ABSTRACT. Keywords: iron oxide, dispersion, deposit control agents, mono-, di-, and trivalent metals effect INTRODUCTION

Transcription

1 Paper No Water Chemistry Impacts on Cooling Water System Iron Oxide Dispersants Zahid Amjad, Libardo Perez, and Robert W. Zuhl The Lubrizol Corporation, Energy and Water, 294 Lakeland Blvd., Wickliffe, Ohio 4492, USA ABSTRACT The effects of water chemistry such as total dissolved solids, polyvalent metal ions, ph, and temperature on particulate iron oxide dispersion by a variety of polymeric additives have been investigated. The deposit control polymers (DCPs) evaluated include synthetic polymers (of varying composition and molecular weight). Results reveal that DCP iron oxide dispersant performance strongly depends on dosage and architecture (e.g., type and amount of monomers, monomer functional group ionic charge, molecular weight). Data show that ph changes cause varying but relatively small changes in DCP dispersant performance. The results also suggest that low levels of divalent and trivalent metal ions reduce DCP dispersant performance. Keywords: iron oxide, dispersion, deposit control agents, mono-, di-, and trivalent metals effect INTRODUCTION Solid/liquid dispersion technology has many domestic and industrial applications. The dispersion is generally defined as a suspension of insoluble particles formed either through de-flocculation or breaking down of agglomerated particles, or from the stabilization of small suspended particles. Industrial applications of dispersant technology includes water treatment, oil and gas recovery, paints, inks, cosmetics, and paper manufacturing. 1 Suspended matter encountered in industrial water systems generally carries a slight negative charge. The type, size, and concentration of suspended mater affect their behavior in water systems. Therefore, anionic polymers are normally the most efficient dispersants because they increase the negative surface charge and keep particles in suspension. Dispersed systems can be achieved by controlling the surface charge of the powders in solution, for example, by the adsorption of charged polymers referred to as polyelectrolytes. 2 Suspension of clays, metal oxides, pigments, ceramic materials, and other insoluble particulate solids in aqueous systems through the use of small quantities of synthetic polymers, polyphosphates, and other polyelectrolytes has become an increasingly important area of study with high technological relevance. A previous study reported the influence of ammonium polyacrylate (NH 4PAA) in dispersing concentrated alumina suspension. 3 A 3.5k molecular weight (MW) NH 4PAA was found to be an effective dispersant for a Bayer * processed alumina that had a point of zero charge at ph 8.. Garris and Sykes 4 in their study on the evaluation of a variety of polyamino acid analogs of biomineral proteins as dispersants for various substrates e.g., clay, calcium carbonate, calcium phosphate, iron oxide, reported that performance of these dispersants was comparable to synthetic polymeric dispersants. In another study by Dubin 5 it was shown that acrylic acid and maleic acid based DCPs performed better * Trade name 1

