In-line monitoring and analysis of polymer melting behavior in an intermeshing counter-rotating twin-screw extruder by ultrasound waves.
The melting process is one of the important steps for controlling processing conditions and product quality in both single- and twin-screw extrusion. The melting process in a single-screw extruder (SSE) was studied by Maddock  and Street  by the "screw pulling-out" method in the 1960s. Since Tadmor  and Tadmor et al.  first introduced a melting model based on the observation of the traditional melt film/solid bed/melting pool melting mechanism, the melting mechanism in SSEs has been extensively investigated and modeled [5-8]. Three kinds of film/solid bed/melting pool melting phenomena were observed for different polyvinyl chloride (PVC) systems at various processing conditions in SSEs: 1) melting with a solid bed against the trailing side of flight [2, 4, 9]; 2) melting with a solid bed in the channel center [1, 10]; and 3) melting with a solid bed against the pushing side of flight [11, 12]. Rauwendaal  proposed a dispersed melting model in an SSE by assuming that at least one-half of the solid particles had been melted, and the particles were dispersed in the polymer melt.
Later, many experiments [14-16] showed that melting in a twin-screw extruder (TSE) was different from that in an SSE, and solid pellets or particles were always melted quickly after mixing elements and suspended in polymer melt. Gogos et al.  proposed a dissipative melting mechanism that was caused by heat conduction, viscous energy dissipation, plastic energy dissipation, friction energy dissipation, and other heat sources. They suggested that plastic energy dissipation and friction energy dissipation were important during melting initiation in a TSE, whereas heat conduction was important for particle melting initiation in an SSE.
Compared to studies on the melting process in co-rotating TSEs [18, 19], studies on polymer melting behavior in an intermeshing counter-rotating TSE are very limited. Janssen  showed that a complete melting sequence could be observed within an individual C-chamber in the extrusion of polypropylene (PP) powders at low die pressure and high die pressure. Wilczynski and White [20-22] recently investigated the melting phenomena of PP and low density polyethylene (LDPE) in pellet form in a Leistritz intermeshing counter-rotating TSE by the traditional screw pulling-out method. Based on the examination of carcass in screw channels, two melting models in calender gaps and in C-chambers were proposed.
However, the conventional screw pulling-out method is not suitable for heat sensitive material such as PVC due to the time delay. A nondestructive ultrasound technique provides an opportunity to in-line monitor the melting process due to its robustness, fast data acquisition speed, and low cost. Depending on the location of the ultrasound probes installed, previous studies on ultrasound in-line monitoring for the extrusion process have been done on two stages: ultrasound probe in-die monitoring and ultrasound probe in-barrel monitoring. Studies with ultrasound probe in-die monitoring include polymer foaming [23-25], polymer melt flow behavior [23, 26, 27], melt flow stability , polymer interface stability in coextrusion , and residence time distribution [30, 31]. Studies with ultrasound probe in-barrel monitoring include barrel and screw wear measurement , the curing process of polyester , residence time distribution measurement , and polymerization monitoring . The ultrasound technique is also applied to characterize the morphology of multiple-phase polymer blends. Experimental studies of ultrasound signal dependence on the compatibility of polymer blends have been widely performed by both off-line and in-line measurements. Hourston and Hughes [36, 37] and Singh and Singh [38, 39] suggested that ultrasound velocity varied linearly with blend composition for miscible blends, while it deviated from linearity when the miscibility of polymer blends decreased. Gendron et al. [40, 41] performed both in-line and off-line measurements of PP/polystyrene (PS) and PP/polyethylene (PE) blends and found ultrasound signal deviations from the additive mixing rule for both wave velocity and attenuation. They suggested that the wave velocity deviation was small, and was influenced by the variation of polymer melt temperature, while attenuation derivation was more significant due to the scattering effect from the dispersed phase.
