This document summarizes research on the eutectic behavior of binary mixtures of polycyclic aromatic hydrocarbons (PAHs). Differential scanning calorimetry was used to measure the melting points and fusion enthalpies of acenaphthene-fluorene and fluorene-phenanthrene mixtures of varying compositions. The enthalpies of fusion of the eutectic mixtures were found to be lower than predicted for ideal mixtures, indicating an interaction energy between the compounds. Future work will further investigate the degrees of deviation from ideal mixture behavior and intermolecular forces involved.

1. Longjiaxin
Zhong1,
Erica
Gunn
Ph.D.2,
Jillian
L.
Goldfarb
Ph.D.3
1. Department
of
Chemistry,
Boston
University,
590
Commonwealth
Ave,
Boston
MA
02215
2.
Department
of
Chemistry,
Simmons
College,
300
The
Fenway,
Boston,
MA
02115
3.
Department
of
Mechanical
Engineering
,
Division
of
Materials
Science
&
Engineering,
Boston
University,
110
Cummington
Mall,
Boston
MA
02215
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Image
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street
light
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July,
1961.
RED
GRANDY/STARS
AND
STRIPES
Fluorene
+
Acenaphthene
Eutec7c
Behavior
of
Binary
Polycyclic
Aroma7c
Hydrocarbon
Mixtures
U n i n t e n d e d
c o n s e q u e n c e s
o f
industrializa2on:
PAH
abound
at
the
former
m a n u f a c t u r e d
g a s
plants
that
lit
the
way
to
our
modern
society.
Eutec7c
Systems
• Phase
diagram
at
low
temperatures
dominated
by
a
two-­‐phase
field
of
two
different
solid
structures,
one
enriched
in
component
A,
other
in
component
B
• Stable,
intermediate
mixtures
form
between
the
extremes
of
pure
component
A
and
pure
component
B
Solid&A&+&B&
Melt&
Tme&
TmA&
TmB&
TA+B!&AB&
Melt&
+&A&
Melt&&
+&B&
100%&A&& &&&&&&&&&&&&&&&&&&&&&100%&B&
Abstract
Polycyclic
aromahc
hydrocarbons
(PAH)
are
byproducts
of
incomplete
combushon.
Despite
their
ubiquitous
environmental
and
industrial
posihoning,
likle
is
known
about
the
phase
behavior
of
PAH
mixtures,
which
is
important
in
predichng
their
fate
and
transport,
and
in
industrial
crystallizahon
processes.
These
compounds
precipitate
during
hydrocracking,
underscoring
the
need
to
fully
understand
their
solid-­‐liquid
equilibrium
behavior
and
the
intermolecular
forces
at
play.
Phase
diagrams
of
binary
polycyclic
aromahc
hydrocarbon
(PAH)
mixtures
display
single
and
mulhple
eutechc
points
depending
on
the
compounds.
We
studied
the
behavior
of
acenaphthene-­‐fluorene
and
fluorene-­‐phenanthrene
mixtures
of
varying
composihon
using
differenhal
scanning
calorimetry
to
measure
their
melhng
points
and
fusion
enthalpies.
As
is
omen
the
case
with
interachng
components,
the
enthalpies
of
fusion
of
these
eutechc
mixtures
are
lower
than
those
calculated
by
an
ideal
mixture
of
the
sum
of
the
individual
components.
Fluorene
+
Phenanthrene
Degrees
of
Devia7on
from
Ideal
Mixtures
and
Future
Work
Ideal
Mixtures
• If
there
were
no
intermolecular
interachons
in
a
mixture,
we
expect
the
enthalpy
of
fusion
to
be
sum
of
its
individual
components
• Eutechc
enthalpies
of
fusion
omen
considerably
lower
than
ideal
predichons
due
to
an
interachon
energy
between
the
compounds
Materials
&
Methods
• Compounds
from
TCI
America
at
minimum
purity
of
98%;
frachonally
sublimed
to
remove
impurihes
• Mixtures
fabricated
by
weighing
on
microbalance,
melted
together
on
hot
plate
at
2°C
above
lowest
melhng
point
• Melhng
points
and
enthalpies
of
fusion
of
pure
components
and
mixtures
determined
on
a
TA
Instruments
Q2000
Differenhal
Scanning
Calorimeter
(DSC)
using
hermehcally
sealed
aluminum
pans
he ability of a binary mixture to form an ideal solution stems from the constituents’ molecular sizes and,
more importantly in the case of these similar sized PAH, specific intermolecular interactions between the
components (Dorset et al. 1989). In an ideal solution, we would expect the liquidous curve to follow the
Schröder equation for freezing point depression, representing the melting point of the mixture, T, as
!" !! = −
∆!!!
!
1
!
−
1
!!,!
(1)
where R is the universal gas constant; x1 is the mole fraction of component 1 (e.g. the solvent); ΔHf1 its
corresponding enthalpy of fusion at an absolute temperature of Tm,1. The same relation would hold for
component 2 as in the binary mixture x2 = 1 – x1. The eutectic temperature, Te, of an ideal binary mixture
is found by setting x1 = xe and T=Te (Hsu and Johnson 1974).
In a similar vein, if there were no intermolecular interactions, one might expect the enthalpy of fusion of a
mixture to be the sum of the individual components, such that:
∆!!!"#,!"#$%
= !!∆!!!
+ !!∆!!!
