Global solutions describing the collapse of a spherical or cylindrical cavity

The collapse of a spherical (cylindrical) cavity in air is studied analytically. The global solution for the entire domain between the sound front, separating the undisturbed and the disturbed gas, and the vacuum front is constructed in the form of infinite series in time with coefficients depending on an ldquoappropriaterdquo similarity variable. At timet=0+, the exact planar solution for a uniformly moving cavity is assumed to hold. The global analytic solution of this initial boundary value problem is found until the collapse time (=(gamma–1)/2) for gamma le 1+(2/(1+v)), wherev=1 for cylindrical geometry, andv=2 for spherical geometry. For higher values of gamma, the solution series diverge at timet — 2(beta–1)/ (v(1+beta)+(1–beta)2) where beta=2/(gamma–1). A close agreement is found in the prediction of qualitative features of analytic solution and numerical results of Thomaset al. [1].

Exact N-Wave Solutions for the Non-Planar Burgers Equation

An exact representation of N-wave solutions for the non-planar Burgers equation u(t) + uu(x) + 1/2ju/t = 1/2deltau(xx), j = m/n, m < 2n, where m and n are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for Absolute value of x < square-root (2Q0 t), where Q0 is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as t tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all j = m/n, m < 2n, and are rather involved; explicit results are written out for j = 0, 1, 1/2, 1/3 and 1/4. The case of spherical symmetry j = 2 is found to be 'singular' and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are compared with those of Crighton & Scott (1979).

Mechanistic studies on the effect of ferrocene bonding agents in composite solid propellents

Five compounds, viz. 1,1'-ferrocenediyldiethylidene bis(thiocarbonohydrazide) (DAFT), 1,1-diacetylferrocene disemicarbazone (DAFS), 1,1-diacetylferrocenebenzoyl hydrazone (FDBAH), 1,1-diacetylferrocene-p-nitrobenzoyl hydrazone (FDNBAH), and p-toluenesulfonic acid 1,1'-ferrocenediyldiethylidene dihydrazide (TFDD) were found to be bonding agents as well as burning-rate modifiers for the ammonium perchlorate + hydroxy-terminated polybutadiene system. The tensile strength and percentage elongation significantly increased in the presence of these bonding agents (except FDBAH). The bonding agents generally did not adversely affect the slurry viscosity during processing. The bonding sites were located by infrared spectroscopy, supported by determination of the dissolution kinetics of the bonding agents and scanning electron microscopy. The bonding agents did not undergo any side-reactions with the curing agents.

Gradient solid electrolytes for thermodynamic measurements: System Na2CO3-Na2SO4

The thermodynamic properties of Na2CO3-Na2SO4 solid solution with hexagonal structure have been measured in the temperature range of 873 to 1073 K, using a composite-gradient solid electrolyte. The cell used can be represented as The composite-gradient solid electrolyte consisted of pure Na2CO3 at one extremity and the solid solution under study at the other, with variation in composition across the electrolyte. A CO2 + O2 + Ar gas mixture was used to fix the chemical potential of sodium at each electrode. The Nernstian response of the cell to changes in partial pressures of CO2 and O2 at the electrodes has been demonstrated. The activity of Na2CO3 in the solid solution was measured by two techniques. In the first method, the electromotive force (emf) of the cell was measured with the same CO2 + O2 + Ar mixture at both electrodes. The resultant emf is directly related to the activity of Na2CO3 at the solid solution electrode. By the second approach, the activity was calculated from the difference in compositions Of CO2 + O2 + Ar mixtures at the two electrodes required to produce a null emf. Both methods gave identical results. The second method is more suitable for gradient solid electrolytes that exhibit significant electronic conduction. The activity of Na2CO3 exhibits positive deviation from Raoult's law. The excess Gibbs' energy of mixing of the solid solution can be represented using a subregular solution model such as the following: DELTAG(E) = X(1 - X)[6500(+/-200)X + 3320(+/-80)(1 - X)J mol-1 where X is the mole fraction of Na2CO3. By combining this information with the phase diagram, mixing properties of the liquid phase are obtained.

