3.1. Phase Behaviour of Ferroparticles in a Liquid Crystal Polymer
Mixtures of the nematic polymer, CBZ6, with different quantities of ferroparticles were prepared in the way described above and observed under a polarizing optical microscope. Selected images are shown in
Figure 7; as the ferroparticle content was increased to around 1.42% by volume, black objects were observed in the mixture (
Figure 7a). As the ferroparticle content was increased further, the quantity of these objects was increased and the birefringence decreased; at around 5.68% by volume of added ferroparticles, a black network was observed in the liquid crystal texture (
Figure 7c). These dark objects were also observed in the isotropic phase and were unchanged in the presence of a magnetic field, although here the birefringence became directional if the polymer was in its nematic phase.
At low concentrations of ferroparticles, the liquid crystal texture appears unchanged; for example, at 1% there appears to be no phase separation. At higher concentrations phase separation occurs; the ferroparticles formed aggregates in the liquid crystal polymer matrix. At the highest concentrations examined, the ferroparticles formed a network structure within the liquid crystal polymer, which became denser with increasing concentration. This network’s formation was related to a decrease in the birefringence.
The influence of the ferroparticles on the phase behaviour was further monitored by measurement of the nematic isotropic transition temperature; the data are presented in
Figure 8. All the samples were prepared by casting films from dichloromethane and so are directly comparable. Small quantities of ferroparticles added to CBZ6 increased its T
NI by up to 2 °C. The addition of ferroparticles has also been reported to increase the smectic A-to-nematic transition temperature in another liquid crystal system [
18]. The behaviour of this system is broadly in line with theoretical expectations [
19]. Once a plateau had been reached, the T
NI was reduced by the addition of further ferroparticles; thus, a small quantity of ferroparticles stabilizes the liquid crystal phase, but once a certain concentration is reached it acts as an impurity and starts to reduce the stability of the liquid crystal phase, causing some phase separation.
3.2. Monodomain Formation
The alignment of the sample to form a monodomain can be observed both from light intensity measurements (see
Figure 5 above) and from WAXS measurements.
Figure 9 shows a plot of the intensity of X-ray scattering recorded parallel and perpendicular to the monodomain director or the direction of the applied magnetic field. The intense broad peak at Q~1.44 Å
−1 arises from the short-range correlations between the mesogenic side chains, and the azimuthal variation in this peak is used to evaluate the global orientation parameter <P
2>, which is the product of the nematic order parameter S and the domain director orientation parameter <D
2> [
20]. This process of quantitative evaluation is described in [
21,
22] and is a mathematically robust procedure which is summarized below. The scattering pattern I(|
Q|,
α) is expressed as a series of amplitudes of spherical harmonics I
2n(|
Q|), where only the even harmonics are required due to the presence of an inversion centre in the scattering pattern [
21]. The amplitude of each harmonic is evaluated using Equation (3) [
21].
where
P2n(
cos α) are a series of Legendre polynomials. The global orientation parameters <
P2n(
cos α)> can be found at a |
Q| value corresponding to the maximum intensity of the structural element of interest using Equation (4)
where
are the values calculated for the scattering from a perfectly aligned structure. Reference [
22] gives some values for common structures. In this study, the scattering arising from the correlations between the mesogenic side groups was used, which gives a peak in the scattering at |
Q|~1.44 Å
−1 which intensifies in the equatorial section. The advantage of using this feature is that it is a more intense feature in the scattering pattern and it is well separated from other structural features.
Figure 10 shows a plot of the I(α) at a fixed value of |
Q|= 1.44 Å
−1, which is used to evaluate the global orientation parameters <
P2n>. The plot shows the symmetrical curve which is inherent to the scattering data for a weakly absorbing sample such as CBZ6. The intensification of the peak at 90° and 270° directly indicates that the long axis of the mesogenic groups lies parallel to the magnetic field direction, as is expected for mesogens which exhibit a positive diamagnetic anisotropy. A more complete structural analysis is given in Reference [
16].
