Crystalline polymers

&

Vibrational spectroscopy of polymers

Glassy: molecules in a random coil conformation. For example fully amorphous PMMA and PPO

Crystalline: Polymer molecules show some degree of ordering. Depending on molecular symmetry (tacticity), molecular weight (kinetics) and branching, etc.

Lamellar growth direction ~10 µm

Lamella thickness

~100 – 200 Å

Microscopy image of a crystal of high density poly(ethylene) - viewed while “looking down” at the lamella.

10 m x 10 m

Lamella grows outwards

Several crystals of isotactic poly propylene G. Ellis*, M. A. Gómez and C. Marco

Polymers with some symmetry are usually polycrystalline. They are usually never completely crystalline but have some amorphous regions and “packing defects”.

competition between polymer chain stretching and coiling on one hand and on reduction in free energy for crystal formation on the other hand determines lamellar thickness.

Why is the lamellar crystal a basic unit?

Tk

gST

k

S

B

B

expratemelt crystal

exprate crystalmelt

1-

1-

is a microscopic frequency, g is negative by definition

Calculating the maximum net rate for a crystal of thickness l gives an estimate of the optimal thickness (fastest growing).

Lamellar thickness of PE grown from a melt

melt crystallization annealing

)(

20

0

cmv

mc TTH

TL

Lamellar Thickness:

Surface energy0mT

vH

Equilibrium melting Temperature

Enthalpy of fusion per unit volume

cT Crystallization temperature

Micellar Structures

When diblock copolymes are asymmetric, lamellar structures are not favoured.

Instead the shorter block segregates into small spherical phases known as “micelles”.

Density within phases is maintained close to bulk value.

Interfacial “energy cost”: (4r2)

Reduced stretching energy for shorter block

Exotic Morphologies

Molecular vibrations – vibrational spectroscopy

Restoring force (the bond): F=k(X2+X1)

m2

X2

m1

m1 m2

X1

equilibrium

F ma kx a d2x

d t2

md2x

d t2 kx d2x

d t2 k

mx

x(t) A cos 2 t k

m

k

Quantum Vibrational Motion

• molecular motion is quantized; vibrational quantum levels (quantum number “v”)

• energy absorbed is energy difference between two levels; for SHO, spacing is same between ALL adjacent levels.

Ev v 12

v 1

2

h

h2

2 12

k

Ev v1 h h

1

2k

Anharmonic Oscillator

• real molecules, vibrations “close to being” harmonic.

• relaxes the selection rules (overtones and combination bands)

• distorts the intensities of the transitions

• changes energy levels so that they come closer together as you go up the vibrational ladder.

• bond can “break”; not so with SHO.

Types of Vibrations

• molecular dipole moment must change during a vibration to be IR active.

• this oscillating dipole interacts with the oscillating E-M field of the photon, leading to absorption.

+ – + +

–

Stretching Vibrations Bending Vibrations

symmetric anti-symmetric rocking scissoring twisting waggingIn-Plane Out-of-Plane

Changes in bond length Changes in bond angle

Vibrational spectroscopy

anti-Stokes

Rayleigh Stokes

E

Virtual states

Excited stateGround state

-3500

400

22900

0

514

19400

3500

630

15900

Raman shift (cm-1)

wavelength (nm)

wavenumber (cm-1)

Raman scattering

Infrared absorption

3500

2850

Infrared is Rovibrational Spectroscopy

• Wavelengths between 0.8 µm to 1 mm.

• Associated with changes in nuclear motion (vibrations and rotations).

• In gas phase, rotational transitions are resolved; in liquid phase, they are broadened. Usually only focus on vibrational character.

• Energy is usually reported in wavenumbers (cm-1); also proportional to frequency

Near IR 0.8 - 2.5 µm 12800 - 4000 cm-

1

Mid-IR 2.5 - 50 µm 4000 - 200 cm-1

Far IR 50 - 1000 µm 200 - 10 cm-1

mostcommonly studied

1

c

The Raman Spectrum

A complete Raman spectrum consists of:

• a Rayleigh scattered peak (high intensity, same wavelength as excitation)

• a series of Stokes-shifted peaks (low intensity, longer wavelength)

• a series of anti-Stokes shifted peaks (still lower intensity, shorter wavelength)

• spectrum independent of excitation wavelength (488, 632.8, or 1064 nm)

Spectrum of CCl4, using an Ar+ laser at 488 nm.

Origin of Raman Effect - Classical

The oscillating electric field of the excitation light.

The induced dipole moment from this oscillating field.

The molecular polarizability changes with bond length.

The bond length oscillates at vibrational frequency.

Hence the polarizability oscillates at same frequency.

Substitute.

Remember trig identity.

Induced dipole has Rayleigh,Stokes, and anti-StokesComponents.

E E0 cos ext induced E E0 cos ex t

0 r req ddr

r req rmax cos vibt

0 ddr

rmax cos vibt

induced 0 ddr

rmax cos vibt

E0 cos ex t 0E0 cos ex t

E0rmaxddr

cos ex t cos vibt

cos x cosy 12

cos x y cos x y induced 0E0 cos ex t

E0rmax

2

ddr

cos ex vib t cos ex vib t

Infrared Spectroscopy Raman Spectroscopy

Interaction Absorption Scattering

Excitation Polychromatic Monochromatic

Frequency measurement Absolute Relative

Activity Dipole moment change Polarizability change

Band intensity

/Q0 /Q0

(/Q /Q)

Raman vs. IR

Compare IR and Raman

Spectra of PETN explosive. From D.N. Batchelder, Univ. of Leeds

Group frequencies

For large molecules - vibrations of some functional groups acts like independent oscillators i.e. always found at ~ same frequencies

Group cm-1

- C-H 2900-3000

- C=O 1700

- C-F 1100

- O-H 3600

- C-C - 900

Factors affecting group frequencies

• Center of Symmetry (i):determine IR active or Raman active.

