AÑO REGIMEN IMPORTE

As noted earlier, processing solvents that include small amounts of additives can alter OSC morphologies, affecting the OSC characteristics. The choice of additive and host solvent and the amount of additive that should be added varies depending on the chemistry of the OSC, to date, remains highly empirical and is often determined through trial-and-error approaches. Here we investigated several solvent and additive molecules that are widely used in OSC processing. The methods developed here provide a framework for further investigations of such multicomponent systems across a range of applications.

Pure solvent equilibration. Prior to the examination of the free energies of mixing, it is

important to establish the appropriate system sizes for the simulations. Since we are particularly interested in following the mixing processes at small concentrations of the additives, it is imperative that the simulation boxes be large enough to allow for this situation. Here, we begin with evaluations of the pure liquids that are subjected to the 2PT method; relevant data is summarized in Figure 4.13 and Figure 4.14. With increasing system size, the entropy changes plateau, as summarized in Figure 4.13. Importantly, as the system sizes are extended, the computational cost for the DoSPT code increases exponentially (Figure 4.15). To balance the computational cost of the exponential system size dependence of the 2PT method with enough additive molecules to ensure entropy convergence, each pure and binary system studied here contains 10,000 total molecules.

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Figure 4.16. Entropy calculated from 2PT method with DoSPT code of different system size.

Figure 4.17. Entropy of the pure solvent from 2PT calculation

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Figure 4.18. Time cost of applying DoSPT code for entropy calculation.

Table 4.7 summarizes the results from six individual simulations for each pure solvent. In general, the liquid densities and the standard molar entropies of CB and DCB show good agreement with experiment. DIO does presents a larger standard deviation of 6.5% with respect to the experimental density; this deviation could be due to the fact that the non-bonded parameter for iodine was derived for aryl halides,⁵⁵ which present slightly different chemistries than one might expect for alkyl halides; two different non-bonded parameters for iodine were evaluated and the input files are included in the SI, with the one that presented the best agreement with the experimental DIO density used in all subsequent calculations. Although the 2PT method has been widely applied to liquids and even mixtures, most of the simulation targets are ions, non-organic liquids,^11-26 or water/organic mixtures.^{23-38, 56} The validation of using 2PT on pure organic solvents here provides us confidence in the application of the method to binary mixtures.

We also determined the solubility parameters of each pure solvent systems. The calculated Hildebrand and Hansen solubility parameters are in good agreement with previous

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reference values.⁵⁷ The solubility parameters of each pure solvent fall within 9.4 to 10 cal^1/2 cm^-3/2, suggesting from an entropic standpoint that each additive should readily mix with the host solvent.

Table 4.7. Hildebrand and Hansen solubility parameter, density and standard molar entropy of solvent systems calculated from simulation.

Density

aDensity and entropy data were retrieved from the NIST WebBook at www.nist.gov. ^bThe experimental solubility parameters were retrieved from literature⁵⁸ and Hansen Solubility Parameters handbook.⁵⁹

Solutions: Free Energy of Solvation and Diffusion. Since experimental solvation energies

of our target systems are not available, we first selected several common organic–aqueous solutions and determined the solvation energy for these reference solutions to validate the approach. The results, presented in Table 4.8, demonstrate that the calculated solvation energies agree reasonably well with reference experimental values.⁵² In turn, we determined the solvation energy of each additive in the three host solvents. All solvation energies are negative, as shown in Figure 4.16, suggesting that the solvation of the additive into the host solvent is an exothermic process. For both CN and DIO, the ∆𝐺 is similar

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across all three solvents, indicating that the energy difference associated with dissolving the additive into different solvent environment is negligible. Solutions with DIO present solvation energies about 10 kJ/mol smaller than the solutions containing CN, suggesting that DIO is more readily solvated.

Table 4.8. Salvation energy of solvent calculated using BAR method as comparing with reference values.

Binary Model Expt. (kJ/mol) MD (kJ/mol)

Methane/Water 8.39 9.84 ± 0.22

Methanol/Water -21.34 -17.87 ± 0.51

Ethanol/Water -20.90 -21.90 ± 3.73

Benzene/Water -3.21 -2.40 ± 0.37

Figure 4.19. Free energy of solvation of two additives in three host solvents.

The relative free energy differences for each interval of the coupling parameter λ are presented in Figure 4.17. The value of λ where the energy changes sign is defined as the critical point (λ_𝐶). Notably, both CN and DIO have similar λ_𝐶, located between 0.7 and 0.8

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in all host solvents. ). For λ value larger than λ_𝐶, scaling out the additive is energetically favorable, while for λ value smaller than λ_𝐶, scaling in additive is energetically favorable.

Notably, both PN and DIO has similar λ_𝐶 located between 0.7 and 0.8 across all host solvents.

