電(dian)(dian)壓(ya)是(shi)鋰(li)離(li)子(zi)電(dian)(dian)池(chi)(chi)的(de)(de)重要參(can)數，直接(jie)決定(ding)電(dian)(dian)池(chi)(chi)的(de)(de)能量，以及電(dian)(dian)池(chi)(chi)包的(de)(de)成組方式。本文對鋰(li)離(li)子(zi)電(dian)(dian)池(chi)(chi)的(de)(de)電(dian)(dian)壓(ya)進行總結，這也是(shi)本人知(zhi)識(shi)梳理與學習的(de)(de)過程(cheng)，理解不對之處請(qing)大家批評指(zhi)正(zheng)。
鋰離(li)子電(dian)池在(zai)充放電(dian)測(ce)試或者實際使用中(zhong)(zhong)，電(dian)壓參數(shu)主要包括平臺電(dian)壓、中(zhong)(zhong)值電(dian)壓、平均電(dian)壓、截止(zhi)電(dian)壓等，典型(xing)放電(dian)曲線(xian)如(ru)圖1所示(shi)。
平(ping)臺電壓(ya)是指電(dian)壓(ya)變(bian)化*小(xiao)而容量變(bian)化較大時(shi)對(dui)應的電(dian)壓(ya)值，磷酸(suan)鐵鋰、鈦酸(suan)鋰電(dian)池具有明(ming)顯的平臺(tai)電(dian)壓(ya)，在充(chong)放電(dian)曲(qu)線中可以(yi)明(ming)確(que)確(que)認(ren)電(dian)壓(ya)平臺(tai)。大部分(fen)電(dian)池的電(dian)壓(ya)平臺(tai)并不明(ming)顯，充(chong)放電(dian)測試時(shi)，通(tong)過(guo)電(dian)壓(ya)間隔采集數據，然后對(dui)電(dian)壓(ya)曲(qu)線做微(wei)分(fen)，通(tong)過(guo)dQ/dV的峰(feng)值確(que)定平臺(tai)電壓。
中值電(dian)壓(ya)是(shi)電(dian)池(chi)容量一半時對應的電(dian)壓(ya)值，對于平臺比較明顯的材料，如磷酸鐵鋰和(he)鈦酸鋰等，中值電(dian)壓(ya)一般(ban)就(jiu)是(shi)平臺電(dian)壓(ya)。
平均電壓是電壓-容量曲線的有效面積（即電池充(chong)/放電能量）除以容(rong)量，計(ji)算(suan)公式為ü = ∫U(t)*I(t)dt / ∫I(t)dt。在充放電(dian)(dian)(dian)測試數據(ju)中，充電(dian)(dian)(dian)或放電(dian)(dian)(dian)能量(liang)除以容量(liang)數據(ju)即(ji)為平均電(dian)(dian)(dian)壓(ya)。反過來，電(dian)(dian)(dian)池能量(liang)密度也(ye)是根據(ju)電(dian)(dian)(dian)池的平均電(dian)(dian)(dian)壓(ya)估算，即(ji)能量(liang)=容量*平(ping)均電壓/電(dian)池質量（或體積）。
截止(zhi)電(dian)壓是是指電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)時允許的*低電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)時允許的*高電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)。如果(guo)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)低于(yu)(yu)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截(jie)止(zhi)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)后繼續(xu)(xu)(xu)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)正極(ji)(ji)的電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)持(chi)續(xu)(xu)(xu)降低，而(er)負極(ji)(ji)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)會(hui)迅速(su)上升，形成(cheng)過(guo)度(du)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)，過(guo)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)可能造(zao)成(cheng)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)極(ji)(ji)活(huo)性(xing)物(wu)質損傷，失去反(fan)應(ying)能力(li)，使電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)壽命(ming)縮短；還會(hui)導致負極(ji)(ji)銅箔分解(jie)并(bing)在(zai)正極(ji)(ji)析出(chu)，存在(zai)短路(lu)風險。