On the Clausius-Planck inequality within theories for differential materials

Summary Within a classical theory of differential materials of complexity one, we prove that the Clausius-Planck inequality is equivalent to another one, here called the extra-stress inequality. Within a Green-Naghdi theory, the first inequality implies the vanishing of a term related to the response function for the internal production of entropy; and the vanishing of this term implies the equivalence of the two aforementioned inequalities.

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Sommario Entro una teoria classica per materiali differenziali di complessità uno si prova che la diseguaglianza di Clausius-Planck equivale ad un'altra diseguaglianza dissipativa, qui detta dell'extra-stress. Entro una teoria alla Green-Naghdi la prima diseguaglianza implica l'annullarsi di un termine legato alla funzione di risposta per la produzione interna di entropia; e l'annullarsi di tale termine implica l'equivalenza tra le diseguaglianze sopra menzionate.

     

Uniqueness theorems for the entropy in any differential body of complexity one

By using in an essential way a certain condition of mutual physical equivalence between admissible response functions for the heat flux, in a previous paper uniqueness theorems were proved for the response functions of the internal energy and of the equilibrium stress, in connection with differential bodies of complexity 1. It was then pointed out that the equality expressing the vanishing of the static internal dissipation uniquely determines the rate of entropy variation in terms of the rate of the internal energy variation and of the equilibrium stress. This paper shows, in a threefold manner, that the last result also holds if one does not impose the condition of physical equivalence. The first proof uses the assumption that the response functions are Euclidean invariant. The second proof uses (i) the weaker assumption of Galilean invariance and (ii) a greater degree of smoothness of the response function for the internal energy. Both of these proofs use an axiom postulating the possibility of putting the body in contact with a vacuum. The third proof of the uniqueness property for the entropy is independent of the isolation axiom and uses the assumptions of the second proof. Whereas any of the first two proofs is a consequence of the uniqueness theorem for the internal energy-proved here by using the afore-mentioned axiom-the third proof does not depend on this theorem. Rather, disregarding the above isolation axiom, it implies that uniqueness of the entropy is compatible with non-uniqueness of both the stress and internal energy.

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Sommario In un precedente articolo, utilizzando in maniera essenziale una certa condizione di mutua equivalenza fisica tra ammissibili funzioni costitutive per il flusso di calore, si dimostrano teoremi di unicità per le funzioni costitutive di energia interna e di stress statico in corpi di tipo differenziale e complessità 1. Inoltre si osserva che, di conseguenza, la uguaglianza esprimente l'annullarsi della dissipazione interna statica permette di determinare univocamente la velocità di variazione dell'entropia in termini della velocità di variazione dell'energia interna e dello stress statico. Nel presente lavoro si dimostra, in triplice maniera, che l'ultimo risultato vale anche se non si impone la accennata condizione di equivalenza fisica. Nella prima dimostrazione si usa l'ipotesi di invarianza Euclidea per le funzioni costitutive. Nella seconda si usa (i) la più debole ipotesi di invarianza Galileiana e (ii) un maggiore grado di regolarità per la funzione costitutiva dell'energia interna. In entrambe le dimostrazioni si usa un assioma che postula la possibilità di porre in contatto il corpo con il vuoto. La terza dimostrazione della proprietà di unicità per l'entropia, che usa le medesime ipotesi della seconda, è indipendente da tale assioma. Mentre nelle prime due dimostrazioni si richiama il teorema il teorema di unicità per l'energia interna-qui dimostrato con l'assioma di isolamento-la terza dimostrazione non dipende da tale teorema. Invece, se non si assume l'assioma di isolamento con il vuoto, l'unicità dell'entropia risulta compatibile con certe non-unicità per stress ed energia interna.

     

Could Carbonaceous Impurities in Reduced Graphenes be Responsible for Some of Their Extraordinary Electrocatalytic Activities?

Thermally and chemically reduced graphene materials contain significant amounts of carbonaceous impurities that are similar in structure to amorphous carbon. Herein, we show that the claimed electrocatalytic activities of these materials for the oxidation of NADH, acetaminophen, and hydroquinone are mainly due to the presence of carbonaceous impurities.     

Bloch Bundles, Marzari-Vanderbilt Functional and Maximally Localized Wannier Functions

We consider a periodic Schrödinger operator and the composite Wannier functions corresponding to a relevant family of its Bloch bands, separated by a gap from the rest of the spectrum. We study the associated localization functional introduced in Marzari and Vanderbilt (Phys Rev B 56:12847–12865, 1997) and we prove some results about the existence and exponential localization of its minimizers, in dimension ${d \leq 3}$ d ≤ 3 . The proof exploits ideas and methods from the theory of harmonic maps between Riemannian manifolds.     

