JOUR N
AL
OF
RESEARC
H
of
the
Notiono
l Bur
eau
of
St
andards-A
. Physics
and
Chemistry
Vol.
78A
, No. J ,
Mo
y-
June 1974
PVT
Relationships for Liquid and Glassy Poly(vinyl acetate)
John
E.
McKinney
Institute for Materials Research ,
National
Bureau of Standards, Washington,
D.C
.
20234
and
Martin
Goldstein
Belfer
Graduate
School
of Science, Yeshiva University,
New
York,
N.Y
.
10033
(J
anuary
23, 19
74
)
PVT m
eas
ur
e me nts we re made on liquid and gl
assy
poly(vinyl acetate) ove r ran
ges
of - 30 to
100 °C
and
0
to
800 bar
(g
age
pr
ess
ur
e).
Th
e d
ata
we re ob tain
ed
by thr
ee
diffe
rent
th e
rmodynami
c
hi stori
es:
(a) variable formation
pr
ess
ur
e. (b) co nsta nt formation pr
ess
ur
e
at
one a tm os ph er
e,
a nd (c)
co
ns
tant
formation press
ur
e at 800 bar. In a
ll
of th
ese
the glass was form ed by iso ba
ri
c c oo lin g at
5°C/
h.
Th
e sali e nt c
har
acte
ri
s
ti
cs
r
es
ulting fr om the diffe re nt h isto
ri
es
are th e followin
g.
History
(a)
pr
o
du
ces
a gla
ss
of
stru c
tur
e varying with forma
ti
on
pr
ess
ur
e
and,
he n
ce,
d
oes
not n
ecessa
ri
ly
,give the prope r th erm od yna
mi
c prope rti
es
of a
"s
in gle ph
ys
i
ca
l s ubsta n
ce."
However, the liquid
·g
lass
inter
sec
tion te mp e
ratur
e,
T
u(
P) ,
is
an importa nt kineti
c,
or relaxa
ti
on
al
, prope rty whi c h a
ppr
ox
im
ates
an
isovi
sc
ous state. Accordingly, the valu
es
of
dTu
l
dP
a re
in
clo
se
agreeme
nt
with those o
bt
a
in
ed
from d yna mic m
ec
ha
ni
c
al
a nd
di
e l
ec
tr
ic time
·t
e
mp
e ra
tur
e·
pr
ess
ur
e s upe rpositi on. Cons
tant
formation
histo
ri
es
(b) and
(c)
g
iv
e
proper
the rmodynamic
pr
operti
es
of th e gla
sses,
but very little
inf
orm a
ti
on
with r
es
p
ec
t
to
kin e
ti
cs. Inc reas ing the
pr
ess
ur
e at whic h the gl
ass
is f
ormed
in
c re
ases
th e densit y
of th e gl
ass
(a
t the g
iv
e n cooling ra te) con side rably in co
ntr
ast to the e
ntr
opy (from othe r work), whic h
appe
ar
s
to
be
esse
ntially inde pende nt of formation
pr
ess
ur
e.
A cons
id
erab
le
part
of th e pa pe r is de finitional.
The
results are re lated to oth er PVT,
dynami
c
mecha
ni
cal , di electri
c,
and th erm od ynamic m
eas
ur
e me nts.
Int
e
rpr
etat
ions are g
iv
e n in te rm s of both
ph enom enological
and
mol
ec
ul
ar
m
ode
l
s.
Key words : De nsit
y;
di!atomet
er;
e
ntr
opy; gl
ass
tran
sitio
n;
gl
ass;
liquid; polyme r; poly(vinyl
ace
ta te);
PVT;
relaxa
ti
on.
C
ont
e
nt
s
1.
Introdu
c tion __________ ________
____
__
___
_
2.
Experimental
apparatus
and
pro
ce
dure
_
__
_
2.
1.
PVT
apparatu
s _________
__
__________ _
2.2 Dilatom
ete
r ___________ ____________ _
a.
D
es
ign _________ ______ ______
__
-
--
b.
