there’s a lot of free volume! density of carbon (as diamond) = 3 g/ml density of 12 c nucleus = r...

There’s a lot of free volume!Density of carbon (as diamond) = 3 g/mL

Density of 12C nucleus =

Rnucleus = [(protons + neutrons)1/3 ][1.2 10-13 cm]

So…carbon could be compressed to about ~ 1 1014 g/mL

3

23

34

1002.612

nucleusRvolume

mass

WOW! I guess those electrons do a great job of repelling each other to fill the volume.

Wiggle Room: as important to polymers as to Hitler.

Crystal of a small alkane

Volume increases with temperature

T

V

“Segmental motion” – many C-atoms move together - ~50 in polyvinyls

Transitions can be followed through thermodynamic

state variables.

T

V

Tm

Melting temperature implies a transition from left to right.We could just as well call it the freezing point

for the transition going from right to left.

T

V

Tm

Of course,water isdifferent!

Equilibrium is highly overrated!

• Slow-cooled SiO2 = Quartz• Fast-cooled SiO2 = window glass• You can also glass water! Just cool it really, really fast.

Practical application of water glass: Freeze-fracture TEM image of aqueous gel. Water in the gel is just “stopped” dead in its tracks without forming ice crystals that would distort the structure.

Stopping polymers dead in their tracks

Amorphous Polymers•Polymers that just can’t crystallize, ever.•Polymers that could crystallize, but weren’t given enough timeat right T.

SemicrystallinePolymers that partially crystallized, but contain amorphous regions.

E.G. – ethylene/octene copolymer – hexyl branch gives amorphous region, higher impact strength at given modulus (E). SCB -1

(e.g., Dow “Elite” PE)

“Toughness” induced by SCBs (S. Chum)

Red – traditional PE; blue - Elite

ImpactStrength,

Izod method B

Modulus, MPa (E)

Less crystalline, so less soluble.Also use some crosslinks to get high E.

Do polymer glasses or crystals shatter?

Does it hurt to dive into water?

Do bookcases sag?

Do glaciers flow?

In all cases, the answer is….it depends. Still, it is easy to identify water as a liquid.Wooden bookshelves and glaciers are clearly solid for most practical purposes.

From how high up?

How long do we wait?

How long do we wait?How steep?

Near Chamonix, France, is a flowing ice tunnel.

Polymer Volume Transitions

T

V

Tm

Totally crystalline

T

V

Tg

Totally glassy

T

V

TmTg

Semi-crystallineThis zone

makes ALLthe difference!TOUGH ZONE

Remember! Tg is for the down-going transition, but

we really care about the stuff above Tg.

That stuff can be melt or tough stuff, depending on crystallinity.

Even “melty”, non-crystallizable polymers can acquire toughness if covalent crosslinks substitute for

the crystalline zones.

Above Tg….

Completely amorphous polymer Viscous fluid

Semicrystalline polymer Tough solid

Very crystalline Often made into fiber.

Frustrated, crystallizable polymer let’s return to that later.

From Rudin

Practical Guide to Polymer Behavior

A molecular level view shows more local volume at

temperatures exceeding Tg

T

V

Tg

Restrictedlocal motion

Greater localmotion

Freevolume

Brittle glass Melt, tough polymeror “other”

Below Tg …….

Polymer is certainly more brittle.

Polymer might not be completely brittle, becausesome motions remain that permit the polymer to dissipate energy. These correspond to “other” transitions that may or may not produce much of a volume change. Transitions usually called a, b, g

T

V

TgTother

Example:Nylon is alwaysused below itsTg, yet is not brittle

Classifying Transitions Thermodynamically

This isn’t a thermo class, but you must recallthis golden oldie from PCHEM:

dG = VdP - SdT + i dni =

j

PTnjnPnT

dnn

GdT

T

GdP

P

G

iii ,,,,

P

T

T

GS

P

GV

Volume is related to a first derivative of G.

So is entropy.

