Fused Filament Fabrication of a Dynamically Crosslinked Network Derived from Commodity Thermoplastics

A massive carbon footprint is associated with the ubiquitous use of plastics and their afterlife. Greenhouse gas (GHG) emissions from plastics are rising and increasingly consuming the global "carbon budget". It is, hence, paramount to implement an effective strategy to reclaim postconsumer plastic as feedstock for technologically innovative materials. Credible opportunity is offered by advances in materials chemistry and catalysis. Here, we demonstrate that by dynamically crosslinking thermoplastic polyolefins, commodity plastics can be upcycled into technically superior and economically competitive materials. A broadly applicable crosslinking strategy has been applied to polymers containing solely carbon-carbon and carbon-hydrogen bonds, initially by maleic anhydride functionalization, followed by epoxy-anhydride curing. These dynamic networks show a distinct rubber modulus above the melting transition. We demonstrate that sustainability and performance do not have to be mutually exclusive. The dynamic network can be extruded into a continuous filament to be in three-dimensional (3D) printing of complex objects, which retain the mechanical integrity of vitrimers. Being covalently crosslinked, these networks show a thermally triggered shape-memory response, with 90% recovery of a programmed shape. This study opens up the possibility of reclaiming recycled thermoplastics by imparting performance, sustainability, and technological advances to the reprocessed plastic.

Rheology of hard glassy materials

Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural (α) relaxation rate and the shear-induced relaxation rate. A different model is formulated here which, instead, assumes that the slowest (global) relaxation process controls the overall relaxation. We show that the first model is not compatible with the existence of finite elastic shear modulus for quasistatic (low-frequency) deformation, while the second model is able to describe all key features of deformation of 'hard' glassy solids, including the yielding transition, the nonaffine-to-affine plateau crossover, and the rate-stiffening of the modulus. The proposed framework provides an operational way to distinguish between 'soft' glasses and 'hard' glasses based on the shear-rate dependence of the structural relaxation time.

Cooperative mechanosensitivity and allostery of focal adhesion clusters

We analyse the role of cooperative interaction between neighbouring adhesion-mechanosensor complexes by constructing an Ising-like Hamiltonian describing the free energy of cell adhesion on a substrate as a lattice of 3-state mechanosensing sites involving focal adhesion kinase (FAK). We use a Monte Carlo stochastic algorithm to find equilibrium configurations of these mechanosensors in two representative geometries: on a 1D ring representing the rim of a cell on a flat surface, and a 2D bounded surface representing the whole area of cell contact with a flat surface. The level of FAK activation depends on the pulling force applied to the individual FAK-integrin via actin-myosin contractile networks, and the details of the coupling between individual sensors in a cluster. Strong coupling is shown to make the FAK sensors experience a sharp on-off behaviour in their activation, while at low coupling the activation/autoinhibition transition occurs over a broad range of pulling force. We find that the activation/autoinhibition transition of FAK in the 2D system with strong coupling occurs with a hysteresis, the width of which depends on the rate of change of force. The effect of introducing a regulating protein (such as Src) in a limited quantity to control FAK activation is explored, and visualizations of clustering in both topologies are presented. In particular the results on the bounded 2D surface indicate that clustering of active FAK occurs preferentially at the boundary, in agreement with experimental observations of focal adhesions in cells.

F1 rotary motor of ATP synthase is driven by the torsionally-asymmetric drive shaft

F₁F₀ ATP synthase (ATPase) either facilitates the synthesis of ATP in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F₀ and F₁, which compete for control of their shared γ -shaft. We present a self-consistent physical model of F₁ motor as a simplified two-state Brownian ratchet using the asymmetry of torsional elastic energy of the coiled-coil γ -shaft. This stochastic model unifies the physical concepts of linear and rotary motors, and explains the stepped unidirectional rotary motion. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the ‘no-load’ angular velocity is ca. 400 rad/s anticlockwise at 4 mM ATP. Increasing the pmf torque exerted by F₀ can slow, stop and overcome the torque generated by F₁, switching from ATP hydrolysis to synthesis at a very low value of ‘stall torque’. We discuss the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the ‘useful outcome’ is measured in the number of H⁺ pushed against the chemical gradient.

Local structure controls the nonaffine shear and bulk moduli of disordered solids

Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices; all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.