Operating
e
quations
_________ _
___
_
2.3.
Sample
__________
__ __
_________ _
___
_
2.4.
Thermodynami
c histori
es
and
relaxa
-
tional
be havior ___________________ _
a.
Variabl
e formation
of
the
gl
ass
___
_
b.
Cons
tant
formation
of
the glass
at
atmo
s
ph
eric
pr
ess
ur
e _______
__
_
c.
Constant
formation
of
th
e g
lass
at
800
bar
_____
___
_________
___
___
_
3.
Pres
e
ntation
of
data
___
___
_________
____
_
3.1.
Liq
uid r egion _______
___
___________ _
3.
2.
Transition
region (glass formation)
___
_
3.3.
Glasses
__________
__
_ - - - - - - - - - - - - - - -
a.
Variable
formation glass _____ _
__
--
b.
Glass
formed
at
atmosph
eri c
pr
es
-
sure
533-558 OL -
74
- 2
Page Page
331 c.
Glass
formed
at
800
bar
__________
341
332 4.
Evaluation
of
data
____________ __________
341
332 4.1.
Equation
s of s
tat
e
and
the
or
d
er
ing
333
param
eter Z
______________________
341
333
4_2.
Evaluation
of
Tg
and
T
;j
'
and
co
rr
e -
333
sponding
prop
erti
es
_
__
_ _
__
_
__
___
_ _ _ 343
334 4_3.
To
and
the isoviscous s
tat
e __________ 345
4-4.
"Perman
e
nt"
densifi
ca
tion
of
the gl
ass
335
and
Tg*
depr
ess
ion _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 345
336
4_5.
Evaluation of
the
fir st
Ehr
e
nf
es
t rela-
tion and its role in time -te
mp
era-
336
ture-pr
ess
ur
e
su
perpo
sition
__
__
__ __
348
4.
6.
Experim
e
ntal
un
cer
tainti
es
including
336
estimate
s on Tg
and
T
,*
_____
___
____
350
337
5.
Concl
u
ding
re
mark
s ______
~__
__
_
__ __
____
352
337 6_
Referen
ces
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 353
337
339
1. Introduction
339
Thi
s work is c
oncerned
with
the
measurem
e
nt
and
340
phenom
enological
evaluation
of
the
PVT
properties
. 331
of
poly(vinyl
acetate)
with
particular
attention
given
to
the
influence
of
thermodynamic
history.
Although
the
properties
of
only
one
polymer
were
evaluated
here,
the
general
behavior
and
concepts
are
con-
sidered
to
be,
at
least
in a
qualitative
sense,
applicable
to
amorphous
polymers
and
glass·forming
liquids
in
general.
It
is well
known
that
the
thermodynamic
history
used
to form a
glass
has
an
important
effect on
its
properties.
Gee
[I]'
and
Ferry,
in his
recent
treatise
[2],
devot
e
considerable
discussion
to
this
point.
For
example,
the
influence
of
the
rate
of
cooling on
the
densification
of
the
glass
and
the
corresponding
shift
of
the
glass
transition
temperature
Tg
on
poly(vinyl
acetate
)
have
been
studied
over
a large
range
of
rates
by Kovacs
[3]. A
similar
effect may
be
obtained
by forming a
glass
at
elevated
pressures
as
shown by
Bianchi
et
al.
[4],
and
later
in
this paper.
In
this
work the densification effect,
among
others,
has
been
demonstrated
extensively.
The
influence
of
thermodynamic
history was
studied
by
using
suitable
temperature-pres
sure-time
vanatIOns
which
were
grouped
into
three
distinct
classes.
In
these
the
glass
was always
formed
using
the
same
isobaric
cooling
rate
at
atmospheric
and
elevated
pressures,
always
commencing
at
equilibrium
in
the
liquid
region,
where
properties
are
independent
of
history.
The
properties
of
the
corresponding
glasses
were
obtained
sub
-
sequently
by
relatively
fast
temperature-pressure
changes
during
which
properties
were
assumed
to
be
independent
of
time
due
to
th
e
slowness
of
the
visco-
elastic
relaxations.
