Pressure and Temperature Behavior of ThermoplasticPolymer Melts During High-Pressure ExpansionInjection Molding

Saso Rogelj,1 Matjaz Krajnc21 Lesnik L.L.C., Zgornje Bitnje 100a, SI 4209 Zabnica, Slovenia, EU

2 Faculty of Chemistry and Chemical Technology, University of Ljubljana, Askerceva 5,SI 1000 Ljubljana, Slovenia, EU

The development of expansion injection molding asnew technology for producing thin plastic parts hasraised questions about polymer melt behavior in theprocess of rapid high pressure compression andexpansion. To investigate those phenomena, the newin-line injection molding machine mounted measure-ment system has been developed. Measuring nozzleequipped with hydraulically driven closing bolts andcontact fast response pressure and infrared tempera-ture sensors enabled us to measure the compressionand expansion of polymer melts at different startingconditions. Results presented for high impact polysty-rene and polyamide show that polymer melt tempera-ture rise is linearly dependent on compression pres-sure as well as it is dependent on compression speed.Comparable effect of temperature fall has beenrecorded during the polymer expansion, resulting in nonoticeable loss of dissipation energy during this re-versible process. Measurements have been comparedwith modified 2-domain Tait equation of state. Curvefitting analysis to manufacturer’s material data showthat measurements fit well with the model, even at veryhigh compression speeds. POLYM. ENG. SCI., 48:1815–1823, 2008. ª 2008 Society of Plastics Engineers

INTRODUCTION

Plastic products are indispensable in our everyday life.

They are made out of different kind of polymeric materi-

als, most commonly out of thermoplastic polymeric mate-

rials.

Thermoplastic polymeric materials consist mostly of

high molecular weight polymers which are deformable

when heated to liquid melts, and plastic when cooled suf-

ficiently to brittle, glassy state. Using processes like injec-

tion molding, these materials can be remelted and

remolded in new shape several times.

Today, the injection molding is the most used method

for producing plastics parts. Process starts with plasticiz-

ing of the polymer granulate in the injection unit. With

the advance of the plasticizing screw, molten polymer

material is injected at high pressure in the mold cavity of

desired product shape. After cooling time and solidifying

of the polymer material, mold halves open and the prod-

uct is ejected. With the closure of the mold, the new

injection molding cycle starts.

Number of products per time unit determines the yield

of the process. Therefore shorter cycle times are an objec-

tive. Parts with thinner wall need shorter cooling time,

which contribute to the trend of the miniaturization of

components but need significantly higher injection speed.

Higher injection speeds are needed, because during the

injection of polymer melt into the cavity, melt quickly

solidifies in contact with colder mold surface. This hap-

pens only to thin melt layer near the mold wall, whereas

the melt core solidifies slower because of small thermal

conductivity of polymers. Polymer thermal conductivity

values are about two or three orders of magnitude lower

than values of most metals [1]. Therefore, when produc-

ing thin products, the whole cavity has to be filled in very

short time to prevent solidification of melt before the end

of the flow path. Classic approach to increase injection

speed is to use the accumulator supported hydraulic. The

hydraulic oil is pressurized in the accumulator and then

released to push plasticizing screw forward and thus

injecting polymer melt. At plasticizing screw speeds over

600 mm/s, this becomes highly demanding because large

amount of oil has to be transferred in controlled condi-

tions in very short time. Highly dynamic servo-valves and

64bit electronics are needed to control rapid acceleration

to full speed in less than a tenth of a second [2]. Today,

fast cycling injection molding machines can achieve plas-

ticizing screw movement speeds of 1000 mm/s [3].

Correspondence to: Matjaz Krajnc; e-mail: matjaz.krajnc@fkkt.uni-lj.si

Contract grant sponsor: Ministry of Higher Education, Science and Tech-

nology of Republic of Slovenia; contract grant number: 3311-03-831832.

DOI 10.1002/pen.21149

Published online in Wiley InterScience (www.interscience.wiley.com).

