Search

In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The numerical scheme is based on the Hermite formula. The Caputo's fractional derivatives in time are discretized by a finite difference scheme of order $\mathcal{O}(k^{(4-\alpha)})$ \& $\mathcal{O}(k^{(4-\beta)})$, $1, Comment: Some major revision needed

The present study was aimed to examine the interaction of two bile salts viz. sodium cholate (NaC) and sodium deoxycholate (NaDC) with three ethylene polyoxide-polypropylene polyoxide (PEO-PPO-PEO) triblock copolymers with similar PPO but varying PEO micelles with a focus on the effect of pH on mixed micelles. Mixed micelles of moderately hydrophobic Pluronic® P123 were examined in the presence of two bile salts and compared with those from very hydrophobic L121 and very hydrophilic F127. Both the bile salts increase the cloud point (CP) of copolymer solution and decreased apparent micelle hydrodynamic diameter (Dh). SANS study revealed that P123 forms small spherical micelles showing a decrease in size on progressive addition of bile salts. The negatively charged mixed micelles contained fewer P123 molecules but progressively rich in bile salt. NaDC being more hydrophobic displays more pronounced effect than NaC. Interestingly, NaC shows micellar growth in acidic media which has been attributed to the formation of bile acids by protonation of carboxylate ion and subsequent solubilization. In contrast, NaDC showed phase separation at higher concentration. Nuclear Overhauser effect spectroscopy (NOESY) experiments provided information on interaction and location of bile salts in micelles. Results are discussed in terms of hydrophobicity of bile salts and Pluronics® and the site of bile salt in polymer micelles. Proposed molecular interactions are useful to understand more about bile salts which play important role in physiological processes.

The present article is devoted to develop a new approach and methodology to find the approximate solution of second order two-dimensional telegraph equations with the Dirichlet boundary conditions. We first transform the telegraph equations into equivalent partial integro-differential equations (PIDEs) which contain both initial and boundary conditions and therefore can be solved numerically in a more appropriate manner. Operational matrices of integration and differentiation of Bernoulli polynomials together with the completeness of these polynomials are used to reduce the PIDEs into the associated algebraic generalized Sylvester equations which can be solved by an efficient Krylov subspace iterative (i.e., BICGSTAB) method. The efficiency of the proposed method has been confirmed with several test examples and it is clear that the results are acceptable and found to be in good agreement with exact solutions. We have compared the numerical results of the proposed method with radial basis function method and differential quadrature method. Also, the method is simple, efficient and produces very accurate numerical results in considerably small number of basis functions and hence reduces computational effort. Moreover, the technique is easy to apply for multidimensional problems.

In this article, we deal with a numerical wavelet collocation method (NWCM) using a technique based on two-dimensional wavelets (TDWs) approximation proposed for the fractional partial differential equations (FPDEs) for electromagnetic waves in dielectric media (EWDM). By implementing the RiemannLiouville fractional derivative, TDWs approximation and its operational matrix along with collocation method are utilized to reduce FPDEs firstly into weakly singular fractional partial integro-differential equations (FPIDEs) and then reduced weakly singular FPIDEs into system of algebraic equation. Using Legendre wavelet approximation (LWA) and Chebyshev wavelet approximation (CWA), we investigated the convergence analysis and error analysis of the proposed problem. Finally, some examples are included for demonstrating the efficiency of the proposed method via LWA and CWA respectively.

