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2021-06-01

深度解讀鋰離子電池的電壓

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電(dian)壓是(shi)(shi)鋰離(li)子電(dian)池的重(zhong)要(yao)參數,直接決(jue)定電(dian)池的能(neng)量(liang),以(yi)及(ji)電(dian)池包(bao)的成組(zu)方式。本文對鋰離(li)子電(dian)池的電(dian)壓進(jin)行總結,這也是(shi)(shi)本人知識(shi)梳理與學習的過程(cheng),理解不對之處請大家批(pi)評指正(zheng)。


 


鋰(li)離子電(dian)池在充放電(dian)測試或者實際使用(yong)中,電(dian)壓(ya)(ya)(ya)參數主要包括(kuo)平臺電(dian)壓(ya)(ya)(ya)、中值(zhi)電(dian)壓(ya)(ya)(ya)、平均電(dian)壓(ya)(ya)(ya)、截(jie)止電(dian)壓(ya)(ya)(ya)等,典型放電(dian)曲線如圖(tu)1所(suo)示。


 


平臺電壓(ya)是指電(dian)(dian)壓變(bian)化(hua)*小而容(rong)量(liang)變(bian)化(hua)較大時對(dui)應的電(dian)(dian)壓值,磷(lin)酸鐵鋰(li)、鈦酸鋰(li)電(dian)(dian)池具有明顯(xian)的平臺電(dian)(dian)壓,在充(chong)放電(dian)(dian)曲(qu)線中可(ke)以明確確認電(dian)(dian)壓平臺。大部(bu)分電(dian)(dian)池的電(dian)(dian)壓平臺并不明顯(xian),充(chong)放電(dian)(dian)測試時,通過電(dian)(dian)壓間隔采(cai)集數據,然后對(dui)電(dian)(dian)壓曲(qu)線做微分,通過dQ/dV的峰值確定(ding)平臺(tai)電壓。


 


中值(zhi)電(dian)壓是電池容量一半時對應的(de)電壓(ya)值,對于平臺比較明顯的(de)材料,如(ru)磷(lin)酸鐵鋰和鈦酸鋰等,中值電壓(ya)一般就是平臺電壓(ya)。


 


平均電壓是電(dian)壓-容量曲線的有效面積(即電池充/放電(dian)能量)除(chu)以容量,計算公式為ü = ∫U(t)*I(t)dt / ∫I(t)dt。在充(chong)(chong)放電(dian)(dian)測試數據中(zhong),充(chong)(chong)電(dian)(dian)或放電(dian)(dian)能量除以容(rong)量數據即為平均電(dian)(dian)壓。反過來(lai),電(dian)(dian)池(chi)能量密度也(ye)是根據電(dian)(dian)池(chi)的平均電(dian)(dian)壓估算,即能量=容量*平均電壓/電池(chi)質量(liang)(或體(ti)積(ji))。


 


截止電壓是是指電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)時允許的(de)*低(di)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya),電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)時允許的(de)*高電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)。如(ru)果電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)低(di)于放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截(jie)(jie)止電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)后繼續(xu)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian),電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)正極的(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)持(chi)續(xu)降(jiang)低(di),而負極電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)會迅速(su)上升,形成過度(du)(du)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian),過放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)可能造成電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)極活(huo)性物質(zhi)損傷,失去反應能力(li),使電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)壽命(ming)縮短(duan);還(huan)會導致負極銅箔分解并在(zai)正極析(xi)出,存(cun)在(zai)短(duan)路風險。如(ru)果充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)高于充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截(jie)(jie)止電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya),電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)正極的(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)持(chi)續(xu)升高,造成正極材料過過度(du)(du)脫(tuo)鋰(li),晶體結(jie)構破壞(huai)失效,電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)解液分解損耗鋰(li)離子。而負極電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)會持(chi)續(xu)下降(jiang),過度(du)(du)嵌鋰(li),石墨層狀瓦解,極片表面析(xi)鋰(li)等問題(ti)。

