Flory theory polyelectrolyte

The thermodynamics of polyelectrolyte solutions is also a strong function of ionic strength and charge density. Very large osmotic second virial coefficients are observed for highly charged macromolecules. The Flory theory of these solutions in presented in Section 10.3. 

The theoretical description of polymeric surfactants, as portrayed above, is based on the Flory theory. In turn, this is a modification of regular solution theory. Each type of monomer is assigned a single Flory % interaction parameter that characterizes the solvent quality. The enthalpic term is assumed to be of the form %( )(1 - ( )). A second characteristic, the dielectric constant e, appeared in the discussion of polyelectrolytes. It is important to note the limitations of this picture. It provides a useful description of many polymer-solvent and polymer-... 

Solvent power parameter entering Flory s theory of dilute solutions, degree of neutralization in polyelectrolyte solutions, free-volume parameter entering Vrentas-Duda theory subscript (1,24) denotes molecular species in solution. 

The theories of polymer solutions upon which steric-stability theories are based are usually formulated in terms of a portmanteau interaction parameter (for example Flory s X Parameter and the excluded volume integral) which does not preclude electrostatic interactions, particularly under conditions where these are short range. It is thus appropriate to consider whether polyelect-roly te-stabilisation can be understood in the same broad terms as stabilisation by non-ionic polymers. It was this together with the fact that polyelectrolyte solutions containing simple salts show phase-separation behaviour reminiscent of that of non-ionic... 

Flory-type free energy calculations show that the root mean square end-to-end distance of a polyelectrolyte increases linearly with the chain length at infinite dilution and without added salt [40]. Using the above perturbation theory, scaling relations at finite densities are obtained. The influence of the interaction with other polymer chains, counterions, and added salt is captured in the Debye screening length xT1. 

This brings us to the question about the applicability of the Flory-Huggins theory for food polymers. For polyelectrolytes, the theory is invalid, unless ionic strength is very high. In Section 7.3 the solubility of proteins will be discussed. Very few polysaccharides are simple homo-... 

Applying the procedure of the theory of Flory on the expansion factor of a polyelectrolyte in dilute solutions, based on the Donnan equilibrium[19], to the polyion chain between entanglement points, we have... 

Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca Freed KF (1987) Renormalization group theory of macromolecules. Wiley, New York Freed KF, Dudowicz J, Stukalin EB, Douglas JF (2010) General approach to polymer chains confined by interacting boundaries. J Chem Phys 133 094901 Fuoss RM, Katchalsky A, Lifson S (1951) The potential of an infinite rod-like molecule and the distribution of the counter ions. Proc Natl Acad Sci USA 37 579-589 Golestanian R, Kardar M, Liverpool TB (1999) Collapse of stiff polyelectrolytes due to counterion fluctuations. Phys Rev Lett 82 4456-4459 Guggenheim FA (1952) Mixtures. The Clarendon Press, Oxford... 

Reliable theories that accurately correlate or predict polyelectrolyte phase diagrams are lacking. Letting electrostatic excluded volume between chain segments be modeled at the level of the Debye-Hiickel approximation, a modified or effective Flory-Huggins parameter Xeff can be determined via the random phase approximation (141) ... 

The Flory-Huggins lattice consideration of the polyelectrolyte solutions presented above incorrectly describes dilute polyelertrolyte solutions. In the Flory-Huggins approach, the monomers are uniformly distributed over the whole volrrme of the system, leading to underestimation of the effect of the short-range monomer-monomer interactions and of the intra-chain electrostatic interactions. A similar problem appears in the Flory-Huggins theory of phase separation of polymer solutions (see for discussion References 32 and 33). This leads to the incorrect expression for the low polymer density branch of the phase diagram. 

The Flory-Huggins theory is only intended to work with non-ionic polymers dissolved in non-polar solvents, so that its use to interpret the results obtained from polyelectrolytes in water must be approached with care. For instance, when changing the calcium concentration the solvent quality will be altered, as well as changing the charge on the chain as a result of ion binding and altering the thickness of the electrical double layer. 

Orofino TA, Flory PJ (1959) The second virial coefficient for polyelectrolyte. Theory and experiment. J Phys Oiem 63 283 290... 

The contribution of the elastic term in lightly cross-linked networks can be described by the Gaussian theory of rubber elasticity (2,3). In fully neutralized polyelectrolytes, in the presence of added salt, the ionic term is not expected to play an exphcit role. Ionic interactions, however, may modify the mixing free energy contribution. In neutral polymer solutions the Flory-Huggins theory (I), based on the lattice model of solutions, expresses the mixing pressure as... 

---