如果(guo)充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)高于(yu)(yu)充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截(jie)止(zhi)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)正極(ji)(ji)的電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)持(chi)續(xu)(xu)(xu)升高，造(zao)成(cheng)正極(ji)(ji)材料過(guo)過(guo)度(du)脫鋰，晶體結構破(po)壞失效，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)解(jie)液分解(jie)損耗鋰離子(zi)。而(er)負極(ji)(ji)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)會(hui)持(chi)續(xu)(xu)(xu)下降，過(guo)度(du)嵌鋰，石墨層狀瓦解(jie)，極(ji)(ji)片表(biao)面析鋰等問題。
而實(shi)際上，電池的電壓(ya)U(電(dian)池)是(shi)由正極的電(dian)極電(dian)勢E(正極)和負極的電極電勢E(負極)之(zhi)差確定的，由公(gong)式(1)所表(biao)示(shi)：
U(電池) = E(正極) - E(負極) (1)
在電(dian)池體(ti)系中，標準鋰(li)電(dian)極(ji)普遍作為參考電(dian)極(ji)，正、負極(ji)材料的電(dian)極(ji)電(dian)勢一般都是反應物和產(chan)(chan)物與參比(bi)鋰(li)電(dian)極(ji)之間反應而(er)產(chan)(chan)生的電(dian)勢。如圖2所示(shi)，在充(chong)放電過程(cheng)中，正負極材(cai)料(liao)脫鋰(li)或嵌鋰(li)，電極電勢發(fa)生變(bian)化(hua)，電池電壓(ya)就是兩者之差。
因此(ci)，認識(shi)電(dian)(dian)池的電(dian)(dian)壓，首先要了解(jie)(jie)各種(zhong)電(dian)(dian)極材料的電(dian)(dian)極電(dian)(dian)勢，了解(jie)(jie)材料的平衡電(dian)(dian)極電(dian)(dian)勢曲線能夠更(geng)好(hao)理解(jie)(jie)電(dian)(dian)池的電(dian)(dian)壓特性。
開路電(dian)壓是指(zhi)電(dian)池(chi)在(zai)非(fei)工作狀態(tai)下(xia)即(ji)電(dian)路中無電(dian)流流過時(shi)，電(dian)池(chi)正負(fu)極(ji)之間(jian)的電(dian)勢(shi)(shi)差。將電(dian)極(ji)材(cai)料與(yu)金(jin)屬(shu)鋰組裝(zhuang)成紐(niu)扣半電(dian)池(chi)，開路電(dian)壓即(ji)電(dian)極(ji)材(cai)料的平(ping)衡電(dian)勢(shi)(shi)。
開路電(dian)壓測試方法
電極材料(liao)的平衡電勢(shi)測(ce)試(shi)過程(cheng)為：電極材料(liao)制(zhi)備成(cheng)極片(pian)，與金屬鋰(li)組裝成(cheng)紐(niu)(niu)扣半(ban)電池(chi)，測(ce)得紐(niu)(niu)扣半(ban)電池(chi)在不同的SOC狀態(tai)下的開路電(dian)壓，并采用多項式或(huo)高斯(si)擬合等確定開路電(dian)壓曲線的數學表達式。開(kai)路電(dian)壓(ya)測試(shi)方法主要包括：
（1）恒(heng)電流間歇滴定技術(shu)（galvanostatic intermittent titration technique，GITT）， 基本(ben)原(yuan)理是在某一特定環(huan)境下對測量體(ti)系施(shi)加一恒定電(dian)流并持續一段時間后切斷(duan)該電(dian)流，觀察(cha)施(shi)加電(dian)流段體(ti)系電(dian)位隨(sui)時間的(de)變(bian)化以及弛豫后達(da)到平衡的(de)電(dian)壓(ya)（即開(kai)路電(dian)壓(ya)）。GITT測試(shi)舉(ju)例如下：（i）在C/50下(xia)充電(dian)直到電(dian)壓達到上限電(dian)壓，如4.2 V；（ii）靜置(zhi)2小時；（iii）1C放電6min，記錄放電(dian)容量；（iv）靜置15min，記(ji)錄電壓(ya)；（v）重(zhong)復步驟（iii）和（iv）共9次；（vi）在C/50下放電(dian)直到電(dian)壓(ya)達到下限電(dian)壓(ya)，如3.0V；（vii）將(jiang)步驟（iii）和（iv）記錄的容(rong)量-電壓曲線，歸一化處理，做成SOC-電壓(ya)(ya)曲(qu)線(xian)，擬合得到開路電壓(ya)(ya)曲(qu)線(xian)的(de)數學表達式。
