電壓是(shi)鋰離(li)子(zi)電池(chi)的(de)重要參數(shu)，直(zhi)接決(jue)定電池(chi)的(de)能量，以(yi)及電池(chi)包的(de)成組方(fang)式。本文(wen)對鋰離(li)子(zi)電池(chi)的(de)電壓進行總(zong)結，這也是(shi)本人(ren)知識梳理與學習的(de)過程(cheng)，理解不對之(zhi)處(chu)請大(da)家批(pi)評指正。
鋰離子電(dian)(dian)(dian)池在充放電(dian)(dian)(dian)測試(shi)或者實際使用中(zhong)，電(dian)(dian)(dian)壓參數(shu)主要包括平臺電(dian)(dian)(dian)壓、中(zhong)值電(dian)(dian)(dian)壓、平均電(dian)(dian)(dian)壓、截止電(dian)(dian)(dian)壓等，典型放電(dian)(dian)(dian)曲(qu)線如圖1所示。
平臺電壓(ya)是指電(dian)(dian)(dian)(dian)壓(ya)變(bian)化(hua)*小而容(rong)量變(bian)化(hua)較大時對應的電(dian)(dian)(dian)(dian)壓(ya)值，磷(lin)酸鐵鋰、鈦(tai)酸鋰電(dian)(dian)(dian)(dian)池具有明顯(xian)的平臺(tai)電(dian)(dian)(dian)(dian)壓(ya)，在充(chong)放電(dian)(dian)(dian)(dian)曲(qu)線中(zhong)可以明確確認電(dian)(dian)(dian)(dian)壓(ya)平臺(tai)。大部(bu)分電(dian)(dian)(dian)(dian)池的電(dian)(dian)(dian)(dian)壓(ya)平臺(tai)并不明顯(xian)，充(chong)放電(dian)(dian)(dian)(dian)測試(shi)時，通過(guo)電(dian)(dian)(dian)(dian)壓(ya)間隔采集數據，然后對電(dian)(dian)(dian)(dian)壓(ya)曲(qu)線做微分，通過(guo)dQ/dV的峰值確定平臺電壓。
中(zhong)值電壓是電池(chi)容量一半時對應的(de)電壓值(zhi)，對于(yu)平(ping)臺(tai)(tai)比較明顯(xian)的(de)材料，如磷酸鐵鋰(li)(li)和鈦(tai)酸鋰(li)(li)等，中值(zhi)電壓一般就是平(ping)臺(tai)(tai)電壓。
平均電壓是電壓-容量曲線的有效面積（即電(dian)池充/放電能量(liang)）除以容量(liang)，計算(suan)公式為(wei)ü = ∫U(t)*I(t)dt / ∫I(t)dt。在充(chong)放電(dian)測試數據(ju)中，充(chong)電(dian)或放電(dian)能量除(chu)以容量數據(ju)即(ji)為平均電(dian)壓。反過來，電(dian)池能量密度也(ye)是根據(ju)電(dian)池的平均電(dian)壓估算，即(ji)能量=容量*平(ping)均電壓(ya)/電池質量（或(huo)體積(ji)）。
截(jie)止(zhi)電壓是是指電(dian)(dian)(dian)池放(fang)電(dian)(dian)(dian)時允(yun)許(xu)的(de)(de)(de)*低電(dian)(dian)(dian)壓，電(dian)(dian)(dian)池充(chong)電(dian)(dian)(dian)時允(yun)許(xu)的(de)(de)(de)*高電(dian)(dian)(dian)壓。如(ru)果(guo)電(dian)(dian)(dian)壓低于放(fang)電(dian)(dian)(dian)截止(zhi)電(dian)(dian)(dian)壓后繼續(xu)放(fang)電(dian)(dian)(dian)，電(dian)(dian)(dian)池正極(ji)的(de)(de)(de)電(dian)(dian)(dian)勢持續(xu)降(jiang)(jiang)低，而(er)負極(ji)電(dian)(dian)(dian)勢會迅(xun)速上升，形成過(guo)度(du)放(fang)電(dian)(dian)(dian)，過(guo)放(fang)電(dian)(dian)(dian)可能(neng)造成電(dian)(dian)(dian)極(ji)活性物(wu)質損傷，失去反應(ying)能(neng)力，使電(dian)(dian)(dian)池壽(shou)命縮短；還(huan)會導致負極(ji)銅箔分解(jie)(jie)并在(zai)正極(ji)析出，存在(zai)短路風險。