Energy Storage Materials and Devices Lecture

Energy Storage Materials and Devices

1. SEE902 – Energy Storage Materials and Devices Week 3, Lecture 5: Battery Parameters Dr. Sudarshan Narayanan Assistant Professor Dept. of Sustainable Energy Engg ., IIT Kanpur

2. Maximum Theoretical Specific Energy Coulombic Efficiency Current rate (C-rate) Discharge capacity Types of Discharge curves Example – Li/I 2 electrochemical system Discharge processes in complex electrode systems Contents

3. PARAMETERS IN BATTERY OPERATION

4. Maximum Theoretical Specific Energy T he e n ergy c o n tained i n a n e l ectr o ch e m i c al s y stem i s t he i n te g r al o f the vo l ta g e mu l t i p l i ed b y t h e ch a rge capac i t y , i . e ., the a mo u nt o f ch a rge av a i l a b l e . It is impo r tant to note that E v aries w ith the state of charge w hich is def i ned as the fract i on of the maximum capa c ity that is still available to be supp l ied. Energy   Edq Let us try to cal c ulate the MTSE in the fol l o w ing insertion reaction. x A  R  A x R Amount of charge (C ) :   MTSE: Wh e re W is t h e sum of the mo le c u l a r w e i g h ts o f the re a cta n ts e n g a g e d in the re a ction  

5. Coulombic Efficiency B a t t er i es a re d e si g n e d such t h a t the % cap a city l o ss p e r c y cle is e x treme l y l o w . In sev e ral a p pl ic a tio n s a b a t t e r y i s e x p ected to mai n t a in i ts ma j or properties ov e r ma n y d i sch a rge - ch a rge c y cl e s. C olu m bic E f ficien c y : F or any battery it is the ratio of cha r ge output to cha r ge inp u t , i.e. D ischarge capacit y / c ha r ge capaci t y . C apacity degradati o n for three differe n t values of C olu m bic efficie n ci e s If the loss in capa c ity is 0.5%, i.e., the Columbic e f ficiency is 0.995, the percentage of capa c ity loss after 50 c y cles is 22% of the orig i nal capa c ity w hich is too large.    

6. Current Rate (C-rate) A parameter that is o f ten used to i n d i cate the ra t e at w h i ch a bat t ery is d i scharged is t he s o -ca l l e d C -R a te. If the b a t t ery is sa i d to be d i sch a rg e d at C / n rat e , it me a ns the curre n t m agn it ud e is s u ch t ha t it w i l l take n hou rs to c o m p l e te l y d is cha r g e its n o mi n al ca p ac i ty If a c e ll h a s a n o mi n al ca p ac i ty of 5 Ah a n d if it is d i sch a rg e d at C/10 a n d C/5 c u rre n t rat e s, th e n w h a t is the actu a l va l ue of the curr e nt? C u rre n t V a l ue C/10 rate C/5 rate 0.5 A T he re a son for re p res e nti n g the ca p ac i ty in terms of Ah inst e ad of C o u l om b s is b e ca u se Ah in d ic a tes w h a t curr e nt rate sh o u l d be us e d to d i sch a rge the b a t t ery in 1 h. 1 A

7. Discharge Capacity The disc h arge c a pa c ity of a bat t ery depends on several factors. Two important ones are C-rate: C discharge de c rea s es w ith the increa s e in C -rate or the rate of drawing c h arge. Temperature: C discharge in c rea s es w ith the increa s e in temperature. Area under the discharge curve rep r esents the energy w hich a l so de c reases w ith the increase i n C- r a te, or decrease in temperature D i sch a rge C u rves C-rate dependence Temperature dependence

8. Types of Discharge Curves C e ll vo l ta g e is d e p e n d e n t on t he ch a rge sta g e or the e x te n t of re a ction Some of the discharge curves are essent i ally flat, others ha v e more than one flat r e gion, and still othe r s have a slanted and str e tched S - shape, at times w ith an appreciable slope. W hy do w e not i ce d i f ferent t y pes of di s cha r ge curves? It is important to understand the orig i n of the s e discharge curves

9. Example: Li/I 2 Electrochemical Cell L e t us try to e x ami n e the Li/ I 2 ce l l (use d in car d i a c p a cem a ker) a n d pr e d i ct its disc h ar g e curve (- ) Li / LiI / I 2 - P2VP (+) Met a l l ic Li is a n e g a tive e l ectr o de or a n o de I 2 + 1 0% Pol y - 2 -vin y lp y ridine (P2 V P) is a p o sitive e l ectr o de or c a th o de C h em i cal re a ction b e t w e e n the Li a nd I 2 form a sol i d L i I e l ectr o l y te Cell voltage w ill depend on the thermod y nam i cs of this chem i cal r x n.  G r   G f ( L iI ) M icrostructure E v olution of Li/ I 2 Cell   t i me Li di f fus e s through the solid Li I and reacts w ith I 2 at the Li I/I 2 interfa c e P2V P is added to render electronic condu c tivity in I 2

