Novel aqueous two-phase system based on a hyperbranched polymer

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Novel aqueous two-phase system based on a hyperbranched polymer Andres Kulaguin-Chicaroux, Tim Zeiner ∗ TU Dortmund, Faculty of Bio- and Chemical Engineering, Chair of Fluid Separations, Emil-Figge Strasse 70, 44247 Dortmund, Germany

a r t i c l e

i n f o

Article history: Received 13 April 2013 Received in revised form 28 July 2013 Accepted 30 July 2013 Available online xxx Keywords: Aqueous two-phase system Lattice cluster theory Wertheim theory Hyperbranched polymer

a b s t r a c t Hyperbranched polymers have increased attention because of their branched structure and the wide range of different functional groups. Because of this feature hyperbranched polymers show an excellent applicability for aqueous two-phase systems (ATPS). In this work an ATPS consisting of a PEGfunctionalized hyperbranched polyesteramide + water + Dextran T40 is compared to an ATPS consisting of PEG8000 + Dextran T40 + water. In addition to the experimental investigation of the ATPS, they will also be modeled using the lattice cluster theory (LCT) in combination with Wertheim theory. The LCT allows the direct incorporation of the polymer architecture in the Helmholtz free energy, so all derived properties are dependent on chain architecture. A multicomponent version of LCT for incompressible polymer solutions/blends is presented in this work. To consider associative interactions the LCT is combined with Wertheim association theory. To obtain the model binary interaction parameters of the hyperbranched polymer + water the subsystem hyperbranched polymer + water was experimentally estimated, and for the subsystem PEG8000–water experimental data from literature were used, the parameters were fitted in both cases. So both ATPS could be modeled. In addition to the phase behavior, the kinematic viscosity of both ATPS was compared. © 2013 Elsevier B.V. All rights reserved.

1. Introduction In recent years the development of pharmaceuticals based on fermentation as recombinant therapeutic proteins, monoclonal antibody have been increased rapidly. These biopharmaceuticals have been applied in different medical areas such as immunization, oncology, autoimmune, cardiovascular, neurological diseases and inflammatory [1,2]. While the titers of biological products in fermentation broths could be increased from mg/L to g/L, the downstream processing often remains the bottleneck in the production process because of limitation of chromatography, as the state of the art technology in terms of capacities and high titers. Aqueous twophase systems (ATPS) show a potential to overcome the limitations of chromatography. ATPS can be formed by dissolving two hydrophilic components as two hydrophilic polymers, a salt and a polymer, a salt and an alcohol or by two surfactants [3]. Beijerinck [4] firstly discovered

Abbreviations: ATPS, aqueous two-phase system; CALM, chemical association lattice model; Exp., experimental; HB, hyperbranched polyesteramide; HPLC, highperformance liquid chromatography; LCT, lattice cluster theory; LCT-EOS, lattice cluster theory-equation of state; LLE, liquid–liquid equilibrium; LCST, lower critical solution temperature; PC-SAFT, perturbed chain statistical association fluid theory; PEG, polyethylene glycol; SAFT-EOS, statistical association fluid theory-equation of state. ∗ Corresponding author. Tel.: +49 2317552670. E-mail address: [email protected] (T. Zeiner).

ATPS by mixing aqueous starch and aqueous gelatin solution in 1896. In the 1950s ATPS were used by Albertson to extract and thereby purify cell organelles and soluble biomolecules such as proteins and nucleic acids [5]. In the last years several groups focused on the establishment of ATPS for industrial application [6]. Until now ATPS consisting of a hydrophilic salt as a phosphate and a hydrophilic polymer as polyethylene glycol are considered for the extraction of biomolecules [6]. But these systems have some disadvantages. Amphiphilic polymers show a poor solubility in salt containing systems, as salts promote the protein aggregation [7]. Moreover, ATPS is not a standalone process. For this reason a capture step of a biomolecule out of one phase is necessary. But if this phase is a salt containing phase, there could be shielding of the proteins from the adsorption sites in a chromatographic separation step [8]. But also by using a salt-free ATPS based on the aqueous solution of two polymers the high viscosity is a problem in industrial use of polymer–polymer ATPS [9]. Kumar et al. [10] proposed the use of smart polymers, which carry on the one hand special functional groups and on the other hand show no denaturation effect on biomolecules. Such a smart polymer is a hyperbranched polymer (Fig. 1), which could be used to form a novel ATPS. The advantages of using hyperbranched polymers as a phase forming component in an ATPS is the lower viscosity of these polymers in melt and solutions [11]. Moreover, hyperbranched polymer can carry a huge number of different functional end-groups [11]. The low melt and solution viscosity of hyperbranched polymers originates in the branched structure, as

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Nomenclature List of symbols A, B constants of densimeter defined by Eq. (36) [–] b3,i number of branching points of three of component i [–] number of branching points of four of component i b4,i [–] E1 energy contribution of the first order [J/mol] energy contribution of the second order [J/mol] E2 F Helmholtz free energy [J/mol] kB Boltzmann constant [J/K] kij parameter defined by Eq. (30) [–] association volume defined by Eq. (29) [–] Kijasso K Mi MM,i ni NL Niasso nV P R S T t V0 ϑ wi z

constant of capillary [mm2 /s] chain length of component i [–] molar mass of component i [g/mol] number of molecules of component i [–] number of lattice sites [–] number of association sites per segment [–] number of holes in lattice [–] pressure [Pa] universal gas constant [J/mol K] entropie contribution [J/mol] temperature [K] time [s] volume of cell [cm3 /mol] Hagenbach correction [s] mass fraction of component i [–] coordination number [–]

