LiquidâLiquid Equilibrium of Aqueous Biphasic Systems Containing

Article pubs.acs.org/jced

Liquid−Liquid Equilibrium of Aqueous Biphasic Systems Containing Ethylene Oxide−Propylene Oxide Block Copolymers and Maltodextrins Elias S. Monteiro Filho,†,§ Pedro A. Pessôa Filho,*,‡ and Antonio José A. Meirelles† †

Department of Food Engineering, University of Campinas, Campinas, São Paulo, Brazil Department of Chemical Engineering, University of São Paulo, São Paulo, São Paulo, Brazil

‡

ABSTRACT: This work presents liquid−liquid phase equilibrium data of ternary systems formed by aqueous mixtures of ethylene oxide−propylene oxide block copolymers and maltodextrin. Phase diagrams were obtained for five copolymers (with EO ratios ranging from 20 % to 80 % and molar masses ranging from 1900 g·mol−1 to 8400 g·mol−1) and three maltodextrins (with number averaged molar masses of 990 g·mol−1, 1500 g·mol−1, and 3000 g·mol−1) at 298.2 K and 308.2 K. The main factor influencing the phase diagrams is the ratio between ethylene oxide and propylene oxide chain sizes. The size distribution of maltodextrin was studied through gel permeation chromatography, and the size distribution of some equilibrium phases was also determined. Maltodextrin was found to partition unevenly between equilibrium phases, with larger molecules being excluded from the polymer-rich phases. The phase equilibrium was modeled using the UNIQUAC equation and with the consideration that maltodextrin can be represented by six pseudocomponents. It was verified not only that the model can adequately describe the phase equilibrium but also that the uneven distribution of maltodextrin molecules can be qualitatively assessed.

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INTRODUCTION Aqueous two-phase systems are formed by the simultaneous dissolution, in water, of certain pairs of substances in certain concentration ranges. Pairs of phase-forming substances include two neutral polymers (poly(ethylene glycol) and dextran, for instance), a neutral polymer and a salt (poly(ethylene glycol) and potassium phosphate), a polyelectrolye and a neutral polymer (poly(sodium acrylate) and poly(ethylene glycol)), and, as recently demonstrated, an ionic liquid and an inorganic salt.1 The use of aqueous two-phase systems in biomolecule downstream can be regarded as a well-established technique, with many applications in both laboratory and industrial scale.2 Although the most extensively used aqueous two-phase systems are those formed by poly(ethylene glycol) and either salts or dextran, there subsists the research on the description of new systems. There are two main reasons for it. First, as aqueoustwo phase extraction is usually placed at the beginning of a separation train, it must be as inexpensive as possible because its resolution is lower than the chromatographic steps. Second, new aqueous two-phase systems may be more suitable for the separation of certain mixtures than existing ones. Maltodextrin is a linear-chain carbohydrate with large applicability in food and pharmaceutical industries as a cheap, tasteless, and noncrystallizing carrier for either food ingredients or pharmaceuticals. It is obtained from starch by enzymatic treatment. Some authors3−5 suggested its use as phase-forming polymer (replacing the more expensive dextran) in aqueous two-phase systems, but no systematic investigation on this use has already been carried out. This carbohydrate is actually a © 2014 American Chemical Society

mixture of many glucose polymers, ranging from monomer (glucose) and dimer (maltose) to polymer chains containing more than one thousand monomer units. This polydispersity may influence the phase equilibrium;6 as an example, dissimilar chains tend to be differently partitioned between equilibrium phases.7 Block copolymers formed by ethylene oxide and propylene oxide (EO−PO) chains have been investigated as phaseforming agents.8−10 Their molecules have a hydrophilic region (the EO chain) and a hydrophobic one (the PO chain). Because of the strong dependence of their solubility in water on temperature, some researchers suggested that these polymers can be recovered by means of controlling the medium temperature once the desired purification process is finished.8,9 Depending on their molar masses and EO/PO ratio, those polymers are also useful as lubricant components and antifoam agents, among other possible usages. The use of EO−PO block copolymers as constituents of aqueous two-phase systems has been long demonstrated. They can induce phase separation along with salts11−13 and polysaccharides such as dextran.14−17 On the other hand, the use of maltodextrin as a phaseforming polymer in aqueous two-phase systems is not common. Among the few examples, one can cite the works by Silva and Meirelles,4 who described systems formed by poly(ethylene glycol) and maltodextrin, Silva and Meirelles,5 with polyReceived: April 28, 2014 Accepted: June 12, 2014 Published: June 23, 2014 2310

dx.doi.org/10.1021/je500375x | J. Chem. Eng. Data 2014, 59, 2310−2319

Journal of Chemical & Engineering Data

Article

(propylene glycol) and maltodextrin, and Picó et al.,18 with EO−PO random copolymers and maltodextrin. These works show that maltodextrin may be a suitable phase-forming polymer. The present work focuses on the determination of phase equilibrium diagrams of aqueous two-phase systems containing block copolymers and maltodextrin. The effect of maltodextrin chain size, copolymer structure and temperature was studied. In order to assess the effect of polydispersity on the phase equilibrium, the partition of phase-forming components between the phases was investigated by means of gel permeation chromatography (GPC) experiments. The thermodynamic modeling of the experimental data was carried out accounting for this polydispersity.

