Macromolecular shape

The values of the exponent for M in Equations 8, 9, and 10 determine the rate at which the size of the respective macromolecular shapes change with the molecular weight. For example, a tenfold increase in molecular weight roughly corresponds to a 10 X 2 X r, or 3 X Rg change in molecular size... 

Mezey, P.G. (1997) Quantum chemistry of macromolecular shape, Internat. Rev. Phys. Chem., 16,361. 

The field of stereochemistry serves as a unifying theme for the expanded definition and diversification of chemistry. The consequences of molecular and macromolecular shape and topology are central to issues of chemical reactivity, physical properties, and biological function. With that view, the importance of stereochemistry had never been greater, and it is hoped that this series will provide a forum for documentation of significant advances in all of these subdisciplines of chemistry. 

Equation (17) has been validated via experiments using simple liquids [35, 37], and has been applied to studies on solutions, and gels, as well as solid foods. PGSE has been used in studies on the obstruction and solvation effects related to the macromolecular shape factor for ovalbumin [38], wheat starch amylopectin [39], and for agarose gel [40]. 

This formula describes dilute solutions (Cp < 1/vN2) fairly well despite the fact that it ignores macromolecular shape changes during binary chain interactions. 

Effects due to macromolecular shape changes during single-contact interactions can, within the Benoit-Benmouna theory, be included in an ad-hoc fashion by renormalizing the single-chain structure factor to make it concentration dependent. This approach is often used to describe polymer solutions up to the concentrated region. 

This has opened the way to a systematic, quantum chemical definition and description of functional groups, to macromolecular shape analysis, to macromolec-ular force computations, and to shape-code-based macromolecular similarity analysis [20-25],... 

Unlike sedimentation equilibrium methods, measurement of sedimentation rates - how fast the molecules fall in the centrifugal field -can give information about both macromolecular shape and the size. These methods use relatively high centrifugal forces and measure the concentration profiles within the centrifuge tube (cell) as a function of time. 

The relationship between [ ] and macromolecular shape is difficult to determine theoretically, except in special cases, but a number of empirical rules have been derived. ... 

Molecular geometry and connectivity can be used to construct descriptors for other shape features. In this section, we introduce another aspect of macromolecular shape the complexity of self-entanglements in a polymer. The analysis is restricted to backbones that is, only main chain atoms are considered. 

This expression is an adaptation of the I(Q) calculation for a sphere and the required integration can be performed numerically. Particles that do not have spherical or near-spherical symmetry do not exhibit the minima and maxima noted above, and the scattering curve I(Q) declines more uniformly as Q increases. Other analytical expressions exist for the calculation of I(Q) for ellipsoids, prisms and cylinders and their hollow equivalents [55]. It should be noted, however, that I(Q) for ellipsoids, prisms and cylinders do not differ greatly. For simple models, a first indication of the macromolecular shape in terms of a triaxial body can be extracted by curve-fitting of the calculated scattering to the experimental curve at low Q. 

Harding, S. E., and Colfen, H., Inversion formulae for ellipsoid of revolution macromolecular shape functions. Ana/. Biochem., 228, 131-142 (1995). 

The term macromolecular architecture has been coined to subsume the realm of polymer stmctures that can be obtained using modem synthetic polymer chemistry. In addition to the control over the bulk properties that results from tunability of the various parameters outlined in Figure 1, each aspert also provides for variability in the individual macromolecular shapes and guidance in their multimolecular assembly processes to lead to well-defined discrete objects of nanoscopic dimensions. 

In summary, much of the current research in organic materials is focused on the creation of macromolecules or interfaces with controlled properties. To control the bulk material properties, chemists must be able to control molecular weights and polydispersities, stereochemistry, sequence, and even macromolecular shape and topology. Many new kinds of materials have emerged in this effort, such as dendrimers, liquid crystals, and fullerenes. Achieving the kinds of control we are discussing often has a basis in the knowledge of the mechanisms of polymerizations, and that is the topic we now consider. 

The above theory was developed basically for flexible molecules which may have some degree of stiffness. However, if it is assumed that xanthan molecules may be modelled as rigid rods to a first approximation, then a theory has been developed which allows the determination of molecular dimensions from viscometric measurements in a similar way to the flexible coil case. The relationship between intrinsic viscosity and macromolecular shape has been derived theoretically for rigid rods (Layec and Wolff, 1974). When the ratio of the length to the diameter of the molecule, p, is large (p 50), the model gives a relationship between the zero shear intrinsic viscosity, Mq, and p of the form ... 

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