Evaluation of activity of a commercial amylase under ultrasound-assisted irradiation

The main objective of this work was to evaluate the effects of ultrasound irradiation on the activity of a commercial amylase. A central composite design was carried out to assess the effects of temperature and pH on the enzyme activity in the presence and absence of ultrasound irradiation. The activation energy, the influence of treatment time as well as the substrate concentration on enzyme activity were also determined in the presence and absence of ultrasound irradiation. The results demonstrated that the effect of temperature was less pronounced in the presence of ultrasound, resulting in a decreasing of about 80% in the activation energy in comparison with the value obtained in the absence. The enzyme showed activities about 3 times higher for temperatures up to 40 °C in the presence of ultrasound. The pH negatively affected the activity in the presence of ultrasound, whereas in the absence a positive effect was verified. The ultrasound irradiation is a promising technology to be used in enzymatic reaction due to its positive effects on enzyme activity.     

Green high‐performance liquid chromatography enantioseparation of lansoprazole using a cellulose‐based chiral stationary phase under ethanol/water mode

A simple and environmentally friendly reversed‐phase high‐performance liquid chromatography method for the separation of the enantiomers of lansoprazole has been developed. The chromatographic resolution was carried out on the cellulose‐based Chiralpak IC‐3 chiral stationary phase using a green and low‐toxicity ethanol‐aqueous mode. The effects of water content in the mobile phase and column temperature on the retention of the enantiomers of lansoprazole and its chiral and achiral related substances have been carefully investigated. A mixed‐mode hydrophilic interaction liquid chromatography and reversed‐phase retention mechanism operating on the IC‐3 chiral stationary phase allowed us to achieve simultaneous enantioselective and chemoselective separations in water‐rich conditions. The enantiomers of lansoprazole were baseline resolved with a mobile phase consisting of ethanol/water 50:50 without any interference coming from chiral and achiral impurities within 10 min.     

Selective catalysis and nanoscience: an inseparable pair

Selective catalysts can be considered as nanomachines designed to perform the synthesis of molecules with high reaction activity and high selectivity. These properties arise from a precise control of the structure of the active sites, of the three-dimensional environment and of their relationship. In both homogeneous and heterogeneous catalysts the active site three-dimensional environment ensemble is always a complex structure resembling the tuneable structure of enzymes, which are the most efficient catalysts optimized by nature over billions of years. To illustrate this concept the structure of a few homogeneous and heterogeneous catalysts for alkenes hydrogenation and for olefin polymerization are chosen and discussed as examples.     

Biosensor analysis for the kinetic study of polyphenols deterioration during the forced thermal oxidation of extra-virgin olive oil

The process of artificial rancidification of extra-virgin olive oil due to heating in an oxidizing atmosphere was studied by testing an actual kinetic model of the process and monitoring the thermal oxidative degradation of the polyphenols contained in it. To this end, a series of oxidative degradation experiments were carried out on extra-virgin olive oil samples under isothermal conditions at 98, 120, 140, 160, and 180 °C using a thermostatic silicon oil bath. The experimental procedure used in this study carefully followed the recommendations regarding the study of olive oil rancidification set out in the AOM procedure. The change in polyphenol concentration with time was monitored at selected temperatures using a tyrosinase biosensor operating in an organic phase (n-hexane). The activation energy for the polyphenol degradation process determined using the MacCallum method was found to be practically constant throughout most of the process.

Furthermore, the application of the so-called “model-fitting” method to this process enabled the specific constant rates to be determined at the above-mentioned selected temperatures. In addition, a confirmation of the activation energy value was obtained by the “model-fitting” method and the algorithm of the kinetic model equation best-fitting the experimental curve representing the whole process was checked.

Finally, further very interesting observations were made, for instance, the half-life concentration values of polyphenols at selected temperatures between 98 and 180 °C.     

Nucleophilic addition of potassium organotrifluoroborates to chiral cyclic N-acyliminium ions: stereoselective synthesis of functionalized N-heterocycles

The stereoselective nucleophilic addition of potassium aryl- and alkynyltrifluoroborates to cyclic N-acyliminium ion derivatives from N-benzyl-3,4,5-triacetoxy-2-pyrrolidinone, affording the respective 5-substituted 2-pyrrolidinone is described. The products were obtained in moderate to good yields and with preference for the syn diastereomer.