Adsorption of polyethylene glycol (PEG) from aqueous solution onto hydrophobic zeolite

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www.elsevier.com/locate/jcis

Adsorption of polyethylene glycol (PEG) from aqueous solution

onto hydrophobic zeolite

C.Y. Chang,

a

_{W.T. Tsai,}

b,∗

_{C.H. Ing,}

a

_{and C.F. Chang}

a a_{Graduate Institute of Environmental Engineering, National Taiwan University, Taipei 106, Taiwan, ROC}

b_{Department of Environmental Engineering and Health, Chia Nan University of Pharmacy and Science, Tainan 717, Taiwan, ROC} Received 14 September 2002; accepted 25 November 2002

Abstract

In the present study, a hydrophobic zeolite was used as an adsorbent for the adsorption of polyethylene glycol (PEG) in water solution and electroplating solution at 25◦C. The adsorption capacities were determined through the adsorption isotherms in a thermostated shaker. The rate of adsorption, on the other hand, was investigated in a batch adsorber under controlled process parameters such as initial PEG concentration (30, 70, 110, 150, 200, and 300 mg dm−3), agitation speed (200, 800, and 1000 rpm), and adsorbent particle size (0.72,

1.44, and 2.03 mm). A batch kinetic model, according to a pseudo-second-order mechanism, has been tested to predict the rate constant of adsorption, equilibrium adsorption capacity, time of half-adsorption, and equilibrium concentration by the fitting of the experimental data. The results of the adsorption isotherm and kinetic studies show that the adsorption process can well be described with the Langmuir and Freundlich models and the pseudo-second-order equation, respectively. Comparing the values of adsorption parameters of PEG in water solution and electroplating solution, there are no significant differences. In addition, the effective diffusion coefficient of the PEG molecule in the microporous adsorbent has been estimated at about 3.20× 10−8cm2s−1based on the restrictive diffusion model.

Keywords: Liquid-phase adsorption; Polyethylene glycol; Hydrophobic zeolite; Isotherm; Kinetic modeling; Restrictive diffusion

1. Introduction

Recently, copper electroplating has been applied to the formation of microelectronics for printed wiring boards (PWB) and ultra-large-scale integration (ULSI) [1], parallel to the rapid growth of the PWB and semiconductor manufac-turing industries in Taiwan since the mid-1990s. However, the wasted electroplating solution may become one of the major wastewater sources in the PWB industry because the main components of the electroplating solution include cop-per sulfate, sulfuric acid, hydrochloric acid, and some mi-nor additives such as polyethylene glycol (PEG), which is a neutral surfactant and acts as a brightener and stabilizer enhancing the copper deposition rate [2]. Therefore, the ef-fluent discharged from the metal finishing industry must also comply with the stringent standards of chemical oxygen de-mand (COD) for water quality control, i.e., 120 mg dm−3 for the PWB manufacturing industry according to the

Efflu-* _{Corresponding author.}

E-mail address: wwtsai@mail.chna.edu.tw (W.T. Tsai).

ent Standards in Taiwan [3]. Obviously, an advanced process needs to be adopted for industrial wastewater treatment.

There are two principal treatment processes for physico-chemical removal of PEG in water and wastewater: destruc-tive processes such as ozonation [4–7], ozonation/UV [8], or H2O2/UV oxidation [9], and recuperative processes such

as adsorption into activated carbon [10–12] or montmoril-lonite clay [13]. However, in wastewater treatment it is well known that the adsorption process has been considered as the best available technology for removing organic pollu-tants [14,15]. Suzuki et al. [10] studied the adsorption of PEG with molecular weight less than 1500 onto activated carbon to elucidate the limiting adsorption due to limited access to the interior pore structure of carbon adsorbents. Arbuckle and Osman [11] used a series of PEG molecules adsorbed onto activated carbon to expand the Suzuki study. They found the maximum adsorption loading occurred with the soluble polymer in the molecular weight range 1000 to 8000, implying restrictive or hindered adsorption as the molecular weight or size of PEG is compared to the pore size of activated carbon. Chang et al. [12] examined the

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sorption equilibrium of PEG with large molecular weight (ave. 6000) from copper electroplating solutions on acti-vated carbon at 288–313 K, and investigated the feasibil-ity of removing the organic additive from the bath. Zhao et al. [13] reported on adsorption of PEG with molecular weight 300–200,000 onto montmorillonite clays; they found the adsorption rate was rapid, and equilibrium was attained within 30 min. Also, the adsorption capacities for all of the clay adsorbents approached constants for molecular weight of PEG over approximately 2000.

