~.. STUDY OF A COUNTER-ROTATING, INTERMESHING EXTRUDER AS A POLYCONDENSATION REACTOR /"

A Thesis Presented to the Faculty of The College of Engineering and Technology Ohio University

In Partial Fulfilment of the Requirements for the Degree Master of Science

by Edward R. Crowe November, 1992

LIBRARY. This Thesis has been approved for the Department of Chemical Engineering and the College of Engineering and Technology

Associate Prof Chem1cal Engineering

Dean of the College of Engineering and Technology iii

Abstract

An experimental study and model development have been performed to better understand the reactive extrusion of polyethylene terephthalate. A process was developed using a

34 mm counter-rotating twin screw extruder to depolymerize a commercial grade of polyethylene terephthalate into an acceptable pre-polymer for reactive extrusion experiments.

Residence time d Ls'tr Ibut.Lon experiments were conducted at different screw speeds and feed rates to characterize the flow patterns of the extruder. Based on these results an idealized plug-flow model was developed to simulate this process. An experimental design using the controllable process variables of zone temperature, feed rate and nitrogen flow sweeping across the surface of the polymer melt was developed to stUdy the individual effects of each of these variables as well as any interactive effects.

The results indicate that the feed rate and nitrogen flow have an effect on the degree of polymerization of the product.

However, the stUdy clearly shows the dominant effect to be ,the average residence time of the polymer melt in the vent zone.

The idealized plug-flow model presents a reasonable representation of this process. The predicted product degree of polymerization is slightly higher than the experimental results due to the exclusion of any degradation reactions.

The model reinforces the importance of residence time and devolatilization effectiveness in the condensation reaction. iv Acknowledgements

I would like to take this opportunity to express my appreciation to the faculty of the Department of Chemical

Engineering for providing a challenging and enjoyable experience and for making a "non-traditional" student feel welcome. My advisor, Dr. K. J. Sampson, deserves a special thanks for his valuable advice and guidance during the course of this research.

Mere words cannot adequately express my feelings of gratitude and affection for my wife, Sarah, for her unselfish. support and encouragement. v

Table of Contents

Page

Abstract iii

Acknowledgements. iv

List of Figures vi

List of Tables vii

Chapter 1: Introduction. 1

Chapter 2: Theoretical and Experimental Background . 5

2.1 Reactive Extrusion with Twin-Screw Extruders . 5 2.2 Co-rotating vs. Counter-rotating Configuration 13 2.3 Processing of Polyethylene Terephthalate 18

Chapter 3: Experimental Methods and Equipment. 25

3.1 Extruder Equipment and Set-up . 27 3.2 Residence Time Distribution Measurement 32 3.3 Depolymerization Procedure . 37 3.4 Polymerization Procedure. 40 3.5 Polymer Characterization. 46

Chapter 4: Results. 54

4.1 Residence Time Distribution Results . 54 4.2 Depolymerization Results. 57 4.3 Polymerization Results 64

Chapter 5: Reactive Extrusion Modelling. 73

5.1 Idealized Plug-Flow Model 74

Chapter 6: Conclusions and Recommendations. 89

6.1 Conclusions . 89 6.2 Recommendations for Future study . 91

References. 94

Appendix A: Dilute Solution Viscosity Test Method 98

Appendix B: Program Listing of Reactive Extrusion Model 104 vi List of Figures

Figure Page

2.1 Classification of Twin-Screw Extruders . 15

2.2 Stages of PET Synthesis • 20

3.1 Schematic Diagram of Experimental Apparatus 26

3.2 Configuration of Screw Elements 29

3.3 Molecular Weight vs Intrinsic Viscosity 53

4.1 Response Curve for Depolymerization Experiment 54

4.2 Response Curve for Polymerization Experiment • 55

4.3 Response Curve for Polymerization Experiment . 55

4.4 Results of Post-processing Experiment 60

4.5 Results of Experiment #1. 65

4.6 Normal Probability Plot of Effects 70

4.7 AC Interaction Plot 70

5.1 . Flow Diagram for Devolatilization Algorithm 84

A.1 Cannon-Ubelohde Dilution Viscometer . • 103 vii

List of Tables

Table Page

3.1 Description of Screw Elements . 30

3.2 2 3 Factorial Design for Experiment #2 46

4.1 Comparison of Residence Time Distributions. 56

4.2 Individual Results of Depolymerization Runs 58

4.3 Test Results from continuous Depolymerization. 59 4.4 Post-processed Test Results from continuous Depolymerization 61

4.5 Test Results from Alternate Depolymerization Process 62 4.6 Post-processed Test Results from Alternate Depolymerization Process. 63

4.7 Results of Experiment #2. 66

4.8 Measured Deviation of the Degree of Polymer­ ization of the Extrudate Compared to the Feed. 66

4.9 Analysis of Variance of Degree of Polymer- ization Data. 68

4.10 Calculated Data for Normal Probability Plot 69

4.11 Calculated DP Values and Residuals 72

5.1 comparison of Theoretical and Experimental Mean Residence Time 79

5.2 Comparison of Model and Experimental Results. 86 5.3 Example of output from Reactive Extrusion Model 88 1

Chapter 1: Introduction

Traditionally, extruders in the plastics industry, whether designed with single or mUltiple screws, have been used to melt and homogenize blends of different polymeric materials as well as to mix polymers with performance enhancing additives or pigments. Although this traditional view of extrusion technology is still dominant in the industry, reactive extrusion is now being viewed as an efficient means of continuously polymerizing monomers as well as chemically modifying existing polymers [1]. As a result of the rapid growth of the polymer industry, the increasing demand for high performance thermoplastic materials and the need for cost competitiveness and manUfacturing flexibility, reactive extrusion has been evolving as a process for efficient continuous polymerization.

The reactive extrusion process effectively combines two traditionally separate manUfacturing operations; the synthesis of the polymeric material and final processing into a finished product. For polymerization processes, extrusion equipment has certain distinct advantages over other continuous and batch processes. First, the intense mixing in an extruder, particularly a twin-screw extruder, continuously creates new, thin surface layers. This surface renewal action facilitates the mass and heat transfer effects. This capability of heat and mass transfer can not be achieved with a high viscosity 2 polymer mixture in a stirred tank reactor. As a result, the equivalent residence time in an extruder is lower, thus avoiding a long exposure to high temperatures that can cause polymer degradation. Also, the ability of an extruder to process polymers of high viscosities without the need for solvents results in a lower raw material cost as well as eliminating the capital costs needed for solvent recovery equipment. Although all of these processing characteristics offer specific advantages over stirred tank reactors, the most attractive advantage for reactive extrusion is the ability to offer a flexible manufacturing alternative. As the polymer industry continues to search for ways to meet the challenge of increased competition and need for cost efficiency, the mechanics of an extruder production line is such that ease of set-up and relatively quick change-over to new products provide a flexibility that can increase small order effectiveness.

This research is a study of the suitability of a counter­ rotating, fUlly-intermeshing twin screw extruder to reactively process polyethylene terephthalate. Using a Leistritz 30.34 laboratory extruder, de-polymerization trials are performed to manufacture a low molecular weight polymer which is then used as the raw material for the polymerization experiments to test the extruder's performance in reactive extrusion. In addition, this research requires the implementation of a test method to estimate the molecular weight of the extruded 3 polymer. Finally, a theoretical reactor model is presented that correlates the empirical results.

The focus of Chapter 2 is the discussion of previous experimental work found in the open literature. Published literature under the general SUbject of reactive extrusion is discussed, as well as other pertinent material, such as the characteristics of co-rotating versus counter-rotating twin screw extruders. ConclUding this chapter is an introductory discussion of condensation polymers with a specific focus on polyethylene terephthalate. The chemistry of PET will be presented along with a discussion of manUfacturing processes.

Chapter 3 discusses the experimental methods and equipment used in this research. A detailed description of the Leistritz laboratory extruder and peripheral equipment is presented as well as an overview of the operating parameters.

In addition a discussion of the method and results of the residence time distribution experiments is presented. Also in this chapter, the two experimental processing methods are discussed. Beginning with a general purpose grade of PET with a number average molecular weight of approximately 23,000, a process for adding ethylene glycol for de-polymerization to obtain a lower molecular weight polymer is presented. The product of this process is the feed material for the polymerization experiments where the investigation focuses on the synthesis of a higher molecular weight polymer.

Concluding Chapter 3 is a discussion of the test method used 4 to characterize the polymer products as well as the correlations used to estimate molecular weight.

The experimental results are presented in Chapter 4.

The results of both the de-polymerization and pOlymerization experiments are presented. Chapter 5 is a discussion of reactive extrusion modelling featuring an idealized plug-flow model simulating this process.

Finally, Chapter 6 presents the conclusions of this research project as well as recommendations for future work. 5

Chapter 2: Theoretical and Experimental Background

2.1 Reactive Extrusion with Twin-Screw Extruders

The practice of using an extruder as a reactor is not a recent innovation. Screw type machines were first used in the

1920's for rubber polymerization and were described in the patent literature in the 1930's [1]. Although within the broad sUbject of reactive extrusion there is pUblished work performed with single screw extruders, the following discussion will focus only on experimental studies performed on twin-screw extruders which are the preferred choice in the industry today. Singl~-screw extruders have performed well in the polymer manufacturing industry for many years as an effective mechanism to homogenize and melt materials of similar consistency. However, there are distinct dis­ advantages in applying these machines to reactive processing.

For example, in a single-screw machine, material is conveyed down the open channel of the screw by the drag forces at the wall, and any low viscosity material will resist being transported down the screw. Material also has a tendency to build-up on the screw because there are insufficient shear forces to drag the high conversion polymer. into the main flow. The past two decades have shown an increasing interest in the application of reactive extrusion to polymer manufactur­ ing. There is, unfortunately, a surprisingly limited number of pUblications in the open literature, which confirms the 6 proprietary nature of the processes developed. A 1985 article

by Sneller [2] refers to a survey conducted by Exxon research scientist Ronald Kowalski reporting a total of over 200 reac­ tive processing patents issued to all resin suppliers, but only three technical articles pUblished by these companies.

In addition, he finds that every resin supplier holds at least

five reactive processing patents. Clearly this illustrates the competitive value of reactive extrusion in today's marketplace.

In one of the earliest experimental works, published in

1968, Gouinlock et al [3], of Hooker Chemicals, described the production of copolyesters from bisphenol A, neopentyl glycol, and terephthaloyl chloride. This poly- condensation reaction was performed in a vented, tangential counter-rotating twin­ screw extruder with a barrel diameter of 20 mm and an LID of

37: 1. The low molecular weight feed was produced in a conventional reactor and then fed to the extruder. Another pUblished article in the 1960's was by Gerhard Illing of the

University of Erlangen [4] • Illing describes the polymerization of caprolactam to form nylon-6 in an intermeshing co-rotating twin screw extruder. The unique feature of Illing's patented design, manufactured by Werner and Pfleiderer, is an adjustable valve by which the effect of variable shear forces on the polymer could be controlled making it possible to adjust the melt viscosity and the average molecular weight. 7

The machine configuration that is predominant in reactive

extrusion is the intermeshing co-rotating twin screw extruder.

Studies of reactive extrusion in these machines can be found

as early as the 1940's, although until the mid-1980's almost

all reports were limited- to patents [5]. A paper presented at the 1987 Annual Technical Conference of the Society of

Plastics Engineers by Mack and Chapman [6] provides a useful

summary of the experimental results of .a co-rotating twin

screw extruder applied to a PET condensation reaction. Of particular interest is the relationship of viscosity to reaction temperature and reactor vacuum. The authors use a melt flow index (MFI) measured with a 2160 gram weight at

350°C to characterize the product. Although they fail to provide a correlation from this MFI value to corresponding values of molecular weight or viscosity, we can predict trends

in molecular weight. In other words, as the MFI value decreases, molecular weight increases. Using a 90 mm co­ rotating twin screw extruder with three venting zones, Mack reports the vacuum applied to the venting zones for removal of the volatile product was reduced from 100 to 20 mbar (15 torr), which was established as the optimum vacuum level. The reaction was carried out with a constant feed rate of 150 lb/hr and a constant screw speed of 120 rpm. The influence of the reactor temperature was studied with a 40 mm co-rotating twin screw extruder with a prepolymer feed of 10 lb/hr, 50 mbar (37.5 torr) vacuum, and a residence time of nine minutes. 8

The barrel temperature was increased in stages from 300°C to

320°C to reach the target viscosity. The authors report that between 317°C and 320°C the degree of pOlymerization was accelerated, and viscosity changes became significant. The authors studied the effects of screw speed and feed rate on residence time distribution in the 40 mm machine. At a screw speed of 60 rpm the feed rate was reduced from 15 lb/hr to 10 lb/hr, which increased the residence time from about 6.5 to about nine minutes. An increase in residence time to almost

12 minutes was achieved by reducing the screw speed to 30 rpm at 10 lb/hr. Although the authors do not provide any information as to the specific screw elements used in their. experiments, or even the length (number of zones) in the extruder, it is useful to know that the PET polycondensation reaction can occur at such seemingly short residence times in an extrusion process.

section 2.2 of this chapter will be devoted to a discussion of the relative merits of co- versus counter­ rotating twin screw extruders because of the relevance each machine has in the study of reactive extrusion. However, with this exception, the focus of this study is the fUlly intermeshing, counter-rotating twin screw extruder, and all further discussion will deal with this system.

In the most recently published text on twin-screw extruders, Dr . White [ 3 ] wri tes "There seem to be no discussions of reactive extrusion in intermeshing counter- 9 rotating twin screw extruders in the published literature."

The following discussion goes beyond that insight offered by

Dr. White and reviews some relevant experimental work performed with these machines.

In a paper presented at the Society of Plastics Engineers

ANTEC 87, Shah, et.al. [7] describe a study' investigating both a devolatilization and a polymerization finishing process in a Leistritz LSM 30.34 counter-rotating twin screw extruder with seven barrel sections (LID ratio of 24:1). This machine was configured with venting zones at sections three and six, but for the reactive extrusion experiments vacuum was only applied to zone six. The screw element configuration contained three pairs of ZS shear elements with FO-3-30-R elements in the vacuum zones (a comprehensive discussion of the Leistritz screw element nomenclature is included in

Chapter 3).

Using an aromatic polyamid (Upjohn's PA 7030) as the prepolymer feed, the authors blended MOl (4,4 - diphenylene methane diisocyanate) at a 3% ratio with prepolymer having a number average molecular weight of 23,800 (measured by GPC).

The MDI was added dropwise in zone three and a vacuum of 28.5 inches of mercury applied to zone six. The processing conditions were 280°C maximum temperature on the barrel, 150 rpm screw rotation, and a 4.85 lb/hr feed rate. with this screw configuration and these operating conditions, the mean residence time is about five minutes. 10 The number average molecular weights of polymer produced in four experimental trials ranged from 24,400 to 25,400. In comparison, the molecular weight of a sample produced without the addition of MDI was 21,800. Dey and Biesenberger [8] used a 34 mm Leistritz counter­ rotating twin screw extruder for a reactive extrusion stUdy of methyl methacrylate. The screw was designed with five FD-1-6­ R elements followed by two FD-3-30-R elements. The feed was

0.1 mole % of the initiator (benzyl peroxide) in methyl methacrylate. Experiments were conducted varying both screw speed and barrel temperature profile. Complete conversion was achieved with a screw speed of 10 rpm and a melt temperature of 300°C. In their discussion, Dey and Biesenberger state that the experimental trials which failed to achieve complete conversion were due to a short residence time in the extruder. Although this may be stating the obvious, they do not give any residence time distribution data to support their conclusions. Van Ballegooie and Rudin [9] conducted experiments blending polystyrene CPS) and polyethylene {PEl via reac~ive extrusion on a DAVO counter-rotating twin screw extruder. The focus of their research was to investigate the effects of treating both a high molecular weight and a low molecular weight series of a 50/50 weight percent PS/PE blend with different levels of dicumyl peroxide and triallyl isocyanurate coupling agent. Their conclusions indicate that the mechanical properties of the PS/PE blends were enhanced by 11 reactive extrusion with the addition of the peroxide and coupling agent. They do note, however, that the observed effects were less pronounced in the high molecular series.

similar research was pUblished later by Van Ballegooie and Rudin [10], but with the focus on enhancing the properties of polyvinyl chloride/polyethylene blends (PVC/PE) and polyvinyl chloride/ethylene-vinyl acetate (PVC/EVA) blends. These experiments were performed on the DAVO counter-rotating twin screw extruder with the addition of the same peroxide and coupling agent as previously discussed in their work with

PS/PE blends. The evidence presented illustrates that the mechanical properties of the PVC/PE blends were enhanced,. however the properties of the PVC/EVA blends were generally worsened with increasing peroxide levels. The application of a fUlly intermeshing counter-rotating twin screw extruder to the continuous polymerization of methylmethacrylate was thoroughly studied by Stuber [11] and published in his doctoral dissertation at the University of

Minnesota. stuber's research incorporated both experimental and modelling studies. The model he developed approximated the C-shaped chambers of the fully intermeshing screws as continuous stirred tank reactors connected by leakage flows through the mechanical clearances of the screw flights. A more complete discussion of this modelling approach and the comparisons to the model developed in this research will be included in Chapter 5. 12 The extruder utilized in the experimental studies was a

Leistritz 34 mm counter-rotating twin screw extruder with a barrel length of 1.2 meters, giving a length to diameter ratio of 35. The 1.2 meter screw length is segmented into 10 zones, with Zone 0 designated as the feed zone and Zones 1 through 9 as the reacting zones. In this particular configuration, fully intermeshing elements were used throughout, with a 12 mm pitch element used in the feed zone ~nd 6 mm pitch elements used in the reacting zones. Residence time distribution studies were conducted by feeding a soluble red dye, Amaplast

LB, in a five percent solution with regu·lar monomer and initiator into the first reactive zone of the extruder.

