PHYSICO-CHEMICAL CRITERION OF POLYMERS HIGHLY LOADED WITH FILLERS

It is well known that the amount of a filler which can be introduced into the poly-mer depends on many factors (filler-polypoly-mer affinity, viscosity of melt or solu-tion, etc.). It is important to give a definition of what should be considered to be high loaded polymer, because, up to now, there is not a distinct understanding of this question. The situation is somewhat similar to that existing some years ago in the field of polymer solution: “what is the meaning of the terms ‘dilute’ and

‘concentrated’ solution?” In the case of solutions, the problem was solved by in-troduction of the concept of coil overlap and critical concentration (cross-over re-gion).⁴² We propose to introduce the definition of a critical loading which corresponds to the filler concentration,ϕ_crit, at which filler particles have maxi-mum packing density (for a given shape of particles), i.e., they begin to touch each other. Above this critical loading, the filled system loses its thermodynamic and mechanical stability.^43-45

In the framework of the classical colloid-chemical concept, filled polymer can be considered as a suspension of solid particles, 1, separated by the interlayers of continuous polymeric phase, 2 (thickness,δ). The energy of inter-action between any two particles of a solid phase is expressed as

U( )δ ≈ −A₁₂₁ /δ² [3.25]

where A121is the parameter of intermolecular interaction. From this equation, it follows that the system, consisting of a structureless continuous phase and uni-formly-distributed uncharged colloid particles, is, from the thermodynamic point of view, unstable, due to the action of the attraction forces between parti-cles which cause coagulation. The system may still be mechanically stable due to a high viscosity of the dispersion media. However, such a hypotetic structureless system does not meet the present experimental data, which support the

pres-ence of surface layers in filled poly-mers, having structure and properties different than bulk.

Taking into account that the only structural feature of polymers in amorphous state is the existence of the network of intermolecular entan-glements, one can suppose that the formation of the surface layers, on filler introduction, can only be caused by the changes in the initial network of entanglements. Consequently, the density of this network, in the surface layers, should differ from the same value for the bulk phase. The average molecular mass, Me, between two adjacent junction points of the network can be used as a measure of network density. It is thus evident that the effect of a solid surface should extend by the distance from the surface of at least equal∆δin relation to Me. Using the empirical relationship 2Me≈Mc(where Mcis critical molecular mass for the entanglements) and avail-able data on Mcfor some flexible chains, it may be shown that the expected val-ues of ∆δshould be in the limits of 40-100 Å.¹⁰This prediction coincides with experimentally-found thicknesses of the surface layers in filled amorphous poly-mers. The values of∆δare thus a measure of effective thickness of the surface layers formed as a result of the contact between the filler particle and polymer melt. It is evident that the formation of a thin polymer film, casted from solution, on a solid surface, gives much higher values of∆δ, because the network density in solution is proportional to 1/M_eand diminishes with solution an increase in concentration. In this case, during solvent evaporation, the gradient of concen-tration is established (and correspondingly the gradient of entanglements) in a direction normal to the surface. Figure 3.13 shows the change of the density of entanglements as a function of the distance from the surface. The entanglement density should either monotonously increase withδ, from some minimum value near the interface, corresponding to the concentration of initial solution, up to

“bulk” value (solid line), or pass through the maximum (dotted line). The first

Figure 3.13. Scheme of the dependence of the entanglement network density and packing density on the distance from the surface:

I-border layer, II-the bulk.

case is typical of a system having low energy of interaction between the solid and polymer, whereas the second case is typical of a strong interaction favoring for-mation of a defective intermediate layer which separates the surface layers and polymer bulk into different structures.

Independent of the formation of filled composition, the increase in the filler content is accompanied by the monotonous increase in the fraction of the surface layers, ϕ₁, up to their overlapping and formation of a continuous surface

“phase”. The amount of filler denoted byϕ′₁should be considered as correspond-ing to the transition of all polymer in the filled system into the state of a surface layer.ϕ′₁ may be considered as the limiting value of a highly loaded system. In the regionϕ₁> ′ϕ ₁, the system preserves its mechanical stability due to adhesive interaction between filler and polymer and due to cohesive strength of the con-tinuous phase. The thermodynamic stability of this system can be a result of compensation of some decrease in entropy of mixing of polymer coils (due to di-minishing density of entanglement network in the surface layer) by decrease of enthalpy due to the thermal movement restrictions in the surface layer. At the same time, with the increasing amount of filler, the decrease in the thickness of the surface layer, up to values lower than the radius of inertion of the molecular coil 2<Rg>, leads to such a drastic decrease in conformational entropy of macromolecules that the thermodynamic stability also sharply diminishes. It means that the region of highly loaded polymer is restricted by some volume fraction of a filler,ϕ′′₁, at which the effective thickness of the surface layer be-comes comparable to the size of a macromolecular coil.

The analysis given above allows for the following definition: highly loaded polymer is a system where all polymeric component was transformed to the state of a surface layer having a thickness exceeding the size of macromolecular coil in the melt. Thus, the critical filler content,ϕ′₁, is a fundamental character-istic of the system and criterion for highly loaded polymer.

According to the experimental data⁴⁴for some crystallizable polymers, the effective thickness of the interlayer, L, between filler particles

L = D[(0.80 /ϕ ′′₁ )¹³ −1] [3.26]

is determined by the size of macromolecular coil in melt, 2Rg(D is the diameter of a filler particle). Because of the scaling dependence Rg≈M^1/3, one may expect a similar relationship between L and M, which was confirmed elsewhere.⁴⁶It was found that, at some concentrations and molecular mass, M, the saturation is reached at the interface PS-fumed silica. Atϕ ϕ> ′′₁, the number of contact points between macromolecules and the surface remains unchanged. The constant value ofν, for highly loaded polymers, independent ofϕ₁, is valid only if with growth inϕ, in the regionϕ ϕ> ′′₁, the diminishing fraction of filler will interact with polymer (meaning the voids will be formed). Thus, the valueϕ₁′′is the up-per limit of the existence of highly loaded polymer, above which the system, as mentioned above, losses its mechanical stability. It was discovered that value L (nm) depends on the molecular mass of polymer, according to the empirical rela-tion:⁴⁷

L = 5.25×10^-3M_w^0.62 [3.27]

Calculated values of L, for various systems, correspond to values Rgand in agreement with the results of theoretical analysis of polymer adsorption, ac-cording to which the thickness of an adsorption layer,δ, and polymerization de-gree, N, are connected by the scaling relationshipδ ≈N¹²atδ >Rg (see reference 22 in Chapter 1).

It is also evident that the limiting amount of a filler depends on the size and shape of its particles. To increase the amount of filler, the polydisperse filler can be used.⁴⁸For such fillers, the geometric criterion of filling can be calculated, which is defined as the difference between the volume fraction of filler at its lim-iting packing density,ϕ_m, in the unitary volume, and its volume fraction in real composition,ϕ, is

ϕ_f =ϕ_m −ϕ [3.28]

whereϕ_f is an unoccupied volume available for polymer in unitary volume. This characteristic is more conveniently compared with the amount of filler.⁴⁹For composites filled with randomly oriented fibers, theoretically, the limiting vol-ume fractionϕ_m = kd/L, where k is a constant and d and L are diameter and length of fiber. This relationship is valid for L/d > 5.3.⁵⁰