Article pubs.acs.org/jced
Cite This: J. Chem. Eng. Data 2019, 64, 3416−3435
Influence of α‑Olefin Concentration and Length on the HighPressure Phase Behavior of (α-Olefin + n‑Hexane + LLDPE) Systems Riccardo M. Swanepoel and Cara E. Schwarz* Department of Process Engineering, Stellenbosch University, Banghoek Road, Stellenbosch 7600, South Africa
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S Supporting Information *
ABSTRACT: Liquid to vapor−liquid, liquid−liquid to vapor−liquid−liquid, and liquid to liquid−liquid transition pressures of (α-olefin + n-hexane + LLDPE) systems were measured using a newly constructed and verified synthetic-visual high-pressure cell and metallocene linear low-density polyethylene (LLDPE: M̅ w = 199 kg·mol−1, M̅ w/M̅ n = 2.62, 2.56 mol % 1hexene). New phase behavior data are reported for a quasibinary (n-hexane + LLDPE) system at polymer mass percentages of wP = (0.5−5) wt % and quasiternary (α-olefin + n-hexane + LLDPE) systems for wP = 3 wt % and polymer-free α-olefin mass percentages of up to 3 wt % ethylene, 20 wt % 1butene, 100 wt % 1-hexene, 30 wt % 1-octene, and 30 wt % 1-decene. The reported data span temperatures of T = (380−470) K and pressures of P = (0.5−13) MPa. They show that (i) transition temperatures and pressures change linearly with α-olefin mass fraction in the solvent; (ii) the C2 to C6 αolefins decrease, and the C8 to C10 α-olefins increase the transition temperatures; and (iii) ethylene has a significant antisolvency effect. The measured data are correlated and predicted successfully with the modified Sanchez−Lacombe equation of state.
1. INTRODUCTION Linear low-density polyethylene (LLDPE) has replaced lowdensity polyethylene (LDPE) in many applications because of LLDPE’s superior mechanical properties.1 It is produced by copolymerising ethylene (C2) monomers with longer α-olefin (Cα) comonomers, such as 1-butene (C4), 4-methyl-1pentene, 1-hexene (C6), and 1-octene (C8), which incorporates short-chain branches (SCBs) onto the polyethylene backbone.2 In the solution process for LLDPE production, the monomers and comonomers are dissolved in an inert hydrocarbon diluent, typically a C4 to C8 alkane and/or its isomers, where they react to produce LLDPE.2,3 The diluent, monomers, and comonomers collectively constitute the solvent in which the LLDPE is dissolved. It is desired to operate the reactors and catalyst separation stages of the solution process at conditions where a single liquid phase exists, and the LLDPE remains completely dissolved in the solvent.4 The incipience of a second liquid phase in these process units is problematic for the control of the molecular mass distribution (MMD) of the product3 and often demands a plant shutdown for the mechanical removal of this phase.5 Consequently, detailed knowledge of the (solvent + LLDPE) fluid phase behavior is required. The phase behavior of (solvent + LLDPE) systems of interest to the solution process, as shown in Figure 1, is usually of type IV, according to the classification of Van Konynenburg and Scott6 and of class 2Pl according to the classification of Bolz et al.7 At high pressures, the entire system exists in a single liquid (L) phase. A reduction in pressure can cause the single liquid © 2019 American Chemical Society
Figure 1. Pressure−temperature (PT) isopleth of a (solvent + LLDPE) system exhibiting type IV phase behavior; LMEP; and VLCP. Adapted from ref 12.
phase to demix into two liquid phases upon crossing the liquid− liquid (LL) line, also called the cloud point curve. The vapor− liquid−liquid (VLL) line is crossed upon further reduction in pressure, which leads to vaporization of the solvent and eventually yields a vapor−liquid (VL) region. The VLL line terminates at the vapor−liquid critical point (VLCP). The Received: March 12, 2019 Accepted: June 27, 2019 Published: July 17, 2019 3416
DOI: 10.1021/acs.jced.9b00224 J. Chem. Eng. Data 2019, 64, 3416−3435
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Table 1. Summary of the Investigated Factors Influencing the High-Pressure Phase Behavior of (Solvent + LLDPE) Systems Published in Open Literature
a
Factor investigated but with limited data.
