carothers equation polymer

In step-growth polymerization the Carothers equation or Carothers equation gives the degree of polymerization X n for a given fractional monomer conversion p. N In step-growth polymerization the Carothers Equation Carothers Equation gives the degree of polymerization Xn for a given fractional monomer conversion p Odain 2004.

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Other Polymers of Interest Obtained by Step-Growth.

. There are several versions of this equation proposed by Wallace Carothers who invented nylon in 1935. Thus the second term of the Carother equation vanishes and the critical extent of the reaction p c is given by. Two monomers in equimolar quantities.

You may be surprised really how high extent of reaction needs to be in order to get polymers of any significant length especially as your reactant ratio deviates more greatly from 1. Pn Approach 8 Network Formation. This equation was originally proposed by Carothers and is often referred to as.

Polymer molecular weight in a step-growth polymerization is determined by the fractional conversion p of the monomer during the polymerization. There are several versions of this equation proposed by Wallace Carothers who invented nylon in 1935. This equation was proposed by Wallace Carothers who invented nylon in 1935.

Derivation of the Carothers equation. In step-growth polymerization the Carothers equation or Carothers equation gives the degree of polymerization X n for a given fractional monomer conversion p. To test his theory he proposed to create polymers by using well-known chemical reactions to join together many small molecules.

The theory was initially conceptualized by Paul Flory in 1941 and then was further developed by Walter Stockmayer in 1944 to. 1 The initial studies by Carothers on the preparation of aliphatic polyesters from the condensation reaction of diacids and diols are often cited as the first intentional synthesis of linear polymers by step-growth reactions. The Carothers equation is based on the assumption of equal reactivity of functional groups which means that the reactivity of one functional group of a bifunctional monomer is the same irrespective of whether the other functional group has reacted and the reactivity of a functional group.

Two monomers in equimolar quantities. In step-growth polymerization the Carothers equation or Carothers equation gives the degree of polymerization X n. A few days after starting work he wrote that he intended.

Condensation polymerization offers the possibility of constructing polymer molecules of accurately known structure. Carothers equation is used to illustrate the extent of reaction for linear polycondensation or polyaddition polymerization reactions. 23 Carothers and his research group studied.

Carothers believed that polymers were molecules hooked together end-to-end in long chains by ordinary bonds. Monomers oligomers and polymers. Derivation of the Carothers equation for molecular mass as a function of the extent of the reaction p and reactant ratio r.

To describe the behavior of linear step-growth polymerization systems in 1930 Carothers proposed a pioneering equation later denoted as the Carothers equation. Carothers equation is applicable only to stoichiometric mixtures of addition monomers or if only one type of functional group undergoes polymerization as it. X n 1 r 1.

The discoveries and theories of Staudinger led Carothers to initiate his work on step-growth polycondensation polymerization. Furthermore the synthesis follows Carothers equation DP 1 1-p which describes the degree of polymerization DP as a function of conversion p the. The Flory-Stockmayer theory represents an advancement from the Carothers equation allowing for the identification of the gel point for polymer synthesis not at stoichiometric balance.

Network Formation and Gelation. In polycondensations the number-average degree of polymer- ization DP can be expressed as DP 1 r1 r 2rp where p is the extent of the polymerization and r is the stoichiometric ratio between the comonomers. P c 2 f avg.

This equation is based on general stochastic insights and gives the degree of polymerization or number average chain length ie x n for a given A or equivalently B FG conversion p with r 1 ignoring intramolecular reactions. Carothers equation In step-growth polymerization the Carothers equation or Carothers equation gives the degree of polymerization Xn for a given fractional monomer conversion p. In step-growth polymerization the Carothers equation or Carothers equation gives the degree of polymerization X n for a given fractional monomer conversion p.

The Carothers Equation High Molecular weights are hard to get this way If there are N omolecules at time 0 and N remaining at time t then the amount reacted is N 0 -N and we can define p as the conversion or fraction reacted then as P N o N N o or N N o 1 P If DP is the average degree of polymerization N 0. N 0 is the number of molecules present initially N is the number of unreacted molecules at time t p. Step-growth polymerization vs chain growth to be covered in more detail later in the course extent of reaction number-average degree of polymerization.

WikiZero Özgür Ansiklopedi - Wikipedia Okumanın En Kolay Yolu. This equation shows that a high monomer conversion is required to achieve a. There are several versions of this equation proposed by Wallace Carothers who invented nylon in 1935.

If X n describes the number of average chain length and P describes the extent of the reaction then starting with N 0 as the number of molecules at the beginning of the polymerization after some time has elapsed N is the number of molecules left in the. One way to express molecular. A Word on MWD for Nonlinear Polymerizations 9.

Segmented and Block Copolymers from Step Condensation Methods 7 Crosslinking and Branching. The simplest case refers to the formation of a strictly linear polymer. An equation attributed to Carothers 1 relates the number-average degree of polymerization to fractional.

FloryStockmayer theory is a theory governing the cross-linking and gelation of step-growth polymers. X n is also the average chain length in monomer units p N 0-NN 0 where. This equation was originally proposed by Carothers and is often referred to as the Carothers equation.

There are several versions of this equation proposed by Wallace Carothers who invented nylon in 1935. The total includes all degrees of polymerization.

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