VVC 2008 Society of Plastics Engineers

POLYMER ENGINEERING AND SCIENCE—-2008

Despite achieving very high plasticizing screw move-

ment speeds, it has been found out that the flow front of

polymeric material has much lower speed [2, 4]. Large

part of energy introduced during the screw movement is

used to compress the melt in the barrel in front of the

screw, which results in delayed and slower movement of

polymer flow front. It is commonly known that polymers

are viscoelastic substances which deform under stress,

and quickly return to their original state once the stress is

removed. When the load is applied, long polymer mole-

cule chains rearrange and change position. Through this

process they dissipate energy and in comparison with

elastic materials lose some energy as heat. Because of its

chemical structure, during compression different polymers

experience different volume deformation. In general, at

about 200 MPa polymer volume reduction for about 10%

may be expected [4]. Volume reduction is defined with

change of specific volume as function of temperature and

pressure. The relationship between those state variables

has been investigated thoroughly through the past. Labo-

ratory machines working on different principles have been

developed especially for measurement of those material

properties. Two such major experimental techniques were

surveyed by Zoller and Fakhreddine [5].

The desirability of formulating an adequate equation of

state (EOS) to follow those measured relations formed

many mathematical models. Spencer and Gilmore pub-

lished simplified version of well-known van der Waals

equation [6]. With desire to predict shrinkage and warp-

age of polymer products while cooling in molds, models

that include also cooling rate effects and crystallization

kinetics when cooling into solid state were developed.

Rodgers [7] reviewed classical Tait equation and six other

theoretical equations of state including lately frequently

used Simha-Somcynsky hole model [8]. Among many

models for representing EOS, Tait equation is purely em-

pirical and assumes that the specific volume only depends

on pressure and temperature [9]. This equation was

derived by Tait in 1888 and is still one of the most used

and proven approximations of actual PVT behavior [10].

2-domain Tait equation uses high temperature asymptote

besides low temperature asymptote to represent solid

state. Both asymptotes are connected with Nakamura

equation at pressure-dependent transition temperature

[11]. This equation is further modified into modified 2-do-

main Tait Equation [12, 13], where in range close to tran-

sitional temperature, low temperature asymptote exponen-

tially approaches melt asymptote, as observed at many

semicrystalline polymers.

Those equations predict compression volume of poly-

mer melts, which may be then used for expansion into a

mold cavity. As a result of that finding, new injection

molding process known as expansion injection molding or

‘‘Xmelt’’ has been recently developed and patented [2, 4,

14]. The expansion injection molding process takes

advantage of the polymer compressibility and is using

compressed polymer melt as the energy accumulator for

expansion into the mold cavity. During the injection

phase, with rotation of the plasticizing screw, polymer

melt is plasticized and transferred in front of plasticizing

screw. With forward movement of the screw, polymer

melt is then compressed against closed shut-off nozzle or

closed hot runner system to high pressure. With opening

of the nozzle or hot runner, the melt is then released to

rapidly expand into the product cavity.

Because of the absence of the screw movement in the

injection phase, expansion injection molding represents a

new step in development of micro and thin wall injection

molding. Using this technology, until now the highest

injection speeds are achieved. Questions how polymer

melts behave in such conditions arise, and therefore pres-

sure and temperature behavior in compression and expan-

sion process has been investigated. Questions also arise,

whether pressure-volume-temperature data measured in

laboratory at isotherm or isobaric conditions also hold for

this highly dynamic industrial process.

To be able to examine the behavior of polymer melts

in the process of compression and expansion, special

measuring nozzle has been developed and mounted to full

electric injection molding machine. Objective of the noz-

zle as the main measurement tool in this research is to

follow pressure and temperature behavior of polymer

melts in this high pressure and high speed process of

compression and expansion at true industrial conditions of

expansion injection molding.

EXPERIMENTAL

Nozzle Design

Measuring nozzle is based on well known slit die rhe-

ometer principle [1], but to be used at true industrial con-

ditions it had to be transferred from lab extruder to an

injection molding machine as already reported before

[15–17]. To be able to follow polymer melt compression

and expansion, nozzle has been further developed and

upgraded with two hydraulically driven bolts able to close

or open the melt channel.

On Fig. 1 presented nozzle consists of conical entrance

orifice which proceeds into long angular slit, equipped

with closing bolts and pressure and temperature trans-

ducers. In this research two nozzles have been built, one

with very thin angular slit of 0.4 mm 3 10 mm and

another with very thick angular slit of 10 mm 3 10 mm.