solvents nor do they characterize the polymers. A systematic investigation into the effects of comonomer concentration and length on the (solvent + LLDPE) phase behavior is therefore lacking and warranted given the fact that the comonomers can constitute a significant portion (up to 30 wt %) of the solvent.5,20 Modern LLDPE plants produce plastics using a variety of comonomers and often switch between various comonomer lengths during different production modes.2 This necessitates knowledge of the influence of α-olefin length on the phase behavior to prevent the unintended crossing of a liquid−liquid boundary during normal operation. Equations of state (EoSs) are required to determine the phase behavior of (solvent + LLDPE) systems at conditions other than those measured. The modified Sanchez−Lacombe (MSL) EoS is Krenz’s23 modification of the original Sanchez−Lacombe (SL) EoS,24−27 which incorporates Neau’s28 expression of the residual Helmholtz energy and a Péneloux volume shift factor.29 Using Gauter and Heidemann’s30 parameterization scheme, only the pure compounds’ critical constants are required to determine the four pure compound parameters. Like the original SL EoS,4 the MSL has shown good flexibility in the correlation of (solvent + LLDPE) phase behaviour.3,12,31−33 Whilst the predictive ability of the MSL EoS is limited due to its extensive use of binary interaction parameters (BIPs),12 it is a commercially accessible EoS as a large number of BIPs is reported by Krenz et al.32 and it is also included in commercial packages, such as VLXE.34 The overarching aim of this contribution was, therefore, to study the effect of α-olefin concentration and length in (α-olefin + diluent + LLDPE) systems for application to the solution process. To achieve this aim, the primary objective of this work was to measure the phase behavior of a (Cα + nC6 + LLDPE) system at constant polymer concentration and industrially relevant α-olefin concentrations for the α-olefins ethylene, 1butene, 1-hexene, 1-octene, and 1-decene (C10). Additionally,
intersection of the LL and VLL lines is frequently referred to as the lower critical end point (LCEP)8−11 but will be termed the lower miscibility end point (LMEP) here, as the cloud point curve is not necessarily the critical locus. The LMEP represents the lowest temperature and pressure at which the two liquids in the liquid−liquid region can become miscible and corresponds to the LCEP if the system is at its critical polymer concentration. Below the LMEP, the system transitions from the liquid to the vapor−liquid region upon crossing the VL line, in which case no second liquid phase forms. (Solvent + LLDPE) phase behavior is influenced by a number of polymer and solvent characteristics, such as: (i) the LLDPE concentration in the solvent; (ii) the LLDPE architecture in terms of its backbone length, MMD modality, dispersity, and SCB length and density; (iii) the ethylene, comonomer, and inert content of the solvent; and (iv) the diluent molar mass and structure (linear, branched, and/or cyclic). Given the industrial importance of (solvent + LLDPE) phase behavior and the number of factors which influence it, considerable effort has been devoted to its experimental measurement.13−16 Table 1 shows that while most factors that influence the solution process’s phase behavior have been investigated, the influence of the dissolved comonomer is lacking. Haruki et al.17,18 investigated the (C2 + C6 + nC6 + LLDPE) system and found that the phase behavior is essentially unaffected by the addition of 1-hexene, given the chemical similarity of n-hexane and 1-hexene. Tork19 found that 1-octene decreases phasetransition pressures in the (C2 + C8 + nC6 + HDPE) system by about 0.07 MPa per wt % 1-octene in the solvent. Buchelli and Todd5 and Costa et al.20 also report industrial operating data for the stream leaving the solution process’s polymerization reactor, but they do not report the compositions of the phases. Phase behavior data, where the solvents contain 1-butene and/ or 1-octene, are also reported by Cameron21 and Lönnqvist,22 but these authors do not publish the compositions of the 3417
DOI: 10.1021/acs.jced.9b00224 J. Chem. Eng. Data 2019, 64, 3416−3435
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Table 2. Names, Abbreviations, CAS Registry Numbers, Suppliers, and Purities of Chemicals Used chemical name
abbr.