Table 2. Characteristics of the Maltodextrins maltodextrin

MD1910 MD1914 MD1920

supplier

% CP20/2100 CP40/2450 CP40/2900 CP50/1900 CP80/8400

99.4 99.4 99.8 99.4 99.4

PE 62 PE 64 43.544-9 43.541-4 41.232-5

Oxiteno Oxiteno Aldrich Aldrich Aldrich

EOb

Mnb

%

g·mol−1

20 40 40 50 80

2100 2450 2900 1900 8400

Mass fraction, calculated from the degree of humidity determined through Karl Fischer titration. bGiven by the manufacturer.

nomenclature was employed instead of the supplier’s commercial nomenclature: each copolymer is identified as CPXX/YYYY, wherein “CP” means copolymer, the first number (XX) represents the EO molar percentage in the polymer molecule, and the second one (YYYY) represents its average molar mass. For instance, the block copolymer of commercial name 43.544-9, which has 40 % of EO in the molecule and average molar mass of 2900 g·mol−1, is identified as CP40/2900. The characteristics of the maltodextrins are presented in Table 2. From the information on dextrose equivalent (DE) given by the manufacturer, the average degree of polymerization DP (i.e., the average number of glucose units in the chain) and the number-average molar mass Mn can be calculated through 1000 − DE(%) 9·DE(%)

M n = 162·DP + 18

11 13 20

10.4 8.4 5.4

Mwe

Mne

g· mol−1

g·mol−1

g· mol−1

1640 1380 900

44300 20500 8800

3000 1500 990

Mw/ Mn

14.8 13.6 8.9

maltodextrins are very polydisperse. Sample humidity (according to Tables 1 and 2) was accounted for when calculating the mass fractions. Methods. System Preparation. To prepare the aqueous two-phase systems, water, copolymer, and maltodextrin were gravimetrically added in definite amounts to test tubes and vigorously mixed in a stirrer. After the complete solubilization of the substances, the tubes were centrifuged at 4000g for at least 20 min in a thermostatted centrifuge (Jouan BR4i, France) and kept overnight in a thermostatic bath at 298.2 K (Cole Parmer, New York, U. S. A.). The temperature was controlled within 0.1 K. After phase separation, samples of top and bottom phase were collected with syringes; to avoid contamination, the top phase was completely withdrawn before sampling the bottom phase. Composition Determination. The concentration of carbohydrate in each sample was obtained through polarimetry at 589 nm (Perkin-Elmer Model 343 Polarimeter, New York, U. S. A.) after proper dilution in either deionized water or mixtures of water and analytical grade ethanol. The water content was determined by freeze-drying (EZ-Dry Model, FTS Systems, New York, U. S. A.), and the synthetic polymer content was determined by difference. The same methodology had been used in previous works with good results.4,20 A mass balance was calculated according to the procedure suggested by Marcilla et al.21 and Rodrigues et al.;22 in the present case, differences of less than 0.5 % were observed for all the experimental compositions. Size Distribution. In order to assess the size distribution of maltodextrin molecules, gel permeation chromatography (GPC) was carried out with some phase samples. The analyses were made on HPLC equipment (Varian Model 9095, Varian Associates, Inc., U. S. A.). Three columns with different size exclusion capacities suited to the reagents employed (columns G 3000 PW, G 4000 PW, and G 6000 PW, Supelco, U. S. A.) and a guard column (Micropak Series, Varian Associates Inc., U. S. A.) were used. They were coupled to a refractive index detector (Varian Model R14, Varian Associates Inc., U. S. A.), maintained at 40 °C. The refractive index detector was calibrated using solutions of glucose, maltose, maltotriose, and dextran of different chain sizes. Deionized water was employed as eluent, and the flow rate was 1.0 mL·min−1. Before the analysis, each sample was diluted to mass fractions of about 1 %. Sample sizes of 2.0 mL were used in each run. Each phase sample was analyzed once. Data analysis was conducted by proper software (Millennium Chromatography Manager, Version 2.1, Waters Corp., U. S. A.) with built-in calibration curves adequate to the carbohydrate.

a

DP =

95.6 95.4 96.0

Mnd

Mass fraction, calculated from the degree of humidity determined through freeze-drying. bDextrose equivalent, as given by the manufacturer. cDegree of polymerization, calculated from the DE value. dNumber-average molar mass, calculated from the DP value. e Obtained through gel permeation chromatography.

