Frustration in Optical Lattices of Interacting Bosons

The realization of optical lattices of cold atoms has opened up the possibility of engineering interacting lattice systems of bosons and fermions, stimulating a frenzy of research over the last decade. More recently, experimental techniques have been developed to apply synthetic gauge fields to these optical lattices. As a result, it has become possible to study quantum Hall physics and the effects of frustration in lattices of cold atoms. In this article we describe the combined effect of frustration and interactions on the superfluidity of bosons. By focussing on a frustrated ladder of interacting bosons, we show that the effect of frustration is for ``chiral'' order to develop, which manifests itself as an alternating pattern of circulating supercurrents. Remarkably, this order persists even when superfluidity is lost and the system enters a Mott phase giving rise to a novel chiral Mott insulator. We describe the combined physics of frustration and interactions by studying a fully frustrated one dimensional model of interacting bosons. The model is studied using mean-field theory, a direct quantum simulation and a higher dimensional classical theory in order to offer a full description of the different quantum phases contained in it and transitions between the different phases. In addition, we provide physical descriptions of the chiral Mott insulator as a vortex-anitvortex super solid and indirect excitonic condensate in addition to obtaining a variational wavefunction for it. We also briefly describe the chiral Mott states arising in other microscopic models.

Shear induced crystallization in different polymorphic forms of PVDF induced by surface functionalized MWNTs in PVDF/PMMA blends

Shear induced crystallization in PVDF/PMMA blends, especially at higher fractions of PMMA, can be quite interesting in understanding the structure-property correlation and processing of these blends. In a recent submission (Phys. Chem. Chem. Phys., 2014, 16, 2693-2704), we clearly demonstrated, using dielectric spectroscopy, that the origin of segmental relaxations concerning the crystalline segments of PVDF in PVDF/PMMA blends in the presence of MWNTs (multiwalled nanotubes) was strongly contingent on the size of the crystallite. We now understand that the fraction of PMMA in the blends governs the origin of polymorphism in PVDF. This motivated us to systematically study the effect of shear on the crystallization behavior of PVDF especially in blends with different polymorphic forms of PVDF. Two model blends were selected; one with a mixture of alpha and beta crystals and the other predominantly rich in alpha crystals. Initially, physical ageing, at different oscillation frequencies (1 rad s(-1) and 0.1 rad s(-1)), was monitored by melt rheology and subsequently, the effect of steady shear was probed in situ without changing the history of the samples. Intriguingly, the rate of crystallization was observed to be significantly higher for higher oscillation frequencies, which essentially suggest that shear has induced crystallization in the blends. More interestingly, the effect of steady shear was more pronounced in the blends rich in alpha crystals (bigger crystallites as observed from SAXS) and at lower oscillation frequencies.

Polymer-grafted multiwall carbon nanotubes functionalized by nitrene chemistry: effect on cooperativity and phase miscibility

The demixing of polystyrene (PS) and poly(vinyl methylether) (PVME) was systematically investigated in the presence of surface functionalized multiwall carbon nanotubes (MWNTs) by melt rheology. As PS-PVME blends are weakly interacting blends, the contribution of conformational entropy increases, resulting in thermo-rheological complexity wherein the concentration fluctuation persists even beyond the critical demixing temperature. These phenomenal changes were followed here in the presence of MWNTs with different surface functional groups. Polystyrene was synthesised by atom transfer radical polymerization and was immobilized onto carboxyl acid functionalized multiwall carbon nanotubes (COOH-MWNTs) via nitrene chemistry in order to improve the phase miscibility in PS-PVME blends. Interestingly, blends with 0.25 wt% polystyrene grafted multiwall carbon nanotubes (PS-g-MWNTs) delayed the spinodal decomposition temperature in the blends by similar to 33 degrees C with respect to both control blends and those with COOH-MWNTs. While the localization of COOH-MWNTs in PVME was explained from a thermodynamic point of view, the localization of PS-g-MWNTs was understood to result from favorable PS-PVME contact and the degree of surface coverage of PS on the surface of MWNTs. The length of the cooperative rearranging region (xi) decreased in presence of PS-g-MWNTs, suggesting confinement effects on large scale motions and enhanced interchain concentration fluctuation.

