dispersant optimization paper
TRANSCRIPT
Systematic Dispersant Optimisation Method For
Mineral Fillers and Pigments in Non-Aqueous Media
K. D. BREESE† AND DR. C. DEARMITT (�)
†Electrolux, Corso Lino Zanussi 30, 33080 Porcia (PN) Italy
�Phantom Plastics, Hattiesburg, Mississippi, USA
Tel: +1 601 466 8342
Abstract
A novel method was developed to allow the systematic design and selection of dispersants for mineral
fillers and pigments in non-aqueous media such as polymers, coatings and lubricants. Dispersant probe
molecules were varied systematically so that the effectiveness of the dispersant “head” and “tail” could be
studied and optimised separately. Rheological tests on particle dispersions in a model fluid, squalane, were
used to assess the effectiveness of each potential dispersant. Calcium carbonate, dolomite and silica were
found to adsorb differing amounts of each probe molecule type. The relative affinity of each mineral for
the various probe molecules could not be predicted or explained using Lewis acid-base concepts. The
dispersant head group functionality was altered to suit the surface chemistry of the mineral whereas the
dispersant tail was tuned to suit the dispersion medium. Using this approach we were able to identify
highly effective dispersants for all minerals tested. Carboxylic acid, sulfonic acid, anhydride, amine and
trichlorosilane were the most effective and versatile head groups found. The dispersant tail length and
chemical composition were also varied. It was observed that the dispersion viscosity was lowered
dramatically when the dispersant tail length was just two to three carbon atoms in length. No further
decrease in viscosity occurred for dispersant tails up to twelve carbon atoms long. The chemical
composition of the dispersant tail was also critical. A hydrocarbon tailed dispersant gave a much lower
dispersion viscosity than did a similar dispersant with a less soluble, perfluoro tail. Our systematic method
is generally applicable to selection and design of dispersants for minerals and pigments dispersed in organic
media such as polymers, lubricants and coatings.
Keywords- dispersant, mineral, pigment, surface-treatment, adsorption, viscosity, method
Introduction
Controlling the degree of particle dispersion is critical in many applications [1-3]. For example, pigments give much higher tinting strength when properly dispersed. In particulate-filled
polymer composites good dispersion of the filler aids processing of the polymer melt [4,5] and gives composites with better mechanical properties, especially impact strength. Dispersants are
a class of surfactants that are commonly employed to control the level of particle dispersion in a
liquid dispersion medium. Particles tend to agglomerate due to the attractive van der Waals
dispersion force that becomes very strong when particles approach each other closely. A dispersant acts by preventing particles from coming into close contact, thereby reducing the
tendency towards particle agglomeration. Use of an effective dispersant can give viscosity reductions of several orders of magnitude (Figs. 2, 3 and 4). Thus, dispersants are often used to
alter the rheological properties of commercial dispersions where appropriate dispersant selection and dosage level are often vital for successful product formulation.
We describe a method that gives a systematic approach to dispersant selection. We used the
method to find suitable dispersants for mineral fillers in polypropylene. However, we wish to
emphasise that our approach is equally useful for dispersion of pigments and minerals in a wide range of different matrices.
