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Lattice model of equilibrium polymerization. VI. Measures of fluid “complexity” and search for generalized corresponding states
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10.1063/1.2785187
/content/aip/journal/jcp/127/22/10.1063/1.2785187
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/22/10.1063/1.2785187
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Typical variation of the dimensionless osmotic pressure with the initial monomer composition for equilibrium polymer solutions at temperatures above the critical temperature. The curves in the figure are computed for the activated equilibrium polymerization model described in the text and specified by , , , , and (i.e., clusters are assumed to be rigid structures). Unless stated otherwise, the same free energy parameters , , , and , the exchange energy , the factor , and the factor (that quantifies the strength of three-body interactions) are used in computations summarized in Figs. 2–11.

Image of FIG. 2.
FIG. 2.

The polymerization transition line (dashed line), coexistence curve (dotted line), and the spinodal curve (solid line) for a model fluid exhibiting activated equilibrium polymerization in the intermediate coupling regime (defined in the text) where the polymerization transition temperature at the critical composition and the critical temperature are comparable in magnitude. The critical point is indicated by a cross, while other symbols denote estimates of the polymerization line that are obtained from the composition variation of the average polymerization index (circles), the isothermal osmotic compressibility (diamonds), and the osmotic pressure (triangles). The coexistence curve (dotted line) is evidently asymmetric, reflecting the “polymeric” nature of the fluid at the critical temperature, and the rectilinear diameter (long dashed line) displays a large slope. The curvature of the rectilinear curve derives from the three-body interactions that generally arise from size anisotropy (between a solvent molecule and a monomer of the associating species) or from the molecular polarizability (see text).

Image of FIG. 3.
FIG. 3.

The critical temperature for the phase separation of equilibrium polymerization solutions as a function of the polymerization energy and computed for the activated polymerization model described in the text. The existence of three different regimes in the qualitative behavior of provides a convenient criterion for defining the weak, strong, and intermediate coupling regimes of associative interactions, which are labeled in the figure by I, II, and III, respectively.

Image of FIG. 4.
FIG. 4.

(a) Temperature variation of the second and third virial coefficients for equilibrium polymer solutions in the weak coupling regime , as computed for the activated polymerization model described in the text. (b) Temperature variation of the second and third virial coefficients for equilibrium polymerization solutions in the strong coupling regime phase as computed for the activated polymerization model described in the text. (c) Temperature variation of the second and third virial coefficients for equilibrium polymerization solutions in the intermediate coupling regime between polymerization and phase separation as computed for the activated polymerization model specified in the text. The second and third virial coefficients as functions of the inverse temperature for (d) the weak, (e) the strong, and (f) the intermediate coupling regimes.

Image of FIG. 5.
FIG. 5.

(a) The mixing component of the osmotic pressure as a function of polymer volume fraction for polyacrylate gels in equilibrium with solutions of NaCl and . Different curves correspond to different salt concentrations, as in Fig. 6 of Ref. 87(a). (b) The second viral coefficient and the ratio (where is the third virial coefficient) as functions of the concentration of . The virial coefficients are obtained from fits of the FH expression for the osmotic pressure to the experimental data shown in (a).

Image of FIG. 6.
FIG. 6.

Temperature variation of the second virial coefficient of equilibrium polymer solutions as computed for different values of the activation entropy that are specified in the figure .

Image of FIG. 7.
FIG. 7.

(a) The characteristic temperatures of equilibrium polymerization solutions as functions of the energy of polymerization and computed for the activated polymerization model described in the text. The temperatures considered include the critical temperature, the theta temperature , and the temperature where the third virial coefficient vanishes. (b) The critical composition as a function of for the system analyzed in (c). Same as (a) but for a system with three-body interactions neglected . (d) Same as (b) but for a system with three-body interactions neglected .

Image of FIG. 8.
FIG. 8.

Ratios of the characteristic temperatures of equilibrium polymer solutions as a function of the sticking energy [see Fig. 7(a)].

Image of FIG. 9.
FIG. 9.

The characteristic temperatures of equilibrium polymer solutions as a function of the exchange energy and computed for the activated polymerization model described in the text. The temperatures considered include the critical temperature, the theta temperature , and the temperature where the third virial coefficient vanishes.

Image of FIG. 10.
FIG. 10.

Ratios of the characteristic temperatures of equilibrium polymer solutions that are analyzed in Fig. 9 as a function of the exchange energy .

Image of FIG. 11.
FIG. 11.

The rectilinear diameter and the critical osmotic compressibility factor (normalized by the corresponding quantity for monomer-solvent systems) computed as functions of the polymerization energy for a solution exhibiting activated equilibrium polymerization. The free energy parameters are specified in the caption to Fig. 1, and the factor , describing the strength of ternary interactions, is set to zero (i.e., the ternary interactions are neglected in this illustrative example).

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/content/aip/journal/jcp/127/22/10.1063/1.2785187
2007-12-11
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Lattice model of equilibrium polymerization. VI. Measures of fluid “complexity” and search for generalized corresponding states
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/22/10.1063/1.2785187
10.1063/1.2785187
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