Table 1. Characteristics of the Block Copolymers commercial name

DPc

a

MATERIALS AND METHODS Materials. Block copolymers of ethylene oxide (EO) and propylene oxide (PO) units were either purchased from Aldrich (U. S. A.) or donated by Oxiteno S/A (Brazil). Maltodextrins were donated by Corn Products Brasil S/A (Brazil). These products were used without subsequent purification. Deionized water (Milli-Q Plus, Millipore Corporation, U. S. A.) was used in all experiments. The characteristics of the copolymers used are presented in Table 1. In order to facilitate understanding, an alternative

puritya

DEb

%

■

copolymer

puritya

(1) (2)

The number-average and the mass-average (Mw) molar masses as calculated from GPC experiments are also presented in Table 2. The ratio Mw/Mn is the so-called dispersity,19 and constitutes an indication of how polydisperse is a certain polymer sample: the values observed show that these 2311



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Table 3. Equilibrium Compositions of Systems Containing MD 1910 at 298.2 K: Mass Fractions of Copolymer (1) and Maltodextrin (2)a overall

a

top phase

bottom phase

copolymer

temperature

w1

w2

w1

w2

w1

w2

CP20/2100

298.2 K

CP40/2450

298.2 K

CP40/2900

298.2 K

CP50/1900

298.2 K

CP80/8400

298.2 K

0.145 0.230 0.232 0.248 0.075 0.098 0.116 0.169 0.084 0.106 0.101 0.117 0.080 0.100 0.118 0.133 0.063 0.119 0.129 0.143

0.118 0.137 0.170 0.202 0.155 0.173 0.204 0.223 0.159 0.193 0.192 0.223 0.231 0.226 0.262 0.285 0.226 0.204 0.221 0.246

0.223 0.401 0.457 0.548 0.120 0.156 0.218 0.327 0.266 0.184 0.312 0.166 0.115 0.152 0.208 0.253 0.126 0.191 0.214 0.251

0.059 0.044 0.045 0.038 0.108 0.093 0.082 0.060 0.075 0.088 0.069 0.098 0.165 0.130 0.113 0.100 0.104 0.077 0.076 0.072

0.046 0.036 0.027 0.028 0.033 0.019 0.008 0.000 0.008 0.019 0.000 0.009 0.030 0.008 0.000 0.000 0.000 0.000 0.000 0.000

0.166 0.243 0.286 0.343 0.233 0.283 0.334 0.406 0.332 0.286 0.393 0.319 0.325 0.390 0.459 0.501 0.357 0.431 0.462 0.496

Estimated standard uncertainties u: u(T) = 0.1 K, u(w1) = 0.002, u(w2) = 0.003.

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MD1910 (Mw = 44 kg·mol−1), 0.58 for MD1914 (Mw = 20.5 kg·mol−1), and 0.66 for MD1920 (Mw = 8.8 kg·mol−1). This analysis shows that, in this case, little change in phase behavior is introduced by replacing dextran by maltodextrin. The effect of maltodextrin average size on the phase equilibrium can be seen in Figure 1, wherein systems containing CP20/2100 and maltodextrins at 298.2 K are presented. In this and in the following figures, for the sake of readability, only the binodal curve and the tie line with higher tie-line length are presented. As the tie-line slope is approximately constant for each system, the general pattern can be straightforwardly inferred from the figures. The biphasic region for MD 1910 is reached at lower concentrations than for MD 1914, and MD 1920 requires even higher concentrations to produce biphasic systems. The tie-line slope, nevertheless, is approximately the same for the different systems. An analogous behavior can be verified by the comparison between samples containing CP40/2450 and CP40/2900 and MD 1920 at 298.2 K, shown in Figure 2. In this case, the small difference between the copolymer chain sizes results in almost coincident phase diagrams; one can assume that the small difference in polymer chain size is mostly within the uncertainty of this kind of measurement. The effect of copolymer EO/PO ratio can be seen in Figure 3, wherein systems containing MD 1910 and CP20/2100, CP40/2450, and CP50/1900 at 298.2 K are presented. One can assume that the differences in copolymer chain size are negligible. Considering the influence of copolymer EO/PO ratio, the higher this ratio is, the smaller the biphasic region and the lower the absolute value of the tie-line slope are. This behavior is related to the fact that the ethylene oxide (EO) part of the molecules is more hydrophilic than the propylene oxide (PO) part, and higher concentrations are needed to induce phase separation. Finally, the effect of temperature can be seen in Figure 4, wherein systems containing CP40/2450 and MD 1914 are presented. The biphasic region is not influenced by

RESULTS AND DISCUSSION Liquid−Liquid Equilibrium. The experimental compositions of coexisting phases are presented in Table 3 (for systems containing MD1910), Table 4 (for systems containing MD 1914), and Table 5 (for systems containing MD 1920). In some aspects, the data herein presented follow the general pattern of two-polymer aqueous biphasic systems, chiefly those systems formed by block-copolymers and other polysaccharides such as dextran. The biphasic region is influenced by the chain size of both the polymer and carbohydrate molecules: in general terms, the larger the molar mass of the constituents, the broader the biphasic region. This behavior is usually related to the so-called “excluded volume” effect. Polymer-rich phases contain appreciable amounts of carbohydrate, but carbohydrate-rich phases contain smaller (in some cases undetectable) amounts of polymer. The water fraction tends to be higher in the polymer-rich phases of molecules with larger EO content (CP50/1900 and CP80/8400). For copolymer with smaller EO content (CP20/2100), the water content is higher in the maltodextrin-rich phase, which can be ascribed to the higher hydrophilic character of the polysaccharide; a similar behavior was observed in systems containing PEG and maltodextrin4 or PPG and maltodextrin,5 as well as in systems containing blockcopolymers and dextran.17 The slope of the tie-lines is approximately independent of the tie-line length, but it does depend on the temperature and on the copolymer structure. Systems containing CP80/8400 and maltodextrin can be compared to systems containing the same copolymer and dextran.17 It can be seen that the tie-line slopes (defined by the ratio of the difference in copolymer mass fractions to the difference in carbohydrate mass fractions) are similar for these systems and follow a definite pattern related to the carbohydrate chain size: average absolute values of tie-line slopes are 0.51 for systems containing dextran 400 (Mw = 410 kg·mol−1), 0.61 for dextran 19 (Mw = 11.6 g·mol−1), 0.54 for 2312



