Degree of polymerization versus

Figure 4.33. (a) PVC examples of degrees of polymerization versus K values (b) PVC examples of molecular weights... 

Previous studies of the decomposition of cellulose reported Ea for absorbent cotton as 54.3 kcal/mol at a high-temperature range of 270-310 °C (23). For temperatures below pyrolysis, Ea = 20 kcal/mol reflects the low-temperature degradation effects of loss of H and OH from adjacent carbon atoms in cellulose (dehydration) and the concomitant creation of C=C bonds (24). In another work Ea = 21 kcal/mol was estimated from Arrhenius plots of the degree of polymerization versus time for cellulose heated in air at 150-190 °C (25). 

A plot of the reciprocal of the number average degree of polymerization versus [T f[M should then be linear, if the analysis is correct. And indeed it is, as illustrated for the polymerization of styrene in various solvents, which act as chain transfer agents (hence the use of the symbol [5] instead of [7] in Figure 4-22). 

The following data were obtained in terms of degree of polymerization versus the intrinsic viscosity of poly(methyl methacrylate) samples (with low monodispersities) in benzene at 25°C ... 

Fig. 29 Virtual degree of polymerization versus association strength (iCa) in supra-molecular polymers. Reprinted with permission from [120]...

Figure 12-3 Plots of the degree of polymerization versus the cumulative number of synthetic steps for various repetitive syntheses (a) conventional linear solid-phase synthesis (b) nonlinear straight-chain sequence synthesis (c) dendrimer synthesis (branching multiplicity of three) (d) double exponential den-drimer synthesis (branching multiplicity of three). In all cases, the degree of polymerization is defined as the total number of monomer units per polymer molecule.

The buildup of the polymer chain with monomer conversion differs significantly depending on the class of polyreaction used. In a chain growth process, the molar mass increases rapidly and reaches a plateau value already at low monomer conversion if chain growth is well controlled or living, then a linear dependency of degree of polymerization versus monomer conversion... 

Figure 5.3.11 Degree of polymerization versus monomer conversion for different polymerization mechanisms. Adapted from Onken (1996).

Values of average degrees of polymerization versus conversion of end groups p shown for / = 2 and / = 3 in Figure 3.1 have been computed using the above... 

Figure 1. Average degree of polymerization versus reaction time for the Pt-MTX polymer.

Figure 5. Reciprocal average degree of polymerization versus time for the degradation of the Pt-MTX polymer in DMSO. 

Figure 3.10 Average degree of polymerization versus conversion at the outlet for Ys = 0.1 and...

Figure 2.10 shows a plot of viscosity versus degree of polymerization for several polymers. Several things should be observed about this graph ... 

Their molecular weight or degree of polymerization, often expressed as K value or K-wert, inferred from viscosity measurements. Figure 4.33 (a b) displays some examples of polymerization degrees and molecular weights versus K values. Slightly different data can be found quoted elsewhere because several methods to measure K values exist. 

Figure 2-8 shows plots of Xn versus the stoichiometric ratio for several values of p in accordance with Eq. 2-78. The stoichiometric imbalance is expressed as both the ratio r and the mole percent excess of the B—B reactant over the A—A reactant. The various plots show how r and p must be controlled so as to obtain a particular degree of polymerization. However, one does not usually have complete freedom of choice of the r and p values in a polymerization. Complete control of the stoichiometric ratio is not always possible, since reasons of economy and difficulties in the purification of reactants may prevent one from obtaining r values very close to 1.000. Similarly, many polymerizations are carried out to less than 100% completion (i.e., to p < 1.000) for reasons of time and economy. The time required to achieve each of the last few percent of reaction is close to that required for the first 97-98% of reaction. Thus a detailed consideration of Fig. 2-2 shows that the time required to go fromp = 0.97 (X = 33.3) to p = 0.98 (X — 50) is approximately the same as that to reach p = 0.97 from the start of reaction. 

Fig. 10. Degree of polymerization, J, versus temperature in CC for equilibrium polymerization of a-methyl-styrene. A. initial concentration of the nonomer 1 mole/kg. B. initial concentration of the monomer 2,5 moles/ kg. Concentration of living ends 0,001 moles/kg. Reproduced, with permission, from Tobolsky and Eisen-...

Tg versus degree of polymerization was linear.254 Similarly, for a series of commercial starch hydrolysis products (polydisperse solutes), there was a linear relationship between Tg (Tg of the maximally freeze-concentrated solute glass) and 1/MW.270... 

Fig. 33. a Volume fraction of deuterated poly(ethylenepropylene), dPEP (full dots) and pro-tonated PEP (open circles) versus depth, for a degree of polymerization N-2300 for both constituents, after a 4 h quench to T=294 K (Tcb 365 K). Profiles are obtained with the time of flight forward recoil spectrometry (TOF-FRES). The dashed line indicates the surface domain thickness l(t). b Plot showing the growth of the surface domain thickness (t) vs t1/3. From Krausch et al. [136]... 

FIGURE 2-27 Graph of the fraction of chains versus the degree of polymerization. 

As discussed in Chapter 5, data from both Auger spectroscopy and optical studies confirm a decreasing polarizability and/or optical basicity for silicate units as the degree of polymerization increases, consistent with the above interpretation. Polarizabilities (or better still, polarizabilities per O atom) have not yet been calculated for silicate polymers, nor have interaction energies of cation pairs such as Mg versus Fe with oxygens of various type yet been studied. 

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