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\begin{document}


\title{Aerogel: Production and Characterization}


\author{Wayne Chan}

\maketitle

\lyxaddress{\protect\( \, \protect \)\protect\( \, \, \, \, \, \, \, \, \protect \)Department
of Physics, University of Cincinnati, Cincinnati, Ohio 45221}

\begin{abstract}
Aerogel is a continously porous solid material which is characterized by nanometer-sized
particles and pores. Typically, aerogel is made using the sol-gel method to
form a solvent filled, high porosity gel that is dried by removing the solvent
without collapsing the tenuous solid phase. Aerogel exhibits many exceptional
properties, such as, lowest thermal conductivity, refractive index, sound velocity,
and dielectric constant. Hence, there is a lot of hope for application.
\end{abstract}

\section{INTRODUCTION}


\paragraph{\textmd{Samuel Stephens Kistler published the first paper on aerogel in Nature
in 1931. It was prepared by the acidic condensation of aqueous sodium silicate.
He attempted to prepare aerogel by converting the water in these gels to a supercritical
fluid, but failed. Ultimately, he succeeded by converting the alcohol to a supercritical
fluid and allowing it to escape. It was a laborious and costly production. Thus,
interest faded and not much happened again until the early 1960's. }}


\paragraph{\textmd{Namely, in 1962, Stanislas Teichner developed the sol-gel process.
It is a much simpler and cost-efficient process than Kistler's. This approach
replaces the sodium silicate with an alkoxysilane. Hydrolyzing this substrate
in a methanol solution fabricates a gel in a single step. Then supercritical
drying is incorporated to avoid the capillary forces. The gel is placed in an
autoclave, together with some of the same liquid that is trapped in the pores
of the gel. The temperature is raised until the critical point is exceeded.
Under these supercritical conditions so as to preserve the tenuous solid network,
the distinction between liquid and vapor vanishes. Successive flushing of the
autoclave by dry Ar then removes all traces of the fluid, leaving a dry, structurally
intact gel called aerogel. Today, the sol-gel method is still used to fabricate
aerogel. }}


\paragraph{\textmd{Aerogel is a transparent, highly porous, open cell, low density foam.
It exhibits some exceptional properties, such as, it has the lowest themal conductivity,
refactive index, sound velocity, and dielectric constant of any solid.}}


\section{Characterization}


\subsection{Thermal properties}

The Arrhenius equation:

\( \qquad  \)\( \qquad \qquad  \)\( \qquad \qquad \qquad \qquad  \)D =D\( _{0} \)e\( ^{-q/kT} \)
\( \qquad \qquad \qquad \qquad \qquad \qquad (1) \)


\paragraph{\textmd{where D is the diffusion coefficient, D\protect\( _{0}\protect \)
is a constant, and q is the activation energy for defect motion, is analogous
to the conduction of heat in solids {[}1{]}. The analog for diffusivity, D,
is thermal conductivity, \protect\( \lambda \protect \), which is defined by
Fourier's law:}}


\paragraph{\protect\( \qquad \qquad \qquad \qquad \qquad \qquad \qquad \protect \)\protect\( \lambda \protect \)=-\protect\( \frac{dQ/dt}{A(dT/dx)}\protect \).\protect\( \qquad \qquad \qquad \qquad \qquad (2)\qquad \qquad \qquad \qquad \protect \)}

Here is an illustration of the equation:

\vspace{0.3cm}
{\centering \resizebox*{10cm}{!}{\includegraphics{ss2d.ps}} \par}
\vspace{0.3cm}

