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Thermal Stability and Phase Composition of Stratifying Polymer Solutions in Small-Volume Droplets

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Journal of Engineering Physics and Thermophysics Aims and scope

Within the framework of the thermodynamic approach the characteristic features of the phase equilibria and of thermal stability of liquid polymer solutions in small-volume systems are considered. Using as an example a stratifying solution of oligomer fractions of polybutadiene and polystyrene in coarsely disperse droplets of different volumes with core–shell configuration, the regions of thermal stability of various heterogeneous states of the core–shell structure that differ by the compositions of core phases and of homogeneous state are obtained. It is shown that these regions of temperatures depend substantially on the droplet volume, with the compositions of the coexisting phases in different states of the core–shell structure being different. A decrease in the droplet volume is accompanied by a substantial change of the mutual solubilities of components, as well as by a decrease of the upper critical temperature of solubility and by the expansion of the temperature region, in which solutions of any composition up to the equimolar one are dynamically stable.

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References

  1. O. J. Dressler, X. Casadeval i Solvas, and A. J. de Mello, Chemical and biological dynamics using droplet-based microfluidics, Annu. Rev. Anal. Chem., 10, 1–24 (2017); DOI: https://doi.org/10.1146/annurev-anchem-061516-045219.

    Article  Google Scholar 

  2. H.-D. Hi, H. Zheng, W. Guo, A. Gañán-Calvo, Y. Ai, C.-W. Tsao, J. Zhou, W. Li, Y. Huang, N. T. Nguyen, and S. H. Tan, Active droplet sorting in microfluidics: A review, Lab. Chip., 17, 751–771 (2017); DOI: https://doi.org/10.1039/c6lc01435f.

    Article  Google Scholar 

  3. P. Gravesen, J. Branebjerg, and O. S. Jensen, Microfluidics — A review, J. Micromech. Microeng., 3, No. 4, 168–182 (1993); DOI: https://doi.org/10.1088/0960-1317/3/4/002.

    Article  Google Scholar 

  4. V. A. Zhabrev, V. T. Kalinnikov, V. I. Margolin, A. I. Nikolaev, and V. A. Tupik, Physiochemical Processes of Synthesizing Nanodimensional Objects [in Russian], Élmor, St. Petersburg (2012).

    Google Scholar 

  5. M. K. Berner, V. E. Zarko, and M. B. Talawar, Nanoparticles of energetic materials: Synthesis and properties (review), Combust., Explos., Shock Waves, 49, 625–647(2013).

    Article  Google Scholar 

  6. V. A. Arkhipov, S. S. Bondarchuk, and A. S. Zhukov, Evolution of a droplet medium in a plasma-chemical reactor, J. Eng. Phys. Thermophys., 86, No. 4, 775–780 (2013); DOI: https://doi.org/10.1007/s10891-013-0894-z.

    Article  Google Scholar 

  7. K. I. Delendik, V. I. Saverchenko, and S. P Fisenko, Pyrolysis of a femtoliter drop in a low-temperature aerosol reactor at a lowered pressure, J. Eng. Phys. Thermophys., 85, No. 3, 549–553 (2012); DOI: https://doi.org/10.1007/s10891-012-0685-y.

    Article  Google Scholar 

  8. O. G. Penyazkov, V. I. Saverchenko, and S. P. Fisenko, Low-temperature synthesis of nanoparticles in the process of evaporation of femtoliter droplets of a solution at a low pressure, J. Eng. Phys. Thermophys., 87, No. 4, 796–801 (2014); DOI: https://doi.org/10.1007/s10891-014-1074-5.

    Article  Google Scholar 

  9. C. Y. Yap, C. K. Chua, Z. L. Dong, Z. H. Liu, D. Q. Zhang, L. E. Loh, and S. L. Sing, Review of selective laser melting: Materials and applications, Appl. Phys. Rev., 2, Article 041101 (2015); DOI: 0.1063/1.4935926.

  10. H. Lee, C. H. J. Lim, M. J. Low, N. Tham, V. M. Murukeshan, and Y.-J. Kim, Lasers in additive manufacturing: A review, Int. J. Precis. Eng. Manuf. — Green Technol., 4, No. 3, 307–322 (2017); DOI: https://doi.org/10.1007/s40684-017-0037-7.

