3.063 Polymer Physics Spring 007 Viewpoint: somewhat more general than just polymers: Soft Matter Polymers, Colloids, Liquid Crystals, Nanoparticles and ybrid rganic- Inorganic Materials Systems. Reference: Young and Lovell, Introduction to Polymer Science (recommended) Demos and Lab Experiences: Molecular Structural Characterization (DSC, GPC, TGA, Xray, AFM, TEM, SEM ) and Mechanical & ptical Characterization
Course Info eltweb.mit.edu/3.063 - course website: notes, hmwks Eric Verploegen Ms. Juliette Braun ffice hours - ow are Wednesdays at 30-330pm? Mini Assignment Send Prof. Thomas contact info/ name/year/major/email/credit/listener and interests relevant to topics in this course Any expertise you have on lab demos, characterization tools, cool samples
ard vs. Soft Solids (for T ~ 300K) ard matter: metals, ceramics and semiconductors: typically highly crystalline. U >> kt Soft matter: polymers, organics, liquid crystals, gels, foods, life(!). U ~ kt Soft matter is therefore sometimes called delicate material in that the forces holding the solid together and causing the particular atomic, molecular and mesoscopic arrangements are relatively weak and these forces are easily overcome by thermal or mechanical or other outside influences. Thus, the interplay of several approximately equal types of forces affords the ability to access many approximately equal energy, metastable states. ne can also tune a structure by application of a relatively weak stimulus. Such strong sensitivity means that soft matter is inherently good for sensing applications.
In 3.063 we aim to understand: The Key rigins of Soft Solid Behavior: relatively weak forces between molecules many types of bonding, strong anisotropy of bonding (intra/inter) wide range of molecular shapes and sizes, distributions large variety of chemistries/functionalities fluctuating molecular conformations/positions presence of solvent, diluent entanglements many types of entropy architectures/structural hierarchies over several length scales Characterization of the molecular structures and the properties of the soft solids comprised of these molecules
Scale in Soft Matter 1 DuPont microstructured fibers. DNA molecule AFM 0.8 0.6 0.4 uman air Photoresist (150 nm) -photon polymerized photonic crystal Nature 1999 Carbon nanotube 0. 0 Red blood cells Intel 4004 Virus Patterned atoms 10 6 10 5 10 4 10 3 10 10 1 10 0 Dimensions (nm)
Interactions in Soft Solids Molecules are predominantly held together by strong covalent bonds. Intramolecular - Rotational isomeric states Intermolecular potential ard sphere potential Coulombic interaction Lennard Jones potential (induced dipoles) ydrogen bonding (net dipoles) hydrophobic effect (organics in water)
Polyelectrolyte Domain Spacing Change by e-field QPVP PS Apply field Photo of tunable gels removed due to copyright restrictions. Fluid reservoir Initial film thickness: ~ 3 μm Total # of layers: ~ 30 layers n PS -n PVP ~ 1.6 n = 1.33
Structure of Soft Solids SR - (always present in condensed phases) intra- and inter- LR - (sometimes present) Spatial: 1D, D, 3D periodicities rientational rder parameters (translational, orientational ) Defects - influence on properties; at present defects are largely under-appreciated; e.g. transport across membranes self assembly-nucleation, mutations, diseases Manipulation of rientation and Defects: Develop methods to process polymers/soft solids to create controlled structures/hierarchies and to eliminate undesirable defects
Polymers/Macromolecules. Staudinger (190 s) colloidal ass y vs. molecule MACRMLECULAR YPTESIS single repeating unit (MER) covalent bonds A SINGLE REPEAT UNIT MANY REPEAT UNITS MNMER (M) PLYMER (M) n Macromolecule - more general term than polymer
