Liquid crystalline elastomers (LCE) are semiflexible polymer networks characterized by spontaneous segment-level mesomorphic ordering.1, 2 Orientational and sometimes positional couplings between neighboring chain segments perturb the statistics of elastic network chains, which adopt oblate or prolate ellipsoidal conformations. LCE therefore exhibit strong deviations from ordinary rubber elasticity, leading to striking physical phenomena such as the polydomain-to-monodomain (P-M) transition3–, 7 and the shape changes and director reorientations observed in globally oriented “monodomain” samples.8–20 The physical factors governing the dynamic mechanical response of LCE are of primary fundamental interest, as it is exceptional mechanical behavior that distinguishes LCE from all other elastomers.
LCE can be broadly classified as either the side-chain type (SCLCE), in which mesogens are attached to the backbone as pendant groups, or the main-chain type (MCLCE), in which mesogens are directly incorporated into the backbone. Several studies of the dynamic mechanical properties of SCLCE3, 5, 8, 21–31 and MCLCE6, 7, 32–34 have appeared in recent years. MCLCE have a more direct coupling between backbone conformation and mesogen orientation compared with SCLCE, and the elasticity of MCLCE is significantly affected by the presence of hairpin folds.34 Thus, one expects fundamental differences in relaxation dynamics between SCLCE and MCLCE. In addition to backbone architecture, the nature of mesomorphic ordering (smectic vs. nematic vs. other) also influences relaxation dynamics. Clarke et al. noted a very high mechanical loss factor [tan δ ≡ G″(ω)/G′(ω) or E″ ((ω)/E′(ω)] in polydomain nematic side-chain LCE. The high values of tan δ noted were attributed in part to the dynamic soft elasticity of nematic elastomers, where internal orientational degrees of freedom permit local director reorientations with little elastic energy cost, essentially reducing the storage modulus.21 Mechanical damping in smectic LCE is thought to be suppressed by the restricting effects of smectic layers,26 leading to the assertion that the nematic phase is more attractive for design of vibration damping materials.21
However, smectic main-chain linear polymers,35, 36 smectic SCLCE,30, 37 and smectic MCLCE33 also exhibit high mechanical damping over certain ranges of temperature and frequency. The relaxation processes underlying the high damping may be quite different compared with those at work in a nematic LCE, leading to dramatic differences in the mechanical loss spectra. This work examines the dynamic mechanical response of polydomain smectic MCLCE which pass directly into the isotropic state at a temperature Tsi without passing through a stable nematic state, in contrast to the SCLCE studied by Clarke et al.21 and Gallani et al.23 For small-strain, oscillatory shear, we find a prominent loss peak at temperatures near the smectic-isotropic (clearing) transition, similar to that observed by Weilepp et al. for SA SCLCE.37 Tan δ passes through a sharp maximum at a temperature near the clearing transition,33 in contrast to nematic SCLCE, which were found to exhibit high damping throughout the temperature range of the nematic phase.21
Stress relaxation in MCLCE is also affected by processes that are common to all polymer networks, namely relaxation of pendant (dangling) and/or free (guest) chains. We therefore explore the effects of structural imperfections on mechanical damping by comparing smectic MCLCE having varying amounts of structural imperfections, as inferred from equilibrium swelling measurements in a good solvent. We also examine the effects of branched units on dynamic mechanical response by varying the crosslink density. Only extracted samples with soluble fraction removed are considered, to avoid the potentially complicating effects of free chains or cyclics not attached to the parent network. The present investigation represents the first attempt to characterize the contribution of structural imperfections to the mechanical loss spectrum in any LCE system.
Polymer and Elastomer Synthesis
2-methylhydroquinone (99%) and allyl bromide (99%) were purchased from Alfa Aesar. Terephthaloyl chloride was purchased from TCI America. 1,1,3,3,5,5 hexamethyltrisiloxane (A2) (99%) and tetrakis(dimethylsiloxy)silane (A4) were purchased from Gelest. Details of synthesis of mesogens (B2) and fractionated linear polymers are presented in a previous report.33 The backbone of the MCLCE studied here had the repeat unit illustrated in Figure 1, with perfectly alternating mesogens and flexible oligosiloxane spacers. The mesogens were a mixture of isomers having varied placement of the methyl groups on the terminal aromatic rings.
