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Lattice cluster theory of associating telechelic polymers. III. Order parameter and average degree of self-assembly, transition temperature, and specific heat
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10.1063/1.4714562
/content/aip/journal/jcp/136/19/10.1063/1.4714562
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4714562
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The temperature variation of the order parameter for self-assembly of weakly interacting (ε s = −300 K) short linear telechelic chains (M = 5) in a single-bead solvent as evaluated from the LCT for various fixed solute volume fraction ϕ. The exchange van der Waals energy ε is taken as ε = 100 K in all figures unless otherwise stated.

Image of FIG. 2.
FIG. 2.

The same as Figure 1, but for the higher sticky interaction energy ε s = −1500 K.

Image of FIG. 3.
FIG. 3.

The temperature variation of the average degree ⟨N⟩ of self-assembly of weakly interacting (ε s = −300 K) short linear telechelic chains (M = 5) in a single-bead solvent as evaluated from the LCT for various fixed solute volume fractions ϕ.

Image of FIG. 4.
FIG. 4.

The same as Figure 3, but for the higher sticky interaction energy ε s = −1500 K.

Image of FIG. 5.
FIG. 5.

The temperature variation of the order parameter for self-assembly of linear telechelic chains in a single-bead solvent as evaluated from the LCT for different fixed lengths M of telechelic chains. Crosses indicate the positions of the inflection points of the order parameter curves. The sticky interaction energy ε s is chosen as ε s = −3000 K, and the solute volume fraction ϕ is taken as ϕ = 0.01.

Image of FIG. 6.
FIG. 6.

The temperature variation of the average degree of self-assembly ⟨N⟩ of linear telechelic chains in a single-bead solvent as evaluated from the LCT for the specified fixed lengths M of telechelic chains. Crosses indicate the values of ⟨N⟩ at the self-assembly transition temperature. The sticky interaction energy ε s is chosen as ε s = −3000 K, and the solute volume fraction ϕ is taken as ϕ = 0.01.

Image of FIG. 7.
FIG. 7.

The temperature dependence of the order parameter for self-assembly of long linear telechelic chains (M = 1000) in a single-bead solvent as evaluated from the LCT for different exchange energies ε. The sticky interaction energy ε s is chosen as ε s = −3000 K, and the solute volume fraction ϕ is taken as ϕ = 0.01.

Image of FIG. 8.
FIG. 8.

The same as Figure 7 but for the temperature dependence for the average degree ⟨N⟩ of self-assembly of long linear telechelic chains (M = 1000).

Image of FIG. 9.
FIG. 9.

The temperature dependence of the order parameter for self-assembly of linear telechelic chains in solutions with a single-bead solvent as evaluated from the LCT for fixed products ϕ x of the solute volume fraction ϕ and the sticker fraction x. Each curve is universal for all lengths M of individual telechelic chains. The sticky interaction energy is ε s = −3000 K.

Image of FIG. 10.
FIG. 10.

The same as Figure 9 but for the temperature dependence of the average degree ⟨N⟩ for self-assembly of linear telechelic chains in solutions.

Image of FIG. 11.
FIG. 11.

The self-assembly transition temperatures T p as a function of the volume fraction ϕ of telechelic chains as evaluated from the LCT. Each self-assembly transition line corresponds to a fixed number M of united atom groups in the individual telechelic chains and to the sticky interaction energy ε s = −1500 K.

Image of FIG. 12.
FIG. 12.

The self-assembly transition temperatures T p as a function of the volume fraction ϕ of telechelic chains as evaluated from the LCT for various sticky interaction energies ε s but fixed chain length M = 5.

Image of FIG. 13.
FIG. 13.

The logarithm of self-assembly transition temperature T p versus the logarithm of the number M of united atom groups in a single telechelic chain as evaluated from the LCT for the dilute solution of linear telechelic chains (ϕ = 0.01) interacting with a fixed sticky interaction energy ε s . Symbols denote calculated results, while lines are least square fits to the calculated data.

Image of FIG. 14.
FIG. 14.

The average degree ⟨N⟩(T = T p ) of self-assembly of linear telechelic chains at the self-assembly transition temperature T p versus the logarithm of the length M of telechelic chains as calculated from the LCT for various volume fractions ϕ of telechelic chains.

Image of FIG. 15.
FIG. 15.

The temperature dependence of the specific heat C V of telechelic polymer solutions as evaluated from the LCT for various sticky interaction energies ε s . The exchange van der Waals energy is taken as vanishing, and the length M of telechelic chains is chosen as M = 5.

Image of FIG. 16.
FIG. 16.

The temperature dependence of the specific heat C V of telechelic polymer solutions as evaluated from the LCT for the specified volume fractions of telechelic polymers, the sticky energy ε s = −1500 K (ε = 0), and the chain length M = 5.

Image of FIG. 17.
FIG. 17.

The temperature dependence of the specific heat C V of dilute solutions of telechelic polymers (ϕ = 0.01) as evaluated from the LCT for several fixed lengths M of telechelic chains. The sticky interaction energy ε s is chosen as ε s = −1500 K, and the van der Waals exchange energy ε is taken as vanishing.

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2012-05-15
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Lattice cluster theory of associating telechelic polymers. III. Order parameter and average degree of self-assembly, transition temperature, and specific heat
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/19/10.1063/1.4714562
10.1063/1.4714562
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