PLYMERIZATIN Common reactions to build polymers: 1. Addition: M n + M M n+1. Condensation: M x + M y M x+y + or Cl / etc. Think of a polymer as the endpoint of a MLGUS SERIES: ow do the properties change with n? N = 1 3 Example: Polyethylene (n 10 4 ) n Degree of Polymerization C =C C C n<100 C C n 100 monomer oligomer polymer
Proteins and Polyamides (Nylons) Proteins are decorated nylon N R n R = various side groups (0 possible amino acids) R = glycine R = C 3 alanine, etc. N N N amide linkage Members of the nylon family are named by counting the number of carbon atoms in the backbone between nitrogen atoms. N N N N C N C N nylon T m > 300 C nylon 6 N C N C 5 5 N T m = 15 C N N N 6 carbon atoms ydrogen bonds note nylon n= = polyethylene (!) T m ~ 140 C
Characteristic Features of Macromolecules uge Range of Structures & Physical Properties Some examples: Insulating --------> Conducting Light emitting Photovoltaic, Piezoelectric Soft elastic ---------> Very stiff plastic Ultra large reversible deformation ighly T, t dependent mechanical properties Zero/few crystals ------> igh Crystallinity Readily Tunable Properties: Weak interactions between molecules, so chains can be readily reorganized by an outside stimulus
Chain Conformations of Polymers: Extremes n is the number of links in the chain with each link a step size l so the contour length of the chain L is nl; As a measure of size of the chain, we can have two situations: 1. Rigid rod: Fully Extended Conformation < r > 1/ n l = L. Flexible coil: Random Walk < r > 1/ n 1/ l - note this is much smaller than L
Extreme Conformations of (Linear) Polymers Isolated molecules Flexible Coil Rigid Rod Entanglements Flexible Coils Rigid Rods
.357 Magnum, layers of Kevlar
Polymer Architectures LINEAR CRSS-LINKED BRANCED DENDRITIC (I) 1930's- (II) 1940's- (III) 1960's- (IV) 1980's- x Flexible Coil Lightly Cross-Linked Random Short Branches Random yperbranched Rigid Rod Densely Cross-Linked Random Long Branches Controlled yperbranched (Comb-burst TM ) Cyclic (Closed Linear) Regular Comb-Branched x Polyrotaxane Interpenetrating Networks Regular Star-Branched Regular Dendrons Dendrimers (Starburst R ) Figure by MIT CW.
1-D Random Walk R = Nb N steps of size b R -4 4 x = 0 (a) -4 0 4 (b) (a) Initial distribution of atoms, one to a line. (b) Final distribution after each atom took 16 random jumps. R is the calculated root mean square for the points shown. Figure by MIT CW.
Gaussian Distribution π nl 3/ P(r,n) = 3 exp 3r nl Note: units are [volume -1 ] P(r,n)4πr dr = 1 normalized probability 0 r = r P(r,n) 4π r dr Probability of distance r between 1 st and n th monomer units for an assembly of polymers is a Gaussian distribution, here shown for 3D p(r)/p(0) 1.00 0.75 0.50 0.5 0.00 0.0 0.5 1.0 1.5.0 R/<R > Figure by MIT CW.
Flexible Coil Chain Dimensions 3 Related Models Mathematician s Ideal Random Walk Chemist s Chain in Solution and Melt r = nl r = nl C α Physicist s Universal Chain r = N b
Mathematician s Ideal Chain n monomers of length l r l,n = l 1 + l +...+ l n = l i n i=1 l i = l r 1,n = 0 since{ r l,n }are randomly oriented No restrictions on chain passing through itself (excluded volume), nopreferred bond angles Consider r 1,n 1 0 r l,n r l,n = l i l j Scalinglaw: = l 1 ( l 1 + l + l 3 +...)+ l ( l 1 + l + l 3 +...)+... ( ) l 1 l 1 l 1 l l 1 l 3... l 1 l n l l 1 l l. l n l 1. l n l n l 0 0... 0. l....... 0 l r l, n 1 n 1 r l,n = nl r l,n 1 = n 1 l
Chemists Chain: Fixed Bond Angle (and Steric inderance) Simpliest case: Chain comprised of carbon-carbon single bonds C 4 Fixed θ: l i l i +1 = l ( cosθ) ( ) l i l i + = l cosθ projections of bond onto immediate neighbor C (1) D C 3 () (3) C 4 C 4 In general: l i l i +m = l ( cosθ) m l, l ( cosθ), l cos θ, l ( cos 3 θ)... C 1 Figure by MIT CW. Factor out l : 1 cosθ cos θ cosθ 1 cosθ cos cosθ 1 θ 3 cos θ cos θ cosθ 1.... cos. θ ( cosθ ) 1 n 1 nl 1 cosθ 1+ cosθ
