Effect of water-soluble polymers, polyethylene glycol and poly(vinylpyrrolidone),on the gelation of aqueous micellar solutions of Pluronic copolymer F127

The micellization of F127 (E98P67E98) in dilute aqueous solutions of polyethylene glycol (PEG6000 and PEG35000) and poly(vinylpyrrolidone) (PVP K30 and PVP K90) is studied. The average hydrodynamic radius (rh,app) obtained from the dynamic light scattering technique increased with increase in PEG concentration but decreased on addition of PVP, results which are consistent with interaction of the micelles with PEG and the formation of micelles clusters, but no such interaction occurs with PVP. Tube inversion was used to determine the onset of gelation. The critical concentration of F127 for gelation increased on addition of PEG and of PVP K30 but decreased on addition of PVP K90. Small-angle X-ray scattering (SAXS) was used to show that the 30 wt% F127 gel structure (fcc) was independent of polymer type and concentration, as was the d-spacing and so the micelle hard-sphere radius. The maximum elastic modulus (G0 max) of 30 wt% F127 decreased from its value for water alone as PEG was added, but was little changed by adding PVP. These results are consistent with the packed-micelles in the 30 wt% F127 gel being effectively isolated from the polymer solution on the microscale while, especially for the PEG, being mixed on the macroscale.

Ex vivo expansion of limbal stem cells is affected by substrate properties

Limbal epithelial stem cells play a key role in the maintenance and regulation of the corneal surface. Damage or destruction of these cells results in vascularisation and corneal opacity. Subsequent limbal stem cell transplantation requires an ex vivo expansion step and preserving cells in an undifferentiated state remains vital. In this report we seek to control the phenotype of limbal epithelial stem cells by the novel application of compressed collagen substrates. We have characterised the mechanical and surface properties of conventional collagen gels using shear rheology and scanning electron microscopy. In doing so, we provide evidence to show that compressive load can improve the stiffness of collagen substrates. In addition Western blotting and immunohistochemistry display increased cytokeratin 3 (CK3) protein expression relating to limbal epithelial cell differentiation on stiff collagen substrates. Such gels with an elastic modulus of 2900 Pa supported a significantly higher number of cells than less stiff collagen gels (3 Pa). These findings have substantial influence in the development of ocular surface constructs or experimental models particularly in the fields of stem cell research, tissue engineering and regenerative medicine.

Design of a biomimetic skin for an octopus-inspired robot– Part I: characterising octopus skin

Octopus skin samples were tested under quasi-static and scissor cutting conditions to measure the in-plane material properties and fracture toughness. Samples from all eight arms of one octopus were tested statically to investigate how properties vary from arm to arm. Another nine octopus skins were measured to study the influence of body mass on skin properties. Influence of specimen location on skin mechanical properties was also studied. Material properties of skin, i.e. the Young's modulus, ultimate stress, failure strain and fracture toughness have been plotted against the position of skin along the length of arm or body. Statistical studies were carried out to help analyzing experimental data obtained. Results of this work will be used as guidelines for the design and development of artificial skins for an octopus-inspired robot.

Design of a biomimetic skin for an octopus-inspired robot - Part II: Development of the skin artefact

In order to develop skin artefact for an octopus-inspired robot arm, which is designed to be able to elongate 60% of its original length, silicone rubber and knitted nylon sheet were selected to manufacture an artificial skin, due to their higher elastic strain and high flexibility. Tensile and scissors cutting tests were conducted to characterise the matrix and reinforcing materials and the skin artefact. Material properties of the individual and the composite materials were compared with the measured properties of real octopus skin presented in Part I. The Young’s modulus of the skin should be below 20 MPa and the elastic strain range should be over 60%. The fracture toughness should be at least 0.9 kJ·m−2. Tubes made of the skin artefact filled with liquid were tested to study volume change under deformation. Finite element analysis model was developed to simulate the material and arm structure under tensile loading. Results show that the skin artefact developed has similar mechanical properties as the real octopus skin and satisfies all the design specifications of the OCTOPUS robot.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

