P Conducting polymers information sheet: page 1 of 5. Intrinsically conducting polymers

Size: px
Start display at page:

Download "P Conducting polymers information sheet: page 1 of 5. Intrinsically conducting polymers"

Transcription

1 oductig polymers iformatio sheet Most textbooks idicate that oe of the most importat properties of polymers is that they are electrical isulators they are used for coverig electrical cables, the bodies of electrical plugs ad sockets, ad so o. This is o loger completely true. Over the past few years several polymeric materials have bee produced that coduct electricity ad a rage of applicatios is beig developed. These coductig polymers are of two basic types: itrisically coductig polymers where the polymeric material itself coducts; ad extrisically coductig polymers which are composites where a coductive material such as carbo black is embedded i a o-coductig polymer such as poly(ethee). Itrisically coductig polymers The simplest itrisically coductig polymer is poly(ethye), sometimes called poly(acetylee), (see below) which, despite its ame, is a alkee ot a alkye. It cosists of a hydrocarbo chai with alteratig sigle ad double bods; called a cojugated system. The p-orbitals which form the double bods ca overlap to form a delocalised π system (similar to the oe i bezee). Electros flow through the delocalised system ad so the polymer ca coduct. I fact, additives such as iodie have to be icorporated to maximise the coductivity by esurig that the polymer does exist i the delocalised form rather tha as localised sigle ad double bods. Suitably doped poly(ethye) ca have a coductivity comparable with that of copper provided the material has bee stretched to alig the chais so that they all ru i the same directio. Poly(ethye) has problems for everyday applicatios as it is attacked by oxyge from the air but other more stable polymers with cojugated systems also have coductig properties. There are some examples o the ext page. ethye poly(ethye) Delocalised π-system Poly(ethye) P oductig polymers iformatio sheet: page 1 of 5 POTOOPY

2 ( 2 ) R N Poly(ethye) S Poly(alkylthiophee) Poly(ailie) S Poly(thiophee) N O Poly(fura) Poly(pyrrole) Examples of itrisically coductig polymers The well-kow coductivity of graphite (see below) ca be explaied i the same way. ere there is a two-dimesioal delocalised system coverig a layer of carbo atoms so that graphite coducts well alog the plaes of carbo atoms but poorly at right agles to them. Delocalised π-system Graphite Extrisically coductig polymers Oe type of extrisically coductig polymer cosists of a matrix of poly(ethee) with a percetage of coductig carbo black (a form of powdered graphite) icorporated i it. If the carbo black particles are close eough to be i cotact with oe aother, the material coducts. If the particles are ot i cotact, it is a isulator. This meas that the degree of electrical coductio depeds o temperature. At high temperature, the poly(ethee) matrix expads ad pulls the particles of carbo black away from each other, decreasig the coductivity. At lower temperatures the poly(ethee) cotracts, the carbo black particles are closer ad the material coducts well. This temperature depedece of coductivity leads to the use of this material i self-regulatig heater cable ad PolySwitch* re-settable circuit protectio devices. * PolySwitch is a registered trademark of Raychem orporatio. oductig polymers iformatio sheet: page 2 of 5 P POTOOPY

3 Beat the freeze the IceStop system Ice ca cause a lot of damage burst pipes, slippery walkways, collapsig roofs - all of which ca be preveted by low level heatig. ovetioal heatig circuits have some disadvatages here as they have a costat curret which ca result i hot spots ad eergy wastage. The IceStop system cosists of parallel copper wires embedded i a coductig polymer. arbo graules form coductig pathways betwee the wires resultig i a large umber of miiature parallel circuits. The polymer coducts electricity well ad thus acts as a heater, oly whe it is cold. As the material warms up the poly(ethee) expads, iterruptig some of the coductig pathways ad switchig off the miiature circuits (see below). + Power supply Polymer holds the carbo black particles i place arbo black particles urret-carryig electrodes oductig pathway of carbo black particles eat is geerated oly where electric curret flows through the carbo black pathways IceStop is a registered trademark of Raychem orporatio. P oductig polymers iformatio sheet: page 3 of 5 POTOOPY

4 OLD eat geerated by flowig curret Electrically isulatig layers oductig pathway of carbo black particles urret carryig electrode old polymer + OT Whe heated the polymer expads. This separates the carbo black particles, breakig the coductig pathway arbo black particles separated by expasio + Expaded hot polymer eater cable IceStop cable ca be laid alog water pipes, uder pathways ad alog gutterig to provide low-level, self-regulatig heatig which keeps the eviromet frost-free. It is flexible ad easy to istall, ca be cut to ay legth required ad ca be overlapped or woud roud a pipe. Protectig batteries the PolySwitch device Lithium batteries are used i may small had-held electrical appliaces such as cameras but a curret overload ca lead to overheatig resultig i, at best, damage to the appliace, ad, at worst, the battery explodig. Lithium batteries are also used i telecom systems, audio speakers, fire ad burglar alarms ad persoal computers. A covetioal fuse could provide the required protectio but eeds to be replaced if it blows. A PolySwitch device does the same job but ca be reset, rather tha havig to be replaced, oce the fault has bee rectified. As i IceStop cable, carbo graules form coductig pathways through the polymer ad these pathways are broke if the material becomes too warm. This protects the appliace from curret overload. Why does t the fuse keep resettig itself? Whe the PolySwitch device gets hot, it does ot switch off the curret completely as does a melted wire i a fuse. A very small curret still flows through the device. This is eough to keep it hot. Oce the fault has bee rectified, the PolySwitch device ca be reset by first turig off the power to allow it to cool. oductig polymers iformatio sheet: page 4 of 5 P POTOOPY