Three fast response Kistler 4013A pressure sensors with

integrated thermocouples were used to record pressure in

the measuring channel. One additional sensor of this kind

has been mounted into the entrance section of the nozzle

to follow polymer properties before entrance into meas-

uring channel. The sensor itself consists of a very stable

and high-temperature-proof silicon sensor element, which

operates according to the piezoresistive principle. This

enables pressure measurement in the range up to 300 MPa

1816 POLYMER ENGINEERING AND SCIENCE—-2008 DOI 10.1002/pen

(3000 bar) and 3508C. Usual piezoelectric pressure

sensors used in injection molding molds are not suitable

for use in the nozzle of an injection molding machine.

Sensor element is located directly behind the extremely

rugged steel diaphragm. The design of the sensor requires

no transmission medium and has very good stability under

load [18]. As those sensors also have integrated thermo-

couples, it was possible to measure temperature as well.

In contrast to fast pressure measurement, fast temperature

readout of the sensor can not be expected. This is due to

contact with the nozzle wall and the thermal capacity of

the sensor itself. This temperature readout was used to

control the nozzle temperature state and to control the

infrared temperature sensor response in an isothermal

state. Because of extremely rapid dynamics of polymer

melt expansion, fast response temperature sensors were

searched. As distinguished from usually used thermocou-

ples or Pt100 resistive temperature sensors, infrared tem-

perature sensors have much shorter response time. There-

fore FOS NTS 2-IR sensors with response time below 15

ms were used [19]. Infrared sensors function on the prin-

ciple of infrared pyrometers and detect heat radiation

from molten plastic. This radiation enters in the sensor

through sapphire window where it is detected by IR

diode. As shown by Obendrauf et al. [20], due to the fact

that plastics are partially penetrable for electromagnetic

radiation in the near infrared range, polymer absorption

coefficient can influence temperature measurement. There-

fore, infrared temperature sensors have been placed

directly in front of the pressure sensors with integrated

thermocouples. In an isothermal state, infrared sensor

response of polymer melt has been calibrated against cor-

responding facing thermocouple.

Sensor signals were guided to corresponding signal

amplifiers, which according to sensor measured value give

0–10 V output. Those outputs were guided into data log-

ger that was further connected to personal computer.

Bolts and sensors are defined and positioned from the

entrance edge of the nozzle as follows: bolt 1 (B1) at

97.5 mm, bolt 2 (B2) at 281.5 mm, pressure sensor 1 (P1)

and temperature sensor (T1) at 129.5 mm, pressure sensor

2 (P2) and temperature sensor 2 (T2) at 189.5 mm and

pressure sensor 3 (P3) and temperature sensor 3 (T3) at

249.5 mm. Additional pressure sensor (P0) has been

mounted into the entrance orifice of the nozzle at 66.44

mm. Injection pressure signal (IP) is taken directly from

the injection molding machine, where it is measured

behind the plasticizing screw via patented membrane

measuring system [21]. Measured signal overview may be

observed on Fig. 2.

Because of extreme high dynamics of expansion phe-

nomena, melt channel opening/closing bolts have to be

able to move with high velocity and therefore accumula-

tor supported hydraulic at 12.5 MPa has been used. Both

bolts were connected to stand alone hydraulic aggregate,

FIG. 1. CAD generated model of the measuring nozzle with closing bolts (a), pressure transducers (b), and

IR temperature transducers (c).

FIG. 2. Layout of the measured signals.

DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2008 1817

monitored and controlled over injection molding machine.

Valves for movement of the bolts were also independently

controlled with the signals from the injection molding

machine. Two stroke transducers monitored bolt move-

ments and their positions. To prevent melt leakage at high

pressures and elevated temperatures, bolt rings and very

tight manufacture tolerances were used. Four separately

regulated heating zones were used along the nozzle, to

keep the nozzle at desired temperature. Heaters were

regulated over four thermocouples, positioned close to the

measuring channel. They were controlled and regulated

directly from the injection molding machine. To prevent

overheating of the hydraulic cylinders on top of the bolts,

water cooling system was also integrated.

Nozzle has been mounted directly on the injection

molding machine plasticizing cylinder. High pressure re-

sistant plasticizing cylinder and abrasion and corrosion re-

sistant screw with 25 mm diameter and L/D 24 on fully

electric tiebarless Engel E-motion 200/100 injection mold-

ing machine have been used. The use of fully electric

injection molding machine is compulsory due to the fact

that during the pressure fall in the expansion process,

plasticizing screw must stay ‘‘locked’’ in the position. In

case of hydraulic injection molding machine, the melt

pressure in front of the plasticizing screw is always in

balance with the hydraulic oil pressure behind the screw.

