李 凱,徐維華,蘇 倩,文 剛,黃廷林

聚醚砜和聚偏氟乙烯超濾膜對(duì)臭氧的耐受性

李 凱*,徐維華,蘇 倩,文 剛,黃廷林

(西安建筑科技大學(xué),陜西省水污染控制與水質(zhì)安全保障協(xié)同創(chuàng)新中心,陜西省環(huán)境工程重點(diǎn)實(shí)驗(yàn)室,西北水資源與環(huán)境生態(tài)教育部重點(diǎn)實(shí)驗(yàn)室,陜西 西安 710055)

通過靜態(tài)浸泡實(shí)驗(yàn)考察了臭氧對(duì)聚醚砜(PES)和聚偏氟乙烯(PVDF)超濾膜透水能力、截留性能、力學(xué)性能等的影響,分析了與臭氧接觸前后膜化學(xué)組成和性質(zhì)的變化,結(jié)果表明,室溫(20±1)℃下與飽和臭氧水接觸2h后,PES膜的透水率增大至原始膜的3倍以上,對(duì)腐殖酸(HA)的截留率降至0左右,結(jié)合膜表面組成和性質(zhì)分析,臭氧在氧化親水添加劑聚乙烯吡咯烷酮(PVP)的同時(shí)使PES分子也發(fā)生了分解,破壞了PES分離層的結(jié)構(gòu)和功能;對(duì)于PVDF膜,與飽和臭氧水接觸1h后膜的透水率增大至原始膜的1.4倍左右,對(duì)HA截留率由原始膜的61.13%降至41.24%,但與臭氧接觸時(shí)間進(jìn)一步延長(zhǎng)時(shí)膜性能無進(jìn)一步下降,對(duì)膜表面組成和性質(zhì)的分析表明臭氧對(duì)PVDF膜分離層的損傷主要是由于PVP的氧化和流失造成的,PVDF本身未發(fā)生分解.PVDF膜分離層對(duì)臭氧的耐受性顯著高于PES膜,但臭氧使2種膜的力學(xué)性能均有明顯下降.

高分子超濾膜；臭氧耐受性；聚醚砜(PES)；聚偏氟乙烯(PVDF)；膜性能

超濾膜對(duì)顆粒物有優(yōu)異的去除效果,且運(yùn)行壓力相對(duì)較低、占地面積較小,在飲用水處理、污水回用以及納濾/反滲透預(yù)處理中的應(yīng)用越來越多[1-3],但水中普遍存在的有機(jī)物對(duì)超濾膜的污染是超濾工藝應(yīng)用中的主要障礙[4-5].臭氧預(yù)氧化能改變有機(jī)物的分子尺寸、親疏水性、荷電性等,從而影響有機(jī)物-膜間的相互作用、減少有機(jī)物在膜上的沉積[6-8],同時(shí)臭氧能抑制膜系統(tǒng)中微生物的繁殖、減少微生物及其代謝產(chǎn)物在膜上的積累從而減緩膜污染[9].因此,臭氧預(yù)氧化已成為國(guó)內(nèi)外研究和應(yīng)用較多的一種超濾膜前預(yù)處理技術(shù)[10-11].

超濾膜與臭氧長(zhǎng)期接觸時(shí)膜結(jié)構(gòu)和性能的穩(wěn)定性是臭氧預(yù)氧化-超濾組合工藝研究應(yīng)用中需重點(diǎn)關(guān)注的問題.陶瓷膜化學(xué)穩(wěn)定性高,適合與臭氧預(yù)氧化聯(lián)用,但成本較高、目前在水處理中應(yīng)用偏少[8,12];高分子膜具有成本較低、裝填密度高的優(yōu)點(diǎn),聚偏氟乙烯(PVDF)、聚醚砜(PES)等是目前水處理中廣泛應(yīng)用的超濾膜材料[13],國(guó)內(nèi)外許多學(xué)者開展了臭氧預(yù)氧化控制高分子超濾膜有機(jī)污染的研究,但對(duì)臭氧作用下高分子膜穩(wěn)定性研究較少.有研究認(rèn)為,為避免臭氧對(duì)高分子膜的損傷,與臭氧聯(lián)用時(shí)應(yīng)將水中殘余臭氧完全分解后再進(jìn)入膜系統(tǒng)[14],但這需要投加還原劑或設(shè)置臭氧分解池,從而增加運(yùn)行或投資成本.但部分高分子膜對(duì)臭氧有較好的耐受性[15-17],例如,Mori等[15]發(fā)現(xiàn)高結(jié)晶度PVDF膜對(duì)臭氧的耐受性顯著高于低結(jié)晶度PVDF膜,但這些研究主要關(guān)注膜的力學(xué)性能和透水能力,未對(duì)臭氧作用下膜結(jié)構(gòu)和性能變化進(jìn)行分析.此外,除了與膜主體材料反應(yīng),臭氧作用下膜中親水性添加劑聚乙烯吡咯烷酮(PVP)的氧化對(duì)PES膜性能的變化有重要影響[18].目前關(guān)于常用高分子超濾膜對(duì)臭氧耐受性的研究較少,對(duì)臭氧作用下膜結(jié)構(gòu)和性能的變化規(guī)律的認(rèn)識(shí)還不夠深入.

