Polymer solutions macromolecular models

Current investigations on dilute polymer solutions are still largely limited to the class of macromolecular solutes that assume randomly coiled conformation. It is therefore natural that there should be a growing interest in expanding the scope of polymer solution study to macromolecular solutes whose conformations cannot be described by the conventional random-coil model. The present paper aims at describing one of the recent studies made under such impetus. It deals with a nonrandom-coil conformation usually referred to as interrupted helix or partial helix. This conformation is a hybrid of random-coil and helix precisely, a linear alternation of randomly coiled and helical sequences of repeat units. It has become available for experimental studies through the discovery of helix-coil transition phenomena in synthetic polypeptides. 

Single-molecule theories originated in early polymer physics work (45) to describe the flow behavior of very dilute polymer solutions, which are free of interpolymer chain effects. Most commonly, the macromolecular chain, capable of viscoelastic response, is represented by the well-known bead-spring model or cartoon, shown in Fig. 3.8(a), which consists of a series of small spheres connected to elastic springs. 

Here we report preliminary results on the multiple fluorescence emission of 1 and 2. From structure-property relationships, solvent effect and temperature effect studies, we are able to show that the multiple emission is from the emission of free squaraine in solution, the emission of the solute-solvent complex and the emission of a twisted relaxed excited state. Further solvent effect study using 2 as a model shows that squaraine forms strong solute-solvent complexes with alcoholic solvent molecules. Analogous complex-ation process is also detected between 1 and the hydroxy groups on the macromolecular chains of poly(vinyl formal). The Important role of this complexation process on the stabilization mechanism of particles of 1 in polymer solution is discussed. 

Hence, the results stated above demonstrated that the cluster model of polymers amorphous state stmcture and fractal analysis allowed quantitative prediction of mechanical properties for pol5miers film samples, prepared from different solvents. Let us note, that the properties prediction over the entire length of the diagram a- was performed within the framework of one approach and with precision, sufficient for practical applications. This approach is based on strict physical substantiation of the analytical intercommunication between structures of a macromolecular coil in solution and pol5miers condensed state [201]. 

The existence of dilute solutions of macromolecules was denied by many experts until the macromolecular hypothesis was largely accepted in the time period from 1930 to 1940. The dilute-solution state is still the basis for characterizing individual macromolecules and the interactions of pairs of macromolecules and the solvent. The structural, thermodynamic, and hydro-dynamic properties of polymer solutions are explained in terms of the random-coil model developed by Kuhn, Debye, Flory, Kirkwood, Yamakawa, and deGennes. While this subject alone could easily be the basis for a one-semester course, the topics are developed so that the material could be presented as part of a complete development of the subject. 

Theoretical attempts to relate dimensions of polymers to chemical structure were pioneered by Flory (2). Statistical macromolecular size in solution can be modeled from first principles by considering the number and length of bonds along with valence bond angles and conformational restrictions. Excluded volume, segmental interactions, specific intramolecular interactions, and chain solvation contribute to dimensions. 

The systems consisting of a macromolecular component and others composed by low molecular weight molecules are of peculiar theoretical and practical importance. The diluted solutions are especially investigated, since the description of different properties of macromolecules could be performed only on this type of models. In diluted solutions the interactions between the macromolecules are practically cancelled. In this way, the determination of the structural particularities of polymer chains (shape, dimensions, and molecular weight) as well as of thermodynamic characteristics of polymer solutions became possible. 

A recent paper describes a mathematical model for the chlorination of polyethylene in a bubble column reactor, the model was used to optimize product quality in the continuous chlorination of polyethylene. Another theoretical treatment deals with the change in polymer reactivity during the course of a macromolecular reactions in solution or in the melt. The reactivity of a transforming unit in the polymer depends on its microenvironment, including nearest neighbours on the same chain and on other chains, as well as small molecules in the reacting system. The equations derived describe the kinetic curve, the distribution of units, and the compositional heterogeneity of the products. 

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. 

As a general comment on the recent polymer integral equation work, we note that applications to date have focused primarily on the structure (intra- and intermolecular) and equation of state (based on a virial or free energy route) of the simple hard core, tangent jointed chain model of polymer solutions and melts. How tractable and generalizable the various approaches are for treating semiflexible and/or atomistic models of macromolecular fluids is unclear for most theories. Little, or no, work has... 

The nature of polymer motion in semidilute and concentrated solutions remains a major question of macromolecular science. Extant models describe polymer dynamics very differently 3-11). Many experimental methods have been used to study polymer dynamics (12). One meAod is probe diffusion, in which inferences about polymer dynamics are made by observing the motions of dilute mesoscopic probe particles diffusing in the polymer solution of interest. Probe diffusion can be observed by several experimental techniques, for example, quasi-elastic light scattering spectroscopy (QELSS), fluorescence recovery after photobleaching (FRAP), and forced Rayleigh scattering (FRS). 

Statistical thermodynamics can be used to calculate both the enthalpic and the entropic contributions to the free energy of mixing by means of statistical calculations. Attempts were first made to apply a theory appropriate to simple regular solutions, the Hildebrand model, to the case of macromolecular solutions. This model does not adequately account for the specific behavior of polymer solutions primarily because the entropy of mixing in a polymer solution is strongly affected by the connectivity of the polymer—that is, by the existence of covalent bonds between the repetitive units. 

Two macromolecular computational problems are considered (i) the atomistic modeling of bulk condensed polymer phases and their inherent non-vectorizability, and (ii) the determination of the partition coefficient of polymer chains between bulk solution and cylindrical pores. In connection with the atomistic modeling problem, an algorithm is introduced and discussed (Modified Superbox Algorithm) for the efficient determination of significantly interacting atom pairs in systems with spatially periodic boundaries of the shape of a general parallelepiped (triclinic systems). 

The initial objective of this paper is to identify, within the context of macromolecular solution modeling, the typical approximations, explicit and implicit, and to discuss the possible impHcations of such approximations. Secondly, we hope to demonstrate that modeling of carbohydrate high polymer solu-... 

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