaps

Fig. 3. Basic steps in generating a computer model.

R.F.G. Brown el al. / Pro<~ress in Organic Coatin<~s 30 (1997) 185 194 187

2. Computer studies

2.1. Theory o[ operation

Three basic techniques are involved in generating models as depicted in Fig. 3.

2.1.1. Technique one: random parking Each packing is generated initially by "random parking'.

The program creates each particle and tries to "park' it at a randomly chosen position within a periodic cell. If any part of the volume of the new particle overlaps with a particle which has already been parked then the location is rejected and a fresh random location generated. If a particle has not been successfully parked after a certain number of attempts then the parking process is aborted. When there is a large size difference between particles of different types, the larger particles must be parked first. This process produces a fairly sparse packing (maximum packing fraction about 0.2).

2.1.2. Technique two: metropolis Monte Carlo [10,11] Once the required number of particles of each type have

been placed in the cell. particles are 'shaken' using the Metropolis Monte Carlo procedure. Metropolis Monte Carlo is a well-established technique for calculating equilibrium thermodynamic properties of systems such as simple liquids. There are difficulties in applying the method to dense systems because thorough sampling of configuration space becomes impossible at higher densities when particles can no longer move freely past each other.

The basis of the method is that each particle in turn is moved to a new test location, randomly chosen within a cubic cell centred on its present position. After each test move, the resultant potential energy change is calculated and used to derive an "acceptance probability' for the move. A random number between 0 and 1 is then generated; if this is less than the acceptance probability the move is

% %)

accepted, otherwise it is rejected. For hard spheres, this process simplifies: a test move is accepted unless it produces an overlap with another particle. When a test move is rejected, the original state of the system counts as the new state in the chain of states (technically a 'Markov chain') which is generated by the Monte Carlo process. Thermody- namic properties can be derived by averaging over a sample set of states, usually taken at fixed intervals along the chain.

In practice, the Metropolis Monte Carlo technique was principally used in this work as a convenient way of 'shak- ing' the packing towards equilibrium. A process in which each particle in the packing is subject to a Monte Carlo test move is referred to here as a Monte Carlo 'sweep' .

2.1.3. Technique three: densification and removal of overhq~s

The computer program was intended to produce systems as close as possible to "dense random packing' (in the case of hard spheres). For this a means of densifying from the initial low packing fraction of around 0.2 is needed.

Each densifying step is a two stage process. First, co- ordinates are scaled by a chosen factor to increase the density. In general, this creates overlaps between particles. Next, each pair of overlapping particles is moved apart in turn to remove the overlap, the distance moved by each overlapping particle being inversely proportional to the volume of the particle. Since moving a particle in a dense packing usually creates new overlaps, this process is iterated until no further overlaps remain.

The Monte Carlo method is used as a "shaker' during the process of densifying a packing to its limit. Typically a packing was subjected to many Monte Carlo 'sweeps' , then densified by a small factor and the overlaps removed. This was followed by a further Monte Carlo 'equilibration' prior to the next densification step.

This densification cycle was repeated until it was no longer possible to remove the overlaps caused by the last densifying step. The program then reversed the last step and

Fig. 4. Packing densilied to limil with radm,; ratio of 0.67 (lalex/pigmenl) Fig. 5. Packing densilied Io limit whh radius ratio of 3.0 {latex/pigment) and PVC of 3(Yk. Pigment spheres dark. and PVC of 30r4. Pigment spheres dark.

188 R.F.G. Brown el al. / Pro eres.s i~ Org~ nic Coatin~,,s 30 (1997) I&g 194

,2

(

I 3 4 5 6 D i s t a n c e ( p i g m e n t r ad ius = 1.0)

10

~ 8

8 6

~ 4 n,"

2

3 4 5 6 D i s t a n c e ( p i g m ~ t radius = 1.0)

0 0 I 3 4 5 6 7

D i s t a n c e ( p i g m e n t r ad ius = 1.0)

1 0 '~!

12 T

1 0 .

._z- ;

~ 4

0

1o

8 6

.~ .