Recently, significant efforts have been made to correlate the size of the dispersed phase with measurable wave velocity and attenuation. Piau and Verdier [42-44] modified the wave propagation theory for viscoelastic emulsion systems by introducing linear viscoelastic effects. They measured the wave velocity and attenuation of a polyamide (PA6)/PP blend at different concentrations of PA6 and with various surfactants, during melt flow through a capillary rheometer . By assuming the polymer blend as an emulsion or suspension of two immiscible phases, they used the modified theory to predict wave parameters as the functions of concentration, radii distribution, and frequency, based on the known thermophysical properties of the material.
Our objective in this work is to investigate polymer melting phenomena in an intermeshing counter-rotating TSE by using the ultrasound in-line monitoring method. The melting level in screw channels is characterized by analyzing wave attenuation in the mixture of unmelted particles and polymer melt.
[FIGURE 1 OMITTED]
PVC (Oxyvinyl 185F) homopolymer resin in powder form was supplied from Polyone Inc. The PVC resin was stabilized by organotin-based Thermolite 31S obtained from Atofina Chemical, Inc. Dimethyl phthalate (DMP) was used as a liquid plasticizer and was obtained from Aldrich Chemical Co.; polybutylene adipate (PBA) (Mw [approximately equal to] 2000, [T.sub.m] [approximately equal to] 60[degrees]C), obtained from Ruco Polymer Corp., was used as a low molecular weight polymeric plasticizer. Calcium carbonate (CaC[O.sub.3]) was supplied by Global Stone PenRoc. Four PVC compounding formulations were used in this study, as listed in Table 1. The purpose for the selection of these four systems is to investigate the additive effects on the PVC melting process by ultrasound signals.
Linear low density polyethylene (LLDPE; Quantum) in pellet form (diameter [approximately] 3 mm) obtained from Quantum Co. was used for a comparative study with the melting phenomena of amorphous PVC.
Equipment Setup and Instrumentation
An intermeshing counter-rotating TSE (Leistritz LSM30.34) was used in this study. The extruder (screw diameter 30 mm, L/D = 32.5, length = 990 mm) has eight modular barrel sections. The feeding zone is water-cooled, and zone 1 to zone 7 are heated by electric heating bands and cooled by air. The temperature in zone 3, where an ultrasound probe was installed, was set at 150[degrees]C for the extrusion of both PVC compounding and LLDPE.
Our in-line monitoring system consists of: 1) a homemade ultrasound probe, assembled by a homemade delay line, an adaptor, and a standard ultrasound transducer with a center frequency of 5 MHz; 2) an ultrasound pulser/receiver; and 3) a data acquisition system on a computer. The ultrasound signals were recorded for one minute by pulse-echo mode with a data acquisition interval of 0.1 second. The schematic setup for both extrusion and in-line monitoring is shown in Fig. 1. Detailed information about the system is explained below.
[FIGURE 2 OMITTED]
To prevent direct contact of the ultrasound transducer from polymers at high temperature and pressure, five homemade delay lines of length 1.45 inch (one with smooth side surface and the other four with threaded side surfaces) shown in Fig. 2a were made to connect transducer with polymer. The material polyetheretherketone (PEEK) is used for these five delay lines due to its heat and chemical resistance, and low heat conductivity. It has an acoustic impedance (product of wave velocity and material density) close to PVC and LLDPE so that received signals have good signal strength. The ultrasound signals of these five delay lines are compared with a standard one from Panametrics Inc. in Fig. 2b. It shows that the signal strength (amplitude of echo [E.sub.D] from delay line/air interface) and signal to noise ratio (SNR) of the homemade delay line with smooth side surface has better quality than the others. Therefore it is used in our extrusion experiments.
[FIGURE 3 OMITTED]
The ultrasound adaptor shown in Fig. 2a has two functions: one is to hold the ultrasound transducer, and the other is to cool the temperature of the ultrasound transducer below its operation temperature by air circulation inside a chamber. It has the same external geometry as the Dynisco pressure transducer PT 460E-5M, and can be flush-mounted in a modular barrel section of the TSE used in this study.
