Simulation of Entangled Polymer Solutions

We present a computer simulation of entangled polymer solutions at equilibrium. The chains repel each other via a soft Gaussian potential, appropriate for semi-dilute solutions at the scale of a correlation blob. The key innovation to suppress chain crossings is to use a pseudo-continuous model of a backbone which effectively leaves no gaps between consecutive points on the chain, unlike the usual bead-and-spring model. Our algorithm is sufficiently fast to observe the entangled regime using a standard desktop computer. The simulated structural and mechanical correlations are in fair agreement with the expected predictions for a semi-dilute solution of entangled chains

Liquid–liquid equilibrium in polymer–fullerene mixtures; an in situ neutron reflectivity study

The composition profiles of a series of model polystyrene/fullerene bilayers are measured, before, during and after thermal annealing, using in situ neutron reflectometry. In combination with grazing-incidence X-ray diffraction measurements, these experiments, which quantify layer compositions as a function of molecular weight using changes in both scattering length density and layer thickness, extend and corroborate recent measurements on ex situ annealed samples and demonstrate that the composition profiles rapidly formed in these systems correspond to two co-existing liquid–liquid phases in thermodynamic equilibrium. The measurements also demonstrate a clear and systematic onset temperature for diffusion of the fullerenes into the PS layer that correlates with the known glass-transition temperatures of both the polymer (as a function of molecular weight) and the fullerene, revealing that the molecular mobility of the fullerenes in these systems is controlled by the intrinsic mobility of the fullerenes themselves and the ability of the polymer to plasticise the fullerenes at the interface. Over the temperature range investigated (up to 145 °C), measurements of equilibrated composition profiles as a function of temperature (during gradual cooling) reveal no significant changes in composition profile, other than those associated with the known thermal expansion/contraction of polystyrene thin-films

Interface-induced d-wave pairing

We discuss a scenario for interface-induced superconductivity involving pairing by dipolar excitations proximate to a two-dimensional electron system controlled by a transverse electric field. If the interface consists of transition metal oxide materials, the repulsive on-site Coulomb interaction is typically strong and a superconducting state is formed via exchange of non-local dipolar excitations in the d-wave channel. Perspectives to enhance the superconducting transition temperature are discussed.Comment: 4 pages, 3 figure

Tuneable interfacial surfactant aggregates mimic lyotropic phases and facilitate large scale nanopatterning.

It is shown that the air-liquid interface can be made to display the same rich curvature phenomena as common lyotropic liquid crystal systems. Through mixing an insoluble, naturally occurring, branched fatty acid, with an unbranched fatty acid of the same length, systematic variation in the packing constraints at the air-water interface could be obtained. The combination of atomic force microscopy and neutron reflectometry is used to demonstrate that the water surface exhibits significant tuneable topography. By systematic variation of the two fatty acid proportions, ordered arrays of monodisperse spherical caps, cylindrical sections, and a mesh phase are all observed, as well as the expected lamellar structure. The tuneable deformability of the air-water interface permits this hitherto unexplored topological diversity, which is analogous to the phase elaboration displayed by amphiphiles in solution. It offers a wealth of novel possibilities for the tailoring of nanostructure

Solid Surface Structure Affects Liquid Order at the Polystyrene/SAM Interface

We present a combined x-ray and neutron reflectivity study characterizing the interface between polystyrene (PS) and silanized surfaces. Motivated by the large difference in slip velocity of PS on top of dodecyl-trichlorosilane (DTS) and octadecyl-trichlorosilane (OTS) found in previous studies, these two systems were chosen for the present investigation. The results reveal the molecular conformation of PS on silanized silicon. Differences in the molecular tilt of OTS and DTS are replicated by the adjacent phenyl rings of the PS. We discuss our findings in terms of a potential link between the microscopic interfacial structure and dynamic properties of polymeric liquids at interfaces

Spin-triplet superconductivity in quasi-one dimension

We consider a system with electron-phonon interaction, antiferromagnetic fluctuations and disconnected open Fermi surfaces. The existence of odd-parity superconductivity in this circumstance is shown for the first time. If it is applied to the quasi-one-dimensional systems like the organic conductors (TMTSF)_2X we obtain spin-triplet superconductivity with nodeless gap. Our result is also valid in higher dimensions(2d and 3d).Comment: 2 page

Neutron Reflectometry of an Anionic Surfactant at the Solid-Liquid Interface under Shear