Although activated carbons are the most widely used ad-sorbent in the removal or recovery of organic compounds from liquid-phase streams due to their large surface area and nearly nonpolar surface [16], they still present some disadvantages in that they are flammable materials, diffi-cult to regenerate high-boiling organics, and may promote polymerization of some polymerizable compounds [17]. On the other hand, hydrophobic zeolite or zeolite DAY, a new synthetically produced adsorbent with high Si/Al ratio, does not have these disadvantages and exhibits good adsorption capacity, similar to that of activated carbon. In contrast to the progress in research on PEG adsorption onto activated carbon, fundamental studies on the adsorption of PEG onto hydrophobic zeolite are scarce. Further, it is noted that the polarity of PEG weakens and the affinity of PEG to wa-ter molecules decreases with the increase of its molecular weight [13]. Thus, the main object of this paper is to study the adsorption equilibrium and adsorption rate or kinetics of PEG with large molecular weight in water solution and cop-per electroplating solution at 25◦C, to further evaluate the applicability of common isotherm models (i.e., Langmuir and Freundlich) and the pseudo-second-order rate model of using this inorganic adsorbent for the removal of PEG from aqueous system. In addition, this paper also determines the effective diffusion coefficient, which was estimated based on the restrictive diffusion model, in order to relate to the slow adsorption process when the molecular size of a solute is comparable to the pore size of an adsorbent.

2. Materials and methods

2.1. Materials

The adsorbate used in the adsorption experiments is polyethylene glycol (PEG), which was purchased from Merck Co. (Catalog No. 807491). The general formula of PEG is H(OCH2CH2)nOH, where its molecular weight

(MW) is in the range of 5000–7000 with average value of n between 109 and 158. Hydrophobic zeolite DAY, supplied by Degussa AG (Germany) and commercially prepared via dealumination of sodium Y-zeolite, was employed as adsorbent in the present study. The zeolite was crushed and sieved to mesh ranges of 20 to 30 (average particle size, 0.72 mm), washed with deionized water to remove the suspension residues, dried at 105◦C for at least 24 h, and

finally stored in the desiccator. Its physical properties were as follows [18]: BET surface area, 601 m2g−1; total pore volume, 0.237 cm3g−1; true density, 2.38 g cm−3; particle density estimated from total pore volume and true density [19], 1.52 g cm−3; particle porosity computed from particle density and true density [19], 0.36. Obviously, the material is a microporous adsorbent having an average pore diameter around 15.8 Å, calculated from BET surface area and total pore volume, if the pores are straight, cylindrical, and not interconnected [19]. In addition, its main components are SiO2and Al2O3, having a high Si/Al ratio (>100), which

makes the zeolite hydrophobic [20]. 2.2. Methods

2.2.1. Adsorption equilibrium

The adsorption equilibrium of PEG was determined by using the batch-shaking method as previously described [12]. In each isotherm experiment, adsorption was carried out by shaking with a fixed value (i.e., 0.1 dm3) of PEG (0.1 g) so-lutions at different initial concentrations (35, 70, 100, 150, 200, and 300 mg dm−3) in a thermostated shaker bath at 25± 0.1◦C for all experiments. These PEG solutions were contacted for about 380 h, which had been shown in the preliminary adsorption kinetics experiments and the sys-tem of PEG adsorption onto microporous carbon adsorbent [12], and was well in excess of the contact time require-ment established to reach equilibrium. Equilibrium con-centration analysis of the solutions after filtration with a 0.45-µm fiber membrane was carried out by a TOC analyzer (O.I.C., Model 700) [7,8,12]. The amount of PEG adsorbed was determined by the difference of the initial and equilib-rium liquid-phase concentrations. The amount of PEG ad-sorbed, qe, was determined as

(1) qe= (C0− Ce)V /W,

where C0 and Ce are the initial and equilibrium

liquid-phase concentrations of PEG solution, respectively, V is the volume of the PEG solution, and W is the mass of the dry zeolite sample.