All the experiments were carried out in the machine pro-

grammed automatic cycle. To be able to free program the

cycle including the nozzle bolt movements the new Engel

CC200 controller was used. Measured signals have been

sent to high speed 16 channel data logger and further to

personal computer. Up to 2000 Hz signal readout per

channel has been used to record fast expansion phenom-

ena. Beside trigger signal, additional 15 signals have been

used: three IR temperature readings, four pressure read-

ings, four temperature readings from pressure sensor inte-

grated thermocouples, two signals from bolt stroke trans-

ducers, reading of plasticizing screw position and machine

injection pressure reading.

Materials and Experimental Conditions

In this work, one amorphous and one semicrystalline

material commonly used in injection molding have been

chosen:

• HIPS high impact polystyrene, Polystyrol 495 F

(BASF)

• PA polyamide (6,6), Durethan A30S (Lanxess)

PA is hygroscopic material and has been dried before use

for 4 h at 858C. Before the measurements, polymeric

materials have been plasticized to desired starting com-

pression volume before the screw. Slightly rising injection

unit temperature profile up to set temperature has been

used.

Polymer melt compression and expansion in the meas-

uring channel have been investigated at following variable

starting conditions:

Injection (compression) rate of 2 to 100 cm3/s;

Temperature from 210 to 2508C for HIPS and from 260

to 3008C for PA;

Compression pressure of 100, 150, 200 and for certain

experiments also of 240 MPa;

Compression volume from 15 to 35 cm3.

All the melts were compressed also with compression

rate of 200 cm3/s. After true screw movement velocity

has been investigated, it has been found out that between

the very short time of compression to desired pressure,

due to servo motor acceleration, above mentioned rates

were not actually achieved. Therefore they are not shown

among the results.

Compression and Expansion Procedure

In addition to in-line rheological measurements, two

independently driven bolts are enabling us to investigate

following phenomena: compression of polymer melts,

expansion of polymer melt into the channel, and expan-

sion of polymer melt out of the channel.

To be able to produce expansion injection molded

parts, polymer melt must first be compressed to high pres-

sure. With the bolts B1 open and the B2 closed, it was

possible to follow polymer compression behavior along

the measuring channel while moving with injection mold-

ing machine screw forward to desired pressure at desired

‘‘injection’’ rate, starting melt volume and temperature.

While expanding into the cavity, it is necessary to

know what happens with compressed melt in the volume

before cavity. This is achieved with the B1 in open and

B2 in closed position. After the compression in the melt

channel and opening of the B2, expansion out of the

channel takes place. In this case it is possible to close B1

and expand only the volume in the measuring channel, or

leave B1 open and expand the whole volume in front of

the plasticizing screw.

RESULTS AND DISCUSSION

Compression

Material has been plasticized at set temperature to

defined volume and then compressed to desired pressure

with variable compression rates. Recorded pressure and

temperature signals from all three nozzle positions, pres-

sure signal P0 from nozzle entry section and machine IP

are represented in Fig. 3. For representation, compression

of PA to 240 MPa at rate of 10 cm3/s and at starting

2808C and 35 cm3 is shown.

For analyses, peak temperature at position 2 (T2) has

been used. The influence of starting conditions on this

1818 POLYMER ENGINEERING AND SCIENCE—-2008 DOI 10.1002/pen

value has been examined. Temperature rise from starting

set temperature at different conditions is represented in

Fig. 4. For each represented point, several measurements

at the same pressure were averaged under the condition

of standard deviation is less than 1.

While compressing the polymer melts, it has been

found out, that beside the pressure, the compression speed

also influences temperature rise of the melt. Temperature

rise during the compression can be explained by moving

the macromolecules closer together, making them less

movable and therefore translating its kinetic energy into

inner thermal energy.

The effect of pressure on polymer melt temperature

has already been investigated by Yue and Wood [22]. In

lower pressure range up to 50 MPa they have concluded

that temperature rise is linearly dependant of pressure. On

larger pressure scale, this effect has been investigated by

Rodriguez and Filisko [23, 24], but only at low tempera-

tures the samples were in solid state.