Figure 3a shows the assembly of an ultrasound probe in a modular barrel section. Figure 3b shows a temperature/pressure transducer aligned in a circumferential direction with the ultrasound probes. Both material pressure and temperature can be obtained with ultrasound signals simultaneously. The circumferential center distance between them is 30[pi]D/360 = 8.90 mm based on the relative position shown in Fig. 3b, thus it is assumed that they are close enough. The data obtained from the temperature/pressure transducer are the same as those where the ultrasound probe is installed. The other end of the aforementioned ultrasound probe is connected to a pulser/receiver, which is used to generate and receive the ultrasound signals. The received data is then digitalized by an analog to digital (A/D) card in a computer. A Windows-based data acquisition software, WINSPECT, is used to transfer the digitized waveforms from the A/D card's memory to a computer for signal analysis.
[FIGURE 4 OMITTED]
Two screw configurations shown in Fig. 4 are used in our experiments. The ultrasound probe is flush-mounted above a thin-flight left-hand screw element (FF-1-20-R2) in zone 3. In both screw configuration I and II, a shearing element (ZS-33-R4) after the screw element (FF-1-20-R2) helps build pressure to make the channel fully filled at the monitoring position. In screw configuration II, a distributive mixing element (ZSS-26-R8) is configured before the screw element (FF-1-20-R2), while screw configuration I does not have this mixing element. The melting behavior in these two screw configurations will be compared to evaluate the polymer melting process with and without the mixing element.
The extrusion experiments were performed at screw speed 40 and 50 rpm for PVC compounds and at a screw speed of 60 rpm for LLDPE. At each screw speed, ultrasound signals were acquired at three feeding rates at a steady extrusion state. Therefore, the effects from PVC additives, screw configurations, and processing conditions (screw speed, feeding rates) can be revealed comprehensively by the ultrasound in-line monitoring system.
RESULTS AND DISCUSSION
General View of Melting Studies by Ultrasound
Figure 5 shows the morphology of PVC resin observed by a scanning electron microscope (SEM). Three types of particle structures are revealed in Fig. 5a and b: PVC grain particles (100-200 [micro]m), agglomerates of primary particles (~50 [micro]m), and primary particles (~1 [micro]m). Besides these structures, other smaller structures such as domains (0.1 [micro]m), microdomains (0.01 [micro]m), and microcrystallites were also suggested . The "melting" process for amorphous PVC resin is defined as disappearance of these particles and domains until it reaches amorphous polymer melt.
The screw is assumed to be stationary and the barrel moves relative to it; and materials in two regions are periodically scanned by ultrasound waves: 1) between the flight and the barrel (Flight region), and 2) in a C-chamber (these regions are shown in Fig. 6a and b, respectively). In these experiments, two intermeshing screws rotate divergently, and thus the ultrasound probe moving direction (Fig. 6b and c) is from the location far from a calender gap to the region close to it. It is worth mentioning that while the ultrasound probe moves from the C-chamber to the Flight region or vice versa, both reflected echoes from the screw root ([E.sub.BR]) and the flight ([E.sub.BF]) are received by the ultrasound transducer simultaneously. This is due to the partial coverage of the delay line on the flight and C-chamber shown in Fig. 6d.
Figures 7 and 8 show different ultrasound signal patterns in one cycle of screw rotation obtained from the melting process of LLDPE and PVC compounds at various processing conditions (screw configurations, feeding rates, and screw speeds). In each signal pattern, the scanning direction (y-axis) with a time interval of 0.1 second between each signal is plotted as a function of the wave flight time (x-axis). In each signal, echo [E.sub.D] denotes reflection from the delay line/polymer interface; [E.sub.BF] and [E.sub.BR] denote reflections from the polymer/flight interface and polymer/screw root interface, respectively; [E.sub.S] denotes the spurious echo from the delay line itself; echo [E.sub.BS] denotes reflection from the polymer melt/solid bed interface.
[FIGURE 5 OMITTED]
Ultrasound Signal Patterns and Melting Phenomena in LLDPE Extrusion
Figure 7a-c are the signal patterns obtained in screw configuration II at the feeding rates of 74, 97, and 127 g/min, respectively; each signal pattern is composed of 11 signals in one cycle of screw rotation at a screw speed of 60 rpm. Three melting states in the C-chambers are implied in Fig. 7: melting initiation at early stage, dispersed melting in the intermediate stage, and fully melted state at final stage.