• For IR active vibration an oscillating electric dipole must be generated.

• For Raman active vibration a change in polarizability of the molecule is produced, which gives rise to induced dipole.

Symmetry factor

• A molecule having a center of symmetry (i) has no permanent dipole moment, so a vibration symmetric to i (sym. mode) does not generate oscillating dipole and therefore it is an IR inactive vibration.

• But vibration anti-symmetric to i (anti-sym. mode) generates transient oscillating dipole, so it will be IR active vibration and show up in the spectrum.

Mutual exclusion rule • Symmetric mode vibration usually gives rise

to Raman scattering which causes changes in polarizability of molecule, and it is a Raman active vibration, showing up in the Raman spectrum.

• Mutual exclusion rule : For IR and Raman spectra, some lines missing in one would show up in the other, due to different symmetry requirement for each spectra. Thus, the information from IR data is complementary to that obtained from Raman.

General rule of symmetry

• Symmetry in molecule reduces the normal modes of vibrations and simplifies spectrum.

• CO2 : sym. stret. = 1340 cm-1 , IR

inactive, but Raman active.

assym. stret. = 2349 cm-1 , IR active.

IR vs. Raman : mutual exclusive.

Symmetry : IR shows only assym. stret.

Symmetry simplify spectra

Mechanical coupling

• Interaction between two vibrational modes through common atom or common bond: Such two identical groups are linked (or fused) by a common atom or a common bond.

• Induce mixing and redistribution of energy states, yielding new energy levels, one being higher and one lower in frequency.

Degrees of freedom

Always 3 N degrees of freedom (N = number of atoms in molecule) with 3N-6 (-5) vibrational degrees of freedom.

For polymers in practice we have 3n-6 modes (n=number of atoms in repeat unit) instead of 3N-6 ☺

Good

news

Quick IR Analysis Algorithm

Infrared spectra: It is important to remember that the absence of an absorption band can often provide more information about the structure of a compound than the presence of a band. Be careful to avoid focusing on selected absorption bands and overlooking others. Use the examples linked to the table to see the profile and intensity of bands. Remember that the absence of a band may provide more information than the presence of an absorption band.Look for absorption bands in decreasing order of importance:1. the C-H absorption(s) between 3100 and 2850 cm-1. An absorption above 3000 cm-1 indicates C=C, either alkene or aromatic. Confirm the aromatic ring by finding peaks at 1600 and 1500 cm -1 and C-H out-of-plane bending to give substitution patterns below 900 cm-1. Confirm alkenes with an absorption at 1640-1680 cm-1. C-H absorption between 3000 and 2850 cm-1 is due to aliphatic hydrogens. 2. the carbonyl (C=O) absorption between 1690-1760cm-1; this strong band indicates either an aldehyde, ketone, carboxylic acid, ester, amide, anhydride or acyl halide. The an aldehyde may be confirmed with C-H absorption from 2840 to 2720 cm-1.3. the O-H or N-H absorption between 3200 and 3600 cm-1. This indicates either an alcohol, N-H containing amine or amide, or carboxylic acid. For -NH2 a doublet will be observed.4. the C-O absorption between 1080 and 1300 cm-1. These peaks are normally rounded like the O-H and N-H peak in 3. and are prominent. Carboxylic acids, esters, ethers, alcohols and anhydrides all containing this peak.5. the CC and CN triple bond absorptions at 2100-2260 cm-1 are small but exposed.6. a methyl group may be identified with C-H absorption at 1380 cm -1. This band is split into a doublet for isopropyl(gem-dimethyl) groups. 7. structure of aromatic compounds may also be confirmed from the pattern of the weak overtone and combination tone

bands found from 2000 to 1600 cm-1.

This is a little recipe from Stanislau State University (California).

Some Raman Advantages

Here are some reasons why someone would prefer to use Raman Spectroscopy.

• Non-destructive to samples (minimal sample prep)

• Higher temperature studies possible (don’t care about IR radiation)

• Easily examine low wavenumber region: 100 cm-1 readily achieved.

• Better microscopy; using visible light so can focus more tightly.

• Easy sample prep: water is an excellent solvent for Raman. Can probe sample through transparent containers (glass or plastic bag).

A Raman disadvantage - Fluorescence

Spectrum of anthracene. A: using Ar+ laser at 514.5 nm. B: using Nd:YAG laser at 1064 nm.

Want to use short wavelength because scattering depends on 4th power of frequency.

…BUT…

Want to use long wavelength to minimize chance of inducing fluorescence.

What is it good for?

• Composition

• Co-ordination

• Conformation

Endgroups - example

CH2 and CH3 stretching and bending modes in saturated hydrocarbons. With increasing chain length the absorption from CH2 groups increases. Introduction to Mol. Spect. Academic press 1970

.

Molecules in motion. A presentation created by Dr Alexander Brodin