而實際上,電池的電壓U(電池)是由正極的電極電勢E(正極)和負極的電極電勢E(負極)之差確定的,由公式(1)所表示:


U(電(dian)池) = E(正(zheng)極) - E(負(fu)極(ji))         (1)

在電(dian)(dian)池體(ti)系中,標(biao)準鋰電(dian)(dian)極(ji)普遍作為(wei)參考電(dian)(dian)極(ji),正、負極(ji)材料(liao)的(de)電(dian)(dian)極(ji)電(dian)(dian)勢一般都是反應(ying)物和(he)產物與參比(bi)鋰電(dian)(dian)極(ji)之間反應(ying)而產生(sheng)的(de)電(dian)(dian)勢。如(ru)圖2所示,在充放電過程中(zhong),正負極材料脫鋰或嵌鋰,電極電勢(shi)發生變化,電池電壓就是兩者之差。

因(yin)此,認識電(dian)池(chi)的(de)(de)電(dian)壓,首先要了解(jie)各種電(dian)極材(cai)料的(de)(de)電(dian)極電(dian)勢,了解(jie)材(cai)料的(de)(de)平衡電(dian)極電(dian)勢曲線能夠更好理解(jie)電(dian)池(chi)的(de)(de)電(dian)壓特性。


 


開(kai)路(lu)電(dian)(dian)(dian)壓(ya)是指電(dian)(dian)(dian)池在非工作(zuo)狀(zhuang)態(tai)下即電(dian)(dian)(dian)路(lu)中無電(dian)(dian)(dian)流流過時,電(dian)(dian)(dian)池正負極之間的電(dian)(dian)(dian)勢(shi)差。將電(dian)(dian)(dian)極材(cai)(cai)料與金屬(shu)鋰(li)組(zu)裝成紐扣半(ban)電(dian)(dian)(dian)池,開(kai)路(lu)電(dian)(dian)(dian)壓(ya)即電(dian)(dian)(dian)極材(cai)(cai)料的平衡電(dian)(dian)(dian)勢(shi)。


 


開路電壓測試方法(fa)


 


電極(ji)材料(liao)的平衡電勢測(ce)試過程為:電極(ji)材料(liao)制(zhi)備(bei)成極(ji)片,與金屬鋰組裝成紐扣半(ban)電池,測(ce)得紐扣半(ban)電池在不同的SOC狀態下的(de)開(kai)路電壓(ya),并(bing)采(cai)用多項(xiang)式或高斯擬(ni)合等(deng)確定(ding)開(kai)路電壓(ya)曲(qu)線的(de)數(shu)學(xue)表達式。開路電壓測試方法主要(yao)包括:


 


1)恒電流間歇(xie)滴定技術(galvanostatic intermittent titration techniqueGITT), 基本原理是(shi)在(zai)某一(yi)特(te)定環境下(xia)對測量(liang)體(ti)(ti)系(xi)施加(jia)一(yi)恒(heng)定電(dian)(dian)流(liu)并(bing)持續一(yi)段(duan)(duan)時(shi)間后(hou)切斷該電(dian)(dian)流(liu),觀察施加(jia)電(dian)(dian)流(liu)段(duan)(duan)體(ti)(ti)系(xi)電(dian)(dian)位(wei)隨時(shi)間的變化以及弛豫后(hou)達(da)到平衡(heng)的電(dian)(dian)壓(即開路(lu)電(dian)(dian)壓)。GITT測試舉例如(ru)下:i)在C/50下充電(dian)直到電(dian)壓達到上(shang)限(xian)電(dian)壓,如4.2 Vii)靜置2小時(shi);iii1C放電6min,記錄(lu)放電(dian)容量;iv)靜置15min,記錄電壓;v)重復(fu)步驟(zou)(iii)和(he)(iv)共9次;vi)在C/50下放電(dian)直到電(dian)壓達到下限電(dian)壓,如(ru)3.0Vvii)將步驟(iii)和(he)(iv)記錄的容量-電壓曲(qu)線,歸一化處理,做成SOC-電(dian)壓曲線(xian),擬合得到開(kai)路電(dian)壓曲線(xian)的數學表達式。


