程大海，伍 川，董 紅，武 俠，張引弟

(杭州師范大學(xué)有機(jī)硅化學(xué)及材料技術(shù)教育部重點(diǎn)實(shí)驗(yàn)室，浙江 杭州 310012)

原子貢獻(xiàn)法估算硅烷及硅氧烷的摩爾折射度

程大海，伍 川，董 紅，武 俠，張引弟

(杭州師范大學(xué)有機(jī)硅化學(xué)及材料技術(shù)教育部重點(diǎn)實(shí)驗(yàn)室，浙江 杭州 310012)

根據(jù)硅烷和硅氧烷的分子結(jié)構(gòu)，利用原子貢獻(xiàn)法考察了中心Si原子及與其相連接的不同原子(C、H、Cl、O)和官能團(tuán)(苯基和碳碳雙鍵)的摩爾折射度，以110種硅烷和硅氧烷折射率和密度實(shí)驗(yàn)數(shù)據(jù)對(duì)建立的摩爾折射度估算方程進(jìn)行了關(guān)聯(lián)，利用SPSS 19.0軟件對(duì)摩爾折射度方程組進(jìn)行了擬合，得到上述原子和官能團(tuán)的摩爾折射度數(shù)值，110種化合物摩爾折射度計(jì)算值與文獻(xiàn)值之間的總體平均絕對(duì)誤差、平均相對(duì)誤差及均方根誤差分別為0.227 cm3.mol-1、0.433%及0.369 cm3·mol-1，為已知結(jié)構(gòu)有機(jī)硅新化合物折射率的預(yù)測(cè)或特定折射率有機(jī)硅化合物的設(shè)計(jì)合成提供了依據(jù).

原子貢獻(xiàn)法;摩爾折射度;硅烷;硅氧烷;估算

前 言

物質(zhì)微觀結(jié)構(gòu)與宏觀性能之間的關(guān)系一直是化學(xué)及材料領(lǐng)域關(guān)注的焦點(diǎn).按照分子內(nèi)原子或官能團(tuán)的組成及相互作用，已采用原子貢獻(xiàn)法、基團(tuán)貢獻(xiàn)法和化學(xué)鍵貢獻(xiàn)法對(duì)各種碳系化合物的摩爾體積、摩爾折射度等具有強(qiáng)度性質(zhì)的狀態(tài)函數(shù)進(jìn)行了廣泛研究，在此基礎(chǔ)上可準(zhǔn)確預(yù)測(cè)烷烴、芳烴、脂肪醇和硫醇等碳系化合物的折射率等光學(xué)性能[1-2].假定原子對(duì)物質(zhì)某一特性的貢獻(xiàn)在不同溶液環(huán)境中不變，那么任一純物質(zhì)或者混合物的某一特性都是由構(gòu)成其所有原子的貢獻(xiàn)之和.人類已合成的化合物數(shù)以萬計(jì)，但這些化合物均由少數(shù)幾種原子構(gòu)成.即使加和規(guī)則只是近似成立，但通過對(duì)少量純物質(zhì)或混合物的實(shí)驗(yàn)數(shù)據(jù)進(jìn)行擬合，回歸得到構(gòu)成物質(zhì)原子特性的貢獻(xiàn)值或參數(shù)值，則可依據(jù)加和規(guī)則對(duì)物性參數(shù)未知的含有同類原子的其它純物質(zhì)或混合物的有關(guān)性質(zhì)進(jìn)行預(yù)測(cè)，從而大大減少人、財(cái)、物和時(shí)間的消耗，用最少的實(shí)驗(yàn)工作量獲得最大的效果[3].例如，利用摩爾折射度的加和性質(zhì)，可由組成化合物的原子種類和數(shù)量及官能團(tuán)的屬性預(yù)測(cè)目標(biāo)化合物的折射率，為開發(fā)高折射率的光學(xué)材料提供有益指導(dǎo)[4].硅烷及以硅氧烷為骨架結(jié)構(gòu)的有機(jī)硅聚合物自20世紀(jì)40年代實(shí)現(xiàn)工業(yè)化生產(chǎn)以來，以其優(yōu)異的光學(xué)、熱性能及耐輻射性能廣泛應(yīng)用于各個(gè)領(lǐng)域，成為不可替代的新材料.雖然碳和硅元素同屬IVA族元素，但兩者原子半徑、電負(fù)性及價(jià)層空軌道差異較大，尤其是硅原子d軌道可通過sp3d或sp3d2等雜化軌道形式參與成鍵，具有很強(qiáng)的pπ-dπ作用，因此，硅烷和硅氧烷等有機(jī)硅化合物與碳系化合物性質(zhì)明顯不同，不能利用以碳系化合物為分子模型推導(dǎo)的各原子或官能團(tuán)的貢獻(xiàn)值對(duì)有機(jī)硅化合物的熱力學(xué)性質(zhì)進(jìn)行預(yù)測(cè).相對(duì)于碳系化合物，有機(jī)硅化合物微觀結(jié)構(gòu)與宏觀性質(zhì)的研究較少，文獻(xiàn)中雖報(bào)道了采用分子連接性預(yù)測(cè)硅烷的摩爾折射度[1-2,5-6]，但僅僅局限于烷基硅烷化合物，對(duì)于取代硅烷及硅氧烷化合物微觀結(jié)構(gòu)與摩爾折射度和摩爾體積等熱力學(xué)性質(zhì)的關(guān)系研究則鮮見報(bào)道.本文采用原子貢獻(xiàn)法研究了硅烷、取代硅烷及低聚二硅氧烷分子結(jié)構(gòu)與其摩爾折射度的關(guān)系.

