Polymer property description, distributions

Kinetic approaches represent realistic and comprehensive description of the mechanism of network formation. Under this approach, reaction rates are proportional to the concentration of unreacted functional groups involved in a specific reaction times an associated proportionality constant (the kinetic rate constant). This method can be applied to the examination of different reactor types. It is based on population balances derived from a reaction scheme. An infinite set of mass balance equations will result, one for each polymer chain length present in the reaction system. This leads to ordinary differential or algebraic equations, depending on the reactor type under consideration. This set of equations must be solved to obtain the desired information on polymer distribution, and thus instantaneous and accumulated chain polymer properties can be calculated. In the introductory paragraphs of Section... 

It is essential for the polymer chemist and analyst to be aware of all possible nonuniformities of polymers in order to interpret the experimental data and understand the properties and behavior of polymers. Two polymer samples may be identical in one or more properties but may differ in others. Although the polymer properties are generally distributed, analysis can provide solely average values. Two polymer samples can be identical in an average property but the property distributions can be different. However, average properties are often used instead of distributions in order to simplify the description of a polymer sample or because the distribution caimot be determined due to the time or instrumental limitations. 

It is generally assumed that the description of polymer properties requires a continuous distribution of relaxation times. Numerous forms of the distribution function have been assumed, often for mathematical simplicity or on the basis of physical intuition. It has been found that a fractional power law distribution of relaxation times of the form t leads to hysteresis absorption with aX = m7il2 (Np), when m < 1 (3). The disadvantage of this model is that attempts to justify this distribution of relaxation times on a molecular basis quantitatively have not been successful. Mathematically, almost any experimental result can be expressed in terms of a distribution of relaxation times, but there may not be any physical significance to the distribution. 

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. 

The molecular weight distribution (MWD) is of vital importance for polymers of all types. It determines the ease of manufacture, the ease of fabrication, and the end-use properties of the polymer. A proper kinetic description of a polymerization requires determination of the molecular weight distribution of the polymer in addition to the usual concepts of conversion and selectivity. 

Descriptions of polymer structures revealed by studies of physical properties focus attention on the distribution of local arrangements present in the molecules, and terms useful in this context are defined in this section. (The terms defined here in relation to complete polymer molecules can also be applied to sequences and to blocks, as in Ref. 2, Definition 3.14.)... 

Most polymerisation reactions occur via a complex reaction scheme. Relatively few reactant species are involved (sometimes only one) and these are usually well-defined. However, the reaction products can be described in a number of ways. The polymer molecules produced in these reactions vary in size in some cases the size distribution can be very wide. In effect, a polymerisation reaction produces a large number of reaction products and reaction selectivity requires special treatment. For some purposes, the polymer molecules can be treated as a combined group which is referred to generally as polymer . However, the physical properties of any given type of polymer depend on its molecular weight distribution. Therefore, it is often necessary to obtain a quantitative description of the product size distribution. This will depend on both the kinetic scheme for the polymerisation reaction and the mixing conditions in the polymerisation reactor. 

Modelling non-isothermal crystallization is the next important step in a quantitative description of reactive processing. This is particularly important, because crystallization determines the properties of the end product. Therefore, the development the spatial distribution of crystallinity, a, and temperature, T, with time throughout the volume of the reactive medium must be calculated. It is also noteworthy that crystallization and polymerization processes may occur simultaneously. This happens when polymerization proceeds at temperatures below the melting point of the newly formed polymer. A typical example of this phenomenon is anionic-activated polymerization of e-caprolactam, which takes place below the melting temperature of polycaproamide. 

Statistical mechanics was originally formulated to describe the properties of systems of identical particles such as atoms or small molecules. However, many materials of industrial and commercial importance do not fit neatly into this framework. For example, the particles in a colloidal suspension are never strictly identical to one another, but have a range of radii (and possibly surface charges, shapes, etc.). This dependence of the particle properties on one or more continuous parameters is known as polydispersity. One can regard a polydisperse fluid as a mixture of an infinite number of distinct particle species. If we label each species according to the value of its polydisperse attribute, a, the state of a polydisperse system entails specification of a density distribution p(a), rather than a finite number of density variables. It is usual to identify two distinct types of polydispersity variable and fixed. Variable polydispersity pertains to systems such as ionic micelles or oil-water emulsions, where the degree of polydispersity (as measured by the form of p(a)) can change under the influence of external factors. A more common situation is fixed polydispersity, appropriate for the description of systems such as colloidal dispersions, liquid crystals, and polymers. Here the form of p(cr) is determined by the synthesis of the fluid. 

A further development should be directed towards the study of the effect of impurities present in the feed monomer and the prediction of polymer quality, through a suitable complication of the kinetic scheme, in order to include the role of chain modifiers. It must be pointed out, however, that while the modifications of the model are relatively simple, a great amount of experimental work is needed to get a satisfactory description of the polymer characteristics, in terms of molecular weight distribution, chain branching and so on, and to correlate these properties to the polymer quality. 

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