（2）小電流充放電曲(qu)線，以特別低的倍率（如0.01C）電(dian)(dian)(dian)流(liu)恒流(liu)充(chong)放電(dian)(dian)(dian)，設置電(dian)(dian)(dian)壓(ya)上下限范圍，得到(dao)(dao)電(dian)(dian)(dian)池小(xiao)電(dian)(dian)(dian)流(liu)充(chong)放電(dian)(dian)(dian)曲線，將電(dian)(dian)(dian)量一(yi)致的點(dian)(dian)作(zuo)為曲線起點(dian)(dian)，對充(chong)放電(dian)(dian)(dian)曲線中的電(dian)(dian)(dian)壓(ya)取平(ping)均值，將曲線的橫坐標(biao)按照理(li)論容(rong)量進行歸一(yi)化處理(li)，然后利用曲線擬合得到(dao)(dao)開(kai)路(lu)電(dian)(dian)(dian)壓(ya)曲線。
電(dian)池極(ji)化(hua)
電(dian)流通過電(dian)極(ji)(ji)(ji)時，電(dian)極(ji)(ji)(ji)偏離平衡電(dian)極(ji)(ji)(ji)電(dian)勢(shi)的現(xian)象稱為電(dian)池的極(ji)(ji)(ji)化，極(ji)(ji)(ji)化產生過電(dian)勢(shi)。根(gen)據極(ji)(ji)(ji)化產生的原因可(ke)以將極(ji)(ji)(ji)化分為歐姆極(ji)(ji)(ji)化、濃差極(ji)(ji)(ji)化和電(dian)化學極(ji)(ji)(ji)化，
（1）歐姆極化(hua)：由電(dian)池連接各部分(fen)的(de)電(dian)阻造(zao)成，其(qi)壓降值遵循歐姆(mu)定(ding)律，電(dian)流(liu)減小，極化立(li)即減小，電(dian)流(liu)停止后立(li)即消失。
（2）電化(hua)學極(ji)化(hua)：由電極表(biao)面電化(hua)學反(fan)應的遲緩性造成(cheng)極化(hua)。隨著電流變小，在(zai)微秒級內(nei)顯著降低(di)。
（3）濃差(cha)極化(hua)：由于溶(rong)液中離子(zi)擴散過程的遲緩性，造(zao)成(cheng)在一定電流(liu)下(xia)(xia)電極(ji)表面(mian)與(yu)溶(rong)液本體濃度(du)差，產生極(ji)化(hua)。這種極(ji)化(hua)隨(sui)著電流(liu)下(xia)(xia)降(jiang)，在宏觀的秒級(幾秒到(dao)幾十(shi)秒)上降(jiang)低或消失(shi)。
電(dian)(dian)池的(de)內(nei)阻隨電(dian)(dian)池放(fang)電(dian)(dian)電(dian)(dian)流的(de)增大而增大，這(zhe)主要是由于大的(de)放(fang)電(dian)(dian)電(dian)(dian)流使得(de)電(dian)(dian)池的(de)極化趨勢增大，并且放(fang)電(dian)(dian)電(dian)(dian)流越大，則極化的(de)趨勢就越明顯，如圖2所示。根據歐姆定律：V=E0-I×RT，內部整(zheng)體電(dian)阻(zu)RT的增加，則電(dian)池電(dian)壓達到放(fang)電(dian)截止電(dian)壓所(suo)需要的時間也相(xiang)應減少(shao)，故放(fang)出的容量(liang)也減少(shao)。
鋰離子電池實質上是一種鋰離子濃(nong)差(cha)電池，鋰離子電池的充放電過程為(wei)鋰離子在(zai)正負極(ji)的嵌入、脫出(chu)的過程。影響鋰離子電池極(ji)化的因素包括：
（1）電解(jie)液(ye)的影響：電解液電導率(lv)低是鋰離(li)子電池(chi)極(ji)化發生的主要原因(yin)。在(zai)一般(ban)溫度范(fan)圍內，鋰離(li)子電池(chi)用電解液的電導率(lv)一般(ban)只有0.01～0.1S/cm,，是水溶液的百分之一(yi)。因此(ci)，鋰離子電(dian)池(chi)在(zai)大電(dian)流(liu)放(fang)電(dian)時，來不及從電(dian)解液中補充Li+，會發(fa)生極化現象。提(ti)高電(dian)解液的導(dao)電(dian)能力是改善鋰離子電(dian)池大電(dian)流放電(dian)能力的關鍵因素(su)。
