REVIEW : INTERATOMIC BONDING : THE LENNARD-JONES POTENTIAL & RUBBER ELASTICITY I DERIVATION OF STRESS VERSUS STRAIN LAWS FOR RUBBER ELASTICITY
|
|
- Brianne Dorsey
- 5 years ago
- Views:
Transcription
1 LECTURE #3 : 3.11 MECHANICS O MATERIALS 03 INSTRUCTOR : Professor Christine Ortiz OICE : PHONE : WWW : REVIEW : INTERATOMIC BONDING : THE LENNARD-JONES POTENTIAL & RUBBER ELASTICITY I DERIVATION O STRESS VERSUS STRAIN LAWS OR RUBBER ELASTICITY
2 SUMMARY : Molecular Origins of Elastic Moduli I.Atomistic Basis for Elastic Moduli lattice strain - uniform distortion of interatomic bonds, e.g. covalent bonds; disturbing outer orbital electron cloud represent an individual bond by a linear elastic Hookean spring which connects two atoms represented by hard spheres atomic =k bond δ bond atomic =interatomic force k bond =bond stiffness δ bond =(r f -r e )= bond displacement r e =equilibrium bond length r f =strained bond length II. Interatomic Parameters : Interatomic Potential or Bond Energy (J or J/mol or k T) : k -A B U(r) or W (r) = U attractive(r) + U repulsive(r) = + = - (r)dr m n r r -du(r) Interatomic (Bond) orce (nn): (r) = = k(r)dr dr -d U(r) d(r) Interatomic (Bond) Stiffness (nn/nm): k(r) = = dr dr r (nm) = interatomic separation distance A,B,m,n = constants determined by the type of interaction B -3 B = Boltzmann's constant = J/K, T = absolute temperature (K) r e r rff + e- e- e- + r e r f w(r)(kbt) Hard-Sphere Repulsion n= σ r(nm) w(r)(kbt) Soft Repulsion Soft Repulsion B= Jm 1 n=1 σ r(nm) w (r)(kbt) London dispersion interaction A=10-77 Jm 6 m=6 r(nm)
3 SUMMARY : LJ Potential I. Lennard-Jones Potential U ( m = 6, n = 1) = = 4E LJ ( m = 6, n = 1) = LJ 7 -A B r r -6A 1B + 13 r r B σ σ r r 1 6 E B = "binding energy," "bond dissociation energy," or depth of potential well r s = distance at which U(r s) exhibits and inflection point, (r s) = minimum = r e = equilibrium bond length, distance at which U(r e) = minimum, (r e) = 0 r = σ = distance at which U(r ) = 0, (r ) o o o 0.4 r o, r e, r s RUPTURE 0. w(r) (k B T) E B anharmonic (asymmetric) -0.6 (r)(nn) RUPTURE V IV I II Interatomic orce versus Separation Distance Curve III r(nm)
4 SUMMARY : Rubber Elasticity I. Structure of Polymer Networks structure and properties of polymers and elastomers : N=degree of polymerization (large) crosslink network strand conformation (spatial arrangement of atoms) crosslink density, ν x =#strands/m strands/cm 3 entropic origin of random coil conformation : Ω=number of available chain conformations <r > 1/ =root-mean-square end-to-end distance=n 1/ a <>= statistical mechanical time average r=instantaneous chain end-to-end separation distance polymer network single random coil polymer chain <r > 1/ At T>0 K the chain is continually in motion due to rotation about backbone bonds macroscopic molecular II. reely-jointed Chain (JC) Model Two molecular level parameters : a= statistical segment length or local chain stiffness (*determined by chemical structure) n= number of statistical segments L contour = L c =na= contour length or length of fully extended chain Assumptions : 1. random walk of rigid segments, all angles between statistical segments are equally probable and each segment is uncorrelated to the next. segments are connected by revolving pivots, free rotation at the bond junctions a 3 a 3. no self-interactions, overlap of different parts of chain allowed 4. no enthalpic deformations, bond length stays constant a 1 r a n- a n-1 a n
