C is very reactive, difficult to control and stabilize
|
|
- Gavin Tyler
- 6 years ago
- Views:
Transcription
1 ynhesis of Polymers Prof. Paula ammond Lecure 25: Living aionic Polymerizaions, Examles of aionic Polymerizaion, Isobuyl ubber ynhesis, Polyvinyl Ehers aionic Polymerizaion ome differences beween caionic and anionic olymerizaion aes are faser for caionic (1 or more orders of magniude faser han anionic or free radical) is very reacive, difficul o conrol and sabilize more ransfer occurs more side reacions more difficul o form living sysems hard o mae olymers wih low PDI or bloc coolymers Living caionic only ossible for a secific subse of monomers Mos indusrial caionic rocesses are no living - recen develomens are imroving his comes off Kineic es for aionic Polymerizaion Iniiaion: Use cids Proonic cids (Bronsed): srong, bu wihou nucleohilic counerion lo 4, F 3 O 3, 2 O 4, FOO - lo wan o avoid recombinaion hrough counerion Lewis cids Ofen as iniiaor/coordinaion comlexes hels sabilize counerions and reven recombinaion BF 3 2 O [ BF - 3 O] ll 3 l [ ll - 4 ] bf 5 F [ bf - 6 ] Equilibrium beween anion-caion air iaion: Professor Paula ammond, ynhesis of Polymers Fall 2006 maerials, MIT OenourseWare (h://ocw.mi.edu/index.hml), Massachuses Insiue of Technology, Dae.
2 arbenium sals wih aromaic sabilizaion l bl 5 bl 6 Proagaion 2 iniiaion secies 2 2 vinyl monomer 2 oe: rearrangemens can occur, esecially if a more sable carbocaion can be formed (e.g. eriary carbocaion) (mos common for 1-alenes, α olefins) e.g. 2 mehyl buene secondary carbocaion eriary carbocaion This occurs via inramolecular hydride ( - ) shifs Usually slow: If rearrangemen rae, will ge rearranged roduc If > rearrangemen rae, will ge random coolymer s T, m (less rearrangemen) ae of rearrangemen does no increase as fas as rae of roagaion. 3 ydride shif OT common for conjugaed monomers lie: syrene, vinyl ehers and isobuylene and oher eriary carbocaions , ynhesis of Polymers, Fall 2006 Lecure 25 Prof. Paula ammond Page 2 of 7 iaion: Professor Paula ammond, ynhesis of Polymers Fall 2006 maerials, MIT OenourseWare (h://ocw.mi.edu/index.hml), Massachuses Insiue of Technology, Dae. 2 3 m
3 Terminaion and Transfer (everal Possibiliies) ) Terminaion wih counerion: ills roagaing caion, ineic chain ( ) i) ombinaion O,comb 2 F 3 OO 2 O F 3 ii) nion liing 2 BF 3 O,s 2 O BF 3 B) Transfer or erminaion o imuriy or solven O To 2 O, O, 3, O, ec. Iniiaor e.g. M M(IZ) X 2 Imuriy or olven r,s M M X(IZ) O 2 O more sable han no as reacive, acs as reardan - will no roagae furher or 2 -O 2 O wea acid will no iniiae ll hese rocesses ill chain lengh , ynhesis of Polymers, Fall 2006 Lecure 25 Prof. Paula ammond Page 3 of 7 iaion: Professor Paula ammond, ynhesis of Polymers Fall 2006 maerials, MIT OenourseWare (h://ocw.mi.edu/index.hml), Massachuses Insiue of Technology, Dae.
4 Transfer (Kineic hain Mainained) ) Proon ransfer o monomer 2 3 roagaes B) ydride ion ransfer from monomer roagaes In general, chain ransfer o monomer is favorable so M r, M can be sizeable. ) Proon ransfer o counerion ( sonaneous erminaion ) r,ci roagaing coninues Usually roagaes (does OT ill chain) usually goes on o iniiae again roic acid iniiaors are ossible Lewis acids are less liely , ynhesis of Polymers, Fall 2006 Lecure 25 Prof. Paula ammond Page 4 of 7 iaion: Professor Paula ammond, ynhesis of Polymers Fall 2006 maerials, MIT OenourseWare (h://ocw.mi.edu/index.hml), Massachuses Insiue of Technology, Dae.