本研究以水處理中常用的PES和PVDF超濾膜為研究對(duì)象,考察了與飽和臭氧水接觸不同時(shí)間對(duì)超濾膜性能、化學(xué)組成和界面性質(zhì)的影響.通過測(cè)定與臭氧接觸前后超濾膜的純水通量、對(duì)腐殖酸(HA)截留率、過濾HA溶液時(shí)膜通量變化及可逆性等分別反映膜透水、截留、抗污染性能的變化;通過測(cè)定膜表面官能團(tuán)、孔隙結(jié)構(gòu)、荷電性、親水性等分析臭氧與膜材料的作用機(jī)理,以期為臭氧預(yù)氧化-超濾組合工藝中膜材料的選擇提供依據(jù).

1 材料與方法

1.1 實(shí)驗(yàn)材料

超濾膜為商品化平板PES膜和PVDF膜,截留分子量均為150kDa,2種膜均為復(fù)合膜,其中PES膜的支撐層為聚乙烯/聚丙烯(PE/PP),PVDF膜的支撐層為聚對(duì)苯二甲酸乙二醇酯(PET).所用試劑均為分析純級(jí)別, HA購(gòu)于Sigma-Aldrich公司,氫氧化鈉(NaOH)和磷酸(H3PO4)購(gòu)置于天津天力化學(xué)試劑有限公司,鹽酸(HCl)購(gòu)置于上海國(guó)藥集團(tuán),磷酸氫二鈉(Na2HPO4)、氯化鈣(CaCl2)、氯化鈉(NaCl)及碳酸氫鈉(NaHCO3)均購(gòu)于科密歐化學(xué)試劑有限公司.

1.2 臭氧與超濾膜反應(yīng)裝置

圖1為臭氧與超濾膜反應(yīng)裝置,反應(yīng)在室溫(20±1)℃下進(jìn)行.取1L超純水(ELGA LabWater,High Wycombe,UK)置于球形反應(yīng)器中,高純氧氣(99.9%)通過流量計(jì)后被送入臭氧發(fā)生器(3S-5A,北京同林科技有限公司,北京),臭氧以1L/min的流量通過微孔曝氣頭連續(xù)注入超純水中,臭氧尾氣用含有KI溶液的洗氣瓶吸收,在平衡狀態(tài)下用靛藍(lán)法測(cè)得的飽和臭氧水中臭氧濃度為(19.2±0.5) mg/L.每次實(shí)驗(yàn)取2張直徑為67mm的超濾膜浸泡于飽和臭氧水中,臭氧與超濾膜反應(yīng)時(shí),每次浸泡的超濾膜面積為90.6cm2,達(dá)到設(shè)定浸泡時(shí)間后取出,用超純水充分清洗后保存于超純水中,用于膜結(jié)構(gòu)和性能表征.臭氧與超濾膜反應(yīng)過程中溶液pH值逐漸下降,加入超濾膜之前飽和臭氧水pH值為(5.46±0.03),反應(yīng)8h后溶液pH值為(3.86±0.01).

圖1 臭氧與超濾膜反應(yīng)裝置示意

1.3 超濾膜性能和性質(zhì)分析

1.3.1 膜性能測(cè)試 使用Amicon 8400超濾杯測(cè)試與臭氧反應(yīng)前后超濾膜的透水性能、截留特性和污染特性.在30kPa跨膜壓力(TMP)下過濾超純水,產(chǎn)水量由與電子天平相連的計(jì)算機(jī)記錄,得到超濾膜的純水通量(w),利用達(dá)西定律計(jì)算超濾膜的純水滲透率(P).