5 SUMMARY : LJ Potential II. reely-jointed Chain (JC) Model (Cont d)_ 1. Qualitative Description of Single Chain Stretching : links rotate so as to uncoil and extend polymer chain along stretching axis disorder and entropy # of available configurations, Ω elastic restoring force, elastic =-externally applied force, elastic r elastic. General Statistical Mechanical ormulas : Ω = number of chain conformations P(r) = probability of finding a free chain end a radial distance, r, away from fixed chain end (origin) ~ Ω S(r) = configurational entropy = kblnp(r) A(r) = Helmholtz free energy = U(r) - TS(r) = - Tk z BlnP(r) -da(r) 0 f(r) = entropic elastic force = 1 dr d(r) -d A(r) k(r) = (global) entropic chain stiffness = = dr dr r 1 3. Gaussian ormulas or Stretching a Single Polymer Chain : 3 4b r 3 P(r) = exp[ b r ] where b = π na 4b r π 3k T A(r) = r 3k T = r 3 S(r) = kbln exp[ b r ] B B na Lca 3k T 3k T 3k T 3k T B B f(r) = - r = r na La c B B k(r) = = cons tan t na = La c x Linear Elasticity y
6 Assemble Strands into a Network λ 3 macroscopically deform rubber cube λ 1 >0 (r 1 r r 3 ) (r 1 r r 3 ) r =0 r molecular level deformation
7 Assemble Strands into a Network 1 >0 (r 1 r r 3 ) (r 1 r r 3 ) =0 λ 3 r <r > 1/ λ molecular level deformation macroscopically deform rubber cube
8 Assemble Strands into a Network 1 >0 (r 1 r r 3 ) (r 1 r r 3 ) =0 λ 3 r <r > 1/ λ molecular level deformation macroscopically deform rubber cube
9 [ λλλ = 1] 1 3 CONSTANT VOLUME CONSTRAINT kbtν A = λ1 λ λ3 3 GAUSSIAN + + CONSTANT VOLUME DEORMATION λ λ 3
10 [ λλλ = 1] 1 3 Stress Equations kbtν A = λ1 λ λ3 3 GAUSSIAN + + CONSTANT VOLUME DEORMATION
11 Stress versus Strain Equations for Uniaxial Deformation kbtν A = λ1 λ λ3 3 GAUSSIAN + + CONSTANT VOLUME DEORMATION [ λλλ = 1] 1 3 λ λ 3
12 Uniaxial Deformation: Comparison of Theory with Experiment 7 6 σ 1 (MPa) // 1 1/λ crosslinks 1// 1 strand
REVIEW : INTRODUCTION TO THE MOLECULAR ORIGINS OF MECHANICAL PROPERTIES QUANTITATIVE TREATMENT OF INTERATOMIC BONDING : THE LENNARD-JONES POTENTIAL
LECTURE #19 : 3.11 MECANICS OF MATERIALS F3 INSTRUCTOR : Professor Christine Ortiz OFFICE : 13-422 PONE : 452-384 WWW : http://web.mit.edu/cortiz/www REVIEW : INTRODUCTION TO TE MOLECULAR ORIGINS OF MECANICAL
More informationMultimedia : Podcast : Sacrificial Bonds in Biological Materials; Fantner, et al. Biophys. J , 1411
3.52 Nanomechanics o Materials and Biomaterials Tuesday 5/1/7 Pro. C. Ortiz, MIT-DMSE I LECTURE 2: THEORETICAL ASPECTS O SINGLE MOLECULE ORCE SPECTROSCOPY 2 : EXTENSIBILITY AND THE WORM LIKE CHAIN (WLC)
More informationLab Week 4 Module α 1. Polymer chains as entropy springs: Rubber stretching experiment and XRD study. Instructor: Gretchen DeVries
3.014 Materials Laboratory December 9-14, 005 Lab Week 4 Module α 1 Polymer chains as entropy springs: Rubber stretching experiment and XRD study Instructor: Gretchen DeVries Objectives Review thermodynamic
More informationChapter 3 Entropy elasticity (rubbery materials) Review basic thermal physics Chapter 5.1 to 5.5 (Nelson)
Chapter 3 Entropy elasticity (rubbery materials) Review basic thermal physics Chapter 5.1 to 5.5 (Nelson) Outline: 3.1 Strain, stress and Young modulus 3. Energy density 3.3 Typical stress-strain curve
More informationPolymers. Hevea brasiilensis
Polymers Long string like molecules give rise to universal properties in dynamics as well as in structure properties of importance when dealing with: Pure polymers and polymer solutions & mixtures Composites
More information3 Biopolymers Uncorrelated chains - Freely jointed chain model
3.4 Entropy When we talk about biopolymers, it is important to realize that the free energy of a biopolymer in thermal equilibrium is not constant. Unlike solids, biopolymers are characterized through
More informationVIII. Rubber Elasticity [B.Erman, J.E.Mark, Structure and properties of rubberlike networks]
