Filler concentrations

There is greater similarity in the behavior of stretched melts and solid samples prepared by, e.g. pressure molding, probably, for the reason of parallelism in structure formation and destruction caused by deformation in melts and the amorphous regions of solid matrices. It is also possible to use identical equations for longitudinal viscosity and strength which present them as functions of the filler concentration [34]. 

Fig. 1. Relative MFI of Diflon polycarbonate (A), HDPE (B) and polycaproamide (C) as function of filler concentration (

MFI of the composition to that of the matrix, as a function of the filler concentration. It can be seen that, as the concentration of a particular filler increases, the index increases too for one matrix but decreases for another, and varies by a curve with an extremum for a third one. Even for one and the same polymerfiller system and a fixed concentration of filler, the stress-strain characteristics, such as ultimate stress, may, depending on the testing conditions (temperature, rate of deformation, etc.) be either higher or lower than in the reference polymer sample [36],... 

To be able to control the PCM properties in the desired direction it is very important to know the relationships between the material composition and properties. Since melt viscosity is one of the most important characteristics of processability of PCM, there have naturally been a large number of equations proposed for describing the viscosity versus filler concentration relationship. For the purpose of this review it may be most interesting to discuss the numerous equations which have in common the use of the value < representing the maximum possible volume filling by filler particles packed in one way or another, as the principal constant. Here are a few examples of such equations. 

Filler Mean particle diameter, m Filler concentration, p.b.v. Degree of crystallinity %... 

The model for a filled system is different. The filler is, as before, represented by a cube with side a. The cube is coated with a polymer film of thickness d it is assumed that d is independent of the filler concentration. The filler modulus is much higher than that of the d-thick coat. A third layer of thickness c overlies the previous one and simulates the polymeric matrix. The characteristics of the layers d and c are prescribed as before, and the calculation is carried out in two steps at first, the characteristics of the filler (a) - interphase (d) system are calculated then this system is treated as an integral whole and, again, as part of the two component system (filler + interphase) — matrix. From geometric... 

The Takayanagi model parameters are related with filler concentration and interphase thickness by the following simple relationships ... 

The behavior of the physico-mechanical characteristics of polymeric composites is easily traceable in the table given in [144] which presents the results of experiments with polyamide matrices filled with resite particles of different shape. The filler concentrations were adjusted so that the integral contact surface area in the filler-matrix system remained the same. 

Specific surface area, m2/g aCl values for filler concentration of (%) ... 

Departing from the known fact that PVC melts have a nodular structure, about 1 micron in size, the authors assumed that white ash particles invaded the inter-nodular spaces, thereby causing the nodules to move apart and the chains between them to be broken as a result the nodules acquire more freedom to move. As the filler concentration is increased, the contribution to viscosity increase... 

For scaly fillers the increase of relative viscosity with filler concentration is not as pronounced as in case of fibrous fillers [177,178]. Owing to filler orientation, the flow curves for systems with different concentrations of a fibrous and a scaly filler may merge together at high shear rates [181]. In composites with a dispersed filler the decrease of the effective viscosity of the melt with increasing strain rate is much weaker. 

Depending on the nature of the polymer-filler interaction and the fracture surface status (smooth or rough), Eq. (34) predicts either a rather smooth variation of the elongation with increasing filler concentration or a sharp drop at some small filler content. 

The three deformation regions are also apparent on the strength versus concentration relationships. The most dramatic drop of the yield point was observed at small filler concentrations (up to 0.15). On further filling the characteristic remained almost unchanged. 

In loading experiments the separation of the matrix from the filler is one of the reasons responsible for the deviation of the stretching diagram deviation from linearity are lower than in case of good adhesion [240]. For good adhesion, the value of e gradually decreases with increasing filler concentration if adhesion is poor, it remains invariant up to a certain concentration and then drops very suddenly. 

Using water repelling agents it is possible to either considerably reduce the viscosity of compositions with a predetermined filler content, or increase the admissible filler concentration for given viscosity [262], In a filled system (e.g. PP + chalk) the treatment of the filler to enhance its polymerophilic properties promotes breakdown of agglomerates [263],... 

Fig. 4. Dependence on filler concentration (

Materials of the second type can be classified as composites with polymerization-modified fillers (PMF) or filler concentrates. 

In a number of works (e.g. [339-341]) the authors sought to superimpose graphically the flow curves of filled melts and polymer solutions with different filler concentrations however, it was only possible to do so at high shear stresses (rates). More often than not it was impossible to obtain a generalized viscosity characteristic at low shear rates, the obvious reason being the structurization of the system. 

Wu [353] who studied extruded fiber-filled composite samples established that the distribution of fibers along the radius of the specimen depended on the extrusion rate at low rates the fiber distribution is uniform, at medium rates the minimum of filler concentration occurs at 0.63 R (R is the extrudate radius) (in case of spherical particles this point corresponds to the maximum filler concentration) at high extrusion rates most of the fibers are concentrated about the flow axis and there are almost none on the extruded sample surfaces. 

Earlier we have said that the flow of filled materials can be raised by modification. One of the modification alternatives consists in using a combination ( flexible ) filler. As shown in [366], addition of a small quantity of glass balls to composites filled with chalk caused a sudden increase of the flow of the system, provided the filler concentration is below critical. Similar behavior was also observed in fiber-filled systems when a small quantity of dispersed particles were added [33],... 

How does yield stress depend on a filler concentration It is shown in Fig. 9 that appreciable values of Y appear beginning from a certain critical concentration cp and then increase rather sharply. Though the existence of cp seems to be quite obvious from the view point of the possibility of contacts of the filler, i.e. the beginning of a netformation in the system, practically the problem turns on the accuracy of measuring small stresses in high-viscosity media. It is quite possible to represent the Y(cp) dependence by exponential law, as follows from Fig. 10, for example, leaving aside the problem of the behavior of this function at very low concentrations of the filler, all the more the small values of are measured with a significant part of uncertainty. 

Fig. 11. Typical flow curves of dispersions of fibre-forming particles in a Newtonian liquid. The arrow indicates the direction in which the filler concentration increases...

At present, the most promising fillers are those with 1/d P 1, i.e. fibers and flaky fillers that make it possible to reduce filler concentration in a composite and, thus, facilitate the processing and improve physical-mechanical properties [17]. Besides cut carbon fibers, carbon fibers coated with a layer of Ni that have higher conductivity have been developed (American cyanamid) [14]. Glass fibers with a layer of aluminium (MB Associates, Lundy Electronics) [16] are in production. 

Fig. 2. Relationship of conductivity of polypropylene-based polymer composites and filler concentration (natural graphite) 1 — polymerization filling 2 — mechanical mixture [24]...

Experimental dependences of conductivity cr of the CPCM on conducting filler concentration have, as a rule, the form predicted by the percolation theory (Fig. 2, [24]). With small values of C, a of the composite is close to the conductivity of a pure polymer. In the threshold concentration region when a macroscopic conducting chain appears for the first time, the conductivity of a composite material (CM) drastically rises (resistivity Qv drops sharply) and then slowly increases practically according to the linear law due to an increase in the number of conducting chains. 

Calculation of dependence of o on the conducting filler concentration is a very complicated multifactor problem, as the result depends primarily on the shape of the filler particles and their distribution in a polymer matrix. According to the nature of distribution of the constituents, the composites can be divided into matrix, statistical and structurized systems [25], In matrix systems, one of the phases is continuous for any filler concentration. In statistical systems, constituents are spread at random and do not form regular structures. In structurized systems, constituents form chainlike, flat or three-dimensional structures. 

---