Samples of the extrudate were taken, dissolved in a solvent, and then measured in a UV spectrophotometer to measure the relative concentration of dye in the sample. Stuber reports a mean residence times varying from 14.9 minutes at a screw speed of 30 RPM to 10. 2 minutes at 120 RPM. This study illustrates that extruder residence time distributions get sharper as temperature or initiator concentration is increased because the polymerization builds viscosity faster. This leads to reduced backflow through the mechanical clearances. Further studies at the University of Minnesota were performed by Bouilloux, et.al. [12] with the Leistritz fUlly intermeshing, counter-rotating. machine. The focus of this research was the reactive extrusion of polyurethane and the modification of the Stuber model to introduce urethane 13 kinetics and rheology. The extruder configuration for this research was essentially the same as reported by Stuber [11].

Support for the ideal reactor approximation approach to modelling the reactive extrusion process is strengthened by this research. Bouilloux confirms Stuber's findings that the model does a reasonable job in predicting reactive extrusion behavior and is able to predict polymer properties and extruder pressures all along the extruder barrel.

2.2 Co-rotating versus Counter-rotating Configurations

Although this research is focused entirely on the

Leistritz fully intermeshing counter-rotating maChine, a discussion such as this would be incomplete without mention of the various twin screw configurations and their comparable features and applications.

A German engineer, Rudolf Erdmenger, was the first to categorize the various types of twin screw extruders [13]. He classed them as either lengthwise open or crosswise open, which describes the possible path of the material within the screws along and across the channel direction. Specifically, lengthwise open describes the extruders in which the material has a path open along the length of the barrel moving from the channels of one screw to the channels of the other. In contrast, crosswise open describes those extruders in which the area common to the two screws is a path across the flights so that the material moves from a channel of one screw to two 14 different channels of the other. Fortunately, this categorization has not become common in the industry. The flow path of the material depends not only on the direction of rotation of the screws but also on the shape of the flights and channels. Because Erdmenger's definitions made it difficult to decide which category a particular twin screw belongs, the accepted nomenclature categorizes twin screw extruders by their geometry. The flow path of the material is then a result of this geometry.

The common classifications in use involve the screw geometry and direction of rotation. For example, partially or full intermeshing and co-rotating or counter-rotating. These combinations, along with reference to the Erdmenger classification, are summarized in Figure 2.1 [14]:

Figure 2.1 illustrates the differences between co­ rotating and counter-rotating as well as between intermeshing and non-intermeshing. For example, the counter-rotating screw (1) is an axially closed, single-chamber pumping system in contrast to the co-rotating intermeshing screw (4) which is an axially open mixing system relying on drag forces. Most commercial intermeshing counter-rotating twin screw extruders are combinations of (1), (9a) and (9b) [14]. The flighted screw elements used in this research are fUlly intermeshing corresponding to (1) in Figure 2.1 (with the exception of the feed zone). 15

SCREW COUNTER-ROTATING CO-ROTATING ENGAGEMENT SYSTEM

LENGTHWISE AND THEORETICALLY CROSSWISE CLOSED NOT POSSIBLE o 2 z LENGTHWISE OPEN >s:: THEORETICALLY ~ :j~ AND ~2 NOT POSSIBLE ~ '-~ CROSSWISE CLOSED 3 ~ 4

~ CI =iB C-' LENGTHWISE AND THEORETICALLY POSSIBLE iSm Z BUT PRACTICAlLY ~tA :r: CROSSWISE OPEN ~5 CI) 5 NOT REAIJZED 6 ~ =U= ::s a::: LENGTHWISE OPEN THEORETICAlLY AND ~ NOT POSSIBLE ~ CROSSWlSE' CLOSED 7 8 >~ ~~ ~ ::il lOA < 0:: ~~ LENTHYISE AND CROSSWISE OPEN

98

0 o Z Z E2 ;: ~ Vl LENTHWISE AND b~ o ~ Z a:::::s! Z ~ CROSSWISE OPEN ~ ~ ~ ~ 11 =- 12

Figure 2.1: Classification of Twin-Screw Extruders

In general, for commercial machines, the main distinction is made between intermeshing and non-intermeshing twin screw extruders. The non-intermeshing screws do not have the benefits of positive conveying characteristics and are closer to single screw extruders in their operational principles and characteristics [15]. Although there is published work in reactive extrusion with both non-intermeshing co-rotating and counter-rotating machines, they will not be addressed any further in this discussion.

The second distinct classification of twin screw 16 extruders are co-rotating and counter-rotating. Intermeshing co-rotating machines can be further divided into low and high speed configurations. Intermeshingcounter-rotating extruders can also be further divided into conical and cylindrical configurations.

Rauwendaal [15] compares a 34 mm Leistritz intermeshing counter-rotating twin screw extruder with a 28 mm Werner and Pfleiderer intermeshing co-rotating machine. He found more positive conveying behavior in the intermeshing counter­ rotating extruder than in the co-rotating machine as well as a much narrower distribution of residence times. He did find, however, a broadening' of the residence time distribution in both machines when run at higher speeds. Rauwendaal also concludes that, attributed to its large shear rates, the intermeshing co-rotating twin screw extruder does a better job in distributive mixing, which is the redistribution of particles uniformly throughout the bulk. The counter-rotating machine is better in dispersive mixing, usually referring to the breakup of agglomerates of solid particles I which is thought to be the result of exposing the material to locally high shear stresses in the intermeshing region. Rauwendaal also found the intermeshing counter-rotating machine to be more effective in devolatilization operations.

Thiele [16] offers a comparison between intermeshing counter-rotating and co-rotating machines which is intended to be focused on those aspects of importance in reactive 17 extrusion. In his discussion, he first points out that the mean residence time is equal to the residence mass divided by the output rate. Therefore screw configurations of equal free volume will have the same residence time regardless of the mode of extrusion. However, Thiele confirms Rauwendaal's findings that the counter-rotating extruder exhibits tighter residence time distribution behavior than the co-rotating machine. He adds the caveat that the tighter distribution shown by the counter-rotating extruder is only significant when the filling degree of the flights is high. Devolatilization is another important aspect for comparison between the extruder types. Thiele states that both counter-rotating and co-rotating machines produce similar amounts of mass transfer for surface renewal. Counter­ rotating screws, in addition to the rolling mass of molten polymer seen in devolatilization zones, produce a film for devolatilization from the transport of polymer through the intermeshing gap.

Two other important criteria in considering reactor performance are mixing intensity and heat transfer capability.

In his paper Thiele [16] briefly discusses both, concluding that counter-rotating and co-rotating are similar and that the specific screw design is much more critical to successful performance.

Sakai, et. ale [17] compared the ability of intermeshing co-rotating and counter-rotating extruders in dispersive 18 mixing as well as their performance in the distributive mixing of glass fibers in a PET melt. Confirming the results of the researchers previously noted, they found that the counter­ rotating machines produced a polymer with better physical properties when compounding polypropylene with an inorganic filler. However, the co-rotating machine exhibited less tendency to break down the glass fibers when producing a 30% glass filled PET blend.

2.3 Processing of Polyethylene Terephthalate

It is appropriate to conclude this chapter with a discussion of the polymer system used in this research. Polyethylene terephthalate was chosen as the experimental polymer for two reasons. First, it is widely produced with demonstrated commercial importance. The most important consideration, however, is the extensive research that has been conducted with the chemistry and processing of PET.

Since our research is directed toward understanding the mechanisms involved in the reactive extrusion process, working with a polymer system with previously studied behavior characteristics facilitates our understanding of the process. The classical subdivision of polymer synthesis into the two groups, condensation and addition polymers, was made in

1929 by W. H. Carothers [19]. Today it is common in the literature to include condensation polymers under the broader classification of step-growth polymers. The addition reaction 19 involves the external chemical activation of molecules that cause them to start combining with each other in a chain reaction without the net loss of any atoms from the polymer molecule. The condensation reaction process differs from the addition process in that the chemical bonding of two molecules can only be achieved by the removal of a molecule at each step. The reaction by-product must be immediately removed from the reacting polymer since it will either inhibit further polymerization or appear as an undesirable impurity in the finished polymer. Polyethylene terephthalate is a condensation polymer with ethylene glycol as the condensation byproduct. Ravindranath and Mashelkar [20] categorize the manufacturing of PET into four distinct stages: (1) transesterification or direct esterification, (2) prepolymerization, (3) melt polyconden­ sation, and (4) solid state polycondensation. These stages are illustrated in Figure 2.2.

In the first stage, bishydroxyethyl terephthalate (BHET) is produced by transesterification or direct esterification.

In the transesterification process, dimethyl terephthalate is reacted with ethylene glycol with the removal of methanol as a byproduct. Alternatively in direct esterification, terephthalic acid is reacted with ethylene glycol and water is removed as a byproduct. Direct esterification was generally not preferred earlier because of difficulties in the purification of terephthalic acid. However, with improvements 20

ESTERIFICATION TPA ANC c:::=::::=::::: STIRRED VESSEL EG 240·280C sao ·500kPa

DP-1.5·4

PREPOlYMERIZAT10N MaT SOLID STATE POLYCONDENSATlON POLYCONDENSAT1ON STIRRED VESSEL DP-20·30 DP-100 DP-160 ~ DISKRING REACTOR ROTARY DRUM 260· 2100 6000 cP 1,OOO,OOO~ 210·2900 200·2400 2·3kPa &0·100 Pa 100kPa

DP-1.6·4

TRANSESTERIFICATION

OUT AND STIRRED VESSEL EO 140·220 0 100kPa

Figure 2.2: stages of PET synthesis in technology, this process is gaining acceptance. [21] In the second, or prepolymerization stage, Ravindranath an~ Mashelkar state that BHET is polymerized in a stirred-tank reactor up to a degree of polymerization of about 30. The third, or melt polycondensation stage, further polymerizes the product under high vacuum using special reactor designs to a degree of polymerization of about 100. It is this stage that provides the focus for our study of the applicability of reactive extrusion. Since, in general, reactors designed with the appropriate mechanical configuration to generate a large interfacial area are used in this stage, it is an appropriate 21

application for the twin-screw extrusion process.

The final stage is the solid state polycondensation

process and is generally used in producing molding grade PET with a degree of polymerization greater than 150. In this

stage, polymer from the ·melt stage is solidified in the form of chips which are then exposed to the solid state

polymerization process. This process is carried out under vacuum at a temperature above the glass transition temperature

but below the polymer melting temperature. It is reported in the literature that ultra-high molecular weight PET (weight

average molecular weight of 440,000) has been achieved using a solvent dissolution, precipitation, and solid state polymerization process. [22]

Since this research is focused exclusively on the melt polycondensation stage, I will restrict the remainder of this discussion of the chemistry and processing of PET to melt polycondensation as well. The main polycondensation reaction is a reversible reaction and the ethylene glycol condensation product must be removed to allow the reaction to proceed. The reaction can be

illustrated from the following condensed structural formula found in sweeting [23]: 22

This is the main reaction taking place in the polycondensation stage, and is generally shown in the literature [24] as

Z + EG

where Eg represents the ester end groups, Z represents the internal ester groups, and EG represents the volatile component, ethylene glycol. In this expression K1 represents the equilibrium constant and k 1 is the temperature dependent rate constant. This reaction expression will be discussed in more detail in Chapter 5 including the specific values used for the rate equation in the plug-flow model developed for this research.

Although the idealized model developed to simulate this reactive extrusion process considers only the main polycondensation reaction, it is important to note that four additional side reactions which have important commercial 23 implications are known to take place [25]. These are (1) the formation of acetaldehyde, (2) diethylene glycol formation,

(3) water formation, and (5) vinyl group formation. The investigation of these side reactions is outside the scope of this research, but in commercial processes these reactions must be controlled since the quality of the polymer is strongly dependent on the amount of side products formed.

In the continuous polycondensation process, Ravindranath and Mashelkar report [26] that the critical process and operational variables are: temperature, vacuum, catalyst concentration, effective interfacial area per unit volume, and axial dispersion.

Of these variables, the effective interfacial area per unit volume is clearly the most dependent on the physical design of the process equipment. For example, the disk ring reactor commonly used in this stage of PET manufacture increases the interfacial area through the use of rotating disks. These disks rotate through the bulk polymer mass in the reactor with a thin film of polymer adhering to each disk as it rotates free of the bulk and is exposed to the applied vacuum. The application of a fUlly intermeshing twin-screw extruder to this process provides the advantage of a high interfacial area per unit volume ratio as well as continuous surface renewal through aggressive mixing characteristics.

The other variable which is very dependent on the geometry of the process equipment, and perhaps the least 24 studied, is axial dispersion. Ravindranath and Mashelkar have developed a simplified, one-dimensional, one-parameter axial dispersion model [26]. They caution that its application is limited and that actual flow patterns in multi­ disk reactors are more complex. The model for the twin-screw extruder used in this research assumes no axial dispersion.

Although this assumption of ideal plug flow greatly simplifies the modelling effort, the residence time distribution study discussed in Chapter 3 justifies this choice. 25

Chapter 3: Experimental Methods and Equipment

The experimental approach used for this study can be categorized into four distinct objectives. The first was to study the general mixing characteristics of this extruder configuration and screw design. This was accomplished by analyzing the residence time distribution for different feed rates and screw speeds using a commercial grade PET. The second goal was to produce a low molecular weight polymer from a commercial grade PET that would be an acceptable raw material for the reactive extrusion experiments. This was necessary since a low molecular weight PET, or pre-polymer, is. not commercially available in the relatively small quantities that would be economically feasible for this research. The third goal was to determine the suitability of a fully intermeshing counter-rotating twin-screw extruder for the reactive processing of a condensation polymer. The fourth and final goal was to develop a method to characterize the polymer product produced from these experiments . The method jUdged to be the most reliable and cost effective was to test for the intrinsic viscosity using an ASTM test method developed specifically for PET. The approach used in achieving these four goals as well as a general discussion of the extruder equipment and peripheral hardware will be discussed in the next five sections of Chapter 3.

A diagram illustrating the general arrangement of the 26 experimental apparatus is shown in Figure 3.1. This diagram is a schematic representation of the Leistritz LSM 30.34 twin- screw extruder showing each zone and the peripheral equipment used in the experimental studies. A complete description of this equipment is included in the next section of this chapter.

ETHYLENE GLYCOL NZ HEAT EXCHANGER

PET FEED

PI VACUUM PUMP

DRIVE FEED MOTOR ZONE

Figure 3.1: Schematic Diagram 'of Experimental Apparatus 27

3.1 Extruder Equipment and Set-up

The experimental studies were carried out on a Leistritz

Model 30.34 laboratory extruder in the Department of Chemical

Engineering at Ohio University. This machine is configured as a fully intermeshing counter-rotating twin-screw extruder.

The extruder's screw diameter is fixed at 34 mm with a barrel of modular construction which allows for a user configured barrel length. This machine has seven barrel segments of

120 mm each, or a total screw length of 840 mm. This gives an

LID ratio of approximately 25. For comparison, the Leistritz

30.34 used in the reactive extrusion research by stuber [11] has a total barrel length of 1.2 meters, or an LID ratio of

35.

The key to extruder performance is the configuration of the screw elements. The terminology that I will use in discussing the screw configuration will be to divide the barrel segments into zones, beginning with the feed zone and proceeding down the barrel in the direction of flow from zones

1 through 6. For purposes of temperature control, the d i.e is referred to as zone 7. The terminology used by Leistritz to describe the variety or screw elements contains an alpha­ numeric descriptor as follows: First, the length of each screw element is labelled by the descriptive suffix R. For example, a full length element of 120 mm is labelled -R, while an element with a length of 60 mm is labelled -R2. This nomenclature is consistent down to the smallest distance 28 element of 7.5 mm which is labelled -R16. Next, the screw elements are identified by their pitch. For example, a 20 mm pitch means that the polymer melt is ideally advanced toward the die by 20 millimeters for every screw revolution. The screw element is also identified by the number of threads.

For example, an element designed with a pitch of 20 mm with two threads moves the polymer melt forward 20 mm for each screw revolution, but the "distance between the leading edge of each flight is only 10 mm since the 20 mm pitch refers to each thread. Finally, the letter combination at the beginning of the label describes the type of screw element. Unfortunately, there is no logical rule to learn to interpret this descriptor, but rather the various types of elements must be committed to memory. For example, the prefix FD refers to a fully intermeshing conveying element where ZD is a non­ flighted distance element. For example, the FD-1-6-R elements positioned in the venting zones are fully intermeshing conveying elements 120 mm in length designed with only one screw thread and a pitch of 6 millimeters. The elements used in the screw design for this study are as follows: In the upstream half of the feed zone an FF-1-20-R2 partially intermeshing conveying element is used. Transferring the polymer from the second half of the feed zone to the first half of zone 1 is a KFD-1-20/20-R compression element. The downstream half of zone 1 consists of a ZD-26-R2 distance element. The fully intermeshing conveying element FD-1-6-R is 29 used in each of zones 2, 3, and 4. Zones 2 and 4 are venting zones used for devolatilization. In the first half of zone 5 is an FD-2-20-R2 element. The remaining screw elements are distance elements with a 26 mm diameter. The downstream half of zone 5 is a ZD-26-R2 and zone 6 is configured with a ZD-26-

R2 followed by two ZD-26-R4 elements. The elements used in this screw design were chosen from the best available elements which would maximize the residence ti~e in each vent zone as well as the overall residence time in the machine. Figure 3.2 is an illustration of this screw configuration.

