Lecture 4 Flashcards
What is the importance of the principle of equal reactivity of functional groups (mentioned in the previous lecture) when it comes to the theoretical treatment of linear step polymerization?
On the basis of the principle, we can conclude that step polymerization involves random reactions occurring between any two mutually reactive molecular species.
Intrinsically, each of the possible reactions is equally probable and their relative preponderance depends only upon the relative numbers of each type of molecular species (i.e. monomer, dimer, trimer, etc.). This assumption of equal reactivity is implicit in each of the theoretical treatments of step polymerization that follow.
What is the Carothers theory?
Look at written notes pt 1
Further analysis of The Carothers Equation:
The equation highlights the need to attain very high extents of reaction of functional groups in order to produce polymers with useful physical properties. Normally, degrees of polymerization of the order of 100 or above are required, hence demanding values of p ≥0.99. This clearly demonstrates the necessity for using monomers of high purity and chemical reactions that are either highly efficient or can be forced towards completion
How is the average molar mass related to the number-average degree of polymerization?
Relation in shown in notes
How do stoichiometric imbalances significantly limit the attainable values of the number-average degree of polymerization?
Check notes pt 1 :)
Analysis and application:
Table 3.3 (shown in digital notes) gives values of xn calculated using the general Carothers Equation and reveals the dramatic reduction in xn when r is less than unity. Thus only very slight stoichiometric imbalances can be tolerated if useful polymers are to be formed, the corollary
of which is that r must be controlled with great accuracy.
It is now absolutely clear that, in order to
control r with the necessary precision, the monomers used in linear step polymerizations must be of very high purity and that the linking reactions must be clean.
Assuming these criteria are satisfied, the equation can be used to exert control of molar mass by using slight imbalances in stoichiometry to place an upper limit on x¯n for reactions taken to very high conversions of functional groups.
How is the general Carothers equation modified to be applicable to reactions in which a monofunctional compound is included to control xn, e.g. RA2+RB2+RB or ARB+RB?
Check written notes
The statistical theory!
The theory of Carothers is restricted to the prediction of number-average quantities. In contrast, simple statistical analyses based on the random nature of step polymerization allow the prediction of the degree of polymerization distributions. Such analyses were first described by Flory.
For simplicity RA2+RB2 and ARB polymerizations in which there is exactly equivalent stoichiometry will be considered here. The first stage in the analysis is to calculate the probability P(x) of the existence of a molecule consisting of exactly x monomer units at time t when the extent of reaction is p. A molecule containing x monomer units is created by the formation of a sequence of (x−1)
linkages. The probability that a particular sequence of linkages has formed is the product of the probabilities of forming the individual linkages. Since p is the probability that a functional group has reacted, the probability of finding a sequence of two linkages is p^2, the probability of finding a sequence of three linkages is p^3 and the probability of finding a sequence of (x−1) linkages is p^(x−1). For a molecule to contain exactly x monomer units, the xth (i.e. last) unit must possess a terminal unreacted functional group. The probability that a functional group has not reacted is (1−p) and so the probability that a molecule chosen at random contains exactly x monomer units is shown in written notes pt 2!
what is the analysis of the equation for the probability that a molecule chosen at random contains exactly x monomer units and the weight fraction of x monomers?
The equations define what is known as the most probable (or Flory or Flory-Schulz) distribution, the most important features of which are illustrated by the plots shown in Figure 3.1 (Shown in digital notes). Thus the mole fraction P(x) decreases continuously as the number of monomer units in the polymer chain increases, i.e. at all extents of reaction, the mole fraction of monomer is greater than that of any other species. In contrast, the weight fraction distribution shows a maximum at a value of x that is very close to x¯n. As the extent of the reaction increases, the maximum moves to higher values of x and the weight fraction of the monomer becomes very small.
How is then the statistical theory related to the Carothrs Equation using the evaluation of molar mass averages?
Find in written notes pt 2 (under bigger picture)
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