如(ru)果(guo)充(chong)電(dian)(dian)(dian)電(dian)(dian)(dian)壓高于充(chong)電(dian)(dian)(dian)截止(zhi)電(dian)(dian)(dian)壓，電(dian)(dian)(dian)池正極(ji)的(de)(de)(de)電(dian)(dian)(dian)勢持續(xu)升高，造成正極(ji)材(cai)料過(guo)過(guo)度(du)脫鋰(li)，晶體結(jie)構破壞失效，電(dian)(dian)(dian)解(jie)(jie)液分解(jie)(jie)損耗鋰(li)離子(zi)。而(er)負極(ji)電(dian)(dian)(dian)勢會持續(xu)下(xia)降(jiang)(jiang)，過(guo)度(du)嵌鋰(li)，石(shi)墨(mo)層狀瓦解(jie)(jie)，極(ji)片表面(mian)析鋰(li)等(deng)問題。
而(er)實際上，電(dian)池的電(dian)壓U(電池)是由正極(ji)的電極(ji)電勢E(正(zheng)極)和負(fu)極的電(dian)極電(dian)勢(shi)E(負極)之差確定的，由公(gong)式(1)所(suo)表示：
U(電池) = E(正(zheng)極) - E(負極) (1)
在電(dian)(dian)池體系中，標準(zhun)鋰電(dian)(dian)極(ji)普遍作為參考(kao)電(dian)(dian)極(ji)，正、負極(ji)材料的電(dian)(dian)極(ji)電(dian)(dian)勢(shi)一般都(dou)是反應物和(he)產(chan)物與參比鋰電(dian)(dian)極(ji)之間反應而產(chan)生的電(dian)(dian)勢(shi)。如圖2所(suo)示，在充放電(dian)過程(cheng)中，正負極(ji)材料脫(tuo)鋰(li)或嵌鋰(li)，電(dian)極(ji)電(dian)勢發生變化，電(dian)池(chi)電(dian)壓就是兩者之差。
因此，認識電池(chi)的(de)(de)電壓，首先要了(le)解(jie)各種電極材料(liao)(liao)的(de)(de)電極電勢(shi)，了(le)解(jie)材料(liao)(liao)的(de)(de)平衡電極電勢(shi)曲線(xian)能夠更(geng)好理解(jie)電池(chi)的(de)(de)電壓特性。
開(kai)路電(dian)(dian)壓(ya)是指電(dian)(dian)池(chi)在非工作狀態下(xia)即電(dian)(dian)路中無電(dian)(dian)流(liu)(liu)流(liu)(liu)過(guo)時(shi)，電(dian)(dian)池(chi)正負極(ji)之(zhi)間的(de)電(dian)(dian)勢差。將電(dian)(dian)極(ji)材料(liao)與金(jin)屬鋰(li)組裝成紐(niu)扣半電(dian)(dian)池(chi)，開(kai)路電(dian)(dian)壓(ya)即電(dian)(dian)極(ji)材料(liao)的(de)平(ping)衡電(dian)(dian)勢。
開路電壓測試方法
電(dian)極材料(liao)的平衡電(dian)勢測試過程為：電(dian)極材料(liao)制(zhi)備(bei)成極片，與金屬(shu)鋰(li)組裝成紐扣(kou)(kou)半(ban)電(dian)池，測得(de)紐扣(kou)(kou)半(ban)電(dian)池在(zai)不(bu)同的SOC狀態下的(de)開路(lu)電壓(ya)，并(bing)采用多項式(shi)或高斯擬(ni)合等確定開路(lu)電壓(ya)曲線的(de)數學表(biao)達式(shi)。開路電壓測試方法主要(yao)包(bao)括：
（1）恒(heng)電流間歇滴(di)定技術（galvanostatic intermittent titration technique，GITT）， 基本原(yuan)理是在某(mou)一特定環境下對測量(liang)體(ti)系施加一恒定電(dian)(dian)流(liu)(liu)(liu)并持續(xu)一段時(shi)間后(hou)切斷該電(dian)(dian)流(liu)(liu)(liu)，觀察施加電(dian)(dian)流(liu)(liu)(liu)段體(ti)系電(dian)(dian)位隨時(shi)間的(de)變(bian)化(hua)以及弛豫后(hou)達到平衡的(de)電(dian)(dian)壓(ya)（即開路電(dian)(dian)壓(ya)）。GITT測試舉例如下：（i）在C/50下(xia)充電直到電壓達到上限(xian)電壓，如4.2 V；（ii）靜置(zhi)2小(xiao)時；（iii）1C放電6min，記錄放電容量；（iv）靜置15min，記錄電壓；（v）重復步驟(zou)（iii）和（iv）共9次；（vi）在C/50下(xia)(xia)放電(dian)直(zhi)到電(dian)壓達到下(xia)(xia)限電(dian)壓，如3.0V；（vii）將(jiang)步驟（iii）和（iv）記錄(lu)的容(rong)量-電壓(ya)曲線，歸一(yi)化處理，做成SOC-電(dian)壓曲線，擬合得到開路電(dian)壓曲線的數學表(biao)達式。
