Molecular radii

Rodbard and Chrambach [77,329] developed a computer program that allows the determination of molecular parameters, i.e., free mobility, molecular radii, molecular weight, and charge or valence, from measured electrophoretic mobilities in gels with different monomer concentrations. For a set of mobility versus gel concentration data they used the Ferguson [18,115,154] equation to obtain the retardation constant from the negative slope and the free mobility from the extrapolated intercept. From the retardation constant they determined the molecular radius using... 

Rodbard, D Chrambach, A, Estimation of Molecular Radius, Free Mobility, and Valence Using Polyacrylamide Gel Electrophoresis, Analytical Biochemistry 40, 95, 1971. 

Molecular radius, R was estimated as the radius of equivalent circle to the projection area of the right configuration in Fig. 1. 

An important phenomenon when considering the differences between ice I and liquid water is that water achieves its maximum density not in the solid state, but at 4 °C, i.e. in the liquid state. The reasons for this were first discussed by Bernal Fowler (1933). They noted that the separation of molecules in ice I is about 0-28 nm, corresponding to an effective molecular radius of 014 nm. Close packing of molecules of such radius would yield a substance of density 1-84 g cm" . To account for the observed density of 10 g cm" , it was necessary to postulate that the arrangement of molecules was very open compared with the disordered, close-packed structures of simple liquids such as argon and neon. 

The Renkin function compares the molecular radius (r) with the pore radius (R) where 0 < F(r/R) < 1.0. With the fixed charges of the pore negative and assuming a linear potential gradient where the sign of the potentials and valences of the ions are accounted for, one gets... 

The Stokes-Einstein equation gives a good approximation of the molecular radius (r) for spherical or nearly spherical molecules ... 

The permeability coefficients and molecular radii are known. The effective pore radius, R, is the only unknown and is readily calculated by successive approximation. Consequently, unknown parameters (i.e., porosity, tortuosity, path length, electrical factors) cancel, and the effective pore radius is calculated to be 12.0 1.9 A. Because the Renkin function [see Eq. (35)] is a rapidly decaying polynomial function of molecular radius, the estimation of R is more sensitive to small uncertainties in the calculated molecular radius values than it is to experimental variabilities in the permeability coefficients. The placement of the perme-ants within the molecular sieving function is shown in Figure 9 for the effective... 

Figure 9 Molecular restriction factor as a function of the ratio of molecular radius to pore radius for paracellular permeants in Caco-2 cell monolayers. Mean pore radius is 1.2 nm.

The plot of permeability coefficient versus molecular radius in Figure 10 shows the interdependence of molecular size and electric charge. The permeability of the solutes decreases with increasing size. The protonated amines permeate the pores faster than neutral solutes of comparable size, and the anions of weak acids permeate the pores at a slower rate. The transport behavior of the ionic permeants is consistent with a net negatively charged paracellular route. These results are phenomenologically identical to those found in the transport kinetics of... 

Figure 10 Paracellular permeability of charged solutes as a consequence of their molecular radius illustrates the mechanism of molecular restricted diffusion across negatively charged pores. Solid line depicts the curve drawn through the permeability coefficients of neutral solutes, and the neutral image of positively and negatively charged permeants.

PC = partition coefficient values from Adson et at. (1995). Molecular density p 1.0 g/mL. Diffusion coefficient and molecular radius calculated by Eqs. (41) and (42). 

As mentioned earlier, ascorbate and ubihydroquinone regenerate a-tocopherol contained in a LDL particle and by this may enhance its antioxidant activity. Stocker and his coworkers [123] suggest that this role of ubihydroquinone is especially important. However, it is questionable because ubihydroquinone content in LDL is very small and only 50% to 60% of LDL particles contain a molecule of ubihydroquinone. Moreover, there is another apparently much more effective co-antioxidant of a-tocopherol in LDL particles, namely, nitric oxide [125], It has been already mentioned that nitric oxide exhibits both antioxidant and prooxidant effects depending on the 02 /NO ratio [42]. It is important that NO concentrates up to 25-fold in lipid membranes and LDL compartments due to the high lipid partition coefficient, charge neutrality, and small molecular radius [126,127]. Because of this, the value of 02 /N0 ratio should be very small, and the antioxidant effect of NO must exceed the prooxidant effect of peroxynitrite. As the rate constants for the recombination reaction of NO with peroxyl radicals are close to diffusion limit (about 109 1 mol 1 s 1 [125]), NO will inhibit both Reactions (7) and (8) and by that spare a-tocopherol in LDL oxidation. 

Van der Waals further finds a relation between the temperature coefficient of surface tension and the molecular surface energy which is in substantial agreement with the Eotvos-Ramsay-Shields formula (see Chapter V.). He also arrives at a value for the thickness of the transition layer which is of the order of magnitude of the molecular radius, as deduced from the kinetic theory, and accounts qualitatively for the optical effects described on p. 33. Finally, it should be mentioned that Van der Waals theory leads directly to the conclusion that the existence of a transition layer at the boundary of two media reduces the surface tension, i.e., makes it smaller than it would be if the transition were abrupt—a result obtained independently by Lord Rayleigh. 

In contrast to a gas, the short-range order in the fluid demands that significant structural relaxation must have occurred when the molecule has diffused a distance equivalent to the distance to the surrounding shell of nearest neighbours. This is of the order of a molecular radius. Since the diffusive process is described by the square of the mean distance moved by a molecule in a time t then... 

Therefore, the potential energy of the molecule shows a minimum at a distance of approximately one molecular radius of the adsorbate. The energy minimum is of the order of 0.01-0.1 eV (1-10 kj mol ) [13]. Due to the weak interaction, a significant physisorption is observed only at low temperatures (<273 K). 

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