As shown on Fig. 4, measurements confirm linear rela-

tionship reported by Yue and Wood. In case of HIPS,

measurements are also comparable with the extrapolation

of their PS curve. Using PA temperature rise of 14.28C at

200 MPa and 10 cm3/s has been recorded, while using

HIPS at the same pressure and compression rate 18.58Ctemperature rise has been recorded.

Influence of compression speed on temperature rise is

driven by macroscopic heat convection from the polymer

melt into the nozzle. Therefore higher compression speeds

are resulting in warmer polymer melt. Although the effect

of compression speed is much weaker than that of com-

pression pressure, it is not negligible. This is particularly

visible at PA, whose thermal conductivity of melt (0.225

W/mK) is much higher than that of HIPS (0.165 W/mK).

Discrepancies between low and high compression speed

result in 38C at 200 MPa for PA and 18C at 200 MPa for

HIPS.

When comparing measurements made with the same

process conditions and only starting volume changed,

very small change in temperature rise have been recorded.

Discrepancies of 0.1–0.58C confirm that starting melt vol-

ume does not influence temperature rise of the melt.

Compressing at higher starting temperatures also does

not influence temperature rise. For example, at PA the av-

erage temperature rise difference between 280 and 3008Cat 240 MPa is 0.2–0.48C over the whole compression

speed range. Very similar differences are also recorded at

HIPS: Between 230 and 2508C at 200 MPa over the

whole compression speed range the discrepancies between

measured temperature rise are less than 0.48C.

Expansion

Expansion measurements were performed with opening

of the bolt B2 and releasing compressed polymer melt out

of the channel. As shown on Fig. 5, pressure in the chan-

nel falls rapidly in 0.01 s to atmospheric pressure. With

expansive pressure drop polymer melt also cools down,

but is then heated back to nozzle set temperature. Again,

pressure and temperature are recorded at three positions

in the nozzle, and the minimum measured value from

middle temperature sensor T2 is compared with other

measurements of this kind. Variable starting conditions

FIG. 3. Typical recorded temperature and pressure compression curves.

FIG. 4. Temperature rise of polymer melt during compression. FIG. 5. Typical recorded temperature and pressure expansion curves.

DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2008 1819

were material, pressure before expansion, temperature

before expansion, and expansion volume.

Like polymer temperature rise at compression, polymer

temperature fall at expansion is also strongly dependent

on pressure difference before and after the expansion.

Temperature fall between and after pressure fall to atmos-

pheric pressure has been recorded. Analyses represented

on Fig. 6 show that like temperature rise at compression,

temperature fall at expansion is also linearly dependant

on pressure.

Influence of staring temperature is insignificant for PA.

Measured values at 3008C are slightly lower as values

measured at starting 2808C. In comparison with compres-

sion close similitude may be found. As much as higher

starting temperature brings lower rise at compression, it

also brings lower temperature fall at expansion. At HIPS

208C higher starting temperature brings up to 28C lower

temperature fall at 200 MPa. Potential explanation of this

phenomenon lies in higher molecular chain flexibility at

higher temperatures that leads to lower shear heat genera-

tion when molecules are arranging together during the

compression.

Because of reversible process of stress deformation, it

is interesting to compare absolute temperature rise during

compression with absolute temperature fall during the

expansion. When comparing high speed PA compression

with expansion, curves cover each other, resulting in no

noticeable loss of dissipation energy. Very similar results

may also be observed using HIPS. Especially at 2508Cpressure-dependent linear temperature rise at high speed

compression covers the absolute pressure-dependent linear

temperature fall at expansion without any discrepancies.

Specific Volume During the Compression

While compressing the polymer melt, it was possible

to follow melt pressure and temperature as well as melt

volume. This dynamic process gives rise to questions of

comparison with pressure-volume-temperature relation-

ships measured in labs and represented with EOS. In

comparison with laboratory measured values, our meas-

urements have been performed with much higher dynam-

ics and have not run at controlled isothermal or isobaric

conditions.

In our case, compression and expansion of polymeric

materials occur at injection molding processing tempera-

tures, which are higher than polymer melting temperature.

This eliminates need for using equations of state which

also cover crystallization phenomena when cooling below

melting point. As it was shown by Zoller and Fakhreddine

[5], Tait equation represents well amorphous as well as

semicrystalline polymer melts. Nonetheless further devel-

oped modified 2-domain Tait Equation has been used:

VðP; TÞ ¼ V0ðTÞ 1� C ln 1þ P

BðTÞ� �� �

þ VtðP; TÞ (1)

V(P,T) is the specific volume of polymer, T is temperature

in Kelvin, P is pressure in Pa, and C is universal constant

(C ¼ 0.894). Melt region above transitional temperature

is represented with four experimentally fitted parameters

b1m, b2m, b3m, b4m, while solid with b1s, b2s, b3s, b4s.