5 Kineic Exressions Iniiaion: ssume Lewis cid Pair I 1. ZY Y(IZ) K i ( IZ) Y I ZY 2. Y(IZ) M YM(IZ) ofen rae limiing If se 2 is rae deermining, hen i i Y ( IZ) M K i I ZY M * i could be deermined based on se 1. Then he exressions would be differen. Proagaion YM j (IZ) M YM j1 (IZ) some number of monomer YMj ( IZ) M M M ssumion: chain lengh has lile effec on reaciviy Le [M ] oal concenraion of all-size roagaing carbocaions (ion airs free ions) Terminaion Mus deermine rimary means of erminaion (solven, imuriies, counerion combinaions, or all?) Examle case: erminaion by counerion combinaion YM(IZ),comb YMIZ, YM IZ, ( ) comb comb If we assume seady sae [M ] K M I ZY eady sae assumion is ha i i i K i i M I ZY M i Going bac o wih 2 i M Ki I ZY M second order in [M] Firs order in i , ynhesis of Polymers, Fall 2006 Lecure 25 Prof. Paula ammond Page 5 of 7 iaion: Professor Paula ammond, ynhesis of Polymers Fall 2006 maerials, MIT OenourseWare (h://ocw.mi.edu/index.hml), Massachuses Insiue of Technology, Dae.
6 (unlie free radical) P : o ransfer (o monomer, solven, counerion) M P P : If ransfer occurs r,m : o monomer creae new roagaing chain r, : o solven creae new caionic secies r,i : o counerion recreae iniiaion P, r, i r, M r wih r, i r, i r, M r, M M r, r, M P M r, i r, M M r, 1 r, i M P M M M r, M r, uose ransfer o solven or imuriy does no resul in furher roagaion. e.g. 3 (IZ) M M(IZ) 3 M M This mus be included in seady sae [M ] exression 2 Ki [][ I ZY ][ M ] erm from ransfer lie r, [ ] *does no effec Is sable o furher roagaion P exression (do no include in P calc) *oe: all of he above assumes he 2 nd iniiaion se is rae deermining. Validiy of eady ae ssumion o really valid - rxn raes very raid (seconds minues) - ofen i > , ynhesis of Polymers, Fall 2006 Lecure 25 Prof. Paula ammond Page 6 of 7 iaion: Professor Paula ammond, ynhesis of Polymers Fall 2006 maerials, MIT OenourseWare (h://ocw.mi.edu/index.hml), Massachuses Insiue of Technology, Dae.
7 - [M ] slowly increases wih ime - [M ] reaches maximum lae in olymerizaion hen decreases wih furher conversion licaion of equaions is merely an aroximaion of wha really haens , ynhesis of Polymers, Fall 2006 Lecure 25 Prof. Paula ammond Page 7 of 7 iaion: Professor Paula ammond, ynhesis of Polymers Fall 2006 maerials, MIT OenourseWare (h://ocw.mi.edu/index.hml), Massachuses Insiue of Technology, Dae.
Kinetics and mechanism of polymerization of methyl methacrylate initiated by stibonium ylide
J. Chem. Sci., Vol. 116, No. 1, January 004,. 55 59. Indian Academy of Sciences. Kineics and mechanism of olymerizaion of mehyl mehacrylae iniiaed by sibonium ylide A K SRIVASTAVA and AJEY KUMAR CHAURASIA
More informationKinetics and Modeling of the Radical Polymerization of Acrylic Acid and of Methacrylic Acid in Aqueous Solution
Kineics and Modeling of he Radical Polymerizaion of Acrylic Acid and of Mehacrylic Acid in Aqueous Soluion Disseraion zur Erlangung des mahemaisch-naurwissenschaflichen Doorgrades Docor rerum nauralium
More informationA First Course on Kinetics and Reaction Engineering. Class 19 on Unit 18
A Firs ourse on Kineics and Reacion Engineering lass 19 on Uni 18 Par I - hemical Reacions Par II - hemical Reacion Kineics Where We re Going Par III - hemical Reacion Engineering A. Ideal Reacors B. Perfecly
More informationSimulation-Solving Dynamic Models ABE 5646 Week 2, Spring 2010
Simulaion-Solving Dynamic Models ABE 5646 Week 2, Spring 2010 Week Descripion Reading Maerial 2 Compuer Simulaion of Dynamic Models Finie Difference, coninuous saes, discree ime Simple Mehods Euler Trapezoid
More informationCHEMICAL KINETICS: 1. Rate Order Rate law Rate constant Half-life Temperature Dependence
CHEMICL KINETICS: Rae Order Rae law Rae consan Half-life Temperaure Dependence Chemical Reacions Kineics Chemical ineics is he sudy of ime dependence of he change in he concenraion of reacans and producs.
