Monomeric unit volume

The partial specific volume of the monomeric unit in PGA was found to be approximately 3 per cent higher than the value of D-galacturonic acid... 

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]

Fig. 4 Curves Xsp versus copolymer composition X = X for macromolecules of length / = 103 at values of parameters (Eq. 20) equal to b- 0.01 and h-2 (2) 5 (3) 15 (4). Asymptotic dependences at h 0 and h oo are depicted by thin lines (Eq. 1) and (Eq. 5), respectively. Volume fraction of monomeric units in a globule = 0.9...

In addition to monomeric compounds, Tabemaemontana plants contain many bisindole alkaloids that are classified on the basis of constituent monomeric units, as in the extensive review by Cordell and Saxton in Volume XX of this series (14). This classification is more rational and comprehensive than others (I, 13, 15) and will be used as a guide for the representation of structural formulas and for the discussion of the chemistry of single alkaloids. 

In earlier experiments the effect of branching on the second virial coefficient was not seriously considered because the accuracy of measurements were not sufficient at that time. With the refinements of modern instruments a much higher precision has now been achieved. Thus A2 can also now be measured with good accuracy and compared with theoretical expectations. The second virial coefficient results from the total volume exclusion of two macromolecules in contact [3,81]. Furthermore, this total excluded volume of a macromolecule can be expressed in terms of the excluded volume of the individual monomeric units. In the limit of good solvent behavior this concept leads to the expression [6,27] as shown in Eq. (24) ... 

The packing geometry may be characterized by the distribution functions p (/) representing the density of monomeric units with partial free-volume /. ... 

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... 

Taking into account the equation derived, the author managed to calculate the distribution of the free-volume for monomeric units p (vf) as a function of v f for vulcanizates of different crosslinking density. 

All excluded volume theories for branched chains suffer, however, from a principal deficiency since the assumption is tacitly made that all monomeric units in the molecule may have, in principle, the chance to interact with each other. This is, however, a too extensive assumption since for sterical reasons two remote segments can never form a contact. Hence, the excluded volume effect is highly overestimated for densely branched chains. In fact, highly branched polymers show the phenomenon of swelling but no detectable distortion of Gaussian chain behavior117,137,138,179. ... 

A theoretical model predicting the shape-structure relationship between the monomeric units and their aggregates was developed by Israelachvili and was based on statistical mechanics of phospholipids.23 This model predicts the type of the aggregate formed on the basis of the packing parameter (P), which relates the volume of the molecule (V) to its length (1) and to the mean cross-sectional (effective) head group surface area (a) ... 

The coordination polymerisation and copolymerisation of heterocyclic monomers have been restricted in industry to a much smaller volume than the polymerisation and copolymerisation of hydrocarbon monomers polyether elastomers from epichlorohydrin and ethylene oxide or propylene oxide, and allyl glycidyl ether as the vulcanisable monomeric unit, are produced on a larger scale [4-7],... 

Using these Va values (va 3 x 10 molcm" ) together with other molecular parameters, i.e. molar mass of monomeric unit M = 71 gmol , density of the dry polymer p = 1.35 gcm , T = 298 K, (p = 0.037, dielectric constant D = 80, molar volumes Vi of the mixtures acetone-water (taken from [6,423), and the degrees of ionizations i = Xmns> the dependences of the interaction parameter x 9i were calculated from experimental (pz values by means of Eq. 

In the following two sections we first consider colls In solutions which are so dilute that coll-coll Interaction does not play a role. Section 5.2a deals with random-walk chains where the Interaction between the units within one chain may be neglected. We denote these as ideal chains. Section 5.2b treats swollen coils In which the monomeric units repel each other due to so-called excluded volume effects. 

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