Isochoric polymer

Figure 4 Cartoon for hidden liquid-liquid spinodal in a polymer melt, calculated for a Flory Rotational Isomeric State chain with a simple coupling between density and conformational order A is the trans-gauche energy gap and a dimensionless density. Shown is the path of an isochoric quence into the unstable regime. r, is the spinodal temperature, T the melting temperature, T the liquid-liquid critical point, and Tp the temperature at which the harrier between dense liquid and crystal is of order ksT ...

The constitutive model used to describe large plastic deformations of glassy polymers involves a separate formulation for temperatures above and below the glass transition Tg, since the underlying deformation mechanisms are different. In either regime, the formulation is based on the decomposition of the rate of deformation into an elastic part and a plastic part Z)P so that 0 = 0° + D. By assuming an isotropic yield stress, the isochoric plastic strain rate is given by the flow rule... 

Consequently, one should banish the simplistic scheme that nodules in a polymer necessarily induce damage in a medium that otherwise would exhibit isochoric deformation by plastic shear. On the contrary, (i) damage processes provide an important contribution to the plastic deformation of most polymers and (ii) dispersed particles often decrease the original damage rate of polymeric matrices, except those that are coarse and poorly adhesive such as glass beads. 

Finally, it should be mentioned that a polymer model for the structural organization of chromatin loops in interphase chromosomes was developed by Oslashevsky (1998) on the basis of isochores. 

Isoharic (constant pressure) and isochoric (constant volume) glass transitions in polymers were first observed for bisphenol A polycarbonate (62). A molecular dynamics study of such transitions in a model amorphous polymer has also been reported (63). This study shows that the glass transition is primarily associated with the freezing of the torsional degrees of freedom of polymer chains (related to chain stiffness), which are strongly coupled to the degree of freedom associated with the nonbonded Lennard-Jones potential (related to interchain cohesive forces). 

Does Equation (5.17) imply that the polymer blending process is isochoric ... 

Mechanical equilibrium between two phases or between a system and an external reservoir can be achieved by allowing the volume of the system to fluctuate. Conventional volume moves, although expensive for molecular systems, are easy to implement. Specialized variants have been proposed to speed up the equilibration in systems of flexible polymers, including branched and crosslinked polymers. In some cases, the relationship between the pressure and other thermodynamic variables of a system can be determined by simulation of an isochoric system the pressure must then be calculated by employing a suitable algorithm (e.g., the virial formula, virtual volume moves, etc. ). 

Temperature lowering at specified isobaric or isochoric conditions is the most often used technique for the determinatian of solvent vapor pressures or activities in polymer solutions. The majority of aU measurements are made using this kind of an isopiestic procedure where the pure solvent is used as the reference system. The equilibrium condition of equal chemical potential of the solvent in the polymer solution as well as in the reference system is realized by keeping the pure solvent at a lower temperature (7)) than the measuring temperature (T-i) of the solution. In equilibrium, the vapor pressure of the pure solvent at the lower temperature is then equal to the partial pressure of the solvent in the polymer solution, i.e., PiiTi) = P Ti). Equilibrium is again established via the common vapor phase for both subsystems. 

Guo, Y., Zhang, C., Lai, C., Priestley, R.D., D Acunzi, M., Fytas, G. Stmctural relaxation of polymer nanospheres under soft and hard confinement Isobaric versus isochoric conditions. ACS Nano 5, 5365 (2011)... 

The volume phase transition can be triggered by different quantities which are able to change the interaaions between polymer and solvent drastically. The macroscopic consequence is a swelling or deswelling (Figure 24). Other properties are changed drastically too. Therefore, it is possible to monitor the transition process by various analytical methods. An understanding of the volume phase transition needs a microscopic model of processes. A two-step model is discussed for the volume phase transition under isochore conditions. ... 

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