CASRN
supplier
catalogue number
final puritya/g·g−1
analysis method
n-hexane n-eicosane ethylene 1-butene 1-hexene 1-octene 1-decene butylated hydroxytoluened
nC6 nC20 C2 C4 C6 C8 C10 BHT
110-54-3 112-95-8 74-85-1 106-98-9 592-41-6 111-66-0 872-05-9 128-37-0
Sigma-Aldrich Sigma-Aldrich Afrox Air Liquide Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich
139386 219274 541202-SH-C 203-449-2 240761 O4806 30650 W218405
0.9952 0.9999 ≥0.9990c ≥0.993c 0.9967 0.9972 0.9852 0.9988
GC-FID/KFb GC-FIDb none none GC-FID/KFb GC-FID/KFb GC-FID/KFb GC-FIDb
All chemicals were used as received. bGas chromatography with a flame ionization detector (GC-FID); all liquid samples were also tested for the water content by means of KF titrations on Metrohm 701 KF Titrino, but the water content was below the limits of detection. cClaimed by the supplier. dUsed in trace amounts as a thermo-oxidative inhibitor. a
a secondary objective was to correlate and predict the experimentally measured results using the MSL EoS. All measurements were performed using a commercially available metallocene LLDPE sample which was characterized fully by high-temperature size-exclusion chromatography (HTSEC) and solution-state carbon-13 nuclear magnetic resonance spectroscopy (13C NMR). The measured (solvent + LLDPE) data are the first where the solvent consists of (C4 + nC6) or (C10 + nC6) mixtures. Additionally, phase behavior data of an (nC6 + LLDPE) system, where the LLDPE is a wellcharacterized polymer of industrial origin, are lacking.
2. EXPERIMENTAL METHODS 2.1. Materials. Information pertaining to the chemicals used is listed in Table 2. The purities of all chemicals were confirmed by gas chromatography and Karl Fischer (KF) titration, which showed no significant impurities; hence, all chemicals were used as received. Technical grade nitrogen (Afrox, 42-SE) was used to flush the phase behavior cell during loading and for pressure control. Technical grade hexane and xylene (Hexane AR, Xylene AR, both from Kimix) were used to clean cell and peripheral equipment. The chemical structure of the LLDPE sample, as confirmed by 13 C NMR, is shown in Figure 2. According to manufacturer’s
Figure 3. PEH199-3 MMD showing the mass fraction wi as a function of molar mass Mi. (□, △) Experimental MMD wexp,i from duplicate HTSEC results; (○) pseudocomponent distribution wpsd,i from Table 16.
refers to the weight-averaged molecular mass of approximately 199 kg·mol−1. A similar convention will be used to refer to polymers in the literature. 2.2. Experimental Equipment. The newly constructed high-pressure phase behavior cell (Figure 4) is of the syntheticvisual type, according to the classification of Dohrn et al.57 It is essentially identical to the one reported by Schwarz and Nieuwoudt58 but differs in the following respects: (i) it operates at higher temperatures (up to 570 K) and lower pressures (up to 20 MPa); (ii) a Pt100 resistance thermometer is placed in direct contact with the high-pressure polymer solution and not in a sensor well; (iii) temperature compensation of the pressure probe is done with a temperature probe that monitors the temperature of the pressure probe; and (iv) a newly constructed manifold with known volume, and temperature and pressure monitoring is used for the precise loading of small quantities of gases. The cell was operated between temperatures of (320− 470) K, pressures of (0.5−20) MPa, and a chamber volume of (15−25) mL. The equipment, constructed from stainless steel 316, consists of a high-pressure section (1) with a variable-volume, highpressure chamber (1.1; ≤20 MPa) and a low-pressure section (3) with a variable-volume, low-pressure chamber (3.1; ≤1 MPa). The high- and low-pressure chambers contain the highpressure solution and nitrogen, respectively. The high-pressure chamber is continuously stirred with a neodymium magnet stirrer bar (1.2) and stirrer/hot plate (5.4; IKA, RCT basic
Figure 2. PEH199-3 structure (as confirmed by 13C NMR). Adapted from ref 55.
