Unit COMPLEMENTS OF CONDENSED MATTER PHYSICS
 Course
 Physics
 Studyunit Code
 GP005934
 Location
 PERUGIA
 Curriculum
 Fisica della materia
 Teacher
 Silvia Corezzi
 Teachers

 Silvia Corezzi
 Hours
 42 ore  Silvia Corezzi
 CFU
 6
 Course Regulation
 Coorte 2021
 Offered
 2022/23
 Learning activities
 Affine/integrativa
 Area
 Attività formative affini o integrative
 Academic discipline
 FIS/03
 Type of studyunit
 Opzionale (Optional)
 Type of learning activities
 Attività formativa monodisciplinare
 Language of instruction
 Italian
 Contents
 (1) Introduction to the Soft Matter Physics
(2) Reology of soft materials: Is soft matter solid or liquid?
(3) Dynamics of soft materials and linear response theory
(4) Colloids and interactions in soft matter  Reference texts
 Slides sent by the teacher and lecture notes.
No specific textbook.  Educational objectives
 The course of COMPLEMENTS OF CONDENSED MATTER PHYSICS aims at developing scientific knowledge in the field of the structure of condensed matter complementary to that given by other courses, by proving the students with an introduction to the physics of soft matter, with notions at a macroscopic and microscopic level, applicable to wide classes of materials in the technological and biophysical field.
The student is expected to learn:
(1) the basic characteristics of soft matter, its viscoelastic and dynamic behavior, and the main investigation methods;
(2) the fundamentals of the linear response theory, which is the basis of the study of the dynamics of disordered systems by means of different experimental techniques;
(3) specific knowledge of colloidal systems and their interactions.
The student is expected to go beyond notionism and demonstrate an ability to develop critical understanding, useful to apply in various fields the specific knowledge acquired.  Prerequisites
 Important yet not mandatory prerequisites:
(1) fundamentals of structure of condensed matter;
(2) basic knowledge of statistical mechanics.  Teaching methods
 The whole body of the program of COMPLEMENTS OF CONDENSED MATTER PHYSICS is presented in facetoface lectures.
Short didactic notes prepared by the teacher can be downloaded through the Unistudium platform, together with material useful (yet not obligated) to the first part of the final examination.  Other information
 Attendance of lessons is strongly encouraged.
 Learning verification modality
 The exam consists in an oral examination in order to verify the knowledge and understanding of the arguments of the lectures.
The oral test is composed of two parts: in the first part the student is requested to present and critically discuss a scientific work from the literature, at its choice, on issues related to the course. In the second part, the specific knowledge acquired by the students is verified through interviews.
For information about DSAstudent support services visit the website http://www.unipg.it/disabilitaedsa  Extended program
  INTRODUCTION TO SOFT MATTER PHYSICS
Wha’s soft matter. Examples of soft materials: polymers, colloids, surfactants, liquid crystals, granular matter, glasses. Polymers: definition; polymeric architectures (linear, branched, crosslinked); main classes of natural and synthetic polymers (thermoplastic, elastomeric, thermoset); mail mechanisms of polymerization (condensation and addition, chain growth and step growth). Colloids: definition; shapes; structures (sol, gel, colloidal crystal, colloidal glass). Surfactants: definition; structures (direct and inverse micelles, microemulsions, lamellae, vesicles, cylinders, cubic phases). Liquid crystals: thermotropic and liotropic; nematic, smectic, cholesteric. Glasses: definition of the glassy state; general information on the glass transition.
Origin of softness in soft materials: supramolecular aggregation; size of structural units and intensity of interactions. Slow dynamics of soft matter.
 RHEOLOY OF SOFT MATERIALS: IS SOFT MATTER SOLID OR LIQUID?
Rheology of elastic solids: macroscopic mechanical characterization in terms of bulk, shear, longitudinal, and Young moduli. Shear elastic modulus at a microscopic level. Rheology of Newtonian liquids: macroscopic description in terms of shear viscosity. Shear viscosity at a microscopic level. The concept of viscoelasticity. Viscoelastic behaviors of soft materials. Constitutive springdashpot models of linear viscoelasticity.
Microscopic origin of elasticity of polymers: the Freely Jointed Chain (FJC) model. Endtoend vector. Average endtoend distance. Probability distribution of the endtoend vector. Expression of the entropic elastic force developed by a single polymer chain for small chain elongations. General expression of the polymer chain elongation as a function of the force it develops: limits of application of the FJC model. Application of the FJC model to calculate the shear modulus of a crosslinked polymer gel. Microscopic origin of viscoelasticity in polymeric materials (notes).
Rotational geometries of different types of rheometers used in dynamic mechanical testing of melt polymers and polymeric solutions: concentric cylinder, plateplate and coneplate geometry.
 DYNAMICS OF SOFT MATTER AND LINEAR RESPONSE THEORY
General information on the methodologies to investigate the dynamics of soft materials. Phenomenology of the linear response. The concept of generalized force and generalized displacement. Response function. Relaxation function. Relation betwee rensponse and relaxation functions. Generalized susceptibility. Genelaralized modulus. Relation between susceptibility and modulus. General properties of generalized susceptibility. Demonstration of the KramersKronig dispersion relations. Connections between causality and dispersion. Connection between imaginary part of the susceptibility and energy absorption.
Phenomenological description of relaxation processes in the time and frequency domains: exponential and stretchedexponential relaxation function; Debye, ColeCole,ColeDavidson, and HavriliakNegami susceptibily.
Temporal fluctuations and timecorrelation function. Power spectrum (or spectral density). Demonstration of the WienerKintchine theorem.
Classic statistical mechanics recalls: phase spacei; Liouville operator; statistical distribution function; Liouville equation. Statistical mechanics of the linear response. Formula of Kubo. Fluctuationdissipation theorem. An example: calculation of the noise tension measured at the ends of a capacitor filled with a dielectric material.
Examples of experimental techniques to acquire fluctualtions in the time and frequency domains: visible light scattering (photocorrelation spectroscopy and FabryPèrot interferometry).
 COLLOIDS AND INTERACTIONS IN SOFT MATTER
Introduction to stocastic processes: casual (or stocastic) variable; casual (or stocastic) process; stationary stocastic processes. Probability and conditional probability. Markovian processes. Smoluchowki’s equation. Derivation of the FokkerPlanck equation. The Brownian motion of colloidal particles. FokkerPlank treatment of the Beownian motion: Langevin equation; FokkerPlanck equation for the velocity and StokesEinstein relation; FokkerPlanck equation for the position and its solution in the diffusive regime. Einstein treatment of the Brownian motion: derivation of the diffusion equation for a Brownian particle; derivation of the StokesEinstein relation.
Introduction to the light scattering theory: the light scattering experiment; fundamental formula of the scattering of light (derivation); scattering geometries. Molecular approach to the light scattering. Light scattering from spherical molecules in dilute solution. Application of photocorrelation spectroscopy to determine the size of brownian colloidal particles.
Colloidal interactions. Van der Waals force. Screened Coulombian force: Debye (or "screening") length. The DLVO theory: colloidal stability and aggregation; diffusioncontrolled and reactioncontrolled regime of colloidal aggregation. Depletion forces. An example: "lock and key" colloids.