5 Questios 1. Explai the term cojugated. 2. The groups attached to the double bods i poly(ethye) ca be either cis or tras. Poly(ethye) exists i two extreme forms all cis ad all tras. Draw the structure of each. You should draw at least five repeatig uits. 3. What is the fuctioal group i poly(ethye)? 4. Why would you expect oxyge to attack poly(ethye)? Suggest a possible product of the reactio. 5. Suggest some advatages which a coductig polymer might have over a coductig metal. Assume that the typical polymer properties are essetially uchaged (except for electrical coductivity). 6. Draw a displayed formula for poly(pyrrole) showig at least three repeatig uits. 7. What is a composite material? What affects its properties? 8. Does the electrical coductio of metals rise or fall as the temperature icreases? (it: thik about supercoductivity.) 9. Look at the formulae of the two polymers below. Predict which oe you might expect to be a itrisic coductor ad explai your choice. a) b) oductig polymers 10. Use a data book to fid the bod legths you would expect for ad for =. What is the carbo carbo distace i bezee? What techique might you use to fid out if poly(ethye) were i the delocalised or o-delocalised form? 11. Describe the way i which electros move i metals ad allow them to coduct electricity. ompare this with the situatio i poly(ethye) ad graphite. Write dow ay similarities ad differeces. P oductig polymers iformatio sheet: page 5 of 5 POTOOPY

6 Shape memory polymers iformatio sheet These polymers remember the shape ito which they have bee moulded ad will retur to it o getle heatig. They are based o thermoplastic polymers. Durig maufacture the polymer is moulded ito a particular shape ad irradiated with β-radiatio. It is the heated, reshaped ad cooled. It does, however, remember the shape which it had whe irradiated ad returs to it whe re-heated. Oe applicatio of this effect is heatshrikable sleeves which are used to hold together budles of wires i car wirig haresses (see below). Bodig withi polymers Applyig a shrikable sleeve ere a cylidrical legth of poly(ethee) sleeve is moulded ito shape so that it has a arrow iteral diameter which firmly holds together a buch of wires. The sleeve is ow irradiated, which causes covalet crossliks betwee the poly(ethee) chais. The tube is ext heated to above its crystallie meltig poit to softe it. The it is stretched ito a larger diameter. This stretches the crossliks. The tube is cooled ad this locks the chais i their stretched positio. Now the large diameter tube ca easily be slipped over a buch of wires. If it is heated (by a hot air gu or blowlamp) above its crystallie meltig poit, the stretched crossliks pull the material back ito the shape it had o irradiatio ad it holds the buch of wires firmly together. Polymers ca be classified as thermoplastic (thermosofteig) or thermosettig. Thermoplastics softe o heatig ad ca be moulded ito a shape which they retai o coolig. They ca be reheated ad moulded idefiitely. They cosist of log chai molecules, each chai beig essetially idepedet of the others. There are o covalet bods betwee the chais. The plastics retai their shape whe cool because of itermolecular forces betwee the chais. I particular there are areas where the the chais lie up i a ordered way so-called areas of crystalliity. If crystallie areas o two adjacet chais lie up, the itermolecular iteractios are particularly strog. This is resposible for much of the stregth of thermoplastics i the solid state. O heatig above the crystallie meltig poit, icreased thermal motio makes the crystallie areas disappear. The polymer softes, the chais become free to move past oe aother ad the plastic ca be moulded. O coolig, ew crystallie areas re-form, which help retai the ew shape (see below). Shape memory polymers iformatio sheet: page 1 of 3 P POTOOPY

7 rystallie areas i a polymer chai Irradiatio Thermosettig plastics have may covalet crossliks betwee the polymer chais which form as the polymer is made. Oce made, the polymer is uaffected by heat (util it begis to bur or decompose). Shape memory plastics have a degree of crosslikig (after irradiatio) which is less tha that of a thermoset but more tha that of a thermosofteig plastic. ow does the irradiatio process produce the cross liks? β-radiatio is a stream of electros each with more tha eough eergy to break covalet bods. β-irradiatio of poly(ethee) breaks some of the bods i the poly(ethee) chais. As carbo ad hydroge atoms have similar electroegativity, the bods ted to break homolytically leavig a free hydroge atom ad a carbo free radical, a carbo atom with a sigle ie upaired electro. Such carbo atoms are extremely reactive ad two close together may form a covalet bod thus pairig up their electros. This forms a crosslik betwee the chais (see below). β-irradiatio The effect of β-irradiatio o poly(ethee) The hydroge atoms, which also have a upaired electro each, ted to come together to form hydroge molecules which escape from the polymer. P Shape memory polymers iformatio sheet: page 2 of 3 POTOOPY

8 Questios 1. What other bods will the β-radiatio break? Suggest what effects this might have o the polymer. 2. What might happe if too may crossliks are formed i the polymer? What effect might this have o its properties? 3. What are the itermolecular forces which operate withi the crystallie regios of a thermosofteig plastic called? ompare the stregth of a sigle itermolecular iteractio with that of a typical covalet bod. Explai why, whe cool, these itermolecular forces have comparable effects to covalet bods ie thermosets ad thermoplastics have comparable stregths. 4. Aother free radical reactio is that of bromie with methae i ultraviolet light. The steps are: 1. Br Br 2Br Br Br + 3 ad Br Br + 3 Br UV 3. Br + Br Br Br Br a) The first step is called iitiatio. Name the other two. b) I this case, there are o hydroge free radicals formed by the reactio Suggest a reaso for this. What does this tell you about the eergy of ultraviolet light compared with that of β-radiatio? c) Which of the three possibilities for step 3 above is most similar to the reactio which occurs i the polymer crosslikig reactio? Explai your choice. 5. Explai the terms homolytically ad electroegativity as used i the passage. Shape memory polymers iformatio sheet: page 3 of 3 P POTOOPY

Homework 7 Due 5 December 2017 The numbers following each question give the approximate percentage of marks allocated to that question.