Polyolefin based antibacterial membranes derived from PE/PEO blends compatibilized with amine terminated graphene oxide and maleated PE

In this study, various strategies like amine terminated GO (GO-NH2), in situ formed polyethylene grafted GO (PE-g-GO) and their combinations with maleated PE (maleic anhydride grafted PE) were adopted to reactively compatibilize blends of low density polyethylene (LDPE) and polyethylene oxide (PEO). These blends were further explored to design porous, antibacterial membranes for separation technology and the flux and the resistance across the membranes were studied systematically. It was observed that GO-NH2 led to uniform dispersion of PEO in a PE matrix and further resulted in a significant improvement in the mechanical properties of the blends when combined with maleated PE. The efficiency of various compatibilizers was further studied by monitoring the evolution of morphology as a function of the annealing time. It was observed that besides rendering uniform dispersion of PEO in PE and improving the mechanical properties, GO-NH2 further suppresses the coalescence in the blends. As the melt viscosities of the phases differ significantly, there is a gradient in the morphology as also manifested from scanning acoustic microscopy. Hence, the membranes were designed by systematically reducing the thickness of the as-pressed samples to expose the core as the active area for flux calculations. Selected membranes were also tested for their antibacterial properties by inoculating E. coli culture with the membranes and imaging at different time scales. This study opens new avenues to develop PE based cost effective anti-microbial membranes for water purification.

An unusual demixing behavior in PS-PVME blends in the presence of nanoparticles

The effect of silver nanoparticles (sNP) on the demixing and the evolution of morphology in off-critical blends of 90/10 and 10/90 (wt/wt) PS/PVME polystyrene/poly(vinyl methyl ether)] was probed here using shear rheology and optical microscopy. The faster component (PVME) has a higher molecular weight (80 kDa) than the slower component (PS, 35 kDa), which makes this system quite interesting to study with respect to the evolving morphology, as the blends transit through the binodal and the spinodal envelopes. An unusual demixing behavior was observed in both PVME rich and PS rich blends. Temperature modulated differential scanning calorimetry measurements showed that the T-g value for the blends with sNP was slightly lower than that of the neat blends. A decreased volume of cooperativity at T-g suggests confined segmental dynamics in the presence of sNP. Although, the addition of sNP had no influence on the thermodynamic demixing temperature, it significantly altered the elasticity of the minor component during the transition of the blend from the homogeneous to the heterogeneous state. This is manifested from energetically driven localization of the sNP in the PVME phase during demixing. As a direct consequence of this, the formation of the microstructures upon demixing was observed to be delayed in the presence of sNP. Interestingly, in the intermediate quench depth, the higher viscoelastic phase evolved as an interconnected network, which subsequently coarsened into discrete droplets in the late stages for the 90/10 PS/PVME blends. Similar observations were made for 10/90 PS/PVME blends where threads of PVME appeared at deeper quench depths in the presence of sNP. The interconnected network formation of the minor phase (here PVME), which is also the faster component in the blend, was different from the usual demixing behavior.

Polyolefin based antibacterial membranes derived from PE/PEO blends compatibilized with amine terminated graphene oxide and maleated PE

In this study, various strategies like amine terminated GO (GO-NH2), in situ formed polyethylene grafted GO (PE-g-GO) and their combinations with maleated PE (maleic anhydride grafted PE) were adopted to reactively compatibilize blends of low density polyethylene (LDPE) and polyethylene oxide (PEO). These blends were further explored to design porous, antibacterial membranes for separation technology and the flux and the resistance across the membranes were studied systematically. It was observed that GO-NH2 led to uniform dispersion of PEO in a PE matrix and further resulted in a significant improvement in the mechanical properties of the blends when combined with maleated PE. The efficiency of various compatibilizers was further studied by monitoring the evolution of morphology as a function of the annealing time. It was observed that besides rendering uniform dispersion of PEO in PE and improving the mechanical properties, GO-NH2 further suppresses the coalescence in the blends. As the melt viscosities of the phases differ significantly, there is a gradient in the morphology as also manifested from scanning acoustic microscopy. Hence, the membranes were designed by systematically reducing the thickness of the as-pressed samples to expose the core as the active area for flux calculations. Selected membranes were also tested for their antibacterial properties by inoculating E. coli culture with the membranes and imaging at different time scales. This study opens new avenues to develop PE based cost effective anti-microbial membranes for water purification.

