Local average density profile

The DFT excess isotherm is found by taking the volume average of the local adsorbate density profile, e.g., for a slit-shaped pore of width 77,... 

Here Rs represents the pore radius measured from the center of the surface atoms, and p is the mean pore density. The radial density profile p(r) is obtained from simulations, while the local viscosity is evaluated using the method of Chung et al. [17], at a density locally averaged over a sphere of radius aj /2 [18]. The radius To in eq. (4) represents... 

In finding the shape of the profile between the two phases it is W n) that is used as the local free energy since the minimization occurs at constant chemical potential (equivalent to constant average density), hence the subtraction of the term fin in g and W. Furthermore, the interfacial free energy is the difference between the free energy of the system with an interface and that of the bulk fluid or gas, hence the subtraction of gh to arrive at... 

It is known that bulk or average density is the major parameter controlling the mechanical properties of polymer foams. Nevertheless, density profile has also a major impact especially for structural foams where an unfoamed skin is enclosing a foamed core. In this study, the effect of density profile on the flexural modulus of a structural foam is discussed in terms of skin thickness and taking into account the local variation of density (related to void fiaction) with position. 

It was proposed (Johnson et al., 1987a) that this local lattice dilation is stabilized by the direct incorporation of hydrogen atoms through the coordinated formation of Si—H bonds. Results from SIMS (Section III. 1) and Raman spectroscopy (following) are consistent with this view. For example, the 60-min deuterium profile in Fig. 7(b) yields an integrated areal density of D in the near-surface peak of —1.7 x 1014 cm-2. The same deuteration conditions applied to this material produced 5 x 10n platelets per cm2 with an average diameter of 7 nm (Ponce et al., 1987). 

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