More informationAdvanced Organic Chemistry
Lalic, G. Chem 53A Chemisry 53A Advanced Organic Chemisry Lecure noes 1 Kineics: A racical Approach Simple Kineics Scenarios Fiing Experimenal Daa Using Kineics o Deermine he Mechanism Doughery, D. A.,
More informationKEY. Math 334 Midterm I Fall 2008 sections 001 and 003 Instructor: Scott Glasgow
1 KEY Mah 4 Miderm I Fall 8 secions 1 and Insrucor: Sco Glasgow Please do NOT wrie on his eam. No credi will be given for such work. Raher wrie in a blue book, or on our own paper, preferabl engineering
More informationEE650R: Reliability Physics of Nanoelectronic Devices Lecture 9:
EE65R: Reliabiliy Physics of anoelecronic Devices Lecure 9: Feaures of Time-Dependen BTI Degradaion Dae: Sep. 9, 6 Classnoe Lufe Siddique Review Animesh Daa 9. Background/Review: BTI is observed when he
More informationd 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3
and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or
More informationh[n] is the impulse response of the discrete-time system:
Definiion Examples Properies Memory Inveribiliy Causaliy Sabiliy Time Invariance Lineariy Sysems Fundamenals Overview Definiion of a Sysem x() h() y() x[n] h[n] Sysem: a process in which inpu signals are
More informationChapter 15: Phenomena. Chapter 15 Chemical Kinetics. Reaction Rates. Reaction Rates R P. Reaction Rates. Rate Laws
Chaper 5: Phenomena Phenomena: The reacion (aq) + B(aq) C(aq) was sudied a wo differen emperaures (98 K and 35 K). For each emperaure he reacion was sared by puing differen concenraions of he 3 species
More informationLAPLACE TRANSFORM AND TRANSFER FUNCTION
CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions
More information10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 10: Non ideal Reactor Mixing Patterns
1.37 Chemical and Biological Reacion ngineering, Spring 27 Prof. K. Dane Wirup Lecure 1: Non ideal Reacor Mixing Paerns This lecure covers residence ime disribuion (RTD), he anks in series model, and combinaions
More informationLecture 2-1 Kinematics in One Dimension Displacement, Velocity and Acceleration Everything in the world is moving. Nothing stays still.
Lecure - Kinemaics in One Dimension Displacemen, Velociy and Acceleraion Everyhing in he world is moving. Nohing says sill. Moion occurs a all scales of he universe, saring from he moion of elecrons in
More information( ) = b n ( t) n " (2.111) or a system with many states to be considered, solving these equations isn t. = k U I ( t,t 0 )! ( t 0 ) (2.
Andrei Tokmakoff, MIT Deparmen of Chemisry, 3/14/007-6.4 PERTURBATION THEORY Given a Hamilonian H = H 0 + V where we know he eigenkes for H 0 : H 0 n = E n n, we can calculae he evoluion of he wavefuncion
More informationAP Chemistry--Chapter 12: Chemical Kinetics
AP Chemisry--Chaper 12: Chemical Kineics I. Reacion Raes A. The area of chemisry ha deals wih reacion raes, or how fas a reacion occurs, is called chemical kineics. B. The rae of reacion depends on he
More information3.1.3 INTRODUCTION TO DYNAMIC OPTIMIZATION: DISCRETE TIME PROBLEMS. A. The Hamiltonian and First-Order Conditions in a Finite Time Horizon
3..3 INRODUCION O DYNAMIC OPIMIZAION: DISCREE IME PROBLEMS A. he Hamilonian and Firs-Order Condiions in a Finie ime Horizon Define a new funcion, he Hamilonian funcion, H. H he change in he oal value of
More informationChapter 14 Chemical Kinetics
# of paricles 5/9/4 Chemical Kineics Raes of Reacions Chemical Kineics is he sudy of he rae of reacion. How fas does i ae place? Very Fas Reacions Very Slow Reacions Chaper 4 Chemical Kineics Acid/Base
More informationNuclear Decay kinetics : Transient and Secular Equilibrium. What can we say about the plot to the right?
uclear Decay kineics : Transien and Secular Equilibrium Wha can we say abou he plo o he righ? IV. Paren-Daugher Relaionships Key poin: The Rae-Deermining Sep. Case of Radioacive Daugher (Paren) 1/2 ()
More informationModule 2 F c i k c s la l w a s o s f dif di fusi s o i n
Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms
More informationMath From Scratch Lesson 34: Isolating Variables
Mah From Scrach Lesson 34: Isolaing Variables W. Blaine Dowler July 25, 2013 Conens 1 Order of Operaions 1 1.1 Muliplicaion and Addiion..................... 1 1.2 Division and Subracion.......................