Melting Crystals vs. Librating Glass

T

V

Tm T

V

Tg

Discontinuity in volume,i.e., discontinuity in a 1st derivative of G

T

dVdT Tm T

dVdT Tg

Discontinuity in derivativeof volume, i.e., discontinuity in a 2nd derivative of G

First order transition Second order transition

Measuring Volume Stinks!Remember that Work = -pdV

System would have to gain some energy, as heat, to perform that work.

It might be easier to measure heat instead.

Order of Magnitude of Transition - g ~ 0.5 r

)(1

))(/1(

0

TV

V

T

VV p

Entropy trends parallel volume

H = T S

1st order transitionwith “latent heat”At transition, you haveto suddenly put in moreheat.

T

S

Tm T

S

Tg

H = 0

2nd order transitionno latent heat. After transition, therate at which heat mustbe supplied changes

Differential Scanning Calorimetry

Suppose we keep track of RPM’s needed to maintain sample and inert reference at same temperature as both are heated….

Primitive Power Supplies

Thermometers

Sample Reference

Or…we could keep track of current.

1st & 2nd Order DSC Transisions

Sample --Reference

Differential heat:the extra heat it takes to get sample through transitions that the inert reference does not have.

T

i

Tm T

i

Tg

Real transitions depend on rate of scanning, qualityof thermal contact between sample & container, etc.

From Campbell Optimal mobility range – Tm – 10 to Tg + 30 (K)

H* = Tm Q dt

Rate of Cryst. Highly Nonlinear

• Avrami eq. - fc = 1 - exp(-k tn) [fraction]• N ~ 2-4. Why? Nucleation triggers rapid

growth at optimal conditions. Then it slows down as advancing fronts meet – diffusional limits.

• Secondary nucleation best – crystals beget crystals.

• Easy way to follow – measure - higher c

(e.g., 1.51 vs. 1.33 g/mL for PET)

Rate and Ultimate Amount of Cryst. Dependent on:

• Conformational regularity – iso, syndio etc.• Polarity, H-bonding (intermolec. forces)• Nucleation conditions• T and P (stress)• Cooling (heating) rate• Side groups – some (-CH2- -CHOH- -CF2-

-C(O)- ) always fit, some don’t

At submicros. level, structures usually either planar zigzag (PE, PVA, nylons) or helical (PP, PMMA, PTFE, poly(peptides))

Jargon – H, 151 = helical, 15 monomers per complete turn

Other Tg Methods• NMR T1, T2, 2H etc.• Dielectric

spectroscopy• Viscoelastic

methods, which can directly probe the entire mechanical spectrum as function of frequency.

• All transitions have characteristic frequencies

• Tg as frequency you really have to

chill something before it cannot slowly deform.

Why is “loss” high at Tg (visco., dielectric)

• T < Tg - rotation restricted, stress or potential stored by vibrational modes (“elastic”).

• T > Tg – stresses stored by uncoiling

• T ~ Tg = chains won’t uncoil, bonds inelastic

From Campbell

Tg (oC)

-75-20-67-6-471081728121811056784

Some Typical Tg’s + Tm’s

Tm (°C)

180137-146

(PE)

176-200 (PP)

280 (PET)265 (N6,6)

700-773 (Tg, PBI)

Poly[2,2’-(m-phenylene)-5,5’-bibenzimidazole

Tg TrendsTg as stiffness (rings, double bonds)

Tg as steric bulk (but not side chain length – e.g., PMMA (105), PEMA (65), PPMA (35 °C))

Tg as M

i.e., Tg = Tg, - (K/Mn) ; K ~ 8 x 104 - 4 x 105

With crosslinks: Tg = Tg, - (Ks/Mn) ; Ks ~ 3.9 x 104

Tg as intermolecular forces

Useful thermo. correlation: 2 ~ 0.5 m R Tg - 25 m ,m = # DOF’s of a link

From Billmeyer

1.4 < Tm/Tg < 2.0

Caveats•A lot about this lecture is schematic; the real picture is more complex.•A lot depends on rate!

