The structure of macromolecules in solution

The detailed chemical structure of many small molecules is dominated by intramolecular interactions, and the shape is independent of the state of macroscopic aggregation (gas, liquid, or solid). On the other hand, the shape of a macromolecule is often a fimction of its environment. One of the earliest evidences of this fact was the large difference in the intrinsic viscosity, [tj], of macromolecules in different solvents. The measurement of solution viscosity has played a central role in the development of polymer science. The theory of hydrodynamics was well developed by the end of the 19th century, and Einstein derived the equation for the viscosity of a dilute solution of rigid spheres with volume fraction 9  

The intrinsic viscosity of globular proteins in a suitable buffer solution is independent of molecular weight This conclusion illustrates another important principle of polymer science proper interpretation of experimental data requires a v id theory. 

Studies of soluble homopolymers in thermodynamically good solvents revealed that the intrinsic viscosity increased with molecular weight. Staudinger attempted to summarize these results with the empirical relation  

A more careful examination of the experimental data by Mark led to a more general relationship between the intrinsic viscosity of macromolecules in solution and molecular weight  

The correct explanation of this result by Kuhn is one of the first triumphs of the statistical theory of polymer chains. He was well aware of the developments in structural chemistry that explained the flexibility of molecules in terms of rotation about single bonds. Since polymers are molecules, rota- 

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Computer simulations have proved to be an exciting advance for electrolyte studies small to moderately large solute molecules are now routinely studied. They are also being developed for the study of large molecules such as those of biological importance, and could possibly enable detail at the molecular level to be correlated with details of the structure of macromolecules in solution and their biological function. 

V.N. Tsvetkov, V.E. Eskin and S. Ya. Frenkel, The Structure of Macromolecules in Solution, Nauka Publishers, Moscow, Russia, 1964, [in Russian]. 

Nuclear Overhauser effect spectroscopy (NOESY) is frequently used in liquid-state NMR, and is one of the standard two-dimensional (2D) methods used to interpret and assign the structures of macromolecules in solution. In addition to solution state, NOESY has been also used in polymeric systems and viscoelastic. 

Most synthetic polymers in which the monomer units are connected via single bonds have rather flexible chains. The bond torsion energy is relatively small and the units can rotate around their bonds [14,30,31]. Each molecule can adopt a large number of energetically equivalent conformations and the resulting molecular geometry is that of a statistical coil, approximately described by a Gaussian density distribution. This coil conformation is the characteristic secondary structure of macromolecules in solution and in the melt. It is entropically favoured because of its... 

Wenz, G., M.A.Muller, M.Schmidt and G.Wegner. The Structure of Polydiacetylenes in Solution, Macromolecules, (1984) in press. 

The overall objective of this chapter is to review the fundamental issues involved in the transport of macromolecules in hydrophilic media made of synthetic or naturally occurring uncharged polymers with nanometer-scale pore structure when an electric field is applied. The physical and chemical properties and structural features of hydrophilic polymeric materials will be considered first. Although the emphasis will be on classical polymeric gels, discussion of polymeric solutions and nonclassical gels made of, for example, un-cross-linked macromolecular units such as linear polymers and micelles will also be considered in light of recent interest in these materials for a number of applications... 

Keeping in mind all three DNA structure levels, primary, secondary, and tertiary, it is essential to understand that the lower level will mediate but not fully determine the higher structural level. In other words, the secondary as well as tertiary DNA structures of ODN in solution will be affected by many physical and chemical parameters, such as temperature, pH, salt content, compound concentration, etc. When evaluating complex biochemical systems, additional factors have to be taken into consideration possible interactions of ODN with a variety of other molecules and macromolecules in solution, local concentration effects and compartmentalization, biological half-life, etc. Hence when designing a DIMS ODN compound, its 3-D structure will not be fully predictable. 

The understanding of the macromolecular properties of lignins requires information on number- and weight-average molecular weights (Mn, Mw) and their distributions (MWD). These physico-chemical parameters are very useful in the study of the hydrodynamic behavior of macromolecules in solution, as well as of their conformation and size (1). They also help in the determination of some important structural properties such as functionality, average number of multifunctional monomer units per molecule (2, 3), branching coefficients and crosslink density (4,5). 