2 than polyphosphates and phosphonates as iron oxide dispersants. Bain et al. 6 tested the performance of poly(aspartic acid) [or PASA] as a dispersant for kaolin clay. Their study results show that low MW PASA performed better than poly(acrylic acid) [or PAA], in dispersing clay in aqueous system. In another study, Amjad 7 evaluated a variety of homo-, co-, and terpolymers containing different functional groups as iron oxide dispersants. Among the homopolymers evaluated in this study, PSA [poly(2-acrylamido-2-methylpropane sulfonic acid)], performs better than PAA and PMA [poly(maleic acid)], suggesting that SO 3H group present in PSA imparts more negative charge on iron oxide particles than COOH present in PAA and PMA. The data further reveal that incorporating SO 3H containing monomers such as SA or SS (sulfonated styrene) results in dramatic increase in co- or terpolymer performance suggesting that incorporation of co-monomers help sterically stabilize iron oxide particles. Similar observations were also reported by Amjad and Zuhl in their studies on the dispersion of iron oxide, 8 clay, 9 hydroxyapatite, 1 and silica. 11 Iron fouling often occurs in cooling water and desalination processes as a result of clarifier carryover where iron salts are used as a coagulants or where the raw water (e.g., well water) contains high iron levels. When the circulating water iron levels are 1 mg/l, the system can normally be controlled by incorporating a dispersant in the water treatment formulation. In cooling waters, Fe 2O 3 (hematite) and FeO (iron oxide or wustite) are the two most common iron deposits. However, magnetite (Fe 3O 4) is rarely encountered in cooling systems because it needs high temperatures and/or anaerobic conditions. Most magnetite found in cooling systems arrives via airborne or water borne solids. In our earlier investigations, we reported the influence of various factors including water chemistry, ph, temperature, and impurities (both soluble & insoluble) on the performance of scale inhibitors. It was shown that, impurities typically exhibit negative impact on scale inhibitor performance. The focus of this study is to examine the effects of water impurities [e.g., metal ions (mono-, -di-, trivalent ions), total dissolved solids (TDS)] on the performance of commercially available DCPs. The influence of ph and temperature on iron oxide dispersants performance was also investigated. Materials EXPERIMENTAL Grade A glassware and analytical grade chemicals were used. Stock solutions of calcium chloride, sodium sulfate, sodium bicarbonate and sodium carbonate were prepared from the respective crystalline solids (Merck ) using distilled water, filtered through.22-µm filter paper and standardized as previously described. 12 Iron oxide (Fe 2O 3) used in this investigation was obtained from Fisher Scientific Co. Powder X-ray diffraction showed that it consisted exclusively of α-fe 2O 3 (hematite). Table 1 lists the commercial DCPs tested including several Carbosperse K-7 polymers and polymers containing AMPS monomer (SA). Additives stock solutions were prepared on a dry weight basis. The desired DCP concentrations were obtained by dilution. Table 1: Deposit Control Polymers Tested Polymer Composition MW Acronym K-752 Solvent polymerized poly(acrylic acid) or SPPAA 2k PAS1 K-728 Water polymerized PAA or WPPAA 2.3k PAW1 CPAAP PAA with phosphinate groups <4k PAAP CPMA Poly(maleic acid) or PMA <1k PMA K-766 Sodium polymethacrylate or PMAA 5k PMAA1 K-775 Poly(acrylic acid : 2-acrylamido-2-methylpropane sulfonic acid]) or <15k CP1 poly(aa/sa) with 74/26 monomer weight ratio K-798 Poly(AA : SA : sulfonated styrene) or AA/SA/SS <15k TP3 CTPD Poly(AA: SA : non-ionic) or AA/SA/NI 4.5k TP4 Trade name 2

3 Dispersion Test Protocol A known amount (.12 g) of iron oxide was suspended in an 8-mL beaker containing 6 ml of simulated industrial water containing known polymer concentration (dispersant). Table 2 shows the three types of water compositions used all with ph in the 7.6 to 7.8 range. Table 2. Water Types Studied Type Polymer (mg/l) Fe2O3 (mg/l) Composition mg/l HCO3, 22 mg/l Na mg/l Ca, 3 mg/l Mg, 314 mg/l Na, 571 mg/l Cl, 192 mg/l SO4, 6 mg/l HCO mg/l Ca, 7.5 mg/l Mg, 78.5 mg/l Na, 143 mg/l Cl, 48 mg/l SO4, 6 mg/l HCO3 All dispersion experiments were done at room temperature ( 22 C). In a typical test, six experiments were run simultaneously using a gang stirrer at 12 revolutions per minute. At known time intervals transmittance readings (%T) were taken with Brinkmann Probe Colorimeter equipped with 42-nm filter. The absorbance of several filtered (.22 µm) suspensions was measured as %T at 42 nm; the absorbance contribution due to dissolved species was insignificant (<3%). DCP performance as percent iron oxide dispersed (%D) was calculated based on %T readings taken as a function of time and using Equation 1 below which includes an adjustment for readings obtained in the absence of DCP. %D = [1 - (1.11 x % transmittance)] (1) The data presented in this study were reproducible (± 5% or better). DCP performance was determined by comparing the %D values for the slurries containing and without DCPs. Increasing %D values suggest more effective dispersion. DCP Performance RESULTS AND DISCUSSION DCPs evaluated (see Table 1) represent a wide range of compositions (monomer type, amount), ionic charges (attributable to monomer functional groups), and MW. The following section discuss results using the protocol described above to runs a series of iron oxide dispersion tests to study the effect of various parameters [e.g., dispersion time, dispersant dosage, polymer composition, metal ions (mono-, di-, and trivalent), solution ph, and temperature]. Test Duration and Dispersant Dosage Effects Figure 1 presents the results showing the performance of TP3 as iron oxide dispersant using Type-1 water composition, at varying DCP dosage and as a function of time. Figure 1 data indicate %D values increase with both increasing time and increasing TP3 dosage. For example, %D values obtained in the presence of 1. mg/l at ½ hr and 1 hr are 25% and 41%, respectively. Increasing the test duration by a factor of three (i.e., from 1 to 3 hr) increases the %D value by >25%. Increasing the test duration another hour (i.e., from 3 to 4 hr) has an insignificant effect on the %D value. Therefore, we conclude that test duration (i.e., TP3 contact time with iron oxide particles) plays an important role in iron oxide particle dispersion in aqueous solution. Other factors including particle size and surface area may play a role in iron oxide dispersion. Trade name 3