Shape instability on swelling of a stretched nematic elastomer filament

Liquid crystalline elastomers combine the ordering properties of liquid crystals with elasticity of crosslinked polymer networks. In monodomain (permanently aligned) elastomers, altering the orientational (nematic) order causes changes in the equilibrium sample length, which is the basis of the famous effect of large-amplitude reversible mechanical actuation. The stimulus for this effect could be a change in temperature, or illumination by light in photosensitized elastomers, but equally the nematic order changes by mixing with a solvent. This work theoretically investigates a competition between the spontaneous contraction on swelling of a monodomain nematic elastomer and the externally imposed stretching. We find that this competition leads to bistability in the system and allows a two-phase separation between a nematic state with lower swelling and an isotropic state with higher solvent concentration. We calculated the conditions in which the instability occurs as well as the mechanical and geometric parameters of equilibrium states. Being able to predict how this instability arises will provide opportunities for exploiting nematic elastomer filaments.

Role of the potential landscape on the single-file diffusion through channels

Transport of colloid particles through narrow channels is ubiquitous in cell biology as well as becoming increasingly important for microfluidic applications or targeted drug delivery. Membrane channels in cells are useful models for artificial designs because of their high efficiency, selectivity, and robustness to external fluctuations. Here, we model the passive channels that let cargo simply diffuse through them, affected by a potential profile along the way. Passive transporters achieve high levels of efficiency and specificity from binding interactions with the cargo inside the channel. This however leads to a paradox: why should channels which are so narrow that they are blocked by their cargo evolve to have binding regions for their cargo if that will effectively block them? Using Brownian dynamics simulations, we show that different potentials, notably symmetric, increase the flux through narrow passive channels - and investigate how shape and depth of potentials influence the flux. We find that there exist optimal depths for certain potential shapes and that it is most efficient to apply a small force over an extended region of the channel. On the other hand, having several spatially discrete binding pockets will not alter the flux significantly. We also explore the role of many-particle effects arising from pairwise particle interactions with their neighbours and demonstrate that the relative changes in flux can be accounted for by the kinetics of the absorption reaction at the end of the channel.

Spatial propagation of protein polymerization

We consider the spatial dependence of filamentous protein self-assembly. Through studying the cases where the spreading of aggregated material is dominated either by diffusion or by growth, we derive analytical results for the spatial evolution of filamentous protein aggregation, which we validate against Monte Carlo simulations. Moreover, we compare the predictions of our theory with experimental measurements of two systems for which we identify the propagation as either growth or diffusion controlled. Our results connect the macroscopic observables that characterize the spatial propagation of protein self-assembly with the underlying microscopic processes and provide physical limits on spatial propagation and prionlike behavior associated with protein aggregation.

Fabrication and electromechanical characterization of near-field electrospun composite fibers

We report the use of near-field electrospinning (NFES) as a route to fabricate composite electrodes. Electrodes made of composite fibers of multi-walled carbon nanotubes in polyethylene oxide (PEO) are formed via liquid deposition, with precise control over their configuration. The electromechanical properties of free-standing fibers and fibers deposited on elastic substrates are studied in detail. In particular, we examine the elastic deformation limit of the resulting free-standing fibers and find, similarly to bulk PEO composites, that the plastic deformation onset is below 2% of tensile strain. In comparison, the apparent deformation limit is much improved when the fibers are integrated onto a stretchable, elastic substrate. It is hoped that the NFES fabrication protocol presented here can provide a platform to direct-write polymeric electrodes, and to integrate both stiff and soft electrodes onto a variety of polymeric substrates.

Theory of thermally activated ionization and dissociation of bound states

Calculating the microscopic dissociation rate of a bound state, such as a classical diatomic molecule, has been difficult so far. The problem was that standard theories require an energy barrier over which the bound particle (or state) escapes into the preferred low-energy state. This is not the case when the long-range repulsion responsible for the barrier is either absent or screened (as in Cooper pairs, plasmas, or biomolecular complexes). We solve this classical problem by accounting for entropic driving forces at the microscopic level. The theory predicts dissociation rates for arbitrary potentials and is successfully tested on the example of plasma, where it yields an estimate of ionization in the core of the Sun in excellent agreement with experiments. In biology, the new theory accounts for crowding in receptor-ligand kinetics and protein aggregation.

Micro-Raman spectroscopy of algae: composition analysis and fluorescence background behavior

Preliminary feasibility studies were performed using Stokes Raman scattering for compositional analysis of algae. Two algal species, Chlorella sorokiniana (UTEX #1230) and Neochloris oleoabundans (UTEX #1185), were chosen for this study. Both species were considered to be candidates for biofuel production. Raman signals due to storage lipids (specifically triglycerides) were clearly identified in the nitrogen-starved C. sorokiniana and N. oleoabundans, but not in their healthy counterparts. On the other hand, signals resulting from the carotenoids were found to be present in all of the samples. Composition mapping was conducted in which Raman spectra were acquired from a dense sequence of locations over a small region of interest. The spectra obtained for the mapping images were filtered for the wavelengths of characteristic peaks that correspond to components of interest (i.e., triglyceride or carotenoid). The locations of the components of interest could be identified by the high intensity areas in the composition maps. Finally, the time evolution of fluorescence background was observed while acquiring Raman signals from the algae. The time dependence of fluorescence background is characterized by a general power law decay interrupted by sudden high intensity fluorescence events. The decreasing trend is likely a result of photo-bleaching of cell pigments due to prolonged intense laser exposure, while the sudden high intensity fluorescence events are not understood.

