Flory interaction parameter measuring

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. 

It is very important to know the value of the Flory interaction parameter X for a given mixture. Methods of measuring this parameter are discussed in Section 4.6 and tables of x parameters are listed in many reference books (see the 1996 review by Balsara). 

At the t -temperature, the interaction parameter — 1/2 and the energetic part of two-body interactions exactly cancels the entropic part, making the net two-body interaction zero (v = (l—2x) Z> = 0). For xbody interactions increase the osmotic pressure of dilute polymer solutions. Hence, measurement of the osmotic pressure in dilute solutions provides a direct way of determining the Flory interaction parameter x-... 

The Flory interaction parameter in miscible polymer blends is measured using small-angle neutron scattering, usually involving deuterium label-... 

Melting point depression data are often used to determine the Huggins-Flory interaction parameter, X12 Table 3.11), that is a measure for the miscibility of the blend, i.e., X12 is negative for a miscible blend. A lack of melting point depression means that is zero. Eq 3.39 is only valid for systems in which the crystalline morphology is not affected by the composition. 

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. 

We present here a forward recoil spectrometry (FRES) study of thermodynamic slowing down" of mutual diffusion in isotopic polymer mixtures and of the diffusion of homopolymers into symmetric diblock copolymer structures. The measurements of "thermodynamic slowing down" were performed on binary mixtures of normal and deuterated polystyrene (PS). Both the Flory interaction parameter, the upper critical... 

Although the emphasis in these last chapters is certainly on the polymeric solute, the experimental methods described herein also measure the interactions of these solutes with various solvents. Such interactions include the hydration of proteins at one extreme and the exclusion of poor solvents from random coils at the other. In between, good solvents are imbibed into the polymer domain to various degrees to expand coil dimensions. Such quantities as the Flory-Huggins interaction parameter, the 0 temperature, and the coil expansion factor are among the ways such interactions are quantified in the following chapters. 

The toughness of interfaces between immiscible amorphous polymers without any coupling agent has been the subject of a number of recent studies [15-18]. The width of a polymer/polymer interface is known to be controlled by the Flory-Huggins interaction parameter x between the two polymers. The value of x between a random copolymer and a homopolymer can be adjusted by changing the copolymer composition, so the main experimental protocol has been to measure the interface toughness between a copolymer and a homopolymer as a function of copolymer composition. In addition, the interface width has been measured by neutron reflection. Four different experimental systems have been used, all containing styrene. Schnell et al. studied PS joined to random copolymers of styrene with bromostyrene and styrene with paramethyl styrene [17,18]. Benkoski et al. joined polystyrene to a random copolymer of styrene with vinyl pyridine (PS/PS-r-PVP) [16], whilst Brown joined PMMA to a random copolymer of styrene with methacrylate (PMMA/PS-r-PMMA) [15]. The results of the latter study are shown in Fig. 9. 

Another study looked at the miscibihty of E-plastomer-polyisobutylene blends. Blends were prepared from linear E-plastomers and a polyisobutylenes in the entire composition range. Flory-Huggins interaction parameters were determined from DMTA and DSC measurements. The usual technique had to be modified in the case of DSC data, since the Tg of E-plastomers cannot be detected by this technique. The two methods yielded identical results and indicated good interaction of the components, which was supported also by a SEM study and the mechanical properties of the blends. 

Here, AGeiastic is the contribution due to the elastic retractive forces developed inside the gel and A6mixi g is the result of the spontaneous mixing of the fluid molecules with the polymer chains. The term AGmjXjng is a measure of the compatibility of the polymer with the molecules of the surrounding fluid. This compatibility is usually expressed by the polymer-solvent interaction parameter, xi (Flory, 1953). 

Two main approaches for osmotic pressure of polymeric solutions theoretical description can be distinguished. First is Flory-Huggins method [1, 2], which afterwards has been determined as method of self-consistent field. In the initial variant the main attention has been paid into pair-wise interaction in the system gaped monomeric links - molecules of solvent . Flory-Huggins parameter % was a measure of above-said pair-wise interaction and this limited application of presented method by field of concentrated solutions. In subsequent variants such method was extended on individual macromolecules into diluted solutions with taken into account the tie-up of chain links by Gaussian statistics [1]. 

The Flory-Huggins interaction parameter, x, indicates the water affinity of the polymer while Ch is a measure of the fraction of bound water in the... 

Flory and Huggins developed an interaction parameter that may be used as a measure of the solvent power of solvents for amorphous polymers. Flory and Krigbaum introduced the idea of a theta temperature, which is the temperature at which an infinitely long polymer chain exists as a statistical coil in a solvent. 

It is conventional to let 1/2 zAw = RT, where x is called the Flory-Huggins interaction parameter. Note that 1/2 Aw is the energy change per 1,2 pair according to Equation (69) therefore, wiih the coordination number z absorbed, the parameter x measures this in units of RT. Finally, Equation (21) establishes the connection between chemical potential and osmotic pressure according to this equation,... 

Equation-of-state theories employ characteristic volume, temperature, and pressure parameters that must be derived from volumetric data for the pure components. Owing to the availability of commercial instruments for such measurements, there is a growing data source for use in these theories (9,11,20). Like the simpler Flory-Huggins theory, these theories contain an interaction parameter that is the principal factor in determining phase behavior in blends of high molecular weight polymers. 

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

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