Flory interaction parameter calculation

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. 

Nn0 is the number of solvent molecules, xn is a dimensionless DP function, and x is the Flory-Huggins interaction parameter calculable from osmometry data (Ulrich, 1975) ... 

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... 

Calculate the thickness of a wet Alexander - de Gennes brush formed by chains with N= 10 Kuhn monomers of length b = 5A, attached to the surface with density a — 1 nm in a good solvent with Flory interaction parameter x==0.3. 

Figure 10.1.7 shows the correlation between the number of carbon atoms in n-aUcanes and the net retention volume of solvent using IGC measurements. Such a correlation must be established to calculate the acid-base interaction s contribution to the free energy of desorption, AGab, as pointed out in discussion of equations [10.1.5] and [10.1.6]. Figure 10.1.8 shows that the Flory interaction parameter (measured by IGC) increases as the temperature increases. 

The effect of polymer-polymer interactions on the miscibility and macroscopic properties of PVC/PMMA, PVC/PS, and PMMA/PS blends were studied and the miscibility of the components was characterized by the Flory-Huggins interaction parameter or by quantities related to it by Fekete et al. (Fekete et al. 2005). The comparison of interaction parameters determined by different methods indicates that PVC and PMMA are nearly miscible, while PS is immiscible either with PMMA or with PVC at all compositions. Hory-Huggins interaction parameters calculated from equihbrium methanol uptake (y jj) are plotted as a function of composition in Fig. 10.24. The negative values obtained for the PVC/PMMA blends hint at complete miscibility, although x,2 depends on composition which indicates limited miscibility. The positive interaction parameters determined for the PVC/PS and PMMA/PS blends suggest immiscibility. 

Inverse-phase gas chromatography (Sect. 3.4) is now used frequently to assess interaction parameters and was used by Riedl and Prud homme to estimate polymer-polymer interaction parameters in polyester-PVC blends, including PCL-PVC blends, at 120 °C and as a function of polymer concentration [72]. Interaction parameters were found to vary with the CH2 ester ratio in the polyester, i.e. with n in 2. From retention volumes they calculated values of the interaction parameter (the Flory interaction parameter per segment) as functions of blend... 

The Flory-Rehner equilibrium swelling method (see Section 4.2.2) was used to evaluate the change in crosslink density of the IPNs, using dioxane as the swelling agent. The Flory interaction parameter was found to be approximately 0.30 for dioxane and either polymer, simplifying the analysis. Table 6.4 gives the results for the effective crosslink densities, vj K where V is the polymer volume in cm. Table 6.4 also shows the theoretical values of vj K calculated in accordance with the law of additivity. 

ASD including the use of in silico solubility parameter (5) calculation (Ghebremeskel et al. 2007), Flory-Huggins (F-H) interaction parameter calculation (Marsac et al. 2006b Zhao et al. 2011), drug-polymer thermodynamic phase diagrams prediction (Tian et al. 2013), crystallization inhibition with molecular dynamic calculation (Pajula et al. 2012), etc. However, in spite of their use and popularity, these theoretical methods have limitations and lack predictability, reliability, and thereby have limited utility. 

Once Tf is determined, equations (6.43) and (6.44) permit the calculation of both the Flory interaction parameter and the heat of fusion of the polymer from the slope and intercept of a plot of (1/7/) - (1/7/) versus (1/7/) (146). The heat of fusion determined in this way measures only the crystalline portion. If heat of fusion data are compared with corresponding data obtained by DSC (see Figure 6.3), which measures the heat of fusion for the whole polymer, the percent crystallinity may be obtained. 

Figure 3 was calculated using NSCFT by Matsen and Bates [2], It shows the equilibrium phases for diblocks with total degree of polymerization Nq and Flory interaction parameter x. An important, general feature of block copolymers is that the corresponding diagrams for many two-species copolymers are very similar in structure to this one, with only small shifts in the phase boundaries that depend on molecular architecture and species [2-14], As described in Chapter 10, the phase diagrams of triblocks can be more complex. 

The method of Benmouna and Benoit, which consists of calculating density correlations for each type of monomer in the block copolymer or network and cross-correlations for the different types of monomer was used for the calculations. In the case in which the different types of monomer are hydrogenated and deuterated versions of the same monomer and the Flory interaction parameter between the different monomer units is assumed zero, the intensity of scattering HQ) is proportional to ... 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

The above values are applicable only in the limiting case of infinite dilution. The interaction parameter varies with the volume fraction of polymer network as has been demonstrated for the PDMS-benzene system by Flory (47) and PDMS-methyl ethyl ketone, PDMS-methyl isobutyl ketone, PDMS-ethyl-n-butyl ketone, and PDMS-diisobutyl ketone by Shiomi et al. (48). Theoretically calculated and experimentally observed values of X as a function of volume fraction of polymer are given for PDMS in alkanes, aromatic hydrocarbons, and dimethyl siloxane oligomers by Gottlieb and Herskowitz (49). In the case of PDMS-alkanes, x was practically independent of the volume fraction of polymer. 

Roult s law is known to fail for vapour-liquid equilibrium calculations in polymeric systems. The Flory-Huggins relationship is generally used for this purpose (for details, see mass-transfer models in Section 3.2.1). The polymer-solvent interaction parameter, xo of the Flory-Huggins equation is not known accurately for PET. Cheong and Choi used a value of 1.3 for the system PET/EG for modelling a rotating-disc reactor [113], For other polymer solvent systems, yj was found to be in the range between 0.3 and 0.5 [96],... 

The bead-bead interaction parameters are generated using classical atomistic MD or they can be calculated from Flory-ITuggins parameters. ... 

In addition to the calculations of changes in the free entropy mixing, Flory introduced the interaction parameter, %, to account for the intermolecular interactions between polymer and solvent molecules, thus giving [53]... 

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]. 

Thermodynamic descriptions of polymer systems are usually based on a rigid-lattice model published in 1941 independently by Staverman and Van Santen, Huggins and Flory where the symbol x(T) is used to express the binary interaction function [16]. Once the interaction parameter is known we can calculate the liquid liquid phase behaviour. 

Analyzes the ability of a paste to spread over a biological surface and calculates the interfacial tension between the two [110], The tension is considered proportional to X1/2, where X is the Flory polymer-polymer interaction parameter. Low values of this parameter correspond to structural similarities between polymers and an increased miscibility... 

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