Biomedical Engineering Reference
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density, porosity, PSD, cumulative surface area, elastic modulus, and hardness
(Table 13.1). They used multiangle single wavelength EP to measure the film
refractive index and applying the known skeletal SiO 2 refractive index to cal-
culate the “full” porosity using the Lorentz-Lorenz equation:
[( n film ) 2
1] / [( n film ) 2 +2]
[( n skeleton ) 2
1] / [( n skeleton ) 2 +2]
π =1
−{
}
/
{
}
(13.4)
and in different media of known refractive index using the effective-medium
theory. They also measured changes in the ellipsometric angles during des-
orption of toluene vapor and calculated the “open” porosity that is accessible
to the vapor penetration. The comparison of the two porosities can indicate
the interconnectivity of the pores. The PSD can also be calculated from the
same set of data using the Kelvin and BET equations (Baklanov et al. 2000).
By integrating the PSD data for a cylindrical pore model, they derived the
cumulative surface area.
More porosimetry techniques have been reported recently by Gidley et al.
(2007) regarding the experimental determination of porosity of low dielectric
constant materials, particularly in thin film forms. Several important prop-
erties of such porous thin films such as density, stiffness, strength, thermal
conductivity, and chemical reactivity depend on the pore structure; thus, the
determination of the pore structure and porosity of these films are of signif-
icant importance to their applications. To achieve the control of pore struc-
ture in these films, it is critical to measure the pore structure quantitatively,
including porosity, average pore size, PSD, and pore interconnectivity. How-
ever, conventional porosimetric techniques for bulk materials such as stere-
ology analysis by microscopic methods, intrusive analysis by gas adsorption,
mercury porosimetry, and nonintrusive methods by radiation scattering and
wave propagation (Julbe and Ramsay 1996) are hardly applicable to thin
films because of the shear size of the total pore volume and surface area, not
to mention that these techniques are ex situ. There are several advanced tech-
niques are thus being developed in the past decade, including EP (Dultsev and
Baklanov 1999; Baklanov et al. 2000), x-ray porosimetry (XRP) (Lee et al.
2003), small-angle neutron and x-ray scattering (SANS and SAXS) (Wu et al.
2000; Huang et al. 2002; Omote et al. 2003), and positron annihilation lifetime
spectroscopy (PALS) (Petkov et al. 1999; Gidley et al. 2000). Here we shall
use examples of the deposition of thin polymer films to illustrate the utility
available from a few of these techniques.
Controlling deposition of redox polymer films has been of interest in the
past few decades (Hamnett and Hillman 1985, 1987; Greef et al. 1989; Redondo
et al. 1988; Rishpon et al. 1990; Rubinstein et al. 1990; Rishpon and Gottesfeld
1991; Sabatani et al. 1993a,b; Tjaernhage and Sharp 1994; Gottesfeld et al.
1995; Severin and Lewis 2000; McMillan et al. 2005; Richter and Brisson 2005;
Hillman and Mohamoud 2006; Wang et al. 2007), because of their potential
in utilizing either passive (e.g., for corrosion protection) or conductive (e.g.,
for energy conversion and storage systems or electronics) properties for many
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