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Table 4. Equilibrium Compositions of Systems Containing MD 1914: Mass Fractions of Copolymer (1) and Maltodextrin (2)a overall

bottom phase

temperature

w1

w2

w1

w2

w1

w2

CP20/2100

298.2 K

0.152 0.168 0.181 0.199 0.150 0.160 0.175 0.215 0.090 0.100 0.125 0.170 0.091 0.100 0.150 0.181 0.087 0.089 0.100 0.125 0.170 0.080 0.102 0.122 0.166 0.010 0.105 0.120 0.175 0.080 0.100 0.118 0.133 0.060 0.093 0.117 0.167

0.149 0.173 0.181 0.199 0.155 0.175 0.185 0.200 0.186 0.211 0.222 0.226 0.181 0.220 0.200 0.222 0.201 0.191 0.220 0.227 0.235 0.197 0.204 0.217 0.223 0.175 0.205 0.220 0.225 0.242 0.237 0.275 0.299 0.211 0.243 0.226 0.307

0.257 0.302 0.324 0.411 0.338 0.386 0.412 0.506 0.121 0.149 0.193 0.263 0.141 0.188 0.245 0.329 0.154 0.140 0.240 0.292 0.362 0.132 0.182 0.230 0.301 0.167 0.233 0.256 0.338 0.115 0.152 0.208 0.253 0.106 0.179 0.202 0.329

0.073 0.067 0.064 0.054 0.055 0.052 0.045 0.037 0.111 0.105 0.091 0.072 0.105 0.093 0.077 0.064 0.124 0.130 0.094 0.081 0.067 0.075 0.093 0.105 0.128 0.121 0.099 0.093 0.074 0.165 0.130 0.113 0.100 0.121 0.100 0.092 0.077

0.032 0.025 0.018 0.021 0.016 0.012 0.011 0.011 0.008 0.002 0.000 0.000 0.023 0.014 0.004 0.007 0.023 0.029 0.015 0.011 0.006 0.057 0.016 0.008 0.003 0.050 0.023 0.018 0.013 0.030 0.008 0.000 0.000 0.000 0.000 0.000 0.000

0.243 0.277 0.310 0.339 0.214 0.243 0.264 0.314 0.342 0.380 0.426 0.465 0.268 0.332 0.371 0.399 0.258 0.244 0.279 0.312 0.365 0.221 0.306 0.347 0.400 0.200 0.254 0.296 0.352 0.325 0.390 0.459 0.501 0.327 0.412 0.450 0.570

308.2 K

CP40/2450

288.2 K

298.2 K

308.2 K

CP40/2900

298.2

308.2 K

a

top phase

copolymer

CP50/1900

298.2 K

CP80/8400

298.2 K


Table 5. Equilibrium Compositions of Systems Containing MD 1920 at 298.2 K: Mass Fractions of Copolymer (1) and Maltodextrin (2)a overall

a

top phase

bottom phase

copolymer

temperature

w1

w2

w1

w2

w1

w2

CP20/2100

298.2 K

CP50/1900

298.2 K

CP80/8400

298.2 K

0.135 0.231 0.202 0.151 0.087 0.093 0.134 0.135 0.057 0.091 0.129 0.166

0.180 0.253 0.230 0.203 0.325 0.326 0.313 0.323 0.288 0.280 0.279 0.298

0.484 0.393 0.233 0.520 0.156 0.181 0.259 0.270 0.113 0.163 0.225 0.292

0.056 0.073 0.119 0.056 0.217 0.195 0.144 0.143 0.194 0.162 0.141 0.127

0.018 0.035 0.041 0.014 0.054 0.041 0.027 0.023 0.004 0.000 0.000 0.000

0.337 0.273 0.234 0.395 0.390 0.409 0.454 0.471 0.367 0.422 0.480 0.532


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Figure 1. Phase diagrams for systems containing copolymer CP20/ 1000 (1) and maltodextrins (2) at 298.2 K. □ and continuous line, systems containing MD1910; ◊ and dotted line, systems containing MD 1914; △ and dashed line, systems containing MD 1920. Binodal curves are shown to guide the eyes.

Figure 3. Phase diagrams for systems containing copolymers (1) and maltodextrin MD 1910 (2) at 298.2 K. □ and continuous line, systems containing CP20/2100; ◊ and dotted line, systems containing CP40/ 2450; △ and dashed line, systems containing CP50/1900. Binodal curves are shown to guide the eyes.

Figure 2. Phase diagrams for systems containing copolymers (1) and maltodextrin MD 1920 (2) at 298.2 K. □ and continuous line, systems containing CP40/2450; ◊ and dotted line, systems containing CP 40/ 2900. Binodal curves are shown to guide the eyes.

