二元溶液完全标度理论及临界指前因子普适标度关系的光散射实验检验
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摘要
设计、构建了适于研究临界现象的高控温精度静／动态光散射仪,测量了苯甲腈+十一烷,苯甲腈+十二烷,苯甲腈+十三烷,苯甲腈+十四烷,苯甲腈十十五烷,苯甲腈+十六烷六个体系在临界点附近共存两相的散射光强,得到关联长度ξ和渗透压缩系数χ,并分析两相ξ和χ的不对称性。结果显示：关联长度无明显不对称性,而渗透压缩系数存在显著的不对称性。计算出渗透压缩系数不对称因子Aχ,并从完全标度理论出发,推导出Aχ的表达式,拟合结果发现Aχ可用和γ分别是与共存曲线和渗透压缩系数相关的临界指数)描述,|△T|β是主导项,从而首次从共存两相渗透压缩系数的不对称性的角度验证了完全标度理论,并说明完全标度理论在对不同热力学量(共存曲线直径和渗透压缩系数)的不对称行为的描述上的一致性。本文结果同时发现|△T|γ-1+β对于准确描述渗透压缩系数的不对称性是不可忽略的。
本文还测量了硝基苯+十一烷,硝基苯+十二烷,硝基苯+十三烷,硝基苯+十四烷,和苯甲腈+十一烷,苯甲腈+十二烷,苯甲腈+十三烷,苯甲腈+十四烷,苯甲腈+十五烷,苯甲腈+十六烷,苯甲腈+十七烷共十一个体系在一相区的浊度,得到一相区关联长度和渗透压缩系数的临界指数υ和γ以及指前因子ξ0和χ0.由于实验仪器和数据分析方法的改进,所得关联长度的指前因子的精确度显著提高。结合由量热实验得到的临界热容的指前因子A+,计算了普适性标度关系和的值,结果与理论预测一致。
A static/dynamic light scattering setup with high temperature control precision was designed and constructed,which is suitable for the study of the c ritical phenomena.The scattered light intensities of the coexisting phases for systems{benzonitrile+undecane},{benzonitrile+dodecane),{benzonitrile+tridecane},{benzonitrile+tetradecane),{benzonitrile+pentadecane),and{benzonitrile+hexadecane}in the critical region were measured,from which the values of the correlation1ength and osmotic compressibility were deduced and no asymmetry was observed for the correlation length,while the asymmetric behavior was clearly detected for the osmotic compressibility.The asymmetry ratio Ax was calculated.An expression of the asymmetry ratiO Ax was derived from the frame of complete sealing theory and used to fit the experimental data.It was found for the first time that the experimental data can be well described by (where△T=(T-Tc)/Tc,β and γ are the critical exponents for the coexistence curve and the susceptibility respectively)and the term|△T|β was dominant,which supports the complete scaling theory and also indicates the consistency Of the complete scaling theory in the description of different asymmetric behaviors(diameter of the coexistence curve and the osmotic compressibility). Moreover, it was found that the contribution of the heat capacity-related term|△T|γ-1+β was also important in precise description of the asymmetric behaviors of the osmotic compressibility.
We also measured the turbidities of{nitrobenzene+undecane},{nitrobenzene+dodecane},{nitrobenzene+tridecane},{nitrobenzene+tetradecane},{benzonitrile+undecane},{benzonitrile+dodecane},{benzonitrile+tridecane},{benzonitrile+tetradecane},{benzonitrile+pentadecane},{benzonitrile+hexadecane},and{benzonitrile+heptadecane}in the critical one-phase region,from which the critical exponents v,and γ and the critical amplitudes ζ0and χ0were deduced for the correlation length and osmotic compressibility,respectively.The higher precision for measurement of the critical amplitudes was achieved because of the improvements of the experimental setup and the data analysis method. The critical amplitudesζ0and χ0together with the critical amplitudes related to the coexistence curve B and the heat capacity in one-phase region A+were used to test the universal ratios and which were in well agreements with the theoretical predictions.
本文还测量了硝基苯+十一烷,硝基苯+十二烷,硝基苯+十三烷,硝基苯+十四烷,和苯甲腈+十一烷,苯甲腈+十二烷,苯甲腈+十三烷,苯甲腈+十四烷,苯甲腈+十五烷,苯甲腈+十六烷,苯甲腈+十七烷共十一个体系在一相区的浊度,得到一相区关联长度和渗透压缩系数的临界指数υ和γ以及指前因子ξ0和χ0.由于实验仪器和数据分析方法的改进,所得关联长度的指前因子的精确度显著提高。结合由量热实验得到的临界热容的指前因子A+,计算了普适性标度关系和的值,结果与理论预测一致。
A static/dynamic light scattering setup with high temperature control precision was designed and constructed,which is suitable for the study of the c ritical phenomena.The scattered light intensities of the coexisting phases for systems{benzonitrile+undecane},{benzonitrile+dodecane),{benzonitrile+tridecane},{benzonitrile+tetradecane),{benzonitrile+pentadecane),and{benzonitrile+hexadecane}in the critical region were measured,from which the values of the correlation1ength and osmotic compressibility were deduced and no asymmetry was observed for the correlation length,while the asymmetric behavior was clearly detected for the osmotic compressibility.The asymmetry ratio Ax was calculated.An expression of the asymmetry ratiO Ax was derived from the frame of complete sealing theory and used to fit the experimental data.It was found for the first time that the experimental data can be well described by (where△T=(T-Tc)/Tc,β and γ are the critical exponents for the coexistence curve and the susceptibility respectively)and the term|△T|β was dominant,which supports the complete scaling theory and also indicates the consistency Of the complete scaling theory in the description of different asymmetric behaviors(diameter of the coexistence curve and the osmotic compressibility). Moreover, it was found that the contribution of the heat capacity-related term|△T|γ-1+β was also important in precise description of the asymmetric behaviors of the osmotic compressibility.
We also measured the turbidities of{nitrobenzene+undecane},{nitrobenzene+dodecane},{nitrobenzene+tridecane},{nitrobenzene+tetradecane},{benzonitrile+undecane},{benzonitrile+dodecane},{benzonitrile+tridecane},{benzonitrile+tetradecane},{benzonitrile+pentadecane},{benzonitrile+hexadecane},and{benzonitrile+heptadecane}in the critical one-phase region,from which the critical exponents v,and γ and the critical amplitudes ζ0and χ0were deduced for the correlation length and osmotic compressibility,respectively.The higher precision for measurement of the critical amplitudes was achieved because of the improvements of the experimental setup and the data analysis method. The critical amplitudesζ0and χ0together with the critical amplitudes related to the coexistence curve B and the heat capacity in one-phase region A+were used to test the universal ratios and which were in well agreements with the theoretical predictions.
引文
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