Anomalous temperature dependence of speed of sound of bulk poly(N-isopropylacrylamide) hydrogels near the phase transition

Bulk Poly(N-isopropylacrylamide) (PNIPAm) hydrogels are thermally responsive polymers that undergo a sharp volumetric phase transition around its lower critical solution temperature of 33 °C. The physical characteristics of bulk, micro-, and nano-form PNIPAm hydrogel have been well-studied, and have applications ranging from biomedical devices to mechanical actuators. An important physical characteristics which reveals lack of available information is speed of sound. Prior studies have utilized Brillouin scattering, multi-echo reflection ultrasound spectroscopy, the sing-around method, and others in measuring the speed of sound. We use a planar resonant cavity with bulk PNIPAm hydrogel in aqueous solution to determine the temperature dependent speed of sound around the lower critical solution temperature. The results show sharp nonmonotonic behavior of the sound velocity in vicinity of the phase transition.     

Limiting Spectral Distribution of Random k-Circulants

Consider random k-circulants A _k,n with n????,k=k(n) and whose input sequence {a _l } _l??0 is independent with mean zero and variance one and $\sup_{n}n^{-1}\sum_{l=1}^{n}\mathbb{E}|a_{l}|^{2+\delta}<\infty$ for some ??>0. Under suitable restrictions on the sequence {k(n)} _n??1, we show that the limiting spectral distribution (LSD) of the empirical distribution of suitably scaled eigenvalues exists, and we identify the limits. In particular, we prove the following: Suppose g??1 is fixed and p ₁ is the smallest prime divisor of g. Suppose $P_{g}=\prod_{j=1}^{g}E_{j}$ where {E _j }_1??j??g are i.i.d. exponential random variables with mean one. (i) If k ^g =?1+sn where s=1 if g=1 and $s=o(n^{p_{1}-1})$ if g>1, then the empirical spectral distribution of n ^?1/2 A _k,n converges weakly in probability to $U_{1}P_{g}^{1/(2g)}$ where U ₁ is uniformly distributed over the (2g)th roots of unity, independent of P _g . (ii) If g??2 and k ^g =1+sn with $s=o(n^{p_{1}-1})$ , then the empirical spectral distribution of n ^?1/2 A _k,n converges weakly in probability to $U_{2}P_{g}^{1/(2g)}$ where U ₂ is uniformly distributed over the unit circle in ?², independent of P _g . On the other hand, if k??2, k=n ^o(1) with gcd?(n,k)=1, and the input is i.i.d. standard normal variables, then $F_{n^{-1/2}A_{k,n}}$ converges weakly in probability to the uniform distribution over the circle with center at (0,0) and radius $r=\exp(\mathbb{E}[\log\sqrt{E}_{1}])$ .     

Interesting periodic variations in physical and chemical properties of homonuclear diatomic molecules

We carry out a systematic study of various ground state and response properties of homonuclear diatomic molecules (from hydrogen to rubidium, including transition metals) as a function of atomic number of constituent atoms. We perform the ground state and response property calculations by using state of the art density functional theory/time dependent density functional theory. We observe that several properties of homonuclear diatomic molecules show periodic variations along rows and columns of the periodic table. The periodic variations in the ground state properties of diatomic molecules may be explained by the nature and type of the bond that exists between the constituent atoms. Similarly, the periodic variations in the response properties such as static dipole polarizability and strength of the van der Waals interaction between diatomic molecules have been correlated with the variations in metallic/nonmetallic character of the elements along the periodic table. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Noncrossing Partitions, Catalan Words, and the Semicircle Law

As is well known, the joint limit distribution of independent Wigner matrices is free with the marginals being semicircular. This freeness is intimately tied to noncrossing pair partitions or, equivalently what are known as Catalan words, each of which contributes one to the limit moments. We investigate the following questions. Consider a sequence of patterned matrices: (i) When do only Catalan words contribute (one), so that we get the semicircle limit? (ii) When does each Catalan word contribute one (with possible nonzero contribution from non-Catalan words)? (iii) For what matrix models do Catalan words not necessarily contribute one each and non-semicircle limits arise, even when non-Catalan words have zero contribution? In particular we show that in a general sense, the semicircle law serves as a lower bound for possible limits. Further, there is a large class of non-Wigner matrices whose limit is the semicircle. This may be viewed as robustness of the semicircle law. Similarly, there is a large class of block matrices whose limit is not semicircular.     