Thermodynamically stable blue phases

We show theoretically that flexoelectricity stabilizes blue phases in chiral liquid crystals. Induced internal polarization reduces the elastic energy cost of splay and bend deformations surrounding singular lines in the director field. The energy of regions of double twist is unchanged. This in turn reduces the free energy of the blue phase with respect to that of the chiral nematic phase, leading to stability over a wider temperature range. The theory explains the discovery of large temperature range blue phases in highly flexoelectric "bimesogenic" and "bent-core" materials, and predicts how this range may be increased further.

Effects of water on aggregation and stability of monoglycerides in hydrophobic solutions

We apply a set of different techniques to analyze the physical properties and phase transitions of monoglyceride (MG)-oil-water ternary systems. The effect of MGs on water absorption in food-grade hazelnut oil and in pure hydrocarbon oil (decane) is reported. Comparison between decane and hazelnut oil backgrounds indicates that the effect of water absorption is significant and universal in different MG ternary systems. Adding small amounts of cosurfactant (stearic acid) is necessary to stabilize the MGs in oil-water combinations by enhancing the swelling capacity of lamellar layers; as a result, the structures become sensitive to the pH of the aqueous phase used. The dramatic changes on increasing the aqueous content are recorded by the calorimetry. In samples with small quantities of water, the phase behavior is almost independent of the pH. Once the proportion of water increases, the effect of pH is prominent. At low pH, the solubility of MG in water is limited, and the ternary system retains key features of the oil-dominated environment, such as the sequence of two transitions on cooling, with the low-temperature sub-alpha crystalline phase. At high pH and a sufficient amount of water, the MG layers remain properly swollen, and the crystalline phase disappears from the phase diagram. We spend considerable effort identifying the inverse lamellar phase of MGs in an oil-dominated environment with the so-called alpha-gel phase that is well-established in water-dominated systems, and distinguishing "demixing" from water and from oil. The rheology is examined in different fluid and gel phases; the storage modulus generally decreased on increasing the water proportion, but a gel-like response is found in the high-temperature lamellar phase over a wide range of water dilution. We then focus on aging phenomena in the inverse lamellar (or alpha-gel) phase and show that the rearranging of hydrogen bonds is slowed down and disrupted by the presence of water, giving the lamellar gel longer life times.

Quenched random disorder and x-ray scattering in smectic elastomers

In this work we examine layer fluctuations in a smectic elastomer with quenched random disorder induced by crosslinks. The system is analyzed in a continuum model and crosslinks are introduced as a random field in a macroscopic picture. In the case of small deformations and replica symmetry the intensity profile for x-ray scattering along the layer normal was determined for layer displacements smaller than the layer separation. In this regime it is predicted that for large enough crosslink densities the first-order diffraction pattern of the solid assumes a characteristic squared-Lorentzian form, showing a decay of short-range order over a length scale of 20 nm. Crosslinks are observed to disorder the system by decreasing the correlation length, which we show not to be a consequence of the random field. The coupling to random crosslinks is predicted to retard the decrease in the correlation length and hence found to stabilize the one-dimensional periodic layer structure against thermal fluctuations. The dependence of the correlation length on the crosslink density leads us to propose an estimate for the percolation limit of a smectic elastomer network.

Aging and metastability of monoglycerides in hydrophobic solutions

Monoglyceride dispersed in oil acts as gel emulsifier to stabilize ordered lamellar structures; however, with time these phases age, leading to separation of oil and lipid. The aging of aggregated structures of monoglycerides in hydrophobic medium is described by a set of different techniques. Polarized microscopy was used to study the mesomorphic behavior as a function of time. Differential scanning calorimetry was utilized to quantitatively monitor changes in the latent heat in different phase transformations that take place in the aging system. The X-ray diffraction patterns fingerprinted the molecular arrangement in different emerging phases. Infrared spectroscopy was used to monitor the states of hydrogen bonding in the system. We conclude that in both inverted-lamellar and sub-alpha crystalline phases, monoglyceride molecules inevitably lose their emulsified ability in the hydrophobic solutions through the gradual change in hydrogen bonding patterns. On aging, the recombination of hydrogen bonding between glycerol groups causes the segregation of chiral (d and l) isomers within the bilayers. Therefore, all structures were eventually forced to reorder into the ground-state beta-crystalline phase. Accordingly, the highly ordered packing of aged structures weakened the emulsifying ability and finally led to the collapse of the percolating gel network.

