MMD Molar mass distribution

Mass spectrometry can be used to measure the molar mass distribution (MMD) of a polymer sample by simply measuring the intensity, Nt, of each mass spectral peak with mass m . This is due to the fact that mass spectrometers are equipped with a detector that gives the same response if an ion with mass 1 kDa or 100 Da (actually any mass) strikes against it. In other words, the detector measures the number fraction and this implies that Nt also represents the number of chains with mass m,. Thus, the number-average molar mass, Mn, is given by ... 

In a polymerization process the chain length distribution or molar mass distribution (MMD) is influenced by a large number of factors and conditions the kinetics of the reaction plays a very important role. The calculation of the resulting MMD is thus very complicated. For one of the simplest cases, a step reaction with polycondensation, a first-order approach is given here. As an example we take a hydroxy acid HO-R-COOH, which, upon condensation, forms the chain -[-O-R-CO-]n. 

The difference between A and B is due to a difference in molar mass distribution MMD for A this is broader than for B (and for C). A broader MMD causes the polymer to deviate more strongly from Newtonian behaviour. A first approximating measure of the width of the distribution is Mw/Mn as far as the effect on the non-Newtonian behaviour is concerned, Mz/Mw would be a better measure. 

The molecular weight distribution (MWD) or molar mass distribution (MMD) informs us about the average molecular size and describes how regular (or irregular) the molecular size is. The MMD may vary greatly, depending on the method of synthesis of the polymer. 

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. 

A HE CHARACTERIZATION OF MODERN HIGH-PERFORMANCE POLYMERS is still a challenge for polymer scientists. Copolymers and complex polymer blends play an important role in many applications (i). A fast, reliable, and comprehensive method is needed to succeed in this task. Size-exclusion chromatography (SEC) is a standard method for the determination of molar mass distributions (MMDs) and molecular weights, if... 

Macromolecular or particulate samples fractionated by the FFF are usually not uniform but exhibit a distribution of the concerned extensive or intensive parameter [8] or, in other words, a polydispersity. Molar mass distribution (MMD), sometimes called molecular weight distribution (MWD), or particle size distribution (PSD) describes the relative proportion of each molar mass (molecular weight), M, or particle size (diameter), d, species composing the sample. This proportion can be expressed as a number of the macromolecules or particles of a given molar mass or diameter, respectively, relative to the number of aU macromolecules or particles in the sample ... 

Using columns with a porosity of 20 /tm is also recommended, in order to minimize shearing the long chains of the polyisoprene. As molar mass distribution (MMD) in natural rubber is quite broad (12 < / < 3), the columns need to offer a considerable separation range. 

Size-exclusion chromatography (SEC) is a well-established method for the determination of the molar mass distribution (MMD) of polymers. However, the determination of the MMD by SEC substantially excludes ultrahigh-molar-mass (UHMM) polymers. Actually, it is well accepted that UHMM polymeric samples degrade, by shearing or elongational forces, in the SEC columns. The upper limit of the molar mass for a successful SEC fractionation without degradation of the sample depends on the broadness of the MMD of the sample, from the SEC columns used and, obviously, from the experimental conditions. Successful SEC fractionations of narrow MMD standards up to 1 X 10 g/mol of molar mass have been reported. Instead, when the MMD of the sample is broad, rarely does the molar mass of the polymeric samples exceed the upper limit of 1 X 10 g/mol. 

The usual means of measuring molar mass distributions (MMDs) is gel permeation chromatography (GPC) which is described in Section 11.2.2.5. Denote the GPC trace as the signal G as a function of elution volume Veil it is assumed that the baseline has been subtracted. Appropriate calibration with monodis-perse standards yields the GPC calibration curve, which is the volumes at which monodisperse standards elute as a function of the molar mass M of the standard this is denoted V(A/ )... 

On-line determination of molar mass (MM) and molar mass distribution (MMD) has become possible with the introduction of an on-line gel permeation chromatograph. Such an instrument does automatic sampling, dilution, injection, elution, detection and analysis, much like an on-line gas chromatograph. Deconvolution is automatic, as is calibration from a mixture of standards. As with all on-line chromatographic techniques, maintenance and reliability are a problem f - large-scale production use. 

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. 

Contrary to the usual organic compounds, polymers are far from being homogeneuos maferials (i.e., polymer chains do not possess the same molar mass and chemical structure). As matter of fact, many synthetic polymers are heterogeneous in several respects. Homopolymers may exhibit both molar-mass distribution (MMD) and end-groups (EG) distribution. Copolymers may also show chemical composition distribution (CCD) and functionality distribution (FTD) in addition to the MMD. Therefore, different kinds of heterogeneity need to be investigated in order to proceed to the structural and molecular characterization of polymeric materials. 

The estimate of molar masses (MM) and of molar-mass distributions (MMD) is of primary interest in polymer characterization work, and much effort has been dedicated to develop suitable methods for their determination. End-group analysis provides important structural information for all the synthetic polymers. It allows also e estimation of molar masses in low polymers and gives clues about the procedure adopted in the synthesis. In fact, polymer samples having the same molecular structure may contain different end groups, due to synthetic routes or to end capping with different agents. If the end groups are chemically reactive, the polymer may be further modified to obtain different materials. 

Molar mass (MM) and molar mass distribution (MMD) values in macromo-lecular compounds can be calculated from their mass spectra, as discussed in Chapter 2. Most industrial polymers have average MM in the range of several tens of thousands and, often being polydisperse, their higher mass tails usually reach MM values of several hundred thousands and even higher. 

The chemical structure of a linear polyethylene homopolymer is solely defined by the molar mass distribution (MMD) of the resin. This important distribution, together with the additives incorporated and the final morphology achieved in the processing, defines the polymer performance in a given application. 

A polymer is a large molecule that contains repeat units of small molecules known as monomers. Polymers possess a molar mass distribution (MMD) and end groups that cap the repeat units. Complete polymer characterization is achieved when aU the above quantities are measured. Routine methods for synthetic polymer characterization exist and many textbooks [1,2] in polymer science extensively describe these methods. There is a definite possibility that, in the near future, mass spectrometry (MS) will be added to routine methods. This possibility implies that textbooks and also encyclopedic works may have to be modified. 

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. 

Due to the statistic character of polymer forming reactions, all quantities have a distribution. Therefore, only a mean value of the discussed properties can be determined. Polymeric properties depend in different ways on the mean values of the different types of distributions. The most important distribution is the molar mass distribution (mmd). The determination of the mmd and their mean values is the main task of polymer characterization. 

The polymerisation reactions are statistically driven processes. Therefore, unlike some natural polymers such as DNA, synthetic polymers always show, due to the reaction mechanisms involved in the production processes, a certain distribution of molar mass and not a distinct molecular weight. The molar mass of S5mthetic polymers can range from some thousand g/mol up to some million g/mol. As an example. Figure 1.4 shows the normalised molar mass distribution (MMD) curves of two different polyethylene samples. 

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