VIII. Rubber Elasticity [B.Erman, J.E.Mark, Structure and properties of rubberlike networks] Using various chemistry, one can chemically crosslink polymer chains. With sufficient cross-linking, the polymer
More informationChapter 2. Rubber Elasticity:
Chapter. Rubber Elasticity: The mechanical behavior of a rubber band, at first glance, might appear to be Hookean in that strain is close to 100% recoverable. However, the stress strain curve for a rubber
More informationChap. 2. Polymers Introduction. - Polymers: synthetic materials <--> natural materials
Chap. 2. Polymers 2.1. Introduction - Polymers: synthetic materials natural materials no gas phase, not simple liquid (much more viscous), not perfectly crystalline, etc 2.3. Polymer Chain Conformation
More informationWeight and contact forces: Young's modulus, Hooke's law and material properties
Weight and contact forces: Young's modulus, Hooke's law and material properties Many objects deform according to Hooke's law; many materials behave elastically and have a Young's modulus. In this section,
More informationRubber elasticity. Marc R. Roussel Department of Chemistry and Biochemistry University of Lethbridge. February 21, 2009
Rubber elasticity Marc R. Roussel Department of Chemistry and Biochemistry University of Lethbridge February 21, 2009 A rubber is a material that can undergo large deformations e.g. stretching to five
More information3.22 Mechanical Properties of Materials Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 3.22 Mechanical Properties of Materials Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Problem Set
More informationRubber Elasticity (Indented text follows Strobl, other follows Doi)
Rubber Elasticity (Indented text follows Strobl, other follows Doi) Elasticity of A Single Chain: The spring constant associated with a single polymer chain is of importance in a wide range of situations
More informationMultimedia : Fibronectin and Titin unfolding simulation movies.
I LECTURE 21: SINGLE CHAIN ELASTICITY OF BIOMACROMOLECULES: THE GIANT PROTEIN TITIN AND DNA Outline : REVIEW LECTURE #2 : EXTENSIBLE FJC AND WLC... 2 STRUCTURE OF MUSCLE AND TITIN... 3 SINGLE MOLECULE
More informationRouse chains, unentangled. entangled. Low Molecular Weight (M < M e ) chains shown moving past one another.
Physical Picture for Diffusion of Polymers Low Molecular Weight (M < M e ) chains shown moving past one another. Z X Y Rouse chains, unentangled Figure by MIT OCW. High Molecular weight (M > M e ) Entanglements
More informationPhys 450 Spring 2011 Solution set 6. A bimolecular reaction in which A and B combine to form the product P may be written as:
Problem Phys 45 Spring Solution set 6 A bimolecular reaction in which A and combine to form the product P may be written as: k d A + A P k d k a where k d is a diffusion-limited, bimolecular rate constant
More informationCE 530 Molecular Simulation
1 CE 530 Molecular Simulation Lecture 14 Molecular Models David A. Kofke Department of Chemical Engineering SUNY Buffalo kofke@eng.buffalo.edu 2 Review Monte Carlo ensemble averaging, no dynamics easy
More informationMechanical Properties of Polymers. Scope. MSE 383, Unit 3-1. Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept.
Mechanical Properties of Polymers Scope MSE 383, Unit 3-1 Joshua U. Otaigbe Iowa State University Materials Science & Engineering Dept. Structure - mechanical properties relations Time-dependent mechanical
More informationWhat we should know about mechanics of materials
What we should know about mechanics of materials 0 John Maloney Van Vliet Group / Laboratory for Material Chemomechanics Department of Materials Science and Engineering Massachusetts Institute of Technology
More information, to obtain a way to calculate stress from the energy function U(r).