1 基本原理和方法

硅原子通常采用sp3雜化方式形成4個(gè)σ成鍵軌道，可與4個(gè)原子相連接，但硅原子除s和p軌道外，還有5個(gè)空3 d軌道可形成pπ-dπ共價(jià)鍵.因此，當(dāng)硅原子作為中心原子時(shí)，與硅直接相連的4個(gè)原子所處的化學(xué)環(huán)境不同于碳原子作為中心原子時(shí)，導(dǎo)致這些原子對(duì)于有機(jī)硅化合物摩爾折射度的貢獻(xiàn)值發(fā)生變化.碳系化合物中部分原子摩爾折射度的數(shù)值已被報(bào)道[4],如果僅僅考慮硅原子對(duì)緊鄰的4個(gè)原子(α位置)的影響而忽略與其分子間距更遠(yuǎn)的β和γ位置原子與硅原子的相互作用，以已確定的碳系化合物中各原子的摩爾折射度為基礎(chǔ)，通過對(duì)各原子摩爾折射度數(shù)值進(jìn)行修正以消除中心的硅原子和碳原子化學(xué)環(huán)境差異對(duì)于有機(jī)硅化合物折射率的影響，則可計(jì)算得到有機(jī)硅化合物中各個(gè)原子、雙鍵和苯基官能團(tuán)的摩爾折射度，進(jìn)而可建立有機(jī)硅化合物或聚合物微觀組成結(jié)構(gòu)與宏觀折射率之間的聯(lián)系.

表1 硅烷及硅氧烷分子中原子修正值的定義

從有機(jī)硅化合物的結(jié)構(gòu)分析可知，與Si原子直接相連的O原子主要包括Si-O-C和Si-O-Si兩種.假定兩種氧原子摩爾折射度的修正值分別為d和h， Si原子的摩爾折射度為a，與Si原子直接相連的C原子、Cl原子、H原子、苯基和雙鍵的修正值分別為b、c、e、f和g，如表1所示.以甲基三甲氧基硅烷(CH3Si(OCH3)3)為例，該化合物分子中，與中心Si原子直接相連的有3個(gè)O原子和1個(gè)C原子，由碳系化合物回歸得到的C原子、H原子、O原子的摩爾折射度數(shù)值分別為2.418、1.100和1.643 cm3.mol-1[4]，因此甲基三甲氧基硅烷的摩爾折射度可表示為MR=a+2.418×4+1.100×12+1.643×3+b+3×d.

物質(zhì)的折射率(nD)與摩爾折射度(MR)之間的關(guān)系可用Lorentz-Lorenz經(jīng)驗(yàn)方程進(jìn)行定量描述(式(1))[4]：

(1)

摩爾折射度(MR)雖為熱力學(xué)強(qiáng)度性質(zhì)，但具有加和性，與組成化合物的原子、分子或基團(tuán)的種類及數(shù)量有關(guān)，如式(2)所示：

(2)

式中n(Gi)、Gi分別為構(gòu)成硅烷分子的原子數(shù)目及其對(duì)于摩爾折射度的貢獻(xiàn)值.

采用式(3)計(jì)算摩爾折射度(MR)文獻(xiàn)值與計(jì)算值之間的均方根誤差(RMSD)：

(3)

式中n為摩爾折射度參數(shù)回歸方程組中化合物的數(shù)目，m為回歸方程組中回歸參數(shù)的數(shù)目.

