Partial Specific Volumes of Polymers

Andersson, G. The Partial Specific Volume of Polymers at High Pressures In The Physics and Chemistry of High Pressures-, Papers read at the symposium held at Olympia, London, lune 27—29, 1962 Society of Chemical Industry London, 1963. 

The second term in Eqs. (1) and (2) corresponds to the ideal volume, of the polymer solution. Partial specific volumes of polymers... 

The partial specific volumes of polymer (1) and solvent (2), Fj F2, spec> are calculated by... 

V is the partial specific volume of polymer, Pq is a constant and Np is Avogadro s number. The expansion factor a is also related to the intrinsic viscosity [tf] by the equation... 

V being the (partial) specific volume of the polymer and m=xV/v the mass of a polymer molecule. The sign and magnitude of the total free energy change AF for a given distance a depends, through J, on or on — exactly as we have pointed out previously... 

Here Vi and v are the partial specific volumes of the polymer (/ = 2,4) and the solvent, respectively M is the molar weight of the solvent and Xu and 724 are the Flory-Huggins interaction parameters, quantifying the energy of interaction between unlike lattice-based polymer segments (%24) or between polymer segments and solvent molecules (%u). 

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. 

In these equations, A/=molecular weight, Xi= interaction parameter, V2=partial specific volume of the polymer, Ki =molar volume of the solvent and o=unperturbed rms end-to-end dimensions. 

Here V2=partial specific volume of the polymer, F=molar volume of the solvent and =rms end-to-end distance of the stabilizing moieties. Although some uncertainty attends the absolute magnitudes of ij/i and determined in this fashion (arising from uncertainty in the modified Flory relationship) the signs of i/>i and are unambiguously fixed by this procedure. 

This can be modified by remembering that r = (VJV and (jtj = CjVj, where Vj is the partial specific volume of the polymer. This can be related to the polymer molecular weight through Vj = so that (t )2/r) = CjVi/Mj and, finally. 

Remembering that = (MV2/V1), where M and V2 are the molar mass and partial specific volume of the polymer, respectively, and is the molar volume of the solvent, the equation states that the critical temperature is a function of M and the value of at infinite M is the theta temperature for the system. 

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