חיפוש חדש  חזור
מידע אישי לתלמיד

שנה"ל תש"ף

  תורת החומר המעובה 2
  Condensed Matter Theory 2  
0321-4410
מדעים מדויקים | פיסיקה ואסטרונומיה
קבוצה 01
סמ'  ב'1500-1800105 פיזיקה-שנקרשיעור פרופ אנדלמן דוד
ש"ס:  3.0

סילבוס מקוצר

פרמטר הסדר (סקלרי, וקטורי, טנזורי), מצבי צבירה והקשר לסימטריות של המערכת, תורת לנדאו ותורת גינזבורג-לנדאו; מבוא לסדר בגבישים נוזליים, פרמטר הסדר הטנזורי, תורות לנדאו, מאייר-סאופה ואונסגר למעבר פאזה נמטי-איזוטרופי, פאזות נמטיות בשדה חשמלי/מגנטי מסדר וליד שפות; פולמרים, מהלך אקראי (RW, SAW) וסטטיסטיקה של שרשרת בודדת, אינטגרלי מסלול, פולימרים בתמיסה, הפרדת פאזות, גורם המבנה (S(q ודינמיקה; אינטראקציות ואן דר ולס, תורת ליפשיץ, אינטראקציות דיפולריות, תורת פואסון-בולצמן ואינטראקציות אלקטרוסטטיות, תורת DLVO.

Course description

Condensed Matter Theory 2 Syllabus

 

Instructor

David Andelman

Email : andelman@post.tau.ac.il

Academic Year, Semesters

Graduate 1 or 2, semester 2

Number of Hours/ Credits

3/3

Mandatory/Elective

Mandatory for condensed matter graduate students

Prerequisites

None

Year in program & how often given, if relevant

Graduate course, given every year

  Course overview – short abstract

The course main objective is to explain how collective many-body phenomena can be addressed in condensed matter using the tools of statistical physics and continuum media. In the first part of the course, the notion of an order parameter is introduced for scalar order parameter as in liquid/liquid or liquid/gas phase transitions. Within a few models (lattice-gas, Landau and Ginzburg-Landau expansions) we calculate the relevant phase diagrams and critical phenomena. In the second part of the course, the tensorial order parameter of nematic liquid crystals is introduced and the isotropic-nematic phase transition is explored within several models. In the third part, we model long-chain disordered materials as random walks. The connection between the statistical properties of long chains and Gaussian distributions is explored and leads to important physical concepts and polymer properties. Finally, in the last part of the course, we introduce the Poisson-Boltzmann theory for mobile charges (ions) dispersed in a liquid medium. The interplay of charges and van der Waals interactions, which results in the DLVO theory for colloidal stability.

Learning outcomes – short description (if you don’t have LOs, then don’t write anything in this part)

Assessment: coursework and grade structure

Final Exam: 80%

Project 15%

Problem Sets – 5%

Week-by-week content, assignments and reading

Note: there is no textbook for this advanced course. The names of the most relevant books are denoted in parenthesis after each week, and correspond to the full references at the end of the list.

Week 1: Introduction to disordered systems, states of matter, phases and their order parameters [CL,S]

Week 2: Free energy of mixing, isotropic phase transitions (liquid/liquid) and their phase diagrams, the bimodal and spinodal lines. The critical point and its critical exponents. [CL,S]

Week 3: Landau and Ginzburg-Landau theories for isotropic phase transitions, density profiles, correlation functions, correlation length and the structure factor in Fourier space. Interfacial phenomena and surface tension. [CL,S] Problem Set #1 on Phase Transitions

Week 4: Introduction to Liquid Crystals. Position and orientation orders. The tensorial nematic order parameter and its scalar magnitude.[dGP,CL]

Week 5: The Isotropic-Nematic phase transition (Landau de Gennes theory). The Isotropic-Nematic transition in presence of a magnetic field. A qualitative explanation on LCD. [dGP,CL]

Week 6: Nematic phases close to boundaries and walls. Twist, splay and bend. The correlation length in nematic phases.  The microscopic Saupe-Maier theory for the Isotropic-Nematic transition. [dGP,CL] Problem Set #2 on Liquid Crystals

Week 7: The Onsager theory for the Isotropic-Nematic transition of hard rods. Introduction to polymers and chains: important properties, architectures of the chains, states of matter, applications. [dGP,CL]

Week 8: Statistical physics of ideal (Gaussian) polymeric chains. End-to-end distance, Kuhn length and gyration radius. Freely jointed chains, freely rotating chains and other chain models. Gaussian distributions in three-dimensions. [RC] Problem Set #3 on Polymers

Week 9: Gaussian distributions in any d dimensions and their connection with random walks and ideal polymer chains. Flexible and semi-flexible chains. The persistence length and Kratky-Porod model. The free energy and entropy of ideal chains. The chain as an entropic spring. [RC]

Week 10: Elongation of ideal chains: force vs. extension models & experiments. The Langevin function for large elongations. Scattering from polymer chains: X-ray, neutron and light. Small angle scattering and measurement of the chain gyration radius. The Debye structure factor. Connection with correlation functions. [RC]

Week 11: The Flory-Huggins free energy of mixing. The phase diagram of polymer-solvent and polymer/polymer mixtures: spinodal line, critical point, coexistence curve. [RC] Problem Set #4 on Polymers

Week 12: The Poisson-Boltzmann theory of mobile charges (ions) in solution. A single charged surface with its mobile counter-ions (Gouy-Chapman problem). The electrostatic potential and ion density profiles. The Debye screening length. Screening of the potential for one charged surface in presence of salt. Linearization of the Poisson-Boltzmann equation (the Debye-Huckel model). [I,S]

Week 13: The forces between two charged surfaces in presence of salt. Calculation of the osmotic pressure in the high salt limit. Van der Waals interactions between two bodies immersed in a 3rd medium. The DLVO theory for colloidal stability. [I,S] Problem Set #5 on Poisson-Boltzmann Theory

Required text – in language of origin

Principles of Condensed Matter Physics, P. Chaikin & T. Lubensky [CL]

Polymer Physics, M. Rubinstein & R. Colby [RC]

Statistical Thermodynamics of Surfaces and Interfaces, S.A. Safran [S]

Intermolecular and Surface Forces, J. Israelachvili [I]

The Physics of Liquid Crystals, P.G. de Gennes and J. Prost [dGP]

 

להצהרת הנגישות


אוניברסיטת ת