Homework 7 Due 5 December 2017 The numbers following each question give the approximate percentage of marks allocated to that question. Name: Homework 7 Due 5 December 2017 The umbers followig each questio give the approximate percetage of marks allocated to that questio. 1. Use the reciprocal metric tesor agai to calculate the agle betwee

More information

Polymerization Lab p. 1 Polymerization Lab

Polymerization Lab p. 1 Polymerization Lab Polymerizatio Lab p. 1 Polymerizatio Lab Itroductio: Polymers (Greek-PLY...may ad MES...parts) have existed sice the begiig of life. Both "atural" ad "sythetic" polymers are a itegral part of our life.

More information

N Goalby chemrevise.org

N Goalby chemrevise.org 21. olymers There are two types of polymerisatio additio ad codesatio Additio olymerisatio A additio polymer forms whe usaturated moomers react to form a polymer Moomers cotai = bods oly(alkees) are chemically

More information

Infinite Sequences and Series

Infinite Sequences and Series Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet

More information

II. Descriptive Statistics D. Linear Correlation and Regression. 1. Linear Correlation

II. Descriptive Statistics D. Linear Correlation and Regression. 1. Linear Correlation II. Descriptive Statistics D. Liear Correlatio ad Regressio I this sectio Liear Correlatio Cause ad Effect Liear Regressio 1. Liear Correlatio Quatifyig Liear Correlatio The Pearso product-momet correlatio

More information

MOTION. The easy stuff; The gaseous state - Translational motion. The crystalline state - Oscillations about a Mean position.

MOTION. The easy stuff; The gaseous state - Translational motion. The crystalline state - Oscillations about a Mean position. The easy stuff; MOTION The gaseous state - Traslatioal motio The crystallie state - Oscillatios about a Mea positio The hard stuff; The liquid state - Coupled motios MOTION IN POLYMERS LARGE SCALE MOTION

More information

Basic Concepts of Electricity. n Force on positive charge is in direction of electric field, negative is opposite

Basic Concepts of Electricity. n Force on positive charge is in direction of electric field, negative is opposite Basic Cocepts of Electricity oltage E Curret I Ohm s Law Resistace R E = I R 1 Electric Fields A electric field applies a force to a charge Force o positive charge is i directio of electric field, egative

More information

SOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T

SOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T SOUIONS: ECE 606 Homework Week 7 Mark udstrom Purdue Uiversity (revised 3/27/13) 1) Cosider a - type semicoductor for which the oly states i the badgap are door levels (i.e. ( E = E D ). Begi with the

More information

Measures of Spread: Standard Deviation

Measures of Spread: Standard Deviation Measures of Spread: Stadard Deviatio So far i our study of umerical measures used to describe data sets, we have focused o the mea ad the media. These measures of ceter tell us the most typical value of

More information

SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES

SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS STANDARD LEVEL PAPER 1 SPECIMEN PAPER 45 miutes INSTRUCTIONS TO CANDIDATES Do ot ope this examiatio paper util istructed to do so. Aswer all the questios. For each questio,

More information

4.3 Growth Rates of Solutions to Recurrences

4.3 Growth Rates of Solutions to Recurrences 4.3. GROWTH RATES OF SOLUTIONS TO RECURRENCES 81 4.3 Growth Rates of Solutios to Recurreces 4.3.1 Divide ad Coquer Algorithms Oe of the most basic ad powerful algorithmic techiques is divide ad coquer.

More information

We will conclude the chapter with the study a few methods and techniques which are useful

We will conclude the chapter with the study a few methods and techniques which are useful Chapter : Coordiate geometry: I this chapter we will lear about the mai priciples of graphig i a dimesioal (D) Cartesia system of coordiates. We will focus o drawig lies ad the characteristics of the graphs

More information

Position Time Graphs 12.1

Position Time Graphs 12.1 12.1 Positio Time Graphs Figure 3 Motio with fairly costat speed Chapter 12 Distace (m) A Crae Flyig Figure 1 Distace time graph showig motio with costat speed A Crae Flyig Positio (m [E] of pod) We kow

More information

NUMERICAL METHODS FOR SOLVING EQUATIONS

NUMERICAL METHODS FOR SOLVING EQUATIONS Mathematics Revisio Guides Numerical Methods for Solvig Equatios Page 1 of 11 M.K. HOME TUITION Mathematics Revisio Guides Level: GCSE Higher Tier NUMERICAL METHODS FOR SOLVING EQUATIONS Versio:. Date:

More information

Series III. Chapter Alternating Series

Series III. Chapter Alternating Series Chapter 9 Series III With the exceptio of the Null Sequece Test, all the tests for series covergece ad divergece that we have cosidered so far have dealt oly with series of oegative terms. Series with

More information

Section 1.1. Calculus: Areas And Tangents. Difference Equations to Differential Equations

Section 1.1. Calculus: Areas And Tangents. Difference Equations to Differential Equations Differece Equatios to Differetial Equatios Sectio. Calculus: Areas Ad Tagets The study of calculus begis with questios about chage. What happes to the velocity of a swigig pedulum as its positio chages?