2.2.2. Adsorption kinetics

For all of the adsorption kinetics experiments, about 3 g of the zeolite was put into a 5-dm3 stirred batch adsorber with four baffles in the wall. The adsorber was maintained at 25◦C by water jacket from a refrigerated circulating-water bath prior to the experiment. In each experiment, ca. 3.7 dm3 of the PEG solution was continuously stirred and samples of the solution (ca. 20 cm3) were withdrawn from the adsorber at different intervals until no significant change in the PEG concentration was measured. It was then filtrated with centrifuge filtration. The concentration analysis of filtrate PEG solution was immediately measured with a TOC analyzer (O.I.C., Model 700). The amount of PEG adsorbed was determined as

(2) qt= (C0− Ct)V /W,

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where C0and Ct are the initial and liquid-phase

concentra-tions of the PEG solution at time t , respectively, V is the volume of the PEG solution, and W is the mass of the dry adsorbent. The effects of experimental parameters, such as the initial PEG concentration (30, 70, 110, 150, 200, and 300 mg dm−3), stirring rate (200, 800, and 1000 rpm), and adsorbent size (2.03, 1.44, and 0.72 mm), were investigated in the present study. In each experiment, the adsorption was carried out under conditions where one parameter changed at a time while the other parameters were held constant. 2.2.3. Adsorption of electroplating solution

To simulate the adsorption of electroplating solution, bath solutions of 0.1 dm3 were prepared with H2SO4 of

17 g dm−3, HCl of 7.6 g dm−3, CuSO4·5H2O of 200 g dm−3,

and 30–300 mg dm−3 of PEG in the isotherm experiments described previously. Further, adsorption kinetics of electro-plating solution with initial concentration 70 mg dm−3 in a stirred batch adsorber was tentatively examined to evaluate the differences between the PEG adsorption of electroplat-ing solutions and that of water solutions, also described pre-viously.

3. Results and discussion

3.1. Adsorption isotherm in water solution

In order to optimize the design of an adsorption system to remove the organic pollutant, it is important to establish the most appropriate correlations for the equilibrium data for each system. Two common isotherm equations have been tested in the present study: Langmuir and Freundlich models [14,15]. Applicability of the isotherm equations was compared by judging the correlation coefficients, R2. 3.1.1. Langmuir model

The Langmuir equation is the most widely used two-parameter equation, commonly expressed as

(3) Ce/qe= 1/(KLqm)+ (1/qm)Ce.

In Eq. (3), Ceand qeare as defined in Eq. (1), KLis a direct

measure for the intensity of the adsorption process, and qm

is a constant related to the area occupied by a monolayer of absorbate, reflecting the adsorption capacity. From a plot of Ce/qevs Ce, qm, and KLcan be determined from the slope

and intercept. Table 1 presents the results of the Langmuir

Fig. 1. Isothermal adsorption of PEG in water solution onto zeolite DAY at 25◦C. ", experimental data; —, simulation of Freundlich model; ···, simulation of Langmuir model.

isotherm fits of PEG to the measured adsorption capacity data at 25◦C. The Langmuir isotherm appears to fit the data reasonably well, as reflected by correlation coefficients (R2) in the range of 0.94. Figure 1 shows such a Langmuir isotherm fit for the adsorption of PEG onto zeolite DAY. 3.1.2. Freundlich model

The Freundlich isotherm is an empirical equation and has been shown to be satisfactory for low concentrations. The equation is commonly given by

