Introduction to Fundamental Concepts

Lecture 1: 09.09.05 Introduction to fundamental concepts Today: THERMODYNAMICS AS A BASIC TOOL FOR MATERIALS SCIENCE & ENGINEERING. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Thermodynamic forces and materials.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 An example: Drug delivery materials that respond to pH: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 WHAT IS THERMODYNAMICS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 points of view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 CHANGES OF STATE AND EQUILIBRIUM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 The balance between internal energy and entropy determines the behavior of real systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 The connection between energies, entropy, and equilibrium: thermodynamics is governed by thermodynamic laws. . . . . . . . . . . . . 10 SO WHAT'S FUNDAMENTAL ABOUT IT? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 A conceptual roadmap... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 THERMODYNAMIC VARIABLES, SYSTEMS, AND FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Thermodynamic Variables.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Reading: Engel and Reid: 1.1, 1.2 Supplementary Reading: H.A. Bent, The Second Law, pp. 1-5 ANNOUNCEMENTS! PROBLEM SET 1 POSTED TODAY DUE: 09.20.05 (WEEK FROM MONDAY) Thermodynamics as a basic tool for materials science & engineering Thermodynamic forces and materials . Materials scientists seek to tune the structure and synthesize materials with properties that provide optimum performance in every type of materials application - the structure-properties-performance triangle performance structure properties THERMODYNAMICS . In order to design materials with optimum performance in various applications, we need to know how properties change in response to their environment These responses determine how we can synthesize/fabricate materials, build devices from materials, and how the devices will operate in a given application: . . Raw materials -(synthesis, processing, fabrication)-> final devices Materials are exposed to a variety of forces (mechanical, chemical, electrical, magnetic, etc.) during synthesis, processing, and in their final applications ? QUESTIONS: 1 CHEMICAL RAN HOW DO I ACHIEVE A CERTAIN STRUCTURE THROUGH PROCESSING? ② WHAT WILL HAPPEN UNDER CONDITION X? synthesis TEMPERATURE processing MAGNETIC FreeD S application 수수수 THERMODYNAMIC FORCES 'INPUTS' temperature MECHANICAL Mechanical stress Chemical reaction Electric fields Magnetic fields STRENGTIN concentration gradients intermolecular forces surface forces etc. RESPONSE? CHANGES IN STRUCTURE (PHASE) VOLUME CHEMICAL SPECIES PRESENT : An example: Drug delivery materials that respond to pH: • The images below show optical micrographs of pH-responsive microporous hydrogels which were fabricated in the Irvine laboratory to have the 3D structure illustrated at left: Figure by MIT OCW. H+H COLLAPSE pH 9 SWEUS 10 μm pH 4 (Data: Yuhua Hu) The gels contain pH-sensitive amine groups that protonate at reduced pH. How does charging of the gel control swelling? What controls the swelling/collapse of these materials? These are questions we can answer qualitatively and quantitatively using thermodynamics. Ο N A thermodynamic driving force called the chemical potential (which will be a major player in our studies this term) drives water into/out of the gel: OUT NH20 OHHO H External solution THERMODYNAMIC FORCES Inorganic cation, e.g. Na+ O Water H+H Inorganic anion, e.g. Cl 00 HO GEL N Gel H20 OEL ہے ουτ ΝΉτο Ντό ... HO, DRIVEN INTO GEL SWELLING/ Figure by MIT OCW. Using thermodynamics, we can predict how these gels should swell: CALCULATION! 1 2 3 4 5 6 7 8 9 10 pH This is a qualitative sketch of a theory developed by Nicholas Peppas¹- who was a graduate student at MIT! (This is an advanced calculation, but one which you will have the basic tools to understand by the end of the term.) What is thermodynamics? 2 points of view Thermodynamics provides the theory to understand how materials respond to all types of forces in their environment- including some forces you may have not thought about or recognized as 'forces'. We will introduce two different points of view during this term: Classical thermodynamics Classical Thermodynamics is the theoretical framework to understand and predict how materials will tend to change internally in response to forces of many types on a macroscopic level. 