    Article  Google Scholar 

  11. Y. Li, X. Zhang, J. M. Manyalo, Z. Tian, and J. Ji, Preparation and thermophysical properties of low temperature composite phase change material octanoic-lauric acid/expanded graphite, J. Mol. Liq., 277, 577–583 (2019); DOI: https://doi.org/10.1016/j.molliq.2018.12.111.

    Article  Google Scholar 

  12. S. Federico and W. Herzog, On the permeability of fi bre-reinforced porous materials, Int. J. Solids Struct., 45, 2160–2172 (2008); DOI: https://doi.org/10.1016/j.ijsolstr.2007.11.014.

    Article  MATH  Google Scholar 

  13. L. M. Bronstein, S. N. Sidorov, and P. M. Valetskii, Nanostructured polymeric systems as nanoreactors for nanoparticle formation, Russ. Chem. Rev., 73, No. 5, 501–515 (2004); DOI: RC2004v073n05ABEH000782.

    Article  Google Scholar 

  14. A. M. Bragov, L. A. Igumnov, A. Yu. Konstantinov, A. K. Lomunov, F. K. Antonov, and P. A. Mossakovski, Impact compressibility of a poly(ethylene glycol)-based nanocomposite fluid, Tech. Phys. Lett., 40, No. 10, 923–925 (2014); DOI: https://doi.org/10.1134/S1063785014100186.

    Article  Google Scholar 

  15. A. Sato, W. Knoll, Y. Pennec, B. Djafari-Rouhani, G. Fytas, and M. Steinhart, Anisotropic propagation and confi nement of high frequency phonons in nanocomposites, J. Chem. Phys., 130, Article 11102 (2009); DOI: https://doi.org/10.1063/1.3096972.

    Article  Google Scholar 

  16. K. Sim and J. Lee, Phase stability of Ag–Sn alloy nanoparticles, J. Alloys Compd., 590, 140–146 (2014); DOI: https://doi.org/10.1016/j.jallcom.2013.12.101.

    Article  Google Scholar 

  17. J. Sopoušek, J. Vřešt’ál, J. Pinkas, P. Broz, J. Buršík, A. Styskalik, D. Skoda, A. Zobak, and J. Lee, Cu–Ni nanoalloy phase diagram — Prediction and experiment, CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, 45, 33–39 (2014); DOI: https://doi.org/10.1016/j.calphad.2013.11.004.

  18. S. Bajaj, M. G. Haverty, R. Arróyave, W. A. Goddard, and S. Shankar, Phase stability in nanoscale material systems: Extension from bulk phase diagrams, Nanoscale, 7, Article 9868 (2015); DOI: https://doi.org/10.1039/C5NR01535A.

    Article  Google Scholar 

  19. F. Monji and M. A. Jabbareh, Thermodynamic model for prediction of binary alloy nanoparticle phase diagram including size effect, CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, 58, 1–5 (2017); DOI: https://doi.org/10.1016/j.calphad.2017.04.003.

    Article  Google Scholar 

  20. V. B. Fedoseev, A. V. Shishulin, E. K. Titaeva, and E. N. Fedoseeva, On the possibility of the formation of a NaCl–KCl solid-solution crystal from an aqueous solution at room temperature in small-volume systems, Phys. Solid State, 58, No. 10, 2095–2100 (2016); DOI: https://doi.org/10.1134/S1063783416100152.

    Article  Google Scholar 

  21. A. V. Shishulin and V. B. Fedoseev, Size effect in the phase separation of Cr−W solid solutions, Inorg. Mater., 54, No. 6, 546–549 (2018); DOI: https://doi.org/10.1134/S0020168518050114.

    Article  Google Scholar 

  22. G. Guisbiers, R. Mendoza-Cruz, L. Bazán-Díaz, J. J. Velázquez-Salazar, R. Mendoza-Pérez, J. Robledo-Torres, J.-L. Rodriguez-Lopez, J. M. Montejano-Carrizales, R. L. Whetten, and M. J. Yakamán, Electrum, the gold–silver alloy, from the bulk scale to nanoscale: Synthesis, properties and segregation rules, ASC Nano, 10, 188–198 (2016); DOI: https://doi.org/10.1021/acsnano.5b05755.

    Article  Google Scholar 

  23. M. Cui, H. Lu, H. Jiang, Z. Cao, and X. Meng, Phase diagram of continuous binary nanoalloys: size, shape and segregation rules, Sci. Rep., No. 7, 1–10 (2017); DOI: https://doi.org/10.1038/srep41990.

