Effects of Cross-Linking and Branching on the Molecular Constitution of Diene Polymers

1948 ◽  
Vol 21 (2) ◽  
pp. 461-470
Author(s):  
Paul J. Flory
Keyword(s):  
Molecular Weight ◽  
Physical Properties ◽  
Reaction Mechanisms ◽  
Structural Unit ◽  
Random Distribution ◽  
Average Chain Length ◽  
Cross Linking ◽  
Gel Formation ◽  
Molecular Constitution ◽  
Kinetic Treatment

Abstract Reaction mechanisms whereby cross-linked and branched polymer structures may be formed during the polymerization of dienes are discussed. A kinetic treatment of the formation of cross-linkages via the occasional addition of a free radical to the unsaturated carbon of a structural unit of a previously polymerized molecule is presented. It is pointed out that the rate of this addition step relative to monomer addition can be deduced from the average chain length and the conversion at which gelation occurs. Cross-linkages introduced by the mechanism under consideration are not distributed at random, but the deviations from a random distribution are unimportant except at high conversions. Conditions are examined under which the cross-linking reaction decreases the total number of molecules more rapidly than they are formed. Physical properties of polymers (with particular emphasis on vulcanized rubbers) are most conveniently interpreted in terms of (1) the primary molecular weight (i.e., molecular weight in the absence of cross-linkages) and its distribution, and (2) the concentration of cross-linkages. The actual molecular-weight distribution, which may be severely distorted by the presence of cross-linkages, is inappropriate for direct correlation with the more important physical properties. The modifiers or regulators commonly employed in diene polymerizations suppress gel formation by reducing the primary molecular weight; they do not actually reduce cross-linking. This reduction in molecular weight is not without other undesired consequences, however.

Gel formation and molecular weight distribution in long-chain polymers

1954 ◽  
Vol 222 (1151) ◽  
pp. 542-557 ◽  
Keyword(s):  
Molecular Weight ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Average Molecular Weight ◽  
Cross Linking ◽  
Average Weight ◽  
Gel Formation ◽  
Theoretical Derivation ◽  
Experimental Values ◽  
Long Chain

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.

Gel formation by main-chain fracture of long-chain polymers

1955 ◽  
Vol 231 (1187) ◽  
pp. 521-534 ◽  
Keyword(s):  
Molecular Weight ◽  
Random Distribution ◽  
Main Chain ◽  
Average Molecular Weight ◽  
Gel Formation ◽  
Fracture Density ◽  
Chain Polymer ◽  
Infinite Extent ◽  
Limiting Value ◽  
Long Chain

The conditions are examined under which the fracture of main-chain bonds in a long-chain polymer, which would normally result in a decrease in average molecular weight, can nevertheless result in formation of a network of infinite extent (gel). It is assumed that the two end-groups produced at a fractured site can attack neighbouring molecules, and link them ­ selves to them. For an initially random distribution it is shown that gel formation will first occur when one molecule in three is thus fractured. The sol fraction is found to equal ( i /3 r ) 2 , where r/i is the average number of fractures per molecule; with increasing fracture density the sol therefore tends to zero. Where only a proportion of the fractures result in linking, the sol fraction decreases to a limiting value. Expressions are derived for many of the parameters of the sol and gel fractions and for the swelling. The results obtained are compared with those for crosslinking of polymers with a similar molecular weight distribution. To distinguish the process considered in this paper from that usually referred to as crosslinking, the term endlinking is proposed.

The Formation and Structure of Vulcanizates

1949 ◽  
Vol 22 (1) ◽  
pp. 96-104
Author(s):  
J. Bardwell ◽  
C. A. Winkler
Keyword(s):  
Mechanical Properties ◽  
Molecular Weight ◽  
Physical Properties ◽  
Network Structure ◽  
Weight Distribution ◽  
Elastic Behavior ◽  
Cross Linking ◽  
Structural Factors ◽  
Experimental Proof ◽  
Vulcanized Rubber

Abstract The characteristic mechanical properties of vulcanized rubber are believed to result from a network structure made up of chainlike molecules bonded together by occasional cross-linkages. In relating the physical properties of the vulcanizate to the structure of the network, it is therefore necessary to consider the concentration of cross-linkages and the molecular-weight distribution of the rubber molecules before cross-linking. Various theories have been proposed for the dependence of elastic properties on these structural factors, but experimental proof of the suggested relations has been meager, largely because of the complexities met with in, vulcanization reactions. In the present investigation some of these difficulties have been overcome, and the quantitative relations between the elastic behavior of GR-S and its network structure have thereby been revealed.

