Quasi-Homogeneous Photocatalysis in Ultrastiff Microporous Polymer Aerogels

The development of efficient and low-cost catalysts is essential for photocatalysis; however, the intrinsically low photocatalytic efficiency as well as the difficulty in using and recycling photocatalysts in powder morphology greatly limit their practical performance. Herein, we describe quasi-homogeneous photocatalysis to overcome these two limitations by constructing ultrastiff, hierarchically porous, and photoactive aerogels of conjugated microporous polymers (CMPs). The CMP aerogels exhibit low density but high stiffness beyond 105 m2 s-2, outperforming most low-density materials. Extraordinary stiffness ensures their use as robust scaffolds for scaled photocatalysis and recycling without damage at the macroscopic level. A challenging but desirable reaction for direct deaminative borylation is demonstrated using CMP aerogel-based quasi-homogeneous photocatalysis with gram-scale productivity and record-high efficiency under ambient conditions. Combined terahertz and transient absorption spectroscopic studies unveil the generation of high-mobility free carriers and long-lived excitonic species in the CMP aerogels, underlying the observed superior catalytic performance.

Significant anisotropic deformation and optical shifts in stretched cholesteric liquid crystal elastomers

This study explores the opto-mechanical response of cholesteric liquid crystal elastomers (CLCEs) subjected to uniaxial stretching along the x-axis, perpendicular to their helical z-axis. A definitive crossover is observed in the strain (εx) dependencies of various optical and mechanical properties, such as the transmission spectra, degree of mesogen orientation, Poisson's ratios, and tensile stress. At low strains, CLCEs exhibit a blue shift in the selective reflection band due to a reduction in the helical pitch, accompanied by a decrease in reflection selectivity for circularly polarized light. Beyond a certain critical strain further pitch alterations halt. This strain regime is marked by substantial anisotropic lateral contractions without any z-axis contraction, as indicated by a Poisson's ratio (μxz) of zero. Within this intermediate strain regime, local directors predominantly reorient towards the x-direction within the xy-plane, resulting in a quasi-plateau of tensile stress. Approaching a higher critical strain a complete loss of reflective selectivity occurs. Past this threshold, while the mechanical responses resemble those of isotropic conventional rubber, they retain a periodic structure albeit without phase chirality. These observed features are accounted for by the Mao-Terentjev-Warner model, especially when the network anisotropy parameter is adjusted to match the critical strain magnitude associated with the cessation of selective reflection.

Unraveling Non-Uniform Strain-Induced Crystallization Near a Crack Tip in Natural Rubber

Strain-induced crystallization (SIC) in natural rubber (NR) near crack tips significantly enhances crack growth resistance, but understanding the interplay between local strain field and crystallization remains challenging due to confined and heterogeneous characteristics. Using micro-scale digital image correlation (DIC) and scanning wide-angle X-ray diffraction (WAXD, with a narrow 10 µm square beam), this study maps local strain tensor properties and SIC in the vicinity of the crack tip and its peripheral zone (≈3 mm × 1 mm area). The analysis reveals a significant correlation between these properties. In the peripheral zone, there is a noticeable deviation of both the principal strain axis and the crystal orientation from the crack opening direction. These deviations are linearly correlated, which indicates that shear strain plays a significant role in determining the crystal orientation. Crucially, the maximum tensile component in the tensor of local principal strains predominantly dictates local crystallinity. This simplicity is attributed to the limited variation in types of deformation within the SIC region, with corresponding to deformations falling between planar and uniaxial stretching. These findings pave the way for predicting crystallinity distribution using solely strain field data, offering valuable insights into the role of SIC in enhancing the crack growth resistance of NR.

Replicating shear-mediated self-assembly of spider silk through microfluidics

The development of artificial spider silk with properties similar to native silk has been a challenging task in materials science. In this study, we use a microfluidic device to create continuous fibers based on recombinant MaSp2 spidroin. The strategy incorporates ion-induced liquid-liquid phase separation, pH-driven fibrillation, and shear-dependent induction of β-sheet formation. We find that a threshold shear stress of approximately 72 Pa is required for fiber formation, and that β-sheet formation is dependent on the presence of polyalanine blocks in the repetitive sequence. The MaSp2 fiber formed has a β-sheet content (29.2%) comparable to that of native dragline with a shear stress requirement of 111 Pa. Interestingly, the polyalanine blocks have limited influence on the occurrence of liquid-liquid phase separation and hierarchical structure. These results offer insights into the shear-induced crystallization and sequence-structure relationship of spider silk and have significant implications for the rational design of artificially spun fibers.