Systematic dispersant selection for minerals and pigments
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Background - Dispersant Selection
Agglomeration of particles occurs mainly due to the omnipresent van der Waals forces that
typically become very strongly attractive at short interparticle distances [6]. Dispersants are a class of surfactants that adsorb onto particles and block interparticle contact so that the
attractive van der Waals forces are lessened. In this way a dispersant may reduce or eliminate the tendency for particle agglomeration. For particles dispersed in a polar solvent two
mechanisms may be invoked to produce a repulsive interparticle force. These two mechanisms
are referred to as steric stabilisation and electrostatic stabilisation [6-8]. They may be used
singly or in combination, the latter combinatorial approach, is known as electrosteric stabilisation. In non-polar or low polarity dispersion media however, the steric stabilisation
mechanism is generally believed to be the most effective way to generate the necessary repulsive force [7,8]. In this study we were interested in this latter case, namely dispersion of
particles in a non-polar medium where steric stabilisation is most effective. The requirements for a dispersant to function as a steric stabiliser are threefold [8]:
• The dispersant molecules must adsorb strongly onto the particles so that they are not displaced when particles collide
• The dispersant “tail” must be well solubilised by the dispersion medium
• The dispersant “tail” must be sufficiently long to keep the particles from approaching too closely
These criteria are well established in the literature and, in principle, they provide a guide to
dispersant selection and design. It can be seen that the dispersant is bifunctional. On the one
hand it has to adsorb strongly to the particles and on the other it must be highly soluble in the dispersion medium. These two contradictory requirements are fulfilled by the use of amphiphilic
dispersant molecules that are typically composed of two chemically different segments. As with other surfactants, a dispersant can be thought of as being composed of a “head” and a “tail”. In
this study, the function of the head moiety was to bind the dispersant to the particle whereas the tail was chosen to be soluble in the dispersion medium in order to confer some steric repulsion
between particles. As the “head” and “tail” of the molecule fulfil different roles we have
developed a method that allows us to optimise each of these two portions of a dispersant
separately. The first task is to determine the appropriate chemistry for the dispersant head because if a dispersant does not adsorb strongly and in sufficient quantities then it cannot be
effective. Most research on this topic has typically been carried out with the aid of techniques such as inverse gas chromatography [9-12], microcalorimetry [9,13,14] and ESCA [9]. These
methods give information about the adsorption of molecules to particles, however, they all suffer
from one major disadvantage. None of these techniques gives any indication about whether an additive is an effective dispersant. Instead of using one of the three traditional methods listed
above we decided to use a rheological method for studying additive adsorption. This rheological test gives not only indirect information about the relative amounts of additive adsorbed, it also
directly shows the influence of the additive on the viscosity of the dispersion. When an additive
is effective in breaking agglomerates a dramatic drop in viscosity results [15,16]. Thus we found
our rheological test method to be very sensitive to additive adsorption, as well as showing the
effectiveness of each additive as a dispersant. This was our rationale for electing to use a
rheological test rather than the other, more commonly employed methods.
Systematic dispersant selection for minerals and pigments
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Experimental Procedure
(1) Powders and Chemicals
The calcium carbonate studied was MicroXtra from Faxe Kalk (mean particle size 1.65µm).
Dolomite was Strådolomit A6 from Sala Mineral (previously Strå Bruken) (70% < 10µm, 35% <
5µm). Silica was Microwhite B1 from Elkem. Chemicals were obtained from Aldrich and were used without further purification.
(2) Preparation and Characterisation of Suspensions
Suspensions were prepared by mixing the filler powder with the model fluid squalane in a
polystyrene beaker, the mixture was then stirred continuously for one hour using a magnetic stirrer bar. Such mixtures were made for each filler and used as a batch supply of the
suspension. A cup was filled with a sample of the batch suspension and 1.00 wt. % of dispersant relative to filler was added whilst stirring. It was calculated that at a concentration of 1.00 wt. %
the dispersant was present in a substantial excess, i.e. there was much more dispersant than
would be required to form a close-packed monolayer of dispersant on the mineral surface. The
mixture was then stirred for one hour afterwards to ensure good mixing and to give ample
opportunity for any adsorption of the dispersant to take place.
Rheological characterisation was performed on a Bohlin VOR Rheometer. A concentric cylinder geometry was used, C25, having a gap between the inner and outer cylinder walls of 1.25 mm.
The equipment was maintained at 25°C. Samples were stirred up to the time of loading into the
measuring geometry to avoid any possible sedimentation.
Samples were pre-sheared at 367 s-1 for one minute to break up any structure induced by loading
into the geometry. Then the sample was allow to rest for 3 minutes, except for dolomite which
settled quickly, so a shorter resting time of 2 minutes was used for that sample. This standard pre-treatment was used to put all the samples of a specific filler at a similar starting structure.
After the pre-treatment, oscillating shear measurements were performed at 0.01 to 20 Hz. We chose the oscillating mode as this is regarded as being particularly sensitive to particle
agglomeration. The shear amplitude for each filler dispersion was chosen so as to be within the
linear viscoelastic region. Oscillating shear measurements, with a sinusoidal applied strain and
measurement of the stress and phase shift, were performed beginning at 0.01 Hz and stepping
up to 20 Hz allowing the determination of the complex viscosity, η*, versus the shear rate.
Results and Discussion
The rheological test operates on the well-known observation that addition of a dispersant to a
dispersion can reduce agglomeration leading to a drop in viscosity [15-20]. There will be a drop
in viscosity only if the dispersant adsorbs to the particles, furthermore, the more dispersant
adsorbed, the greater the drop in viscosity [19].