2+

O! : ~ :

0 1

: : i i i i 2 3 4 5 6

D i s t a n c e (pigment radius = 1.0)

12

10

~ 6 -

2~ 2 .

0

12

lO

a 6 .=

2

11'~ lO

e~ 6

N 4

2

, , p

1 3 4 6 D i s t a n c e (p igmen t rad ius --51.0)

1 2 3 4 =51.0) 6 7 D i s t a n c e ( p i g m e n t r a d i u s

Figs. 6- l l . Radial distribution functions for model packings created by computer with varying size ratios. Key': RR, radius ratio (latex radius/pigment radius): PF, final packing fraction: N. total number of particles.

Fig. 6. Radius ratio 0.667 864 particlcsl: Fig. 7. Radius ratio 0.800 (864 particles); Fig. 8. Radius ratio 1.00 {500 particles}: Fig. 9. Radius ratio 1.50 (500 particles): Fig. 10. Radius ratio 2.00 I500 particles): Fig. I1. Radius ratio 3.0 {500 particles).

optionally carried out a final Monte Carlo shake (although by this stage the packing was too close for more than local equilibration to take place). Examples of binary packings created in this manner are shown in Figs. 4 and 5.

2.2. C h a r a c t e r i s a t i o n o f ' p a c k i n g

A radial distribution function (RDF) shows the mean particle density as a function of radial distance from a typical particle, normalised by dividing by the overall particle density. The densified packings were analysed by calculating radial distribution functions. 'Pigment ' particles were assigned a radius of one program unit. Therefore, a neigh- bouring pigment particle could not be closer than 2 units (centre-to-centre). In a dense packing, the first peak in the radial distribution function always occurs at this distance. Any long range order will cause further peaks to be observed at larger distances.

Example radial distribution functions illustrating the efl~ct of increasing the size ratio are shown in Figs. 6-1 1. Note that RDFs shown are calculated for pigment particles only. ignoring latex particles.

Care is needed in the interpretation of radial distribution functions. For example, a sharp first peak at a centre-to- centre distance of 2.0 program units shows that all nearest neighbours of a typical pigment sphere are in close contact with the central particle, but need not imply that the packing is highly clustered. The most likely explanation of the broader first peak for radius ratio 3.0 (Fig. 11) is that pigment spheres are more loosely packed into the gaps between much larger latex spheres. This happens because the great difference in size between the two types of sphere (a volume ratio of 27:1) reduces the interference between the two components of the packing (the components are said to be more nearly 'non-crowding ') .

Integrating the number of nearest neighbours out to the first minimum in the RDF yields the mean number of pigment particles in the 'first nearest neighbour shell ' , which is a very useful measure of clustering. Since the density of pigment particles in all models was very nearly the same, the larger the number of first nearest neighbours in the pigment radial distribution function, the more clustered the pigment (up to the limit of about 14 neighbours found for a single-component random close packing [12]).

R.F.G. Brown e/ al. /Progre.~s in Organic Coe Jing.~ 3(I (1997) 185 194 189

We have also calculated 'single fraction" (the proportion of all spheres which are not in contact with at least one neighbour) for comparison with results from the image analysis of model latexes. Two-dimensional single fractions were calculated by taking multiple cross-sections through the periodic cell and averaging.

Any single fraction measurement requires a threshold distance (or critical gap) as part of its definition. A panicle is defined as single if the surface-to-surface distance to its nearest neighbour is greater than this critical gap. The best value to be used for the critical gap is hard to decide: the higher the value, the more latitude in the definition of 'contact' between particles, and the lower the single fraction (Table 1 and Fig. 12). Typically, a critical gap of 30 nm was used for particles of nominal 270 nm diameter in the analysis of SEM images and the colTesponding value of 0.222 program units was used for analysis of the computer simulations.

The three-dimensional version of single fraction is much more sensitive to the size of critical gap than two dimensional single fraction. However, 2D values are the only measurements possible on the experimental model systems and therefore the only means of direct comparison between computer and experimental results.

In the method described above, single fraction is calculated directly from the computer model. However, we were also able to develop a theoretical description of two-dimensional and three-dimensional single fractions so that each measurement could be derived from the radial distribution function for the calculated packing. The results from both methods are compared in Fig. 13 and Fig. 14.

