Flory’s principle

A kinetic study for the polymerization of styrene, initiated with n BuLi, was designed to explore the Trommsdorff effect on rate constants of initiation and propagation and polystyryl anion association. Initiator association, initiation rate and propagation rates are essentially independent of solution viscosity, Polystyryl anion association is dependent on media viscosity. Temperature dependency correlates as an Arrhenius relationship. Observations were restricted to viscosities less than 200 centipoise. Population density distribution analysis indicates that rate constants are also independent of degree of polymerization, which is consistent with Flory s principle of equal reactivity. 

The second method is based on Flory s principle of the independence of the reactivity of the bonding sites is independent of their position in the long chain or a low-molecular weight analogue with a correct selection of the model reaction components (a central particle in the form of a metal ion). For a single-site bonding the K value is determined as in the case of low-molecular weight compounds... 

In isodesmic polymerizations, the individual monomers associate with an association constant that is independent of the polymer size. This is comparable to the simplest description of a step-growth polycondensation given by Flory s principle of equal reactivity [10]. The mechanism gives rise to a PDI of 2 in the high-concentration regime. 

Even though it has now been in print for over 50 years, the essential single book for every physical chemist who desires to understand macromolecules is Flory s Principles cf Polymer Chemistry There is a good introduction and considerable historical material in that volume. 

The pubhcation of his monograph. Viscoelastic Properties of Polymers, in 1961 provided a solid basis for all future work, and a key guide to all previous work [7]. It ranks with Flory s Principles of Polymer Chemistry as an essential record of the paradigm of polymer science. 

P. J. Floryt whose outstanding overall contributions in polymer chemistry won him the Nobel Prize in 1974. Flory s book Principles of Polymer Chemistry contains an admirable discussion of these topics. 

While a number of introductory or comprehensive texts dealing with polymer chemistry were written, the most influential was probably Paul J. Flory s textbook "Principles of Polymer Chemistry", published in 1954. No prior knowledge of polymers was assumed with particular chapters directed at the beginner. It also contained much information useful to the experienced investigator. A wealth of experimental data was included to illustrate the applicability of the presented concepts and conclusions. Admittedly missing are topics related to the mechanical properties of polymers and to the application of polymers in industry - i.e. fabrication, synthesis, etc. Even so Flory s text is a landmark book in science. 

The observed stoichiometrically imbalanced polymerization behavior is rationalized by involvement of olefin-Pd(O) complex 14, which leads to cascade bidirectional allylation. Thus, after the first allylation of 13, 14 selectively forms the allylpalladium(II) complex at the other allylic terminal. Therefore, the polymer end groups are always the malonic ester moiety even in the presence of excess 13, which would not terminate the polycondensation by the attack on both polymer end groups. This behavior is dependent on the ligand of the Pd(0) catalyst bis(diphenylphosphino)butane (dppb) is indispensable, and use of PPh3 results in low molecular weight polymer as expected by Carothers and Flory s basic principle [1-3]. 

In Section 7.1 we discussed the thermodynamic condition for a stable mixture given in the Flory-Huggins equation (Eq. 7.1-6), where AS denotes the increase of entropy due to mixing. This equation is based on Boltzmann s principle stating that the entropy of a... 

FIGURE 5-23 Flory s experimental results [replotted from the data of P. J. Rory. Principles of Polymer Chemistry, Cornell University Press (1953)]. 

As in so many things in this field, if you want to work through the arguments yourself, you cannot do better than go to Flory— see Principles of Polymer Chemistry, Chapter EX. Stockmayer s equation illustrates the point we wish to make with dazzling simplicity as f the number of branches, increases, the polydispersity decreases. Thus for values of/equal to 4, 5 and 10, the polydispersity values are 1.25, 1.20 and 1.10, respectively. Note also that for / = 2, where two independent chains are combined to form one linear molecule (Figure 5-28), the polydispersity is predicted to be 1.5. Incidentally, an analogous situation occurs in free radical polymerization when chain termination is exclusively by combination. 

