Znd. Eng. Chem. Res. 1996,34, 1501-1516
1601
REVIEWS Phase Equilibria in High-pressure Polyethylene Technology Bernard Folie Exxon Chemical International, 20 Canadastraat, B-2070 Zwyndrecht, Belgium
Maciej Radosz" Exxon Research and Engineering Company, Annandale, New Jersey 08801
This is a review of the phase equilibria in supercritical monomer solutions of ethylene homopolymers and copolymers, such as low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE), poly(ethy1ene-m-methacrylate) (EMA), poly(ethylene-co-vinyl acetate) (EVA), poly(ethylene-co-methacrylicacid) (EMAA), and poly(ethy1ene-m-acrylicacid) (EM). The knowledge of such phase equilibria underlies the high-pressure polyethylene (HPPE) technology. The ability to estimate such phase equilibria allows for smooth and robust process optimization during grade transitions. This is important because the HPPE technology makes it possible t o minimize the product cross-contamination and, hence, to make higher-value, fluctuating-demand speciality polymers. Experimental data, phase diagrams, and patterns of phase disengagement presented in this paper are related to the reactor system, the high-pressure separator (HPS), and the high-pressure recycle system. These data and diagrams are used to characterize the monomer-polymer miscibility defined as a cloud point transition. The cloud point pressures in such systems are found to depend on thermodynamic parameters, such as temperature and composition, and on the dissimilarity between the polymer and the monomer. This dissimilarity is characterized in terms of the differences in molecular weight and density (e.g., for LDPE and LLDPE), in polarity (e.g., for EVA and EMA), and in association (e.g., for EA4 and EMAA).
Introduction Understanding the phase behavior of polymer solutions in supercritical fluids (SCFs) is of great theoretical and practical interest. Predicting phase boundaries (e.g., cloud points) and phase compositions (e.g., solubilities) for such systems is difficult because (i) they are highly nonideal at high pressures, (ii) the polymer and solvent greatly differ in size, thus critical conditions, and (iii) commercial polymers are composed of many molecules differing in molar mass and chemical composition. Nevertheless, the phase boundaries and compositions are required for the safe and efficient operation of polymer processes such as the high-pressure polyethylene (HPPE)process, where the bulk polymerization reaction and the main polymer-monomer separation step are carried out in supercritical The objective of this work is to review the phase equilibria of ethylene-based polymers and copolymers in sub- and supercritical monomer fluids, which underlie the HPPE technology.
The High-Pressure Polyethylene Process Low-density polyethylene (LDPE) is one of the most widespread plastic materials, synthesized commercially at relatively high temperatures (180-300 "C) and high pressures (1000-3000 bar) by free-radical bulk polymerization in supercritical ethylene.1>2The polymerization is carried out in a well-stirred single-stage or multistage autoclave or a tubular reactor. A generic
* Corresponding author. Current address: Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA 70803.
flow diagram of the HPPE process is shown schematically in Figure 1. In brief, fresh ethylene, after primary compression, is combined with recycled ethylene and, optionally, with a comonomer. This stream is pressurized to the desired reactor pressure in a second compression stage. Polymerization of the monomers is initiated by adding free-radical initiators (e.g., organic peroxides); in tubular reactors, oxygen from air is also used as initiator. The heat of reaction is removed by either controlling the rate of initiator addition in autoclave reactors or by through-wall heat transfer in tubular reactors. The polymer molecular weight (MW) is controlled by adjusting the reactor temperature and pressure and, optionally, by adding a chain-terminating agent. In this process, ethylene is both the reactant and the solvent for the polymer. Due to the short reactor residence time (30-90 s), the monomer conversion is relatively low, between 10 and 20 wt % in autoclaves and up to 30 wt % in tubular reactors. The reactor effluent stream is depressurized across a pressurereduction valve down to 150-250 bar to allow separation of the product from the unreacted ethylene in a high-pressure separator (HPS). The overhead monomerrich stream is cooled and recycled back to the reactor whereas the bottom polymer-rich stream undergoes a second separation step at near atmospheric pressures in a low-pressure separator (LPS). The LPS overhead is recycled back to the reactor, whereas the residual ethylene and comonomers dissolved in the molten polymer can optionally be stripped under vacuum in a devolatilizing extruder. Finally, the extrudate is pelletized under water, and the pellets are dried and stored in silos that are continuously purged with warm air. Recently, Exxon Chemical retrofitted the HPPE pro-
0888-588519512634-1501$09.00/00 1995 American Chemical Society
1502 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995
I COMONOMER
PRIMARY COMPRESSOR
e
ETHYLENE
I
CATALYST
COMONOMER
-
t HIGH-PRESSURELOOP WITH SUPERCRITICAL ETHYLENE
1I b-, LPS
1
TO EXTRUDER AND FINISHING
Figure 1. Simplified flow diagram of the HPPE process. HIGH-PRESSURE LLDPE MADE WITH METALLOCENECATALYSTS: CH2=CH2
NARROW MWD NARROW CD LINEAR MOLECULES APOLAR COMONOMERS
HIGH-PRESSURE LDPE MADE WITH FREE-RADICAL INITIATORS:
$+
BROAD MWD BROAD SCBD
polymerizing ethylene with a polar comonomer (e.g., vinyl acetate, methyl acrylate, and acrylic acid). LLDPE, on the other hand, is made of linear molecules of similar sizes (MWD = 2) to which short-chain branches (SCB) can be added by polymerizing ethylene with various higher a-olefins (e.g, 1-butem and 1-hexene). Due to the large diversity of polyolefins that -can be produced via the HPPE process today, it is essential to understand the effect of the polyolefin size, microstructure, and chemical composition on the phase behavior in supercritical solvents, for example, the phase boundaries in the reactor and the phase compositions in the HPS.
./CH2=CH2
LCB
.
POLAR COMONOMERS NARROW-BROAD CD
high polymers + oligomers
Figure 2. Schematic diagram illustrating the differences in microstructure and chemical composition between LDPEs and LLDPEs made in the HPPE process.
cess to allow for commercial production of linear lowdensity polyethylene (LLDPE) using single-site homogeneous metallocene catalyst^^-^ in high-pressure autoclave reactors. The LLDPE produced this way has different microstructure and chemical composition compared to LDPE. As illustrated in Figure 2, LDPE is made of branchy macromolecules differing in size (molecular weight distribution (MWD) or polydispersity (Mw/Mn)between 5 and 20) and in branch size (from short to long chain branches) and density (number of branches per 100 backbone carbons). Polar pending groups can be incorporated into the LDPE backbone by
Thermodynamic Issues in the HPPE Process The phase state of the reaction mixture controls the polymerization kinetics and, therefore, the polymer structure and end-use properties. In a stirred autoclave reactor, the exothermic polymerization reaction is usually carried out in a single-phase region to facilitate the reaction heat removal and hence ensure adequate reaction temperature control and to avoid fouling and forming cross-linked materials. Moreover, the presence of a viscous polymer-rich phase increases the probability of forming hot spots in the reactor and hence initiating explosive runaway reactions via the autoacceleration or Trommsdorf e f f e ~ t . ~This ? ~ effect is illustrated schematically in Figure 3. In brief, when phase separation occurs, polymer-rich microdroplets are formed. Termination of the live macroradicals entrapped in those highviscosity regions becomes severely diffusion-controlled, resulting in a rapid increase of the ratio of the propagation rate constant (K,) to the termination rate constant The resulting increase in polymer MW, combined
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1503
n
LOW VlSCOSrPl BULK PHASE MACRORADICALS
molecules (the so-called “waxes”) that can have relatively high solubility in the HPS monomer-rich phase. This leads to recurrent fouling of the heat exchangers in the high-pressure recycle system. Therefore, some processes include one or more additional phase separation steps, solid-liquid (SL) or LL, in the recycle system to remove the waxes from the recycled monomer stream. In fact, one faces a difficult optimization problem whereby the pressure in the HPS should be high enough to reduce the ethylene recompression cost but, at the same time, low enough to reduce the wax solubility in the monomer-rich phase and the monomer solubility in the polymer-rich phase.
