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There’s a lot of free volume!

There’s a lot of free volume!. Density of carbon (as diamond) = 3 g/mL Density of 12 C nucleus = 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

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There’s a lot of free volume!

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

  2. Volume increases with temperature V T Wiggle Room: as important to polymers as to Hitler. Crystal of a small alkane “Segmental motion” – many C-atoms move together - ~50 in polyvinyls

  3. Of course, water is different! V V T Tm T Tm Transitions can be followed through thermodynamic state variables. 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.

  4. 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.

  5. Stopping polymers dead in their tracks • Amorphous Polymers • Polymers that just can’t crystallize, ever. • Polymers that could crystallize, • but weren’t given enough time • at right T. • 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)

  6. “Toughness” induced by SCBs (S. Chum) Red – traditional PE; blue - Elite Impact Strength, Izod method B Less crystalline, so less soluble. Also use some crosslinks to get high E. Modulus, MPa (E)

  7. From how high up? How long do we wait? How long do we wait? How steep? 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.

  8. Near Chamonix, France, is a flowing ice tunnel.

  9. Totally crystalline Totally glassy V V T Tm T Tg Semi-crystalline This zone makes ALL the difference! TOUGH ZONE V T Tg Tm Polymer Volume Transitions

  10. 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.

  11. Above Tg…. Completely amorphous polymer  Viscous fluid Frustrated, crystallizable polymer  let’s return to that later. Semicrystalline polymer  Tough solid Very crystalline  Often made into fiber.

  12. Practical Guide to Polymer Behavior From Rudin

  13. Free volume A molecular level view shows more local volume at temperatures exceeding Tg Greater local motion Restricted local motion V Tg T Brittle glass Melt, tough polymer or “other”

  14. V Tg T Tother Below Tg ……. 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 Example: Nylon is always used below its Tg, yet is not brittle

  15. Classifying Transitions Thermodynamically This isn’t a thermo class, but you must recall this golden oldie from PCHEM: dG = VdP - SdT +  i dni= Volume is related to a first derivative of G. So is entropy.

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

  17. 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

  18. S S Tm T Tg T Entropy trends parallel volume DH = T DS 1st order transition with “latent heat” At transition, you have to suddenly put in more heat. DH = 0 2nd order transition no latent heat. After transition, the rate at which heat must be supplied changes

  19. 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.

  20. i i Tm Tg T T Real transitions depend on rate of scanning, quality of thermal contact between sample & container, etc. 1st & 2nd Order DSC Transisions Differential heat: the extra heat it takes to get sample through transitions that the inert reference does not have. Sample -- Reference

  21. From Campbell H* = Tm Q dt Optimal mobility range – Tm – 10 to Tg + 30 (K)

  22. 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)

  23. 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

  24. 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. Other Tg Methods

  25. 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

  26. Tg (oC) -75 -20 -67 -6 -47 108 172 8 121 81 105 67 84 Some Typical Tg’s + Tm’s Tm (°C) 180 137-146 (PE) 176-200 (PP) 280 (PET) 265 (N6,6) 700-773 (Tg, PBI) Poly[2,2’-(m-phenylene)-5,5’-bibenzimidazole From Campbell

  27. Tg Trends Tg 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

  28. 1.4 < Tm/Tg < 2.0 FromBillmeyer

  29. Slow V Fast Tg Tg T T time Modern DSC’s (like ours!) use sophisticated temperature ramping sequences to sort out reversible (fast) from irreversible (slow) transitions. Caveats • A lot about this lecture is schematic; the real picture is more complex. • A lot depends on rate!

  30. It really, really matters! Challenger space shuttle. Feynmann: http://www.feynman.org/

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

  32. Tg behavior or plasticizers Rough 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!

  33. 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

  34. Effects of Additive on Tm • 3 types of additives – • Isomorphous – Additive doesn’t disrupt lattice. • One-crystallizable – shows min. • Plasticizer – amorphous additive 320 Two different blends of poly(amides) Tm, ºC 260 200 0 60 2

  35. 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 Break - b Stress  Necking Strain softening Strain =  - 1 = (L/L0) - 1

  36. 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:

  37. 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, 

  38. 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

  39. WLF Theory –”Universal??”

  40. For Polymer Liquids (Melts, Conc. Solutions) Slope = 3.4 – zero shear Log  High shear Slope = 1.7 Xw ~ 600 Log(Xw) 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.

  41. 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 t • to exit ~ Maxwellian time constant, • = /E Then, using Einstein eq.,  ~ L2/Dc Where L is the path length and Dc is a diffusivity along the path.

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