Chemical potential change with polymerization

Escobedo and de Pablo have proposed some of the most interesting extensions of the method. They have pointed out [49] that the simulation of polymeric systems is often more troubled by the requirements of pressure equilibration than by chemical potential equilibration—that volume changes are more problematic than particle insertions if configurational-bias or expanded-ensemble methods are applied to the latter. Consequently, they turned the GDI method around and conducted constant-volume phase-coexistence simulations in the temperature-chemical potential plane, with the pressure equality satisfied by construction of an appropriate Cla-peyron equation [i.e., they take the pressure as 0 of Eq. (3.3)]. They demonstrated the method [49] for vapor-liquid coexistence of square-well octamers, and have recently shown that the extension permits coexistence for lattice models to be examined in a very simple manner [71]. 

Polymerization reactions are in most cases conducted under conditions remote from polymer-monomer equilibrium, i.e., these reactions are, to a great extent, irreversible. A polymer can have different molecular and supramolecular structures for example it can be iso- or syndiotactic, amorphous, or crystalline. Differences in the chemical potential of polymers with different structures are small in comparison with the changes observed in the chemical potential at conversion of a monomer into a polymer. This means that the possibility for a polymer of a certain structure to be formed will be determined by kinetic causes the nature of the catalyst, solvent, etc. According to the scheme in Fig. 5, the polymer with structure 2 will be mainly produced. 

The difference in the free energy of a system between two thermodynamic states is related to the ratio of their partition functions. Since the partition function is proportional to the probability with which the system visits the relevant state, such a ratio can be obtained in a single, expanded simulation that samples both states. If the transition between them is difficult, additional intermediate conditions can be simulated. This principle was exploited by Lyubartsev et al. [72] to simulate changes of free energy with temperature for simple systems. Similar ideas have been implemented by others to address a variety of problems, including the simulation of chemical potentials for polymeric systems [73-76]. 

A straightforward, but tedious, route to obtain information of vapor-liquid and liquid-liquid coexistence lines for polymeric fluids is to perform multiple simulations in either the canonical or the isobaric-isothermal ensemble and to measure the chemical potential of all species. The simulation volumes or external pressures (and for multicomponent systems also the compositions) are then systematically changed to find the conditions that satisfy Gibbs phase coexistence rule. Since calculations of the chemical potentials are required, these techniques are often referred to as NVT- or NPT- methods. For the special case of polymeric fluids, these methods can be used very advantageously in combination with the incremental potential algorithm. Thus, phase equilibria can be obtained under conditions and for chain lengths where chemical potentials cannot be reliably obtained with unbiased or biased insertion methods, but can still be estimated using the incremental chemical potential ansatz [47-50]. 

The fate of organic contaminants in soils and sediments is of primary concern in environmental science. The capacity to which soil constituents can potentially react with organic contaminants may profoundly impact assessments of risks associated with specific contaminants and their degradation products. In particular, clay mineral surfaces are known to facilitate oxidation/reduction, acid/base, polymerization, and hydrolysis reactions at the mineral-aqueous interface (1, 2). Since these reactions are occurring on or at a hydrated mineral surface, non-invasive spectroscopic analytical methods are the preferred choice to accurately ascertain the reactant products and to monitor reactions in real time, in order to determine the role of the mineral surface in the reaction. Additionally, the in situ methods employed allow us to monitor the ultimate changes in the physico-chemical properties of the minerals. 

Chemical polymerizations are usually in situ, with a host conventional polymer, such as poly(ethylene terephthalate) (PET) typically used to sorb monomer vapors, e.g. of pyrrole, then exposed to oxidant, e.g. FeClj, which results in polymerization of the sorbed monomer. The sorption may be reversed, with oxidant sorbed and exposed to monomer vapor or solution. Catalytic in situ chemical polymerizations, with e.g. a transition metal catalyst sorbed into the host polymer and then exposed to monomer vapor, are used primarily for P(Ac) composites. One variant of chemical polymerization uses a solution of the monomer and oxidant as solvent evaporates, the oxidation potential changes to a value conducive to polymerization. 

Materials that readily undergo violent chemical change at elevated temperatures and pressures Materials that exhibit an exotherm at temperatures less than 200° C and materials that polymerize vigorously and evolve heat Materials that react violently with water or form potentially explosive mixtures with water heat of mixing less than 600 but greater than 100 cal/g Less than 100 but greater than 10 W/mL... 

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