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LIQUID CRYSTALLINE THERMOSETS Introduction Liquid crystalline thermosets (LCTs) may generally be defined as low molar mass, multifunctional monomers, which can be cured thermally, chemically, or photochemically in the melt state, leading to a highly cross-linked, high glass-transition temperature material which exhibits liquid crystalline order. These materials are expected to exhibit properties that combine the useful benefits of both cross-linked thermosets and liquid crystals, such as low viscosity for ease of processing, good dimensional stability, high glass-transition temperatures, good thermal stability, high mechanical properties, the ability to be oriented, and good barrier properties. Among the applications envisioned for these materials are high performance resins for composites, optical thin films, and packaging material for microelectronics. The eventual use of LCTs for these types of applications will depend on the continued investigation and development of their properties. The first mention of LCTs is in a paper by de Gennes in 1969 (1). The first experimental investigations occurred in the 1970s (2,3). However, significant numbers of publications did not appear in the literature until the 1990s. Early efforts focussed primarily on the liquid crystalline structure of the monomers or the cured networks, whereas more recently there have been efforts to examine the evolution of structure during cure, the nature of the cure process, and a variety of properties.
Molecular Structure of Monomers Quite a large number of different monomer structures have been synthesized (4). Reactive end groups utilized include epoxy (5–10), acrylate and methacrylate
Encyclopedia of Polymer Science and Technology. Copyright John Wiley & Sons, Inc. All rights reserved.
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(11–14), maleimide and nadimide (15–21), vinyl (22,23), isocyanate and cyanate ester (24–27), and ethynyl (28–30). In one case, a dual-curing monomer containing both acrylate and ethynyl groups has been made (31). The mesogen is generally aromatic, and may include ester (6–8,10,16,19–21,25–30,32–34), amide (15,18), or azomethine (35,36) linkages. There may also be a flexible spacer, typically between the mesogen and the reactive group (10,13,37). Two fairly unusual structures involve twin mesogen LCTs, in which there are two mesogenic units separated by a flexible spacer (34,36,38,39), and LCTs in which the reactive group is placed between the flexible unit and the mesogen (40). It is also possible to create branched monomers that exhibit a liquid crystalline phase (41). While most monomers exhibit either achiral nematic or smectic phases, by appropriate choice of the monomer structure it is possible to create chiral smectic (42) and discotic phases (43). Tables 1 and 2 provide a representative list of monomers that have been synthesized. Two epoxies that have been extensively compared are shown below.
Diglycidyloxy-α-methylstilbene (1) is a liquid crystalline epoxy, while the diglycidyl ether of bisphenol A (2) is a typical non-liquid-crystalline epoxy. LCT monomers follow the general rules for liquid crystalline behavior that have been found for nonreactive low molar mass liquid crystals (44–48). Thus, bulky substituents tend to destabilize the liquid crystalline phase (16,27– 30,33,35), longer flexible units favor the formation of smectic phases (40,49), and odd–even effects are seen in the transition temperatures as a function of flexible spacer length (36,40,49). Rigid mesogens that form liquid crystalline order upon cure may not be liquid crystalline themselves. For example, 1 is itself a monotropic nematic, with a melting temperature of 128◦ C and an isotropic to nematic transition upon cooling of 95◦ C (50). Extension of 1 with a flexible unit such as glutaric acid creates an oligomer which is enantiotropic (8). In this case the structure may be likened to that of a main chain liquid crystalline polymer containing rigid and flexible segments. The phase diagram for binary mixtures of LCT monomers may be calculated using the same techniques as are employed for low molar mass liquid crystals, although slight discrepancies are found between theoretical and experimental phase diagrams (51). These discrepancies may be accounted for by the reactive nature of LCTs, whereby a complex mixture of partially reacted species is formed during the experiment that is not accounted for in the theory. It has also been found that the type of linkage can have an effect on the phases shown. For example, Lee and co-workers have examined the effect of an ester group versus an ether group between the mesogen and the flexible spacer of an epoxy LCT
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Table 1. Representative Epoxy LCTs Mesogen
End group
References 9 8 8 8 8 8 8 10 10 10 10 35
(R1 and R2 may be hydrogen or methyl) 35 52 38 36 (x ranges from 6 to 9)
(52). They found that the ester group leads to a monomer with a smaller nematic temperature range. As in low molar mass liquid crystals, this can be attributed to reduced intermolecular interactions due to the electron-withdrawing character of the ester group, and lower geometrical anisotropy due to the larger size of the ester group.