Figure 4. Phase diagrams for systems containing copolymer CP40/ 2450 (1) and maltodextrin MD 1914 (2) at different temperatures. □ and continuous line, systems at 288.2 K; ◊ and dotted line, systems at 298.2 K; △ and dashed line, systems at 308.2 K. Binodal curves are shown to guide the eyes.

the change in temperature, except for the fact that at 308.2 K, this region is slightly smaller due to an increase in the amount of maltodextrin in the copolymer phase. The tie-line slope and length, however, are strongly affected by the temperature. This behavior can be related to the aggregation of block-copolymers, which is strongly dependent on temperature.23 Polydispersity. As shown by the ratio Mw/Mn, the maltodextrin samples used in this work are highly polydisperse.

The mass distribution obtained through GPC is presented in Figure 5 for the three maltodextrin samples. The size distribution has a common shape with two maxima, but all samples show a broad mass distribution, ranging from monomer and oligomers to high molar mass polymer chains. Some equilibrium phases were also analyzed through GPC to assess the effect of polydispersity on the phase equilibrium; 2314



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Figure 6. Size distribution in equilibrium phases (system CP20/2100 and MD 1920, with overall composition presented in Table 6) as obtained through gel permeation chromatography. Continuous line, top phase; dotted line, bottom phase.

Table 7. Area and Surface Parameters for UNIQUAC Equationa component

r

q

MD 1920 MD 1914 MD 1910 CP20/2100 CP40/2450 CP40/2900 CP50/1900 CP80/8400 Water

39.6 60.0 118.9 80.9 92.5 110.2 72.1 308.6 0.92

36.5 54.8 107.8 66.6 76.4 90.9 59.7 255.0 1.40

a

Carbohydrate parameters calculated from Peres and Macedo,26 copolymer parameters calculated from Balsev and Abildskov.27 Figure 5. Size distribution in maltodextrin samples as obtained through gel permeation chromatography. (A) Mass fractions; (B) cumulative mass fractions. Continuous line, MD 1920; dotted line, MD 1910; dashed line, MD 1914.

these systems are identified in Table 6, wherein the results for the average molar masses for top and bottom phases are presented. Segregation differences can be observed by comparing these data with those for hypothetical systems

Table 6. GPC Analysis of Equilibrium Phases at 298.2K for Systems Containing Copolymer (1) and Maltodextrin (2) GPC data feed composition

top phase

calculated bottom phase

top phase

bottom phase

maltodextrin

copolymer

w1

w2

Mn

Mw

Mn

Mw

Mn

Mw

Mn

Mw

MD 1910

CP20/2100

0.145 0.230 0.063 0.152 0.060 0.135 0.140 0.087 0.057

0.118 0.137 0.226 0.149 0.211 0.180 0.200 0.325 0.288

1200 1350 2250 1150 2450 1150 1650 900 2150

1900 2700 4400 1600 4800 2000 5300 1600 4300

2800 2850 2850 2500 2550 1950 2150 2450 2550

25100 35400 27600 24000 24000 18300 24900 21200 12500

2300 2200 6000 2000 4700 2000 2200 1300 3700

11100 6300 24950 6200 14800 2800 3500 1700 8650

2800 2900 3000 1550 1500 1050 1000 1100 1100

35800 39500 45000 18300 20450 8450 8700 8000 8800

MD 1914 MD 1920

CP80/8400 CP20/2100 CP80/8400 CP20/2100 CP40/2450 CP50/1900 CP80/8400

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Table 8. Description of Maltodextrin Samples with Six Pseudocomponents. MD 1920

MD 1914

wi

pseudocomponent

Mi

wi −1

g mol 1 2 3 4 5 6

0.0577 0.4984 0.2618 0.1333 0.0407 0.0080

MD 1910 Mi g mol

241.258 685.896 3492.91 21955.1 111806 317864

0.0346 0.3863 0.2942 0.2373 0.0441 0.0036

wi

Mi

−1

248.104 789.367 4790.04 36699.6 222700 708542

g mol−1 0.0159 0.2430 0.3050 0.3536 0.0760 0.0066

320.691 1062.46 6866.83 56494.5 365132 1209691

Table 9. Interaction Parameters for the UNIQUAC Equation. component i component j CP20/2100 CP40/2450 CP40/2900 CP50/1900 CP80/8400 Water

Aij/K Aji/K Aij/K Aji/K Aij/K Aji/K Aij/K Aji/K Aij/K Aji/K Aij/K Aji/K

MD 1920

MD 1914

MD 1910

Water

62.3 47.57 224.68 −2.11 −94.87 227.96 1999.97 2184.26 −345.92 190.2 −213.03 −221.55

42.3 97.41 215.91 −21.6 −90.74 229.69 2647.11 2999.34 −350.03 188.32 −197.1 −536.44

165.43 −927.59 218.12 −24.06 383.24 −63.81 1700.86 2019.26 −360.42 184.17 −199.81 −380.03