（2）正負極材料的(de)影響：正(zheng)負極材料顆粒(li)大鋰離(li)子(zi)擴散到表面(mian)的通道加長，不利于大倍率放電。
（3）導(dao)電劑：導電(dian)劑(ji)的(de)含量是(shi)影(ying)響高倍率放電(dian)性能的(de)重要因素。如果正極配方中(zhong)的(de)導電(dian)劑(ji)含量不(bu)(bu)足，大電(dian)流放電(dian)時(shi)電(dian)子不(bu)(bu)能及(ji)時(shi)地轉移，極化內阻迅速增大，使電(dian)池的(de)電(dian)壓很快降低到放電(dian)截止電(dian)壓。
（4）極片設計的影響：
極(ji)片厚(hou)度(du)(du)：大電流放電的(de)(de)情(qing)況下，活性物質反應速度(du)(du)很(hen)快，要(yao)求(qiu)鋰離(li)子(zi)能在材料中(zhong)迅速的(de)(de)嵌入、脫(tuo)出，若(ruo)是極(ji)片較(jiao)厚(hou)，鋰離(li)子(zi)擴散的(de)(de)路徑增加，極(ji)片厚(hou)度(du)(du)方向會產生很(hen)大的(de)(de)鋰離(li)子(zi)濃度(du)(du)梯度(du)(du)。
壓(ya)實(shi)密度：極片的壓(ya)實(shi)密度較大，孔(kong)隙變得更(geng)(geng)小，則極片厚(hou)度方向鋰離子運動的路(lu)徑更(geng)(geng)長。另外，壓(ya)實(shi)密度過大，材料與電解液(ye)之間接觸(chu)面(mian)積減小，電極反應場(chang)所減少，電池內阻也會增大。
（5）SEI膜(mo)的(de)影(ying)響：SEI 膜的形(xing)成增加了(le)電極/電(dian)(dian)解液界面的電(dian)(dian)阻，造成(cheng)電(dian)(dian)壓滯后即極化。
電池的工作電壓
工作電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)又稱端電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)，是指電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)在(zai)工作狀態下即電(dian)(dian)(dian)(dian)(dian)(dian)(dian)路(lu)中有(you)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)流流過時(shi)(shi)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)正負極(ji)之間的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢差。在(zai)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)放電(dian)(dian)(dian)(dian)(dian)(dian)(dian)工作狀態下，當(dang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)流流過電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)內(nei)部(bu)時(shi)(shi)，需克服電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)內(nei)阻(zu)所造成阻(zu)力，會造成歐(ou)姆壓(ya)(ya)降和電(dian)(dian)(dian)(dian)(dian)(dian)(dian)極(ji)極(ji)化(hua)，故工作電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)總是低于(yu)(yu)開路(lu)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)，充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)時(shi)(shi)則(ze)與之相反，端電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)總是高于(yu)(yu)開路(lu)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)。