Steric hindrance parameter

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

G (a) Steric hindrance parameter (usually measured in dilute solutions). 

Some important properties of polymer chains in dilute solutions [steric hindrance parameter, characteristic ratio, persistence length, radius of gyration, statistical chain segment length (introduced earlier, in Chapter 11), intrinsic viscosity, and viscosity at small but finite concentrations] will be discussed, and new correlations will be presented for the steric hindrance parameter and the molar stiffness function, in Chapter 12. 

Several parameters, most of which are interrelated and can be estimated in terms of each other, are utilized to describe the conformational properties of polymer chains [1,2]. These quantities include the steric hindrance parameter a, the characteristic ratio Cx, the persistence length Ip, the statistical chain segment (or Kuhn segment) length lk, the root mean square radius of gyration Rg (often briefly referred to as simply the "radius of gyration"), and the molar... 

The steric hindrance parameter a is the simplest conformational property of a polymer chain. If o denotes the mean-square end-to-end distance of an unperturbed linear chain molecule in solution, and of denotes the mean-square end-to-end distance of the idealized and hypothetical "freely rotating" state of the chain, o is defined formally by Equation 12.1 ... 

A dataset consisting of the a values of 54 polymers was prepared by using experimental data from the Polymer Handbook [16] and then used to develop a direct correlation, with four adjustable parameters, between the structures of polymers and their steric hindrance parameters. The intuitively expected trends summarized in Section 12.A.2 were used to guide this effort. 

Table 12.3. Experimental values [16] o(exp) of the steric hindrance parameter, the quantities used in the correlation equation for o, and the fitted values o(fit), for 53 polymers. 

Figure 12.8. Comparison of the experimental values [16] of the steric hindrance parameters c of 53 polymers with the calculated values obtained by a four-parameter linear regression.

Table 12.4. Experimental steric hindrance parameters o and characteristic ratios [16] of 51 polymers. Some of the a values listed below differ from those in Table 12.3, because only the results of those measurements for which both o and CM were reported are utilized in this table.

Step 21. Calculate the key properties of polymers in dilute solutions. The steric hindrance parameter a is predicted by using equations 12.22-12.26. For polystyrene, the result is 0-2.22. The characteristic ratio is predicted from the value of a, by using Equation... 

Steric hindrance parameter Atactic in benzene or chloroform 1.98 (16)... 

For a chain with completely free rotation, (cos 0 > = 0 and Equation (4-26) becomes Equation (4-25). An dAVtrans chain is a rigid chain with 6 = 0, which is, however, physically absurd with regard to Equation (4-26). Thus, o is a measure of the hindrance to rotation it is often called the steric hindrance parameter. With tactic polymers, the relationship between 0 and a is more complicated. One can, however, always use an equation analogous to Equation (4-26) ... 

The steric hindrance parameter o measures the hindrance to rotation about main chain bonds, and, so, is a measure of the thermodynamic flexibility of the coiled molecule. It can be calculated from the radius of gyration of unperturbed coils via Equations (4-29) and (4-27) if the bond length, valence angle, and number of main chain bonds is known. 

The steric hindrance parameter a is a constant only in the case of apolar polymers in apolar solvents. A distinct dependence of the hindrance parameter on the type of solvent can be observed, however, for polar polymers and/or polar solvent combinations (see Table 4-7). Such effects are to be expected because of changes brought about in the trans I gauche ratios of conformers in the chain. 

According to Equation (4-27), the chain end-to-end distance depends on parameters independent of the constitution and configuration, such as the number of bonds, as well as on parameters which are dependent, like bond length, valence angle, and steric hindrance parameter. A certain stiffness of the chain can be caused by increased bond length and valence angle, as well as... 

The intrinsic viscosity is a measure of the macromolecular dimensions. Thus, for flexible macromolecules, chain skeleton parameters (bond lengths, valence angles, degree of polymerization, mass of the monomeric unit), the steric hindrance parameter a, or a measure of the hindrance to rotation, and the expansion factor a as a measure of the interaction with the solvent, determine the magnitude of the intrinsic viscosity. In theta solvents, a = 1. Thus, from Equations (9-148) and (9-152)... 

Figure 10-21. The relationship between the glass transition temperature Tg and the steric hindrance parameter a for carbon-carbon chains (O) carbon-oxygen chains ( ), and carbon-nitrogen chains (0).

Polymers of higher tacticity have more rigid chains than atactic polymers, since more base units are fixed in conformational sequences of the coil, which corresponds formally to an increase in the steric hindrance parameter a. With a predominantly iso tactic poly(methyl methacrylate), for example, a X = 0.087 cm /g was obtained in heptanone-3 (0 = 40.0°C), whereas an at-PMMA in the same solvent gave only K = 0.063 cm /g (0 = 33.7°C). At higher temperatures, potential barriers to rotation can be more readily surmounted. The K values then become practically identical 0.057 for it-PMMA (0 = 152.rC) and 0.058 for at-PMMA (0 = 159.7°C) in p-cymene. 

For polymers with a more complicated backbone structure and different bond lengths along the backbone (for example polysaccharides), it is not possible to assume a simple bond length b. In this case, the average end-to-end distance is not described via the characteristic ratio, but the steric hindrance parameter cr. 

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