2 resultados para contractive and strictly contractive self-mappings
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Resumo:
Self-assembled materials produced in the reaction between alkanethiol and Ag are characterized and compared. It is revealed that the size of the Ag substrate has a significant role in the self-assembly process and determines the reaction products. Alkanethiol adsorbs on the surface of Ag continuous planar thin films and only forms self-assembled monolayers (SAMs), while the reaction between alkanethiol and Ag clusters on inert surfaces is more aggressive and generates a significantly larger amount of alkanethiolate. Two dissimilar products are yielded depending on the size of the clusters. Small Ag clusters are more likely to be converted into multilayer silver-alkanethiolate (AgSR, R = CnH2n+1) crystals, while larger Ag clusters form monolayer-protected clusters (MPCs). The AgSR crystals are initially small and can ripen into large lamellae during thermal annealing. The crystals have facets and flat terraces with extended area, and have a strong preferred orientation in parallel with the substrate surface. The MPCs move laterally upon annealing and reorganize into a single-layer network with their separation distance approximately equal to the length of an extended alkyl chain. AgSR lamellar crystals grown on inert surfaces provide an excellent platform to study the melting characteristics of crystalline lamellae of polymeric materials with the thickness in the nanometer scale. This system is also unique in that each crystal has integer number of layers – magic-number size (thickness). The size of the crystals is controlled by adjusting the amount of Ag and the annealing temperature. X-ray diffraction (XRD) and atomic force microscopy (AFM) are combined to accurately determine the size (number of layers) of the lamellar crystals. The melting characteristics are measured with nanocalorimetry and show discrete melting transitions which are attributed to the magic-number sizes of the lamellar crystals. The discrete melting temperatures are intrinsic properties of the crystals with particular sizes. Smaller lamellar crystals with less number of layers melt at lower temperatures. The melting point depression is inversely proportional to the total thickness of the lamellae – the product of the number of layers and the layer thickness.
Resumo:
The objective of this study was to extend the use of combined longitudinal (P-wave) and shear (S-wave) ultrasonic wave reflection (UWR) to monitor the setting and stiffening of self-compacting pastes and concretes. An additional objective was to interpret the UWR responses of various modified cement pastes. A polymeric buffer with acoustic impedance close to that of cement paste, high impact polystyrene, was chosen to obtain sensitive results from the early hydration period. Criteria for initial and final set developed by our group in a prior study were used to compute setting times by UWR. UWR results were compared with standard penetration measurements. Stiffening behavior and setting times for normal cement pastes, pastes modified with mineral and chemical admixtures, self-compacting pastes, and concretes were explored using penetration resistance, S-wave and P-wave reflection. All three methods showed that set times of pastes varied linearly with w/c, that superplasticizer and fly ash delayed the set times of pastes, and that differences in w/cm, sp/cm, and fa/cm could be detected. Final set times determined from UWR correlated well with those from penetration resistance. Initial set times from S-wave reflection did not correlate very well with those from penetration resistance. Final set times from P-wave and S-wave reflection were roughly the same. Pastes with different chemical admixtures were tested, and the effects of these admixtures on stiffening were determined using UWR. Self-compacting concretes were studied using UWR, and their response and setting times were largely similar to that of corresponding self-compacting pastes. The P-wave reflection response was explored in detail, and the phenomenon of partial debonding and the factors affecting it were explained. Partial debonding is probably caused by autogenous shrinkage at final set, and was controlled and limited by water. The extent of partial debonding was higher with the transducers placed on the side as opposed to the bottom, and the S-wave transducer seemed to promote debonding in the P-wave reflection, whereas the P-wave transducer seemed to reduce debonding in the S-wave reflection. Simultaneous formwork pressure testing and UWR were performed; however, no clear correlation was seen between the two properties.