Polymers equilibrium characterization

Michailov YM, Ganina LV, Smirnov VS. (2002) Phase equilibrium in biphase polymer systems based on Diglycidyl Ether of Bisphenol A. In Rozenberg BA, Sigalov GM (eds.). Heterophase Network Polymers Synthesis, Characterization, and Properties, pp. 33-42, CRC Press. 

As any ring-opening polymerization, the polymerization of lactams is characterized by competition between the intermolecular reaction resulting in a linear polyamide and the intramolecular reaction of cyclization. Thus, if thermodynamically feasible, as indicated by a negative value of the free-energy change of polymerization AGp, the conversion of lactam to the linear polyamide can be realized if an appropriate reaction path exists for a reasonable rate in a polymer-monomer equilibrium characterized by a preponderance of linear macromolecules. The corresponding equilibrium monomer concentration [M]g is related to the standard enthalpy and entropy ASp of polymerization and to... 

The study of optico-mechanical properties of one of ladder polyphenyIsesquioxanes in bulk has revealed the complex nature of the photoelasticity effect in the films of this polymer. Ladder polymers are characterized by high equilibrium rigidity of double stranded chains. ... 

If, in their use conditions, polymers are subjected to a residual molecular mobility (Ji motions in glassy polymers, a motions in the rubbery amorphous phase of semi-crystalline polymers), they will undergo a molecular reorganization towards the thermodynamic equilibrium, characterized by ... 

The phase equilibrium in systems containing rigid-chain polymers is characterized by the formation of a liquid-crystalline state, which fact can be illustrated by the diagram due to Flory reproduced in Figure 3. At x values below 0,the polymer-solvent system forms either an isotropic (one-phase) solution mixture of... 

Equilibrium characterization of polymers usually takes place in dilute solution where 1 > > 2A.cM > > iAx M, and over an angular range such that <5 x1. As seen in Chapters 11-13, in this case, Zimm equation reduces to one of its most freqnently nsed forms ... 

Although we have referred to the change in the emission spectrum of freeze-dried mixtures of donor and acceptor labeled polymers as characterizing self-diffusion, it should be pointed out that the "unfolding" of a globule containing a collapsed polymer chain to its equilibrium conformation is a very different process than the transport of the unfolded chain. Both processes are opposed by the viscosity of the medium and the conjecture that they are closely related seems reasonable, although data on their interrelationship are not available at this time. 

In systems of LP the dynamic response to a temperature quench is characterized by a different mechanism, namely monomer-mediated equilibrium polymerization (MMEP) in which only single monomers may participate in the mass exchange. For this no analytic solution, even in terms of MFA, seems to exist yet [70]. Monomer-mediated equilibrium polymerization (MMEP) is typical of systems like poly(a-methylstyrene) [5-7] in which a reaction proceeds by the addition or removal of a single monomer at the active end of a polymer chain after a radical initiator has been added to the system so as to start the polymerization. The attachment/detachment of single monomers at chain ends is believed to be the mechanism of equilibrium polymerization also for certain liquid sulphur systems [8] as well as for self-assembled aggregates of certain dyes [9] where chain ends are thermally activated radicals with no initiators needed. 

Lack of termination in a polymerization process has another important consequence. Propagation is represented by the reaction Pn+M -> Pn+1 and the principle of microscopic reversibility demands that the reverse reaction should also proceed, i.e., Pn+1 -> Pn+M. Since there is no termination, the system must eventually attain an equilibrium state in which the equilibrium concentration of the monomer is given by the equation Pn- -M Pn+1 Hence the equilibrium constant, and all other thermodynamic functions characterizing the system monomer-polymer, are determined by simple measurements of the equilibrium concentration of monomer at various temperatures. 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

In the following paper, the possibility of equilibration of the primarily adsorbed portions of polymer was analyzed [20]. The surface coupling constant (k0) was introduced to characterize the polymer-surface interaction. The constant k0 includes an electrostatic interaction term, thus being k0 > 1 for polyelectrolytes and k0 1 for neutral polymers. It was found that, theoretically, the adsorption characteristics do not depend on the equilibration processes for k0 > 1. In contrast, for neutral polymers (k0 < 1), the difference between the equilibrium and non-equilibrium modes could be considerable. As more polymer is adsorbed, excluded-volume effects will swell out the loops of the adsorbate, so that the mutual reorientation of the polymer chains occurs. 

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