Voids radius

When the density of the gas changes much less rapidly than the radius of the void, then the equation of continuity which the void radius a(t) satisfies is ... 

Figure 2. Intensity dependence of narrow ACAP spectra s component (SN) from nano void radius (R) for first fraction of tri-glucerids in crystalline state at 22 0C ( ) and 36 0C, the sixth fraction of tri-glucerids in liquid state (A), the mix of first and sixth fractions at 25 0C (A) for two patterns La(Cl2H25COO)3 ( ) and with fullerens ( ) at 22 0C.

Analyzing adsorption (Section III,C) and desorption (Sections ni,D and III,E), we assumed that the pore volume is concentrated in voids, whereas necks do not possess volumes of their own (Fig. 2). Seaton (34) has recently considered an alternative model of porous solids assuming the pore volume to be concentrated in necks (Fig. 3). In the framework of this model, the adsorption process is described by analogy with Eq. (18) (one should only replace the void radius distribution by the neck radius distribution), and consequently the analysis of the adsorption branch of the isotherm allows one to obtain the neck-size distribution. The desorption process can be described by using the same ideas as in Sections III,D and III,E because this process is mathematically equivalent to the bond problem in percolation theory, even if the pore volume is concentrated in the necks. In particular, the volume fraction of emptied necks under desorption [1 - C/des(fp)] can... 

All of the isotherms shown in Figs. 16-18 have been calculated for the same void radius distribution (Fv = 30 A and = 0.5) and different neck radius distributions. The desorption branch of the isotherm is seen to shift to higher pressures with increasing Zo (Fig. 16), F (Fig. 17), and a (Fig. 18). 

Mason (20) has analyzed in detail the isotherms for xenon on Vycor porous glass (Fig. 14). The void radius distribution has been derived employing the adsorption branch of the isotherm. The void and neck radius distributions were assumed to be connected by the relationship given by Eq. (35). The latter assumption allows one to obtain from the desorption data the value of z (for Vycor glass Zo = 3.3) and to calculate the neck radius distribution (Figure 22). 

Fig. 22. Neck and void radius distributions for Vycor glass. The neck distribution has been calculated employing Eqs. (35) and (37). (From Ref. 20, with permission.)...

The results of simulations demonstrating the effect of various factors on mercury intrusion into porous solids are shown in Figs. 24-26. All the intrusion curves presented have been calculated for the same void radius distribution [Eq. (41) with v = 3000 A and = 0.5]. The mercury intrusion process is seen to start at higher pressures with decreasing Zo (Fig. 24), r (Fig. 25), and o- (Fig. 26). 

Equation (44) [or Eq. (46)] allows one to determine the neck radius distribution provided that the void radius distribution is known from independent experiments. For example. Fig. 27 shows the integral radius distributions for necks and voids, 4>(r) and F(r) [Eqs. (32) and (33)], obtained for a model porous structure formed by a dense random package of glass balls having diameters of =250 /xm (S8). The account of interconnection of various pores is seen to lead to an essentially different distribution of necks over radii compared to the independent cylinder model the distribution shifts toward small radii and its slope is less steep. It is also seen that the neck radius distribution is significantly affected by the overlapping of the void and neck radius distributions. 

Equations (44) and (46) take into account the overlapping of the neck and void radius distribution. However, these equations have been derived employing the assumptions similar to those used in the mean-field approximation in statistical physics. In particular, Eqs. (44) and (46) ignore the effect of pore-size correlations on mercury intrusion. The latter effect has been recently studied in detail by Tsakiroglou and Payatakes (4J) employing the Monte Carlo method. Simulations were made on a square lattice... 

Figure 29B shows the influence of the mean void radius on the deactivation process. An increase in the mean void radius results in a sharper threshold, below which the network loses its global connectivity. The effect of the mean coordination number on the deactivation kinetics is shown in... 

Fig. 29. Relative activity as a function of time at various values of the deactivation rate constant (A) and at various values of the mean void radius (B). The time dependence of the critical radius is described by Eq. (49).

Fig.l Ortho-positronium lifetime r=l/(Apu+ t) as a function of the void radius a-cylindrical void (infinitely long), lowest state b- spherical void, lowest state c- cylindrical void, first excited state d- spherical void, first excited state. The penetration parameter AR is assumed 0.166 nm. 

FIGURE 1.98 Relationships between the changes in the Gibbs free energy of water bound to different silicas and (a) volume of voids filled by unfrozen water and (b) void radius. (Adapted from Arfv. Colloid Interface Sci., 118, Gun ko, V.M., Ihrov, V.V., Bogatyrev, V.M. et al, Unusual properties of water at hydrophilic/hydrophobic interfaces, 125-172, 2005d. Copyright 2005, with permission from Elsevier.)... 

Type V is also of log-normally sized particles/voids and bi-modal size distribution. It is a type of combination of Type III and Type IV with the same nominated mean particle/void radius (f,) with standard deviations (for rj of 0.2 and 0.4, respectively, and volume fractions of 0.054 and 0.096, respectively. 

Figure 7.16 Dependence of resulting reduced void radius xf = on the C-parameter...

Figure 7.19 Time dependencies of (a) void radius and (b) segregation magnitude during shrinkage at various ratios of diffusivities K = 1,2,4, 8,15, 32 (actually, preexponential factors) in the phenomenological model. The parameters are chosen as = 10 , Cg = 0.5, r " = a, r = 17o,...

In the process of internal void growth, the initial reserves of the chemical driving force (concentration and chemical potential gradients) ran out, so that at some moment (at some void radius) the chemical driving force becomes less than the capillary forces (and the corresponding vacancy drop between internal and external boundaries). Thus, one has a crossover from formation to shrinkage. 

Having used the model for void electromigration at the copper/dielectric interface, we simulated the voids with radii 4a, 6a, and 8a (a standing for the lattice parameter). Despite the observed faceting, we find that the velocity is inversely proportional to the void radius, which conforms to analytical predictions... 

ANA- YUGAMI PNC, Japan ANA code claculates temperature and central void radius. YUGAMI code calculates steady-state fuel-clad deformation using a method similar to DEFORM 90... 

---