電壓是鋰離(li)子電池的(de)重要參數，直接決(jue)定電池的(de)能量，以及電池包的(de)成組方式。本文對(dui)鋰離(li)子電池的(de)電壓進行總結，這也是本人知識梳理與學習的(de)過(guo)程，理解(jie)不對(dui)之(zhi)處請大家批評指(zhi)正。
鋰(li)離(li)子電(dian)池(chi)在充放(fang)(fang)電(dian)測試或者實際使用中，電(dian)壓(ya)(ya)(ya)參數主要包括平臺電(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(xing)放(fang)(fang)電(dian)曲(qu)線(xian)如圖1所示。
平(ping)臺電(dian)壓是指(zhi)電(dian)壓(ya)變(bian)化*小而容量變(bian)化較大時對(dui)(dui)應的(de)電(dian)壓(ya)值，磷酸鐵鋰、鈦酸鋰電(dian)池具有明(ming)顯(xian)的(de)平臺電(dian)壓(ya)，在充放電(dian)曲(qu)線(xian)中可以明(ming)確確認(ren)電(dian)壓(ya)平臺。大部(bu)分電(dian)池的(de)電(dian)壓(ya)平臺并(bing)不(bu)明(ming)顯(xian)，充放電(dian)測試時，通過(guo)電(dian)壓(ya)間隔采集數(shu)據，然后(hou)對(dui)(dui)電(dian)壓(ya)曲(qu)線(xian)做微(wei)分，通過(guo)dQ/dV的峰值確(que)定(ding)平臺電壓。
中值電(dian)壓是電(dian)池容量一(yi)半時對應的(de)電(dian)壓值(zhi)(zhi)，對于平(ping)臺(tai)比(bi)較明顯的(de)材(cai)料，如磷酸(suan)鐵鋰和鈦酸(suan)鋰等(deng)，中值(zhi)(zhi)電(dian)壓一(yi)般就是平(ping)臺(tai)電(dian)壓。
平均電壓是電(dian)壓-容量曲線的有效(xiao)面積（即電池充/放電(dian)能量(liang)）除以(yi)容量(liang)，計算公式為ü = ∫U(t)*I(t)dt / ∫I(t)dt。在充放(fang)電(dian)(dian)測(ce)試數據(ju)中，充電(dian)(dian)或放(fang)電(dian)(dian)能量除(chu)以(yi)容量數據(ju)即為平均電(dian)(dian)壓。反過(guo)來，電(dian)(dian)池(chi)能量密度也(ye)是根據(ju)電(dian)(dian)池(chi)的平均電(dian)(dian)壓估算，即能量=容量(liang)*平(ping)均電壓/電池質(zhi)量（或(huo)體積(ji)）。
截止電(dian)壓是是指電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)放(fang)(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)時允許的(de)*低(di)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(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)時允許的(de)*高電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)。如果電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)低(di)于(yu)(yu)放(fang)(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截止電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)后繼續(xu)放(fang)(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)正極的(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢持續(xu)降低(di)，而(er)(er)負極電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢會迅速上升(sheng)(sheng)，形成(cheng)過度(du)放(fang)(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)，過放(fang)(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)可能(neng)造成(cheng)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)極活性(xing)物質損(sun)傷，失去反應能(neng)力，使電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)壽命縮短(duan)；還(huan)會導(dao)致負極銅箔分(fen)解(jie)(jie)并(bing)在(zai)正極析出(chu)，存在(zai)短(duan)路風險(xian)。