Floiy temperature

GUP Gupta, A., Mohanty, B., and Bohidar, H.B., Floiy temperature and upper critical solution temperature of gelatin solutions. Biomacromolecules, 6,1623, 2005. 

There are of course, other sources of nonldeahty in a macromolecular solution in addition to the excluded volume. To make a solution behave as an ideal one, a temperature can be foimd (0 temperature or Floiy temperature) at which the above enthalpic and entroplc terms cancel each other. The second virial coefficient, B, then becomes nil and the solution behaves Idealfy. 

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... 

FIGURE 10-63 Schematic plot of glass transition temperature versus reciprocal molecular weight (redrawn from the data of T. G. Fox and P. J. Floiy, J. Appl Phys., 21,581 (1950)1. 

You may recall that the temperature where % 2is what Floiy called the theta tern--perature and can now be seen to describe the situation where the second virial coefficient becomes zero (Figure 12-10). This means that at this point pair-wise interactions cancel and the chain becomes nearly ideal, as we discussed in the section on dilute solutions (Chapter 11), where we referred to the Floiy excluded volume model in which the chain expansion factor is given by Equation 12-18 ... 

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. 

Chiang and Floiy used three conditions to demonstrate the presence of a latent heat in polyethylene. They cleaned the sample of possible impurities to eliminate adventitious sites for heterogeneous nucleation and annealed the sample before melting commenced to ensure that the highest possible crystallization was achieved. Finally, Flory and Chiang heated the polyethylene sample slowly (over the period of a week before each increase in temperature) to allow the sample to equilibrate. 

In the binary cluster approximation, A3 as well as A2 must vanish simultaneously under the 6 condition. This prediction, however, does not agree with the osmotic pressure data of Floiy and Daoust [92] on poly (isobutylene) in benzene, which gave positive A3 at the 6 temperature (24° C). More definite evidence for non-v mishing A3 under the 0 condition can be seen from the osmotic pressure data of Vink [89] on polystyrene in cyclohexane. Thus it seems mandatory to abandon the binary cluster approximation in the region near the 6 condition. 

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. 

The free volume theory originated some years later than the lubricity and the gel theories, when the evolution of different properties of polymers as a function of temperature, specific volume, thermal expansion coefficients, or viscosity was attempted to be explained.The relationships between these properties and some variables corresponding to polymer stracture, such as molecular weight or terminal groups content, the presence of another monomer and, of course, the presence of plasticizers, was also explained. For plasticized polymers the theory attempted to explain the diminution of the glass transition temperature with the plasticizer content. This theory is a contribution of different authors, but it was postulated by Fox and Floiy. The theory is still being used to explain some properties of plasticized polymers, i.e., viscoelastic properties. ... 

It was established by the earlier authors that the specific volume of polymers diminishes linearly with the temperature until the Tg. Below this temperature the diminution continues but at a small rate, as shown in Figure 5.4 obtained by Fox and Floiy for fractions of polystyrene of different molecular weights. Moreover, it was observed " that all the volume-temperature curves of the liquid state above the transition temperature, if they are extrapolated, intersect each other practically at the same point, at absolute zero temperature (V(o)iiq = 0.7674 cm /g). This volume was considered as the remaining space between atoms and molecules when no movement is allowed. Kanig ° proposed that the difference between the volume observed at absolute zero temperature and the volume measured at the transition temperature was constant for all polymers and equal to 0.0646 cm /g. This volmne difference was considered the space which, in the amorphous solid, is available for oscillations. 

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... 

Fox TG, Floiy PJ (1948) Viscosity-molecular weight and viscosity- temperature relationships for polystyrene and polyisobutylene. J Am Chem Soc 70 2384—2395 Frischknecht AL, Milner ST (2000) Diffusion with contour length fluctuations in linear polymer melts. Macromolecules 33 5273-5277... 

Let us first consider the high temperature side of the transition and determine the main effects that indicate the onset of ferromagnetic order. A first method applies a small magnetic field H to the system and measures the average magnetization M induced by H. For small H this must be of the form M = where is called the susceptibility (not to be confused with the Floiy interaction parameter), xu depends on tenverature and diverges when = (t - Tc)/r becomes veiy small ... 

KRI Krigbaum, W.R. and Geymer, D.O., Thermodynamics of polymer solutions. The polystyrene-cyclohexane system near the Floiy theta temperature, J. Amer. Chem. Soc., 81, 1859, 1959. 

The simple Floiy-Huggins %-function, combined with the solubihty parameter approach may be used for a first rough guess about solvent activities of polymer solutions, if no experimental data are available. Nothing more should be expected. This also holds true for any calculations with die UNIFAC-fv or oflier group-contribution models. For a quantitative representation of solvent activities of polymer solutions, more sophisticated models have to be applied. The choice of a dedicated model, however, may depend, even today, on the nature of die polymer-solvent system and its physical properties (polar or non-polar, association or donor-acceptor interactions, subcritical or supercritical solvents, etc.), on the ranges of temperature, pressure and concentration one is interested in, on the question whether a special solution, special mixture, special application is to be handled or a more universal apphcation is to be found or a software tool is to be developed, on numerical simplicity or, on die other hand, on numerical stability and physically meaningful roots of the non-linear equation systems to be solved. Finally, it may depend on the experience of the user (and sometimes it still seems to be a matter of taste). 

As our main interest is dedicated to the expected difference of the collapse and freezing temperatures, we will focus here on the discussion of the scaling behavior of the finite-size deviation of the maximum specific-heat temperature of a finite-length polymer from the temperature, TdN) — T [127,128,130,132,133]. For polymer solutions, Floiy-Huggins mean-field theory [145] suggests... 

With temperature decreasing, the first term on the right side of the expression [4.2.6] increases and the second term decreases. Such behavior implies the piesenee of the upper and lower critical temperatures of mixing. Later Floiy developed another expression for Xi that includes the parameter of contact interactions,... 

Figure 9.1.8 shows that the Floiy interaction parameter (measured by IGC) increases as the temperature increases. 

The degree to which a cross-linked polymer will swell when immersed in a solvent depends upon the polymer-solvent interaction parameter at the test temperature and the average moleeular weight of the chain segments separating crosslinks (effective chains). This relationship is defined by the Floiy-Rehner equation [89,90]. 

For star polymers the temperature at which 2 = 0 is lower than the Floiy 0-temperature of the linear polymer and depends on the molecular weight and the functionality [103]. Several studies have confirmed this phenomenon for polystyrene stars [37,38] and polyisoprene stars [41-43]. All studies have assumed that the lower temperature of the star polymer is exclusively due to their branched structure and is not affected by the increased weight fraction of foreign chemical groups present in the multiple chain ends or in the central coupling unit of the star. There is experimental evidence that such groups affect the observable [104]. Furthermore, in the discussion it should be kept in mind that determination of 0 usually has a 1 to 2 K accuracy. 

AG is normalized by the gas constant R and absolute temperature T. The free enthalpy of mixing AG of polymer blends was originally formulated within the mean-field approximation for incompressible polymer blends by Floiy and Huggins as... 

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