式中:w為超濾膜的純水通量,L/(m2·h);為D時(shí)間內(nèi)濾過的體積,L;為有效膜面積,m2;D表示時(shí)間間隔,h;P為純水滲透率,L/(m2·h·bar),P0表示原始膜的純水滲透率.采用相對(duì)透水率(P/P0)表征膜透水性能變化.

HA作為天然地表中的主要有機(jī)污染物[19],可以造成超濾膜的嚴(yán)重污染[20],本實(shí)驗(yàn)采用HA作為模型有機(jī)物評(píng)價(jià)與臭氧反應(yīng)前后超濾膜的截留性能和污染特性.HA溶液采用超純水配制,HA濃度為10mg/L,添加1mmol/L 的NaHCO3、6mmol/L的NaCl和1mmol/L的CaCl2模擬天然水中的背景離子條件,并使用HCl和NaOH調(diào)節(jié)pH值至(7.5± 0.1)[21].采用比通量(0)反映超濾膜過濾HA溶液的污染過程.HA濃度通過紫外-可見光分光光度計(jì)(U3900,日本日立)測(cè)量254nm處吸光度進(jìn)行定量[22],并根據(jù)膜進(jìn)水和膜出水中HA濃度計(jì)算膜對(duì)HA的截留率:

式中:表示截留率,%;P為膜出水的HA濃度,mg/L;f為膜進(jìn)水的HA濃度,mg/L.

1.3.2 膜理化性質(zhì)分析 采用衰減全反射-傅里葉變換紅外光譜儀(ATR-FTIR,NicoletiS50,美國(guó)Thermo Fisher Scientific公司)測(cè)定與臭氧反應(yīng)前后膜表面的紅外光譜反映膜表面特征官能團(tuán)的變化;采用掃描電子顯微鏡(SEM,FEI Quanta 600,美國(guó)FEI 公司)觀察膜表面形貌的變化;使用動(dòng)態(tài)接觸角分析儀(JC2000D4A,上海中辰數(shù)字技術(shù)設(shè)備有限公司)測(cè)定膜表面的純水接觸角反映膜表面親疏水性的變化;采用固體表面電動(dòng)分析儀(SurPASS,奧地利Anton Parr公司)分析膜表面Zeta電位的變化;使用電子萬能試驗(yàn)機(jī)(CMT4204,MTS 公司)測(cè)定膜的拉伸強(qiáng)度和斷裂伸長(zhǎng)率反映其力學(xué)性能.

2 結(jié)果與討論

2.1 臭氧接觸時(shí)間對(duì)PES和PVDF超濾膜性能的影響

透水性能反映了超濾膜對(duì)水流的固有阻力,是評(píng)價(jià)膜老化的常用指標(biāo)[23].如圖2所示,對(duì)于PES膜,與臭氧接觸1h后,膜的相對(duì)透水率達(dá)到1.34;與臭氧接觸2h時(shí)相對(duì)透水率達(dá)到3.25;接觸時(shí)間繼續(xù)延長(zhǎng)時(shí)膜的相對(duì)透水率未繼續(xù)增大,說明與臭氧接觸使PES膜的透水性能顯著增大,且PES膜透水性能的變化主要發(fā)生在與臭氧接觸的前2h內(nèi).對(duì)于PVDF膜,與臭氧接觸1h時(shí),膜的相對(duì)透水率為1.44,接觸時(shí)間繼續(xù)增大時(shí)膜的相對(duì)透水率為1.22～1.44,并未進(jìn)一步增大.透水性能的改變間接反映了膜孔隙率、孔徑等微觀結(jié)構(gòu)的變化[24],臭氧使PES和PVDF膜的透水性能均有所增大,但PVDF膜透水性能的增加幅度顯著低于PES膜,表明PVDF膜對(duì)臭氧的耐受性明顯高于PES 膜,與之前研究的結(jié)果一致[16].