Pluronics® and Tetronics® are used in industry for solubilizing various kinds of hydrophobic compounds since decades. In present study, moderately hydrophobic linear and star block copolymer viz. Pluronic® P104 and Tetronic® T1304 are employed for the solubilization of four polycyclic aromatic hydrocarbons (PAHs) viz. naphthalene (Np), anthracene (An), phenanthrene (Ph) and pyrene (Py). The aggregation behaviour of these block copolymers in an aqueous media has been investigated by cloud point (CP), viscometry, dynamic light scattering (DLS), and small angle neutron scattering (SANS) techniques. The aqueous solubilities of these PAHs are quite poor, hence their extractions from contaminated areas are difficult. Cloud point of block copolymers linearly decreases as a function of PAHs concentration and strongly depends on the structure of PAHs. The aqueous solutions of both block copolymers are Newtonian fluid. The solubilization of PAHs in these copolymeric micelles leads to increase in the viscosity of solution suggesting the growth of micelles. The effect of concentration and temperature on the size and shapes of micelles were evaluated from DLS and SANS studies. The study provides an alternative method for the remediation of PAHs using inexpensive commercially available block copolymers.

Aqueous solution behaviour of worm-like micelles of cetyltrimethylammonium tosylate (CTAT) was examined in the presence of some water soluble nonionic polymers viz. poly(ethylene oxide) 4000 (PEO 4K), poly(propylene oxide) 1000 (PPO 1K), poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) and poly(propylene oxide)-poly(ethylene oxide)-poly(propylene oxide) (PPO-PEO-PPO) type linear triblock copolymers and nonlinear octablock copolymers by an array of techniques. CTAT forms worm-like micelles at very low concentrations. Very hydrophilic PEO 4K molecules surround micelle surface leading to viscosity increase while PPO 1K and linear triblock copolymers demonstrates distinct interaction with worm-like CTAT micelles. They form smaller mixed micelles strongly depending on their structure and hydrophobicity. Structurally different PEO-PPO-PEO type nonlinear block copolymer display dissimilar effect on morphology of CTAT micelles. Small angle neutron scattering (SANS) measurements provide clear idea about structural transitions from worm-like to spherical/ellipsoidal micelles with different dimensions. The different behaviour shown by the polymers is explained on the basis of their interaction with different interiors of CTAT micelles. 1 H NMR and nuclear overhauser enhancement spectroscopy (NOESY) experiments provide idea about location of these additives and site of interaction. The present study validates how the size of worm-like micelles can easily be tuned up by different polymers.

Microstructural evolution of a cationic gemini surfactant butanediyl-1,4-bis(dodecyldimethylammonium bromide) (hereafter referred to as 12-4-12) micelles in the presence of two bile salts viz. sodium deoxycholate (NaDC) and sodium cholate (NaC) was investigated using surface tension, viscosity, nuclear magnetic resonance (NMR), and small angle neutron scattering (SANS) measurements. A negative value of interaction parameter (β) evaluated from surface tension measurements is a signature of strong synergistic interaction between oppositely charged surfactants. Other micellar parameters have also been calculated at different mole fractions. Both the bile salts induced a shape transitions in 12-4-12 micelles on account of their hydrophobicity. Viscosity measurements disclose that loading of bile salts induces morphological changes in gemini micelles; NaDC is more efficient in altering the aggregation behaviour compared to NaC and presents a pronounced increase in viscosity and micellar growth which is suppressed at elevated temperatures. A remarkable growth observed in micelles in the presence of NaDC at low pH has been ascribed to the solubilization of bile acids formed in acidic medium. The size and shape of gemini mixed micelles obtained from SANS measurements are explicated on the basis of the hydrophobicity of bile salts. The location of bile salts in the micelle was determined from NOESY. The present study characterizes gemini–bile salt mixed systems which significantly enriches our knowledge and such a structural transition provides an opportunity to use these bioamphiphiles (bile salt containing mixed micelles) as delivery vehicles and in some pharmaceutical formulations.

