Electric permittivity anomaly close to the critical mixing point: An improved method of estimation of the exponent describing a weak critical anomaly

Temperature, concentration, and frequency dependence of the dielectric constant near the critical point of the binary liquid mixture nitrobenzene-tetradecane

“…Many data showed that the observed singularity in the static dielectric constant in the homogeneous phase was consistent with including a ͉t͉ 1−␣ term ͓with t = ͑T − T c ͒ / T c and ␣ the heat capacity critical exponent͔, [12][13][14][15][16][17] in agreement with the predictions of a scaling formulation for fluids under an electric field. 18 Moreover, the anomalous behavior of ⑀ in the one-phase region was experimentally confirmed to be an intrinsic effect, 13,14,19,20 different from the critical behavior of the density .…”

Electric Permittivity Anomaly Close to the Critical Consolute Point of a Nitrobenzene + Octane Liquid Mixture

“…Recently a "critical increment" method has been proposed, convenient for an analysis of weak critical anomalies. 33,34 The method has its advantages: (a) it reduces the number of matched parameters, (b) it does not produce an increase in the error (like the derivative method), (c) it makes it possible to omit the correction-to-scaling element (analysis is performed in Table 1. Fitting of eq 1 to the Experimental Points Obtained in Run 1 a the vicinity of T c only), and (d) it makes it possible to avoid correlations between the critical amplitudes.…”

“…Because the analyzed range is close to the critical temperature, the correction-to-scaling element could be omitted. Consequently, the critical increment has the following form 33…”

“…Recently a “critical increment” method has been proposed, convenient for an analysis of weak critical anomalies. , The method has its advantages: (a) it reduces the number of matched parameters, (b) it does not produce an increase in the error (like the derivative method), (c) it makes it possible to omit the correction-to-scaling element (analysis is performed in the vicinity of T c only), and (d) it makes it possible to avoid correlations between the critical amplitudes. The method consists of analyzing the differences between the experimental values and the tangent line calculated at some arbitrarily selected reference temperature T x in the precritical region normalΔ false( normalε normalρ̑ − 1 false) normalc = ( ε ρ̑ − 1 ) − ( B 0 + B 1 T ) where ( B 0 + B 1 T ) is the tangent to the ερ̑ –1 ( T ) calculated at T x .…”

“…Because the analyzed range is close to the critical temperature, the correction-to-scaling element could be omitted. Consequently, the critical increment has the following form normalΔ false( normalε normalρ̑ − 1 false) normalc = prefix− italicC 1 − normalα ( α · t x 1 − α + false( 1 − normalα false) · t x − α · t − t 1 − α ) where t x = ( T x / T c – 1) is the reduced reference temperature. The results of the fitting of eq to the critical increment obtained in run 1 are presented in Table .…”