4 LAWS DICTATE RESPONSES DOES NOT REUL ON A MOLECULAR-LEVEL UNDERSTANDING OF A MATERIAL "[Thermodynamics] is the only physical theory of universal content which, within the framework of the applicability of its basic concepts, I am convinced will never be overthrown." - Albert Einstein Statistical mechanics Statistical mechanics (or statistical thermodynamics) is the calculation of thermodynamic properties starting from molecular models of materials- either simple lattice models or quantum mechanical models. QUANTUM MECH. (OR COARSE-GRAINED) MOLECULAR MODELS AND MAKS PREDICTIONS OF THERMODYNAMIC PROPERTIES -(STILL OBEY 4 LAWS!) Why 2 approaches? Useful in different applications CLASSICAL: GENERALLY APPLICABLE TO ALL MATERIALS, BUT OFFERS NO MOLECULAR-LEVEL INSIGHT STAT MECH UNDERSTAND THE ROLE OF MOLECULAR DETAILS, BUL LIMITED TO SIMPLE PROBLEMS, AND APROXIMATIONS Changes of state and equilibrium A sentence of new concepts Thermodynamics is concerned with predicting the state of materials at equilibrium using thermodynamic functions, particularly internal energy, entropy, and free energy. State U S GOR F A unique set of values for the variables that describe a material on the macroscopic level. For example: P PRESSURE V VOWME SIMILE SYSTEM! T TEMPERATURE N MOLECULES (n #MOLEL) . 2 LINKED! SUBSES DEFINES SYSTEM The molecules in materials heat up, react, rearrange, change shape, form and break bonds with one another, and undergo myriad other changes in response to changes in their environment. The changes in macroscopic properties that occur due to these internal molecular interactions are changes in the state of the material. Material State A (Vo, No) THERMODYNAMICS SEEKS TO PREDICT WHEN CHANGES OCCUR, AND WHAT THEY Aㅈ石... Thermodynamic forces State B State C State D (V < Vo. No) (V > Vo, No) (Vo, N > No) Pressure Temperature Magnetic fields Light (more later) Let's continue to define a few key terms, as a brief introduction to the concepts we will focus on for much of the term: Equilibrium Equilibrium is defined as a state from which a material has no tendency to undergo a change. Analogy to potential energy: a ball rolling on hills and valleys: V(x) (1) (2) (3) (4) X G FREE ENERGY (1) Unstable state system is actively tending toward a new equlibrium state (2) Metastable equilibrium state - system can change to a lower total energy state (3) Unstable equilibrium state any perturbation will cause the material to change to a new equilibrium state (4) Stable equilibrium state material does not change its state in response to small perturbations STABLE EQUILIBRIUM STATE We will return to define the different types of equilibrium states in mathematical terms later in the term. In physics, you learn that stable mechanical equilibrium is achieved when the potential energy is at its lowest level- when the potential energy is minimized. Similar extremum principles will come into play in reaching internal equilibrium in materials- we may look for the maximum or minimum of a thermodynamic function to identify equilibrium states. Internal energy (U) Internal energy is a quantity that measures the capacity to induce a change which would not otherwise occur. In freshman physics you learned: ETOTAL = V KE KINETIC POTENTIAL QUERGY U INTERNAL ENERGY ENERGY OF POSITION ENERGY STORED WITHIN A MATERIAL! IN BONDS, VIBRATIONS, IN MAGNETIC MOMENTS, IN POLARIZATION Internal energy in a material is 'stored energy'- energy is transferred to a material via all the possible forces that act on it- pressures, thermal energy, chemical energy, magnetic energy, etc. and is stored within the random thermal motions of the molecules, their bonds, vibrations, rotations, and excitations. ++ TYPICAL THERMO CHAC: ASTUGAL = AK+AKE Entropy (S) ΔΕ = ΕFINAL-ENTIAL Entropy is a non-intuitive but absolutely critical parameter of materials- along with the more common extensive parameters like volume and number of molecules. We will introduce a rigorous thermodynamic definition for entropy in the coming lectures, but let's start with a conceptual interpretation of entropy to aid in our grasp of what entropy is: ENTROPY IS AN INDEX OF #WAYS A MATERIAL HAS TO STORE ENERGY Suppose we consider a glass of water: A snapshot of the molecules in our glass of water at one instant: (()) VIBRATIONS TRANSLATIONS MODES OF STORING ENERGY ROTATIONS The 1023 individual molecular details position, velocities, states of vibration) of each water molecule together give rise to a macroscopically observed (T, P, V) ... AT FINITE TEMPERATURE : MANT SNAPSHOTS (MICLASTATES) ARE EVOLVING IN TIME MICROSTATES - Ω↑ THEN ST The 2nd law of thermodynamics: The system is equally likely to be in any of the possible microstates (consistent with the macroscopic (T,V.P). S=konsu BATEMANN CONSTRANT The balance between internal energy and entropy determines the behavior of real systems If I drop a crystal of table salt (NaCl) into a beaker of pure water, the salt will dissolve quite rapidly. It is equally common experience that once dissolved, the salt crystal will never spontaneously re-form- even though the bonding energy between ions in the crystal would be quite strong. This is common knowledge, but why should it happen? BONDING ENERGY! ~ 787 kJ/mole • Na Dissolution of a salt crystal HHI I 1 I Na 409 60 I 4 CI . ENERO1 ~ 342 kJ/mole DISKOLVED LONS So what drives the dissolution and non-resolidification of this crystal in water? The answer is that dissolution increases the entropy of the system, while resolidification would decrease the entropy: A VERY VEX VERY VERY BIG CRYSTAL enl AS↑ AS ? There are many cases when the increase in entropy occurring for a given process is not obvious, but for any spontaneous process ever analyzed, entropy increases have been found. On a molecular level, once the atoms are released from the crystal, their thermal energy will scramble them thoroughly (and randomly) through the solution- and because this thermally-driven process is random, it extremely unlikely that it will ever randomly reverse. Finding the balance between energies (like bonding between molecules, or forces induced by an electric field) and entropy (random thermally-induced disorder) is what defines equilibrium states. The connection between energies, entropy, and equilibrium: thermodynamics is governed by thermodynamic laws. There are 4 thermodynamic laws in total, but the 2 most practically important laws, which will use thoughout the term, can be summarized as follows: FIRST LAW: SECOND LAW: AU = (work in/out) + (heat in/out) The entropy of the universe increases in any spontaneous process. -THE LAWS HAVE NEVER BEEN PROVEN, ONLY NEVER DISPRAVEN THE LAWS PROVIDE A DESCRIPTION OF HOW UNIVERSE WOLKS, NOT AN EXPLANATION So what's fundamental about it? • Thermodynamics has many practical uses. It provides the theory to answer the following sorts of practical materials questions:2 Thermodynamics in Materials Science Thermodynamics explains many phenomena in the natural world: • -HOW DO I FORMULATE PREDICTIONS FOR A MATERIAL'S BEHAVIOR? • -WHY PROCESSES MAKE A MATERIAL UNSTABLE? WHAT'S THE MAX VALVE A PROPERTY CAN TAKE? ... and it continues to be a fundamental part of new materials discoveries. Thermodynamics in Materials Engineering • The interpretation of a material's response to the forces in its environment is the basis of many technologies. Some examples: Thermodynamic Driving Force: Temperature Electrostatic potential Mechanical stress concentration gradients Chemical reactions Electric fields surface forces Magnetic fields Technology Based Upon It: internal combustion engines, phase change materials batteries, dielectrics All materials for load-bearing and structural applications dialysis systems corrosion-resistant materials, batteries piezoelectric materials engineered crystals and composites disk drives and magnetic storage materials A conceptual roadmap Road map of the thermodynamics component: Lectures 1-2 Topic Basic concepts for thermodynamics 3-7 8-14 15-20 21-24 The first law, work, and heat The second law and free energy at equilibrium Phase diagrams and thermodynamics of solutions Introduction to statistical mechanics, microscopic models of materials What are we after? DEFINITIONS, HOW DO WE DESCRIBE MATERIALS AU = (WORK) + (HEAT) HEATT ENTROPY HOW DO PREDICT SPONTANEOUS CHANGES? DETERAINING STABLE FORMS OF MATERIALS HEAT TO ENTROPY MICROSCOPIC VIEWPOINT! Thermodynamic variables, systems, and functions Thermodynamic Variables Remember that classical thermodynamics is concerned with macroscopic properties MACROSCOPIC VAANBIES: 2 types of variables intensive Extensive PV,T, n... MAGNITUDE DOUS VARDI W/ THE SIZE OF SYSTEM Intensive variables: P (P.T) (P,T) (P.T) ... BUT CAN VARY PB IN SPACE FROM PONT TO POINT: E ミコ(メリッ记) ↓↓↓ ↑ P2P = PB fimse extensive variables: (U.V)(UV) (2U,2V) intensive and extensive variables form coupled pairs: • • e.g. pressure and volume P <-> V the product of one intensive variables multiplied by its coupled extensive variables is work References 1. 2. Peppas, N. A. & Brannon-Peppas, L. Equilibrium swelling of pH-sensitive hydrogels. Chem. Eng. Sci., 715-722 (1989). Carter, W. C. (2002).