The Cross-Linking of Rubber by Pile Radiation

1955 ◽  
Vol 28 (1) ◽  
pp. 1-11
Author(s):  
Arthur Charlesby
Keyword(s):  
Molecular Weight ◽  
Radiation Dose ◽  
Average Molecular Weight ◽  
High Energy ◽  
Cross Linking ◽  
Gel Formation ◽  
Gel Fraction ◽  
Cross Links ◽  
The Cross ◽  
The Relationship

Abstract The degree of cross-linking produced in a rubber by high-energy radiation is proportional to the radiation dose. Unit radiation, as defined in the text, links 1.1 per cent of the isoprene units. The distribution of molecular weight prior to cross-linking agrees with a Poisson distribution. Gel formation begins for γ=0.5. From the radiation dose required to initiate gel formation, the initial average molecular weight can be deduced. The increase of gel fraction with radiation dose follows the relationship deduced theoretically in the first part of the article. Measurement of gel fraction gives an alternative method of calculating the initial average molecular weight. Where some cross-linking is present in the rubber prior to cross-linking, this may be evaluated. In accordance with the theory presented in the article, the viscosity of the sol fraction rises initially, then decreases as the radiation dose increases. This provides a third method of measuring molecular weight, or of relating viscosity to molecular weight, which can be deduced from measurement of gel fraction. The swelling of very lightly cross-linked gel has been compared with the Flory-Huggins relationship, which is found to hold down to very lightly cross-linked gels for which the cross-linking index is only 0.2. To obtain this agreement, it is necessary to consider the swelling of the dry gel, rather than the whole specimen, and to ignore the cross-links required to form the gel itself.

Network Chain Distribution and Strength of Vulcanizates

1969 ◽  
Vol 42 (3) ◽  
pp. 659-665 ◽  
Author(s):  
S. D. Gehman
Keyword(s):  
Physical Properties ◽  
Chain Length ◽  
Random Distribution ◽  
Length Distribution ◽  
Chain Scission ◽  
Point Of View ◽  
Average Chain Length ◽  
Chain Length Distribution ◽  
Network Chain ◽  
Chain Molecules

Abstract Physical characteristics of rubber network structures usually enumerated and discussed are network chain density, crosslink functionality, average chain length between crosslinks, entanglements which act somewhat like crosslinks, and free chain ends which are network defects. Chemical factors include structure of the chain molecules, type of crosslinks, whether monosulfide, disulfide or polysulfide, or direct carbon-to-carbon bonds. Side effects of vulcanization reactions such as chain scission or combination of minor quantities of chemical fragments from the vulcanizing system are also recognized. One might think that these variables would be adequate to account for physical properties of elastomers but explanations of strength aspects of vulcanizates are still unsatisfactory. Something is missing in these considerations, that is, the distribution of crosslinks along a main chain or the length sequences of monomer units in network chains. Usually a random distribution is implicitly assumed. If the distribution is always random and nothing can be done about it and it cannot be measured anyway, there may seem to be little point in writing about it. However, an ideally random distribution for all crosslinking systems and polymers seems very improbable. The importance of network chain length distribution for physical properties has been, of course, well recognized in theory. Bueche's calculations showed that viscoelastic resistance to deformation increased markedly with increased crosslink functionality, that is, as more chains are involved in the displacement of a crosslink. His molecular theory of tensile strength was based on the concept of short, overloaded network chains which snapped and transferred their loads to neighboring chains. An alternate point of view is that short chains are detrimental because they do not stress orient as well as longer chains.

scholarly journals The preparation of an alkali-soluble collagen from demineralized bone

1971 ◽  
Vol 124 (5) ◽  
pp. 915-919 ◽  
Author(s):  
G. D. Kemp ◽  
G. R. Tristram
Keyword(s):  
Molecular Weight ◽  
Physical Properties ◽  
High Molecular Weight ◽  
Soluble Protein ◽  
Weight Fraction ◽  
Cross Linking ◽  
High Molecular Weight Fraction ◽  
Soluble Collagen ◽  
Acid Soluble Collagen ◽  
Calf Skin

Ossein was solubilized by the action of alkali and a resulting high-molecular-weight fraction isolated. The chemical and physical properties of this fraction were studied and compared with those of an acid-soluble collagen prepared from calf skin by conventional techniques. From the results it is concluded that the alkali-soluble protein exhibits only minor differences from acid-soluble collagen, and that these differences can be ascribed for the most part to a decrease in the inter- and intramolecular cross-linking.

