Floiy parameter

The classical size-independent combinations are the Floiy parameters that combine the intrinsic viscosity, [rj], and the radius of gyration, Rg. 

In discussing the interaction between a polymer and a solvent in Section III.l we were led to define the interactions in terms of a Floiy parameter x the energy of interaction per site was of the form... 

Interaction parameter, employed in the Floiy-Huggins theory, to account for the contribution of the noncombinatorial entropy of mixing and the enthalpy of mixing to the Gibbs energy of mixing. 

The effect of intermolecular interactions is characterized by the Floiy-Huggins interaction parameter. For the polymer brush with 400 bonds, three values of the interaction parameter were selected in the calculations and the segment density profiles are plotted in Fig. 9. x 0 corresponds to a good solvent and x 0.5 to a poor one. With increasing value of x, the height of the polymer bmsb decreases. For the poor solvent ( =0.5), the chant segments tend to be more uniformly distributed (curve 3). 

In the present calculations, the interaction parameter (x or x") is the only undetermined parameter. For the PI chains-toluene interactions, x is selected 0.35, which is close to the experimental values of the Floiy-Huggins interaction parameter45 OfFH=0.32—0.36 in the concentration range temperature range 25-55 °C). For the PS chains-toluene interactions, x is taken 0.2, which is in the lower range of the experimental Floiy-Huggins interaction parameters45 (a,fh=0.04-0.67 in the concentration... 

Interpretation of the second and third virial coefficients, A2 and A3, in terms of Floiy-Huggins theory is apparent from Eq. (3.82). The second virial coefl[icient A2 evidently is a measure of the interaction between a solvent and a polymer. When A2 happens to be zero, Eq. (3.82) simplifies greatly and many thermodynamic measurements become much easier to interpret. Such solutions with vanishing A2 may, however, be called pseudoideal solutions, to distinguish them from ideal solutions for which activities are equal to the molar fractions. Inspection of Eq. (3.83) reveals that A2 vanishes when the interaction parameter X equal to. We should also recall that %, according to its definition given by Eq. (3.40), is inversely proportional to temperature T. Since x is positive for most polymer-solvent systems, it should acquire the value at some specific temperature. 

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

In addition, as the objective of starch formylation is to improve its compatibility with PCL, we need to examine the effect of functionalization in terms of increasing the interactions between the two polymers. The compatibility between the two polymer phases is better when the Floiy-Huggins interaction parameter fi2 is close to 0, i.e. when the solubility parameters S i of the two polymers are similar, if we look at equation [10.2] ... 

FIGURE 28 The dependences of enthalpic component of Floiy-Huggins interaction parameter on formal blocks contents for PESF solutions in tetrachloroethane (1) and chloroform (2). 

FIGURE 45 The relationship between fractal dimension of solvent molecules swarm 8 and Floiy-Huggins interaction parameter for poly(methyl methacrylate) (1), poly stirene (2), poly(vinyl acetate) (3) and polysulfone (4). 

X Floiy-Huggins polymer-solvent interaction parameter... 

Figure 10-13 substantiates this prediction for three quench temperatures. Finally, using eq 2.44, we evaluate Dapp and 2Mok from the intercept and slope of the straight line obtained. If separate information about f u) is available, we can calculate the more basic parameters and k from them. Sometimes the Floiy-Huggins theory is used for f u), but probably it is only of semi-quantitative use for the two-phase region. 

Hence, the proposed above assumption about intercommunication of Df and Xj corresponds to the experimental data Floiy-Huggins interaction parameter describes exactly enough interactions system for macromolecular coil in solution, controlling its fractal dimension value. The main problem at the Eq. (12) usage with the purpose of Dj. predicting is the empirical parameter xs calculation method absence [17]. 

The parameter gives the rate of recombination to dead chains or 1/yS is the waiting time until termination occurs. It becomes obvious, the greater the waiting time yS the broader the molecular mass distribution. The y-distribution was first time adjusted to molecular mass distributions of polymers by Schulz (1935) and Flory (1936). Therefore, it is called Schulz-Floiy distribution in macromo-lecular science. 

Miscible blends of poly(styrene) (PS) and poly(vinyl methyl ether) (PVME) show LCST behavior as presented in Figure 18. Phase separation occurs above 152 °C. This liquid-liquid phase separation, we may discuss in terms of Floiy-Huggins parameter given as a function of temperature. We see parameter i as a free-energy parameter comprising energy and entropy contribution, Xv Xs... 

The data presented indicate the complex thermodyn unic behavior of the system. Actu dly, as Fig 2.3 shows, the Floiy-Huggins thermodynamic interaction parameter between the system components has a value lower than the critical value in the region of surfactant concentrations up to 30% that characterizes the thermodynamic stability of the system. The xl,3 critical parameter for the given oligomeric system was calculated using the equation... 

Here, the term A includes the contribution of interaction entropy (Floiy 1970). Such a contribution can be miderstood from the concept of compressible free volume in the fluids. When two fluids are mixed with each other, part of molecules of one species enters the free volume of another species, and then the total volume is not a simple addition of the two individual components. Yamakawa made an approximate estimation from the expansion theory (Yamakawa 1971). Prigogine attributed this contribution to a combinatorial contribution of molecular geometry and a non-combinatorial contribution of molecular stmctures, and proposed an equation-of-state theory (Prigogine 1957b). Hory, Orwell and Vrij further considered the contribution of free volume, and employed separate parameters to describe the hard-core volume and surface contacts of chain units (Flory et al. 1964 Flory 1965 OrwaU and Rory 1967). This work makes the equation of state fit better to the e erimental results, and derives the so-called Flory-Orwell-Vrij equation of state for pure polymers, as given by... 

Xi is a dimensionless quantity characterizing the difference between the interaction energy of solvent molecule immersed in the pure polymer compared with interaction energy in the pure solvent. It is a semi-empirical constant. This parameter was introduced by Floiy and Huggins in the equation for solvent activity to extend their theory for athermic processes to the non-athermic processes of mixing ... 

The large amount of experimental data is then an essential advantage of the Floiy s theory. Simple expressions exist for parameter X,2 in the terms of Xij characteristic parameters for chemically different segments of molecules of components 1 and 2. Each segment or chemical group has an assigned value of characteristic length (Oj, Oj) or surface area as a fraction of the total surface of molecule ... 

Starting with a theory, one has an advantage, particularly in multicomponent systems such as PLC -I- EP -I- solvent it is easy to define the concentration of a flexible polymer (EP) and the average concentratiOTi q of LC sequences in PLC chains. The average concentration of flexible sequences in PLC molecules is of course 1 — and other model parameters such as in the Floiy theory can be defined as well. Somewhat similarly, it is easy in molecular dynamics (MD) simulations to set up certain chains with > 0 and other chains with 9 = 0. 

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