電壓是(shi)鋰離子(zi)(zi)電池的重要參數，直(zhi)接(jie)決定(ding)電池的能量(liang)，以及電池包的成組(zu)方式(shi)。本(ben)文對鋰離子(zi)(zi)電池的電壓進(jin)行總結，這(zhe)也是(shi)本(ben)人(ren)知識梳理與學習的過程，理解不對之處請大家批評(ping)指正。
鋰離子電(dian)(dian)池在充放(fang)電(dian)(dian)測試(shi)或者(zhe)實際(ji)使用中(zhong)，電(dian)(dian)壓(ya)參數主要包(bao)括平(ping)臺電(dian)(dian)壓(ya)、中(zhong)值電(dian)(dian)壓(ya)、平(ping)均電(dian)(dian)壓(ya)、截(jie)止電(dian)(dian)壓(ya)等，典型放(fang)電(dian)(dian)曲線如圖1所示(shi)。
平臺電壓(ya)是(shi)指(zhi)電(dian)(dian)(dian)壓(ya)變化*小(xiao)而容量變化較(jiao)大時(shi)(shi)對(dui)應的(de)(de)電(dian)(dian)(dian)壓(ya)值，磷酸(suan)鐵鋰、鈦酸(suan)鋰電(dian)(dian)(dian)池具有明(ming)顯的(de)(de)平(ping)臺電(dian)(dian)(dian)壓(ya)，在(zai)充(chong)放電(dian)(dian)(dian)曲線中可(ke)以明(ming)確(que)確(que)認電(dian)(dian)(dian)壓(ya)平(ping)臺。大部分電(dian)(dian)(dian)池的(de)(de)電(dian)(dian)(dian)壓(ya)平(ping)臺并不明(ming)顯，充(chong)放電(dian)(dian)(dian)測試時(shi)(shi)，通(tong)過電(dian)(dian)(dian)壓(ya)間隔采集數據，然后(hou)對(dui)電(dian)(dian)(dian)壓(ya)曲線做微分，通(tong)過dQ/dV的峰值確定平臺電(dian)壓。
中值電壓是(shi)電池容量一半時對(dui)應的電壓值，對(dui)于平臺(tai)比(bi)較(jiao)明顯的材料，如磷酸鐵鋰和鈦酸鋰等，中值電壓一般就是(shi)平臺(tai)電壓。
平均電(dian)壓是電壓-容量(liang)曲線的有效(xiao)面積（即電(dian)池充/放電能量(liang)）除以容量(liang)，計算公式為(wei)ü = ∫U(t)*I(t)dt / ∫I(t)dt。在充放(fang)電(dian)測試數據中，充電(dian)或放(fang)電(dian)能量(liang)除以容(rong)量(liang)數據即(ji)為(wei)平均(jun)電(dian)壓(ya)。反過來，電(dian)池(chi)能量(liang)密度也是根據電(dian)池(chi)的平均(jun)電(dian)壓(ya)估算(suan)，即(ji)能量(liang)=容量*平均電壓/電池質量（或體(ti)積）。
截止電(dian)壓是是指電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)時允(yun)許(xu)的*低(di)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)時允(yun)許(xu)的*高(gao)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)。如(ru)果電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)低(di)于放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截止(zhi)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)后繼(ji)續放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)正(zheng)(zheng)(zheng)極(ji)(ji)(ji)的電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)持(chi)續降(jiang)低(di)，而負(fu)極(ji)(ji)(ji)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)會迅(xun)速上升，形成(cheng)過(guo)(guo)(guo)度(du)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)，過(guo)(guo)(guo)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)可(ke)能造成(cheng)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)極(ji)(ji)(ji)活性物質損(sun)傷，失(shi)去反應(ying)能力，使電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)壽(shou)命縮短；還會導致負(fu)極(ji)(ji)(ji)銅箔分解并在正(zheng)(zheng)(zheng)極(ji)(ji)(ji)析(xi)出，存在短路風(feng)險。