PET FEED VENT ZONE VENT ZONE

,,

FEED ZONE ZONE 1 ZONE 2 ZONE 3 ZONE 4 ZONE 5 ZONE 6 D I l...... --...Ill 120 mm 120 mm 120 mm 120 mm 120 mm 120 mm 120 mm E ~

(1) FF-1-20-R2 (4) FD-1-6-R (7) FD-2-20-R2 (2) KFD-1-20/20-R (5) FD-1-6-R (8) ZD-26-R2 (3) ZD-26-R2 (6) FD-1-6-R (9) ZD-26-R2 (10) ZD-26-R4 (11) ZD-26-R4

Figure 3.2: Configuration of Screw Elements

Table 3.1 is a listing of the elements in Figure 3.2 in the same sequence as they are installed in the direction of 30 material flow from the feed zone to the die. This listing includes the alpha-numeric descriptor, length, and description of each element pair. The screw tip and the centering disks used to connect each element in series have been omitted from this discussion since their use is common to any screw configuration.

Table 3.1: Description of Screw Elements

Element Pair Length Description

FF-1-20-R2 60 nun Conveying element, partially intermeshing KFD-1-20/20-R 120 nun Compression element, partially intermeshing ZD-26-R2 60 nun Non-flighted distance element FD-1-6-R 120 nun Conveying element, fully intermeshing FD-1-6-R 120 mrn Conveying element, fully intermeshing FD-1-6-R 120 rnrn Conveying element, fully intermeshing FO-2-20-R2 60 rnrn Conveying element, fully intermeshing ZD-26-R2 60 rnrn Non-flighted distance element ZD-26-R2 60 rnrn Non-flighted distance element ZD-26-R4 30 rnrn Non-flighted distance element ZD-26-R4 30 rnrn Non-flighted distance element

Total length: 840 nun

The barrel sections, with the exception of the feed zone, are heated with 700 watt electrical resistance heaters and cooled with attached air blowers. The die is also heated with a 350 watt resistance heater but does. not have cooling capability. The primary sensing elements are thermocouples which read the barrel temperature of zones 1 through 6. The die has both a thermocouple and a pressure transducer.

The main drive consists of a 10 kilowatt variable speed 31 drive with a DC motor and tachometer feedback. The screw speed is variable from 8 to 230 RPM, although the minimum speed of 8 RPM was used exclusively for the polymerization experiments to maximize residence time. The feed mechanism consists of a hopper and screw feeder designed to convey solid polymer pellets. A minor modification to the original design was necessary to restrict the flow of pellets to the feed screw to lower the overall feed rate. However, even with this modification, the very low feed rates and screw speed required for the polymerization study require a manual feed. This extruder is controlled with the Leistritz Micromatex

Model 16.1 microprocessor based controller. From the control panel, the operator can set input digital setpoints for zone temperatures (in Fahrenheit), screw speed, and relative feed rate. The vacuum pump is also controlled from the control panel. In addition to the visual readout of operating parameters, fault conditions and diagnostic assistance, a built-in printer will provide a hard copy of this same information.

The vacuum pump was originally designed to provide a suction power of 20 CFM at 50 torr of vacuum. It should be noted that this vacuum pump was not functional at the beginning of this research stUdy and after being rebuilt can only provide about 160 torr of vacuum. The vacuum system is attached to zones 2 and 4 for devolatilization. 32 Other peripheral equipment added to the equipment set-up includes a nitrogen system consisting of a rotameter, a heat exchanger designed with copper tUbing and resistance heating, and associated piping to provide a supply of heated nitrogen to zones 2 and 4 to sweep across the polymer surface to enhance devolatilization. For the depolymerization experiments, ethylene glycol was fed from a one liter flexible container of the type used in medical applications for intraveneous injection. The non-vented polypropylene tUbing, inclUding a drip chamber and a flow regulator, were attached to the container with the discharge end of the tUbing routed to the entrance of the feed zone.

The Leistritz extruder has proven to be a well designed machine capable of accurate speed and temperature control.

There are, however, limitations with the experimental set-up such as the necessity for manual feed at low feed rates.

Other desirable additions such as a system to remove extrudate from the die would be helpful to future researchers. Detailed recommendations will be discussed further in Chapter 6.

3.2 Residence Time Distribution Measurement

The knowledge of the residence time distribution in the extruder is important in the study of reactive extrusion.

Residence time distributions can be used to describe the overall mixing characteristics of the machine. In this study, the response curves will also validate the choice of an 33 idealized plug-flow model to represent this process. Most importantly, the molecular weight distribution of the polymer is largely determined by the spread in residence times of the reacting material [18].

Several techniques used to measure residence time distribution appear in the literature. Janssen [18] adds Mn02 as a tracer and measures the concentration by the induced

S6 S6 radioactive decay of Mn 'to Fe • This system gives accurate measurements of low concentrations. Stuber [ 11] uses a soluble red dye, Amaplast LB, in his studies of reactive extrusion of MMA. After feeding a solution of five percent dye and 95 percent monomer, he collects samples of the polymer effluent until the red dye is no longer visible. These samples are then dissolved in a solvent and the concentration of dye is quantified in a UV spectrophotometer by the 320 nm absorbance using a sample of the polymer without dye as a reference.

Because the Leistritz twin screw extruder used in this at.udy does not have the facility for liquid injection, a variation of Stuber's approach was first tried. Since a dye cannot be directly injected into the polymer melt, the first attempt to run a residence time distribution experiment consisted of adding a small quantity of emerald green PET pellets (Kodapak PET Polyester 9900U) as a pulse input along with the constant feed of clear PET (Kodapak PET Polyester

7352). The intent was to measure the dye present in the green 34 pellets in the extrudate. Samples of the extrudate were taken every minute and dissolved in phenol/tetrachloroethane solvent. These samples were then measured in a spectrophotometer with the absorbance compared to an extrudate sample with no dye present. The results of, this method were useless because of the excessive scatter of data.

The next approach was similar. Again, a solid polymer sample was used as the die carrier. It was added to the feed zone as a pulse input to convey a dye to the polymer melt.

The polymer for this experiment was a black nylon (BASF

ULTRAMID~). Extrudate samples were taken at one minute time intervals and pressed into flat "pancakes" of a thickness of

0.045" to 0.055". Because the previous experiment yielded poor results using the spectrophotometer, a simpler approach was used in this experiment. The relative light transmitted through each extrudate sample was measured with a cadmium sulfide photocell (Radio Shack 276-118). Although the res.ponse curve of the photocell varies greatly over the visible light spectrum, the carbon black in the nylon effectively blocks all visible light resulting in surprisingly good results. The direct readings from the photocell are in ohms. These readings are then converted to concentrations using a correlation developed from reading known samples containing zero, one, and two percent concentrations of nylon.

Three experiments were conducted to determine the residence time distributions at the feed rates and screw 35 speeds used in both the depolymerization and polymerization trials. The clear commercial grade PET (Kodapak 7352) with a degree of polymerization of 120 was used in all three experiments. The first RTD experiment was conducted with a feed rate of 36 grams per minute and a screw speed of 25 rpm.

These conditions were also used for the first set of depolymerization experiments. The two RTD experiments representing the polymerization trials were conducted with feed rates of approximately 13 and 7 grams per minute respectively, both with screw speeds of 8 rpm. In all of the

RTD experiments, the temperature setpoints of all the extruder zones were set at 505 of (263 Oe).

To negate the effect of thickness variations in each polymer sample, two readings were taken at different locations on the sample and then averaged. To obtain the conversion correlation from the resistance data to percent concentration, samples of known concentrations of one and two percent nylon were prepared. The readings used in this correlation were

2.068 kohms for 0% nylon, 4.017 kohms for 1%, and 6.480 kohms for 2%. Although this is nearly a linear fit, the following quadratic expression was used to correlate percent concentration to kilohms:

% Cone = -1.26345 + O.66047-(kohms) - O.02420S·(kohmS)2

After the conversion to concentration, the first and second moments of each residence time distribution were 36 calculated. The first moment, ""'1 , is equal to the mean residence time, T, which is defined as:

fo" t·C( t) dt 1J.1 = "t' = fo"C( r) dt

The second moment, ""'2' is defined as:

From the first and second moments the variance of the response curve can be calculated. The magnitude of the variance is an indication of the spread of the distribution. The greater the· variance, the greater the spread of the distribution. The standard deviation is the square root of the variance. The variance is defined as:

A useful benchmark for model development is the number of equivalent ideal CSTRs in series that would be required to approximate an experimental response curve. This number can be calculated by dividing the square of the mean residence time by the variance as shown in the following equation [31]:

2 No. of ideal CSTRs = ..!­ 0 2

By sUbstituting the first and second moments in this equation 37 we get the following expression:

No. of ideal CSTRs =

The results of these experiments are shown in Chapter 4.

Figures 4.1 to 4.3 show the concentration response curves for each of the experimental conditions described above.

3.3 Depolymerization Procedure

The strategy for this experimental study was to use a low molecular weight PET pre-polymer with a degree of polymerization in the range of 10 to 20 as the feed for the reactive extrusion experiments. A polymer feed in this molecular weight range should give good devolatilization performance yet be sUfficiently viscous to be transported by the screw flights. Unfortunately, a polymer in this molecular weight range is not sold as a commercial product. It is an intermediate product in the industrial PET manufacturing processes and cannot be practically extracted, packaged, and shipped to customers. Since the polycondensation reaction is reversible, however, a process was developed to depolymerize the commercial grade PET.

There are two process technologies which are used in the depolymerization of PET. These are hydrolysis/methanolysis and glycolysis. Treating PET with excess water at an elevated temperature of 150 - 250 °C with a sodium acetate catalyst 38 will produce terephthalic acid and ethylene glycol in four hours [29]. Acids (such as sUlfuric) as well as bases (such as ammonium hydroxide) can be used as catalysts in hydrolysis.

Alternatively, methanolysis is treating PET with excess methanol to produce dimethyl terephthalate and ethylene glycol. Glycolysis is the transesterification reaction resulting from the treatment of PET with an excess of a glycol. An experimental study by Baliga, et. ale [30] showed that the product of the depolymerization of recycled PET in excess ethylene glycol at 190 °C in the presence of a metal acetate catalyst contains over 75 mol % BHET. Companies that are pursuing recycling strategies with PET are interested in depolymerizing PET back to its monomers or oligomers to enable them to reuse them in the manufacture of food grade PET.

For this research, the glycolysis approach was used to reduce· the degree of polymerization from the value of 120

(molecular weight of 23,000) of the commercial grade clear PET

(Kodapak 7352) to the targeted range of 10 to 20. The follow- ing equations illustrate the calculations used to deter~ine the degree of polymerization (OP) for a PET feed rate of 36 gm/min and an ethylene glycol feed rate of 34 drops/min (29 drops of ethylene glycol are equivalent to 1 ml):

34 dr0p's EG • .l:.- ml . 1. 1 gm EG =1.29 gm. EG nu.n 29 drops EG ml nu.n

.l:.- min . 23000 gIrl PET • 1.29 gIn. EG • .l:.- mole EG = 13.29 mole EG 36 gm PET mole PET nu.n 62 gm EG mole PET 39

If the DP of the feed is 120, then the theoretical DP of the extrudate is: DP = 120 = 8.40 13.29 + 1

The depolymerization process was conceptually very simple. The commercial PET was fed at a constant rate by the screw feeder into the feed zone of the extruder. The ethylene glycol was gravity fed from the reservoir mounted above the extruder via the tubing attached to the discharge of the screw feeder to allow a regulated flow of glycol to drip on the bulk pellets as they entered the feed zone. Nitrogen tUbing was also routed to the feed zone to supply a steady stream of inert nitrogen to inhibit polymer degradation. The entrance to the feed zone was sealed to contain the ethylene glycol vapor and nitrogen. A variation to this process was used for a second series of dep~lymerization trials. Instead of a continuous feed of polymer pellets and ethylene glycol, a batch process was implemented where several pounds of commercial PET pellets were blended with ethylene glycol in the same ratio as used in the continuous process. The pellet/glycol blend was fed in equal weight increments every minute. A ball valve was installed at the entrance of the feed zone providing a tight seal to contain the glycol vapor. A positive pressure in the feed zone was created by a nitrogen purge. Post-processing of the low molecular weight extrudate was performed to reduce the potential of unreacted glycol in the 40 polymer mixture. There is the possibility that unreacted glycol, since it is not chemically bonded in the PET molecular structure, would more readily devolatilize during the polymerization experiments. This would bias the results of that experimental procedure. The post-processing procedure used was to bake the low molecular weight material for a predetermined time interval. This time interval was determined from the results of an experiment where a small quantity of low molecular weight material was baked at 200 °c. Samples were taken at two, four, six, and eight hours. As expected, the molecular weight increased from that of the original extrudate. However after six hours there was no significant difference in the samples tested. Based on these results, the post-processing conditions of baking the polymer at 200 °C for six hours were established.

The results of these individual experiments are included in detail in section 4.2 of Chapter 4.

3.4 Polymerization Procedure

The outcome of this study to determine the suitability of using the Leistritz twin screw extruder as a polycondensation reactor depended on the success of implementing two fundamental strategies. The first strategy was to maximize the mean residence time and the second was to maximize the devolatilizing capability of the process.

The key to maximizing the residence time was to design a 41 screw with elements that minimized the axial transport of the polymer product for every screw revolution (refer to section

3.1 for details of the screw design). The non-flighted spacer elements are a major contributor to increasing the overall residence time since the polymer melt in these zones is transported only by displacement. The 6 mm pitch elements installed in the devolatilizing zones provide the maximum residence time of any of the available conveying elements.

The spacer elements would provide a longer residence time in these zones for devolatilization, but the mass transfer limitations due to the diffusion of ethylene glycol through the polymer melt would be a significant concern because there is no mixing and consequently no continuous surface renewal action. The other factors that had to be controlled to maximize residence time were the screw speed and polymer feed rate.. Because of torque limitations, the minimum screw speed is 8 RPM. This value was set as a constant in all of the polymerization experiments. The polymer feed rate has an effect on residence time and was included as a controlled variable to determine its effect on the reaction. There is a complete discussion of the results of the residence time distribution study in section 4.1.

Maximizing the devolatilizing capability of the process required a dual approach. The first step was to refurbish the vacuum pump. Next the vacuum piping and associated couplings were assembled to connect the vacuum pump to the two vent 42 zones of the extruder. Due to the worn condition of the vacuum pump the minimum attainable pressure in the vent zones from this system was approximately 160 torr. This level of vacuum is much less than normally used. In industrial processes the partial pressure of ethylene glycol in the vapor space must be reduced to less than 6 torr to maintain a reaction driving force to achieve a molecular weight in a commercially useful range [32]. To supplement the vacuum system performance, nitrogen was passed through a heat exchanger and injected into the devolatilizing zones. In theory, under equilibrium conditions the weight fraction of the volatile component in the polymer is related to its mole fraction in the vapor by Henry's law. Henry's law is expressed by Biesenberger [33] in the form:

p w = n e_ e G K PI where Kw is a Henry's law constant, we is the weight fraction of the volatile substance in the polymer melt, no is the mole fraction in the vapor, and P is the total pressure. Without the introduction of noncondensables, no would be equal to one.

It is clear from this equation that sweeping the polymer surface with an inert gas such as nitrogen causes no to drop thereby reducing the fraction of the volatile component remaining in the polymer at equilibrium. A detailed discussion of the theoretical calculations used in the model will be included in Chapter 5. 43 The experimental design for the polymerization study consisted of two experimental procedures. Experiment #1 determined the minimum time needed to reach steady state conditions after the low molecular weight feed is introduced. For this experiment, neither the nitrogen nor vacuum was applied. The commercial grade PET was fed to the extruder for a sufficient time to insure that no residue of degraded polymer was left in the extruder. Th~n the feed was stopped and the machine was purged. Low molecular weight polymer with a low feed rate (6. 7 gm/min) was then fed manually. Extrudate samples were taken at 30, 45, 60, and 90 minutes from the time the feed was initiated. There were two viscosity tests performed for each sample and the-two results were averaged.

The results of this experiment, illustrated in Figure 4.5, showed that the molecular weight of the extrudate dropped over the duration of the experiment until it reached a level equivalent to the feed. This point determined the minimum sampling time required for Experiment #2. These results are discussed in detail in Chapter 4.

Experiment #2 was a 2 3 factorial design to determine the effects of three factors; zone temperature profile, polymer feed rate, and the flow rate of nitrogen injected in the vent zone for stripping. Factorial designs are orthogonal arrays where the number of treatment combinations equals the number of levels raised to a power equal to the number of factors.

For example, in a 2 3 factorial design, two represents the 44 number of levels in the design and three represents the number of factors. The number of treatment combinations equals 2 3 , or eight. The advantage of a factorial design is that it requires relatively few runs. If the variables interact over the range of interest, the factorial design measures that interaction more efficiently than a "one-at-a-time" experiment. In this study, for instance, to gain the same precision by running experiments to study one factor at a time would require 24 experimental runs. The 2 3 factorial design requires only eight runs. This efficiency was desirable in view of the arduous process required to produce low molecular weight polymer. The disadvantage of the factorial design is that, because there are only two levels for each factor, a linear response over the range of factor levels chosen must be assumed. However, it clearly points out trends and can determine the appropriate direction for further experimentation.