The
parallel
method
of
forming
the
glass by iso-
thermal
compressions
at
nearly
constant
rate
used
in
references
[5
-8
] was not
employed
here;
however,
some
correlation
between
results
from
the
two
types
of
formations
is
included
in
the
discussions.
The
pressure
range
was limited to 800
bar
(gage
pressure)2. Although
this
range
may
appear
to
be
small
in
comparison
to
that
obtained
in
some
other
high
pressure
experiments,
the
compressibilities
of
polymers
are
relatively
large
,
and
accordingly,
large
changes
in
the
transition
propertie
s
are
observed
with
pressure.
On
the
other
hand,
as will
be
seen,
a fourfold
increase
in
the
pressure
range
would
be
useful
to
study
some
of
the
limiting
transitional
phenomena
predicted
by
some
interpretations
of
these
and
other
data.
In
experimental
observations
on liquid-glass sys-
tems,
one
is
faced
with finding a
suitable
or
appro-
priate
definition
of
the
glass
transition
temperature.
A definition
of
Tg(P)
which
is
unique
for
eac
h sub-
stance
in
that
it is
independent
of
the
exper
imental
mode
by
which
it
was
det
ermined
is
of
co
urse
not
possible. Different definitions
of
Tg
are
usually
not
equivalent.
It
has
been
proposed
that
with PVT
measurements,
a
pressure
dependent
transItIOn
temperature
should
be
defined
from
the
intersection
of
the
liquid
and
glass
surfaces
in PVT
space
[3, 4,
8]
.
Since,
in
this
work,
the
glasses
were
formed
by
differ-
ent
histories,
the
intersection
temperatures
at
each
I
Fi
g
ur
es
in
brac kets indi cate
lit
e
ratur
e refere nce
at
end
of
this
paper.
2
Th
e co
rr
es
ponding qu a ntit y
in
5 1 units is 80 me
gapa
sca) (MPa).
pressure
will
often
take
on
different
values,
and
also
may
have
markedly
different
pressure
dependences.
In
order
to
make
appropriate
distinctions,
it is con-
venient
to
adopt
the
convention
proposed
by Goldstein
[9], which is
applicable
to
the
histories
used
here.
With
this
convention
Tg(P) is defined
as
the
tempera-
ture
of
the
liquid-glass
intersection,
where
the
glass
was
formed
by
isobaric
cooling
repeated
at
different
pressures
at
the
same
constant
rate.
The
values
of
Tg(P) may
be
viewed as a
set
of
characteristic
tempera-
tures
at
which a
mean
volume relaxation
time
is
essentially
constant
as
pressure
is varied. Although
Tg(P)
depends
upon
the
rate
of
cooling,
dTg/dP
has
been
found to
be
essentially
independent
of
rate.
The
other
quantity
from
Goldstein's
convention,
Tg*(P)
,
is
the
temperature
of
the
liquid-glass
intersection
where
the
glass is
formed
by
isobaric
cooling
at
con-
stant
rate
only
at
one
pressure,
with
the
values
at
other
pressures
in
the
glassy region
being
obtained
by
extrapolation
of
the
volume
isobars
.
It
is
thus
equiva-
lent
to
the
definition
mentioned
earlier
(3, 4, 8).
Although
the
values
of
Tg
and
Tg*
are
identical
at
the
formation
pressure,
it will be
seen
that
dTg/dP
and
dTg*/dP
differ
considerably.
The
meaning
of
these
quantities
in
terms
of
the
experimental
data
will
become
clearer
in
later
dis-
cussion.
At
this
time
it is
important
to
remember
that
Tg(P) ,
as
defined
here,
measures
a
relaxational
or
kinetic
property,
whereas
T;(P)
measures
a thermo-
dynamic
property
defined from
the
equations
of
state
for
the
liquid
and
glass (in
pseudoequilibrium)
formed
by a
particular
history.
To
the
extent
that
the
glass
transition
is
as
defined
in
a
relaxational
context,
Tg
may
be
regarded
as
the
more
significant
parameter.