In an experiment {[}2{]}, thermal conductivity measurements of a typical silica
aerogel sample are conducted at atmospheric pressure and room temperature. The
thermal conductivity at room temperature is found to be 0.0131 Wm\( ^{-1} \)K\( ^{-1} \).
Figure 2 shows that \( \lambda  \) increases linearly with T up to 40 \( ^{0} \)C
where there is a sudden change of slope. At a temperature of 50 \( ^{0} \)C,
\( \lambda  \) reaches a value of 0.0178 Wm\( ^{-1} \)K\( ^{-1} \). When
the temperature is lowered, \( \lambda  \) decreases with a slope of only 35\( \times  \)10\( ^{-6} \)Wm\( ^{-1} \)K\( ^{-2} \)
giving a hysteresis to the curve. There is, however, no hysteresis effect when
cooling down to -20 \( ^{0} \)C and then going back to room temperature. The
value of \( \lambda  \) after this cycling is 0.0167 Wm\( ^{-1} \)K\( ^{-1} \).
The drastic increase in \( \lambda  \) around 40 \( ^{0} \)C is due to an
increase in density and is not a temperature effect. When the temperature is
increased, there is less friction in the moving parts of the pressurized apparatus
where the sample is stored, causing a higher pressure on the aerogel. This effect
also accounts for the hysteresis. This phenomenon is very common in this type
of experiment.

\vspace{0.3cm}
{\centering \resizebox*{10cm}{!}{\includegraphics{ss2f.ps}} \par}
\vspace{0.3cm}


\subsection{Refraction index}

The index of refraction for aerogel spans from \( \eta  \)\( \cong  \)1.006
to 1.1, corresponding to densities from 3 to 500 kg m\( ^{-3} \) {[}3{]}. Due
to this feature, high-energy physicists have an interest in aerogel as Cherenkov
detectors. Cherenkov radiation occurs if a charged particle penetrates a medium,
having an index of refraction, \( \eta  \), with a speed \( \nu  \), which
is higher than the velocity of light, c/\( \eta  \), in that medium. Under
the action of the fast moving electric field which the particle carries along,
the medium is polarized and gives off light in a cone-shaped pattern (reminiscent
of the sound waves of a sonic boom) around the flight path. For the detection
of relativistic particles, such as. pions, koans, and protons, a medium with
\( \eta  \)\( \cong  \)1 is needed.


\subsection{Acoustic property}

The sound velocities of aerogel ranges from 100 m/s for an aerogel density \( \rho  \)=71
g/l up to 310 m/s for \( \rho  \)=285 g/l {[}4{]}. Aerogel is acoustically
microporous, i.e. its pores are small compared to the ultra-sonic wavelengths.
This feature suggests that the low sound velocities are caused by the air-skeleton
interaction and not to the small Young's modulus. Such an effect is known from
ordinary sound absorbers (where the fibrous structures are also small compared
to the sound wavelength in the auditory range). In an experiment, measurements
are conducted on the sound velocity of evacuated aerogel slabs. There was no
change of the sound velocity compared to the air-filled samples. Thus, one can
conclude that the sound propagation occurs via the skeleton and not though the
air within the porous system.


\subsection{Dielectric property}

Aerogel has the lowest dielectric constant of any known solid. Typically, the
values range from 1.07 to 1.79. The dielectric property of aerogel is dominated
by the large volume fraction of trapped gas in the pores and the high concentraion
of adsorbed molecules on the abundant surfaces. Measurements of the dielectric
constants and loss tangents (i.e. loss factor/dielectric constant) for several
aerogel varieties at the microwave frequency range show that they both vary
linearly with the aerogel density, indicating that the dielectric behavior of
aerogel is more gas-like than solid-like {[}5{]}. Also, the dielectric strength
is very high due to the high volume resistivity and the nano-sized pores confining
the charge carriers to spaces that are about the same size as the mean-free
path for collisions.


\section{Conclusion}

Like most research on material, the growth of aerogel research hinges on commercial
exploitation. Since aerogel has the lowest thermal conductivity, refractive
index, sound velocity, and dielectric constant, the applications for aerogels
are potentially vast and huge in impact. Many scientists from numerous fields
have an interest in aerogel. For instance, high energy physicists would use
it to study the Cherenkov radiation. Material scientists would use it to produce
commercial products, such as refrigerator insulation and wall insulation.

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\end{document}