Diethyldisulfoammonium chlorometallates as heterogeneous Brønsted–Lewis acidic catalysts for one‐pot synthesis of 14‐aryl‐7‐(N‐phenyl)‐14H‐dibenzo[a,j]acridines

A new series of Brønsted–Lewis acidic diethyldisulfoammonium chlorometallates, [DEDSA][FeCl₄] and [DEDSA]₂[Zn₂Cl₆], were synthesized as solid materials from the reaction of [(Et)₂N(SO₃H)₂][Cl] ionic liquid with transition metal chlorides (FeCl₃ and ZnCl₂) at 80 °C in neat condition for 2 h. The chlorometallates were fully characterized using various spectroscopic and analytical techniques such as Fourier transform infrared, UV–visible and Raman spectroscopies, powder X‐ray diffraction, scanning electron microscopy, energy‐dispersive X‐ray and thermogravimetric analyses, Hammett acidity and elemental analyses. Their catalytic activity was studied as reusable heterogeneous catalysts for the three‐component synthesis of novel 14‐aryl‐7‐(N‐phenyl)‐14H‐dibenzo[a,j]acridines under solvent‐free conditions at 100 °C.     

Radiation (60Co)-Induced Graft Copolymerization of Acrylamide on Jute Fiber

The radiation induced graft copolymerization of acrylamide onto jute fibers was studied following preirradiation of jute in air using a⁶⁰Co source of γ-radiation and subsequent polymerization of acrylamide in a limited aqueous system under nitrogen at 607°C. An increase of the time of preirradiation (at a fixed dose rate) increased the percent grafting measurably and the grafting efficiency marginall Grafting effects showed further improvement on addition of Fe²⁺ or Co²⁺ ions to the system prior to the polymerization step. Increasing the concentration of Fe²⁺ or Co²⁺ ion led to an increase in the grafting parameters with a leveling off effect in the higher concentration range, however. An increase in the polymer (jute) content for a fixed monomer content produced a significant increase in the efficiency of grafting, while % grafting followed a slowly decreasing trend.     

Mechanistic aspects of ligand substitution on <Emphasis Type="Italic">cis</Emphasis>-diaqua(<Emphasis Type="Italic">cis</Emphasis>-1,2-diaminocyclohexane)platinum(II) by Glycine-<Emphasis Type="SmallCaps">l</Emphasis>-Leucine

The kinetics of the interaction of glycine-l-leucine (Glyleu) with cis-[Pt(cis-dach)(OH₂)₂]²⁺ (dach = 1,2-diaminocyclohexane) has been studied spectrophotometrically as a function of [cis-[Pt(cis-dach)(OH₂)₂]²⁺], [Glyleu] and temperature at pH 4.0, where the complex exists predominantly as the diaqua species and Glyleu as a zwitterion. The substitution reaction shows two consecutive steps: the first is the ligand-assisted anation and the second is the chelation step. The activation parameters for both the steps were evaluated using Eyring’s equation. The low ∆H₁^≠ (51.9 ± 2.8 kJmol⁻¹) and large negative value of ∆S₁^≠ (−152 ± 8 JK⁻¹mol⁻¹) as well as ∆H₂^≠ (54.4 ± 1.7 kJmol⁻¹) and ∆S₂^≠ (−162 ± 5 JK⁻¹mol⁻¹) indicate an associative mode of activation for both the aqua ligand substitution processes.     

Kinetics and mechanism of the reaction of hydroxopentaaquarhodium(III) ion with <Emphasis Type="SmallCaps">l</Emphasis>-Arginine in aqueous solution

The kinetics of the aqua ligand substitution from hydroxopentaaquarhodium(III) ion, [Rh(H₂O)₅(OH)]²⁺, by l-Arginine has been studied spectrophotometrically as a function of Arginine concentration, and temperature, at pH 4.3. The reaction proceeds via a rapid outer sphere association complex formation step followed by two consecutive steps. The first of these involves ligand-assisted anation, while the second involves chelation as the second aqua ligand is displaced. The association equilibrium constant for the outer sphere complex formation has been evaluated together with the rate constants for the two subsequent steps. The activation parameters for both steps have been evaluated using Eyring’s equation. Thermodynamic parameters calculated from the temperature dependence of the outer sphere association equilibrium constants are also consistent with an associative mode of activation. The product of the reaction has been characterized by conductivity measurement and IR spectroscopic analysis.     