2.
Experimental
Apparatus
and
Procedure
2.1. PVT
Apparatus
All
of
the
measurements
,
except
for
the
reference
density
determinations,
were
obtained
by
pressurized
volume dilatometry.
The
dilatometer
was
placed
in a
pressure
chamber
with glass windows to
permit
visual
observations
of
the
height
of
the
mercury
column
in
the
dilatometer.
The
ch
amber
, in
turn,
was
placed
in
a liquid
thermostat,
also with glass windows.
The
height
of
the
mercury
column
was
read
with a
cathe-
tometer
at
various
values
of
the
independent
variables,
temperature
and
pressure.
A low-viscosity silicone oil
capable
of
withstanding
temperatures
of
250°C
was
used
as
a
thermo
stating
liquid
over
the
high
temperature
range.
At
lower
temperatures,
where
the
silicone oil
became
too
viscous,
and
temperature
gradients
became
evident
from
striations,
ethyl
alcohol
was
used
.
The
bath
temperature
was
co
ntrolled
by a
proportional
controller
with a
thermister
element.
For
the
isobaric
cooling
runs
the
multi
turn
potentiom
eter
con
trol was varied
at
constant
angular
velocity
using
a
variable
speed
gear
box driven by a
synchronous
motor.
Since
the
resistance-temperature
relationship
is
essentially
lin-
ear,
the
bath
temperature
was,
accordingly, varied
at
332
constant
rate.
At
temperatures
below
40°C
accurate
control
was
made
possible
by usi
ng
a
refrigerator
with
an
adjustable
back·
pres
s
ure
valve
located
between
the
suction
side
of
the
compressor
and
evapo
rator
coil.
The
valve was
manually
set
in
accordance
with
the
heat
load
to
be
removed.
Final
control
was
established
by
adding
the
appropriate
amount
of
heat
automatically
with
the
proportional
controller.
The
chamber
tempera-
ture
was
read
and
recorded
using a c
hromel-alumel
thermocouple
lo
ca
ted
within
the
chamber
through
a
pressure
seal.
Although
it would
have
been
marginally
desirable
to
con
trol
the
chamber
with a
sensing
element
within
the
chamber,
this is very difficult,
because
of
the
massiven
ess
of
the
chamber
and
the
difficulties e
ncountered
in
using
suitable
sensing
elements
at
elevated
pressures.
As a
result
a
transi
e
nt
was
introdu
ced
in
the
c
hamber
temperature
when
a
constant
rate
of cooling
was
initiated
or
terminated
in
the
bath
. A
steady
state
of
0.4
°c
difference
between
bath
and
chamber
temperatures
at
a
rate
·
of
cooling ' of
5 °C/h was
rea
che
d in
about
20 min.
This
transient
res
ponse
was
of
no
conseq
uence
in
these
measurements
because
the
run
s
were
initiated
well
in
the
liquid regions
and
terminated
in
the
g
la
ss
.
In·
both
of
these
regions
the effect
of
thermodynami
c history is insignificant
over
the
time
scales
which
were
used. By
separate
ex-
periment
at
atmospheric
pressure
at
the
same
cooling
rate,
the
c
hamb
er
temperature
(at
the
thermocouple)
and
sample
temperature
were
found
to
be
the
same
within
the
experimental
uncertainty.
The
pressur
e
chamber
with
glass
windows is
similar
to
that
used
by
Martin
and
Mandelkern
[10].
Di(ethyl hexyl)
sebacate
was
used
as
the
pressure
transmitting
fluid.
The
pressure
was
generated
by a
hand
screw
pump
and
measured
with a 16-in
bourdon
tube
gage.
The
bourdon
gage is
calibrated
periodically
against
a
dead
weight piston gage.
In
the
isobaric
cooling
runs
the
pressure
was
held
constant
by
manual
adjustment
to co
mpensate
for
the
pressure
drop
resulting
from
the
volume
contractions
of
the
con-
stituents
in
the
pressure
c
hamber.