Special case: Rotational conformations of n-butane Potential energy of a n-butane molecule as a function of the angle φ of bond rotation. C 3 C C C 3 V(φ) Potential energy/kj mol -1 0 15 10 5 eclipse eclipse gauche planar trans eclipse gauche 0-180 o - 10 o - 60 o 0 60 o 10 o 180 o φ eclipse Planar trans conformer is lowest energy C 3 3 C C 3 C 3 Views along the C-C3 bond C3 C 3 eclipsed conformations C 3 C 3 C 3 igh energy states 3 C C 3 C 3 V(φ) Gauche Planar Gauche Figure by MIT CW. Low energy states
Conformers: Rotational Isomeric State Model Rotational Potential V(φ) Probability of rotation angle phi P(φ) ~ exp(-v(φ)/kt) Rotational Isomeric State (RIS) Model e.g. Typical 3 state model : g -, t, g + with weighted probabilities Again need to evaluate l i l j+1 taking into account probability of a φ rotation between adjacent bonds This results in a bond angle rotation factor of combining where 1 cosθ 1+ cosφ r = nl 1+ cosθ 1 cosφ = nl C C 1 cosθ 1+ = 1+ cosθ 1 cosφ cosφ 1+ 1 cosφ cosφ The so called Characteristic ratio and is compiled for various polymers cosφ = cos(φ)p(φ)dφ P(φ)dφ with P(φ) = exp(-v(φ)/kt)
The Chemist s Real Chain Preferred bond angles and rotation angles: θ, φ. Specific bond angle θ between mainchain atoms (e.g. C-C bonds) with rotation angle chosen to avoid short range intra-chain interferences. In general, this is called steric hinderance and depends strongly on size/shape of set of pendant atoms to the main backbone (F, C 3, phenyl etc). Excluded volume: self-crossing of chain is prohibited (unlike in diffusion or in the mathematician s chain model): Such contacts tend to occur between more remote segments of the chain. The set of allowed conformations thus excludes those where the path crosses and this forces <r l,n > 1/ to increase. Solvent quality: competition between the interactions of chain segments (monomers) with each other vs. solvent-solvent interactions vs. the interaction between the chain segments with solvent. Chain can expand or contract. monomer - monomer solvent - solvent ε M-M vs. ε S-S vs. ε M-S monomer - solvent
Excluded Volume The excluded volume of a particle is that volume for which the center of mass of a nd particle is excluded from entering. Example: interacting hard spheres of radius a volume of region denied to sphere A due to presence of sphere B V= 4/3π(a) 3 = 8 V sphere but the excluded volume is shared by spheres so V excluded = 4 V sphere
Solvent Quality and Chain Dimensions Theta θ Solvent Solvent quality factor α Solvent In Local Picture Good Solvent α < r > = < r > θ Global Picture Solvent quality factor 0 10 Good solvent Solvent ut 0 10 10 0 10 θ Solvent Poor Solvent 10 0 10 10 10 Poor solvent Figure by MIT CW. Solvent quality: M-M, S-S, M-S interactions: ε M-M, ε S-S, ε M-S
Solvent Quality (α) good solvent: favorable ε SM interaction so chain expands to avoid monomer-monomer contacts and to maximize the number of solvent-monomer contacts. -ε SS -ε MM -ε SM good α > 1 0 -ε SM -ε SS -ε MM poor α < 1 0 poor solvent: unfavorable ε SM, therefore monomer-monomer, solvent-solvent interactions preferred so chain contracts. r = nl C α
Theta Condition: Choose a solvent and temperature such that Excluded volume chain expansion is just offset by somewhat poor solvent quality and consequent slight chain contraction: called Θ condition (α =1) r θ = local steric influence nl = nl C bond angles, rotation angles α = r r θ solvent quality factor Actually expect a radial dependence to alpha, since segment density is largest at center of chain segment cloud.
Random Walks RW Figure by MIT CW. SARW 3.01 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 005) Figure by MIT CW.