Morphological mapping and analysis of poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] and its clay nanocomposites by atomic force microscopy

Atomic force microscopy was successfully applied for comprehensive nanoscale surface and bulk morphological characterization of thermoplastic elastomeric triblock copolymers: poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] (SEBS) having different block lengths and their clay based nanocomposites. Commercially available Cloisite®20A and octadecyl (C₁₈) ammonium ion modified montmorillonite clay (OC) prepared in our laboratory by cation exchange reaction were used. The phase detected images in the tapping mode atomic force microscopy exhibited a well‐ordered phase separated morphology consisting of bright nanophasic domains corresponding to hard component and darker domains corresponding to softer rubbery ethylene‐co‐butylene (PEB) lamella for all the neat triblock copolymers. This lamellar morphology gave a domain width of 19–23 nm for styrenic nanophase and 12–15 nm for ethylene‐co‐butylene phase of SEBS having end to mid block length ratio of 30:70 and block molecular weights of 8800–41,200–8800. On increasing the ratio of block lengths of the polymer matrix and the selectivity of the solvent toward the blocks used for casting, the morphological features of the resultant films altered along with change in domain thickness. The phase images showed position and distribution of the brightest clay stacks in the dark‐bright contrast of the base matrix of the nanocomposite. Exfoliated and intercalated‐exfoliated morphology obtained in the case of Cloisite®20A and OC‐based SEBS nanocomposites, respectively, is further supported by X‐ ray diffraction and transmission electron microscopy studies. The lamellar thickness of the soft phases widened to 50–75 nm, where the layered clay silicates (40–54 nm in length and 4–17 nm in width) were embedded in the soft rubbery phases in the block copolymeric matrix of the nanocomposite. The marginally thicker width of the hard styrenic phases and slightly shrinked width of the soft rubbery lamella can be observed from the regions where no nanofiller is present. Distinct differences in bulk morphologies of the nanocomposites prepared in the melt and the solution processes were obtained with nanocomposites. The presence of clay particles was evident from the almost zero pull‐off and snap‐in force in the force‐distance analysis of SEBS based nanocomposite. This analysis also revealed stronger tip interaction resulting in highest contact and adhesive forces with the softer PEB region relative to the harder PS region. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 52–66, 2007     

A theoretical analysis of acoustic microscopy with converging acoustic beams

A theoretical analysis is carried out to synthesize acoustic material signatures (AMS) of solid plates immersed in water. The distinctive feature of this analysis is that it avoids three major simplifying assumptions of the presently available techniques, which are, paraxial approximation, assumption of perfect reflection and Gaussian summation of the incident field. Presently available techniques can avoid some but not all of these simplifying assumptions for computing the AMS. In this paper the analysis is carried out for lowfrequency acoustic waves generated by a cylindrical transducer without a lens rod. Reasons for these changes in the conventional acoustic microscope geometry is given. The AMS is synthesized for an aluminium plate in presence as well as in absence of water on its one side. As expected a significant difference is observed between the signatures generated under these two situations.     

A factorization theorem for a certain class of graphs

In this note we give a necessary and sufficient condition for factorization of graphs satisfying the “odd cycle property”. We show that a graph G with the odd cycle property contains a [k_i] factor if and only if the sequence [H]+[k_i] is graphical for all subgraphs H of the complement of G.A similar theorem is shown to be true for all digraphs.     

Bounds on the number of disjoint spanning trees

It is shown that an n-edge connected graph has at least ?$\text{(n ? 1)}\text{2}$? pairwise edge-disjoint spanning trees. This bound is best possible in general. A maximal planar graph with four or more vertices contains two edge-disjoint spanning trees. For a maximal toroidal graph, this number is three.     