certificate of analysis, it was produced by copolymerization of ethylene and 1-hexene, using a metallocene catalyst to yield a resin with a density of 0.918 g·mL−1 and a melt flow index of 1.0 g/10 min. The MMD (Figure 3) and molecular mass averages (Table 3) were determined by HT-SEC, according to standard literature procedures.54 The average comonomer content (Table 3) of the LLDPE resin was determined by 13C NMR, as described elsewhere.55,56 Because the LLDPE sample was synthesized with a metallocene catalyst, the comonomer content is uniform across all chain lengths,2 and it is not necessary to characterize the polymer in terms of its comonomer content distribution. This LLDPE sample will be referred to as PEH199-3: PEH abbreviates poly(ethylene-co-1-hexene); 3 refers to the approximate 1-hexene content expressed in mole percent; and 199 3418
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2CB) in direct contact with the high-pressure polymer solution. The high-pressure chamber’s pressure is adjusted by controlling the pressure in the low-pressure chamber (3.1) either by evacuation (3.4) or by addition of compressed nitrogen (3.3), of which the pressure can be regulated manually up to 1 MPa. For temperature control, heating oil is continuously circulated in a heating jacket (5.1) surrounding the high-pressure section, with additional heating provided by the hot plate (5.4). The temperature of the oil is controlled to ±0.2 K of the set point by a Julabo ME-4 heating circulator, and the hot plate temperature is controlled to ±1 K of the set point. The temperature of the polymer solution in the high-pressure chamber (1.1) was measured by a 4-wire Pt100 probe [6.2; Wika Instruments (Pty) Ltd, 1/10 DIN, manufactured according to Standard DIN EN 60751:2009]. Both the high- and low-pressure sections are insulated by 20 mm thick glass wool insulation and covered with additional 50 mm thick mineral rock wool insulation (1.5 and 3.5). The contents in the high-pressure chamber (1.1) was monitored through a sapphire window (1.3; SITEC, 742.0106-2) and a Stryker 0°/10 mm laparoscope connected to a Stryker 1188 HD camera. The signal from the camera was upscaled to 1080i resolution and projected onto a 23″ display (6.3). The high-pressure chamber (1.1) was illuminated with a Smith & Nephew AutoBrite Illuminator II halogen light source. To load gaseous compounds, the removable manifold (2) was used. The manifold allows connection of the sample cylinder (2.1) to the cell inlet valve (1.4). Connecting lines and the cell were evacuated using a vacuum pump (2.4) and flushed with nitrogen (2.5). Pressure and temperature in the manifold were monitored during loading by a pressure indicator (2.6; Yoto, PG801C-100bar-A) and infrared thermometer (Lasa). 2.3. Experimental Procedure. Known amounts of PEH199-3, n-hexane [containing 500 mg·kg−1 butylated
Table 3. PEH199-3 Characterization polymer property
value
unit