（2）小電流充放電曲線(xian)，以特別低的倍(bei)率(lv)（如0.01C）電(dian)(dian)流(liu)恒流(liu)充(chong)放電(dian)(dian)，設置電(dian)(dian)壓上下限(xian)范圍，得到(dao)電(dian)(dian)池(chi)小電(dian)(dian)流(liu)充(chong)放電(dian)(dian)曲(qu)線(xian)(xian)(xian)，將電(dian)(dian)量一致(zhi)的點作為(wei)曲(qu)線(xian)(xian)(xian)起(qi)點，對充(chong)放電(dian)(dian)曲(qu)線(xian)(xian)(xian)中(zhong)的電(dian)(dian)壓取(qu)平均值，將曲(qu)線(xian)(xian)(xian)的橫坐標按照理(li)論(lun)容量進行(xing)歸一化處理(li)，然后(hou)利用(yong)曲(qu)線(xian)(xian)(xian)擬合得到(dao)開路電(dian)(dian)壓曲(qu)線(xian)(xian)(xian)。
電池極化
電(dian)(dian)流通過(guo)電(dian)(dian)極(ji)時，電(dian)(dian)極(ji)偏離平衡電(dian)(dian)極(ji)電(dian)(dian)勢的現象稱(cheng)為電(dian)(dian)池的極(ji)化(hua)(hua)，極(ji)化(hua)(hua)產生(sheng)過(guo)電(dian)(dian)勢。根據極(ji)化(hua)(hua)產生(sheng)的原因可以將(jiang)極(ji)化(hua)(hua)分(fen)為歐姆極(ji)化(hua)(hua)、濃差(cha)極(ji)化(hua)(hua)和電(dian)(dian)化(hua)(hua)學極(ji)化(hua)(hua)，
（1）歐姆極化：由電池連接各部(bu)分的電阻(zu)造成，其壓降值遵(zun)循歐姆定(ding)律(lv)，電流減小，極化立即(ji)減小，電流停(ting)止后立即(ji)消失。
（2）電化學極化：由電(dian)極表面電(dian)化(hua)學反應的遲緩(huan)性(xing)造(zao)成(cheng)極化(hua)。隨著電(dian)流(liu)變小，在微秒級內顯著降低。
（3）濃差極化：由于溶(rong)液(ye)中離子擴(kuo)散過程的遲緩性，造(zao)成(cheng)在一定電(dian)流下(xia)電(dian)極(ji)表面與溶(rong)液(ye)本體濃(nong)度差，產生極(ji)化。這種極(ji)化隨著電(dian)流下(xia)降，在宏觀(guan)的秒級(ji)(幾秒到(dao)幾十秒)上(shang)降(jiang)低或消失。
電(dian)池的內阻隨電(dian)池放(fang)(fang)電(dian)電(dian)流的增(zeng)大而(er)增(zeng)大，這(zhe)主要是(shi)由于(yu)大的放(fang)(fang)電(dian)電(dian)流使得電(dian)池的極(ji)化趨(qu)勢增(zeng)大，并且(qie)放(fang)(fang)電(dian)電(dian)流越(yue)大，則極(ji)化的趨(qu)勢就越(yue)明(ming)顯(xian)，如(ru)圖2所示。根據歐姆(mu)定(ding)律(lv)：V=E0-I×RT，內(nei)部整體電(dian)阻RT的(de)(de)增加，則電池電壓(ya)達到(dao)放電截止電壓(ya)所(suo)需(xu)要的(de)(de)時(shi)間也(ye)相應減少，故放出的(de)(de)容量也(ye)減少。
鋰離子(zi)(zi)電(dian)(dian)池(chi)實質上(shang)是一(yi)種鋰離子(zi)(zi)濃(nong)差電(dian)(dian)池(chi)，鋰離子(zi)(zi)電(dian)(dian)池(chi)的(de)充放電(dian)(dian)過程為(wei)鋰離子(zi)(zi)在正負極的(de)嵌(qian)入、脫出的(de)過程。影響鋰離子(zi)(zi)電(dian)(dian)池(chi)極化的(de)因(yin)素(su)包(bao)括：