Figure 11 shows the plot of the global orientation parameter against time in a magnetic field of 2.1 T. As can be seen, there is a rapid increase in orientation followed by a more gradual increase to eventually reach a steady value; by which time the cross-linking reaction is complete. From this it is possible to identify a value of time at which the orientation value reaches 50% of its final value (the alignment time) and this provides us with a route to understanding the factors which influence the rate of alignment.
Figure 12 shows the variation in the alignment times as a function of the applied magnetic field strength. The plot shows the strong effect that the magnetic field strength has on the alignment time. The magnetic fields used in this work are at their limit due to the saturation of the magnetic field in the iron core pole pieces. Larger magnetic fields are available with air-cored magnetics, as in the case of superconducting magnets, where fields up to 45 T are possible. Clearly, heating the sample in a cryogenically cooled bore is more challenging than the methodology presented here. It is interesting that the alignment times follow the 1/B
2 model (Equation (2)).
On the basis of our previous experience forming monodomains [
11], it was expected that that the molecular weight would have a strong influence on the alignment times.
Figure 13 shows the global orientation parameter <P
2> plotted against time in a fixed magnetic field of 2.1 T and at 90 °C for two liquid crystalline polymers, CBZ6 (SIP 198) and SIP 127, with differing molecular weights but that are otherwise chemically equivalent (see
Table 1). The lower-molecular-weight sample aligns much more rapidly. These differences can be attributed to the greater viscosity of the higher-molecular-weight polymer. The ratio of their alignment times is more than a factor of 16.
The techniques used to probe the orientation of the liquid crystal polymers were also used to evaluate the behaviour of mixtures of the polymer with ferro nanoparticles. Wide-angle X-ray scattering was used to probe their intermediate-range structure (distances between neighbouring molecules). The curves in
Figure 14 are essentially the same as those shown in
Figure 9 for the polymer, apart from the superposition of some small sharp Bragg reflections arising from the magnetite in the nanoparticles. It is clear from the comparison of the curves in the parallel and perpendicular sections that the magnetite scattering is isotropic. This was confirmed by azimuthual sections at peak positions for the magnetite [
23] (for example, at |
Q| = 2.1 Å
−1(220), |
Q| = 2.48 Å
−1(311), |
Q| = 3.89 Å
−1(511), and |
Q| = 4.26 Å
−1(440)). The background in these sections is higher than the polymer alone due to the X-ray fluorescence of the iron. For these samples, the Kapton substrate used in their fabrication before measurement of their X-ray scattering has not been removed and so this also contributes to the background, and this is also shown in
Figure 14.
Figure 15 shows the development of the global orientation parameter <P
2> over time for samples of the polymer plus a small fraction of nanoparticles. A comparison of the two curves in
Figure 15 shows a remarkable change in the alignment time with the addition of ferro nanoparticles. The time taken to reach 90% of the maximum value of <P
2> observed was reduced by a factor of 4 by the addition of 0.28%
v/
v of ferroparticles.
In order to develop an understanding of the mechanism of action and the optimum fraction of ferroparticles, a range of polymer films with different compositions, ranging from 0.07% to 28.4% of the inorganic material, were prepared and their alignment time evaluated through repeated X-ray scattering measurements.
Figure 16 shows the maximum value of <P
2> for each composition held in a magnetic field of 2.1 T at a temperature of 110 °C. There are two regions to this plot. At lower concentrations of ferroparticles, the value of <P
2> appears to exhibit a more or less constant value; the second region shows a rapidly reducing value above a concentration of 0.52%. In the first region, the ferroparticles appear to enhance or at least stabilize the maximum value of <P
2>, whereas above a volume fraction of 0.52%, orientational order appears inhibited.
Figure 17 shows a plot of the alignment times of the monodomains formed from a mixture of the polymer CBZ6 and a small fraction of ferroparticles; remarkably, the alignment time is independent of the applied magnetic field. Note that for the mixture with 0.28% ferroparticles, this invariance could be observed at a very low field of ~0.15 T, this was the lowest field which could be obtained from the electromagnet used in the preparation system due to the remanent magnetisation of the iron pole pieces. To emphasize this remarkable observation, the alignment time τ is invariant with the magnetic field from 15 T to 2.1 T. This is in marked contrast to the alignment times for the monodomains prepared from the polymer, which show a strong dependence on the strength of the applied magnetic field, as shown in
Figure 12.