MCLCE were prepared by nonlinear polymerization of mesogen (B2), spacer (A2), and crosslinker (A4) by Pt-catalyzed hydrosilylation, similar to the route described by Finkelmann and coworkers.38 The reaction was started by mixing monomers in CH2Cl2 solution at 45–50 °C, which was necessary to dissolve the (solid) mesogen and homogenize the immiscible monomers. CH2Cl2 represented ∼65 mass % of the initial reaction mixture in all cases. The hydrosilylation polycondensation reaction was catalyzed by platinum(0)-1,3-divinyl-1,1,3,3-tetramethyldisiloxane complex (Alfa Aesar) at a concentration of 1.0 mass % of the total concentration of combined monomers. After 14 days of cure, the CH2Cl2 was allowed to evaporate by air drying. Curing proceeded in air at 45–50 °C for an additional 1 day, then under vacuum for 1 day. The mole fraction of A groups (SiH) belonging to crosslinkers was defined as
and ρ was set to 0.04, 0.06, 0.08, or 0.10. Higher values of ρ correspond to higher effective crosslink densities. The mole ratio of total A groups (SiH) to B groups (allyl) was calculated as
For each value of ρ studied, several MCLCE were prepared that had different values of r. All MCLCE were swollen and extracted in toluene for 7 days to measure equilibrium swelling and to remove solubles, during which time the toluene was replaced with fresh solvent daily until a constant equilibrium mass was reached. The equilibrium volume swelling ratio, Qs, was calculated according to
where Ms is the total mass at equilibrium swelling, Mex is the dry mass of the extracted elastomer, and ρ1 and ρ2 are the densities of toluene and polymer in the solution state, approximated as (0.865 g/cm3 and 1.00 g/cm3), respectively. MCLCE swollen in toluene were de-swollen by slow addition of methanol (a poor solvent) to the toluene over a period of a few days, to avoid cracking from rapid evaporation of solvent, followed by air drying and vacuum drying at 50 °C. The soluble fraction was calculated according to
where Munex is the dry mass of the elastomer prior to extraction, including solubles.
Dynamic Mechanical Thermal Analysis
Shear storage moduli of extracted MCLCE were measured using a TA Instruments Q800 DMTA with the shear sandwich fixture. Sample thickness was approximately 0.3 mm. For selected samples, the complex modulus was measured at a small strain (amplitude γ0 = 0.005) using a constant temperature frequency sweep, which was repeated at temperature intervals of 5 °C, from −20 to 100 °C. Storage and loss moduli were plotted versus reduced frequency to generate a “master curve” by applying time–temperature superposition (TTS) with shift factors aT (frequency scale) and bT (storage and loss moduli). Constant frequency (ω = 1 Hz) temperature sweeps were also performed for several samples, from T = −20 to 190 °C at a temperature ramp of 10 °C/min.
Wide-Angle X-Ray Diffraction
Wide-angle X-ray diffraction (WAXD) experiments were performed on samples of 0.3 mm approximate thickness at ambient temperature (22 ± 2 °C) in transmission using a Rigaku D/MAX Rapid II instrument equipped with graphite monochromator, 300 μm pinhole collimator, and CuKα source (λ = 1.5418 Å). Corrections for polarization and oblique incidence were applied to raw data using Rigaku AreaMax software. To obtain a fiber photo of a drawn MCLCE, the sample was subjected to a uniaxial extension of magnitude λ= (L/L0) = 2.0, where L and L0 are the final and initial sample lengths, and the incident X-ray beam was normal to the axis of extension. Diffraction data were converted to grayscale images using commercial image processing software.
Differential Scanning Calorimetry
A Seiko Instruments DSC 220 CU equipped with a liquid nitrogen cooling tank was used to characterize thermal transitions in MCLCP and MCLCE under a flowing N2 atmosphere. After crimping 7 to 8 mg of sample into a TA Instruments aluminum pan, a 10 °C/min heating ramp to 195 °C was applied followed by a −10 °C/min cooling ramp to −70 °C, then followed by a final 10 °C/min heating ramp to 195 °C. DSC heating traces were recorded during the final heating ramp. Indium was used as a calibration standard for the temperature scale. The clearing temperature (Tsi) reported for the linear polymer was taken from heating traces as the temperature at which the peak of the endotherm was observed at a heating rate of 10 °C/min; uncertainty in the peak position was ± 2 °C. Glass transition temperatures (Tg) reported are based upon the midpoint of the inflection in the heating trace.
