(198a) Film Formation From Aqueous Suspensions of Polymer-Silica Nanocomposites

Polymer films find wide application in the coatings, adhesives, and cosmetic industries. These are often formed from a suspension of colloidal polymer particles that come into contact and coalesce as the solvent (either organic or aqueous) evaporates. After evaporation and coalescence, the film resembles a compressed packed bed of zero voidage although the particle surfaces are still identifiable. Polymer molecules subsequently diffuse across the once-distinct interparticle boundaries giving a continuous polymer film as a final product.

Higher performance polymer films may be obtained by using nanocomposite particles as building blocks for the films. These are either polymer-polymer or polymer-inorganic nanocomposites in type. Polymer-polymer nanocomposites are useful in that they combine the properties of widely different polymers to provide multi-purpose industrial materials. Polymer-inorganic nanocomposites often include a silica or clay particle within a polymer particle. The latter class shows good potential in providing tough, optically transparent, scratch-resistant coatings. And last but not least, the solvent employed may be aqueous or organic, with the use of the former demonstrating a clear environmental advantage.

In the current paper, our main focus is on polymer (latex)-inorganic (silica) nanocomposites. Almost all applications of these nanocomposites demand that the suspensions form a continuous, crack-free film under suitable conditions, and the contribution of this work is a process model predicting the stable environmental conditions (minimum temperature) for which a given suspension of latex-silica nanoparticles will form a crack-free film. This parameter is termed the Minimum Film Formation Temperature (MFFT). The most conveniently controlled process parameter when manufacturing the feedstock suspension is the volume fraction (i.e. loading) of silica within each nanocomposite particle. The approach of the process model is as follows.

Film formation has been studied from a modelling standpoint for over fifty years. The process is generally agreed to comprise three stages, namely excess solvent evaporation, particle coalescence and finally polymer interdiffusion to form a continuous film. The focus of this work is on the intermediate stage. Existing models relate to simple single polymer particles. Here we extend the modelling to include a hard component (silica) within the particles.

A driving force is required to induce particle coalescence and there are three potential candidates. The first is surface tension between the polymer and the aqueous solvent. When particles come into contact they coalesce relatively rapidly at the contact point and are resisted by the inherent stiffness of the particles. The mechanical constitutive behaviour of the polymer (latex) may be elastic, viscous, or some combination. In this model, the latex is assumed to be linear viscoelastic and incompressible.

When the characteristic solvent evaporation time is large, or the latex viscosity and/or shear modulus is small, the nanoparticles will coalesce into larger and larger groups prior to full evaporation of the solvent. An apparently continuous film is formed upon the substrate although at this stage the particle boundaries are still identifiable within the film. As this process is complete before the solvent evaporates, a rarefied layer of solvent remains on top of the film. This mode of film formation is termed wet sintering.

If the polymer is slightly more resistant to deformation, solvent will evaporate until the underlying particles are compressed into a contacting network or particulate skeleton, although the porosity is still well above zero at this time. At this point, a second potential driving force arises, namely capillary pressure at the air-polymer-water interface at the top of the particulate skeleton. This stress acts perpendicularly to the film surface and tends to compress the skeleton, driving coalescence. This mode of film formation is termed capillary deformation (CD).

The use of even stiffer polymers or a smaller evaporation time means evaporation is essentially complete prior to the onset of significant coalescence within the skeleton. However, the dry skeleton still experiences air-polymer surface tension and will slowly coalescence under its influence. Due to the obvious parallels with wet sintering, this mode of film formation is termed dry sintering (DS).

In cases intermediate between CD and DS, a mixed mode of film formation arises where the solvent front recedes in the general direction of the substrate surface with DS above (behind) the front and CD below (ahead) of the front. This mode is termed the receding water front (RWF) mode.

This work extends a previous process model of film formation (Routh and Russel 1999; Routh and Russel 2001) to include a hard component and each of the above formation mechanisms is predicted as a function of the environmental conditions, in particular the ambient temperature and humidity, and the silica loading.

The polymer viscosity decays exponentially with increasing temperature (allowing more rapid particle coalescence) whereas the evaporation rate changes much more slowly, particularly if the air is saturated with vaporised solvent and/or the rate of mass transfer of vapour away from the film is limited. If one assumes the influence of humidity is small and the mass transfer rate is relatively independent of temperature (at least when compared to the change in viscosity), one may perform a temperature-time superposition such that for a given suspension and evaporation rate, the temperature is all that is required to predict which mode of film formation occurs and thus the time required for complete formation. CD is the most industrially relevant mode and the existing model provides the minimum temperature at which a given film will deform by this mode (MFFT mentioned previously).

The current work extends the existing model to films incorporating nanocomposites featuring silica inclusions; this particular problem has received little attention in the modelling literature. The model is mostly analytical with the final ODEs solved numerically. The inclusions are assumed to be rigid relative to the polymer which is assumed to feature linear viscoelastic, incompressible rheology. The particles are assumed to be of a single size and each is assumed to be loaded with a single cylindrical inclusion of identical dimensions that is initially centrally located within the particle. The range of inclusion-particle volume fractions studied was 0-10% which corresponds to the range most easily manufactured in parallel experimental work by the authors' collaborators.

The major terms arising in the extended model are the interfacial normal and shear stresses that exist between the particle and inclusion. These correspond to surface tension and hydrodynamic drag stress acting to oppose coalescence, respectively.

Interestingly, the results obtained predict that surface tension has no effect on the time required or alternatively the difficulty of film formation, and thus has no influence on the MFFT. However, the validity of this result is restricted to linear viscoelastic polymer particles. If a drag stress is included, the results predicted are unaffected by the magnitude of the surface tension stress. The model produces a dimensionless group that incorporates the effects of interfacial shear stress (divided by capillary pressure), inclusion-particle volume fraction and the shape of the inclusions (aspect ratio). The parameters are strongly coupled. Thus, while the film formation time may be processed into a MFFT via a temperature time superposition, the drag dimensionless group does not permit simple manipulation into an inclusion volume fraction (an industrially relevant parameter).

The model was applied to the four film formation modes described previously (WS, CD, RWF and DMS). As expected the MFFT rose with increasing values of the drag dimensionless group, indicating a higher inclusion loading and/or the use of more aspherical and more ?sticky' or rougher inclusions retards film formation.

References

Routh, A. F. and W. B. Russel (1999). "A Process Model for Latex Film Formation: Limiting Regimes for Individual Driving Forces." Langmuir 15(22): 7762-7773.

Routh, A. F. and W. B. Russel (2001). "A Process Model for Latex Film Formation: Limiting Regimes for Individual Driving Forces." Langmuir 17(23): 7446-7447.