BIOEN 36 014 LECTURE : MOLECULAR BASIS OF ELASTICITY Estimating Young s Modulus from Bond Energies and Structures First we consider solids, which include mostly nonbiological materials, such as metals,
More informationElasticity of biological gels
Seminar II Elasticity of biological gels Author: Gašper Gregorič Mentor: assoc. prof. Primož Ziherl Ljubljana, February 2014 Abstract In the seminar we discuss the elastic behavior of biological gels,
More informationLecture 1 NONLINEAR ELASTICITY
Lecture 1 NONLINEAR ELASTICITY Soft-Matter Engineering: Mechanics, Design, & Modeling Mechanics Rigid/Hard Systems bending or torsion (but not stretching) small strains (~0.1% metals; ~1% plastics) linearized
More informationMechanical Properties of Tetra-Polyethylene and Tetra-Polyethylene Oxide Diamond Networks via Molecular Dynamics Simulations
Supplemental Information Mechanical Properties of Tetra-Polyethylene and Tetra-Polyethylene Oxide Diamond Networks via Molecular Dynamics Simulations Endian Wang and Fernando A. Escobedo Table S1 Lennard-Jones
More informationExample: Uniaxial Deformation. With Axi-symmetric sample cross-section dl l 0 l x. α x since α x α y α z = 1 Rewriting ΔS α ) explicitly in terms of α
Eample: Uniaial Deformation y α With Ai-symmetric sample cross-section l dl l 0 l, d Deform along, α = α = l0 l0 = α, α y = α z = Poisson contraction in lateral directions α since α α y α z = Rewriting
More informationImperfect Gases. NC State University
Chemistry 431 Lecture 3 Imperfect Gases NC State University The Compression Factor One way to represent the relationship between ideal and real gases is to plot the deviation from ideality as the gas is
More information3.091 Introduction to Solid State Chemistry. Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS
3.091 Introduction to Solid State Chemistry Lecture Notes No. 5a ELASTIC BEHAVIOR OF SOLIDS 1. INTRODUCTION Crystals are held together by interatomic or intermolecular bonds. The bonds can be covalent,
More informationStructural Analysis of Truss Structures using Stiffness Matrix. Dr. Nasrellah Hassan Ahmed
Structural Analysis of Truss Structures using Stiffness Matrix Dr. Nasrellah Hassan Ahmed FUNDAMENTAL RELATIONSHIPS FOR STRUCTURAL ANALYSIS In general, there are three types of relationships: Equilibrium
More information2.1 Traditional and modern applications of polymers. Soft and light materials good heat and electrical insulators
. Polymers.1. Traditional and modern applications.. From chemistry to statistical description.3. Polymer solutions and polymer blends.4. Amorphous polymers.5. The glass transition.6. Crystalline polymers.7.
More informationHow materials work. Compression Tension Bending Torsion
Materials How materials work Compression Tension Bending Torsion Elemental material atoms: A. Composition a) Nucleus: protons (+), neutrons (0) b) Electrons (-) B. Neutral charge, i.e., # electrons = #
More informationMATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?
MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition
More informationV(φ) CH 3 CH 2 CH 2 CH 3. High energy states. Low energy states. Views along the C2-C3 bond
Example V(φ): Rotational conformations of n-butane C 3 C C C 3 Potential energy of a n-butane molecule as a function of the angle φ of bond rotation. V(φ) Potential energy/kj mol -1 0 15 10 5 eclipse gauche
More informationJohns Hopkins University What is Engineering? M. Karweit MATERIALS
Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: MATERIALS A. Composition
More informationAbvanced Lab Course. Dynamical-Mechanical Analysis (DMA) of Polymers
Abvanced Lab Course Dynamical-Mechanical Analysis (DMA) of Polymers M211 As od: 9.4.213 Aim: Determination of the mechanical properties of a typical polymer under alternating load in the elastic range
More informationThe broad topic of physical metallurgy provides a basis that links the structure of materials with their properties, focusing primarily on metals.
