Molecular inhomogeneity

The pronounced dependence of the Kerr constant on molecular weight observed for poly(vinyl chloride) and poly(vinyl bromide) solutions appears to be due to their molecular inhomogeneity. The presence of agpegates in solutions of these two polymers has often been detected experimentally - . ... 

Identification of such eflFects is made difficult, however, by the complexity of a crystallization experiment. Crystallization typically occurs from a molecularly inhomogeneous, aqueous gel, prepared by combination of a silica and an alumina source together with varying amounts of hydroxide ion. Since the product obtained is often nucleation-controlled, variables in an experiment can include not only the silica source (gel, sol, sodium silicate) and the alumina source (sodium aluminate, aluminum sulfate) but also the detailed mixing and crystallizing procedures (temperatures, aging, stirring rate, etc.). 

The development of surface charge at the interface between soil particles and the soil solution is a reflection of inhomogeneities in the molecular environment of the interface, as discussed in Sec. 3.1. These molecular inhomogeneities also influence the thermodynamic properties of both the charged species in the soil particles and those in the soil solution. In particular, the distribution of a charged species between the two bulk phases, regardless of their composition, is determined by the electrochemical potential of that species, jx. The gradient of the electrochemical potential of a species drives its diffusive transfer between phases, and equilibrium with respect to this transfer is described by the equality... 

With monomolecular substances, Q = 1 and (7=0. Molar mass ratios and molecular inhomogeneities can, of course, be defined as the quotients of other averages besides the number and mass averages. 

Figure 8-6. Gaussian distribution for samples of degrees of polymerization < A n > = 200, 600, or 1200 of constant standard deviation a (and consequently, variable molecular inhomogeneity U) or constant molecular inhomogeneity (and variable standard deviation).

The width of the elution curve increases with the width of the distribution. But unimolecular substances do not give a sharp signal an elution curve is also obtained. This is produced by what is known as the axial dispersion. According to the model described above, it signifies a distribution of residence times in the pores. The effect must also be taken into account when calculating molar mass distributions. For this, it is assumed that the total standard deviation atm is composed of the standard deviation associated with molecular inhomogeneity Omoi and the standard deviation resulting from axial dispersion Oad ... 

Chemical thermodynamics and kinetics provide the formalism to describe the observed dependencies of chemical-conformational reactions on the external physical state variables temperature, pressure, electric and magnetic fields. In the present account the theoretical foundations for the analysis of electrical-chemical processes are developed on an elementary level. It should be remarked that in most treatments of electric field effects on chemical processes the theoretical expressions are based on the homogeneous-field approximation of the continuum relationship between the total polarization and the electric field strength (Maxwell field). When, however, conversion factors that account for the molecular (inhomogeneous) nature of real systems are given, they are usually only applicable for nonpolar solvents and thus exclude aqueous solutions. Therefore, in the present study, particular emphasis is placed on expressions which relate experimentally observable system properties (such as optical or electrical quantities) with the applied (measured) electric field, and which include applications to aqueous solutions. 

Thus, the molecular inhomogeneity U and, consequently, the value of Q depend also on the number-average molecular weight. The standard deviation remains as a more sensitive measure of the distribution width than either Q or U, but with one exception, it is not an absolute measure of the width of the distribution (see also Section 8.3.2.1). To be an absolute measure of the width of the molecular-weight distribution, the standard deviation must encompass a fraction of the original material that is independent of the width of the distribution, and this only holds for a Gaussian distribution. 

Polymeric materials are very complex in nature. Their high molecular weights, molecular inhomogeneity and their chemical inertness often present difficulties in their identification which therefore requires special techniques and the use of advanced methods of analysis. The problem of characterisation is further complicated by the market availability ofan extremely wide range of materials and the presence of compounding materials such as plasticizers, stabilizers and fillers (which change the physical properties of the product) and thus a complete identification of polymeric materials may not always be po.ssible. 

As the mol. wt. de ermined by any one of the different methods (p.l76) is always some sort of an average, it docs not convey anything about the spread of the molecular weigiit or molecular inhomogeneity or polydispersity. 

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