Melting initiation. Figure 7a suggests that most of the LLDPE pellets with a size larger than the wavelength (i.e., D [much greater than] [lambda]) were at solid state at the monitoring location even though they passed through several screw elements from the feeding port. However, local melting initiation may occur between the pellets due to friction energy dissipation or plastic energy dissipation. Therefore, the wave mainly propagates through the particles by reflection and transmission between local melt/pellet interfaces, so that echoes [E.sub.BS] were reflected intermittently as noise in some signals. Figure 7a shows that the amplitudes of echoes [E.sub.BR] close to the calender region are lower than those far away from the calender region. It suggests that the particle size in the location close to the calender region is comparable to the wavelength (i.e., D [approximately] [lambda]) and that the wave amplitude [E.sub.BR] decreases due to the dominant scattering effect, while the particle size at the region far away is much larger than the wavelength (i.e., D [much greater than] [lambda]), and only absorption is dominant in wave attenuation.
Dispersed melting state. Figure 7b suggests that LLDPE pellets have been broken up into smaller particles with the size comparable to the wavelength (i.e., D [approximately] [lambda]), so that the amplitude of echo [E.sub.BR] apparently decreased due to the scattering effect. Uniformly distributed amplitudes of echoes [E.sub.BR] across the channel suggest that the particles were uniformly melted and suspended in polymer melt in the C-chamber.
Fully melting state. Compared to Fig. 7b, the amplitudes of echoes [E.sub.BR] in Fig. 7c increase again because almost all of the particles were melted, and less or no scattering effect contributes to the wave attenuation in the C-chamber. It suggests that the pellets in both the Flight region and the C-chamber have been totally melted and have reached the same melting state.
The ultrasound signal patterns in the C-chambers show that the melting process of LLDPE is highly dependent on feeding rates, which is related to pressure buildup inside the material. It implies that high pressure induced by high feeding rate not only helps to break up the pellets through all gaps (side gaps, calender gaps, tetrahedron gaps, and flight gaps) during their leakage flow, but also speeds up the local melting initiation by friction energy dissipation or plastic energy dissipation between particles.
Figure 7a-c shows that the amplitudes of echoes [E.sub.BF] in the Flight region almost remain the same with the increase in feeding rates, i.e., pressure. This suggests that the pellets in this region have melted much faster than those in the C-chambers, due to efficient heat conduction from barrel and viscous energy dissipation.
[FIGURE 6 OMITTED]
Ultrasound Signal Patterns and Melting Phenomena in Extrusion of PVC Compounds
Figure 8a-f shows the ultrasound signal patterns in one cycle of screw rotation for four PVC compounds, and various melting phenomena were observed depending on the processing conditions and additives used. Because the ultrasound wavelength [lambda] (~200 [micro]m) in melt is comparable with the particle size of grain particles (~100 [micro]m) and agglomerates of primary particles (~50 [micro]m) in PVC resin (as shown in Fig. 5), the scattering effect is dominant in wave attenuation, which is related to the measurable amplitude of echo [E.sub.BR] or [E.sub.BF]. The higher the value of the amplitude echo [E.sub.BR] or [E.sub.BF], the less wave is scattered and the fewer particles exist in the melt matrix, if the contribution from scattering of each particle is equal.
Figure 8a shows a typical ultrasound signal pattern for the melting process of unplasticized PVC (uPVC) at a feeding rate of 107.9 g/min, screw speed of 40 rpm, and screw configuration I, without a distributive mixing element before monitoring position. In most cases, no echo [E.sub.BR] could be detected from the polymer/screw root interface even though very high pressure was built up, except some weak [E.sub.BF] echoes. This implies that PVC particles are closely compacted there without melting initiation, and air bubbles between the particles scatter ultrasound waves effectively so that the wave energy is completely attenuated. However, the melting initiation in the thin Flight region happened due to the direct heat conduction from barrel.