Physical Metallurgy The broad topic of physical metallurgy provides a basis that links the structure of materials with their properties, focusing primarily on metals. Crystal Binding In our discussions
More informationFinal Project: Indentation Simulation Mohak Patel ENGN-2340 Fall 13
Final Project: Indentation Simulation Mohak Patel ENGN-2340 Fall 13 Aim The project requires a simulation of rigid spherical indenter indenting into a flat block of viscoelastic material. The results from
More informationStructure, molecular dynamics, and stress in a linear polymer under dynamic strain
Structure, molecular dynamics, and stress in a linear polymer under dynamic strain arxiv:112.5588v1 [cond-mat.soft] 27 Dec 21 Stress σ (MPa) 2 15 1 5 N=128, ρ=1., dε/dt=1.x1 9 /sec n = 1 n = 2 n = 5 n
More informationAdvantages of a Finite Extensible Nonlinear Elastic Potential in Lattice Boltzmann Simulations
The Hilltop Review Volume 7 Issue 1 Winter 2014 Article 10 December 2014 Advantages of a Finite Extensible Nonlinear Elastic Potential in Lattice Boltzmann Simulations Tai-Hsien Wu Western Michigan University
More informationXI. NANOMECHANICS OF GRAPHENE
XI. NANOMECHANICS OF GRAPHENE Carbon is an element of extraordinary properties. The carbon-carbon bond possesses large magnitude cohesive strength through its covalent bonds. Elemental carbon appears in
More information3.22 Mechanical Properties of Materials Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 3.22 Mechanical Properties of Materials Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Problem Set
More informationDeformation of Elastomeric Networks: Relation between Molecular Level Deformation and Classical Statistical Mechanics Models of Rubber Elasticity
Deformation of Elastomeric Networks: Relation between Molecular Level Deformation and Classical Statistical Mechanics Models of Rubber Elasticity J. S. Bergström and M. C. Boyce Department of Mechanical
More information3.052 Nanomechanics of Materials and Biomaterials Assignment #3 Due :
.5 Nanomechanics of Materials and Biomaterials : Spring 7 Assignment # Due Date : Thursday.5.7 You are encouraged to use additional resources (e.g. journal papers, internet, etc. but please cite them (points
More informationPractical 1P9 Polymers - Molecular weight effects
Practical 1P9 Polymers - Molecular weight effects What you should learn from this practical Science The main theme of the Polymer Synthesis lectures is that molecular weight, and the ability to control
More information3.22 Mechanical Properties of Materials Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 3.22 Mechanical Properties of Materials Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Quiz #1 Example
More informationPractical 1P9 Polymers - Molecular weight effects
Practical 1P9 Polymers - Molecular weight effects What you should learn from this practical Science The main theme of the Polymer Synthesis lectures is that molecular weight, and the ability to control
More information3.032 Problem Set 4 Fall 2007 Due: Start of Lecture,
3.032 Problem Set 4 Fall 2007 Due: Start of Lecture, 10.19.07 1. A microelectronic sensor is to be made of conductive wires deposited on a thin Si wafer. During design considerations, it was decided that
More informationIdeal Gas Behavior. NC State University
Chemistry 331 Lecture 6 Ideal Gas Behavior NC State University Macroscopic variables P, T Pressure is a force per unit area (P= F/A) The force arises from the change in momentum as particles hit an object
More information4. Thermal properties of solids. Time to study: 4 hours. Lecture Oscillations of the crystal lattice
4. Thermal properties of solids Time to study: 4 hours Objective After studying this chapter you will get acquainted with a description of oscillations of atoms learn how to express heat capacity for different
More information3.032 Problem Set 4 Solutions Fall 2007 Due: Start of Lecture,
3.032 Problem Set 4 Solutions Fall 2007 Due: Start of Lecture, 10.19.07 1. A microelectronic sensor is to be made of conductive wires deposited on a thin Si wafer. During design considerations, it was
More information3.032 Problem Set 5 Solutions Fall 2007 Start
3.032 Problem Set 5 Solutions Fall 2007 Due: Start of Lecture, Monday 10.29.07 (NOTE THAT THIS DATE IS LATER THAN IN YOUR SYLLABUS DUE TO NEW DUE DATE OF LAB 2.) 1. We have discussed that linear viscoelastic
More informationTHEORY OF MOLECULE. A molecule consists of two or more atoms with certain distances between them
THEORY OF MOLECULE A molecule consists of two or more atoms with certain distances between them through interaction of outer electrons. Distances are determined by sum of all forces between the atoms.
