A thermoresponsive supramolecular polymer network comprising pyrene-functionalized gold nano-particles and a chain-folding polydiimide.

A thermoresponsive, supramolecular nanocomposite has been prepared by the addition of pyrenyl functionalized gold nanoparticles (AuNPs) to a polydiimide that contains receptor residues designed to form defined complexes with pyrene. The novel pyrenyl-functionalized AuNPs (P-AuNPs) were characterized by transmission electron microscopy, with surface functionalization confirmed by infrared and UV–visible spectroscopic analyses. Mixing solutions of the P-AuNPs and a π-electron-deficient polydiimide resulted in the formation of electronically complementary, chain-folded and π–π-stacked complexes, so affording a new supramolecular nanocomposite network which precipitated from solution. The P-AuNPs bind to the polydiimide via π–π stacking interactions to create supramolecular cross-links. UV–visible spectroscopic analysis confirmed the thermally reversible nature of the complexation process, and transmission electron microscopy (TEM), infrared spectroscopy (IR), and differential scanning calorimetry (DSC) were used to characterize the supramolecular-nanocomposite material. The supramolecular polymer network is insoluble at room temperature, yet may be dissolved at temperatures above 60 °C. The thermal reversibility of this system is maintained over five heat/cool cycles without diminishment of the network characteristics. In contrast to the individual components, the nanocomposite formed self-supporting films, demonstrating the benefit of the supramolecular network in terms of mechanical properties. Control experiments probing the interactions between a model diimide compound that can also form a π-stacked complex with the π-electron rich pyrene units on P-AuNPs showed that, while complexation was readily apparent, precipitation did not occur because a supramolecular cross-linked network system could not be formed with this system.

CLSM method for the dynamic observation of pH change within polymer matrices for oral delivery

If acid-sensitive drugs or cells are administered orally, there is often a reduction in efficacy associated with gastric passage. Formulation into a polymer matrix is a potential method to improve their stability. The visualization of pH within these materials may help better understand the action of these polymer systems and allow comparison of different formulations. We herein describe the development of a novel confocal laser-scanning microscopy (CLSM) method for visualizing pH changes within polymer matrices and demonstrate its applicability to an enteric formulation based on chitosan-coated alginate gels. The system in question is first shown to protect an acid-sensitive bacterial strain to low pH, before being studied by our technique. Prior to this study, it has been claimed that protection by these materials is a result of buffering, but this has not been demonstrated. The visualization of pH within these matrices during exposure to a pH 2.0 simulated gastric solution showed an encroachment of acid from the periphery of the capsule, and a persistence of pHs above 2.0 within the matrix. This implies that the protective effect of the alginate-chitosan matrices is most likely due to a combination of buffering of acid as it enters the polymer matrix and the slowing of acid penetration.

Mutual binding of polymer end-groups by complementary π–π-stacking: a molecular “Roman Handshake”

Self-complementary tweezer-molecules based on a naphthalenediimide core self-assemble into supramolecular dimers through mutual π–π-stacking and hydrogen bonding. The resulting motif is extremely stable in solution (Ka = 105 M−1), and its attachment to one terminal position of a poly(ethylene glycol) chain leads to a doubling of the polymer's apparent molecular weight.

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

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.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

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.

Self-assembly and bioactivity of a polymer/peptide conjugate containing the RGD cell adhesion motif and PEG

The self-assembly and bioactivity of the peptide–polymer conjugate DGRFFF–PEG3000 containing the RGD cell adhesion motif has been examined, in aqueous solution. The conjugate is designed to be amphiphilic by incorporation of three hydrophobic phenylalanine residues as well as the RGD unit and a short poly(ethylene glycol) (PEG) chain of molar mass 3000 kg mol-1. Above a critical aggregation concentration, determined by fluorescence measurements, signals of b-sheet structure are revealed by spectroscopic measurements, as well as X-ray diffraction. At high concentration, a self-assembled fibril nanostructure is revealed by electron microscopy. The fibrils are observed despite PEG crystallization which occurs on drying. This suggests that DGRFFF has an aggregation tendency that is sufficiently strong not to be prevented by PEG crystallization. The adhesion, viability and proliferation of human corneal fibroblasts was examined for films of the conjugate on tissue culture plates (TCPs) as well as low attachment plates. On TCP, DGRFFF–PEG3000 films prepared at sufficiently low concentration are viable, and cell proliferation is observed. However, on low attachment surfaces, neither cell adhesion nor proliferation was observed, indicating that the RGD motif was not available to enhance cell adhesion. This was ascribed to the core–shell architecture of the self-assembled fibrils with a peptide core surrounded by a PEG shell which hinders access to the RGD unit.

