J. Phys.: Condens. Matter 12 (2000) L281–L286. Printed in the UK PII: S0953-8984(00)12410-5
LETTER TO THE EDITOR
Does temperature fluctuate? Indirect proof by dynamic glass
transition in confined geometries
E Donth†, E Hempel† and C Schick‡
† Fachbereich Physik, Universit¨ at Halle, D-06099 Halle (Saale), Germany
‡ Fachbereich Physik, Universit¨ at Rostock, D-18051 Rostock, Germany
Received 7 March 2000
Abstract. The Gibbs canonical distribution, dw ∼ exp(-E(p,q)/k
B
T)dpdq , seems one of
the most solid pillars of statistical physics. Thermodynamics is believed to be a derivative of
this distribution. Since the temperature T is introduced, de facto, from a heat bath by the zeroth
law of thermodynamics, this distribution cannot represent a genuine temperature fluctuation; all
fluctuations are derived from energy fluctuations (δE). Increasingly, nanoscale problems are
attacked by physics (e.g. glass transition), physical chemistry (e.g. nucleation), or biology (e.g.
protein folding). The fluctuations are relatively large because the nano-subsystems are small. The
fluctuations should, therefore, completely be collected. The von Laue approach [1–3] to subsystem
thermodynamics via minimal work for generation of fluctuations also allows the temperature to
fluctuate (δT ). For this alternative, statistical physics is a derivative of thermodynamics. Here we
show that a decision between the alternatives is possible by a calorimetric determination of the
characteristic length of dynamic glass transition in confined geometries.
The alternatives give different formulas for these lengths. From dynamic calorimetry of glass
transition (for polyethylene-terephtalate (PET) in mobile layers of partially crystalline samples,
for salol, and for benzoin-iso-butyl-ether (BIBE) as guests in host pores of size 2.0, 2.5, 5.0,
and 7.5 nanometer diameter) we partly get lengths, if calculated from the Gibbs distribution,
which are significantly larger than the morphological lengths of the host geometry. This seems
impossible. Alternatively, if the lengths are calculated from the von Laue approach they are
always smaller than, or of order the morphological lengths. This seems reasonable. The final
consequence of these findings is that thermodynamics seems more fundamental than the Gibbs
distribution, and that a new basic distribution should be derived from thermodynamics.
The formula derived from energy fluctuations is [4–6]
V
α
(δE) = ξ
3
α
(δE) = k
B
T
2
/c
V
ρδT
2
g
(1)
and from temperature fluctuation [7]
V
α
(δT) = ξ
3
α
(δT) = k
B
T
2
(1/c
V
)/ρδT
2
. (2)
No ad hoc assumptions (besides the decision whether temperature can fluctuate or not) are
necessary for their derivation. All calorimetric variables needed are well defined by fully
reproducible (for a given sample) experiments with dynamic scanning calorimetry (DSC)
corrected by partial freezing-in [8], or heat capacity spectroscopy (figure 1) [9–11]. V
α
is
the volume of a cooperatively rearranging region (CRR) as defined by Adam and Gibbs [12]
via statistical independence, from the environment, of fluctuations in the dispersion zone
of dynamic glass transition. In any case, the CRR size is microscopically small, since all
quantities in equations (1) and ( 2) do not depend on the macroscopic sample size. The walls
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