More informationLecture 8 Polymers and Gels
Lecture 8 Polymers and Gels Variety of polymeric materials Polymer molecule made by repeating of covalently joint units. Living polymers (not considered in this lecture) long-chain objects connected by
More informationSection 2.5 Atomic Bonding
Section 2.5 Atomic Bonding Metallic bond, Covalent bond, Ionic bond, van der Waals bond are the different types of bonds. Van der Waals interactions: London forces, Debye interaction, Keesom interaction
More informationUntangling the Mechanics of Entangled Biopolymers
Untangling the Mechanics of Entangled Biopolymers Rae M. Robertson-Anderson Physics Department University of San Diego students/postdocs: Cole Chapman, PhD Tobias Falzone, PhD Stephanie Gorczyca, USD 16
More informationSolid State Theory Physics 545
olid tate Theory hysics 545 Mechanical properties of materials. Basics. tress and strain. Basic definitions. Normal and hear stresses. Elastic constants. tress tensor. Young modulus. rystal symmetry and
More informationPHASE TRANSITIONS IN SOFT MATTER SYSTEMS
OUTLINE: Topic D. PHASE TRANSITIONS IN SOFT MATTER SYSTEMS Definition of a phase Classification of phase transitions Thermodynamics of mixing (gases, polymers, etc.) Mean-field approaches in the spirit
More informationThe lattice model of polymer solutions
The lattice model of polymer solutions Marc R. Roussel Department of Chemistry and Biochemistry University of Lethbridge February 25, 2009 1 The lattice model of polymer solutions In the last note, we
More informationMechanical properties of polymers: an overview. Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore
Mechanical properties of polymers: an overview Suryasarathi Bose Dept. of Materials Engineering, IISc, Bangalore UGC-NRCM Summer School on Mechanical Property Characterization- June 2012 Overview of polymer
More informationMATERIALS SCIENCE POLYMERS
POLYMERS 1) Types of Polymer (a) Plastic Possibly the largest number of different polymeric materials come under the plastic classification. Polyethylene, polypropylene, polyvinyl chloride, polystyrene,
More informationSwelling and Collapse of Single Polymer Molecules and Gels.
Swelling and Collapse of Single Polymer Molecules and Gels. Coil-Globule Transition in Single Polymer Molecules. the coil-globule transition If polymer chains are not ideal, interactions of non-neighboring
More informationLecture 8. Polymers and Gels
Lecture 8 Polymers and Gels Variety of polymeric materials Polymer molecule made by repeating of covalently joint units. Many of physical properties of polymers have universal characteristic related to
More informationSELECTED PROBLEMS OF SHORT CIRCUIT WITHSTANDABILITY Section II - POWER TRANSFORMER October 2004, Vigo - Spain
Dr. Władysław Pewca Institute of Power Engineering, Transformer Division (IenOT( IenOT), Poland SELECTED PROBLEMS OF SHORT CIRCUIT WITHSTANDABILITY Section II - POWER TRANSFORMER 28-30 October 2004, Vigo
More informationStrain hardening of polymer glasses: Entanglements, energetics, and plasticity
PHYSICAL REVIEW E 77, 8 8 Strain hardening of polymer glasses: Entanglements, energetics, and plasticity Robert S. Hoy* and Mark O. Robbins Department of Physics and Astronomy, Johns Hopkins University,
More informationThe viscosity-radius relationship from scaling arguments
The viscosity-radius relationship from scaling arguments D. E. Dunstan Department of Chemical and Biomolecular Engineering, University of Melbourne, VIC 3010, Australia. davided@unimelb.edu.au Abstract
More informationMagnetic tweezers and its application to DNA mechanics
Biotechnological Center Research group DNA motors (Seidel group) Handout for Practical Course Magnetic tweezers and its application to DNA mechanics When: 9.00 am Where: Biotec, 3 rd Level, Room 317 Tutors:
More informationIntroduction to Liquid Crystalline Elastomers
Introduction to Liquid Crystalline Elastomers Harald Pleiner Max Planck Institute for Polymer Research, Mainz, Germany "Ferroelectric Phenomena in Liquid Crystals" LCI, Kent State University, Ohio, USA
More informationProteins polymer molecules, folded in complex structures. Konstantin Popov Department of Biochemistry and Biophysics
Proteins polymer molecules, folded in complex structures Konstantin Popov Department of Biochemistry and Biophysics Outline General aspects of polymer theory Size and persistent length of ideal linear
More informationPolymer Gels. Boulder Lectures in Soft Matter Physics July 2012 Yitzhak Rabin
Polymer Gels Boulder ectures in Soft Matter Physics July Yitzhak abin M. ubinstein and.h. Colby, Polymer Physics (Oxford, ), Chapters 6 and 7 P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell,
More informationExploiting pattern transformation to tune phononic band gaps in a two-dimensional granular crystal
Exploiting pattern transformation to tune phononic band gaps in a two-dimensional granular crystal The Harvard community has made this article openly available. Please share how this access benefits you.
More informationAnnouncements. Homework 3 (Klaus Schulten s Lecture): Due Wednesday at noon. Next homework assigned. Due Wednesday March 1.
Announcements Homework 3 (Klaus Schulten s Lecture): Due Wednesday at noon. Next homework assigned. Due Wednesday March 1. No lecture next Monday, Feb. 27 th! (Homework is a bit longer.) Marco will have
More informationPhysics of Materials: Bonding and Material Properties On The basis of Geometry and Bonding (Intermolecular forces) Dr.