3. Latex model systems

To compare the results of the computer simulations with the nearest experimental equivalent, physical systems were required in which packing behaviour would approximate that of hard spheres. It is not possible to produce stable sub-micron panicles which interact as hard spheres, so the approach adopted was to equalise the electrostatic surface potentials of two distinguishable latexes. The polymers used

0 .5 ¢-

. 0

~ o4

I i

"~ o.a L"

0 02 G)

t'-

o5 o.1

0 T

,- I - - I i I I , {

0.5 I 1.5 2 25 3

Radius Ratio ('latex'/'pigrnent')

Tablc l

Effecl of critical gap on 2D single fraction

Critical gap/ Radius ralio (latex/pigment) (pigment radius I

0.667 (1.8() 1.00 1.50 2 .00 3.00

1.0e-3 0.427 0.354 0.294 0.307 0.290 (I.352 1.Oe 2 0.399 0.291 0.263 0.280 0.260 0.327 0.1 0.330 0.217 0.205 0.177 0.136 0.163 0.222 0.290 0.197 0.199 0.148 0.099 0.076

needed to be chemically similar and the surfactant the same. However, it was necessary for the different latexes within a mixture to be distinguishable by electron microscopy. The system chosen comprised mixtures of poly (methyl methacrylate) and poly (methyl methacrylate-co-butyl acrylate) which are chemically similar but have different minimum film-forming temperatures.

It was found that when films were cast from mixtures of fi lm-lbrming and non-fihn-forming latexes, contrast was observed due to the topography of the spherical non-film- forming particles. Enough contrast was present for the hard particles to be distinguished by SEM. The hard particles showed up as lighter coloured circles (Fig. 15).

It was tbund that, by casting films on acetate sheets and with careful use of a microtome, it was also possible to distinguish hard particles within a cross-section of a film cast from a mixture of hard and soft latexes.

The scanning electron microscope (SEM) images were enhanced and processed using a Quantimet 520 Image Ana- lyser to calculate single fractions and cluster sizes.

Fine particle size latexes were prepared by a semi-con- tinuous 'seed and feed" method [131 using 0 .1-0 .2% (w/w monomer) of Aerosol OT I, all present during the seed for- mation stage. Latexes of predetermined intermediate particle size were synthesised by controlled growth [14] of previously prepared seed particles. A series of film-forming latexes was prepared at ca. 40% solids with particle sizes ranging between 105-830 rim. A non-film-forming latex was prepared at ca. 40% solids in two stages to yield a particle size of ca. 280 ran, this being representative of the mean particle size of a commercial grade of titanium

dioxide. Originally', it was found that (for a given HSVC) the

number of hard particles detected per unit area decreased as the panicle size of the film-forming panicles decreased. This phenomenon was attributed to flooding [151 and was overcome by the incorporation of a thickener.

As it was necessary to include a thickener in the model systems, it was also necessary to assess whether changing the concentration of the thickener had any effect on the degree of dispersion of the hard panicles. This was achieved

Fig. 12. Single crystal fraction xersus radius ratio, showing the c('flzct of varying the critical gap (gap is in multiples of typc 1 particle radius), t Tradcnamc for dioctyl sullosuccmatc, sodium sah (surfactant).

1 9 0 R.F.G. Brown et al. /Progress in Organic Coatings 30 (1997) 185 194

35

3O

20

u_ 10

0.5 1 1.5 2 25 3 3.5 Radius Ratio ('latex'tpigment')

~ 3 D SCF (Model) Q 2D SCF (Model) J ]

35

g 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . O

15 . . . . . . . . . . . . . . . "F . . . . . . . . . . ~ _

U. 10

0 I i I ~ I i I ~ 1 4 I '

0.5 1 1.5 2 2.5 3 Radius Ratio (r2/rl)

[m ao scv (cal~) e 2D scv (cae) i k |

3.5

F ig . 13. S C F v a l u e s f r o m c o m p u l e r .

by preparing systems at different HSVCs, surfactant loading and thickener loading. It was found that changing the surfactant concentration and the thickener concentration within the ranges used had no observed effect on the system. The number of particles detected per unit area depended linearly on HSVC. This indicates that the flooding effects observed with early model systems had been overcome.