如(ru)果充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)高(gao)于充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截止(zhi)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)正(zheng)(zheng)(zheng)極(ji)(ji)(ji)的電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)持(chi)續升高(gao)，造成(cheng)正(zheng)(zheng)(zheng)極(ji)(ji)(ji)材料過(guo)(guo)(guo)過(guo)(guo)(guo)度(du)脫鋰，晶體(ti)結構破壞失(shi)效，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)解液分解損(sun)耗(hao)鋰離(li)子。而負(fu)極(ji)(ji)(ji)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)會持(chi)續下降(jiang)，過(guo)(guo)(guo)度(du)嵌鋰，石墨層狀(zhuang)瓦解，極(ji)(ji)(ji)片表面析(xi)鋰等問(wen)題。
而實(shi)際(ji)上(shang)，電池的電壓U(電池)是由正(zheng)極的電極電勢E(正極)和負(fu)極(ji)的電極(ji)電勢E(負極)之差(cha)確定的，由公(gong)式(shi)(1)所表示：
U(電池(chi)) = E(正極) - E(負極(ji)) (1)
在電(dian)(dian)池(chi)體(ti)系中，標準鋰電(dian)(dian)極(ji)(ji)普遍作(zuo)為(wei)參(can)考電(dian)(dian)極(ji)(ji)，正、負極(ji)(ji)材(cai)料的電(dian)(dian)極(ji)(ji)電(dian)(dian)勢一般都(dou)是反應(ying)物(wu)和(he)產(chan)物(wu)與參(can)比鋰電(dian)(dian)極(ji)(ji)之(zhi)間(jian)反應(ying)而產(chan)生的電(dian)(dian)勢。如圖2所示(shi)，在充放電(dian)過程中，正負極(ji)材料脫鋰(li)或嵌鋰(li)，電(dian)極(ji)電(dian)勢(shi)發生變(bian)化，電(dian)池電(dian)壓就是兩者之差。
因此，認識電(dian)(dian)池(chi)(chi)的(de)電(dian)(dian)壓(ya)，首先要(yao)了(le)解(jie)各種電(dian)(dian)極材料的(de)電(dian)(dian)極電(dian)(dian)勢(shi)，了(le)解(jie)材料的(de)平衡電(dian)(dian)極電(dian)(dian)勢(shi)曲線能夠更好理解(jie)電(dian)(dian)池(chi)(chi)的(de)電(dian)(dian)壓(ya)特(te)性。
開路(lu)電(dian)壓是指電(dian)池(chi)(chi)在非工(gong)作狀態下即電(dian)路(lu)中無電(dian)流流過時(shi)，電(dian)池(chi)(chi)正(zheng)負極(ji)之間的電(dian)勢差。將電(dian)極(ji)材料與金(jin)屬鋰組(zu)裝(zhuang)成紐扣(kou)半(ban)電(dian)池(chi)(chi)，開路(lu)電(dian)壓即電(dian)極(ji)材料的平衡電(dian)勢。
開路(lu)電壓測試方法
電(dian)極(ji)材(cai)(cai)料的(de)平衡電(dian)勢測(ce)試過程為：電(dian)極(ji)材(cai)(cai)料制備成極(ji)片，與金屬(shu)鋰(li)組裝成紐扣半電(dian)池(chi)，測(ce)得(de)紐扣半電(dian)池(chi)在(zai)不同的(de)SOC狀態下的開(kai)路電壓(ya)，并采用多項式(shi)或(huo)高(gao)斯擬合等確定開(kai)路電壓(ya)曲線的數(shu)學表達式(shi)。開路電壓測試方法主要包括：