−413.97 −340.76 −136.01 −104.99 −591.16 36.95 544.15 −526.56 −355.64 −402.01

Table 10. Average Deviations (in Mass Percent) for Phase Equilibrium Calculations Using the UNIQUAC Equation system CP20/2100 CP20/2100 CP20/2100 CP40/2900 CP40/2900 CP40/2900 CP50/1900 CP50/1900 CP50/1900 CP80/8400 CP80/8400 CP80/8400

+ + + + + + + + + + + +

MD 1910 MD 1914 MD 1920 MD 1910 MD 1914 MD 1920 MD 1910 MD 1914 MD 1920 MD 1914 MD 1920 MD1910

number of pseudocomponents 1

6

1.71 0.70 1.95 1.99 2.12 2.08 1.46 0.98 5.78 4.58 0.31 0.22

1.99 0.68 1.87 1.47 1.17 1.03 1.39 0.89 0.63 0.36 0.31 0.67

Figure 7. Liquid−liquid equilibrium for the system CP 40/2450 (1) and MD 1914 (2) at 298.2 K. Triangles and continuous line, experimental compositions; dotted line, UNIQUAC equation considering maltodextrin as a monodisperse compound; dashed line, UNIQUAC equation considering maltodextrin as a mixture of six pseudocomponents.

from the literature that molecules with different sizes may be segregated between the equilibrium phases.24 The data obtained confirms this fact for systems containing maltodextrins and sheds light upon this phenomenon. This fact also explains the few exceptions observed in Table 6 (calculated dispersities larger than the actual ones): they occur for systems containing larger copolymer molecules. In this case, the fact that larger maltodextrin molecules are excluded from the top phase leads to a decrease of the dispersity of that phase. Modeling. The liquid−liquid equilibrium was modeled using the UNIQUAC equation for the excess Gibbs energy; the activity coefficient of a certain compound i is given by

calculated by considering that the values of Mn and Mw correspond to an even distribution of carbohydrate molecules, that is, considering the fact that the carbohydrate in either top or bottom phase has the same size distribution as the maltodextrin sample. In most cases, these hypothetical systems show larger dispersities, which indicates that the actual distribution is narrower than the calculated ones. An example of GPC distributions is shown for equilibrium phases of the system containing CP20/2100 and MD 1920 in Figure 6. The largest peak for the distribution in the top phase in this figure corresponds to the copolymer. The GPC curve for larger molecule sizes in the top phase is observed to vanish, even though the maltodextrin mass fraction in that phase is 5.6 %, indicating that high molar mass carbohydrate molecules are virtually excluded from the polymer-rich phases. It is known

⎛θ ⎞ ⎛ϕ⎞ ϕ z ln γi = ln⎜ i ⎟ + qi ln⎜⎜ i ⎟⎟ + li − i xi 2 ⎝ xi ⎠ ⎝ ϕi ⎠ − qi ln ∑ θτ j ji + qi − qi ∑ j

j

∑ xjlj j

θτ j ij ∑k θkτkj

(3)

wherein γ is the activity coefficient, q is the surface parameter, r is the volume parameter, ϕ is the volume fraction, θ is the surface fraction, x is the mole fraction, T is the absolute temperature, and z is the number of nearest neighbors, which 2316



Article D

S=

N K−1

∑∑ ∑ m

n

i

2 ⎡⎛ I,ex I,calc ⎞ ⎛ w II,ex − w II,calc ⎞2 ⎤ i ,n,m ⎟ ⎥ ⎢⎜ wi , n , m − wi , n , m ⎟ ⎜ i ,n,m ⎟ +⎜ ⎟⎥ ⎢⎜ I II σ σ wi , n , m wi , n , m ⎠ ⎝ ⎠⎦ ⎣⎝

(6)

in which wi,n,m is the mass fraction of component i in tie line n and in data group m, the superscripts I and II stand for phases I or II, respectively, superscripts ex and calc stand for experimental and calculated data points, respectively, D is the total number of data groups, N is the total number of tie lines in each group, and m and K are the number of components in the mth data group. σwIi,n,m and σwIIi,n,m are the average standard deviations observed in the compositions of the two liquid phases. The minimization was performed through a modified Simplex method. For the modeling, the maltodextrin sample was considered a mixture of different pseudocomponents. The number and structure of these pseudocomponents were obtained through the Gauss-Laguerre procedure, as follows: considering a certain distribution function F(M), as presented in Figure 5A

∫0

∞

F(M )dM = 1.0

(7)

wherein M is the molar mass. One can replace the above integral by a summation

∫0

n

∞

F(M )dM =

∑ ωiF(Mi)exp(Mi) i=0

(8)

wherein ωi is the weight corresponding to the root Mi of the Laguerre polynomial. These roots correspond to the molar masses of the pseudocomponents. The mole fraction of each pseudocomponent (xi) is given by xi =

(9)

The minimization procedure was conducted considering different number of pseudocomponents. It was observed that using more than six pseudocomponents did not change equilibrium calculations, in agreement with literature.25 Therefore, the calculations were carried out considering either a single pseudocomponent (i.e., considering a monodisperse system) or six pseudocomponents. When considering polydispersity, the structure parameters for the maltodextrin pseudocomponents were calculated through ri = 0.03982·(Mi/ g·mol−1) and qi = 0.03627·(Mi/g·mol−1), wherein Mi is the molar mass of each pseudocomponent. The characterization of the six pseudocomponents of each sample of maltodextrin is presented in Table 8. The parameters obtained through the minimization procedure are presented in Table 9, whereas the average deviations (given by equation 6) are presented in Table 10. It can be seen that considering the polydispersity of maltodextrin does improve equilibrium calculations for most systems. A comparison between both approaches (with and without considering polydisperisty) can be seen in Figure 7 for the system CP40/2450 and MD 1914 at 298.2 K. As the equation used to describe liquid-phase nonideality is the same, the consideration of polydispersity is the main factor affecting the phase equilibrium calculations. The most important aspect of considering the polydispersity in equilibrium calculations is that it allows a reasonable description of the size segregation of the maltodextrin sample.