Kinetic and mechanistic studies on the reaction of thiosemicarbazide with [(H<Subscript>2</Subscript>O)(tap)<Subscript>2</Subscript>RuORu(tap)<Subscript>2</Subscript>(H<Subscript>2</Subscript>O)]<Superscript>2+</Superscript> {tap = 2-(m-tolylazo)pyridine}

The interaction of thiosemicarbazide with the title complex has been studied spectrophotometrically in aqueous medium as a function of [complex], [thiosemicarbazide], pH and temperature at constant ionic strength. At pH 7.4, the reaction shows two distinct paths; both of which are [thiosemicarbazide] dependent. A parallel reaction scheme fits well with the experimental findings. An associative interchange mechanism is proposed for both the paths; the activation parameters calculated from Eyring plots are ΔH₁^≠ = 14.2 ± 0.8 kJ mol⁻¹, ΔS₁^≠ = −241 ± 2 JK⁻¹ mol⁻¹, ΔH₂^≠ = 30.8 ± 1.4 kJ mol⁻¹ and ΔS₂^≠ = −236 ± 4 JK⁻¹ mol⁻¹. From the temperature dependence of the outer sphere association complex equilibrium constants, the thermodynamic parameters calculated are ΔH₁^° = 34.25 ± 1.9 kJ mol⁻¹, ΔS₁^° = 146 ± 6 J K⁻¹ mol⁻¹ and ΔH₂^° = 9.4 ± 1.1 kJ mol⁻¹, ΔS₂^° = 71 ± 3 JK⁻¹ mol⁻¹, which gives a negative ΔG° at all temperatures studied, supporting the spontaneous formation of an outer sphere association complex.     

Mapping the Transformation [{RuII(CO)3Cl2}2]→[RuI2(CO)4]2+: Implications in Binuclear Water–Gas Shift Chemistry

The complete sequence of reactions in the base‐promoted reduction of [{Ru^II(CO)₃Cl₂}₂] to [Ru^I₂(CO)₄]²⁺ has been unraveled. Several μ‐OH, μ:κ²‐CO₂H‐bridged diruthenium(II) complexes have been synthesized; they are the direct results of the nucleophilic activation of metal‐coordinated carbonyls by hydroxides. The isolated compounds are [Ru₂(CO)₄(μ:κ²‐C,O‐CO₂H)₂(μ‐OH)(NP^F‐Am)₂][PF₆] ( 1 ; NP^F‐Am=2‐amino‐5,7‐trifluoromethyl‐1,8‐naphthyridine) and [Ru₂(CO)₄(μ:κ²‐C,O‐CO₂H)(μ‐OH)(NP‐Me₂)₂][BF₄]₂ ( 2 ), secured by the applications of naphthyridine derivatives. In the absence of any capping ligand, a tetranuclear complex [Ru₄(CO)₈(H₂O)₂(μ³‐OH)₂(μ:κ²‐C,O‐CO₂H)₄][CF₃SO₃]₂ ( 3 ) is isolated. The bridging hydroxido ligand in 1 is readily replaced by a π‐donor chlorido ligand, which results in [Ru₂(CO)₄(μ:κ²‐C,O‐CO₂H)₂(μ‐Cl)(NP‐PhOMe)₂][BF₄] ( 4 ). The production of [Ru₂(CO)₄]²⁺ has been attributed to the thermally induced decarboxylation of a bis(hydroxycarbonyl)–diruthenium(II) complex to a dihydrido–diruthenium(II) species, followed by dinuclear reductive elimination of molecular hydrogen with the concomitant formation of the Ru^I? Ru^I single bond. This work was originally instituted to find a reliable synthetic protocol for the [Ru₂(CO)₄(CH₃CN)₆]²⁺ precursor. It is herein prescribed that at least four equivalents of base, complete removal of chlorido ligands by Tl^I salts, and heating at reflux in acetonitrile for a period of four hours are the conditions for the optimal conversion. Premature quenching of the reaction resulted in the isolation of a trinuclear Ru^I₂Ru^II complex [{Ru(NP‐Am)₂(CO)}{Ru₂(NP‐Am)₂(CO)₂(μ‐CO)₂}(μ₃:κ³‐C,O,O′‐CO₂)][BF₄]₂ ( 6 ). These unprecedented diruthenium compounds are the dinuclear congeners of the water–gas shift (WGS) intermediates. The possibility of a dinuclear pathway eliminates the inherent contradiction of pH demands in the WGS catalytic cycle in an alkaline medium. A cooperative binuclear elimination could be a viable route for hydrogen production in WGS chemistry.