Aggregates typical values

The term D is called the fractal index and represents the packing change with distance from the centre of the floe. Computer simulation and experiments allow the value of D to be related to the mechanism of aggregation. Typical values are for ... 

In combination with Equation 9.9 it is now possible to calculate the dimensions of the rod-shaped micelles from the minimum of G Tco). Kern et al. performed systematic studies of the average micellar lengths of wormlike aggregates. Typical values are of the order of several micrometers, but extreme values of more than 0.1 mm were also sometimes observed. These data are in fairly good agreement with results of cryo-TEM, which also show the presence of entangled wormlike micelles with dimensions as long as several micrometers. 

It is possible to vary the addition level of water-reducing admixtures when an increase in dosage level will generally produce an increase in the amount of water which it is possible to remove from the mix proportions whilst maintaining the required slump. Typical values are shown in Table 1.13 for an aggregate-cement ratio of 5.85 1 and a slump of 50 mm. 

The critical packing parameter can be used as a guide to the aggregate architecture for a given surfactant (as shown in Figure 4.6). Typical values and their corresponding aggregate structures are ... 

The cac (critical aggregate concentration) values for oleate are in the millimolar range, which means that at the operational concentration of 10-50 mM there will be a signihcant concentration of monomer in equilibrium with the aggregate. This consideration allows us to go back to the question of whether vesicles are chemical equilibrium systems. Oleate vesicles cannot be considered proper chemical equilibrium systems, however they behave in a mixed way, with some features that are typical of micelles in equilibrium (Luisi, 2001). 

An equivalent surface area of 460 m g was determined from the monolayer volume, Vj. The value obtained for the dimensionless energetic constant, C=260, was characteristic of a microporous material. Although the BET surface area may not be a physically precise quantity due to the fact that the nitrogen molecule does not exhibit the same cross-sectional area in a microporous environment as on a flat surface, the BET value is useful for comparisons of relative porosities among a related class of adsorbents. For instance, smectite clays pillared by metal oxide aggregates typically exhibit BET surface areas in the range 150 - 400 m /g. Thus, the TSLS complex is among the more porous intercalated nanocomposites derived from smectite clays. 

Substitution of a typical value for HAF black (A = 105 cc/100 g) leads to ceff/c = 2.2, which is also of the order required to reconcile Smit s relative viscosity data. (Eq. 17 comes reasonably close to predicting the effective filler concentration for the quasi-equilibrium stress data of Fig. 11, giving rise to shift factors a — 0.62, 0.76, 1.00 and 1.10 see Section V-3.) The possibility of a significant occluded polymer contribution was considered by Smit, but dismissed on the basis of what appears to be an overestimate of the packing density of the particles in the primary structure aggregates. 

Abrasion resistance. The resistance of aggregates to abrasion is measured in terms of the aggregate abrasion value and the polished stone value (see section 6.4.3). An alternative measure is the Bond Work Index [3.3], which ranges from 4 kW-hr/t for soft limestones, to about 10 for typical dense limestones. 

The frequency dispersion of the absorption coefficient k and the refractive index n of the films of PIC long chain derivatives in J-aggregated and monomer forms were determined in the wavelength region from 500 to 650 nm. The typical value of measured thin films thickness was 20-30nm. As an illustration, the resulting spectra for two films are shown in Fig. 12. The spectra for other films were similar. One shows anomalous dispersion for n within the region of dye absorption (500-570 nm), with the values n = 3.05 and k = 0.8 at the maximum of the J-peak dispersion curve at the absorption maximum of the J-peak, n = 2.5 and fe = 1.25 for film 21 nm thick. 

Combustor ash is highly absorptive with absorption values ranging from 5-17% for fine particles and from about 4-10% for coarse particles. Conventional aggregates typically exhibit absorption values of less than 2%. 

The typical value of the surface tension for bitumen at 100°C is about 24 mN/m (Drelich et al. 1994) and a characteristic value of the shear modulus is about 0.6 GPa (Batzle and Zhijing 1992 Kato et al. 2008). It can be calculated by substituting these values into Equation 15.15 that the depth of shear spreading will be 1-2 mm for a characteristic aggregate size of 2-3 nm. This estimate is in agreement with the experimental data. 

Thermotropic polyesters are melt-spun from the nematic phase and orient easily in an elongational flow field (moderate drawdowns/forces are sufficient). In the fiber case, highly oriented fibers form easily with an initial modulus close to theory—typical values range from about 70 to 150 GPa. Ward [46] has shown that the tensile modulus may be described by an aggregate model, i.e., the modulus is a function of the inherent chain modulus, the molecular chain orientation, and the shear modulus (which described the stress transfer between chains). The tensile strength of LCP fibers follows the prediction of the lag-shear model [47]. Both the aggregate model and the lag shear model treat the LCP as though it... 

The range and typical values of key elements found in asphaltene fractions are summarized in Table 1. One primary delimiter of asphaltene structure is the atomic H/C ratio, which correlates directly with aromaticity (40). An even more telling indicator of asphaltene structure is the distribution of H/C ratio, or equivalently, the Jurkiewicz TV fee-tor (41), over the range of molecular weights, whieh characterizes the aromaticity and polydispersity of asphaltenes. As we will discuss below, the tendeney of asphaltenes to associate and aggregate eertainly increases with acidity, but may also increase with moleeular weight... 

The spectral dimension S is a function of the branching rate of the set and indicates how the whole aggregate can vibrate. The vibration density is proportional to co at low frequencies co. The specific heat of the fractal aggregate is then proportional to (in which T is the absolute temperature). The heat conductivity is a function of the distance a and is proportional to typical value for... 

The normalised scattering curves in Fig. 4.13 are plotted over a broad range of ( -values, which cannot be covered by just one instrument (typical values for SLS are 0.002 to 0.03 nm and for SAXS 0.05 to 2 nm cf. Sect. 2.3.4). That causes tremendous difficulties in deriving reliable parameters on size and stmcture of particle aggregates. For the purpose of illustration. Fig. 4.13 shows the normalised... 

---