The first proposal of mixing ferroparticles with liquid crystals was made by de Gennes and Brochard in a paper published in 1970 [
24]. They suggested that there was both a magnetic field effect on liquid crystal alignment due to the anisotropic magnetic field surrounding even a spherical particle and a mechanical effect due to the elongated particle that they used. The invariant nature of the alignment time with the magnetic field in the current work suggests that there is indeed another alignment mechanism in place which is strong enough to mask the inherent magnetic field effect due to the diamagnetic anisotropy of the mesogenic units.
Ferrofluids, essentially a suspension of magnetic particles in a carrier fluid, were first developed in the 1960s and subsequently developed for a wide variety of applications [
25,
26], ranging from rocket fluid [
26] through to magnetic hyperthermia in medical physics [
27] and to fluid seals [
28]. Magnetic polymer composites offer the potential for the controlled release of bioactive materials; for example, as coatings on implants [
29]. Due to their size, nanoparticles are readily magnetized but usually have no magnetization when the applied magnetic field is removed; consequently, they readily form dipolar chains of nanoparticles [
30]. Zubarev et al. [
19] have developed a theoretical model (which predicts the mean number of particles
in a chain due magneto-dipole inter-particle interactions as shown in Equation (5):
where
ϕ is the solid fraction and
λ is the dimensionless coupling coefficient, which is a measure of the strength of particle–particle interactions and determines the probability of aggregate formation due to magneto-dipole interactions.
λ can be derived using Equation (6):
where
Md is the saturation moment of the bulk,
V is the particle volume, and
μ0 is the permeability of the free space. To give an example, for a 10 nm magnetite particle at 298 K with
Md = 466 kAm
−1, n = 1.36, so little chaining occurs. However, for a 13 nm particle n is infinite. In this situation
λ~0.4 and this is the regime under which long chains are formed. A
λ ≥ 3 is required for spherical aggregates. At higher concentrations, Dubois et al. [
31] observed a cellular-like structure.
It is to be expected that the chains of ferroparticles form parallel to the magnetic field and present a series of internal surfaces in a similar manner to polymer stabilized liquid crystals [
32]. Just as the interactions with any surface will affect the alignment of the nematic domains, we propose a simple model to explain the results in
Figure 17. In the absence of an external magnetic field, the ferroparticles are randomly arranged. Realistically, it is difficult to place the sample in a zero magnetic field due to the earth’s magnetic field of ~30 μT. Increasing the applied magnetic field to 0.15 T is sufficient to align the chains of the nanoparticles; the response time will depend on the threshold magnetic field, the viscosity of the polymer, and the number of internal surfaces. The latter gives rise to the composition dependence shown in
Figure 17.
Figure 16 shows the dependence of the maximum value of <P
2> observed during the formation of the monodomain. Clearly, all of the compositions in the first region of this plot are sufficient to drive the domain alignment towards a monodomain, and we attribute this to the fact that these chains are organized in a parallel 2D manner. As the proportion of ferroparticles increases, the morphology of the chains becomes more 3D [
30] and starts to inhibit monodomain formation.
In order to explore whether there is any additional evidence to support this chain model of the invariance of the monodomain formation time, both laser and X-ray scattering were used to probe the appropriate samples. A dispersion of ferroparticles in kerosene readily yields a highly anisotropic light scattering pattern between crossed polarizers lying normal to the applied magnetic field direction. The characteristics of the light scattering yielded objects 24 µm long and 5 µm wide. The external surface of a cross-linked sample of the polymer with a 0.28% volume fraction of ferroparticles showed a rippled surface when examined under a scanning electron microscope, with ripples which were µm wide. Although it is tempting to associate these with the chains of particles, the work of Zubarev et al. [
19] predicts this rippled surface as the ferroparticles generate such a surface according to their field lines.