Semisoft elastic response of nematic elastomers to complex deformations

We consider a relaxed semisoft elastomer with its director oriented along the z axis that is first subjected to a large stretch in the x direction then to a slight x-z shear. We give a general argument that in any theory including director rotation, at the onset and end of the director rotation induced by these large stretches, there will be kinks in the stress-large strain curve (forming a stress-strain plateau) and zeros in the x-z shear modulus (C5) associated with small shears imposed on top of the stretches. We then find the analytical forms of the C5 -strain curves for a particular model of semisoftness (arising from compositional fluctuations) and show that it, together with the known stress-strain curve, provides the basis for a strong test of this theory. Finally, we consider the scope for other semisoft models and show that the compositional fluctuations model in fact yielded a generic form, that is, it is the most general quadratic free energy that does not explicitly include a final state direction other than the director. By introducing such additional directions, a large range of alternative models could be developed.

Universal kinetics of helix-coil transition in gelatin

By covering a much wider concentration range than previous studies we find a very unusual exponential dependence of the rate of helix formation on concentration of gelatin in water and ethylene glycol solutions. By applying a procedure of concentration-temperature superposition we build a master curve describing the initial renaturation rates in both solvents. The growth of the normalized helical fraction chi(t) is a first-order process, with a rate constant consistent with cis-trans isomerization, in most situations. We propose that association of three separate chains to form a triple helical nucleus occurs rapidly and contributes less to the helical onset than previously thought. The measured helix content is a result of lengthening of the triple helix after nucleation, by zipping from the associated nuclei.

Thermal diffusion and bending kinetics in nematic elastomer cantilever

Vertically aligned monodomain nematic liquid-crystal elastomers contract when heated. If a temperature gradient is applied across the width of such a cantilever, inhomogeneous strain distribution leads to bending motion. We modelled the kinetics of thermally induced bending in the limit of a long thin strip and the predicted time variation of curvature agreed quantitatively with experimental data from samples with a range of critical indices and nematic-isotropic transition temperatures. We also deduced a value for the thermal diffusion coefficient of the elastomer.

Concentration-temperature superposition of helix folding rates in gelatin

Using optical rotation as the primary technique, we have characterized the kinetics of helix renaturation in water solutions of gelatin. By covering a wide range of solution concentrations we identify a universal exponential dependence of folding rate on concentration and quench temperature. We demonstrate a new concentration-temperature superposition of data at all temperatures and concentrations, and build the corresponding master curve. The normalized rate constant is consistent with helix lengthening. Nucleation of the triple helix occurs rapidly and contributes less to the helical onset than previously thought.

Role of polarization and alignment in photoactuation of nematic elastomers

Changing the orientational order in liquid-crystal elastomers leads to internal stresses and changes of the sample shape. When this effect is induced by light, due to photoisomerization of constituent molecular moieties, the photomechanical actuation results. We investigate quantitatively how the intensity and the polarization of light affect photoactuation. By studying dissolved, as well as covalently bonded azo-dyes, we determine the changes in absorption and the response kinetics. For the first time we compare the response of aligned monodomain, and randomly disordered polydomain nematic elastomers, and demonstrate that both have a comparable photoresponse, strongly dependent on the polarization of light. Polarization-dependent photoactuation in polydomain elastomers gives an unambiguous proof of its mechanism since it is the only experiment that distinguishes from the associated thermal effects.

Colloidal interactions and transport in nematic liquid crystals

We describe a new nematic liquid-crystal colloid system which is characterized by both charge stabilization of the particles and an interaction force. We estimate the effective charge of the particles by electrophoretic measurements and find that in such systems the director anchoring energy W is very low and the particles have little director distortion around them. The interaction force is created by producing a radial distribution of the nematic order parameter around a locally isotropic region created by ir laser heating. We theoretically describe this as being due to the induced flexoelectric polarization, the quadrupolar symmetry of which provides the required long-range force acting on charged particles.

Stretching globular polymers. I. Single chains

We review the force-extension behavior of polymers collapsed in poor solvent, modified to include the effects of semiflexibility and considered for globules with "ordered" and "disordered" internal structures. A series of ordered globules is used as a model for the unbinding of a disordered globule beneath its glass transition and for multiple-repeat proteins such as the poly-Ig-domain titin used in atomic force microscopy studies. These single-chain results form the foundation for the treatment of cross-linked networks of globular polymers.