In
past
experience
the
windows
were
found
to
be
in
danger
of
fracture
at
pressures
in
excess
of
1
kbar.
Accordingly, for a
reasonabl
e
margin
of
safety,
the
maximum
pressure
was
restricted
to 800 bar.
2.2.
Dilatometer
(o) Design
The
dilatometer
is a
composite
version which
is
described
in
detail
in
reference
[11].
Only
a
brief
description
is given
here
for
which
a
schematic
diagram
is
shown
in figure
1.
Mercury
was
used
as
a
confining fluid.
The
sample
of
polymer
(0)
was
inserted
into
thimble
(M), which
at
high
temperatures
prevented
the
molten
sample
from
en
t
ering
bore
(B).
The
slots
(N) in
the
thimble
facilitated
evac
uation
after
assembly
of
the
dilatometer.
Sample
bore (P), which is
optional,
reduced
the
thermal
relaxation
time
of
the
sample.
(This is
true
only
if
a s
trong
conductor
like
mercury
is
used,
as
in
this
case,
for
the
confining liquid.)
The
sample
and
thimble
were
inserted
in
cavity
(F)
which
A
B
c
D---..JrIr---hl
E
F
:~:
J
'\
~K
\
L
FI
GU RE
1.
Schematic
diagram
of
the dilatometer: (A)
tap
er
ed
seal,
(B) capi
llar
y bore,
(C-L)
brass
clamp,
(D) rubber
"0"
ring, (E)
female
thr
ead, (F) cavit
y,
(C) flange,
(H)
rubber
"0"
ring, (I)
matin
g surface,
(J)
stainless steel base,
(K)
mal
e thread, (M)
thimble,
(N)
slots,
(0)
sample,
(P) sample bore.
was
closed
with
stainless
steel
base
(J).
The
base
was
secured
by
screwing
a
brass
clamp
(C-
L), having very
fine
threads,
until a
seal
was
made
completely
by
contact
between
flange
(G)
and
surface
(I).
The
dilatometer
was
then
evacuated
and
filled with
mercury.
The
chief
advantage
of
a
composite
dilatom·
eter
with
respect
to
polymers
is
that
no
heat
sealing
of
the
glass,
from which
there
would
be
the
danger
of
damaging
the
sa
mple
, is
necessary.
This
composite
dilatometer
was
found
to be
as
stable
over
many
cycles
of
varying
temperature
and
pressure
as
the
unit
construction
type.
(b)
Operating
Equations
The
operating
equations
for
the
dilatometer
relate
the
experimental
observables,
which
are
temperature,
pressure,
and
displacement
of
the
mercury
column,
to
the
corresponding
density,
or
specific
volume,
of
the
sample.
In
the
derivations
of
these
equations
it is
assumed
that
the
volumes
of
the
dilatometer
constit·
uents
are
additive,
and
all
deformations,
including
those
of
the
dilatomer
itself
are
homogeneous.
The
assumption
of
volume
additivity
implies
that
the
associated
compliances,
!:J.VdP,
are
additive
under
hydrostatic
conditions.
The
total
available volume V
of
the
dilatometer
up
to
the
meniscus
of
th
e
mercury
column
taken
at
some
333
arbitrary
reference
condition
is
(1)
where
V
T
, V
s
,
and
V
Hg
are
the
volumes
of
the
thimble,
sample
and
mercury
at
conditions
T,
P.
The
sub-
script
0
indicates
that
these
quantities
are
taken
at
reference
conditions
To,
Po.
At
general
conditions
T, P
the
available
volume
up
to
the
reference
reading
ho
is
where
r is
the
capillary
radius
and
h is
the
height
of
the
mercury
column
at
conditions
T,
P.
The
right-
hand
term
is
therefore
the
volume
of
mercury
above
the
referen
ce
reading
.
The
temperature
and
pressure
dependences
of
the
dilatometer
glass
contained
in
the
terms
V-V
T
and
r
may
be
expressed
explicitly
by
rewriting
eq
(2)
as
V s = x
3
(V
- V
T)
25 - V H g +
7Txr~
5
(h - h
o
)
(3)
where
x is
an
effective
extension
ratio
approximated
linearly by
x
3
= 1 +
ao(T
- 25) - {3oP.
