1. Introduction
The study of structural ordering of liquid crystals (LCs) is of great importance for both the development of physics of condensed matter and application. There exist a few general LC structures. First of all, it should be noted that, on untreated solid substrates in the absence of polar forces, nematic LC molecules align parallel to one another and bounding surfaces. In this case, we deal with an inhomogeneous orientation smoothly varying over the substrate plane. Depending on an LC layer thickness, either thread-like or schlieren texture is observed [
1,
2]. The former consists of homogeneous mesophase regions separated by movable linear disclinations; the latter has singular points with outgoing lines (distorted regions of the planar orientation). In these textures, defects are the nematic medium objects that obey topological laws.
Another type of the structure is local formations in the volume or on the surface of a nematic LC. The most typical of them are nematic droplets floating in an isotropic liquid [
3]. They arise in the form of a dispersive phase distributed in a dispersive medium with the formation of a dispersive system. Similar droplets form at the decay of a three-component system LC-solvent-polymer [
4]. Nonuniform orientation of the nematic director in droplets is caused by the boundary conditions (normal or tangential) and the orientational anisotropy of the LC elastic free energy. Configuration of the nematic director is completed on point defects (one in the center and two on the poles of a droplet), which are locally restricted and do not interact with one another and defects of neighboring droplets. The conditions for the existence of droplets are more complex when the latter are located on the LC surface, e.g., the nematic-isotropic liquid (NI) interface [
5]. Varying the temperature, one can change the position of the interface in an LC cell; then, the director configuration will be additionally affected by external factors (bounding surfaces of LC cells, forces of gravity,
etc.). Under such conditions, point defects interact with one another as on the untreated solid surfaces. Placing droplets on water, one can obtain stable local formations of a nematic LC on the liquid surface [
6]. The objects arising in this case have the form of hemispheres (lenses) suspended to the water boundary. The lenses with two surface defects at the diameter ends are stable and independent of one another and external factors. Study of the LC behavior on non-solid boundaries are of interest, since such boundaries make it possible to observe a regular network of point defects that can arise, e.g., on a free nematic LC surface. The network consists of domains formed by protrusions and troughs where the nematic director configuration is determined by the competing effects of elastic, surface, and gravity forces [
7]. The similar network arose at the NI interface [
8] and in hybrid ordered thin (~1 μm) nematic films with a liquid (glycerol or polyethylene glycol) surface [
9].
One more type of the structure can arise in a nematic LC layer with the orienting centers occurring during the transition of the metastable isotropic phase to the stable nematic one. As was demonstrated in [
10], upon gradual cooling of nematics from an isotropic liquid on the polyimide surface, nucleation occurs either in the volume of a nematic LC or on its surface, depending on polymer polarity. In such systems, under the temperature variation, spherical domains spontaneously occur that grow in time. The domains are stable and do not interact with one another. The kinetics of the phase ordering during the domain growth was studied in [
11].
In this study, we investigate the alignment of nematic LCs on polymer surfaces in the presence of different solvents. We demonstrate that, on polymer structural elements, a network of stable domains arises, which can be considered as a superposition of three different configurations of the director.
3. Discussion
Study of the LC domain structures on the PC surface showed that the b-domains are the c-domains with the superimposed planar LC layer. However, from the topological point of view, the c-domains should have a singular point with the force
s = ± 1 at their centers [
2]. Changing the angular position of a domain relative to the crossed polarizers, one can determine the sign of a topological defect. At the rotation of a c-domain in
Figure 3, the extinction band positions relative the polarizer directions remain invariable, which corresponds to the sign (+) of the point defect force. This behavior of the domains is characteristic of the schlieren texture; however, in contrast to it, the c-domains with the sign (−) were never observed in our experiments. Thus, we may conclude that the structures under study are not objects of the nematic medium in itself [
1,
2], but autonomous formations. In this case, the polymer surface should be considered as a source of the domain formation.
One of the possible reasons for the occurrence of domains and disclinations in the LC on the PC surface is the presence of mechanical defects (cracks, protrusions, troughs,
etc.). The defects can occur under the action of surface tension resulting from diffusion of a free volume during evaporation of the solvent [
13], which remains in the film after its drying in air (
Figure 10). In addition, one may suggest that the domain ensembles shown in
Figure 2b,c are the domain networks with protrusions and troughs, similar to those described in [
6–
9], in which the LC director configuration is significantly affected by forces of gravity. However, since the domain formation was not affected by the spatial position of the PC substrate and no relief on the polymer surface was found after removal of the LC in optical and scanning electron microscopes (
Figure 11c,d), the surface profiling cannot be considered as an origin of the domain formation.
The results of our experiments can neither be treated within the nucleophilic decay of the three-component system LC-polymer-solvent at a constant temperature. First, these components are spatially separated in the sandwich and it is difficult to find the conditions of their intermixing and the phase separation, which were met in the LC structures described in [
3–
5]. Second, the domain formation in the LC on the PC surface is poorly compatible with the classical concept of nucleation and growth in the LC systems, according to which the time dependence of the diameter of a growing nucleus obeys the universal growth law
d(
t) ~
tk. In this law, growth component
k in the well-known experiments reported in [
11] changes from 0.5 to 1 only near temperature
TNI. At the exponential growth, the value
k = 1 can be obtained. In our experiment, the time dependence of the diameter of a growing domain (
Figure 7) can be described by the universal growth law for the only value
k = 1. In addition, as can be seen in
Figure 5, the domains grow to this size until the neighboring domains limit their propagation.