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Table 2. Representative Miscellaneous LCTs Mesogen
End group
References 11
(R is hydrogen or methyl; n = 3, 6, 11) 12,14 (R is hydrogen or methyl)
(R is hydrogen or methyl; n = 6) 11,13 15
16 (R is hydrogen, methyl, or chlorine) 20 (n = 5, 6, 8, 9) 22 (R is hydrogen or methyl) 24
(R is methyl or chlorine) 25,26 25,26 25,26 25,26 26 (R is hydrogen) 26 (R is hydrogen)
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Table 2. (Continued) Mesogen
End group
References 28
(R is hydrogen, methyl, methoxy, or chlorine) 29,30 (R is hydrogen, methyl, methoxy, or chlorine) 90
Cure Behavior Reaction Kinetics. The presence of a liquid crystalline phase can have a dramatic effect on polymerization rates. The activation energy can be lower in the liquid crystalline phase, implying a higher rate constant (53). For those monomers which are initially isotropic, isothermal differential scanning calorimetry measurements show an initial exotherm due to the polymerization in the isotropic phase, followed by a second exotherm due to a rate acceleration when the reacting system undergoes a phase transition to a liquid crystalline phase. This phenomenon appears to be general, as it appears in both chain-growth (54–56) and step-growth (57–59) systems. Mormann and Br¨ocher found a similar second exotherm for an epoxy system that was undergoing a smectic to nematic transition during cure (60). This may be due to the lower viscosity of the nematic phase. Several studies have compared the kinetic parameters that result from polymerization in different phases for chain-growth systems. Douglas and co-workers used Raman spectroscopy to compare liquid crystalline and non-liquid crystalline bisacetylene monomers (28). They found that the initial polymerization rate was higher in the liquid crystalline phase. Other studies have examined the photopolymerization of methacrylates and acrylates using differential scanning calorimetry. Hoyle and co-workers found there was no change in the initial polymerization rate as a function of phase, but the maximum rate was reached at lower conversions as the order of the phase increased (56). Guymon and Bowman performed a detailed kinetic study for liquid crystalline and non-liquid-crystalline diacrylates polymerized in a liquid crystalline solvent (61). Remarkably, they found that the polymerization rate is higher at lower temperatures, again due to the greater order present in the lower temperature liquid crystalline phases. A detailed analysis showed that this rate increase is caused by a decrease in the termination rate constant rather than by an increase in the propagation rate constant. Kinetic studies have also been conducted on epoxy systems. For amine cure, it is generally assumed that the primary amine has a greater reactivity than the secondary amine. However, two studies found that for liquid crystalline epoxies the secondary amine is more reactive than the primary amine (62,63). There is no
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complete explanation for this behavior, but it has been suggested that it is caused by the lower viscosity of the nematic phase. More detailed kinetic analysis has been done to model the kinetics during the complete reaction. Non-liquid crystalline epoxies are typically found to follow an autocatalytic model, in which one considers the reaction between an epoxide and an amine or anhydride hardener, with the reaction catalyzed by a species formed during the reaction (eg hydroxyl group). This model fits the isothermal differential scanning calorimetry data for both isotropic epoxies, and for liquid crystalline epoxies that show only a single exothermic peak during cure (57,64). For systems that do show a second peak due to a phase change during cure, modifications to the autocatalytic model are needed. The basic concepts inherent in these modifications are that the reaction proceeds at a different rate in the liquid crystalline phase than in the isotropic phase, and the isotropic and liquid crystalline phases contribute to the rate according to the relative proportion of each phase present. Liu and co-workers developed a model by modifying the autocatalytic model with a rate-enhancement term (57,59) and also introduced an error function so that the contribution of the rate-enhancement term increases as the conversion increases. Micco and co-workers also developed a model by assuming that the reaction rate is autocatalytic in the isotropic phase but linear with conversion to the liquid crystalline phase (58). They also assumed a form for the rate of growth of the liquid crystalline phase, and that the isotropic and liquid crystalline phases contributed to the overall rate in proportion to their volume fractions. Given the similarities of the two models, it is not surprising that both are able to model the double exotherm. Unfortunately, these models do not give much insight into the mechanism behind the rate enhancement, although Liu and co-workers do propose that their rate-enhancement term is associated with an increased concentration of reactive groups at the layer boundaries in the smectic phase. Network Formation. Only very little work has been conducted on examining the effect that the liquid crystalline phase may have on the network formation. The two studies conducted indicate that in fact the liquid crystalline phase has no effect on gelation. Jahromi and co-workers examined the viscoelastic behavior of a liquid crystalline epoxy during cure at a single temperature (65). They found that the critical gelation exponent was equal to 0.5, which is also found for isotropic epoxies. Cho and Douglas performed measurements on a different epoxy at multiple temperatures, and found that the conversion at gelation was independent of cure temperature, as would be expected for a purely statistical step-growth process (66). Both studies found that the conversion at gelation was in good agreement with that calculated from standard theories of gelation via step growth. Thus it appears that, at least in epoxy systems, gelation is independent of the phase in which the cure reaction occurs. Phase Evolution during Cure. Although the liquid crystalline properties of LCT monomers are easily understood on the basis of low molar mass liquid crystals, the structures of the resulting networks are much more complicated, resulting from an interplay among the monomer structure, the effect of crosslinking, and the cross-linking agent, if one is present. In some cases, there is no change in the liquid crystalline texture during cure, and the network exhibits the same liquid crystallinity as does the monomer (28,30,67). Even in such cases, however, there may be a slight loss of order at the molecular level due to the cross-linking reaction. Such an effect has been predicted theoretically (68),