Dispersant Head/Anchor Group Selection
The choice of model liquid for this study was critical. We needed to use a pure, non-toxic, low
vapour pressure, apolar liquid. Our choice was squalane, a wholly aliphatic hydrocarbon. It is
important to use an aliphatic dispersion medium when examining additive adsorption because
aromatic hydrocarbons such as toluene can themselves adsorb to the mineral surface [16] thus competing with the dispersant for adsorption sites. Such competitive adsorption can hinder the
Systematic dispersant selection for minerals and pigments
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clear interpretation of adsorption data and consequently the use of a wholly aliphatic medium is
recommended in the literature [21]. When a potential dispersant is added to the mineral
dispersed in squalane it will only adsorb if there is a driving force for adsorption. It is entropically
favourable for the dispersant to remain in solution and there must be some stronger, enthalpic
interaction present if adorption is to occur. Thus, whenever adsorption takes place, we can deduce that there is some specific interaction between the head of the dispersant and some of
the surface sites of that particular mineral.
We have tested several different potential dispersants for each mineral, in each case the
dispersant tail was kept constant, it was always a linear hydrocarbon chain, twelve carbons
atoms in length. Whilst keeping the tail constant we varied the surfactant head to be one of a
wide range of common organic functionalities, such as carboxylic acid, amine, alcohol, aldehyde,
and ester groups. We added an excess of the additive (1.00 weight % versus filler), that is, much
more than would be needed to form a close-packed monolayer. Then we measured the viscosity of the dispersion. Additives that did not adsorb gave little or no change in viscosity whilst
additives that adsorbed in substantial amounts gave a large reduction in viscosity as compared to the dispersion containing no dispersant. The viscosity dropped by a factor of up to 104 or 105 for
the dispersants adsorbing in the highest concentrations. Thus our rheological method was found
to be extremely sensitive to dispersant adsorption. Using this system, we tested the
effectiveness of several common head functionalities at adsorbing onto commercial samples of different mineral fillers. For each mineral we were able to compile a set of rheological curves
that revealed the affinity of that particular mineral for each chemical type tested. It should be
noted that the magnitude of the viscosity drop is related solely to the amount of surfactant
adsorbed but not necessarily to the strength of the adsorption.
We assumed that the viscosity drop per molecule of dispersant adsorbed is not dependent on the
chemistry of the head group. That is, we assume that the same viscosity drop would result for
adsorption of an equimolar amount of any of the different potential dispersants. Only the tail
moiety contributes to dispersion as the head of an adsorbed molecule is not in contact with the solvent. Because the surfactant tail structure is held constant, we can directly compare the
relative amount of each potential dispersant that adsorbed onto a given mineral. The results were plotted in the conventional way for such data, that is, on a log-log scale of complex
viscosity η* versus shear rate. By examination of the rheological results it is possible to make
several important conclusions. As stated previously, the method was found to be extremely sensitive. Using just 20 weight % of filler, the measured viscosity drop upon dispersant addition was typically 103 for the better dispersants. It is therefore possible to detect very small
differences in the amount of additive adsorbed. Another, key observation is that no two minerals displayed the same surface chemistry, the relative affinity of each mineral towards the
various chemical types was unique.
For each mineral, we have identified one or more suitable dispersant head group chemistries. Calcium carbonate, (CaCO3) and dolomite (CaCO3.MgCO3) are similar chemically and are
often therefore assumed to behave in the same manner with respect to additive adsorption [9]. Our tests showed that, in fact, even these two chemically similar minerals displayed noticeably
different surface chemistry. In particular, for dolomite the strong, sulfonic acid adsorbed to the
greatest extent followed by the carboxylic acid, then the silane, the acid anhydride and the amine (Fig. 1).
Systematic dispersant selection for minerals and pigments
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Figure 1 Rheological screening of 16.7 weight % Calcium carbonate in Squalane and addition of 1 weight % probe molecule relative to filler. The probe molecules are: ���� base system (no probe molecule), ▲▲▲▲ 1-dodecanol, ���� dodecylbenzenesulfonic acid, ���� dodecyltrichlorosilane, ○○○○ dodecylamine, ���� dodecanoic acid, and ���� 2-dodecen-1-ylsuccinic anhydride.