Mechanical Propertiesa melt flow index 1.0 g/10 min resin density 0.918 g·mL−1 Molecular Mass Distributionb minimum molar mass, M0 1750 g·mol−1 number average molar mass, 75 700 g·mol−1 M̅ n weight average molar mass, 198 700 g·mol−1 M̅ w higher average molar mass, 373 700 g·mol−1 M̅ z maximum molar mass, M∞ 2 573 g·mol−1 950 dispersity, D̵ M = M̅ w/M̅ n 2.62 Comonomer Contentc mole percent 1-hexene 2.56 mol % 1-hexene weight percent 1-hexene 7.32 wt % 1-hexene branching density 1.28 branches per 100 backbone carbons branching density 2.56 branches per 100 backbone ethylene units branch number fraction 0.0512 number fraction of carbons in branches branch weight fraction 0.0497 weight fraction of carbons in branches a
According to the certificate of analysis from the manufacturer. Determined by high-temperature size exclusion chromatography (HT-SEC). cDetermined by solution-state carbon-13 nuclear magnetic resonance (13C NMR) spectroscopy. b
IKAMAG) and is sealed off from the atmosphere by a carbonfilled polytetrafluoroethylene seal (4.2). Pressure in the high-pressure chamber (1.1) is monitored with a pressure transmitter (6.1; ONEHalf20, CTDLX6MA-
Figure 4. Schematic representation of the high-pressure phase behavior cell. (1) High-pressure section; (1.1) high-pressure chamber; (1.2) neodymium magnet stirrer bar; (1.3) sapphire sight glass; (1.4) high-pressure chamber inlet valve; (1.5) high-pressure chamber insulation; (2) detachable manifold; (2.1) gas sample cylinder; (2.2) gas inlet valve; (2.3) sample cylinder outlet valve; (2.4) valve to vacuum; (2.5) valve to nitrogen purge; (2.6) manifold pressure indicator; (3) low-pressure section; (3.1) low-pressure chamber; (3.2) Viton O-rings; (3.3) inlet from compressed nitrogen; (3.4) outlet to vacuum; (3.5) low-pressure chamber insulation; (4) free piston; (4.1) high-pressure piston face and rod; (4.2) carbon-filled polytetrafluoroethylene seal; (4.3) bronze tightening nut; (4.4) low-pressure piston face; (5.1) heating oil jacket; (5.2) heating oil inlet; (5.3) heating oil outlet; (5.4) magnetic stirrer and hot plate; (6.1) direct pressure probe; (6.2) direct temperature probe; and (6.3) laparoscope, high-definition camera, light source, and monitor. After ref 58. 3419
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Figure 5. (a) Deviations from literature D = Pexp − Pref relative to the combined standard uncertainty in pressure uc(P). (Green ◀) (C2 + nC20) L → FL;62,63 (blue ▶) (C2 + C4) L → FL;64 (red ●) (C2 + nC6) L → FL;31 (grey ■) (nC6 + PEH199-3) L → VL and LL → VLL relative to nhexane vapour pressure;65 (b) distribution of the D/uc(P) values.
hydroxytoluene (BHT) to inhibit α-olefin polymerization and thermo-oxidative polymer degradation59,60], and liquid αolefins were loaded gravimetrically to the high-pressure chamber at ambient conditions (approximately 290 K). The chamber was then sealed, the liquids were degassed, and the chamber was evacuated to liquid’s bubble point pressure. Gaseous compounds were then loaded using the removable manifold (2), after which the cell was heated to the desired temperature and pressurized to obtain a homogeneous solution. After attaining thermal equilibrium, the pressure was slowly decreased until a liquid to vapor−liquid (L → VL), liquid to fluid−liquid (L → FL), liquid to liquid−liquid (L → LL), or liquid−liquid to vapor−liquid−liquid (LL → VLL) transition was observed visually, at least three times. This procedure was repeated at all temperatures of interest. More details on the experimental procedure can be found in the Supporting Information.