Stress-independent delay time in yielding of dilute colloidal gels

We investigate the yielding under shear for dilute poly(N-isopropyl acrylamide-co-fumaric acid) (PNIPAM-FAc) colloidal gels obtained above the volume phase transition temperature. In this temperature range, the microgel suspensions form colloidal gels due to hydrophobic interparticle interactions under appropriate pH and ionic strength conditions. Step-strain tests revealed that yielding occurs when the applied strain exceeds a specific threshold, requiring a finite, stress-independent delay time (tD). This is distinct from previous findings on delayed yielding in other colloidal gels, where tD decreases with increasing stress. In the start-up shear tests, yield strain (γy) at a higher strain rate () increases with escalating , while γy at lower  remains constant. This characteristic γy- relationship is successfully explained by a simple model using the stress-independent tD value without an adjustable fitting parameter. The distinctive yielding behavior, underscored by a stress-independent tD, is expected to originate from strain-induced macroscopic phase separation into a dense colloidal gel and water, observable separately from rheological measurements.

Strain hardening in biaxially stretched elastomers undergoing strain-induced crystallization

We reveal strain hardening due to strain-induced crystallization (SIC) in both cross-linked natural rubber (NR) and its synthetic analogue (IR) under planar extension, a type of biaxial stretching where the rubber is stretched in one direction while maintaining the dimension in the other direction unchanged. Utilizing a bespoke biaxial tensile tester, planar extension tests were conducted on geometrically designed and optimally shaped sheet specimens to achieve a uniform and highly strained field. Evident strain hardening due to SIC was observed in both stretching (x) and constrained (y) directions when the stretch (λx) exceeded a critical value λx,c. The λx,c value aligned with the onset stretch of SIC in planar extension, as determined by wide-angle X-ray scattering measurements. Interestingly, the nominal stress ratio between the constrained (σy) and stretching (σx) axes as a function of λx exhibited a distinct minimum near λx,c. This minimum signifies that the increment of σx induced by an increase in λx surpasses that of σy before strain hardening (λx < λx,c), while the relationship is reversed in the strain hardening region (λx > λx,c). The λx,c value in planar extension (4.7 for IR and 4.5 for NR) was slightly lower than that in uniaxial extension (5.7 for IR and 5.2 for NR). This difference in λx,c values can be explained by considering a single mechanical work required for strain hardening, owing to the relatively small dissimilarities between the two stretching modes. This investigation contributes significantly to the understanding of SIC phenomena in biaxial stretching, and provides valuable insights for predicting the mechanical response of SIC rubber under various deformation conditions.

Porous supramolecular gels produced by reversible self-gelation of ruthenium-based metal-organic polyhedra

Supramolecular gels based on metal-organic polyhedra (MOPs) represent a versatile platform to access processable soft materials with controlled porosity. Herein, we report a self-gelation approach that allows the reversible assembly of a novel Ru-based MOP in the form of colloidal gels. The presence of cationic mixed-valence [Ru2(COO)4]+ paddlewheel units allows for modification of the MOP charge via acid/base treatment, and therefore, its solubility. This feature enables control over supramolecular interactions, making it possible to reversibly force MOP aggregation to form nanoparticles, which further assemble to form a colloidal gel network. The gelation process was thoroughly investigated by time-resolved ζ-potential, pH, and dynamic light scattering measurements. This strategy leads to the evolution of hierarchically porous aerogel from individual MOP molecules without using any additional component. Furthermore, we demonstrate that the simplicity of this method can be exploited for the obtention of MOP-based gels through a one-pot synthetic approach starting from MOP precursors.

Pore-Networked Gels: Permanently Porous Ionic Liquid Gels with Linked Metal-Organic Polyhedra Networks

