Flory construction

A schematic representation of the Flory construction for a polymer network. 

Estimate the fraction of the tensile force at 300 K that has energetic origins by using a Flory construction on the following data for the temperature dependence of tensile force for a crosslinked rubber with 1 cm cross-sectional area held at constant elongation. 

The history of dendrimer chemistry can be traced to the foundations laid down by Flory [34] over fifty years ago, particularly his studies concerning macro-molecular networks and branched polymers. More than two decades after Flory s initial groundwork (1978) Vogtle et al. [28] reported the synthesis and characterization of the first example of a cascade molecule. Michael-type addition of a primary amine to acrylonitrile (the linear monomer) afforded a tertiary amine with two arms. Subsequent reduction of the nitriles afforded a new diamine, which, upon repetition of this simple synthetic sequence, provided the desired tetraamine (1, Fig. 2) thus the advent of the iterative synthetic process and the construction of branched macromolecular architectures was at hand. Further growth of Vogtle s original dendrimer was impeded due to difficulties associated with nitrile reduction, which was later circumvented [35, 36]. This procedure eventually led to DSM s commercially available polypropylene imine) dendrimers. 

The total product spectrum for a typical precipitated iron catalyst in an LTFT process is shown in Figure 13.3. Constructing an Anderson-Schulz-Flory (ASF) plot from the total product spectrum does not give a straight line and can conveniently be separated in two distinct regions, one from C, to C8 and another from C20 onward (as shown in Figure 13.4). The light olefins and... 

Whereas the well-characterized, perfect (or nearly so) structures of dendritic macromolecules, constructed in discrete stepwise procedures have been described in the preceding chapters, this Chapter reports on the related, less than perfect, hyperbranched polymers, which are synthesized by means of a direct, one-step polycondensation of A B monomers, where x > 2. Flory s prediction and subsequent demonstration 1,2 that A B monomers generate highly branched polymers heralded advances in the creation of idealized dendritic systems thus the desire for simpler, and in most cases more economical, (one-step) procedures to the hyperbranched relatives became more attractive. 

This result can be derived from a simple extension of the Flory calculation more detailed pictures of the swollen star can be constructed cite[ 13] and lead to the same form. (An attentive reader will note that if we put N=/1/2 in eq. (7), we end up with R=aX1/3, i.e. a compact nodule as announced). 

Most theoretical procedures for deriving expressions for AG iix start with the construction of a model of the mixture. The model is then analyzed by the techniques of statistical thermodynamics. The nature and sophistication of different models vary depending on the level of the statistical mechanical approach and the seriousness of the mathematical approximations that are invariably introduced into the calculation. The immensely popular Flory-Huggins theory, which was developed in the early 1940s, is based on the pseudolattice model and a rather low-level statistical treatment with many approximations. The theory is remarkably simple, explains correctly (at least qualitatively) a large number of experimental observations, and serves as a starting point for many more sophisticated theories. 

Here

Flory-Huggins lattice, but ultimately one wishes to consider some coarse-graining over many cells of the lattice to construct a smoothly varying field q>(f) defined in continuous space. 

The free volume theory, which was developed subsequently by Flory and coworkers, is much more elaborate in its innate construction. It attempts to rectify the omissions of the Flory-Huggins theory whilst retaining certain important elements therefrom. Whereas the Flory-Huggins theory has found wide application in the development of theories of polymeric stabilization, the free volume theory has not yet proved to be quite so productive, although it remains crucial to the understanding of the effects of temperature. Both theories will therefore be outlined in this chapter. 

Quantitative predictions of surfactant phase behavior can be made by constructing a thermodynamic model. The classical expression for the free energy of a microemulsion is a function of the interfacial tension, bending moment, and micelle-micelle interactions [47]. Two quantitative models have been developed to describe supercritical microemulsions based on this concept. Here, the key challenge is to find accurate expressions for the oil-surfactant tail interactions and the tail-tail interactions. To do this, the first model uses a modified Flory-Krigbaum theory [43,44], and the second a lattice fluid self-consistent field (SCF) theory [25]. 

Queslel combined the Ball model with the Flory model of restricted junction fluctuations to explain the origin of junction and trapped entanglement contributions to the total modulus exhibited by networks. There, the total contribution to the reduced force is considered to be the sum of the full Flory term (see Sect. 4.2) and the entanglement contribution of the Ball term. Such an expression has the practical advantage that it is valid over the entire range of deformation, but it seems to be an artificial construction. 

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