Highly selective sulfur transfer reaction in the solid state

Benzyltriethylammonium tetrathiomolybdate 1 reacts readily with benzyl halides, alkyl iodides and acyl halides in the solid state to give the corresponding disulfides in good yields and with remarkable selectivity.

Mechanistic studies on the effect of ferrocene bonding agents in composite solid propellents

Five compounds, viz. 1,1'-ferrocenediyldiethylidene bis(thiocarbonohydrazide) (DAFT), 1,1-diacetylferrocene disemicarbazone (DAFS), 1,1-diacetylferrocenebenzoyl hydrazone (FDBAH), 1,1-diacetylferrocene-p-nitrobenzoyl hydrazone (FDNBAH), and p-tolenesulfonic acid, 1,1'-ferrocenediyldiethylidene dihydrazide (TFDD) were found to be bonding agents as well as burning-rate modifiers for the ammonium perchlorate + hydroxy-terminated polybutadiene system. The tensile strength and percentage elongation significantly increased in the presence of these bonding agents (except FDBAH). The bonding agents generally did not adversely affect the slurry viscosity during processing. The bonding sites were located by infrared spectroscopy, supported by determination of the dissolution kinetics of the bonding agents and scanning electron microscopy. The bonding agents did not undergo any side-reactions with the curing agents.

Diffusion path during internal displacement reactions in multi-component oxides: Reaction between Fe and (Co,Mg)TiO3 solid solution at 1273 K

The reaction between Fe foil and a disc of ilmenite solid solution (Co-0.48 Ni-0.52) TiO3 was studied at 1273 K. At the metal/oxide interface, the displacement reaction, Fe + (Co,Mg)TiO3 = Co + (Fe,Mg)TiO3 occurs, resulting in an ilmenite solid solution containing three divalent cations. Ferrous ions diffuse into the oxide solid solution and cause the precipitation of Co-Fe alloy as discrete particles inside the oxide matrix. The morphology of the product layer was characterized by SEM. Only two phases, alloy and ilmenite, were detected in the reaction zone. This suggests that the local flux condition imposed by ilmenite stoichiometry (Co + Fe + Mg):Ti = 1:1] was satisfied during the reactive diffusion: (J(Co) + J(Fe) + J(Mg)) = J(Ti). The composition of the alloy and the oxide was determined using EPMA as a function of distance in the direction of diffusion. Although Mg does not participate in the displacement reaction, its composition in the ilmenite phase was found to be position dependent inside the reaction zone. The up-hill diffusion of inert Mg is caused by the development of chemical potential gradients as a result of displacement reaction. The evolution of composition gradients inside the reaction zone and the diffusion path in a ternary composition diagram of the system CoTiO3-FeTiO3-MgTiO3 are discussed. (C) 2010 Elsevier B.V. All rights reserved.

Reaction of normal and pseudo 2-formylbenzenesulfonyl chlorides with amines:experimental and theoretical studies on the structure of 2-formyl benzenesulfonamides in solid, solution and gas phases

The reaction of 2-formylbenzenesulfonyl chloride 1 and its pseudo isomer 2 with primary amines give either the corresponding sulfonamido Schiff bases or the corresponding 2-formylbenzenesulfonamide depending on the concentration of the amine used. The derivatives exist as an equilibrium mixture of the corresponding sulfonamide and 2-alkyl-3-hydroxy(or 3-aminoalkyl)-benzisothiazole-1,1-dioxide. Spectroscopic studies suggest that 2-formylbenzenesulfonamides exist as benzisothiazole-1,1-dioxides in the solid state, as a mixture of 2-formylbenzenesulfonamide and the corresponding benzisothiazole-1,1-dioxide in solution and as 2-formyl-benzenesulfonamides in the gas phase.