Porous liquids (PLs) are attractive materials because of their capability to combine the intrinsic porosity of microporous solids and the processability of liquids. Most of the studies focus on the synthesis of PLs with not only high porosity but also low viscosity by considering their transportation in industrial plants. However, a gap exists between PLs and solid adsorbents for some practical cases, where the liquid characteristics and mechanical stability without leakage are simultaneously required. Here, we fill in this gap by demonstrating a new concept of pore-networked gels, in which the solvent phase is trapped by molecular networks with accessible porosity. To achieve this, we fabricate a linked metal-organic polyhedra (MOPs) gel, followed by exchanging the solvent phase with a bulky liquid such as ionic liquids (ILs); the dimethylformamide solvent trapped inside the as-synthesized gel is replaced by the target IL, 1-butyl-3-methylimidazolium tetrafluoroborate, which in turn cannot enter MOP pores due to their larger molecular size. The remaining volatile solvents in the MOP cavities can then be removed by thermal activation, endowing the obtained IL gel (Gel_IL) with accessible microporosity. The CO₂ capacities of the gels are greatly enhanced compared to the neat IL. The exchange with the IL also exerts a positive influence on the final gel performances such as mechanical properties and low volatility. Besides ILs, various functional liquids are shown to be amenable to this strategy to fabricate pore-networked gels with accessible porosity, demonstrating their potential use in the field of gas adsorption or separation.

Four distinct network patterns of supramolecular/polymer composite hydrogels controlled by formation kinetics and interfiber interactions

Synthetic composite hydrogels comprising supramolecular fibers and covalent polymers have attracted considerable attention because their properties are similar to biological connective tissues. However, an in-depth analysis of the network structures has not been performed. In this study, we discovered the composite network can be categorized into four distinct patterns regarding morphology and colocalization of the components using in situ, real-time confocal imaging. Time-lapse imaging of the network formation process reveals that the patterns are governed by two factors, the order of the network formation and the interactions between the two different fibers. Additionally, the imaging studies revealed a unique composite hydrogel undergoing dynamic network remodeling on the scale of a hundred micrometers to more than one millimeter. Such dynamic properties allow for fracture-induced artificial patterning of a network three dimensionally. This study introduces a valuable guideline to the design of hierarchical composite soft materials.

Negative and Positive Energetic Elasticity of Polydimethylsiloxane Gels

We investigated the thermoelasticity of polydimethylsiloxane (PDMS) gels containing six types of solvents with different solubilities. The contribution of energetic elasticity to the total stress (σ_E/σ) ranges from +0.20 to -0.20 depending on the solvent species. The σ_E/σ values are positive for the solvents with low molecular mass. By contrast, it is negative for oligodimethylsiloxane (ODMS) or PDMS solvents acting as athermal solvents, each of which has the same chemical structure as the network strands. The investigation using a PDMS rubber without a solvent and the PDMS gels with various ODMS contents reveal a crossover of the σ_E/σ value from positive to negative with increasing ODMS content. The pronounced dependence of σ_E/σ on the solvent species and the negative energetic elasticity specific to the high contents of ODMS and PDMS unveil previously unknown aspects of thermoelasticity of polymer gels. The orientation coupling between the segments of the free polymeric chains and network strands is one of the possible scenarios to explain the negative energetic elasticity specific to the ODMS and PDMS solvents, because it stabilizes the aligned state, reducing the elastic energy.

Transition of rupture mode of strain crystallizing elastomers in tensile edge-crack tests

We revisit the classical results that the fracture energy density (W_b) of strain crystallizing (SC) elastomers exhibits an abrupt change at a characteristic value () of initial notch length (c₀) in tensile edge-crack tests. We elucidate that the abrupt change of W_b reflects the transition in rupture mode between the catastrophic crack growth without a significant SIC effect at c₀ > and the crack growth like that under cyclic loading (dc/dn mode) at c₀ < as a result of a pronounced SIC effect near the crack tip. At c₀ < , the tearing energy (G) was considerably enhanced by hardening via SIC near the crack tip, preventing and postponing catastrophic crack growth. The fracture dominated by the dc/dn mode at c₀ < was validated by the c₀-dependent G characterized by G = (c₀/B)^1/2/2 and the specific striations on the fracture surface. As the theory expects, coefficient B quantitatively agreed with the result of a separate cyclic loading test using the same specimen. We propose the methodology to quantify the tearing energy enhanced via SIC (G_SIC) and to evaluate the dependence of G_SIC on ambient temperature (T) and strain rate (). The disappearance of the transition feature in the W_b-c₀ relationships enables us to estimate definitely the upper limits of the SIC effects for T (T*) and  (*). Comparisons of the G_SIC, T*, and * values between natural rubber (NR) and its synthetic analog reveal the superior reinforcement effect via SIC in NR.

