Rigid Solute Molecules

Several theories based on elongated rigid axisymmetric models for a macromolecule predict frequency dependence of the dynamic shear moduli and intrinsic viscosities which can be expressed in the following form  

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In the first section we have discussed a general methodology for the theoretical description of rotational dynamics of rigid solute molecules in complex solvents. Many-body Fokker-Planck-Kramers equations (MFPKE), including collective solvent degrees of freedom (either rotational ones, i.e., rigid bodies, or translational ones, i.e., vector fields), and their conjugate momenta, have been described as convenient tools to reproduce (or simulate) the complexity of an actual liquid system. 

Typical singlet lifetimes are measured in nanoseconds while triplet lifetimes of organic molecules in rigid solutions are usually measured in milliseconds or even seconds. In liquid media where drfifiision is rapid the triplet states are usually quenched, often by tire nearly iibiqitoiis molecular oxygen. Because of that, phosphorescence is seldom observed in liquid solutions. In the spectroscopy of molecules the tenn fluorescence is now usually used to refer to emission from an excited singlet state and phosphorescence to emission from a triplet state, regardless of the actual lifetimes. 

With this terminology in mind, we can restate the objective of this section as the interpretation of the intrinsic viscosities of solutions of rigid molecules. If the solute molecules are known to be spherical, comparison of Eqs. (9.10) and (9.14) shows that the intrinsic viscosity for such systems is given by... 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

In one of their solutions to the problem, Corey and his coworkers solved the first problem by starting with a preconstructed cyclopentane the stereochemistry was steered by deriving the oxygen atoms from a rigid bicyclic molecule. Alkylation of... 

Procedures are now available that allow for the presence of several solvent molecules around a solute molecule. This approach takes into account the effect of molecular interactions with the solvent on properties such as the enthalpy of formation and the shape adopted by a non-rigid molecule, such as a protein or a region of DNA. These studies are important for investigating the structures and reactions of biological molecules in their natural environment. 

Existing SEC retention theories have been independently developed for each of the molecular-shape models shown in Figure 1. The deep hollow cyclin-drical pore in the figure (A, B, and C) illustrates the SEC exclusion effect on three types of solute molecules, hard-sphere, rigid-rod, and random-coil, respectively. The individual theories and their bases of commonality are now reviewed briefly. 

One of the first explanations for the afterglow of organic compounds in rigid solutions after exposure to UV light was offered by Perrin.<12) Perrin postulated that the excited molecules could undergo a transition to a metastable state of lower energy. Emission from this state was thought to be... 

The inhomogeneous broadening effect will be apparent in practically all cases, and the character of this broadening may be both stationary (in rigid solutions or when time of relaxation xr is less than lifetime of fluorescence x, or xr>t) and dynamic in nature. Inhomogeneous broadening affects all spectral characteristics of organic molecules in solutions. 

Whilst the electric moment so calculated is in reality not an absolute value since it is actually only the alteration in electric moment of the surface produced by substituting the adsorbed solute molecules for solvent molecules, yet it is clear that the ionisable substances possess large values which vary within wide limits as the surface concentration is altered. We must conclude that since the apparent molecular electric moment varies with the concentration that Helmholtz s conception of a rigid double layer must be replaced by some species of boundary layer which varies in structure with the surface concentration. Gouy loo. cit) was the first to consider in detail the mechanism by which the ions are kept away from the charged surface. He put forward the view that the finite value of S is due to their thermal agitation. On this M... 

Wada 109, 110) pioneered studies of polypeptide conformation by the dielectric method. He found 110) a linear dependence of (ft2)1 2 on Mw for a series of PBLG samples (ranging from 7 x 104 to 18 x 104 in Mw) in EDC at 25° C and obtained 3.5 D for gh, where D stands for debye units. He computed (ft2) by the use of an approximate equation derived by himself 109) for rigid-rod molecules, which for very dilute solutions may be written... 

If we turn from phenomenological thermodynamics to statistical thermodynamics, then we can interpret the second virial coefficient in terms of molecular parameters via a model. We pursue this approach for two different models, namely, the excluded-volume model for solute molecules with rigid structures and the Flory-Huggins model for polymer chains, in Section 3.4. 

The essence of this model for the second virial coefficient is that an excluded volume is defined by surface contact between solute molecules. As such, the model is more appropriate for molecules with a rigid structure than for those with more diffuse structures. For example, protein molecules are held in compact forms by disulfide bridges and intramolecular hydrogen bonds by contrast, a randomly coiled molecule has a constantly changing outline and imbibes solvent into the domain of the coil to give it a very soft surface. The present model, therefore, is much more appropriate for the globular protein than for the latter. Example 3.3 applies the excluded-volume interpretation of B to an aqueous protein solution. 

The experimental data show that for photo-colourability in either the crystal or rigid solution there is required an ortho- hydroxyl group which is hydrogen bonded to the nitrogen of the same molecule. There is no direct evidence as to the quinoid nature of the coloured form— we have only the suggestive analogy with the azonaphthols and the relative behaviour of the anils from 2 3- and l 2-hydroxynaphth-aldehydes. 

Solution of the wave equation for rotation of a rigid diatomic molecule leads to the following expression for rotational energy ... 

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