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and there is at least some experimental evidence that this may actually occur (69). In many cases, however, the liquid crystalline order of the network is not the same as that of the monomer. Most common is the case in which the order of the network is actually greater than that of the monomer, in seeming contradiction with the theoretical calculations mentioned above. The most common example is 1, which is a monotropic nematic liquid crystal as a monomer, and can be cured from the isotropic phase to give a liquid crystalline network (50,67,70). There are also other examples of this behavior (38,39,71–74), including systems which are initially nematic and then cure to give a smectic network (3,67,71). In general this behavior is explained on the basis of a minimum aspect ratio for the molecule that is required for liquid crystallinity to occur (28,39). It is assumed that the cure reaction increases the aspect ratio such that the molecules organize into a liquid crystalline phase. However, this explanation does not account for transitions from a monomer that is nematic to a network that is smectic, nor why some monomers that are initially isotropic form a network that is smectic. Therefore, it has also been suggested that specific molecular interactions between either the mesogens or the cross-linking molecules may be operative in the formation of smectic phases (38,69). There are also several cases in which the molecular order decreases during cure, with the formation of a nematic network from a smectic monomer (75,76) or isotropic networks from both nematic and smectic monomers (28,40,76). This phenomenon is explained as being due to the disruption of the order due to the formation of cross-links. For example, Gavrin and Douglas synthesized a series of bisethynyl LCTs in which the cross-linking group is attached directly to the mesogen (40). In this particular case the cross-linking group is not decoupled from the mesogen through a flexible spacer, and thus if the distance between the molecules in the liquid crystalline phase is inconsistent with the bonding distance, the liquid crystallinity will be disrupted. This behavior is therefore similar to the general requirements for a flexible spacer to decouple the mesogen from the backbone in side-chain liquid crystalline polymers. However, other bisethynyl LCTs do not lose liquid crystallinity during cure (28), and thus there are clearly some details of this behavior that are not yet understood. Another important factor affecting the network structure, at least in epoxies, is the cross-linking agent that is used. A study on this factor was conducted by Mihara and co-workers (77). They examined several combinations of mesogenic and nonmesogenic epoxies and amines. The most significant result from their study was that it is possible to create a liquid crystalline network if a mesogenic amine is used, even if the epoxy used is nonmesogenic. This clearly indicates the strong role that the hardener may play in determining the liquid crystalline structure of the network. Another example of this phenomenon occurs with 1 (50,70). When cured with a difunctional amine the resulting network forms a nematic structure. However, when cured with the unsymmetric tetrafunctional amine sulfanilamide, the resulting network forms a smectic structure. The authors propose that this difference is caused by the unequal reactivities of the two amine groups in sulfanilamide. The aromatic amine tends to react more easily, causing chain extension with little cross-linking, which is assumed to favor formation of the smectic phase. Only at the later stages of cure does the sulfonamide group react, resulting in cross-linking. However, Barclay and co-workers have found
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that 1 and its oligomers cross-linked with the symmetric tetrafunctional amine methylenedianiline can form either a nematic or smectic phase, depending on the molecular weight distribution; oligomers with a narrower distribution tend to form the smectic phase (67). This result suggests that the most important factor may be the presence of molecular interactions that drive the formation of the smectic phase, and that a broader molecular weight distribution disrupts the regularity of that structure, leading to a nematic phase. Similarly, use of an aliphatic acid to cure 2,6-diglycidyloxynaphthalene results in a nematic network, despite the low aspect ratio of the epoxy monomer (72). In this case, hydrogen bonding may play an important role in the formation of the liquid crystalline structure. It is apparent, then, that the formation of liquid crystalline structure in cured LCT networks is a complicated process and is currently difficult to predict. Nevertheless, for practical applications it is desirable to at least have knowledge of the liquid crystallinity that may form as a function of the cure conditions. To achieve this, a number of workers have created transformation diagrams that show the liquid crystalline phases that form as a function of cure temperature and cure time (28,30,36,38–40,70,71,73,78). Figure 1 is one example of these types of diagrams. One of the interesting questions that arises from these types of diagrams is the conversion dependence of the phase transformation. Several studies have addressed this issue by performing independent measurements of conversion versus time at various cure temperatures, and then converting the time axis to conversion (63, 66,78). They find that the conversion at which the transformation occurs increases with increasing cure temperature. This is because at higher cure temperatures the critical molecular length for liquid crystallinity to occur is higher, and thus a greater conversion is needed. This explanation is supported by experimental results on other systems, for which an increase in isotropization temperature as a function of cure time at a single cure temperature has been reported (50). 200 I 180 LC
Temperature, °C
160 140 I
120 100
LC
80 60
K
40 0
10
20
30 Time, min
40
50
60
Fig. 1. Transformation diagram for 1 cured with sulfanilamide showing changes in morphology as a function of the cure time. This particular diagram shows the time at which phase transformations occur when the sample is cured isothermally at a given temperature. I, isotropic; LC, liquid crystalline; K, crystalline. Reprinted from Ref. 70, Copyright (1994), with permission from Elsevier Science.