Following the strategy of maximizing residence time and devolatilization capability, the screw speed was set at a minimum (8 RPM) and the vacuum pump was to be run during all experiments. Although it will be discussed in more detail in the conclusions and recommendations in Chapter 6, it should at least be mentioned at this point that the use of the vacuum pump was abandoned because the molten polymer was being

"pulled" away from the extruder screw and into the vacuum system. As the polymer cooled in the hose it solidified, 45 effectively blocking any effect the vacuum would have on devolatilization. The experimental strategy was then focused entirely on using nitrogen to strip the ethylene glycol vapor from the polymer surface. The final 2 3 factorial design is summarized in Table 3.2.

In conducting this experiment, a random order of treatment combinations was selected for the run order. The experiment was carried out over four days, with two runs occurring each day. Each day, in preparation for the first run, commercial grade polymer was processed through the machine to clean out any degraded material created during heating the extruder. This material was then purged from the machine and the feed of the low molecular weight polymer was initiated, simulating as closely as possible the conditions of Experiment #1. Also between experiments each day, commercial grade polymer was again processed through the machine to clean out any remaining product from the previous experimental run.

Samples of the extrudate were taken at the time period determined from the results of Experiment #1. Two dilute solution viscosity tests were performed on a sample from each treatment combination and averaged to minimize any variation due to testing. These results are presented in detail in

Chapter 4. 46 Table 3.2: 2 3 Factorial Design for Experiment #2

Low Level High Level Variable (-) (+)

A: Zone Temperature 260 -c 275 °c B: Feed Rate 7 gm/min 13 gm/min C: Nitrogen Flow 1850 ml/min 6800 ml/min

The treatment combinations are as follows: Treatment Run A Combinations

1 (1) 2 + a 3 + b 4 + + ab 5 + c 6 + + ac 7 + + bc 8 + + + abc

3.5 Polymer Characterization The selection of a test method that would accurately evaluate polymer properties was an essential element of this study. Some of the commonly used polymer testing methods, such as those testing mechanical properties, would not provide sufficient information to assess the results of this study. Therefore, only polymer characterization tests were investigated. The four most common and widely accepted groups of tests are: (1) the melt index and capillary rheometer tests, (2 ) viscosity tests, (3) gel permeation chromatography, and (4) thermal analysis tests, specifically thermogravimetric 47 analysis, thermomechanical analysis, and differential scanning calorimetry [34]. The melt index test measures the rate of extrusion of a polymer melt through an orifice under fixed conditions of temperature and pressure. Melt index values distinguish between polymers of different molecular weights since a higher molecular weight increases the resistance to flow, resulting in a lower melt index value. The disadvantage of the melt index test is that it is a single point test. The flow rates are measured at a single shear stress and shear rate at one temperature. The capillary rheometer test, however, measures the melt flow rate over a range of shear stresses and shear rates. A capillary rheometer consists of an electrically heated cylinder, a pressure ram, temperature controllers, timers, and interchangeable capillaries. Different load and speed settings can be established for the polymer being tested. The ram is moved at a constant velocity which correlates to a constant shear rate with the force required to move the ram measured by a load cell and plotted by a chart recorder.

Gel permeation chromatography (GPC) is a method for determining the molecular weight distribution of a polymer. The separation of polymer molecules by GPC is based upon the differences in their size in solution. The GPC instrumentation consists of a delivery system that pumps the polymer solution through the system, columns of highly porous, 48 dense packing media such as glass beads packed together in a tube which separate the sample by molecular weight, and an analyzer and recorder to provide a continuous plot of the molecular weight distribution. The average molecular weight can be determined from the GPC curve, but more importantly the shape of the molecular weight distribution curve provides information that can predict the physical and processing characteristics of the polymer.

The thermal analysis techniques, differential scanning calorimetry (DSC) , thermogravimetric analysis (TGA) , and thermomechanical analysis (TMA) are commonly used in the polymer industry. DSC is a thermal analysis technique that measures the quantity of energy absorbed or liberated by a polymer sample as its temperature is raised. TGA is a test procedure in which changes in the weight of a specimen are recorded as the sample is progressively heated. TMA consists of measuring the physical expansion or contraction of a material as a function of temperature. The maximum benefit of thermal analysis is gained by combining all three of these test procedures to characterize a polymer. From a combination of these tests, properties such as glass transition temperature, heat capacity, percent crystallinity, percent of inert material, degradation profiles, thermal expansion, and heat deflection temperature can be measured [34]. This is only a partial list of the useful information that can be determined from thermal analysis. 49 These polymer characterization test methods are commercially relevant and in widespread use in the industry.

However, the barrier to applying them to this study was the purchase cost of instrumentation for in-house testing or the prohibitive cost for external laboratory testing. since the success of the experiments conducted in this feasibility s cudy can be determined from the average molecular weight, the dilute solution viscosity test was chosen as a practical alternative. This test is performed by dissolving a specified amount of a polymer sample in a specified solvent. When the solution has reached temperature equilibrium after insertion in a constant temperature bath, a predetermined amount of this solution is transferred to a viscometer which is also immersed in the bath. The liquid level in the viscometer is brought above an upper graduation mark by applying a slight vacuum from a bulb pipet filler. The vacuum is then removed so the liquid level will drop. The time that the meniscus passes from the upper graduation mark to the lower mark is called the efflux time. This time is recorded for both the pure solvent and the soLut.Lon, From the ratio of efflux times, the relative viscosity, the intrinsic viscosity, the average molecular weight, and the degree of polymerization can be calculated. The detailed test method used in this stUdy is adapted from ASTM Standard Test Method D4603 and is included in its entirety in Appendix A. 50

The relative viscosity is calculated by the equation

"rel = where t is the efflux time of the solution and to is the efflux time of the pure solvent.

The inherent viscosity is the ratio of the natural logarithm of the relative viscosity to the concentration as shown by the equation

In Tlrel 'linb = C where, by convention, c is the solution concentration defined in grams per deciliter.

The intrinsic viscosity, or limiting viscosity number, is defined as

11rel - 1 [TIl = lim c C" 0 where the concentration c is also in grams per deciliter. The intrinsic viscosity can be determined by calculating the value of ~m - 1 divided by the concentration, called the reduced viscosity, for a range of concentrations. By plotting these values against the respective concentrations and drawing a line through the points extrapolating to zero concentration, the intrinsic viscosity is found as the intercept of the line on the axis. Similarly, a plot of the inherent viscosities at different concentrations extrapolated to zero would also 51 intercept the axis at the intrinsic viscosity.

An alternate method of calculating the intrinsic viscosity is the Billmeyer relationship [27]. This is an estimate of the intrinsic viscosity that can be determined from a single measurement of the relative viscosity using the following relationship:

'lIel - 1 + 3·1n ('lrel) []'l = 0.25------­ c

For the tests conducted in this study, this relationship was used exclusively to determine the intrinsic viscosity. A concentration of 0.5 gm/dl was used throughout the experimental procedures.

Although the value of the intrinsic viscosity is adequate for comparing polymer samples, it is more instructive to compare the molecular weight or the degree of polymerization.

To convert from intrinsic viscosity to molecular weight, the empirical Mark-Houwink relationship is commonly used. This general relationship appears in the literature [28] in the form where Mv is the viscosity average molecular weight. The empirically determined constants K and a depend on the type of polymer, solvent, and the solution temperature. The Mark- Houwink relationship used in this study was formulated for PET in a 60:40 mixture of phenol and tetrachloroethane at 25 °c. This relationship is expressed as [35] 52

3 [11 ] = 3. 7 21 -10-4 ~. 7 where [~] is in dl/gm and ~ is the number average molecular weight. Rearranging this equation to calculate the number average molecular weight from the intrinsic viscosity gives the following expression:

Mn = 49,857 [11] 1.37

The dilute solution viscosity test method used in this study specifies a 60:40 phenol to tetrachloroethane solvent mixture at 30 °C. Figure 3.3 illustrates the comparison of the relationship used in this study with two other empirical expressions presented by Hergenrother [28]. These were formulated with mixtures of 1:1 and 3:5 phenol to tetrachloroethane at 25 °C and 30 °C respectively. It appears from Figure 3 . 3 that changes in the ratio of phenol to tetrachloroethane do not have a major effect on the empirical relationship. Four dilute solution viscosity tests performed on the commercial grade Kodapak PET Polyester 7352 had an average intrinsic viscosity of 0.564 dl/gm. This can be equated to a number average molecular weight of 22,750 using the Mark-Houwink expression. The physical property data sheet supplied by Eastman Chemical lists a typical value for the number average molecular weight for this product of 23,000.

The degree of polymerization, sometimes referred to as the chain length, is the number of repeating units in the 53

(OOO's) 60 r------,

M 0 50 L E C 40 U L A R 30 W E 20 I G H 10 T

0 a 0.1 0,2 0.3 0.4 0.5 0.6 0.7 0.8 0,9 1.0 INTRINSIC VISCOSITY (dl/g)

-- 3:2 PTCE @ 25 C -f- 1:1 PTCE @ 25 C ---*- 3:5 PTCE @ 30 C

Number average molecular weight VS. IV of PET in phenol/tetrachloroethane (PTCE) so/vents,

Figure 3.3: Molecular Weight vs Intrinsic Viscosity

polymer molecule. Referring back to the structural formula for the main polycondensation reaction in section 2.3, the repeat unit is enclosed in parenthesis and has a molecular weight of approximately 192. Therefore, to calculate the degree of polymerization the number average molecular weight is simply divided by 192. For example, the calculated molecular weight of the commercial PET was 22,750. This is equivalent to a degree of polymerization of 118.5. 54

Chapter 4: Results

4.1 Residence Time Distribution Results

The concentration response curve for the first residence time distribution experiment is shown in Figure 4.1.

1.6 ..,.------,

% 1.4- oC 1.2­ N C 1 - E N 0.8 - T R 0.6 - A T 0.4 - I o 0,2 - N * * o I ~1'IIIIIJ'JJ~~~ o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TIME (minutes) 36 qm/min clear PET with 2 gm black nvton as the pulse input and a screw speed of 25 rpm

Figure 4.1: Response Curve for Depolymerization Experiment

This response curve has a mean residence time of 11.0 minutes with a standard deviation of 1. 7 minutes. It is clearly evident from the concentration response curves shown in Figures 4.2 and 4.3 that the scatter in the data increases as the feed rate and screw speed is decreased. 55

0,7

% 0.6 - * ** c * 0 0.5 - * N * C * E 0.4 N T 0.3 ~ * R A ** T 0.2 ~ *** I 0 0.1 r- *** N * ****~ J/ *~ I I ~ 0 * 0 10 20 30 40 50 60 TIME (minutes) 13 gm/min clear PET with 1 gm of black nylon as the pulse input and a screw speed of 8 rpm

Figure 4.2: Response Curve for Polymerization Experiment

0.7 % 0.6 - * C * * 0 0.5 - * * N * C E 0.4 - * * N * ** T 0.3 - R A ~ T 0.2 - ~ I 0 0.1 - * N ** * I ..L I I I * *I 0 * 0 10 20 30 40 50 60 70 80 TIME (minutes) 7 gm/min clear PET with 0,5 gm black nylon 8S the pulse Input and 8 screw speed of 8 rpm

Figure 4.3: Response Curve for Polymerization Experiment 56 Figures 4.2 and 4.3 show that the flow patterns in the extruder are dependent on the feed rate. The effect of the non-flighted screw elements is more apparent at lower feed rates. At the low feed rates there is less filled volume and with the material in these sections being transported forward only by displacement of the polymer melt that exits the flighted elements there is a longer residence time. A rotational velocity distribution created in the annulus by the melt adhering to the rotating screw shafts and the barrel wall could result in a mixing action. since the residence time is higher in these zones at lower feed rates, we can postulate there is more time for the polymer melt to mix resulting in a broader distribution of the tracer material in the extrudate. Even with this broadening characteristic, the residence time distribution is sUfficiently narrow to reasonably approximate this process with an idealized plug-flow model. The following table summarizes the results of the three residence time distribution experiments.

Table 4.1: Comparison of Residence Time Distributions

Experiment Number: (1) (2) (3) PET Feed Rate (gm/min) : 36.0 12.7 7.1 Screw Speed (RPM): 25.0 8.0 8.0 Black Nylon Tracer (gm) : 2.0 1.0 0.5 Mean Residence Time (min): 11.0 29.2 37.5 Variance (min2 ): 2.9 39.0 65.3 Number of CSTRs in Series: 41.7 21.8 21.5 57

4.2 Depolymerization Results

The results from the depolymerization experiments verify that the experimental procedure discussed in Chapter 3 will successfully depolymerize commercial grade PET into a low molecular weight pre-polymer. However, these results also show the lack of repeatability in the procedure. This can be attributed to the necessity of adding a liquid component with the bulk feed. Although the twin-screw extruder screws are designed with a close tolerance to the barrel walls, this machine is not designed to convey liquids. From visual observation of the process it appears that most of the ethylene glycol adheres to the surface of the pellets as the pellets enter the feed zone. There is, however, a significant amount of the glycol that remains in the feed zone as well as some that is vaporized before it can be mixed with the molten polyme~. The feed rate of ethylene glycol can be accurately regulated, but the amount lost can not be controlled. The build-up of liquid ethylene glycol in the feed zone is evident by observing the glycol actually leaking through the bushings along the screw shafts after a few hours of operation. There were 6626 gm (14.6 lbs) of low molecular weight PET produced by applying the procedure of continuously feeding PET and ethylene glycol. There were seven separate production runs made using this method. The material from the first six of these runs were tested to determine the degree of polymerization. The samples were taken at the beginning of 58 each run after the process appeared to reach steady state and near the end of each run. Individual samples from the seventh production run were not tested. Runs one through four had a feed rate of 36 gm/min of PET and an ethylene glycol feed rate of 34 drops/min. The ratio of glycol to PET was increased in runs five through seven with a PET feed rate of 30 gm/min and

36 drops/min of ethylene glycol. During all seven runs the screw speed was 25 RPM and the temper~ture profile was 265 °C

(510 OF) for zones 2, 3, and 4 and 260 °C (500 OF) for zones

1, 5, 6 and the die. These results are summarized in the following table:

Table 4.2: Individual Results of·Depolymerization Runs

Degree of Run PET Glycol Speed Polymerization Number (gm/min) (drops/min) (RPM) Sample 1 Sample 2

1 36 34 25 10.9 12.0

2 36 34 25 18.6 7.2

3 36 34 25 20.1 29.1

4 36 34 25 15.7 13.4

5 30 36 25 9.1 9.2

6 30 36 25 11.3 11.1

This table clearly shows ~he inconsistent performance from run to run. A conclusion that can be drawn from this data is that when compared to the theoretical calculations 59 discussed in Chapter 3, there is a 35 to 50% loss of ethylene glycol due to vapor escaping at 'the feed section, unreacted glycol being carried through the extruder in the polymer melt and turning to vapor at the die, and liquid glycol collecting in the feed section and leaking through the bushings where the screw shafts extend from the gearbox into the feed section.

There is a discussion in Chapter 6 on equipment recommendations to improve this process for future work.

The low molecular weight polymer from all of the individual runs was collected and processed in small batches in a ordinary food blender to break down the extrudate into small particles. The individual batches were then manually mixed together in a large container. Five random samples were selected and tested to obtain an average DP. These results are shown in Table 4.3.

Table 4.3: Test Results from continuous Depolymerization

Sample Intrinsic Number Average Degree of Number Viscosity Molecular Weight Polymerization

1 0.129 3014 15.7

2 0.134 3176 16.5

3 0.130 3047 15.9

4 0.133 3143 16.4

5 0.134 3176 16.5

Average 0.132 3111 16.2 60

An experiment was then conducted to determine if the low molecular weight polymer contained any unreacted ethylene glycol. A small sample of the polymer product was baked in an oven for eight hours at 200 °C. Samples were then taken at two hour intervals and tested. Two dilute solution viscosity tests were performed on each sample. The results of this experiment are shown graphically in Figure 4.4.

o E G 35 R E 30 - * . E * ~ o 25 - """""""'" F ~ P 20 - * . o <~ yL 15 - . M E 10 - . R I Z 5 - . A T O-+------r------r------~------r------' I I I I I o N o 2 4 6 8 10 TIME (hours) Low molecular weight PET baked at 200 C for eight hours to evaporate unreacted ethylene glycol

Figure 4.4: Results of Post-processing Experiment

The conclusion drawn from this experiment is that the apparent DP as determined by the dilute solution viscosity test is increased by baking the polymer at 200°C up to six hours with no significant increase beyond six hours. This is 61 due to the evaporation of ethylene glycol in solution with the polymer as well as possibly a slow condensation reaction occurring. It is possible, however, that the "levelling off" of the DP curve after six hours could be a result of polymer degradation offsetting any molecular weight gain due to the evaporation of ethylene glycol. Based on these results, the total quantity of low molecular weight polymer was baked for six hours at 200 °C. After baking, five random samples were taken and tested. These results are shown in Table 4.4.