4. Results and discussion

4.1. The e~k, ct ~¢ volume concentration on single particle fraction

In the latex model systems described above, the number of hard particles detected on the surface or within the cross- section of a film was found to increase linearly as the volume concentration of hard spheres (HSVC) increases as expected.

It was also observed that the single particle fraction decreases with increasing HSVC. This is expected because the density of particles detected increases with HSVC and so the probability that another particle will be closer than the defined critical gap increases. This is a type of 'crowding' effect in which the spheres are inevitably found closer to each other on average as their density increases. For example, model systems with higher HSVCs will have a higher density of hard particles on any surface or section examined, and hence will tend to have lower single fractions purely as a result of crowding.

To study the effect of particle size ratio and polydisper- sity, this crowding effect must first be understood and com- pensated for, if possible.

A simple statistical model (essentially a Poisson distribution) can be derived for randomly placed overhq)ping disks in two dimensions. If f is the single traction of particles in a 2D image frame and k is a constant, N, is the number of particles in the image frame and s is the side length of the image frame, then we expect the following relationship to hold:

ln/"=k • Ne/s 2 (1)

F i g . 14. S C F v a l u e s f r o m t h e o r y a n d R D F s .

These approximations do not apply for two-dimensional distributions of pigment crystals because they are not free to overlap, but results can still be usefully analysed by plotting In f against N,.

The effect of number detected on single fraction values for the experimental systems can clearly be seen by select- ing results for a narrow range of latex sizes (Fig. 16). The approximate theory predicts an exponential dependence and this is demonstrated by plotting log(single fraction) against number detected, as in Fig. 17.

Based on this simple relationship it was possible to develop a 'normalisation factor', which is a function only of the number of particles detected in the 2D image frame. Single fraction results can then be corrected for crowding by normalising all results to a fixed number of particles detected. The success of this /'actor in mapping results for various PVC's onto a single curve can be seen by comparing Fig. 18 with Fig. 19. One conclusion which can be drawn from this result is that the effect of PVC in the model systems can be fully explained by the crowding effect produced by the larger number of particles. This is confirmed by a statistical 'sum of squares' analysis of the normalised single fraction values.

PVC in the latex model systems is expected to have a simple linear effect on the number of particles detected in the 2D SEM images since the size of the image frame was constant. This was true in general although some images showed fewer particles than expected while others showed more. Such variation amounts to experimental noise but since the crowding effect depends only on the number detected, correcting for the effect of crowding actually reduces the effect of this type of noise on the "normalised' single fraction values.

The same normalisation factor was also be applied to the computer simulation results and made possible a direct comparison between experimental and computer results despite the difference m PVCs.

4.2. The £ffect qfl latex particle size

A series of hard sphere computer models were created to investigate the effect of particle size ratio on distribution of

R.F.G. Brown el al. / Progress in Ot'~ t t'c Coating,s 30 (1997) 185-194 191

Fig. 15, Scanning electron micrograph of surface of iihll containing film- forming and non filrn-fornfing latex.

pigment particles. Each hard sphere packing was created initially by random parking to give a packing fraction of roughly 0.2. The packing was then densified in three stages, to packing fractions of 0.3, 0.4 and 0.5, each densification followed by removal of overlaps and 2500 Metropolis Monte Carlo sweeps for equilibration. The program's den- sify to limit operation was then performed with 1000 Monte Carlo sweeps following each densification stage. Pigment single fraction was calculated by averaging over a series of I00 sample states taken from a sequence of Monte Carlo sweeps, taking one sample every 10 sweeps. Two indepen- dent calculations were made for each radius ratio.

Each pigment sphere has a radius of one program unit, and all single fraction values refer to a critical gap of 0.222 program units, corresponding to a gap between panicles at

'contact ' of 30 nm it pigment particles are assumed to have a diameter of 270 nm.

