Abstract
In pressurized glass-forming systems, the apparent (changeable) activation volume Va(P) is the key property governing the previtreous behavior of the structural relaxation time (τ) or viscosity (η), following the Super-Barus behavior: $${\boldsymbol{\tau }}{\boldsymbol{(}}{\boldsymbol{P}}{\boldsymbol{)}}{\boldsymbol{,}}{\boldsymbol{\eta }}{\boldsymbol{(}}{\boldsymbol{P}}{\boldsymbol{)}}{\boldsymbol{\propto }}{\bf{\exp }}{\boldsymbol{(}}{{\boldsymbol{V}}}_{{\boldsymbol{a}}}{\boldsymbol{(}}{\boldsymbol{P}}{\boldsymbol{)}}{\boldsymbol{/}}{\boldsymbol{R}}{\boldsymbol{T}}{\boldsymbol{)}}$$
τ
(
P
)
,
η
(
P
)
∝
exp
(
V
a
(
P
)
/
R
T
)
, T = const. It is usually assumed that Va(P) = V#(P), where $${{\boldsymbol{V}}}^{{\boldsymbol{\#}}}{\boldsymbol{(}}{\boldsymbol{P}}{\boldsymbol{)}}={\boldsymbol{R}}{\boldsymbol{T}}{\boldsymbol{d}}\,{\boldsymbol{ln}}\,{\boldsymbol{\tau }}{\boldsymbol{(}}{\boldsymbol{P}}{\boldsymbol{)}}{\boldsymbol{/}}{\boldsymbol{d}}{\boldsymbol{P}}$$
V
#
(
P
)
=
R
T
d
ln
τ
(
P
)
/
d
P
or $${{\boldsymbol{V}}}^{{\boldsymbol{\#}}}{\boldsymbol{(}}{\boldsymbol{P}}{\boldsymbol{)}}{\boldsymbol{=}}{\boldsymbol{R}}{\boldsymbol{T}}{\boldsymbol{d}}\,{\boldsymbol{ln}}\,{\boldsymbol{\eta }}{\boldsymbol{(}}{\boldsymbol{P}}{\boldsymbol{)}}{\boldsymbol{/}}{\boldsymbol{d}}{\boldsymbol{P}}$$
V
#
(
P
)
=
R
T
d
ln
η
(
P
)
/
d
P
. This report shows that Va(P) ≪ V#(P) for P → Pg, where Pg denotes the glass pressure, and the magnitude V#(P) is coupled to the pressure steepness index (the apparent fragility). V#(P) and Va(P) coincides only for the basic Barus dynamics, where Va(P) = Va = const in the given pressure domain, or for P → 0. The simple and non-biased way of determining Va(P) and the relation for its parameterization are proposed. The derived relation resembles Murnaghan - O’Connel equation, applied in deep Earth studies. It also offers a possibility of estimating the pressure and volume at the absolute stability limit. The application of the methodology is shown for diisobutyl phthalate (DIIP, low-molecular-weight liquid), isooctyloxycyanobiphenyl (8*OCB, liquid crystal) and bisphenol A/epichlorohydrin (EPON 828, epoxy resin), respectively.
How to “measure” a structural relaxation time that is too long to be measured?