Detection of kissing bonds by Lamb waves

Closed cracks under compressive normal stresses are difficult to detect by the conventional ultrasonic techniques. When the crack surfaces stay in very close contact with each other then the bond between the two surfaces of the crack is called a ‘kissing bond’. This is a very dangerous bond. Catastrophic failures can result if the system is subjected to crack opening normal stresses or shear stresses. When the crack surfaces are smooth then kissing bonds cannot transmit shear stress very well but can carry compressive normal stress, these bonds are called ‘slip bonds’. Conventional P-wave scans (C-scan or A-scan) are based on the assumptions that P-waves are reflected by the defective interface. However, an interface subjected to a large compressive stress cannot reflect P-waves effectively, hence these bonds remain invisible to the conventional P-wave based C-scan or A-scan techniques. In this paper it is shown that the kissing bonds can be effectively detected by some leaky Lamb mode. Theoretical and experimental results are presented to show that using the Lamb waves is an effective way of detecting kissing bonds.     

Orientational order in liquid crystals exhibited by some binary mixtures of rod-like and bent-core molecules

We report measurements of the temperature variations of the optical birefringence in the nematic (N) and partial bilayer SmA (SmA_d) phases in 4-n-octyloxy 4^′ -cyanobiphenyl made of rod-like (R) molecules and five mixtures of this compound with 1,3-phenylene bis[4-(3-methylbenzoyloxy)] 4^′ -n- dodecylbiphenyl 4^′ -carboxylate, made of bent-core (BC) molecules. The birefringence decreases with the concentration x of the BC molecules but the macroscopic order parameter initially decreases upto 11mol% of BC molecules and subsequently increases with x . This is attributed to the possible formation of polar clusters of BC molecules. Orientation of BC molecules changes between the N and SmA_d phases and the birefringence data in the two phases imply that the kink angle of the BC molecules is ∼ 90^° rather than ∼ 110^° as obtained from calculations which minimize the energy of the molecule. IR spectroscopic measurements on the mixture with 11mol% of BC molecules have been used to estimate the molecular order parameter S of the R molecules, and to provide additional support for a relatively small kink angle of BC molecules.     

Nano-powders of Na0.5K0.5NbO3 made by a sol–gel method

Sodium potassium niobate (NKN) nano-particle powders were synthesised through the thermal decomposition of a sol–gel NKN precursor. Powders and gels were characterised by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA) and transmission electron microscopy (TEM). Hydrated carbonate phases formed as a result of reaction with evolved vapours during organic decomposition, and by reaction of NKN powders with H₂O and CO₂ on exposure to air. The primary particle size of the powders increased from <50 to <250 nm as decomposition temperatures were raised from 500 to 950 °C.     

Exponents of class groups of real quadratic function fields (II)

Let be an even positive integer. We show that there are polynomials with such that the ideal class group of the real quadratic extensions have an element of order .

     

Numerical simulation of electromagnetic acoustic transducers using distributed point source method

In spite of many advances in analytical and numerical modeling techniques for solving different engineering problems, an efficient solution technique for wave propagation modeling of an electromagnetic acoustic transducer (EMAT) system is still missing. Distributed point source method (DPSM) is a newly developed semi-analytical technique developed since 2000 by Placko and Kundu (2007) [12] that is very powerful and straightforward for solving various engineering problems, including acoustic and electromagnetic modeling problems. In this study DPSM has been employed to model the Lorentz type EMAT with a meander line and flat spiral type coil. The problem of wave propagation has been solved and eddy currents and Lorentz forces have been calculated. The displacement field has been obtained as well. While modeling the Lorentz force the effect of dynamic magnetic field has been considered that most current analyses ignore. Results from this analysis have been compared with the finite element method (FEM) based predictions. It should be noted that with the current state of knowledge this problem can be solved only by FEM.     

Nature of Nonlocality in Triangle Network based on Elegant Joint Measurement

Defining nonlocality in a no-input closed quantum network scenario is a new area of interest nowadays. Gisin, in [Entropy 21, 325 (2019)], proposed a possible condition for non-tri-locality of the trivial no-input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In [npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, it finds the nature of the correlation in a triangle network scenario. This study observes how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here, it uses the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non-locality on the entanglement of these joint measurement bases. It also checks the probability bound for the polygon structure.