The Measurement of Molecular Weight Distribution in Polymers by Cross Linking—Solubility Methods1a

1964 ◽  
Vol 68 (8) ◽  
pp. 2258-2263 ◽  
Author(s):  
William W. Graessley

In long-chain polymers an insoluble network or gel may be produced when a number of the separate molecules are linked together. A theoretical derivation is given of the relationship between the amount of gel formed and the degree of cross-linking, in terms of the initial molecular weight distribution. It is shown that whatever the initial molecular weight distribution, incipient gelling occurs when there is on the average one cross-linked monomer per weight average molecule. The shape of the gel-cross-linking curve depends on the ratio of z average, z +1, . . . average molecular weight to the weight average. From experimental values of the curve it becomes possible to determine many of the constants of the molecular weight distribution in the original polymer. Expressions are derived for the number average, weight average and z average of the polymer as a function of cross-linking prior to gel formation, as well as the number and weight averages of the sol fraction after gelation. The average molecular weight between cross-links in the gel is calculated. A number of other functions of the sol and gel fractions are also given.


Author(s):  
Burak Erman ◽  
James E. Mark

Until quite recently, there was relatively little reliable quantitative information on the relationship of stress to structure, primarily because of the uncontrolled manner in which elastomeric networks were generally prepared. Segments close together in space were linked irrespective of their locations along the chain trajectories, thus resulting in a highly random network structure in which the number and locations of the cross-links were essentially unknown. Such a structure is shown in figure 10.1. New synthetic techniques are now available, however, for the preparation of “model” polymer networks of known structure. More specifically, if networks are formed by end linking functionally terminated chains instead of haphazardly joining chain segments at random, then the nature of this very specific chemical reaction provides the desired structural information. Thus, the functionality of the cross links is the same as that of the end-linking agent, and the molecular weight Mc between cross-links and the molecular weight distribution are the same as those of the starting chains prior to their being end-linked. An example is the reaction shown in figure 10.2, in which hydroxyl-terminated chains of poly(dimethylsiloxane) (PDMS) are end-linked using tetraethyl orthosilicate. Characterizing the un-cross-linked chains with respect to molecular weight Mn and molecular weight distribution, and then carrying out the specified reaction to completion, gives elastomers in which the network chains have these characteristics; in particular, a molecular weight Mc between cross-links equal to Mn, a network chain-length distribution equal to that of the starting chains, and cross-links having the functionality of the end-linking agent. It is also possible to use chains having a known number of potential cross-linking sites placed as side chains along the polymer backbone, so long as their distribution is known as well. Because of their known structures, such model elastomers are now the preferred materials for the quantitative characterization of rubberlike elasticity. Such very specific cross-linking reactions have also been shown to be useful in the preparation of liquid-crystalline elastomers. Trifunctional and tetrafunctional PDMS networks prepared in this way have been used to test the molecular theories of rubber elasticity with regard to the increase in non-affineness of the network deformation with increasing elongation.


2021 ◽  
Author(s):  
Fanfan Li ◽  
Yi Yu ◽  
Hanyu Lv ◽  
Guiting Cai ◽  
Yanwu Zhang

To overcome aggregation of porphyrins and realize heterogeneous catalysis with high active site loadings, the twisted ZnTHP-Me2Si and layered ZnTHP-Ph2Si are synthesized through cross-linking zinc tetraphenylporphyrin (ZnTHP) respectively with dichlorodimethylsilane...


Foods ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 591 ◽  
Author(s):  
Tae-Kyung Kim ◽  
Hae In Yong ◽  
Hae Won Jang ◽  
Young-Boong Kim ◽  
Yun-Sang Choi

Global concern about food supply shortage has increased interest on novel food sources. Among them, edible insects have been studied as a potential major food source. This study aimed to improve the functional properties of protein solutions extracted from Protaetia brevitarsis (PB) by use of transglutaminase (TG) as a cross-linking agent. After various incubation times (10, 20, 30, 60, and 90 min) with TG, the protein solutions were assessed with regard to their amino acid composition, protein nutritional quality, pH, color (yellowness), molecular weight distribution, thermal stability, foam ability (capacity and stability), and emulsion ability (capacity and stability). Incubation with TG changed the amino acid composition of the proteins and shifted the molecular weight distribution towards higher values, while improving the rest of the aforementioned properties. Since the incubation time for 90 min decreased the protein functionality, the optimum incubation time for cross-linking PB-derived protein with TG is 60 min. The application of TG to edible insect proteins ultimately increases its functionality and allows for the development of novel insect processing technology.


2013 ◽  
Vol 10 (2) ◽  
pp. 29
Author(s):  
Normah Ismail ◽  
Nur' Ain Mohamad Kharoe

Unripe and ripe bilimbi (Averrhoa bilimbi L.) were ground and the extracted juices were partially purified by ammonium sulfate precipitation at the concentrations of 40 and 60% (w/v). The collected proteases were analysed for pH, temperature stability, storage stability, molecular weight distribution, protein concentration and protein content. Protein content of bilimbi fruit was 0.89 g. Protease activity of both the unripe and ripe fruit were optimum at pH 4 and 40°C when the juice were purified at 40 and 60% ammonium sulfate precipitation. A decreased in protease activity was observed during the seven days of storage at 4°C. Molecular weight distribution indicated that the proteases protein bands fall between IO to 220 kDa. Protein bands were observed at 25, 50 and 160 kDa in both the unripe and ripe bilimbi proteases purified with 40% ammonium sulfate, however, the bands were more intense in those from unripe bilimbi. No protein bands were seen in proteases purified with 60% ammonium sulfate. Protein concentration was higher for proteases extracted with 40% ammonium sulfate at both ripening stages. Thus, purification using 40% ammonium sulfate precipitation could be a successful method to partially purify proteases from bilimbi especially from the unripe stage. 


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