There are difficulties in obtaining results from the computer model at small relative latex particle sizes. A minimum of about 100 'pigment ' panicles in the cell is needed to allow meaningful measurements of pigment distribution. The smallest latex:pigment diameter ratio used was 0.50, requiring a total of almost 2000 panicles per cell. Latex panicles smaller than this cannot easily be modelled because the total number of particles becomes too large to be manageable. However, it is possible to model a system in which the latex particles become so small that they behave as a continuum. In this case we expect the distribution of particles to be unaffected by the presence of the latex, so that pigment distribution will be the same as if the panicles were randomly distributed in a solvent or vacuum. Results from single-component simulations of this type, corresponding to a latex: pigment diameter ratio of zero, are also included here.

Films formed ti"om mixtures of hard and soft latex particles were prepared as described earlier to validate the results of computer simulations against simplified model systems. The model latexes consisted of mixtures of film-forming and non-film-forming particles. The hard particles were poly (methyl methacrylate) with diameter of 270 nm. The soft, film-forming panicles were poly (methyl methacrylate- co-butyl acrylate) with particle sizes ranging from 150 to 830 nm.

The results from the computer and the model latexes were normalised as described above to compensate for the effect of HSVC on single fraction.

Results of the hard sphere models are shown in Table 2 and Fig. 20.

There is a good correlation between the results from the computer and the model latexes. Single fraction decreases as the size of latex particles increases, and the curve is steeper when latex panicles are smaller. There is no evi- dence from the computer model to suggest the existence of a

- 100

16 r0 t . . . . ' ; ; - . . . . . . . . . . . . . . . . . .

6 0 4 . . . . . ~ - • _; . . . . . . . . . 8 0

" i - 00 /

~2a2 . . . . . . . . . . . . . . . Y--- . . . . . . . . . . . i • -20

0 100 200 300 400 500 600 Number Detected

1 7 25 m

15 i l l / : _ - i z i u. /

j -

J

O i l " + + + - - -

0 100 200 300 400 500 600 Number Detected

Figs. 16, 17. Relationship o f two-dimensional single fraction ~alue to ntnllber (it" particles detected in an image fralne (experinlental results at two similar

particle sizes).

Fig. 16. Data plotted as I two-dimensional) single traction versus number detected: Fig. 17. Data plotted as logarithm of sitlgle fi'action versus number detected.

192 R.F.G. Brown et aim /Progress in Organic Coatings 30 (1997) 185 194

18 7O

o•60 m . . . . . . . . . . . . . . . .

~ 20

10

0 ~ i ! i I I i I I ; ~

0 0.5 1 1.5 2 2.5 3 3.5 Radius Ratio ('Latex'/'Pigment')

H S V C - l O %

H S V C = 1 5 %

H S V C = 2 0 %

H S V C - 1 0 % (L inoae Fi i}

H S V C - 1 5 % (L inear Fit}

H S V C = 2 0 % (L inear Fit}

19 7O

~ 6 0

~- 50

u- 40

~ 3(1

~ 2o

0 0.5 1 1.5 2 2.5 3 3.5 Radius Ratio ('Latex'/'Pigment')

m H S V C = 1 0 %

H S V C = 1 5 %

H ? V C = 2 0 %

H S V C = 1 0 % (L inea r Fi t )

HSVC = 1 5 % (Lir , aa r Fit)

H S V C = 2 0 % (L im~ar Fff)

Figs. 18, 19. Experimental single fraction data as a function of radius ratio, showing use of normalization to map curves at differet hard sphere concentrations (HSVCs) onto a single master curve.

Fig. 18. Experimental single fraction ,,alLies: Fig. 19. Normalised single fraction values.

maximum at small latex particle sizes. The composite results from the physical models suggest that the increase in single fraction levels out below l:l size ratio (Fig. 20). However, examination of the individual plots for different HSVC (Fig. 18 and Fig. 19) shows that experimental error increases as size ratio decreases making it difficult to deter- mine the shape of the curve conclusively in this region.

We deduce that, in the absence of other effects, a fine particle latex is necessary to give good pigment distribution and hence optimise pigment utilisation.

