Size-controlled and water-soluble gold nanoparticles using UV-induced ligand exchange and phase transfer

Pure water is a weak electrolyte; only a small amount ionizes into hydrogen and hydroxide ions. At any given temperature, the concentration of undissociated water is almost constant, so the ionic product of water is the product of the hydrogen and hydroxide ion concentrations, denoted as Kw. The square root of Kw gives the individual ion concentrations.
The ionic product of water varies with temperature, and its value is 1.0 x 10−14 at standard experimental conditions. Per Le...

Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass...

Compared with pure water, the solubility of an ionic compound is less in aqueous solutions containing a common ion (one also produced by dissolution of the ionic compound). This is an example of a phenomenon known as the common ion effect, which is a consequence of the law of mass action that may be explained using Le Chȃtelier’s principle. Consider the dissolution of silver iodide:

Solubility equilibria are established when the dissolution and precipitation of a solute species occur at equal rates. These equilibria underlie many natural and technological processes, ranging from tooth decay to water purification. An understanding of the factors affecting compound solubility is, therefore, essential to the effective management of these processes. This section applies previously introduced equilibrium concepts and tools to systems involving dissolution and precipitation.
The...

The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...

Solubility is the measure of the maximum amount of solute that can be dissolved in a given quantity of solvent at a given temperature and pressure. Solubility is usually measured in molarity (M) or moles per liter (mol/L). A compound is termed soluble if it dissolves in water.