Figure 18a shows that the 2D small-angle scattering pattern of the monodomain shows strong scattering clustered around the zero-angle point (see also
Supplementary Materials Figures S1 and S2 and Table S1). Although much of the scattering is obscured by the beam stop, it can be seen that it shows some highly anisotropic scattering, in which the scattering is highly constrained in the vertical direction, indicating some highly extended objects, and spread out in the horizontal direction, indicating that the extended objects are quite narrow in the horizontal direction. The analysis of these data using a log–log plot of the intensity vs. the scattering vector (
Figure 18b) shows at a small q there is a linear relationship with a slope close to (-)1. This is suggestive of a one-dimensional structure [
33], and we believe such features to arise from individual chains of ferroparticles. The strength of the scattering increases with an increasing volume fraction of the ferroparticles and an increasing level of anisotropy, and with increasing time in the magnetic field. The tentative analysis of these features by fitting a Gaussian peak to the observable data yields a width of the anisotropic object of 195 nm, with the length evaluation probably limited by the resolution of the setup but in excess of 1000 nm. Further information and SAXS data can be seen in the
Supplementary Materials (see Figures S3 and S4).
3.4. Director Rotation
In order to further understand the role of ferroparticles in the orientation of liquid crystal polymers, we conducted experiments to reorientate the aligned polymer systems. A 2.1 T magnetic field was applied at 90° to the director of an aligned ferronematic polymer (with a 0.28% volume fraction) and the change in its mesogenic side-group orientation was monitored using X-ray scattering with a three-circle diffractometer. The angle of the side-group orientation gradually changed to correspond to the new magnetic field direction over approximately 30 min. This time appears to be independent of the magnetic field strength at the fields investigated (0.8 T–2.1 T). It was also found that this reorientation resulted in a decrease in the global orientation parameter as the mesogens rotated; this decrease is independent of the field strength both in depth and time. The orientation level is recovered at the same time as the new angle of orientation is reached. This behaviour can be compared with the reorientation of CBZ6 without ferroparticles.
Figure 15 shows that this system takes longer than the ferronematic polymer to reorganize (as with its initial monodomain formation). The intermediate decrease in orientation is much larger and there is a discontinuity in the change in orientation angle.
The difference in behaviour can be seen more clearly by looking at the X-ray scattering azimuthal scans, which show intensity as a function of alpha, where alpha is their angle to the original director. For the non-ferronematic polymer,
Figure 20a shows a gap in the plots where the maximum orientation angle discontinuity occurs. In contrast, for the ferronematic polymer,
Figure 20b shows a continuous array of plots where the orientation angle changes smoothly to the applied magnetic field direction.
As discussed above, the non-ferronematic polymer exhibits a discontinuity in its maximum orientation angle and a decrease in its level of orientation as director rotation occurs. This suggests that the mesogens are first unaligned and then realigned in the new direction, whereas the ferronematic polymer exhibits a continuous change in maximum orientational angle and only a small decrease in its level of orientation. Thus, for the ferronematic sample, it appears that the mesogens rotate together to the new direction, and this appears to a be a collective behaviour. This strikingly different behaviour lends itself to two potential explanations: The first one is that it is more energetically favourable for the ferroparticle chains to rotate to the new magnetic field direction rather than dissolve and re-assemble; since they influence the mesogens, the director follows the same behaviour. However, as we have seen above, the ferroparticle chains are particularly unstable and lose their alignment relatively easily, even without the additional influence of a change in the magnetic field direction. An alternative explanation is that for materials aligned in the presence of ferroparticles, it is a general realignment of the polymer backbone which is occurring; in this case, a loss of local mesogen alignment is energetically unfavourable, since it will require a greater distortion of the elastic network. This arises because the polymer backbone was originally better aligned with the ferroparticles and the backbone as a whole reorientates.
Figure 21 shows the shape change of an initially circular sample which was cut from a monodomain sample held in an isotropic phase. We have measured the dimensions of the sample at specific angular positions, a process easily achieved with digital imaging, as the sample temperature was varied. This approach also compensates for any error in aligning the sample with respect to the original magnetic field direction. As
Figure 21 shows, the maximum change was observed at an angle slightly titled from the horizontal. This measurement was performed with the chemically identical polymer SIP 136 (see
Table 1), which has a lower molecular weight.