Number of monomeric units

Chain length is another factor closely related to the structural characterization of conducting polymers. The importance of this parameter lies in its considerable influence on the electric as well as the electrochemical properties of conducting polymers. However, the molecular weight techniques normally used in polymer chemistry cannot be employed on account of the extreme insolubility of the materials. A comparison between spectroscopic findings (XPS, UPS, EES) for PPy and model calculations has led some researchers to conclude that 10 is the minimum number of monomeric units in a PPy chain, with the maximum within one order of magnitude n9- 27,i28) mechanical qualities of the electropolymerized films,... 

Another kind of situation arises when it is necessary to take into account the long-range effects. Here, as a rule, attempts to obtain analytical results have not met with success. Unlike the case of the ideal model the equations for statistical moments of distribution of polymers for size and composition as well as for the fractions of the fragments of macromolecules turn out normally to be unclosed. Consequently, to determine the above statistical characteristics, the necessity arises for a numerical solution to the material balance equations for the concentration of molecules with a fixed number of monomeric units and reactive centers. The difficulties in solving the infinite set of ordinary differential equations emerging here can be obviated by switching from discrete variables, characterizing macromolecule size and composition, to continuous ones. In this case the mathematical problem may be reduced to the solution of one or several partial differential equations. 

In order to analyze the rate of the decay of chemical correlations in macromolecules of proteinlike copolymers, it is necessary to calculate the dependence on n of the irreducible correlator o>ap(n) = Yap(n) - XaXp where the reducible correlator Yap(n) is obtained by formula (Eq. 45). Correlator coap(n) is calculated as the sum of series (Eq. 45), each item of which is the product of two cofactors. The first of them is controlled just by the number of monomeric units l in a globule, as well as by their volume fraction [Pg.160]

Data concerning the chain conformations of isotactic polymers are reported in Table 2.1. In all the observed cases the torsion angles do not deviate more than 20° from the staggered (60° and 180°) values and the number of monomeric units per turn MIN ranges between 3 and 4. Chains of 3-substituted polyolefins, like poly(3-methyl-l-butene), assume a 4/1 helical conformation (T G )4,45,46 while 4-substituted polyolefins, like poly(4-methyl-1-pentene), have less distorted helices with 7/2 symmetry (T G )3.5-39 When the substituent on the side group is far from the chain atoms, as in poly(5-methyl-1-hexene), the polymer crystallizes again with a threefold helical conformation (Table 2.1). Models of the chain conformations found for the polymorphic forms of various isotactic polymers are reported in Figure 2.11. 

Number of monomeric units in a macromolecule an oligomer molecule, a block, or a chain. 

Important characteristics of chitosan are its MW, viscosity, DD (Bodek, 1994 Ferreira et al., 1994a,b), crystallinity index, number of monomeric units, water retention value, pKa, and energy of hydration (Kas, 1997). Chitosan has a high charge density, adheres to negatively charged surfaces, and chelates metal ions. 

Miller37 supposed that the right side of Eq. (48) was equal to the number of monomeric units in a so-called cooperative unit Z at Tg. In this case... 

In Eq. (93) the coefficient a is supposed to be the sum of the expansivities of each region, taking into account their number fraction [Eq. (91)]. In deriving Eq. (93) it was assumed that at temperature T some monomeric units are in the glassy and some in the liquid state in accordance with the distribution function. The integral value, representing the number of monomeric units in the liquid state diminishes from NpjifM at the temperature above Tg where a = a( to zero below Tg (a = Og). If all monomeric units have the same partial free-volume/, the transition to the liquid... 

Number of monomeric units per turn Identity period referred to one monomeric unit, A Ref. 

According to the proposed model, the experimentally found variation of optical activity with temperature should be connected with numerous factors the most important of them are the absolute values of the optical activity of each allowed conformation, the variation with temperature of the ratio between the number of monomeric units spiraled in one and in the other screw sense and the variation with temperature of the percentage of monomeric units having a different conformation from that of the monomeric units included in the spiraled sections. 

Fig. 31. Molecular weight dependence of (S2) for the ABC model. The numbers indicate the branching probability p in Oq = aAp. The value 1/p gives the number of monomeric units between two branching points104 ...

Another membrane property physically affected by flavonoids is the surface potential. Working with liposomes composed of PC and PS, we found that (—)-epicatechin and certain procyanidins (dimer to hexamer) decreased liposome surface potential. This effect relied on both, procyanidin concentration and number of monomeric units [Verstraeten et al., 2003]. On the other hand, when liposomes were composed exclusively of PC, it was found that (—)-epi-catechin dimers Al and B2, and the trimers A and C2 increased liposome surface potential in a concentration-dependent manner [Verstraeten et al.,... 

The results of the first four polymers are listed in Table I the internal rotation angles of the main chain, x. and x , the number of monomeric units per turn, N, for the calculated stable conformations, and also the values for the structure determined by x-ray analyses. In the case of polypropylene, the number of monomeric units per turn is 2.91, very close to the x-ray value of 3.0. This result for polypropylene is essentially the same as those of Natta et al. (32) and Liquori et al. (33). For the three other polymers, good agreements were also obtained between the predicted models and x-ray structures in spite of the simple assumption of considering only intramolecular interactions. This... 

The chain length can be expressed as degree of polymerisation P (number of monomeric units in the chain), or, in most cases, as molar mass (or molecular weight) in g/mol. Sometimes the better unit, kg/mol is used the difference is a factor of 1000. In this book the older unit, g/mol, will mostly be used. 

All theoretical treatments of the molecular weight dependence indicate the number of monomeric units in loops increases monotonically with molecular weight, whereas the number of units in tails approaches an asymptotic limit, i.e., the fraction of units in tails must be a decreasing function of molecular weight. The molecular weight invariance we observe indicates the mobile units are predominantly in loops, and not tails. 

The statistical polymer method proposed recently by the author [6] considers polymeric systems as sets of assemblages possessing structures averaged over all these of polymers containing the same numbers of monomeric units, i.e., statistical polymers. For the case when one is interested in the evaluation of the weight distribution and/or additive (extensive) parameters like energy, entropy, etc., one can consider statistical polymers instead branched cross-linked ones. 

Statistical polymer is defined as the averaged structure exhibiting all possible structures of polymers containing the same number of monomeric units. 

On the other hand, the same parameters are easily estimated from the total number of monomeric units ... 

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