Interfacial interactions play a decisive role in the determination of the mechanical properties of particulate-filled polymers, but they strongly influence other characteristics like processability or aesthetics as well.

Type and Strength of Interaction

Both the polymers used as matrices in particulate-filled composites and the fillers or reinforcements have the most diverse physical and chemical structures; thus, a wide variety of interactions may form between them. Two boundary cases of interactions can be distinguished: covalent bonds, which rarely form spontaneously, but can be created by special surface treatments, and zero interaction, which does not exist in reality, since at least secondary, van der Waals forces always act between the components. In practice, the strength of the interaction is somewhere between the two boundary cases.

The theory of adsorption interaction is applied most widely for the description of interaction in particulate-filled or reinforced polymers. The approach is based on the theory of contact wetting, in which interfacial adhesion is created by secondary forces. Accordingly, the strength of the adhesive bond is assumed to be proportional to the reversible work of adhesion (W_{AB}), which is necessary to separate two phases with the creation of new surfaces. The Dupre equation relates W_{AB} to the surface (y_{A }and y_{b}) and interfacial (y_{AB}) tension of the components in the following way

Unfortunately, interfacial tension cannot be measured directly; it is usually derived from thermodynamic calculations. (Fowkes 1964) assumed that surface tension can be divided into components, which can be determined separately. The theory can be applied relatively easily for apolar interactions when only dispersion forces act between surfaces. Its generalization for polar interactions is more complicated and the geometric mean approximation gained the widest acceptance. This considers only the dispersion and a polar component of surface tension, but the latter includes all polar interactions (Wu 1974). According to the approach, interfacial tension can be calculated as

The surface tension of two thermoplastics and three fillers are listed in Table 2. Large differences can be observed both in the dispersion, but especially in the polar component. The surface tension of the majority of polymers is in the same range as shown in Table 2, in fact between that of PP and PMMA. The examples listed in the table represent the most important particulate fillers and reinforcements used in practice, since clean glass fibers possess similar surface tensions as SiO_{2}.

Although Eq. 5 tries to take into account the effect of the polarity of the surfaces to some extent, the role of acid-base interactions in adhesion became clear and theories describing them are more and more accepted. Fowkes (1981) suggested that the reversible work of adhesion should be defined as

where W_{AB} ab is the part of the reversible work of adhesion created by acid-base interactions. According to Fowkes, the polar component can be neglected, i.e., W_{AB }p~0; thus W_{AB} can be expressed as

Table 2 Surface tension of selected polymers and fillers, dispersion (g ^{d}) and polar (g ^{p}) components

Surface tension (mJ/m^{2})

Material

Y^{d}

Y^{p}

Y

PP^{a}

32.5

0.9

33.4

PMMA^{a}

34.3

5.8

40.1

CaCO3^{b}

54.5

153.4

207.9

Talc^{c}

49.3

90.1

139.4

SiO2^{c}

94.7

163.0

257.7

^{a}Contact angle ^{b}IGC

^{c}Gravimetric measurement

Fig. 8 Effect of interfacial adhesion on the tensile yield stress ofPP/CaCO_{3} (covered with different amounts of stearic acid surfactant) composites; filler: CaCO_{3},

9_{f} = 0.1, R = 0.9 |rm

where ДH_{ab} is the change in free enthalpy due to acid-base interactions, n is the number of moles interacting with a unit surface, and f is a conversion factor, which takes into account the difference between free energy and free enthalpy (f ~ 1) (Fowkes 1981). The enthalpy of acid-base interaction, ДH_{ab}, necessary for the determination of the specific component of the reversible work of adhesion, can be calculated from the acid-base constants of the interacting phases by using the theory of (Drago et al. 1971) or (Guttman 1978).

In most cases, the strength of the adhesive bond is characterized acceptably by the reversible work of adhesion values calculated by the above theory. Often, especially in apolar systems, a close correlation exists between and the macroscopic properties of the composite (Fig. 8). In spite of the imperfections of the approach, the reversible work of adhesion can be used for the characterization of matrix/filler interactions in particulate-filled polymers. The quantities necessary for the calculation of W_{A}b can be determined by inverse gas chromatography (Fekete et al. 2004), while parameters related to interfacial adhesion can be derived from appropriate models (Pukanszky 1990; Pukanszky and Maurer 1995).