(4) qe= KFCe1/n,

where KF is a constant for the system, related to the

bond-ing energy. KF can be defined as an adsorption or

distri-bution coefficient and represents the quantity of adsorbate adsorbed onto adsorbents for a unit equilibrium concentra-tion (i.e., Ce = 1 mg dm−3). The slope 1/n, ranging

be-tween 0 and 1, is a measure for the adsorption intensity or surface heterogeneity, becoming more heterogeneous as its value gets closer to zero. A value for 1/n below one indi-cates a normal Langmuir isotherm while 1/n above one is indicative of cooperative adsorption. A plot of ln qevs Ce

en-ables the empirical constants KF and 1/n to be determined

from the intercept and slope of the linear regression. Table 1 presents the Freundlich parameters, also indicating the satis-factorily good correlation between the model predictions and the experimental data. The value of the exponent n is 3.76, depicting favorable adsorption in the present study. On the other hand, it can be seen that the Freundlich model yields a somewhat better fit than the Langmuir model by comparing the results of correlation coefficients (i.e., 0.99 vs 0.94) in

Table 1

Isotherm parameters for adsorption of PEG onto zeolite DAY in water and copper electroplating solutions

Solution Langmuir Freundlich

qm KL R2 KF 1/n R2

(mg g−1) (cm3mg−1) [mg g−1(cm3mg−1)1/n]

Water 155.1 234.4 0.9393 317.9 3.76 0.9856

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Table 1. It is also seen (Fig. 1) that the data for each adsorp-tion isotherm closely lie on the Freundlich line as expected by Eq. (4).

3.2. Adsorption kinetics

The adsorption process on a porous adsorbent in a stirring chamber generally involves several transport stages [14,15]; external diffusion, internal diffusion, and actual adsorption. The model for the separation process should adequately account for the mass balance and the equilibrium isotherm if the system is isothermal. In most cases, the resistance to internal diffusion can be significant. However, the local rate of adsorption is assumed to be relatively fast and the resistance to external diffusion is experimentally controlled to be negligible, compared to the intraparticle diffusion. Although many theoretical model equations have been proposed to describe the adsorption kinetics based on mass balance, pore diffusion rate, and initial/boundary conditions, these equations are not only complicated and impractical in industry, but also require detailed data such as the characteristics of adsorbate and adsorbent.

In the present work, a simple kinetic analysis of adsorp-tion, a pseudo-second-order equaadsorp-tion, was used to fit exper-imental data in the form [21–23]

(5) dqt/dt= k(qe− qt)2,

where k is the pseudo-second-order rate constant (g mg−1 h−1), qe is the amount of PEG adsorbed at equilibrium

(mg g−1), and qt is the amount of PEG adsorbed at time

t (mg g−1). Integrating Eq. (5) for the boundary conditions t= 0 to t = t and qt= 0 to qt= qt gives

(6) 1/(qe− qt)= 1/qe+ kt.

Equation (6) can be rearranged to obtain a linear form, (7) t/qt= 1/(kqe2)+ (1/qe)t.

Rate parameters, k and qe, can be directly obtained from

the intercept and slope of the plot of (t/qt) against t . The

equilibrium concentration (i.e., Ce) can be further calculated

from Eq. (1) as the value of qe has been obtained from the

fitting of Eq. (7). Also, half of the PEG adsorption time, t1/2,

is the time required for the adsorbent to take up half as much PEG as it will at equilibrium (i.e., t= t1/2 as qt = qe/2).

This time is often used as a measure of the rate of adsorption and is given from the rearrangement of Eq. (6) as follows:

(8) t1/2= 1/(kqe).

The effects of the initial PEG concentration, stirring (mix-ing) speed, and adsorbent size on the rate and extent of ad-sorption of PEG were studied at 25◦C and are presented be-low.