Generic Phase Diagrams
HIGH VISCOSITY MICRO-DROPLET
TERMINATION BECOMES DIFFUSION-CONTROLLED kp I kt INCREASES RAPIDLY
II FORMATION OF “HOT SPOTS + ETHYLENE DECOMPOSITION
Figure 3. Schematic diagram illustrating the autoacceleration (Trommsdorf) effect.
with the high exothermicity of such a vinyl polymerization reaction, can eventually lead, locally, to crosslinking, visible as tiny gels in films, to reactor fouling, and, in the worst instances, to the decomposition reaction of ethylene. Nevertheless, in some instances, it is desirable to carry out the polymerization reaction in a two-phase region. Phase separation in autoclave reactors is typically achieved by lowering the pressures or by adding an inert antisolvent, such as N2, to the reaction mixt ~ r e .As ~ reported by Bogdanovic et a1.,8 LDPE produced in a two-phase system exhibits superior film properties because of narrower MWD and less longchain branches (LCB). However, ethylene polymerization in a two-phase system requires higher initiator cons~mption.~Since the entropy of mixing (AS,) decreases as polymerization proceeds in the reactor, the supercritical polymerization mixture has a tendency to split into two phases.1° An example of an undesirable phase transition in high-pressure tubular reactors is polymer precipitation due to cooling of the reaction mixture (through-wall heat transfer) that leads to the deposition of polymer films on the tube inner wall. This impairs heat transfer and hence requires continuous online def~uling.~,~ Therefore, it is crucial to know the temperature, pressure, and mixture composition corresponding to the demixing point (the cloud point). As it is discussed later, the cloud point curve (binodal) depends to a large extent on the polymer size, structure, and chemical composition. For separating the polymer from the unreacted monomers, a combination of phase transitions is used, including fluid-fluid equilibria in the HPS, which we will refer to as liquid-liquid (LL) equilibria even if one of the phases is supercritical with respect to the solvent, vapor-liquid (VL) equilibria in the LPS and extruder, and solid-vapor (SV) equilibria in the silos. The polymers produced in this process are always polydisperse (MWD > 1.0) and contain a fraction of low MW
(i) Solvent-Solvent Systems. Although polymersolvent mixtures are multicomponent systems by virtue of the polymer polydispersity, their phase behavior can be related to those of true binaries whose components differ in size, structure, and p01arity.ll-l~ Pressuretemperature (P-T) projections of generic pressuretemperature-composition (P-T-X) phase diagrams for binary mixtures of increasing degree of molecular asymmetry are shown in Figure 4. In Figure 4a (type A behavior), characteristic of binaries with a low degree of molecular asymmetry, a continuous critical locus joins the critical points (Cl and C2) of the pure components which terminate their respective vapor pressure curves. Also depicted in Figure 4a is a region of liquid-liquid immiscibility at low temperatures, bounded by a liquid-liquid-vapor (LLV)line ending at an upper critical end point (UCEP) and, at higher pressures, by the upper critical solution temperature (UCST) curve, along which increasing temperature induces transition from two liquid phases to a single liquid phase. For the record, type A behavior shown in Figure 4a, is referred to as type I (with no LLV curve) or type I1 in the classification of van Konynenburg and Scott.14 Type B behavior shown in Figure 4b is characteristic, for instance, of hydrocarbon binaries with a high degree of molecular size asymthe critical locus is discontinuous and is represented by two separate dashed curves: one connects the lower critical end point (LCEP) to the heavy component critical point (Cz), while the other connects the higher UCEP to the light component critical point ((21). Type B behavior corresponds to type IV or type V (special case with no LLV curve) in the classification of van Konynenburg and Scott. For ethane and propane, for example, the change from type A to type B phase behavior (without a known LLV curve, however) occurs The at c18 and between c29 and C30, re~pective1y.l~~ type C P-T projection shown in Figure 4c (corresponding to type I11 in the classification of van Konynenburg and Scott) is typical of binaries with a very high degree of molecular asymmetry. In this case the LLV line intersects the critical locus only once at the UCEP. The other part of the critical locus starts at C2 and rises with pressure without ever meeting the LLV line or C1. As this second part of the critical locus is shifted toward higher temperatures (see Figure 4c), it progressively becomes smoother until it loses its pressure minimum and maximum. Such critical loci are characteristic of gas-gas (GG) equilibria of the first (type y ) and the second (type b) kind.14 (ii) Polymer-Solvent Systems. In general, polymer-solvent mixtures exhibit phase behavior patterns similar to those depicted in Figure 4 for binary mixtures
1504 Ind. Eng. Chem. Res., Vol. 34,No. 5,1995 M : molecular weight
TEMPERATURE
-
8
TEMPERATURE
(b)
\
TEMPERATURE
I$)
-
- iGG- 1
I
I\ \,\ \
2 PHASES
TEMPERATURE
-
Figure 5. P-T isopleth typical of an amorphous and monodisperse hydrocarbon polymer-solvent binary system showing the effect of increasing degree of molecular asymmetry between the polymer and the solvent. The cloud point pressure (at constant temperature) increases, and the UCST and LCST curves merge into one single curve (U-LCST) with increasing differences in molecular weight (AM-)and density (&) for nonpolar systems, with increasing differences in polarity (Ap) for polar nonassociating systems and with increasing differences between self-association and cross-association (AA)due to specific chemical forces (e.g., hydrogen bonding) for polar associating systems.
1 PHASE
1
\
0
“1.
-
Figure 4. Two-dimensional P-T projections of generic P-T-X phase diagrams for binary mixtures of increasing degree of molecular asymmetry, going from a to c, between component 1 (light) and component 2 (heavy). The dashed curves represent the mixture critical loci.