如果充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)高于(yu)(yu)充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)截止電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)正極的(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢持續(xu)升(sheng)(sheng)高，造成(cheng)正極材料過過度(du)脫鋰(li)，晶體(ti)結構破壞失效，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)解(jie)(jie)液(ye)分(fen)解(jie)(jie)損(sun)耗鋰(li)離子。而(er)(er)負極電(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢會持續(xu)下降，過度(du)嵌鋰(li)，石墨層狀瓦(wa)解(jie)(jie)，極片(pian)表面析鋰(li)等問題。
而實際上，電池(chi)的電壓U(電池(chi))是由正(zheng)極的(de)電極電勢E(正極)和(he)負(fu)極的電極電勢E(負極)之差確定的，由公式(1)所(suo)表示(shi)：
U(電(dian)池(chi)) = E(正極) - E(負極) (1)
在電(dian)(dian)(dian)(dian)池體系中，標準鋰電(dian)(dian)(dian)(dian)極(ji)(ji)普遍作(zuo)為參考電(dian)(dian)(dian)(dian)極(ji)(ji)，正、負極(ji)(ji)材(cai)料的電(dian)(dian)(dian)(dian)極(ji)(ji)電(dian)(dian)(dian)(dian)勢(shi)(shi)一般(ban)都(dou)是(shi)反應物和產物與(yu)參比鋰電(dian)(dian)(dian)(dian)極(ji)(ji)之間反應而產生(sheng)的電(dian)(dian)(dian)(dian)勢(shi)(shi)。如圖2所示，在充放(fang)電(dian)過程中，正負極材料(liao)脫鋰或嵌鋰，電(dian)極電(dian)勢發生變化(hua)，電(dian)池電(dian)壓就是兩者之(zhi)差。
因此(ci)，認(ren)識電(dian)(dian)(dian)池的(de)電(dian)(dian)(dian)壓，首先(xian)要了解各(ge)種電(dian)(dian)(dian)極(ji)(ji)材(cai)料的(de)電(dian)(dian)(dian)極(ji)(ji)電(dian)(dian)(dian)勢(shi)，了解材(cai)料的(de)平衡電(dian)(dian)(dian)極(ji)(ji)電(dian)(dian)(dian)勢(shi)曲線能夠(gou)更(geng)好理解電(dian)(dian)(dian)池的(de)電(dian)(dian)(dian)壓特性。
開(kai)路電(dian)壓是指電(dian)池在(zai)非工作(zuo)狀態下即(ji)電(dian)路中無電(dian)流流過時，電(dian)池正負極(ji)之間的電(dian)勢差。將電(dian)極(ji)材料與金(jin)屬鋰組裝成(cheng)紐扣(kou)半電(dian)池，開(kai)路電(dian)壓即(ji)電(dian)極(ji)材料的平衡電(dian)勢。
開(kai)路電(dian)壓測試方(fang)法
電極(ji)材料的(de)平衡電勢測試過程為：電極(ji)材料制備成(cheng)極(ji)片(pian)，與(yu)金屬鋰組裝成(cheng)紐扣半電池(chi)，測得(de)紐扣半電池(chi)在(zai)不同的(de)SOC狀態下的(de)開(kai)路電壓，并(bing)采用多(duo)項式(shi)或高斯擬合等確定開(kai)路電壓曲線的(de)數學(xue)表達式(shi)。開(kai)路(lu)電壓(ya)測試(shi)方法主要(yao)包括(kuo)：
