Molar mass distribution. See

Strictly speaking, Balke s system combined SEC in the first dimension with a mixed mode separation in the second dimension. Since SEC separates with respect to hydrodynamic volume and not molar mass, the copolymers under investigation could not be quantified with respect to molar mass distribution (see discussion in Sect. 3). The effect of the SEC separation was simply to obtain fractions with narrower molar mass distribution as compared to the total sample. Considering this fact, it is clear that for chemically heterogeneous copolymers no quantitative data can be obtained from the first dimension. Only the second dimension, separating with respect to chemical composition, can provide quantitative information on the chemical composition distribution. Accordingly, a coupled information on both MMD and CCD was not available for this system. 

Since chain transfer to polymer does not change the numbo- of polymo molecules formed, it has no effect upon the number-average molar mass, M . Furthermore, although it results in the formation of branched polymer molecules, only in the case of intermolecular diain transfer to polymer is thrae an effect upon molar mass distribution (see Section 1.3.4) which broadens, leading to increases... 

The kinetics of chain-reaction polymerization is illustrated in Fig. 3.28 for a free radical process. Analogous equations, except for termination, can be written for ionic polymerizations. Coordination reactions are more difficult to describe since they may involve solid surfaces, adsorption, and desorption. Even the crystallization of the macromolecule after polymerization may be able to influence the reaction kinetics. The rate expressions, as given in Appendix 7, Fig. A7.1, are easily written under the assumption that the chemical equations represent the actual reaction path. Most important is to derive an equation for the kinetic chain length, v, which is equal to the ratio of propagation to termination-reaction rates. This equation permits computation of the molar mass distribution (see also Sect. 1.3). The concentration of the active species is very small and usually not known. First one must, thus, ehminate [M ] from the rate expression, as shown in the figure. The boxed equation is the important equation for v. 

By calibrating the column or column set with a set of standards, a calibration curve of retention versus the logarithm of molar mass is constructed so that molar mass averages may be calculated for unknown polymers. Figure 6.10 is an example chromatogram of a separation of a polyDADMAC coagulant polyelectrolyte. The molar mass distribution, see Figure 6.11, is relative to the calibration standards used, polyethylene oxide in this example. 

Chain-transfer side reactions (see Scheme 1.1) can also cause substantial increases in D-values. Macrocychzation is particularly poor in this respect, leading to a complete equihbrium and an especially broad molar mass distribution (see e.g. Figure 1-4). On the other hand, a reversible polymerization devoid of macro-cyclization, but accompanied by the segmental exchange reactions, can fulfill the criteria of the living process [95-99]. However, in this case the D-value also increases with conversion, reaching at equilibrium a value which is predicted by Equation 1.24 and characteristic of the most probable molar mass distribution. Figure 1.7 illustrates the dependence of M /M determined for LA polymerization initiated with Sn(ll) alkoxide [98]. 

The melt flow index is a useful indication of the molar mass, since it is a reciprocal measure of the melt viscosity p. p depends very strongly on 77 ( ) (doubling of results in a 10.6 times higher 77 ). This relation is valid for the zero-shear viscosity the melt index is measured at a shear stress where the non-Newtonian behaviour, and thus the width of the molar mass distribution, is already playing a part (see MT 5.3.2). The melt index is a functional measure for the molar mass, because for a producer of end products the processability is often of primary importance. 

This produces a rise in the concentration of active centers and a corresponding increase in the propagation rate. Chains produced at this stage are longer, and this leads to a broadening of the molar mass distribution. The term gel effect is widely used to describe this effect, although no gel is actually formed in the system. The effect is also called the Trommsdorff effect (see Chapter 5). 

The structural complexity of synthetic polymers can be described using the concept of molecular heterogeneity (see Fig. 1) meaning the different aspects of molar mass distribution (MMD), distribution in chemical composition (CCD), functionality type distribution (FTD) and molecular architecture distribution (MAD). They can be superimposed one on another, i.e. bifunctional molecules can be linear or branched, linear molecules can be mono- or bifunctional, copolymers can be block or graft copolymers, etc. In order to characterize complex polymers it is necessary to know the molar mass distribution within each type of heterogeneity. 

For copolymers, in particular random copolymers, instead of discrete functionality fractions a continuous drift in composition is present (see Fig. 3). To determine this chemical composition drift in interrelation with the molar mass distribution, a number of classical methods have been used, including precipitation, partition, and cross-fractionation [2]. The aim of these very laborious techniques is to obtain fractions of narrow composition and/or molar mass distribution which are then analyzed by spectroscopy and SEC. 

From the Th-FFF retention data, it is possible to obtain a molar mass distribution after a suitable calibration for the determination of the Mark-Houwink constants (straight-line plot of log(D/DT) vs. log M [15]). Another possibility is to couple an absolute molar mass detector like MALLS (see Sect. 4.3.2) or a suitable detector combination such as an on-line viscometer coupled with a refractive index detector. This possibility does not require prior knowledge of DT... 

