了解高分子混合物在失穩分解行為及界面特性是凝態物理的古老議題之一。在這裡我們提出了新的科學研究方法，來藉由實驗觀察及理論分析，了解PEG/PPG 混合物在界面形成和演化之過程行為。在第一章中，Temperature-Transmittance Tracing實驗可以透過Flory-Huggins 格子理論來建立熱力學狀態方程。透過相圖反映出的平衡組成，相互作用參數(interaction parameter ?)可由分析計算出相應的溫度依賴性關係。從等溫條件下觀察的2D Fourier transform 相差顯微鏡相分離動力學粗化指數中，可發現接近臨界點的粗化機制屬於擴散界面模型所描數之界面擴散機制行為。從結構形態的觀察，我們還指出reduced hump energy ψ 對溫度依賴性的驅動力影響，來為後續理論模型架構提供所需參數。

在第二章中，我們為PEG/PPG 相分離平衡態進行Axisymmetric Drop Shape Analysis (ADSA) 分析法來量測兩相平衡界面張力值。為進行此研究，我們同時與thermo-optical apparatus一起架設開發設計了臨界標度行為分析之用途儀器。此外，為了精確的量測懸垂液滴之低界面張力值，我們引入了自動同步控制滴定及影像擷取功能，藉此得到更精確、更高重複率的懸垂液滴形狀因子優化測定之技術。實驗結果驗證了平均場理論（mean-field theory）對序参量的解析及狀態方程的預測。最後，我們首次提出比界面張力(reduced interfacial tension)在最大懸垂液滴尺寸隨時間緩和之指數衰減的主曲線(master curve) ，並非溫度依賴行為。

在第三章中，我們着重於透過先前實驗數據，而解析Cahn-Hilliard模型所呈現的失穩分解粗化數值計算結果，並將失穩分解中的三個階段過程，藉由自由能及gradient energy coefficient κ溫度依賴性做進一步結構與界面形成和演化過程詳細的了解。而於數值分析結果為非量化分析，其粗化機制與實驗比較後，我們可以確認熱力學及界面張力在相變原理上是可被部分表述的。

Understanding the phenomenon of interfacial properties of spinodal decomposition in polymer mixtures is one of the long-standing challenges in condensed matter physics. Here we study this question by developing an experimental and theoretical method to investigate the various behaviors of structure formation and transformation in PEG/PPG mixtures. In the first section, the thermodynamic characteristic of phase behavior is constructed by temperature-transmittance tracing experiments, where Flory-Huggins Lattice model was used to calculate the temperature dependence of the interaction parameter ?. From the kinetic scaling of growing under isothermal phase separation using 2D Fourier transform phase contrast microscope images, we have found the diffusing mechanism appears to happen at near critical temperature, which follows the description of diffuse interface model. From the morphological observation, we also indicate the evidence of temperature dependence reduced hump energy ψ driving force, which provided us with a useful framework for theoretical comparison.

In the second section, the interfacial tension γ of macroscopic phase separated PEG/PPG mixtures at equilibrium was measured with Axisymmetric Drop Shape Analysis (ADSA) technique. The apparatus we specifically designed and developed with thermo-optical apparatus together for critical scaling behavior analyzing purpose. Because of the interfacial tension of the two phases are partially miscible and ultralow, obtaining an accurate and repeatable was addressed by development of automatic control and precise dispensing control to form an optimized pendant drop on the Teflon capillary. The results were evaluated to mean-field theory on the reduced critical temperature and was realized with reduced hump energy prediction. Additionally, we proposed a new physical phenomenon from a master curve of reduced interfacial tension exponential decay dynamic at maximum drop size, which is independent of scaling laws.

In the third section, we put attention on using only experimental data to manipulate coarsening kinetics by Cahn-Hilliard model. We found that with temperature dependent free energy and gradient energy coefficient κ, the three stages of spinodal decomposition and composition dependence was able to presented detailed information on the structural and interfacial evolution processes. This is confirmed by comparison between experimental observation and offer valuable insights into the nature of the state.

[1] Domb, C. and Lebowitz, J. (1983). Phase transitions and critical phenomena, Volume 8. London: Academic Press.