Table 4.4: Post-processed Test Results from' continuous Depolymerization

Sample Intrinsic Number .Average Degree of Number Viscosity Molecular Weight Polymerization

1 0.169 4374 22.8

2 0.175 4582 23.9

3 0.175 4596 23.9

4 0.178 4692 24.4

5 0.172 4465 23.3

Average 0.174 4541 23.7

The alternate process used for depolymerization, as discussed in Chapter 3, consisted of blending eight lb of PET and 150 ml of ethylene glycol in.a bulk container. This blend was manually fed at 14 gm/min. The extruder screw speed during these runs was set at 15 RPM and the temperature set- 62 points of all zones were set to 263 °C (505 OF). A low molecular weight polymer was produced in three separate runs.

The material from the individual runs was not tested. As in the previous experiment, five randomly selected samples from the total blend of 5.6 lb were tested. These results are shown in Table 4.5.

Table 4.5: Test Results from Alternate Depolymerization Process

Sample Intrinsic Number Average Degree of Number Viscosity Molecular Weight Polymerization

1 0.207 5758 30.0

2 0.192 5190 27.0

3 0.178 4700 24.5

4 0.184 4902 25.5

5 0.207 5777 30.1

Average 0.194 5261 27.4

As in the previous experiments, the total blended sample of low molecular weight polymer was baked for six hours at

200 °C. Again, five random samples were selected and tested.

These results are shown in Table 4.6.

These test results are an interesting contrast to the results obtained from the continuous process. When comparing the data in Tables 4.5 and 4.6, the conclusion can be drawn that the baking process produces no significant difference in 63

Table 4.6: Post-processed Test Results from Alternate Depolymerization Process

Sample Intrinsic Number Average Degree of Number Viscosity Molecular Weight Polymerization

1 0.187 5019 26.1

2 0.192 5201 27.1

3 0.193 5218 27.2

4 0.193 5241 27.3

5 0.193 5236 27.3

Average 0.192 5183 27.0

molecular weight in the polymer product. This is dramatically different to the previous results where post-processing resulted in a 46% increase in the degree of polymerization.

The primary differences in this method compared to the continuous depolymerization method were the blending of the bulk pellets with the liquid glycol resulting in complete surface coverage and the possibility of pre-absorption into the solid pellets, the lower feed rate, and the lower screw speed. The lower feed rate and screw speed resulted in a longer residence time. During the second trial the liquid glycol collected in the feed zone and leaked out of the barrel through the bushings along the screw shafts in a similar fashion to that observed during previous runs. It was observed, however, that there was less vapor exiting the die along with the extrudate. 64

A total of 20.179 lbs of low molecular weight polymer was produced. There were 6.223 lbs with a OP of 23.7 used in

Experiment #1 and in preparation for Experiment #2. Of the

13.956 lbs remaining for use in Experiment #2 of the polymerization study, there were 8.371 lbs with a OP of 23.7 from the previous runs and 5.585 lbs with an average OP of

27.0 from the last set of runs. A weighted average of the total blend of polymer gives an average degree of polymerization of 25.0. This material was then used as the feed for the polymerization experiment discussed in the next section.

4.3 Polymerization Results

The results from Experiment #1 show that the degree of polymerization of the extrudate reaches an equilibrium value after one hour with a feed rate of 6.7 gm/min and a screw speed of 8.0 RPM. After first purging the extruder of commercial grade PET (DP of 120), the degree of polymerization decreased from a high of 65.6 (most likely reduced from 120 as a result of mechanical shear) to a OP of 24.3 in one hour after initiating a feed of low molecular weight PET (OP of

23.7). The DP of the extrudate tested after 90 minutes was

24.2. These results are illustrated in Figure 4.5. Each point on the graph represents the average of two extrudate samples taken at each sampling period. There appears to be no discernible difference between the degree of pOlymerization of 65

o GE 70..,.------. R ~ § 60 _ .

~ 50 _ .

P 40 - *: . o L y 30 - . 'IE M 'IE E 20 -- . R I Z 10 - . A T O-+-----,-----~---..------.------..------J I 1 I I I I o N o 15 30 45 60 75 90 TIME (minutes) Polymer with a DP of 23.7 fed at a rate of 6,7 gmlmin after purging ex truder of commercial PET Screw speed was 8 RPM.

Figure 4.5: Results of Experiment #1

the feed and the extrudate after one hour. Based on the previous residence time distribution experiments, a higher feed rate would reduce the time to reach equilibrium. Since the feed rate of 6.7 gm/min is lower than either of the feed rates used in Experiment #2, an operating period of one hour before collecting the two extrudate samples was established for each of the eight trials of the experiment. The results of Experiment #2 are shown in Table 4.7.

Table 4.8 is a complete listing of the algebraic symbols assigned to the 2 3 factorial design, with a + representing a high level and a - representing a low level. Once the signs for the main effects have been established, the signs for the 66 Table 4.7: Results of Experiment #2

Run Treatment Degree of Polymerization Order Combinations Sample #1 Sample #2 Average

8 (1) 25.0 24.9 25.0 1 a 24.2 23.7 24.0 4 b 23.8 23.5 23.7 2 ab 22.6 22.6 22.6 3 c 25.2 24.6 24.9 7 ac 25.2 26.1 25.7 5 bc 23.3 23.4 23.4 6 abc 24.5 23.1 23.8

Table 4.8: Algebraic Symbols for Effects. in 2 3 Design

Treatment Factorial Effect Average Combinations A ~ .Q AB AC BC ABC DP (1) + + + 25.0 a + + + 24.0 b + + + 23.7 ab + + + 22.6 c + + + 24.9 ac + + + 25.7 bc + + + 23.4 abc + + + + + + + 23.8

remaining columns can be obtained by mUltiplying the ap~ropriate preceding columns row by row. The main effects and the interactions are then easily grouped together to see the magnitude of the effects.

Table 4.8 can also be represented in equation form.

Using the average DP results, the factor effects can be 67 estimated by the following equations [36]:

A = -1.... [a - (1) + ab - b + ae - e + abc - be] 4n

B= -1...·[b+ab+be+abe- (1) -a-e-ae] 4n

C = -1.... [e + ae + be + abc - (1) - a - b - ab] 4n

AB = -1...·[ab - a - b + (1) + abc - be - ae + e] 4n

AC = -1.... [ (1) - a + b - ab - e + ae - be + abc] 4n

BC = -1.... [ (1) + a - b - ab - c - a e + be + abe] 4n

ABC = -1...·[abe-be- ae+ e- ab+b+ a - (1)] 4n

In the previous set of equations, n represents the number of replicates and the quantity within the brackets is defined as the contrast, or total effect. The sums of squares are easily calculated from the contrast values. In a 2 3 factorial design with n replicates, the sum of squares for any effect is calculated by the equation

88 = (Contrast) 2 8n

A summary of the calculated values of the effects and the sum of squares for each treatment combination is shown in 68

Table 4.9.

Table 4.9: Summary of Calculated Effects

Treatment Average Sum of Combination Result Effect Squares

(1) 25.0 a 24.0 -0.225 0.101 b 23.7 -1.525 4.651 ab 22.6 -0.125 0.031 c 24.9 0.625 0.781 ac 25.7 0.825 1.361 bc 23.4 -0.175 0.061 abc 23.8 -0.075 0.011

There are three standard approaches commonly discussed- in the literature to analyze a single replicate of a factorial design. One approach is to assume that high order interactions are negligible and combine their mean squares to estimate the error. However, if there are high order interactions that are significant this method is not applicable. A second method that is useful is to determine if any of the main effects can be neglected. If so, then that variable is discarded and a 2 3 factorial design with one replicate becomes a 2 2 design with two replicates. Both of these methods were inappropriate for this experiment since, although the main effect from A (zone temperature) appeared to be negligible, the AC interaction was significant.

A method of analysis attributed to Daniel [37] overcomes this problem by plotting the effects on normal probability 69 paper. The negligible effects will behave like a random sample drawn from a normal distribution and will lie approximately along a straight line. Those effects that do not lie near the line are significant factors. The calculated data for the normal probability plot is shown in Table 4.10.

Table 4.10: Calculated Data for Normal Probability Plot

Treatment Probability Order (j) Combination Effect (j - 0.5)/7

1 B -1.525 0.071 2 A -0.225 0.214 3 BC -0.175 0.357 4 AB -0.125 0.500 5 ABC -0.075 0.643 6 C 0.625 0.786 7 AC 0.825 0.929

The normal probability plot for these effects is shown in

Figure 4.6. The significant effects that are clearly evident are the main effects of Band C and the AC interaction. A plot of the AC interaction is also shown in Figure 4.7. 70

99

95 • AC ~ 0 90 0 x 80 •C "'-'"

-+->- 70 .o 0 50 .o 0 '- a.. 30 0 20 E '- 0 10 z •B 5

1

-2 -1 o 1 2 Effects (in DP) Figure 4.6: Normal Probability Plot of Effects

26 ~------,

c o :g 25 c+ N ·C (I) E >-. ci: 24 ~o (I) Q) '- ~23 o

22 ....1...----+------_-01__-----'

Effect A + Figure 4.7: AC Interaction Plot 71

The AC interaction indicates that the nitrogen flow C has little effect at the low temperature level but a large effect at the high temperature level.

A regression analysis was performed as a diagnostic check to test the validity of the conclusion that the only significant effects are the feed rate (B), nitrogen flow (C), and the interaction (AC) of the zone temperature and nitrogen flow. In the analysis, the average DP for each treatment combination was identified as the dependent variable and the

B, C, and AC effects were selected as the independent variables. The values of 0 or 1 were used in the analysis representing the algebraic symbols - or + as listed in Table

4.8. Using the linear regression algorithm in Quattro Pro version IV, the reSUlting regression equation is

Dp· = 24.17S - 1.S2S·B + O.62S·C + O.82S·AC

A·comparison of the observed DP value, the calculated value of Dp·, and the residuals are shown in Table 4.11. The

R2 value of this regression analysis calculated by Quattro Pro

IV is 0.971 with an estimated standard error of 0.160 for each coefficient. The estimated standard error of the values of

Dp· is 0.226.

The results in Table 4.11 confirm that, within the limits of this experiment, decreasing the feed rate and increasing the nitrogen flow have a measurable effect on the degree of polymerization of the extrudate. The interactive effect of 72

Table 4.11: Calculated OP Values and Residuals

Treatment Observed Calculated Combination OP OP· Residual

(1) 25.0 25.0 0 a 24.0 24.2 -0.2 b 23.7 23.5 0.2 ab 22.6 22.6 0 c 24.9 24.8 0.1 ac 25.7 25.6 0.1 bc 23.4 23.3 0.1 abc 23.8 24.1 -0.3

the zone temperature and nitrogen flow is also significant.

The low molecular weight of the average of all the extrudate samples compared to the feed will be discussed in Chapter 6. 73

Chapter 5: Reactive Extrusion Modelling

A reactive extrusion model was developed as part of this study to provide a theoretical comparison to the experimental results presented in Chapter 4. This model is based on three key assumptions. First, the flow characteristics of the polymer melt can be represented by ideal plug flow based on the results of the residence time distribution studies. An alternate modelling approach proposed by Stuber [11] uses a series of continuous stirred tank reactors to model the flow characteristics which considers the leakage flows between the individual c-shaped sections. The next approximation, and perhaps the most significant, assumes the reaction mechanism consists of only the main polycondensation reaction. The four additional side reactions discussed in Chapter 2 are not considered in this model. The third key assumption is that the devolatilization that occurs as a result of sweeping nitrogen across the surface of the polymer obeys Raoult's law.

Even with these simplifying assumptions, the model reasonably represents the extrusion process and the calculated results offer an interesting comparison to the experimental results. section 5.1 includes a discussion of the equipment details, physical properties, and the processing conditions used in the model as well as a comparison of calculated and experimental results. A variable list and the complete FORTRAN code listing is included in Appendix B. 74

5.1 Idealized Plug Flow Model

. The first section of the FORTRAN code sets the physical properties of the individual species, the reaction kinetics,

and the operating parameters of the extruder, including the

relevant physical characteristics of the screw elements.

The polyethylene terephthalate polymer is represented in

the model by three species. The ester end groups are

identified with the suffix one in the variable name, the internal ester groups with two, and the volatile component,

ethylene glycol, with three. For example, the molecular weight of the end groups has the variable name MW1 and the molar flow rate is FL1.

The following parameters used in the model were obtained

from the physical property data sheet (DS-185H dated August,

1990) for Kodapak PET Polyester 7352 supplied by Eastman

Chemical Company. The melt density at 285°C is 1.2 gm/cm3 , which was assumed to be constant within the allowable range of the model (255-282 °C). The heat of fusion is 59 kJ/kg and the thermal conductivity is 0.25 W/m·K. The data for the specific heat capacity is given over a selected range of temperatures from 23°C (1130 J/kg·K) to 280°C (2050 J/kg·K). A second degree polynomial was fitted to this data with the following equation:

CP = -1221.77 + 10.2552-T - O.00784-T2 where T is the temperature of the polymer mixture in degrees

Kelvin. 75 The value of the activation energy (18,500 kcal/kgmole) and the equilibrium constant (0.5) were taken from Kumar and

Sainath [25]. Different values of the pre-exponential constant are reported in the literature depending upon the catalyst system used in the reaction. since the catalyst in the commercial PET used in this study is unknown, the value of the pre-exponential constant (4. 08 _1012 em> /kgmole -hr) was chosen because it approximately fit ~he experimental data. This value is a factor of ten lower than the value reported by

Kumar and Sainath [25]. Ravindranath and Mashelkar [20] report a constant value for the diffusivity of ethylene glycol in molten PET (0.82-10~ cm2/s) in the range of 20 to 150 DP at

270°C. The vacuum applied to the vent zones is an input variable with a choice of ON or OFF. The pressure in the vent zone is then set to 167 torr or 760 torr respectively. Since the operation of the vacuum pump would create a pressure in each vent zone of 167 torr (measured at the vacuum pump), which is not adequate for devolatilization, nitrogen was injected in the vent zone to lower the partial pressure of the ethylene glycol. A study was conducted to calculate a continuous function equating a direct reading on the rotameter scale to the nitrogen flow rate at a pressure of 205 torr (measured at the outlet of the rotameter). ~he pressure difference of 38 torr is due to the pressure drop across the heat exchanger. with the nitrogen flow at a specific rotameter setting, the 76 vacuum pump was turned on and a new reading was taken. After repeating this procedure several times, volumetric flow rates were calculated by the equation

where PA is 205 torr, PB is 760 torr, QB is the vOlumetric flow at atmospheric pressure taken from the rotameter calibration

chart, and QA is the calculated vOlumetric flow rate with the vacuum pump ON. A nitrogen molar flow rate was then calculated from the ideal gas law, assuming a temperature of 20°C. A regression analysis with the rotameter setting as the independent variable and the equivalent molar flow rate was calculated for both cases. The equation calculated for atmospheric pressure when the vacuum pump is OFF is

FN2 = 0.007 OS·N2 - 0.0311 where N2 is the direct reading from the rotameter and FN2 is the calculated flow rate in moles/min. The applicable equation when the vacuum pump is ON is

FN2 = O. 0019S·N2 - 0.0213

The physical dimensions of the extruder used in the model are the diameter of the screw (3.4 em), the cross-sectional area of the c-shaped section formed by the meshing of the

flighted screw elements (3.14 cm2 ), the cross-sectional area of the annulus formed by the inside wall of the barrel and the 77 circumference of the spacer elements (6.91 cm2 ), and the cir- cumference of the interior of the extruder barrel (17.57 cm). The pitch of the individual elements for this screw config- uration are also set for each zone. The vapor pressure of ethylene glycol is calculated with

Antoine's equation using the following parameters [38]:

PVAP = 750. O· exp (13 . 6 3 _ 6 022 · 18 ) T - 28.25 where T is in degrees Kelvin and PVAP is calculated in torr. Calculating the molar feed rates of each species from the

PET feed rate and OP is an iterative process. There are three equations used to calculate the variables FL1, FL2, and FL3. The first equation is a relationship between OP, FLI, and FL2

[26]: DPO = 1 + 2·FL2 FLl where OPO represents the degree of polymerization of the feed, FLl is the molar feed rate of the ester end groups (kgmole/hr) and FL2 is the molar feed rate of the internal ester groups (kgmole/hr). Rearranging this equation to solve for FLI gives

2·FL2 FLl = DPO - 1

The second equation is the mass balance of all three species:

FEED = MWl-FLl + MW2·FL2 + MW3·FL3 where the feed is in kg/hr and the molecular weight is in kg/kgmole. SUbstituting the first equation into the second to solve for FL2 gives 78

FL2 = FEED - MW3-FL3 2·MWl + MW2 DPO - 1

By initially setting the ethylene glycol molar feed rate (FL3) to zero, FLl and FL2 can be solved with these two equations.

Assuming that the PET feed is in reaction equilibrium, a value for FL3 can then be calculated from the equation for the polycondensation reaction [26]:

K-FL1 2 FL3 = 4-FL2 where the equilibrium constant K is equal to 0.5. The sequence in the iterative procedure sets FL3 equal to zero, calculates FL2 from the second equation with the known values of FEED and OPO, and then calculates FL1. with the values of

FLl and FL2, FL3 is calculated. All three values are then substituted into the mass balance equation. If FEED minus the sum of all three species multiplied by their respective molecular weights is greater than a predetermined error criteria, the calculated value of FL3 is substituted back into the second equation to solve for FL2 and the procedure is repeated.

The second section of the FORTRAN code applies Euler's method in solving the change in molar flow rates for each species as well as calculates the physical properties of the polymer in each of the six extruder zones.