3.2.1. Effect of initial concentration

The effect of the initial PEG concentration on the intake rate by zeolite DAY adsorption at adsorbent dosage of 3 g 3.7 dm−3and mixing speed of 800 rpm is shown in Fig. 2, where the experimental data are shown as discrete points and those obtained from the model by solid lines. It is evident from Fig. 2 that the rate of adsorption decreased with time until it gradually approached a plateau due to the continuous decrease in the concentration driving force. The kinetic data obtained from batch studies have been analyzed using the pseudo-second-order model. Values of k, qe, correlation

coefficient (R2), t1/2, and Cefor the PEG adsorption system,

computed from (5)–(8), are listed in Table 2, from which it will be seen that the kinetics of PEG adsorption on zeolite DAY follows this model with regression coefficients higher than 0.99 for all the systems in this study. Clearly, the adsorption capacity (i.e., qe) increases with the initial PEG

concentration (i.e., C0) and equilibrium concentration (i.e.,

Ce), which is also consistent with their adsorption isotherms

described previously. Further, it was found that the variation of rate constant (i.e., k) and t1/2seemed to have a significant

trend with initial PEG concentration.

Fig. 2. Plots of adsorbed amount versus time at various initial PEG concen-trations (adsorbent dosage 3 g 3.7 dm−3, adsorbent particle size 0.72 mm, agitation speed 800 rpm, and temperature 25◦C; symbols: experimental data; full lines: calculated from Eq. (7) and Table 2).

Table 2

Kinetic parameters for adsorption of PEG onto zeolite DAY at various initial concentrations C0 k qe Correlation t1/2 Ce (mg dm−3) (g mg−1h−1) (mg g−1) coefficient (h) (mg dm−3) 30 0.012200 37.037 0.9987 2.213 0.000 70 0.001961 84.746 0.9984 6.017 1.287 110 0.000719 128.205 0.9944 10.848 6.050 150 0.000607 140.845 0.9994 11.697 35.801 200 0.000365 181.818 0.9905 15.069 52.580 300 0.000293 212.766 0.9989 16.041 127.487 Adsorption conditions: adsorbent dosage 3 g 3.7 dm−3, agitation speed 800 rpm, and temperature 25◦C.

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Fig. 3. Plots of adsorbed amount versus time at various agitation speeds (initial PEG concentration 70 mg dm−3, adsorbent dosage 3 g 3.7 dm−3, adsorbent particle size 0.72 mm, and temperature 25◦C; symbols: experi-mental data; full lines: calculated from Eq. (7) and Table 3).

Table 3

Kinetic parameters for adsorption of PEG onto zeolite DAY at various agitation speeds Agitation k qe Correlation t1/2 Ce speed (rpm) (g mg−1h−1) (mg g−1) coefficient (h) (mg dm−3) 200 0.001974 88.496 0.9973 5.724 0.000a 800 0.001961 84.746 0.9984 6.017 1.287 1000 0.000981 94.340 0.9975 10.815 0.000a Adsorption conditions: initial concentration 70 mg dm−3, adsorbent dosage 3 g 3.7 dm−3, and temperature 25◦C.

a_{Values of C}

eare negative based on the rough calculation in Eq. (1). 3.2.2. Effect of agitation speed

The effect of agitation speed on PEG adsorption at an adsorbent dosage of 3 g 3.7 dm−3 and an initial PEG concentration of 70 mg dm−3is shown in Fig. 3 and Table 3. The correlation between the experimental and the model results is again excellent. The data listed in Table 3 indicates that the adsorption capacity (i.e., qe) has no significant

increase and the equilibrium concentration has thus no relative decrease as the agitation speed increases from 200 to 1000 rpm. This effect can be attributed to the strong turbulence and the very small thickness around the adsorbent particles in the boundary layer as a result of the high degree of mixing [24]. However, the variation of rate constant (i.e., k) and t1/2 seemed to have significant trend with the

