Realizing and testing de Gennes' semi-fast artificial muscle: light-pulse-driven, acoustically limited actuation in a lamellar rubber–nematic–rubber (RNR) composite

In a 1997 note, P.-G. de Gennes proposed a 'semi-fast' artificial muscle: a lamellar composite built from an RNR triblock copolymer, in which uncrosslinked nematic polymer layers (N) alternate with crosslinked elastomeric layers (R) sharing a common axial strain. A short optical pulse, absorbed uniformly, collapses the nematic order of the N layers essentially instantaneously, and the composite contracts axially at a rate limited by elastic-wave propagation ($\tau_e=L/4c$) rather than by diffusion, while the reverse isotropic-to-nematic step on cooling is slow and inhomogeneous. His free-energy analysis predicts a composition-dependent transition and a spontaneous strain that can reach order unity for backbone nematogens. Whether the lamellar RNR composite can be realized and operated in this semi-fast optical regime, and whether the note's quantitative free-energy predictions are borne out, remains an open question.

Background

An artificial muscle is a material that converts a stimulus into a reversible macroscopic contraction capable of doing mechanical work. Early candidates — polymer gels swollen and deswollen by chemical effectors — are limited by diffusion of small molecules, so their switching is slow and their transient stress inhomogeneities can fracture the gel. Liquid crystal elastomers (LCEs) offered a faster route: an LCE is a crosslinked polymer network carrying rod-like mesogenic units; in the nematic phase the mesogens share a common average orientation (the director), and the network backbone is statistically elongated along it. When the sample is heated through the nematic–isotropic ($N\to I$) transition, orientational order is lost and the network contracts along the director by an amount coupled to the nematic order parameter. If the director is uniform across the sample (a monodomain, or 'liquid single crystal' elastomer, first made by Küpfer and Finkelmann in 1991 by crosslinking a partially cured network while it was mechanically aligned), the contraction is macroscopic and reversible; if the orientation varies from domain to domain (a polydomain), the strains cancel. Bulk LCE switching is nevertheless still rate-limited by heat diffusion into the sample and by the latent heat of the transition. In a 1997 note in Comptes Rendus de l'Académie des Sciences (Série IIb), de Gennes asked how to make this switching genuinely fast and fracture-tolerant. His proposal was a composite: a triblock copolymer R–N–R, where R denotes an ordinary elastomeric block and N a nematogenic polymer block, self-assembles by microphase separation (the segregation of chemically unlike blocks of a copolymer chain into periodic nanometre-scale domains) into a lamellar phase of alternating R and N layers (thicknesses of order 100 nm); the R blocks are then crosslinked to form a continuous rubbery matrix in which the active N layers remain uncrosslinked. Because thin incompressible lamellae share transverse strains, the composite deforms with a common axial strain $e$. Writing a Landau-type free energy for the nematic layers coupled linearly to strain (coupling coefficient $\Lambda$, measuring how strongly nematic order elongates the chain), plus rubber elasticity of the R layers, de Gennes derived a spinodal condition — the limit of metastability of the isotropic state — of the form $A(T_{NI})=\Lambda^{2}\Omega_{N}/(\Omega_{N}\mu_{N}+\Omega_{R}\mu_{R})$, where $A(T)$ is the Landau coefficient of the nematic ordering free energy evaluated at the transition temperature $T_{NI}$, $\Omega_{N},\Omega_{R}$ are layer volumes and $\mu_{N},\mu_{R}$ shear moduli, and a spontaneous axial strain in the nematic state, $e_{A}=\Lambda Q_{A}\Omega_{N}/(\mu_{N}\Omega_{N}+\mu_{R}\Omega_{R})$, with $Q_{A}$ the nematic order parameter — of order unity when the layer volumes are comparable and the mesogens sit in the backbone. The intended operation is a short light pulse (the note's mechanism: a pulse uniformly absorbed so as to raise the temperature above $T_{NI}$) with duration $\tau_p$ chosen so that $\tau_{N}<\tau_{p}<\tau_{e}$: nematic orientational relaxation ($\tau_{N}\sim10^{-7}$–$10^{-5}\ \mathrm{s}$) is faster than the pulse, and the pulse is faster than mechanical relaxation across the specimen, $\tau_{e}=L/4c$ with $c=(\mu/\rho)^{1/2}\approx40\ \mathrm{m\,s^{-1}}$ for a soft rubber — so the contraction stroke is limited by elastic-wave propagation, not by heat or mass transport. The reverse step is intrinsically slow: cooling back into the nematic state is set by thermal diffusion, $\tau_{T}\sim\ell^{2}/\pi^{2}D\approx1\ \mathrm{s}$ for a millimetre-thick specimen, and proceeds inhomogeneously, generating internal stresses — hence 'semi-fast'. Since 1997 the field has advanced along adjacent lines: photo-driven actuation of monodomain LCEs via cis–trans isomerization of azobenzene chromophores (azobenzene is a rod-like molecule that switches between an extended trans and a bent cis shape on absorbing light, thereby disrupting nematic order; Finkelmann et al. 2001; Li et al. 2003; Camacho-López et al. 2004; high-frequency photodriven oscillators by White et al. 2008 and Gelebart et al. 2017), reviewed by Bisoyi and Li (2016); and the RNR architecture itself has been synthesized (Li, Keller, Yang and Albouy 2004; Ahir, Tajbakhsh and Terentjev 2006; main-chain liquid-crystalline polyester ABA triblocks by Tokita's group 2013–2015). What none of these delivers is de Gennes' composite operating in its intended regime.