V0 ¼ b1m þ b2mðT � b5Þ; T > T�

V0 ¼ b1s þ b2sðT � b5Þ; T < T� (2)

BðTÞ ¼ b3m exp½�b4mðT � b5Þ�; T > T�

BðTÞ ¼ b3s exp½�b4sðT � b5Þ�; T < T� (3)

Exponential approach to high temperature asymptote is

fitted with parameters b7, b8, and b9:

VtðT;PÞ ¼ 0; T > T�

VtðT;PÞ ¼ b7 expððb8ðT � b5ÞÞ � ðb9PÞÞ; T < T� (4)

Zoller and coworkers [25, 26] found that the pressure

dependence of the transitional temperature T* is linearly

dependent on pressure with parameters b5 and b6:

T� ¼ b6Pþ b5: (5)

Parameters were then fitted to material manufacturers’

data [27]. The equation parameters are quoted in Table 1.

Overall average specific volume discrepancy between the

material data and the model for PA is 0.000037 cm3/g

with standard deviation of 0.0032, while for HIPS the

model covers data almost without discrepancies. The

results presented on Figs. 7 and 8 show that the fit covers

material data well and that the overall averages are com-

parable with data from the literature [5, 7]. Experimental

data of polymer melt compression were then examined.

During the measurement in automatic machine cycle,

polymer melt was compressed from atmospheric pressure

at set initial temperature at desired compression rate to

chosen final pressure.

FIG. 6. Temperature fall of polymer melt during expansion.

1820 POLYMER ENGINEERING AND SCIENCE—-2008 DOI 10.1002/pen

Beside temperature and pressure measurement also

screw position has been recorded. With known nozzle ge-

ometry, melt volume was calculated. At 50 MPa it is safe

to confirm that the plasticizing screw nonreturn valve is

completely closed and therefore at this point mass of the

melt has been calculated. This constant mass is further

compressed, giving us the measured specific volume of

the melt.

Because the process is not isothermal, three-dimen-

sional graph has to be used to represent the results. These

are represented on Fig. 9, together with fitted modified 2-

domain Tait equation represented with grid. Over this grid

compression measurements are plotted. Results show that

measurements fit well with the model, even at very high

compression speeds and high dynamics. However at high

pressures over 200 MPa slightly lower specific volume

may be observed, than predicted by EOS. This phenom-

enon occurs due to elastic steel deformation of nozzle and

plasticizing screw, which leads to larger volume as calcu-

lated [4]. Consequently to larger volume, discrepancies to

EOS reduce.

Figure 9 represented the curve at compression rate of

100 cm3/s and at 2808C that stretches from atmospheric

pressure to 241 MPa, which has been recorded in 0.24 s.

At this rapid compression there is no time for heat

exchange between polymer melt and surrounding nozzle

and therefore adiabatic conditions may be assumed. An

examination of slow compression speeds show that even

at very small compression speeds isothermal compression

does not occur. This result is consequence of low thermal

conductivity of polymer melts and high ratio between

bulk volume of compressed melt and contact surface with

nozzle.

Expansion Speed Through the Nozzle

Expansion process is highly dynamic and occurs at

very high speed. The speed of pressure fall along the hot

runner during the expansion of polymer melt out of the

hot runner into the mold cavity determines the maximum

theoretical speed of injection. With presented measuring

nozzle, it is possible to measure pressure drop travel

along the nozzle. In addition it is also possible to measure

TABLE 1. Parameters for modified 2-domain Tait equation for

Durethan A30S and Polystyrol 495 F.

Parameter Values for PA Values for HIPS Units

b1m 0.0011 0.0010 m3/kg

b2m 6.97 3 1027 6.51 3 1027 m3/kg K

b3m 6.96 3 1027 1.72 3 108 Pa

b4m 0.0039 0.0043 1/K

b1s 0.0010 0.0010 m3/kg

b2s 6.44 3 1027 2.49 3 1027 m3/kg K

b3s 6.68 3 107 2.51 3 108 Pa

b4s 0.0032 0.0032 1/K

b5 528.01 373.71 K

b6 2.19 3 1027 2.39 3 1027 K/Pa

b7 4.55 3 1025 0.00 m3/kg

b8 0.0312 0 1/K

b9 6.89 3 1029 0.00 1/Pa

C 0.0894 0.0894

FIG. 7. Modified 2-domain Tait equation fit to Durethan A30S manu-

facturer’s data.

