Equations Huggins

Linking this molecular model to observed bulk fluid PVT-composition behavior requires a calculation of the number of possible configurations (microstmctures) of a mixture. There is no exact method available to solve this combinatorial problem (28). ASOG assumes the athermal (no heat of mixing) FIory-Huggins equation for this purpose (118,170,171). UNIQUAC claims to have a formula that avoids this assumption, although some aspects of athermal mixing are still present in the model. 

The symbol Xs stands for the interaction energy per solvent molecule divided by kT. Combining equations (5.7) and (5.8) gives the Flory-Huggins equation for the free energy of mixing of a polymer solution ... 

Equation (6.20) is known as the Huggins equation. From it, we can see that the limiting case as c tends to zero is that the term (p - PoVho c tends to a... 

The intrinsic viscosity [ti] and Huggins constant Kjj were calculated according to Huggins equation (11). 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

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

Next, we use the following relationship, which we sometimes call the Huggins equation [1 ] ... 

In many applications a capiiiary viscometer is used to measure the viscosity of poiymer soiutions of differing concentrations, and then the data are piotted to obtain the intrinsic viscosity. Severai techniques have been used to determine intrinsic viscosity from soiution. One is the Huggins equation for intrinsic viscosity [1] ... 

The combination of entropy and enthalpy changes finally lead to the well-known Flory-Huggins equation [53] ... 

The Flory-Huggins equation (Eq. 10) allows one to reconstruct schematic phase diagrams to express the phase separation behavior as discussed below. 

One of the most common techniques for determining x parameters for polymer-solvent systems is the vapor pressure method.(10) In this approach, the uncrosslinked polymer is exposed to solvent vapor of known pressure, p. The polymer absorbs solvent until equilibrium is established, x is related to p and V2, the volume fraction of polymer at equilibrium, by the Flory-Huggins equation (ll)... 

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... 

The polymer-solvent interaction is described by the famous Flory-Huggins equation [38]... 

Tanaka and collaborators [31] further investigated the polyacrylamide behavior. Based on the Flory-Huggins equation for osmotic pressure, they... 

The relation between the specific viscosity (tjsp) of a dilute solution and that of a concentrated solution is shown by the Huggins equation,... 

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