In a real water-borne paint, there is a practical limit to the size of the latex particles unless the polymer is water solu- ble. Small particles also require more surfactant than large particles, the presence of which may have undesirable effects on the final film properties.

Table 2

Hard sphere packing restlhs

Radius ratio Experimental Computer (latex/pigmenl) single fraction single fraction

(normalised) (normalised)

0.000 62.4 0.426 42.4 0.500 51.4 0.593 42.1 0.667 45.3 0.800 41.9 0.852 43.9 1.000 36.5 1.167 37.7 - 1.250 31.5 1.500 - 31.2 1.870 29.9 2.000 24.4 2.50O 24.2 3.00O 21.2 3.074 26.4

4.3. Comparison of SEM observations and computer simulations

A series of TiO2 pigmented paints were formulated at different latex particle size and PVC. Electron micrographs are presented in Fig. 21. The quality of pigment dispersion improves with decreasing latex particle size and decreasing PVC. This demonstrates that the physical effects observed in the hard sphere models are still valid in pigmented systems even though small latex particles will have a much greater surface area and be much more likely to destabilise the pigment dispersion. The results obtained suggest that the geometry of the system remains important even though chemical interactions have become competitive in nature.

All computer models described previously used a PVC of 30% to ensure that enough 'pigment' particles were present to give meaningful estimates of single fraction. For a direct visual comparison with the micrographs of pigment distribution, computer packings were created using hard sphere potentials at 20% PVC and radius ratios of 0.6, 1.2 and 1.8, respectively. This required a very large number of particles

70 . . . .

g ~= 604 o

50

( D

C3 40 t " , l

-g 30

70 2o 0

m m mmm

• " ~ m . . . . . .

m

0.5 1 1.5 2 2.5 3 3.5 Relative Latex Diameter (pigment = 1 )

Fig. 20. Hard sphere models: results from computer (light) and experimental (dark) systems.

R.F.G. Brow~z el al. /P rogresx in Orgam'c Coatings 30 ~1997) 185-194 193

Latex Particle Size: 185nm, PVC: 20%

.+ ,+ ; t', .:~ + +t+,,4 ~ ++,, a .+,,... . :~p+" + ~ ' * - • . .+ , , : .

• . . . . . :~ •

• + -

: + .~+ ". ",ai:"+~ .,." . .ik+,." +

- + , ,,..,,.+!:i: -+ . +..+,+-+. "b • e + * , * ' + * * ' " ~ ,4

, , . . " . ' : , '~" ~ . " , , .

+" '+" "++"'J"+ +~ " " ' 4 ++it ~ " :+ "+.~- " ..LL*+,, _+.,,,. o.,~ , "- --,,,~+ .s +,,,+. .,a~ ',,,+- ,'~ ,,,+ +-+ , , ' . .+" . t - " . L , " +,,,',+ ,t ~ ., . ", +.

Latex Particle Size: 285nm, PVC: 20% Latex Particle Size: 450nm, PVC: 20%

Latex Particle Size: 185nm, PVC: 15%

a , +~ . +4 ~'%,- . . Z I

+I I ~ " + +i~ " +

, . , ; - " " ,-, o ".,,,+ '~'q, + + ~ 4, +,

, r -+ ~ . . ,

4 1 , +

+ " . . , . + a ' ~ - =~ t .~ + +r • ~ , : + ; ' " ~ ' , , "

. " + . ' 4 ~ . I lr " t4,,41" " 44" i

k ~* "1%,+*'~" " +.,, ~t +

.++ , ~ : . . e .

Latex Particle Size: 285nm, PVC: 15% Latex Particle Size: 450nm, PVC: 15%

Latex Particle Size: 185nm, PVC: 10% Latex Particle Size: 285nm, PVC: 10% Latex Particle Size: 450nm, PVC: 10%

Fig. 21. Electron micrographs showing pigment dispersion. -+ Increasing particle size, 1" increasing PVC.

in the periodic cell with correspondingly long calculat ion

times. The single cell of each of these models is shown in Fig. 22. Cross-sections, each consist ing of nine periodic cells, are shown in Fig. 23.