: Bonding and Material Properties On The basis of Geometry and Bonding (Intermolecular forces) Dr. Anurag Srivastava Atal Bihari Vajpayee Indian Institute of Information Technology and Manegement, Gwalior
More informationUnderstanding Frequency Domain Viscoelasticity in Abaqus
Paper # 12 Understanding Frequency Domain Viscoelasticity in Abaqus By Saurabh Bahuguna, Randy Marlow*, and Tod Dalrymple Dassault Systèmes Simulia Corp., Great Lakes Region Presented at the Fall 172 nd
More informationINTRODUCTION TO STRAIN
SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,
More information9 MECHANICAL PROPERTIES OF SOLIDS
9 MECHANICAL PROPERTIES OF SOLIDS Deforming force Deforming force is the force which changes the shape or size of a body. Restoring force Restoring force is the internal force developed inside the body
More informationChapter 2: Atomic structure and interatomic bonding
Chapter 2: Atomic structure and interatomic bonding Fundamental concepts Electrons in atoms Periodic table Bonding forces and energies Chapter 2 - Chapter 2: Atomic structure and interatomic bonding Fundamental
More informationSimulation of Coarse-Grained Equilibrium Polymers
Simulation of Coarse-Grained Equilibrium Polymers J. P. Wittmer, Institut Charles Sadron, CNRS, Strasbourg, France Collaboration with: M.E. Cates (Edinburgh), P. van der Schoot (Eindhoven) A. Milchev (Sofia),
More informationIAP 2006: From nano to macro: Introduction to atomistic modeling techniques and application in a case study of modeling fracture of copper (1.
IAP 2006: From nano to macro: Introduction to atomistic modeling techniques and application in a case study of modeling fracture of copper (1.978 PDF) http://web.mit.edu/mbuehler/www/teaching/iap2006/intro.htm
More informationComplete and precise descriptions based on quantum mechanics exist for the Coulombic/Electrostatic force. These are used to describe materials.
The forces of nature: 1. Strong forces hold protons and neutrons together (exchange of mesons) 2. Weak interactions are involved in some kinds of radioactive decay (β-decay) 3. Coulombic or electrostatic
More informationInteratomic bonding 1
Interatomic bonding 1 Bonding forces of atoms All forces playing role in bonding are electrostatic Coulomb forces. Nuclei attract electrons, but nuclei repulse each other as well as electrons do. So, bonding
More informationA Molecular Modeling Approach to Predicting Thermo-Mechanical Properties of Thermosetting Polymers
A Molecular Modeling Approach to Predicting Thermo-Mechanical Properties of Thermosetting Polymers Natalia Shenogina, Wright State University Mesfin Tsige, University of Akron Soumya Patnaik, AFRL Sharmila
More informationChemistry C : Polymers Section. Dr. Edie Sevick, Research School of Chemistry, ANU. 3.0 The size of chains in good and poor solvent conditions
Chemistry C3102-2006: Polymers Section Dr. Edie Sevick, Research School of Chemistry, ANU 3.0 The size of chains in good and poor solvent conditions Obviously, the ideal chain is a simple, first approximate
More informationChapter 2: Atomic structure and interatomic bonding. Chapter 2: Atomic structure and interatomic bonding
Chapter 2: Atomic structure and interatomic bonding Fundamental concepts Electrons in atoms Periodic table Bonding forces and energies Chapter 2: Atomic structure and interatomic bonding Fundamental concepts
More informationMECHANICS OF CARBON NANOTUBE BASED COMPOSITES WITH MOLECULAR DYNAMICS AND MORI TANAKA METHODS. Vinu Unnithan and J. N. Reddy
MECHANICS OF CARBON NANOTUBE BASED COMPOSITES WITH MOLECULAR DYNAMICS AND MORI TANAKA METHODS Vinu Unnithan and J. N. Reddy US-South American Workshop: Mechanics and Advanced Materials Research and Education
More informationCE 530 Molecular Simulation
1 CE 530 Molecular Simulation Lecture 1 David A. Kofke Department of Chemical Engineering SUNY Buffalo kofke@eng.buffalo.edu 2 Time/s Multi-Scale Modeling Based on SDSC Blue Horizon (SP3) 1.728 Tflops
More information1.3 Molecular Level Presentation
1.3.1 Introduction A molecule is the smallest chemical unit of a substance that is capable of stable, independent existence. Not all substances are composed of molecules. Some substances are composed of
More informationMaterial Properties & Characterization - Surfaces