4 8 Figure 1: Iron Oxide Dispersion vs. TP3 Dosage using Type-1 Water mg/l.5 mg/l 1. mg/l Time (hr) TP3 dosage impact on iron oxide dispersion was also studied. Figure 1 shows that TP3 iron oxide dispersion performance strongly depends on polymer dosage but the relationship is not linear. For example, %D values obtained at 3 hr in the presence of.25 and.5 mg/l TP3 are 43% and 55%, respectively. Doubling the TP3 concentration (i.e., from.5 to 1. mg/l) increases the %D value only 12% (from 55 to 67%). This is not surprising considering that the extent of adsorption depends largely on the DCP conformation on the iron particles. Although outside of the scope of the work herein, studies of adsorption mechanism(s) would help provide a better understand this behavior of the DCPs. Figure 1 data clearly show that iron oxide dispersant performance depends on DCP concentration. Metal Ions Effect Monovalent Ions The influence of monovalent metal ions (i.e., Na + ) on the performance of TP3 was investigated by conducting dispersion experiments in the presence of varying sodium chloride concentrations using Type-1 water. Figure 2 dispersion data collected at 3 hr for 1. mg/l TP3 clearly show that adding a small amount (49 mg/l) of sodium chloride (NaCl) enhances performance. For example, %D values obtained in the presence of 49 mg/l NaCl is 89% compared to 7% without NaCl ( 2% improvement). As shown, increasing the NaCl concentration from 49 to 11 mg/l results in TP3 performance increasing 1%. However, increasing the NaCl concentration (ionic strength) further has an insignificant effect on TP3 performance. Divalent Ions Homopolymers: High hardness waters either due to harsh feed waters or high cycles of concentration (COC) are well known to create difficult operating conditions that demand high performance dispersants. A series of experiments was conducted with Type-1 water to determine the influence of Ca 2+ ions on PAA (i.e., PAS1 and PAW1) performance. Figure 3 presents dispersion data in the presence of 1. mg/l PAAs and varying concentration of Ca 2+ ions. In the absence of Ca 2+ ions, both PAAs exhibit excellent iron oxide dispersion performance. 4

5 1 Figure 2: Iron Oxide Dispersion by 1 mg/l TP3 in Presence of NaCl using Type-1 Water Control 49 mg/l NaCl 11 mg/l NaCl 44 mg/l NaCl 659 mg/l NaCl 1 Figure 3: Iron Oxide Dispersion by Polyacrylates in Type-1 Water as a Function of Ca 2+ Concentration PAS1 PAW Ca 2+ (mg/l as Ca) Figure 3 shows that adding Ca 2+ ions has an antagonistic effect on PAA performance. The data indicate that PAS1 performs better than PAW1 especially at a higher Ca 2+ ions concentration (i.e., 15 mg/l). This difference may be attributed to poor compatibility with Ca 2+ and/or poor adsorption of PAW1 on iron oxide particles. To study the impact of Ca 2+ on iron dispersion by homopolymers of acrylic acid and maleic acid of varying molecular weight (MW), several dispersion experiments were carried out in the presence of 1. mg/l DCP and 15 mg/l Ca 2+ using Type-1 water. Results presented in Figure 4 clearly show that homopolymer performance is affected by Ca 2+ to a varying degrees and can be ranked (highest to lowest) as PAS1 PMA >PAW1 ~ PMAA1 > PAAP. This DCP performance trend is consistent with an 5