of small molecules, except that the polymer vapor pressure curve is usually not shown in P-T diagrams, because polymer vapor pressures are very low and polymers decompose before they reach their critical temperatures (Ca shown in Figure 4 does not exist for polymers). A qualitative example of a P-T isopleth (constant polymer volume fraction) phase diagram typical of a monodisperse and amorphous polymer-solvent mixture with a high degree of molecular asymmetry (type B behavior) is shown in Figure 5. In most cases, there is a pair of LL boundaries, one at higher temperatures, labeled the lower critical solution temperature (LCST) curve, and one at lower temperatures, labeled the UCST curve. These curves are not critical loci but are labeled LCST and UCST because they correspond to the LCST and UCST boundaries in T-X coordinates. In a P-T projection, these boundaries intersect the
mixture VL curve near, respectively, the LCEP and UCEP. Also depicted in Figure 5 are two three-phase regions (LLV), one below the UCEP temperature and one above the LCEP temperature. In general, the mixture VL curve is close, but not identical, to the solvent vapor pressure curve and typically extends up to 3-5 “C above the solvent critical point. Therefore, the LLV curve is extended toward higher temperatures with increasing solvent critical temperature. For polydisperse polymers, LLV is not a single curve but a band.15a The line between the UCEP and the LCEP represents the bubble-point side of the mixture VL curve. As the degree of molecular asymmetry between the polymer and the solvent increases, the LCST and UCST curves approach each other and eventually merge into a single curve with a minimum, labeled the U-LCST curue16J7(type C behavior), as shown in Figure 5. In this case, as in Figure 4c for binaries of small molecules, there is only one three-phase LLV line which extends all the way to near the solvent critical point. For polyethylene-solvent mixtures relevant to the HPPE process, the degree of molecular asymmetry between the polymer and the solvent can be characterized in terms of the difference in molecular weight (AM)and density (A@)for nonpolar systems, in terms of the difference in polarity (Ap) for polar nonassociating systems, and in terms of the difference between self-association and cross-association (AA) due to specific chemical forced2 (e.g., hydrogen bonding) for polar associating systems. These effects are illustrated qualitatively in Figure 5 for an amorphous polymer-solvent mixture. In addition to P-T isopleths which allow one to determine the number of phases present at given T, P, and overall mixture composition, one often needs phase composition diagrams, such as T-X or P-X. These diagrams are illustrated in Figure 6 as cuts of a qualitative P-T-X phase diagram for a monodisperse and amorphous polymer-solvent mixture exhibiting a U-LCST critical locus. For the polyethylene-solvent systems of interest here, increasing pressure always
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1506 @ P1
T U-LCST crlllcal I o w a
WT U POLYMER
T
E
l
shadow c ~ r v e . The ~ ~ shadow , ~ ~ curve does not coincide with either the cloud point curve or the coexistence curve. These curves are illustrated qualitatively with a generic P-X phase diagram shown in Figure 7. The weight fraction ratio of the two phases in equilibrium can be calculated according the the lever rule. The weight fraction ratio of the polymer-rich phase t o the polymer-lean phase (w'lw'') is equal to the ratio of the distance between points F and V to the distance between points F and L:
WT X POLYMER
T
WT X POLYMER
Figure 6. Three-dimensional P-T-X
phase diagram typical of an amorphous and monodisperse polymer-solvent system exhibitthe LL ing a U-LCST critical locus. At elevated pressures (PI), miscibility gap in T-X coordinates is continuous with a maximum (UCST);at intermediate pressures (Pz), it becomes discontinuous with a maximum (UCST) and a minimum (LCST); at pressures (P3)lower than the minimum critical pressure, an hourglassshaped T-X diagram is obtained, without critical point.
induces mixing because of a negative excess volume of mixing (AVm < 0). This pressure-induced mixing is illustrated qualitatively with P-X isotherms in the P-T-X phase diagram in Figure 6. The maximum on each isotherm is a critical point, called the upper critical solution pressure (UCSP). While these isotherms have similar shapes a t all temperatures, the T-X isobars shown on the right-band side in Figure 6 change their shape depending upon pressure. At elevated pressures (e.g., PI), the miscibility gap in T-X coordinates is continuous with a maximum a t UCST; a t intermediate pressures (e.g., P2), it becomes discontinuous with a maximum a t UCST and a minimum a t LCST; a t pressures lower than the minimum critical pressure (e.g., P3),it becomes an hourglass-shaped miscibility gap without critical points. In the latter case, the system is immiscible a t all temperatures within a limited concentration range. (iii) The Polydispersity Effect. Several features distinguish a typical P-X phase diagram for polymersolvent systems from those of true binary systems consisting of small molecules of similar sizes. First, the cloud point P-X curve is highly asymmetric with the maximum shifted toward the solvent-rich concentration end.l0 As the size difference between the polymer and the solvent decreases, this maximum is shifted to higher polymer concentrations.16J7For polydisperse polymers, the critical point (UCSP) does not coincide with the maximum on the phase boundary (called the precipitation threshold1*) but is shifted to higher polymer concentrations. Finally, for the true binary systems, the compositions of the liquid phases in equilibrium, given by the tie lines, coincide with the binodal compositions at the same pressure, temperature, and overall composition. By contrast, for the polydisperse polymers, the binodal (cloud point) compositions usually do not coincide with the phase compositions which must be measured independently as tie lines and are given by the so-called coexistence curves. In addition, the pressurecomposition dependence of the minor phase being formed at the cloud point is represented by a so-called
where point L and V are located on the coexistence curves and point F corresponds to the feed or initial concentration shown for a bubble-point-type transition in Figure 7, where the feed concentration is lower than the critical concentration. A similar approach can be used for a dew-point-type transition also shown in Figure 7, where the feed concentration is higher than the critical concentration. A quantitative example of the cloud point, shadow, and coexistence curves is shown in Figure 8 for a LDPE wax-ethylene system.
Thermodynamic Basis of UCST and LCST Behavior In general, the thermodynamic requirements to form a homogeneous solution of two pure components can be expressed by
AGm = AHm- TAS,
0) because the like interactions are more energetically favorable than the unlike interactions, thus favoring the two-phase state. In fact, according to the principle "like-dissolves-like", the more alike the pure components, the smaller the AHm, On the other hand, the more dissimilar the solute and the solvent, the larger the AH,. Hence, for long chains, A H m dominates the always favorable AS,,,. At high enough temperatures, the -TM, term compensates for the positive A H m to give the negative AGm value required for solubilization. For example, in the system polyethylene-n-alkane, the cloud point pressure decreases substantially with increasing solvent size.21For these nonpolar systems, the dispersion (London) forces between polymer segments and solvent are strengthened (larger A H m ) as a result of an increase in solvent polarizability with increasing solvent size.22 This effect alone would make AG, more positive, resulting in higher cloud point pressures. In this case, the observed decrease in cloud point pressure is due to a comparatively larger increase in AS,.
1506 Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 FREE-VOLUME DIFFERENCE Ap
BUBBLE POINT-TYPE TRANSITION: Xi > X,t
----
cloud point curve shadow curve
LIQUID
(a)
W
a 3 v) v)
W
a
R
PHYSICAL INTERMOLECULAR FORCES
CHEMICAL INTERMOLECULAR FORCES :AA
- Londonor dispersionforces (AM)
- hydrogenbonds
-permanent dipole moments (4)
XCrt
Xi,i
- charge transfer complexes
Figure 9. The phase behavior of any polymer-solvent system ultimately depends upon the balance of physical and chemical intermolecular forces acting between polymer segment-segment, solvent-solvent, and polymer segment-solvent and upon the difference in pee volume between polymer and solvent.
Xi,2
POLYMER CONCENTRATION ---+
DEW POINT-TYPE TRANSITION: Xi < Xcr+
----
cloud point curve shadowcurve existence curve
LIQUID
I
ation threshold
t W
a
3 v) v)
W
a R
Xi,i Xi,2
POLYMER CONCENTRATION
-
Figure 7. Typical P-X isotherms for polydisperse polymersolvent systems exhibiting UCSP behavior. (a) A bubble-point transition occurs when the initial polymer concentration (Xi)is larger than the critical polymer concentration (Xcrt), whereas (b) a dew-point transition occurs when Xi is smaller than Xd.
1
Spahl and Luft (1981)
60
L U J
a30
t
P 20
-
cloud point curve shadow curve coexistence curves
10
"0
10
20
30
LO
50
60
70
80
90
100
weight % LDPE
Figure 8. P-X isotherm (160 "C) for a polydisperse LDPE wax (M,= 1130 g/mol, M , = 4040 g/mol) in ethylene. The coexistence curves shown correspond to dew-point type transitions with Xi < Xd (E 40 wt %). The feed compositions are, from left to right, 6.1, 14.0, 18.6,28.0, and 36.5 wt %. These data were taken from ref 19.
