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Evolution of the Dynamics in 1,4-Polyisoprene from a Nearly Constant Loss to a Johari-Goldstein -Relaxation to the R-Relaxation
Evolution of the Dynamics in 1,4-Polyisoprene from a Nearly Constant
Loss to a Johari-Goldstein -Relaxation to the R-Relaxation
C. M. Roland,*
,
M. J. Schroeder, J. J. Fontanella, and K. L. Ngai*
,
Naval Research Laboratory, Washington, D.C. 20375-5320, and United States Naval Academy,
Annapolis, Maryland 21402
Received December 1, 2003; Revised Manuscript Received January 15, 2004
ABSTRACT: The Johari-Goldstein (JG) secondary relaxation, presumed to be universal, has never been
seen in 1,4-polyisoprene (PI) by dielectric spectroscopy, despite very many measurements extending over
the past half-century. By using a high-resolution capacitance bridge, we are able to show the existence
of a secondary relaxation in PI that has the properties of the JG process. Measurements were also carried
out at lower temperatures, which probe the dynamics of chain units caged by neighboring segments
comprising the local structure. The caged dynamics precede by decades of time the JG relaxation and,
from general physical principles, are also expected to be a property of all glass-forming materials.
Collectively, the caged dynamics and JG relaxation serve as precursors to structural relaxation (i.e., the
glass transition) and thus are of central importance to understanding vitrification. The present data
show that the dynamics of caged PI repeat units are manifested as a nearly constant loss (NCL). This
NCL has been found in other glass-formers, both molecular and polymeric, and its temperature dependence
in PI is similar to that for other materials. The experimental results are consistent with the predictions
from the coupling model.
Introduction
Substances having diverse chemical and physical
structures vitrify, with the glass transition phenomenon
characterized by dynamic and thermodynamic proper-
ties common to all glass-formers. An immense amount
of experimental data has been accumulated over the
years, particularly on the structural R-relaxation; nev-
ertheless, a consensus regarding a theory of the glass
transition is lacking.
1,2
Fundamental understanding
requires examination of the dynamics that precede
(earlier in time) the cooperative R-relaxation, since these
faster processes serve as the precursor to structural
relaxation. At early times, before either rotational or
translational diffusion has transpired, molecular mo-
tions are confined to a cage, defined by the intermo-
lecular potential of neighboring molecules. For molec-
ular glass-formers, caging is effected by the neighboring
molecules, while for polymers, a segment is caged by
segments from other chains as well as repeat units from
the same chain. In both cases, the caging is effected by
intermolecular (intersegmental) repulsive forces. The
short time dynamics within the cage, occurring before
the onset of structural relaxation, are of fundamental
interest. One familiar short-time process is the second-
ary relaxation, which is local (noncooperative) and
thermally activated. However, at times shorter than the
secondary relaxation, but longer than the Boson peak
or Poley absorption,
3
the motions of the caged molecules
are not well understood. Herein, we refer to the pro-
cesses in this regime as caged dynamics.
The best-known description of the caged dynamics is
from mode coupling theory (MCT),
4
based on nonlinear
coupling of density fluctuations in condensed matter.
According to MCT, the caged relaxation is the so-called
fast -process, which transpires at temperatures above
a critical temperature, T
c
. When the time dependence
of this -process is Fourier transformed to a susceptibil-
ity, the imaginary part, (), has a minimum defined
by two power laws,
-b
and
a
, on the respective low-
and high-frequency sides. The exponents a and b are
related by the equation [
2
(1 - a)/(1 - 2a)] ) [
2
(1 +
b)/(1 + 2b)], where is the gamma function. The
susceptibility minimum has a frequency dependence
that bears no resemblance to the loss associated with a
relaxation process, and hence the fast -process of MCT
is not a relaxation in the conventional sense. Note that
the MCT -process is distinct from the above-mentioned
secondary relaxations commonly observed in glass-
formers; the latter are genuine relaxations, involving
local rotation and/or translational diffusion (in MCT
parlance, these comprise the slow -process). According
to MCT, the fast -process is followed by the R-relax-
ation, described by the Kohlrausch-Williams-Watts
(KWW) function
where
R
is the R-relaxation time and
KWW
is a fraction
less than unity.
