Chain-molecule solutions

Polymer solutions figure in a vast array of practical materials and processes in the modern world. Ideas about polymers are also relevant to understanding solutions of DNA, proteins, polysaccharides, and other solutions of biological interest. Because of the size and complexity of the chain molecule solutes, polymer solutions present challenging problems in solution theory, and a great deal of work has been directed toward a theoretical understanding of these solutions over the last century. 

The chain molecule solution will be characterized by a set of rotational isomeric states. After the initial thermalization, this set will still be in a nonequilibrium state due to the overall shear deformation. For the internal torsional angle distribution to relax to equilibrium, it is necessary for the solution liquid structure to relax and the solvent molecule distribution to reach equilibrium. In a concentrated polymer solution, these processes are highly coupled. Rotational isomeric state changes depend on both internal potentials and the local viscosity and are often in the nanosecond range, well above the glass transition for the solution. Total stress relaxation cannot occur any faster than the chains can change their local rotational isomeric states. 

Fig. 2. A representation of the cellulose chain ia solution, projected against three two-dimensional surfaces. The circles represent the oxygen atoms that link the iadividual glucose residues, and the lines take the place of the sugar residues. This result of a modeling study (39) iadicated a molecule somewhat more...

In Sec. 3 our presentation is focused on the most important results obtained by different authors in the framework of the rephca Ornstein-Zernike (ROZ) integral equations and by simulations of simple fluids in microporous matrices. For illustrative purposes, we discuss some original results obtained recently in our laboratory. Those allow us to show the application of the ROZ equations to the structure and thermodynamics of fluids adsorbed in disordered porous media. In particular, we present a solution of the ROZ equations for a hard sphere mixture that is highly asymmetric by size, adsorbed in a matrix of hard spheres. This example is relevant in describing the structure of colloidal dispersions in a disordered microporous medium. On the other hand, we present some of the results for the adsorption of a hard sphere fluid in a disordered medium of spherical permeable membranes. The theory developed for the description of this model agrees well with computer simulation data. Finally, in this section we demonstrate the applications of the ROZ theory and present simulation data for adsorption of a hard sphere fluid in a matrix of short chain molecules. This example serves to show the relevance of the theory of Wertheim to chemical association for a set of problems focused on adsorption of fluids and mixtures in disordered microporous matrices prepared by polymerization of species. 

The changes in the average chain length of a solution of semi-flexible selfassembling chains confined between two hard repulsive walls as the width of the sht T> is varied, have been studied [61] using two different Monte Carlo models for fast equihbration of the system, that of a shthering snake and of the independent monomer states. A polydisperse system of chain molecules in conditions of equilibrium polymerization, confined in a gap which is either closed (with fixed total density) or open and in contact with an external reservoir, has been considered. 

J. A. Marques, K. A. Dill. Solute partitioning into chain molecule interphases monolayers, bilayer membranes and micelles. J Chem Phys 55 434—444, 1986. 

Free energy of solution, containing chain molecules of a definite length (before the beginning of degradation), can be written as follows ... 

Solvent disturbs chain deflection by interacting with it. At first, solvent molecules must be moved at chain deflection. In this case it may sufficiently decrease the distance between interacting atoms, which are closely disposed and valently disconnected. The model of a homogenous chain in solution is described [12]. The chain in the solvent possesses a higher observable local rigid-... 

Hence, the main aim of the technological process in obtaining fibres from flexible-chain polymers is to extend flexible-chain molecules and to fix their oriented state by subsequent crystallization. The filaments obtained by this method exhibit a fibrillar structure and high tenacity, because the structure of the filament is similar to that of fibres prepared from rigid-chain polymers (for a detailed thermodynamic treatment of orientation processes in polymer solutions and the thermokinetic analysis of jet-fibre transition in longitudinal solution flow see monograph3. ... 

The influence of the a-bond isomerism is in agreement with the slow exchange spectra of 2,3-dimethylbutane and 1,2-dimethycylohexane in solution 16,17). Taking into account the different isomeric states of the bonds in a- and P-position on both sides of the observed carbons the slow exchange spectra of CH2-chain molecules have to be explained by conformational variations in chain segments of five carbon atoms. 

Huggins M.L. The Viscosity of Dilute Solutions of Long-Chain Molecules. IV. Dependence on Concentration. J. Am. Chem. Soc., 64,11 (1942) 2716-2718. 

Albersheim P., Neukom H. Deuel H. (1960) Splitting of pectin chain molecules in neutral solutions. Archives of Biochemistry and Biophysics 90, 46-51. 

Diffusion and sedimentation measurements on dilute solutions of flexible chain molecules could be used to determine the molecular extension or the expansion factor a. However, the same information may be obtained with greater precision and with far less labor from viscosity measurements alone. For anisometric particles such as are common among proteins, on the other hand, sedimentation velocity measurements used in conjunction with the intrinsic viscosity may yield important information on the effective particle size and shape. ... 

When a compound that can form several modifications crystallizes, first a modification may form that is thermodynamically unstable under the given conditions afterwards it converts to the more stable form (Ostwald step rule). Selenium is an example when elemental selenium forms by a chemical reaction in solution, it precipitates in a red modification that consists of Se8 molecules this then converts slowly into the stable, gray form that consists of polymeric chain molecules. Potassium nitrate is another example at room temperature J3-KN03 is stable, but above 128 °C a-KNOs is stable. From an aqueous solution at room temperature a-KN03 crystallizes first, then, after a short while or when triggered by the slightest mechanical stress, it transforms to )3-KN03. 

One of the most remarkable features of polymer crystallization is that such chain molecules can form lamellar crystals that contain heavily folded polymer chains. In experiments, the structural analysis of these lamellar crystals became possible when polyethylene single crystals were first prepared from a solution [100-102]. It was found that the orientation of the polymer chains... 

Real polymer processes involved in polymer crystallization are those at the crystal-melt or crystal-solution interfaces and inevitably 3D in nature. Before attacking our final target, the simulation of polymer crystallization from the melt, we studied crystallization of a single chain in a vacuum adsorption and folding at the growth front. The polymer molecule we considered was the same as described above a completely flexible chain composed of 500 or 1000 CH2 beads. We consider crystallization in a vacuum or in an extremely poor solvent condition. Here we took the detailed interaction between the chain molecule and the substrate atoms through Eqs. 8-10. 

The adsorption of chain molecules at the solid/solution interface differs in many respects from that of small molecules. Some of these differences are listed below. 

Finally, there is a large body of experimental and theoretical contributions from investigators who are mainly interested in the dynamic and conformational properties of chain molecules. The basic idea is that the cyclisation probability of a chain is related to the mean separation of the chain ends (Morawetz, 1975). Up to date comprehensive review articles are available on the subject (Semiyen, 1976 Winnik, 1977, 1981a Imanishi, 1979). Rates and equilibria of the chemical reactions occurring between functional groups attached to the ends or to the interior of a flexible chain molecule are believed to provide a convenient testing ground for theories of chain conformations and chain dynamics in solution. 

Early interest in the relation between the shape of chain molecules and solvent in ring-closure reactions can be traced in the work of Salomon (1936a). More recently, the problem has been given much attention by Winnik (1977). Though being small (see p. 64), the corresponding effects on the ease of cyclisation are believed to be of considerable importance in probing the shape of hydrocarbon and other flexible chains in solution. 

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