Heating Rate Effects Large sample size Tm > Tm 400 Extended Chains Dendrites 395 Single Crystals 1 10 100 1,000 Heating Rate ( K / min )
Single crystals melting pint increases as heating rate decreases at lw heating rates there is a lnger time fr the crystal t anneal. Extended chain crystals 'superheating' heat supplied faster than the crystal can melt and rerganize t a randm cil. Dendrites are suppsedly s defective they can rerganize r anneal faster than single crystals; they therefre melt at higher temperatures.
Small sample size single crystals T 1 2 3 40 20 5 Peak psitin independent f heating rate, but peak size changes. Third peak frm melting f annealed r rerganized plymer. Ts
Tm 400 3 395 2 1 1 10 100 1,000 Heating Rate ( K / min )
CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 CH 2 H H C C H H
110 200 TEM Crystals grwn at different temperatures have different thicknesses and therefre melting pints. They als have different sectr area ratis (SAR) as measured using TEM. Different sectrs crrespnd t different directins f flding in the crystal; different fld planes.
Determine the rati f the first tw peaks in DTA r DSC fr these crystals. Curve reslve t separate. Tc = 80 c Tc = 90 c 1 DTA 3 2 3 1 2 Nte:- there s less annealing fr crystals grwn at higher temperatures; third peak smaller.
Cmpare SAR by TEM t ratis f the first tw peaks by DSC/DTA. Excellent 1:1 crrelatin TEM als shws preferential melting f 200 sectr. 4 TEM Sectr Area Rati (110:200) The first tw peaks in DSC/DTA are due t melting f 110 and 200 sectrs in the crystal. Differences in melting pint arise frm different surface energies. 2 Surface energy differences frm different fld structures in 110 and 200 directins. 2 DTA Peak rati (2:1) 4
Mdeling Melting in Plymer Crystals Wt. Input Average crystal cre thickness fr lamellae. Sme measure f thickness distributin. Wt. Thickness Tm Temperature Use Hffman Weeks t calculate Tm fr each δ (thickness). Expected melting curve fr given distributin f crystal thicknesses, assuming n rerganizatin.
Tw pssible frms f Rerganizatin:- Annealing Crystals thicken n heating up t Tm which leads t melting pint changes. Recrystallizatin Melting at Tm prduces a melt belw Tm, which may then recrystallize (the melt is belw Tm ) and finally remelt. Assume recrystallizatin nly takes place; (there's mre data in the literature t predict expected changes in thickness and Tm).
Fr each riginal element that melts we ask :- Hw much melted? Des previusly melted material recrystallize? Did any recrystallize? What is the new Tm fr recrystallized plymer? Melting elements frm the riginal curve will nt crystallize until later, at a higher temperature. Equatin fr Tm f recrystallized plymer:- Tm(recryst) = (Tm [2β -1] + Tc)/2β (β 1 fr PE)
Percent Crystallinity by DSC Assume :- Tw phase system in a stress free state. Heat capacity (Cp) f amrphus can be extraplated frm the melt. Amrphus and crystalline Cp's are additive. By definitin Ø = Hf / Hf Ø = fractinal crystallinity Hf = Measured heat f fusin f my sample. Hf = Heat f fusin f 100% cryst. plymer. Need t measure Hf f the sample and determine Hf f pure 100% crystalline plymer.
Measuring Hf fr the sample Calibrate the DSC using a knwn weight f a material with a knwn heat f fusin. Measure area under the melting curve and find the cnversin factr fr area > heat f fusin. Run a knwn weight f sample and cnvert area t heat f fusin using the previusly determined cnversin factr.
Prblems Defining the apprpriate area fr the melting sample. A prblem f defining the baseline. H = Ø.Hc + (1 - Ø).Ha + dø/dt. Hf Cp Befre melting n change in Ø. After melting n change in Ø. Cnnect pre and pst melting baselines. Indium Plymer All this assumes:- instrument is well calibrated; n curvature in instrument baseline withut sample in the unit. Temperature r Time
Determinatin f Hf fr 100% crystalline plymer Measure Hf fr a number f samples prepared under different cnditins and having different measured crystallinities by (fr example) density. Extraplate t 100% crystalline. The abve samples als prbably have different crystal thicknesses (L); extraplate measured Hf vs. (1/L) t infinite thickness crystal. Measure Hf vs. heating rates fr the same material. Extraplate t infinitely slw heating rate. Sample anneals t infinitely thick crystals!!
Determinatin f Hf fr 100% crystalline plymer Use mdel cmpunds in fully extended chain crystal frm. Fr example fr PE we culd use a series f paraffin's f varius mlecular weights; extraplate t infinite mlecular weight. Make extended chain crystals by high pressure crystallizatin; measure melting pint. Many plymer have been reprted Lk it up!! Fr cplymers use the hmplymer Hf!!
Thermdynamics f Melting HEAT The abve cartn shws what happens t the chain in a crystal n melting; we can split the melting prcess int tw cmpnents; belw:- ( Hf ) ( S)
Ignre the flds they are already amrphus; Pull ff a stem frm the crystal H term Allw this stem length t disrder S term. Given G = H - T. S at T = Tm ; G = 0 therefre Tm = Hf / Sf Mlecular parameters that increase Hf will tend t increase Tm. Parameters that increase Sf (chain disrdering) will tend t decrease Tm.
Effects f structural parameters n Tm (regular hmplymers) Structure Tm PE CH 2 CH 2 140 Standard State PEO CH 2 CH 2 O 66 O linkage flexible; S PE,PØ CH 2 CH 2 (Ø) 380 Ring hinders flexibility; S PTFE CF 2 CF 2 327 F bulkier than H; S Ply Amides Ply Urethanes Ply Urea O -C-N-(-CH 2 -)- 6 H O -O-C-N-(-CH 2 -)- 6 H O -N-C-N-(-CH 2 -)- 6 H H 225 165 300 H-bnding; H Added -O- fr flexibility; S Mre H bnds; H
Effects f Side Chain Substituents n Tm Cnsider the mnmer CH 2 =CHX; where X is:- Tm CH 3 165 CH2-CH3 125 Increasing side chain length leads t lser CH 2 -CH 2 -CH 3 75 crystal structure. H CH 2 -CH 2 -CH 2 -CH 3-55 CH2-CH-CH2-CH3 CH 3 CH 3 CH 2 -C-CH 2 -CH 3 CH3 196 Increasing side chain 350 bulk hinders chain mbility in the liquid state. S
Finding Tm free f the effects f annealing r superheating As fr Hf, extraplate Tm versus: lng perid t infinite lng perid; percentage crystallinity t 100% crystallinity; heating rate t infinitely slw rate; mdel cmpund mlecular wt. t infinite ml. wt. extended chain crystals by high pressure.
Finding Tm free f the effects f annealing r superheating Plt experimental Tm versus experimental Tc and extraplate t the line Tm = Tc. Tm The line whse equatin is Tm = Tc. x x x x Tc The ne pint (Tm ) where experimental data fit the equatin; namely Tm = Tc = Tm If crystals culd be grwn at Tc = Tm (crystallize fr infinite time) they wuld als melt at Tm. Infinitely large crystals and plymer melt are in equilibrium at Tm.