（1）恒電流(liu)間歇滴定技術（galvanostatic intermittent titration technique，GITT）， 基本原理(li)是在某一特定環境下(xia)對測(ce)量體系施加(jia)一恒定電流(liu)并持(chi)續一段(duan)時間(jian)(jian)后切斷該電流(liu)，觀察施加(jia)電流(liu)段(duan)體系電位(wei)隨時間(jian)(jian)的(de)變化(hua)以(yi)及弛豫后達到平衡的(de)電壓（即(ji)開路電壓）。GITT測試舉例如下：（i）在(zai)C/50下充(chong)電(dian)直到電(dian)壓達(da)到上限電(dian)壓，如(ru)4.2 V；（ii）靜置2小時；（iii）1C放電6min，記錄放電容量；（iv）靜(jing)置15min，記(ji)錄電壓；（v）重復步(bu)驟（iii）和（iv）共9次；（vi）在C/50下(xia)放電(dian)直(zhi)到電(dian)壓達到下(xia)限(xian)電(dian)壓，如3.0V；（vii）將步驟（iii）和（iv）記錄(lu)的容量-電壓曲(qu)線(xian)，歸一化處理，做成SOC-電壓曲線，擬合(he)得到開路電壓曲線的數學表(biao)達(da)式(shi)。
（2）小電(dian)流充(chong)放電(dian)曲線，以特(te)別低的倍率（如0.01C）電(dian)流恒流充放電(dian)，設(she)置電(dian)壓(ya)上下限范圍，得到(dao)電(dian)池小電(dian)流充放電(dian)曲線(xian)(xian)(xian)，將(jiang)電(dian)量(liang)(liang)一致(zhi)的(de)點作為曲線(xian)(xian)(xian)起點，對充放電(dian)曲線(xian)(xian)(xian)中的(de)電(dian)壓(ya)取平(ping)均值，將(jiang)曲線(xian)(xian)(xian)的(de)橫坐標(biao)按照理論(lun)容量(liang)(liang)進行歸一化處理，然(ran)后利用曲線(xian)(xian)(xian)擬合(he)得到(dao)開路電(dian)壓(ya)曲線(xian)(xian)(xian)。
電池(chi)極化
電(dian)流通過(guo)電(dian)極(ji)(ji)時，電(dian)極(ji)(ji)偏離平衡電(dian)極(ji)(ji)電(dian)勢的(de)現象稱為電(dian)池的(de)極(ji)(ji)化(hua)(hua)，極(ji)(ji)化(hua)(hua)產(chan)生(sheng)過(guo)電(dian)勢。根據極(ji)(ji)化(hua)(hua)產(chan)生(sheng)的(de)原因可以(yi)將極(ji)(ji)化(hua)(hua)分為歐姆極(ji)(ji)化(hua)(hua)、濃差極(ji)(ji)化(hua)(hua)和電(dian)化(hua)(hua)學極(ji)(ji)化(hua)(hua)，
（1）歐(ou)姆(mu)極化(hua)：由電(dian)池連接(jie)各部分的電(dian)阻造成，其壓降(jiang)值遵循歐姆定(ding)律(lv)，電(dian)流減小，極(ji)化立即減小，電(dian)流停止后立即消(xiao)失。
（2）電化學極(ji)化：由電極表面(mian)電化學(xue)反應(ying)的遲緩性造成極化。隨著(zhu)電流變小，在微秒(miao)級內顯(xian)著(zhu)降低(di)。
（3）濃差極化(hua)：由于溶液中離子擴(kuo)散過程的(de)遲(chi)緩性，造成在一(yi)定電(dian)(dian)流(liu)下電(dian)(dian)極(ji)表面(mian)與溶液本(ben)體濃(nong)度差，產(chan)生極(ji)化。這種(zhong)極(ji)化隨著(zhu)電(dian)(dian)流(liu)下降，在宏(hong)觀的(de)秒級(幾(ji)秒(miao)到幾(ji)十(shi)秒(miao))上降低(di)或消失。
電(dian)池的(de)內阻隨電(dian)池放電(dian)電(dian)流的(de)增(zeng)(zeng)大(da)(da)而增(zeng)(zeng)大(da)(da)，這主要(yao)是由(you)于大(da)(da)的(de)放電(dian)電(dian)流使得電(dian)池的(de)極(ji)化(hua)趨(qu)勢增(zeng)(zeng)大(da)(da)，并(bing)且放電(dian)電(dian)流越(yue)大(da)(da)，則極(ji)化(hua)的(de)趨(qu)勢就越(yue)明顯，如圖2所(suo)示。根據歐姆定律：V=E0-I×RT，內(nei)部整(zheng)體電阻RT的增加(jia)，則(ze)電(dian)池(chi)電(dian)壓(ya)達到(dao)放電(dian)截止電(dian)壓(ya)所需要(yao)的時間也相應(ying)減少，故放出的容(rong)量也減少。
鋰(li)(li)(li)離(li)子(zi)(zi)(zi)電池(chi)(chi)(chi)實(shi)質上是(shi)一種鋰(li)(li)(li)離(li)子(zi)(zi)(zi)濃差電池(chi)(chi)(chi)，鋰(li)(li)(li)離(li)子(zi)(zi)(zi)電池(chi)(chi)(chi)的充放電過程為鋰(li)(li)(li)離(li)子(zi)(zi)(zi)在正負極的嵌入(ru)、脫出(chu)的過程。影(ying)響(xiang)鋰(li)(li)(li)離(li)子(zi)(zi)(zi)電池(chi)(chi)(chi)極化的因素包括(kuo)：