The Collagenic Molecular Structural Unit of Solid State Complexes

1971 ◽  
Vol 29 ◽  
pp. 478-479
Author(s):  
Kenneth M. Richter ◽  
John A. Schilling
Keyword(s):  
Molecular Weight ◽  
Solid State ◽  
Structural Unit ◽  
X Ray Diffraction ◽  
X Ray ◽  
Naoh Treatment

The structural unit of solid state collagen complexes has been reported by Porter and Vanamee via EM and by Cowan, North and Randall via x-ray diffraction to be an ellipsoidal unit of 210-270 A. length by 50-100 A. diameter. It subsequently was independently demonstrated by us in dog tendon, dermis, and induced complexes. Its detailed morphologic, dimensional and molecular weight (MW) aspects have now been determined. It is pear-shaped in long profile with m diameters of 57 and 108 A. and m length of 263 A. (Fig. 1, tendon, KMnO4 fixation, Na-tungstate; Fig. 2a, schematic of unit in long, C, and x-sectional profiles of its thin, xB, and bulbous, xA portions; Fig. 2b, tendon essentially unmodified by ether and 0.4 N NaOH treatment, Na-tungstate). The unit consists of a uniquely coild cable, c, of ṁ 22.9 A. diameter and length of 2580-3316 A. The cable consists of three 2nd-strands, s, each of m 10.6 A.

Cross-Linked αsγt-Chain Hybrids in Plasma Clots Studied by 1D- and 2D Electrophoresis and Western Blotting

1993 ◽  
Vol 70 (03) ◽  
pp. 438-442 ◽  
Author(s):  
B Grøn ◽  
C Filion-Myklebust ◽  
S Bjørnsen ◽  
P Haidaris ◽  
F Brosstad
Keyword(s):  
Molecular Weight ◽  
Monoclonal Antibodies ◽  
Human Plasma ◽  
Western Blotting ◽  
Isoelectric Point ◽  
Factor Xiii ◽  
Cross Linking ◽  
2D Electrophoresis ◽  
Complex Phenomenon ◽  
Fibrinopeptide A

SummaryFibrinogen and fibrin related chains in reduced human plasma as well as the bonds interlinking partially cross-linked fibrin from plasma clots have been studied by means of 1D- and 2D electrophoresis and Western blotting. Immunovisualization of reduced plasma or partially cross-linked fibrin with monoclonal antibodies specific for the α-chains or the γ-chains have shown that several bands represent material belonging to both chains. In order to decide whether these bands constitute αγ-chain hybrids or superimposed α- and γ-chain dimers, the cross-linked material was separated according to both isoelectric point (pI) and molecular weight (MW) using Pharmacia’s Multiphor II system. Western blotting of the second dimension gels revealed that partially cross-linked fibrin contains αsγt-chain hybrids and γ- polymers, in addition to the well-known γ-dimers and α-polymers. The main αsγt-chain hybrid has a pI between that of the α- and the γ-chains, a MW of about 200 kDa and contains Aα-chains with intact fibrinopeptide A (FPA). It was also observed that soluble fibrinogen/fibrin complexes as well as partially cross-linked fibrin contain degraded α-dimers with MWs close to the γ-dimers. These findings demonstrate that factor XIII-catalyzed cross-linking of fibrin is a more complex phenomenon than earlier recognized.

Effect of Plasticizer and Cross-Linking Agent on the Physical Properties of Protein Films

2005 ◽  
Vol 10 (1) ◽  
pp. 88-91 ◽  
Author(s):  
Myoung-Suk Lee ◽  
Se-Hee Lee ◽  
Yu-Hyun Ma ◽  
Sang-Kyu Park ◽  
Dong-Ho Bae ◽  
...  
Keyword(s):  
Physical Properties ◽  
Cross Linking ◽  
Protein Films
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