More information

Mark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University

Mark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University Mark udstrom Sprig 2015 SOUTIONS: ECE 305 Homework: Week 5 Mark udstrom Purdue Uiversity The followig problems cocer the Miority Carrier Diffusio Equatio (MCDE) for electros: Δ t = D Δ + G For all the

More information

Solids - types. correlates with bonding energy

Solids - types. correlates with bonding energy Solids - types MOLCULAR. Set of sigle atoms or molecules boud to adjacet due to weak electric force betwee eutral objects (va der Waals). Stregth depeds o electric dipole momet No free electros poor coductors

More information

ELECTRICAL PROPEORTIES OF SOLIDS

ELECTRICAL PROPEORTIES OF SOLIDS DO PHYSICS ONLINE ELECTRICAL PROPEORTIES OF SOLIDS ATOMIC STRUCTURE ucleus: rotos () & electros electros (-): electro cloud h h DE BROGLIE wave model of articles mv ELECTRONS IN ATOMS eergy levels i atoms

More information

POLYMERS

POLYMERS POLYMERS Short Aswer Questios: **1.What is PHBV? How is it useful to ma? As. PHBV is Poly β-hydroxy butyrate-co- β-hydroxy valerate.it is a biodegradable polymer. It is used i speciality packig, orthopaedic

More information

Physics Supplement to my class. Kinetic Theory

Physics Supplement to my class. Kinetic Theory Physics Supplemet to my class Leaers should ote that I have used symbols for geometrical figures ad abbreviatios through out the documet. Kietic Theory 1 Most Probable, Mea ad RMS Speed of Gas Molecules

More information

Overview. p 2. Chapter 9. Pooled Estimate of. q = 1 p. Notation for Two Proportions. Inferences about Two Proportions. Assumptions

Overview. p 2. Chapter 9. Pooled Estimate of. q = 1 p. Notation for Two Proportions. Inferences about Two Proportions. Assumptions Chapter 9 Slide Ifereces from Two Samples 9- Overview 9- Ifereces about Two Proportios 9- Ifereces about Two Meas: Idepedet Samples 9-4 Ifereces about Matched Pairs 9-5 Comparig Variatio i Two Samples

More information

Chem Discussion #13 Chapter 10. Correlation diagrams for diatomic molecules. Key

Chem Discussion #13 Chapter 10. Correlation diagrams for diatomic molecules. Key Chem 101 017 Discussio #13 Chapter 10. Correlatio diagrams for diatomic molecules. Key 1. Below is a plot of the first 10 ioizatio eergies for a sigle atom i 3 rd row of the periodic table. The x- axis

More information

11 Correlation and Regression

11 Correlation and Regression 11 Correlatio Regressio 11.1 Multivariate Data Ofte we look at data where several variables are recorded for the same idividuals or samplig uits. For example, at a coastal weather statio, we might record

More information

Roberto s Notes on Infinite Series Chapter 1: Sequences and series Section 3. Geometric series

Roberto s Notes on Infinite Series Chapter 1: Sequences and series Section 3. Geometric series Roberto s Notes o Ifiite Series Chapter 1: Sequeces ad series Sectio Geometric series What you eed to kow already: What a ifiite series is. The divergece test. What you ca le here: Everythig there is to

More information

MID-YEAR EXAMINATION 2018 H2 MATHEMATICS 9758/01. Paper 1 JUNE 2018

MID-YEAR EXAMINATION 2018 H2 MATHEMATICS 9758/01. Paper 1 JUNE 2018 MID-YEAR EXAMINATION 08 H MATHEMATICS 9758/0 Paper JUNE 08 Additioal Materials: Writig Paper, MF6 Duratio: hours DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO READ THESE INSTRUCTIONS FIRST Write

More information

CHAPTER 11. Practice Questions (a) OH (b) I. (h) NH 3 CH 3 CO 2 (j) C 6 H 5 O - (k) (CH 3 ) 3 N conjugate pair

CHAPTER 11. Practice Questions (a) OH (b) I. (h) NH 3 CH 3 CO 2 (j) C 6 H 5 O - (k) (CH 3 ) 3 N conjugate pair CAPTER 11 Practice Questios 11.1 (a) O (b) I (c) NO 2 (d) 2 PO 4 (e) 2 PO 4 (f) 3 PO 4 (g) SO 4 (h) N 3 (i) C 3 CO 2 (j) C 6 5 O - (k) (C 3 ) 3 N 11.3 cojugate pair PO 3 4 (aq) C 3 COO(aq) PO 2 4 (aq)

More information

Random Models. Tusheng Zhang. February 14, 2013

Random Models. Tusheng Zhang. February 14, 2013 Radom Models Tusheg Zhag February 14, 013 1 Radom Walks Let me describe the model. Radom walks are used to describe the motio of a movig particle (object). Suppose that a particle (object) moves alog the

More information

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30. Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before 4:15, Moday, April 30. The PHYS 213 fial exam times are * 8-10 AM, Moday, May 7 * 8-10 AM, Tuesday, May 8

More information

There are 7 crystal systems and 14 Bravais lattices in 3 dimensions.

There are 7 crystal systems and 14 Bravais lattices in 3 dimensions. EXAM IN OURSE TFY40 Solid State Physics Moday 0. May 0 Time: 9.00.00 DRAFT OF SOLUTION Problem (0%) Itroductory Questios a) () Primitive uit cell: The miimum volume cell which will fill all space (without

More information

Lecture 10: P-N Diodes. Announcements

Lecture 10: P-N Diodes. Announcements EECS 15 Sprig 4, Lecture 1 Lecture 1: P-N Diodes EECS 15 Sprig 4, Lecture 1 Aoucemets The Thursday lab sectio will be moved a hour later startig this week, so that the TA s ca atted lecture i aother class

More information

Roberto s Notes on Series Chapter 2: Convergence tests Section 7. Alternating series

Roberto s Notes on Series Chapter 2: Convergence tests Section 7. Alternating series Roberto s Notes o Series Chapter 2: Covergece tests Sectio 7 Alteratig series What you eed to kow already: All basic covergece tests for evetually positive series. What you ca lear here: A test for series

More information

For example suppose we divide the interval [0,2] into 5 equal subintervals of length