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Properties Mechanical Properties. Liquid crystalline polymers are known to have outstanding mechanical properties due to their microdomain morphology and their ability to be oriented. It is expected, therefore, that LCTs may have the same advantages. The effects of orientation are considered in a later section; here we consider only macroscopically unoriented systems. As part of their study on orientation effects, Benicewicz and co-workers measured the tensile modulus of 1(69). They obtained a value of 3 GPa, which is typical for non-liquid-crystalline epoxies. Earls and co-workers also found flexural modulus values of approximately 3–4 GPa for both 1 and 2(9). Tan and co-workers found even lower values of modulus for different liquid crystalline epoxies, although they did not make a direct comparison to isotropic systems (79). Ortiz and co-workers also found no enhancement in modulus for 1, with the storage modulus in the glassy state actually lower than for an isotropic epoxy and the compressive modulus the same (80). From this limited data it appears that the liquid crystalline phase has no advantage for tensile modulus. This may not be surprising since modulus in the glassy state is governed by bond deformations and rotations, which will be relatively unaffected by the liquid crystalline state. Ortiz and co-workers did find, however, an increase in the dynamic modulus in the rubbery state above what is predicted from rubber elasticity theory (80). This increase is greater for the smectic phase than for the nematic phase. They explain this behavior by proposing that deformation due to motion of the cross-links in an ordered phase will disrupt that ordered phase, resulting in an additional free energy penalty due to the deformation. They also examined additional compressive properties, and found that the liquid crystalline phase results in a lower yield stress, no strain-softening region, and a lower strain at failure. They propose that this behavior occurs because the rigid and extended nature of the network segments prevents plastic deformation. Similarly, Earls and co-workers found a slightly lower flexural strength for 1 compared to that for 2(9). Enhancements in fracture toughness for LCTs are greater than for other properties. Several studies have examined the fracture behavior of LCT epoxies. Both Sue and co-workers and Ortiz and co-workers found that 1 cured in the liquid crystalline phase had a higher fracture toughness than 1 cured in the isotropic phase (80,81). Robinson and co-workers conducted a detailed investigation, comparing 1 and 2 cured with the same curing agent with the same cure cycle (82). By varying the epoxy-to-hardener ratio, they found that the morphology of 1 changed, with the domain size decreasing with increasing deviation from balanced stoiochiometry. As a result, the fracture toughness for 1 was higher than that for the isotropic epoxy only at and near the stoichiometric formulation. Carfagna and coworkers found that this increased fracture toughness extends to fiber-reinforced composites, although the increase in impact resistance for LCTs was not as great in the composites as for the neat resin (83). The mechanism for this enhanced fracture toughness has been investigated by TEM. Sue and co-workers found that the crack appears to grow preferentially at the boundaries of the liquid crystalline domain, resulting in crack deflection and segmenting, with this mechanism becoming less effective as the domain size decreases (81). Ortiz and co-workers found that failure occurs by formation of individual microcracks, which grow and
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Fig. 2. Thin films of (a) 2 and (b) 1, both cured with methylene dianiline, strained in tension, and observed between crossed polars in an optical microscope. In (a) can be seen the typical behavior of an isotropic epoxy: a single crack with birefringence caused by a shear deformation zone ahead of the crack tip. In (b) there are multiple cracks; these cracks undergo slow, stable propagation due to failure of individual liquid crystalline domains in front of and at the crack tip. Reprinted with permission from Ref. 84, Copyright (2000), Kluwer Academic Publishers.