T

V

Tg Tg

Slow

Fast

Modern DSC’s (like ours!) use sophisticated temperature ramping sequences to sort out reversible (fast) fromirreversible (slow) transitions.

T

time

It really, really matters!

Challenger space shuttle. Feynmann: http://www.feynman.org/

Plasticizers can change polymer bricks into polymer pillows by modifying Tg.

O

O

O

O

Di-sec-octylphthalate (DOP)Other uses: lubricant for textiles rocket propellant insect repellant perfume solvent nail polish to prevent chipping

http://www.chemicalland21.com/industrialchem/plasticizer/DOP.htm

Tg behavior or plasticizersRough eq. –Tg-1 = 1 Tg1

-1 + 2Tg2-1

(Fox-Flory eq.)

More exact – based on thermo. -

ln(Tg/Tg1) =

[2 ln(Tg2/Tg1)] /[1 (Tg2/Tg1) + 2 ]

- Works for copolymers too!

Heat Deflection T (HDT)

• Widely reported

• T at which sample bar deflects by 0.25 mm under center load of 455 kPa, at 2 K/min ramp.

• Amorphous – 10-20 K less than Tg

• Crystalline – closer to Tm

Effects of Additive on Tm

• 3 types of additives – • Isomorphous – Additive doesn’t disrupt

lattice.• One-crystallizable – shows min.• Plasticizer – amorphous additive

0 60

Tm, ºC

200

320

260

Two different blends of poly(amides)

2

Mechanical Behavior of Crystalline Polymers

• For already crystallized polymer – many polymers go amorphous cryst. on drawing.

• Lamellae distort to “shish-kebabs” – slip, tilt, twist to fibrils. Annealing helps.

Strain = - 1 = (L/L0) - 1

Stress

y

NeckingBreak - b

Strain softening

PVT Behavior of Amorphous Polymers

• Rheo. Behavior – follows WLF theory.

Above Tg:

V ~ V(Tg) + [d(V0 + Vf)/dT] (T – Tg)

The dV0 accounts for polymer, the dVf for the FV. Knowing that:

= r - g = (1/V0) (dVf/dT), we obtain:

Williams-Landel-Ferry (WLF) Eqs.

f = fg + (T – Tg) ; f = Vf/V0

Can subs. any ref. T0, f0 to >Tg - 20 and it should still work. WLF proposed:

ln(/0) = f-1 – f0-1 ; subs. previous eq. to

get:

log(/0) = -C1(T – T0) / [C2 + (T – T0)] Where: C1 = (2.303 f0)-1 and C2 = (f0/).

dTg/dP ~ 0.16-0.43 K/MPa , so P,

WLF Theory

(/0) called the “shift factor”, aT. WLF postulated

that:aT is universal for ANY mechanical or

rheological property related to segmental motion (relax. times, moduli).

aT ‘s use depends on type of property – up or down WRT T? The “shifting” described by aT is known as time-T superposition.

“Universal” WLF constants are:0 = 1012 Pa*s ; C1 = 17.44; C2 = 51.6 K

WLF Theory –”Universal??”

For Polymer Liquids (Melts, Conc. Solutions)

Log(Xw)

Log

Slope = 1.7

Slope = 3.4 – zero shear

Xw ~ 600

The critical Xw is where “critical entanglement” happens.(Xw)c ~ 2 Xe , where the entanglement chain length can be

found from “overlap criterion” – where:(# coils/vol)*(vol/coil) = 1 in dilute solution.

High shear

Entangled Melts – Reptation Theory

Constraints imposed by nearby chains – path is the “primitive path”; constraint surface is the “tube”. Leave tube -- you’re free (like a corn maze).

Characteristic tto exit ~ Maxwellian time constant,

= /EThen, using Einstein eq.,

~ L2/Dc

Where L is the path length and Dc is a diffusivity along the path.