#
APS March Meeting 2011

## Volume 56, Number 1

##
Monday–Friday, March 21–25, 2011;
Dallas, Texas

### Abstract: Y42.00001 : Twinkling Fractal Analysis of Confinement Effects on the Glass Transition of Thin Films

8:00 AM–8:12 AM

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The Twinkling Fractal Theory (TFT) of the Glass Transition has
recently been
verified experimentally [J.F. Stanzione, et al., ``Observing the
twinkling
fractal nature of the glass transition'', J. Non-Cryst. Solids
(2010),
doi:10.1016/j.jnoncrysol.2010.06.041] Here we apply the TFT to
understand
nanoconfinement effects on T$_{g}$ for amorphous thin films of
thickness h
with free and adhered surfaces. The TFT states that T$_{g}$
occurs when the
dynamic clusters percolate rigidity at the rate of testing
$\gamma $. The
lifetime $\tau $ of these fractal clusters of size R behaves as
$\tau \sim
$R$^{\delta }$ exp $\Delta $E/kT, where $\delta $=D$_{f}$/d$_{f}$
in which
D$_{f}$ is the fractal dimension and d$_{f}$=4/3 is the fracton
dimension
for the vibrational density of states g($\omega )\sim \omega ^{df}$.
The activation energy $\Delta $E = $\beta $[T$^{\ast
2}$-T$_{g}^{2}$] in
which $\beta \quad \approx $ 0.3 cal/mol $^{o}$K$^{2}$ and
T*$\approx
$1.2T$_{g}$. In confined spaces, only clusters of size R$<$h can
exist and
these have a very fast relaxation time compared to the bulk.
Thus, for free
surfaces, T$_{g}$ must be dropped at that test rate to percolate
rigidity
and we obtain the familiar expression T$_{g}$(h)/T$_{g\infty }
\quad \approx $
[1-(B/h)$^{\delta }$] where $\delta \approx $1.8 when D$_{f}
\quad \approx
$2.5 and B is a known constant. For thin films adhered to solid
substrates,
T$_{g}$ increases in accord with the adhesion energy$\Delta $A as
$\Delta
$E$\to \Delta $E+$\Delta $A and the adhered cluster lifetime
increases. As
the rate of testing $\gamma $ increases, the confinement effects
diminish as
T$_{g}$ increases in accord with T$_{g}(\gamma )$ = T$_{go}$ +
(k/2$\beta
)$ ln $\gamma $/$\gamma _{o}$.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.Y42.1