coalesce, eventually resulting in failure (84). This is in contrast to the isotropic epoxy, which fails by formation and growth of a single crack. Figure 2 shows a comparison between the two systems. Ortiz and co-workers proposed that the individual microcracks undergo stable propagation due to failure of individual liquid crystalline domains (84). These mechanisms are consistent with the results of Robinson and co-workers (82), in that it would be expected for these toughening mechanisms to become less effective as the domain size decreases. Several studies have examined the adhesive properties of LCTs. Ochi and Takashima, and Carfagna and co-workers both found an increase in the lap shear strength for an LCT epoxy compared to an isotropic LCT (85,86). However, Frich and Economy (87) found that the lap shear strength with a titanium substrate for an LCT that cures by transesterification was lower than that for an isotropic resin. Given the limited data available, it is not clear whether these differences are due to the substrates, surface pretreatment, the type of cure reaction, the liquid crystalline phase, or some other factor. However, most of these studies did find
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that the failure mode for the LCT was cohesive or mixed cohesive and adhesive, as opposed to only adhesive for the isotropic thermosets. Thus, it appears that regardless of the lap shear strength, the LCT has a greater bonding strength to the substrates. In one case both materials failed in a cohesive manner, and thus the increased lap shear strength appears to be related to the higher fracture toughness of the liquid crystalline material (86). Thermal Stability. Only a few studies have examined the thermal stability of LCTs. When the monomers are specifically designed to contain no aliphatic carbons, the thermal stabilities can be very high. For example, Melissaris and coworkers synthesized rigid rod monomers with ethynyl end groups (88,89), while Gavrin and co-workers synthesized monomers with phenylethynyl end groups (90). In both cases degradation temperatures were reported to be at least 400◦ C in both air and nitrogen atmospheres. Thermal stability has also been examined for epoxy LCTs. The thermal stability is affected by the type and concentration of hardener used; as the aliphatic content of the resin mixture increases, the thermal stability decreases (91,92). One study showed that an anhydride hardener resulted in lower thermal stability than an amine hardener, perhaps due to the difference in cross-link structure (93). In one study liquid crystalline epoxies were compared directly to 2(94). When the epoxies were cured with an anhydride hardener the liquid crystalline epoxies showed a higher onset temperature for degradation, but when an amine hardener was used 2 had a higher onset temperature. In general, the results suggest that the high thermal stability is a consequence of the types of bonds present and is not significantly affected by the liquid crystalline phase. Permeability. Liquid crystalline polymers are known to exhibit very low permeability to various permeants due to the packing of molecules in the liquid crystalline and crystalline states. The low permeability of LCPs can be understood on the basis of a two-phase model, in which it is assumed that the permeant does not penetrate into the domains, but can only diffuse through the domain boundaries (95–97). On the basis of these results, it might be expected that LCTs would also show low permeability. Carfagana and co-workers measured the sorption isotherm for 1 and found no difference in water sorption between the nematic and isotropic states (98). In contrast, Earls and co-workers found that 1 cured in the smectic state absorbed considerably less methylene chloride, methylethyl ketone, dimethyl formamide, and bleach after 30 days compared to that adsorbed by 2; weight gains for 1 were all less than 1%, while weight gains for 2 ranged from 1.0% (bleach) to 26.6% (methylene chloride)(9). Feng also found considerable differences between 1 and 2 in the smectic phase (99). Using a permeation technique to measure the transport of water vapor through thin films, he found that the permeability, diffusion coefficient, and sorption coefficient were all substantially lower for 1. From the limited data available, it appears that the liquid crystalline state present in the cured resin has an important effect on the diffusion properties, with the smectic phase being considerably less permeable than the nematic or isotropic phases. Optical Properties. All of the optical applications of LCTs have considered the cholesteric phase. The cholesteric phase is interesting because thin films of a cholesteric liquid crystal oriented such that the helical axis is perpendicular to the plane of the film will selectively reflect circularly polarized light with a wavelength determined by the pitch of the helix. For low molar mass liquid crystals,
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films are typically created by mixing a nematic liquid crystal with small amounts of a chiral molecule. The pitch of the helix is determined by both the concentration and the temperature, and thus they are utilized as simple temperature sensors. The goal of creating a cholesteric LCT is driven by the desire to permanently fix the helical pitch, and thus the reflected wavelength, for use in optical devices. There are several approaches that have been used to create cholesteric LCTs. These include polymerizing nematic LCTs in the presence of a nonpolymerizable chiral molecule (100–104), polymerizing a non-liquid-crystalline monomer in the presence of a nonpolymerizable chiral molecule (105), and copolymerizing nematic and chiral LCTs (100,106). As with low molar mass liquid crystals, in general the pure cholesteric compounds do not reflect light in the visible range, although there is at least one example of a diacrylate which reflects red light when it is not polymerized (106). Several studies have examined the properties of the cross-linked cholesteric LCTs and proposed some interesting applications. Hikmet and Zwerver showed that removal of the nonpolymerizable molecule leads to an irreversible change in the helical pitch, and thus the wavelength of reflected light (101). This change could be induced locally by writing with a laser beam, suggesting that these materials could be used for optical storage. Ishihara and co-workers used cholesteric LCTs as optical notch filters that filter light of specific wavelengths for displays, allowing better color purity for those displays (105). Heynderickx and Broer also considered cholesteric LCTs for display applications (104). In their case they used a cholesteric LCT film as a compensation foil to eliminate the wavelength dependence of transmission for a supertwisted nematic display.