Time-strain inseparability in multiaxial stress relaxation of supramolecular gels formed via host-guest interactions

Supramolecular hydrogels utilizing host-guest interactions (HG gels) exhibit large deformability and pronounced viscoelasticity. The inclusion complexes between β-cyclodextrin (host) and adamantane (guest) units on the water-soluble polymers form transient bonds. The HG gels show significant stress relaxation with finite equilibrium stress following the step strain. The stress relaxation process reflects the detachment dynamics of the transient bonds which sustain the initial stress, while the finite equilibrium stress is preserved by the permanent topological cross-links with a rotaxane structure. Nonlinear stress relaxation experiments in biaxial stretching with various combinations of two orthogonal strains unambiguously reveal that time and strain effects on stress are not separable. The relaxation is accelerated for a short time frame (<10² s) with an increase in the magnitude of strain, whereas it is retarded for a longer time window with an increase in the anisotropy of the imposed biaxial strain. The time-strain inseparability in the HG gels is in contrast to the simple nonlinear viscoelasticity of a dual cross-link gel with covalent and transient cross-links in which the separability was previously validated by the same assessment. We currently interpret that the significant susceptibility of the detachment dynamics to the deformation type results from the structural characteristics of the HG gels, i.e., the host and guest moieties covalently connected to the network chains, the considerably low concentrations (<0.1 M) of these moieties, and the slidability of the permanent rotaxane cross-links.

Impact of Strain-Induced Crystallization on Fast Crack Growth in Stretched cis-1,4-Polyisoprene Rubber

cis-1,4-Polyisoprene (IR) elastomers harden via strain-induced crystallization (SIC) when the imposed stretch (λ) exceeds the onset value of SIC (λ*). We investigate the Mode-I fast crack growth in the IR sheets as a function of λ in a pure shear geometry. The steady-state crack velocity (V) increases with increasing λ, and V exceeds the shear wave speed of sound at λ > λ_s. Further stretch beyond λ* (>λ_s) causes SIC-driven hardening, resulting in a pronounced increase in V. The characteristics of the crack-tip strain field are also significantly influenced by the SIC-driven hardening: The crack-tip opening displacement increases with increasing λ at λ < λ* but exhibits an abrupt reduction beyond λ*. The crack-tip singularity and the area of strain increment caused by the crack growth change discontinuously around λ*. The abrupt variations in these crack-tip characteristics result from the considerable differences in the mechanical properties prior to the crack growth between the entirely amorphous state at λ < λ* and the partially crystallized state at λ > λ*.

Control of Extrinsic Porosities in Linked Metal-Organic Polyhedra Gels by Imparting Coordination-Driven Self-Assembly with Electrostatic Repulsion

The linkage of metal-organic polyhedra (MOPs) to synthesize porous soft materials is one of the promising strategies to combine processability with permanent porosity. Compared to the defined internal cavity of MOPs, it is still difficult to control the extrinsic porosities generated between crosslinked MOPs because of their random arrangements in the networks. Herein, we report a method to form linked MOP gels with controllable extrinsic porosities by introducing negative charges on the surface of MOPs that facilitates electrostatic repulsion between them. A hydrophilic rhodium-based cuboctahedral MOP (OHRhMOP) with 24 hydroxyl groups on its outer periphery can be controllably deprotonated to impart the MOP with tunable electrostatic repulsion in solution. This electrostatic repulsion between MOPs stabilizes the kinetically trapped state, in which an MOP is coordinated with various bisimidazole linkers in a monodentate fashion at a controllable linker/MOP ratio. Heating of the kinetically trapped molecules leads to the formation of gels with similar colloidal networks but different extrinsic porosities. This strategy allows us to design the molecular-level networks and the resulting porosities even in the amorphous state.

Hypercrosslinked Polymer Gels as a Synthetic Hybridization Platform for Designing Versatile Molecular Separators

Hypercrosslinked polymers (HCPs), amorphous microporous three-dimensional networks based on covalent linkage of organic building blocks, are a promising class of materials due to their high surface area and easy functionalization; however, this type of material lacks processability due to its network rigidity based on covalent crosslinking. Indeed, the development of strategies to improve its solution processability for broader applications remains challenging. Although HCPs have similar three-dimensionally crosslinked networks to polymer gels, HCPs usually do not form gels but insoluble powders. Herein, we report the synthesis of HCP gels from a thermally induced polymerization of a tetrahedral monomer, which undergoes consecutive solubilization, covalent bond formation, colloidal formation, followed by their aggregation and percolation to yield a hierarchically porous network. The resulting gels feature concentration-dependent hierarchical porosities and mechanical stiffness. Furthermore, these HCP gels can be used as a platform to achieve molecular-level hybridization with a two-dimensional polymer during the HCP gel formation. This method provides functional gels and corresponding aerogels with the enhancement of porosities and mechanical stiffness. Used in column- and membrane-based molecular separation systems, the hybrid gels exhibited a separation of water contaminants with the efficiency of 97.9 and 98.6% for methylene blue and KMnO₄, respectively. This result demonstrated the potentials of the HCP gels and their hybrid derivatives in separation systems requiring macroscopic scaffolds with hierarchical porosity.

