Molecular mass, determination polydispersity

The development of mass spectroscopic techniques such as matrix assisted laser desorption (MALDI) and electrospray mass spectrometry has allowed the absolute determination of dendrimer perfection [7,8], For divergent dendrimers such as PAMAM and PPI, single flaws in the chemical structure can be measured as a function of generation to genealogically define an unreacted site of or a side reaction producing a loop at a particular generation level. Mass spectromet-ric results on dendrimers, not only demonstrate the extreme sensitivity of the technique, but also demonstrate the uniformity of the molecular mass. The polydispersity index of Mw/Mn for a G6 PAMAM dendrimer can be 1.0006 which is substantially narrower than that of living polymers of the same molecular mass [7],... 

Very precise appraisals of polydispersities due to branch defects can be made by HPLC fractionation, electrophoresis and mass-spectral analyses of the components. The molecular-mass and polydispersity values thus obtained, corroborate branch-defect ranges determined by high-field 13C-NMR spectroscopy. 

Synthetic polyelectrolytes can be separated by capillary electrophoresis applying the same rules derived for the electrophoresis of biopolymers. In the reptation regime, determination of the molecular mass and polydispersity of the polyelectrolytes is possible. Introduction of chromophores facilitates the detection of non-UV-absorbing polymers. Indirect detection techniques can probably be applied when analytes and chromophores of similar mobilities are available. 

When the averaged molecular masses determined by CGE are compared with those given by the suppliers (measured via SEC), molecular masses determined by SEC are always lower. When the CGE values are compared with results from MALDI-TOF measurements a closer correlation could be found. This may be an indication that in SEC polymer adsorption on the matrix was the reason for higher elution volumes, resulting in lower molecular masses. Of course, polydispersity is also affected by adsorption. Consequently CGE is a fast and reliable method for characterization of the molecular masses of polyelectrolytes and their distribution. 

Finally, in the three last columns, we find quantities characterizing the polydispersion of the samples ratios Mw/Mn and Mz/Mw (different averages of the molecular mass) and polydispersity p. In Chapter 7, Section 3.2 we indicated how to determine the average Mw and M from the scattered intensity. We shall indicate in the next section how Mz is determined. 

Montaudo, M. S., Puglisi, C., Samperi, E, and Montaudo, G., Application of Size Exclusion Chromatography Matrix-assisted Laser Desorption/Ionization Time-of-flight to the Determination of Molecular Masses in Polydisperse Polymers, Rapid Comm. Mass Spectrom., 12, 519, 1998. 

The determination of polymer molecular mass and distribution by MALDI-MS requires not only accurate mass measurement but also quantitative measurement of ions. The equations used for molecular mass determination and polydispersity (PD) calculation are ... 

The analysis of a broad-polydispersity polymer (PD > 1.2) can be carried out by combining GPC or size-exclusion chromatography (SEC) with MALDI-MS [161-172]. In this approach, a wide-polydispersity polymer is first separated by GPC and fractions at a defined time interval are collected. The time interval is properly chosen so that the individual fraction would contain only a narrow-polydispersity (PD < 1.2) polymer, which can then be analyzed by MALDI-MS for accurate molecular mass determination. The molecular mass information generated from the MALDl analysis of aU individual fractions can be used to convert the time domain in the GPC chromatogram into a mass domain. The polymer distribution can be determined from this chromatogram. 

Mineo, P., Vitalini, D., Scamporrino, E., Bazzano, S., and Alicata, R. (2005) Effect of delay time and grid voltage changes on the average molecular mass of polydisperse polymers and polymeric blends determined by delayed extraction matrix-assisted laser desorption/ ionization time-of-flight mass spectrometry. Rapid Commun. Mass Spectrom., 19, 2773-2779. 

Montaudo MS, Puglisi C, Samperi F, Montaudo G. Application of size exclusion chromatography matrix-assisted laser desorption/ionization time-of-flight to the determination of molecular masses in polydisperse polymers. Rapid Comm Mass Spec 1998 12 519-28. 

Similar to off-line LC-MALDI, the coupling of SEC with ESI-MS can be applied not only for an accurate molecular mass determination of polymers with higher polydispersities, but also for monitoring the mechanism and synthesized products in photoinitiated, radical and controlled radical reversible addition-fragmentation chain transfer (RAFT)... 

The observation of molecular size or polydispersity and the subsequent determination of relative molecular mass, (MJ or molecular mass (weight) distribution (MWD), is the most common analytical application of SEC. The goal of these types of experiments is to either observe the solvated size of one or more molecular species or to observe the distribution of sizes present in a mixture... 

It should be stressed that the observed critical strain-rate for bond fracture (sf) in the case of a polydisperse fraction refers to the longest chain present in the sample. This quantity is significantly different from the critical strain-rate (r ) defined with respect to an average molecular mass whose value could be determined only after careful consideration of the degradation kinetics. 

A measure of the breadth of the molecular mass distribution is given by the ratios of molecular mass averages. The most commonly used ratio Mw/Mn — H, is called the polydispersity index. Wiegand and Kohler discuss the determination of molecular masses (weights) and their distributions in Chapter 6. 

Although MALDI-MS plays an outstanding role in dendrimer analysis, additional use is also made of modern ESI mass spectrometers for monitoring syntheses, for determination of relative molecular masses, and for studying the purity and polydispersity of dendrimers, including those of higher generations [34]. 