10. Example: Li/I 2 Electrochemical Cell Pred i ction of C e l l V o l tage in L i / I 2 C e ll T he e x p e rime n tally d et e rmin e d d i schar g e curve o f L i / I 2 ce l l sh o w s a p l at e a u a t 2 .8 V ∆ G f ( L i I ) = -2 6 9. 6 7 kJ / mol z i = +1; F = 9650 C / m o l  E  2. 7 9 5 V   The resi s tan c e is a ls o found to in c rea s e w hi c h c an be attributed to the in c rea s e in the thi ck ne s s of LiI electrol y te. This value is close to the experimentally found voltage t i me  G r   G f ( L i I )

11. Example: Li/I 2 Electrochemical Cell MTSE of Li/I 2 cell Le t u s try to estim a te the M T SE o f L i / I 2 ce l l Given, E = 2 .7 9 5 V T otal Ch a rge = 1 × 9 6 5 C W e i g h t of L iI = 6 .94 + 126 .9 = 133 .84 g T emperature Dep e nd e nce of C e ll V o l tage  G r   H r  T  S r N o w , At 2 5 o C S ( L iI )  85.7 7 J / K / m ol S ( L i )  29.0 8 J / K / m ol S ( I 2 )  116.1 4 J / K / m ol           Cell voltage varies slight l y in Li/I 2 cell.

12. Example: Li/I 2 Electrochemical Cell L e t us a ssume a h y p o th e tical case in w h i ch some I 2 d i sso l ve in Li el e ctro d e Now app l y ing Gibb ’ s pha s e ru l e , In this case, C = 2 and P = 1. T aking into a c count T and P , value of F = 1   T he electri c al potential of the lithiu m – iodine alloy is not fi x ed, but v aries, depending on other para m et e r s , such as the a m ount of iodine in the Li – I solid solution. Please note that this is a h y pothetical case in w hich it is assu m ed that iodine di f fuse s into the Li.

13. Example: Li/I 2 Electrochemical Cell T he p o sitive e l ectr o de ha s o n ly on e active com p o n e n t (e l em e nt), i o d i n e , w h i ch i s a n e l ectr o ch e mic a l l y active p h as e . T h u s , b o th C an d P h a ve va l u e s o f 1 . (- )Li / LiI / I 2 - P2VP(+) As a re s u l t, F = 0, if T and P are fi x ed. All the other inten siv e v ar i ables are f i xed and are independent of the s tate of c harge for the po sitiv e ele c trode ( I 2 ). Sin c e the c e l l v o l tage i s def i ned as the d i f feren c e in the potential of po sit i v e and negat i v e e l e c tro d e s, its v a l ue rema i ns independent of the s tate of c harge for L i / I 2 cell. T his e x planation m atches w ell w ith the discharge cur v e obser v e e x peri m entall y .

14. Discharge Process in Complex Electrode Materials A number of m a t eria l s are used as e l ec t rodes i n e l ec t roche m i c al ce l ls i n w h i ch mo r e t han on e re a c t ion occu r s i n sequenc e as t he ove r all discharge pr o cess occu r s S ome mat e r i als e x hi b it a ser i es of mult i -phase r e actions in w hi c h the r e sultant degr e es of f r eedom i s S ome mat e r i als under g o sequential r e actions w hi c h a re not simi l a r . In the Li-Ti-O system, a solid-solution of Spinel phase is formed followed by two-phase region and then Rocksalt phase. A discharge curve with a set of constant voltages plateau.

15. Discharge Process in Complex Electrode Materials Reconstitu t ion reac t ion t akes p l ace w hen mo r e t han 1 Li is added w h i ch result s in t w o phases contain i ng d i f f erent amoun t s of L i . The relat i ve amount of pha s es changes as the guest species (here, Li) is introduced into the host material. T he pha s e conta i ning high c on c entration of Li increases at the e x pen s e of pha s e w ith low Li amount. T h is oc c u r s th r ough mov i ng interface recon s titution reaction. Mo v ing Inter f ace R ea c tion It is important to note that the compositions of these two phases does not change but their relative amount changes. As a result, plateau in the potential is observed.

16. Bard, Allen J., and Larry R. Faulkner.  Electrochemical Methods: Fundamentals and Applications . 2nd ed. Wiley, 2000. ISBN: 9780471043720. Huggins, Robert A.  Energy Storage: Fundamentals, Materials and Applications. 2 nd ed. Springer, 2016. ISBN: 9783319212388. Reddy, Thomas B. Handbook of Batteries . Fourth ed. McGraw-Hill, 2011. Further Readings

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