6 earlier study on the calcium ion tolerance by homopolymers. 13 The effect of Ca 2+ on DCP performance may be attributed to several factors including Ca-DCP complexation, Ca-DCP salt precipitation, and iron oxide particle surface charge. 1 Figure 4: Iron Oxide Dispersion by Homopolymers (1 mg/l) using Type-1 Water mg/l Ca 15 mg/l Ca PAS1 PAW1 PAAP PMAA1 PMA Co/terpolymers: The role of DCP functional group(s) was investigated by conducting a series of iron oxide dispersion experiments using Type-1 water and 1. mg/l co/terpolymers (e.g., CP1, TP3, TP4) containing several functional groups [e.g., ionic (-COOH, -SO 3H)] and comparing performance to various homopolymers. Figure 5 shows 3-hr dispersion data for PAW1 and TP3 collected in the presence of varying Ca 2+ ion concentrations leading to three observations: 1. In the absence of Ca 2+, PAW1 performs better than TP3, 2. At low Ca 2+ (i.e., <5 mg/l), TP3 outperforms PAW1, and 3. PAW1 and TP3 performance decreases with increasing Ca 2+ concentration Figure 5: Iron Oxide Dispersion by Polymers (1 mg/l) as a Function of Ca 2+ Concentration using Type-1 Water PAW1 TP Ca 2+ (mg/l as Ca) 6

7 From a practical viewpoint, Figure 5 data suggest that incorporating TP3 (a terpolymer) used in a low hardness water system (e.g., a boiler) treatment program would be expected to perform better than PAW1 (a homopolymer). This is because TP3 s carboxyl content is lower than for PAW1 and thus is more tolerant to Ca 2+ ions Figure 6 presents dispersion data for several polymers using Type-1 water conducted in the absence and presence of 15 mg/l Ca 2+. The data in the absence of Ca 2+ ions show that the two homopolymers (i.e., PAS1 and PAAP) perform better than the co/terpolymers. However, all DCPs lose dispersion activity in the presence of Ca 2+ and the extent of the performance loss is dependent on polymer architecture (e.g., manufacturing process, MW, type and amount of co-monomers). More specifically, co/terpolymers resist perform loss much better in the presence of 15 mg/l Ca 2+ than the homopolymers. This polymer trend observed is consistent with an earlier study focusing on DCP calcium ion tolerance Figure 6: Iron Oxide Dispersion by Polymers (1 mg/l) Impacted by 15 mg/l Ca 2+ using Type-1 Water mg/l Ca 15 mg/l Ca PAS1 PAAP CP1 TP3 TP4 Trivalent Ions Aluminum and iron-based compounds (e.g., alum, sodium aluminate, ferric sulfate) have been used for decades as coagulant aids in municipal and industrial water clarification processes. These inorganic flocculating agents neutralize the charge of water borne turbidity particles and hydrolyze to form insoluble hydroxide particles that entrap additional particles. In most cases, these large particles (or flocs) are removed via settling in a clarifier and extracted as sludge. Occasionally, clarifier upsets cause these metal-ion containing flocs and/or fugitive flocculants to carry over or escape pretreatment systems and become contaminants or impurities in cooling or boiler feed waters and can adversely impact treatment program performance. Figure 7 presents the impact of varying Al(III) and Fe(III) concentrations on TP3 iron oxide dispersion performance using Type-1 water. Low levels of trivalent metal ions exhibit antagonistic effects on TP3 performance; e.g., %D values obtained in the presence of.25 mg/l Al(III) is 67% compared to 73% in the absence of Al(III). Increasing the Al(III) concentration fourfold (i.e., from.25 to 1. mg/l) decreases the TP3 %D by 33% (from 73 to 4%). Increasing Al(III) from 1. to 5. mg/l further decreases TP3 performance. As shown, Fe(III) concentrations also have an antagonistic effect on TP3 performance which is less impactful than Al(III). The iron dispersant performance decrease caused by trivalent metal ions may be attributed several factors: 7

