Polymers, Colloids, Liquid Crystals, Nanoparticles … · 3.063 Polymer Physics ... Polymers,...
Transcript of Polymers, Colloids, Liquid Crystals, Nanoparticles … · 3.063 Polymer Physics ... Polymers,...
3.063 Polymer Physics Spring 2007
• Viewpoint: somewhat more general than just polymers:
“Soft Matter”Polymers, Colloids, Liquid Crystals, Nanoparticles and Hybrid Organic-
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 & Optical Characterization
Course Info
eltweb.mit.edu/3.063 - course website: notes, hmwks…Eric VerploegenMs. Juliette Braun Office hours - How are Wednesdays at 230-330pm?
Mini AssignmentSend 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…
Hard vs. Soft Solids(for T ~ 300K)
• Hard 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 equalenergy, metastable states. One 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 Origins of Soft Solid Behavior:
relatively weak forces between moleculesmany types of bonding, strong anisotropy of bonding (intra/inter)
wide range of molecular shapes and sizes, distributionslarge variety of chemistries/functionalitiesfluctuating molecular conformations/positionspresence of solvent, diluententanglementsmany types of entropyarchitectures/structural hierarchies over several length scales
• Characterization of the molecular structures and the properties of the soft solids comprised of these molecules
1
0.8
0.6
0.4
0.2
010 6 10 5 10 4 10 3 10 2 10 1 10 0
Carbon nanotube
Photoresist (150 nm)
Intel 4004 Patterned atoms
HumanHair
Red blood cells
Dimensions (nm)
Virus
DuPont microstructured fibers.
2-photon polymerized photonic crystal Nature 1999
DNA molecule AFM
Scale in Soft Matter
Interactions in Soft Solids
• Molecules are predominantly held together by strong covalent bonds.
• Intramolecular - Rotational isomeric states• Intermolecular potential
– Hard sphere potential– Coulombic interaction– Lennard Jones potential (induced dipoles)– Hydrogen bonding (net dipoles)
• “hydrophobic effect” (organics in water)
Polyelectrolyte Domain Spacing Change by e-Field
nPS - nP2VP ~ 1.6nH2O = 1.33
Fluid reservoir
PS
QP2VP
Apply field
Photo of tunable gels removed dueto copyright restrictions.
Initial film thickness: ~ 3 μm
Total # of layers: ~ 30 layers
Structure of Soft Solids• SRO - (always present in condensed phases)
– intra- and inter-• LRO - (sometimes present)
– Spatial: 1D, 2D, 3D periodicities– Orientational
• Order 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 Orientation and Defects: Develop methods to process polymers/soft solids to create controlled structures/hierarchies and to eliminate undesirable defects
Polymers/Macromolecules
H. Staudinger (1920’s) colloidal ass’y vs. molecule
“MACROMOLECULAR HYPOTHESIS”
single repeating unit(MER)
covalent bonds
A SINGLE REPEAT UNIT → MONOMER (M)MANY REPEAT UNITS → POLYMER (M)n
“Macromolecule” - more general term than polymer
POLYMERIZATIONCommon reactions to build polymers:1. Addition: Mn + M → Mn+1
2. Condensation: Mx + My → Mx+y + H2O or HCl / etc.
Think of a polymer as the endpoint of a HOMOLOGOUS SERIES:
N = 1 2 3 nDegree of
Polymerization
CH2=CH2 → – CH2 – CH2 – → – CH2 – CH2 – n≥100
Example: Polyethylene (n ≈ 104)
n<100monomer oligomer polymer
How do the properties change with n?
N
H
O
N
H
O
N
H
O
amide linkage• Members of the nylon family are named by counting thenumber of carbon atoms in the backbone betweennitrogen atoms.
O
N
H
O
N CH2
H
O
N
H
CH2
nylon 6O
N
H
O
N CH2
H
O
N
H
CH25 5
6 carbonatoms
Tm = 215°C
note nylon n=∞ = polyethylene (!) Tm ~ 140°C
nylon 2 Tm > 300°C
Proteins are “decorated nylon 2”
O
N
R
H
H
n
R = various side groups(20 possible amino acids)
R = H → glycineR = CH3 → alanine, etc.