[2] Binder K. Phase transition of polymer blends and block copolymer melts in thin films. In: Advances in Polymer Science, vol. 138, Polymers in Confined Enviroments, Springer, 1999.
[3] Granick, S. and Binder, K. (1999). Phase transition of polymer blends and block copolymer melts in thin films. In: Advances in Polymer Science, vol. 138, Polymers in confined environments. Berlin: Springer.
[4] Ōnuki, A. (2007). Phase transition dynamics. Cambridge: Cambridge Univ. Press.
[5] Akcasu, A. (2011). Scattering and Dynamics of Polymers: Seeking Order in Disordered System. Wiley.
[6] Kenel, C. and Leinenbach, C. (2015). Influence of cooling rate on microstructure formation during rapid solidification of binary TiAl alloys. Journal of Alloys and Compounds, 637, pp.242-247.
[7] Kundin, J., Pogorelov, E. and Emmerich, H. (2015). Phase-field modeling of the microstructure evolution and heterogeneous nucleation in solidifying ternary Al–Cu–Ni alloys. Acta Materialia, 83, pp.448-459.
[8] Wang, H., Zhang, X., Lai, C., Kuang, W. and Liu, F. (2015). Thermodynamic principles for phase-field modeling of alloy solidification. Current Opinion in Chemical Engineering, 7, pp.6-15.
[9] Hashimoto, T., Takenaka, M. and Jinnai, H. (1991). Scattering studies of self-assembling processes of polymer blends in spinodal decomposition. Journal of Applied Crystallography, 24(5), pp.457-466.
[10] Bates, F. and Wiltzius, P. (1989). Spinodal decomposition of a symmetric critical mixture of deuterated and protonated polymer. The Journal of Chemical Physics, 91(5), pp.3258-3274.
[11] Bates, F. and Wiltzius, P. (1989). Spinodal decomposition of a symmetric critical mixture of deuterated and protonated polymer. The Journal of Chemical Physics, 91(5), pp.3258-3274.
[12] Siggia, E. (1979). Late stages of spinodal decomposition in binary mixtures. Physical Review A, 20(2), pp.595-605.
[13] Aarts, D., Dullens, R. and Lekkerkerker, H. (2005). Interfacial dynamics in demixing systems with ultralow interfacial tension. New Journal of Physics, 7, pp.40-40.
[14] McMaster, L. (1975). Aspects of Liquid-Liquid Phase Transition Phenomena in Multicomponent Polymeric Systems. Advances in Chemistry, pp.43-65.
[15] Flory, P. (2010). Principles of polymer chemistry. Ithaca: Cornell Univ. Press.
[16] Rubinstein, M., & Colby, R. H. (2003). Polymer physics. Oxford: Oxford University Press.
[17] Cahn, J. (1965). Phase Separation by Spinodal Decomposition in Isotropic Systems. The Journal of Chemical Physics, 42(1), pp.93-99.
[18] Lifshitz, I. and Slyozov, V. (1961). The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids, 19(1-2), pp.35-50.
[19] Shimizu, R. and Tanaka, H. (2015). A novel coarsening mechanism of droplets in immiscible fluid mixtures. Nature Communications, 6, p.7407.
[20] Cahn, J. and Hilliard, J. (1958). Free Energy of a Nonuniform System. I. Interfacial Free Energy. The Journal of Chemical Physics, 28(2), pp.258-267.
[21] Enders, S., Wolf, B. and Binder, K. (1995). Interfacial tension of phase‐separated polymer solutions and relation to their equation of state. The Journal of Chemical Physics, 103(9), pp.3809-3819.
[22] Young, T. (1805). An Essay on the Cohesion of Fluids. Philosophical Transactions of the Royal Society of London, 95(0), pp.65-87.
[23] Bashforth, F. and Adams, J. (1883). An attempt to test the theories of capillary action. Cambridge [England]: Cambridge University Press.
[24] Lambert, J. (2000). Numerical methods for ordinary differential systems. Chichester: John Wiley & Sons.
[25] Hu, H. and Joseph, D. (1994). Evolution of a Liquid Drop in a Spinning Drop Tensiometer. Journal of Colloid and Interface Science, 162(2), pp.331-339.
[26] Enders, S., Huber, A. and Wolf, B. (1994). Interfacial tension and interaction parameters. Polymer, 35(26), pp.5743-5747.
