Conjugate pairs internal energies

Table 1.1 Conjugate pairs of variables in work terms for the fundamental equation for the internal energy U. Here/is force of elongation, Z is length in the direction of the force, <7 is surface tension, As is surface area, , is the electric potential of the phase containing species i, qi is the contribution of species i to the electric charge of a phase, E is electric field strength, p is the electric dipole moment of the system, B is magnetic field strength (magnetic flux density), and m is the magnetic moment of the system. The dots indicate scalar products of vectors.

The fundamental equation for U is in agreement with the statement of the preceding section that for a homogeneous mixture of Ns substances, the state of the system can be specified by Ns + 2 properties, at least one of which is extensive. The total number of variables involved in equation 2.2-8 is 2NS + 5. Ns + 3 of these variables are extensive (U, S, V, and (nj), and Ns + 2 of the variables are intensive (T, P, /.q ). Note that except for the internal energy, these variables appear in pairs, in which one property is extensive and the other is intensive these are referred to as conjugate pairs. These pairs are given later in Table 2.1 in Section 2.7. When other kinds of work are involved, there are more than 2Ns + 5 variables in the fundamental equation for U (see Section 2.7). 

The sign of the derivatives can be determined simply by writing down the variables in two rows, the intensive variables above, the extensive variables below so that conjugate pairs are in the same column. The signs attached to the intensive variables are those of the corresponding terms in the fundamental equation (4.23) for the internal energy. 

MALDI-conditions [47] and also predicted by molecular modeling [40, 50], However, these model calculations also predicted that large clusters would have insufficient internal energy for a complete dissociation with evaporation of the neutrals. This result may also originate from insufficient simulation times and/or to too-hmited sizes of the simulation box [58], and does not necessarily reflect the situation for smaller to medium-sized clusters. While the initially charged matrix - analyte cluster ions never appear in the MALDI spectra with the typical solutes used, such as trifluoroacetic acid (TFA) or ammonium salts, they have been detected for extremely strong acids [60] their conjugate anions are extremely weak bases and thus stabiUze the formed ion pairs with protonated analyte sites. 

---