Orientation of LCTs in External Fields The liquid crystalline order of LCTs allows them to be oriented by external fields. Orientation may be induced at a surface, or by electric or magnetic fields. Curing the material subsequent to, or during, orientation leads to a cured thermoset which has some degree of macroscopic order. Unlike liquid crystalline polymers, shear fields and mechanical deformation in the uncured state are not considered to be as effective, because of the rapid relaxation of the monomers and the difficulty in maintaining such fields during the cure process. Nevertheless, mechanical deformation has been shown to be effective at orienting lightly cross-linked materials by heating above their T g and subsequently cooling to lock in the orientation, although the ability to orient decreases dramatically with increasing cross-link density and the orientation is lost upon heating above T g (107,108). The orientation process tends to enhance certain properties of the cured LCT, although the potential benefits have not yet been fully explored. Surface Induced Orientation. Liquid crystals are well known to orient at surfaces (109). This effect is utilized in liquid crystal displays, in which orientation of the liquid crystal at a surface is transmitted throughout a thin film. Often this orientation can be achieved simply by rubbing a polymer such as polyimide repeatedly along a given direction. This rubbing process results in orientation of the liquid crystal along the rubbing direction. Given that this technique works well for low molar mass liquid crystals, it is not surprising that it has been utilized
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to align thin films of LCTs (12,22,23,56,110). The technique appears to be very general, and has been applied to epoxies, vinyl ethers, and methacrylates, using both thermal and photoinitiated polymerization. The orientation in these systems can be measured using either infrared spectroscopy or X-ray scattering. The resulting orientation is expressed in terms of the second moment of the orientation function, or the orientation parameter, which is given by 1 P2 = (3cos2 α − 1) 2
(1)
where α is the angle a molecule makes with respect to the alignment direction and the angular brackets denote an average over all molecules. The limiting values for are −0.5 for perfect orientation perpendicular to the alignment direction, 0 for no orientation, and 1.0 for perfect orientation parallel to the alignment direction. Values for resulting from surface-induced orientation typically range from 0.6 to 0.94, indicating a high degree of alignment. An interesting application of surface-induced alignment of LCTs is orientation at the surface of fibers in fiber-reinforced composites. Adams and Mallon have shown that a low molar mass liquid crystal is oriented at the surface of a carbon fiber parallel to the fiber direction (111), while Sue and co-workers found that 1 can be oriented along the fiber direction, depending on the cure schedule and the epoxy/hardener formulation (112). These findings raise the possibility of creating fiber-reinforced composites with controlled matrix orientation and/or tailored interfaces, which may improve the fiber/matrix interface and result in improved properties (see REINFORCEMENT). Electric-Field-Induced Orientation. Despite the fact that electric field orientation of liquid crystals is an important technology used, for example, in liquid crystal displays, there has been almost no work on the electric field alignment of LCTs. This may be because electric fields are effective only for thin films; the high field strengths required, on the order of 104 V/cm or greater, can lead to dielectric breakdown in thick samples. Nevertheless, although bulk orientation cannot be obtained via electric fields, use of electric fields does provide a complement to the surface-induced techniques described above. The only description of electric field orientation comes out of work by Ober and co-workers (37,113). They used ac electric fields, which allowed them to control orientation either parallel or perpendicular to the field direction. This is caused by an electrohydrodynamic effect, by which there exists a critical field frequency, below which the molecule orients parallel to the electric field and above which the molecule orients perpendicular to the electric field. Ober and co-workers were able to show control over the direction of orientation in a cyanate ester LCT by changing the frequency of the applied field during the cure (113). In contrast, an epoxy LCT flipped from a parallel to a perpendicular orientation during isothermal cure at a given applied frequency (37). This was attributed to a change in the critical frequency due to the increase in viscosity during cure. Magnetic-Field-Induced Orientation. Liquid crystals may be oriented in magnetic fields, even though they are diamagnetic, due to the anisotropy in their diamagnetic susceptibility. The advantage of magnetic fields over surfaceinduced orientation or electric fields is that samples are not confined to thin films.
