There’s a lot of free volume!

Density of carbon (as diamond) = 3 g/mL Density of 12 C nucleus =

mass volume

 12 6 .

02  10 23 4  3

R nucleus

3 R nucleus = [(protons + neutrons) 1/3 ][1.2  10 -13 cm] So…carbon could be compressed to about ~ 1  10 14 g/mL 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 V T “Segmental motion” – many C-atoms move together - ~50 in polyvinyls

V

Transitions can be followed through thermodynamic state variables.

Of course, water is different!

V T T T m T m 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.

Equilibrium is highly overrated!

• Slow-cooled SiO 2 • Fast-cooled SiO 2 = Quartz = 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 at right T. could crystallize, but weren’t given enough time Semicrystalline Polymers 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)

Impact Strength, Izod method B Red – traditional PE; blue - Elite Less crystalline, so less soluble.

Also use some crosslinks to get high E.

Modulus, MPa (E)

Do polymer glasses or crystals shatter?

Does it hurt to dive into water?

From how high up?

Do bookcases sag?

Do glaciers flow?

How long do we wait?

How long do we wait?

How steep?

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.

Near Chamonix, France, is a flowing ice tunnel.

V

Polymer Volume Transitions

Totally crystalline Totally glassy T m V V T Semi-crystalline T g T This zone makes ALL the difference!

TOUGH ZONE T g T m T

Remember! T

g

is for the down going transition, but we really care about the stuff above T

g

.

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 T

g

….

Completely amorphous polymer  Viscous fluid Frustrated, crystallizable polymer  let’s return to that later.

Semicrystalline polymer  Tough solid Very crystalline  Often made into fiber.

Practical Guide to Polymer Behavior From Rudin

A molecular level view shows more local volume at temperatures exceeding T

g V Restricted local motion Greater local motion Free volume Brittle glass T g T Melt, tough polymer or “other”

Below T

g …….

Polymer is certainly more brittle.

Polymer might not be completely brittle, because some 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 V T other T g T Example: Nylon is always used below its T g , yet is not brittle

Classifying Transitions Thermodynamically This isn’t a thermo class, but you must this golden oldie from PCHEM: recall

dG = VdP - SdT

+   i dn i = 

G



P



T

,

n i dP

  

V S

   

G



P



G



T T P G T P

,

n i dT

  

G



n j n i

,

T

,

P

So is entropy.

dn j

Volume is related to a first derivative of G .

V Melting Crystals vs. Librating Glass First order transition Second order transition V T m T dV dT T m T Discontinuity in volume, i.e., discontinuity in a 1 st derivative of G T g T dV dT T g T Discontinuity in derivative of volume, i.e., discontinuity in a 2 nd derivative of G

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 /

V

)( 

V



T

)

p V V

0  1   ( 

T

)

S

Entropy trends parallel volume

S T m T  H = T  S 1 st order transition with “latent heat” At transition, you have to suddenly put in more heat.

 H = 0 T g T 2 nd order transition no latent heat. After transition, the rate at which heat must be supplied changes

Differential Scanning Calorimetry

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

Or…we could keep track of current.

i

1

st

& 2

nd

Order DSC Transisions

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

i T m T T g T Real transitions depend on rate of scanning, quality of thermal contact between sample & container, etc.

 H* =  Tm Q dt From Campbell Optimal mobility range – T m – 10 to T g + 30 (K)

Rate of Cryst. Highly Nonlinear

• Avrami eq. - f c = 1 - exp(-k t n ) [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 (-CH 2 - -CHOH- -CF 2 -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, 15 1 = helical, 15 monomers per complete turn

Other T

g

Methods

• NMR T1, T2, 2 H etc.

