Theoretical interpretation polymer

EDXRF vs. WDXRF, sequential vs. simultaneous XRF), geometry (TXRF, SEXAFS, glancing angle), theoretical interpretations (EXAFS, XANES), microanalysis ( xXRF, EPMA), hyphenation or on-line analysis. There is sufficient scope for polymer/additive analysis by means of XRS tools. 

Since Meyer ) introduced the concept of kinetic molecular chain into the physics of polymers in 1932, remarkable progress has been made in the molecular-theoretical interpretation of elastic behavior of rubber vulcanizates and polymer solids in general2- ), and one can appreciate the present status of knowledge on this subject by a number of review articles and reference books. On the other hand, the phenomeno-logic approach to rubber elasticity has not aroused much interest in the field of polymer research. This is understandable because polymer scientists are primarily concerned with affairs of the molecular world. 

Originally, Fox and Flory (121) found that the zero shear viscosity of polymer melts increases with the 3.4-th power of the molecular weight. Bueche (122) has shown that this relationship holds only above a certain critical molecular weight Mc which depends on the structure of the polymer chain. Below Mc the zero shear viscosity is found to depend on a significantly lower power of molecular weight. A theoretical interpretation of these facts has been given by the latter author on the basis of the free-draining model (Section 3.4.1.). 

Thus the theories on the conformation of the macromolecules in solution, which have already been well developed, can be proved experimentally. However, in order to attain further progresses in this fields it is necessary to acquire a deeper theoretical knowledge of the relationships between chemical structure and rotatory power and to investigate other series of homologous polymers having simple monomer unit structure in order to facilitate the theoretical interpretation of the experimental results. 

The very strong influence of molecular mass on the viscosity of polymer melts required some mechanism of molecular interaction for a theoretical interpretation. Bueche (1952) could derive Eq. (15.28) with certain assumptions on the influence of chain entanglements on polymer flow. Later, numerous other interpretations have been offered which will not be discussed here. 

This test may be useful for a rapid comparison of a number of polymers. A theoretical interpretation of the results is almost impossible, however, because temperature and stress history of the polymer are completely undefined. 

Order-disorder, or rod-to-coil , transitions in dilute solution have been reported for polydiacetylenes (2, 5-11), polysilylenes (12-15), and alkyl-substituted polythiophenes (16). The interpretation of the experimental observations has been the subject of considerable controversy with respect to whether the observations represent a single-polymer-molecule phenomenon or a many-chain aggregation or precipitation process (3-16). Our own experimental evidence (12, 13) and that of others (5-8, 10, 16) weigh heavily in favor of the single-chain interpretation. In our theoretical interpretation, we will assume that the order-disorder transitions observed in dilute pol-ysilylene solutions represent equilibrium, single-chain phenomena. 

Huh, C., Pope, G.A., 2008. Residual oil saturation from polymer floods Laboratory measurements and theoretical interpretation, paper SPE 113417 presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, 19—23 April. 

The morphological characterization of structured latexes is a fundamental aspect of their study, because (1) it provides very useful information on the nature of the mechanisms that regulate the formation of the particle, and (2) knowledge of the organization of the polymer within the particle is the essential foundation for the theoretical interpretation of the behavior of the resulting latex films (mechanical properties, permeability, etc.). From this perspective, there are a great many techniques that require examination to eliminate artifacts and incorrect conclusions deduced from their use. 

Previous explanations of the impact modification effect and its phase transition like the brittle-to-tough transition have assumed a basically statistical distribution of the dispersed rubber phase in the continuous polymer matrix [139], From there the critical interparticle distance model originated [139b], which is essentially a percolation-type theoretical interpretation. Experimental results like those reported by Bucknall [139a], but also many crack surfaces published in the literature, show that more rubber phase is present in the visible area of the crack surface than would be expected from a statistical distribution, SEM evaluations are consistent with our findings of a non-statistical distribution, but a phase separation of the dispersed material into some kind of layer. 

In a study using C-labeled benzene, it was found fliat at a degree of polymerization of 700, the average polymer molecule contained about 20 benzene units [37], Thus there is evidence of retardation attributable to a degradative chain-transfer process [37, 38]. In addition, there is evidence that actual copolymerization of vinyl acetate and benzene takes place. As a matter of fact, there may be controversy whether the observations discussed here are a result of chain transfer or of copolymerization. The point in question may be rather subtle [39], The facts, regardless of theoretical interpretation, are that aromatic solvents retard the polymerization of vinyl acetate, and the polymer contains substantial quantities of covalently bound solvent. 