圖2 臭氧接觸時(shí)間對(duì)PES和PVDF膜透水性能的影響

由圖3可以看出,原始PES膜在第1和第2過濾周期對(duì)HA的截留率分別為37.59%和45.62%,第2周期截留率高于第1周期;原始PVDF膜在第1和第2過濾周期對(duì)HA的截留率分別為61.13%和52.59%,2個(gè)周期截留率變化與PES膜相反,這與2種膜界面性質(zhì)和對(duì)HA截留機(jī)理的差異有關(guān).超濾膜對(duì)HA的截留機(jī)理主要包括吸附和尺寸排阻,其中吸附主要是疏水作用力下HA分子與膜材料結(jié)合,尺寸排阻是大于膜孔的HA分子被膜截留[22].由表1可見,PES膜親水性好于PVDF膜,疏水吸附貢獻(xiàn)相對(duì)較小,尺寸排阻作用所占比例較大,第1周期運(yùn)行后膜孔阻塞使膜孔尺寸減小、尺寸排阻作用增強(qiáng),第2周期截留率升高;PVDF膜疏水性較強(qiáng),疏水吸附對(duì)HA截留的貢獻(xiàn)較大,第1周期運(yùn)行后部分吸附位點(diǎn)已被占據(jù),第2周期吸附量減小,總體截留率有所下降.

與臭氧接觸1h后,PES膜對(duì)HA截留率分別降至28.83%和33.94%;與臭氧接觸時(shí)間繼續(xù)增大時(shí),PES膜對(duì)HA的截留率降至0左右,說明此時(shí)PES膜已失去了對(duì)HA的截留能力;對(duì)于PVDF膜,與臭氧接觸1h后,在第1和第2過濾周期對(duì)HA截留率分別降至41.24%和36.50%;與臭氧接觸時(shí)間繼續(xù)增大時(shí),PVDF膜的截留率未進(jìn)一步下降.臭氧作用下PES和PVDF膜對(duì)HA截留率的變化與其透水性能的變化趨勢(shì)一致,其中PES膜透水性能和截留率的變化主要發(fā)生在接觸的前2h內(nèi),而PVDF膜性能的變化主要發(fā)生在前1h內(nèi).

如圖4(a)所示,與臭氧反應(yīng)1h時(shí),PES膜第1周期通量下降曲線與原始膜相似,但反沖洗后通量恢復(fù)效果顯著高于原始膜,說明與臭氧接觸使PES膜的HA污染可逆性增加;與臭氧接觸2h后,PES膜過濾HA溶液時(shí)比通量始終在1.0左右,這一結(jié)果和與臭氧接觸2h后的PES膜對(duì)HA幾乎無截留的結(jié)果一致,進(jìn)一步說明與臭氧反應(yīng)2h時(shí)PES膜分離層已被破壞.對(duì)于PVDF膜(圖4(b)),與原始膜相比,與臭氧接觸1h后PVDF膜的通量下降略有減緩,反沖洗后通量恢復(fù)率顯著增加,這可能與臭氧對(duì)膜界面性質(zhì)的改變有關(guān),有研究表明臭氧氧化會(huì)在PVDF分子鏈上引入含氧親水基團(tuán),這能夠減小HA分子與PVDF分子之間的疏水結(jié)合力,從而使污染可逆性提高[25];與臭氧反應(yīng)時(shí)間繼續(xù)延長(zhǎng)時(shí),PVDF膜的污染行為沒有進(jìn)一步變化,這與膜透水性能和截留特性的變化一致,進(jìn)一步說明臭氧對(duì)PVDF膜的改變主要發(fā)生在接觸的第1h.

2.2 臭氧對(duì)PES和PVDF超濾膜性質(zhì)的影響

如圖5(a)所示,原始PES膜在1580,1486,1320, 1296,1240,1150,1105cm-1處具有很高的吸收強(qiáng)度,這些是PES分子的特征峰[26];在與臭氧反應(yīng)4h后,這些峰的強(qiáng)度均有所降低,同時(shí)在1032cm-1處有新峰的生成,該峰是PES分子鏈斷裂形成的磺酸基的特征峰[27-28],這說明臭氧使PES分子發(fā)生了分解.原始PVDF膜(圖5(b)), PVDF分子的特征吸收峰(1402,1277,1178,1072cm-1)與文獻(xiàn)報(bào)道一致[29],在與臭氧接觸4h后,這些峰的強(qiáng)度無明顯變化,說明臭氧未造成PVDF分子分解.PES和PVDF膜在1668cm-1處均有明顯的吸收峰,該峰是親水性添加劑PVP中酰胺基的特征峰;與臭氧接觸4h后,2種膜在1668cm-1處的峰均消失,在1700cm-1處有新峰生成,說明部分PVP從膜上流失,部分PVP被氧化生成了琥珀酰亞胺[26].

