Effective molecular radius

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. 

Transferrin, fhe iron-transporting protein, occurs in urine at concentrations that are about 15 times lower fhan that of albumin. The protein has a shghtly larger effective molecular radius (around 4.0 run) than albumin (3.6 run). Its detection in fhe urine allows a more sensitive indicator of early glomerular involvement in some nephropathies such as cadmium nephropathy. A strong association has been found between the presence of albumin and transferrin in fhe urine of patients with fhe nephrotic syndrome. In these patients, increased transferrin synthesis is insufficient to compensate for urinary losses and plasma levels are reduced [94]. 

From measurements of diffusion coefficients, the effective molecular radius of phosgene in the gas phase was calculated to be 0.242 nm [1129]. 

Assuming that phosgene packs as a "cubic molecule" with cube sides equal to its diameter, then (from density data) its effective molecular radius in the liquid state is 0.245 nm [1129]. 

Figure 1. Enlargement of starch-filled pore showing space requirements for enzyme and product diffusion. Open and solid circles represent glucose and pesticide molecules, respectively. Dotted circles indicate the effective molecular radius due to molecular rotation, a pesticide is adsorbed to the starch, b pesticide is covalently bonded to the starch.

The molecular attraction parameter, a = 111.07 atm L mol and the effective molecular radius, r = 4.23, were calculated from E and the molar volume [41]. 

Ruiz et aP have investigated the linear polarizability, a, of icosahedral fiillerenes in the range C60-C720 using the PPP ( r-electron) method. They find that the calculated polarizability is given by the formula, a = 0.75R] in terms of the effective molecular radius. It is argued that the fiillerenes should exhibit the maximum possible polarizability for carbon shells. 

For an isotropic distribution of angular momentum, the rotational diffusion constant can be related to the effective molecular radius a and a microscopic viscosity 7] as ... 

In the most frequent case, the acceptor component in the nanofibers interacts with a distribution of donor chromophores. The distance between individual donors and the low-energy gap acceptor unit can be limited not only by the effective molecular radius, as in bulk samples, but also by the nanofiber radius (a condition especially relevant for very thin, 10 nm fibers). We will come back to this issue in the next pages. In general, the energy transfer dynamics can be described by means of rate equations for the populations, Hdo tiAc) of D (A) in the excited state, also taking into account that a fraction of molecules of the donor polymer can be directly excited (i.e., by direct absorption of incident excitation photons) ... 

Many substances with fairly small molecules have liquid-state diffusion coefficients near 1 x 10 m s . What effective molecular radius corresponds to this value if water is the solvent and if the temperature is... 

In a good solvent, polymer coils expand, increasing the effective molecular radius, which results in a lowering of the diffusion coefficient. Coil expansion is usually expressed as follows [see Eq. (8.6.14)] ... 

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