Secondary energy minimum

Redman JA, Grant SB, Olson TM, Estes MK (2001) Pathogen filtration, heterogeneity, and the potable reuse of wastewater. Environ Sci Technol 35 1798-1805 Redman JA, Walker SL, Elimelech M (2004) Bacterial adhesion and transport in porous media Role of the secondary energy minimum. Environ Sci Technol 38 1777-1785 Reeves CP, CeUa MA (1996) A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour Res 32 2345-2358 Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics 1 318-333... 

Figure 6.11 Gibbs free interaction energy (in units of ki>T) versus distance for two identical spherical particles of R = 100 nm radius in water, containing different concentrations of monovalent salt. The calculation is based on DLVO theory using Eqs. (6.57) and (6.32). The Hamaker constant was Ah = 7 x 10 21 J, the surface potential was set to )/>o = 30 mV. The insert shows the weak attractive interaction (secondary energy minimum) at very large distances.

A closer look at the interaction at large distances shows the weak attractive energy. This secondary energy minimum can lead to a weak, reversible coagulation without leading to direct molecular contact between the particles. 

Attempts to determine the dimensions of the unit cell by use of X-ray diffraction were not successful. It was, however, concluded that the cell is large and triclinic. Computer-based conformational analysis showed that the energy difference between the extended lowest-energy isomer and the non-linear conformer (secondary energy minimum) was 16.2 kJ/mol. 

The second, unstable, state can be realized if the secondary energy minimum is deep enough, and the repulsion barrier is well above kT (usually > 15 kT). 

Redman J, Walker S, Elimelech M. (2004). Bacterial adhesion and transport in porous media Role of the secondary energy minimum. Environmental Science Technology 38 1777-1785. 

For 0 = 110° or 120° the conformational energy map of hydrated GABA is extremely restricted, steric hindrance preventing rotation about which is constrained to the value of 180°. The rotation about T2 presents more freedom, the most stable conformation corresponding to Tj = 180°, 13 = 30° with a secondary energy minimum for the totally extended form at Tj = 13 = 180°, 4 kcal mole" above the global one for 0 = 110°... 

For noncohesive or weakly cohesive particulate films the contact cross-sectional area, A, [42] can be related to the characteristic length of repulsion or the p-p distances at the secondary energy minimum [27, 36]. To determine ylk, a line was fitted to the most steeply rising part of the H-A isotherms (see the leftmost isotherm in Fig. 4) at the surface pressure of 2 mN/m < IT < ric-2mN/m (lie is the collapse pressure) and the intersection of the fitted line and the horizontal axis (A) gives the parameter, Tk. Dividing A by Z, the total number of particles in the boundary layer, one gets this parameter for an individual sphere, Ai. 

FIG U RE 6.8 Spectral distribution for 0 mM (a) and 20 mM KBr (b). The data show that field-induced aggregation may occur in a primary or in a secondary energy minimum, depending on the electrolyte concentration. 

Figure 2. A schematic of the free energy density of an aperiodic lattice as a function of the effective Einstein oscillator force constant a (a is also an inverse square of the locahzation length used as input in the density functional of the liquid). Specifically, the curves shown characterize the system near the dynamical transition at Ta, when a secondary, metastable minimum in F a) begins to appear as the temperature is lowered. Taken from Ref. [47] with permission.

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

One recent study [44], used a protein of known structure. They examined every possible conformation and whether it lead to the correct protein fold, in essence the kinetics of the folding process. Surprisingly, they found no correlation between the presence of secondary structural elements and finding the correct fold Instead the important feature that lead to the correct fold was the presence of the native state as a well-defined energy minimum. The correct energy landscape of configuration is the determinant feature for the correct folding. 

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