5,6
Thus, MCT regards its putative
-process to be the precursor of structural relaxation.
The MCT description of caged dynamics is restricted
to temperatures above T
c
. However, there exists a
plethora of experimental data for both above and well
below T
c
, which must be reconciled with any theoretical
description. At lower temperatures, the duration over
which molecules are caged is extended because the
primary and secondary relaxations that cause decay of
the cage are slower. Since the caged dynamics continues
to longer times at lower temperatures, it should be
experimentally observable over a wider frequency range
at T < T
c
than for T > T
c
. Dielectric data for both small
molecules and polymers show
7-12
that at lower temper-
atures the caged dynamics can be described by a slowly Naval Research Laboratory. United States Naval Academy.
* To whom correspondence should be addressed. E-mail: roland@
nrl.navy.mil. (t) ) exp[-(t/
R
) KWW
]
(1)
2630
Macromolecules 2004, 37, 2630-2635
10.1021/ma0358071
This article not subject to U.S. Copyright.
Published 2004 by the American Chemical Society
Published on Web 03/06/2004 decreasing function of frequency, -
(where is a
small positive exponent), or as a logarithmic function
of . Similar behavior is found in glassy, molten, and
even crystalline ionic conductors for temperatures at
which the ions are caged and thus unable to move to
another site in the experimental time range.
7
The
variation of this dispersion with frequency is very weak,
and hence, in the field of ionic conductors, it is referred
to as the nearly constant loss (NCL). A good example is
the glass-forming molten salt, 0.4Ca(NO
3
)
2
-0.6KNO
3
(CKN), which is both a glass-former and an ionic
conductor.
7
The observation of the NCL in glass-formers is not
limited to dielectric relaxation measurements. Dynamic
light scattering experiments on polyisobutylene,
13
poly-
(methyl methacrylate),
14
and glycerol
14
have revealed
a nearly constant loss in the imaginary part of both the
depolarized and polarized susceptibilities, (), at high
frequencies (gGHz) for temperatures ranging from
below T
g
to near or above T
c
. Studies of several organic
glass-forming liquids
15
found a power law decay of the
optical Kerr effect response given by t
-1+c
, where c 0.1 at temperatures below the T
c
of MCT. Since the
optical Kerr effect signal is the Fourier transform of the
imaginary part of the susceptibility,
15
the latter is a
nearly constant loss.
At high temperatures, NCL as a background loss can
give rise to a minimum in the susceptibility, having
-b
and
a
dependences on the low- and high-frequency
sides. This occurs at high temperatures (such as above
T
c
), when
R
becomes short. Then, the temporal extent
of the NCL is reduced by the encroaching high-
frequency flank of the R-loss peak, which has a
-
KWW
dependence on the low-frequency side (viz., the one-
sided Fourier transform of eq 1), which can give rise to
the
-b
dependence of the susceptibility minimum. On
the high-frequency side, there is always a contribution
from the low-frequency flank of the Boson peak or Poley
absorption. Thus, the structural relaxation at high
temperatures (for which
R
is typically on the order of
nanoseconds), in combination with the Boson peak and
the NCL, can yield a minimum in the susceptibility, as
observed by dielectric, neutron, and light scattering
experiments at sufficiently high temperatures.
4
This
explains why
R
invariably has this magnitude (
10
-9
s) at T
c
, where T
c
is obtained by extrapolation of the
MCT scaling laws. It is also obvious that the suscepti-
bility minimum predicted by the standard MCT cannot
account for the NCL.
At T
c
and above, with
R
in the range of nanoseconds,
all nontrivial secondary relaxations have merged with
the R-relaxation. Under these conditions, the claim of
MCT that the caged dynamics is the precursor of the
R-relaxation has validity. However, at lower tempera-
tures, the secondary relaxation and the R-relaxation
become well-separated in time. Since the secondary
relaxation falls intermediate in time between the faster
caged dynamics and the slower R-relaxation, evidently
the secondary relaxation must play some role in the
development of the R-relaxation. However, it is not