For example suppose we divide the interval [0,2] into 5 equal subintervals of length Math 120c Calculus Sec 1: Estimatig with Fiite Sums I Area A Cosider the problem of fidig the area uder the curve o the fuctio y!x 2 + over the domai [0,2] We ca approximate this area by usig a familiar

More information

PH 425 Quantum Measurement and Spin Winter SPINS Lab 1

PH 425 Quantum Measurement and Spin Winter SPINS Lab 1 PH 425 Quatum Measuremet ad Spi Witer 23 SPIS Lab Measure the spi projectio S z alog the z-axis This is the experimet that is ready to go whe you start the program, as show below Each atom is measured

More information

Response Variable denoted by y it is the variable that is to be predicted measure of the outcome of an experiment also called the dependent variable

Response Variable denoted by y it is the variable that is to be predicted measure of the outcome of an experiment also called the dependent variable Statistics Chapter 4 Correlatio ad Regressio If we have two (or more) variables we are usually iterested i the relatioship betwee the variables. Associatio betwee Variables Two variables are associated

More information

1 Lesson 6: Measure of Variation

1 Lesson 6: Measure of Variation 1 Lesso 6: Measure of Variatio 1.1 The rage As we have see, there are several viable coteders for the best measure of the cetral tedecy of data. The mea, the mode ad the media each have certai advatages

More information

Name Solutions to Test 2 October 14, 2015

Name Solutions to Test 2 October 14, 2015 Name Solutios to Test October 4, 05 This test cosists of three parts. Please ote that i parts II ad III, you ca skip oe questio of those offered. The equatios below may be helpful with some problems. Costats

More information

Doped semiconductors: donor impurities

Doped semiconductors: donor impurities Doped semicoductors: door impurities A silico lattice with a sigle impurity atom (Phosphorus, P) added. As compared to Si, the Phosphorus has oe extra valece electro which, after all bods are made, has

More information

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)

2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i) Math PracTest Be sure to review Lab (ad all labs) There are lots of good questios o it a) State the Mea Value Theorem ad draw a graph that illustrates b) Name a importat theorem where the Mea Value Theorem

More information

Math 116 Second Exam

Math 116 Second Exam Math 6 Secod Exam November, 6 Name: Exam Solutios Istructor: Sectio:. Do ot ope this exam util you are told to do so.. This exam has 9 pages icludig this cover. There are 8 problems. Note that the problems

More information

For example suppose we divide the interval [0,2] into 5 equal subintervals of length

For example suppose we divide the interval [0,2] into 5 equal subintervals of length Math 1206 Calculus Sec 1: Estimatig with Fiite Sums Abbreviatios: wrt with respect to! for all! there exists! therefore Def defiitio Th m Theorem sol solutio! perpedicular iff or! if ad oly if pt poit

More information

PRACTICE PROBLEMS FOR THE FINAL

PRACTICE PROBLEMS FOR THE FINAL PRACTICE PROBLEMS FOR THE FINAL Math 36Q Fall 25 Professor Hoh Below is a list of practice questios for the Fial Exam. I would suggest also goig over the practice problems ad exams for Exam ad Exam 2 to

More information

Example: Find the SD of the set {x j } = {2, 4, 5, 8, 5, 11, 7}.

Example: Find the SD of the set {x j } = {2, 4, 5, 8, 5, 11, 7}. 1 (*) If a lot of the data is far from the mea, the may of the (x j x) 2 terms will be quite large, so the mea of these terms will be large ad the SD of the data will be large. (*) I particular, outliers

More information

Chapter 22. Comparing Two Proportions. Copyright 2010, 2007, 2004 Pearson Education, Inc.

Chapter 22. Comparing Two Proportions. Copyright 2010, 2007, 2004 Pearson Education, Inc. Chapter 22 Comparig Two Proportios Copyright 2010, 2007, 2004 Pearso Educatio, Ic. Comparig Two Proportios Read the first two paragraphs of pg 504. Comparisos betwee two percetages are much more commo

More information

Wave Motion

Wave Motion Wave Motio Wave ad Wave motio: Wave is a carrier of eergy Wave is a form of disturbace which travels through a material medium due to the repeated periodic motio of the particles of the medium about their

More information

17 Phonons and conduction electrons in solids (Hiroshi Matsuoka)

17 Phonons and conduction electrons in solids (Hiroshi Matsuoka) 7 Phoos ad coductio electros i solids Hiroshi Matsuoa I this chapter we will discuss a miimal microscopic model for phoos i a solid ad a miimal microscopic model for coductio electros i a simple metal.

More information

The Interval of Convergence for a Power Series Examples

The Interval of Convergence for a Power Series Examples The Iterval of Covergece for a Power Series Examples To review the process: How to Test a Power Series for Covergece. Fid the iterval where the series coverges absolutely. We have to use the Ratio or Root

More information

Estimation of a population proportion March 23,

Estimation of a population proportion March 23, 1 Social Studies 201 Notes for March 23, 2005 Estimatio of a populatio proportio Sectio 8.5, p. 521. For the most part, we have dealt with meas ad stadard deviatios this semester. This sectio of the otes

More information

IV. COMPARISON of CHARGE-CARRIER POPULATION at EACH SIDE of the JUNCTION V. FORWARD BIAS, REVERSE BIAS

IV. COMPARISON of CHARGE-CARRIER POPULATION at EACH SIDE of the JUNCTION V. FORWARD BIAS, REVERSE BIAS Fall-2003 PH-31 A. La Rosa JUNCTIONS I. HARNESSING ELECTRICAL CONDUCTIVITY IN SEMICONDUCTOR MATERIALS Itrisic coductivity (Pure silico) Extrisic coductivity (Silico doed with selected differet atoms) II.

