Coil molecules dimensions

This thermodynamic behaviour is consistent with stress-induced crystallisation of the rubber molecules on extension. Such crystallisation would account for the decrease in entropy, as the disorder of the randomly coiled molecules gave way to well-ordered crystalline regions within the specimen. X-Ray diffraction has confirmed that crystallisation does indeed take place, and that the crystallites formed have one axis in the direction of elongation of the rubber. Stressed natural rubbers do not crystallise completely, but instead consist of these crystallites embedded in a matrix of essentially amorphous rubber. Typical dimensions of crystallites in stressed rubber are of the order of 10 to 100 nm, and since the molecules of such materials are typically some 2000 nm in length, they must pass through several alternate crystalline and amorphous regions. 

Perhaps the most striking feature of this equation is that the friction factor has disappeared. It cancels out in the product alv. Physically this means that only some overall dimensions of the coiled molecule are of importance for its hydrodynamic behaviour. These dimensions are proportional to / = < > / (3.58a)... 

Deriving molecular dimensions in solution from viscosities depends on the model assumed for the conformations of the free molecules. Since any a- or - triple helical sections of our gelatins vrc>uld be melted at 30 C. we assume near randomness for the chains, and a lew ellipticity for the molecular envelopes. Further, the success of Flory s viscosity theory (17) has shown that the hydrodynamically effective volume of randomly coiled (and of many other) chain molecules is not very different from the volume encompassed by the meandering segments. Thus we treated our data as if they pertained to random coil molecules. The measured layer thicknesses then describe the level within the adsorbed interphase below v ich the segmental density is equal to, or larger, than the effective coil density of the free molecules. 

Hence, the results stated above have shown that the macromolecular coil fractal dimension D can serve as volume effects measure. The value D for coil in 0-solvent characterizes such effects absence (D=2.0, e=0). Dj.<2.0 means repulsive interactions availability, >2.0—attractive interactions between randomly drawing closer to one another chain links and also between chain links and solvent molecules. The repulsive interactions weakening and, respectively, attractive interactions intensification means macromolecular coil coimectivity degree enhancement, characterized by the spectral dimension d. Thus, the dimensions D, and d variation (at fixed d) characterizes completely enough biopol5miers (and polymers at all) macromolecular coil behavior in diluted solutions [39]. 

In fact, neutron scattering studies show that coiled molecules have the same unperturbed dimensions as they would have in the appropriate dilute solution (see Figure 4-20). The experimental conclusion is independent of the method of preparation of the solid solution. In one case, such a solid solution was prepared by dissolving a protonated polymer in deuterated monomer and... 

Molecular composites as an extension of fiber reinforcement Molecular composites is designed to use rigid rodlike molecules as reinforcement for the flexible coil molecules as matrix. The patent applications on the molecular composites were made almost in the same age independently by Takayanagi in Japan in 1977 and by Helminiak in the United States in 1978. Takayanagi proposed thermoplastic nylon reinforced by poly(p-phenylene terephthalamide)(PPTA) and Helminiak proposed wet process using poly(p-phenylene benzobisthiazole)(PBT)-reinforced poly(2,5(6)benzimidazole) (ABPBI). In molecular composite (MC) [15,16,17], the fineness of reinforcement was pursued to its limit, i.e. to the molecular dimension. 

The polymer molecules are isolated from each other in solution. They take on the statistically most likely conformation and form a coil. The dimension of this coil in dilute solution is what affects the viscous properties of a polymer solution. Despite of the regional isolation between the coils, as shown in Fig. 4.1, there are interactions that take effect during the flow process. These interactions are only prevented when the state of the so-called ideal dilute solution is reached. In this case, the polymer concentration c O and the single polymer molecule only interacts with the solvent. The following description for the determination of the intrinsic viscosity is based on this idealized state of solution. 

