Fillers particle density

The determination of filler particle density is carried out using the pyknometer method. The pyknometers used are smaller than those used for determining the density of aggregates. The capacity of the pyknometer used is usually 50 ml. 

Bulk Density. Bulk density, or the apparent density, refers to the total amount of space or volume occupied by a given mass of dry powder. It includes the volume taken up by the filler particles themselves and the void volume between the particles. A functional property of fillers in one sense, bulk density is also a key factor in the economics of shipping and storing fillers. 

It is precisely the loosening of a portion of polymer to which the authors of [47] attribute the observed decrease of viscosity when small quantities of filler are added. In their opinion, the filler particles added to the polymer melt tend to form a double shell (the inner one characterized by high density and a looser outer one) around themselves. The viscosity diminishes until so much filler is added that the entire polymer gets involved in the boundary layer. On further increase of filler content, the boundary layers on the new particles will be formed on account of the already loosened regions of the polymeric matrix. Finally, the layers on all particles become dense and the viscosity rises sharply after that the particle with adsorbed polymer will exhibit the usual hydrodynamic drag. 

Note that, apart from the filler particle shape and size, the molecular mass of the base polymer may also have a marked effect on the viscosity of molten composites [182,183]. The higher the MM of the matrix the less apparent are the variations of relative viscosity with varying filler content. In Fig. 2, borrowed from [183], one can see that the effect of the matrix MM on the viscosity of filled systems decreases with the increasing filler activity. In the quoted reference it has also been shown that the lg r 0 — lg (MM)W relationships for filled and unfilled systems may intersect. The more branches the polymer has, the stronger is the filler effect on its viscosity. The data for filled high- (HDPE) and low-density polyethylene (LDPE) [164,182] may serve as an example the decrease of the molecular mass of LDPE causes a more rapid increase of the relative viscosity of filled systems than in case of HDPE. When the values (MM)W and (MM)W (MM) 1 are close, the increased degree of branching results in increase of the relative viscosity of filled system [184]. 

Atomistic simulation of an atactic polypropylene/graphite interface has shown that the local structure of the polymer in the vicinity of the surface is different in many ways from that of the corresponding bulk. Near the solid surface the density profile of the polymer displays a local maximum, the backbone bonds of the polymer chains develop considerable parallel orientation to the surface [52]. This parallel orientation due to adsorption can be one of the reasons for the transcrystallinity observed in the case of many anisotropic filler particles. 

Figure 7 shows the effect of filler particle shape on the viscosity of filled polypropylene melts, containing glass beads and talc particles, of similar density, loading and particle size distribution. The greater viscosity of the talc-filled composition was attributed to increased contact and surface interaction between these irregularly shaped particles. 

In the case of filled systems, the two latter effects provide a substantial contribution to C2 compared with the influence of trapped entanglements [80]. For filled systems, the estimated or apparent crosslinking density can be analyzed with the help of the Mooney-Rivlin equation using the assumption that the hard filler particles do not undergo deformation. This means that the macroscopic strain is lower than the intrinsic strain (local elongation of the polymer matrix). Thus, in the presence of hard particles, the macroscopic strain is usually replaced by a true intrinsic strain ... 

The variations in the positron intensities in HDPE with different amounts of glass filler were satisfactorily explained by the proposed composite model for positron annihilation. The composite model takes into account the size of the filler particles and the density difference between the filler and matrix. 

The value of x, which is needed to calculate P, and Pm, was chosen here as the thickness of a disc with the same diameter as the glass spheres, i.e. 4r/3 — 7.7 rim, where r is the radius of the glass beads. This gave a value of the ratio Pf/Pm of 2.54, which is almost the same as the density ratio dt dm = 2.60. It can be seen from equations (Al) and (A2) that P,/P will approach the density ratio d1/dm if the filler particles tire small enough, Le. when x approaches zero. Equation (A7) then becomes... 

The properties and densities of the mixtures and their resultant syntactic foams not only depend on the binder/filler ratio but also on the microspheres themselves, their size, sphericity, polydispersity, apparent and bulk density, the thickness and uniformity of their shells. Thus, at a given binder/filler ratio, the fluidity of a mixture depends on the size of the microspheres (Fig. 2) and the apparent density depends on their bulk density (Fig. 3)l). As the bulk density of the microspheres increases (the filler particles become larger), the final strength of the material decreases3 76>. 