（1）恒電流間歇(xie)滴定技術(shu)（galvanostatic intermittent titration technique，GITT）， 基本(ben)原(yuan)理(li)是在某一特定環境下對(dui)測量體(ti)系施(shi)加一恒定電(dian)流并持續一段時(shi)間(jian)后切(qie)斷該電(dian)流，觀察施(shi)加電(dian)流段體(ti)系電(dian)位隨時(shi)間(jian)的(de)變化以及弛豫(yu)后達(da)到平衡的(de)電(dian)壓(ya)（即開路電(dian)壓(ya)）。GITT測試舉例如下：（i）在(zai)C/50下充電(dian)直到(dao)電(dian)壓達(da)到(dao)上(shang)限(xian)電(dian)壓，如4.2 V；（ii）靜置2小時；（iii）1C放電6min，記(ji)錄放電(dian)容量(liang)；（iv）靜置15min，記(ji)錄(lu)電壓(ya)；（v）重(zhong)復步(bu)驟（iii）和（iv）共9次；（vi）在C/50下(xia)放電(dian)直到電(dian)壓(ya)達到下(xia)限電(dian)壓(ya)，如3.0V；（vii）將步(bu)驟（iii）和（iv）記錄的(de)容量(liang)-電壓曲線，歸一(yi)化處理，做成SOC-電壓(ya)曲線，擬(ni)合得到開路電壓(ya)曲線的數學表(biao)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)(dian)流(liu)恒流(liu)充放(fang)電(dian)(dian)，設置(zhi)電(dian)(dian)壓(ya)上下限范圍，得到(dao)電(dian)(dian)池小電(dian)(dian)流(liu)充放(fang)電(dian)(dian)曲(qu)(qu)線(xian)(xian)，將電(dian)(dian)量(liang)一(yi)致的(de)點作為(wei)曲(qu)(qu)線(xian)(xian)起點，對(dui)充放(fang)電(dian)(dian)曲(qu)(qu)線(xian)(xian)中的(de)電(dian)(dian)壓(ya)取平均(jun)值，將曲(qu)(qu)線(xian)(xian)的(de)橫坐標按照理(li)(li)論容量(liang)進(jin)行歸一(yi)化處理(li)(li)，然后利(li)用曲(qu)(qu)線(xian)(xian)擬合(he)得到(dao)開(kai)路電(dian)(dian)壓(ya)曲(qu)(qu)線(xian)(xian)。
電(dian)池極化
電(dian)流通(tong)過電(dian)極(ji)(ji)(ji)(ji)(ji)時，電(dian)極(ji)(ji)(ji)(ji)(ji)偏離平(ping)衡電(dian)極(ji)(ji)(ji)(ji)(ji)電(dian)勢(shi)的現象稱為電(dian)池的極(ji)(ji)(ji)(ji)(ji)化(hua)，極(ji)(ji)(ji)(ji)(ji)化(hua)產(chan)(chan)生(sheng)過電(dian)勢(shi)。根據極(ji)(ji)(ji)(ji)(ji)化(hua)產(chan)(chan)生(sheng)的原因可以將極(ji)(ji)(ji)(ji)(ji)化(hua)分為歐姆極(ji)(ji)(ji)(ji)(ji)化(hua)、濃差(cha)極(ji)(ji)(ji)(ji)(ji)化(hua)和(he)電(dian)化(hua)學極(ji)(ji)(ji)(ji)(ji)化(hua)，
（1）歐姆(mu)極化(hua)：由電(dian)池連接各部(bu)分的電(dian)阻造(zao)成，其壓降值(zhi)遵循歐(ou)姆定(ding)律，電(dian)流(liu)減小，極(ji)化(hua)立即減小，電(dian)流(liu)停止后立即消失。
（2）電化學極化：由電極(ji)表面(mian)電化學反應的遲緩性造(zao)成極(ji)化。隨著(zhu)電流變小，在(zai)微秒級內顯著(zhu)降低。
（3）濃差極化(hua)：由(you)于(yu)溶(rong)液中離(li)子擴散過程的遲緩性，造成(cheng)在(zai)一定電流下(xia)(xia)電極(ji)表面與溶(rong)液本體濃度差，產生極(ji)化。這(zhe)種極(ji)化隨(sui)著(zhu)電流下(xia)(xia)降(jiang)，在(zai)宏(hong)觀的秒級(幾秒(miao)到幾十(shi)秒(miao))上降低或消失。
電(dian)池(chi)的(de)(de)內阻隨電(dian)池(chi)放電(dian)電(dian)流的(de)(de)增(zeng)大(da)(da)而增(zeng)大(da)(da)，這(zhe)主要是(shi)由于大(da)(da)的(de)(de)放電(dian)電(dian)流使得電(dian)池(chi)的(de)(de)極化趨(qu)勢增(zeng)大(da)(da)，并且放電(dian)電(dian)流越(yue)大(da)(da)，則極化的(de)(de)趨(qu)勢就(jiu)越(yue)明顯，如圖2所示。根(gen)據歐(ou)姆定(ding)律：V=E0-I×RT，內部整體電阻RT的增加(jia)，則(ze)電(dian)池電(dian)壓達到(dao)放(fang)電(dian)截止電(dian)壓所需要的時(shi)間也(ye)相應減少，故放(fang)出的容量也(ye)減少。