8 1. Dispersant concentration is reduced due to possible polymer removal via adsorption by freshly formed Al(III) and Fe(III) hydroxide particles, 2. Al(III) and Fe(III) may form soluble and/or insoluble complexes with polymer, 3. Al(III) and Fe(III) may interfere in the adsorption of polymer-iron oxide particles, and 4. Combinations of the processes above. 8 Figure 7: Iron Oxide Dispersion by TP1 (1 mg/l) Impacted by Trivalent Ions using Type-1 Water Al3+ Fe Trivalent Ion Concentration (mg/l) The antagonistic effect of trivalent ions on TP3 iron oxide dispersant performance has also been observed for scaling systems, e.g., calcium phosphate, calcium phosphonate, calcium sulfate dihydrate Effect of ph Increasing cooling system ph has two key effects on system performance: (1) decreases metal corrosion rates and (2) increases potential scaling due to increasing supersaturation of scaling salts (e.g., calcium carbonate, calcium phosphate, and calcium phosphonates). To study solution ph impact on PAW1 and TP3 performance, a series of dispersion experiments were conducted using Type-2 water. Figure 8 presents results indicating that DCP iron oxide dispersion performance varies with solution ph. The performance for both PAW1 and TP3 at 1 mg/l dosages increases as ph increases from 2.5 to 9.2 with more dramatic increase observed for TP3. The DCP performance on solution ph dependence may be attributed to the increased ionization of the COOH and -SO 3H groups present in PAW1 and TP3, respectively. Similar solution ph vs. DCP performance profiles have been reported in a calcium sulfate dihydrate seeded growth inhibition using PAA. 17 8

9 8 Figure 8: Iron Oxide Dispersion by Polymers (1 mg/l) as a Function of ph using Type-2 Water PAW1 TP Test Solution ph Temperature Effect It is well known that water chemistry parameters including ph, total dissolved solids (TDS) water composition, and temperature affect the solubility of scale forming salts. The solubility of most scale forming salts (e.g., calcium carbonate, calcium sulfate, and calcium phosphate) is inversely dependent on solution temperature. This solubility-temperature relationship suggests that scaling tendency is greater at heat exchanger surfaces than in the other parts of the circulating water system. Figure 9 shows the effect of temperature on iron oxide dispersion of PAW1 and TP3 at 1 mg/l dosages. It is evident that temperature, within the range studied (i.e., 23 to 6 C), exhibits insignificant effect on DCP performance Figure 9: Iron Oxide Dispersion by Polymers (1 mg/l) as a Function of Temperature using Type-2 Water PAW1 TP3 23 C 4 C 6 C Test Solution Temperature 9

10 Cycles of Concentration Effect It is well known that increasing the cycles of concentration (COC) in cooling water systems increases the potential for scaling salt formation and/or deposition of unwanted materials on equipment surfaces. Under normal conditions, the water treatment additive (e.g., antiscalant, dispersant, corrosion inhibitor) concentrations also increase with increasing COC. However, at high COC, scaling potential increases dramatically and/or the re-circulating water suspended matter loading increases and may exceed the inhibitor s ability to provide control even if product dosages are increased. To understand the impact of COC on TP3 performance, a series of experiments were conducted using Type-3 water. The experiments were designed such that both iron oxide particles and TP3 concentrations were increased directly with COC increases. Figure 1 shows that TP3 performance increases as COC increases from one to four and then levels out; i.e., TP3 performance increases only slightly when COC doubles (goes from 4 to 8). The observed dependence of TP3 s iron oxide dispersion properties with increasing COC may be attributed to several factors including water chemistry changes, kinetics of TP3 adsorption and/or desorption on suspended iron oxide particles, and TP3 s conformational changes in aqueous solution Figure 1: Iron Oxide Dispersion by TP3 (1 mg/l) as Function of COC using Type-3 Water 1 COC 2 COC 3 COC 4 COC 8 COC Figure 11 presents iron oxide dispersion data using Type-3 water, eight COC, and TP3 dosages ranging from 1 to 1 mg/l. The data indicate no change in TP3 performance as dosage increases which is likely due to a combination of two competing processes summarized below: 1. Hardness ion concentration increase due to COC increase thereby decreasing TP3 performance, 2. TP3 dosage increasing from 1 to 1 mg/l should increase TP3 adsorption thereby increasing TP3 performance. 1