Whereas for calcium carbonate, the acid anhydride was adsorbed in the highest amount
followed by the acid, then the amine, the silane and lastly the sulfonic acid (Fig. 2). It can be concluded that the acid anhydride and carboxylic acid head groups are the best choices for
calcium carbonate. For dolomite the sulfonic acid and carboxylic acid are the two best choices. As expected, these acidic test molecules are able to adsorb in high concentrations to the basic
mineral. Somewhat surprisingly, the basic, amine probe molecule also adsorbed in a very high
concentration onto these two basic minerals. The data shows that it is not possible to predict
the relative adsorbed amounts of different head groups based on Lewis acid-base concepts. If
the best dispersant head group is needed, then it is essential to actually measure the amount of
each additive type adsorbed as we have done here. Silica is known to be predominantly acidic at the surface [22,24] and so it is expected that silica should have a markedly different surface
chemistry than the two basic minerals. For silica, the silane was the best treatment by a clear margin.
Systematic dispersant selection for minerals and pigments
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Figure 2 Rheological screening of 16.7 weight % Dolomite in Squalane and addition of 1 weight % probe molecule relative to filler. The probe molecules are: ���� base system (no probe molecule), ▲▲▲▲ 1-dodecanol, ○○○○ dodecylamine, ���� 2-dodecen-1-ylsuccinic anhydride, ���� dodecyltrichlorosilane, ���� dodecanoic acid, and ���� dodecylbenzenesulfonic acid.
That was not unexpected because the standard surface treatments for (silica) glass fibres are silanes which are well known to form strong, covalent bonds to silanol groups on the silica
surface [22]. Furthermore, it has been shown that trichlorosilanes are especially reactive
towards the different types of silanol groups present on silica [22]. After the silane, the sulfonic
acid and the acid anhydride were the next best treatments followed by the amine and then the
carboxylic acid (Fig. 3). Thus, the silica did have a significantly different surface chemistry than
the two basic minerals but again, the surface was amphoteric in nature, adsorbing significant concentrations of both acidic and basic probe molecules.
It could be argued that the results seen in this study are different from other studies because of trace impurities in the fillers used. The minerals in this study are commercial products and not
totally pure materials. We recognise that even though the samples used here are chemically
pure, even small levels of impurity on the surface may significantly alter the results affinity of the
dispersants. In practice, totally pure minerals are not used commercially to any great extent, due
to their prohibitively high cost. As commercial materials all have some level of impurity likely to
affect the surface properties, it makes sense to measure the behaviour of the precise material grade of interest rather than relying on generic data from other sources.
Systematic dispersant selection for minerals and pigments
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Figure 3 Rheological screening of 16.7 weight % Silica in Squalane and addition of 1 weight % probe molecule relative to filler. The probe molecules are: ���� base system (no probe molecule), ▲▲▲▲ 1-dodecanol, ���� dodecanoic acid, ○○○○ dodecylamine, ���� 2-dodecen-1-ylsuccinic anhydride, ���� dodecylbenzenesulfonic acid, and ���� dodecyltrichlorosilane.
Aside from allowing us to identify suitable head / anchor groups for dispersants, this test also gives information that can be useful in other ways. For example, using the results from the
rheological test it is possible to predict whether other additives in a specific formulation are likely to adsorb onto a given mineral. Simply examining the chemical structure of an additive will
show if it contains functional groups that could potentially cause it to adsorb to the mineral in
question. Additives with the potential to adsorb include antioxidants in filled polymers or catalysts used to cure coatings. Another use for the adsorption data is in predicting and
understanding adhesion between the filler and the polymer matrix [23,24]. If the polymer contains functional groups that are able to adsorb onto the mineral then it is anticipated that
adhesion would be increased by any such polymer-filler interactions [23,24]. Naturally, in both
of these cases, steric factors must also be considered when attempting to predict the feasibility
of adsorption for a certain functional group within a molecule.
The rheological test proved to be an extremely effective and sensitive way of indirectly
determining two important parameters. It was of utility both for studying additive adsorption and for directly measuring the viscosity drop caused by the improvement in the dispersion of the
Systematic dispersant selection for minerals and pigments
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particles. We found that each mineral displayed its own unique surface chemistry and were able
to identify an effective dispersant head moiety to anchor dispersant molecules onto each
mineral. We therefore believe that this technique is suitable for the systematic development of
new, improved dispersants in the future.