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In fact, orientation in magnetic fields is more efficient in thicker samples, due to anchoring effects at walls. The result is that magnetic fields are the only way to obtain samples of highly cross-linked materials on which bulk properties can be measured. de Gennes has described the fundamental physics behind the orientation of liquid crystals in magnetic fields (109). Essentially, we can consider an isolated rod placed in a magnetic field. This rod experiences a torque due to the presence of the field, given by (109,114) 1 LM = − χ B2 sin 2θ 2
(2)
where χ is the anisotropy in the diamagnetic susceptibility parallel and perpendicular to the molecular axis (χ par - χ perp ), B is the magnetic field strength, and θ is the angle of the molecular axis with respect to the magnetic field direction. Most liquid crystals have a positive χ , meaning that the molecular axis aligns parallel to the applied field. Opposing this magnetic torque is a viscous torque, given by LV = − γ1
dθ dt
(3)
where γ 1 is the rotational viscosity coefficient. Essentially, this viscous torque is caused by the drag exerted on the molecule by the surrounding medium. The time dependence of the orientation process can be obtained by assuming that steady state has been reached, i.e. the sum of these torques is zero. Solving the resulting differential equation leads to −t tan θ = tan θ 0 exp (4) τ where θ 0 is the initial angle of the molecule when the field is first applied, and τ is a relaxation time given by γ1 (5) τ= χ B2 There are two important assumptions in this approach. The first is that the viscosity is a constant. Clearly for LCTs this cannot be true, as the viscosity increases during cure. It is straightforward to include a time-dependent viscosity in the model, although it makes the solution of the differential equation more complicated. The implications of this time-dependent viscosity will be discussed below. The other assumption is that this is a monodomain sample, with all molecules at the same angle with respect to the magnetic field. To account for polydomain samples, it is possible to integrate equation 4 over all possible domain orientations. When this is done, the distribution function for domain orientations is given by (114) ρ(θ,t) =
sin θ 0 dθ0 sin θ dθ
(6)
where the relationship between θ 0 and θ is defined by equation 4. Finally, the model prediction for average orientation angle of the domains, < cos2 θ >, is
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cos2 θ =
153
ρ(θ,t)sin θ cos2 θ dθ
0 π/2
(7) ρ(θ,t)sin θ dθ
0
which can then be used to calculate using equation 1. Experimentally, it has proven quite feasible to orient LCTs in magnetic fields. Two classes of materials have been studied: epoxies, which are thermally polymerized in the presence of a magnetic field (69,79,107,115–118). and acrylates or methacrylates, which are oriented in a magnetic field and then photopolymerized (12,56,119,120). Most of the work understanding the factors affecting the degree of orientation have been conducted on epoxies. From the model described above, we see that the factors that could improve orientation are higher field strength; lower initial viscosity and slower viscosity increase; longer time in the magnetic field; and a more anisotropic diamagnetic susceptibility. However, very few studies have examined these factors in detail. Benicewicz and co-workers have shown that orientation increases for 1 cured with sulfanilamide system up to a field strength of approximately 10 T (69). Lincoln and Douglas examined the combined effects of field strength, time in the field, and B-staging (prereaction) (118). They found that orientation increases with higher field strength, longer time in the field, and less B-staging (due to the lower viscosity). The liquid crystalline phase present during the orientation process is also an important factor. Theoretically, the decrease in energy upon orientation of a single molecule in the gas phase is orders of magnitude less than the thermal energy, and thus a single molecule is randomized by thermal fluctuations. In a liquid crystalline phase, however, motions of the molecules are coupled, and thus the total energy decrease of the system is much greater than the thermal energy. In addition, it has been shown theoretically that packing constraints in a smectic liquid crystal cause orientation to be considerably more difficult than in a nematic (121). Thus, we would expect that under identical conditions nematic LCTs would show the greatest degree of orientation, smectic LCTs would show a lower degree of orientation, and isotropic thermosets would show no orientation. These expectations are confirmed by experimental results. Hoyle and co-workers photopolymerized a methacrylate LCT at various temperatures in a 0.53-T field (56). Substantial orientation was observed when polymerization was conducted at low temperatures in the nematic phase. However, no orientation was observed at high temperatures, when the monomer existed in the isotropic phase. Barclay and co-workers examined 1 and oligoethers of 1, cured with methylene dianiline (67,107). Compound 1 showed much lower orientation compared to the oligoethers, because 1 itself is initially isotropic, while the oligoethers are initially nematic. Thus, the oligoethers have more time for orientation to occur, and presumably also have lower viscosity since orientation can occur before any chain branching or cross-linking can occur due to the cure reaction. Jahromi used deuterium NMR to show that the rate of orientation is lower in the smectic phase than in the nematic phase (115). Very little work has been done to understand the kinetics of the orientation process. The model described above has been used to examine the factors affecting the degree of orientation (122). The rate of orientation is determined
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70 60
θ , deg
50 40 30 20 10 0
0
4000
8000
12000
Time, s 70 60
θ , deg
50 40 30 20 10 0
0
8000
4000
12000
Time, s
Fig. 3. Model calculations of the magnetic field orientation of liquid crystals. Calculations were conducted using equations 2 and 3. In (a) comparison is made between a nonreactive liquid crystal with a constant viscosity and a reactive liquid crystal with an exponentially increasing viscosity due to the cure reaction —— reactive; unreactive. In (b) is seen the effects of magnetic field strength for the reactive liquid crystal 0.01 T; 0.025 T; – – - 0.05 T; 0.1 T. From Ref. 122. To convert T to gauss, multiply by 104 .