2 計(jì)算結(jié)果及討論

以表2所示110種硅烷和硅氧烷化合物作為樣本，利用已報(bào)道的碳系化合物中原子摩爾折射度的數(shù)據(jù)[4]，采用原子貢獻(xiàn)法研究硅烷化合物中分子結(jié)構(gòu)與摩爾折射度之間的關(guān)系.利用文獻(xiàn)值按式(1)計(jì)算各有機(jī)硅化合物的摩爾折射度(MRexp)，對(duì)每一樣本化合物采用式(2)描述原子和官能團(tuán)種類和數(shù)量與化合物摩爾折射度之間的關(guān)系，構(gòu)成由110個(gè)多元一次線性方程形成的方程組，采用SPSS 19.0數(shù)理統(tǒng)計(jì)軟件對(duì)方程組進(jìn)行回歸擬合，利用學(xué)生t-分布的區(qū)間估計(jì)公式，計(jì)算得到各原子和基團(tuán)摩爾折射度的修正值及其在置信水平為0.95上的置信區(qū)間(見表3).

表2 110種硅烷及硅氧烷化合物的摩爾折射度

注：RE=(MRpredt-MRexp)/MRexp

表3 有機(jī)硅化合物各原子和基團(tuán)摩爾折射度計(jì)算結(jié)果

備注：MR′為碳系化合物中各原子和官能團(tuán)的摩爾折射度

利用回歸得到的各原子和基團(tuán)摩爾折射度修正值，由硅烷或硅氧烷分子結(jié)構(gòu)出發(fā)，計(jì)算得到各化合物的摩爾折射度(MRpredt).例如，甲基三氯硅烷(CH3SiCl3)的摩爾折射度表達(dá)式為：

MRpredt=a+2.418+b+1.100×3+5.967×3+3×c

將回歸得到的修正值a=8.304，b=-0.246，c=-0.842代入上式計(jì)算得到甲基三氯硅烷的摩爾折射度MRpredt=29.151 cm3.mol-1，與實(shí)驗(yàn)值MRexp=29.110 cm3.mol-1非常接近，兩者之間的相對(duì)誤差僅為-0.141%.分別計(jì)算110個(gè)樣本的摩爾折射度數(shù)值(MRpredt)并與實(shí)驗(yàn)值進(jìn)行對(duì)比，結(jié)果列于表2中，計(jì)算值與實(shí)驗(yàn)值之間的總體平均絕對(duì)誤差、平均相對(duì)誤差及均方根誤差分別為0.227 cm3.mol-1、0.433%及0.369 cm3·mol-1，可見摩爾折射度預(yù)測(cè)值與實(shí)驗(yàn)值之間的偏差小，兩者之間的一致性令人滿意(見圖1).

為進(jìn)一步驗(yàn)證原子貢獻(xiàn)法估算得到各原子及苯基和乙烯基官能團(tuán)的摩爾折射度，任意選取17種化合物，計(jì)算其摩爾折射度并與文獻(xiàn)計(jì)算值進(jìn)行對(duì)比，結(jié)果如表4和圖2所示.17個(gè)樣本預(yù)測(cè)結(jié)果的平均絕對(duì)誤差為0.329 cm3.mol-1、平均相對(duì)誤差為0.470%、均方根誤差為0.724 cm3.mol-1.可見預(yù)測(cè)值與實(shí)驗(yàn)值的一致性令人滿意.

圖1 摩爾折射度預(yù)測(cè)值與實(shí)驗(yàn)值的比較Fig. 1 Comparisons between predicted and experimental values for molar refraction

圖2 17種有機(jī)硅化合物摩爾折射度預(yù)測(cè)值與實(shí)驗(yàn)值的比較Fig. 2 Comparisons between predicted and experimental values of molar refraction for 17 kinds of silicone compounds

表4有機(jī)硅化合物摩爾折射度的驗(yàn)證

Tab.4Verificationofmolarrefractionforsiliconecompounds

序號(hào)物質(zhì)名稱CASRNρ/g．cm-3n20DMRexpMRpredtAE100×RE1二乙基四甲基二硅氧烷[8]2295?17?20．79691．401258．08458．1120．0280．0492乙烯基五甲基二硅氧烷[8]1438?79?50．7871．393052．88553．0690．1830．3463正丙基二甲基乙氧基硅烷[56]18387?29?60．78491．396944．87644．876-0．001-0．0024正丙基乙基二氯硅烷[57]18147?34?71．03431．437043．35043．3520．0030．00651，7?二乙烯基?1，7?二乙基?1，3，3，5，5，7?六甲基四硅氧烷[58]21121?15?30．90021．4240102．829103．8641．0361．00761，1，3，3，5，5，7，7?八甲基?1，7?二苯基四硅氧烷[59]18588?96?00．97851．4790126．012125．903-0．110-0．08771，1，1，3，3，5，5，7，7?九甲基四硅氧烷[41]17478?07?80．86641．392181．55481．8620．3070．37781，9?二乙基?1，3，3，5，5，7，7，9?八甲基?1，9?二乙烯基五硅氧烷[58]21121?16?40．89601．4170122．626122．548-0．077-0．06391，1，1，5，5，9，9，9?八乙基?3，3，7，7?四甲基五硅氧烷[60]21380?16?50．89911．4270141．939141．872-0．067-0．048101，1，3，3，5，5，7，7，9，9?十甲基五硅氧烷[41]995?83?50．88181．390295．95796．1630．2060．21411乙基二乙氧基氯硅烷[61]18171?16?90．98721．400644．93045．3570．4280．95212乙烯基二乙氧基氯硅烷[62]18187?22?90．99251．400144．14744．9320．7851．77813四乙基二氯二硅氧烷[63]18825?03?11．03011．443066．74066．654-0．086-0．12814二乙基甲氧基氯硅烷[64]18157?18?10．96391．414139．59339．9100．3180．80315二乙基乙氧基氯硅烷[61]18171?09?00．94231．414544．25944．5280．2690．60916二乙基乙氧基硅烷[61]4087?42?70．78971．400040．60840．493-0．115-0．282171，3，5，7，9?五乙基?1，1，3，5，7，9，9?七甲基五硅氧烷[65]18557?66?90．9011．4150126．451128．0181．5671．239

