End groups analysis

End-group analysis can be used to determine of polymer samples if the substance contains detectable end groups, and the number of such end groups per molecule is known beforehand. 

End-group an ysis has been applied mainly to condensation polymers, since these polymers by their very nature have reactive functional end groups. The end groups are often acidic or basic in nature, as exemplified by the carboxylic groups of polyesters or the amine groups of polyamides such groups are conveniently estimated by titration. From the experimental data M is derived according to 

Problem 4.3 A sample (3.0 g) of carboxyl terminated polybutadiene (CTPB) required titration with 20 mL 0.1 N KOH to reach a phenolphthalein end point. Calculate M of the polymer. 

End-group analysis yields the equivalent weight of the polymer. Me, which is the mass of the polymer per mole of end groups and related to by 

The functionality / of low-molecular-weight functionalized prepolymers (e.g., polyether polyols used in the preparation of polyurethanes) is often determined by combining the functional group analysis (which yields the equivalent weight of the polymer. Me) with another suitable method of molecular weight (M ) determination, such as vapor phase osmometry. Note that in this respect the functional groups do not have to be end groups. 

End-group analysis is a chemical method used for calculating the of a polymer sample whose molecules contain reactive functional groups at one end or both ends. can be expressed as shown next  

Problem 4.4 A sample (2.0 g) of polyether polyol prepolymer (M = 2048) dissolved in chlorohydrocar-bon solvent was treated with excess succinic anhydride to convert each hydroxyl group in the polyol to a carboxyl group by formation of succinic half-ester. A sample (1.0 g) of this treated polymer recovered from the solution by precipitation (in excess of ethanol) required 12.8 mL of N/10 KOH for carboxyl titration. Determine the hydroxyl functionality of the polyol. 

In cases where the end-groups are known and their concentration can be determined, knowledge of their abundance allows a determination of M . The sensitivity of this method decreases and the chain length becomes greater. Some end-groups can be determined using spectroscopic techniques and others through titration. 

Example 8.1 In order to determine the number of carboxyl end groups in a sample of polyethylene terephthalate, Pohl dissolved 0.15 g of the polymer in hot benzyl alcohol, to which some chloroform was subsequently added [7]. This solution, when titrated with 0.105 N sodium hydroxide, required 35 pL of the 

Solution Because 30 pL of 0.105 gram equivalent per liter of the base reacted with the polymer, the concentration of gram equivalents of end groups was 

The number-average molecular weight is calculated from the analytically determined end-group content according to the following relationship  

The non-thermodynamic methods for evaluation of M have their basis in the determination of the number of moles of end-groups of a particular 

Thus end-group analysis is restricted to low molar mass polymers with well-defined structures and stinguishable end-groups. The upper limit for accurate measurement of Mn is dependent upon the sensitivity of the technique used to determine the end-group concentration, but typically is IxlO tol.SxlO gmor  

End-group analysis yields the equivalent mass (sometimes called the equivalent weight) of the polymer, Af, which is the mass of polymer per mol of end-groups. If for a polydisperse polymer sample, is the number of moles of polymer molecules of molar mass M/, and / is the number of analysable end-groups per polymer molecule then 

TABLE 3.5 Theoretical effects of low molar mass impurities upon the value of M as calculated using Equation (1.6) 

Chemical methods can also be applied to determine in cases where the chemical structure of the polymer, especially its end group, is known in advance. The requirements are that a definite end group exists in each molecule, the polymer is linear and the molecular weight of the polymer is relatively low (up to about 10 ). Polyamides (mainly nylon-6 and nylon-6, 6) and poly (ethylene terephthalate) are good examples. 

Condensation polymerisation of nylon salt or an addition polymerisation of e-caprolactam yields polymers having a carboxyl group and an amino group at either end of the chain. If we express the mole number of the carboxyl and amino groups per one gram of the sample by [COOH] and [NHt], is given by  

Eqn (5.23) is derived for the case when [COOH] = [NH2]. In the case when the number of moles of carboxyl groups formed is not equivalent to the number of amino groups formed ([CCOHj [NH2]),M is given by  

Step addition and step condensation polymerization processes give rise to polymers containing distinctive functional groups at chain ends. The nature of the end groups will depend on the precise chemistry of the polymerization process. For example, linear polyurethanes are produced by reaction between diisocyanates and diols. If a perfect 1 1 stoichiometry of the reactants is used in the synthesis, on average each polymer chain must contain one isocyanate functional group and one alcohol group. If a 2 1 molar ratio of reactants is used, when the isocyanate is in excess, all the chain ends will have isocyanate functionality, and all will have alcohol functionality at the chain ends if a two-fold excess of diol is used. 

End-group methods produce an equivalent mass, namely the mass of polymer per mol of end-groups. For a polydisperse polymer of molecular weight Mf containing iV,. moles of polymer molecules, if the number of functional groups is /, then 

Knowing that M = liVf Af,/SyV, and that it is a constant, then the equivalent mass is given by M //, from which can be calculated. 

If it is possible to analyse end groups of a particular specimen of polymer, it may be possible to use the data to determine number average relative molar mass. If the molecules are branched the degree of branching can be measured from a combination of end group analysis and relative molar mass determination (determined by an alternative method). 

One major drawback of end group analysis is that it rapidly becomes inaccurate as relative molar mass increases. This arises because the percentage of the end groups becomes smaller and smaller, and hence more and more uncertainty attaches to the numerical values of end group content that may be obtained. To illustrate this point, let us consider a polyester with acid end groups being determined by titration. Results for such titrations are shown in Table 6.5. 