Dispersant Tail Selection
Having identified suitable head / anchor groups which can be used to adsorb a dispersant to each
mineral we then moved on to look at the influence of the dispersant tail. Several research groups
have shown that even subtle changes in tail structure can have dramatic effects on the rheology
and colloidal stability of dispersions [1,15,18,21]. We used our rheological method to look at two of the factors that determine the effectiveness of the dispersant tail moiety in dispersing
particles. Factors such as polarity, solubility, chemical structure and size are generally considered to be critical in determining how well a dispersant performs. In this paper we
demonstrate the utility of our rheological method for developing dispersants with the optimal tail group in terms of both chemical composition and structure. For this part of the study the mineral examined was calcium carbonate and the selected head group was carboxylic acid. This
combination was chosen because it has been established that carboxylic acids adsorb strongly and in high concentrations onto calcium carbonate [9-12, 25-27] hence the popular use of stearic
acid as a dispersant for that mineral. By keeping the head group constant we were able to isolate
the effect of changing the tail moiety upon the effectiveness of dispersants. Only one mineral
was studied because the relative effect of different tails is not expected to be dependent on the
mineral used. Again, we concentrated on hydrocarbon tailed molecules as these can be expected
to be soluble in the hydrocarbon test fluid squalane and thus, they should have the potential to provide good steric stabilization.
Tail Length
Steric stabilisation relies on the dispersant to prevent the close approach of particles. If the
particles are allowed to approach each other too closely then the attractive Van der Waals forces, which dominate over short distances will cause strong particle agglomeration.
Therefore, in order to be effective, the steric layer created by the dispersant must be thick enough to keep the particles separated by a sufficient distance. The required thickness of the
steric layer will depend upon the magnitude of the attractive forces between the particles these, in turn, are dependent upon the Hamaker constant of the dispersed material in the dispersion
medium [28,29]. Our results are therefore only quantitatively valid for the dispersion of calcium
carbonate in squalane. Minerals and pigments dispersed in other hydrocarbon liquids are expected to behave somewhat differently [16,28,29] although our results should remain
qualitatively valid to those systems. If one wishes to find the optimal dispersant for a mineral in a
more polar medium, e.g. PVC, nylon, polyester etc., then it would be appropriate to choose a
model fluid other than squalane to more closely matching the solubility parameter and Lewis
acid-base characteristics of the more polar medium.
Systematic dispersant selection for minerals and pigments
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Figure 4 Effect of probe tail length on dispersant efficiency, ηηηη* obtained from rheological screening at frequencies of ���� 1 Hz, ▲▲▲▲ 2 Hz, ���� 3 Hz.
We measured the viscosity of calcium carbonate in squalane with different dispersants added
(Fig. 4). The dispersants chosen were a homologous series of carboxylic acids, each dispersant had a linear hydrocarbon tail of different length. Excess dispersant was used in all cases so we
were able to measure the effectiveness of the dispersants. Effectiveness has been defined as the maximum effect achievable using a given surfactant when excess is present [30]. The use of a
dispersant with only a two carbon tail was sufficient to reduce the dispersion viscosity η* (as measured at 3 Hz) by almost two orders of magnitude (Fig. 4). A greater drop in viscosity was
achieved using the analogous dispersant with a three carbon tail. It was interesting to note that
further lengthening of the dispersant tail did not give a further drop in viscosity. Thus, the use of
a longer dispersant tail does not give any noticeable advantage. As mentioned previously, the industry standard dispersant for calcium carbonate in PP is stearic acid, which is eighteen
carbons in length. According to our results, a similar degree of dispersion could be attained using
a much shorter dispersant tail. It should be mentioned that our work here is performed on
dispersants that are so-called semi-steric stabilisers. These short chain dispersants enhance the degree of dispersion considerably but the molecules are too short to completely prevent
agglomeration. This can be seen in our results where the slope seen for each plot is indicative of non-Newtonian behaviour caused by agglomeration. Longer chain, oligomeric and polymeric
steric stabilisers often much more effective leading to a more Newtonian response.
Systematic dispersant selection for minerals and pigments
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Unfortunately, it was not possible to obtain longer, polymeric molecules in the same homologous
series for our studies.