Figure 8b shows the ultrasound signal patterns during the melting process of uPVC at a feeding rate of 78 g/min, screw speed of 40 rpm, and screw configuration II. In this signal pattern, there are some signals in which no [E.sub.BR] echo is found in the location close to the trailing side of the flight flank, and this suggests that PVC grain particles are closely packed with air bubbles between them. However, [E.sub.BR] echoes appear when the ultrasound probe moves to the intermeshing region, which implies that there is polymer melt between particles possibly due to the backflow of polymer melt from the calender gap. Therefore, a dispersed melting mechanism occurs close to the pushing side of the flight flank, while unmelted PVC powders are packed at the trailing side of the flight. When the feeding rate is increased to 82.8 g/min, the amplitudes of the [E.sub.BR] echoes shown in Fig. 8c reach a maximum value, and do not change with a further increase of the feeding rate to 89.2 g/min. This strongly suggests that the PVC powders in the C-chambers have been totally melted at both feeding rates.
[FIGURE 7 OMITTED]
Similar signal patterns such as those in Fig. 8b have been obtained at a screw speed of 50 rpm, at the feeding rates of 89.2, 101.0, and 107.9 g/min, respectively. However, when the feeding rate is increased to 107.9 g/min, there are still some signals that do not show [E.sub.BR] echo close to the trailing side of flight. This suggests that the melting process in the C-chambers at a screw speed of 50 rpm is delayed compared to that at a screw speed of 40 rpm. The delayed melting process at higher feeding rates was also observed by Wilczynski and White  during the melting process of PP pellets by the screw pullingout method in the same machine.
Figure 8d shows the ultrasound signal patterns during the melting process of PVC/DMP at a feeding rate of 111.3 g/min, screw speed of 40 rpm, and screw configuration II. Similar to the melting of uPVC described above, melting of PVC/DMP in the C-chambers occurs in the pushing side of the Flight region first, and then extends to the trailing side. However, additional [E.sub.BS] echoes (Fig. 8d) suggest that the polymer melt due to the leakage flow from the Flight region covers the solid bed (gelled PVC particles) at the trailing side of flight, and forms a flat boundary between them. Contrary to the dissipation-dominant melting process of uPVC with high-pressure buildup, the melting process of PVC/DMP in C-chambers finishes at low pressure because heat conduction significantly contributes to the melting process and the addition of liquid plasticizer DMP lowers the glass temperature of PVC.
Figure 8e and f shows the ultrasound signal patterns during the melting process of PVC/PBA at a feeding rate of 101.7 g/min and screw speeds of 40 and 50 rpm, respectively. Contrary to the melting mechanism suggested in Fig. 8a, Fig. 8e suggests that the melting pool with dispersed powders was always observed at the trailing side of the flight. Previous studies of Kulas and Thorshaug  and Menges and Klent  showed a similar melting phenomena in the melting process of PVC in an SSE. The [E.sub.BS] echoes in Fig. 8f suggest that a PBA melt film develops above the packed PVC powders and works as an external lubricant for the PVC material due to its low melting temperature (~60[degrees]C). This melt film was observed at a screw speed of 50 rpm, and might be formed by a dragging effect from the Flight region. Our experimental results show that the melting process of the PVC/PBA system is delayed compared to the uPVC system due to the lubrication effect of the melted PBA between PVC particles.
Distribution of Wave Velocity Across the Screw Channel
Figure 9 illustrates the traveling path of ultrasound wave through the delay line and polymer when the dispersed melting phenomena occurs in the C-chambers. The incident wave (amplitude [A.sub.0]) is reflected at the delay line/polymer interface and comes back into the transducer as echo [E.sub.D] (traveling distance in delay line 2[L.sub.D], traveling time [t.sub.D], amplitude [A.sub.D]). Another part is transmitted into the polymer in the channel and is reflected back from the polymer/screw root interface into the transducer as echo [E.sub.BR] (traveling distance in polymer 2H, traveling time [t.sub.C], amplitude [A.sub.BR]).