圖5 臭氧對(duì)PES和PVDF膜表面FTIR光譜的影響

如圖6所示,與原始PES膜相比,與臭氧接觸4h后PES膜表面結(jié)構(gòu)已嚴(yán)重破壞,這與臭氧接觸4h后PES膜的透水性能大幅增大、截留性能喪失的結(jié)果一致.對(duì)于PVDF膜,與臭氧接觸4h后,膜孔數(shù)量有所增加,膜孔徑略有增大,這應(yīng)該是由于PVP氧化流失引起的[26],這一結(jié)果也與膜透水性能略有增加、HA截留率略有下降一致,進(jìn)一步證明了PVDF超濾膜對(duì)臭氧的耐受性顯著高于PES膜.

由圖7可見,PES膜在與臭氧反應(yīng)4h后負(fù)電荷顯著增加,pH=3條件下負(fù)電荷的增加說明臭氧使PES膜表面形成了強(qiáng)酸性官能團(tuán),進(jìn)一步說明臭氧使PES分子鏈斷裂形成了磺酸基團(tuán)[28],這與FTIR譜圖(圖5)中1032cm-1處形成新的吸收峰一致;同時(shí)pH值增大時(shí)膜表面電負(fù)性增大趨勢(shì)更為明顯,這可能是由于PVP氧化使膜表面羧酸基團(tuán)增加[30].對(duì)于PVDF膜,強(qiáng)酸性條件下膜表面Zeta電位無明顯變化,pH值增大時(shí)膜表面電負(fù)性增大趨勢(shì)也有所增加,這應(yīng)該也是由于PVP被臭氧氧化使羧酸基團(tuán)有所增加.

圖7 臭氧對(duì)PES和PVDF膜表面Zeta電位的影響

測(cè)試溶液1mmol/L KCl溶液

原始PES膜表面的純水接觸角為(62.40 ± 1.38)°,與臭氧接觸4h后變?yōu)?29.16±7.26)°,這主要是由于臭氧使PES分離層結(jié)構(gòu)破壞,支撐層孔隙很大因而測(cè)得的接觸角顯著下降[31].原始PVDF膜的純水接觸角為 (77.03±1.72)°,與臭氧反應(yīng)4h后變?yōu)?78.07±2.00)°,雖然親水添加劑PVP的流失會(huì)造成膜親水性的降低,但有研究表明臭氧能在PVDF分子鏈上引入含氧親水基團(tuán)[25],因此,綜合作用的結(jié)果使膜表面純水接觸角無明顯變化.此外,與臭氧反應(yīng)后的PVDF膜污染的可逆性大大提高,也應(yīng)該是由于PVDF分子鏈上親水基團(tuán)增加造成的.

膜的力學(xué)性能對(duì)膜的完整性和使用壽命至關(guān)重要,圖8中,原始PES膜的拉伸強(qiáng)度和斷裂伸長(zhǎng)率分別為(16.72±1.24) MPa和(44.00±1.43)%,與臭氧反應(yīng)4h后,拉伸強(qiáng)度和斷裂伸長(zhǎng)率分別下降31.0%和30.2%,表明臭氧使PES膜的機(jī)械性能降低.原始PVDF膜的拉伸強(qiáng)度和斷裂伸長(zhǎng)率分別為(28.76± 3.70) MPa和(32.86±0.66)%,與臭氧接觸4h后,拉伸強(qiáng)度下降53.3%,斷裂伸長(zhǎng)率無明顯變化.本研究中使用的商品化PES和PVDF膜均為復(fù)合膜,分離層的厚度一般在1μm以下,支撐層的厚度一般為100～ 200μm[32],所以膜的力學(xué)性能主要取決于支撐層[29], PES和PVDF膜與臭氧反應(yīng)4h后拉伸強(qiáng)度均降低,說明兩種膜的支撐層在臭氧作用下發(fā)生了不同程度的降解.臭氧作用下PVDF分離層的結(jié)構(gòu)和性能保持穩(wěn)定,但臭氧與PET支撐層的反應(yīng)使PVDF膜的拉伸強(qiáng)度下降,因此將PVDF膜與臭氧聯(lián)用時(shí)應(yīng)采用耐臭氧性較好的材料作為支撐層.