At temperatures approaching the solvent critical temperature, polymer-solvent systems exhibit LCST behavior, characteristic of the temperature-induced phase separation. For the LCST phase separation A H m
is exothermic ( A H m < 0), thus favoring the solution state. In order for the phase separation to take place upon raising the temperature, A S m must necessarily be negative in this case. It is now well established that such a negative noncombinatorial AS, does exist due to free-volume (density) dissimilarities between the solvent and the polymer. In brief, as the system temperature approaches the solvent critical temperature at a moderate constant pressure, the solvent molecules tend to take a more expanded gas-like configuration, resulting in a rapid drop in density with increasing temperature. Since the polymer density is still far removed from its hypothetical critical density, the polymer does not undergo such a dilation effect with increasing temperature. It is precisely this growing difference in density (A@)between the polymer and the solvent that induces demixing upon raising the temperature. As it is shown directionally in Figure 5, the LCEP temperature decreases with increasing 4 values, either as a result of increasing polymer density or decreasing solvent density. In fact, the polymer has a contracting effect on the solvent molecules by confining them to a more rigid matrix (AVm < 0). The negative A S m results from this lesser degree of spatial disorder for the solvent in such a confined state, compared to that in an expanded state. The phase behavior of any polymer-solvent system ultimately depends upon the balance of physical and chemical intermolecular forces driving the polymer segment-segment, solvent-solvent, and polymer segment-solvent interactions and upon the difference in free volume between the polymer and the solvent. As shown in Figure 9, examples of the physical intermolecular forces are the dispersion forces acting among nonpolar molecules and the polar forces acting among molecules with permanent dipole or higher pole moments. Examples of specific chemical forces are hydrogen bonding and charge transfer complexing, which can lead to self-association that favors demixing or crossassociation that favors mixing.
Phase Disengagement Patterns The HPPE process is a continuous process. Therefore, the kinetics of phase disengagement play a crucial role in the design of efficient separators. In order to minimize the separator volume and polymer residence time, the phase disengagement patterns and the phase stability have to be taken into account.
Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 1507 PATTERNS OF PHASE DISENGAGEMENT 0
1 Phase
... . Dew Point
VL
Bubble Point
VL
u homogeneoussystem
1-Phase
Figure 10. Schematic diagram of phase disengagement patterns upon lowering pressure at constant temperature. The shaded area represents the polymer-rich phase.
On a macroscopic scale, there are two patterns of phase separation, as illustrated in Figure 10. One pattern is similar to a dew-point separation in vaporliquid equilibria (VLE), where one observes the onset and growth of the high-density phase (liquid) upon lowering the pressure. The other pattern is similar to a bubble-point separation in VLE, where one observes the onset and growth of the low-density phase (vapor) upon lowering the pressure.16 As shown in Figure 7, the dew-point transition occurs when the initial polymer concentration (Xi) is smaller than the critical polymerconcentration (Xd),whereas the bubble-point transition occurs when it is larger than Xed. Hence, the type of the phase disengagement pattern in a particular separation process depends on Xi and Xch. Since XCh is k n o w n to increase with decreasing polymer MW, concentrated solutions of high MW polymers (e.g., in HPS) 0.0 xcrt 1.o will tend to separate according to a bubble-point-like Polymerweight fraction pattern, whereas dilute solutions of low MW waxes (e.g., Figure 11. Constructing a P-X phase diagram (binodal and high-pressure recycle separator) will tend to separate spinodal) from the shape and curvature of the Gibbs free energy according to a dew-point-like pattern. of mixing (AG,) curve as a function of composition, X,a t constant Whereas the shape of the Gibbs free energy of mixing temperature. (AGm) curve as a function of composition X determines the phase state of the system at a given T and P, its matrix of the other phase. This energy-intensive decurvature determines the phase stability and hence the mixing mechanism is known as the nucleation and microscopic mechanism by which the system d e m i x e ~ . ~ ~growth mechanism. These mechanisms are illustrated This is illustrated qualitatively in P-X coordinates in in 2'-X coordinates in Figure 12. In general then, Figure 11 for a polymer-solvent binary exhibiting a crossing the binodal (from a one- to a two-phase region) negative excess volume of mixing (AVm < 0). At is a necessary condition for demixing to occur, whereas elevated pressures (PI), the system is homogeneous crossing the spinodal is a sufficient condition for sponbecause the AGm curve has a positive curvature (@AGm/ tanous and irreversible demixing. At equilibrium, after 3x2 > 0) across its entire concentration range, hence, a sufficient settlement time, both mechanisms will such a system cannot lower its free energy of mixing at eventually lead to two homogeneous liquid phases albeit any composition. At lower pressures (P& the system at different rates. demixes because the AGm curve has, locally, a negative curvature ( @ A G m / t P .c 0). The compositions of the two Polymer Solubility in Solvents phases in equilibrium, given by the double tangent to the AGm curve, correspond to the binodal compoxiPolyethylene solubility in supercritical ethylene detions (X'b and d'b). At these points, the chemical pends on temperature and pressure. This dependence, potential of each species is the same in both phase (&'i similar to that of many solutes in SCFS,~ is illustrated = +"i). The compositions at the two inflection points, qualitatively in Figure 13. The two solubility isotherms where the curvature of the AGm curve changes from shown in Figure 13 describe the solubility behavior of concave to convex and vice versa, correspond to the polyethylene in sub- and supercritical ethylene. In the spinodal compositions (dSp and x " ~ ~ )The . pressure subcritical pressure (e.g., LPS), where the vapor pres(UCSP) and composition ( X h )at which these four points sure- and enthalpy-related effects are dominant, the merge into one single point corresponds to the critical solubility increases (due to solute evaporation) with point. increasing temperature and decreasing pressure. In the The LL domain, bounded by the binodal, is divided supercritical pressure range (e.g., HPS), the solubility into two distinct regions: one unstable and one metaalways increases with increasing pressure, as reported stable, each region corresponding to a different microby LuR and Lindnel.24 for several high and low MW LDPEs in ethylene. The effect of temperature is not as scopic separation mechanism.23 In the unstable region, straightforward, however. At intermediate pressures, bounded by the spinodal curve, the system demixes spontaneously, forming two cocontinuous phases. This the free-volume (density) effect is dominant and the is k n o w n as the spinodal decomposition mechanism. In solubility drops with increasing temperature ((a In the metastable region, nuclei of the new phase must XlaT), < 0). At higher HPS pressures and at reactor form and grow into dispersed droplets in a continuous pressures, the solubility is controlled by energy-related
1508 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 DEW-POINT TRANSITION
BUBBLE-POINT TRANSITION
stable
4
1
t 2
t
1
metastable POLYMER CONCENTRATION
-
3'
t t
Figure 12. T-X phase diagram typical of a monodisperse and amorphous polymer-solvent binary system, illustrating the difference between demixing through the spinodal decomposition mechanism and the nucleation and growth mechanism.
enthalpy effects dominant 8
energy effects dominant
free-volume effects dominant -
4
I
-
0
W fn U
I a. I
0 a
G
5
2
fn
E
> t d
/I
m
I I I I I I I I I I 1 I I
3
s:a W
B
3
8
1
1 LPS
! subcritical a
0.1
10
100
1000
PRESSURE (bar)
Figure 14. Effect of pressure and temperature on PEP790 solubility in ethylene as predicted by SAFT. kg was fitted to experimental cloud point data taken from ref 48.
PRESSURE
supercritical -
HPS
1
REACTOR
Figure 13. Qualitative diagram showing the effect of pressure and temperature on polymer solubility in a subcritical and supercritical solvent.
effects, hence it increases with increasing temperature ((3 In X/aT>, =- 0). Notice that at the crossover point labeled 1 in Figure 13, the solubility is independent of the temperature. The location of this point is systemdependent as illustrated by the following two examples.