Based on the traveling distance in Fig. 9 and the traveling time obtained from ultrasound signal patterns, the wave velocities in both the delay line and polymer are simply calculated during in-line monitoring by Eqs. 1a and 1b as follows:
[V.sub.D] = 2[L.sub.D]/[t.sub.D] (1a)
[V.sub.C] = 2H/[t.sub.C] (1b)
where the length of the delay line [L.sub.D] is 34.544 mm and the channel depth H is 4 mm. The ultrasound traveling time [t.sub.D] in the delay line and [t.sub.C] in the C-chamber are 31.2 and 8 [micro]s, respectively. The wave velocity [V.sub.D] in the delay line and [V.sub.C] in polymer melt in the C-chamber are 2214.36 and 1000 m/s, respectively. The acoustic impedances of delay line [Z.sub.D] and polymer melt [Z.sub.P] are calculated from Eq. 2 simultaneously from in-line monitoring.
Z = [rho]V (2)
where [rho] is material density and V is wave velocity.
The calculated acoustic impedances of polymer melt and delay line as well as those of screw root and solid PVC are listed in Table 2 for further attenuation analysis.
Figure 10 shows the distribution of wave velocity across the screw channel in the melting process of uPVC at three feeding rates. The wave velocity in both the Flight region and the C-chamber seems unchanged with the increase of feeding rate or pressure build-up. This suggests that there is a limitation to using wave velocity to analyze the melting level because the variation in wave velocity [V.sub.C] with particle size and concentration is so small that it cannot be differentiated from the temperature or pressure effect.
However, the velocity in the Flight region shows a large difference from that in the C-chamber region. The wave velocity for longitudinal wave is given by
E' = [rho][V.sub.L.sup.2] (3)
where [V.sub.L] is the wave velocity, E' is the longitudinal storage modulus, and [rho] is the density. Therefore, E' in the Flight region is much lower than that in the C-chamber because of the high shearing rate in the Flight region.
Furthermore, if the wave frequency in the uPVC melt is same as the transducer center frequency (5 MHz), the ultrasound wavelength [lambda] is estimated as 200 [micro]s based on the following equation
[lambda] = [V.sub.C]/f. (4)
According to the relationship between the particle size and the ultrasonic wavelength, it is convenient to divide the ultrasonic propagation in the polymer mixture into the three regimes shown in Fig. 11: 1) long wavelength regime (LWR), i.e., [lambda] [much greater than] R; 2) intermediate wavelength regime (IWR), i.e., [lambda] [approximately] R; and 3) short wavelength regime, [lambda] [much less than] R (SWR). In the melting process of LLDPE pellets (R [approximately] 1.5 mm) to total amorphous melt, ultrasonic propagation covers these three regimes, while it falls into either the LW or IW regime for the melting process of PVC resins (R [approximately] 50-100 [micro]m) and agglomerates of primary particles (R [approximately] 25 [micro]m). If we consider the mixture of PVC in the C-chambers as a suspension system and assume only volume concentration changes during the melting process, i.e., the radius of PVC resins is a constant, the melting level can be characterized by the analysis of wave attenuation.