（1）電解液的(de)影(ying)響(xiang)：電(dian)解液電(dian)導率低(di)是鋰離子(zi)電(dian)池極化發生(sheng)的(de)主要原(yuan)因。在(zai)一般(ban)溫度范(fan)圍內，鋰離子(zi)電(dian)池用電(dian)解液的(de)電(dian)導率一般(ban)只有0.01～0.1S/cm,，是(shi)水溶液的百分之(zhi)一。因此，鋰離子電池(chi)在大電流(liu)放電時，來不及從電解液中補充Li+，會發(fa)生極化現象。提高電解液(ye)的(de)導電能(neng)力(li)(li)是改善鋰離子電池大電流放電能(neng)力(li)(li)的(de)關鍵因素。
（2）正負(fu)極材(cai)料的影響：正負(fu)極材料顆粒大鋰離子擴散到(dao)表面的通道(dao)加長，不利于大倍率(lv)放電(dian)。
（3）導電劑(ji)：導電(dian)(dian)劑的含(han)量是(shi)影(ying)響高倍率放(fang)電(dian)(dian)性能(neng)的重要因素(su)。如果正極配方(fang)中的導電(dian)(dian)劑含(han)量不足(zu)，大電(dian)(dian)流放(fang)電(dian)(dian)時電(dian)(dian)子不能(neng)及時地轉移(yi)，極化內(nei)阻(zu)迅速(su)增(zeng)大，使電(dian)(dian)池的電(dian)(dian)壓很快降低(di)到放(fang)電(dian)(dian)截(jie)止電(dian)(dian)壓。
（4）極片設(she)計的影響：
極(ji)片厚度(du)(du)：大(da)電(dian)流放(fang)電(dian)的情況下，活性(xing)物質反應速度(du)(du)很(hen)快，要求鋰(li)離(li)子(zi)(zi)能在材(cai)料(liao)中迅速的嵌入、脫出，若是極(ji)片較厚，鋰(li)離(li)子(zi)(zi)擴散(san)的路徑增加，極(ji)片厚度(du)(du)方向會產生很(hen)大(da)的鋰(li)離(li)子(zi)(zi)濃度(du)(du)梯度(du)(du)。
壓實(shi)密(mi)度：極片(pian)的壓實(shi)密(mi)度較大(da)(da)，孔隙變得(de)更(geng)(geng)小(xiao)，則極片(pian)厚(hou)度方向鋰離子運動的路徑更(geng)(geng)長。另外，壓實(shi)密(mi)度過大(da)(da)，材(cai)料與電解液之間接觸面積(ji)減(jian)小(xiao)，電極反(fan)應場所減(jian)少，電池內阻也會增大(da)(da)。
（5）SEI膜的影響：SEI 膜的形成增加(jia)了電(dian)極/電解液界面的(de)電阻，造成電壓滯(zhi)后即極化。
電池的工作電壓(ya)
工作(zuo)(zuo)(zuo)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)又(you)稱(cheng)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(zuo)(zuo)(zuo)狀態下即電(dian)(dian)(dian)(dian)(dian)(dian)(dian)路中有電(dian)(dian)(dian)(dian)(dian)(dian)(dian)流流過時電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)正負極(ji)之(zhi)間的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)勢(shi)(shi)差。在(zai)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)工作(zuo)(zuo)(zuo)狀態下，當電(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)(nei)部時，需克服電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)內(nei)(nei)阻(zu)所造(zao)成(cheng)阻(zu)力，會造(zao)成(cheng)歐姆壓(ya)(ya)降和電(dian)(dian)(dian)(dian)(dian)(dian)(dian)極(ji)極(ji)化，故工作(zuo)(zuo)(zuo)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)總是低(di)于(yu)開路電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)，充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)時則與(yu)之(zhi)相反(fan)，端電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)總是高于(yu)開路電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)。