Using the free-volume theory to estimate the solubility of a high MW and polydisperse LDPE (M, = 13 kg/mol, MWD = 10) in ethylene, Bogdanovic et reported an increase in solubility with increasing temperature in the pressure range 250-290 atm. The opposite temperature effect is shown in Figure 14, which illustrates the solubility of a low MW (790 g/mol) model polyolefin, a nearly-monodisperse, amorphous, and alternating ethylene-propylene copolymer (PEP), in ethylene. These curves were calculated from an equation of state (EOS) derived from statistical associating fluid theory (SAFT). In this case, the simulation results indicate a decrease in PEP solubility with increasing temperature in the HPS pressure range (200-300 bar). al.25926
Ind. Eng. Chem. Res., Vol. 34, No. 5,1995 1509 Polyethylene solubility in ethylene not only depends upon the HPS temperature and pressure but also depends upon the polymer yield or conversion in the reactor and upon its MW and MWD prior t o fractionation. As a rule of thumb, it has been observed that, as the conversion increases, the polymer solubility increases while its average MW in the ethylene-rich phase decreases.% This is expected because the polymer solubility increases with decreasing MW. In copolymerizationprocesses, the polymer solubility can be controlled by tuning the solvent mixture density not only with temperature and pressure but also with solvent c o m p o s i t i ~ n . ~ ~
Experimental Approaches The equilibrium phase behavior of polymer solutions in supercritical solvents, for example, characterized by the cloud point curve, the spinodal curve, the coexistence curves, and the critical point, is usually determined experimentally in small high-pressure variable-volume optical batch cells where it is possible t o vary the pressure and observe the phase transitions at constant temperature and composition. The cloud points are determined by light scattering or simply by visual inspection when there is enough difference in the refractive index between the two demixed phases. Modern light-scattering techniques involve irradiation of a solution of known polymer concentration with a He-Ne laser and measurement of the scattered light intensity as the system is brought from the homogeneous to the heterogeneous region by a change in pressure. At the cloud point, the intensity of the scattered light increases drastically. Such phase transitions can also be observed visually in optical cells equipped with sapphire windows, by displaying the window image, via a borescope and a video camera, on a video screen.16 At the cloud point, the initially-clear solution becomes turbid. The phase compositions can be determined by Sampling and analysis of the equilibrated phases. A volumetric-gravimetric method combined with gas chromatography or mass spectrometry analysis of the light components, suitable for polymer solutions, was recently reported.28 Flow that allow continuous sampling and production of relatively large samples have also been used for that purpose. One of the most recent techniques developed to measure both the spinodal and binodal at elevated pressures is a pressure-pulse-induced critical scattering (PPICS) developed by Kiepen and BrochardZ9and Wells et al.30 PPICS is based on the fact that the reciprocal of the light intensity (1d-l scattered from a homogeneous polymer solution is proportional to the second derivative of AGm with respect to composition which is the spinodal. Another, more effective, approach to measuring the spinodal is through a light-scattering pressure-jump e ~ p e r i m e n t . ~ ~ The LL critical point can be determined by a method described by de Loos et al.32 In order t o estimate the critical temperature, one measures the phase volume (or height) ratio as a function of the pressure difference between the separation pressure and the cloud point pressure at a fixed temperature. The interface rises in the dew-point region, as the volume of the polymer-rich phase increases. The interface drops in the bubble-point region, as the volume of the polymer-rich phase decreases. By decreasing the dew-point temperature and
increasing the bubble-point temperature, one converges around the critical temperature.
Theoretical Approaches Thermodynamic models applicable to polymer solutions have recently been reviewed by W ~ h l f a r t h .Only ~~ a brief overview of the most popular models, especially those useful for calculations of high-pressure phase equilibria, is given here. The starting point for calculations of phase equilibria of solutions is usually a model for the excess Gibbs free energy (P), from which the activity coefficient (yi) of each component i in the mixture can be estimated, and/ or an EOS, from which the fugacity coefficient (vi)of each component i can be calculated. With the chemical potential hi)or fugacity f i of each component i being equal in all phases at equilibrium, the phase compositions can be estimated by solving the following set of equations (for two coexisting phases): ,uIi
=PI'&
or f i = f,
(4)
vi
(5)
Hence,
(piyip= y p g
Bi= 1.0
si
= 1.0
(7)
where f i 0 is the standard state fugacity of component i and xi and yi are the unknown mole fractions of component i in each phase. The most popular P model for polymer solutions is a lattice model first derived by Flory and H ~ g g i n s . ~ ~ J ~ , ~ ~ The Flory-Huggins model is widely used in industry because of its simplicity. However, it suffers several important shortcomings, especially for high-pressure phase equilibria calculations involving polymers in SCFs. First, it is only applicable to incompressible liquid solutions, since it assumes that there is no excess volume of mixing (AV, = 0). Second, it fails to predict the LCST type phase behavior. In other words, it neglects the effect of the free volume dissimilarity between the polymer and the solvent. Three different approaches have been used t o develop EOSs for polymer solutions.33The corresponding states free-volume theory, first developed by P r i g ~ g i n eand ~~ put in practice later by F ~ o $ and ~ P a t t e r ~ o ntakes ,~~ into account the dissimilarity in free volume between the polymer and the solvent as a result of their great difference in size. The basic deficiency of this theory is that it is essentially limited to liquid-like densities. The lattice-fluid models, such as those developed by Sanchez and L a ~ o m b eand ~ ~Koningsveld and K l e i n t j e n ~ac,~~ count for compressibility and excess volume of mixing by allowing for unoccupied sites (holes)in a rigid lattice. Those models, with the exception of the lattice-gas model of Koningsveld and Kleintjens, suffer the same drawback as the fi-ee-volumemodels; they are only valid a t liquid-like densities. The third group of EOSs is those derived from thermodynamic perturbation theory, such as the perturbed-hard-chain (PHC),39the chainof-rotators and the statistical associating fluid theory (SAFT).40-45These EOSs are useful because they are generally applicable over a wide range of densities (from dilute gases to dense liquids) and over a wide range of molecular sizes (from small to large,
1510 Ind. Eng. Chem. Res., Vol. 34,No. 5,1995
polymeric molecules). Since SAFT is also applicable to associating molecules and has been demonstrated for high-pressure polyolefin systems, it is briefly described below. SAFT is a molecularly based EOS that incorporates terms accounting for the molecular size and shape (e.g, chain length and branchiness), association (e.g., hydrogen bonding) energy, and mean-field (e.g., dispersion) energy. SAFT development and approximations and tests against molecular simulation data are described el~ewhere.~O-~~ A SAFT fluid is a collection of spherical segments that are not only exposed to repulsive (hard sphere) and attractive (dispersion) forces but can also aggregate through covalent bonds to form chains (chain effect) and through hydrogen-like bonds to form shortlived clusters (association effect). The reference part of SAFT includes the hard-sphere, chain, and association terms. The perturbation part of SAF'T accounts for the relatively weaker, mean-field dispersion-likeeffects. The SAFT residual Helmholtz free energy (Ares)relative to an ideal gas reference state is given by = Aref
Ares
+ AdiSp
(8)
with Aref
= AhS
+ AChain
+ Aassoc
(9)
Using the thermodynamic relationship (W&)T = -P, SAFT can be expressed in terms of the compressibility factor, 2:
600
400
A LL
0
t
tt
. L (DP)
50
100
150
200
250
TEMPERATURE ("C)
Figure 15. P-T isopleths for PEP790 (at 15 wt %) in l-butene, propylene, and ethylene, illustrating the phase behavior shift from type A to type B to type C, respectively, with decreasing solvent size and density (data are from refs 16 and 48).