The micellar characteristics of an aqueous solution of the polyoxyethylene based alkyl aryl type non-ionic surfactant Triton X-100 (TX-100) in the presence of several 1-alkyl-3-methylimidazolium (Cnmim+) based non-amphiphilic, amphiphilic and biamphiphilic ionic liquids (ILs) varying in the alkyl chain length of the cation (C4–C10) and different anions viz. chloride [Cl−], tetrafluoroborate [BF4−], trifluoromethanesulfonate [CF3SO3−], hexaflurophosphate [PF6−] and octylsuphate [C8SO4−] have been systematically investigated by cloud point (CP), viscosity, dynamic light scattering (DLS), nuclear magnetic resonance (NMR), fluorescence and small-angle neutron scattering (SANS) measurements. These ILs interact with TX-100 micelles on account of their hydrophobicity; ILs with a hydrophilic counter ion (Cl−) favour demicellization, increase CP, decrease the solution viscosity and apparent hydrodynamic diameter (Dh) of micelle, whereas ILs with a hydrophobic counter ion (PF6−) increase the solution viscosity and exhibit micellar growth. SANS data on the size/shape of TX-100 micelles in the presence of different ILs are reported to provide information on microstructural changes in the micelles. The location of ILs, which has a dominating effect on the structure of the micelles, was evaluated using fluorescence and 1H NMR studies, and these results are discussed in terms of the insertion of the ILs in TX-100 micelles. IL molecules with long alkyl chains penetrate deeper in the TX-100 micelles. The present study provides useful information on tuning the solution characteristics of TX-100 in the presence of ILs that may have industrial applications.

A selective, practical, and large-scale synthesis of [6]cycloparaphenylene, the second smallest cycloparaphenylene to be synthesized, was achieved in nine steps starting from commercially available 1, 4-dibromobenzene and 4′-bromobiphenyl-4-ol. The key intermediate, cis-1, 4-(4-bromophenyl)-1, 4-bis(triethylsiloxy)cyclohexa-2, 5-diene, was prepared on a large scale (>20 g) and was selectively dimerized to form a cyclic precursor of [6]cycloparaphenylene by platinum-mediated assembly and subsequent reductive elimination. Deprotection of the triethylsilyl group and subsequent tetrachlorostannic acid (H2SnCl4)-mediated reductive aromatization gave [6]cycloparaphenylene in 23% overall yield from the commercially available substrates on gram scale.

The cationic surfactant cetyltrimethylammonium tosylate (CTAT) forms highly viscous/viscoelastic solutions and worm-like micelles at relatively low concentrations. The effect of 1-alkanols with short to long alkyl chains viz. ethanol, 1-butanol, 1-hexanol and 1-octanol on CTAT micelles was examined. In particular, a detailed study on the effect of 1-hexanol was carried out by viscosity, cryogenic transmission electron microscopy (cryo-TEM), nuclear magnetic resonance (NMR) and small-angle neutron scattering (SANS) to observe microstructural changes in CTAT micelles. 1-Hexanol displays a distinct interaction with CTAT micelles strongly dependent on CTAT concentration. Up to a certain critical CTAT concentration, 1-hexanol molecules penetrate into the micelles and show growth. Characterization by direct cryo-TEM imaging implies that upon progressive addition of 1-hexanol, worm-like CTAT micelles first grow and finally transform into vesicles. The course of vesicle formation was followed by SANS measurements. The site of 1-hexanol in the micelles close to the palisade layer was evaluated using 2D NMR. This study devotes a fundamental knowledge for controlling the shape and size of worm-like micelles that find many industrial applications particularly in personal- and home-care products.

Tadpole-shaped β-cyclodextrin-tagged poly(N-vinylpyrrolidone) (β-CD-PNVP) has been synthesised via the click reaction of alkyne-terminated PNVP and azide-functionalized β-CD. The formed polymer is characterized by 1H NMR, FTIR, and TGA study. The complexing ability of such a polymer with phenolphthalein is considerably lower with respect to that with β-CD alone. Doxorubicin (DOX)-loaded β-CD-PNVP (DOX-β-CD-PNVP) exhibits higher tumoricidal activity against a panel of tumor cell lines derived from sarcoma (U2-OS) and carcinomas (MCF-7 and HEPG2), causing significant lysis of tumor cells compared to free DOX. The formulation also demonstrates significantly higher uptake by the tumor cells and enhances apoptosis compared to free DOX.