[27] Escudie, E., Graciaa, A. and Lachaise, J. (1986). Pendent drop measurements of the polypropylene/polystyrene interfacial tension between 220°C and 270°C. Materials Chemistry and Physics, 14(3), pp.239-246.
[28] Composto, R., Kramer, E. and White, D. (1988). Mutual diffusion in the miscible polymer blend polystyrene/poly(xylenyl ether). Macromolecules, 21(8), pp.2580-2588.
[29] Chen, L. and Shen, J. (1998). Applications of semi-implicit Fourier-spectral method to phase field equations. Computer Physics Communications, 108(2-3), pp.147-158.
[30] Li, Y., Wang, C. and Liu, X. (2009). Thermodynamic assessments of binary phase diagrams in organic and polymeric systems. Calphad, 33(2), pp.415-419.
[31] Kapur, J., Sahoo, P. and Wong, A. (1985). A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision, Graphics, and Image Processing, 29(3), pp.273-285.
[32] Lifshitz, I. and Slyozov, V. (1961). The kinetics of precipitation from supersaturated solid solutions. Journal of Physics and Chemistry of Solids, 19(1-2), pp.35-50.
[33] Bansil, R. (1993). Phase separation in polymer solutions and gels. Le Journal de Physique IV, 03(C1), pp.C1-225-C1-235.
[34] Henry, C., Meunier, M. and Morel, S. (1993). Helium diffraction study of the nucleation and growth of palladium clusters on MgO (100). Journal of Crystal Growth, 129(3-4), pp.416-420.
[35] Bailey, A., Poon, W., Christianson, R., Schofield, A., Gasser, U., Prasad, V., Manley, S., Segre, P., Cipelletti, L., Meyer, W., Doherty, M., Sankaran, S., Jankovsky, A., Shiley, W., Bowen, J., Eggers, J., Kurta, C., Lorik, T., Pusey, P. and Weitz, D. (2007). Spinodal Decomposition in a Model Colloid-Polymer Mixture in Microgravity. Physical Review Letters, 99(20).
[36] Roux, D. (1986). Spinodal decomposition in microemulsions. Journal de Physique, 47(5), pp.733-738.
[37] Veenstra, H., van Lent, B., van Dam, J. and Posthuma de Boer, A. (1999). Co-continuous morphologies in polymer blends with SEBS block copolymers. Polymer, 40(24), pp.6661-6672.
[38] Veenstra, H., Van Dam, J. and Posthuma de Boer, A. (1999). Formation and stability of co-continuous blends with a poly(ether-ester) block copolymer around its order–disorder temperature. Polymer, 40(5), pp.1119-1130.
[39] Veenstra, H., Verkooijen, P., van Lent, B., van Dam, J., de Boer, A. and Nijhof, A. (2000). On the mechanical properties of co-continuous polymer blends: experimental and modelling. Polymer, 41(5), pp.1817-1826.
[40] Veenstra, H., Van Dam, J. and Posthuma de Boer, A. (2000). On the coarsening of co-continuous morphologies in polymer blends: effect of interfacial tension, viscosity and physical cross-links. Polymer, 41(8), pp.3037-3045.
[41] Veenstra, H., Norder, B., van Dam, J. and Posthuma de Boer, A. (1999). Stability of co-continuous polystyrene/poly(ether–ester) blends in shear flow. Polymer, 40(18), pp.5223-5226.
[42] Russell, T., Anastasiadis, S., Menelle, A., Felcher, G. and Satija, S. (1991). Segment density distribution of symmetric diblock copolymers at the interface between two homopolymers as revealed by neutron reflectivity. Macromolecules, 24(7), pp.1575-1582.
[43] Karim, A., Felcher, G. and Russell, T. (1994). Interdiffusion of Polymers at Short Times. Macromolecules, 27(23), pp.6973-6979.
[44] Escudie, E., Graciaa, A. and Lachaise, J. (1986). Pendent drop measurements of the polypropylene/polystyrene interfacial tension between 220°C and 270°C. Materials Chemistry and Physics, 14(3), pp.239-246.
[45] Arashiro, E. and Demarquette, N. (1999). Use of the pendant drop method to measure interfacial tension between molten polymers. Materials Research, 2(1), pp.23-32.