(5)
However, this if often not the case; the enthalpies of fusion of eutectic mixtures are often considerably
lower than those calculated by equation (5), attributed to an interaction energy between the compounds,
equal to the difference between the measured and mixing law prediction (Gupta et al. 2012).
xi
=
Mole
frachon
of
component
i
ΔHfi
=
Enthalpy
of
fusion
component
I
n, if there were no intermolecular interactions, one might expect the enthalpy of fusion of a mixture to be
the sum of the individual components, such that:
∆!!!"#,!"#$%
= !!∆!!!
+ !!∆!!!
(5)
However, this if often not the case; the enthalpies of fusion of eutectic mixtures are often considerably
lower than those calculated by equation (5), attributed to an interaction energy between the compounds,
equal to the difference between the measured and mixing law prediction (Gupta et al. 2012).
∆!!"#$%&'#!(" = ∆!!!"#,!"#$%&"'
− ∆!!!"#,!"#$%
(6)
Sample Calculation (Acenaphthene-fluorene mixture in 50:50):
[Not pretty sure how to use this equation]
66.55℃ = 339.7!K
Fluorene
C13H10
Molecular
Weight:
166.2185
Acenaphthene
C12H10
Molecular
Weight:
154.2078
g/mol
Heat/Cool
Thermal
cycle
at
5°C/min,
50wt%
(0.14mol%)
Fluorene
69.5°C
64.3°C
56.5°C
51.5°C
49.3°C
46.0°C
44.5°C
48.5°C
50.5.3°C
55.3°C
51.5°C
67.5°C
72.0°C
72.8°C
Cooling
and
reheahng
of
mixture.
Some
evidence
of
low
temperature
phase
growing
back
in
at
low
temperature,
and
then
re-­‐converhng
as
the
sample
is
heated.
RT# 50.8#°#C# 55.0#°#C#
55.5#°#C#
(b)#
66.0°#C# 67.0#°#C#
(b)#
Sample
quenched
from
melt
between
coverslips.
(b)
Images
taken
between
crossed
polarizers;
crystalline
material
appears
bright,
melt
appears
dark.
Appearance
changes
with
temperature,
but
sample
remains
crystalline.
Changes
very
possibly
due
to
solid-­‐solid
phase
transformahon,
which
completes
around
66°C.
1mm
Mixtures
of
40-­‐60wt%
(46-­‐63mol%)
acenapthene
in
fluorene
show
single
melhng
points
across
composihon
range
Mixtures
of
40-­‐60wt%
(46-­‐63mol%)
acenapthene
in
fluorene
have
enthalpies
of
fusion
similar
to
that
predicted
by
an
ideal
mixture.
Outside
of
this
range,
we
find
negahve
interachon
enthalpies.
Fluorene
C13H10
Molecular
Weight:
166.2185
Phenanthrene
C14H10
Molecular
Weight:
178..2292
Conclusions
&
Implica7ons
Mixtures
with
more
than
20wt%
of
either
compound
show
single
melhng
points
Enthalpies
of
fusion
are
fairly
close
to
ideal
mixture
predichons
Fluorene
+
Phenanthrene
mixtures
show
considerably
lower
enthalpies
of
interachon
than
Fluorene
+
Acenaphthene
mixtures
The degree to which a mixture deviates from ideal behavior can also be described by
excess functions for enthalpy (ΔHE
), Gibbs free energy (ΔGE
), and entropy (ΔSE
).
∆!!
= −!!!
!!
!"#!!
!"
+ !!
!"#!!
!"
(7)
∆!!
= !" !!!"!! + !!!"!! (8)
∆!! = −! !!!"!! + !!!"!!+!!!
!"#!!
!"
+ !!!
!"#!!
!"
(9)
!
The
degree
to
which
a
mixture
deviates
from
ideal
behavior
can
also
be
described
by
excess
funchons
for
enthalpy
(ΔHE),
Gibbs
free
energy
(ΔGE),
and
entropy
(ΔSE).
We
will
explore
the
degree
to
which
deviahons
from
ideality
stem
from
entropic
versus
enthalpic
contribuhons
based
on
Gibbs
minimizahon
at
the
eutechc
The
acenaphthene-­‐fluorene
system
exhibits
both
single
and
double
melhng
peaks
from
low
mass
frachon
to
high
mass
frachon.
The
fluorene-­‐phenanthrene
mixture
goes
from
eutechc
to
non-­‐eutechc
and
then
going
back
to
eutechc
behavior.
As
a
result,
the
range
of
acenaphthene’s
mass
frachon
across
the
single
phase
melhng
for
the
acenaphthene-­‐fluorene
mixture
was
between
44.6
and
64.3%,
and
the
range
of
temperature
of
the
eutechcs
was
between
67.5
and
66.6
°C.
The
range
of
fluorene’s
mass
frachon
to
achieve
this
eutechc
for
the
fluorene-­‐phenanthrene
mixture
is
between
5.27
to
54.89%
and
79.89
to
95.06%,
and
the
eutechcs
formed
for
these
mass
frachons
between
97.98
and
114.85
°C.
The
fluorene-­‐phenanthrene
system
has
a
considerably
broader
eutechc.
As
is
omen
the
case
with
interachng
components,
the
enthalpies
of
fusion
of
these
eutechc
mixtures
are
lower
than
those
calculated
by
an
ideal
mixture
of
the
sum
of
the
individual
components.