For mass of polymer pellets loaded, uc(mP) = 6 μg, based on the 4 μg standard uncertainty of the calibrated analytical balance (Ohaus Discovery DV214C calibrated by CME Metrology cc). When preparing the liquid mixtures, constituents were added to the glass vial with an uncertainty of uc(mi) = 3 mg. This includes contributions due to chemical purities, the 4 μg standard uncertainty of the calibrated analytical balance (Ohaus Discovery DV214C), and the 1 mg standard uncertainty associated with possible evaporative losses during preparation. For the mass of the prepared liquid mixture loaded to the cell, uc(mmix) = 0.14 g, which includes contributions from the 1 mg standard uncertainty of the calibrated analytical balance (Ohaus Pioneer PA423C calibrated by CME Metrology cc), and the 0.14 g standard uncertainty associated with possible evaporative losses during loading, degassing, and evacuation. Ethylene and 1-butene were loaded with an uncertainty of uc(mgas) = 8 mg, based on the chemical purities, the 4 mg standard uncertainty of the calibrated analytical balance (Precisa EP2220M calibrated by CME Metrology cc) and 5 mg (ethylene) and 2 mg (1-butene) standard uncertainties associated with the correction of the gas lost during loading. The uncertainties of this correction stem from standard uncertainties in the determination of the manifold volume, temperature, and pressure. 3.3. Pressure. The combined standard uncertainty in the pressure measurement is uc(Pmeas) = 0.05 MPa for L → VL and LL → VLL transitions and 0.06 MPa for L → LL transitions. These include contributions from: (i) sensor−indicator precision (0.03 MPa) and resolution (0.01 MPa); (ii) hysteresis errors resulting from a maximum hysteresis band of 0.12 MPa; (iii) 0.02 MPa standard uncertainty of the calibration; (iv) pressure fluctuations (less than 0.03 MPa); and (v) inherent errors associated with the synthetic-visual determination of phase-transition pressures, expressed as a standard error from literature data (s(D̅ ) = 0.01 MPa; see section 4). Because pressure sensor’s diaphragm is in direct contact with the fluid, negligible uncertainty is introduced by the measuring method. The pressure probe was calibrated against a reference dead weight balance, calibrated independently by Unique Metrology (Pty) Ltd. The uncertainty uc(Pmeas), however, represents only the uncertainty of pressure measurement, but the actual position of the transition is also determined by the temperature, polymer concentration, and solvent composition. Hence, the combined
3. UNCERTAINTY ANALYSIS Uncertainties in this work are expressed as combined standard uncertainties uc and were estimated in accordance with the Evaluation of measurement dataGuide to the expression of uncertainty in measurement (GUM).61 Only the key contributions to the uncertainty in temperature, composition, and pressure are presented below; the Supporting Information gives a detailed account of uncertainty estimation methods and detailed uncertainty analysis reports. 3.1. Temperature. For temperature, uc(T) = 0.4 K, which includes contributions due to the 0.3 K standard uncertainty of the calibration, temperature fluctuations (less than 0.2 K), and sensor−indicator precision (0.2 K), resolution (0.1 K), and hysteresis (0.002 K). Because the probe is in direct contact with the fluid, negligible uncertainty is introduced by the measuring method. The probe was calibrated relative to a reference probe which was independently calibrated by Wika Instruments (Pty) Ltd. 3.2. Composition. Uncertainties in composition uc(w) were calculated by propagating the uncertainties of the compound masses uc(m) loaded to the cell. These uncertainties vary depending on the compounds loaded and are provided with the tabulated experimental data. Even though chemical purity was accounted for the uncertainty analyses, this had a small contribution to the final composition uncertainty, given the high purities of the chemicals used. 3420
DOI: 10.1021/acs.jced.9b00224 J. Chem. Eng. Data 2019, 64, 3416−3435
