Branching frequency,

The short side chain branching frequency is inversely proportional to polymer crystallinity. Short branches occur at frequencies of 2—50 per 1000 carbons in chain length their corresponding crystallinity varies from 35 to 75%. Directiy proportional to the polymer density, crystallinity can be calculated by the following formula,... 

For star polymers a value of e = 0.5 has been obtained (1, V7) and studies (18) of model comb polymers indicate a value of 1.5. Other work (191 has suggested that e is near 0.5 at low LCB frequencies. For a random LCB conformation of higher branching frequency an e value between 0.7 and 1.3 might be expected, i.e. somewhere between a star and a comb configuration. 

Figure 2 compares the conformational transition curves of wild-type yeast glucan (branch frequency = 0.20) and PGG (branch frequency = 0.50). Wild-type yeast glucan required approximately 0.1M NaOH to disrupt the triple helical conformation, whereas this transition is observed at approximately 0.04 M NaOH with PGG. This trend is consistent with the observation that curdlan, an entirely linear p-D(l-3)-linked glucan, requires approximately 0.25M NaOH to disrupt the ordered conformation (76). Hence, it is concluded that the highly branched PGG molecules only form weak inter-chain associations resulting in the formation of predominantly single-helical zones. 

Branching Frequency - number of branches/number of glucose moieties per repeating unit. 

Figure 2 Effect of branch frequency on glucan conformation. Conformational characterization of glucans was carried out as described in the experimental section. Curdlan is a linear p(l-3)linked glucan Yeast glucan has a 30% P(l-6) branch frequency and PGG-R glucan has a 50% p(l-6) branch frequency. The Congo Red-single/triple helix complex absorption maxima are indicated.

Models for emulsion polymerization reactors vary greatly in their complexity. The level of sophistication needed depends upon the intended use of the model. One could distinguish between two levels of complexity. The first type of model simply involves reactor material and energy balances, and is used to predict the temperature, pressure and monomer concentrations in the reactor. Second level models cannot only predict the above quantities but also polymer properties such as particle size, molecular weight distribution (MWD) and branching frequency. In latex reactor systems, the level one balances are strongly coupled with the particle population balances, thereby making approximate level one models of limited value (1). 

It can also be expected that any calculations of long chain branching frequency (12,13) will be severely compromised by errors resulting from supermolecular structures. This is because the frequency of long branches resulting from chain transfer to... 

Pannell (38) has studied a range of polystyrenes with comb-like branching, but with relatively long branches. He has correlated the low-shear melt viscosities with calculated values of , finding i/o°c(so)4 8, whereas the exponent for linear polymers is about 3.4. Fujimoto s results can be correlated in a similar way, but with a rather higher exponent, 5.1, though rather better correlations would be obtained if separate lines were used for each branching frequency. 

The relative sensitivity of short-chain alkyl branches of different sizes to elimination on irradiation with formation of the corresponding alkane has been variously reported as being constant or varying (13,14). Figure 9 compares G values for formation of the alkane corresponding to the short-chain branch from samples of these three polymers with branch frequencies from 0.5 to 6 per 1,000 C atoms. There is a notably higher scission efficiency for ethyl branches. 

This technique has been used to investigate the distribution of short-chain branches in LDPE and the relatively higher scission efficiency of ethyl branches would rationalize the yields with 13C NMR measurements of branch frequencies (2). 

Narrow distribution in the backbone length as well as in the chemical composition or the branch frequency may be expected from a living-type copolymerization between a macromonomer and a comonomer provided the reactivity ratios are close to unity. This appears to have been accomplished to some extent with anionic copolymerizations with MMA of methacrylate-ended PMMA, 29, and poly(dimethylsiloxane) macromonomers, 30, which were prepared by living GTP and anionic polymerization, respectively [50,51]. Recent application [8] of nitroxide (TEMPO)-mediated living free radical process to copolymerizations of styrene with some macromonomers such as PE-acrylate, la, PEO-methacr-ylate, 27b, polylactide-methacrylate, 28, and poly(e-caprolactone)-methacrylate, 31, may be a promising approach to this end. 

For PE, the so-called Igepal transition time, which is the time during an experiment in which the medium becomes effective, was found to increase significantly with a rising degree of crystallinity when the molecular weight and weight distribution as well as the branch frequency were kept similar [35]. 

The number of discrete k values is N/2, the number of primitive unit cells in the crystal. Each of these is assumed to yield the same set of 12 branch frequencies Vj. Thus we can simplify Eq. (30) to... 

Although the density of the polymer can be varied by copolymerization with higher olefins to match that of polyethylene produced by high-pressure free-radical processes, the two types differ in branch frequency and character and in molecular weight distributions. As a result, they do not have comparable processing and mechanical properties. 

It is plausible to suppose that the temperature dependence should not be affected by branching unless the branching frequency is unusually high, since the friction factor f is presumed to reflect the behavior of relatively short (ca. five to twenty mer units) segments of the chain. Results on star-shaped branched polymers support this view 101, 136, 196). For example, the ratio exhibited the same dependence... 

Many of the symbols used here are those which have found favor in the literature over the years and which are presently being used. As such, they may differ from the symbols used in the original publications.) From the number of branches, the branching frequency (A) of the molecule may be calculated by Eq. (6),... 

Once g is determined, the branching number (number of branches per molecule), the branching frequency A (number of branches per arbitrarily selected repeat unit of molecular weight), and / (number of arms for a star) can be calculated. Determinations of A and / require equations specific to the type of branching for... 

Fig. 2 In the triple-detector overlay of dextran, the shift of the LS detector toward a higher M indicates polydispersity. Both the M-H and branching frequency plots show a randomly branched polysaccharide, with both short- and long-chain branching. = 230,000, = 540,000, M, =...

Table 1 Average molecular weights, polydispersity index, mole-percent branching agent, branching frequency, Mark-Houwink-a value, and melting temperature for the synthesized polyesters. L = linear PBA, TMP = trimethylol propane was used as a branching agent, BT = 1,2,4-butanetriol was used as branching agent ...

The content of the different branches is given in Table 5. The relation between the methyl branch frequency and the polymerization conditions is somewhat different compared to that of the others. The content of this branch structure decreases with decreasing polymerization temperature and monomer concentration, Figure 8. This is what could be expected from the mechanism for chain transfer to monomer ... 

The information in Table 35 is plotted in a three-dimensional form in Figure 105. The X-axis is the logarithm of MW. The y-axis is the branch concentration, in branches per 1000 carbon atoms. On the z-axis, one would normally plot the amount of polymer found at each (x,y) location. However, it is more informative to know where the branches are rather than where the polymer is in this 3D plot. Therefore, in Figure 105, the z-axis is the number of branches found at each (x,y) location. To clarify this point again The y-axis represents the branch frequency, and the z-axis is the number of branches, or the percentage of all branches. This... 

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