Combinatorial effect of rolling and carbonaceous nanoparticles on the evolution of crystallographic texture and structural properties of ultra high molecular weight polyethylene

Ultra high molecular weight polyethylene (PE) is a structural polymer widely used in biomedical implants. The mechanical properties of PE can be improved either by controlled crystalline orientation (texture) or by the addition of reinforcing agents. However, the combinatorial effect has not received much attention. The objective of this study was to characterize the structure and mechanical properties of PE composites incorporating multiwall carbon nanotubes (MWCNT) and reduced graphene oxide (RGO) subjected to hot rolling. The wide angle X-ray diffraction studies revealed that mechanical deformation resulted in a mixture of orthorhombic and monoclinic crystals. Furthermore, the presence of nanoparticles resulted in lower crystallinity in PE with smaller crystallite size, more so in RGO than in MWCNT composites. Rolling strengthened the texture of both orthorhombic and the monoclinic phases in PE. Presence of RGO weakened the texture of both phases of PE after rolling whereas MWCNT only mildly weakened the texture. This resulted in a reduction in the elastic modulus of RGO composites whereas moduli of neat polymer and the MWCNT composite increased after rolling. This study provides new insight into the role of nanoparticles in texture evolution during polymer processing with implications for processing of structural polymer composites.

Anomalous structural relaxations in PVDF rich blends with PMMA in the presence of surface functionalized CNTs

The structural relaxations in PVDF rich blends with PMMA can be quite interesting in understanding the origin of the different molecular relaxations associated with the crystalline and amorphous phases, crystal-amorphous interphase and the segmental motions. In light of our recent findings, we understood that the origin of these molecular relaxations were strongly contingent on the concentration of PMMA in the blend, crystalline morphology and the surface functional moieties on multiwall carbon nanotubes (CNTs). In addition, for the blends with concentration of PMMA >= 25 wt%, the structural relaxations often merge and are dielectrically indistinguishable. In this study, we attempted to determine the critical width in composition where the structural relaxations can be distinctly realized both in the control as well as blends with amine functionalized CNTs (NH2-CNTs). Intriguingly, we observed that in a narrow zone in composition (with PMMA concentration >= 10 wt% and <= 25 wt%), the molecular relaxations can be dielectrically distinguished and they often merge for all other compositions. Furthermore, we attempted to understand how this critical width in composition is related to the crystalline morphology using small angle X-ray scattering and polarizing optical microscopy and the crystal structure using FTIR and Raman spectroscopy. We now understand that although the formation of beta crystals in the blends has no direct correlation with the observed molecular relaxations, the amorphous miscibility and the interphase regions seem to be dictating the origin of different molecular relaxations in the blends. The latter was observed to be strongly contingent on the concentration of PMMA in the blends.

Thermally Induced Demixing in an LCST Mixture in the Presence of Densely Grafted Nanoparticles: Tuning the Graft Chain Length To Induce Thermodynamic Miscibility

The demixing in an LCST mixture of PS/PVME (polystyrene/poly(vinyl methyl ether)) was probed here by melt rheology in the presence of gold nanoparticles which were densely coated with varying graft lengths of PS. The graft density for the gold nanoparticles coated with 3 kDa PS was ca. Sigma = 1.7 chains/nm(2), and that for 53 kDa PS was ca. Sigma = 1.2 chains/nm(2). The evolution of morphology, as the blends transit through the metastable and the unstable envelopes of the phase diagram, and the localization of the gold nanoparticles upon demixing were monitored using in situ hot-stage AFM and confocal Raman imaging. Interestingly, gold nanoparticles coated with 3 kDa polystyrene (PS(3 kDa)-g-nAu) were localized in the PVME phase, whereas gold nanoparticles coated with 53 kDa polystyrene (PS(53 kDa)-g-nAu) were localized in the PS phase of the blend. While the localization of PS(3 kDa)-g-nAu in the PVME phase can be expected to be of entropic origin due to expulsion from the PS phase as R-g,R-matrix chains > R-g,R-grafted chains (where R-g is the radius of gyration of the polymer chain), the localization of PS(53 kDa)-g-nAu in the PS phase is believed to be facilitated by favorable melt/graft interactions. The latter nanoparticles also delayed the demixing by 12 degrees C with respect to the neat mixture. The observed changes were addressed in context to enthalpic interactions between the grafted PS and the free PS, the entropic losses (deformational entropic losses on blending, translational entropic loss of the free PS, and the conformational entropic loss of the grafted PS), and the interface of the grafted and the free chains.