Marked Sensitivity of Ultimate Elongation to Loading Axiality in Polyrotaxane Gels with Largely Slidable Cross Links

Polyrotaxane (PR) gels with low ring densities have figure-of-eight cross links that can slide along network strands. The slidable cross links have a unique ability to increase the network strand length between adjacent cross links in the loading direction via chain supply from the stress-free direction, thereby enhancing the ultimate elongation (λ_m) of the gels. We reveal that this enhancement of λ_m due to the slidable cross links is pronounced specifically in uniaxial stretching, while it is considerably modest in biaxial stretching. The sensitivity of λ_m to loading axiality becomes larger as the ring densities decrease. The corresponding difference in λ_m is markedly larger for the PR gels with low ring densities than that for the networks with fixed cross links. The exceptional sensitivity of λ_m to loading axiality unveils a previously unidentified aspect of the chain-supply mechanism based on slidable cross links.

Phototriggered Spatially Controlled Out-of-Equilibrium Patterns of Peptide Nanofibers in a Self-Sorting Double Network Hydrogel

Out-of-equilibrium patterns arising from diffusion processes are ubiquitous in nature, although they have not been fully exploited for the design of artificial materials. Here, we describe the formation of phototriggered out-of-equilibrium patterns using photoresponsive peptide-based nanofibers in a self-sorting double network hydrogel. Light irradiation using a photomask followed by thermal incubation induced the spatially controlled condensation of peptide nanofibers. According to confocal images and spectroscopic analyses, metastable nanofibers photodecomposed in the irradiated areas, where thermodynamically stable nanofibers reconstituted and condensed with a supply of monomers from the nonirradiated areas. These supramolecular events were regulated by light and diffusion to facilitate the creation of unique out-of-equilibrium patterns, including two lines from a one-line photomask and a line pattern of a protein immobilized in the hydrogel.

Multiscale structural control of linked metal-organic polyhedra gel by aging-induced linkage-reorganization

Assembly of permanently porous metal-organic polyhedra/cages (MOPs) with bifunctional linkers leads to soft supramolecular networks featuring both porosity and processability. However, the amorphous nature of such soft materials complicates their characterization and thus limits rational structural control. Here we demonstrate that aging is an effective strategy to control the hierarchical network of supramolecular gels, which are assembled from organic ligands as linkers and MOPs as junctions. Normally, the initial gel formation by rapid gelation leads to a kinetically trapped structure with low controllability. Through a controlled post-synthetic aging process, we show that it is possible to tune the network of the linked MOP gel over multiple length scales. This process allows control on the molecular-scale rearrangement of interlinking MOPs, mesoscale fusion of colloidal particles and macroscale densification of the whole colloidal network. In this work we elucidate the relationships between the gel properties, such as porosity and rheology, and their hierarchical structures, which suggest that porosity measurement of the dried gels can be used as a powerful tool to characterize the microscale structural transition of their corresponding gels. This aging strategy can be applied in other supramolecular polymer systems particularly containing kinetically controlled structures and shows an opportunity to engineer the structure and the permanent porosity of amorphous materials for further applications.

Linear Dynamic Viscoelasticity of Dual Cross-Link Poly(Vinyl Alcohol) Hydrogel with Determined Borate Ion Concentration

We investigated the linear dynamic viscoelasticity of dual cross-link (DC) poly(vinyl alcohol) (PVA) (DC-PVA) hydrogels with permanent and transient cross-links. The concentrations of incorporated borate ions to form transient cross-links in the DC-PVA hydrogels (CBIN) were determined by the azomethine-H method. The dynamic viscoelasticity of the DC-PVA hydrogel cannot be described by a simple sum of the dynamic viscoelasticity of the PVA gel with the same permanent cross-link concentration and the PVA aqueous solution with the same borate ion concentration (CB = CBIN) as in the DC-PVA gel. The DC-PVA hydrogel exhibited a considerably higher relaxation strength, indicating that the introduction of permanent cross-links into temporary networks increases the number of viscoelastic chains with finite relaxation times. In contrast, the relaxation frequency (ωc) (given by the frequency at the maximum of loss modulus) for the DC-PVA hydrogel was slightly lower but comparable to that for a dilute PVA solution with the same CB. This signifies that the relaxation dynamics of the DC-PVA hydrogels is essentially governed by the lifetime of an interchain transient cross-link (di-diol complex of boron). The effect of permanent cross-linking on the relaxation dynamics was observed in the finite broadening of the relaxation-time distribution in the long time region.

