Summary_Exam_1_Brennan

Summary_Exam_1_Brennan - Polymer Physics Overview Lecture 1...

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Unformatted text preview: Polymer Physics Overview Lecture 1 Dr. Anthony Brennan University of Florida Department of Materials Science & Engineering EMA 6165 Polymer Physics AB Brennan 1 Agenda Introduction Chapter 1 Definitions/Nomenclature Configurational States Structure/Property Relationships Polymer Classifications Molar Mass Distribution Thermal Transitions (General) EMA 6165 Polymer Physics AB Brennan 2 Syllabus and Schedule http://brennan.mse.ufl.edu/ema6165_new.h Syllabus Schedule Proposal Expectations Questions? EMA 6165 Polymer Physics AB Brennan 3 Properties Chemical Physical Electronic Magnetic Optical CERAMICS METALS PROPERTIES ELECTRONIC MATERIALS POLYMERS EMA 6165 Polymer Physics AB Brennan 4 Vocabulary Polymer monomer (repeat unit) oligomers Bond energies Chain Structure Homopolymer Copolymer Branching Stereoregular Isomeric Reactions Condensation Polymerization Addition Polymerization Chain Growth Molar Mass Number, Weight Ave Degree of polymerization (DP) Polydispersity (PDI) Refer to Table 2.7 Intro to Polymer Sci 4th Ed, L. H. Sperling, Wiley & Sons, 2006 5 Structure Thermoplastics Thermosets Elastomers EMA 6165 Polymer Physics AB Brennan Importance of Chemistry Protein Tertiary Structure Conformational Structure Random Confirmation - Dilute Lamellar Configuration - Secondary Helical Configuration - Tertiary 6 EMA 6165 Polymer Physics AB Brennan Importance of Chemistry Balance of Three Energies Intermolecular Intramolecular Thermal (kT) Structures Linear Branched EMA 6165 Polymer Physics AB Brennan 7 Optical Isomers Amino Acids:Alanine Chiral Center EMA 6165 Polymer Physics AB Brennan 8 Configurational States Configuration permanent stereostructure. Rearrangement requires bond disruption. Tacticity Isotactic Syndiotactic Atactic EMA 6165 Polymer Physics AB Brennan 9 Copolymer Chain Terminology Unknown/specified Statistical Random Alternating Block Graft Star Blend Cross-linked Interpenetrating -co-stat-rand-alter-block-graft-star-blend-net-interpoly (A-co-B) poly(A-stat-B) poly(A-rand-B) poly(A-alter-B) poly(A-block-B) poly(A-graft-B) poly(A-star-B) poly(A-blend-B) poly(A-net-B) poly(A-inter-B) Adapted from Intro Phys Poly Sci-Sperling, 4th Ed, Wiley & Sons EMA 6165 Polymer Physics AB Brennan 10 Characteristics Condensation polymerization Addition polymerization chain reaction stepwise reaction one group added monomer consummed early per reaction DP peaks instantly DP rises steadily long reaction time long reaction time gives high molar gives high mass conversion only polymer and monomers, dimers, trimers, etc. monomer present present no reaction by reaction by products products 6165 Polymer Physics AB Brennan EMA 11 Polymeric Materials Structure-Property Behavior Dr. Anthony Brennan University of Florida Department of Materials Science & Engineering EMA 6165 Polymer Physics AB Brennan 12 Stress - Strain Response A: High frequency ( << t), Low temperature (T<<Tg,Tm), high crystallinity B: Decreasing frequency, ( ~t) (T~Tg, T<Tm) C: Decreasing frequency ( >t), decreasing crystallinity, (T>Tg, T<Tm) D: Low frequency ( >>t), high temperature (T>>Tg, T~Tm), low crystallinity Stress (A.U.) A B C D Strain EMA 6165 Polymer Physics AB Brennan 13 Stress Strain Behavior - Comparison Note Scales Note Differences = ETensile E = 2 (1 - ) G E = 2 (1 - 2 ) B yield = 0.028 ETensile EMA 6165 Polymer Physics AB Brennan 14 apted from Polymer Processing, TA Osswald, Hanser, 1998. Chain Energy (Thermodynamics) HEAT H - bonding COOL G = - S 15 EMA 6165 Polymer Physics AB Brennan Chain Thermodynamics Order of Thermodynamic Transitions Chain Dimensions Characterization Methods EMA 6165 Polymer Physics AB Brennan 16 Polymer Structure -Property Behavior Thermodynamics Glass transition (Tg) solid to liquid second order transition modulus decreases by 2 to 3 orders of magnitude elongation increases volume expansion rate increases (CTE) ~2/3 Tm Melting transition (Tm) solid to liquid first order transition modulus decreases by 2 to 3 orders of magnitude volume expansion