High-strength, healable, supramolecular polymer nanocomposites

A supramolecular polymer blend, formed via π-π interactions between a π-electron rich pyrenyl endcapped oligomer and a chain-folding oligomer containing pairs of π-electron poor naphthalene-diimide (NDI) units, has been reinforced with cellulose nanocrystals (CNCs) to afford a healable nanocomposite material. Nanocomposites with varying weight percentage of CNCs (from 1.25 to 20.0 wt.%) within the healable supramolecular polymeric matrix have been prepared via solvent casting followed by compression molding, and their mechanical properties and healing behavior have been evaluated. It is found that homogeneously dispersed films can be formed with CNCs at less than 10 wt.%. Above 10 wt.% CNC heterogeneous nanocomposites were obtained. All the nanocomposites formed could be re-healed upon exposure to elevated temperatures although, for the homogeneous films, it was found that the healing rate was reduced with increasing CNC content. The best combination of healing efficiency and mechanical properties was obtained with the 7.5 wt.% CNC nanocomposite which exhibited a tensile modulus enhanced by as much as a factor of 20 over the matrix material alone and could be fully re-healed at 85 °C within 30 minutes. Thus it is demonstrated that supramolecular nanocomposites can afford greatly enhanced mechanical properties relative to the unreinforced polymer, while still allowing efficient thermal healing.

The mechanical properties of amniotic membrane influence its effect as a biomaterial for ocular surface repair

The human amniotic membrane (AM) is a tissue of fetal origin and has proven to be clinically useful as a biomaterial in the management of various ocular surface disorders including corneal stem cell transplantation. However, its success rate displays a degree of clinical unpredictability. We suggest that the measured variability inAMstiffness offers an explanation for the poor clinical reproducibility when it is used as a substrate for stem cell expansion and transplantation. Corneal epithelial stem cells were expanded upon AM samples possessing different mechanical stiffness. To investigate further the importance of biological substrate stiffness on cell phenotype we replaced AM with type I collagen gels of known stiffness. Substrate stiffness was measured using shear rheometry and surface topography was characterized using scanning electron microscopy and atomic force microscopy. The differentiation status of epithelial cells was examined using RT-PCR, immunohistochemistry and Western blotting. The level of corneal stem cell differentiation was increased in cells expanded upon AM with a high dynamic elastic shear modulus and cell expansion on type I collagen gels confirmed that the level of corneal epithelial stem cell differentiation was related to the substrate’s mechanical properties. In this paper we provide evidence to show that the preparatory method of AM for clinical use can affect its mechanical properties and that these measured differences can influence the level of differentiation within expanded corneal epithelial stem cells.

Measurement of intrinsic properties of amyloid fibrils by the peak force QNM method

We report the investigation of the mechanical properties of different types of amyloid fibrils by the peak force quantitative nanomechanical (PF-QNM) technique. We demonstrate that this technique correctly measures the Young’s modulus independent of the polymorphic state and the cross-sectional structural details of the fibrils, and we show that values for amyloid fibrils assembled from heptapeptides, a-synuclein, Ab(1–42), insulin, b-lactoglobulin,lysozyme, ovalbumin, Tau protein and bovine serum albumin all fall in the range of 2–4 GPa.

Microbiological, chemical and rheological properties of low fat set yoghurt produced with exopolysaccharide (EPS) producing Bifidobacterium strains.

In this work, the microbiological and physicochemical differences of three types of low fat set yoghurts were studied, as well as the changes taking place during storage at 4 °C for 28 days. The first yoghurt was produced with yoghurt starters and exopolysaccharide (EPS) producing Bifidobacterium longum subsp. infantis CCUG 52486 (CCUGY), the second with yoghurt starters and Bifidobacterium infantis NCIMB 702205 (NCIMBY) and the third with just yoghurt starters (control yoghurt). No significant differences were observed in terms of cell concentrations; for all three yoghurts, similar final cell concentrations were obtained for the yoghurt starter cultures (~7.5 log cfu g−1) and the Bifidobacterium strains (~7.8 log cfu g−1). Both Bifidobacterium survived well during storage, as in both cases the cell viability decreased by less than 0.5 log cfu g−1after 28 days of storage. A decrease in pH followed by an increase in lactic acid was observed during storage for all three yoghurts, which was mostly attributed to the activity of the yoghurt starter cultures. The two yoghurts with the EPS producing Bifidobacterium strains exhibited lower syneresis than the control yoghurt. The lowest was shown by CCUGY, which also exhibited the highest storage modulus and firmness, and a well defined porous web-like structure in cryo-SEM. Examination of the micro-structure of the yoghurts using cryo-scanning electron microscopy (cryo-SEM) indicated that the above observations were due to the interaction between the EPS and the milk proteins. Overall, the results indicated that the EPS producing Bifidobacterium longum subsp. infantis CCUG 52486 is the most promising strain, and can be used with yoghurt starter cultures to manufacture low fat set yoghurt with probiotic activities and at the same time enhanced physicochemical and rheological properties.