即極(ji)化的(de)(de)結(jie)果使電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)放(fang)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)時端電(dian)(dian)(dian)(dian)(dian)(dian)(dian)壓(ya)(ya)低(di)于(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)動勢(shi)(shi)，電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)充(chong)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)時，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)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)池(chi)(chi)(chi)(chi)的(de)(de)電(dian)(dian)(dian)(dian)(dian)(dian)(dian)動勢(shi)(shi)。
由于極化(hua)現(xian)象的(de)存(cun)在(zai)(zai)，會導(dao)致電(dian)(dian)(dian)池(chi)在(zai)(zai)充(chong)放(fang)電(dian)(dian)(dian)過程中瞬時(shi)電(dian)(dian)(dian)壓(ya)(ya)與實(shi)際電(dian)(dian)(dian)壓(ya)(ya)會產(chan)生(sheng)一(yi)定(ding)的(de)偏(pian)差。充(chong)電(dian)(dian)(dian)時(shi)，瞬時(shi)電(dian)(dian)(dian)壓(ya)(ya)略高于實(shi)際電(dian)(dian)(dian)壓(ya)(ya)，充(chong)電(dian)(dian)(dian)結束后(hou)極化(hua)消失(shi)，電(dian)(dian)(dian)壓(ya)(ya)回落；放(fang)電(dian)(dian)(dian)時(shi)，瞬時(shi)電(dian)(dian)(dian)壓(ya)(ya)略低(di)于實(shi)際電(dian)(dian)(dian)壓(ya)(ya)，放(fang)電(dian)(dian)(dian)結束后(hou)極化(hua)消失(shi)，電(dian)(dian)(dian)壓(ya)(ya)回升。
綜合以上所述(shu)，電池端電壓的組成如圖3所示，表(biao)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)些(xie)材料具有(you)明顯的(de)電壓平(ping)臺而有(you)些(xie)沒有(you)？
熱力學中，自(zi)由度 F 是當(dang)系統(tong)為平(ping)衡狀(zhuang)態時，在不改變相態的數量情(qing)況下，可獨立改變的因素(su)（如(ru)溫度和壓力），這些變量(liang)的數目(mu)叫做自(zi)由度數。系(xi)統的自(zi)由度跟其(qi)他變量(liang)的關系(xi)：
F = C - P + n
其中 F：表示系統的自(zi)由度；C ：系統(tong)的獨立(li)組元數；P ：相態數目；n ：外界因素，多(duo)數取n=2，代表壓力和溫度。
針(zhen)對鋰離(li)子電(dian)化學體(ti)系，外界因素n=2，分別取電壓和溫度。假定鋰(li)離子電極(ji)材料在(zai)充放電過(guo)程(cheng)中溫度和壓力(li)恒定不(bu)變。在(zai)此，我們討(tao)論二元系（C=2），如果(guo)在一個粒(li)子(zi)中含(han)有一個相，即P=1，則F=1，化學勢是一個自由(you)度(du)，隨鋰濃度(du)的變(bian)(bian)化而變(bian)(bian)化（例如固溶體(ti)鈷酸鋰，一個相，鋰濃度(du)不斷變(bian)(bian)化）。
如果粒子中包含(han)兩個(ge)相，即P=2，則F=0。當兩相(xiang)共存(cun)(cun)(cun)時，在一(yi)個二元系電極材料中存(cun)(cun)(cun)在平坦(tan)的電壓平臺(tai)（例(li)如磷(lin)酸(suan)鐵(tie)鋰，兩相(xiang)共存(cun)(cun)(cun)，每(mei)個相(xiang)中鋰濃度是不變的）。