即極(ji)化(hua)的(de)(de)結果使電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)放電(dian)(dian)(dian)(dian)(dian)(dian)(dian)時(shi)(shi)端電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)低于(yu)(yu)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)動(dong)勢，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)充電(dian)(dian)(dian)(dian)(dian)(dian)(dian)時(shi)(shi)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)端電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)高于(yu)(yu)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)動(dong)勢。
由于(yu)極(ji)化(hua)現象的(de)存在，會(hui)導致電(dian)(dian)(dian)(dian)池在充(chong)(chong)放(fang)電(dian)(dian)(dian)(dian)過程中(zhong)瞬時(shi)電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)與實(shi)際(ji)電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)會(hui)產生一定的(de)偏(pian)差。充(chong)(chong)電(dian)(dian)(dian)(dian)時(shi)，瞬時(shi)電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)略高于(yu)實(shi)際(ji)電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)，充(chong)(chong)電(dian)(dian)(dian)(dian)結束后極(ji)化(hua)消(xiao)失，電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)回(hui)落(luo)；放(fang)電(dian)(dian)(dian)(dian)時(shi)，瞬時(shi)電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)略低于(yu)實(shi)際(ji)電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)，放(fang)電(dian)(dian)(dian)(dian)結束后極(ji)化(hua)消(xiao)失，電(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)回(hui)升。
綜合以上所述，電池(chi)端電壓的(de)組成如圖3所示，表達(da)式(shi)為：
充(chong)電：VCH = （E+ - E-）+ VR =（E+0+η+）- （E-0 - η-）+ VR
放電：VD = （E+ - E-）- VR =（E+0-η+）- （E-0 + η-）- VR
為什么有些材料具有明顯的電壓平臺而(er)有些沒有？
熱力學(xue)中，自(zi)由度(du) F 是當系統(tong)為平衡狀(zhuang)態時，在(zai)不改變相態的數量情況下(xia)，可獨立改變(bian)的(de)(de)因素（如(ru)溫度(du)和壓力），這些(xie)變(bian)量的(de)(de)數(shu)(shu)目叫做自由(you)(you)度(du)數(shu)(shu)。系統的(de)(de)自由(you)(you)度(du)跟其(qi)他變(bian)量的(de)(de)關系：
F = C - P + n
其(qi)中 F：表(biao)示系(xi)統的自由度(du)；C ：系統的(de)獨立組元數；P ：相態(tai)數(shu)目(mu)；n ：外界因素，多數取n=2，代表壓力(li)和(he)溫(wen)度。
針對鋰離子電化學體系，外界(jie)因(yin)素n=2，分(fen)別(bie)取電壓(ya)和(he)溫度(du)。假定鋰(li)離子電極(ji)材料(liao)在(zai)(zai)充放電過程中(zhong)溫度(du)和(he)壓力恒定不(bu)變。在(zai)(zai)此，我(wo)們討論二元系（C=2），如果(guo)在一個(ge)粒子中含有一個(ge)相，即(ji)P=1，則(ze)F=1，化(hua)學勢(shi)是一個自(zi)由度，隨鋰(li)濃度的變(bian)化(hua)而變(bian)化(hua)（例如固溶體鈷酸鋰(li)，一個相(xiang)，鋰(li)濃度不斷變(bian)化(hua)）。
如果(guo)粒子中包含兩個相(xiang)，即P=2，則F=0。當兩相共存時，在一個二元系電極材料中(zhong)存在平坦的(de)電壓平臺（例如(ru)磷酸鐵鋰，兩相共存，每(mei)個相中(zhong)鋰濃度(du)是(shi)不變的(de)）。
