Search results
Results from the WOW.Com Content Network
In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “universal” group having these properties, in the sense that any two homomorphisms from G and H into a group K factor uniquely through a ...
The Hildebrand parameter for such non-polar solvents is usually close to the Hansen value. A typical example showing why Hildebrand parameters can be unhelpful is that two solvents, butanol and nitroethane, which have the same Hildebrand parameter, are each incapable of dissolving typical epoxy polymers. Yet a 50:50 mix gives a good solvency ...
Note the decrease in ΔG ‡ activation for the polar-solvent reaction conditions. This arises from the fact that polar solvents stabilize the formation of the carbocation intermediate to a greater extent than the non-polar-solvent conditions. This is apparent in the ΔE a, ΔΔG ‡ activation. On the right is an S N 2 reaction coordinate diagram.
For example, the coproduct in the category of groups, called the free product, is quite complicated. On the other hand, in the category of abelian groups (and equally for vector spaces ), the coproduct, called the direct sum , consists of the elements of the direct product which have only finitely many nonzero terms.
The hydrophobic effect can be quantified by measuring the partition coefficients of non-polar molecules between water and non-polar solvents. The partition coefficients can be transformed to free energy of transfer which includes enthalpic and entropic components, ΔG = ΔH - TΔS. These components are experimentally determined by calorimetry ...
In mathematics, an operator or transform is a function from one space of functions to another. Operators occur commonly in engineering , physics and mathematics. Many are integral operators and differential operators .
This phenomenon leads to minimum exposed surface area of non-polar molecules to the polar water molecules (typically spherical droplets), and is commonly used in biochemistry to study protein folding and other various biological phenomenon. [22] The effect is also commonly seen when mixing various oils (including cooking oil) and water.
Capillary action of water (polar) compared to mercury (non-polar), in each case with respect to a polar surface such as glass (≡Si–OH). Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space without the assistance of external forces like gravity.