discontinuous EMA 6165 Polymer Physics AB Brennan 17 Polymer Structure -Property Behavior Chain Dimensions Gel Permeation Chromatography c NM Mn = = c/M N cM NM2 Mw = = c NM 2 3 cM NM MZ = = 2 cM NM EMA 6165 Polymer Physics AB Brennan detector 18 Viscosity Viscosity (solution) hydrodynamic volume relative inherent intrinsic (Mv) Mark-Houwink -0 =lim c0 c 0 a 0 V = KM M N < MV < MW < M Z 19 EMA 6165 Polymer Physics AB Brennan Polymer Structure -Property Behavior Chain Dimensions Polydispersity Mechanical Properties Processing Stability Mw PDI = Mn = Mn EMA 6165 Polymer Physics AB Brennan Mw -1 Mn 20 Thermal Transitions EMA 6165 Polymer Physics AB Brennan 21 DSC/Complex Viscosity Influence of Cooling Rate http://scholar.lib.vt.edu/theses/available/etd-0898-145634/unrestricted/CH5.PDF Hydroxybenzoic Acid-Terephthalic Acid-Hydroquinone EMA 6165 Polymer Physics AB Brennan 22 EMA 6165 - Polymer Physics Polymer Solubility Lecture 15 Dr. Anthony Brennan University of Florida Department of Materials Science & Engineering EMA 6165 Polymer Physics AB Brennan 23 Polymer Solubility Entropy of Mixing The Classical Approach has been... The mixing of an G = H - TS "Ideal" Solution V = V1 + V2 For where V = Molar Volume P = P o ni i i ni -mole fraction P -vapor pressure i 24 T = 0 , P = 0 Vmix = 0 Hmix = 0 for gases, acceptable Hmix 0 for liquids EMA 6165 Polymer Physics AB Brennan Raoult's Law Obeyed, i.e. Polymer Solubility Entropy of Mixing V 1 = N 1k ln S V1 where N = # of molecules 1 Smix = S1 + S2 V = N1k ln + N1k ln V1 V2 EMA 6165 Polymer Physics AB Brennan 25 V Polymer Solubility Entropy of Mixing Gmix = N 1 G1 + N 2 G2 Where then N1 = # of molecules and n1 = mole fraction Gmix =- kT ( N 1 ln n1 + N 2 ln n2 ) Where n1 = mole fraction of solvent n2 = mole fraction of solute EMA 6165 Polymer Physics AB Brennan 26 Polymer Solubility Entropy of Mixing Statistical Approach - Lattice mix = k ln S N1 identical molecules # of lattice sites identical in size No = (N No ! 1 ! N 2 !) 27 EMA 6165 Polymer Physics AB Brennan Polymer Solubility Entropy of Mixing Now, one can use this to define the free Energy of Mixing for an Athermal Process: Gmix = RT n ln n i =1 i a. Solvent - Solute b. Solvent - Solvent c. Solute - Solute i Restrictions: } Interactions are equal Consider: head to head head to tail d. Size of lattice sites identical EMA 6165 Polymer Physics AB Brennan 28 One 0ligomer with Small Molecules Bethe Lattice X X X O O O O O O O X X X X X X O O O X O O O 29 EMA 6165 Polymer Physics AB Brennan Polymer Solubility Entropy of Mixing These conditions simulate concentrated solutions, However, we assume very dilute for ideality. Another restriction. Sum all sites to get: N - x i w1 =( N - x i ) z * N EMA 6165 Polymer Physics AB Brennan N - x i ( z -1) N ( x -2 ) 30 Polymer Solubility Entropy of Mixing and 1 = N2 w i= 1 N2 i which leads to the following in terms of volume fraction: Smix = - R ( X 1 ln1 + X 2 ln 2 ) EMA 6165 Polymer Physics AB Brennan 31 EMA 6165 - Polymer Physics Polymer Solubility Lecture 16 Dr. Anthony Brennan University of Florida Department of Materials Science & Engineering EMA 6165 Polymer Physics AB Brennan 32 Polymer Solubility Enthalpy of Mixing Since Then =0 H for an ideal solution Gmix = kT N i ln ni i =1 Normalization with respect to Avogadro's No. yields Gmix = RT N i lnni EMA 6165 Polymer Physics AB Brennan i =1 33 Polymer Solubility Enthalpy of Mixing Combinatorial Entropy S = -k N i ln i =- k ( N 1 ln 1 + N 2 ln 2 ) S and based upon the assumption of Ideality, Which for a two-phase system =0 H EMA 6165 Polymer Physics AB Brennan 34 Polymer Solubility Enthalpy of Mixing Therefore: Gmix = kT ( N 1 ln + 1 Where N1 = # N2 = # N 2 ln ) 2 of molecules of segments = volume fraction EMA 6165 Polymer Physics AB Brennan 35 Polymer Solubility Enthalpy of Mixing S R X1 Xi= n=500 n=100 n=50 mole fraction of segments X2 Why? 0 H Consider: London van der Waals Dipole H-bonding Acid-Base, etc. 36 EMA 6165 Polymer Physics AB Brennan Polymer Solubility Enthalpy of Mixing Use pairwise interaction energy and arguments similar to the Combinatorial Entropy =2 w1,2 -w1,1 -w2 ,2 w Segment i is surrounded by z and 1 z 