Figure 8. Size distribution in equilibrium phases (system CP80/8400 and MD 1920, with overall composition presented in Table 6) (A) top phase and (B) bottom phase. Continuous line, cumulative mass fractions obtained through gel permeation chromatography; dashed line, cumulative mass fractions calculated using the UNIQUAC equation considering maltodextrin as a mixture of six pseudocomponents.

was considered to be constant equal to 10. Parameters li and τij are defined respectively by z li = (rj − qj) − (rj − 1) (4) 2 and ⎛ Aij ⎞ τij = exp⎜ − ⎟ ⎝ T⎠

ωiF(Mi)exp(Mi) n ∑ j = 0 ωjF(Mj)exp(Mj)

(5)

wherein Aij is the binary interaction parameter. The structure parameters of the UNIQUAC equation are presented in Table 7. The interaction parameters were obtained through the minimization of the following objective function S 2317



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(3) Szlag, D. C.; Giuliano, K. A.; Snyder, S. M. A low cost aqueous two-phase system for enzyme extraction. Biotechnol. Technol. 1990, 4, 277−282. (4) Silva, L. H. M.; Meirelles, A. J. A. Phase equilibrium in poly(ethylene glycol)/maltodextrin aqueous two-phase systems. Carbohydr. Polym. 2000, 42, 273−278. (5) Silva, L. H. M.; Meirelles, A. J. A. Phase equilibrium in aqueous mixtures of maltodextrin with polypropylene glycol. Carbohydr. Polym. 2001, 46, 267−274. (6) Cabezas, H., Jr. Theory of phase formation in aqueous two-phase systems. J. Chromatogr. B: Biomed. Sci. Appl. 1996, 680, 3−30. (7) Conneman, M.; Gaube, J.; Leffrang, U.; Müller, S.; Pfennig, A. Phase equilibria in the system poly(ethylene glycol) + dextran + water. J. Chem. Eng. Data 1991, 36, 446−448. (8) Persson, J.; Johansson, H.-O.; Galaev, I.; Matiasson, B.; Tjerneld, F. Aqueous polymer two-phase systems formed by new thermoseparating polymers. Bioseparation 2000, 9, 105−116. (9) Persson, J.; Kaul, A.; Tjerneld, F. Polymer recycling in aqueous two-phase extractions using thermoseparating ethylene oxide− propylene oxide copolymers. J. Chromatogr. B: Biomed. Sci. Appl. 2000, 743, 115−126. (10) Rabelo, A. P. B.; Tambourgi, E. B.; Pessoa, A., Jr. Bromelain partitioning in two-phase aqueous system containing PEO-PPO-PEO block copolymers. J. Chromatogr. B: Anal. Technol. Biomed. Life Sci. 2004, 807, 61−68. (11) Kitahara, T.; Kamihira, M.; Takeuchi, H. Application of Pluronic F68 for Aqueous Two-Phase Extraction of Proteins. J. Chem. Eng. Jpn. 1993, 26, 183−188. (12) Haraguchi, L. H.; Mohamed, R. S.; Loh, W.; Pessôa Filho, P. A. Phase equilibrium and insulin partitioning in aqueous two-phase systems containing block copolymers and potassium phosphate. Fluid Phase Equilib. 2004, 215, 1−15. (13) Oliveira, M. C.; Abreu Filho, M. A. N.; Pessôa Filho, P. A. Phase equilibrium and protein partitioning in aqueous two-phase systems containing ammonium carbamate and block copolymers PEO-PPOPEO. Biochem. Eng. J. 2007, 37, 311−318. (14) Svensson, M.; Linse, P.; Tjerneld, F. Phase Behavior in Aqueous Two-Phase Systems Containing Micelle-Forming Block Copolymers. Macromolecules 1995, 28, 3597−3603. (15) Svensson, M.; Joabsson, F.; Linse, P.; Tjerneld, F. Partitioning of hydrophobic amino acids and oligopeptides in aqueous two-phase system containing self-aggregating block copolymer effects of temperature, salts and surfactants. J. Chromatogr. A 1997, 761, 91− 101. (16) Svensson, M.; Berggren, K.; Veide, A.; Tjerneld, F. Aqueous two-phase systems containing self-associating block copolymers: Partitioning of hydrophilic and hydrophobic biomolecules. J. Chromatogr. A 1999, 839, 71−83. (17) Tada, E. S.; Loh, W.; Pessôa Filho, P. A. Phase equilibrium in aqueous two-phase systems containing ethylene oxide-propylene oxide block copolymers and dextran. Fluid Phase Equilib. 2004, 218, 221− 228. (18) Picó, G.; Romanini, D.; Nerli, B.; Farruggia, B. Polyethyleneglycol molecular mass and polydispersivity effect on protein partitioning in aqueous two-phase systems. J. Chromatogr. B: Anal. Technol. Biomed. Life Sci. 2006, 830, 286−292. (19) Stepto, R. F. T. Dispersity in polymer science (IUPAC Recommendations 2009). Pure Appl. Chem. 2009, 81, 351−353. (20) Monteiro Filho, E. S.; Coimbra, J. S. R.; Minim, L. A.; Silva, L. H. M.; Meirelles, A. J. A. Liquid-liquid equilibrium for ternary systems containing a sugar + a synthetic polymer + water. J. Chem. Eng. Data 2002, 47, 1346−1350. (21) Marcilla, A.; Ruiz, F.; García, A. N. Liquid-liquid-solid equilibria of the quaternary system water-ethanol-acetone-sodium chloride at 25 °C. Fluid Phase Equilib. 1995, 112, 273−289. (22) Rodrigues, C. E. C.; Filipini, A.; Meirelles, A. J. A. Phase Equilibrium for Systems Composed by High Unsaturated Vegetable Oils + Linoleic Acid + Ethanol + Water at 298.2 K. J. Chem. Eng. Data 2006, 51, 15−21.