More informationInventory Analysis and Management. Multi-Period Stochastic Models: Optimality of (s, S) Policy for K-Convex Objective Functions
Muli-Period Sochasic Models: Opimali of (s, S) Polic for -Convex Objecive Funcions Consider a seing similar o he N-sage newsvendor problem excep ha now here is a fixed re-ordering cos (> 0) for each (re-)order.
More informationPolymerization Technology Laboratory
Versuch eacion Calorimery Polymerizaion Technology Laboraory eacion Calorimery 1. Subjec Isohermal and adiabaic emulsion polymerizaion of mehyl mehacrylae in a bach reacor. 2. Theory 2.1 Isohermal and
More informationSolutions Problem Set 3 Macro II (14.452)
Soluions Problem Se 3 Macro II (14.452) Francisco A. Gallego 04/27/2005 1 Q heory of invesmen in coninuous ime and no uncerainy Consider he in nie horizon model of a rm facing adjusmen coss o invesmen.
More informationDesigning Information Devices and Systems I Spring 2019 Lecture Notes Note 17
EES 16A Designing Informaion Devices and Sysems I Spring 019 Lecure Noes Noe 17 17.1 apaciive ouchscreen In he las noe, we saw ha a capacior consiss of wo pieces on conducive maerial separaed by a nonconducive
More informationPhysics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle
Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,
More informationLinear Quadratic Regulator (LQR) - State Feedback Design
Linear Quadrai Regulaor (LQR) - Sae Feedbak Design A sysem is expressed in sae variable form as x = Ax + Bu n m wih x( ) R, u( ) R and he iniial ondiion x() = x A he sabilizaion problem using sae variable
More information( ) is the stretch factor, and x the
(Lecures 7-8) Liddle, Chaper 5 Simple cosmological models (i) Hubble s Law revisied Self-similar srech of he universe All universe models have his characerisic v r ; v = Hr since only his conserves homogeneiy
More informationTwo Coupled Oscillators / Normal Modes
Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own
More informationIB Physics Kinematics Worksheet
IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?
More information1 birth rate γ (number of births per time interval) 2 death rate δ proportional to size of population
Scienific Comuing I Module : Poulaion Modelling Coninuous Models Michael Bader Par I ODE Models Lehrsuhl Informaik V Winer 7/ Discree vs. Coniuous Models d d = F,,...) ) =? discree model: coninuous model:
More information5.1 - Logarithms and Their Properties
Chaper 5 Logarihmic Funcions 5.1 - Logarihms and Their Properies Suppose ha a populaion grows according o he formula P 10, where P is he colony size a ime, in hours. When will he populaion be 2500? We
More information6.003 Homework 1. Problems. Due at the beginning of recitation on Wednesday, February 10, 2010.
6.003 Homework Due a he beginning of reciaion on Wednesday, February 0, 200. Problems. Independen and Dependen Variables Assume ha he heigh of a waer wave is given by g(x v) where x is disance, v is velociy,
More informationChapter 14 Chemical Kinetics
/5/4 Chaper 4 Chemical Kineics Chemical Kineics Raes of Reacions Chemical Kineics is he sudy of he rae of reacion. How fas does i ake place? Very Fas Reacions Very Slow Reacions Acid/Base Combusion Rusing
More informationPhysics 180A Fall 2008 Test points. Provide the best answer to the following questions and problems. Watch your sig figs.
Physics 180A Fall 2008 Tes 1-120 poins Name Provide he bes answer o he following quesions and problems. Wach your sig figs. 1) The number of meaningful digis in a number is called he number of. When numbers
More informationRelaxation in Glass. Transition
Relaxaion in Glass Lecure 2: he Glass ransiion as a Kineic Lecure 2: he Glass ransiion as a Kineic ransiion Enhalpy Changes in he Glass ransiion Range H decreases coninuously wih cooling Slope of he H
More informationTraveling Waves. Chapter Introduction
Chaper 4 Traveling Waves 4.1 Inroducion To dae, we have considered oscillaions, i.e., periodic, ofen harmonic, variaions of a physical characerisic of a sysem. The sysem a one ime is indisinguishable from
More informationGuest Lectures for Dr. MacFarlane s EE3350 Part Deux
Gues Lecures for Dr. MacFarlane s EE3350 Par Deux Michael Plane Mon., 08-30-2010 Wrie name in corner. Poin ou his is a review, so I will go faser. Remind hem o go lisen o online lecure abou geing an A
More informationON DETERMINATION OF SOME CHARACTERISTICS OF SEMI-MARKOV PROCESS FOR DIFFERENT DISTRIBUTIONS OF TRANSIENT PROBABILITIES ABSTRACT
Zajac, Budny ON DETERMINATION O SOME CHARACTERISTICS O SEMI MARKOV PROCESS OR DIERENT DISTRIBUTIONS O R&RATA # 2(3 ar 2 (Vol. 2 29, June ON DETERMINATION O SOME CHARACTERISTICS O SEMI-MARKOV PROCESS OR
More informationCosumnes River College Principles of Macroeconomics Problem Set 1 Due January 30, 2017
Spring 0 Cosumnes River College Principles of Macroeconomics Problem Se Due Januar 0, 0 Name: Soluions Prof. Dowell Insrucions: Wrie he answers clearl and concisel on hese shees in he spaces provided.