2 An interaction energy can be calculated for each segment and solvent molecule, w 37 EMA 6165 Polymer Physics AB Brennan Polymer Solubility Enthalpy of Mixing Since we are interested in 1,2 pairwise interactions, a new term is defined 1 w = z 2 kT Chi Parameter mix = N 1 k T H 2 Flory-Huggins Pairwise interaction 38 EMA 6165 Polymer Physics AB Brennan Polymer Solubility Enthalpy of Mixing Gmix = kT [ N 1 - 2 (X Where 1 ln 1 + X 2 ln 2 ) ] EMA 6165 Polymer Physics AB Brennan molar X = volume fraction Positive } Positive Zero Negative 39 } Polymer Solubility Enthalpy of Mixing = N H kT 1 2 = N 1 kT 2 w = 2 w1,2 - w1,1 - w2 ,2 V E 1 = zNwii 2 Cohesive energy density, Vaporization 40 EMA 6165 Polymer Physics AB Brennan Polymer Solubility Enthalpy of Mixing Substitute in for Hmix 1 2 Hmix E E 2 1 - 12 = Vm V2 V1 1 2 1 E V1 Hildebrand and Scott Cohesive Energy Density 41 EMA 6165 Polymer Physics AB Brennan Polymer Solubility Enthalpy of Mixing Which provides a definition for the Solubility Parameter: = E1 V1 1 2 cal 3 cm 1 2 which for an Athermal Process: 1 = 2 EMA 6165 Polymer Physics AB Brennan 42 Polymeric Materials Models for Calculating Chain Dimensions Dr. Anthony Brennan University of Florida Department of Materials Science & Engineering EMA 6165 Polymer Physics AB Brennan 43 Chain Dimensions Characteristic Dimensions r where: 2 0 = Cnl 2 <r2>o - chain dimensions at Theta conditions C - Characteristic Chain Ratio n - number of segments l - segment dimension (length) EMA 6165 Polymer Physics AB Brennan 44 Chain Dimensions Chain Expansion Factor = 1: when T = -> n 1/10; T > - = C n 1 - T 5 3 <r2> = <r2>o at T = q Chains behave as phantoms 12 - 1 - M T 5 3 EMA 6165 Polymer Physics AB Brennan 45 Freely Jointed Chain Conditions End - to - end distance and radius of gyration : all valence angles are allowed No excluded volume EMA 6165 Polymer Physics AB Brennan 46 Freely Jointed Chain Vector Analysis r 2 = nl 2 1 + cos 1 - cos For the Freely Jointed Model there are no restrictions on the valence bond angle, thus EMA 6165 Polymer Physics AB Brennan 47 Freely Jointed Chain Vector Analysis cosij = 0; for i j Thus, the FREELY JOINTED CHAIN is defined as: r 2 = nl 2 Consider how <r2> scales with Molar Mass EMA 6165 Polymer Physics AB Brennan 48 Freely Rotating Chain Vector Analysis Mean Square End to End Distance r 2 = nl 2 2 As shown previously: ri rj = l cosij 49 EMA 6165 Polymer Physics AB Brennan Freely Rotating Chain Model Vector Analysis r 2 = nl 2 2 1 + cos(180 - ) 1 - cos(180 - ) 2 (Fixed angle = 109.5) 50 r = 2nl EMA 6165 Polymer Physics AB Brennan Freely Rotating Chain Vector Analysis r 2 = 2 Ml 2 Freely rotating model: high temperature solvated Fixed bond angle of 109.5 expands by 2 Ignores bond rotational energy barriers (RIS) EMA 6165 Polymer Physics AB Brennan 51 Hindered Rotating Chain Model Ilustration of RIS C H C H C H C H H H H C C H Periodic fluctuations as 2 /3 EMA 6165 Polymer Physics AB Brennan 52 Freely Rotating Chain Vector Analysis r 2 = 2nl 2 Which clearly demonstrates the increase in the chain dimensions by the restriction of bond angle. This is thus critical in terms of relative measurements such as viscosity for complex polymer and copolymer structures EMA 6165 Polymer Physics AB Brennan 53 Summary Freely Jointed Chain dimensions scale with Molar Mass Freely Rotating Model increases chain dimensions of simple polyolefins by a factor of 2 compared to the freely jointed model. EMA 6165 Polymer Physics AB Brennan 54 References Introduction to Physical Polymer Science, 4th Edition, Lesley H. Sperling, Wiley Interscience (2006) ISBN 13-978-0-471-70606-9 Principles of Polymer Chemistry, P.J. Flory (1953) Cornell University Press, Inc., New York. The Physics of Polymers, Gert Strobl (1996) Springer-Verlag, New York. Figures were reproduced from Polymer Physics, (1996) Ulf Gedde, Chapman & Hall, New York. EMA 6165 Polymer Physics AB Brennan 55 ...
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This note was uploaded on 07/20/2011 for the course EMA 6165 taught by Professor Brennan during the Spring '08 term at University of Florida.

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