agitation speed, as depicted in Table 3. 3.2.3. Effect of adsorbent size

The effect of varying the zeolite particle size on PEG ad-sorption at the initial concentration of 70 mg dm−3and mix-ing speed of 800 rpm is shown in Fig. 4. The values of rate parameters for the adsorption system have been obtained and listed in Table 4. It is evident from Fig. 4 that the correlation between the experimental and the model results is also good. It can be expected that the PEG concentration in the solution decreased and the adsorbed amount thus increased at a faster rate as the adsorbent size decreased. Table 4 shows that the adsorption capacity (i.e., qe) increased and equilibrium

con-Fig. 4. Plots of adsorbed amount versus time at various adsorbent particle sizes (initial PEG concentration 70 mg dm−3, adsorbent dosage 3 g 3.7 dm−3, agitation speed 800 rpm, and temperature 25◦C; symbols: experimental data; full lines: calculated from Eq. (7) and Table 4).

Table 4

Kinetic parameters for adsorption of PEG onto zeolite DAY at various adsorbent sizes Size k qe Correlation t1/2 Ce (mm) (g mg−1h−1) (mg g−1) coefficient (h) (mg dm−3) 0.72 0.001961 84.746 0.9984 6.017 1.287 1.44 0.000718 78.740 0.9697 17.688 6.157 2.03 0.000573 70.423 0.9438 24.782 12.900 Adsorption conditions: initial concentration 70 mg dm−3, agitation speed 800 rpm, and temperature 25◦C.

centration thus decreased as the adsorbent size decreased. This behavior can demonstrate that larger surface areas of adsorbent particles are associated with smaller particle size. Also, the intradiffusional resistance to mass transfer is more significant with large particle sizes and consequently most of the internal surface of the particle may not be utilized for adsorption; hence the amount of PEG adsorbed is relatively small [25]. The results obtained from this section of exper-iments also indicated that the rate constant (k) seemed to decrease significantly as the adsorbent size increased. 3.3. Adsorption of electroplating solution

The purpose of electroplating solution adsorption is to evaluate the applicability of isotherm models and pseudo-second-order models described previously. The Langmuir and Freundlich parameters were computed and also are given in Table 1. It is seen that the two models still appear to fit the data well. The Freundlich model yields a somewhat better fit than the Langmuir model when the R2 are com-pared (0.9944 vs 0.9660) (Fig. 5), which is consistent with the results of PEG adsorption in water solution. Compar-ing the values of the monolayer adsorption capacity (qm) of

PEG adsorbed by activated carbon F-400 (qm= 303 mg g−1,

BET surface area = 1026 m2/g) and zeolite DAY (qm=

144 mg g−1, BET surface area= 601 m2/g) in electroplat-ing solution [12], one sees that the ratio of the value of qmof

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Fig. 5. Isothermal adsorption of PEG in electroplating solution onto zeolite DAY at 25◦C. ", experimental data; —, simulation of Freundlich model; ···, simulation of Langmuir model.

Table 5

Kinetic parameters for adsorption of PEG onto zeolite DAY in copper electroplating solution and water solution

Solution k qe Correlation t1/2

(g mg−1h−1) (mg g−1) coefficient (h) Electroplating 0.002079 96.956 0.9984 4.961

Water 0.001961 84.746 0.9984 6.017

Adsorption conditions: initial concentration 70 mg dm−3, adsorbent dosage 3 g 3.7 dm−3, and temperature 25◦C.

Fig. 6. Plots of adsorbed amount versus time in electroplating solution vs water solution (initial PEG concentration 70 mg dm−3, adsorbent dosage 3 g 3.7 dm−3, adsorbent particle size 0.72 mm, agitation speed 800 rpm, and temperature 25◦C; symbols: experimental data; full lines: calculated from Eq. (7) and Table 5).

of their surface areas. The adsorption kinetics in electroplat-ing solution, in the other hand, are given in Table 5 under the conditions of an adsorbent dosage of 3 g 3.7 dm−3, ini-tial PEG concentration of 70 mg dm−3, and mixing speed of 800 rpm. Obviously, there are no significant differences be-tween the adsorptions in electroplating solution and water solution from the data of qe, k, and t1/2(Table 5 and Fig. 6).