• Dielectric spectroscopy • Viscoelastic methods, which can directly probe the entire mechanical spectrum as function of frequency. • All transitions have characteristic frequencies • T g  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

Some Typical T

g

’s + T

m

’s

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

T g ( o C) -75 -20 -67 -6 -47 108 172 8 121 81 105 67 84

Tm (°C) 180 137-146 (PE) 176-200 (PP) 280 (PET) 265 (N6,6) 700-773 (T g , PBI) From Campbell

T

g

Trends

T g  as stiffness  (rings, double bonds) T g  as steric bulk  (but not side chain length – e.g., PMMA (105), PEMA (65), PPMA (35 °C)) T g  as M  i.e., T g = T g ,  - (K/M n ) ; K ~ 8 x 10 4 - 4 x 10 5 With crosslinks: T g = T g,  - (K s /M n ) ; K s ~ 3.9 x 10 4 T g  as intermolecular forces  Useful thermo. correlation:  2 m = # DOF’s of a link ~ 0.5 m R T g - 25 m ,

1.4 < T m /T g < 2.0

From Billmeyer

Caveats

•A lot about this lecture is schematic; the real picture is more complex.

•A lot depends on rate! V Slow Fast T g T g T T time Modern DSC’s (like ours!) use sophisticated temperature ramping sequences to sort out reversible (fast) from irreversible (slow) transitions.

It really, really matters!

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

Plasticizers can change polymer bricks into polymer pillows by modifying T

g

.

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

T

g

behavior or plasticizers

Rough eq. – Tg -1 =  1 T g1 -1 +  2 T g2 -1 (Fox-Flory eq.) More exact – based on thermo. -

ln(T

g

/T

g1

) = [

 2

ln(T

g2

/T

g1

)] /[

 1

(T

g2

/T

g1

) +

 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 T g • Crystalline – closer to T m

Effects of Additive on T m • 3 types of additives – • Isomorphous – Additive doesn’t disrupt lattice.

• One-crystallizable – shows min.

• Plasticizer – amorphous additive 320 Two different blends of poly(amides) T m , ºC 260 200 0  2 60

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.

 y Stress  Necking Strain softening Break  b Strain =  - 1 = (L/L 0 ) - 1

PVT Behavior of Amorphous Polymers

• Rheo. Behavior – follows WLF theory.

Above Tg: V ~ V(T g ) + [d(V 0 + V f )/dT] (T – T g ) The dV 0 accounts for polymer, the dV f FV. Knowing that: for the  =  r  g = (1/V 0 ) (dV f /dT), we obtain:

Williams-Landel-Ferry (WLF) Eqs.

f = f g +  (T – T g )

; f = V

f

/V

0 Can subs. any ref. T 0 , f 0 to >Tg - 20 and it should still work. WLF proposed: ln(  /  0 ) = f -1 – f 0 -1 ; subs. previous eq. to get: log(  /  0 ) = -C 1 (T – T 0 ) / [C 2 + (T – T 0 )] Where: C 1 = (2.303 f 0 ) -1 and C 2 = (f 0 /  ).

dT g /dP ~ 0.16-0.43 K/MPa , so P  , 

WLF Theory (  /  0 ) called the “shift factor”, a T .

that: WLF postulated a T is universal for ANY mechanical or rheological property related to segmental motion (relax. times, moduli). a T ‘s use depends on type of property – up or down WRT T? The “shifting” described by a T is known as

time-T superposition

.

“Universal” WLF constants are:  0 = 10 12 Pa*s ; C 1 = 17.44; C 2 = 51.6 K

WLF Theory –”Universal??”

For Polymer Liquids (Melts, Conc. Solutions) Slope = 3.4 – zero shear Log  High shear Slope = 1.7

Log(X w ) X w ~ 600 The critical X w (X w ) c ~ 2 X e is where “critical entanglement” happens.

, where the entanglement chain length can be found from “overlap criterion” – where: (# coils/vol)*(vol/coil) = 1 in dilute solution.

Entangled Melts – Reptation Theory

Characteristic t to exit ~ Maxwellian time constant,  =  /E Then, using Einstein eq.,  ~ L 2 /D c Where L is the path length and Dc is a diffusivity along the path.

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