From Table 6.5 quantitative determination of end groups can be seen to be increasingly uncertain particularly above a value of of 10 000. Nonetheless, end group analysis may be useful in certain circumstances, particularly for lower molar mass polymers and oligomers, where it may be a fairly straightforward approach to obtaining useful data. 

One major drawback of end group analysis is that it rapidly becomes inaccurate as relative molar mass increases. This arises 

Tivo other techniques are also used to measure Af of relatively low-molecular-weight polymers. These are end-group analysis and vapor phase osmometry. 

Problem 4.5 A sample (2.0 g) of polyether polyol prepolymer (M = 2048) dissolved in chlorohydrocarbon solvent was treated with excess succinic anhydride 

Since each polypeptide contains an iV-terminal and a C-terminal residue, the number of distinct subunits in a protein can be determined by identifying the 

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The method of end group analysis for molecular weight determination is not only simple to understand, but can also be done with ordinary laboratory equipment in many instances. 

Note that the method of end group analysis is inapplicable to copolymers, since the presence of more than one repeat unit adds extra uncertainty as to the nature of chain ends. The above example included the remark that the molecular weights calculated in the example were average values. In the next section we shall examine this point in greater detail. 

This expression is consistent with the analysis of each of the lines in Table 5.1 as presented above and provides a general answer to one of the questions posed there. It is often a relatively easy matter to monitor the concentration of functional groups in a reaction mixture as we saw in discussing end group analysis as a method for molecular weight determination in Sec. 1.7. Equation (5.4) is... 

Table 9.3 lists the intrinsic viscosity for a number of poly(caprolactam) samples of different molecular weight. The M values listed are number average figures based on both end group analysis and osmotic pressure experiments. Tlie values of [r ] were measured in w-cresol at 25°C. In the following example we consider the evaluation of the Mark-Houwink coefficients from these data. 

Polyester composition can be determined by hydrolytic depolymerization followed by gas chromatography (28) to analyze for monomers, comonomers, oligomers, and other components including side-reaction products (ie, DEG, vinyl groups, aldehydes), plasticizers, and finishes. Mass spectroscopy and infrared spectroscopy can provide valuable composition information, including end group analysis (47,101,102). X-ray fluorescence is commonly used to determine metals content of polymers, from sources including catalysts, delusterants, or tracer materials added for fiber identification purposes (28,102,103). 

Hydroxyl number and molecular weight are normally determined by end-group analysis, by titration with acetic, phthaUc, or pyromellitic anhydride (264). Eor lower molecular weights (higher hydroxyl numbers), E- and C-nmr methods have been developed (265). Molecular weight deterrninations based on coUigative properties, eg, vapor-phase osmometry, or on molecular size, eg, size exclusion chromatography, are less useful because they do not measure the hydroxyl content. 

Among the techniques employed to estimate the average molecular weight distribution of polymers are end-group analysis, dilute solution viscosity, reduction in vapor pressure, ebuUiometry, cryoscopy, vapor pressure osmometry, fractionation, hplc, phase distribution chromatography, field flow fractionation, and gel-permeation chromatography (gpc). For routine analysis of SBR polymers, gpc is widely accepted. Table 1 lists a number of physical properties of SBR (random) compared to natural mbber, solution polybutadiene, and SB block copolymer. 

The molecular weight and molecular weight distribution may be determined by conventional techniques. As the resins are of comparatively low molecular weight it is possible to measure this by ebullioscopic and by end-group analysis techniques. 

End-group analysis reveals several things. First, it identifies the N- and C-ter-minal residues in the polypeptide chain. Second, it can be a clue to the number of ends in the protein. That is, if the protein consists of two or more different polypeptide chains, then more than one end group may be discovered, alerting the investigator to the presence of multiple polypeptides. 

Although the initial radical formed from the reaction of Ce(rV) ion and acetylanilide (AA) and N-p-tolylacet-amide (PTA) has never been observed in the ESR studies, the presence of AA, PTA moieties in the end group of PAN obtained from initiating the CAN-AA, CAN-PTA system have been detected by the FT-IR spectra analysis method. Similar results were observed in the end group analysis of CAN-phenylcarbamate, CAN-N-acyl-N -tolylurea initiation systems. 

Based on the ESR studies and the end group analysis, the initiation mechanism of Ce(IV) ion redox systems is proposed as ... 

MMA and DMAPMA poly(MMA-co-DMAPMA) 23, obtained by radical copolymerization, can produce a photografting reaction with acrylonitrile (AN) using BP as the initiator [61]. The formation of a graft copolymer, poly[(MMA -c<7-DMAPMA)- -AN] was confirmed by FT-IR spectrophotometry. Based on ESR studies and end group analysis, the mechanism of grafting reaction is proposed as follows ... 

Most recent work is in accord with mechanism (b). In an effort to distinguish these mechanisms studies on model propagating species have been carried out.IS6 liW For S-MMA polymerization initiated by AIBMe- -13C (Scheme 8.13) it has been established by end group analysis that extremely small amounts of ethyl aluminum sesquichloride (<10 3M with 1.75 M monomers) are sufficient to cause a substantial enhancement in specificity for adding S in the initiation step. This result suggests that complexation of the propagating radical may be sufficient to induce alternating copolymerization but does not rule out other hypotheses. 

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