鋰(li)離(li)子(zi)電池(chi)實質上是一種鋰(li)離(li)子(zi)濃差電池(chi)，鋰(li)離(li)子(zi)電池(chi)的(de)充放電過(guo)程(cheng)為鋰(li)離(li)子(zi)在正負(fu)極的(de)嵌(qian)入、脫(tuo)出的(de)過(guo)程(cheng)。影(ying)響鋰(li)離(li)子(zi)電池(chi)極化的(de)因(yin)素包括：
（1）電解液的影響：電(dian)解(jie)液(ye)電(dian)導率低是(shi)鋰離子(zi)電(dian)池(chi)極化發生的主要原(yuan)因(yin)。在一般(ban)溫(wen)度范圍內，鋰離子(zi)電(dian)池(chi)用(yong)電(dian)解(jie)液(ye)的電(dian)導率一般(ban)只有0.01～0.1S/cm,，是水溶(rong)液(ye)的百分之一。因此，鋰離(li)子電池(chi)在大電流放電時，來不(bu)及從(cong)電解液(ye)中(zhong)補充Li+，會發(fa)生極化現象。提高電(dian)解液的導電(dian)能力(li)是改(gai)善鋰離子(zi)電(dian)池大電(dian)流放電(dian)能力(li)的關(guan)鍵(jian)因素。
（2）正負極材料的影響：正負極材料顆(ke)粒大鋰(li)離子擴散到表面的通道加長(chang)，不利于(yu)大倍率放電。
（3）導電劑：導(dao)電(dian)(dian)(dian)(dian)劑(ji)的含量是影響高倍率放電(dian)(dian)(dian)(dian)性能(neng)的重要因(yin)素。如果正極配方中的導(dao)電(dian)(dian)(dian)(dian)劑(ji)含量不足，大電(dian)(dian)(dian)(dian)流(liu)放電(dian)(dian)(dian)(dian)時電(dian)(dian)(dian)(dian)子不能(neng)及時地轉移，極化內阻迅速增大，使電(dian)(dian)(dian)(dian)池的電(dian)(dian)(dian)(dian)壓很快降(jiang)低到放電(dian)(dian)(dian)(dian)截止電(dian)(dian)(dian)(dian)壓。
（4）極片(pian)設計(ji)的影響：
極(ji)片厚度(du)：大(da)電流放(fang)電的(de)情況下，活性物(wu)質反應速(su)度(du)很快，要求鋰離子能在材料中迅(xun)速(su)的(de)嵌入(ru)、脫出，若(ruo)是極(ji)片較厚，鋰離子擴(kuo)散(san)的(de)路徑增加，極(ji)片厚度(du)方向會產(chan)生很大(da)的(de)鋰離子濃度(du)梯度(du)。
壓(ya)實密(mi)度(du)(du)：極片(pian)的壓(ya)實密(mi)度(du)(du)較大，孔隙變得更(geng)小，則極片(pian)厚度(du)(du)方向(xiang)鋰離子運動的路徑更(geng)長。另(ling)外(wai)，壓(ya)實密(mi)度(du)(du)過大，材料與電(dian)解液之間接觸面(mian)積減小，電(dian)極反應(ying)場所減少，電(dian)池內阻也會增大。
（5）SEI膜的影響：SEI 膜的形成增加了電極(ji)/電(dian)(dian)解液界面的電(dian)(dian)阻，造成(cheng)電(dian)(dian)壓滯后即極(ji)化。
電池的(de)工作電壓
工(gong)作電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)又(you)稱端電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)，是(shi)指電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)在工(gong)作狀態(tai)下即電(dian)(dian)(dian)(dian)(dian)(dian)路中有電(dian)(dian)(dian)(dian)(dian)(dian)流流過時(shi)電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)正(zheng)負極之間的(de)電(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)差。在電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)放電(dian)(dian)(dian)(dian)(dian)(dian)工(gong)作狀態(tai)下，當電(dian)(dian)(dian)(dian)(dian)(dian)流流過電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)內部時(shi)，需克服電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)的(de)內阻(zu)所造成(cheng)阻(zu)力(li)，會造成(cheng)歐姆壓(ya)(ya)(ya)降和電(dian)(dian)(dian)(dian)(dian)(dian)極極化，故工(gong)作電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)總(zong)是(shi)低(di)于開(kai)路電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)，充電(dian)(dian)(dian)(dian)(dian)(dian)時(shi)則與之相反，端電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)總(zong)是(shi)高于開(kai)路電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)。