Florys Parameter

Xaf. the Flory parameter of pair interaction between units Ma and M ... 

In these formulas the letter X stands for the average copolymer composition, while of denotes the dispersion of the SCD quantitatively characterizing its width. The second of these statistical characteristics is extremely significant for the thermodynamics of the melt of a heteropolymer specimen, being in a simple way AHmix = RT jof connected with the specific enthalpy of mixing Affmix per mole of monomeric units. Here T is the absolute temperature, R represents the gas constant, whereas / denotes the Flory /-parameter whose values are available from the literature for many pairs of monomeric units (see, for example, [7]). 

The Flory parameter is in essence analogous to the activity coefficient of the HOC in the DOM phase and consists of two components %u and 5Cs> which are the enthalpic and entropic contributions, respectively ... 

Where V2/V1 (r) is the ratio of the molar volume of the polymer to that of the solvent and x is the Flory parameter which depends primarily on the intermolec-ular forces between solute and solvent. According to the original formulation, this parameter is zero for athermal mixtures. However, subsequent work has shown that both the excess entropy and the excess enthalpy contribute to x ... 

Monte Carlo calculations based on the lower bound method were applied to estimate the Flory parameter for asymmetric stars, whereas, for the symmetric stars, experimental results on three- and four-arm homopolymer stars were used. The obtained values of gg for different macroscopic states together with those obtained from RG and MC calculations are presented in Table 2. p is the ratio of the lengths of the B and A arms (p=NB/NA). 

In practice, the Flory-Huggins theory fails to predict many features of polymers solutions, either qualitatively or quantitatively, but remains widely used because of its simplicity. The Flory parameter x, assumed to be constant, often increases with interaction-energy scaled on kT, often exhibits a more complicated temperature dependence than 1/T (Flory, 1970). Such behavior stems from energetic effects, such as directional polar... 

This fact can be demonstrated as follows. Let us determine the value of the well-known Flory parameter x, which corresponds to the 6 point (i.e. to the point of inversion of the second virial coefficient of the solution of rods) in the Flory theory of Ref.9). This can be done by expanding the chemical potential of the solvent in the isotropic phase (Eq. (16) of Ref.9 ) into powers of the polymer volume fraction in the solution, and by equating the coefficient at the quadratic term of this expansion to zero this procedure gives Xe = 1/2 independently of p. On the other hand, it is well known26,27) that the value of x decreases with increasing p and that X < 1 at p > 1. The contradiction obtained shows that the expressions for the thermodynamic functions used in Ref.9) are not always correct... 

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... 

Figure 16 shows a schematic diagram of phase transformations for rigid-chain polymers separated from isotropic solutions by introducing a nonsolvent into the system (this is a usual method of obtaining fibres and films) (cf. >). The initial isotropic solution with the polymer concentration V2 and the value of the Huggins-Flory parameter is in the monophase region. The critical concentration of the transition into liquid crystalline state for this system is v. When a nonsolvent is introduced, i.e. when x is increased up to the value >0.5 (x ), two routes of the phase transition... 

Mantovani F, Grassi M, Colombo I, Lapasin R. A combination of vapor sorption and dynamic laser light scattering methods for the determination of the Flory parameter chi and the crosslink density of a powdered polymeric gel. Fluid Phase Equilib 2000 167(1) 63— 81. 

Product distributions can be evaluated for reaction probabilities of elemental surface reaction steps with the model of non trivial surface polymerisation [2]. Specific inhibition of desorption of a chemisorbed organic species has been postulated to be the intrinsic principle of the FT-synthesis [5]. A chemisorbed species can react further by linear chain prolongation or chain branching or it can desorb as a paraffin, olefin or an organic oxygen compound. Growth probabilities pg, that contain a similar information as the Anderson-Schulz-Flory parameter a. 

So while not perfect, the value of the Flory parameter chosen, 0.475, gives a reasonably good description of the cyclohexane-polyisobutylene system. 

The SEC columns were calibrated using narrow molecular weight distribution water soluble polymer standards sodium polystyrene sulfonate, NaPSS (Pressure Chemical Company, Pittsburgh, PA) and dextrans (Pharmacia Fine Chemicals, Piscataway, NJ). The universal calibration curve proposed by Grubisic et al. (13) was found not to be applicable for these polymer standards. The alternative calibration procedure of Coll and Prusinowski (J ) which incorporates excluded volume effects in the numerical value of the Flory parameter was found to be applicable for this system ( ). The calibration curve for the two-column network system described above is shown in Figure 3. The Kyyy parameter used on the abscissa of Figure 3 is a normalized elution volume parameter defined by Equation 1,... 

Depending on the Flory parameter x, there is a particular special temperature T = 6 at X = 1/2, which corresponds to an exact cancellation between steric repulsion and van der Waals attraction between monomers, and thus the chains are nearly ideal. This temperature is known as the collapse temperature or theta temperature [15]. Equation (15.10) for the free energy of mixing is an expression that finds wide use in physical chemistry. A quantitative understanding of hydrophobie eollapse is required to understand the initial stage of protein folding, as proteins are often a finite chain consisting of a 50-300 amino acid residue linear chain, which in many aspects resembles a heteropolymer. 

The A/B diblock copolymer melt is characterized by two parameters /=iV>W and %N, where Na is the number of A monomers in a chain of N=Na- Nb monomers, and is the so-called Flory parameter characterizing the... 

The usual one is to take into account only tte active chains and jum tions. The difunctional junctions are thus not iiKluded. Therefore the molecular wdght between crosslinks can be different from M and its distribution is unknown. Nevertheless one gains more knowledge about the functionality of the considered juiKtims, three in an imperfect trifunctional network, a mixture of three and four in a tetrafunctional one. The Flory parameter v. and the Graessley parameter h are not defined. One can take an average over the distribution of molecular weights between crosslinks and the different functionalities. 

Table 7. Values of the Flory parameter x for imperfect trifunctkxial networks = 0), using e p i-mental data from Ref. S2...

The aim of this paper is to clarify current discussions about rubber elasticity particularly with regard to entanglement contributions. [A similar review convering some of the same topics has recmtly been prqjared by Eichinger After a brief review of the existing molecular theories, it is shown that the Flory parameters can be determined by a new method of fitting the stress-strain curves obtained for perfect end-linked PDMS nrtworks. For networks assumed to be imperfect, the branching... 

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