More informationFishing limits and the Logistic Equation. 1
Fishing limis and he Logisic Equaion. 1 1. The Logisic Equaion. The logisic equaion is an equaion governing populaion growh for populaions in an environmen wih a limied amoun of resources (for insance,
More informationUnsteady Mass- Transfer Models
See T&K Chaper 9 Unseady Mass- Transfer Models ChEn 6603 Wednesday, April 4, Ouline Conex for he discussion Soluion for ransien binary diffusion wih consan c, N. Soluion for mulicomponen diffusion wih
More informationLecture 4 Notes (Little s Theorem)
Lecure 4 Noes (Lile s Theorem) This lecure concerns one of he mos imporan (and simples) heorems in Queuing Theory, Lile s Theorem. More informaion can be found in he course book, Bersekas & Gallagher,
More informationLogistic growth rate. Fencing a pen. Notes. Notes. Notes. Optimization: finding the biggest/smallest/highest/lowest, etc.
Opimizaion: finding he bigges/smalles/highes/lowes, ec. Los of non-sandard problems! Logisic growh rae 7.1 Simple biological opimizaion problems Small populaions AND large populaions grow slowly N: densiy
More informationThe fundamental mass balance equation is ( 1 ) where: I = inputs P = production O = outputs L = losses A = accumulation
Hea (iffusion) Equaion erivaion of iffusion Equaion The fundamenal mass balance equaion is I P O L A ( 1 ) where: I inpus P producion O oupus L losses A accumulaion Assume ha no chemical is produced or
More informationINDEX. Transient analysis 1 Initial Conditions 1
INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera
More informationModule 3: The Damped Oscillator-II Lecture 3: The Damped Oscillator-II
Module 3: The Damped Oscillaor-II Lecure 3: The Damped Oscillaor-II 3. Over-damped Oscillaions. This refers o he siuaion where β > ω (3.) The wo roos are and α = β + α 2 = β β 2 ω 2 = (3.2) β 2 ω 2 = 2
More informationt is a basis for the solution space to this system, then the matrix having these solutions as columns, t x 1 t, x 2 t,... x n t x 2 t...
Mah 228- Fri Mar 24 5.6 Marix exponenials and linear sysems: The analogy beween firs order sysems of linear differenial equaions (Chaper 5) and scalar linear differenial equaions (Chaper ) is much sronger
More informationהמחלקה : ביולוגיה מולקולרית הפקולטה למדעי הטבע
טל : 03-9066345 פקס : 03-9374 ראש המחלקה: ד"ר אלברט פנחסוב המחלקה : ביולוגיה מולקולרית הפקולטה למדעי הטבע Course Name: Physical Chemisry - (for Molecular Biology sudens) כימיה פיזיקאלית )לסטודנטים לביולוגיה
More informationModule 4: Time Response of discrete time systems Lecture Note 2
Module 4: Time Response of discree ime sysems Lecure Noe 2 1 Prooype second order sysem The sudy of a second order sysem is imporan because many higher order sysem can be approimaed by a second order model
More information04. Kinetics of a second order reaction
4. Kineics of a second order reacion Imporan conceps Reacion rae, reacion exen, reacion rae equaion, order of a reacion, firs-order reacions, second-order reacions, differenial and inegraed rae laws, Arrhenius
More informationMath 333 Problem Set #2 Solution 14 February 2003
Mah 333 Problem Se #2 Soluion 14 February 2003 A1. Solve he iniial value problem dy dx = x2 + e 3x ; 2y 4 y(0) = 1. Soluion: This is separable; we wrie 2y 4 dy = x 2 + e x dx and inegrae o ge The iniial
More informationRise-Time Distortion of Signal without Carrying Signal
Journal of Physics: Conference Series PAPER OPEN ACCESS Rise-Time Disorion of Signal wihou Carrying Signal To cie his aricle: N S Bukhman 6 J. Phys.: Conf. Ser. 738 8 View he aricle online for udaes and
More informationContinuous Time Markov Chain (Markov Process)
Coninuous Time Markov Chain (Markov Process) The sae sace is a se of all non-negaive inegers The sysem can change is sae a any ime ( ) denoes he sae of he sysem a ime The random rocess ( ) forms a coninuous-ime
More informationSOLUTIONS TO ECE 3084
SOLUTIONS TO ECE 384 PROBLEM 2.. For each sysem below, specify wheher or no i is: (i) memoryless; (ii) causal; (iii) inverible; (iv) linear; (v) ime invarian; Explain your reasoning. If he propery is no
More informationψ(t) = V x (0)V x (t)
.93 Home Work Se No. (Professor Sow-Hsin Chen Spring Term 5. Due March 7, 5. This problem concerns calculaions of analyical expressions for he self-inermediae scaering funcion (ISF of he es paricle in