即極化的(de)結果使電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)放電(dian)(dian)(dian)(dian)(dian)(dian)時(shi)端電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)低(di)于電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)的(de)電(dian)(dian)(dian)(dian)(dian)(dian)動勢(shi)，電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)充電(dian)(dian)(dian)(dian)(dian)(dian)時(shi)，電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)的(de)端電(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)(ya)高于電(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)的(de)電(dian)(dian)(dian)(dian)(dian)(dian)動勢(shi)。
由(you)于極化現(xian)象的存在，會導(dao)致電(dian)(dian)池在充(chong)放電(dian)(dian)過程中(zhong)瞬(shun)時電(dian)(dian)壓(ya)(ya)(ya)與實際(ji)電(dian)(dian)壓(ya)(ya)(ya)會產生一定的偏差(cha)。充(chong)電(dian)(dian)時，瞬(shun)時電(dian)(dian)壓(ya)(ya)(ya)略高于實際(ji)電(dian)(dian)壓(ya)(ya)(ya)，充(chong)電(dian)(dian)結束(shu)后極化消失，電(dian)(dian)壓(ya)(ya)(ya)回落；放電(dian)(dian)時，瞬(shun)時電(dian)(dian)壓(ya)(ya)(ya)略低(di)于實際(ji)電(dian)(dian)壓(ya)(ya)(ya)，放電(dian)(dian)結束(shu)后極化消失，電(dian)(dian)壓(ya)(ya)(ya)回升。
綜合以上所述，電(dian)池端電(dian)壓的組成如圖3所示(shi)，表(biao)達式為：
充電(dian)：VCH = （E+ - E-）+ VR =（E+0+η+）- （E-0 - η-）+ VR
放(fang)電：VD = （E+ - E-）- VR =（E+0-η+）- （E-0 + η-）- VR
為什(shen)么有些材料具有明顯(xian)的電壓平臺而(er)有些沒有？
熱力學中，自由度 F 是當系統為平衡狀態(tai)時，在不(bu)改變相(xiang)態的數量(liang)情況下，可獨(du)立(li)改(gai)變(bian)的因素（如溫度和(he)壓力），這些變(bian)量(liang)(liang)的數目(mu)叫做自(zi)由度數。系統(tong)的自(zi)由度跟其他(ta)變(bian)量(liang)(liang)的關系：
F = C - P + n
其中 F：表(biao)示系統的自(zi)由(you)度；C ：系統的獨立組元數；P ：相(xiang)態數目；n ：外界因素(su)，多數取n=2，代表壓力(li)和溫度。
針對鋰離子電化學體系，外界(jie)因素n=2，分(fen)別取(qu)電壓和溫(wen)度。假定(ding)鋰離子電(dian)極(ji)材料在充放電(dian)過(guo)程中(zhong)溫(wen)度和壓力恒定(ding)不變。在此，我們討論二(er)元系(xi)（C=2），如果在一個(ge)粒子中含有一個(ge)相，即P=1，則F=1，化學勢是一個(ge)自由度(du)，隨鋰(li)(li)濃度(du)的變化而變化（例如(ru)固(gu)溶體鈷(gu)酸鋰(li)(li)，一個(ge)相，鋰(li)(li)濃度(du)不斷變化）。
如果粒子中包含(han)兩個相，即P=2，則F=0。當兩相共存時(shi)，在(zai)一個(ge)二元系電極材料中(zhong)存在(zai)平坦的電壓平臺(tai)（例如磷酸鐵鋰(li)，兩相共存，每(mei)個(ge)相中(zhong)鋰(li)濃度是不變(bian)的）。