Characterization of Melting Level by Attenuation Analysis
The wave energy loss occurs at the interface between two media and inside the materials. As a longitudinal wave normally travels from medium 1 to medium 2 with acoustic impedances [Z.sub.1] = [[rho].sub.1][V.sub.1] and [Z.sub.2] = [[rho].sub.2][V.sub.2], respectively, the wave is partially reflected and partly transmitted. The amplitudes of reflected wave ([A.sub.R]) and transmitted wave ([A.sub.T]) are given as follows :
[FIGURE 8 OMITTED]
[A.sub.R] = R[A.sub.0] = [[[Z.sub.1] - [Z.sub.2]]/[[Z.sub.2] + [Z.sub.1]]][A.sub.0] (5a)
[A.sub.T] = T[A.sub.0] = [[2[Z.sub.2]]/[[Z.sub.2] + [Z.sub.1]]][A.sub.0]. (5b)
By assuming that the mixture of unmelted PVC particles and melt is similar to the suspension or emulsion system, the ultrasound wave energy losses inside this viscoelastic system is originated mainly from scattering effect, intrinsic wave absorption, and thermal and viscous effects . The scattering mechanism does not produce dissipation of acoustic energy. Particles simply redirect a part of the wave energy so that this portion of the energy cannot be received by the ultrasound transducer. The intrinsic mechanism refers to the loss of wave energy due to the absorption of sound wave inside particles and medium, which are considered to be homogeneous on a molecular level. The thermal mechanism is thermodynamic in nature and is related to temperature gradients generated near the particle surface. Dissipation of wave energy is dominant for soft particles. The viscous mechanism is hydrodynamic in nature and is related to shear waves generated by the particle oscillating in the wave pressure field. These shear waves appear because of the density difference between particle and medium. The density difference causes particle motion with respect to the medium. As a result, liquid layers in the vicinity of the particle slide relative to each other and cause losses of wave energy due to shear friction. Viscous dissipative losses are dominant for small rigid particles with size less than 3 [micro]m. Therefore, by the superposition approach, the total wave attenuation [[alpha].sub.Total] inside the mixture is expressed as
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[[alpha].sub.Total] = [[alpha].sub.Scattering] + [[alpha].sub.Intrinsic] + [[alpha].sub.Thermal] + [[alpha].sub.Viscous] (6)
where [[alpha].sub.Scattering] is scattering attenuation, [[alpha].sub.Intrinsic] is intrinsic absorption, and [[alpha].sub.Thermal] and [[alpha].sub.Viscous] are attenuations from thermal and viscous effects, respectively. According to the wave traveling path in Fig. 9, echo [E.sub.D]'s traveling path is: traveling in delay line (D), reflection through the delay line/polymer (D/P) interface, and traveling in delay line (D) again; echo [E.sub.BR]'s traveling path is: traveling in delay line (D), transmission through the D/P interface, traveling in polymer (P), reflection through polymer/screw root (P/S), traveling in polymer (P) again, transmission through the polymer/delay line (P/D) interface, and traveling in delay line (D). Therefore, the amplitudes [A.sub.D] and [A.sub.BR] can be determined by the superposition approach of all attenuation mechanisms, respectively, as follows
[FIGURE 10 OMITTED]
[A.sub.D] = [R.sub.DP][e.sup.-2[[alpha].sub.D]L][A.sub.0] (7a)
[FIGURE 11 OMITTED]
[A.sub.BR] = [T.sub.DP][R.sub.PS][T.sub.PD][e.sup.-2([[alpha].sub.P.A][H.sub.P] + [[alpha].sub.M.A][H.sub.M])][e.sup.-2[[alpha].sub.D]L][e.sup.-2[[alpha].sub.S]H][A.sub.0] (7b)
where [[alpha].sub.D] is the attenuation coefficient of the delay line, [[alpha].sub.P.A] is the absorption coefficient of particles, [[alpha].sub.M.A] is the absorption coefficient of polymer melt, and [[alpha].sub.S] is scattering coefficient of the mixture. If we assume that the scattering contribution from each particle is equal, we can neglect absorption of solid particles ([[alpha].sub.P.A]), and viscous and thermal effects on wave attenuation. At a high melting level, polymer melt absorption ([[alpha].sub.M.A]) is constant and the sum of the traveling distance in polymer melt 2[H.sub.M] [approximately equal to] 2H. Therefore, the normalized amplitude ratio K of [A.sub.BR] to [A.sub.D] is simplified as in Eq. 8a, in which the measurable value K varies with the scattering coefficient [[alpha].sub.S]. One of advantages of using the normalized amplitude ratio K is to eliminate the wave attenuation in the delay line, and correlate it to the polymer melting state in the screw channels directly. Furthermore, the scattering coefficient [[alpha].sub.S] is calculated from the K value by Eq. 8b. Both Eqs. 8a and 8b imply that the higher the normalized value K, the less wave losses in material and the fewer particles suspended in the C-chambers.