Nematic-isotropic transition with quenched disorder

Nematic elastomers do not show the discontinuous, first-order, phase transition that the Landau-De Gennes mean field theory predicts for a quadrupolar ordering in three dimensions. We attribute this behavior to the presence of network crosslinks, which act as sources of quenched orientational disorder. We show that the addition of weak random anisotropy results in a singular renormalization of the Landau-De Gennes expression, adding an energy term proportional to the inverse quartic power of order parameter Q. This reduces the first-order discontinuity in Q. For sufficiently high disorder strength the jump disappears altogether and the phase transition becomes continuous, in some ways resembling the supercritical transitions in external field.

Fast relaxation of carbon nanotubes in polymer composite actuators

Silicone elastomer composites containing multiwalled carbon nanotubes have been irradiated with near-infrared light to study their mechanical actuation response. We show that the speed of the stimulated response is faster than Debye relaxation, instead following a compressed-exponential law. However, the relaxation after switching off the light source follows the simple-exponential relaxation, as does the stimulated response at very low nanotube concentration. We discuss possible models and explanations to account for the fast photomechanical response.

Spontaneous size selection in cholesteric and nematic emulsions

We study the spontaneous size selection in lyotropic cholesteric (W/O) and thermotropic nematic (O/W) liquid crystal emulsions. The droplet sizes have been characterized by dynamic light scattering, which indicates a narrow monomodal distribution of droplets achieved spontaneously even without emulsion filtration. Anchoring of the director, provided by the chosen surfactant on the interface, may generate a topological defect inside the droplet. Below the critical radius R = K/W, determined by the ratio of Frank elastic and the surface anchoring constants, the effective anchoring strength is weak and droplets are not topologically charged; this allows them to coalesce freely, depleting the size distribution in this range. Large droplets possess a topological charge of +1 and present a high elastic energy barrier for pair coalescence; the resulting size distribution is skewed, with R > R, and effectively frozen.

Chirality transfer and stereoselectivity of imprinted cholesteric networks

Imprinting of cholesteric textures in a polymer network is a method of preserving a macroscopically chiral phase in a system with no molecular chirality. By modifying the elastic properties of the network, the resulting stored helical twist can be manipulated within a wide range since the imprinting efficiency depends on the balance between the elastic constants and twisting power at network formation. One spectacular property of phase chirality imprinting is the created ability of the network to adsorb preferentially one stereo component from a racemic mixture. In this paper we explore this property of chirality transfer from a macroscopic to a molecular scale. In particular, we focus on the competition between the phase chirality and the local nematic order. We demonstrate that it is possible to control the subsequent release of a chiral solvent component from the imprinting network and the reversibility of the stereo-selective swelling by racemic solvents.

Stability of cellulose lyotropic liquid crystal emulsions

We studied a new kind of W/O emulsions based on a lyotropic liquid crystal as the aqueous droplet phase. The cholesteric phase, a solution hydroxypropyl cellulose in water was dispersed in the continuous oil matrix, paraffin oil or heptane. We made a specific choice of surfactant in order to impose director anchoring conditions at the oil-water interface and orient the liquid crystal inside the droplet. The strong anchoring conditions resulted in a topological defect inside the droplets of size above the critical value R(*). The defect elastic energy creates a barrier against droplet coalescence, the effect of topological size selection. We have studied the orientation of the director inside the droplets and their size distribution.

Induced helicity in biopolymer networks under stress

By combining dynamic mechanical and optical measurements in probing the internal structure of a biopolymer network (gelatin gel), we studied the quasi-equilibrium evolution of helical content as a function of the applied stress. Assuming that the net optical activity is proportional to the concentration of secondary helices of collagen chains, and assuming that affine mechanical deformation, we find a nonmonotonic relationship between the helical domains and an imposed deformation. The results are in qualitative agreement with theoretical predictions of alpha-helices induced by chain end-to-end stretching, and give a consistent picture of mechanically stimulated helix-coil transition in networks of denatured polypeptides.

Constrained Rouse model of rubber viscoelasticity

In this work we use a new approach to investigate the equilibrium and linear dynamic-mechanical response of a polymer network. The classical Rouse model is extended to incorporate quenched constraints on its end-boundary conditions; a microscopic stress tensor for the network system is then derived in the affine deformation limit. To test the model we calculate the macroscopic stress in equilibrium, corresponding to the long-time limit of relaxation. Particular attention is paid to the treatment of compressibility and hydrostatic pressure in a sample with open boundaries. Although quite different in general, for small strains the model compares well with the classic equilibrium rubber-elasticity models. The dynamic shear modulus is obtained for a network relaxing after an instantaneous step strain by keeping track of relaxation of consecutive Rouse modes of constrained network strands. The results naturally cover the whole time range--from the dynamic glassy state down to the equilibrium incompressible rubber plateau.