The
values
ao
= 0.99 X
1O
-
5°C
- 1 [12]
and
{3o
= 2.92 X
10-
5
bac
l
[13],
taken
as
constants,
are
the
thermal
expansivity
(cubic)
and
compressibility
of
boro-
silicate glass
taken
at
25
°C.
The
linear
dependence
of
the
right-hand
term
of
eq
(3)
on
x
results
from
the
fact
that
the
radius
and
the
distance
between
any
two
graduations
on
the
capillary
both
vary linearly with
x.
Accordingly,
the
multiplying
factor
is x
2
/x
= x.
If
the
readings
were
read
solely
with a
cathetometer
(at
ambient
conditions)
the
right-
hand
term
would
depend
upon
x
2
•
In
our
work
the
cathetometer
was
used
only to
interpolate
between
adjacent
graduations.
From
eq
(3)
the volume
available
for
the
sample
and
mercury
at
reference
conditions
is
This
result
is
used
to e
liminate
(V
- V
T
)25
in
eq
(3).
With
some
rearrangement
and
division
by
W
s
,
the
sample
mass,
the
final,
desired
result
for
the
sample
specific volume is
obtained:
Vs
=
~
s
{Vso
-
[VH
g-
(VHg)O]
-(1-:~)
[(VH
g
)O+(V
S)o
]+7Txr~5(h-ho)}
.
(4)
In
the
above
equations
the
contributions
to
the
sample
volume given
by
the
terms
in
the
braces
may
be
id
ent
ified
as
the
reference
sample
volume,
the
change
in
the
total volume
of
mercury,
the
change
in
the
available
volume
of
the
dilatometer
up
to
ho
,
and
the
volume
of
mer
cury
above
h
o
•
Since
the
thimqle
is
made
from
the
same
material
(borosilicate
glass)
as
the
dilatometer,
V
T
does
not
enter
into
equation
(4).
The
values
for
the
specific volume
of
mercury
were
taken
from
the
data
of
Carnazzi
[14].
2.3.
Sample
All
measurements
wer
e
made
on
a single
sample
of
high
molecular
weight poly(vinyl
acetate),
grade
A Y
AT,
supplied
by
the
Plastics
Division
of
the
Union
Carbide
Company.3
The
intrinsic
viscosity
[11]
is given
as
0.69 dljg
at
20 °C in cyclohexanone.
The
corres-
ponding
molecular
weight may be
estimated
from
the
Mark-Houwink
Equation
[15],
[11]
=
KM
:
where
Mv is
the
viscosity
average
molecular
weight.
The
values
K=15.8xlO
- 5 dljg
and
a=0.69
are
taken
from
reference
[16] which
apply
to
acetone
solutions
at
20 °C.
Since
acetone
and
cyclohexanone
ha
ve
the
same
solubility
parameter,
0 =
9.9
[17], it is
expected
that
the
above
values
of
K
and
a
are
appli-
cable
to cycl
ohexanone
solutions to within
the
accuracy
desired
here.
Using
these
values
in
the
above
equation,
the
value Mv = 189,000
was
obtained
for
this
sample.
The
viscosity-average lies
between
the
number-
and
- weight-average
molecular
weights,
but
is usually
closer
to
the
weight-average.
The
above
value
of
Mv
is
expected
to
be
sufficiently
high for
Tg
to be
essentially
independent
of
molecular
weight.
The
validity
of
this
assumption
is
indicated
from
the
relation
[18]
where
M is
the
molecular
weight
of
a
monodisperse
polymer.
From
references
[19]
and
[20]4
experimental
values
of
K~,r~nging
over
a
factor
of
two,
may
be
approxi-
mated
by
1.0 X 10
5
for
the
several
polymers
investigated.
Although poly(vinyl
acetate)
was not
included
in the
above
investigations,
it
seems
reasonable
to
assume
that
this value
of
K is also roughly
applicable
to
this
polymer.
