122
L. V. Karabanova et al.
heated at a rate of 3 ◦ C min −1 . Loss modulus E”, storage modulus (dynamic
modulus) E’ and mechanical loss factor tan δ = E”/E’ as functions of temperature
were measured.
In two cases, for neat PU and for one nanocomposite (PU-MWCNT-ox), the
effective activation energy Q of segmental motion versus temperature dependence
was estimated within the −70 to +150 ◦ C range covering the extraordinarily broadened glass transition range. This was determined from the DMA measurements
performed at frequencies of 0.1, 1 and 10 Hz. Typically, Q values are calculated
by the displacement of temperature in the maximum of the relaxation peak with
frequency; where partial overlap of neighbouring peaks occurs, their separation into
Gaussian or Lorentz peaks is analyzed. However, very complicated DMA spectra
in the broad temperature region of the glass transition were observed for the PU
network and PU-based composites (see below) suggesting the substantial overlapping of a few constituent peaks, that is, the pronounced dynamic heterogeneity
within the glass transition range. This prevented the possibility for calculating the
strict Q values. Therefore, we chose the nontraditional way for estimating, semiquantitatively, a tendency of changing Q with temperature over the temperature
range of the glass transition. This was performed proceeding from the displacement
of the experimental points in the complicated tan δ spectrum along temperature axis
with frequency at a series of chosen tan δ levels, using the initial equation for a
frequency of relaxation acts (ν = ν 0 exp. (−Q/RT)), and the resultant relation:
Q = 0.038T 1 T 2 / (T 2 − T 1 ) kJ mol
−1
(8.5)
where T 1 and T 2 (in Kelvin) relate to the temperature points in the DMA spectra
obtained at 0.1 and 10 Hz, respectively, for a chosen mechanical loss level.
8.2.2.7 Laser-Interferometric Creep Rate Spectroscopy (CRS)
CRS, an original high-resolution method of relaxation spectrometry and thermal
analysis, allows the characterization in a discrete way of the dynamics, dynamic
heterogeneity and creep resistance of materials over a broad temperature region; the
CRS setups, experimental technique and numerous possibilities have been described
in detail elsewhere [29]. This technique comprises precise measuring of creep rates
at a constant low stress, much less than the yield stress, as a function of temperature
(creep rate spectrum). To this end, the laser interferometer, based on the Doppler
effect, is used. The time evolution of deformation is registered as a sequence of
low-frequency beats in an interferogram whose beat frequency ν yields a creep rate:
˙
ε =
λv
2I 0
(8.6)
Here λ = 630 nm is a laser wavelength, and I 0 is the initial length of the
working part of a sample. The film samples with 0.6 × 10 mm 2 cross-section and
L. V. Karabanova et al.
heated at a rate of 3 ◦ C min −1 . Loss modulus E”, storage modulus (dynamic
modulus) E’ and mechanical loss factor tan δ = E”/E’ as functions of temperature
were measured.
In two cases, for neat PU and for one nanocomposite (PU-MWCNT-ox), the
effective activation energy Q of segmental motion versus temperature dependence
was estimated within the −70 to +150 ◦ C range covering the extraordinarily broadened glass transition range. This was determined from the DMA measurements
performed at frequencies of 0.1, 1 and 10 Hz. Typically, Q values are calculated
by the displacement of temperature in the maximum of the relaxation peak with
frequency; where partial overlap of neighbouring peaks occurs, their separation into
Gaussian or Lorentz peaks is analyzed. However, very complicated DMA spectra
in the broad temperature region of the glass transition were observed for the PU
network and PU-based composites (see below) suggesting the substantial overlapping of a few constituent peaks, that is, the pronounced dynamic heterogeneity
within the glass transition range. This prevented the possibility for calculating the
strict Q values. Therefore, we chose the nontraditional way for estimating, semiquantitatively, a tendency of changing Q with temperature over the temperature
range of the glass transition. This was performed proceeding from the displacement
of the experimental points in the complicated tan δ spectrum along temperature axis
with frequency at a series of chosen tan δ levels, using the initial equation for a
frequency of relaxation acts (ν = ν 0 exp. (−Q/RT)), and the resultant relation:
Q = 0.038T 1 T 2 / (T 2 − T 1 ) kJ mol
−1
(8.5)
where T 1 and T 2 (in Kelvin) relate to the temperature points in the DMA spectra
obtained at 0.1 and 10 Hz, respectively, for a chosen mechanical loss level.
8.2.2.7 Laser-Interferometric Creep Rate Spectroscopy (CRS)
CRS, an original high-resolution method of relaxation spectrometry and thermal
analysis, allows the characterization in a discrete way of the dynamics, dynamic
heterogeneity and creep resistance of materials over a broad temperature region; the
CRS setups, experimental technique and numerous possibilities have been described
in detail elsewhere [29]. This technique comprises precise measuring of creep rates
at a constant low stress, much less than the yield stress, as a function of temperature
(creep rate spectrum). To this end, the laser interferometer, based on the Doppler
effect, is used. The time evolution of deformation is registered as a sequence of
low-frequency beats in an interferogram whose beat frequency ν yields a creep rate:
˙
ε =
λv
2I 0
(8.6)
Here λ = 630 nm is a laser wavelength, and I 0 is the initial length of the
working part of a sample. The film samples with 0.6 × 10 mm 2 cross-section and