1) XPS Spectrum analysis: The figure below shows an XPS spectrum measured on the surface of a clean insoluble homo-polyether. Using the formulas and tables in this document, answer the following questions:
More informationENAS 606 : Polymer Physics
ENAS 606 : Polymer Physics Professor Description Course Topics TA Prerequisite Class Office Hours Chinedum Osuji 302 Mason Lab, 432-4357, chinedum.osuji@yale.edu This course covers the static and dynamic
More informationHyeyoung Shin a, Tod A. Pascal ab, William A. Goddard III abc*, and Hyungjun Kim a* Korea
The Scaled Effective Solvent Method for Predicting the Equilibrium Ensemble of Structures with Analysis of Thermodynamic Properties of Amorphous Polyethylene Glycol-Water Mixtures Hyeyoung Shin a, Tod
More informationChemical Engineering 160/260 Polymer Science and Engineering. Lecture 14: Amorphous State February 14, 2001
Chemical Engineering 160/260 Polymer Science and Engineering Lecture 14: Amorphous State February 14, 2001 Objectives! To provide guidance toward understanding why an amorphous polymer glass may be considered
More informationDensity. Physical Properties of Materials. Which Ones? THEORETICAL DENSITY, ρ. What would make a material dense? Concept Question. Physical Properties
Physical Properties of Materials Let s get physical!! density Physical Properties electrical thermal expansion shock Density Which Ones? melting point What is density? = THEORETICAL DENSITY, ρ Concept
More informationThermal-Mechanical Decoupling by a Thermal Interface Material
Thermal-Mechanical Decoupling by a Thermal Interface Material Haibing Zhang, Ph.D. Research and Development Chemist Andy Cloud Product Development Manager Abstract Thermal-mechanical decoupling by a silicone
More informationWORCESTER POLYTECHNIC INSTITUTE
WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT STRESS ANALYSIS ES-2502, C 2012 Lecture 07: Stress and Strain 24 January 2012 General information Instructor: Cosme Furlong HL-151 (508)
More informationICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below
ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below Introduction In statistical physics Monte Carlo methods are considered to have started in the Manhattan project (1940
More informationXiaoming Mao Physics, University of Michigan, Ann Arbor. IGERT Summer Institute 2017 Brandeis
Xiaoming Mao Physics, University of Michigan, Ann Arbor IGERT Summer Institute 2017 Brandeis Elastic Networks A family of discrete model networks involving masses connected by springs 1 2 kk( ll)2 Disordered
More information6.730 Physics for Solid State Applications
6.730 Physics for Solid State Applications Lecture 8: Lattice Waves in 1D Monatomic Crystals Outline Overview of Lattice Vibrations so far Models for Vibrations in Discrete 1-D Lattice Example of Nearest
More informationChapter 3. Crystal Binding
Chapter 3. Crystal Binding Energy of a crystal and crystal binding Cohesive energy of Molecular crystals Ionic crystals Metallic crystals Elasticity What causes matter to exist in three different forms?
More informationSupplementary Information
Supplementary Information Ballistic Thermal Transport in Carbyne and Cumulene with Micron-Scale Spectral Acoustic Phonon Mean Free Path Mingchao Wang and Shangchao Lin * Department of Mechanical Engineering,
More informationElasticity. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Modified by M.
Elasticity A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Modified by M. Lepore Elasticity Photo Vol. 10 PhotoDisk/Getty BUNGEE jumping utilizes
More informationElasticity of the human red blood cell skeleton
Biorheology 40 (2003) 247 251 247 IOS Press Elasticity of the human red blood cell skeleton G. Lenormand, S. Hénon, A. Richert, J. Siméon and F. Gallet Laboratoire de Biorhéologie et d Hydrodynamique Physico-Chimique,
More informationIntroduction to Materials Science Prof. Michael Roth
Introduction to Materials Science Prof. Michael Roth Chapter 3 Crystal Binding and Elasticity Introduction What holds a crystal together? Atoms in a solid are bound together by Coulomb forces; Others,
More informationModeling Biological Systems Opportunities for Computer Scientists
Modeling Biological Systems Opportunities for Computer Scientists Filip Jagodzinski RBO Tutorial Series 25 June 2007 Computer Science Robotics & Biology Laboratory Protein: πρώτα, "prota, of Primary Importance
More information