    Article  Google Scholar 

  24. V. B. Fedoseev and A. V. Shishulin, Shape effect in layering of solid solutions in small volume: Bismuth–Antimony alloy, Phys. Solid State, 60, No. 7, 1398–1404 (2018); DOI: https://doi.org/10.1134/S1063783418070120.

    Article  Google Scholar 

  25. A. V. Shishulin and A. V. Fedoseev, On some peculiarities of stratifi cation of liquid solutions within pores of fractal shape, J. Mol. Liq., 278, No. 7, 363–367 (2019); DOI: https://doi.org/10.1016/j.molliq.2019.01.050.

    Article  Google Scholar 

  26. A. V. Shishulin, V. B. Fedoseev, and A. V. Shishulina, Melting behavior of fractal-shaped nanoparticles (The example of Si−Ge system), J. Tech. Phys., 89, No. 9, 1343–1349 (2019); DOI: https://doi.org/10.1134/S1063784219090172.

    Article  Google Scholar 

  27. V. B. Fedoseev and E. N. Fedoseeva, Formation of bi- and polymodal distributions and the non-Ostwald behavior of disperse systems, J. Eng. Phys. Thermophys., 92, No. 5, 1191–1200 (2019); DOI: https://doi.org/10.1007/s10891-019-02033-2.

    Article  Google Scholar 

  28. V. B. Fedoseev, Formation of mono- and narrow disperse ensembles of droplets of water-organic solutions in vapors of volatiles, J. Eng. Phys. Thermophys., 93, No. 5 (in press) (2020).

  29. V. B. Fedoseev, Oscillating “solution–gas” and “solution–crystal” phase transitions in solution droplets with one crystallizing component, Nelinein. Dinam., 13, No. 2, 195–206 (2017).

    Article  Google Scholar 

  30. B. Straumal, B. Baretzky, A. Mazilkin, S. Protasova, A. Myatiev, and P. Straumal, Increase of Mn solubility with decreasing grain size in ZnO, J. Eur. Ceram. Soc., 29, 1963–1970 (2009); DOI: https://doi.org/10.1016/j.jeurceramsoc.2009.01.005.

    Article  Google Scholar 

  31. E. K. Titaeva and V. B. Fedoseev, Specific features of crystallization of supersaturated solution in femtoliter-volume systems, Crystallogr. Rep., 59, No. 3, 437–441 (2014); DOI: https://doi.org/10.1134/S1063774514030195

    Article  Google Scholar 

  32. G. Kaptay, Nano-CALPHAD: extension of the CALPHAD method to systems with nano-phases and complexions, J. Mater. Sci., 47, No. 24, 8320–8335 (2012); DOI: https://doi.org/10.1007/s10853-012-6772-9.

    Article  Google Scholar 

  33. M. N. Magomedov, The change in the phase diagram of a simple substance at decreasing of the nano-system size, J. Mol. Liq., 285, 106–113 (2019); DOI: https://doi.org/10.1016/j.molliq.2019.04.032.

    Article  Google Scholar 

  34. A. V. Shishulin, V. B. Fedoseev, and A. V. Shishulina, Phonon thermal conductivity and phase equilibria of fractal Bi–Sb nanoparticles, Tech. Phys., 64, No. 4, 512–517 (2019); DOI: https://doi.org/10.1134/S1063784219040200.

    Article  Google Scholar 

  35. A. V. Shishulin and V. B. Fedoseev, On mutual solubility in submicron-sized particles of the Pt–Au catalytic system, Kinet. Catal., 60, No. 3, 315–319 (2019); DOI: https://doi.org/10.1134/S0023158419030121.

    Article  Google Scholar 

  36. A. V. Shishulin and V. B. Fedoseev, Peculiarities of phase transformations of polymer solutions in deformable porous matrices, Tech. Phys. Lett., 45, No. 7, 697–699 (2019); DOI: https://doi.org/10.1134/S1063785019070289.

    Article  Google Scholar 

  37. A. V. Shishulin and V. B. Fedoseev, Concerning the characteristic features of the phase diagrams of polymer solutions in systems of limited volume, Ext. Abstracts of the Korshakovsk. All-Union Conf. (with foreign participants)"Polycondensation Processes and Polymers," February 18–20, 2019, Moscow (2019), p. 53.