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Measured L → FL pressures of the (C2 + C4) system are compared in Figure 7 to data reported by Laugier et al.64 These data were selected for comparison because they are consistent with those of another group,66 they were measured with three different methods, and ethylene is loaded accurately in this work, limiting loading errors in this work to 1-butene. The measured pressures agree well with those of Laugier et al.,64 but they were slightly lower than the published data (Table 4 and Figure 5a). These deviations are, however, still within the 99.7% level of confidence of the pressure measurement; thus the loading of 1butene is deemed sufficiently accurate. L → FL pressures of the (C2 + nC6) system were measured (Figure 8) and are compared (Table 4 and Figure 5a) to data from Nagy et al.31 These comparisons confirm the accuracy of nhexane loading and high-temperature measurement using the new direct temperature probe. The data of Nagy et al.31 were chosen as reference because this group’s equipment and procedure have been verified previously,67 n-hexane is the major constituent of solvents in this work, and the data are at high temperatures (>400 K), which allows for testing of the high-temperature measurement. 4.2. Transition Measurement in Polymer-Containing Systems. L → VL and LL → VLL pressures (Figure 9) and L → LL pressures (Figure 10) of the (nC6 + PEH199-3) system were measured (Table 8) and are compared to the vapor pressure of n-hexane65 and cloud points reported by Chen et al.47 and Haruki et al.17 (same research group using the same equipment). Whilst the L → VL and LL → VLL pressures in the (nC6 + PEH199-3) system should coincide with the vapor pressure of nhexane,10 only qualitative comparisons will be possible to verify the L → LL pressures because of the variation of polymers and the lack of consensus regarding the experimental identification of a cloud point pressure (CPP).68 To confirm the accuracy of the L → VL and LL → VLL transitions, the vapor pressure of pure n-hexane was considered. Because of the substantial molar masses of the polyethylene samples shown in Figure 9, they are nonvolatile and will decompose before reaching the temperatures theoretically required to vaporize. Therefore, these polymers have a negligible effect on the vapor phase behavior such that the L → VL and LL → VLL transitions will essentially coincide with the vapor pressure of n-hexane.10 Consequently, the accuracy of the L → VL and LL → VLL pressures is confirmed in Table 4, where it is seen that the measured transition pressures agree with the nhexane vapor pressure within experimental uncertainty. The measured pressures also fall between the pressures reported by Chen et al.47 and Haruki et al.17 (Figure 9), again confirming their accuracy. For the L → LL transitions, despite the lack of consensus regarding the experimental identification of CPPs68 and the slight differences in polymer architecture, the measured and published data are in remarkable agreement (Figure 10). A
standard uncertainty in the reported phase-transition pressure uc(P) accounts for the temperature dependence of the pressure (∂P/∂T), the composition dependence of the pressure (∂P/∂w), and the uncertainties in the measured pressure, temperature, and composition. Because (∂P/∂T) and (∂P/∂w) (estimated in the Supporting Information) depend on the nature of the system and the type of transition, uc(P) will vary and is listed separately for each system in the tabulated experimental data. Generally, uc(P) is 0.06 MPa for the L → VL and LL → VLL transitions, 0.14 MPa for the L → LL pressures of ethylene- or 1-butenecontaining systems, and 0.08 MPa for the L → LL pressures of the other systems.
4. METHOD VERIFICATION The experimental method’s accuracy was verified by measurement of transition pressures for systems and conditions at which reliable reference data from independent sources are published. The deviations D = Pexp − Pref between the experimentally measured pressures Pexp and the reference values Pref are shown relative to uc(P) in Figure 5a, for which statistics are reported in Table 4. Reference pressures were estimated at the experimental Table 4. Statistical Summary of the Deviations D = Pexp − Pref in MPa from Literature (n, Number of Comparisons; D̅ , Average Deviation; s(D), Experimental Standard Deviation of D; s(D̅ ), Experimental Standard Deviation of D̅ ) system
n
D̅
s(D)
s(D̅ )
(C2 + nC20) (C2 + C4) (C2 + nC6) (nC6 + PEH199-3) overall
12 6 12 56 86
−0.01 −0.12 −0.02 0.00 −0.01
0.13 0.04 0.07 0.04 0.07
0.04 0.02 0.02 0.01 0.01
temperature and composition by polynomial interpolation of the literature data. BHT was added in the order of 500 mg·kg−1 (based on total load) to inhibit α-olefin polymerization. 4.1. Accuracy of Solvent Loading. The accuracy of solvent loading was confirmed by measurement of L → FL pressures of (C2 + nC20), (C2 + C4), and (C2 + nC6) systems (Tables 5−7 and Figures 6−8). The (C2 + nC20) system was selected to verify the accuracy of ethylene loading because two sets of independent and consistent data62,63 exist, and this system’s L → FL pressures increase steeply with the increasing ethylene content, making it a sensitive test for the ethylene loading accuracy. Further, the data are at relatively low temperatures (