Electromagnetic shielding materials and coatings derived from gelation of multiwall carbon nanotubes in an LCST mixture

Thermally induced demixing in an LCST mixture, polystyrene (PS)/polyvinyl methyl ether] (PVME), was used as a template to design materials with high electrical conductivity. This was facilitated by gelation of multiwall carbon nanotubes (MWNTs) in a given phase of the blends. The MWNTs were mixed in the miscible blends and the thermodynamic driven demixing further resulted in selective localization in the PVME phase of the blends. This was further confirmed by atomic force microscopy (AFM). The time dependent gelation of MWNTs at shallow quench depth, evaluated using isochronal temperature sweep by rheology, was studied by monitoring the melt electrical conductivity of the samples in situ by an LCR meter coupled to a rheometer. By varying the composition in the mixture, several intricate shapes like gaskets and also coatings capable of attenuating the EM radiation in the microwave frequency can be derived. For instance, the PVME rich mixtures can be molded in the form of a gasket, O-ring and other intricate shapes while the PS rich mixtures can be coated onto an insulating polymer to enhance the shielding effectiveness (SE) for EM radiation. The SE of the various materials was analyzed using a vector network analyzer in both the X-band (8.2 to 12 GHz) and the K-u-band (12 to 18 GHz) frequency. The improved SE upon gelation of MWNTs in the demixed blends is well evident by comparing the SE before and after demixing. A reflection loss of -35 dB was observed in the blends with 2 wt% MWNTs. Further, by coating a layer of ca. 0.15 mm of PS/PVME/MWNT, a SE of -15 dB at 18 GHz could be obtained.

Electromagnetic interference shielding through MWNT grafted Fe3O4 nanoparticles in PC/SAN blends

In this study, multiwall carbon nanotubes (MWNTs) were chemically grafted onto dopamine anchored iron oxide (Fe3O4) nanoparticles via diazotization reaction to design electromagnetic (EM) shielding materials based on PC (polycarbonate)/SAN poly (styrene-co-acrylonitrile)] blends. A two step mixing protocol was adopted to selectively localize the nanoparticles in a given phase of the blends. In the first step, MWNT-g-Fe3O4 nanoparticles were solution blended with PC, followed by dilution with SAN during melt mixing in the subsequent step. This strategy, besides improving the quality of dispersion of MWNTs in the blends, facilitated enhanced EM interference shielding effectiveness (SE). Both, the MWNTs and the modified MWNTs, selectively localized in the PC phase and led to high electrical conductivity, in striking contrast to PC filled MWNT composites. The SE was measured on toroidal samples over a broad range of frequencies; X-band (8.2-12 GHz) and K-u-band (12-18 GHz). It was observed that the shielding mechanism mostly involved reflection in the blends with MWNTs, whereas absorption dominated in the case of blends with MWNT-g-Fe3O4. To realize the efficacy of this strategy, a few compositions were prepared by physical mixing MWNTs with Fe3O4 nanoparticles. Intriguingly, blends with MWNT-g-Fe3O4 nanoparticles manifested enhanced microwave absorption over physically mixed nanoparticles. An SE of -32.5 dB was observed (at 18 GHz) for MWNT (3 wt%)-g-Fe3O4 (3 vol%) in PC/SAN blends.