[46] Demarquette, N. and Kamal, M. (1994). Interfacial tension in polymer melts. I: An improved pendant drop apparatus. Polymer Engineering and Science, 34(24), pp.1823-1833.
[47] Helfand, E. and Tagami, Y. (1972). Theory of the Interface between Immiscible Polymers. II. The Journal of Chemical Physics, 56(7), pp.3592-3601.
[48] Helfand, E. and Sapse, A. (1975). Theory of unsymmetric polymer–polymer interfaces. The Journal of Chemical Physics, 62(4), pp.1327-1331.
[49] Anastasiadis, S., Chen, J., Koberstein, J., Sohn, J. and Emerson, J. (1986). The determination of polymer interfacial tension by drop image processing: Comparison of theory and experiment for the pair, poly(dimethyl siloxane)/polybutndiene. Polymer Engineering and Science, 26(20), pp.1410-1418.
[50] Anastasiadis, S., Gancarz, I. and Koberstein, J. (1988). Interfacial tension of immiscible polymer blends: temperature and molecular weight dependence. Macromolecules, 21(10), pp.2980-2987.
[51] Wu, S. (1982). Polymer interface and adhesion. New York: M. Dekker.
[52] Elemans, P., Janssen, J. and Meijer, H. (1990). The measurement of interfacial tension in polymer/polymer systems: The breaking thread method. Journal of Rheology, 34(8), pp.1311-1325.
[53] López-Barrón, C. and Macosko, C. (2010). A new model for the coarsening of cocontinuous morphologies. Soft Matter, 6(12), p.2637.
[54] Xing, P., Bousmina, M., Rodrigue, D. and Kamal, M. (2000). Critical Experimental Comparison between Five Techniques for the Determination of Interfacial Tension in Polymer Blends: Model System of Polystyrene/Polyamide-6. Macromolecules, 33(21), pp.8020-8034.
[55] Ferguson, A. (1912). XXXVIII.Photographic measurements of Pendent Drops. Philosophical Magazine Series 6, 23(135), pp.417-430.
[56] Berry, J., Neeson, M., Dagastine, R., Chan, D. and Tabor, R. (2015). Measurement of surface and interfacial tension using pendant drop tensiometry. Journal of Colloid and Interface Science, 454, pp.226-237.
[57] Jasper, J. (1972). The Surface Tension of Pure Liquid Compounds. Journal of Physical and Chemical Reference Data, 1(4), pp.841-1010.
[58] Inaba, H. and Sato, K. (1996). A measurement of interfacial tension between tetradecane and ethylene glycol water solution by means of the pendant drop method. Fluid Phase Equilibria, 125(1-2), pp.159-168.
[59] Kulaguin Chicaroux, A., Górak, A. and Zeiner, T. (2017). Demixing behavior of binary polymer mixtures.
[60] Grunert, T., Rudolph, H. and Enders, S. (2013). Prediction of Interfacial Tensions between Demixed Ternary Mixtures. Zeitschrift für Physikalische Chemie, 227(2-3), pp.269-284.
[61] Enders, S. and Quitzsch, K. (1998). Calculation of Interfacial Properties of Demixed Fluids Using Density Gradient Theory. Langmuir, 14(16), pp.4606-4614.
[62] Holgado-Terriza, J., Gómez-Lopera, J., Luque-Escamilla, P., Atae-Allah, C. and Cabrerizo-Vı́lchez, M. (1999). Measurement of ultralow interfacial tension with ADSA using an entropic edge-detector. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 156(1-3), pp.579-586.
[63] Cook, H. (1970). Brownian motion in spinodal decomposition. Acta Metallurgica, 18(3), pp.297-306.
[64] Cahn, J. (1961). On spinodal decomposition. Acta Metallurgica, 9(9), pp.795-801.
[65] de Gennes, P. (1980). Dynamics of fluctuations and spinodal decomposition in polymer blends. The Journal of Chemical Physics, 72(9), pp.4756-4763.
[66] Biner, S. (2017). Programming Phase-Field Modeling.
[67] Tanaka, F., Doi, M., Ohta, T. and Fulde, P. (1989). Space-time organization in macromolecular fluids. Berlin: Springer.