K = |[A.sub.BR]/[A.sub.D]| = |[[T.sub.DP][T.sub.PD][R.sub.PS]]/[R.sub.DP]|[e.sup.-2([[alpha].sub.M.A] + [[alpha].sub.S])H] = [Ce.sup.-2([[alpha].sub.M.A] + [[alpha].sub.S])H] (8a)
[[alpha].sub.S] = [1/[2H]]ln(C/K) - [[alpha].sub.M.A] (8b)
where T is the transmission coefficient, R is the reflection coefficient, and C is a constant defined as
C = |[[T.sub.DP][T.sub.PD][R.sub.PS]]/[R.sub.DP]| = |[4[Z.sub.P][Z.sub.D]([Z.sub.P] - [Z.sub.S])]/[([Z.sub.D.sup.2] - [Z.sub.P.sup.2])([Z.sub.P] + [Z.sub.S])]|. (9)
[FIGURE 12 OMITTED]
Based on Eq. 8a and ultrasound signal patterns at screw speeds of 40 and 50 rpm for extrusion of uPVC, the distribution of normalized amplitude K is plotted in Figs. 12 and 13, respectively, in both the Flight region and the C-chamber. This suggests that the melting level increases with the increase of feeding rates, and that polymer melts less uniformly at higher screw speeds.
The ultrasound in-line monitoring method is used successfully to investigate the melting phenomena of various polymer systems fed in powder form or pellet form. Ultrasound signal patterns were used to investigate the polymer melting behavior in both the Flight region and the C-chamber.
[FIGURE 13 OMITTED]
Melting in the Flight region finishes much faster than in the C-chamber, due to the combination of heat conduction and viscous energy dissipation in the extrusion process of both LLDPE and PVC.
Generally, melting in the C-chamber always starts at the pushing side of the flight first, and then spreads to the trailing side. Melting level and uniformity in the C-chamber increases with the increase of pressure buildup in the material because the pressure buildup might accelerate local melting, which is associated with energy dissipation between particles (particle friction and plastic deformation) and viscous energy dissipation. Higher pressure can also contribute to particle compaction so that heat transfer from the barrel is more efficient.
Various melting phenomena in the C-chamber have been observed depending on materials and processing conditions. During the extrusion of LLDPE and PVC compounds, dispersed or dissipation melting phenomena are dominant under most processing conditions. However, film/solid bed melting behavior with solid bed at the trailing side of the flight is observed for the PVC/DMP system, while solid bed at the pushing side is observed for the PVC/PBA system due to the lubricant effect.
The experimental results suggest that wave velocity across the screw channel is insensitive to processing conditions such as feeding rates and screw speeds. An attenuation analysis method is proposed to characterize the melting level in the C-chamber.
TABLE 1. The formulations of PVC compounds in this study. Material I (phr) II (phr) III (phr) IV (phr) PVC resin 100 100 100 100 Stabilizer 2 2 2 2 DMP 20 20 PBA 20 CaC[O.sub.3] 20 TABLE 2. The data of material density, wave propagation velocity, and acoustic impedance. Acoustic Density Wave impedance (X [10.sup.3] velocity (X [10.sup.5] Material kg/[m.sup.3]) (m/s) kg/([m.sup.2] * s)) Polymer melt 1.33 (a) 1000 (b) 13.30 Solid material 1.40 (e) 1400 (c) 33.53 PEEK delay line 1.30 (e) 2214.36 (b) 28.79 Steel 4340 (d) 7.80 5850 456.3 (a) Measured from capillary rheometer at 150[degrees]C. (b) Measured from ultrasound in-line monitoring at 150[degrees]C. (c) From off-line ultrasound measurement at room temperature. (d) Refer to "Non-destructive Testing Handbook." (e) From MSDS.
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Dongbiao Wang, Kyonsuku Min
Polymer Engineering Department, The University of Akron, Akron, Ohio 44325-0301
Correspondence to: K. Min; e-mail: email@example.com
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|Author:||Wang, Dongbiao; Min, Kyonsuku|
|Publication:||Polymer Engineering and Science|
|Date:||Jul 1, 2005|
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