More information2.4 Cuk converter example
2.4 Cuk converer example C 1 Cuk converer, wih ideal swich i 1 i v 1 2 1 2 C 2 v 2 Cuk converer: pracical realizaion using MOSFET and diode C 1 i 1 i v 1 2 Q 1 D 1 C 2 v 2 28 Analysis sraegy This converer
More informationCHEMICAL KINETICS Rate Order Rate law Rate constant Half-life Molecularity Elementary. Complex Temperature dependence, Steady-state Approximation
CHEMICL KINETICS Rae Order Rae law Rae consan Half-life Moleculariy Elemenary Complex Temperaure dependence, Seady-sae pproximaion Chemical Reacions Kineics Chemical ineics is he sudy of ime dependence
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 31 Signals & Sysems Prof. Mar Fowler Noe Se #1 C-T Signals: Circuis wih Periodic Sources 1/1 Solving Circuis wih Periodic Sources FS maes i easy o find he response of an RLC circui o a periodic source!
More informationKinetic and Structural Features of Furan Compounds as Inhibitors of the Radical Polymerization of Vinyl Acetate.
A R G É N E N Í F Kineic and Srucural Feaures of Furan ompounds as nhibiors of he Radical Polymerizaion of Vinyl Aceae. Rebeca Vega and Jacques Rieumon Absrac: Some furan compounds bearing a double bond
More informationTSC 220X Spring 2011 Problem Set #5
Name: TSC 220X Spring 2011 Problem Se #5 This problem se is due in class on Monday 21 March 2011. The problem se should be yped. We do no expec Pulizer Prize winning wriing, bu answers should be complee,
More informationLinear Dynamic Models
Linear Dnamic Models and Forecasing Reference aricle: Ineracions beween he muliplier analsis and he principle of acceleraion Ouline. The sae space ssem as an approach o working wih ssems of difference
More informationMath 2214 Solution Test 1A Spring 2016
Mah 14 Soluion Tes 1A Spring 016 sec Problem 1: Wha is he larges -inerval for which ( 4) = has a guaraneed + unique soluion for iniial value (-1) = 3 according o he Exisence Uniqueness Theorem? Soluion
More informationSolutions for Assignment 2
Faculy of rs and Science Universiy of Torono CSC 358 - Inroducion o Compuer Neworks, Winer 218 Soluions for ssignmen 2 Quesion 1 (2 Poins): Go-ack n RQ In his quesion, we review how Go-ack n RQ can be
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. A/Prof Tay Seng Chuan
Ground Rules PC11 Fundamenals of Physics I Lecures 3 and 4 Moion in One Dimension A/Prof Tay Seng Chuan 1 Swich off your handphone and pager Swich off your lapop compuer and keep i No alking while lecure
More informationReaction Order Molecularity. Rate laws, Reaction Orders. Determining Reaction Order. Determining Reaction Order. Determining Reaction Order
Rae laws, Reacion Orders The rae or velociy of a chemical reacion is loss of reacan or appearance of produc in concenraion unis, per uni ime d[p] d[s] The rae law for a reacion is of he form Rae d[p] k[a]
More informationEE 435. Lecture 31. Absolute and Relative Accuracy DAC Design. The String DAC
EE 435 Lecure 3 Absolue and Relaive Accuracy DAC Design The Sring DAC . Review from las lecure. DFT Simulaion from Malab Quanizaion Noise DACs and ADCs generally quanize boh ampliude and ime If convering
More informationSolutions to Assignment 1
MA 2326 Differenial Equaions Insrucor: Peronela Radu Friday, February 8, 203 Soluions o Assignmen. Find he general soluions of he following ODEs: (a) 2 x = an x Soluion: I is a separable equaion as we
More informationChapter 13 Homework Answers
Chaper 3 Homework Answers 3.. The answer is c, doubling he [C] o while keeping he [A] o and [B] o consan. 3.2. a. Since he graph is no linear, here is no way o deermine he reacion order by inspecion. A
More information2001 November 15 Exam III Physics 191
1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses:
More informationPHYSICS 220 Lecture 02 Motion, Forces, and Newton s Laws Textbook Sections
PHYSICS 220 Lecure 02 Moion, Forces, and Newon s Laws Texbook Secions 2.2-2.4 Lecure 2 Purdue Universiy, Physics 220 1 Overview Las Lecure Unis Scienific Noaion Significan Figures Moion Displacemen: Δx
More informationF This leads to an unstable mode which is not observable at the output thus cannot be controlled by feeding back.