Small-angle neutron scattering (SANS) of labelled (deuterated) amorphous samples and rubber samples detects the size of the coiled molecules and the response of individual molecules to macroscopic deformation and swelling. It has been shown that uncrosslinked bulk amorphous polymers consist of molecules with dimensions similar to those of theta solvents in accordance with the Flory theorem (Chapter 2). Fernandez et al (1984) showed that chemical crosslinking does not appreciably change the dimensions of the molecules. Data on various deformed network polymers indicate that the individual chain segments deform much less than the affine network model predicts and that most of the data are in accordance with the phantom network model. However, defmite SANS data that will tell which of the affine network model and the phantom network model is correct are still not available. 

The above discussion points out the difficulty associated with using the linear dimensions of a molecule as a measure of its size It is not the molecule alone that determines its dimensions, but also the shape in which it exists. Linear arrangements of the sort described above exist in polymer crystals, at least for some distance, although not over the full length of the chain. We shall take up the structure of polymer crystals in Chap. 4. In the solution and bulk states, many polymers exist in the coiled form we have also described. Still other structures are important, notably the helix, which we shall discuss in Sec. 1.11. The overall shape assumed by a polymer molecule is greatly affected... 

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

Strauss and Williamst have studied coil dimensions of derivatives of poly(4-vinylpyridine) by light-scattering and viscosity measurements. The derivatives studied were poly(pyridinium) ions quaternized y% with n-dodecyl groups and (1 - y)% with ethyl groups. Experimental coil dimensions extrapolated to 0 conditions and expressed relative to the length of a freely rotating repeat unit are presented here for the molecules in two different environments ... 

In addition to an array of experimental methods, we also consider a more diverse assortment of polymeric systems than has been true in other chapters. Besides synthetic polymer solutions, we also consider aqueous protein solutions. The former polymers are well represented by the random coil model the latter are approximated by rigid ellipsoids or spheres. For random coils changes in the goodness of the solvent affects coil dimensions. For aqueous proteins the solvent-solute interaction results in various degrees of hydration, which also changes the size of the molecules. Hence the methods we discuss are all potential sources of information about these interactions between polymers and their solvent environments. 

The structure of any molecule is a unique and specific aspect of its identity. Molecular structure reaches its pinnacle in the intricate complexity of biological macromolecules, particularly the proteins. Although proteins are linear sequences of covalently linked amino acids, the course of the protein chain can turn, fold, and coil in the three dimensions of space to establish a specific, highly ordered architecture that is an identifying characteristic of the given protein molecule (Figure 1.11). 

Although R2 is the easiest quantity to be obtained theoretically, there is no straigthforward experimental method for its determination. For this reason, two other quantities are widely in use to characterize the dimensions of a randomly coiled polymer molecule ... 

The quantity b has the dimension of a volume and is known as the excluded volume or the binary cluster integral. The mean force potential is a function of temperature (principally as a result of the soft interactions). For a given solvent or mixture of solvents, there exists a temperature (called the 0-temperature or Te) where the solvent is just poor enough so that the polymer feels an effective repulsion toward the solvent molecules and yet, good enough to balance the expansion of the coil caused by the excluded volume of the polymer chain. Under this condition of perfect balance, all the binary cluster integrals are equal to zero and the chain behaves like an ideal chain. 

In the unstressed state the molecules of an elastomer adopt a more-or-less randomly coiled configuration. When the elastomer is subjected to stress the bulk material experiences a significant deformation, as the macromolecules adopt an extended configuration. When the stress is removed, the molecules revert to their equilibrium configurations, as before, and the material returns to its undeformed dimensions. 

Apart from their utility in determining the correction factor 1/P( ), light-scattering dissymmetry measurements afford a measure of the dimensions of the randomly coiled polymer molecule in dilute solution. Thus the above analysis of measurements made at different angles yields the important ratio from which the root-mean-square... 

According to the interpretation given above, the intrinsic viscosity is considered to be proportional to the ratio of the effective volume of the molecule in solution divided by its molecular weight. In particular (see Eq. 23), this effective volume is represented as being proportional to the cube of a linear dimension of the randomly coiled polymer chain,... 

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