Probing the in-plane liquid-like behavior of liquid crystal elastomers

When isotropic solids are unequally stretched in two orthogonal directions, the true stress (force per actual cross-sectional area) in the larger strain direction is typically higher than that in the smaller one. We show that thiol-acrylate liquid crystal elastomers with polydomain texture exhibit an unusual tendency: The true stresses in the two directions are always identical and governed only by the area change in the loading plane, independently of the combination of imposed strains in the two directions. This feature proves a previously unidentified state of matter that can vary its shape freely with no extra mechanical energy like liquids when deformed in the plane. The theory and simulation that explain the unique behavior are also provided. The in-plane liquid-like behavior opens doors for manifold applications, including wrinkle-free membranes and adaptable materials.

Porous Colloidal Hydrogels Formed by Coordination-Driven Self-Assembly of Charged Metal-Organic Polyhedra

Introduction of porosity into supramolecular gels endows soft materials with functionalities for molecular encapsulation, release, separation and conversion. Metal-organic polyhedra (MOPs), discrete coordination cages containing an internal cavity, have recently been employed as building blocks to construct polymeric gel networks with potential porosity. However, most of the materials can only be synthesized in organic solvents, and the examples of porous, MOP-based hydrogels are scarce. Here, we demonstrate the fabrication of porous hydrogels based on [Rh₂ (OH-bdc)₂ ]₁₂ , a rhodium-based MOP containing hydroxyl groups on its periphery (OH-bdc=5-hydroxy-1,3-benzenedicarboxylate). By simply deprotonating [Rh₂ (OH-bdc)₂ ]₁₂ with the base NaOH, the supramolecular polymerization between MOPs and organic linkers can be induced in the aqueous solution, leading to the kinetically controllable formation of hydrogels with hierarchical colloidal networks. When heating the deprotonated MOP, Na_x [Rh₂₄ (O-bdc)_x (OH-bdc)_24-x ], to induce gelation, the MOP was found to partially decompose, affecting the mechanical property of the resulting gels. By applying a post-synthetic deprotonation strategy, we show that the deprotonation degree of the MOP can be altered after the gel formation without serious decomposition of the MOPs. Gas sorption measurements confirmed the permanent porosity of the corresponding aerogels obtained from these MOP-based hydrogels, showing potentials for applications in gas sorption and catalysis.

Effect of stretching angle on the stress plateau behavior of main-chain liquid crystal elastomers

The equilibrium nonlinear stress-stretch relationships for a monodomain main-chain nematic elastomer (MNE) are investigated by varying the angle between the stretching and initial director axes (θ₀). Angle θ₀ has pronounced effects on the ultimate elongation as well as on the width of the low stress plateau regime (Λ_p) during director rotation, whereas θ₀ has no appreciable effect on the plateau stress (σ_p). In the stretching normal to the initial director (θ₀ = 90°), the plateau end exceeds 200% strain. At oblique angles of 90° > θ₀≥ 35°, Λ_p decreases with decreasing θ₀, whereas the definite plateau regime vanishes at θ₀ < 24°. Wide-angle X-ray scattering and polarized optical microscopy measurements reveal that the director rotates uniformly in the biased direction for the MNE of θ₀°≪ 90°, whereas directors rotating clockwise and counterclockwise are coexistent for θ₀ = 90°. Over the entire plateau regime, the MNEs exhibit pure shear deformation characterized by a Poisson's ratio of zero in the direction of the rotation axis. The Λ_p for the corresponding polydomain NE (PNE) undergoing a transition to the monodomain alignment is smaller than that of the MNE of θ₀ = 90°, while the σ_p values for both NEs are almost similar. The semi-soft elasticity concept satisfactorily explains the effects of θ₀ on Λ_p, and the Λ_p value of the PNE, using a single anisotropy parameter which is evaluated from the degree of thermally induced deformation of MNEs.