Liquid-liquid demixing in solutions of polymers in low molar mass solvents is not a rare phenomenon. Dembcing depends on concentration, temperature, pressure, molar mass and molar mass distribution function of the polymer, chain branching and end groups of the polymer, the chemical nature of the solvent, isotope substitution in solvents or polymers, chemical composition of copolymers and its distributions, and other variables. Phase diagrams of polymer solutions can therefore show a quite complicated behavior when they have to be considered in detail (see Ref la). 

Other strategies for controlling copolymer composition Although the use of monomer-starved conditions for control of copolymer composition is widespread, the low monomer feed rates which need to be used give rise to low rates of copolymerization and have significant effects upon the molar mass and molar mass distribution of the copolymers formed (see Section 7.4.4.4). Hence, alternative procedures have been developed which facilitate higher feed rates, but nevertheless allow for control of copolymer composition. These procedures are briefly described in this section. 

When functional homopolymers are synthesized, in addition to macromolecules of required functionality, functionally defective molecules are formed (see Fig. 4). For example, if a target functionality of f = 2 is required, then in the normal case species with f = 1, f = 0 or higher functionalities are formed as well [7], Deviation of the average functionality from the pre-assigned one may result in a decreased or increased reactivity, cross-linking density, surface activity etc. Each functionality fraction has its own molar mass distribution. Therefore, to fully describe the chemical structure of a functional homopolymer, the determination of the molar mass distribution (MMD) and the functionality type distribution (FTD) is required. 

When the molar mass distribution is not too wide, the mass average and area average for random coils and flexible rods are, within the experimental error, practially identical. A whole series of other averages, besides these two averages, may also be defined (see also Section 8),... 

Numerous Hevea varieties, referred to as clones in professional jargon, can be found in estates. Subramaniam was the first to study NR from different clone by size-exclusion chromatography (SEC) and to know about the native molar mass distribution (MMDq). MMDo is the molar mass distribution of polyisoprene leaving the tree, without any treatments (drying, shearing) that could modify it. As we see later, MMDq is a very important clonal parameter for prediction of some properties of raw commercial NR. 

Many different physico-chemical properties can be investigated by chromatographic techniques. Some special applications of SFC in these fields, not yet mentioned above, are, for example, the measurement of virial coefficients and partial molar volumes of mixtures, the determination of molar mass distributions, the investigation of adsorption phenomena, etc. for details see [7,13]. 

The ultrasonic degradation of polymers is an established and capable method for the production of homologues series of molar masses. Ultrasonic degradation does not lead to a broadening of the molar mass distribution and a separation of monomer units and is therefore an indispensable operation for the determination of [rj]-M-relationships (see above) from a single polymer sample. 

Here several [ j]-M-relationships are listed. Table 6.7 shows [rj]-M-relationships of important polymer-solvent systems. Most of these relationships where determined from sample sets with a very narrow molar mass distribution Q, the heterogeneity class is specified for each [/jJ-M-relationship (see Heterogeneity classes and the influence of the polydispersity on the [rj]-M-relationship in Chap. 8). The [ j]-M-re-lationships are only valid for the listed range of molar masses. More [ j]-M-rela-tionships are listed in Tables 6.2,6.4,6.5 and 8.5. For rare polymer-solvent systems and copolymers with a defined composition, the reader is referred to the Polymer Handbook [48], Gnamm and Fuchs [45] as well as [67,68]. 

The molar mass determined with an [/jJ-M-relationship is the so-called viscosity average molar masses M, rather than mass (M ) or number average (MJ molar mass (see Chap. 2). This seems to be peculiar on first glance, since the molar masses used for the determination of the [ /]-M-relationships were either number or mass average molar masses (depending on the determination method). However, the samples used for the determination of the [/j]-M-relationship should have had a very narrow molar mass distribution. The unknown sample on the other hand has an unknown distribution function of the molar mass. Only in the case that the distribution function of the unknown sample and the sample used for the determination are the same, or M are determined directly from the viscosimetric measurement. 

Diagrams like fig.l characterize upper critical miscibility behavior (UCM), mutual solubility increasing when the temperature is raised. The reverse behavior, lower critical miscibility (LCM) is also known and appears to be a general phenomenon in polymer mixtures. Fig.2 shows an example in which we see that the location of the miscibility gap is very sensitive to polymer chain length, an observation consistent with theoretical prediction [9]. Fig.3 illustrates the sensitivity to chain length, not only with respect to location but also with respect to the shape of the miscibility gap. In fig.4 we see that the molar-mass distribution (mmd) in one of the constituents may also influence the shape of the cloud-point curve. 

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