Boltzmann factor Water

FIGURE 11.4 Van der Waals energy for three sizes of spherical particles (AI2O3 in water). R = radius of the spherical particle. The ordinate is normalized by a Boltzmann factor to make for easy comparison to Brownian energy (Eg = 2/3 kg T). 

Figure 6. Temperature dependence of 5 (see the text on its definition) determined by the fitting of our prediction to the experimental data of p, Kj, and Cp at various pressures. Open squares, triangles, and circles represent, respectively, data onp.Ax.andCpat ambient pressure. All the other symbols are data at higher pressures. The dashed line is our theoretical prediction for S. The values of S determined from the 23 sets of data of bulk liquid water are all collapsed on the master curve, which is described by the single Boltzmann factor. The figure is reproduced from Fig lb of [25]...

Factor 1 The exponential of the empty water lattice Helmholtz free energy divided by kT, where k is Boltzmann s constant,... 

The 0 term is a Boltzmann temperature, T, factor the <1) term is a Debye-Waller (DW) factor, well known from diffraction work and finally, the I are Bessel functions of the first kind. This single, simple, harmonic system is quite unrepresentative of any realistic molecular solid, however, it is instructive to express the equation with appropriate experimental parameters. The translational optic modes of water (see below) appear at about 35 meV (260 cm ) and typical experimental temperatures are about 20 K (= 2 meV). 

According to Boltzmann s entropy formula (S = kB In 2), the entropy of a polymer chain approaches zero when the chain is highly stretched by an external stretching force. That is, the entropies of the final state are the same (S 0) in the two conditions. However, it is known that the conformation of PNIPAM in water at 35°C is much more compact than that in water at RT, i.e., the initial entropy of PNIPAM at 35°C is much less than that at RT. Thus, the energy cost of a compact conformation would be less than that of a coil conformation. This factor may roughly correspond to the energy difference between water at 35°C and organic solvents. 

A damped oscillating charge distribution of the interfacial structure was also obtained by Sotnikov and Esin/ assuming a Boltzmann distribution of ion vacancies in the interface cf. the case of dilute solutions of ions in water. Additionally, they introduced a polarizability factor to account for the deformation of ion charge under the influence of the electric field within the multilayer. Their revised formula for the interfacial capacitance gave... 

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