More information

Chemical Kinetics CHAPTER 14. Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop. CHAPTER 14 Chemical Kinetics

Chemical Kinetics CHAPTER 14. Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop. CHAPTER 14 Chemical Kinetics Chemical Kietics CHAPTER 14 Chemistry: The Molecular Nature of Matter, 6 th editio By Jesperso, Brady, & Hyslop CHAPTER 14 Chemical Kietics Learig Objectives: Factors Affectig Reactio Rate: o Cocetratio

More information

6.3 Testing Series With Positive Terms

6.3 Testing Series With Positive Terms 6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial

More information

SECTION 2 Electrostatics

SECTION 2 Electrostatics SECTION Electrostatics This sectio, based o Chapter of Griffiths, covers effects of electric fields ad forces i static (timeidepedet) situatios. The topics are: Electric field Gauss s Law Electric potetial

More information

: Transforms and Partial Differential Equations

: Transforms and Partial Differential Equations Trasforms ad Partial Differetial Equatios 018 SUBJECT NAME : Trasforms ad Partial Differetial Equatios SUBJECT CODE : MA 6351 MATERIAL NAME : Part A questios REGULATION : R013 WEBSITE : wwwharigaeshcom

More information

Semiconductors. PN junction. n- type

Semiconductors. PN junction. n- type Semicoductors. PN juctio We have reviously looked at the electroic roerties of itrisic, - tye ad - time semicoductors. Now we will look at what haes to the electroic structure ad macroscoic characteristics

More information

Fall 2018 Exam 3 HAND IN PART 0 10 PIN: 17 INSTRUCTIONS

Fall 2018 Exam 3 HAND IN PART 0 10 PIN: 17 INSTRUCTIONS MARK BOX problem poits HAND IN PART 0 10 1 10 2 5 NAME: Solutios 3 10 PIN: 17 4 16 65=13x5 % 100 INSTRUCTIONS This exam comes i two parts. (1) HAND IN PART. Had i oly this part. (2) STATEMENT OF MULTIPLE

More information

The axial dispersion model for tubular reactors at steady state can be described by the following equations: dc dz R n cn = 0 (1) (2) 1 d 2 c.

The axial dispersion model for tubular reactors at steady state can be described by the following equations: dc dz R n cn = 0 (1) (2) 1 d 2 c. 5.4 Applicatio of Perturbatio Methods to the Dispersio Model for Tubular Reactors The axial dispersio model for tubular reactors at steady state ca be described by the followig equatios: d c Pe dz z =

More information

Castiel, Supernatural, Season 6, Episode 18

Castiel, Supernatural, Season 6, Episode 18 13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio

More information

7-1. Chapter 4. Part I. Sampling Distributions and Confidence Intervals

7-1. Chapter 4. Part I. Sampling Distributions and Confidence Intervals 7-1 Chapter 4 Part I. Samplig Distributios ad Cofidece Itervals 1 7- Sectio 1. Samplig Distributio 7-3 Usig Statistics Statistical Iferece: Predict ad forecast values of populatio parameters... Test hypotheses

More information

ARISTOTELIAN PHYSICS

ARISTOTELIAN PHYSICS ARISTOTELIAN PHYSICS Aristoteles (Aristotle) (384-322 BC) had very strog ifluece o Europea philosophy ad sciece; everythig o Earth made of (mixture of) four elemets: earth, water, air, fire every elemet

More information

ECEN Microelectronics. Semiconductor Physics and P/N junctions 2/05/19

ECEN Microelectronics. Semiconductor Physics and P/N junctions 2/05/19 ECEN 3250 Microelectroics Semicoductor Physics ad P/N juctios 2/05/19 Professor J. Gopiath Professor J. Gopiath Uiversity of Colorado at Boulder Microelectroics Sprig 2014 Overview Eergy bads Atomic eergy

More information

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER / Statistics

ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER / Statistics ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER 1 018/019 DR. ANTHONY BROWN 8. Statistics 8.1. Measures of Cetre: Mea, Media ad Mode. If we have a series of umbers the

More information

Chapter 6: Numerical Series

Chapter 6: Numerical Series Chapter 6: Numerical Series 327 Chapter 6 Overview: Sequeces ad Numerical Series I most texts, the topic of sequeces ad series appears, at first, to be a side topic. There are almost o derivatives or itegrals

More information

MEMS: Microelectromechanical Systems

MEMS: Microelectromechanical Systems MEMS: Microelectromechaical Systems What are MEMS? Micro-electro-mechaical systems miiaturized mechaical ad electro-mechaical elemets havig some sort of mechaical fuctioality Covert betwee measured mechaical

More information

DESCRIPTION OF THE SYSTEM

DESCRIPTION OF THE SYSTEM Sychroous-Serial Iterface for absolute Ecoders SSI 1060 BE 10 / 01 DESCRIPTION OF THE SYSTEM TWK-ELEKTRONIK GmbH D-001 Düsseldorf PB 1006 Heirichstr. Tel +9/11/6067 Fax +9/11/6770 e-mail: ifo@twk.de Page

More information

Chapter 6 Overview: Sequences and Numerical Series. For the purposes of AP, this topic is broken into four basic subtopics:

Chapter 6 Overview: Sequences and Numerical Series. For the purposes of AP, this topic is broken into four basic subtopics: Chapter 6 Overview: Sequeces ad Numerical Series I most texts, the topic of sequeces ad series appears, at first, to be a side topic. There are almost o derivatives or itegrals (which is what most studets

More information

What is Physical Chemistry. Physical Chemistry for Chemical Engineers CHEM251. Basic Characteristics of a Gas

What is Physical Chemistry. Physical Chemistry for Chemical Engineers CHEM251. Basic Characteristics of a Gas 7/6/0 hysical Chemistry for Chemical Egieers CHEM5 What is hysical Chemistry hysical Chemistry is the study of the uderlyig physical priciples that gover the properties ad behaviour of chemical systems