On the other hand, it can be supposed that the domain formation originates from the occurrence of supramolecular structures on the polymer film surface during evaporation of the solvent, which are visualized by the LC due to the molecular interaction. Since PC is a rigid chain polymer, upon slow evaporation of the solvent from the solution such crystal structures as packs, fibrils, and spherulites can form in it. [
14]. Packs and fibrils contain 10–50 polymer chains and are characterized by molecular close packing. Spherulites are tens and hundreds of microns in size and can be seen in a polarizing microscope in crossed polarizers. However, in observation of the PC film (
Figure 11c) with the removed structured LC layer in polarized light, the optically dark field is always seen and the crystal polymer structure is not observed. In addition, as follows from
Figure 10, evaporation of the solvent from a solution is not slow if the LC film is deposited onto the PC film right after its formation, although in this case no domain formation was observed.
At the same time, the dependence of the domain growth time on temperature and exposure of the polymer film prior to the LC deposition and the different forms of domains depending on the solvent used indicate that the solvent plays an important role in the formation of the LC texture. As is known, in the polymer films there is a surface layer with the chemical structure and density different from those in the volume [
13]. This layer forms a potential barrier at the interface preventing solvent output. On the other hand, there exists a well-known phenomenon of extraction of substances in solvents [
15]. In particular, in study [
16] the authors showed that dichloromethane used by us effectively extracts nematic LC molecules from the droplets emulsified in the polymer matrix. We suppose that extraction of solvent molecules by LC molecules creates the solvent excess in the surface layer and causes the mobility of polymer chains. The amount of the solvent in the thin PC film is not sufficiently large to transfer the polymer surface to the diluted solution state with separate macromolecules. Such a system could be described by methods of statistical physics of volume interactions [
17] with the exact analysis of the structural transformations on the polymer surface in the presence of the LC. However, in our case, structuring is the surface of the amorphous PC film with entangled polymer chains. Parts of this surface transfer to the plastic state during the solvent entry. The quantitative analysis of such a system is complicated by the significant mutual effects of statistical factors. Nevertheless, structuring of the PC surface capable of retaining the LC domain configuration can be roughly estimated by energy
E consisting of characteristic energies
Eps of the polymer − solvent interaction, energy
Epp of attraction of polymer links and, additionally, energy
Eplc of the interaction of polymer links with nematic molecules:
E = Eps +
Eplc −
Epp. To estimate
Eps of the investigated systems, we calculated the Huggins constants asη
sp/
c = [η] +
KH [η]
2c [
14], where
c is the solution concentration, η
sp/c = (η − η
0)/η
0c is the reduced viscosity of the solvent, η and η
0 are the solvent and solution viscosities, and [η] is the viscosity at the infinite dilution. We measured η
sp for different
c and applied standard calculation technique with extrapolation of the curve η
sp/
c to the limit value [
18]. Defining [η] from the Staudinger-Kun equation [η] =
KMα with a value of the molecular
weight M = 45000 and the coefficients
K/α = 1.11 × 10
−2/0.82; 2.77 × 10
−1/0.5; 2.01 × 10
−2/0.7 [
14], we obtained
KH = 0.43,
KH = 0.3, and
KH = 0.13 for the PC solutions in dichloromethane, chloroform, and pyridine, respectively. Apparently, when dichloromethane or chloroform yielding high values of
KH and, consequently, high
Eps are used [
14], we have
Eps +
Eplc >>
Epp >
kT. When the amount of the solvent in the surface layer is sufficiently large, then movable parts occur in the polymer chains. On these parts, the
b- and
c-domains form. At the same time, when pyridine with low
KH is used under the same condition, we have
Eps +
Eplc >
Epp >
kT, which is insufficient to strain a part of the polymer chain, which results in the formation of island-shaped domains on the PC surface (
Figure 2d). As the amount of the solvent is decreased, e.g., upon drying the polymer film at the temperature
T = 50 °C (
Figure 10), the mobility of the polymer chains drops and the domain formation degrades: randomly formed structural formations with entangled thread visualized by the LC arise on the PC film that are hard to analyze (
Figure 9a) or granular textures are observed (
Figure 9b). When the solvent is completely removed from the PC film at
T = 120 °C (
Figure 10), the thread-like or schlieren texture forms on the polymer surface.