  38. C. D. Han, S. B. Chun, S. F. Hahn, S. Q. Harper, P. J. Savickas, D. M. Meunier, L. Li, and T. Yancin, Phase behavior of polystyrene/polybutadiene and polystyrene/hydrogenated polybutadiene mixtures: Effect of the microstructure of polybutadiene, Macromolecules, 31, 394–402 (1998); DOI: https://doi.org/10.1021/ma971309e.

    Article  Google Scholar 

  39. Y. S. Li, C. P. Wang, and X. J. Liu, Thermodynamic assessments of binary phase diagrams in organic and polymeric systems, CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, 33, 415–419 (2009); DOI: https://doi.org/10.1016/j.calphad.2008.12.007.

    Article  Google Scholar 

  40. A. Shirinyan, Two-phase equilibrium states in individual Cu–Ni nanoparticles: Size, depletion and hysteresis effects, Beilstein J. Nanotechnol., 6, 1811–1820 (2015); DOI: https://doi.org/10.3762/bjnano.6.185.

    Article  Google Scholar 

  41. A. A. Tager, Physical Chemistry of Polymers [in Russian], Khimiya, Moscow (1978).

    Google Scholar 

  42. S. Wu, Interfacial and surface tensions of polymers, J. Macromol. Sci. C, 10, 1–73 (1974); DOI: https://doi.org/10.1080/15321797408080004.

    Article  Google Scholar 

  43. V. I. Saverchenko, S. P. Fisenko, and Yu. A. Khodyko, Evaporation of a picoliter drop on a wetted substrate at reduced pressure, J. Eng. Phys. Thermophys., 84, No. 4, 723–729 (2011); DOI: https://doi.org/10.1007/s10891-011-0527-3.

    Article  Google Scholar 

  44. V. M. Samsonov, N. Yu. Sdobnyakov, M. V. Samsonov, D. N. Sokolov, and N. V. Novozhilov, Thermodynamic model of melting of thin metal films, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech., 9, No. 4, 831–835 (2015); DOI: https://doi.org/10.1134/S1027451015040333.

    Article  Google Scholar 

  45. A. V. Shishulin, V. B. Fedoseev, and A. V. Shishulina, On the influence of external medium on phase conversions in a small-volume system on the example of the decay of the Bi–Sb solid solution, Butler Commun., 51, No. 7, 31–37 (2017).

    Google Scholar 

  46. A. A. Amooey, A novel model for predicting the surface tension of binary solutions, J. Eng. Phys. Thermophys., 87, No. 3, 533–540 (2014); DOI: https://doi.org/10.1007/s10891-014-1042-0.

    Article  Google Scholar 

  47. L. Jia and B. Shi, A new equation between surface tensions and solubility parameters without molar volume parameters simultaneously fi tting polymers and solvents, J. Macromol. Sci. B, 50, 1042–1046 (2011); DOI: https://doi.org/10.1080/00222348.2010.497439.

    Article  Google Scholar 

  48. A. Shirinyan, G. Wilde, and Y. Bilogorodskyy, Solidification loops in the phase diagrams of nanoscale alloy particles: from a specific example towards a general vision, J. Mater. Sci., 53, 2859–2879 (2018); DOI: https://doi.org/10.1007/s10853-017-1697-y.

    Article  Google Scholar 

  49. A. V. Shishulin and V. B. Fedoseev, Effect of initial composition on the liquid–solid phase transition in Cr–W alloy nanoparticles, Inorg. Mater., 55, No. 1, 14–18 (2019); DOI: https://doi.org/10.1134/S0002337X19010135.

    Article  Google Scholar 

  50. V. B. Fedoseev and A. V. Shishulin, Influence of the original composition on phase equilibria in the Cr–W system of nanometer dimension, Coll. Ext. Abstracts of papers submitted to the IX Int. Sci. Conf. "Kinetics and Mechanism of Crystallization. Crystallization and Materials of the Future," September 13–16, 2016, Ivanovo (2016), pp. 28–29.

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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 93, No. 4, pp. 831–840, July–August, 2020.

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Shishulin, A.V., Fedoseev, V.B. Thermal Stability and Phase Composition of Stratifying Polymer Solutions in Small-Volume Droplets. J Eng Phys Thermophy 93, 802–809 (2020). https://doi.org/10.1007/s10891-020-02182-9

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  • DOI: https://doi.org/10.1007/s10891-020-02182-9

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