Interactions Flory interaction parameter

KF Freed, AI Pesci. Computation of the cross-link dependence of the effective Flory interaction parameter % for polymer networks. Macromolecules 22 4048-4050, 1989. 

Flory Interaction Parameters for Illinois Number 6 Coal Extracts and Benzene... 

The extent to which these Flory interaction parameters apply to the pyridine-insoluble portion of the Illinois No. 6 coal is open to question. We cannot address this aspect fully here, but we have noted that the pyridine-soluble and -insoluble portions of the Illinois No. 6 coal studied here have similar carbon, hydrogen and oxygen contents. Maciel has observed that the aromaticities of the two portions of an Illinois No. 6 coal are similar as well.(12) Based on this alone, it seems that the pyridine-soluble portion is representative of the larger, crosslinked portion, at least for the Illinois No. 6 coal, but this aspect remains controversial,(12) so caution is warranted. 

Here, nt is the moles of the swelling agent, and u2 are the corresponding volume fractions of swelling agent and polymer, yA is the Flory interaction parameter, and k and T are the Boltzmann constant and absolute temperature, respectively. 

Table I Phase transitions, Flory interaction parameters (/), free energies (AG) and differences of Hildebrand solubility parameters (A<5) depending on the molecular structure (fluorination of the alkyl chain) [25]...

Olvera de la Cruz and Sanchez [76] were first to report theoretical calculations concerning the phase stability of graft and miktoarm AnBn star copolymers with equal numbers of A and B branches. The static structure factor S(q) was calculated for the disordered phase (melt) by expanding the free energy, in terms of the Fourier transform of the order parameter. They applied path integral methods which are equivalent to the random phase approximation method used by Leibler. For the copolymers considered S(q) had the functional form S(q) 1 = (Q(q)/N)-2% where N is the total number of units of the copolymer chain, % the Flory interaction parameter and Q a function that depends specifically on the copolymer type. S(q) has a maximum at q which is determined by the equation dQ/dQ=0. 

A more detailed study of the phase diagram of the polyelectrolyte complex must take into account the non-electrostatic interactions between the two polymers characterized by the Flory interaction parameter %. This inter-... 

When the concentration of the free polymer is set equal to zero, the situation corresponds to pure steric stabilization. The free energy of interaction due to the interpenetration of the adsorbed polymer chains has a range of 26, where 6 is the thickness of the adsorbed layer. This free energy is proportional to the quantity (0.5 - x), where x is the Flory interaction parameter for the polymer-solvent system. Thus, a repulsive potential is expected between two particles when x < 0.5 and this repulsion is absent when x = 0.5. For this reason, it was suggested [25] that instabilities in sterically stabilized dispersions occur for x > 0.5, hence for theta or worse-than-theta conditions. However, the correlation with the theta point only holds when the molecular weight of the added polymer is sufficiently high... 

The solubility parameter can be used to estimate the Flory interaction parameter, /, via ... 

Since the Flory interaction parameter, x> was derived by considering only interaction energies between the molecules, it should not contain any entropic contributions and Equation (2D-9) should yield the correct value for the Flory-/ parameter. Unfortunately, x contains not only enthalpic contributions from interaction energies, but also entropic contributions. The solubility parameter includes only interaction energies and by the definition of regular solutions does not include any excess entropy contributions. Blanks and Prausnitz (1964) point out that the Flory / parameter is best calculated from... 

As we will see in Chapter 11, it is usual to describe interactions in polymers using the Flory interaction parameter x, which varies as the inverse of the temperature. Thus if x is relatively small it is possible to form a single phase at temperatures below the degradation point of the polymer. Then, as you cool and X gets larger, the system phase-separates. The temperature or value of x at which this occurs, the order-disorder transition, varies with composition and it is possible to... 

The Flory interaction parameter x is defined to characterize the difference of interaction energies in thomiixture ------------------------------------... 

It is very important to know the value of the Flory interaction parameter X for a given mixture. Methods of measuring this parameter are discussed in Section 4.6 and tables of x parameters are listed in many reference books (see the 1996 review by Balsara). 

Substituting Eqs (4.27)-(4.29) into the definition of the Flory interaction parameter [Eq. (4.21)] allows it to be written in terms of solubility para-meter difference. 

Since x is related to the square of the difference in solubility parameters it is clear why the Flory interaction parameter is usually positive x > 0- Th above approach works reasonably well for non-polar interactions, which only have van der Waals forces between species, and does not work in... 

Table 4.3 Temperature dependence of the Flory interaction parameters of polymer blends [Eq. (4.31)1 with vq= 100 A ...

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