The maximum feed rate, identified as MAXFD, is defined as the theoretical value for the maximum rate that can be 79 transported by a screw element based on the pitch of the element and the rotational speed. This is calculated by multiplying the pitch of the element, the rotational speed, the cross-sectional area of the c-shaped section, and the density of the polymer melt. The filled cross-sectional area is then calculated by mUltiplying the cross-sectional area of the c-shaped section by the ratio of the feed to the theoretical maximum feed. In the zones that contain the non- flighted screw elements, the filled cross-sectional area is defined as the annulus between the interior wall of the barrel and the screw element. Residence time is completely dependent upon the feed rate in 'these sections since the axial flow of the polymer melt occurs only by displacement. The theoretical mean residence time for each zone is calculated by dividing the total filled volume by the feed rate. Table 5.1 shows the comparison between the mean residence times calculated in the model and the mean residence times determined experimentally.

Table 5.1: Comparison of Theoretical and Experimental Mean Residence Time

Experiment Number: (1) (2) (3)

PET Feed Rate (gm/min): 36.0 12.7 7.1 Screw Speed (RPM): 25.0 8.0 8.0

Mean Residence Time (min): Model: 8.2 24.0 36.4 Experimental: 11.0 29.2 37.5 80 The model reasonably represents the mean residence time of the extruder. The theoretical value calculated by the model is predictably lower than the experimental value since the plug flow model does not consider any leakage flow between the c-shaped volume sections of the flighted screw elements. The heat transfer calculation is based' on a heat transfer coefficient determined experimentally for a co-rotating intermeshing twin screw extruder. This relationship, reported by White [39], is represented by the equation

where h is the heat transfer coefficient, D is the screw diameter, N is the rotational speed, 11 and lIw are the viscosity of the bulk and at the wall, and k, cP and p are the thermal conductivity, heat capacity and density of the polymer melt. For the purposes of this model, the viscosity ratio was assumed to be unity and the dimensionless coefficient, C, was set. at 0.9 based on actual temperature measurements of the polymer melt taken with a thermocouple probe in zone 2. The heat transfer to the polymer melt is calculated by

Newton's Law, Q = h·A·aT, where A is the area defined by mUltiplying the inside circumference of the extruder barrel by the incremental length set by the Euler's loop and ~T is the temperature difference between the barrel and the polymer melt. In the zones with non-flighted elements, the heat transfer coefficient was arbitrarily divided by 10 to reflect 81 that no mixing was taking place. Finally, the incremental temperature change in the melt is calculated by dividing Q by the product of the polymer feed rate and heat capacity.

The reaction rate expression for the main polycondensation reaction, as reported by Ravindranath and

Mashelkar [26], is

o Rl = k/[e; _ 4 z ·g ] K where the concentrations of the end groups, the internal ester groups, and ethylene glycol are represented by e g , z, and 9 respectively.

since the polycondensation reaction will not proceed to high conversion without the removal of the volatile byproduct, an algorithm is included in the FORTRAN code to calculate the removal of the ethylene glycol in zones 2 and 4 . The relationship used to calculate the devolatilization of ethylene glycol is developed by Ravindranath and Mashelkar

[26] for an idealized polycondensation process occurring in a semi-infinite film with an exposed surface. The criterion for the semi-infinite film model is presented by Biesenberger [41] with the equation

where Af is the time of exposure of the film to devolatilization and An is the characteristic time for 82

diffusion. Biesenberger defines the characteristic time, Ao , as the square of the film thickness divided by the diffusivity. This model assumes that the aggressive surface renewal action of the intermeshing screw elements meets this criteria for a semi-infinite film. Ravindranath and Mashelkar's linearized penetration theory model is expressed in the form

where N is the rate of devolatilization expressed in moles/volume-time, D is the diffusivity of ethylene glycol in molten PET, a i is the interfacial area per unit volume of the polymer melt, go and gj are the concentrations of glycol in the bulk and at the interface respectively. The rate constant k

is defined as

k = 4·k'·z K

The concentration at the interfacial surface is assumed to obey Raoult's law, which states that the partial pressure of a component is equal to its vapor pressure multiplied by its mole fraction in the liquid, represented by the equation

Applying Dalton's law of partial pressures,

where the mole fraction of the component in the vapor is equal 83 to its partial pressure divided by the system pressure, these equations can be combined and solved for the mole fraction in the liquid, xA. This results in the equation

y .p x = _A_ A pvap which implies that the only ways to reduce'xA are to increase the temperature thereby increasing pvap, reduce the system pressure, or reduce the mole fraction of A in the vapor. The injection of nitrogen into the vent zones to sweep across the surface of the polymer melt would reduce the mole fraction of ethylene glycol in the vapor. The algorithm used in this model for calculating the devolatilization of ethylene glycol is illustrated by the flow diagram in Figure 5. 1. As an example, for the case where the vacuum pump is off and there is nitrogen flow to the vent zones, the vapor flow rate is initialized to zero. The mole fraction of ethylene glycol in the vapor phase is then calculated. Applying Raoult's law, the glycol mole fraction in the liquid phase is calculated. A provisional molar flow rate of glycol is calculated from this mole fraction and, when divided by the vOlumetric flow rate, represents the calculated value of the interfacial surface concentration of ethylene glycol in the polymer melt. The rate of devolatilization is then calculated and mUltiplied by the incremental volume to calculate the molar flow rate of the vapor. This calculated vapor molar flow rate is compared to the initialized value. 84

PVAP calculated form Antoine's Eq. FL3 calculated from reaction kinetics FLT = FL1 + FL2 + FL3 XL3 = FL3/FLT PP = XL3*PVAP

No Yes Yes ZONE 2 or 4? FN2 > O?

No

No VAC < PP? XV3 = FV3/(FV3 + FN2/1200} Yes· XL3 = XV3*VAC/PVAP FL3A = XL3*FLT N=(CN3-FL3A/VFR)*AI*SQRT(DEG*KR1) FV3A = N*(AR*DY)

XV3 = 1.0 XLS = XVS*VAC/PVAP FL3A = XL3*FLT Yes N= (CN3-FL3A/VFR)*AI*SQRT(DEG*KR 1) FV3 = FV3A? FV3 = N*(AR*DY) FL3 = FL3 - FV3

Return new value of FL3 to Euler"s loop and add value ot FV3 to the lolal glycol removed in the zone.

Figure 5.1: Flow Diagram for Devolatilization Algorithm

If the difference is greater than a predetermined error criteria then a new value is set at the beginning of the IF ­

THEN loop and another iteration is performed. After the final iteration, the liquid molar flow rate of ethylene glycol is set equal to the provisional value and returned to the Euler's loop.

The linearized penetration theory model is applicable to 85 a geometry which can be modeled as a semi-infinite film. The analytical form of the solution used here is valid for long exposure times. These approximations may not be valid in this application; however, the practical significance of this possible error is low since quantitatively similar results were achieved with a simple kinetic model that is not diffusion limited. The last calculation in the model is the relationship between melt viscosity, degree of polymerization, and temperature. This correlation is derived from a more general relationship reported in the literature by Gregory [40]. It is included in the model in the form

T'J = 0.012538· exp (-11. 9755 + 6802 .1) · Dp3.5 T where '7 is the melt viscosity in centipoise, T is the temperature in Kelvin, and OP is the degree of polymerization.

Table 5.2 shows the calculated degree of polymerization from the model in comparison to the experimental results.

In comparing the main effects overall, the model results show a slightly higher DP than the experimental results. In comparing the temperature effect, the higher temperature setting had a theoretical increase in OP while the experimental results showed no significant change. This may be explained in part by the exclusion of the degradation reactions from the model. Both the theoretical and experimental results show a small increase in DP with a lower 86 Table 5.2: Comparison of Model and Experimental Results

Treatment Degree of Polymerization Combinations Experimental Model

(1) 25.0 25.7 a 24.0 26.0 b 23.7 25.6 ab 22.6 25.9 c 24.9 25.7 ac 25.7 26.0 bc 23.4 25.6 abc 23.8 25.9

feed rate. The experimental results show a more significant increase at the lower feed rate which may be an effect of the difference between the actual residence time distribution and the idealized plug flow in the model. The calculations in the model show no difference between the two levels of nitrogen flow. This is notably different in the experimental case where the higher nitrogen flow results in more effective devolatilization. The results of the model indicate that the

model is not mass transfer limited due to the value of a j nor is it limited by the reverse reaction since the nitrogen level has no effect. However, since the experimental results show that the nitrogen does have an effect, the polymerization process probably is reaction limited. Although it is not certain this is the case, it is reasonable to expect a low mass transfer resistance leaving only the reaction limitation to explain the results.

A source of error in the model could be the application 87 of Raoult's law representing the vapor-liquid equilibrium relationship rather than another approximation such as Henry's law. The choice of the reaction equilibrium constant could also be in error. The model is also applicable for the depolymerization process with an input variable assigned to a fixed rate of ethylene glycol to be added with the feed. The results from the model compare reasonably well with the experimental results if you assume that a large percentage of the additional glycol is vaporized and does not mix with the polymer melt.

A sample of the direct output from the model is shown in

Table 5.3 on the next page. These calculations are based on treatment combination (1) with a feed rate of 7.2 gm/min, the temperature setpoints on the zones are 500oF, and the nitrogen flow is set at 15 on the rotameter scale. 88

Table 5.3: Example of Output from Reactive Extrusion Model

FEED CONDITIONS

Feed rate of PET is 7.2 g/min (.432 kg/hr) Feed rate of ethylene glycol is .000 kg/hr Screw speed is 8.0 RPM Nitrogen flow to zones 2 & 4 is .113E-02 kgmole/hr

Degree of polymerization of the feed is 2S.0 Molar flowrate of the hydroxyl end groups is .1775E-03 kgmole/hr Molar flowrate of the diester groups is .2130E-02 kgmole/hr Molar flowrate of the ethylene glycol is .1849E-OS kgmole/hr

PRODUCT PROPERTIES AND EXTRUDER CONDITIONS BY ZONE

Molar flow rates exiting each zone (kgmole/hr):

ZONE 1 ZONE 2 ZONE 3 ZONE 4 ZONE 5 ZONE 6 End Groups: .177E-03 .177E-03 • 176E-03 .175E-03 • 174E-03 .172E-03 Diester: .213E-02 .213E-02 .213E-02 .213E-02 .213E-02 .213E-02 Glycol: • 18SE-OS .OOOE+OO .34SE-06 .OOOE+OO .816E-06 • 146E-OS

DP: 25.000 25.109 25.208 25.317 25.555 25.745

Average Residence Time (minutes) : 7.296 2.500 2.500 2.500 7.296 13.820 Barrel Temperature (deg C): 260.0 260.0 260.0 260.0 260.0 260.0 Product Temperature (deg C): 259.8 260.0 260.0 260.0 260.0 260.0 Zone Pressure (torr) : 760.0 760.0 760.0 760.0 760.0 760.0 Parti~l Pressure of EG (torr) : 3.274 .001 .616 .001 1.455 2.598 Melt Viscosity (cP) : 2155. 2176. 2206. 2239. 2314. 2375.

The mean residence time is 35.912 minutes

The total mass of ethylene glycol vapor removed: ZONE 2: .2235E-09 kg/hour ZONE 4: .1813E-10 kg/hour 89

Chapter 6: Conclusions and Recommendations

6.1 Conclusions In general, this study clearly indicates that the length of time the polymer melt is under an applied vacuum and the partial pressure of ethylene glycol in the vapor are the dominant factors needed for the effective devolatilization essential for achieving high conversipn in the PET reaction. The specific conclusions that can be drawn from this research study are: • The Leistritz twin-screw extruder is effective in a depolymerization process. The screw configuration used in this study provided ample mixing and residence time to produce a low molecular weight polymer. • The key to increasing the molecular weight in the polycondensation reaction is the effective removal of the volatile product. In the reactive extrusion process this can be achieved by maximizing the residence time of the polymer melt in the vent zones while minimizing the partial pressure of the vapor product by sweeping an inert gas across the polymer surface. • The experimental results show that reducing the feed rate

had a significant effect on the product DP. A lower feed rate will slightly increase the residence time and provide a higher surface to volume ratio of the polymer melt. This resulted in a higher product DP than that achieved at the 90 higher feed rate. • The results also indicate that increasing the nitrogen flow into the vent zone to lower the partial pressure of the ethylene glycol vapor increases the product DP. • Although increasing the zone temperatures did not have a significant effect, a second order interaction appeared to occur which did have an effect on the product OP. The interaction of the higher zone temperatures and increased nitrogen flow increased the product DP. • While the factors previously mentioned showed a statistically significant effect on the product OP, the average OP of the eight experiments is slightly lower than the OP of the feed. A plausible hypothesis is that there is a degradation effect caused by the side reactions. • This process can be reasonably represented, in both the polymerization and depolymerization processes, by an idealized plug flow model. with only an average increase of

0.8 OP for all eight experiments, the model supports the hypothesis of the effect of residence time on devolatili­ zation. It would be reasonable to expect product OP values closer to the experimental results if degradation reactions were included as well as a more accurate method to predict the mass transfer effects. In conclusion, the Leistritz twin-screw extruder has the potential to perform successfully in a reactive extrusion process. The hardware limitations of the experimental system 91 preclude an efficient process due to the lack of devolatilization capability. However, the basic design of this equipment to aggressively mix and transport very viscous, high molecular weight polymers provides the potential for successful reactive extrusion research.

6.2 Recommendations for Future study The following equipment recommendations are presented to facilitate any future reactive extrusion research with condensation polymers. • Additional screw elements are necessary to replace the non­ flighted elements in the present screw configuration. The overall residence time does not appear to be as important as the length of time in each vent zone. Also, an aggressive mixing action in all of the zones may provide a more effective depolymerization process. The FD-1-6-R elements are recommended in all six heated zones. • The vacuum pump with the present equipment configuration is inadequate. A new vacuum system is essential for future reactive extrusion research with polycondensation reactions. • The depolymerization process must be improved to provide a means to efficiently manufacture a low molecular weight pre­ polymer since it is not commercially available. The recommended equipment would be a liquid injection port and a small positive displacement pump to transfer the ethylene glycol directly into the polymer melt. 92 • A new screw mechanism for the bulk feeder is strongly recommended. The existing feeder cannot convey the polymer at the low feed rates suitable for reactive extrusion experiments requiring a manual feed. It is also desirable to have a feeder capable of conveying small particles at a consistent feed rate. There is a substantial reduction in particle size created by grinding and blending the low molecular weight polymer produced in the depolymerization process . •A modification to the current equipment design is required to meet the residence time criteria for effective devolatilization. Since this study was conducted at the minimum extruder speed and with the proper elements (FD-1-6­

R) to maximize the residence time in the vent zones, a novel design is needed to provide better results. One approach

would be to replace the closed barrel sections in zones 3

and 5 with venting sections. with the proper vacuum system, this would double the devolatilization capability. However, a more cost effective approach would be to install a recycle loop from the die back to zone 2. This would involve minor modifications to the extruder die, an adapter plate for the vent zone, and the associated piping. The critical design consideration is a reliable heating system for the recycle piping. The following are recommendations for future study in characterizing the Leistritz twin-screw extruder for reactive 93 extrusion applications. • The effect of mechanical shear on the molecular weight is an area that will require study as the system is modified to produce polymers at a high conversion. This was an aspect that was disregarded in this research study since a high molecular weight product could not be achieved. • The relationship between melt viscosity and residence time distribution may be an important aspect in characterizing the process. Determining if leakage flows between c-shaped sections of the screw elements increase as the melt viscosity decreases will provide useful information for future model development. The following recommendations to the reactive extrusion model would· establish a closer correlation to the experimental results. • The model could be improved by revising the devolatilization algorithm. The assumption that the glycol concentration in the polymer melt at the interfacial surface is in equilib­ rium with the vapor estimated by Raoult's law may be in error. • Including the side reactions in the polycondensation stage of PET formation would improve the model results at elevated product temperatures. 94 References

1. Tzoganakis, C. "Reactive Extrusion of Polymers: A Review." Advances in Polymer Technology, Vol. 9, (1989): 321-330. 2. Sneller, J. A., "Reactive Processing: New Era of Innovation Begins in Resin PrOduction." Modern Plastics (July, 1985): 56-60. 3. White, J. L. Twin Screw Extrusion: Technology and Principles. Hanser Publishers, New York. (1990): 94-95

4. Ibid., 210-211.

5 . Ibid., 265 • 6. Mack, M. H. and T. F. Chapman. "Performing continuous Polymer Reactions on Co-Rotating Intermeshing Twin Screw Extruders." ANTEC 87 Conference Proceedings. Society of Plastics Engineers 45th Annual Technical Conference, Los Angeles, California. (May, 1987): 136-139. 7. Shah, S., S. F. Wang, N. Schott and S. Grossman. 'tcounter-Rotating Twin Screw Extruder as a Devolitizer and as a continuous Polymer Reactor." ANTEC 87 Conference Proceedings. Society of Plastics Engineers 45th Annual Technical Conference, Los Angeles, California. (May, 1987): 122-127. 8. Dey, S. K. and J. A. Biesenberger. "Reactive Extrusion of Methyl Methacrylate." ANTEC 87 Conference Proceedings, Society of Plastics Engineers 45th Annual Technical Conference, Los Angeles, California. (May, 1987): 133-.135. 9. Van Ballegooie, P. and A. Rudin. "Reactive Extrusion of Polystyrene/Polyethylene Blends." Polymer Engineering and Science, Vol. 28. (1988): 1434-1442.

