4.1. Temperature-Dependent Measurements
At the beginning, Young’s modulus (E) of unannealed and annealed PMMA and DR1/PMMA fibers is measured at room temperature. The results in
Table 1 show that Young’s modulus
E in DR1/PMMA fibers is greater than in PMMA fibers and is lower in annealed fibers compared with the unannealed ones.
Young’s modulus as a function of temperature determines the effect of heating and population changes on the stiffness of the samples. Samples are heated from 296.15 °K to 323.15 K in 3 K increments and their elasticity is measured.
Figure 4 shows Young’s modulus as a function of temperature for unannealed and annealed plain PMMA and DR1/PMMA fibers. The graphs are fitted to the Equation (
10), where
,
T,
, and
are Young’s modulus at
, the oven temperature, the characteristic temperature, and the critical exponent, respectively.
Table 2 summarizes the results of the parameters of the fitting function.
Figure 4 shows that increasing temperature decreases the elasticity of the samples and DR1/PMMA fibers have larger elasticity than plain PMMA fibers. Moreover, annealed fibers show lower Young’s modulus compared with the unannealed ones.
The glass transition temperature
of the fiber material is measured using differential scanning calorimetry (DSC) with a scanning rate of 10 °C/min. The DSC unit is manufactured by Mettler Toledo and has a temperature accuracy of ±0.2 K and precision of ±0.02 K based on metal standards. The samples’ masses are between 2 and 3 mg. The results show that adding DR1 decreases
. Moreover, annealing the samples increases their
. This is consistent with the results of the characteristic temperature
that is derived using the fitting function, which shows that
in annealed PMMA and DR1/PMMA is greater than in unannealed ones. However,
is unchanged between plain PMMA and DR1/PMMA fibers, implying that adding DR1 did not affect the characteristic temperature.
values of the unannealed fibers are the same within experimental uncertainties, as are the annealed ones.
Figure 5 shows the derivative of the heating flow as determined from DSC measurements used to determine
.
Table 3 shows the correlations between various combinations of samples using the data in
Table 2. The first row shows that there is a significant difference between annealed and unannealed PMMA polymer, as determined from the parameter
—the low temperature limit of Young’s modulus, and
—the critical temperature parameter. The difference is not as dramatic for DR1/PMMA. However, adding dye to PMMA has a statistically significant effect on increasing the parameter
. The effect of annealing and dye doping on critical temperature is less obvious, partially due to the fact that the uncertainties are large in the critical exponent
, which affects the accuracy in the determination of
.
In summary, Young’s modulus at room temperature results
The temperature-dependent Young’s modulus of the unannealed fibers are given by
and
The annealed fibers give
and
We observe that adding DR1 to PMMA decreases the glass transition temperature , while Young’s modulus E increases. Annealed samples have a measured in DR1/PMMA fiber that is lower than annealed PMMA fiber, while its E is greater. Moreover, in both fibers, annealing increases and decreases E.
Adding DR1 to PMMA is expected to decrease its
due to DR1’s plasticizing effect on PMMA [
30] and to reduce the stiffness of the polymer compared with the plain PMMA fibers. However, these fibers show that while
in DR1-doped samples decreases, their
E increases. This phenomenon is known as antiplasticization [
2,
25,
26,
27,
28,
29]. Here, it is observed that DR1 molecules can induce an antiplasticization effect that can decreases the mobility of the chains and their free volume and increases the packing efficiency of the sample, which increases the modulus [
2,
25,
26,
27,
28,
29]. Moreover, annealing decreases polymer chain alignment, which reduces their stiffness and increases their entropy [
2]. This process decreases the free volume, thus, yielding a higher
compared with unannealed fibers.
Stress as a function of temperature is measured for unannealed and preannealed DR1-doped and undoped PMMA fibers. The results for the samples that are heated from 293.15 K to 323.15 K over 4 min are shown in
Figure 6. Stress as a function of temperature data is fit to the function
where
T is the sample temperature and the fit parameters are
,
,
, and
n.
These parameters have physical meaning.
is the temperature-dependent stress contribution in the limit of zero temperature while
is a stress offset due to the stress applied by the clamps when the sample is mounted.
is the temperature at which the temperature-dependent stress falls to half its value.
n is an exponent that quantifies the rate at which the stress changes as a function of temperature at
. For samples that have multiple phase transitions, the stress would be a sum over expressions of the form given by Equation (
15)—one for each phase transition. The stress for the temperature range in the present studies is described well by a single transition.
