Polymer chain structures

CALCULATION OF AVERAGE DIMENSIONS FOR VARIOUS POLYMER CHAIN STRUCTURES... 

Several assumptions were made in using the broad MWD standard approach for calibration. With some justification a two parameter equation was used for calibration however the method did not correct or necessarily account for peak speading and viscosity effects. Also, a uniform chain structure was assumed whereas in reality the polymer may be a mixture of branched and linear chains. To accurately evaluate the MWD the polymer chain structure should be defined and hydrolysis effects must be totally eliminated. Work is currently underway in our laboratory to fractionate a low conversion polydlchlorophosphazene to obtain linear polymer standards. The standards will be used in polymer solution and structure studies and for SEC calibration. Finally, the universal calibration theory will be tested and then applied to estimate the extent of branching in other polydlchlorophosphazenes. 

Figure 10. The polymer chain structure of 1,6-bis(2,4-dinitrophenoxy)-2,4-hexadiyne (DNP). Two repeating units are shown (15).

Since its early beginnings more than a half-century ago, the field of polymers has attracted a number of brilliant minds and has benefitted from the contributions of many bright minds. The scientific researches of Herman Mark, especially his pioneering work on polymer chain structure by X-ray diffraction, are part of such contributions. But that is not where his uniqueness lies. His special and unique contribution has been and still is in "spreading the gospel" of polymers, to borrow the phrase from great spiritual movements. But unlike the proselytes of such movements, who seek to "convert" people,... 

Figure 2.8 Schematic of common polymer chain structures...

It should not be taken for granted that all polymers that are defined as condensation polymers by Carothers classification will also be so defined by a consideration of the polymer chain structure. Some condensation polymers do not contain functional groups such as ester or amide in the polymer chain. An example is the phenol-formaldehyde polymers produced by the reaction of phenol (or substituted phenols) with formaldehyde... 

The Tg increases as the intermolecular forces in the polymer and the regularity or crystallinity of the polymer chain structure increase. Thus polyvinyl chloride (PVC) has a higher Tg than linear polyethylene (hdpe) because of the presence of dipole-dipole interactions between the chains in PVC. 

Fig. 8. Linear swelling ratio calculated for ionized NIPA gels. Numbers on curves represent the effective number of charges per polymer chain. Structural parameters were calculated from the preparation condition of the samples. Other parameters were identical with those used in the calculations for neutral NIPA gels...

Here D is the translational diffusion coefficient of the solute molecule at C —> 0 with C the mass concentration of the solute, kd the diffusion second virial coefficient, f a dimensionless parameter depending on polymer chain structure and solvent, and the mean square radius of gyration of the polymer chain. Hence, for C and q small enough, Eq. (2.3) may be approximated by... 

Perhaps the widest application is that of conventional high-resolution spectroscopy in solution for the purpose of learning in detail about polymer chain structure. In this field, proton NMR, formerly dominant, has given way to carbon-13 NMR with the development of pulse Fourier transform spectrometers with spectrum accumulation. Carbon spectroscopy is capable of giving very detailed and often quite sophisticated information. For example, a very complete accounting can be provided of comonomer sequences in vinyl copolymers and branches can be identified and counted, even at very low levels, in polyethylenes. 

The correlation between the data on the electric conductivity of the system in the presence of monomer and those on the relationship between the structures of the catalytic complex and the polymer makes it possible to represent the general polymerization scheme (Reaction 14). In so doing, cis-trans isomerism of the polymer chain structure is not dealt with, although the same approach can be applied to this phenomenon as well. 

It is easy to see that in our case the system exists in several discrete states of one catalytic center, and their ratio affects the polymer chain structure and the polymerization rate. 

The cellulose II structure is more complex to unravel, since it involves two symmetry-independent chains. Polymer chain structures have been proposed that involve six different intrachain hydrogen-bond arrangements [344] ... 

Polyacrylonitrile (PAN) is the most common precursor used to make carbon fibers. A flow diagram showing the steps involved in making PAN-based carbon fiber is shown in Fig. 8.3. The PAN precursor has a flexible polymer chain structure like any other polymer, but it has an all carbon backbone chain that contains polar nitrile groups, as shown in Fig. 8.4. During the stabilization treatment, the PAN precursor fiber is heated to 200-220 C, under tension. When this is done oxygen is absorbed, and it serves to cross-link the chains the fibers turn black, and a stable ladder structure is formed. A ladder polymer is a rigid... 

In this case the metal atom is a part of the polymer chain (structure G). To realize sudh an arrangement with the mentioned ligands four-or hi er valent metal atoms like Si, Se, Sn and other may be taken. 

The structure of cellulose has only relatively recently been tackled through the examination of its trinitrate, that is. nitrocellulose of ca, 14% N. Trinitrate of cellulose was chosen as a readily available cellulose ester, soluble in polar solvents, of an almost unique unbranched polymer chain structure having a broad range of molecular weights manifested by the degree of polymerization 250-9000. 

The model thus has been defined in terms of polymer chain structure, solution structure, and interactions. Now statistical mechanics can be applied to it. We use the partition function devised by Flory (27, 28). For simplicity, instead of the entire system, we study a subsystem containing one polymer molecule plus its share of N /N2 monomer molecules. The partition function of the subsystem has the same form as that for the entire system (27,28) that is... 

Chromophores attached to a polymer present an Inhomogeneous medium for excitation transport. Rather than being randomly distributed, as in a solution, the positions of the chromophores are correlated through the covalent bonds of the polymer. Also, the finite size of the polymer limits the number of sites the excitation can sample. This inhomogeneity in the chromophore distribution resulting from the requirements of polymer chain structure can... 

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