FIG. 8. Modified 2-domain Tait equation fit to Polystyrol 495 F manu-

facturer’s data.

FIG. 9. PA compression measurements plotted over PVT equation of

state grid: ( PA 3008C 4 cm3/s, PA 3008C 10 cm3/s,

PA 3008C 100 cm3/s, PA 2808C 4 cm3/s,

PA 2808C 10 cm3/s, PA 2808C 100 cm3/s).

DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2008 1821

pressure fall to atmospheric pressure at certain position in

the nozzle. Measurements were made with nozzle with

thick 10 mm 3 10 mm cross section channel and also

with very thin 0.4 mm 3 10 mm cross section channel.

Figure 10 shows one of the representative measurements

with PA at 2808C. It may be observed that pressure falls

very rapidly from almost 220 MPa to atmospheric pres-

sure in 0.01 s. Pressure drop is firstly perceived by sensor

P3 near the exit gate of the nozzle, followed successively

by the others in direction to the start of the nozzle chan-

nel. Several measurements reveal that pressure at sensor

P2 and P1 falls almost simultaneously, while sensors P0

and IP respond with few milliseconds delay. This is due

to smaller volume in the channel in comparison with the

compressed melt volume in the screw barrel. Even with

this delay, it may still be found out that the pressure sig-

nal travels along the nozzle with very high velocity.

Between P3 and P0 at 150 MPa, signal speed of 102 m/s

is measured. Interesting is also pressure fall speed along

the measuring nozzle. Results of Fig. 10 unveil that the

pressure fall is equally rapid at all positions in the nozzle.

Down to 50 MPa linear pressure fall may be assumed,

before the true exponential pressure fall is observed. In

this apparent linear pressure fall speeds between 27 and

30 GPa/s at different locations in the Nozzle were

recorded. Because of good resemblance between actual

melt behavior in the nozzle and PVT EOS, actual melt

flow front expansion speed for given geometry can be cal-

culated. In our case, during apparent linear pressure fall

at the first 7 ms of expansion, flow front velocity of 13.4

m/s is calculated. This is the maximum expansion speed

in hot runner system of such geometry. Pressure drop

speed is considerably slower at thin channel nozzle shown

on Fig. 11, which presents pressure fall of PA at 2808Cfrom 180 MPa. In this thin measurement channel, only at

pressure sensor P3 near the exit of the nozzle linear pres-

sure fall may be assumed, where the pressure fall speed

of 10 GPa/s is recorded. At thin nozzle polymer flow is

restricted with velocity profile for pseudo plastic polymers

with no slip at the wall condition, and is thus representing

noticeable polymer expansion resistance. In comparison

with the thick nozzle, pressure fall in the thin nozzle is

not rapid, but is falling slowly with time.

CONCLUSIONS

New in-line injection molding machine mounted meas-

uring nozzle has been developed to follow polymer melt

compression and expansion at true industrial conditions of

expansion injection molding. It has been found that dur-

ing the compression, temperature is linearly rising with

pressure. The results show that up to 18.58C temperature

rise when compressing polymer melt up to 200 MPa may

be expected. Likewise to temperature rise during com-

pression, temperature fall during the rapid polymer expan-

sion has been recorded. Comparison shows no noticeable

loss of dissipation energy during the process of compres-

sion and expansion. During dynamic polymer compres-

sion at conditions used in industrial process, pressure,

temperature, and volume have been measured. Compari-

son with modified 2-domain Tait equation fitted to mate-

rial manufacturer’s pressure-volume-temperature data

shows comparable and representative results. Results

show that this dynamic process still follows PVT data

acquired in laboratories at isothermal or isobaric condi-

tions. They also show that equations of state can be used

to predict polymer melt behavior during high speed and

high pressure industrial expansion injection molding.

ACKNOWLEDGMENT

The authors thank Engel Austria GmbH for extensive

partnership on the present work.

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FIG. 11. PA expansion pressure drop in nozzle with 0.4 mm 3 10 mm

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