Interactive model surface plot

Figure 6 An interactive model three-dimensional response surface plot for fines in the milling study.

The surface plot in Figure 9(a) indicated that there was a considerable interaction between apphed voltage and solution concentration and this is in agreement with the presence of the term XX in the model of AFD. In the present study, applied voltage influenced AFD regardless of spinning distance and volume flow rate as shown in Figure 9(d) and (e). The absence of 2 3 and X X in the model of AFD proves this observation. 

The generated equations for tensile modulus can also be pictorially represented as surface plots, as shown in Figure 10.10. The presence of a two-way interaction leads to the curvature in the surface plot for the properties and thus provides the ways to carefully consider the different components of the mixture to achieve an optimum enhancement of the properties. Unlike conventional models, which depend on oversimplified assumptions and are not applicable in reality, these models do not suffer from these limitations and can still predict the composite properties using a set of simple equations. 

Interpretation of IC-AFM images is complicated by the fact that the tip-sample force is a nonlinear function of tip-sample separation. The tip-surface interactions in IC-AI have been modeled extensively and have been recently reviewed [109, 143]. Two important conclusions have come from the modeling. First, the nonlinear interaction of the dynamic tip with the surface can lead to two stable oscillation states one that follows a net attractive path and the other that follows a net repulsive path [147, 148]. A hint of this is seen in the phase versus frequency plot (see Fig. 3.32) where the cantilever initially oscillates along an adhesive path and then abruptly transitions to the repulsive path. Simulated amplitude and phase (z-sweep) curves can reproduce those determined experimentally. These have been interpreted in terms of force based interaction models that include the effect of capillary forces and adhesive forces when they are known or can be estimated. The transition between the bistable states depends on a number of factors including the cantilever Q, Ao, and r p, and the drive frequency as well as the surface properties [149]. In general high Q cantilevers or small Ao favor the net attractive path. 

The model in Figure 3.20a applies to ACM-silica, while Figure 3.20b suits the ENR-silica system. Kraus constant, C, determined from the slope of the plots in Figure 3.19, quantifies the mbber-silica interaction in these systems. CACM/siUca is 1-85 and CENR/siika is 2.30 and these values are significantly higher than the reinforcing black-filled mbber composites [65]. Hydrogen-bonded interaction between the SiOH and the vicinal diols in ENR is responsible for this, whereas dipolar interaction between ester and SiOH in ACM-silica only results in weaker adsorption of the mbber over the filler surfaces. 

Figure 8.5 Interaction potential for model whey protein layer consisting of densely packed brush-like tethered chains with small a fraction of the whev protein replaced by p-casein chains as represented by a copolymer model. The energy A d) calculated from SCF theory is plotted as a function of surface-surface separation d A, no p-casein B, 2.5% p-casein C, 5% p-casein D, 5% p-casein alone (without whey protein layer). Potentials A, B and D imply that the emulsion system is flocculated potential C implies a stable emulsion state. Reproduced from Dickinson (2006b) with permission.

Fig. 7. Detailed models of surface free energies based on quasi-chemical metal-metal interactions allow detailed Wulff plots, and hence particle shapes, to be predicted as a function of temperature, (a) Interfacial phase diagram for simple cubic lattice model with nearest-neighbor and next-nearest-neighbor attraction, (b) Representative Wulff plots and equilibrium crystal shape of (a) (103).

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