（1）電解液的影響：電(dian)解液(ye)電(dian)導(dao)率(lv)低是鋰離子電(dian)池極化發生的(de)主要原(yuan)因。在一般溫(wen)度范(fan)圍內，鋰離子電(dian)池用電(dian)解液(ye)的(de)電(dian)導(dao)率(lv)一般只有0.01～0.1S/cm,，是水溶(rong)液的百(bai)分之(zhi)一。因(yin)此，鋰離子(zi)電(dian)池在大電(dian)流放(fang)電(dian)時，來不(bu)及(ji)從電(dian)解液中補充Li+，會發生極化現象。提(ti)高電(dian)解液的導電(dian)能(neng)力是改善鋰離子電(dian)池大電(dian)流放電(dian)能(neng)力的關鍵因素。
（2）正負極材料(liao)的影響：正(zheng)負極(ji)材料顆(ke)粒大(da)鋰離子擴散到表面的通(tong)道(dao)加長，不利(li)于大(da)倍(bei)率放電。
（3）導電劑(ji)：導(dao)電(dian)劑(ji)的含量是影響高倍率(lv)放電(dian)性能(neng)的重要因素。如果正極配(pei)方(fang)中的導(dao)電(dian)劑(ji)含量不足，大(da)電(dian)流放電(dian)時電(dian)子不能(neng)及時地轉移，極化內(nei)阻迅速增大(da)，使電(dian)池的電(dian)壓很快降低到(dao)放電(dian)截止(zhi)電(dian)壓。
（4）極(ji)片(pian)設計的影響(xiang)：
極(ji)(ji)片厚度(du)：大(da)電流放電的情(qing)況下，活性物質反應速度(du)很快，要求鋰(li)(li)離子能在材(cai)料中迅速的嵌入、脫(tuo)出，若是極(ji)(ji)片較厚，鋰(li)(li)離子擴散的路徑增加(jia)，極(ji)(ji)片厚度(du)方向(xiang)會產生很大(da)的鋰(li)(li)離子濃度(du)梯度(du)。
壓(ya)實密度(du)(du)(du)：極片的壓(ya)實密度(du)(du)(du)較大(da)，孔隙變得(de)更小，則(ze)極片厚度(du)(du)(du)方向鋰離子運動的路徑(jing)更長(chang)。另(ling)外，壓(ya)實密度(du)(du)(du)過大(da)，材(cai)料與電(dian)解液之間接觸面積減小，電(dian)極反應場所減少，電(dian)池(chi)內阻也會增大(da)。
（5）SEI膜的影響(xiang)：SEI 膜的(de)形成增加了電極/電解液界面(mian)的電阻，造成電壓滯后即極化。
電(dian)池的工作電(dian)壓
工(gong)(gong)(gong)作(zuo)(zuo)電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)又稱端(duan)電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)，是指電(dian)(dian)(dian)(dian)(dian)池在工(gong)(gong)(gong)作(zuo)(zuo)狀態下即電(dian)(dian)(dian)(dian)(dian)路中有電(dian)(dian)(dian)(dian)(dian)流(liu)流(liu)過時(shi)電(dian)(dian)(dian)(dian)(dian)池正負極(ji)之間(jian)的(de)(de)電(dian)(dian)(dian)(dian)(dian)勢(shi)差。在電(dian)(dian)(dian)(dian)(dian)池放電(dian)(dian)(dian)(dian)(dian)工(gong)(gong)(gong)作(zuo)(zuo)狀態下，當電(dian)(dian)(dian)(dian)(dian)流(liu)流(liu)過電(dian)(dian)(dian)(dian)(dian)池內(nei)部時(shi)，需克(ke)服電(dian)(dian)(dian)(dian)(dian)池的(de)(de)內(nei)阻所(suo)造(zao)成阻力，會造(zao)成歐姆壓(ya)(ya)降和電(dian)(dian)(dian)(dian)(dian)極(ji)極(ji)化，故工(gong)(gong)(gong)作(zuo)(zuo)電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)總(zong)是低于(yu)開路電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)，充(chong)電(dian)(dian)(dian)(dian)(dian)時(shi)則與(yu)之相反(fan)，端(duan)電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)總(zong)是高于(yu)開路電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)。