Interface tension of silica hydroxylated nanoparticle with brine: a combined experimental and molecular dynamics study

We have used molecular dynamics simulations to calculate the interfacial tension of hydroxylated SiO(2) nanoparticles under different temperatures and solutions (helium and brine with monovalent and divalent salts). In order to benchmark the atomistic model, quartz SiO(2) interfacial tension was measured based on inverse gas chromatography under He atmosphere. The experimental interfacial tension values for quartz were found between 0.512 and 0.617 N/m. Our calculated results for the interfacial tension of silica nanoparticles within helium atmosphere was 0.676 N/m, which is higher than the value found for the system containing He∕α-quartz (0.478 N/m), but it is similar to the one found for amorphous silica surface. We have also studied the interfacial tension of the nanoparticles in electrolyte aqueous solution for different types and salts concentrations (NaCl, CaCl(2), and MgCl(2)). Our calculations indicate that adsorption properties and salt solutions greatly influence the interfacial tension in an order of CaCl(2) > MgCl(2) > NaCl. This effect is due to the difference in distribution of ions in solution, which modifies the hydration and electrostatic potential of those ions near the nanoparticle.     

Path-following gradient-based decomposition algorithms for separable convex optimization

A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require any smoothness assumption on the objective function. This allows us to handle more general classes of problems arising in many real applications than in the path-following Newton methods. The new algorithm is a combination of three techniques, namely smoothing, Lagrangian decomposition and path-following gradient framework. The algorithm decomposes the original problem into smaller subproblems by using dual decomposition and smoothing via self-concordant barriers, updates the dual variables using a path-following gradient method and allows one to solve the subproblems in parallel. Moreover, compared to augmented Lagrangian approaches, our algorithmic parameters are updated automatically without any tuning strategy. We prove the global convergence of the new algorithm and analyze its convergence rate. Then, we modify the proposed algorithm by applying Nesterov’s accelerating scheme to get a new variant which has a better convergence rate than the first algorithm. Finally, we present preliminary numerical tests that confirm the theoretical development.     

Invariant-point theorems and existence of solutions to optimization-related problems

To consider existence of solutions to various optimization-related problems, we first develop some equivalent versions of invariant-point theorems. Next, they are employed to derive sufficient conditions for the solution existence for two general models of variational relation and inclusion problems. We also prove the equivalence of these conditions with the above-mentioned invariant-point theorems. In applications, we include consequences of these results to a wide range of particular cases, from relatively general inclusion problems to classical results as Ekeland’s variational principle, and practical situations like traffic networks and non-cooperative games, to illustrate application possibilities of our general results. Many examples are provided to explain advantages of the obtained results and also to motivate in detail our problem settings.     

Iterative methods for solving monotone equilibrium problems via dual gap functions

This paper proposes an iterative method for solving strongly monotone equilibrium problems by using gap functions combined with double projection-type mappings. Global convergence of the proposed algorithm is proved and its complexity is estimated. This algorithm is then coupled with the proximal point method to generate a new algorithm for solving monotone equilibrium problems. A class of linear equilibrium problems is investigated and numerical examples are implemented to verify our algorithms.     

Topologically‐based characterizations of the existence of solutions of optimization‐related problems

Necessary and sufficient conditions for the existence of solutions of optimization‐related problems, defined on general sets, are established by using topologically‐based structures, without the usual linear structure. First, we prove that the existence of solutions to a variational relation problem is equivalent to the existence of either a KKM‐structure or a connectedness structure, satisfying additionally some verifiable conditions. Then, applying these results, we obtain such full (two‐way) characterizations for the existence of invariant points, solutions of quasiequilibrium problems of the Stampacchia‐Minty type, saddle points, and Nash equilibria for noncooperative games. The main advantages of our scheme with the mentioned two structures are that full characterizations for existence are obtained in a unified way, with no convexity assumptions, and also that one has flexibility to choose a suitable structure in investigations. (This flexibility is decisive when the natural underlying structure of the given problem is scarcely employed.)     