Stretching globular polymers. II. Macroscopic cross-linked networks

We expand upon the results for the force-extension behavior of single-collapsed polymer chains to consider the mechanical response of networks of cross-linked globular polymers in poor solvent. Force-strain curves are obtained under the affine deformation approximation for networked globules with both disordered and ordered globule conformations. Due to their large stored lengths, these networks would be capable of reaching extremely large strains. They also show anomalous nonmonotonic force-strain response, as a consequence of the nonmonotonic force-extension curves of their constituent globules. Finally, we consider the stability of ordered and disordered globules in these networks and propose means taken from biological and colloid science to stabilize networked globules.

Viscoelasticity of a protein monolayer from anisotropic surface pressure measurements

We present a method to completely characterize the viscoelasticity of Langmuir monolayers. In contrast to existing techniques, both the compression and shear moduli are determined at the same time, in a single experiment and with a standard apparatus. This approach relies on the measurement of anisotropy in the surface pressure: the tension is measured in orientations perpendicular and parallel to the compression direction. We apply this technique to the study of beta-lactoglobulin spread monolayers, a system that has been shown to develop a shear modulus at high concentration. Beta-lactoglobulin monolayers are interesting both because of their importance in food science and because they exhibit universally slow dynamical behavior that is not fully understood. Our results confirm that the compressional modulus dominates the total viscoelastic response and also provide a complex shear modulus, emerging above a critical concentration. We are able to describe how each of the dynamical response moduli is related to the surface concentration and to the equilibrium osmotic pressure.

Commentary on "Mechanical properties of monodomain side-chain nematic elastomers" by P. Martinoty, P. Stein, H. Finkelmann, H. Pleiner and H.R. Brand

We discuss the background to static and dynamic soft elasticity. The evidence in the static case and the symmetry basis for soft and semi-soft elasticity is well understood. By contrast the dynamic analogy is less clear. Lack of clean time scale separation clouds the interpretation of director relaxation keeping up, or not, with imposed strains. However, the reduction in modulus between geometries obtaining at low frequencies and being lost at high frequencies confirms that director reaction indeed determines dynamical semi-softness.

Photonic gaps in cholesteric elastomers under deformation

Cholesteric liquid crystal elastomers have interesting and potentially very useful photonic properties. In an ideal monodomain configuration of these materials, one finds a Bragg reflection of light in a narrow wavelength range and a particular circular polarization. This is due to the periodic structure of the material along one dimension. In many practical cases, the cholesteric rubber possesses a sufficient degree of quenched disorder, which makes the selective reflection broadband. We investigate experimentally the problem of how the transmittance of light is affected by mechanical deformation of the elastomer, and the relation to changes in liquid crystalline structure. We explore a series of samples which have been synthesized with photonic stop gaps across the visible range. This allows us to compare results with detailed theoretical predictions regarding the evolution of stop gaps in cholesteric elastomers.

Phase chirality and stereo-selective swelling of cholesteric elastomers

Cholesteric elastomers possess a macroscopic "phase chirality" as the director n rotates in a helical fashion along an optical axis z and can be described by a chiral order parameter alpha. This parameter can be tuned by changing the helix pitch p and the elastic properties of the network at formation. The cholesterics also possess a local nematic order, changing with temperature or during solvent swelling. In this paper, by measuring the power of optical rotation d upsilon /dz , we discover how these two parameters vary as functions of temperature or solvent adsorbed by the network. The main result is a finding of pronounced stereo-selectivity of cholesteric elastomers, demonstrating itself in the retention of the "correct" chirality component of a racemic solvent. It has been possible to quantify the amount of such stereo-separation, and the basic dynamics of the effect.

Stereo-selective swelling of imprinted cholesteric networks

Molecular chirality, and the chiral symmetry breaking of resulting macroscopic phases, can be topologically imprinted and manipulated by cross-linking and swelling of polymer networks. We present a new experimental approach to stereo-specific separation of chiral isomers by using a cholesteric elastomer in which a helical director distribution has been topologically imprinted by cross-linking. This makes the material unusual in that is has a strong phase chirality, but no molecular chirality at all; we study the nature and parameters controlling the twist-untwist transition. Adding a racemic mixture to the imprinted network results in selective swelling by only the component of "correct" handedness. We investigate the capacity of demixing in a racemic environment, which depends on network parameters and the underlying nematic order.