RESULTS AND DISCUSSION
The MCLCE studied here form a smectic mesophase with inter-layer d-spacing of (30.5 ± 1.0) Å at 22 °C. In a previous study, we characterized smectic ordering in the linear polymer prepared from the same mesogen (B2) and flexible connector (A2).33 The linear polymer exhibits SCA ordering with inter-layer d-spacing of (28.0 ± 1.0)Å, with a glass transition temperature (Tg) of 8 °C and a clearing temperature (Tsi) of 72 °C. The smectic state in the elastomers is characterized by a slightly higher interlayer d-spacing, and X-ray diffraction patterns are consistent with SA ordering or perhaps SCA ordering with a low tilt angle.33 Figure 2 compares DSC traces of a low molar mass, fractionated linear polymer (Mw = 11 kg/mol, Mw/Mn = 1.1) and an extracted elastomer having (r = 1.36, ρ = 0.08). The elastomer has approximately the same Tg as the linear polymer, but the endotherm expected at Tsi is indistinct, despite clear evidence of smectic ordering from WAXD and DMTA. The smectic-isotropic transition is known to be weakly first order, and the endotherm associated with clearing was difficult to detect in these elastomers, regardless of sample size or heating rate. It is possible that the enthalpy change of isotropization in the elastomers differs from that in the fractionated linear polymer. DMTA is better suited for detecting Tsi in the elastomers because it is quite sensitive to the changes in storage and loss moduli associated with loss of smectic ordering.
All MCLCE studied here are randomly oriented, polydomain elastomers prepared by crosslinking in the absence of any external aligning fields. Upon uniaxial stretching to a macroscopic draw ratio of L/L0 ≈ 2, the smectic layer normals were oriented predominantly in the direction of stretching, judging by the intensification of the low-angle reflection centered at 2θ = 2.8° (Fig. 3). No evidence of a stable nematic state was found by WAXD, differential scanning calorimetry, or optical microscopy in either the linear polymer or the elastomers at any temperature.33 DSC traces revealed that a linear polymer of moderately high molar mass (Mw = 77kg/mol) also forms a higher order smectic phase that melts near T2 ≈ 30 °C after several days of equilibration at 22 °C.33 We did not find any evidence of the higher order smectic phase in either the low molar mass linear polymer (Mw = 11 kg/mol) or the the elastomers considered in this study, however. The higher order smectic state may be destabilized by the presence of numerous chain ends (in the low molar mass linear polymer) or by the branched A4 units (in the elastomers), or the kinetics of its formation may be slowed greatly in the crosslinked elastomers.
Elastomers were prepared by varying the stoichiometric parameters ρ (eq 1) and r (eq 2). Table 1 summarizes elastomer compositions and equilibrium swelling data in toluene. Values of 0.04, 0.06, 0.08, and 0.10 were selected for ρ(mole fraction of SiH units belonging to A4), with higher values of ρ corresponding to higher chemical crosslink densities. For a given series of elastomers having constant ρ, the reaction stoichiometry was further optimized by systematic variation of the r parameter (mole ratio of SiH groups to allyloxy groups). An optimal value ropt was found for each value of ρ, assigned to the value of r producing a network having the minimum equilibrium swelling ratio (Qs) in toluene, a thermodynamically good solvent for the linear polymer. The value of ropt observed varied from ∼1.32 to 1.38, with little dependence on ρ over the range of compositions studied.
Table 1. Compositions and Equilibrium Swelling Ratios in Toluene for All MCLCE
Values of G/RT were determined in the isotropic state at 175 °C and ω = 1 Hz.