Flory presented a more detailed analysis of the molecular theory of the hquid crystalline state of polymeric systems. This theory is discussed in the first chapter of this book, so we here shall only describe the principle of calculating the equilibrium phase composition without going into details. Note that Flory s theory embraces a wide range of concentrations, while Onsager s analysis is valid only for low concentrations, since it is based on the second virial approximation. 

Flory s theory has been formulated in various nearly equivalent manners1,2,3,4 and there does not exist any classical approach. Consequently, we shall begin with a rough description of the basic principles, and afterwards we shall expound this theory more precisely by using the trial probability technique in a rather novel way. 

Flory s equal reactivity principle, which has been validated on mechanistic and experimental grounds, has greatly simplified an otherwise complicated kinetic analysis of condensation polymerization. This... 

If the two interacting monomeric primary molecules are not present in equivalent amounts, the conditions are more complicated but remain in principle within the scope of the present discussion. It would lead too far to examine these more complex conditions further and it will suffice to cite the literature,especially Flory s work mentioned previously. ... 

Figure 5.5 Models of the amorphous state in pictorial form, (a) Flory s random coil model the (b) Privalko and Lipatov randomly folded chain conformations (c) Yeh s folded-chain fringed-micellar model and (d) Pechhold s meander model. Models increase in degree of order from (a) to (d). References, (a) P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953. (b) V. P. Privalko and Y. S. Lipatov, Makromol. Chem., 175, 641 (1972). (c) G. S. Y. Yeh, J. Makoromol. Scl. Phys., 6, 451 (1972). (cf) W. Pechhold, M. E. T. Hauber, and E. Liska, KolloIdZ. Z. Polym., 251, 818 (1973). W. Pechhold, lUPAC Preprints, 789 (1971).

Chapters 4 and 5 are closely related in providing fundamental principles of modem polymer physical chemistry. Chapter 4 duly emphasizes Flory s work and Chapter 5 emphasizes de Gennes work, de Gennes work, in a sense, refutes some of Flory s theory and orients polymer physical chemistry in a new direction. 

As we see, Flory s simple mean-field treatment leads to the same result as the exact analysis by renormalization group methods. In fact, this comes as a real surprise because there is no good reason to expect that a mean-field treatment which in principle is not allowed for a single chain in view of the pronounced concentration variations would give the correct result. However, it does, and so it appears that different faults in the treatment mutually cancel out. 

Flory, PJ., Principles of Polymer Chemistry, Cornell University Press, Ithaca, 1953. Gehrke, S. and Lee, R, in Tyle, P. (Ed.), Specialized Drug Delivery Systems Manufacturing and Production Technology, Marcel Dekker, New York, 1989, p. 333. Rieka, J., and Tanaka, T., Macromolecules, 17 (1984) 2916. 

In the 50 years after the appearance of Flory s book Principles... numerous authors published contributions to the theory of step-growth polymerization covering the following aspects ... 

Flory, Paul John (1910-85) American polymer chemist. Flory s early work consisted of helping Wallace CAROTHERS to develop nylon and neoprene. He began to investigate the properties of polymers in the 1930s. Flory solved the difficulty that a polymer molecule does not have a fixed size and structure by using statistical techniques to calculate a distribution of polymer chain lengths. Flory also worked on polymers in which there are links between chains. This led to work on the elasticity of rubber. Flory summarized his work in the classic books Principles of Polymer Chemistry (1953) and Statistical Mechanics of Chain Molecules (1969). Flory won the 1974 Nobel Prize for chemistry for his work on polymers. 

Flory (11) improved the notation and form of Prigogine s expressions, and it is essentially the Flory form of Prigogine s free-volume theory that is of most use for design purposes. The Flory work (11) leads to an equation of state which obeys the corresponding-states principle ... 

In this case the role of kinetically independent elements in accordance with the extended Flory principle is performed by monomeric units of different kinds S0,...,Sf, while here the rate constants of the elementary reactions of condensation ky(z, =0,...,f-l) between functional groups belonging to units S and S act as the parameters of the FSSE model. It has been suggested [76] to characterize every molecule by vector 1 with components /0,...,/(,...,Zf equal to the numbers of units of types S0,...,S ,...,Sf that this molecule is comprised of. Kinetic schemes of the reactions between monomeric units as well as between molecules may be written down as follows ... 

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