Course Identification

Emergent states of matter in materials and biomolecules

Lecturers and Teaching Assistants

Prof. Sam Safran
Dr. Avraham Moriel, Dr. Dan Deviri

Course Schedule and Location

First Semester
Monday, 14:15 - 16:00

Field of Study, Course Type and Credit Points

Chemical Sciences: Lecture; Elective; Regular; 2.00 points
Physical Sciences: Lecture; Elective; Regular; 1.00 points


Course will be given if there are 10 or more students registered.
All courses in the first semester will be held on-line via zoom.





Language of Instruction


Attendance and participation

Required in at least 80% of the lectures

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)


Evaluation Type

Final assignment

Scheduled date 1


Estimated Weekly Independent Workload (in hours)



Emergent states of matter in materials and biomolecules

  • Schedule:
  • Mondays at 14:15-16:00:  First lecture Monday October 26, 2020; last lecture Monday January 25, 2021

    No Class (FGS Calendar): Sigd Holiday, Monday   November 16, 2020

    Monday October 26: Lecture 1A: Introduction – what is emergence, examples of emergent states of matter, structure and properties; Lecture 1B – Molecular interactions that can lead to emergence.

    Monday November 2: Lecture 2: Conventional and exotic states of matter: emergent structure as revealed by scattering of light, X-rays, neutrons, electrons; liquids, crystals, fractals, polymers, liquid crystals

    Monday November 9: Lecture 3: Statistical thermodynamics - govern the competition of interactions and entropy that determine the properties of emergent states of matter.

    Monday November 16: No class Sigd holiday

    Monday November 23: Lecture 4: Phase separation of mixtures - equilibrium: simplest example of emergence that applies ubiquitously to materials, polymers, biomolecules and cells. Experimental examples, free energy, phase diagrams, generic theory.

    Monday November 30: Lecture 5: Phase separation of mixtures – dynamics: unstable and metastable emergence of structures in crystallization and mixtures.  Spinodal decomposition vs. nucleation and growth.

    Monday December 7: Lecture 6: Interfaces in phase separation originate in the same physics that determines phase separation thermodynamics.  Interfacial tension and its importance in emergent structures. Thermal fluctuations of interfaces – Rayleigh instability, capillary waves, roughening transition of crystal surfaces.

    Monday December 14: Lecture 7: Solids vs. liquids in materials and biomolecule assemblies. Solid vs. crystal vs. liquid.  Generic response of solids to applied force: shear elasticity (strain and stress).  Thermal fluctuations of solids: thermal expansion, destruction of crystalline order in 1 and 2 dimensions – lack of Bragg peaks in scattering. Inclusions in materials and in biological cells.

    Monday December 21: Lecture 8: Polymers – 1d “crystals” in a 3d world, dominated by their entropy in solution.  Self-assembly of molecules in solution into 1d equilibrium polymers.  Non-equilibrium assembly in biopolymers such as actin and its “treadmilling” dynamics.  Properties of chains in dilute solution: Flory theory in both good and bad solvents.  Why polymer solutions become “entangled” (and thus highly viscous) at very small concentration.

    Monday December 28: Lecture 9: DNA emergent behavior: in the nucleus, DNA is not in dilute solution.  “Screening” of chain self-repulsion in concentrated solutions, self-attraction and DNA organization in the nucleus. Phase separation of DNA in the nucleus. Non-equilibrium organization of DNA – fractal globules, chromosome territories. What is the biological advantage of different DNA organization modes in the nucleus?

    Monday January 4, 2021: Lecture 10: Elastic gel formation of synthetic and biopolymers: How do crosslinks give rise to gels that respond to forces as solids even though they are not at all “crystals”. Rubber elasticity theory using simple Flory free energy.  Gels that stiffen or soften under shear, biomolecular examples.

    Monday January 11: Lecture 11: Dynamics response and memory of interactions: viscoelasticity of gels in both synthetic and biopolymer systems. Friction of molecules and solvent – low Reynolds number. Delayed force response of mechanical propagation of both static and time varying mechanical signals in gels.

    Monday January 18: Lecture 12: Electrostatics and emergence: ions in solution self-organize to create an emergent concentrations profile; screening of charges by ions in solution. Common features of ionic crystals and DNA collapse in solution. Why are cells “salty” and how does screening impact biological function.

    Monday January 25: Lecture 13: Open questions, review, summary, preparation for final report and exam.



Learning Outcomes

Students will understand the origin, structure and properties of emergence, which refers to structures, patterns or functions that arise in systems in a spontaneous manner – without external templating.  These include the novel structures and forms that exist in both materials science, assemblies of biomolecules, cells and tissues. These properties cannot be attributed only to the individual molecules but originate in their cooperative interactions.  In many cases, the emergence can be understood as a result of phase transitions in thermal equilibrium, but in many others, they are non-equilibrium and are due to a dynamical balance of forces in the system. Students will learn a compact understanding of the laws of thermodynamics and their relation to the statistical properties of matter.  They will be able to identify the conceptual, and quantitative physical basis for archteypical examples emergent phenomena common to both materials science and structural and cell biology.  These include: phase separation (e.g., in alloys vs. biomolecules in solution in cells), nucleation and growth, the elasticity of crystals and biopolymer gels, and the properties of thin solid sheets (e.g., graphene) vs. lipid membranes that are important in biology.

Reading List

K. Dill, Molecular Driving Forces

B. Fultz, Phase Transitions in Materials

M. Rubinstein and R. Colby, Polymer Physics

R. Phillips et al., Physical Biology of the Cell

D. Tabor, Gases, Liquids and Solids