Stripe instability in thin films of smectic liquid-crystal polymers

Two-dimensional nanostripes are formed in thin films of side-chain liquid-crystalline polymer films when the material enters the smectic phase. The structure is investigated using transmission electron microscopy. Electron diffraction patterns show that the chain molecules are mostly aligned in the film plane and the average molecular director is parallel to the direction of the stripes. We discuss factors affecting the stripe amplitude and periodicity, such as the film thickness and the temperature of annealing in the nematic phase, and suggest a possible mechanism for their formation. We propose that an equilibrium instability occurs due to a competition between the layer-aligning effect of the substrate and the planar director alignment, forcing smectic layers perpendicular to the film surface. The stripes decorate the overall patterns of nematic director in the polymer film and provide a means of high-resolution imaging for observation of textures and disclinations.

Liquid crystalline elastomers: dynamics and relaxation of microstructure

The equilibrium mechanical response of nematic elastomers can be soft or hard depending on the relation between the imposed strains and the nematic director, in particular, if the local nematic director is able to respond by rotating. The dynamical response proves to be equally unusual. We examine the linear dynamic mechanical response of monodomain nematic elastomers under shear and the aspects of time-temperature superposition of the dynamical data across phase-transition regions. In the low-frequency region of the master curves, one finds a dramatic reduction of rubber plateau modulus and the rise in internal dissipation: in the shear geometries compatible with dynamic soft elasticity. Power-law variation of the storage modulus with frequency G' proportional, variant omega(a) agrees very well with the results of static stress relaxation, where each relaxation curve obeys the analogous power law G' proportional, variant t(-a) in the corresponding region of long times and temperatures.

Dynamic soft elasticity in monodomain nematic elastomers

We study the linear dynamic-mechanical response of monodomain nematic liquid crystalline elastomers under shear in the geometry that allows the director rotation. The aspects of time-temperature superposition are discussed at some length and Master Curves are obtained between the glassy state and the nematic transition temperature Tni. However, the time-temperature superposition did not work through the clearing point Tni, due to the transition from the "soft-elasticity" nematic regime to the ordinary isotropic rubber response. We focus on the low-frequency region of the Master Curves and establish the power law dependence of the modulus G' alpha w(a). This law agrees very well with the results of the static stress relaxation, where each relaxation curve obeys the analogous power law G' alpha t(-a) in the corresponding region of long times and temperatures.

UV isomerisation in nematic elastomers as a route to photo-mechanical transducer

The macroscopic shape of liquid-crystalline elastomers strongly depends on the order parameter of the mesogenic groups. This order can be manipulated if photo-isomerisable groups, e.g. containing N=N bonds, are introduced into the material. We have explored the large photo-mechanical response of such an azobenzene-containing nematic elastomer at different temperatures, using force and optical birefringence measurements, and focusing on fundamental aspects of population dynamics and the related speed and repeatability of the response. The characteristic time of "on" and "off" regimes strongly depends on temperature, but is generally found to be very long. We were able to verify that the macroscopic relaxation of the elastomer is determined by the nematic order dynamics and not, for instance, by the polymer network relaxation.

Propagation of acoustic waves in nematic elastomers

We develop a theory of elastic waves in oriented monodomain nematic elastomers. The effect of soft elasticity, combined with the Leslie-Ericksen version of dissipation function, results in an unusual dispersion and anomalous anisotropy of shear acoustic waves. A characteristic time scale of nematic rotation determines the crossover frequency, below which waves of some polarizations have a very strong attenuation while others experience no dissipation at all. We study the anisotropy of low-frequency Poynting vectors and wave fronts, and discuss a "squeeze" effect of energy transfer nonparallel to the wave vector. Based on these theoretical results, an application, the acoustic polarizer, is proposed.

Networks of helix-forming polymers

Biological molecules can form hydrogen bonds between nearby residues, leading to helical secondary structures. The associated reduction of configurational entropy leads to a temperature dependence of this effect: the helix-coil transition. Since the formation of helices implies a dramatic shortening of the polymer dimensions, an externally imposed end-to-end distance R affects the equilibrium helical fraction of the polymer and the resulting force-extension curves show anomalous plateau regimes. In this article, we investigate the behaviour of a crosslinked network of such helicogenic molecules, particularly focusing on the coupling of the (average) helical content present in a network to the externally imposed strain. We show that both elongation and compression can lead to an increase in helical domains under appropriate conditions.

Evolution of photonic structure on deformation of cholesteric elastomers

We subject a monodomain cholesteric liquid crystal elastomer to uniaxial strain perpendicular to its helical axis and study the response of its texture to deformation. A combination of mechanical, optical, and x-ray scattering measurements confirms the prediction for the director rotation, coarsening, and then unwinding the cholesteric helix. The study of optical absorption of circularly polarized light quantifies the complex dependence of the photonic band-gap structure on strain and directly relates to the microscopic deformation of elastomer. Agreement is found with the recently proposed theoretical prediction of the photonic structure of cholesteric elastomers.