found by fitting SAFT to pure component vapor pressures and saturated liquid densities; these parameters are found to be well-behaved and hence easy to generalize for large molecules.44 In order t o extend SAFT t o real fluid mixtures, one also often needs a binary parameter, k,, which is used to fine-tune the unlike-segment interaction energy estimated from mixing rules. The SAFT mixing rules, however, are only required for the dispersion term because the three reference terms can be extended to mixtures based on rigorous statistical mechanics. SAFT was applied to many real pure components44 and fluid m i ~ t u r e s including , ~ , ~ ~ supercritical and nearcritical solutions of polymers, such as PEP and polyisobutylene (PIB). For example, SAFT was found to account for phase transitions in binary and ternary ~ ~ , ~data ~ ~for ~ ~pure PEP systems of P E P - a - ~ l e f i n , PVT and the associating effects in binary systems of monohydroxy and dihydroxy telechelic PIB in nonpolar and polar solvents.50
Amorphous Polyethylene Systems i
j
where 3 is the reduced fluid density, m is the number of segments per molecule, is the molar density, v is the molar volume, XAis the mole fraction of molecules not bonded at site A, u/k is a temperature-dependent dispersion energy of interaction between segments, DG and t are constants, and the summation is over all the sites. Knowing Ares and 2, vi can be estimated from the following thermodynamic identity: In v i= {a(Ares//RT)/ani}r,",~,~~ -In2
(15)
where V is the total volume of the system and ni is the number of moles of substance i. In order to extend SAFT to real fluids, one needs three pure component parameters for nonassociating fluids: uo, the temperature-independent segment-segment interaction energy, uoo, the temperature-independent segment volume, and m, the segment number. Also needed are two association parameters that characterize each site-site interaction: E , the energy of association between sites on a molecule, and K, the reduced volume of association. The nonassociating parameters are
P-T isopleths were recently reported by Chen et al.16J7and Gregg et al.48for solutions of PEP in suband supercritical a-olefins, including ethylene. In those well-defined systems, it was demonstrated that the greater the size difference (AMI between the polymer and the solvent (i) the higher the probability of type B and C phase behavior and (ii) the higher the cloud point pressure. An example of each type of phase behavior is shown in Figure 15 where experimental data are shown for 790 g/mol PEP in three different solvents. The PEP-1butene system exhibits type A behavior with no LL split. The PEP-propylene system exhibits type B behavior of the LCST type. The PEP-ethylene system, for which part of the U-LCST curve is shown in Figure 15, exhibits type C behavior. As expected, the size of the singlephase region (at pressures above the cloud point curves) increases with increasing solvent power, which, in this case, increases with increasing solvent MW and density. While both LCST and U-LCST transitions were observed for PEP solutions in propylene, only U-LCST transitions were observed for PEP solutions in ethylene in the MW range investigated (790-96 000 This is illustrated in Figure 16 where, for comparison,
Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 1511 . . . . . . . . . . . . . . . . . . . . . . . . .
2000
1500
z
UCST
1 t
0
'
PEP 0.79k
f , , N u ., w-- c20
C36 0.5k
LCST
50
1.6k
I
0.28k
100 150 TEMPERATURE ("C)
200
t
l
'
l
'
*
LL-*L (BP)
w
a
3 v)
3
200
a a
LOO
250
Figure 16. P-T isopleths for semicrystalline LDPEs, amorphous PEPs, and n-alkanes in ethylene showing the shift in phase transition from LCST type to UCST type with increasing solute MW. In all the cases, the polymer concentration is close to 15 wt % (data are from refs 48, 51-55). Not shown in this figure are the solid-liquid transitions expected at low temperatures for the semicrystalline LDPEs and n-alkanes. 500
A
'
PEP 96k
I
500
-
l
--
P
-
l ' -SAFT
*
P-1 ISOPLETH (i I S Ut% rolul.)
0 40
80
120 ieo TEMPERATURE ("C)
200
240
Figure 18. P-T isopleths for PEP26k (at 15 wt %) in a mixture of 1-butene and ethylene, showing the effect of increasing ethylene concentration (in weight percent on a polymer-free basis) in the solvent mixture. For 23.4 wt % ethylene in the mixture, SAFT predicts that the UCST and LCST merge (data are from ref 17).
transition, while PEP5.9K (and below) exhibits an LCST transition. It turns out that, as the LCEP drops, the O8k initial LCST slope, (aP/aT)x,increases.I6 In addition, 28k 15k the phase disengagement is of the dew-point type for IOk PEP790 and PEP5.912, whereas it is of the bubble-point 5.0k type for PEP2612 and PEP96K. For these systems, SAFT successfully predicts the increase in temperature and pressure of the U-LCST minimum with increasing polymer Mw, as shown by the curves in Figure 17. During production of LLDPE with the metallocenes, 700 ethylene is polymerized with a higher a-olefin. The stream entering the HPS consists of a ternary system LLDPE/ethylene/a-olefin for which the ethylene/a-olefin ratio depends on such factors as the weight percent -, a-olefin incorporated in the polymer and the a-olefin reactivity ratio. In these mixed olefin cases, Chen et a1.16 found that ethylene behaves like an antisolvent 0 -150 -100 -50 0 60 LOO 150 200 250 while the higher a-olefins behave like cosolvents for the TEMPERATURE ("C) polymer. This is illustrated in Figure 18 for a PEP26M 1-butene/ethylene system where the size of the LL Figure 17. P-T isopleths for PEPs (at 15 wt %) in propylene, showing the shift from type B (LCST) to type C (U-LCST) phase region rapidly increases, hence the single-phase region behavior with increasing polymer MW. The curves were calculated decreases, with increasing ethylene concentration in the from SAFT (data are from ref 17). mixture. The monomer density, and consequently its solvent cloud point data for several semicrystalline LDPEpower, also depends on its molecular structure, as ethylene and n-alkane-ethylene systems (for which the illustrated in Figure 19 for a low MW (ethyleneSL transitions are not shown) are also i n c l ~ d e d . ~ ~ s ~ lpropylene-diene) -~~ elastomer in straight, branched, and As shown in Figure 16, the slope of the cloud point curve cyclic saturated paraffins of the same carbon number changes sign with decreasing polymer MW. In the ( C S ) . ~The ~ difference in solvent power between the temperature range shown, the phase transition for high linear (n-hexane) and the branched parafin (methylMW polymers is of the UCST type, while for low MW pentane) is small, whereas the cyclic compound (methpolymers, it is of the LCST type. Although the LCST ylcyclopentane) is a much better solvent because of its transitions shown in Figure 16 are the LCST branches higher critical dencity (ec). As the density difference of U-LCST curves, the UCST transitions may or may (he)between the polymer and the solvent increases, the not be the UCST branches of U-LCST curves. The latter LCST curve shifts to lower temperatures, which means will depend on whether or not the critical locus shown that the size of the two-phase region increases. in Figure 4c has a minimum. The effect of polymer M W on the cloud point curve is Semicrystalline Polyethylene Systems illustrated for various PEP-propylene systems in Figure 17. As shown, the cloud point pressure at a fxed Both LDPE and LLDPE manufactured in the HPPE temperature increases with increasing polymer M W , as process significantly differ from the model PEP compounds in the following ways: (i) they are usually expected. The phase transition also shifts from type B to type C phase behavior with increasing polymer MW. semicrystalline and therefore precipitate below their For examples, PEPlOK (and above) exhibits a U-LCST crystallization temperature, (ii) they are polydisperse,
1512 Ind.Eng. Chem. Res., Vol. 34,No. 5, 1995 I I .
1400
.
I
I
I
I .
'
"
1
.
'
.
I
'
.
'
i
"
I I .
'
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:-
..........
1200
..........................
..............
1000
..........
........ ......
..............
t
.......
...............
800
PA
W
U
........
3
cn ......................
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-
* ..
..........................
......; ..................
. . . . . . . ...................
/i
,'
.
:
,
i/
.
.
-1 .................. i..r/ .. 1
.A.......:.
..i . . . . . . . . .
..........
v
I
i
................... . . . ...........
..I
I
i
/
j
I ......................... j
EPDM-140 k
r...i...i...i...i...l... 1
I
I
140
160
180
R
:
:
!