11 Figure 11: Iron Oxide Dispersion as Function of TP3 Dosage using Type-3 Water TP3 dosage (mg/l) SUMMARY This study on the effects of water chemistry on performance of iron oxide dispersion by deposit control polymers (DCPs) indicates: 1. Fe 2O 3 particle dispersion increases with increasing DCP concentration and contact time. 2. Fe 2O 3 dispersant performance strongly depends on DCP architecture, e.g., monomer type(s) and amounts, functional group(s), and molecular weight. 3. The ranking (best to worst) of DCPs evaluated as iron oxide dispersants is: Terpolymer > Copolymer > Homopolymer 4. Metal ions charge and concentration are the two most important water quality factors impacting DCP performance. 5. Metal ion antagonistic impact ranking (greatest to least) on DCP performance is: Trivalent Ions [(Al(III) > Fe(III)] >> Divalent Ions > Monovalent Ions. 6. Temperature (23 to 6 C range) has minimal impact on DCP performance. 7. DCP performance increases as solution ph increases from 2.5 to 6. and incrementally above ph 6.. ACKNOWLEDGEMENTS The authors thank The Lubrizol Corporation for support to conduct this research and present the findings at NACE International s annual convention. 11

12 REFERENCES 1. R. D. Athey, Polymeric Organic Dispersants for Pigments: Useful Structures and Their Evaluations, TAPPI, 58, 1 (1975): pp P. Somasundaran and V. Runkana, Interactions of Polyelectrolytes with Particulate Matter in Aqueous Systems, in The Science and Technology of Industrial Water Treatment, Z. Amjad (Ed), (Boca Raton, FL, CRC Press, 21), pp J. Davis, J. G. P. Binner, The Role of Ammonium Polyacrylate in Dispersing High Solids Content Alumina Suspensions, J. Eur. Ceram. Soc., 2, 5 (2): pp J. P. Garris and C. S. Sikes, Use of Polyamino Acid Analogs of Biomineral Proteins in Dispersion of Inorganic Particulates Important to Water Treatment, Colloids and Surfaces A, 8 7, (1993): pp L. Dubin and K. E. Fulks, The Role of Water Chemistry on Iron Dispersant Performance, CORROSION 1984, Paper No. 118 (Houston, TX: NACE, D. J. Bain, G. Fan, J. Fan, H. Brugman, and K. Enoch, Laboratory and Field Development of a Novel Environmentally Acceptable Scale and Corrosion Inhibitors, CORROSION 22, Paper No. 223, (Houston, TX: NACE, 22). 7. Z. Amjad, Dispersion of Iron Oxide Particles in Industrial water, Tenside Surfactants Detergents 36, 1 (1999): pp Z. Amjad and R. Zuhl, Particle Size and Microscopic Investigation of Iron Oxide Foulants in the Presence of Dispersants, Association of Water Technologies Annual Convention, Charlotte, NC (26). 9. Z. Amjad and R. W. Zuhl, Silica Control in Industrial Waters with a Novel Polymeric Dispersant, Association of Water Technologies Annual Convention, Hollywood, FL (29). 1. Z. Amjad and D. Morgan, Efficacy of Hydroxyapatite Dispersants in the Presence of Surfactants, Phos. Res. Bull., 25, 3 (211): pp Z. Amjad and R. W. Zuhl, Effects of Thermal Stress on Silica-Silicate Deposit Control Agent Performance, Association of Water Technologies Annual Convention, Reno, NV (21). 12. Z.Amjad, Robert W. Zuhl, and John F. Zibrida, The Use of Polymers to Improve Control of Calcium Phosphonate and Calcium Carbonate in High Stressed Cooling Water Systems, Association of Water Technologies Annual Convention, Nashville, TN (24). 13. Z. Amjad, Interactions of Hardness Ions with Polymeric Scale Inhibitors, Tenside Surfactants Detergents, 42, 2 (25): pp Z. Amjad, J. Pugh, J. Zibrida, and R. Zuhl, Polymer Performance in Cooling Water: The Influence of Process Variables, Mat. Perf. 36, 1, (1997): pp Z. Amjad, R. Zuhl, and J. A. Thomas-Wholever, Advances in Crystal Growth Inhibition Technologies, (New York, New York: Kluwer Academic Press, 2), pp S. K. Hamdona, R. B. Nessim and S. M. Hamza, Spontaneously Precipitation of Calcium Sulfate Dihydrate in the Presence of Some Metal Ions, Desalination 94, 5 (1983) pp Z. Amjad, Kinetics of Crystal Growth of Calcium Sulfate Dihydrate. The Influence of polymer Composition, Molecular Weight, and Solution ph, Can J. Chem., 66, 2 (1988): pp