 


2)小電流充放電曲線,以特別低的(de)倍率(lv)(如0.01C)電(dian)流恒(heng)流充放(fang)電(dian),設置電(dian)壓上下限范圍,得到(dao)電(dian)池(chi)小(xiao)電(dian)流充放(fang)電(dian)曲(qu)(qu)線(xian),將電(dian)量一致的點(dian)作為曲(qu)(qu)線(xian)起點(dian),對充放(fang)電(dian)曲(qu)(qu)線(xian)中的電(dian)壓取平均值,將曲(qu)(qu)線(xian)的橫坐標按照理(li)論容量進行歸一化處理(li),然后利(li)用曲(qu)(qu)線(xian)擬合得到(dao)開路電(dian)壓曲(qu)(qu)線(xian)。


 


電池極化


 

電流(liu)通過電極(ji)(ji)時,電極(ji)(ji)偏(pian)離(li)平(ping)衡電極(ji)(ji)電勢的(de)現(xian)象稱為(wei)電池(chi)的(de)極(ji)(ji)化(hua),極(ji)(ji)化(hua)產生(sheng)過電勢。根(gen)據極(ji)(ji)化(hua)產生(sheng)的(de)原因(yin)可以將極(ji)(ji)化(hua)分為(wei)歐姆極(ji)(ji)化(hua)、濃差極(ji)(ji)化(hua)和電化(hua)學極(ji)(ji)化(hua),

1)歐姆極化:由電池(chi)連接各部(bu)分的電阻造成,其壓降值遵循歐姆定律,電流減(jian)小,極化立即減(jian)小,電流停(ting)止后(hou)立即消失。


2)電化(hua)學極化(hua):由電(dian)極(ji)(ji)表(biao)面電(dian)化學反應的遲緩性(xing)造成極(ji)(ji)化。隨著電(dian)流變小,在微秒級內顯著降低。


3)濃(nong)差(cha)極化:由(you)于溶(rong)液(ye)中離子擴散過程(cheng)的(de)遲緩(huan)性,造(zao)成在(zai)一(yi)定(ding)電(dian)(dian)流下電(dian)(dian)極表面與(yu)溶(rong)液(ye)本(ben)體濃度(du)差,產(chan)生(sheng)極化。這種極化隨(sui)著電(dian)(dian)流下降,在(zai)宏(hong)觀的(de)秒級(幾(ji)秒到幾(ji)十秒)上降低或消失(shi)。


 


電(dian)池(chi)(chi)的內阻隨電(dian)池(chi)(chi)放電(dian)電(dian)流(liu)的增大(da)而增大(da),這主要是由于大(da)的放電(dian)電(dian)流(liu)使得電(dian)池(chi)(chi)的極化趨勢增大(da),并(bing)且(qie)放電(dian)電(dian)流(liu)越大(da),則極化的趨勢就越明(ming)顯,如圖2所示。根據(ju)歐姆定律:V=E0-I×RT,內部整體(ti)電阻RT的(de)增加,則電池(chi)電壓達到放電截止電壓所需要的(de)時間也相應減(jian)少(shao),故放出的(de)容量也減(jian)少(shao)。


 


鋰(li)(li)離子(zi)(zi)電(dian)池(chi)實質上是一(yi)種(zhong)鋰(li)(li)離子(zi)(zi)濃(nong)差電(dian)池(chi),鋰(li)(li)離子(zi)(zi)電(dian)池(chi)的充放電(dian)過(guo)程為鋰(li)(li)離子(zi)(zi)在正負(fu)極(ji)的嵌入、脫(tuo)出的過(guo)程。影響鋰(li)(li)離子(zi)(zi)電(dian)池(chi)極(ji)化的因素包括:


1)電解液的影響:電(dian)解液電(dian)導率(lv)低是鋰(li)離子(zi)電(dian)池極化發生的主要原因(yin)。在一般溫度范圍內,鋰(li)離子(zi)電(dian)池用電(dian)解液的電(dian)導率(lv)一般只有0.010.1S/cm,,是水(shui)溶液的百分之一。因此,鋰離(li)子電(dian)(dian)池在大電(dian)(dian)流放電(dian)(dian)時,來不及從電(dian)(dian)解液中補充Li+,會發生極化現象。提(ti)高電解液的導電能力是改善鋰離子電池大電流放(fang)電能力的關(guan)鍵因(yin)素。


2)正負極材料的影響(xiang):正負極(ji)材料顆粒大鋰離子擴散(san)到(dao)表面的通道加長,不利于大倍率放(fang)電。


3)導電劑(ji):導(dao)電劑的含量是影響高(gao)倍率放電性能(neng)(neng)的重(zhong)要(yao)因素。如(ru)果正極配方中的導(dao)電劑含量不足,大(da)電流放電時(shi)電子不能(neng)(neng)及時(shi)地(di)轉移(yi),極化內(nei)阻迅(xun)速增大(da),使(shi)電池的電壓很快降低到放電截止電壓。


4)極(ji)片設計的影響:


極片厚度(du):大電流放電的(de)情(qing)況下,活性物(wu)質反(fan)應速(su)度(du)很快,要求鋰(li)(li)離子能在材料中(zhong)迅速(su)的(de)嵌入、脫(tuo)出(chu),若是極片較(jiao)厚,鋰(li)(li)離子擴散的(de)路徑增加,極片厚度(du)方向會產(chan)生很大的(de)鋰(li)(li)離子濃度(du)梯度(du)。


壓(ya)實(shi)密(mi)度(du)(du):極片的壓(ya)實(shi)密(mi)度(du)(du)較大,孔隙變得更小,則極片厚度(du)(du)方向鋰離子(zi)運動的路徑更長(chang)。另外,壓(ya)實(shi)密(mi)度(du)(du)過大,材料與電(dian)解液之間接(jie)觸面積減小,電(dian)極反(fan)應場所減少,電(dian)池內(nei)阻也會增大。


5SEI膜的影響:SEI 膜的形成(cheng)增加(jia)了電極/電(dian)(dian)解液界面的電(dian)(dian)阻(zu),造成電(dian)(dian)壓滯后即極化。


 


電池的工作(zuo)電壓


 


工作電(dian)(dian)(dian)(dian)(dian)(dian)壓又稱端(duan)電(dian)(dian)(dian)(dian)(dian)(dian)壓,是(shi)指電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)在工作狀(zhuang)態下即(ji)(ji)電(dian)(dian)(dian)(dian)(dian)(dian)路(lu)中有電(dian)(dian)(dian)(dian)(dian)(dian)流流過(guo)(guo)時(shi)(shi)電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)正負極之間(jian)的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)差。在電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)放電(dian)(dian)(dian)(dian)(dian)(dian)工作狀(zhuang)態下,當電(dian)(dian)(dian)(dian)(dian)(dian)流流過(guo)(guo)電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)內部時(shi)(shi),需克(ke)服電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)內阻所造成阻力,會造成歐(ou)姆(mu)壓降和電(dian)(dian)(dian)(dian)(dian)(dian)極極化,故(gu)工作電(dian)(dian)(dian)(dian)(dian)(dian)壓總是(shi)低于(yu)開路(lu)電(dian)(dian)(dian)(dian)(dian)(dian)壓,充電(dian)(dian)(dian)(dian)(dian)(dian)時(shi)(shi)則與之相(xiang)反(fan),端(duan)電(dian)(dian)(dian)(dian)(dian)(dian)壓總是(shi)高于(yu)開路(lu)電(dian)(dian)(dian)(dian)(dian)(dian)壓。即(ji)(ji)極化的(de)(de)結果使電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)放電(dian)(dian)(dian)(dian)(dian)(dian)時(shi)(shi)端(duan)電(dian)(dian)(dian)(dian)(dian)(dian)壓低于(yu)電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)動勢(shi),電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)充電(dian)(dian)(dian)(dian)(dian)(dian)時(shi)(shi),電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)端(duan)電(dian)(dian)(dian)(dian)(dian)(dian)壓高于(yu)電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)動勢(shi)。


