Theoretical models for polymer

In the first part of this article the review of various theoretical models for polymer chains is given. The models of freely jointed chains, freely rotating chains (including wormlike chains), and chains with fixed bond angles and independent rotational potentials and with interdependent potentials, including rotatimial isomeric state approximation, are presented. 

DiolOCtriC Thoory. The piezoelectricity in amorphous polymers differs from that in semicrystalline polymers and inorganic crystals in that the polarization is not in a state of thermal equilibrium, but rather a quasi-stable state because of the freezing-in of molecular dipoles. The result is a piezoelectric-hke effect. A theoretical model for polymers that have frozen-in dipolar orientation was presented to explain piezoelectricity and p5Toelectricity in amorphous polymers such as poly(vinyl chloride) (39). 

Both theoretical and experimental evidence suggest that the precise nature of the charge carriers in conjugated polymer systems varies from material to material, and it is still a subject of debate in many cases. A discussion of the various theoretical models for the electronic structure of conjugated polymers is given below, using polyacetylene and poly(paraphenylene) as examples. More detailed information on these materials and the applicability of these theoretical models is given in subsequent sections. 

A basic theoretical model for flexible polymers is the Gaussian chain which assumes N ideal beads with intramolecular distance between them following a Gaussian distribution, so that the mean quadratic distance between two beads separated by n-1 ideal and not correlated bonds is given by [ 15,20]... 

Despite the lack of theoretical models for interfacial recombination processes in excitonic solar cells, it is obvious empirically that those cells which function efficiently must have a very slow rate of recombination. In DSSCs, this can be explained simply by the slow electron self-exchange rate of the I /I2 redox couple and the absence of field-driven recombination. However, in the case of solid-state, high-surface-area OPV cells, such as the conducting polymer/C60-derivative cells [36,39], the slow rate of interfacial recombination is an important problem that is not yet understood. 

Theoretical Model for Determining Monomer-Polymer Reaction Stoichiometry from Equilibrium Gel Partition... 

Permeability measurements for polymer blends prepared by mixing different latices have been reported by Peterson (14). Interpreting transport data for such heterogeneous systems as polymer blends is extremely difficult, however (3, 9,15). The main purpose of the present investigation is, therefore, to study the applicability of gas permeation measurements to characterize polymer blends and not to evaluate the different theoretical models for the permeation process in heterogeneous polymer systems. 

Z. Tadmor, Fundamentals of Plasticating Extrusion. I. A Theoretical Model for Melting, Polym. Eng. Sci., 6, 185-190 (1966). First presented at the Society of Plastics Engineers Annual Technical Conference, Montreal Canada, April 1966. 

C. E. Wyman, Theoretical Model for Intermeshing Twin Screw Extruders Axial Velocity Prohle in Shallow Channels, Polym. Eng. Sci., 15, 606-611 (1975). 

In order to understand the role played by surface-anchored chains in adhesion and friction, it is essential to understand under which conditions a surface layer, when in contact with a melt, is penetrated by free chains. The question has been addressed theoretically mostly for polymer brushes, and more recently for Guiselin s pseudo-brushes. We want to review here some of these analysis, and compare the predictions of the models with the available experimental data. 

One cannot, and should not, separate the computational studies from theoretical solutions to problems. Some aspects of the theoretical models for single chains are therefore discussed briefly. After all, the major goal of polymer simulations is to assist in the reliable prediction of experiment and, at the same time, the quantitative molecular understanding of the structure of matter. 

Cohen DS. Theoretical models for diffusion in glassy polymers. J. Polym. Set B Polym. Phys. 1983 21 2057-2065. 

Confined Complex Fluids. - Because of their important technological relevance, the study of alkanes and polymers under extreme confinement continues to gain popularity in the simulation community. The difficulty in making experimental measurements for nano-confined systems, and the lack of confirmed theoretical models for such systems, makes molecular simulation the ideal tool to explore thermodynamics, structure and transport at such scales. 

A theoretical treatment of aqueous two-phase extraction at the isoelectric point is presented. We extend the constant pressure solution theory of Hill to the prediction of the chemical potential of a species in a system containing soivent, two polymers and protein. The theory leads to an osmotic virial-type expansion and gives a fundamentai interpretation of the osmotic viriai coefficients in terms of forces between species. The expansion is identical to the Edmunds-Ogston-type expression oniy when certain assumptions are made — one of which is that the solvent is non-interacting. The coefficients are calculated using simple excluded volume models for polymer-protein interactions and are then inserted into the expansion to predict isoelectric partition coefficients. The results are compared with trends observed experimentally for protein partition coefficients as functions of protein and polymer molecular weights. 

To close this paper, we believe that both the theoretical and experimental aspects of excited-state relaxation in aromatic polymers will continue to be the subject of lively debate in the near future. Thus, the analyses of non-equilibrium transport based upon asymmetric energy-space master equations (43., 53) as well as theoretical models for a description of EET and rotational sampling are challenging many-partlole problems in polymer photo-physios. From an experimental standpoint of view, the time resolution of fluorescence system-configurations requires further Improvement in order to test these concepts. Moreover, site-selective pulse-and-probe techniques should help to reveal transient excited-state distributions, energy relaxation and trapping on sub-ps time scales in forthcoming measurements. 

Two theoretical models for polysaccharides in aqueous solution come from polymer physics ... 

Theoretical Models for Sds-sirm. Random chain sdssion characterized by a yield of G(s) increases the number of polymer chains in a system while crosslinking... 

The reason why the random flight model has proved so popular theoretically stems from its simplicity, which offers hope for the development of analytic solutions. The problem can usually be cast in the form of a diffusionlike or a Schrodinger-wave-equation-like differential equation, the solutions of which are reasonably well explored. A tendency has developed in recent times to apply extremely sophisticated mathematical procedures to what are really very primitive models for polymer chains (see, e.g. Levine et al., 1978). Whether the ends merit the means in such instances cannot yet be assessed objectively. A strategy that might be more productive in terms of the development of a practical theory for steric stabilization is to aim for a simpler mathematical description of more complex models of polymer chains. It should also be borne in mind in developing ab initio theories that a simple model that may well suffice in polymer solution thermodynamics may be quite inadequate for the simulation of the conformational properties of polymers. Polymer solution thermodynamics seem to be relatively insensitive to molecular architecture per se whereas the conformation of a polymer chain is extremely sensitive to it. 

Reinforcement factor e=(E/E2)"1> where E and E2 are the moduli of blend and polymer matrix, respectively, as a function of volume fraction of the reinforcing material (v) is proposed for treatment of experimental data, as well as for comparison of different theoretical models for the elastic modulus of polymer blends. 

The most important theoretical models for attempting to accoimt for liquid-crystal alignment are the lattice model, introduced by Flory in 1956, and the mean-field model introduced about 1960 by Maier and Saupe. Of these, the former has proved to be more readily applicable to polymers. It is based on the rather obvious idea that, as the number of rigid impenetrable rods in a given volume is increased, they must eventually become aligned approximately parallel to each other, at least in local regions, and it attempts to predict the concentration at which this will tend to happen. In this model there is no specific interaction between the rods except for the short-range repulsive force that corresponds to their mutual impenetrability. 

As already mentioned, SANS on partially deuterated networks allows a direct measurement of polymer chain deformation (stretching or swelling). This makes SANS a unique tool for assessing the validity of theoretical models of polymer... 

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