0
i
. . . . . .; . . . . . . . . j.. ..:... ....... i... .......................................... .........._ j .6 I e
200
.
3 U
..........................
1
I
I
I
200
220
240
260
::
0 triple point TEMPERATURE
280
-
TEMPERATURE ("C)
Figure 19. P-T isopleths for EPDM (at 6 w t %) in straight, branched, and cyclic saturated paraffins of the same carbon number (CS), showing the effect of the solvent density on the position of the LCST cloud point curve (data are from ref 56).
I
Berghmans' critical point
a polymer melting point
,/-\
t
\
(b)
I
L
with polydispersity ranging from narrow for LLDPE (MWD = 2.0) to broad and very broad for LDPE (MWD w = 5-20), and (iii)they are made of molecules differing U 3 in SCB (comonomer) content and therefore must also Ibe characterized on the basis of their SCB (composition) m.p. W distribution, SCBD (CD). Moreover LDPE is not linear R but branched with a variable number of LCBs. Hence, 3Iunderstanding the effects of crystallinity, MWD, SCB, SCBD, and LCB on the high-pressure phase behavior of polyethylene-solvent solutions is key to HPPE technology. The system most extensively studied during the past 30 years is the LDPE-ethylene ~ y ~ t e m . The ~ ~ , ~ ~ , ~ ~ POLYMER VOLUME FRACTION 1.0 qualitative P-T and T-X phase diagrams shown in Figure 20. (a) P-T isopleth phase diagram typical of semicrysFigure 20 represent typical phase diagrams for semitalline, high M W LDPE-ethylene solutions, showing the interseccrystalline LDPE-ethylene systems exhibiting a LL tion (point A) between the cloud point curve and the crystallization phase transition of the UCST type. These phase boundary. Typical operating conditions for the reactor, HPS, and diagrams were constructed on the basis of Ehrlich's the recycle separators are also indicated. (b) T-X phase diagram three-dimensional (P-T-X)phase diagram^^^?^^ for the (constant P ) for the same system as in part a showing the effect of decreasing pressure and increasing polymer MW on the phase same system. Figure 20a shows a P-T isopleth phase boundaries. diagram; upon decreasing temperature, the cloud point curve intersects the crystallization boundary at point A, beyond which one solid phase coexists with one liquid ether system. In general, point B moves toward higher phase (SL). Along the crystallization boundary below polymer concentrations and higher temperatures with point A, three phases coexist, two liquid phases and one either increasing polymer MW, decreasing pressure, or solid phase (SLL). Figure 17b shows a T-X phase both. diagram; we see that LL demixing and crystallization Spahl and Luft19,20,61 investigated the phase boundoccur side by side and that the polymer melting point aries of LDPE waxes in supercritical ethylene. They is depressed with increasing solvent concentration. The reported a phase boundary with a positive slope ((W cloud point curve intersects the crystallization boundary 82')~ > 0),typical of the LCST branch of a U-LCST type at the critical point B (Berghmans's point). According phase transition, for an LDPE wax (M, = 1.1 kg/mol) to the phase rule: in ethylene (Figure 21). For comparison, the phase boundaries of other LDPEs and linear high-density polyethylene (HDPEs) in ethylene are also included in the crystallization temperature is independent of conFigure 21. These data illustrate the shift from a LCSTcentration only for true binary systems.60 Indeed, if the to a UCST-type phase transition with increasing type number of components, m, is two and the number of LDPE size, as already inferred from Figure 16. Also phases, n,three, there is no degree of freedom left (F= worth noticing in Figure 21 is that the cloud point 0) when the pressure is fixed. For polydisperse polymerpressure increases with increasing polymer size, albeit solvent systems (m > 2), the crystallization temperature at a considerably reduced rate for the largest polymers. either decreases with decreasing concentration, as sugMoreover, as the polymer size increases, the cloud point gested by the data of Condo et al.59for the quasi-binary pressure becomes more and more temperature dependHDPE-propane system, or increases with decreasing ent. This is one possible explanation for the recurrent concentration, as recently reported by Koningsveld and BerghmansG0for the quasi-binary HDPE-diphenyl fouling observed in high-pressure tubular reactors at
s
I
O e 0
Ind. Eng. Chem. Res., Vol. 34, No. 5,1995 1513 2000 4 . 1 .
;. . . ; . ..; .. . ; . . .; . ..
Spahl~and Lu(r (1981)-
1
700
1
1
I
I
ElWK 1800-
-
1600-
_-
L 1400--
e
I
w
! ! j
1200
A
In
8
A
l3
0
w In
g
1000
0 800
0 0
600
22
0
8
P 4 100
0 120
140
0 160
6 180
200
220
TEMPERATURE ('C) 200
Figure 21. P-T projections for LDPEs and HDPEs in ethylene (data are from ref 20).
the tube entrance during low-temperature start-up or directly downstream of the cold side-stream injection points.20 By comparing the cloud point curves for LDPE and HDPE of similar MW and MWD, others20,62 concluded that the presence of LCBs (absent in HDPEs) enhances polymer solubility and, consequently, lowers the cloud point pressures, as illustrated in Figure 21. However, the cloud point data recently collected by Chen,63with nearly-monodisperse linear poldethylene-1-butene) (PEB) samples of varying 1-butene content in sub- and supercritical propane indicate that SCBs play a significant role in shifting the phase boundaries. As shown in Figure 22, the cloud point pressure increases with decreasing 1-butene content and, hence, with decreasing SCB density (number of ethyl branched100 carbon atoms). Moreover, the cloud point curve shifts from an LCST-type to a U-LCST type with decreasing 1-butene content. The data are consistent with the known facts that the higher the polymer crystallinity (or density), the less soluble the polymer becomes, thereby requiring higher pressures for complete solubilization. These results also suggest that the higher cloud point pressures exhibited by HDPEs are probably due to their lower SCB content and consequentlytheir higher densities and, to a lesser extent, t o their lack of LCBs. Looking back at Figure 21, one can see also that, as for the size effect, branchiness has a more significant effect on the cloud points of the smaller polyethylene molecules. In other words, the presence of highly branched LDPE waxes in the polymer, as indicated for instance by a broad SCBD, is particularly undesirable with respect t o recycle fouling because it is likely t o increase the LDPE solubility in the HPS overhead stream.
Polar Ethylene Copolymer Systems Polymerizing ethylene with polar monomers, such as vinyl esters (e.g., vinyl acetate (VA), methyl acrylate (MA), and butyl acrylate (BA)),unsaturated carboxylic acids (e.g., acrylic acid (AA)and methacrylic acid (MAA)), or mixtures of these, in the presence of freeradical initiators, results in polymers with enhanced optical, mechanical, and thermal properties compared to traditional LDPE homopolymers. Phase behavior studies for these polar systems are relatively scarce in the literature, the most comprehensive ones being those
8
24
c
0
Propane
0
0
20
40
60
I
I
I
I
80
100
120
140
I 160
I
180
2
Temperature ("C)
Figure 22. P-T isopleths for PEBs (at 5 wt % in propane) varying in 1-butene content but of similar MW, illustrating the effect of the SCB density (branched100 C) on the cloud point pressure (data are from ref 63). from Hnrch et al. (1993)
2600
=b
w
\.
2200
a
3
EMA/58wt%MA/99i
3
*
.
4
a
' P-T isopleth 'f 5.5 wl% EMA
1000
*
LL ; . .
EMA/25wt%MA/75k *
.