10~ Van Ballegooie, P. and A. Rudin. "Reactive Extrusion of Poly(Vinyl Chloride) Compounds with Polyethylene and with Ethylene-Vinyl Acetate Copolymers." Journal of Applied Polymer Science, Vol. 39. (1990): 2097-2117. 11. Stuber, N. P. "Studies of continuous Methylmethacrylate Polymerization in a Twin-Screw Extruder." Ph.D. diss., University of Minnesota. (1986). 95

12. Bouilloux, A., C. W. Macosko and T. Kotnour. "Urethane Polymerization in a Counterrotating Twin-Screw Extruder." Ind. Eng. Chern. Res., Vol. 30. (1991): 2431­ 2436. 13. Martelli, F. G. Twin-Screw Extruders: A Basic Understanding. Van Nostrand Reinhold, New York. (1983) 14. Cheremisinoff, N. P. Polymer Mixing and Extrusion Technology. Marcel Dekker, Inc., New York. (1987). 15. Rauwendaal, C. J. "Analysis and Experimental Evaluation of Twin Screw Extruders." ANTEC 81 Conference Proceedings. Society of Plastics Engineers 39th Annual Technical Conference, Boston, Massachusetts. (May, 1981): 618-622. 16. Thiele, W. "Co- and Counterrotating Reaction Extruders." COMPALLOY '90 Conference Proceedings. New Orleans, Louisiana. (1990). 17. Sakai, T., N. Hashimoto and N. Kobayashi. "Experimental Comparison Between Counter-Rotation and Co-Rotation on the Twin Screw Extrusion Performance." ANTEC 87 Conference Proceedings. Society of Plastics Engineers 45th Annual Technical Conference, Los Angeles, California. (May, 1987): 146-151. 18. Janssen, L. P. Twin Screw Extrusion. Elsevier Scientific PUblishing Company, Amsterdam. (1978). 19. Odian, G. Principles of Polymerization, McGraw-Hill, New York. (1970). 20. Ravindranath, K. and R. Mashelkar. "Polyethylene Terephthalate - I. Chemistry, Thermodynamics and Transport Properties." Chemical Engineering Science, Vol. 41, No.9. (1986): 2197-2214. 21. Gupta, S. K. and A. Kumar. Reaction Engineering of step Growth Polymerization. Plenum Press, New York. (1987). 22. Cohn, G. "Preparation of Ultra-High Molecular Weight Poly(ethylene terephthalate)." Polymer Preprints, Division of Polymer Chemistry, American Chemical Society, Vol 30, No.2. (1989): 160-161. 23. Sweeting, o. J. The Science and Technology of Polymer Films, Volume II. John Wiley & Sons, New York. (1971). 96 24. Ravindranath, K. and R. Mashelkar. "Finishing stages of PET Synthesis: a Comprehensive Model." AICHE Journal, VaI . 30 , No. 3. (May, 1984): 415 - 422 . 25. Kumar, A. and A. Sainath. "Optimization of the Polycondensation Step of Polyethylene Terephthalate Formation in Semibatch Reactors." Polymer Engineering and Science, Vol. 27, No. 10. (May, 1987): 740-752. 26. Ravindranath, K. and R. Mashelkar. "Modeling of Poly(Ethylene Terephthalate) Reactors: 6. A continuous Process for Final stages of Polycondensation." Polymer Engineering and Science, Vol. 22, No. 10. (July, 1982): 628-636. 27. Billmeyer, F. W. "Methods for Estimating Intrinsic Viscosity." Journal of Polymer Science, Vol. IV. (1949): 83-86. 28. Hergenrother, W. L. and C. J. Nelson. "Viscosity­ Molecular Weight Relationship for Fractionated Poly(ethylene Terephthalate)." Journal of Polymer Science: Polymer Chemistry Edition, Vol. 12. (1974): 2905-2915. 29. Ehrig, R. J., Ed. Plastics Recycling: Products and Processes. Hanser PUblishers, New York. (1992): 59-60. 30. Baliga, S. and W. Wong. "Depolymerization of Poly(ethylene Terephthalate) Recycled from Post­ Consumer Soft-Drink Bottles." Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 27. (1989): 2071-2082. 31. Fogler, H. S. Elements of Chemical Reaction Engineering. Prentice-Hall Inc., Englewood Cliffs, New Jersey. (1986): 656. 32. Forney, R., L. McCune, N. Pierce, and R. Thompson. "Synthetic Fibers: Where the Chemical Engineer Fits In.'' Chemical Engineering Progress, Vol. 62. (March, 1966): 88-97. 33. Biesenberger, J., Ed. Devolatilization of PolYmers: Fundamentals - Equipment - Applications. Hanser Publishers, New York. (1983): 9-10. 34. Shah, V. Handbook of Plastics Testing Technology. John Wiley and Sons, Inc., New York. (1984): 166. 97

35. Kroschwitz, J., Ed. Encyclopedia of Polymer Science and Engineering, Second Edition, Volume 12. John Wiley and Sons, Inc., New York. (1988): 226. 36. Montgomery, D. Design and Analysis of Experiments, Third Edition. John Wiley and Sons, Inc., New York. (1991). 37. Daniel, c. Applications of statistics to Industrial Experimentation. John Wiley and Sons, Inc., New York. (1976). 38. Reid, R., J. Prausnitz and B. Poling. The Properties of Gases and Liquids. Fourth Edition, McGraw-Hill. (1987). 39. White, J. L. Twin Screw Extrusion: Technology and Principles. Hanser Publishers, New York. (1990): 264. 40. Gregory, D. "Rheological Properties of Molten Poly(ethylene Terephthalate)." Journal of Applied Polymer Science, Vol. 16. (1972): 1479-1487. 41. Biesenberger, J., Ed. Devolatilization of Polymers: Fundamentals - Equipment - Applications. Hanser PUblishers, New York. (1983): 19-20. 98

APPENDIX A

Test Method for Determining the Intrinsic Viscosity

of Polyethylene Terephthalate (PET)

1. Scope

This test method has been adapted from the ASTM Standard Test Method 04603 for determining the inherent viscosity of PET. This method directly measures the relative viscosity of polyethylene terephthalate soluble at 0.50% concentration in a 60/40 phenol/l,1,2,2-tetrachloroethane solution. The intrinsic viscosity is then calculated using the Billmeyer relationship [27]. An additional relationship [28] is also provided to estimate the number average molecular weight from the intrinsic viscosity.

2. Referenced Documents

ASTM Standards:

D4603 Standard Test Method for Determining Inherent Viscosity of Poly(Ethylene Terephalate) (PET) 0445 Test Method for Kinematic Viscosity of Transparent and Opaque Liquids (and the Calculation of Dynamic Viscosity) 0446 Specification for Operating Instructions for Glass Capillary Kinematic Viscometers E177 Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods El Specification for ASTM Thermometers

Eastman Chemical Company Test Method:

ECC-A-AC-G-V-1-6 Determination of Dilute Solution Viscosity of Polyesters

3. Summary of Test Method

The relative viscosity is determined by measuring the flow time of a solution of known polymer concentration and the flow time of the pure solvent in a capillary viscometer at a fixed temperature. The intrinsic viscosity value is then calculated from the flow time values. 99

4. Significance and Use

The intrinsic viscosity directly correlates to the average molecular weight of a polyester resin. It must be controlled so that the processability and end properties of the resin remain in a desired range.

5. Apparatus

1. Cannon Ubbelohde Type 1B viscometer.

2. Constant temperature bath, controllable at 30 °C ±0.01 °C. 3. Thermometer calibrated from 28.5 °c to 31.5 °C with 0.05 °C subdivisions (conforms to ASTM Standard E-l).

4. Digital stop·watch.

5. Temperature controllable magnetic stirring hot plate.

6. Volumetric flasks and stoppers, 50 ml capacity.

7. Analytical balance accurate to 0.001 gram.

8. Filter funnels with coarse fritted disc (40 to 60 ~m).

9. TFE-flourocarbon coated stirring bar (3.2 x 13 mm) and bar retreiver.

10. Bulb type safety pipet filler.

6. Reagents and Materials

Reagent grade chemicals should be used in all test procedures.

1. Phenol/1,1,2,2-tetrachloroethane solution, 60/40 weight % mixture with 0.2 weight % of alpha-pinene as a stabilizer.

2. Reagent grade methylene chloride and acetone, rinsing solvents.

3. Chromic acid, cleaning solution. 100

7. Hazards

The material safety data sheets (MSDS) for each of the chemicals specified in this procedure are kept in Room 039. It is strongly recommended that the first step in performing this procedure is to review each MSDS and understand the precautions that must be taken in handling each of these chemicals.

The phenol/1, 1, 2, 2-tetrachloroethane solution used as the solvent in this procedure is toxic and requires proper care and handling. Using the hood for proper ventilation and avoiding skin contact is essential.

8. Procedure

1. Accurately weigh between 0.2475 and 0.2525 g (accurate to ±0.001 g) of PET sample into a clean, dry 50 mL vOlumetric flask.

2. Place a TFE-flourocarbon coated stirring bar into the flask and add approximately 25 mL of solvent. Prepare an additional flask without any sample present. Cap the flasks.

3. Place the flasks in steel beakers and place on a preheated magnetic hot plate. Heat the flasks to 110°C ±10 °C (set temperature control dial to 5.5 on the Model 210T hot plate) for 15 min while stirring. Remove flasks and inspect for undissolved PET. If a sample does not dissolve completely, extend the stirring time for up to 30 more minutes while inspecting the sample at 10 minute intervals. If the sample fails to dissolve completely at this time, this procedure is not applicable.

4. When the samples have completely dissolved, remove the flasks from the hot plate and allow them to cool to approximately room temperature. Remove the stirring bar. Add additional solvent to a level about 1 cm below the 50 mL mark. Place the flasks in the constant temperature bath preset at 30°C ±0.05°C. Allow the flasks to sit for 10 minutes to reach the bath temperature. Invert the stoppered flasks to wash down solvent droplets adhering to the flask walls above the polymer solution, and add sufficient solvent to raise the liquid level up to the 50 mL mark. 101

5. Pour the solution into a clean, dry, Cannon-Ubbelohde viscometer by passing it through a filter funnel into the top of the larger viscometer tUbe (tube G in Figure A.l). Fill the viscometer to a level between the level lines (J and K in Figure A.1) on the large reservoir bulb at the bottom of the larger tUbe. Remove the funnel and place the viscometer in the constant temperature bath preset at 30°C fO.OSoC. Allow at least 15 minutes for the temperature of the solution in the viscometer to reach equilibrium. 6. Using the bulb type pipet filler, draw the solution through the capillary to a level above the top calibration mark {D in Figure A.1). Regulate the level by capping the breather tube (tube B in Figure A.l) with one rUbber-gloved finger and carefully applying suction to the top of the capillary tube (tube A in Figure A.1). Use care to prevent splashing or bubble formation.

7. Let the sample solution or solvent flow back down the capillary tube by removing the suction from the top of the capillary tUbe and by removing the finger from the top of the capillary tube. The first flow is a rinse to wet the capillary bulb and finally equilibrate the sample solution to the bath temperature.

8. After the solution has drained out of the capillary, repeat steps 6 and 7 and time the period required . for the liquid to fall back from the higher calibration mark to the lower calibration mark above the capillary (D and F in Figure A.l). Use the digital stopwatch for this measurement. The bottom of the meniscus of the liquid surface is used for determining the times at which the liquid surface flows past the calibration marks. 9. Record the flow time and repeat the measurement three more times. Average these results unless the range in time exceeds 0.2 seconds, in which case make additional measurements until four within a range of 0.2 seconds are obtained for averaging. Measure the solvent flow time in the same manner as the flow time of the solution samples. 10. During the measurements, record the bath temperature to the nearest 0.05 °C. The range in temperature should not exceed 0.05 °C. 102

11. When the measurements are completed, remove the viscometer from the bath and carefully pour the solution from the viscometer into a safety disposal container.

9. Sources of Error

1. Incomplete sample solution with resulting undissolved polymer will give low viscosity values.

2. The presence of moisture, pigment, and inert material in the sample will cause the measured viscosity to be lower than the true viscosity of the polymer.

3. Other sources of erro~ include excessive heating during dissolution of samples, foreign particles in the capillary, inaccuracies in the temperature of the bath or not allowing adequate time for the samples to reach equilibrium, and a variation of the solvent mixture from the specified 60/40 weight percent.

10. Calculation

1. Determine the intrinsic viscosity as follows:

where "1 = intrinsic viscosity at 30 °C in dl/g, "1 r = relative viscosity (t/to)' t = average solution flow time in seconds, to = average solvent flow time in seconds, C = polymer solution concentration in g/dl.

2. Estimate the number average molecular weight as follows:

where "1 = intrinsic viscosity at 30 °C in dl/g, M.. = number average molecular weight. 103 FIGURE A.I Cannon-Ubbelohde Dilution Viscometer for Transparent Liquids

..-r-----A

r!eI-----B c .....------D

E ------F

'-----G

------H 104 APPENDIX B

VARIABLE LIST

Variable Description

A, B, e Antoine's constants for ethylene glycol. AI cm2/cm3 Interfacial area/volume of polymer melt. AR cm2 Filled cross-sectional area of zone. ARC cm2 Cross-sectional area of C-shaped section. eIRC cm Internal circumference of extruder barrel. CHl kgmolejcm3 Concentration of species 1. CH2 kgmolejcm3 C~ncentration of species 2. CH3 kgmolejcm3 Concentration of species 3. CP joulesj(kgeK) Specif~c heat capacity of polymer mixture. D m Diameter of extruder screw. DEG cm2/hr Diffusivity of ethylene glycol in PET. DFLl kgmole/(hrecm) Change in molar flow rate of species 1. DFL2 kgmole/(hrecm) Change in molar flow rate of species 2. DFL3 kgmole/(hrecm) Change in molar flow rate of species 3. DL kg/cm3 Density of polymer mixture. DP Degree of polymerization. DPO Degree of polymerization of polymer feed. DT K Incremental temperature rise. DY cm Incremental step size (zone length). EG kgjhour Rate of ethylene glycol feed. FEED kg/hour Rate of polymer feed. FLl kgmole/hr Molar flow rate of species 1. FL2 kgmole/hr Molar flow rate of species 2. FL3 kgmole/hr Molar flow rate of species 3. FL3A kgmole/hr Dummy variable in devolatilization algorithm. FLT kgmole/hr Total liquid product molar flow rate. FLTO kgmole/hr Total initial molar feed rate. FN2 kgmole/hr Nitrogen flow. FV3 kgmole/hr Molar flow rate of glycol vapor per DY. G Coefficient in heat transfer correlation. B Wattsj(m2eK) Heat transfer coefficient. Ie Equilibrium constant. ICR cm3j(kgmoleehr) Reaction rate constant. ICRl l/hr Devolatilization rate constant. ICRA cm3/(kgmoleehr) Pre-exponential constant. ICRB kcaljkgmole Activation energy. MAXFD kg/hour Maximum mass flow through extruder zone. MRT minute Mean residence time in extruder zone. MY cP Melt viscosity of liquid product. MVT kg/hour Total mass flow rate of vapor stream. MWl kgmole/kg Molecular weight of hydroxyl end groups. MW2 kgmole/kg Molecular weight of diester groups. MW3 kgmole/kg Molecular weight of ethylene glycol. MWV kgmole/kg Molecular weight of vapor. H kgmole/cm3ehr Rate of ethylene glycol devolatilization. HZ Extruder zone identifier. PCB cm Thread pitch of conveying elements. PP torr Partial pressure of ethylene glycol. PVAP torr Vapor pressure of ethylene glycol. Q Watts Heat transferred to polymer mixture. 105

Rl kgmole/(cm3·hr) Polycondensation reaction rate. RG kcal/(kgmole·X) Ideal gas constant. RT minutes Mean residence time of extruder. STATUS ON - OFF identifier for vacuum pump. T X Temperature of polymer mixture. TC Watts/(m·K) Thermal conductivity of polymer mixture. TZ K Wall temperature of each extruder zone. V cm3 Filled volume of extruder zone. VFR cm3jhour Liquid product volumetric flowrate. XLl Liquid product mole fraction of species 1. XL2 Liquid product mole fraction of species 2. XL3 Liquid product mole fraction of species 3. XV3 Glycol vapor mole fraction per DY. ZDP Variable DP assigned to formatted output. ZFLl kgmolejhr Variable FLl assigned to formatted output. ZFL2 kgmolejhr Variable FL2 assigned to formatted output. ZFL3 kgmole/hr Variable FL3 assigned to formatted output. ZGVT kgjhr Variable GVT assigned to formatted output. ZMV cP Variabte MV assigned to formatted output. ZPP torr Variable PP assigned to formatted output. 106

C Program TSE

C Idealized plug-flow model of a Leistritz Model 30.34 C counter-rotating twin-screw extruder reactively processing C poly(ethylene terephthalate).