Problem Statement

Can de Gennes' semi-fast artificial muscle be realized and quantitatively verified? Specifically: fabricate a lamellar rubber–nematic–rubber (RNR) composite — a microphase-separated triblock-copolymer architecture of alternating uncrosslinked nematic polymer layers (N) and crosslinked elastomeric layers (R) sharing a common axial strain — and operate it in the regime the 1997 note defines. Resolving the question therefore requires jointly establishing, for one and the same material system: (i) evidence that the lamellar morphology and a monodomain nematic texture in the N layers are achieved and preserved through crosslinking and through repeated nematic–isotropic–nematic cycles (with the fabrication tolerances — crosslink density, block lengths, layer-volume ratio — identified), this evidence being new for the same specimen system as components (ii)–(iv) rather than the structural characterization already reported for existing RNR syntheses; (ii) driving of the nematic-to-isotropic step by a short optical pulse (photothermal) that is spatially uniform across the specimen, with pulse duration $\tau_{p}$ satisfying $\tau_{N}<\tau_{p}<\tau_{e}$ (where $\tau_{N}$ is the nematic orientational relaxation time and $\tau_{e}$ the elastic-wave time across a specimen of length $L$), and demonstration that the resulting axial contraction occurs on the elastic-wave timescale $\tau_{e}=L/4c$, with $c=(\mu/\rho)^{1/2}$ the shear-wave speed set by the shear modulus $\mu$ and density $\rho$, rather than being heat- or diffusion-limited, with a strain magnitude comparable to the predicted spontaneous strain $e_{A}=\Lambda Q_{A}\Omega_{N}/(\mu_{N}\Omega_{N}+\mu_{R}\Omega_{R})$ (where $\Lambda$ is the nematic–strain coupling coefficient, $Q_{A}$ the nematic order parameter, $\Omega_{N},\Omega_{R}$ the nematic and rubber layer volumes, and $\mu_{N},\mu_{R}$ the corresponding shear moduli; the measured value is to be reported against $e_{A}$, with any gap accounted for through the measured order parameter, layer-volume ratio, or coupling strength); (iii) measurement of the reverse (cooling-induced, isotropic-to-nematic) step — its timescale, spatial inhomogeneity, internal-stress distribution, and how these stresses and repeated cycling affect mechanical integrity (fatigue); and (iv) a quantitative comparison of the measured transition behavior and actuation strain with the note's composite free-energy relations, including the composition-dependent transition condition $A(T_{NI})=\Lambda^{2}\Omega_{N}/(\Omega_{N}\mu_{N}+\Omega_{R}\mu_{R})$ ($A(T)$ being the Landau coefficient of nematic ordering at the transition temperature $T_{NI}$; symbols as in (ii)), thereby confirming, correcting, or refuting the theoretical estimates that motivated the architecture. These four components serve one objective — establishing whether the self-assembled lamellar RNR composite works as the fast-stroke, slow-recovery actuator the note predicted — so what the question asks for is the self-assembled lamellar RNR composite operating in the semi-fast optical regime the note defines — not a material realized only as a slow thermal actuator, nor fast optical switching demonstrated only in a different liquid-crystal-elastomer architecture.

References

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