Mixtures Flory-Huggins parameter

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]. 

A quantitative comparison between the mean field prediction and the Monte Carlo results is presented in Fig. 15. The main panel plots the inverse scattering intensity vs. xN. At small incompatibility, the simulation data are compatible with a linear prediction (cf. (48)). From the slope, it is possible to estimate the relation between the Flory-Huggins parameter, x, and the depth of the square well potential, e, in the simulations of the bond fluctuation model. As one approaches the critical point of the mixture, deviations between the predictions of the mean field theory and the simulations become apparent the theory cannot capture the strong universal (3D Ising-like) composition fluctuations at the critical point [64,79,80] and it underestimates the incompatibility necessary to bring about phase separation. If we fitted the behavior of composition fluctuations at criticality to the mean field prediction, we would obtain a quite different estimate for the Flory-Huggins parameter. 

As a consequence, the chains can be considered as being rescaled into chains of blobs [2] of size each of these blobs containing only monomers of the considered chains, and no monomers of other chains being present inside such a blob. As a consequence, in the limit 4> - 0 the mixture becomes compatible A renormalization group analysis [238, 239] shows that the effective renormalized Flory-Huggins parameter vanishes as... 

Fig. 33a. Effective Flory-Huggins parameter xert(4>> T) plotted vs volume fraction of deuterated polyethylethylene in a mixture with protonated polyethylethylene. Filled symbols refer to N = 1710, open symbols to NJ = 818, while Nj = 1330. From Bates et al. [68]. b Effective Flory-Huggins parameter X fif4>. T) plotted vs relative concentration a/(1 — <(>,) for the model of Fig. 3 (in d = 3 dimensions) and the case , = 0.2, N = 16, eAB = 0,...

Another very interesting problem concerns the concentration dependence of the effective Flory-Huggins parameter XeffM T) that can be extracted from small angle scattering data by fitting Eqs. (37), (46) or (55) to them. It has been found that Xrff T) for symmetric mixtures (such as mixtures of protonated and... 

Chremos A, Nikoubashman A, Panagiotopoulos AZ Flory-Huggins parameter X, from binary mixtures of Lennard-Jones particles to block copolymer melts, J Chem Phys 140(5) 054909, 2014. 

In Section II we look more closely at the computational aspects of DPD, before focusing attention on the specific application to polymer systems. Section III describes the matching of simulation parameters to the properties of real polymer systems, with an emphasis on the relation between the conservative force field and the common Flory-Huggins / parameter for mixtures. The dynamics of individual polymer chains in a solvent and in a melt are discussed in Section IV, and the ordering dynamics of quenched block copolymer systems is described in Section V. A summary and conclusions are given in Section VI. 

Flory-Huggins parameter (binary mixture) (dimensionless)... 

Fig. 3.17. Endothermal symmetrical mixture with a constant heat of mixing. Temperature dependence of the Flory-Huggins parameter (left) and phase diagram showing a lower miscibility gap right)...

The quantity x is called the Flory-Huggins interaction parameter It is zero for athermal mixtures, positive for endothermic mixing, and negative for exothermic mixing. These differences in sign originate from Eq. (8.39) and reaction (8.A). 

Haeany Solution Model The initial model (37) considered the adsorbed phase to be a mixture of adsorbed molecules and vacancies (a vacancy solution) and assumed that nonideaUties of the solution can be described by the two-parameter Wilson activity coefficient equation. Subsequendy, it was found that the use of the three-parameter Flory-Huggins activity coefficient equation provided improved prediction of binary isotherms (38). 

Schwahn, D. Willner, L. Phase Behavior and Flory-Huggins Interaction Parameter of Binary Polybutadiene Copolymer Mixtures with Different Vinyl Content and Molar Volume. Macromolecules 2002,35, 239-247. 

Note 1 The definition and the name of the term have been modified from that which appears in ref. [5] to reflect its broader use in the context of polymer blends. In its simplest form, the %. parameter is defined according to the Flory-Huggins equation for binary mixtures... 

Flory-Huggins Approach. One explanation of blend behavior lies in the thermodynamics of the preceding section, where instead of a polymer-solvent mixture, we now have a polymer-polymer mixture. In these instances, the heat of mixing for polymer pairs (labeled 1 and 2) tends to be endothermic and can be approximated using the solubility parameter. The interaction parameter for a polymer-polymer mixture, Xi2, can be approximated by... 

Here, N is the volume fraction of the network units within the network j is the volume fraction of i-th component, a is size of monomer units Xu> XNi ate Flory-Huggins interaction parameters between component of the mixture and between components of solvent and network monomer units, respectively V is the volume of network sample. 

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