注：AE=MRexp-MRpredt

由表3和表4及圖1和圖2可以看出，含有苯基或乙烯基的硅烷和硅氧烷的摩爾折射度預(yù)測(cè)值與實(shí)驗(yàn)值之間的誤差較大,這是由于計(jì)算過程中將苯基與雙鍵當(dāng)作單個(gè)原子進(jìn)行了簡(jiǎn)化處理，實(shí)際上，苯基和雙鍵與中心Si原子之間存在更為復(fù)雜的pπ-dπ作用，若忽略苯基和雙鍵中β和γ位置上其它原子對(duì)于中心Si原子的長(zhǎng)程作用，將導(dǎo)致含苯基或乙烯基的硅烷和硅氧烷的摩爾折射度及摩爾體積預(yù)測(cè)值與實(shí)驗(yàn)值之間出現(xiàn)較大的誤差.

3 結(jié) 論

根據(jù)硅烷和硅氧烷分子的結(jié)構(gòu)，對(duì)其進(jìn)行合理拆分，在文獻(xiàn)報(bào)道的碳系化合物原子摩爾折射度數(shù)值基礎(chǔ)上，對(duì)與硅原子直接相連的原子和基團(tuán)進(jìn)行修正，通過回歸分析得到Si、Cl、H、C、C=C、O(Si—O—C中)、O(Si—O—Si中)及苯環(huán)的摩爾折射度數(shù)值；除含苯環(huán)和C=C雙鍵的有機(jī)硅化合物外，計(jì)算得到的原子摩爾折射度數(shù)值可成功用于有機(jī)硅化合物摩爾折射度的預(yù)測(cè)，預(yù)測(cè)值與實(shí)驗(yàn)值之間相對(duì)誤差較小，為已知結(jié)構(gòu)有機(jī)硅新化合物折射率的預(yù)測(cè)或特定折射率的有機(jī)硅化合物的設(shè)計(jì)合成提供了有力工具.

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TheMolarRefractionEstimationofSilanesandSiloxanesbyAtomContributionMethod

CHENG Dahai, WU Chuan, DONG Hong, WU Xia, ZHANG Yindi

(Key Laboratory of Organosilicon Chemistry and Material Technology, Ministry of Education, Hangzhou Normal University,Hangzhou 310012, China)

The molar refraction of the central Si atom and different atoms (C, H, O, Cl) as well as or functional groups (phenyl group and C=C double bond) that directly connected with the central Si atom in silane or siloxane molecules was investigated by atom contribution method. The molar refraction values and density experimental data of 110 kinds of silanes and siloxanes were used to correlate with the established estimation formula of molar refraction. The equation set of molar refraction was fitted by SPSS 19.0 software and the values of molar refraction of each studied atoms and groups were estimated. The overall mean absolute error, the mean relative error and the root-mean-square deviation between the estimated and calculated values of the molar refraction of 110 kinds of chemicals were 0.227 cm3.mol-1, 0.433% and 0.369 cm3·mol-1, respectively. The results are beneficial to the prediction of the refractive index of the novel silicone compounds with known structure or the design and synthesis of the novel silicone compounds with specific refractive index.

atom contribution method; molar refraction; silane; siloxane; estimation

2013-05-10

浙江省公益技術(shù)應(yīng)用研究資助項(xiàng)目(2011C21026)；石油和化工行業(yè)科技指導(dǎo)計(jì)劃資助項(xiàng)目(2011-07-06).

伍 川(1970—),男，研究員，主要從事有機(jī)硅樹脂研究.E-mail:catalyst88@163.com

10.3969/j.issn.1674-232X.2013.05.003

O642.1

A

1674-232X(2013)05-0395-09