Lecure 8 Las ime: Semi-free configuraion design This is equivalen o: Noe ns, ener he sysem a he same place. is fixed. We design C (and perhaps B. We mus sabilize if i is given as unsable. Cs ( H( s = +
More informationME425/525: Advanced Topics in Building Science
ME425/525: Advanced Topics in Building Science Indoor environmenal qualiy for susainable buildings: Lecure 6 Dr. Ellio T. Gall, Ph.D. Lecure 6 Today s objecives o Error propagaion Apply o SS soluion (venilaion,
More informationSummary of shear rate kinematics (part 1)
InroToMaFuncions.pdf 4 CM465 To proceed o beer-designed consiuive equaions, we need o know more abou maerial behavior, i.e. we need more maerial funcions o predic, and we need measuremens of hese maerial
More informationLinear Time-invariant systems, Convolution, and Cross-correlation
Linear Time-invarian sysems, Convoluion, and Cross-correlaion (1) Linear Time-invarian (LTI) sysem A sysem akes in an inpu funcion and reurns an oupu funcion. x() T y() Inpu Sysem Oupu y() = T[x()] An
More information(1) (2) Differentiation of (1) and then substitution of (3) leads to. Therefore, we will simply consider the second-order linear system given by (4)
Phase Plane Analysis of Linear Sysems Adaped from Applied Nonlinear Conrol by Sloine and Li The general form of a linear second-order sysem is a c b d From and b bc d a Differeniaion of and hen subsiuion
More informationBiol. 356 Lab 8. Mortality, Recruitment, and Migration Rates
Biol. 356 Lab 8. Moraliy, Recruimen, and Migraion Raes (modified from Cox, 00, General Ecology Lab Manual, McGraw Hill) Las week we esimaed populaion size hrough several mehods. One assumpion of all hese
More informationNEWTON S SECOND LAW OF MOTION
Course and Secion Dae Names NEWTON S SECOND LAW OF MOTION The acceleraion of an objec is defined as he rae of change of elociy. If he elociy changes by an amoun in a ime, hen he aerage acceleraion during
More informationSome Basic Information about M-S-D Systems
Some Basic Informaion abou M-S-D Sysems 1 Inroducion We wan o give some summary of he facs concerning unforced (homogeneous) and forced (non-homogeneous) models for linear oscillaors governed by second-order,
More informationL1, L2, N1 N2. + Vout. C out. Figure 2.1.1: Flyback converter
page 11 Flyback converer The Flyback converer belongs o he primary swiched converer family, which means here is isolaion beween in and oupu. Flyback converers are used in nearly all mains supplied elecronic
More informationChapter 7: Inverse-Response Systems
Chaper 7: Invere-Repone Syem Normal Syem Invere-Repone Syem Baic Sar ou in he wrong direcion End up in he original eady-ae gain value Two or more yem wih differen magniude and cale in parallel Main yem
More informationLecture 3: Exponential Smoothing
NATCOR: Forecasing & Predicive Analyics Lecure 3: Exponenial Smoohing John Boylan Lancaser Cenre for Forecasing Deparmen of Managemen Science Mehods and Models Forecasing Mehod A (numerical) procedure
More informationAP Calculus BC Chapter 10 Part 1 AP Exam Problems
AP Calculus BC Chaper Par AP Eam Problems All problems are NO CALCULATOR unless oherwise indicaed Parameric Curves and Derivaives In he y plane, he graph of he parameric equaions = 5 + and y= for, is a
More informationEchocardiography Project and Finite Fourier Series
Echocardiography Projec and Finie Fourier Series 1 U M An echocardiagram is a plo of how a porion of he hear moves as he funcion of ime over he one or more hearbea cycles If he hearbea repeas iself every
More informationSterilization D Values
Seriliaion D Values Seriliaion by seam consis of he simple observaion ha baceria die over ime during exposure o hea. They do no all live for a finie period of hea exposure and hen suddenly die a once,
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 3 Signals & Sysems Prof. Mark Fowler Noe Se # Wha are Coninuous-Time Signals??? /6 Coninuous-Time Signal Coninuous Time (C-T) Signal: A C-T signal is defined on he coninuum of ime values. Tha is:
More informationChapter #1 EEE8013 EEE3001. Linear Controller Design and State Space Analysis
Chaper EEE83 EEE3 Chaper # EEE83 EEE3 Linear Conroller Design and Sae Space Analysis Ordinary Differenial Equaions.... Inroducion.... Firs Order ODEs... 3. Second Order ODEs... 7 3. General Maerial...