The small number of particles in these computer images (even though each frame contains nine tiled images of a

single cell) does not allow any firm conclusions to be drawn from this comparison with experiment.

5. C onc lu s ions

The decrease in hard particle single fraction observed as HSVC increases is a purely geometric effect caused by the increase in density of the hard particles. A simple mathe-

matical t reatment can be used to normal ize results to a nominal HSVC. This al lows us to study the effects of other geometric effects such as particle size ratio indepen-

150nm

30Ohm 45onm

Fig. 22. Single cells of models corresponding to micrographs of Fig. 21.

194 R.F.G. Brown et al. /Progress in Organic" Coatings 30 (1997) 185 194

. . . . . . . . ' , , , . , • • ,• • • • • • • •

.% ~ . . % . • . • • • • • • • • . oo o . e o . = • o o O • I ; o o • o o O • •

o ° • O o • e • • • o ; • . . . . • . o O o ~ , o O . , ~ ,ooq;f= • •

"% ~ " • " " "" " ' J " " ~ . 8 " - . . _ , , . . _ , , . . ~ . • • . . . . . . .

• oOO • o o o • c o o ~, • • O!

• e • " ° ° " ° ° "D " | "

300 nrn (g cells) o • 0 O °O 0 O

• . • .

450 nm (9 cells)

Fig. 23. Cross-sections of models in Fig. 22.

dently and to compare results f rom exper iments and com-

puter s imulat ions made at different H S V C or PVC.

In terms of geomet r ic factors alone, the compute r s imula-

tion and mode l latexes clearly show that single particle

fraction increases as the size o f the f i lm-forming part icles

is reduced. There is probably no m a x i m u m or plateau in the

curve at small latex particle sizes due to geomet r ic effects.

In real paints the particle surface potentials as well as

compet i t ive absorpt ion of surfactant and dispersant will

compl ica te matters. However , a series of mode l paints pig-

mented with t i tanium dioxide (ca. 250 nm diameter) show

that the predict ions o f the compute r model are qual i ta t ively

valid f o r latex particles in the range 1 8 5 - 4 5 0 nm.

R e f e r e n c e s

[1[ W.D. Ross, J. Paint Technol.. 43 (1971) 50. [2] J. Balfour and D. Huchette, Pai/~t and htk Int., 8 (1995) $2.

[3] S. Fitzwater and J.W. Hook, J. Coat. Technol., 57 (1985) 39. [4] L. Cutrone, J. Coat. Techno/., 58 (1986) 83. [5] A. Brisson and A. Haber, J. Coat. Technol., 63 (1991) 59. [6] J. Temperley, M.J. Westwood, M.R. Hornby and L.A. Simpson,

Proc. XXth FATIPEC Congress, Nice, 1990, p. 330. [7] M.R. Hornby and R.D. Murley, J. Oil Col. Chem. Assoc., 52 (1969)

1035. [8] D.J. Rutherford and L.A. Simpson, Double Liason. 31 (1984) 17. [9] F. Cansell, F. Henry and C. Pichot, J. Appl. Polym. Sci., 41 (1990)

547. [10] W.W. Wood and J.D. Jacobson, in Proceedings of the Western Joint

Computer Confi, renee, San Francisco, 1957, pp. 261-269. [11] M. Moon, and S.G. Croll, Polymer Preprints (ACS), 32 (1991) 301. [ 12] R. Zallen, The Physics of Amorphous Solids, John Wiley, New York,

1983, p. 56. [13] G. Arzamendi and J.M. Asua, Proc. 2rid CNRS Int. Conf. on Copo-

lymerisation and Copolymers in Disperse Media, Lyon, 1989, p. 70. [14] J. Ugelstad et al., in 1. Piirma (Ed.), Emulsion Polymerisation, Aca-

demic Press, New York, 1982, Chapter I 1, pp. 396-399. [15] H.D. Jefferies, in G.D. Parlitt (Ed.), Dispersion of Powders in

Liquids. Applied Science Publishers Ltd., Barking, 1981, 3rd edn., Chapter 9, pp. 462-464.

effect of pigment volume concentration and latex particle size on pigment distribution

Documents