京都大学 京都大学

Special Topics in Chemical Engineering III

Numbering Code G-ENG17 6E033 LJ76 Year/Term 2022 ・ First semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Tue.5
Instructor name TANIGUCHI TAKASHI (Graduate School of Engineering Associate Professor)
Outline and Purpose of the Course Lectures on basic phenomena, theoretical backgrounds, and calculation methods in soft matter systems.
Course Goals Understand the theory and simulation method of phase transition and flow phenomena that occur in soft matter systems.
Schedule and Contents I. Overview of phenomena related to soft matters and their simulation methods (1)
II. Computational science of macromolecules
　　--- Focusing on the contents related to the phase separation phenomenon ---
A. Equilibrium state (twice)
　　1. Example of phase separation phenomenon
　　2. Order parameter, free energy
　　3. Thermodynamic conditions for phase separation to occur
　　　(a). Chemical potential, osmotic pressure (← functional derivative)
　　　(b). Geometric meaning of free energy shape, chemical potential, and osmotic pressure
　　　(c). Nucleation, spinodal decomposition → morphology
　　4. Critical point conditions => (derivation of critical temperature and critical composition)
　　5. Derivation of interface profile and interface energy in equilibrium state
　　6. Laplace's law (from variational principle)

B. Phase separation dynamics (3)
　　1. Equation of Continuity
　　2. Thermodynamic variables conjugate with thermodynamic force
　　3. Material flow in non-equilibrium state (phenomenon theory)
　　4. Effect of thermal noise ⇒ Stochastic differential equation (Langevin equation)
　　5. Spinodal decomposition and Scattering function)
　　　　Fokker-Planck equation　
　　　　Linear stability analysis → Non-linear analysis Langer-Baron-Miller theory
　　6. Growth of droplets
(a) Ostwald growth,
　　　　(b) Lifshitz--Slozov--Wagner theory
　　　　(c) Thomson's relational expression
　　7. Fluid dynamics effect →
　　　　(a) Navier-Stokes equation
　　　　(b) Reynolds number, Re
　　　　(c) Oseen Tensor
　　　　(d) Derivation of stress expression
　　8. Domain growth law,

C. Advanced calculation method for polymer meso-structure prediction (2)
　　1. Self-consistent field theory for equilibrium state
　　2. Dynamic self-consistent field theory
　　3. Density functional theory for macromolecules with an arbitrary branched structure

D. Polymer rheology (3)
　　1. Non-entangled polymer model
(a) Dumbbell model,
(b) Rouse model
2. Entangled polymer model
(a) Tube model
(b) Primitive Chain Network model
(c) Slip-Link model

III. Feedback
(Topics on which students want to discuss) (1)
Evaluation Methods and Policy Evaluation will be judged by the submitted your reports for questions given during the course of lectures.
Course Requirements knowledge of vector analysis, fluid mechanics, thermodynamics, and statistical mechanics studied in the undergraduate school
Study outside of Class (preparation and review) Before taking this course, students should review the fundamental knowledge for vector analysis, fluid mechanics, thermodynamics, and statistical physics.
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