Chemical Composition of the Tail
One of the criteria for steric stabilisation is that the dispersant tail must be well solvated in the
dispersion medium. We decided to look at the effect of changing the chemical composition of the dispersant tail, once again the head group was kept constant. The dispersants tested were
dodecanoic acid and perfluorododecanoic acid. Thus the tail length is constant, only the
chemical composition is different. The viscosity data show that the chemical composition of the
dispersant tail is critical in determining how effective the dispersant is. We assume that both dispersants can adsorb in similar concentrations because they have the same head group. As
expected, the hydrocarbon tail gave a very large reduction in dispersion viscosity because it is similar in chemical composition to the hydrocarbon dispersion medium (Fig. 5).
Figure 5 Effect of probe tail chemical composition on dispersant efficiency (16.7 weight % Calcium carbonate in Squalane and addition of 1 weight % to filler of probe molecule.) The probe molecules are: ���� base system (no probe molecule), ���� perfluorododecanoic acid, and ���� dodecanoic acid.
The fluorocarbon tail however gives much poorer dispersion. Whilst the fluorocarbon tail is
somewhat effective, it only gives a drop in viscosity of 10 fold compared to the viscosity with no dispersant added whereas the hydrocarbon tailed dispersant gives a 1000 fold drop in viscosity.
Systematic dispersant selection for minerals and pigments
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These results illustrate that it is vital to choose a dispersant with the correct tail in terms of
chemical composition. It is well known that fluorocarbons have very poor solubility in
hydrocarbons and this is why the perfluoro dispersant is so poor in this case. Thus, matching the
solubility of the tail to the polarity of the dispersion medium is of paramount importance if
effective dispersion is required.
Conclusions
Dispersants are a class of surfactant used in many industries world-wide. The correct choice of
dispersant is vital in countless applications for controlling both the level of particle dispersion and
for tuning the viscosity of such dispersions. Despite the importance of dispersants, there has not previously been a good way to systematically choose the correct dispersant, nor to design new,
better dispersants. We have developed a systematic, rheologically based methodology that clearly shows the relationship between dispersant structure and effectiveness. The dispersants
were viewed as a surfactant containing a head / anchor group and a tail moiety, each of these
two portions were varied and optimised separately. The chemistry of the head was selected to
be one that bonded in high concentrations to the mineral particles. It was found that the optimal choice of head group is individual for each mineral depending upon the surface chemistry of that
mineral and that no two minerals showed the same adsorption behaviour. The optimal structure
of the dispersant tail was chosen so that it would sufficient length and solubility in the dispersion
medium. The chemical composition and length of the tail were found to dramatically affect the
effectiveness of the dispersants in terms of lowering the viscosity of the mineral dispersions. Specifically, the tail was more effective when it was similar in chemical composition to the
dispersion medium. The length of the tail was also seen to be very important. The viscosity of the dispersion was lowered as the dispersant tail moiety was increased up to three carbons in
length. Further increase in the carbon tail length up to twelve carbons had virtually no further
impact on dispersion viscosity. By varying the two parts of the dispersant separately we were
able to identify very effective dispersants for each mineral dispersed in a non-polar aliphatic
hydrocarbon liquid medium.
This study has highlighted some of the main parameters determining the effectiveness of dispersants. It also provides a way to choose dispersants from sets of existing chemicals as well
as insight into how new, improved dispersants and coupling agents for minerals and pigments can be designed. We performed this study using a rheometer for the viscosity measurements,
however, we wish to emphasise that qualitatively similar results can be obtained using much less
expensive equipment. A flow cup, DIN cup, or ISO cup as commonly used in industry, can be
used instead of a rheometer, to measure relative viscosity more quickly and cheaply. We
therefore anticipate that our method will be of value in academia and in industry for improved
surface treatment of particles in applications including nanocomposites, flame-retardant-filled polymers, polymer composites, coatings, lubricants and other particulate-filled systems.
Acknowledgements
We sincerely thank Borealis AB, Borealis Oy, MinFo, Faxe Kalk, Finnminerals Oy, Kemira Oy,
Strå Bruken AB, Aros Mineral AB, Akzo Nobel Surface Chemistry AB, Laxå Bruks AB, Elkem AS and NUTEK for funding this work and for valuable input.
Systematic dispersant selection for minerals and pigments
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© Chris DeArmitt and Kevin Breese 2009