Flory hydrodynamic parameter

Flory hydrodynamic parameter relating intrinsic viscosity to the... 

Oo Flory hydrodynamic parameter for a flexible linear unperturbed coil ... 

In practice, there is a growing body of experimental evidence that shows that the choice of theta solvent can have an impact on the magnitude of measured unperturbed dimensions [39, 42-44] and/or the Flory hydrodynamic parameter d> under theta conditions [30, 45]. Theory anticipated [46] and has rationalized [45, 47] such effects. In fact, today, polymer chains are viewed by theory as being only quasi-ideal at the theta state [48-50]. 

With regard to differences in polymer behavior in solution versus the bulk state, several points must be made. Clearly, it is now well-established that the choice of theta solvent can affect chain dimensions to some extent [42-44, 46, 47]. Hence, only the chain in an amorphous melt of identical neighbors can be considered to be in the unperturbed state. Particularly striking are some of the differences noted in temperature coefficients measured by different techniques. Is it possible that the thermal expansion of a polymer molecule is fundamentally different in the bulk and in solution Can specific solvent effects exist and vary in a systematic way within a series of chemically similar theta solvents Does the different range of temperatures usually employed in bulk versus solution studies affect K Are chains in the bulk (during SANS and thermoelastic experiments) allowed adequate time to completely relax to equilibrium All of these issues need further attention. Other topics perhaps worthy of consideration include the study of the impact of deuterium labelling on chain conformation (H has lower vibrational energy than does H ) and the potential temperature dependence of the Flory hydrodynamic parameter . 

At the largest length scales, field theoretic and continuum mechanics models are able to predict the equiUbriirm stmcture of multicomponent systems and macroscopic flow response of a polymer system. However, these models do not contain molecular detail. They are based either on a phenomenological description of the free energy of the system, such as the Flory-Hu ns or Landau free energies, or on actual hydrodynamic parameters such as viscosity. 

In GPC, the product [77] M, (or the hydrodynamic radius Re) has been widely accepted as a universal calibration parameter. In the Ptitsyn-Eizner modification of the Flory-Fox equation the quantity 4>, which relates the dimensional parameters to the above product, is taken as a variable. The value of < depends upon molecular expansion in solution as represented by a function f(e). Because of this dependence polymeric species having the same [77] M value cannot have the same statistical dimensions (radius of gyration or end-to-end distance) unless they have the same e value. Thus, if [77] M is a universal calibration parameter, the statistical parameters cannot be used as such. A method is presented for obtaining the Mw/Mn ratio from GPC data even though universal calibration is used. 

Calculate the for solutions in chlorobenzene of polystyrenes with molar weights of 2 x 105,5 x 105 and 106 g/mol the intrinsic viscosity, the critical concentration, the swelling factor, the hydrodynamic swollen volume, the second virial coefficient and the Flory-Huggins interaction parameter. 

M and v are the molecular weight and the partial specific volume of the polymer, jjo p are the viscosity and the density of the solvent, respectively, and P and O are functions of relative chain length L/A and of the parameter of hydrodynamic interaction, d/A, respectively. These functions have been represented in an analytical form and tabulated over a wide range of changes in the L/A and d/A parameters At extremely high molecular weights (at IVA -> ), functions P and ap oach an asymptotic limit P— Po = 5.11 — 4>, = 2.862 x 10 (the Flory constant). This corresponds to the conformation of a hydrodynamically undrained Gaussian coil. 

Fig. 2.5. Flory constant 0 from Zimm theory evaluated by various methods of calculation plotted against hydrodynamic interaction parameter h Circles from eigenvalues of difference equation (2.18) thin lines from Eq. (2.41) thick line result of Tschoegl from Eq. (2.20). Values of h are shown, and cross mark indicates N = 104 for a given value of h = hN 112 (72)...

The polymers influence the rheological properties of fluids, due to acquiring a large volume in solution as compared to the total of the molecular dimensions of the repeating unite [3]. The solution volume occupied by the solvated polymer chain is known as the hydro-dynamic volume (HDV). The hydrodynamic volume is determined by polymer structural parameters (e.g., chain length and chain stifihiess), polymer-solvent interactions, polymer associations or repulsions, temperature, concentration, and molecular weight. The effective HDV of a random-coil polymer is generally equated to the product [ti]M defined by Flory [3] ... 

Several parameters determined in dilute solutions used in the following to characterize the chain conformation, hydrodynamics and thermodynamics are presented here for convenience - additional parameters are presented as needed. Further details on the functional forms summarized may be found elsewhere [1, 10-16]. For example, under Flory Theta conditions, given by the condition that the second virial coefficient A2 is zero, the root mean square radius of gyration... 

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