Synthesis and Dilute-Solution Behavior of Model Star-Branched Polymers

1978 ◽  
Vol 51 (3) ◽  
pp. 406-436 ◽  
Author(s):  
B. J. Bauer ◽  
L. J. Fetters

Abstract The occurrence of polymers branched in a random fashion is common. Chain transfer reactions can cause short- and long-chain branching in polymerizations such as the high-pressure polymerization of ethylene. Branching can also be introduced intentionally by the use of a polyfunctional monomer in end-linking polymerizations. Similar branching can be produced in addition polymerizations by the use of a small amount of difunctional monomer, e.g., divinylbenzene. There also has been much interest in graft polymerization by which long chain branches can be introduced onto a backbone, which is often a different polymer from the branches. The properties of branched polymers can be quite different from those of linear polymers of the same molecular weight. For example, bulk viscosities as well as concentrated and dilute solution viscosities can be lower for branched polymers than for a linear material of equivalent molecular weight. As an example, the melt processing behavior of polymers can be manipulated by alterations in the average molecular weight, molecular weight distribution, and the frequency and length of long branches in the molecules. Thus, there is an obvious need to correlate and characterize the type and degree of branching in a polymer with its effect on the physical properties in solution or melt. In all of the above examples of branching, there is a mixture of branched and unbranched material. The unbranched and branched polymers can have a wide molecular weight distribution, as can the branches themselves. Also, the frequency of branches and the segment lengths between branch points can vary. Hence, the physical properties of such materials represent an average of the properties of all the different species present.

1965 ◽  
Vol 38 (4) ◽  
pp. 907-920
Author(s):  
Gerard Kraus ◽  
J. T. Gruver

Abstract The steady-state viscosity of a number of cis-polybutadienes was determined as a function of shear rate and temperature by use of a capillary rheometer. Polymers investigated differed in molecular weight distribution and long chain branching. None of the polymers exhibited Newtonian behavior, even at the lowest shear rates attainable. Nevertheless, for polymers of similar molecular weight distribution and minimum branching, all the capillary viscometer data could be reduced to a single curve by a reduced variable treatment. The molecular weight shift function was found to be the same as for polymers exhibiting a Newtonian flow range, i.e., a 3.4th power law in weight-average molecular weight. Broadening the molecular weight distribution or increasing the degree of long-chain branching led to increasingly pronounced non-Newtonian behavior. Tensile creep experiments showed nonlinear viscoelastic behavior for all polymers studied, even at small strains. This behavior was most pronounced in the more highly branched polymers. At very low stresses some of these polymers exhibited extremely high viscosities, the strain being almost completely recoverable. Under larger stresses the viscosity of these rubbers dropped several decades and in the capillary extrusion experiments these polymers flowed readily. This is the same behavior observed previously in high molecular weight branched (multichain) narrow distribution polybutadienes. It is tentatively explained by a constraint of the branch points on the slippage of chain entanglements. The fact that all cis-polybutadienes exhibit this behavior, while linear polybutadienes made by organolithium initiation do not, suggests that all cis-polybutadienes may be branched to some extent.


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.


2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Sachin Shanbhag

The extreme sensitivity of rheology to the microstructure of polymer melts has prompted the development of “analytical rheology,” which seeks inferring the structure and composition of an unknown sample based on rheological measurements. Typically, this involves the inversion of a model, which may be mathematical, computational, or completely empirical. Despite the imperfect state of existing models, analytical rheology remains a practically useful enterprise. I review its successes and failures in inferring the molecular weight distribution of linear polymers and the branching content in branched polymers.


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