Colloidal systems are generally of a polydispersed nature - i.e. the molecules or particles in a particular sample vary in size. By virtue of their stepwise build-up, colloidal particle and polymer molecular sizes tend to have skew distributions, as illustrated in Figure 1.2, for which the Poisson distribution often offers a good approximation. Very often, detailed determination of relative molecular mass or particle size distribution is impracticable and less perfect experimental methods, which yield average values, must be accepted. The significance of the word average depends on the relative contributions of the various molecules or particles to the property of the system which is being measured. 

The problem, of course, comes from the implicit assumption that the gel matrix has no specific interactions with the soluble polymer, and that the relationship between effective volume and molecular weight is the same for the polysaccharide of interest and the standards. A recent development has been to place instruments which measure molecular weight at the exit of a GPC column, so that the column is used only for fractionation, and a full molecular weight distribution of a polydisperse polymer can be obtained. Viscometers and light-scattering monitors can be so employed, as can on-line electrospray mass spectrometers. The last technique is particularly powerful, since the masses determined by the mass spectrometer are absolute. 

Noda, Kato, Kitano, and Nagasawa23 have made systematic measurements of the osmotic pressure in order to verify (15.4.21). They used seven samples of poly(a-methyl) styrene of different molecular masses (see Table 15.13). Each sample was obtained by anionic polymerization, followed by a fractionation aimed at a reduction of polydispersity. The latter is characterized by the ratio Mw/Afn < 1.01. The solvent used was toluene. The interaction b for poly(a-methyl)styrene in toluene, experimentally determined, is about 1.5 nm1. 

An absolute method for molecular weight determination is matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF) (Kona et al., 2005 Creel, 1993 Nielsen, 1999 Cho et al., 2001). The sample is dispersed in a UV-absorbing matrix (e.g., trans -cinnamic acid or 2,5-dihydroxybennzoic acid). Irradiation with a UV laser induces evaporation of ionized polymer chains, which are then detected using TOF. The technique requires relatively narrow MWD samples. Alternative ionization methods have been employed, such as electrospray ionization mass spectrometry (ESI-MS), which may have advantages for certain polymer end groups (Vana et al., 2002). IFFF and MALDI-TOF can be coupled to analyze polydisperse samples and polymer mixtures (Kassalainen and Williams, 2003). 

Montaudo, G., Montaudo, M.S., Puglisi, C., and Samperi, E, Molecular Weight Determination and Structural Analysis in Polydisperse Pol3miers by Hyphenated Gel Permeation Chromatography/MALDI-TOF Mass Sp>ectrometry Method, Intemat. J. of Polym. Anal. Charact, 3, 177 (1997). 

High-temperature SEC finds wide application in polymerization studies, as the molecular mass distribution is an artefact of the various reactions involved in polymerization, initiation, termination, and transfer. It is diagnostic of living systems and random polymerization reactions, such as condensation and radical initiated polymerizations, for which the distributions are Poisson and normal respectively. In the polymerization of ethene and propene by Ziegler-Natta catalysts, the determination of the concentration of active centres as a function of conversion defines catalyst type. Similar studies have been made in the study of chain scission by thermal degradation or by irradiation, in defining the number of molecules produced from the inverse of the number average molecular mass and random chain scission eventually leads to a normal molecular mass distribution, with polydispersities close to 2.0. This has, of course, been widely used to produce narrow from broad molecular mass distribution samples prior to fractionation. 

The determination of extremely low values of polydispersity can be made using eqns (8.11) and (8.12), as pointed out in section 8.3. For this purpose, the plate height is measured at a number of values of the flow velocity , and a plot of H versus

is constructed (see Figure 8.13). The intercept of the plot is then determined by least squares this intercept is identified with as shown by eqn (8.12). From this, fi values are obtained by eqn (8.11), using known values of channel length L and selectivity S. For the 170000 molecular mass polystyrene plotted in Figure 8.13, the polydispersity is calculated to be )U = 1.0034 the reported value was no more specific than /z<1.06. Similar results were obtainedJbr other polystyrene standards jU = 1.005 for = 179000, fi = 1.006 for = 300000, and = 1.006 for = 411000. Thus the polymers characterized in this study were found to have much narrower distributions than anticipated by the suppliers [32]. 

MALDI-MS is a powerful tool for polymer characterization. Compared with analytical techniques currently used for polymer analysis, it provides several unique features. In MALDI-MS, molecular mass and molecular mass distribution information can be obtained for polymers of narrow polydispersity with both precision and speed. The accuracy, though difficult to determine due to the lack of well-characterized standards, also appears to be good [150]. The MALDI analysis of polymers does not require the use of polymer standards for mass caUbration. Furthermore, this technique uses a minimum amount of solvents and other consumables, which translates into low operational costs. MALDI-MS can also provide structural information, if the instrumental resolution is sufficient to resolve oligomers. In this case, monomer and end-group masses can be deduced from the accurate measurement of the mass of individual oligomers. This is particularly true when a FT-ICR MS is used for polymer analysis. With the use of MALDI-MS/ MS, stmctural characterization can be facilitated. Finally, impurities, byproducts, and subtle changes in polymer distributions can often be detected even for relatively complex polymeric systems such as copolymers. 

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