0.040 ± 0.001
1.38 ± 0.05
37 ± 4
0.040 ± 0.001
1.26 ± 0.05
16 ± 2
0.060 ± 0.001
1.32 ± 0.05
28 ± 3
0.060 ± 0.001
1.22 ± 0.05
14 ± 1
0.080 ± 0.002
1.36 ± 0.05
34 ± 6
0.080 ± 0.002
1.22 ± 0.05
18 ± 3
0.100 ± 0.002
1.38 ± 0.05
31 ± 3
0.100 ± 0.002
1.24 ± 0.05
11 ± 1
All other elastomers having (r ≠ ropt) exhibited higher Qs and were termed “imperfect.” Compositions having values of r less than about 1.2 did not reach the gel point, forming highly branched polymers or microgels rather than elastomers. Networks having r only slightly above 1.2 are therefore considered highly imperfect and are presumed to contain larger fractions of pendant chains and other defects than the “optimal” networks. The pendant chains in these networks are not necessarily linear, as some pendant structures with branches are also likely to form. Pendant chains are elastically ineffective and do not contribute to the elastic retractive force of the swollen network that balances the osmotic pressure of the solvent at the equilibrium swelling condition, leading to higher Qs.39
The observed value of ropt deviated substantially from 1, the value one might expect to be optimal for a polycondensation, where the numbers of “A” groups and “B” groups are equal. In fact, elastomer formulations having r = 1 did not even reach the gel point in the present study. Observing ropt ≠ 1.0 is not unusual for hydrosilylation crosslinking, however. Substantial deviations from stoichiometric conditions have been previously observed in Pt-catalyzed hydrosilylation end-linking studies with A4 crosslinker and B2 = either polydimethylsiloxane (PDMS)39, 40 or poly(diethylsiloxane) (PDES).41, 42 The origin of the deviation has been debated, and appears to have more than one underlying cause.39, 43
For each value of ρ studied, the optimal network also exhibited the lowest value of wsol, in addition to the lowest Qs. Soluble fractions of the MCLCE studied here ranged from 23 mass % to 52 mass %. Finkelmann et al. also reported relatively high soluble fractions of 18 to 22 mass % for a very similar crosslinking approach (with different mesogens).38 Even the optimal networks have wsol values substantially higher than the accepted range for “model” networks, which can have wsol < 1.0 mass %.39, 41, 44, 45 Thus, although the “optimal” samples are presumed to have a lower concentration of architectural defects than the “imperfect” networks, they cannot be fairly described as “model” networks. The high soluble fractions may be attributed to intramolecular cyclization reactions, encouraged by the presence of solvent during crosslinking and by the flexibility of the oligosiloxane connectors. The term “optimal” is specific to the crosslinking conditions employed in this study, and does not exclude the possibility that networks with lower equilibrium swelling and/or soluble fractions could be obtained under different crosslinking conditions, for example, reduced solvent concentration.
All networks, optimal and imperfect, were exhaustively extracted in toluene to remove solubles and thoroughly dried before characterization by DMTA in small-strain (γ0= 0.005) oscillatory shear. Figures 4 and 5 illustrate constant frequency (ω= 1 Hz) temperature ramps for samples Opt-10 and Imp-10 (ρ = 0.10). (Data at temperatures near and below Tg ≈ 10 °C may not be reliable, as slippage of a glassy sample is possible in the shear sandwich geometry.) For both samples, G′(ω) drops sharply above about 30 °C and a maximum in G″(ω) is noted as the sample passes through the glass transition. Above about 60 °C, the storage modulus drops abruptly, because of the loss of ordering upon clearing of the smectic phase. In contrast, nematic LCE are known to sometimes exhibit an increase in storage modulus above the clearing temperature,21, 24, 46 an effect which has been attributed in part to the dynamic soft elasticity of the nematic state.21, 24 For T ≫ Tsi, the storage modulus in our elastomers increases with temperature, as expected for an isotropic, rubber-like network. Comparing Opt-10 and Imp-10, the storage modulus of the imperfect network is much lower in the isotropic state at T ≫ Tsi. For example, at 175 °C and ω = 1 Hz, G′ = 0.12 MPa for Opt-10 and G′ = 0.04 MPa for Imp-10. For an isotropic, rubber-like network, one expects G ∼ νRT, where ν is the density of elastically effective chains. Values of (G/RT) determined at 175 °C and ω = 1 Hz, well above the clearing transition temperature, are presented in Table 1. The measured values of (G/RT) for the imperfect networks are substantially lower than the values of (G/RT) for the optimal networks in all cases, which is consistent with the higher equilibrium swelling of the imperfect networks. The lower values of (G/RT) and higher equilibrium swelling of the imperfect networks result from higher concentrations of elastically ineffective (pendant) chains.
Figure 6 illustrates the dependence of tan δ on temperature for optimal and imperfect elastomers with different values of ρ. Regardless of the values of ρ or r, all imperfect elastomers exhibit markedly higher loss in the isotropic phase compared with the optimal elastomers because of relaxation of pendant chains and other imperfections in the imperfect networks. The contribution of pendant chain relaxation to mechanical damping is not unique to MCLCE, of course. Pendant chains enhance vibration damping behavior of amorphous elastomers as well (e.g., polydimethylsiloxane, PDMS).40 Urayama et al. recently verified experimentally that long linear pendant chains greatly enhance mechanical loss in end-linked PDMS networks, which do not exhibit liquid crystalline or mesomorphic ordering.47 By simply increasing the fraction of long pendant chains, PDMS elastomers having tan δ > 0.5 over several decades of frequency were obtained.
