Rigid molecules spheres model

Rigid, unsolvated spheres. Stokes law, Eq. (9.5), provides a relationship between f and the radius of the particle. Since this structure is a reasonable model for some protein molecules, experimental D values can be interpreted, via f, to yield values of R for such systems. Note that this application can also yield a value for M, since M = N pj [(4/3)ttR ], where pj is the density of the unsolvated material. 

IB. Hard Sphere Model. Here the molecule is assumed to be the equivalent of a billiard ball. That is, the molecule is presented as a rigid sphere of diameter or, mass m (the molecular weight), and the capability... 

We consider the rigid body system consisting of one solute molecule with an arbitrary shape and solvent molecules with a spherical shape. The solute molecule is modeled as fused hard spheres with different radii and the solvent molecules ate modeled as hard spheres with the same radius. This represents aqueous soludon of organic solute at infinite diludon. 

Adopting the molecular billiard ball model considering molecules that are smooth and symmetric rigid elastic spheres not surrounded by fields of force, the molecules affect each other motion only at contact. 

In view of the failure of the rigid sphere model to yield the correct isochoric temperature coefficient of the viscosity, the investigation of other less approximate models of the liquid state becomes desirable. In particular, a study making use of the Lennard-Jones and Devonshire cell theory of liquids28 would be of interest because it makes use of a realistic intermolecular potential function while retaining the essential simplicity of a single particle theory. The main task is to calculate the probability density of the molecule within its cell as perturbed by the steady-state transport process. 

A rigorous treatment of the rigid sphere model was presented by Mason and McDaniel " here, we give an abbreviated version. According to this model, the collision between an ion and a gas molecule is treated as that of rigid spheres in which the ion is eqnaUy likely to be scattered in any direction (in the center-of-mass coordinate system). Mason and McDaniel" described the mean ion energy (14 mv ) in Equation 10.12 ... 

In the rigid sphere model, the sum of the radii of the ion and the neutral molecule d will increase slightly as the chain length and ion mass in the homologous series increase. In the polarization limit model, the ion size is totally neglected, whereas in the hard-core potential model, (the minimum in the interaction potential) depends on the ion mass, as shown in Equation 10.22 ... 

In addition to an array of experimental methods, we also consider a more diverse assortment of polymeric systems than has been true in other chapters. Besides synthetic polymer solutions, we also consider aqueous protein solutions. The former polymers are well represented by the random coil model the latter are approximated by rigid ellipsoids or spheres. For random coils changes in the goodness of the solvent affects coil dimensions. For aqueous proteins the solvent-solute interaction results in various degrees of hydration, which also changes the size of the molecules. Hence the methods we discuss are all potential sources of information about these interactions between polymers and their solvent environments. 

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