On the role of specific interactions in the diffusion of nanoparticles in aqueous polymer solutions

Understanding nanoparticle diffusion within non-Newtonian biological and synthetic fluids is essential in designing novel formulations (e.g., nanomedicines for drug delivery, shampoos, lotions, coatings, paints, etc.), but is presently poorly defined. This study reports the diffusion of thiolated and PEGylated silica nanoparticles, characterized by small-angle neutron scattering, in solutions of various water-soluble polymers such as poly(acrylic acid) (PAA), poly(Nvinylpyrrolidone) (PVP), poly(ethylene oxide) (PEO), and hydroxyethylcellulose (HEC) probed using NanoSight nanoparticle tracking analysis. Results show that the diffusivity of nanoparticles is affected by their dimensions, medium viscosity, and, in particular, the specific interactions between nanoparticles and the macromolecules in solution; strong attractive interactions such as hydrogen bonding hamper diffusion. The water-soluble polymers retarded the diffusion of thiolated particles in the order PEO > PVP > PAA > HEC whereas for PEGylated silica particles retardation followed the order PAA > PVP = HEC > PEO. In the absence of specific interactions with the medium, PEGylated nanoparticles exhibit enhanced mobility compared to their thiolated counterparts despite some increase in their dimensions.

Cobalt incorporation in calcite: Thermochemistry of (Ca,Co)CO3 solid solutions from density functional theory simulations

The incorporation of cobalt in mixed metal carbonates is a possible route to the immobilization of this toxic element in the environment. However, the thermodynamics of (Ca,Co)CO3 solid solutions are still unclear due to conflicting data from experiment and from the observation of natural ocurrences. We report here the results of a computer simulation study of the mixing of calcite (CaCO3) and spherocobaltite (CoCO3), using density functional theory calculations. Our simulations suggest that previously proposed thermodynamic models, based only on the range of observed compositions, significantly overestimate the solubility between the two solids and therefore underestimate the extension of the miscibility gap under ambient conditions. The enthalpy of mixing of the disordered solid solution is strongly positive and moderately asymmetric: calcium incorporation in spherocobaltite is more endothermic than cobalt incorporation in calcite. Ordering of the impurities in (0001) layers is energetically favourable with respect to the disordered solid solution at low temperatures and intermediate compositions, but the ordered phase is still unstable to demixing. We calculate the solvus and spinodal lines in the phase diagram using a sub-regular solution model, and conclude that many Ca1-xCoxCO3 mineral solid solutions (with observed compositions of up to x=0.027, and above x=0.93) are metastable with respect to phase separation. We also calculate solid/aqueous distribution coefficients to evaluate the effect of the strong non-ideality of mixing on the equilibrium with aqueous solution, showing that the thermodynamically-driven incorporation of cobalt in calcite (and of calcium in spherocobaltite) is always very low, regardless of the Co/Ca ratio of the aqueous environment.

Polymer brushes under shear: molecular dynamics simulations compared to experiments

Surfaces coated with polymer brushes in a good solvent are known to exhibit excellent tribological properties. We have performed coarse-grained equilibrium and nonequilibrium molecular dynamics (MD) simulations to investigate dextran polymer brushes in an aqueous environment in molecular detail. In a first step, we determined simulation parameters and units by matching experimental results for a single dextran chain. Analyzing this model when applied to a multichain system, density profiles of end-tethered polymer brushes obtained from equilibrium MD simulations compare very well with expectations based on self-consistent field theory. Simulation results were further validated against and correlated with available experimental results. The simulated compression curves (normal force as a function of surface separation) compare successfully with results obtained with a surface forces apparatus. Shear stress (friction) obtained via nonequilibrium MD is contrasted with nanoscale friction studies employing colloidal-probe lateral force microscopy. We find good agreement in the hydrodynamic regime and explain the observed leveling-off of the friction forces in the boundary regime by means of an effective polymer–wall attraction.

Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Exploiting thermally-reversible chemistry for controlling the crosslinking of polymer networks

High explosives are highly sensitive to accidental detonation by impact, fire, shrapnel and small arms fire. This sensitivity can be reduced by storing the energetic material within a rubbery polymer matrix and are known as plastic bonded explosives (PBX). The current procedure used to manufacture PBX involves mixing the energetic material with a hydroxy-functionalised aliphatic polymer. Upon the addition of an isocyanate crosslinker an immediate polymerisation occurs and thus the rapidly curing mixture must be used to fill the missile or shells, referred to as ‘stores’. This process can lead to poor distribution of the crosslinker resulting in the formation of an inhomogeneously crosslinked matrix and the formation of voids. One solution to this problem involves containing the crosslinker within polyurethane microcapsules that are uniformly dispersed in the explosive-polymer mixture. Upon the application of a stimulus the crosslinker can be released from the microcapsules and the formation of a uniformly crosslinked PBX achieved. Herein is reported the design and synthesis of polyurethane microcapsules that release isocyanate crosslinkers when desired using a thermal stimulus. This has been achieved by exploiting the thermally-reversible nature of oxime-urethane and Diels-Alder adducts that have been incorporated into the shell wall of the microcapsules. An alternative approach to controlling the polymerisation of PBX materials has also been achieved using thermally-reversible blocked isocyanates that regenerate the isocyanate crosslinker when exposed to heat.