 


由于(yu)(yu)極化(hua)(hua)現象的存在(zai),會導(dao)致電(dian)(dian)池在(zai)充放電(dian)(dian)過程中(zhong)瞬(shun)時(shi)(shi)電(dian)(dian)壓(ya)與實(shi)(shi)(shi)際(ji)電(dian)(dian)壓(ya)會產生一定的偏差。充電(dian)(dian)時(shi)(shi),瞬(shun)時(shi)(shi)電(dian)(dian)壓(ya)略高于(yu)(yu)實(shi)(shi)(shi)際(ji)電(dian)(dian)壓(ya),充電(dian)(dian)結(jie)束后(hou)極化(hua)(hua)消(xiao)失,電(dian)(dian)壓(ya)回落(luo);放電(dian)(dian)時(shi)(shi),瞬(shun)時(shi)(shi)電(dian)(dian)壓(ya)略低于(yu)(yu)實(shi)(shi)(shi)際(ji)電(dian)(dian)壓(ya),放電(dian)(dian)結(jie)束后(hou)極化(hua)(hua)消(xiao)失,電(dian)(dian)壓(ya)回升。

綜合以(yi)上所述,電池(chi)端電壓的組成如圖3所示(shi),表達式(shi)為:


充(chong)電:VCH E- E-+ VR =E+0+E-0 - η-+ VR


放電:VE- E-- VR =E+0+E-0 + η-- VR


 


 


為什么(me)有(you)(you)些材料(liao)具有(you)(you)明(ming)顯的電壓平臺而有(you)(you)些沒有(you)(you)?


熱力學中,自由度 F 是當系統為平衡狀態時,在不改變相(xiang)態的情況下,可(ke)獨立改變(bian)的(de)因素(如(ru)溫度和壓力),這些變(bian)量的(de)數目叫做自由度數。系統的(de)自由度跟其他變(bian)量的(de)關系:


F = C - P + n


其中 F表示系統的(de)自(zi)由度(du);系統的(de)獨(du)立組元數;相(xiang)態(tai)數目;外(wai)界(jie)因素(su),多數取n=2,代表(biao)壓力和溫度。


 


針對鋰(li)離子電化學體(ti)系,外界因(yin)素n=2分別(bie)取電(dian)壓(ya)和(he)溫度(du)。假(jia)定(ding)鋰離(li)子(zi)電極材料在(zai)充(chong)放電過程中(zhong)溫度(du)和(he)壓力恒定(ding)不變。在(zai)此,我(wo)們討論(lun)二(er)元系(xi)(C=2),如果在(zai)一個(ge)粒(li)子中(zhong)含有一個(ge)相,即P=1,則F=1,化(hua)學勢是一個(ge)自由(you)度(du),隨鋰濃度(du)的(de)變(bian)化(hua)而(er)變(bian)化(hua)(例如固溶體(ti)鈷酸鋰,一個(ge)相,鋰濃度(du)不斷變(bian)化(hua))。


 


如(ru)果(guo)粒子中包含兩個相,即P=2,則F=0當兩相(xiang)共存(cun)(cun)時,在(zai)一(yi)個二元系電(dian)極材(cai)料(liao)中存(cun)(cun)在(zai)平坦的(de)電(dian)壓平臺(例(li)如磷(lin)酸鐵鋰,兩相(xiang)共存(cun)(cun),每個相(xiang)中鋰濃度是不變(bian)的(de))。


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