From Figure 6, one can also compare tan δ for optimal MCLCE having different values of ρ. The concentration of A4 crosslinker units appears to have little effect on either the magnitude of tan δ (in the smectic state) or the temperature at which its maximum value is observed. Little difference in tan δ is noted between the optimal and imperfect networks in the smectic state. At low strains, the mechanical damping in the smectic state arises from segment-level relaxation processes that are insensitive to the details of chain connectivity, at least at the chosen frequency of observation (ω = 1 Hz). The relaxation of pendant chains occurs on a significantly longer time scale in the smectic state because of the overall slowing of chain dynamics with the constraints imposed by layering.
Networks Opt-8 and Imp-8 were further characterized by constant-temperature frequency sweeps at temperature intervals of 5 °C. Data near Tg and above were collapsed to master curves by temperature–time superposition (TTS). Frequency scale shifting of tan δ data was performed with respect to an arbitrary reference temperature Tref = 50 °C. Shift factors aT were first applied to the frequency scale to maximize the superposition of tan δ data across the entire temperature/frequency range. To achieve superposition of G′(ω) and G″(ω) data, an additional shift factor bT was applied to the moduli. At a given temperature, the value of bT applied to G′(ω) was constrained to be the same as the value of bT applied to G″(ω). The superposition of the G′(ω) and G″(ω) data appears to be quite reasonable with this shifting approach, although some regions of imperfect overlap are still seen in tan δ (most obvious in the data obtained at temperatures just above Tg and near Tsi). Shift factors applied to the data in Figures 7 and 8 are plotted in Figure 9 for the sake of documenting the shifting procedure. The values of aT determined for Opt-8 are remarkably close to those determined independently for Imp-8. The dependence of aT on temperature cannot be satisfactorily represented by the well-known Williams–Landel–Ferry (WLF) expression.48, 49
The failure of TTS is not surprising for a system that undergoes loss of positional ordering with increasing temperature. Attempts to extract physical meaning from the shift factors may be misguided, given that TTS fails for all smectic elastomers studied so far. The shifting approach assumes that the shape of the relaxation spectrum is temperature-independent, which is not true if a change in polymer backbone conformation occurs because of a phase transition. Giamberini et al. report failure of TTS for both nematic and smectic MCLCE,50 for example. The apparent reasonable superposition obtained for the moduli in Figures 7 and 8 is therefore probably an artifact of the comparatively narrow frequency range studied at each temperature (1–100 Hz). We would expect more obvious deviations from superposition had a larger frequency range been covered at each temperature.
In Figure 8, the enhanced mechanical damping due to pendant chains is again seen as a prominent shoulder in tan δ in the low frequency (high temperature) limit, which is substantially weaker in sample Opt-8. The tan δ plots for all samples in Figures 6–8 are also characterized by prominent loss peaks near Tg and Tsi. Tan δ approaches a peak value of about 1.0 in the transitional region separating the smectic and isotropic states. This temperature range defines the region of steepest decline in the storage modulus, corresponding to the loss of positional ordering associated with smectic layering. The behavior of the MCLCE studied here contrasts with the behavior of side-chain smectic elastomers studied by Clarke et al.,21 which exhibited little if any enhancement in tan δ near the smectic–nematic phase boundary. Clarke et al. observed that the total area under the loss curve between Tg and the clearing temperature appears to be proportional to the total entropy increase associated with the underlying phase transitions. This idea is consistent with the behavior of the MCLCE in this study, which undergo a significant gain in conformational entropy over a comparatively narrow temperature window, perhaps accounting for the strength of the relaxation peak near Tsi.
The dynamic mechanical response of polydomain smectic MCLCE is affected by the relaxation of structural imperfections such as pendant chains, although the effects are most obvious in the isotropic state. The value of tan δ in the isotropic state in the highly imperfect networks studied here may be enhanced by the high polydispersity of the pendant chains, which possibly include both linear and branched structures. The effects of structural imperfections are less pronounced in the smectic state at ω = 1 Hz, where the restricting effects of smectic layers slow the relaxation dynamics considerably. The relaxation of pendant chains in the smectic state may affect dynamic mechanical response at low frequencies or long times, an idea that could be examined by conducting static stress relaxation experiments in the smectic state to characterize the long-time stress relaxation power law. The strong relaxation noted in the transitional region near the clearing temperature appears to arise from segment-level relaxations that are essentially unaffected by the details of structural perfection in the network. From an engineering standpoint, smectic MCLCE are promising vibration damping materials because of the possibility of tuning the loss peak at Tsi to match a desired temperature/frequency range.33 In addition, deliberate introduction of high fractions of pendant chains or other defects provides a means to broaden temperature/frequency range of high damping.
The authors thank Mark Angelone for help with the WAXD experiments and Ralph Colby for helpful discussions.