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes.

On the power amplifier nonlinearity in MIMO transmit beamforming systems

In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT.

Molecular recognition between functionalized gold nanoparticles and healable, supramolecular polymer blends – a route to property enhancement

A new, healable, supramolecular nanocomposite material has been developed and evaluated. The material comprises a blend of three components: a pyrene-functionalized polyamide, a polydiimide and pyrenefunctionalized gold nanoparticles (P-AuNPs). The polymeric components interact by forming well-defined p–p stacked complexes between p-electron rich pyrenyl residues and p-electron deficient polydiimide residues. Solution studies in the mixed solvent chloroform–hexafluoroisopropanol (6 : 1, v/v) show that mixing the three components (each of which is soluble in isolation), results in the precipitation of a supramolecular, polymer nanocomposite network. The precipitate thus formed can be re-dissolved on heating, with the thermoreversible dissolution/precipitation procedure repeatable over at least 5 cycles. Robust, self-supporting composite films containing up to 15 wt% P-AuNPs could be cast from 2,2,2- trichloroethanol. Addition of as little as 1.25 wt% P-AuNPs resulted in significantly enhanced mechanical properties compared to the supramolecular blend without nanoparticles. The nanocomposites showed a linear increase in both tensile moduli and ultimate tensile strength with increasing P-AuNP content. All compositions up to 10 wt% P-AuNPs exhibited essentially quantitative healing efficiencies. Control experiments on an analogous nanocomposite material containing dodecylamine-functionalized AuNPs (5 wt%) exhibited a tensile modulus approximately half that of the corresponding nanocomposite that incorporated 5 wt% pyrene functionalized-AuNPs, clearly demonstrating the importance of the designed interactions between the gold filler and the supramolecular polymer matrix.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Stability of an ice sheet on an elastic bed

The stability of stationary flow of a two-dimensional ice sheet is studied when the ice obeys a power flow law (Glen's flow law). The mass accumulation rate at the top is assumed to depend on elevation and span and the bed supporting the ice sheet consists of an elastic layer lying on a rigid surface. The normal perturbation of the free surface of the ice sheet is a singular eigenvalue problem. The singularity of the perturbation at the front of the ice sheet is considered using matched asymptotic expansions, and the eigenvalue problem is seen to reduce to that with fixed ice front. Numerical solution of the perturbation eigenvalue problem shows that the dependence of accumulation rate on elevation permits the existence of unstable solutions when the equilibrium line is higher than the bed at the ice divide. Alternatively, when the equilibrium line is lower than the bed, there are only stable solutions. Softening of the bed, expressed through a decrease of its elastic modulus, has a stabilising effect on the ice sheet.

Multivalency in healable supramolecular polymers: the effect of supramolecular cross-link density on the mechanical properties and healing of noncovalent polymer networks

Polymers with the ability to heal themselves could provide access to materials with extended lifetimes in a wide range of applications such as surface coatings, automotive components and aerospace composites. Here we describe the synthesis and characterisation of two novel, stimuli-responsive, supramolecular polymer blends based on π-electron-rich pyrenyl residues and π-electron-deficient, chain-folding aromatic diimides that interact through complementary π–π stacking interactions. Different degrees of supramolecular “cross-linking” were achieved by use of divalent or trivalent poly(ethylene glycol)-based polymers featuring pyrenyl end-groups, blended with a known diimide–ether copolymer. The mechanical properties of the resulting polymer blends revealed that higher degrees of supramolecular “cross-link density” yield materials with enhanced mechanical properties, such as increased tensile modulus, modulus of toughness, elasticity and yield point. After a number of break/heal cycles, these materials were found to retain the characteristics of the pristine polymer blend, and this new approach thus offers a simple route to mechanically robust yet healable materials.