Neutron reflectometry with in situ rheology is used to measure the shear response of an adsorbed anionic surfactant (sodium bis(2-ethylhexyl) sulfosuccinate, AOT) at the alumina-water interface. A low surfactant concentration is measured where a single bilayer adsorbs at the interface as well as a higher concentration where a multilamellar structure forms. The low concentration structure does not change with the imposed shear (oscillatory or steady). However, the lamellar phase shows a loss of structure under both steady and oscillatory shear. There are differences between the steady and oscillatory cases, which are discussed, with both showing a strong dependence on the strain amplitude.We thank BP plc [grant number EP/J501876/1] and the Engineering and Physical Sciences Research Council, UK (EPSRC) for financial support for this work

Measurement of molecular mixing at a conjugated polymer interface by specular and off-specular neutron scattering

Measurements have been performed on thermally equilibrated conjugated-polymer/insulating-polymer bilayers, using specular and off-specular neutron reflectivity. While specular reflectivity is only sensitive to the structure normal to the sample, off-specular measurements can probe the structure of the buried polymer/polymer interface in the plane of the sample. Systematic analysis of the scattering from a set of samples with varying insulating-polymer-thickness, using the distorted-wave Born approximation (DWBA), has allowed a robust determination of the intrinsic width at the buried polymer/polymer interface. The quantification of this width (12 Å ± 4 Å) allows us to examine aspects of the conjugated polymer conformation at the interface, by appealing to self-consistent field theory (SCFT) predictions for equilibrium polymer/polymer interfaces in the cases of flexible and semi-flexible chains. This analysis enables us to infer that mixing at this particular interface cannot be described in terms of polymer chain segments that adopt conformations similar to a random walk. Instead, a more plausible explanation is that the conjugated polymer chain segments become significantly oriented in the plane of the interface. It is important to point out that we are only able to reach this conclusion following the extensive analysis of reflectivity data, followed by comparison with SCFT predictions. It is not simply the case that conjugated polymers would be expected to adopt this kind of oriented conformation at the interface, because of their relatively high chain stiffness. It is the combination of a high stiffness and a relatively narrow intrinsic interfacial width that results in a deviation from flexible chain behaviour

Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model

We study the long time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural networks model. The system has a finite number of possible states so it is not possible to use the term chaos in the usual sense of sensitive dependence on the initial condition. Nevertheless, at varying the asymmetry parameter, $k$, one observes a transition from ordered motion (i.e. short transients and short periods on the attractors) to a ``complex'' temporal behaviour. This transition takes place for the same value $k_{\rm c}$ at which one has a change for the mean transient length from a power law in the size of the system ($N$) to an exponential law in $N$. The ``complex'' behaviour during the transient shows strong analogies with the chaotic behaviour: decay of temporal correlations, positive Shannon entropy, non-constant Renyi entropies of different orders. Moreover the transition is very similar to that one for the intermittent transition in chaotic systems: scaling law for the Shannon entropy and strong fluctuations of the ``effective Shannon entropy'' along the transient, for $k > k_{\rm c}$.Comment: 18 pages + 6 figures, TeX dialect: Plain TeX + IOP macros (included

On Approximating the Entropy of Polynomial Mappings

We investigate the complexity of Polynomial Entropy Approximation (PEA): Given a low-degree polynomial mapping p : F^n-> F^m, where F is a finite field, approximate the output entropy H(p(U_n)), where U_n is the uniform distribution on F^n and H may be any of several entropy measures. We show: Approximating the Shannon entropy of degree 3 polynomials p : F_2^n->F_2^m over F_2 to within an additive constant (or even n^{.9}) is complete for SZKPL, the class of problems having statistical zero-knowledge proofs where the honest verifier and its simulator are computable in logarithmic space. (SZKPL contains most of the natural problems known to be in the full class SZKP.) For prime fields F\neq F_2 and homogeneous quadratic polynomials p : F^n->F^m, there is a probabilistic polynomial-time algorithm that distinguishes the case that p(U_n) has entropy smaller than k from the case that p(U_n) has min-entropy (or even Renyi entropy) greater than (2+o(1))k. For degree d polynomials p : F_2^n->F_2^m, there is a polynomial-time algorithm that distinguishes the case that p(U_n) has max-entropy smaller than k (where the max-entropy of a random variable is the logarithm of its support size) from the case that p(U_n) has max-entropy at least (1+o(1))k^d (for fixed d and large k).Engineering and Applied Science