3 結(jié)論

3.1 臭氧對(duì)PES和PVDF超濾膜性能的影響不同.PES膜與臭氧反應(yīng)2h后透水性能增加至原始膜的3倍以上,對(duì)HA的截留能力降至0左右,表明臭氧使PES膜分離層功能喪失;PVDF膜與臭氧接觸前1h內(nèi)膜的透水性能有所升高,對(duì)HA的截留率有所下降,但接觸時(shí)間繼續(xù)增加時(shí)膜的透水性能不再增加,截留率不再下降,膜性能保持穩(wěn)定.

3.2 膜表面化學(xué)組成和界面性質(zhì)分析表明,臭氧使PES和PVDF膜上的親水性添加劑PVP均氧化流失,同時(shí)使PES分子鏈斷裂、PES分離層結(jié)構(gòu)破壞,但未造成PVDF分子結(jié)構(gòu)的破壞,表明PVDF對(duì)臭氧的耐受性顯著高于PES對(duì)臭氧的耐受性.

3.3 臭氧使PES膜的拉伸強(qiáng)度和斷裂伸長(zhǎng)率分別下降31.0%和30.2%,使PVDF膜的拉伸強(qiáng)度下降53.3%,這主要是由于臭氧對(duì)膜支撐層的損傷引起.PVDF分離層對(duì)臭氧耐受性較強(qiáng),用于臭氧預(yù)氧化-超濾組合工藝的PVDF膜應(yīng)使用耐臭氧材料作為支撐層.

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Ozone resistance of polyethersulfone (PES) and polyvinylidene fluoride (PVDF) ultrafiltration membranes.

LI Kai*, XU Wei-hua, SU Qian, WEN Gang, HUANG Ting-lin

(Collaborative Innovation Center of Water Pollution Control and Water Quality Security Assurance of Shaanxi Province, Shaanxi Key Laboratory of Environmental Engineering, Key Laboratory of Northwest Water Resource, Environment and Ecology, Ministry of Education, Xi'an University of Architecture and Technology, Xi’an 710055, China)., 2022,42(3)：1157～1163

The effect of ozone on permeability, retention ability and mechanical properties of polyethersulfone (PES) and polyvinylidene fluoride (PVDF) membranes were investigated by static immersion experiments, and the changes in chemical composition and properties of PES and PVDF ultrafiltration membranes were analyzed. The pure water permeability of PES membrane increased to more than 3times of the original membrane and the retention rate of humic acid (HA) by ozonated membrane decreased to about 0after exposed to saturated ozonated water for 2h at room temperature (20±1) ℃. Combing the analysis of composition and properties of the membrane surface, the hydrophilic additives polyvinylpyrrolidone (PVP) were oxidized, while PES molecules were seriously degraded, leading the destruction of the structure and function of PES separation layer. For the PVDF membrane, the pure water permeability of ozonated membrane was about 1.4times of the original membrane and the HA rejection rate decreased from 61.1% to 41.2% after exposure to saturated ozonated water for 1h. Moreover, the performances of the ozonated membranes did not further decrease with the extension of the exposure time. The analysis of the composition and properties of the membrane surface showed that the damage of the separation layer of PVDF membrane was mainly caused by the oxidation and loss of PVP, and PVDF matrix was not decomposed. The ozone resistance of PVDF membrane separation layer was significantly higher than that of PES membrane, but the mechanical properties of both membranes were significantly decreased by ozonation.

polymeric ultrafiltration membrane；ozone resistance；PES；PVDF；membrane performance

X703

A

1000-6923(2022)03-1157-07

李 凱(1987-),河南泌陽人,男,副教授,博士,主要研究方向?yàn)槟し嬘盟幚砗退此|(zhì)安全保障技術(shù).發(fā)表論文40余篇.

2021-08-12

陜西省重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2019ZDLSF06-01);陜西省自然科學(xué)基金青年基金資助項(xiàng)目(2020JQ-672);國(guó)家自然科學(xué)基金資助項(xiàng)目(51608427)

*責(zé)任作者, 副教授, likai@xauat.edu.cn