Using
the
values
K'
= 1.0 X 10
5
and
M = 190,000 in
the
above
equation,
the
difference
between
Til
and
Ty
x is
only
0.5
°C,
which is
generally
within
th
e
range
of
experimental
uncertainty.
Since
the
presence
of
even
small
traces
of
residual
solvent
lower
s
the
value
of
Til
considerably
[21],
the
following
procedure
was
used
to
remove
the
solvent.
The
PV
Ac
pellets
which
averaged
about
5
mm
in
diameter
were
placed
in a cy
lindrical
glass
tube
with
a
tapered
sea
l
and
diameter
slightly
larger
than
the
thinble
shown in figure L
The
tube
containing
the
sample
was
evacuated
to
less
than
one
torr
(133
Pal
3 Co
mmer
cial materi al used
in
this expe rime
nt
does not impl y reco mm e nd a
ti
on or
endor
se
me nt b y
th
e
Na
ti
on
al
Bur
ea
u
of
Standard
s,
nor d
oes
it
imply
thai
th
e mate ri al
id
entified is n
ecessa
ril y
th
e b
es
t availabl e for th e
purpo
se.
"The
va
lue
of K
'=
1.2 x
10
5
for po
ly
(te
tram
ethyl·p
-s
ilphe nylene)-sil
oxane
is not given
ex plic itl y in
this
referen
ce,
but was obtaine d fro m calculations on
data
obtain
ed the rei n.
334
and
brou
ght up to 120 °C using a sili c
one
oil
bath.
Th
ese
conditions
wer
e
maintain
ed for
about
three
w
ee
ks ,
which
was
more
than
s
uffi
cie
nt
time for the
sam
pI
e weight to stabilize.
Th
e loss
of
weig
ht
over
the
e
ntir
e pro
cess
was
about
1
percent,
whi c h is
attributed
to r
es
idual solvent.
Durin
g this period
th
e pellets
flow
ed
together
and
the
sample
assumed
the s
hape
of
the
co
ntainer.
Over
several
days
the
sa
mple
was
coole d
to room
temperature
.
The
tube
was
broken,
and
one
end
of
the
sample
was
faced
on
a
lath
e to a length slightly
s
horter
than
the
thimble. A two millim e
ter
hole was
drilled
through
the
sampl
e,
as
shown in
fi
gure 1, in
order
to
shorten
the
time
to
r
eac
h the
rmal
equilibrium.
The
final
dimensions
of
th
e
sa
mple shown on
fi
g
ure
1
are
35 X 15
mm
diam
with a 2
mm
diam
bor
e.
A
reference
value
of
the
specific volume for
the
polymer
was
obtained
using
the
usual
hydrostatic
weighing
procedure
[22]. A value
of
0.8487
cm
3
/g
at
40 °C
was
obtained
after
making
the
air
buoyancy
co
rrection
s [23]. 40 °C is a high e nough te
mperature
for
the
sample
to
reach
viscoelastic
equilibrium
in a
short
time
and
low
enough
not to
unduly
complicate
the
hydrostati
c weighing
proc
e
dur
e.
'.2
.4. Ther
modynam
ic Hist
or
i
es
and
Re
la x
at
ion
al
Behav
ior
As
stated
earlier
the
thermodynami
c hi story
of
a
polyme
r,
or
glassforming
liquid,
has
co
nsid
e
rable
influence on the
experimental
prop
erti
es
in
the
tran-
sition
and
glass regions. In this work
comparisons
were
made
betw
ee
n
data
obtained
from
the
histori
es
us
ed to form
the
glass. All
of
th
ese
involve d co
mmen
c-
ing a
"run"
at
true
equilibrium
in
th
e liquid region,
where
the
prope
rties
are
independent
of
history,
and
forming
the
g
la
ss
isobarically
at
differe nt pr
ess
ures
at
a
constant
rate
of
cooling
at
5 °
C/hr.
This
rate
is
small
enough
to
essentially
maintain
the
rmal
equilibrium
within
the
sample.