More information

FINALTERM EXAMINATION Fall 9 Calculus & Aalytical Geometry-I Questio No: ( Mars: ) - Please choose oe Let f ( x) is a fuctio such that as x approaches a real umber a, either from left or right-had-side,

More information

Chemical Engineering 374

Chemical Engineering 374 Chemical Egieerig 374 Fluid Mechaics NoNewtoia Fluids Outlie 2 Types ad properties of o-newtoia Fluids Pipe flows for o-newtoia fluids Velocity profile / flow rate Pressure op Frictio factor Pump power

More information

Nonequilibrium Excess Carriers in Semiconductors

Nonequilibrium Excess Carriers in Semiconductors Lecture 8 Semicoductor Physics VI Noequilibrium Excess Carriers i Semicoductors Noequilibrium coditios. Excess electros i the coductio bad ad excess holes i the valece bad Ambiolar trasort : Excess electros

More information

Chapter 7: Numerical Series

Chapter 7: Numerical Series Chapter 7: Numerical Series Chapter 7 Overview: Sequeces ad Numerical Series I most texts, the topic of sequeces ad series appears, at first, to be a side topic. There are almost o derivatives or itegrals

More information

6 Integers Modulo n. integer k can be written as k = qn + r, with q,r, 0 r b. So any integer.

6 Integers Modulo n. integer k can be written as k = qn + r, with q,r, 0 r b. So any integer. 6 Itegers Modulo I Example 2.3(e), we have defied the cogruece of two itegers a,b with respect to a modulus. Let us recall that a b (mod ) meas a b. We have proved that cogruece is a equivalece relatio

More information

Chapter 22. Comparing Two Proportions. Copyright 2010 Pearson Education, Inc.

Chapter 22. Comparing Two Proportions. Copyright 2010 Pearson Education, Inc. Chapter 22 Comparig Two Proportios Copyright 2010 Pearso Educatio, Ic. Comparig Two Proportios Comparisos betwee two percetages are much more commo tha questios about isolated percetages. Ad they are more

More information

EECS130 Integrated Circuit Devices

EECS130 Integrated Circuit Devices EECS130 Itegrated Circuit Devices Professor Ali Javey 9/04/2007 Semicoductor Fudametals Lecture 3 Readig: fiish chapter 2 ad begi chapter 3 Aoucemets HW 1 is due ext Tuesday, at the begiig of the class.

More information

a b c d e f g h Supplementary Information

a b c d e f g h Supplementary Information Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;

More information

LECTURE 11: POSTNIKOV AND WHITEHEAD TOWERS

LECTURE 11: POSTNIKOV AND WHITEHEAD TOWERS LECTURE 11: POSTNIKOV AND WHITEHEAD TOWERS I the previous sectio we used the techique of adjoiig cells i order to costruct CW approximatios for arbitrary spaces Here we will see that the same techique

More information

Introduction to Solid State Physics

Introduction to Solid State Physics Itroductio to Solid State Physics Class: Itegrated Photoic Devices Time: Fri. 8:00am ~ 11:00am. Classroom: 資電 206 Lecturer: Prof. 李明昌 (Mig-Chag Lee) Electros i A Atom Electros i A Atom Electros i Two atoms

More information

Lecture 6. Semiconductor physics IV. The Semiconductor in Equilibrium

Lecture 6. Semiconductor physics IV. The Semiconductor in Equilibrium Lecture 6 Semicoductor physics IV The Semicoductor i Equilibrium Equilibrium, or thermal equilibrium No exteral forces such as voltages, electric fields. Magetic fields, or temperature gradiets are actig

More information

ARITHMETIC PROGRESSIONS

ARITHMETIC PROGRESSIONS CHAPTER 5 ARITHMETIC PROGRESSIONS (A) Mai Cocepts ad Results A arithmetic progressio (AP) is a list of umbers i which each term is obtaied by addig a fixed umber d to the precedig term, except the first

More information

Data Analysis and Statistical Methods Statistics 651

Data Analysis and Statistical Methods Statistics 651 Data Aalysis ad Statistical Methods Statistics 651 http://www.stat.tamu.edu/~suhasii/teachig.html Suhasii Subba Rao Review of testig: Example The admistrator of a ursig home wats to do a time ad motio

More information

Lecture 9: Diffusion, Electrostatics review, and Capacitors. Context

Lecture 9: Diffusion, Electrostatics review, and Capacitors. Context EECS 5 Sprig 4, Lecture 9 Lecture 9: Diffusio, Electrostatics review, ad Capacitors EECS 5 Sprig 4, Lecture 9 Cotext I the last lecture, we looked at the carriers i a eutral semicoductor, ad drift currets

More information

Comparing your lab results with the others by one-way ANOVA

Comparing your lab results with the others by one-way ANOVA Comparig your lab results with the others by oe-way ANOVA You may have developed a ew test method ad i your method validatio process you would like to check the method s ruggedess by coductig a simple

More information

CONFIDENCE INTERVALS STUDY GUIDE

CONFIDENCE INTERVALS STUDY GUIDE CONFIDENCE INTERVALS STUDY UIDE Last uit, we discussed how sample statistics vary. Uder the right coditios, sample statistics like meas ad proportios follow a Normal distributio, which allows us to calculate

More information

Math 116 Final Exam December 19, 2016

Math 116 Final Exam December 19, 2016 Math 6 Fial Exam December 9, 06 UMID: EXAM SOLUTIONS Iitials: Istructor: Sectio:. Do ot ope this exam util you are told to do so.. Do ot write your ame aywhere o this exam. 3. This exam has 3 pages icludig

More information

Tennessee Department of Education

Tennessee Department of Education Teessee Departmet of Educatio Task: Comparig Shapes Geometry O a piece of graph paper with a coordiate plae, draw three o-colliear poits ad label them A, B, C. (Do ot use the origi as oe of your poits.)