The analytical form of Equation (
15) with the fitting parameters determined from a fit to the data is used to determine
for each fiber for a range of temperatures. Using an analytical fit function provides a cleaner determination of the derivative than would the raw data. The derivative
is related to the thermal expansion coefficient. As the fiber is slightly stretched when mounted to prevent buckling when its length increases, an expanding fiber will result in a decrease of the stress; so,
. This can be understood from the fact that the fiber’s resting length is less than its stretched length at the start of the experiment. If the fiber’s resting length increases due to light actuation, the force read by the sensor decreases as the resting length grows closer to the stretched length, which is fixed by the distance between the clamps.
Figure 7 shows that all dye-doped fibers have a positive thermal expansion coefficient. For temperatures above 308.15 K, the temperature-induced stress change is larger for unannealed DR1/PMMA fibers than for annealed ones. Similarly, the stress derivative
in annealed plain PMMA fiber is lower than in the unannealed ones. So, annealing is observed to decrease the thermal expansion coefficient. Finally, dye-doped fibers show greater thermal expansion than plain fiber, an effect that is most pronounced at the highest temperatures.
To understand the results, we consider two processes that lead to thermal expansion. First, the polymer expands as the temperature increases due to the polymer chains getting excited with thermal energy. Secondly, a change in temperature affects the relative populations of the two isomers of the dopant molecules [
16,
23]. The competition between these two processes determines the net response.
Figure 7 shows that the thermal expansion coefficient of the dye-doped fibers grows relative to the undoped fibers with temperature. The dye dopant appears to enhance the thermal expansion coefficient. The cis isomer population increases at higher temperatures and, given its larger volume, adds to thermal expansion in the DR1/PMMA fibers. The glass transition temperature
is lower in DR1-doped fibers than in plain ones. Since the thermal expansion coefficient increases as the temperature is increased, the larger stress change in DR1/PMMA relative to plain PMMA at a fixed temperature might be explained by this depression in the glass transition in doped polymers. Moreover, annealing the samples increased their
by decreasing their free volume; so, the rearrangement of molecules in the annealed samples is smaller than the unannealed ones, leading to a smaller thermal expansion coefficient in the annealed samples.
Intensity-Dependent Measurements
Here, we characterize the mechanical properties of fibers that are exposed to 488 nm-wavelength light produced by a krypton/argon laser as a function of intensity and polarization. Young’s modulus is measured before, during, and after irradiation to determine the immediate and persistent effects of the light.
Figure 8 and
Figure 9 show typical stress–strain curve data for unannealed PMMA and DR1/PMMA fibers illuminated with vertical and horizontal pump light polarizations.
The flat part in
Figure 8 and
Figure 9 is due to mechanical backlash in the mounts and is excluded when determining Young’s modulus. The stress is observed to decrease during irradiation and persists to varying degrees in both PMMA and DR1/PMMA fibers after irradiation at the maximum intensity. In plain PMMA, the horizontally polarized pump has a larger influence on the stress change than the vertically polarized pump. In both cases, the stress persists when the pump is turned off at the same level as when the pump is on at its maximum intensity.
In dye-doped fiber, the horizontal pump also has the largest influence on the stress change. However, the level of persistent stress after the pump is turned off is less than at its maximum value when the pump is on. These observations imply that the DR1 dopant contributes to the stress change in the presence of light but that its contribution is reversible, while that of PMMA is not. Since these are unannealed samples, the irreversible part of the stress change is most likely due to a light-induced relaxation of the polymer chains, perhaps from photothermal heating.
To observe the process directly in real-time, the light-induced stress at fixed strain is measured as a function of time as the fibers are irradiated with the maximum light intensity in the mW range for 15 min for both horizontal and vertical pump polarizations.
Figure 10 shows the stress as a function of time for unannealed PMMA and DR1/PMMA fibers for 5 min with the pump off, 15 min with the pump on, then 5 min with the pump off. A slight monotonic decrease in stress over time is observed for unannealed PMMA. Upon illumination with 488-nm light, the stress in the DR1/PMMA fiber decreases by about 0.4 MPa. Blocking the pump light after 15 min returns the stress to a level about 0.1 MPa below the starting value. The behavior is the same for both polarizations and for unannealed and annealed fibers.
Stress versus strain curves are used to determine Young’s modulus as a function of absorbed pump intensity for both vertical and horizontal polarization in both plain and dye-doped fibers.
Figure 11 and
Figure 12 show that for both fibers, Young’s modulus is constant before, during, and after irradiation and is not polarization dependent. So, while there is an offset in the strain induced by light, it does not affect the slope of the stress versus strain curve.
Next, we illuminate each sample with maximum light intensity for almost an hour and its Young’s modulus is measured before, during, and after illumination with both polarizations of light.