Proteins and Polyamides (Nylons)
N
H
O
N
H
O
N
H
O
N
H
O
N
H
O
N
H
O
Hydrogen bonds
Characteristic Features of Macromolecules• Huge Range of Structures & Physical Properties• Some examples:
• Insulating --------> Conducting• Light emitting• Photovoltaic, Piezoelectric• Soft elastic ---------> Very stiff plastic
– Ultra large reversible deformation– Highly T, t dependent mechanical properties
• Zero/few crystals ------> High Crystallinity
• Readily Tunable Properties:
Weak interactions between molecules, so chains can be readily reorganized by an outside stimulus
Chain Conformations of Polymers: 2 Extremes
• 1. Rigid rod: Fully Extended Conformation – < r2>1/2 ≈ n l = L
• 2. Flexible coil: Random Walk – < r2>1/2 ≈ n1/2 l - note this is much smaller than L
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:
Flexible Coil
Flexible Coils
Rigid Rod
Rigid Rods
Extreme Conformations of (Linear) Polymers
Entanglements
Isolated molecules
.357 Magnum, 22 layers of Kevlar
Polymer Architectures
x
x
Flexible Coil
Rigid Rod
Cyclic (Closed Linear)
PolyrotaxaneInterpenetrating
Networks
Densely Cross-Linked
Lightly Cross-Linked
Regular Star-Branched
Regular Comb-Branched
Random Long Branches
Random Short Branches
Regular Dendrons
Controlled Hyperbranched(Comb-burstTM)
Random Hyperbranched
Dendrimers(StarburstR)
LINEAR CROSS-LINKED BRANCHED DENDRITIC(I) (II) (III) (IV)1930's- 1940's- 1960's- 1980's-
Figure by MIT OCW.
1-D Random Walk
R2 = N b2
-4 4x = 0
(a)
(a) Initial distribution of atoms, one to a line.
-4 4
(b)
0
2 R2
2 R2
(b) Final distribution after each atom took 16 random jumps. is the calculated root mean square for the points shown.
N steps of size b
Figure by MIT OCW.
Gaussian Distribution
P(r,n) =2π nl2
3
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
−3/2
exp −3r2
2nl2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ Note: units are [volume-1]
P(r,n) 4π r2 dr0∞
∫ = 1 normalized probability
r2 = r2 P(r ,n) 4π r2 dr∫
Probability of distance rbetween 1st and nth
monomer units for an assembly of polymers
is a Gaussian distribution, hereshown for 3D
1.00
0.75
0.50
0.25
0.000.0 0.5 1.0 1.5 2.0
p(R
)/p(0
)
R/<R2>
Figure by MIT OCW.
Flexible Coil Chain Dimensions
• Mathematician’s Ideal Random Walk
• Chemist’s Chain in Solution and Melt
• Physicist’s Universal Chain
3 Related Models
22 bNr =
r2 = n l2 C∞ α 2
22 nlr =
Mathematician’s Ideal Chain
21
21
2, :law Scaling nr nl ∝
n monomers of length l li = l
r l ,n = l 1 + l 2 + ......+ l n = l i
i=1
n
∑
r1,n = 0 since r l ,n{ }are randomly oriented
Consider r1,n2
12 ≠ 0
r l ,n ⋅ r l ,n = li ⋅ l j∑∑= l 1 ⋅ l 1 + l 2 + l 3 + ...( )+ l 2 ⋅ l 1 + l 2 + l 3 + ...( )+ ...( )
l1 ⋅ l1 l1 ⋅ l2 l1 ⋅ l3 ... l1 ⋅ ln
l2 ⋅ l1 l2 ⋅ l2
..
ln ⋅ l1 ln ⋅ ln
→
l2 0 0 ... 0. l2 .. . .. . .0 l2
r l ,n
2 = nl2 r l ,n
212 = n
12 l
No restrictions on chain passing through itself (excluded volume), nopreferred bond angles
Chemists’ Chain: Fixed Bond Angle (and Steric Hinderance)
Fixed θ:
• projections of bond onto immediate neighbor
li ⋅ li +1 = l2 −cosθ( )li ⋅ li +2 = l2 −cosθ( )2
In general: li ⋅ li +m = l2 −cosθ( )m
l2 , l2 −cosθ( ) , l2 cos2 θ , l2 −cos3 θ( )....