3.4. Diffusion coefficient

According to the typical adsorption model [14,15], there are two main mass transfer resistances, external diffusion across the boundary layer surrounding each adsorbent parti-cle and internal diffusion into the porous partiparti-cle. In the pre-vious discussion, it seems that the effect of agitation speed on the rate and capacity of adsorption is negligible in this in-vestigation, implying that the rate of adsorption in the porous adsorbent should be controlled by transport within the pore network. For the liquid-phase diffusion of a solute with large molecular size in porous materials, its effective diffusion co-efficient (De) can be related to the equation describing the

restrictive or hindered diffusion [26,27] as

(9) De= [Dbε/τ]F (λ),

where Db is the bulk diffusion coefficient or diffusivity in

free solution, ε is the porosity, τ is the tortuosity factor of the porous particle ranging from 2 to 7 [20], and F (λ) is a func-tion dependent on the ratio of critical molecular size and pore size (i.e., λ) accounting for steric hindrance/exclusion and hydrodynamic drag effects. In the present study, the bulk diffusivity of PEG in water at 25◦C was estimated using the equation [28]

(10) Db= 1.465 × 10−4× Ma−0.557,

where Ma is the average molecular weight of PEG with the

value of 6000. Substituting in Eq. (10), we obtain 1.152× 10−6cm2s−1for bulk diffusivity of PEG in water. The criti-cal molecular size is defined as the minimum cross-sectional diameter of the adsorbate molecule and may be estimated from bond lengths, bond angles, and van der Waals radii [20]. According to the side view of the PEG molecule and the data on the molecular structure [29], the critical dimen-sion is approximately to 0.55 nm. Therefore, the value of λ is approximately 0.348 (= 0.55 nm/1.58 nm) based on average pore diameter, commonly calculated from the total pore vol-ume and BET surface area [19]. For λ < 0.5, a commonly used expression for the restrictive diffusion effect was de-rived by Renkin [30], given by

(11) F (λ)=1− λ21− 2.104λ + 2.09λ3− 0.95λ5.

De for the intraparticle transport of PEG within the pores

of zeolite DAY has been estimated to 3.204× 10−8cm2s−1 based on Db= 1.152 × 10−6cm2s−1, ε= 0.36, τ = 4 [20]

and F (λ)= 0.309. The obtained value of the effective dif-fusivity is compared to the typical reported diffusion coeffi-cients (ca. 10−8 cm2s−1) in zeolites found in the literature [20]. Further work would be helpful in order to elucidate sur-face diffusion of flexible chains of PEG molecule [31] and simulate the adsorption system based on either liquid film resistance or pore diffusion resistance [14,15].

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4. Conclusions

The use of hydrophobic zeolite for the adsorption of PEG from aqueous solutions has been examined at 25◦C. The following conclusions can be drawn:

• The adsorption isotherm can be well correlated by Langmuir and Freundlich models.

• The adsorption kinetics can be well described by the pseudo-second-order model equation.

• The effect of the initial PEG concentration and adsor-bent particle size on the rate of adsorption and the equi-librium adsorption was found to be of considerable sig-nificant.

• The intraparticle diffusion mechanism plays a signifi-cant role in the adsorption system based on the results of the effect of adsorbent size on the rate of adsorption and the equilibrium adsorption capacity.

• The results of this research were found to be in agree-ment with those for similar adsorption systems, e.g., the PEG–activated carbon adsorption system.

• The effective diffusion coefficient, estimated based on the restrictive diffusion model, is compared to the published data in the literature.

• A feasible process option would comprise the adsorp-tion of PEG from copper electroplating soluadsorp-tion by hy-drophobic zeolite and then recycle the bath with subse-quent addition of new organic additive.

Acknowledgments

This research was partly supported by the NSC (National Science Council), Taiwan, under Contracts NSC 89-2211-E-002-025 and NSC 89-2211-E-041-006. The authors also thank the Powder Technology Laboratory of Chemical Engineering Department of National Taiwan University for assistance in characterizing the zeolite adsorbent.

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