Phase diagram snapshots - Results and discussion

5.4 Results and discussion

5.4.4 Phase diagram snapshots

Additionally, we built phase diagram using snapshots. The diagrams was built for pH−pK=1,ε =0.5 (see Fig.5.6) and pH−pK=1,ε=0.7 (see Fig.5.7). Both diagrams were built for different salt concentrationc_sas a function of applied pressure (or gel density φ). The colored frame on some snapshots illustrated the two-phase region, which is calculated by Maxwell construction procedure. As it is seen, the two-phase region shrinks with an increase of salt concentration. That refers to one of the ideas of the article, namely, deteriorate the solvent quality condition in order to get the effect at high salt concentrations.

(a)

14.5 pH-pK ≈ 1.29 pH-pK ≈ 1.12

7.73 pH-pK ≈ 0.47

pH-pK ≈ 0.15

pH-pK ≈ -0.04 pH-pK ≈ -0.17

3.92 1.05 0.19 -0.03

16.5 -1.32 8.2

-0.23 1.48

ptr = 2.62 simulations, pH-pK = 2, ɛ = 0.7 simulations, pH-pK = 2, ɛ = 0.5 box-model, different pH-pK, χ = 1.12 box-model, different pH-pK, χ = 0.9

Salt concentration, cs [mol/L]

10⁻³ 0.01 0.1

Gel density, ρ [mol/L]

10⁻³ 0.01 0.1 1 10 100

(b)

pH-pK ≈ 1.2 12.24 pH-pK ≈ 0.98

5.85 pH-pK ≈ 0.41

pH-pK ≈ 0.16 pH-pK ≈ -0.4

pH-pK ≈ -0.47 pH-pK ≈ -0.48

8.01 3.31 0.4 0.05 -0.04

16.5 -0.62 8.2

-0.46 -0.02

1.55 ptr = 4.07 bar simulations, pH-pK = 1, ɛ = 0.5 simulations, pH-pK = 2, ɛ = 0.5 box-model, different pH-pK, χ = 0.96 box-model, different pH-pK, χ = 0.9

Salt concentration, cs [mol/L]

10⁻³ 0.01 0.1

Gel density, ρ [mol/L]

10⁻³ 0.01 0.1 1 10 100

(c)

pH − pK ≃

box- mode

pH − pK = 1, χ

= 0.96 ptr = 25.22

18.41 12.26 6.93 4.9 0.41

0.16

−0.40

−0.47

−0.48

-0.04 0.05 0.29 0.59 ptr = 0.94 ptr = 8.01 7.89 3.68 1.95 1.33 ptr = 8.01

3.31 0.4 0.05 -0.04-0.62

-0.46 -0.02

1.55 ptr = 4.07 bar simulations: pH − pK = 1, ɛ = 0.5 box-model: different pH − pK, χ = 0.96 box-model: pH − pK ≃ 0.41, χ = 0.96 box-model: pH − pK ≃ −0.48, χ = 0.96

Salt concentration, cs [mol/L]

10⁻³ 0.01 0.1

Gel density, ρ [mol/L]

10⁻³ 0.01 0.1 1 10 100

FIGURE5.5: Phase diagrams of hydrophobic gel in salt concentration cs– gel concentration coordinates obtained from MD simulations (a) at constant pH−pK = 2 and different solvent quality εand (b) at constant solvent qualityε=0.5 and different pH−pK. (c) Compar- ison of simulation results at constant pH−pK =1 andε=0.5 with analytical theory results at constant solvent qualityχ=0.96 and different pH−pK. Numbers near by points correspond to transition pressure values. Results of fitting see in the supporting information

of original manuscript Fig. 5, Fig. 6, Fig. 7.

c_s[M]

0.2

./Figures/tga/pK6.0/cs0.2/pwgel_100.0_100.0_100.0_try0_mpc50_pK6.0_cs0.2_muexcess-0.6145_lB2.0_eps0.5_pp_step16_2-tga-converted-to.jpg./Figures/tga/pK6.0/cs0.2/pwgel_100.0_100.0_100.0_try0_mpc50_pK6.0_cs0.2_muexcess-0.6145_lB2.0_eps0.5_pp_step16_2-tga-converted-to.jpg./Figures/tga/pK6.0/cs0.2/pwgel_100.0_100.0_100.0_try0_mpc50_pK6.0_cs0.2_muexcess-0.6145_lB2.0_eps0.5_pp_step16_2-tga-converted-to.jpg./Figures/tga/pK6.0/cs0.2/pwgel_100.0_100.0_100.0_try0_mpc50_pK6.0_cs0.2_muexcess-0.6145_lB2.0_eps0.5_pp_step16_2-tga-converted-to.jpg./Figures/tga/pK6.0/cs0.2/pwgel_100.0_100.0_100.0_try0_mpc50_pK6.0_cs0.2_muexcess-0.6145_lB2.0_eps0.5_pp_step16_2-tga-converted-to.jpg

0.12

0.072

0.043

0.026

0.015 0.01 0.006 0.003 0.002

φ[mol/L]: 0.03 0.25 1.16 1.78 3.91 6.15 8.99 12.79 17.37 22.06 FIGURE5.6: Snapshots of hydrophobic gel with pH−pK = 1, ε = 0.5. Each row corresponds to a certain salt concentrationcsand each column – gel density. Snapshots in colored frame show the gel in the

coexistence region.

c_s[M]

0.2

0.12

0.072

0.043

0.026

0.015 0.01 0.006 0.003 0.002

φ[mol/L]: 0.03 0.25 1.16 1.78 3.91 6.15 8.99 12.79 17.37 22.06 FIGURE5.7: Snapshots of hydrophobic gel with pH−pK = 1, ε =

0.7. Each row corresponds to a certain salt concentrationcsand each column – gel density. Snapshots in colored frame show the gel in the

coexistence region.

No documento Computer Simulation Methods of Soft Matter (páginas 55-58)