INTEGER I, NZ, STATUS

DOUBLE PRECISION AI, AR, ARC, A, B, C, CIRC, D, DEG, CNl, CN2, + CN3, CP, DL, DPO~ DP, DT, DY, EG, FEED, G, H, K, KR, KRA, + FLl, FL2, FL3, FL3A, FLT, FLTO, FV3, FV3A, PCH, KR1, KRB, + MAXFD, MRT, MV, MWl, MW2, MW3, RPM, MVT, Q, TF, TZ, TC, + N, N2, RT, T, VFR, Rl, DFL1, DFL2, DFL3, PP, PVAP, RG, + V, VAC, XLI, XL2, XL3, XV3

DIMENSION ZFLl(6), ZFL2(6), ZFL3(6), ZDP(6), ZGVT(6), ZPP(6), + PCH(6), TZ(6), MRT(6), V(6), TF(6), T(6), MVT(6), + ZMV(6) C******************************************************************** C SET POLYMER PROPERTY VALUES AND OPERATING PARAMETERS c******************************************************************** C Molecular weights of each species (k9/kgmole)

MWI = 127.12 MW2 = 192.17 MW3 = 62.07

C Density of polymer mixture (kg/cmA 3 )

DL = 0.00120

C Thermal conductivity (watts/m K) TC = 0.25

C Pre-exponential constant (cm A3/kgmole hr)

KRA = 4.08E12

C Equilibrium constant

K = 0.5 C Activation energy (kcal/kgmole) KRB = 18500.0

C Diffusivity of ethylene glycol (cm A2/hr)

DEG = 0.02952

C Ideal gas constant (kcal/kgmole K)

RG = 1.987 C Degree of polymerization of feed

PRINT *, 'Enter the degree of polymerization of the feed:' READ *, DPO 107

C Polymer feed rate (kg/hour)

PRINT *, 'Enter the polymer feed rate in grams per minute:' READ -, FEED FEED = (FEED/I000.0)*60.0 C Ethylene glycol feed rate (kg/hour)

PRINT *, 'Enter any additional glycol feed in drops per minute:' READ -, EG

EG = EG*(1.0/29.0)*I.I*60.0*(1.0/1000.0)

C Zone temperatures (degrees F)

PRINT *, 'Enter the temperature setpoints for each zone in degree +s fahrenheit:' PRINT *, ,

DO 10 I = 1, 6 1 PRINT 2, I 2 FORMAT (' Enter the temperature setpoint of Zone'I2':') READ *, TZ(I)

C Limit zone temperatures between 490 F and 540 F

IF (TZ(I) .LT. 490.0) THEN PRINT *, 'THE ZONE TEMPERATURE MUST BE ABOVE 490 FI' GOTO 1 ENDIF IF (TZ(I) .GT. 540.0) THEN PRINT *, 'THE ZONE TEMPERATURE MUST BE BELOW 540 FI' GOTO 1 ENDIF 10 CONTINUE

C Vacuum applied to devolitalizing zones

3 PRINT *, 'If the vacuum pump is ON, enter 1:' PRINT *, ' If the vacuum pump is OFF, enter 0:'

READ *, STATUS IF (STATUS .EQ. 1) THEN VAC = 79.0 ELSE IF (STATUS .EQ. 0) THEN VAC = 0.0 ELSE GOTO 3 ENDIF

C Nitrogen flow to zones 2 and 4 (converted to kgmole/hr from C direct reading from rotameter scale)

PRINT *, 'Enter nitrogen flow (direct from rotameter):' READ *, N2 IF (N2 .EQ. 0) THEN FN2 = 0.0 GOTO 8 ENDIF 108

C Calculate nitrogen flow in mole/min from regression equation

IF (STATUS .EQ. 1) THEN FN2 = 0.00198*N2 - 0.0213 ELSE IF (STATUS .EQ. 0) THEN FN2 = 0.00708*N2 - 0.0311 ENDIF C IF (FN2 .LE. 0) THEN FN2 = 0.0 PRINT *, 'CALCULATED NITROGEN FLOW IS BELOW MINIMUM LIMIT OF +ROTAMETERl ' PRINT *, PRINT *, 'NITROGEN FLOW IS SET TO 01!1' ENDIF

C Convert nitrogen flow to kgmole/hr

FN2 = (FN2*60)/1000

C Divide by 2 to calculate the value for each vent zone

FN2 = FN2/2.0

C Calculate pressure of vent zone in torr 8 VAC = 760 - VAC*7.5

C Area of C-shaped section (cm A2) ARC = 3.14 C Circumference of extruder barrel (em) CIRC = 17.57 C Diameter of extruder screw (m) D = 0.034

C Interfacial area of polymer melt per unit volume (cmA2/cmA 3 ) AI = 5.0 C Dimensionless heat transfer correlation coefficient

G = 0.9

C Thread pitch of conveying elements (em) PCH(1) = 2.0 PCH(2) = 0.6 PCH(3) = 0.6 PCH(4) = 0.6 PCH(5) = 2.0 PCH(6) = 0.0

C Extruder screw RPM

4 PRINT *, 'Set the extruder screw speed in RPM:' PRINT *, 'Note: Speed setting MUST be at least 8 RPM!' READ -, RPM 109

IF (RPM.LT.8.0) THEN PRINT *,'EXTRUDER DRIVE SHUT DOWN DUE TO LOW TORQUE LIMIT!' STOP ENDIF

C Parameters (ethylene glycol) for Antoine's equation C to calculate vapor pressure in bar

A = 13.629 B = 6022.18 C = -28.25 C Calculate initial molar feed rates (kgmole/hour)

FL3 = 0 5 FL2 = (FEED-FL3*MW3)/«2.0*MW1)/(DPO-1)+MW2) FL1 = 2.0*FL2/(DPO-1) FL3 = (0.125*FL1*FL1)/FL2

IF (ABS(FL1*MW1+FL2*MW2+FL3*MW3 - FEED) .GT. (1.0E-9» THEN GOTO 5 ENDIF

FL3 = FL3 + EG/MW3 FLTO = FLl + FL2 + FL3

WRITE (1,100) 100 FORMAT (' ') WRITE (1,101) 101 FORMAT (20X,'FEED CONDITIONS') WRITE (1,102) 102 FORMAT (' ') WRITE (1,103) FEED*1000.0/60.0, FEED 103 FORMAT (4X,'Feed rate of PET is',F5.1,' g/min ('F4.3,' kg/hr)') WRITE (1,104) EG 104 FORMAT (4X,'Feed rate of ethylene glycol is',F5.3,' kg/hr') WRITE (1,105) RPM 105 FORMAT (4X,'Screw speed is',F5.1,' RPM') WRITE (1,106) FN2/2.0 106 FORMAT (4X,'Nitrogen flow to zones 2 & 4 is ',E8.3,' kgmole/hr') WRITE (1,107) 107 FORMAT (' ') WRITE (1,108) DPO 108 FORMAT (4X, 'Degree of polymerization of the feed is ' + F5.1) WRITE (1,109) FL1 109 FORMAT (4X, 'Molar flowrate of the hydroxyl end groups is', + E10.4,' kgmole/hr') WRITE (1,110) FL2 110 FORMAT (4X, 'Molar flowrate of the diester groups is', + E10.4,' kgmole/hr') WRITE (1,111) FL3 111 FORMAT (4X, 'Molar flowrate of the ethylene glycol is', + EI0.4,' kgmole/hr')

WRITE (1,112) 112 FORMAT (' , ) 110

C************************************************************** C CALCULATE CHANGE IN MOLAR FLOW RATES AND PHYSICAL C PROPERTIES IN EACH OF THE SIX EXTRUDER ZONES c************************************************************** C Initialize feed temperature T(l} = 50 + 273.15

DO 20 NZ = 1, 6

C Calculate filled cross-sectional area (cmA2) IF (PCH(NZ).EQ.O.O) THEN AR = 6.91 ELSE MAXFD = RPM*60.O*PCH,( NZ) *ARC*DL AR = (FEED/MAXFD)*ARC ENDIF C Check feed rate versus maximum theoretical output IF (FEED.GT.MAXFD) THEN PRINT *, ,********************************************, PRINT *, 'THE FEED RATE EXCEEDS THE OUTPUT FLOW RATE:' PRINT *,' ---INCREASE THE SCREW SPEED---' PRINT *, ,********************************************, PRINT *, GOTO 4 ENDIF C Initialize variables V(NZ) = 0.0 MRT(NZ) = 0.0 MVT(NZ) = 0.0 C Convert zone temperature to Kelvin TZ(NZ) = (5.0j9.0)*(TZ(NZ}-32) + 273.15 C Set incremental zone length for Euler's Loop (em)

DY = 0.01 C Euler's Loop to calculate the molar flow rate of each species C along the length of the zone DO 30 I = 1, 1200 C Adjustment for element change within Zone 1 and Zone 5 IF «NZ.EQ.1 .OR. NZ.EQ.5) .AND. I.GE.600) THEN AR = 6.91 ENDIF

C Calculate filled volume (cmA3) V(NZ) = V(NZ) + AR*DY 111

C Calculate theoretical mean residence time (minutes) MRT(NZ) = (V(NZ)/FEED)*DL*60.0 C Calculate specific heat capacity (Joules/kg K) CP = -O.00784*T(NZ)*T(NZ) + 10.2552*T(NZ) - 1221.77

C Calculate heat transfer coefficient (Watts/mA2 K)

H = G*(TC/D)*«(D*D*(RPM/60.0)*DL*1.OE6*CP)/TC)**O.333) C Calculate heat transfer (Watts)

IF (PCH(NZ).EQ.O) THEN Q = (H/10.0)*(CIRC/100.0)*(DY/100.0)*(TZ(NZ) - T(NZ» ELSE Q = H*(CIRC/100.0)*(DY/100.0)*(TZ(NZ) - T(NZ» ENDIF

C Calculate polymer temperature change with reactor length

DT = Q/«FEED/3600.0)*CP)

C Calculate total volumetric flowrate of polymer (cm A3/hour)

VFR = (FL1*MWI + FL2*MW2 + FL3*MW3)/DL

C Calculate species concentrations (kgmole/cmA3)

CN1 = FL1/VFR CN2 = FL2/VFR CN3 = FL3/VFR

C Calculate reaction rate constants (cm A3/kgmole hr)

KR = KRA*EXP(-KRB/RG/T(NZ» C Calculate rate constant for devolatilization (1/hr)

KRI = (4.0*KR*CN3)/K

C Calculate reaction rates (kgmole/cmA3 hr)

Rl = KR*(CNl*CN1 - (4.0*CN2*CN3)/K) C Calculate the change of molar flow rate of each species with C reactor length (dFi/dy)

DFLI = -2*Rl*AR DFL2 = Rl*AR DFL3 = R1*AR

C Update the species molar flow rates (kgmole/hour) FLI = FL1 + DFL1*DY FL2 = FL2 + DFL2*DY FL3 = FL3 + DFL3*DY C Update the temperature of the polymer melt

T(NZ) = T(NZ) + DT 112

C Calculate product molar flowrate FLT = FLI + FL2 + FL3 C Calculate mole fractions of each species

XLI = FLI/FLT XL2 = FL2/FLT XL3 = FL3/FLT C Calculate ethylene glycol vapor pressure (torr)

PVAP = 7S0.0*EXP(A-B/(C+T(NZ») C Calculate partial pressure (in torr) using Raoult's Law. PP = XL3*PVAP C Initialize vapor flow rate FV3 = 0 C Calculate change in glycol mole fraction, molar flow C rate and total molar flow rate in devolatilizing zones IF (NZ.EQ.2 .OR. NZ.EQ.4) THEN IF (FN2 .GT. 0) THEN FV3 = 0 6 XV3 = FV3/(FV3 + FN2/(12.0/DY» XL3 = (XV3*VAC)/PVAP FL3A = XL3*FLT N = (CN3-FL3A/VFR)*AI*SQRT(DEG*KRl) FV3A = N*(AR*DY) IF (ABS(FV3A-FV3) .GT. (ABS(FV3A*O.01») THEN FV3 = (FV3 + FV3A)/2.0 GOTO 6 ENDIF FL3 = FL3A ENDIF IF (VAC .LT. PP) THEN XV3 = 1.0 XL3 = XV3*VAC/PVAP FL3A = XL3*FLT N = (CN3-FL3A/VFR)*AI*SQRT(DEG*KRl) FV3 = N*(AR*DY) FL3 = FL3 - FV3 ENDIF ENDIF C Calculate total mass of ethylene glycol vapor IF (NZ.EQ.2 .OR. NZ.EQ.4) THEN MVT(NZ) = MVT(NZ) + FV3*MW3 ENDIF

C Calculate degree of polymerization

DP = 1 + 2*FL2/FLI 113

C Calculate melt viscosity in centipoise MV = 0.012538*«EXP(-11.9755+6802.1/T(NZ»)*(DP**3.5» C Assign variables for formatted output ZDP(NZ) = DP ZFL1(NZ) = FL1 ZFL2(NZ) = FL2 ZFL3(NZ) = FL3 ZGVT(NZ) = GVT ZPP(NZ) = PP ZMV(NZ) = MV 30 CONTINUE

C Initialize melt temperature for the next zone T(NZ + 1) = T(NZ) 20 CONTINUE C Calculate mean residence time of extruder

RT = 0 DO 40 NZ = 1, 6 40 RT = RT + MRT(NZ) C Convert both zone and bulk temperatures to Centigrade

DO 50 NZ = 1, 6 TZ(NZ) = TZ(NZ)-273.15 50 TF(NZ) = T(NZ)-273.15

WRITE (1,200) 200 FORMAT (' ') WRITE (1, 201) 201 FORMAT (12X,'PRODUCT PROPERTIES AND EXTRUDER CONDITIONS BY ZONE') WRITE (1, 202) 202 FORMAT (' ') WRITE (1,203) 203 FORMAT (4X,'Molar flow rates exiting each zone (kgmole/hr):') WRITE (1,204) 204 FORMAT (' ') WRITE (1,205) 205 FORMAT (lSX,' ZONE 1 ZONE 2 ZONE 3 ZONE 4 ZONE +5 ZONE 6') WRITE (1,206) ZFL1(1),ZFL1(2),ZFL1(3),ZFL1(4),ZFL1(S),ZFL1(6) 206 FORMAT (4X,'End Groups:'E10.3, E11.3, El1.3, E1l.3, E11.3, + Ell.3) WRITE (1,207) ZFL2(l),ZFL2(2),ZFL2(3),ZFL2(4),ZFL2(S),ZFL2(6) 207 FORMAT (4X,'Diester: 'E10.3, E11.3, El1.3, E1l.3, El1.3, + E11.3) WRITE (1,208) ZFL3(1),ZFL3(2),ZFL3(3),ZFL3(4),ZFL3(S),ZFL3(6) 208 FORMAT (4X,'Glycol: 'E10.3, E11.3, E11.3, E11.3, E11.3, + E11.3) WRITE (1, 209) 209 FORMAT (' ') WRITE (1,210) ZDP(1),ZDP(2),ZDP(3),ZDP(4),ZDP(S),ZDP(6) 210 FORMAT (4X,'DP: 'F8.3,3X,F8.3,3X,F8.3,3X,F8.3,3X,F8.3, + 3X,F8.3) 114

WRITE (1,211) 211 FORMAT (' ') WRITE (1,212) 212 FORMAT (4X,'Average Residence Time') WRITE (1,213) MRT(l), MRT(2), MRT(3), MRT(4), MRT(5), MRT(6) 213 FORMAT (4X,'(minutes):'F8.3,3X,F8.3,3X,F8.3,3X,F8.3,3X,F8.3, + 3X,F8.3) WRITE (1,214) 214 FORMAT (4X,'Barrel Temperature') WRITE (1,215) TZ(1), TZ(2), TZ(3), TZ(4), TZ(5), TZ(6) 215 FORMAT (4X,'(deg C): 'F8.1,3X,F8.1,3X,F8.1,3X,FS.1,3X,FS.1, + 3X,F8.1) WRITE (1,216) 216 FORMAT (4X,'Product Temperature') WRITE (1,217) TF(l), TF(2), TF(3), TF(4), TF(5), TF(6) 217 FORMAT (4X,'(deg C): 'FS.1,3X,F8.1,3X,F8.1,3X,FS.1,3X,F8.1, + 3X,F8.1) WRITE (1,218) 21S FORMAT (4X,'Zone Pressure') WRITE (1,219) 760.0, VAC, 760.0, VAC, 760.0, 760.0 219 FORMAT (4X,'(torr): 'F8.1,3X,F8.1,3X,FS.1,3X,FS.1,3X,F8.1, + 3X,F8.1) WRITE (1,220) 220 FORMAT (4X,'Partial Pressure of EG') WRITE (1,221) ZPP(l), ZPP(2), ZPP(3), ZPP(4), ZPP(5), ZPP(6) 221 FORMAT (4X,'(torr): 'F8.3,3X,F8.3,3X,F8.3,3X,FS.3,3X,F8.3, + 3X,F8.3) WRITE (1,222) 222 FORMAT (4X, 'Melt Viscosity') WRITE (1, 223) ZMV(l), ZMV(2), ZMV(3), ZMV(4), ZMV(5), ZMV(6) 223 FORMAT (4X,'(cP): 'FS.0,3X,F8.0,3X,F8.0,3X,F8.0,3X,F8.0, + 3X,F8.0) WRITE (1,224) 224 FORMAT (' ') WRITE (1,225) RT 225 FORMAT (lOX, 'The mean residence time is ',F7.3,' minutes') WRITE (1,226) 226 FORMAT (' ') WRITE (1,227) 227 FORMAT (lOX, 'The total mass of ethylene glycol vapor removed:') WRITE (1,228) MVT(2) 228 FORMAT (20X, 'ZONE 2: ' E11.4,' kg/hour') WRITE (1,229) MVT(4) 229 FORMAT (20X, 'ZONE 4: ' E11.4,' kg/hour')

STOP E~