UV manipulation of order and macroscopic shape in nematic elastomers

A range of monodomain nematic liquid-crystal elastomers containing differing proportions of photoisomerizable mesogenic moieties, which turn from a rodlike to a kinked shape upon ultraviolet (uv) irradiation, was studied. Depending on the proportion and positional role of the photosensitive groups in the crosslinked polymer network, different types and magnitudes of response were found. The principle consequence of such photoisomerization is the destabilization of the nematic phase, whose order parameter depends on temperature in a near-critical fashion. Accordingly, the effect of uv irradiation is dramatically enhanced near the critical temperature, with the associated reduction in the nematic order parameter manifesting as a change in the macroscopic shape of the elastomer samples, producing a large uniaxial contraction. Theoretical analysis of this phenomenon gives a good quantitative agreement with experiment.

Effect of cross-linker geometry on dynamic mechanical properties of nematic elastomers

We study three monodomain (single-crystal) nematic elastomer materials, all side-chain siloxane polymers with the same mesogenic groups but with different types of cross linking: (i) short flexible siloxane linkage affine to the network backbone, (ii) short flexible aliphatic cross links miscible with mesogenic side-chain groups, and (iii) long segments of main-chain nematic polymer. The dynamic mechanical response of these three systems shows a characteristically universal decrease of storage modulus and a corresponding increase of loss factor. This effect of "dynamic soft elasticity" is strongly anisotropic, depending on the nematic director orientation. We examine the important role of the average backbone chain anisotropy r(T)=l(parallel)/l(perpendicular), which is affected by the cross-linking geometry and contributes to the magnitude and frequency dependence of the dynamic anomaly, and discuss possible applications in mechanical damping and polarized acoustic technology.

Effect of crosslinker geometry on equilibrium thermal and mechanical properties of nematic elastomers

We study three monodomain (single-crystal) nematic elastomer materials, all side-chain siloxane polymers with the same mesogenic groups but with different types of crosslinking: (i) short flexible siloxane linkage affine to the network backbone, (ii) short flexible aliphatic crosslinks miscible with mesogenic side chain groups, and (iii) long segments of main-chain nematic polymer. Equilibrium physical properties of these three systems are very different, especially the spontaneous thermal expansion and anisotropic stress-strain response along and perpendicular to the uniform nematic director. In the latter case, we examine the soft elastic plateau during the director reorientation. We compare the nematic order-parameter Q(T), provided primarily by the side mesogenic groups and relatively constant between the samples, and the average backbone chain anisotropy r(T)=l( parallel)/l( perpendicular), which is strongly affected by the crosslinking geometry. The experimental data is compared quantitatively with theoretical models of nematic elastomers.

Topographic contrast of partially wetting water droplets in environmental scanning electron microscopy

Partially wetting water droplets with sizes smaller than the capillary length acquire a distinct spherical cap shape controlled by the equilibrium contact angle, which is specific for different substrates and conditions. Images of such droplets in an environmental scanning electron microscope (ESEM) show strong topographic contrast. This contrast across the droplets can be analysed within a simple theoretical model, as the droplet sides are inclined smooth surfaces. Very small droplets have ESEM intensity profiles which deviate from this topographic model. Such deviations indicate that other sources of electron signal may be important for such droplets, and also demonstrate the limits of the analytical model. For droplets sufficiently large that they lie within the range of the topographic contrast model, values of contact angles on different substrates can be deduced. These are found to agree with independent direct measurements, as well as the results given in the literature. The possibilities of using this technique to analyse physical properties of different substrates are discussed.

Cholesteric elastomers: deformable photonic solids

A mechanical strain applied to a monodomain cholesteric elastomer modulates and eventually unwinds the helical director distribution. There are similarities with the classical problem of an electric field applied to a cholesteric liquid crystal, but also differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is rather between the director being helically anchored to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Below the critical strain the coarsening of the director distribution is not accompanied by an increase but rather by an affine decrease in the pitch. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis. Finally we consider cholesteric elastomers in a classical device geometry with an electric field applied along the pitch axis and hence transverse to the director orientation.

Anomalous viscoelastic response of nematic elastomers

We report a combined theoretical and experimental study of linear viscoelastic response in oriented monodomain nematic elastomers. The model predicts a dramatic decrease in the dynamic modulus in certain deformation geometries in an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics. Dynamic mechanical measurements on monodomain nematic elastomers confirm our predictions of dependence on shear geometry and on nematic order, and also show a very substantial mechanical loss clearly associated with director relaxation.