More informationSuggested Problem Solutions Associated with Homework #5
Suggesed Problem Soluions Associaed wih Homework #5 431 (a) 8 Si has proons and neurons (b) 85 3 Rb has 3 proons and 48 neurons (c) 5 Tl 81 has 81 proons and neurons 43 IDENTIFY and SET UP: The ex calculaes
More information6.003 Homework #9 Solutions
6.00 Homework #9 Soluions Problems. Fourier varieies a. Deermine he Fourier series coefficiens of he following signal, which is periodic in 0. x () 0 0 a 0 5 a k sin πk 5 sin πk 5 πk for k 0 a k 0 πk j
More informationThis is an example to show you how SMath can calculate the movement of kinematic mechanisms.
Dec :5:6 - Kinemaics model of Simple Arm.sm This file is provided for educaional purposes as guidance for he use of he sofware ool. I is no guaraeed o be free from errors or ommissions. The mehods and
More information2) Of the following questions, which ones are thermodynamic, rather than kinetic concepts?
AP Chemisry Tes (Chaper 12) Muliple Choice (40%) 1) Which of he following is a kineic quaniy? A) Enhalpy B) Inernal Energy C) Gibb s free energy D) Enropy E) Rae of reacion 2) Of he following quesions,
More informationMATHEMATICAL DESCRIPTION OF THEORETICAL METHODS OF RESERVE ECONOMY OF CONSIGNMENT STORES
MAHEMAICAL DESCIPION OF HEOEICAL MEHODS OF ESEVE ECONOMY OF CONSIGNMEN SOES Péer elek, József Cselényi, György Demeer Universiy of Miskolc, Deparmen of Maerials Handling and Logisics Absrac: Opimizaion
More informationME 452 Fourier Series and Fourier Transform
ME 452 Fourier Series and Fourier ransform Fourier series From Joseph Fourier in 87 as a resul of his sudy on he flow of hea. If f() is almos any periodic funcion i can be wrien as an infinie sum of sines
More informationHOTELLING LOCATION MODEL
HOTELLING LOCATION MODEL THE LINEAR CITY MODEL The Example of Choosing only Locaion wihou Price Compeiion Le a be he locaion of rm and b is he locaion of rm. Assume he linear ransporaion cos equal o d,
More informationEmbedded Systems and Software. A Simple Introduction to Embedded Control Systems (PID Control)
Embedded Sysems and Sofware A Simple Inroducion o Embedded Conrol Sysems (PID Conrol) Embedded Sysems and Sofware, ECE:3360. The Universiy of Iowa, 2016 Slide 1 Acknowledgemens The maerial in his lecure
More informationUNIVERSITY OF CALIFORNIA College of Engineering Department of Electrical Engineering and Computer Sciences EECS 121 FINAL EXAM
Name: UNIVERSIY OF CALIFORNIA College of Engineering Deparmen of Elecrical Engineering and Compuer Sciences Professor David se EECS 121 FINAL EXAM 21 May 1997, 5:00-8:00 p.m. Please wrie answers on blank
More informationChapter 2 The Derivative Applied Calculus 107. We ll need a rule for finding the derivative of a product so we don t have to multiply everything out.
Chaper The Derivaive Applie Calculus 107 Secion 4: Prouc an Quoien Rules The basic rules will le us ackle simple funcions. Bu wha happens if we nee he erivaive of a combinaion of hese funcions? Eample
More informationLecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481/581 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih
More informationUnit Root Time Series. Univariate random walk
Uni Roo ime Series Univariae random walk Consider he regression y y where ~ iid N 0, he leas squares esimae of is: ˆ yy y y yy Now wha if = If y y hen le y 0 =0 so ha y j j If ~ iid N 0, hen y ~ N 0, he
More information