Structural similarities among eight benzoylhydrazones

The crystal structures of eight benzoylhydrazones with different substituents have been investigated, namely 1‐benzoyl‐2‐(propan‐2‐ylidene)hydrazone, C₁₀H₁₂N₂O, (I), 1‐benzoyl‐2‐(1‐cyclohexylethylidene)hydrazone, C₁₅H₂₀N₂O, (II), 1‐benzoyl‐2‐[1‐(naphthalen‐2‐yl)ethylidene]hydrazone, C₁₉H₁₆N₂O, (III), 1‐benzoyl‐2‐(1‐cyclohexylbenzylidene)hydrazone, C₂₀H₂₂N₂O, (IV), 1‐benzoyl‐2‐(1‐phenylbenzylidene)hydrazone, C₂₀H₁₆N₂O, (V), 1‐benzoyl‐2‐[1‐(4‐chlorophenyl)benzylidene]hydrazone, C₂₀H₁₅ClN₂O, (VI), 1‐benzoyl‐2‐(4‐hydroxybenzylidene)hydrazone methanol monosolvate, C₁₄H₁₂N₂O₂·CH₃OH, (VII), and 1‐benzoyl‐2‐(1,1‐diphenylpropan‐2‐ylidene)hydrazone, C₂₂H₂₀N₂O, (VIII). The ten molecules in the eight crystal structures [there are two independent molecules in the structures of (V) and (VI)] show similar conformations and hydrogen‐bonding patterns. The C=N—NH—C=O group is planar, but the plane of the phenyl ring of the benzoyl group is rotated by about 30° with respect to that of the keto group [except for (IV), where the groups are coplanar]. Only in the amide group of (VIII) is the N—H group syn to the C=O bond, whereas the seven other compounds exhibit the anti conformation. Unless prevented by steric hindrance, N—H...O hydrogen bonds help to stabilize the crystal structure, which leads to infinite chains or dimers depending upon the molecular conformation. The molecular packing is supported by intermolecular C—H...O interactions. In the crystal structure of (VII), the methanol solvent molecule participates in two strong hydrogen bonds and two weak C—H...O interactions, thus acting as a link between the molecular chains.     

Efficient, enantioselective assembly of silanediol protease inhibitors

A five-step assembly of silicon-protected dipeptide mimics from commercially available reagents is described. This methodology makes silanediol protease inhibitors readily available for the first time. The sequence features asymmetric hydrosilylation, a novel reduction of a silyl ether to a silyllithium reagent, and addition of this dianion to a sulfinimine, to produce the complete inhibitor skeleton with full control of stereochemistry. Oxidation of the primary alcohol to an acid completes the synthesis.     

Metal ion affinity-based biomolecular recognition and conjugation inside synthetic polymer nanopores modified with iron-terpyridine complexes

Here we demonstrate a novel biosensing platform for the detection of lactoferrin (LFN) via metal-organic frameworks, in which the metal ions have accessible free coordination sites for binding, inside the single conical nanopores fabricated in polymeric membrane. First, monolayer of amine-terminated terpyridine (metal-chelating ligand) is covalently immobilized on the inner walls of the nanopore via carbodiimide coupling chemistry. Second, iron-terpyridine (iron-terPy) complexes are obtained by treating the terpyridine modified-nanopores with ferrous sulfate solution. The immobilized iron-terPy complexes can be used as recognition elements to fabricate biosensing nanodevice. The working principle of the proposed biosensor is based on specific noncovalent interactions between LFN and chelated metal ions in the immobilized terpyridine monolayer, leading to the selective detection of analyte protein. In addition, control experiments proved that the designed biosensor exhibits excellent biospecificity and nonfouling properties. Furthermore, complementary experiments are conducted with multipore membranes containing an array of cylindrical nanopores. We demonstrate that in the presence of LFN in the feed solution, permeation of methyl viologen (MV(2+)) and 1,5-naphthalenedisulphate (NDS(2-)) is drastically suppressed across the iron-terPy modified membranes. On the basis of these findings, we envision that apart from conventional ligand-receptor interactions, the designing and immobilization of alternative functional ligands inside the synthetic nanopores would extend this method for the construction of new metal ion affinity-based biomimetic systems for the specific binding and recognition of other biomolecules.     

Synergistic degradation to prepare oligochitosan by γ-irradiation of chitosan solution in the presence of hydrogen peroxide

Synergistic degradation of chitosan by γ-irradiation of chitosan solution (3%) in the presence of hydrogen peroxide (0.25%, 0.5% and 1%) was investigated. The efficiency of the degradation process was demonstrated by gel permeation chromatography (GPC) analysis of the average molecular weight of degraded chitosan (oligochitosan). Structures of resultant oligochitosan were characterized by Fourier-transform infrared spectra (FT-IR) and X-ray diffraction (XRD). Results showed that oligochitosan with Mw from 5000 to 10,000 could be efficiently prepared by γ-irradiation of chitosan solution containing a small amount of hydrogen peroxide at low dose less than 10 kGy. There was almost no significant change in the main chain structure of oligochitosan; however, the obtained oligochitosans lost about 10% of amino groups and the formation of carboxyl groups could not be specified by FT-IR spectra. The morphology state of oligochitosan was essentially amorphous, which differs from that of original chitosan. The combined γ ray/H₂O₂ method is significantly efficient for scale-up manufacture of oligochitosan.     

Singularity and blow-up estimates via Liouville-type theorems for Hardy–Hénon parabolic equations

We consider the Hardy–Hénon parabolic equation ${u_t-\Delta u =|x|^a |u|^{p-1}u}$ with p > 1 and ${a\in \mathbb{R}}$ . We establish the space-time singularity and decay estimates, and Liouville-type theorems for radial and nonradial solutions. As applications, we study universal and a priori bound of global solutions as well as the blow-up estimates for the corresponding initial-boundary value problem.