Soft-chemical routes to synthesis of solid oxide materials

We describe three different families of metal oxides, viz., (i) protonated layered perovskites, (ii) framework phosphates of NASICON and KTiOPO4 (KTP) structures and (iii) layered and three-dimensional oxides in the H-V-W-O system, synthesized by 'soft-chemical' routes involving respectively ion-exchange, redox deinteracalation and acid-leaching from appropriate parent oxides. Oxides of the first family, HyA2B3O10(A = La/Ca; B = Ti/Nb), exhibit variable Bronsted acidity and intercalation behaviour that depend on the interlayer structure. V2(PO4)3 prepared by oxidative deintercalation from Na3V2(PO4)3 is a new host material exhibiting reductive insertion of lithium/hydrogen, while K0.5Nb0.5 M0.5OPO4(M = Ti, V) are novel KTP-like materials exhibiting second harmonic generation of 1064 nm radiation. HxVxW1-xO3 for x = 0.125 and 0.33 possessing alpha-MoO3 and hexagonal WO3 structures, prepared by acid-leaching of LiVWO6, represent functionalized oxide materials exhibiting redox and acid-base intercalation reactivity.

Solid state physics through the years: Need for new initiatives

Solid state physics developed in India later than elsewhere in the world. What is particularly disconcerting is the poor state of experimental solid state physics today. A new thrust and better funding are essential if this field has to thrive in the country.

Study of the reaction between 1,2,3-trihydroxybenzene and 8-hydroxyquinoline in the solid state

1.2,3-Trihydroxybenzene (THB) reacts with 8-hydroxyquinoline (8HQ) in the solid state forming an orange-coloured charge transfer complex THB* (8HQ)(2). When the reaction was carried out in a petri dish, or when the vapours of 8HQ were allowed to react with solid THB (gravimetric study), the reaction product separated out as good quality, shiny single crystals. X-Ray diffraction studies on single crystals showed that they belong to the orthorhombic system with a = 15.408(1), b = 16.276(1), c = 7.825(1) Angstrom, Z = 4, D-x = 1.413 g cm(-3) and space group Pnaa. From the crystallographic evidence it has been found that the proton of the middle OH group of THB is transferred to the N atom of 8HQ. This accounts for the observed colour change. Kinetic studies on the solid state reaction showed that the 8HQ molecules diffuse towards THB, and the lateral diffusion occurs through surface migration, grain boundary diffusion and vapour phase diffusion. Gravimetric studies of the reaction between solid THB and 8HQ vapour showed that the diffusion of 8HQ molecules into the crystal lattice of THB has a higher energy of activation than that observed when the reactants are in contact. The nature of the crystal packing in the reaction product indicates diffusion of 8HQ molecules into the crystal lattice of THB along the c-axis, to occupy the cavities present between the THB molecules in the unit cell.

Reversible Insertion of a Trivalent Cation onto MnO2 Leading to Enhanced Capacitance

Supercapacitor properties of MnO2 are studied generally in aqueous alkali metal salt solutions, often in a Na salt solution. During electrochemical discharge-charge processes, Na+ ions from the electrolyte get reversibly inserted/deinserted on the surface of MnO2 particles, which leads to redox reaction between MnOONa and MnO2. In the present study, it has been shown that MnO2 exhibits enhanced capacitance behaviour in a rare earth metal salt solution, namely, La(NO3)(3) solution in comparison with NaNO3 and Mg(NO3)(2) aqueous solutions. The specific capacitance increases with an increase in charge on the solution cation (Na+, Mg2+ and La3+). It is proposed that the number of surface sites for adsorption of cations remains unaltered in all solutions. The surface insertion of cation facilitates the reduction of Mn4+ in MnO2 to Mn3+ equivalent to the charge present on the cation. As the specific capacitance is related to the quantity of charge that is exchanged between the solid MnO2 and the aqueous solution, the trivalent cation (La3+) provides greater specific capacitance than in Mg(NO3)(2) and NaNO3 electrolytes. Accordingly, the number of Mn(IV)/Mn(III) redox pairs involved in the neighbourhood of the adsorption site is one, two and three when Na+, Mg2+ and La3+ ions, respectively, are adsorbed. (C) 2011 The Electrochemical Society. DOI: 10.1149/1.3565177] All rights reserved.

Whither solid state physics

The physics of the solid state has grown into that of condensed matter and is now expanding into the study of a bewildering variety of complex systems. After a brief survey of this progression, I enquire into the health of solid state physics; many signs of vitality and growth are found. The Indian scene in this field is briefly sketched, and some suggestions are offered on how to make it more lively,