Methods used to obtain conformational information and establish secondary, tertiary, and quaternary structures involve electron microscopy, x-ray diffraction, refractive index, nuclear magnetic resonance, infrared radiation, optical rotation, and anisotropy, as well as a variety of rheological procedures and molecular weight measurements. Extrapolation of solid state conformations to likely solution conformations has also helped. The general principles of macromolecules in solution has been reviewed by Morawetz (17), and investigative methods are discussed by Bovey (18). Several workers have recently reexamined the conformations of the backbone chain of xylans (19, 20, 21). Evidence seems to favor a left-handed chain chirality with the chains entwined perhaps in a two fold screw axis. Solution conformations are more disordered than those in crystallites (22). However, even with the disorder-... 

Many of the methods used to extract information related to the structure of macromolecules come from studying the behavior of isolated macromolecules in solution. These techniques are based primarily on the flow behavior in a velocity gradient, the rate of Brownian motion of a particle, or osmotic effects associated with the size of individual molecules. The techniques that have been employed to study size and shape of macromolecules most extensively include viscometry, light scattering, analytical ultracentrifugation, and electron microscopy. 

The most commonly used generic term for a dissolved substance is solute, and this is the term that we will employ in most contexts, for both large and small compounds, that is, for macromolecules and micromolecules. A closely related term, cosolvent, is often used by physical chemists when the issue in question involves a dissolved substance that either stabilizes or destabilizes the structures of macromolecules. For instance, cosolvent is often used in literature on the effects of solutes on protein stability. A more restrictive and specific term that will be employed when we discuss the osmotic relationships of organisms is osmolyte. 

The diffusion of small molecules in polymeric solids has been a subject in which relatively little interest has been shown by the polymer chemist, in contrast to its counterpart, i.e., the diffusion of macromolecules in dilute solutions. However, during the past ten years there has been a great accumulation of important data on this subject, both experimental and theoretical, and it has become apparent that in many cases diffusion in polymers exhibits features which cannot be expected from classical theories and that such departures are related to the molecular structure characteristic of polymeric solids and gels. Also there have been a number of important contributions to the procedures by which diffusion coefficients of given systems can be determined accurately from experiment. It is impossible, and apparently beyond the author s ability, to treat all these recent investigations in the limited space allowed. So, in this article, the author wishes to discuss some selected topics with which he has a relatively greater acquaintance but which he feels are of fundamental importance for understanding the current situation in this field of polymer research. Thus the present paper is a kind of personal note, rather than a balanced review of diverse aspects of recent diffusion studies. 

The solution behavior of polymers has been intensively investigated in the past. Dilute solutions, where polymer-polymer interactions may be excluded, have become the basis for the characterization of the primary structure of macromolecules and their dimensions in solution. Besides this "classical" aspect of macromolecular science, interest has focussed on systems, where - due to strong polymer/polymer interactions - association of polymers causes supermolecular structures in homogeneous thermo-dynamically-stable isotropic and anisotropic solutions or in phase-separated multi-component systems. The association of polymers in solutions gives rise to unconventional properties, yielding new aspects for applications and multiple theoretical aspects. 

Influence of the Chemical Structure of the Potyn on the Intramdecular Mobflity (JMM) of Macromolecules in Solution... 

Statistical theories of macromolecules in solutions have recently attracted considerable attention of theorists because of remarkable and wide-ranged properti of macromolecules, of their close connection to the theories of phase transitions in lattices, and relations to ferromagnetism and adsorption problems and of the discoveries in the structures and functions of DNA and other biological macromolecules. Needless to say, a great many papers and books have been pubUshed recently, but we confine our attention to statistical theories of macromolecules in solutions. In spite of the great number of papers in this field, however, the development of rigorous statistical theories of macromolecular solutions has been rather slow, and there have been presented many different approaches some of which have probably confused readers. Therefore, in this paper we aim at a rather unified and simplified theory of macromolecular solutions and at the same time we discuss some of the feattues of various other macromolecular solution theories and elucidate the present situation. In so doing we hope to attract attention of more theoretical chemists and physicists whose participation in this field is certainly needed. 

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