Some possible approximations have been considered by Cates [56], who concentrated attention on macromolecular entanglements, which play an important role in the description of the behaviour of block polymers [86-89]. Cates believes that the fact that the concept of polymer fractal neglects the effects of macromolecular entanglements is the main drawback of this theory. Nevertheless, Cates [56] introduced several simplifications that make it possible to ignore these effects for dilute solutions and relatively low molecular masses. However, in the opinion of Cates, even in the case of predominant influence of entanglements, theoretical interpretation of this phenomenon is impossible without preliminary investigation of the properties of the system in terms of Rouse-Zimm dynamics, which can serve as the basis for a more complex theory. It was assumed [56] that the effects of entanglement can be due to the substantially enhanced local friction of macromolecules. 

For the above reasons, theoretical interpretation of the glass transition process of polymers was developed witWn the framework of two directions - kinetic and thermodynamic (the last one simplified it and considered it as an equilibrium process). Simple empirical expressions were developed. 

To sum up, we may say that application to high polymers of proved experimental and theoretical methods used in the region of low molecular substances can be successful only if the greatest possible degree of accuracy is employed in carrying out the experiments and every kind of fundamental relation involved is taken into consideration in the theoretical interpretation. 

D.N. Bennion, Experimental Measurement and Theoretical Interpretation of Membrane Transport of Concentrated Electrolytic Solutions, In E.B. Yeager, B. Schuum, K. Mauritz, K. Abbey, D. Blankenship, and J. Akridge (eds). Proceedings Symposium on Membranes and Ionic and Electronic Conducting Polymers, PV 83-3, The Electrochemical Society Inc. (1983), p. 78. 

While the measurement of osmotic pressure n and the calculation of the second virial coefficient A2 are relatively simple, their theoretical interpretations are rather comphcated. Throughout the past half century, many investigators have tried to set up a model and derive equations for n and A2. Because of the unsymmetrical nature with respect to the sizes of solute (macromolecule) and solvent (small molecule), polymer solutions involve unusually large intermolecular interactions. Furthermore, since n is directly related to pj, any theoretical knowledge learned from the osmotic pressure and the second virial coefficient contributes to the knowledge of the general thermodynamic behavior of polymer solutions. For this reason. Chapter 4 and 9 are closely related in macromolecular chemistry. 

In Section 6.3.3 some of the experimental evidence for and theoretical interpretation of a depleted layer effect close to the pore wall was reviewed. This is discussed here in the context of a narrow cylindrical capillary in which the hydrodynamic problem can be formulated. Figure 6.7 shows that there is a polymer concentration profile, C(r), across the capillary and that the depleted layer extends over a distance S from the wall. Some notation is introduced in Figure 6.6 r is the radial co-ordinate, i 2 is the tube radius, is the radius of the inner bulk region, and the depleted layer thickness, d, is given by d = R2 — Ri). In order to perform calculations on the hydrodynamic effects which are caused by this profile, it is necessary to have a single analytic form for either the concentration profile, C(r), or the resulting viscosity profile, rj r), directly. The latter quantity must be derived in the calculations if it is not directly available. In the absence of a depleted layer. 

Heat capacities form an important link between macroscopic laop-erties of materials and their microscqpic origin. Since the method of heat capacity measurements is well establidied and the theoretical interpretation has achieved a high degree of success, valuable information should result from the study of heat capacities of linear h h polymers and the interpretation of the data. 

The theoretical interpretation, via Eq. (6.19) or (6.20), that logG versus logG" plots are independent of temperature for flexible homopolymers is used in Chapter 8 to determine a critical temperature at which phase transition from an anisotropic phase to the homogeneous phase takes place in block copolymers, and in Chapter 9 to determine a critical temperature at which phase transition from an anisotropic phase to the homogeneous phase takes place in thermotropic liquid-crystalline polymers. Friedrich et al. (1996) and Neumann et al. (1998) have referred to the log G versus log G" plot as the Han plot. ... 

THEORETICAL INTERPRETATION OF VALENCE XPS SPECTRA OF STEREOREGULAR ORGANIC POLYMERS... 

The theoretical interpretation will be based on band theory results where electronic states "extend" over the length of the polymer molecule. In such a case the removal of an electron should have little effect on the energy level structure and Koopmans theorem should be a valid approximation to account for the photoemission process involved in step 1. More precisely step 1 of the photoionization corresponds to an excitation between two states with the same k-point in the reduced Brillouin zone of respective energies i(k) and f(k). In a photoelectric experiment the number of photoelectrons with a particular energy is measured, this is represented by the energy distribution of the joint density of states which is expected to contain much of the same physical information as experiment does. 

---