Study of the growth kinetics of the domains located close to one another (
Figure 6) or the domain ensembles arising at the repeated deposition of the LC on the structured PC surface (
Figure 11e) allows us to make the following assumption. The disclination lines in the domains occur in the presence of structural elements
L that are the movable parts of the polymer chains with LC molecules absorbed by them perpendicular. The absorbed molecules tend to orient the polymer chains perpendicular to director n
p of the planar volume LC layer (
Figure 4). The mechanism of absorption of nematic molecules will be investigated in the next work. We denote the averaged alignment of the absorbed molecules along the polymer chain by unit vector n
l (
Figure 13). Under the action of the local torques from the side of n
p, element
L will tend to reduce its free energy. If the chain ends are fixed on the surface, then a more bent element will be found on
L on which the chain will twist and, owing to this, straighten up. The twisted part will appear an orienting center around which LC molecules will align with the formation of the radial configuration. This process should be slow due to the molecular interactions of the LC and the polymer surface [
19,
20]. Owing to the absorption of nematic molecules on the PC film, the twist will fix on the surface. At the formation of the structure in an external field, e.g., magnetic, the twist can break away from the surface and pass in the volume (
Figure 12). The proposed scenario of the development of the radial configuration (
R) of the director field n(r) is consistent with the domain growth observed in our experiments.
The occurrence and shape of the disclination lines can be explained by studying the behavior of configurations
L within
R. On the texture parts where local director n
r and vector n
l coincide, lines
L are indistinguishable. They become visible where n
r significantly diverges from n
l. The divergence should be larger at the periphery of
R when the consideration is made along
L and smaller near the
R center where n
r and n
l are the closest to one another. Under these conditions, the disclination lines should occur along
L and they were really observed in the optical microscope. Without polarizers, they looked like wide bands narrowing near their centers (
Figure 11b). If under the action of an external factor, a polymer chain part is forced out into the LC layer, the disclination line corresponding to this part looks like a double line (
Figure 11f). Thus, the disclination lines arising at the developed configuration
R and following its radius are the factors visualizing the polymer chain during the domain growth (
Figures 5 and
6). Dark defect areas in
Figure 6 near the domain centers can be identified as the polymer chain twists visualized by large light scattering due to the sharp change in the refractive index in the strongly strained LC layer. In this figure, one can also see that during the domain growth, molecules of the volume nematic layer do not extend the polymer chains, which could occur due to the anisotropy of the LC surface tension, and only visualize them.
Thus, the domain growth is the gradual radial alignment of LC molecules on the PC surface around the polymer chain twists with the formation of the disclination lines along them. The LC molecules forming the configuration
R are absorbed on the polymer surface, retaining the surface ordering memory. After removal of the LC layer, the polymer chains are released but the
R imprint on the PC surface and the twist fixing points remain. At the repeated LC deposition on the PC film, configuration
R is instantly visualized, but the polymer chains released from the LC form new structural elements
L aligned in the new direction (
Figure 11e). The surface configuration
R ensures the memory of the planar LC alignment above the domains. The orientation of
L in the surface polymer layer favors the formation of the stable azimuth direction of nematic director n
p in the volume layer.
Figure 14 presents the main possible orientational structures at different LC configurations in the volume and on the surface of PC. If the LC alignment in the volume layer is planar (
P), then at its superposition on the surface configuration
R with four extinction bands, we will observe the configuration
PR with two narrow dark bands where the n
p and n
r orientations are close. In the wide bright regions, these orientations have a large angular divergence. At the superposition of
L on
PR, horizontal in the geometry presented in the figure, the configuration
PR will not change due to the large angular divergence of directors n
p, n
r, and n
l, but
L will be seen as a dark line against the bright background. If
L were located vertically, the dark branches in the configuration
PRL would brighten due to the large difference between the n
r and n
l orientations and the entire configuration disk would become bright. However, since n
p and n
l tend to orient perpendicular to one another, this configuration is not shown in the figure and the bright domains were not observed in our experiments. The presented configuration
PRL corresponds to the
b-domain shown in
Figure 3a. If
L makes a certain angle with the light polarization directions (
L′), then the orientational divergence between n
p and n
l decreases and brightened sectors will appear in the configuration
PRL′. The configuration
PRL′ corresponds to the b-domain shown in
Figure 3c. If in the volume layer the LC has the homeotropic alignment (
H), then at the superposition of the latter on the surface configuration
R with four extinction bands, the configuration
HR will also be seen with narrow dark bands. At the superposition of
L on
HR, vertical or horizontal in the geometry presented in the figure, the dark bands through which
L passes will brighten due to the large angular divergence of directors n
r and n
l, and
L will be visualized as a dark line against the bright background. The configuration
HRL corresponds to the c-domain shown in
Figure 3f. In the configuration
HRL′, the bright regions will remain due to the large angular divergence between n
r and n
l, but
L will be seen as a dark line against the bright background. The configuration
HRL′ corresponds to the
c-domain shown in
Figure 3d. The orientation change
P→
H should lead to the configuration transformation
PRL→
HRL. This transformation can occur at the growing effect of the oblique alignment of the nematic on the free droplet surface on the planar LC alignment on the PC surface because of a decrease in the thickness of the volume nematic LC layer at approaching the droplet periphery, similar to the LC cell with the homeoplanar orientation [
21]. The domain ensembles in
Figure 2b,c correspond to the considered transformation. The transformation
PRL→
HRL can occur also at the temperature variation (
Figure 8). The orientational transition can be caused by different temperature dependences of the polar energies of the nematic anchoring to movable polymer chains
WL and radially absorbed LC molecules with polymer surface
WR.