Carothers relation

As a fledgling faculty member at Harvard that fall, Carothers was somewhat surprised by its working conditions. In a cheery letter to Jack Johnson, Carothers related how a chemistry assistant pried ten thumbtacks out of the Harvard administration. The assistant was permitted to put in a requisition for thumb tacks to the number of ten (10), said thumb tacks to be purchased by the University and given to the assistant for use in connection with Chemistry 5, and the cost (purchase price + expenses incurred in their purchase) to be pro rated among the students of the course charged to their individual accounts. ... 

To establish the relation—also called the Carothers relation—between the number average degree of polymerization (X ) and the extent of reaction (p), it is necessary first to define these two quantities. The extent of reaction is defined as the fraction of reacted functional groups at that instant (t). If all molecules are bifiuictional and bivalent and if No and Nt are the number of (monomer or polymer) molecules present in the reaction medium at time 0 and t, respectively, the extent of reaction can be written as... 

The Carothers relation shows that a high degree of polymerization can be obtained only for an extent of reaction close to unity. Thus, to obtain... 

The addition of monovalent molecules, such as X-A or Y- , induces a deviation from the Carothers relation because they form nonreactive chain ends of or type. Addition of monovalent molecules is currently used to limit the degree of polymerization to a previously selected value. If N represents the number of -Y monovalent molecules used in excess and r=N N2 the stoichiometric imbalance with respect to N2, then the number average degree of polymerization can be written as... 

The gel point can be approximately predicted through an approach similar to that used to establish the Carothers relation. 

In the absence of any by-product eliminated, the reaction is naturally driven toward the product and high molar mass polymers can be obtained by satisfying the Carothers relation. 

The Carothers relation (Section 7.2.1) for nonstoichiometric conditions gives... 

The Carothers equation relates the number-average degree of polymerization to the extent of reaction and average functionality of a step-growth polymer. In the Carothers equation, the number-average degree of polymerization, X , relates to the extent of reaction, p, and average functionality, /avg, of the polymer system ... 

The name Nylon was given by the Du Pont company of America to their first synthetic condensation polymer formed by the reaction of difuncfional acids with difuncfional amines, ft had been made as part of the fundamental programme of W. H. Carothers to investigate the whole topic of polymerisation. The term has gradually been extended to other related polymers. These materials are strictly polyamides, but this term includes that otherwise distinct class of natural macromolecules, the proteins. The term nylon is retained for its usefulness in distinguishing synthetic polyamides from the broader class of such polymers. 

Carothers returned to Illinois chemistry department that fall to concentrate for two more years on organic chemistry with minors in physical chemistry and mathematics. His thesis topic was related to Adams signature discovery, a catalyst used to hydrogenate unsaturated fats for the shortening and soap industries. Carothers and 11 other collaborators produced 18 papers about the catalyst with Adams. At the same time, Carothers... 

Science, politics, labor relations, philosophy, music, literature, and sports—it seemed that everything interested Carothers. Soon after Sinclair Lewis novel Babbitt was published in 1920, he praised it as a literal depiction of Midwestern conformity and provincialism. When Marvel introduced him to fly-fishing in the Wisconsin woods, Carothers loved it. Although friends often found it difficult to tell when Carothers was pleased and happy, he was so excited trying to land a muskie from a rowboat that he almost jumped in after the fish. 

For the remainder of 1934 and throughout 1935, Carothers team continued to hunt for fibers. They focused on compounds related to Coffman s exciting polyamide filament. It was stronger than silk but Carothers was looking for filaments that were easier to polymerize and spin. Bolton, on the other hand, urged Carothers to focus on polymers made from cheap and plentiful materials. 

This equation relating the degree of polymerization to the extent of reaction was originally set forth by Carothers [1936] and is often referred to as the Carothers equation. 

Carothers pioneering studies were also based on aliphatic polyesters and then culminated in laying the foundations for condensation and step-growth polymerization and in establishing a relationship between molar mass and extent of reaction and the stoichiometric imbalance of functional groups. Fundamental studies relating structure to properties were carried out using these polymers. 

Tonic Dendrimers and Related Materials [R. Engel, Chapt. 3, pp. 73-99]. Silicon-based Stars, Dendrimers, and Hyperbranched Polymers [L. J. Mathias, T. W. Carothers, Chapt. 4, pp. 101-121]. 

A step polymerization yields high molecular weight polymer only after very high conversion is reached (Fig. 1) as described by Carother s equation [Eq. (2)] relating the number average degree of polymerization (DP ) to conversion (p). 

This section develops the relation between the number average size of polymers produced in a Step-growth polymerization and the fraction of functional groups which have been reacted at any point in the process. The basic equation which will be developed, Eq. (5-19), is called the Carothers equation. It illustrates the fundamental principles which underlie the operation of such polymerizations to produce good yields of polymers with the desired molecular weights. 

Carothers (17) recognized very early that if monomers with more than two reactive sites were polymerized, gelation resulted. He proposed a simple formula to relate the average functionality (/, number of reactive sites) to the degree of reaction (Pc) at which gelation could be expected. 

Farrington SM, McKinley AJ, Carothers AD, Cunningham C, Bubb VJ, Sharp L, et al. Evidence for an age-related influence of microsateUite instability on colorectal cancer survival. Int J Cancer 2002 98 844-50. 

One of the best-known polymer condensation processes is the reaction between hexa-methylenediamine and adipic acid, shown in Figure 25.6. The final product, called nylon 66 (because there are six carbon atoms each in hexamethylenediamine and adipic acid), was first made by Wallace Carothers at Du Pont in 1931. The versatility of nylons is so great that the annual production of nylons and related substances now amounts to several billion pounds. Figure 25.7 shows how nylon 66 is prepared in the laboratory. 

We shall follow Carothers definition of polymerizability 27), described in thermodynamic terms, and relating the polymerizability to the free energy of polymerization (AGp). According to this definition, the more negative AGp the higher the polymerizability. Since AGp = RT In [M]e, the more negative AGp, the lower the equilibrium monomer concentration. 

Carothers s early research at Du Pont focused on products related to acetylene, whose molecules were known to form long chains. With Arnold Collins, in 1931, he produced polychlorobutadiene, better known by its commercial name Neoprene, the first wholly synthetic rubber to be manufactured commercially (beginning in 1933). 

Completely synthetic fibers were also to take their place in the world. The leader, here, was the American chemist Wallace Hume Carothers (1896-1937). He, together with a Belgian-American chemist, Julius Arthur Nieuwland (1878-1936), had investigated polymers related to, and having some of the elastic properties of, rubber. The result, in... 

W.H. Carothers, the pioneer of step-growth reactions, proposed a simple equation relating to a quantity p describing the extent of the reaction for linear polycondensations or polyadditions. 

The Carothers equation is particularly enlightening when we examine the numerical relation between x andp thns, for p = 0.95 (i.e., 95% conversion), x = 50 and when p = 0.99, then x = 100. In practical terms, it has been fonnd that for a fiberforming polymer such as nylon-6.6 NH(CH2)6NHCO(CH2)4CO the value of... 

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