Relaxation in Glass. Transition

Transcription

1 Relaxaion in Glass Lecure 2: he Glass ransiion as a Kineic Lecure 2: he Glass ransiion as a Kineic ransiion

2 Enhalpy Changes in he Glass ransiion Range H decreases coninuously wih cooling Slope of he H curve is he hea capaciy which changes from liquid-like o solid-like values in he ransiion region Change in hea capaciy a he glass ransiion Cpg measures he differences beween he liquid and solid glassy Cp values Sub-g annealing and relaxaion can occur if liquid is given sufficien ime o relax o lower enhalpy sae Mola ar enhal lpy glass fas Cp glass slow crysal supercooled liquid emperaure liquid Cp liquid H meling Cp crysal swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 2

3 Enropy Changes in he Glass ransiion Range supercooled liquid lar enro opy glass fas S meling Cp liquid / liquid Mo slow crysal Cp crysal / emperaure m swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 3

4 Gibb s Free-Energy Changes in he Glass ransiion Range G = H - S Gibbs Free-Energy change a m is coninuous, here is no Laen Free-Energy Change as is he case for he enhalpy and enropy A he meling poin G liquid = G crysal Below he meling poin G liquid > G crysal and G crysallizaion < O Above he meling gpoin Gibb b s Free-E Energy Liquid Crysal G liquid > G crsyal G meling < O G A any poin P S emperaure m swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 4

5 Gibb s Free-Energy Changes in he Glass ransiion Range Glasses hen fall off he liquid line a progressively lower emperaures he slower he cooling rae Gibbs Free-Energy of he glass behaves more like he crysal han he liquid Glass ransiion range is he range of where he Gibb s Free-Energy changes from liquid-like values o solid-like values ergy Gibb s Free-En Liquid Glasses Crysal emperaure m swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 5

6 Fundamenals of he Glass ransiion he Glass ransiion is a Kineic ransiion Coninuous changes in srucure and properies Srucure and properies are coninuous wih emperaure Srucures and properies can be changed coninuously by changing he kineics of he cooled or reheaed liquid swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 6

7 ime and emperaure Dependence of Properies A high emperaures, he liquid can reach equilibrium afer sep, relaxaion ime is shor compared o ime allowed Prope ery P or H << liquid ~ Sample Enhalpy hea conen of sample or Propery volume of sample A low emperaures, he liquid canno reach equilibrium afer sep sep, is long compared o ime allowed Average cooling rae, = / ime >> glass swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 7

8 emperaure dependence of he inernal ime scale While he exernal ime scale, mos ofen does no change, / he inernal imescale can be srongly emperaure dependen, E ac Rearrangemen of he liquid requires breaking of bonds beween aoms ions his requires hermal energy he relaive magniude of he energy barrier o moion, E ac o he available hermal energy, k deermines he probabiliy of geing over he energy barrier E o k ac Arrhenius emperaure dependence of he relaxaion ime swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 8

9 emperaure dependence of he inernal relaxaion ime For E ac > / E E k ac I is a hermal probabiliy of moion High, k ~ E ac, high probabiliy of moion Low, k << E ac low probabiliy of moion au/ /au.e+2.e+8 8.E+6.E+4.E+2 E+.E+.E+8.E+6.E+4.E+2.E+ o E k ac emperaure dependence of au K swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 9

10 emperaure dependence of he inernal relaxaion ime For E ac > Eac log o 2. 33k I is a hermal probabiliy of.e+2 moion.e+8 High, k ~ E ac, high probabiliy of moion Low, k << E ac low probabiliy bili of moion au/au u.e+6.e+4 E+2.E+2.E+.E+8.E+6.E+4.E+2.E+ Arrhenius emperaure dependence of au /K swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion

11 Glass ransiion is a Kineic ransiion Glass formaion is a kineic ransiion, herefore, i depends upon he kineics of he process he inernal imescale,, for he process is conrolled by he aomic or ionic bonding beween aoms or ions Srong and numerous bonding increases he viscosiy Weak and limied bonding decreases he viscosiy iscosiy relaxaion ime, = G he exernal imescale,, is conrolled by he erimen or process, i.e., how fas is he liquid cooled Is i purposefully quenched very fas? is shor Is i jus allowed o cool naurally under prevailing condiions? Or is i insulaed and allowed o cool very slowly, is long swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion

12 Glass ransiion is a Kineic ransiion Assume ha he relaxaion following a emperaure jump is also onenial Noe ha ~ 5 relaxaion ime are required for nearly complee relaxaion ~. ~ % Noe ha 99% of change has occurred Now consider E ac ~ 5, J/mol, ~ -3 sec au/au.e+2.e+8 8.E+6.E+4.E+2.E+.E+8 8.E+6.E+4.E+2 Arrhenius emperaure dependence of au 5.E /K swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 2

13 Glass ransiion is a Kineic ransiion Now consider an example: Consider saring a a emperaure, above m where he viscosiy is low and he relaxaion ime is shor compared o an erimenal ime sep following a emperaure sep :,, Now, for he second sep suppose he relaxaion ime is sill shor compared o an erimenal ime sep following a emperaure sep : Mol lar olum me, 2..., n n supercooled liquid glass liquid liquid fusion crysal crysal emperaure swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 3

14 Glass ransiion is a Kineic ransiion Now consider he case where he exen of relaxaion depends upon he ime i akes for relaxaion o occur: he amoun of relaxaion: Mo olar olu ume supercooled liquid glass liquid liquidid fusion crysal crysal - -/ = complee emperaure change - -/ =, no change swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 4

15 Glass ransiion is a Kineic ransiion Relaxaion, herefore depends upon he and relaionship:,, he original volume he insananeous volume change due o change o h f l i f i ih l i i he exen of relaxaion afer ime sep a wih relaxaion ime swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 5

16 emperaure and ime Dependen olume Afer wo ime seps,,,,,, ,2 2 swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion

17 Exercises.. = second = -3 seconds E ac = 5, cal/mole 3K? Fully relaxed 8K? no relaxed 6K? For E ac = 5, cal/mole 3K? No relaxed For E ac = 5, cal/mole K? Relaxed E Eac o R R.987 cal / mole K swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 7

18 Exercises.. Now consider he elasic volume change ake ~ 35 ml/mol l ake liquid ~ 4 ppm/k ake =K Sar a 2 K Wha is a 7K? Wha is a 8K? Wha is a 8K? Wha is ~ g? Wha is a 7K?, n n swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 8

19 Exercises Now add relaxaion componen ake ~ 35 ml/mol ake liquid ~ 4 ppm/k ake = K ake = second Sar a 2 K Wha is a 99K, second? Wha is a 98K, 2 seconds? Wha abou a 7K? Wha abou K? Eac o R R.987cal / mole K, swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 9

20 he Glass ransiion from Arrhenius dependence of au and onenial relaxaion olume vs. emperaure ml/mol o C/sec - o C/sec - o C/sec 3 -"" o C/sec au = x -3 secs 5,cal/mol/R cal/mol/r emperaure K swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 2

21 Homework Reconsruc Glass ransiion cooling behavior using - C/second cooling rae, Arrhenius emperaure dependence of relaxaion ime and onenial relaxaion funcion. Exra Credi Reconsruc faser C/sec and slower cool C/sec cooling raes Exra Exra Credi Consruc reheaing curve for - C/second cooling curve a a rehea rae of + C/second Exra Exra Exra Credi, Consruc reheaing curve for - and - C/second cooling curves a a rehea rae of + C/second swmarin@iasae.edu Lecure 2: hermodynamics of he Glass ransiion 2