Parameter Flory-Huggins

In many applications the phase stmcture as a function of the temperature is of interest. The discussion of this issue requires the knowledge of the temperature dependence of the Flory-Huggins parameter x (T). If the interactions... 

This involves the Flory-Huggins parameter x and hence assumes the same limitation as the rest of the Flory-Huggins approach, i.e. a moderately concentrated solution. Flory and Krigbaum rewrote this equation in terms of some other parameters, i.e. 

Fig. 28 Mean-field phase diagram for ABCD tetrablock quaterpolymer melts with 0=1/4. Flory-Huggins parameters are xab = X except /Ad- Phases abbreviations MCS BC mixed centrosymmetric NCS non-centrosymmetric CS centrosymmetric. From [90]. Copyright 2004 American Chemical Society...

The energy of interaction between the components is conveniently described by means of three mutually independent Flory Huggins parameters x X ° and xP° Indices refer to the respective component pairs. 

The experimental thickness measurements may also be compared with theoretical results based on profiles generated by the S.F., Scheutjens Fleer, theory (11). For this calculation we use a value for xs °f 1 (net adsorption free energy), for x of 0.45 (experimental value of the Flory-Huggins parameter) and a polymer solution concentration of 200 ppm. Although the value for xs seems rather arbitrary it has been shown (10) that 6jj is insensitive to this parameter. 

Predicting the characteristic sizes and morphologies of these nanostructures has been an intense topic of investigation from both the theoretical and experimental points of view. Critical parameters are the degree of polymerization and the volume fraction of the constituent blocks, as well as the Flory-Huggins parameter between them. More complete information about microphase separated structures in bulk block copolymers can be found in the book of Hamley [2],... 

Two main approaches for osmotic pressure of polymeric solutions theoretical description can be distinguished. First is Flory-Huggins method [1, 2], which afterwards has been determined as method of self-consistent field. In the initial variant the main attention has been paid into pair-wise interaction in the system gaped monomeric links - molecules of solvent . Flory-Huggins parameter % was a measure of above-said pair-wise interaction and this limited application of presented method by field of concentrated solutions. In subsequent variants such method was extended on individual macromolecules into diluted solutions with taken into account the tie-up of chain links by Gaussian statistics [1]. 

Flory-Huggins parameters Xy do not influence the mobility. For the case of Rouse dynamics, which only depends on the local friction, the bare mobility matrix ... 

The general agreement between mean-field prediction and experimental results was excellent. Other than PE-PEE, PEP-PEE (sample VI) undergoes an ODT which is observed at 473 K. An analysis by the modified RPA theory due to Fredrickson [265] yields a strong stretching of the radii of gyration around the ODT and a temperature-dependent Flory-Huggins parameter ... 

Similar observations were made on the higher molecular weight PEP-PEE diblock, which undergoes an ODT at 473 K. Figure 6.11 presents the initial slopes obtained at 473 and 533 K. The RPA predicted collective mode was calculated on the basis of the effective Flory-Huggins parameter and structural... 

The deterioration of the solvent qnality, that is, the weakening of the attractive interactions between the polymer segments and solvent molecules, brings about the reduction in the coil size down to the state when the interaction between polymer segments and solvent molecules is the same as the mutual interaction between the polymer segments. This situation is called the theta state. Under theta conditions, the Flory-Huggins parameter % assumes a value of 0.5, the virial coefficient A2 is 0, and exponent a in the viscosity law is 0.5. Further deterioration of solvent quality leads to the collapse of coiled structure of macromolecules, to their aggregation and eventually to their precipitation, the phase separation. 

So, let us suppose that the network is immersed in the mixture of two solvents a good solvent A and a poor solvent B. Let yAB, %m and yvBN be the Flory-Huggins parameters of interaction between A-B, A-network units, B-network units, respectively. The specific calculations for this system along the lines described in Sect. 2.1. were made in Ref. [31]. 

Here a is the Kuhn or segment length. The delta functional selects out only those configurations satisfying the incompressibility constraint. The Flory-Huggins parameter, measures the incompatibility between A and B monomers. The dimensionless A monomer-density operator is given by... 

In mean field theory, two parameters control the phase behavior of diblock copolymers the volume fraction of the A block /A, and the combined interaction parameter xTak- V. where Xab is the Flory-Huggins parameter that quantifies the interaction between the A and B monomers and N is the polymerization index [30], The block copolymer composition determines the microphase morphology to a great extent. For example, comparable volume fractions of block copolymer components result in lamella structure. Increasing the degree of compositional asymmetry leads to the gyroid, cylindrical, and finally, spherical phases [31]. 

Table 5.6 The number a of solvent molecules sorbed per phenyl group and the limiting Flory -Huggins parameter x0 for polystyrene-divinylbenzene copolymers- solvent systems (Errede 1989)...

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