Figure 13 and
Figure 14 show that visible light does not induce any permanent changes to the Young’s modulus of all the fibers for both polarizations. Since PMMA is transparent in the visible range, no change in its Young’s modulus is expected. It was shown that the elastic modulus of PMMA thin films remains constant upon irradiation with UV and visible light [
48]. Adding an isomerizable dye does not result in a persistent change of Young’s modulus after visible irradiation, but it does induce a persistent and transient stress.
The photomechanical effect in DR1/PMMA fibers is known to be reversible; so, it restores the stress to its initial value [
16]. In contrast, a DR1/PMMA film in which the DR1 dye is grafted as a side chain pendent shows a persistent decrease in the elastic modulus after irradiating the sample with 487-nm light [
33]. In addition, azobenzene-containing films showed that upon visible irradiation the elastic modulus can increase or decrease [
49,
50,
51,
52]. These differences can be due to differences in azobenzene molecules used, sample preparation methods, sample geometry, wavelength, the polarization of the pump light, and the experimental protocols.
To measure the contribution of photothermal heating to the photomechanical stress response, the PMMA fibers are painted with black markers that absorb all of the light, converting all of the energy to heat. These fibers are irradiated with 488 nm-wavelength light and the stress response as a function of time is measured for vertically and horizontally polarized pump light.
Figure 15 shows typical data for the stress versus time for one full cycle of painted fiber. The black points are the smoothed data and the solid curve is a fit to a single exponential. The fit is based on the model developed previously [
16,
23], given by
and
where
,
, and
are the amplitudes, turn-on time constant when the pump is on, and turn-off time constant when the pump is off, respectively.
is the time duration of the beam being on and off.
represents the strength of the photomechanical stress response of the material. This stress, when divided by the intensity of the light
I that induces this stress, is the definition of the photomechanical constant. Details of this definition can be found in the literature [
16,
22].
If the sole mechanism is photothermal heating, as it should be in such painted fibers, then
and
should be the same as the Newton heating and cooling time constants [
23].
Figure 16 and
Figure 17 show the turn-on and turn-off time constants
and
as a function of intensity that are derived using the fitting functions in Equations (
16) and (
17). We will assume that these are the Newton heating/cooling time constants to determine the photothermal heating contribution.
The photothermal heating contribution to the photomechanical response can be determined from Equation (
7).
is determined using Equation (
5).
Table 4 lists the independently determined values of
and
c for PMMA and
w is measured with a caliper for the fiber used in our measurements.
is calculated from the values in
Table 5, which are determined from fits to the temperature-dependent stress as described above. The heating contribution to the photomechanical response are shown in
Figure 18. “|” and “—” denote the response along and perpendicular to the long axis of the fibers, which are mounted vertically [
23].
The photomechanical response for PMMA fibers marked with black ink and DR1/PMMA fibers as a function of temperature cluster at about s/m for both polarizations as well as for the painted and unpainted fibers. The response in painted PMMA fibers is only due to heating. The fact that this is the same as the response in unpainted DR1/PMMA fibers strongly suggests that the contribution of photoisomerization and/or molecular reorientation in DR1/PMMA fibers to the photomechanical response is negligible. Furthermore, the fact that the time constants of the response for both painted and unpainted fibers are the same also suggests that the heating mechanism dominates.
The inset of
Figure 7 shows the photomechanical response for the dye-doped fiber and the painted plain PMMA fiber, unannealed and annealed. There are several important features of the data. First, in all of the fibers, the thermal contribution to the photomechanical response is approximately independent of the polarization of the pump beam. The difference between the two polarizations for each fiber is at most about
% from the mean. As such, the largest contribution from other mechanisms is bounded by
%. Secondly, the photothermal response is smaller when the fibers are annealed. This could be due to the fact that after annealing, the internal stress that adds to the photomechanical response has been released. Further, the photomechanical response for pump beam polarization perpendicular to the strain direction is consistently lower than for the parallel polarization. This effect, though small, could be from the broken symmetry by the uniaxial strain direction. Finally, we find the plain PMMA fibers that are marked with ink have the same photomechanical response as the dye-doped ones when comparing the unannealed ones as well as the annealed ones.
The temperature-dependent figure of merit is also measured to determine if elevated temperature can increase their efficiencies. It is derived using Equation (
11) and is shown in
Figure 19. The result shows that increasing temperature increases the figure of merit and indicates that controlling the temperature can improve the response of such materials. The largest change is for unannealed DR1-doped PMMA, which shows a linear dependence with a slope of 10% K
−1—a dramatic increase.