Figure 4.20. Relative free energy differences as function of each interval of λ.

Turning to diffusion, there is a large variation in the additive diffusion coefficients at low additive concentrations, Figure 4.18. At low additive concentrations, only a few additive molecules are present in the system, resulting in larger standard deviations. At concentrations larger than 10%, the diffusion constant stabilizes in all mixtures. Additive

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diffusion in each host solvent follows the order of CB > DCB > TCB, which is expected in part due to the increasing size of the host molecule. When CB was the host solvent, at low additive concentrations, both CN and DIO showed the largest diffusion coefficient, around 0.8×10^-5 cm²/s, which then decreased significantly as the concentration increased; this suggests that there was more solvent-additive interaction at lower additive concentration in CB solution. In DCB and TCB mixtures, however, the diffusion constants for DIO and CN were less affected by the additive concentration.

Figure 4.21. Diffusion constant of two additive, DIO (left) and CN (right), in three host solvents as a function of the additive concentration.

Gibbs free energy of mixing

The density of each binary solution at various additive concentrations was checked to guarantee a mixed condition was achieved for free energy prediction. The results were shown in Figure 4.21. Each density change was following the trend to recover the density of the two components, suggesting a complete mixed feature throughout the concentrations.

We then calculated the energies with these equilibrated systems.

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Figure 4.22. Density of the two additive mixtures, CN (top) and DIO (bottom), in the three host solvents as a function of the additive concentration.

All binary mixtures present ∆𝐺_𝑚𝑖𝑥 less than zero across all additive fractions, Figure 4.22, indicating the additives are soluble with three host solvent at various concentrations. The minimum of ∆𝐺_𝑚𝑖𝑥 occurs between 0.2 – 0.4 additive mole fraction. Interestingly, when DIO is the additive, the enthalpy terms are all positive, suggesting that the mixing of DIO with the host solvent is enthalpically unfavorable. For mixtures containing CN as the

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additive, the enthalpy is nearly unchanged and zero across all mole fractions. In every case,

∆𝐺_𝑚𝑖𝑥 follows the trends set by −𝑇∆𝑆, suggesting that the mixing between the additive and host solvents re driven by entropy. Notably, when CB and DCB are the host solvent, both DIO and CN show a slightly higher ∆𝐺_𝑚𝑖𝑥 than when TCB is the solvent.

Figure 4.23. Enthalpy, entropy and Gibbs free energy of mixing as function of the additive mole fraction of the binary solutions.

For the purpose of solution printing OSC, there has been a move towards developing non-halogenated “green” solutions. To show further generality of the method, we also examined the mixing of 1,2,4-trimethylbenzene (TMB) as the host solvent and 1-phenylnaphthalene (PN) as the additive (Figure 4.23).⁶⁰ Here, the minimum of ∆𝐺_𝑚𝑖𝑥 occurs between 0.4 – 0.6 additive mole fraction. The enthalpy term is again slightly positive, suggesting that the mixing of PN with the TMB is enthalpically unfavorable. The overall entropy and free energy of mixing are similar to the halogenated solutions using CN as the additive, which is expected due to the chemical similarity of the CB–CN and TMB–PN mixtures.

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Figure 4.24. Enthalpy, entropy and Gibbs free energy of mixing as function of the additive mole fraction of the TMB–PN solutions.

4.5 Conclusion

In this chapter, we have shown that the 2PT method is a practical tool to calculate the entropy of various liquid solutions. When the shape of the molecule is spherical, 2PT gives a good agreement with experimental measurement. For the non-spherical molecules, however, a linear relation with the entropy calculated from low-concentration solutions can provide a good estimation of the standard molar entropy of the solute.

We then explored the energy properties of the LJ liquids and several common molecular models, for the pure and binary systems, our results showed reasonable agreement with experiment and expectations. ∆𝐺_𝑚𝑖𝑥 < 0 was shown to be a necessary but not sufficient condition for miscibility. Turning to ternary solutions, we found that the introduction of the additional component can further stabilize the ∆𝐺_𝑚𝑖𝑥 and the lowest energy becomes

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comparable to the fully mixed solution while all components are equivalent in concentration.

Accurate and expedient determinations of the free energy of mixing can hold important consequence across a number of fields, including the development of emerging technologies. Here, with a focus on beginning to develop in silico protocols to understand and design printing inks for OSC, we determined the free energies of mixing for commonly used halogenated solvents and additives across a range of concentrations. We show that the mixing in these systems is predominantly entropically driven, which highlights the importance of needing robust methods to determine entropic terms. This work represents a first step along the path to implementing in silico design of OSC that includes the processing conditions.

127 CHAPTER 5

INFLUENCE OF THE SOLVENT ENVIRONMENT ON THE MOLECULAR