In the example shown in Figure 8 (system CP80/8400 and MD 1920), the size distribution in the equilibrium phases is verified to be somehow emulated by the UNIQUAC equation. One cannot expect a perfect concordance in this case, as the procedure of choosing pseudocomponents entails an arbitrary choice of their number and molar masses, and from the equilibrium calculations, both equilibrium phases must be described by the same pseudocomponents (which may be a too restrictive hypothesis). Moreover, the very fact that UNIQUAC interaction parameters are different for different sizes of maltodextrin shows that the description of the equilibrium is somehow incomplete with this equation, as one should expect that these parameters are independent of the carbohydrate chain size. Nevertheless, the very fact that the shape and relative position of the GPC curves are described shows that the phase equilibrium is more correctly calculated by considering the pseudocomponents than otherwise.

■

CONCLUSIONS The liquid−liquid phase equilibrium of aqueous two-phase systems containing maltodextrins and EO/PO block copolymers was experimentally determined. The phase diagrams show that these systems have a similar phase behavior than other systems containing EO/PO block copolymers and dextran, and this carbohydrate can thus be replaced (at least with regard to the phase equilibrium) by the less expensive maltodextrin. Equilibrium phases had their polymer content analyzed through gel permeation chromatography, allowing an assessment of the uneven distribution of carbohydrate molecules of different sizes in equilibrium phases. The phase equilibrium was modeled using the UNIQUAC equation, and the carbohydrate was described by six pseudocomponents. A good description of the phase equilibrium and of the size distribution was obtained by this procedure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +(55) 11 3091 1106. Fax: +(55) 11 3091 2284. Present Address §

Department of Food Engineering and Technology, State University of São Paulo, São José do Rio Preto, São Paulo, Brazil. Funding

This work was supported by the Brazilian agencies CAPES, CNPq and FAPESP. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors gratefully acknowledge Prof. Dr. Francisco Maugeri and Dr. Fátima Aparecida Costa from the Bioengineering Laboratory of the Food Engineering Department at UNICAMP for their help with GPC analyses.

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REFERENCES

(1) Dreyer, S.; Kragl, U. Ionic liquids for aqueous two-phase extraction and stabilization of enzymes. Biotechnol. Bioeng. 2008, 99, 1416−1424. (2) Benavides, J.; Rito-Palomares, M.; Asenjo, J. A. Aqueous TwoPhase Systems. In Comprehensive Biotechnology, 2nd ed.; Murray MooYoung, Ed.; Elsevier: Amsterdam, 2011, v. 2, pp. 697−713. 2318



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(23) Alexandridis, P.; Hatton, T. A. Poly(ethylene oxide)+poly(propylene oxide)+poly(ethylene oxide) block copolymer surfactants in aqueous solutions and at interfaces: thermodynamics, structure, dynamics, and modeling. Colloid Surf., A 1995, 96, 1−46. (24) Loret, C.; Schumm, S.; Pudney, P. D. A.; Frith, W. J.; Fryer, P. J. Phase separation and molecular weight fractionation behaviour of maltodextrin/agarose mixtures. Food Hydrocolloids 2005, 19, 557−565. (25) Pessoa Filho, P. A.; Mohamed, R. S. Thermodynamic modeling of the partitioning of biomolecules in aqueous two-phase systems using a modified Flory-Huggins equation. Process Biochem. 2004, 39, 2075−2083. (26) Peres, A. M.; Macedo, E. A. Prediction of thermodynamic properties using a modified UNIFAC model: application to sugar industrial systems. Fluid Phase Equilib. 1999, 158−160, 391−399. (27) Balsev, K.; Abildskov, J. UNIFAC Parameters for four new groups. Ind. Eng. Chem. Res. 2002, 41, 2047−2057.

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