by a competition between the magnetic field and the viscosity. Figure 3a show the effect of the time-dependent viscosity as predicted by the above model. For a liquid crystal with a constant viscosity, the viscosity only serves to retard the orientation process; thus at long times the monodomain sample becomes completely oriented in the direction of the magnetic field. However, when the viscosity increases exponentially with time, there comes a point where the magnetic field strength is not sufficient to overcome the viscosity, and orientation ceases. In real systems, this point may correspond to the gel point. Figure 3b shows that if
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10
9
Modulus, GPa
8 7
6
5
4
3 2 −0.2
0
0.2
0.4
0.6
0.8
1
Orientation parameter
Fig. 4. Effect of magnetic field strength on the tensile modulus of compound 1 cured with sulfanilamide. The line is a quadratic fit to the data, which indicates that the modulus is determined by the average orientation of the molecules. Reprinted with permission from Ref. 69, Copyright (1998), American Chemical Society. To convert GPa to psi, multiply by 145,000.
the field strength is high enough complete orientation can be achieved before the viscosity increase overcomes the magnetic field. Unfortunately, there have been no detailed comparisons to date between this model and experimental results, and so the quantitative accuracy of this model cannot be evaluated. However, predicted trends do correspond to the experimental results described above. A few studies have examined the effect of orientation on bulk properties. Figure 4 shows the change in tensile modulus with orientation for 1 cured with sulfanilamide. Overall, the tensile modulus can be increased three times by orientation. The authors interpret the quadratic dependence of the modulus on orientation parameter as indicating that the modulus depends on the average orientation of the smectic layers (69). Tan and co-workers also found an increase in tensile modulus upon orientation (79). It has also been shown that orientation leads to an anisotropic coefficient of thermal expansion (low thermal expansion in the direction of orientation) (69,107), as well as a higher tensile strength and elongation at break (79). In contrast, experiments using a non-liquid-crystalline epoxy show no enhancements in properties after curing in a magnetic field (123), further confirming that the liquid crystalline phase is needed for orientation to occur.
Future Directions for Research The synthesis of LCT monomers and understanding of their cure behavior appears to be fairly well established. Although further effort may be needed to
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identify LCT monomers appropriate for specific situations, the general principles of how molecular structure affects the phases present, and the development of different phase structures during cure, is well understood. Future work is likely to be focussed on properties and applications of LCTs. For example, only relatively little work has been conducted on bulk mechanical properties or permeability of solvents or gases in LCTs. Important fundamental questions remain regarding the mechanism of enhancement in these properties over conventional isotropic thermosets, as well as the origin of differences in properties between different liquid crystalline phases (eg nematic vs smectic). Considerable work is also needed to fully understand and control the orientation of LCTs using external fields. Finally, applications for LCTs are not yet developed. A few optical devices have been constructed using LCTs, but general application of LCTs to optical applications has not been demonstrated. Similarly, the use of LCTs in composite structures remains limited in scope. Substantial effort is needed to show whether LCTs can exhibit performance benefits that will justify their use in future applications.
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ELLIOT P. DOUGLAS University of Florida
LITERATURE OF POLYMERS.
See INFORMATION RETRIEVAL.
LIVING POLYMERIZATION, ANIONIC. LLDPE.
See ANIONIC POLYMERIZATION.
See ETHYLENE POLYMERS, LLDPE.
LOW DENSITY POLYETHYLENE.
See ETHYLENE POLYMERS, LDPE.