The key role of polymer grafted nanoparticles in the phase miscibility of an LCST mixture

Blends of bromo-terminated polystyrene (PS-Br) and poly(vinyl methylether) (PVME) exhibit lower critical solution temperatures. In this study, PS-Br was designed by atom transfer radical polymerization and was converted to thiol-capped polystyrene (PS-SH) by reacting with thiourea. The silver nanoparticles (nAg) were then decorated with covalently bound PS-SH macromolecules to improve the phase miscibility in the PS-Br-PVME blends. Thermally induced demixing in this model blend was followed in the presence of polystyrene immobilized silver nanoparticles (PS-g-nAg). The graft density of the PS macromolecules was estimated to be ca. 0.78 chains per nm(2). Although the matrix and the grafted molecular weights were similar, PS-g-nAg particles were expelled from the PS phase and were localized in the PVME phase of the blends. This was addressed with respect to intermediate graft density and favourable PS-PVME contacts from microscopic interactions point of view. Interestingly, blends with 0.5 wt% PS-g-nAg delayed the spinodal decomposition temperature in the blends by ca. 18 degrees C with respect to the control blends. The scale of cooperativity, as determined by differential scanning calorimetry, increased only marginally in the case of PS-g-nAg; however, it increased significantly in the presence of bare nAg particles.

Tailoring the interface of an immiscible polymer blend by a mutually miscible homopolymer grafted onto graphene oxide: outstanding mechanical properties

A unique strategy was adopted here to improve the compatibility between the components of an immiscible polymer blend and strengthen the interface. PMMA, a mutually miscible polymer to both PVDF and ABS, improved the compatibility between the phases by localizing at the blends interface. This was supported by the core-shell formation with PMMA as the shell and ABS as the core as observed from the SEM micrographs. This phenomenon was strongly contingent on the concentration of PMMA in the blends. This strategy was further extended to localize graphene oxide (GO) sheets at the blends interface by chemically coupling it to PMMA (PMMA-g-GO). A dramatic increment of ca. 84% in the Young's modulus and ca. 124% in the yield strength was observed in the presence of PMMA-g-GO with respect to the neat blends. A simultaneous increment in both the strength and the modulus was observed in the presence of PMMA-g-GO whereas, only addition of GO resulted in a moderate improvement in the yield strength. This study reveals that a mutually miscible polymer can render compatibility between the immiscible pair and can improve the stress transfer at the interface.

Poly(vinylidene fluoride)-Based Flexible and Lightweight Materials for Attenuating Microwave Radiations

Two unique materials were developed, like graphene oxide (GO) sheets covalently grafted on to barium titanate (BT) nanoparticles and cobalt nanowires (Co-NWs), to attenuate the electromagnetic (EM) radiations in poly(vinylidene fluoride) (PVDF)-based composites. The rationale behind using either a ferroelectric or a ferromagnetic material in combination with intrinsically conducting nanoparticles (multiwall carbon nanotubes, CNTs), is to induce both electrical and magnetic dipoles in the system. Two key properties, namely, enhanced dielectric constant and magnetic permeability, were determined. PVDF/BT-GO composites exhibited higher dielectric constant compared to PVDF/BT and PVDF/GO composites. Co-NWs, which were synthesized by electrodeposition, exhibited saturation magnetization (M-s) of 40 emu/g and coercivity (Hc) of 300 G. Three phase hybrid composites were prepared by mixing CNTs with either BT-GO or Co-NWs in PVDF by solution blending. These nanoparticles showed high electrical conductivity and significant attenuation of EM radiations both in the X-band and in the Ku-band frequency. In addition, BT-GO/CNT and Co-NWs/CNT particles also enhanced the thermal conductivity of PVDF by ca. 8.7- and 9.3-fold in striking contrast to neat PVDF. This study open new avenues to design flexible and lightweight electromagnetic interference shielding materials by careful selection of functional nanoparticles

Strings vs. spins on the null orbifold

We study the null orbifold singularity in 2+1 d flat space higher spin theory as well as string theory. Using the Chern-Simons formulation of 2+1 d Einstein gravity, we first observe that despite the singular nature of this geometry, the eigenvalues of its Chern-Simons holonomy are trivial. Next, we construct a resolution of the singularity in higher spin theory: a Kundt spacetime with vanishing scalar curvature invariants. We also point out that the UV divergences previously observed in the 2-to-2 tachyon tree level string amplitude on the null orbifold do not arise in the at alpha' -> infinity limit. We find all the divergences of the amplitude and demonstrate that the ones remaining in the tensionless limit are physical IR-type divergences. We conclude with a discussion on the meaning and limitations of higher spin (cosmological) singularity resolution and its potential connection to string theory.