Factor out l2:
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
−−−−
−−− −
1.1
coscos1coscos.coscos1cos
)cos(...coscoscos1
22
2
132
θθθθθθθ
θθθθ n
⎟⎠⎞
⎜⎝⎛
+−
≈∑ θθ
cos1cos12nl
Simpliest case:
Chain comprised ofcarbon-carbon single
bonds
Figure by MIT OCW.
C4
C4
C4
C2
C1
C3
(1)
(2) (3)
D
2
Special case: Rotational conformations of n-butane
CH3CH2CH2CH3
Views along the C2-C3 bond
Planar trans conformer is lowest energyV(φ)
V(φ)
High energy states
Low energy states
5
00- 180o - 120o - 60o 60o 120o 180o
10
15
20
gauche gaucheplanar trans
φ
φPotential energy of a n-butane molecule as a function of the angle of bond rotation.
Pote
ntia
l ene
rgy/
kJ m
ol-1
H
H H
H
H
H
H
H
H
HHH
H
HH
H
HH HH
H
H
HHCH3
CH3
CH3 CH3 CH3
CH3
CH3
H3C
H3C
CH3 CH3
CH3
eclipsed conformations
Gauche GauchePlanar
eclipse
eclipse eclipse
eclipse
Figure by MIT OCW.
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 taking into account probability of a φ
rotation between adjacent bonds
• This results in a bond angle rotation factor of
where
with P(φ) = exp(-V(φ)/kT)
1+⋅ ji ll
r2 = nl2 1− cosθ1+ cosθ
⎞ ⎠ ⎟
1+ cosφ1− cosφ
⎛
⎝ ⎜
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ = nl2C∞
φφ
cos1cos1
−+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛⎜⎜⎝
⎛
−+
⎟⎠⎞
+−
=∞ φφ
θθ
cos1cos1
cos1cos1C
cosφ =cos(φ)P(φ)dφ∫
P(φ)dφ∫
combining
The so called “Characteristic ratio”and is compiled for various polymers
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, CH3, 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 remotesegments of the chain. The set of allowed conformations thus excludes those where the path crosses and this forces <rl,n
2 >1/2 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 εM-M vs. εS-S vs. εM-S• monomer - solvent
Excluded Volume
• The excluded volume of a particle is that volume for which the center of mass of a 2nd 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(2a)3 = 8 Vsphere
but the excluded volume is shared by 2 spheres so Vexcluded = 4 Vsphere
Solvent Quality and Chain Dimensions
• Solvent quality: – M-M, S-S, M-S interactions: εM-M, εS-S, εM-S
Solvent quality factor αTheta θ Solvent
20
20
20
20
10
10
10 10
10
10
10 10Poor Solvent
Good Solvent
Solvent In
Solvent Out
Local Picture Global PictureSolvent quality factor
α2 = < r2 >θ
< r2 >
θ − Solvent
Good solvent
Poor solvent
Figure by MIT OCW.
Solvent Quality (α)
• good solvent: favorable εSM interaction so chain expandsto avoid monomer-monomer contacts and to maximize the number of solvent-monomer contacts.
• poor solvent: unfavorable εSM, therefore monomer-monomer, solvent-solvent interactions preferred so chain contracts.
r2 = n l2 C∞ α 2
0-εSS
-εMM-εSM
α > 1
0-εSM-εSS
-εMM
α < 1poorgood
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)
r2
θ = n l2 ⋅local steric influence
bond angles, rotation angles⎛
⎝ ⎜
⎞
⎠ ⎟ = n l2 C∞
θ=α
2
22
r
r“solvent quality factor”
Actually expect a radial dependence to alpha, since segment density is largest at center of “chain segment cloud”.
Random Walks
3.012 Fundamentals of Materials Science: Bonding - Nicola Marzari (MIT, Fall 2005)
RW
SARW
Figure by MIT OCW.
Figure by MIT OCW.