From a fit of Equation (10) to spatially resolved relaxation curves, images of the parameters A, B, T2, q M2 have been obtained [3- - 32]. Here A/(A + B) can be interpreted as the concentration of cross-links and B/(A + B) as the concentration of dangling chains. In addition to A/(A + B) also q M2 is related to the cross-link density in this model. In practice also T2 has been found to depend on cross-link density and subsequently strain, an effect which has been exploited in calibration of the image in Figure 7.6. Interestingly, carbon-black as an active filler has little effect on the relaxation times, but silicate filler has. Consequently the chemical cross-link density of carbon-black filled elastomers can be determined by NMR. The apparent insensitivity of NMR to the interaction of the network chains with carbon black filler particles is explained with paramagnetic impurities of carbon black, which lead to rapid relaxation of the NMR signal in the vicinity of the filler particles. 

H and 2H NMR have been used in styrene-butadiene rubber (SBR) with and without carbon-black fillers to estimate the values of some network parameters, namely the average network chain length N. The values obtained from both approaches were checked to make sure that they were consistent with each other and with the results of other methods [71, 72, 73]. To this purpose, a series of samples with various filler contents and/or crosslink densities were swollen with deuterated benzene. The slopes P=A/ X2-X 1) obtained on deuterated benzene in uniaxially stretched samples were measured. The slopes increase significantly with the filler content, which suggests that filler particles act as effective junction points [72, 73]. 

It was shown that the stress-induced orientational order is larger in a filled network than in an unfilled one [78]. Two effects explain this observation first, adsorption of network chains on filler particles leads to an increase of the effective crosslink density, and secondly, the microscopic deformation ratio differs from the macroscopic one, since part of the volume is occupied by solid filler particles. An important question for understanding the elastic properties of filled elastomeric systems, is to know to what extent the adsorption layer is affected by an external stress. Tong-time elastic relaxation and/or non-linearity in the elastic behaviour (Mullins effect, Payne effect) may be related to this question [79]. Just above the melting temperature Tm, it has been shown that local chain mobility in the adsorption layer decreases under stress, which may allow some elastic energy to be dissipated, (i.e., to relax). This may provide a mechanism for the reinforcement of filled PDMS networks [78]. 

The elastic properties of rubbers are primarily governed by the density of netw ork junctions and their ability to fluctuate [35]. Therefore, knowledge of the network structure composed of chemical, adsorption and topological junctions in filled elastomers as well as their relative weight is of a great interest. The H T2 NMR relaxation experiment is a well established method for the quantitative determination of the network structure in the elastomer matrix outside the adsorption layer [14, 36]. The method is especially attractive for the analysis of the network structure in filled elastomers since filler particles are "invisible" in this experiment due to the low fraction of protons at the Aerosil surface as compared with those in the host matrix. 

Fig. 11). It is, therefore, highly probable that the bulky filler particles impose geometrical hindrances (entropy constraints) for the chain dynamics at the time scale of the NMR experiment (of the order of 1 ms). This effect may be compared with the effect of transient chain entanglements on chain dynamics in polymer melts. It should be remarked that the entanglements density estimated for PDMS melts by NMR is close to its value fi om mechanical experiments [38]. Therefore, it can be assimied that topological hindrances from the filler particles can also be of importance in the stress-strain behavior of filled elastomers. 

A large number of macroscopic properties of elastomer networks are closely related to the density of network junctions and the extent of their fluctuations. Qualitatively, any increase of network density causes an increase in stress, whereas fluctuations of network junctions leads to a decreasing stress. It is generally believed that a formation of additional network junctions resulting fi-om the presence of filler particles in the elastomer matrix is one of the reasons for the improvement of mechanical properties of filled elastomers. However, the application of macroscopic techniques does not provide reliable results for the network structure in filled elastomers. Furthermore, a lack of information exists on the dynamic behavior of adsorption junctions. The present study fills the gap of knowledge in this area. 

The main contribution to the network density in filled PDMS is provided by adsorption junctions and topological hindrances from the filler particles... 

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