The
co
nstant
rat
e
was
te
rminat
ed
at
some
temperature
well within
the
glassy region
characterized
by viscoelastic relaxation
times
suffi-
ciently
long
in
comparison
to
experimental
times
that
no
further
changes
in de nsity with time
at
c
onstant
te
mperature
were
observed.
Subsequent
measure-
ments
in
the
glass
wer
e
taken
by an
accelerated
procedure.
A typical
volume-temperature
curve
obtained
by
isobaric
cooling
at
constant
rate,
used
to form
the
glass,
is
shown
schematically
on
figure 2a.
The
glass tem-
perature,
T
g
,
is
manifested
here
by the
rapidly
changing
slope as shown.
In
the
liquid
region
at
temperatures
well above T
g
,
for
example
T
a
,
th
e
time-dependent
response
in volume
resultin
g from a s
udd
en c
hange
in
temperature
or
pr
ess
ure
is shown on figure
2b,
where
two relaxation 5
processes
may
be re alize d.
The
first is a vis co
elastic,
or
structural
relaxation,
which
may
be
co
mpleted
so
rapidly
at
very high tem-
peratures
that
it will
not
be
observed
by this tec
hnique.
The
second
is a
thermal
relaxation,
which
results
from a
time
dependent
macroscopic
distribution
of
5 M ore stric tly , " reta rd
ation"
is use d to ex
pr
ess
time-depen
den
t strain
at
c
onstant
s
tr
ess
in c
ontra
st to " relaxation" for
time-depend
ent s
tr
ess
a l con stant strain. In thi s work " relax-
ation" is u
se
d
in
a more general se n
se
10
co
ver both.
>
> Vi
scoe
la
s
tic
Relaxation
>
Therma
l
Re
la
xa
t
ion
(a)
T
(b
)
log
t
(c)
log
t
Liquid
1 V£
a
Th
er
mal
Relaxation
~
V
iscoe
la
stic
Re
la
x
ation
V
R
FIGURE
2.
Relaxational Response
in
Liquid
and
Class.
te
mperatur
es
and
co
rr
es
ponding
de nsities over
the
sa
mple
and
apparatus
c
omponents
equilibrating
through
heat
tran
sfer.
Th
e
inf
or
mation
obtained
from
th
ermal relaxations is
of
no
int
er
es
t he re.
In
our
work
the
thermal
relaxations
e
quilibrat
ed in
about
20 min
essentially
ind
e
pendent
of
temperature
and
pres
sure.
At
th
e co
nclusion
of
both
relaxations
the
true
equi-
librium
value,
VI,
was
obtained.
A
se
t
of
valu
es
in
the
liquid region was
obtained
by rapidly c
hanging
the
temperatur
e
or
pressure
to
th
e
desired
valu
es
and
allowing
true
equilibrium
to
be
attain
ed
at
e
ach
point
.
This
procedure
reaching
either
tru
e
or
apparent
equi-
librium
at
each
point
is
referred
to
here
as
the
tem-
perature-pres
s
ure
jump
method
.
As a
result
of
the
larg
e
increase
in
vi
scoel
asti c relax-
ation
tim
es
with
de
c
r
eas
in
~
temp
e
ratur
e
and
the
constancy
of
the
thermal
relaxation tim
es,
the
order
of
the
two
relaxation
proce
sses
is re versed
at
tem-
perature
s well below
Tg.
Figure
2c shows
the
time-
dep
e
nd
e
nt
response
r
es
ulting from
thermodynamic
r
es
pon
se
in
th
e glass,
say
at
T
b
,
on figure 2a.
The
thermal
re
laxation
is
completed
in
about
the
usual
20 min followed by
the
viscoelastic
one
which
may
be
e
xtended
over
many
years
depending
upon
the
tem-
pe
rature
and
pressure.
Since
the
observed
volume
is
essentially
stationary
during
and
well
after
the
thermal
relaxation,
th
e value
of
volume
obtained
at
the
comple·
tion
of
the th
er
mal
relaxati
on
appears
to
have
reached
335