; ' . . .
of Luft,64,65 McHugh,22,66 W~hlfarth,~'-'~ and their collaborators. These systems can be divided into nonassociating and associating. (i) Nonassociating Systems. Both poly(ethy1eneco-methyl acrylate) ( E m ) and poly(ethylene-co-vinyl acetate) (EVA) are weakly polar polymers whose ester groups interact electrostatically with each other, because of their permanent dipole moments, but do not hydrogen bond with each other significantly. An example of a P-T phase diagram for EMA in ethylene is shown in Figure 23, prepared on the basis of experimental data taken by Hasch et The EMAs shown in Figure 23 have high MW and varying MA content. As for the high MW LDPE in ethylene, the cloud point
1514 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1 6 0 0 ' .
.
. : .
.
. : .
. .
: . .
. : .
.
.
2200
EVA1: 29.3k10.935 ocm-3
=z h
- 1400
w
2000
I
1
1
+
L
'
160
9
'd
1
I
L
i-
I
from Luft and W l n i (1982)
+
a
3
v)
3a
1800
a
+ 1600 z
2 1400 a
3
5 1200
'""t, 0
EVA3-28MtKVA 180°C 15 vi%EVA
0:2
0:4
t
i
VA WEIGHT FRACTION (POLYMER-FREE BASIS)
Figure 24. Cloud point pressure vs free VA weight fraction in the solvent mixture (VA ethylene) for three EVAs of varying VA content and one LDPE homopolymer. M,, and the density are indicated for each polymer in the upper right corner. The temperature is constant at 160 "C (data are from ref 71).
+
0
15 wI% polymer 1000
I
0
LL
I . . . . I . . . . l . . . . I . . . . l . . . . I I 1 I I
5
10
15
20
25
I
30
WEIGHT PERCENT COMONOMER IN POLYMER Figure 25. Cloud point pressure vs weight percent comonomer in the polymer backbone for two different polar systems: the associating EAA-ethylene system and the nonassociating EVAethylene system. The temperatures and composition are as indicated in the figure (data are from ref 65).
(comonomer-free) systems is plotted as a function of the polymer AA content at constant temperature and polycurves for EMA are UCST-type phase boundaries. As mer concentration (15 wt % polymer). Also shown in shown in Figure 23, however, the cloud point pressure Figure 25 are the cloud point curves for EVA-ethylene first drops with increasing MA content (up to 25 wt %) (comonomer-free) systems. Figure 25 illustrates a and then increases again a t higher MA concentrations dramatic difference in the phase behavior between in the polymer. The same behavior was reported by EAAs and EVAs in the presence of supercritical ethylLuft and Wind65for the EVA-ethylene system. This ene. nonmonotonic dependence can be explained by the For the associating systems, to a first approximation, difference in polarity (Ap) between the polymer and the it is the balance between the self- and cross-association solvent. Since ethylene has a quadrupole moment, it (AA)which controls the cloud point pressure. In pure is more polar than an LDPE homopolymer. As MA or ethylene, as the polymer AA content increases, the VA is incorporated into the backbone, the polymer degree of self-association is likely to increase. This is becomes more polar and Ap is reduced, favoring more expected to favor demixing and therefore higher cloud and stronger polymer segment-solvent interactions. point pressures. Conversely, in the presence of free AA This results in lower cloud point pressures. At some in the solvent mixture, the cross-association between higher VA or MA weight percent, however, Ap will start polymer segments and the solvent is expected t o favor increasing, requiring higher cloud point pressures again. mixing and therefore lower cloud point pressures. In the presence of free VA or MA in the solvent P-T isopleths for several high MW EAAs,73varying mixture, the cloud point pressure consistently drops with increasing MA or VA content in the p ~ l y m e r . ~ ~ in , ~AA ~ content, in pure ethylene are shown in Figure 26 along with a reference LDPE homopolymer and EVA. This is illustrated for several high MW EVAs in Figure In all the cases shown in Figure 26, the cloud point 24, where the cloud point pressure is plotted as a curves are UCST-type phase transitions. The important function of the VA weight fraction in the solvent mixture point to notice here is that, as the cloud point curves at constant temperature and polymer concentration (15 are extrapolated toward higher temperatures, the difw t % polymer). Also illustrated in Figure 24 is the ferences in the cloud point pressures rapidly diminish. observation that the polymer and solvent VA content This can be explained by the fact that the average have a much greater effect on the cloud point pressure potential energy (r,)or energy of attraction between two than do small differences in molecular size22,64and species i a n d j due to polarity and hydrogen bonding density between the polymer and solvent. Although the rapidly decreases at elevated temperatures.13 At such polymer density, and therefore he, increases with temperatures, the phase behavior is primarily controlled increasing VA content (which should drive the cloud by the dispersion interactions among the polymer segpoint toward higher pressures), the cloud point pressure ments and the solvent molecules and by the differences consistently drops with increasing polymer VA content in free volume. These trends are quantitatively exat all VA weight fractions. Obviously, the Ap effect is pressed by the followieg relation for r,: stronger than the A@effect in this case. The effect of Ap on the cloud point pressure of the EVA-ethylenerli= - c 1 ( ~ 4 / r 6-) c z b i2,uj2/ r6KT) VA pseudo-ternary system was successfullymodeled by the SAFT c3bi2Qj2/r8hT) ... H - bonding (17) (ii) Associating Systems. The pending carboxylic acid groups (COOH)in poly(ethy1ene-m-acrylic acid) (EAA)and in poly(ethylene-co-methacrylic acid) (EMAA) where the first term represents the temperature indecan hydrogen bond intra- and intermolecularly. Therependent dispersion interactions, the second term the fore, the cloud point pressure of these polymers in dipole-dipole interactions, and the third one the dipoleethylene rapidly increases with increasing acid percent quadrupole interactions (with ,u the permanent dipole in the polymer backbone.64 This is illustrated in Figure moment, r the intermolecular distance, Q the quadru25 where the cloud point pressure for EAA-ethylene pole moment, K the Boltzmann constant, and ci con-
+ +
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1515 .
2400
...:. .
.
.:.
. .
.:....:..
15 wt% polymer
t e
. .
L
A
2200;
w
a
3 v)
3 a L
4
1000 50
100
150
.
200
250
4
300
TEMPERATURE (“C)
Figure 26. P-T isopleths for three EAAs of increasing AA content, one LDPE homopolymer, and one EVA (all at 15 wt % in ethylene), illustrating the rapidly diminishing differences in cloud point pressures at elevated temperatures (data are from refs 52, 71, and 73). The curves are labeled with weight percent incorporation and with weight average MW, e.g., 138k (if not given, it means it is not available).
is related t o the interchange energy of stants). mixing o as follows:
(18) where z is the number of dissimilar solvent-polymer segment pairs. The EM-ethylene phase diagram presented in Figure 26 can be used to explain the heterogeneity due to formation of “microgels”in commercial EAA products. Because AA is much more reactive than ethylene in the high-pressure free-radical process, a local depletion of free AA, combined with an excess of AA in the polymer, can lead to a local phase separation in the reactor. Such a phase separation, in turn, underlies formation of the microgel domains in the final EAA products.
Conclusions All the cloud point curves for commercial semicrystalline, polydisperse LDPE-monomer systems are of the UCST or U-LCST type. For the homopolymer LDPEethylene system, the cloud point pressure increases while the cloud point curve is shifted t o higher temperatures with increasing polymer MW (AM) and crystallinity/density (A@). For the polar LDPE-monomer systems, on the other hand, the difference in polarity ( A p )and the difference in self-association versus crossassociation (AA)control the shape and position of the cloud point curve..
Acknowledgment We gratefully acknowledge Professor Gerhard Luft’s unpublished data that we used to prepare Figures 24 and 26. We thank Doctors David Walsh, Paul Ehrlich, Ludo Kleintjens, Christopher Gregg, and Richard Shutt for their helpful comments that enhanced this paper.
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Received for review November 21, 1994 Accepted November 29, 1994@ I39401770 Abstract published in Advance A C S Abstracts, February 15, 1995. @
