Abstract— <p>Correlation dependence <i>B</i><sub>0</sub> = <i>B</i><sub>0</sub>(β, ω) is determined as a function of β and acentric factor ω, based on an analysis of experimental information about critical amplitude <i>B</i><sub>0</sub> and critical index β of the saturation line. The proposed correlation uses 20 substances for which there are experimental data on <i>B</i><sub>0</sub> in ranges 3.15&#xa0;≤ β ≤ 3.85 and ω ≤ 0.365. It is established for all considered substances that the absolute values of the maximum relative deviations <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11504_2025_6104_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta {{B}_{{0,{\text{max}}}}}\)</EquationSource> <!--PhysChA2570027Rykov-m1--> </InlineEquation> of the experimental values of critical amplitude <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11504_2025_6104_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\({{B}_{{0,{\text{exp}}}}}\)</EquationSource> <!--PhysChA2570027Rykov-m2--> </InlineEquation> from ones calculated using correlation <i>B</i><sub>0</sub>(β, ω) are no greater than 6%. Some values of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11504_2025_6104_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\({{B}_{{0,{\text{exp}}}}}\)</EquationSource> <!--PhysChA2570027Rykov-m3--> </InlineEquation> for H<sub>2</sub>O (|<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11504_2025_6104_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta {{B}_{{0,{\text{max}}}}}\)</EquationSource> <!--PhysChA2570027Rykov-m4--> </InlineEquation>| = 6.64%), SF<sub>6</sub> (|<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11504_2025_6104_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta {{B}_{{0,{\text{max}}}}}\)</EquationSource> <!--PhysChA2570027Rykov-m5--> </InlineEquation>|&#xa0;= 8.75%), and <sup>4</sup>He (|<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11504_2025_6104_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta {{B}_{{0,{\text{max}}}}}\)</EquationSource> <!--PhysChA2570027Rykov-m6--> </InlineEquation>| = 10.3%) are exceptions. In the course of this work, D.Yu. Ivanov’s hypothesis of (2007) of the universality of the critical amplitude <i>B</i><sub>0</sub> (up to the critical index β) is considered. It is shown that his proposed correlation dependence <i>B</i><sub>0</sub> = <i>B</i><sub>0</sub>(β) produces values of |<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11504_2025_6104_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta {{B}_{{0,{\text{max}}}}}\)</EquationSource> <!--PhysChA2570027Rykov-m7--> </InlineEquation>| that reach 35%. It is also established that new correlation <i>B</i><sub>0</sub> = <i>B</i><sub>0</sub>(β, ω) agrees with correlation dependence <i>B</i><sub>0</sub> = <i>B</i><sub>0</sub>(ω) proposed by R. A. Perkins et al. (Int. J. Thermophys. <b>34</b>, 191 (2013)) at β = 0.326. However, deviations δ<i>B</i><sub>0</sub> for all considered groups of substances are greater than 10% when <i>B</i><sub>0</sub> = <i>B</i><sub>0</sub>(ω), even for β ≥ 0.34. The assertion that amplitude <i>B</i><sub>0</sub> characterizes a substance is confirmed because it is affected by the nonsphericity of the molecules, which is characterized by ω. The possibility of using new correlation <i>B</i><sub>0</sub> = <i>B</i><sub>0</sub>(β, ω) to determine the critical amplitude of the saturation line of <sup>4</sup>He is discussed as well.</p>

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Correlation between a Critical Index and the Critical Amplitude of a Saturation Line

  • S. V. Rykov,
  • I. V. Kudryavtseva

摘要

Abstract—

Correlation dependence B0 = B0(β, ω) is determined as a function of β and acentric factor ω, based on an analysis of experimental information about critical amplitude B0 and critical index β of the saturation line. The proposed correlation uses 20 substances for which there are experimental data on B0 in ranges 3.15 ≤ β ≤ 3.85 and ω ≤ 0.365. It is established for all considered substances that the absolute values of the maximum relative deviations \(\delta {{B}_{{0,{\text{max}}}}}\) of the experimental values of critical amplitude \({{B}_{{0,{\text{exp}}}}}\) from ones calculated using correlation B0(β, ω) are no greater than 6%. Some values of \({{B}_{{0,{\text{exp}}}}}\) for H2O (| \(\delta {{B}_{{0,{\text{max}}}}}\) | = 6.64%), SF6 (| \(\delta {{B}_{{0,{\text{max}}}}}\) | = 8.75%), and 4He (| \(\delta {{B}_{{0,{\text{max}}}}}\) | = 10.3%) are exceptions. In the course of this work, D.Yu. Ivanov’s hypothesis of (2007) of the universality of the critical amplitude B0 (up to the critical index β) is considered. It is shown that his proposed correlation dependence B0 = B0(β) produces values of | \(\delta {{B}_{{0,{\text{max}}}}}\) | that reach 35%. It is also established that new correlation B0 = B0(β, ω) agrees with correlation dependence B0 = B0(ω) proposed by R. A. Perkins et al. (Int. J. Thermophys. 34, 191 (2013)) at β = 0.326. However, deviations δB0 for all considered groups of substances are greater than 10% when B0 = B0(ω), even for β ≥ 0.34. The assertion that amplitude B0 characterizes a substance is confirmed because it is affected by the nonsphericity of the molecules, which is characterized by ω. The possibility of using new correlation B0 = B0(β, ω) to determine the critical amplitude of the saturation line of 4He is discussed as well.