More information

4.7 Organic Chemistry

4.7 Organic Chemistry 4.7 rgaic hemistry rude oil rude oil is a fiite resource foud i rocks. rude oil is the remais of a aciet biomass cosistig maily of plakto that was buried i mud. Alkaes Most of the hydrocarbos i crude oil

More information

CALCULUS BASIC SUMMER REVIEW

CALCULUS BASIC SUMMER REVIEW CALCULUS BASIC SUMMER REVIEW NAME rise y y y Slope of a o vertical lie: m ru Poit Slope Equatio: y y m( ) The slope is m ad a poit o your lie is, ). ( y Slope-Itercept Equatio: y m b slope= m y-itercept=

More information

Induction: Solutions

Induction: Solutions Writig Proofs Misha Lavrov Iductio: Solutios Wester PA ARML Practice March 6, 206. Prove that a 2 2 chessboard with ay oe square removed ca always be covered by shaped tiles. Solutio : We iduct o. For

More information

(3) If you replace row i of A by its sum with a multiple of another row, then the determinant is unchanged! Expand across the i th row:

(3) If you replace row i of A by its sum with a multiple of another row, then the determinant is unchanged! Expand across the i th row: Math 5-4 Tue Feb 4 Cotiue with sectio 36 Determiats The effective way to compute determiats for larger-sized matrices without lots of zeroes is to ot use the defiitio, but rather to use the followig facts,

More information

P1 Chapter 8 :: Binomial Expansion

P1 Chapter 8 :: Binomial Expansion P Chapter 8 :: Biomial Expasio jfrost@tiffi.kigsto.sch.uk www.drfrostmaths.com @DrFrostMaths Last modified: 6 th August 7 Use of DrFrostMaths for practice Register for free at: www.drfrostmaths.com/homework

More information

Introduction to Semiconductor Devices and Circuit Model

Introduction to Semiconductor Devices and Circuit Model Itroductio to Semicoductor Devices ad Circuit Model Readig: Chater 2 of Howe ad Sodii Electrical Resistace I + V _ W homogeeous samle t L Resistace R V I L = ρ Wt (Uits: Ω) where ρ is the resistivity (Uits:

More information

Exponents. Learning Objectives. Pre-Activity

Exponents. Learning Objectives. Pre-Activity Sectio. Pre-Activity Preparatio Epoets A Chai Letter Chai letters are geerated every day. If you sed a chai letter to three frieds ad they each sed it o to three frieds, who each sed it o to three frieds,

More information

CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination MATHEMATICS 9740/01

CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination MATHEMATICS 9740/01 CATHOLIC JUNIOR COLLEGE Geeral Certificate of Educatio Advaced Level Higher JC Prelimiary Examiatio MATHEMATICS 9740/0 Paper 4 Aug 06 hours Additioal Materials: List of Formulae (MF5) Name: Class: READ

More information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENIOR CERTIFICATE GRADE 1 MATHEMATICS P1 NOVEMBER 016 MARKS: 150 TIME: 3 hours This questio paper cosists of 9 pages ad 1 iformatio sheet. Please tur over Mathematics/P1 DBE/November 016 INSTRUCTIONS

More information

Homework 5 Solutions

Homework 5 Solutions Homework 5 Solutios p329 # 12 No. To estimate the chace you eed the expected value ad stadard error. To do get the expected value you eed the average of the box ad to get the stadard error you eed the

More information

1 Review of Probability & Statistics

1 Review of Probability & Statistics 1 Review of Probability & Statistics a. I a group of 000 people, it has bee reported that there are: 61 smokers 670 over 5 960 people who imbibe (drik alcohol) 86 smokers who imbibe 90 imbibers over 5

More information

ENGI 4421 Confidence Intervals (Two Samples) Page 12-01

ENGI 4421 Confidence Intervals (Two Samples) Page 12-01 ENGI 44 Cofidece Itervals (Two Samples) Page -0 Two Sample Cofidece Iterval for a Differece i Populatio Meas [Navidi sectios 5.4-5.7; Devore chapter 9] From the cetral limit theorem, we kow that, for sufficietly

More information

Discrete Mathematics for CS Spring 2005 Clancy/Wagner Notes 21. Some Important Distributions

Discrete Mathematics for CS Spring 2005 Clancy/Wagner Notes 21. Some Important Distributions CS 70 Discrete Mathematics for CS Sprig 2005 Clacy/Wager Notes 21 Some Importat Distributios Questio: A biased coi with Heads probability p is tossed repeatedly util the first Head appears. What is the

More information

Vector Quantization: a Limiting Case of EM

Vector Quantization: a Limiting Case of EM . Itroductio & defiitios Assume that you are give a data set X = { x j }, j { 2,,, }, of d -dimesioal vectors. The vector quatizatio (VQ) problem requires that we fid a set of prototype vectors Z = { z

More information

CHAPTER 8 SYSTEMS OF PARTICLES

CHAPTER 8 SYSTEMS OF PARTICLES CHAPTER 8 SYSTES OF PARTICLES CHAPTER 8 COLLISIONS 45 8. CENTER OF ASS The ceter of mass of a system of particles or a rigid body is the poit at which all of the mass are cosidered to be cocetrated there

More information

CHAPTER 10 INFINITE SEQUENCES AND SERIES

CHAPTER 10 INFINITE SEQUENCES AND SERIES CHAPTER 10 INFINITE SEQUENCES AND SERIES 10.1 Sequeces 10.2 Ifiite Series 10.3 The Itegral Tests 10.4 Compariso Tests 10.5 The Ratio ad Root Tests 10.6 Alteratig Series: Absolute ad Coditioal Covergece

More information