Space-Filling Properties

The effects mentioned in the last sub-section are all local ones and do not depend upon the macromolecular nature of the material. A more important group of properties comprises those that are affected by the changes that LCB produces in the space-filling behaviour of polymer molecules under conditions in which they are free or relatively free from conformational constraints, that is in solution or in the melt, or in the amorphous state below 7.  

It has been recognised for several decades that most of the characteristic properties of polymers (except the untypical globular proteins), such as their high solution and melt viscosities, their rubber-like elasticity, and their viscoelastic behaviour generally, can be ascribed to the fact that their molecules, unless constrained as in the crystal, are free to adopt extended but coiled configurations, so that each molecule affects a region of space of many times its own volume  

The viscoelastic properties of long-branched polymers in the melt are understood even less well than their solution properties the former are profoundly affected by entanglements, unless the polymer is of low DP, and it is intuitively obvious that entanglements involving branched molecules may be more difficult to unravel than those of linear molecules, especially those involving segments between two branch points but to treat this quantitatively would be difficult. 

The sizes and space-filling properties of polymer molecules are most conveniently expressed in terms of a mean-square radius s2 , the square root of which is the radius of gyration. It is given by  

If interactions between parts of the molecule separated by many links (the excluded volume effect ) is absent, so that the chains obey random-flight statistics, s2 takes its unperturbed value, (s ). Theoretical calculations of the dimensions of branched molecules usually assume random flight chains, and values of the mean-square radius so obtained are estimates of So . 

---

It is known that sweet-tasting compounds are quite common and their chemical structures vary widely. In order to establish a structure-taste relationship, a large number of compounds have been tested, and several molecular theories of sweet taste have been proposed by different groups. At present, the phenomenon of sweet taste seems best explained by the tripartite functioning of the postulated AH, B (proton donor-acceptor) system and hydro-phobic site X (1, 2, J3, 4 5). Sweet-tasting compounds possess the AH-B-X system in the molecules, and the receptor site seems to be also a trifunctional unit similar to the AH-B-X system of the sweet compounds. Sweet taste results from interaction between the receptor site and the sweet unit of the compounds. Space-filling properties are also important as well as the charge and hydro-phobic properties. The hydrophile-hydrophobe balance in a molecule seems to be another important factor. 

After the finding of a sweet taste in L-Asp-L-Phe-OMe (aspartame) by Mazur et at. (6), a number of aspartyl dipeptide esters were synthesized by several groups in order to deduce structure-taste relationships, and to obtain potent sweet peptides. In the case of the peptides, the configuration and the conformation of the molecule are important in connection with the space-filling properties. The preferred conformations of amino acids can be shown by application of the extended Hiickel theory calculation. However, projection of reasonable conformations for di- and tripeptide molecules is not easily accomplished. 

One problem that remains is the mode of interaction between the sweet peptides and the receptor site. Despite a great number of studies, the mechanism of action of sweet stimuli on the receptor is not well known. Stereoisomerism can be responsible for differences in taste responses, and space-filling properties are also very important. These facts suggest that the receptor site exists in a three-dimensional structure. In this connection, the sense of sweet taste is subject to the "lock and key" of biological activity. 

Steric. Pertaining to the spatial relationships of atoms in a molecular structure, and in particular, to the space-filling properties of a molecule. 

The term stereochemistry refers to the three-dimensional nature of molecules and to their space-filling properties. Many computer models can give a perception of three dimensions, but printed and hand-drawn representations of molecules are two-dimensional images that are meaningful only to those who understand implicit rules for visualizing the third dimension. Furthermore, such drawings have meanings on many levels. 

Steric effect (Section 6.13A) An effect on relative reaction rates caused by the space-filling properties of those parts of a molecule attached at or near the reacting site. 

Thus, supermolecular liquid crystals with a cyclotriphosphazene dendritic core and polycatenar mesogenic units (144) were obtained in three steps by the conventional sequence of substitution (i), derivatization (ii and iii) methods from [N3P3CI6] (Scheme 9). Due to the microsegregation of the alkyl chains and the aromatic central cores and the space-filling properties, compounds (144) adopt a discotic conformation assembled in a columnar mesophase and illustrate the possibilities of using cyclotriphosphazenes for the design of columnar assemblies at room temperature, in the mesophase or in a vitrified solid state with interest for applications in material science. Similarly, the new family of solution processable, photoluminescent, monodisperse nanocomposite dendrimers (145) (Tg > 165 °C, > 465 °C)... 

In recent years, numerous attempts have been made to correlate the geometry of catalyst/substrate intermediates with the l/b ratio of product aldehydes derived from the hydroformylation of 1-olefins [38]. Conclusions are mainly based on spectroscopic measurements or chemical calculations [39]. Especially, Tolman s cone angle (9) [40] and the natural bite angle ( ) [38], respectively, are used to estimate the space-filling properties of a ligand (see Chapter 2). These studies mainly refer to phosphorus-modified rhodium catalysts and 1-olefins as substrates, but they can also contribute to a better understanding of the isomerization - hydroformylation [41]... 

It has been shown with numerous compounds that as the hydrophobicity and the space-filling properties of hydrophobic groups increase, the sweetening strength increases, passes through a maximum, and finally reaches a limit beyond which the sweet taste is either quenched or changes into a bitter taste. 

Figure 1 The basic concept of the fractal description of rugged systems is that one can add a fractional number to the topological dimension of systems to describe its space filling properties. ...

We can describe these complex geometrical shapes mathematically, and if the space-filling properties of the objects are consistent over a wide range of length scales, the system can be characterized using a quantity known as the fractal dimension. The concept is that these objects are somewhere between the integer dimensions—they have a fractional dimension. By calculating the fractal dimension we can obtain a measure of how space is filled by the material. 

What is steric repulsion The generic term refers to the space-filling property of atoms and molecules, as manifested in crystal packing densities, molecular collision cross-sections, and other lines of experimental evidence. Indeed, space-filling molecular models are among the most useful tools of the chemistry studenL and atomic radii are among the first properties called to the student s attention to illustrate atomic periodicity trends. 

---