即極(ji)化的(de)(de)結果使(shi)電(dian)(dian)(dian)(dian)(dian)池放電(dian)(dian)(dian)(dian)(dian)時(shi)端(duan)電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)低于(yu)電(dian)(dian)(dian)(dian)(dian)池的(de)(de)電(dian)(dian)(dian)(dian)(dian)動(dong)勢(shi)，電(dian)(dian)(dian)(dian)(dian)池充(chong)電(dian)(dian)(dian)(dian)(dian)時(shi)，電(dian)(dian)(dian)(dian)(dian)池的(de)(de)端(duan)電(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)高于(yu)電(dian)(dian)(dian)(dian)(dian)池的(de)(de)電(dian)(dian)(dian)(dian)(dian)動(dong)勢(shi)。
由(you)于(yu)極化現象的(de)存在，會導(dao)致電(dian)(dian)(dian)(dian)池在充(chong)放(fang)電(dian)(dian)(dian)(dian)過程(cheng)中瞬(shun)(shun)時(shi)電(dian)(dian)(dian)(dian)壓(ya)(ya)與實際電(dian)(dian)(dian)(dian)壓(ya)(ya)會產生一(yi)定的(de)偏差。充(chong)電(dian)(dian)(dian)(dian)時(shi)，瞬(shun)(shun)時(shi)電(dian)(dian)(dian)(dian)壓(ya)(ya)略(lve)高于(yu)實際電(dian)(dian)(dian)(dian)壓(ya)(ya)，充(chong)電(dian)(dian)(dian)(dian)結束后極化消(xiao)失，電(dian)(dian)(dian)(dian)壓(ya)(ya)回落(luo)；放(fang)電(dian)(dian)(dian)(dian)時(shi)，瞬(shun)(shun)時(shi)電(dian)(dian)(dian)(dian)壓(ya)(ya)略(lve)低于(yu)實際電(dian)(dian)(dian)(dian)壓(ya)(ya)，放(fang)電(dian)(dian)(dian)(dian)結束后極化消(xiao)失，電(dian)(dian)(dian)(dian)壓(ya)(ya)回升。
綜合(he)以上所述(shu)，電池端電壓的組成如圖3所示(shi)，表達式為：
充電：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(you)(you)(you)(you)些材料具有(you)(you)(you)(you)明(ming)顯的(de)電壓平臺而有(you)(you)(you)(you)些沒(mei)有(you)(you)(you)(you)？
熱力(li)學(xue)中，自由(you)度 F 是當系統(tong)為平衡(heng)狀態時，在不改變相態的數量(liang)情況下(xia)，可獨立改變(bian)的因素（如溫度(du)和壓力），這些(xie)變(bian)量的數目叫做自(zi)由度(du)數。系統的自(zi)由度(du)跟其他變(bian)量的關系：
F = C - P + n
其(qi)中(zhong) F：表(biao)示系統的自由度；C ：系統的獨立組元數；P ：相(xiang)態數目；n ：外界因素，多數取(qu)n=2，代(dai)表壓力和溫度。
針對鋰離子電化學體(ti)系，外界因素(su)n=2，分別取電(dian)壓和溫度。假定鋰(li)離子電極材料在充放電過(guo)程中溫度和壓力恒定不變。在此(ci)，我們討論二元系（C=2），如果在一(yi)個粒(li)子(zi)中(zhong)含(han)有一(yi)個相，即(ji)P=1，則(ze)F=1，化學(xue)勢(shi)是一(yi)個自由(you)度(du)，隨鋰濃度(du)的變(bian)化而(er)變(bian)化（例如固溶體鈷酸鋰，一(yi)個相，鋰濃度(du)不斷變(bian)化）。
如果粒(li)子中包含(han)兩個相(xiang)，即P=2，則F=0。當(dang)兩相(xiang)共存時，在(zai)一(yi)個二元系電極材料中存在(zai)平坦的電壓平臺(tai)（例如磷(lin)酸鐵鋰，兩相(xiang)共存，每個相(xiang)中鋰濃度是不(bu)變(bian)的）。