Greek letters ij association strength between molecule i and molecule j defined by Eq. (28) εij interaction energy defined by Eq. (1) association energy between segments of molecule i εasso ij and molecule j  dynamic viscosity , , , , ω,  component indexes kinematic viscosity

density ˚i volume (segment) fraction of component i 2 XiS , Xiε , Xiε coefficients defined by Eqs. (5)–(9), (11)–(16), (18)–(25) XAi non-bonded segment fraction of component i Superscripts asso association Subscripts air air asso association lattice cluster theory LCT mix mixing water H2 O

affected and the thermal recovery of the hyperbranched polymers is ensured. For the optimization of extraction processes with an ATPS a modeling of the ATPS is essential. In literature there are some models for the phase equilibria of ATPS. To calculate this phase equilibria gE models [12] (e.g. UNIQUAC or NRTL) or equations of state as PC-SAFT [13] can be used; whereas the influence of salts is considered by an Debye–Hueckel term [12,13] or an Pitzer equation [12]. By the use of hyperbranched polymers as a phase forming component the polymer architecture has to be considered in the thermodynamic framework. Based on the Flory–Huggins theory [14], Freed and coworkers [15–18] developed the lattice cluster theory (LCT). Similar as the Mayer Expansion of real gases, correction terms to the Flory–Huggins theory were calculated. Using these expansions the polymer architecture can directly be considered in the Helmholtz free energy. Jang and Bae [19] used the LCT to model the phase equilibria of hyperbranched polymer solutions for the first time, but they did not consider the corrections made by Dudowicz et al. [18]. Zeiner et al. [20] have published a revised version of the LCT. Using this version they could successfully predict the critical concentration by just using one adjustable parameter and the knowledge of the chemical structure of the hyperbranched polymer. By using just one adjustable parameter the low concentrated branch of the cloud point curve could be modeled in good accordance with experimental data, but there were deviation between the calculated high concentrated branch and the experimental data. This expression was also used by Domanska et al. [21], to model the phase behavior of a hyperbranched polymer in a organic solvent. One way to improve the calculation of Zeiner et al. [20] could be the incorporating of associative interactions. For these reason the LCT was combined with the Wertheim association theory [22] and the Chemical Association Lattice Model [23,24]. By this combination a good accordance between experimental data and calculations could be achieved. In addition to the calculation of the phase behavior of a polymer in a single solvent, also the phase behavior of a hyperbranched polymer in mixed [25] and demixed [26] solvent was modeled. In the case of the hyperbranched polymer solution in a mixed solvent, the ternary phase behavior could be calculated in a good agreement with experimental data by adjusting the interaction parameters of the two solvents on the ternary phase behavior. In the work of Schrader et al. [26] the LCT in combination with Wertheim theory could predict the ternary phase behavior in good accordance with experimental data, based on all binary subsystems. Furthermore, the LCT was used to calculate high pressure phase behavior of hyperbranched polymer solutions [27], using the newly developed lattice cluster theory-equation of state [27–29] (LCTEOS). In this work ATPS consisting of hyperbranched polyesteramide (HB), Dextran T40 and water is experimentally investigated and modeled using a multicomponent version of the incompressible LCT. To account for associative interactions the LCT is combined with Wertheim association theory [30–33]. Moreover, this ATPS is compared with an ATPS consisting of polyethylene glycol 8000 (PEG8000), Dextran T40 and water. In addition to the experimental and theoretical investigation of the phase behavior, also the viscosity of both ATPS is analyzed. 2. Theory

the chain entanglement is lower (Fig. 1). Hyperbranched polymers show a good biocompatibility and high thermal and chemical stability [11]. These properties are very important for the potential use to form an ATPS, because by the presence of the hyperbranched polymers the microorganisms in the fermentation broth are not

In this chapter the used model will be introduced. Here a version of the LCT applicable for a multicomponent polymer solution/blend is introduced. As the LCT cannot consider associative contributions, the LCT will be combined with a lattice Wertheim theory as developed by Van Durme et al. [32,33].

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2.1. Lattice cluster theory Dudowicz and Freed [17] proposed a version of the LCT applicable to arbitrary chain architecture. The LCT derives in the form of a cluster expansion in the inverse coordination number 1/z and the reduced interaction energy εij /kB T , here kB is the Boltzmann constant, T is the temperature and εij is defined as: εij = εii + εjj − 2εij

(1)



 S X3,k

=

where εii describes the interaction energy between two segments of the same kind and εij is the interaction energy of different kind. In order to account for the chain size, the polymer between two segments will be divided into chain segments, which will be placed on a lattice. For this reason the polymer volume (segment) fraction ˚i will be introduced as follows: ˚i =

Mi ni NL

(2)



1−

1 Mk

n

=

n n  

k=1

+

z2 =1

2 − 2 z

=1

n n n    4

k=1

S X1,k ˚k ˚

n n  

k=1 S X4,k ˚k ˚ ˚ +

S X2,k ˚k ˚

1 + 2 z

=1

n n n n     2

z2

=1

k=1

=1

=1

n n  

k=1

Whereas the coefficients S X1,k =



1−

 1 1 Mk

n

n





1 −2 Mk

(9)

n

n

n

=1

k=1 =1

 1  ε X3,k ˚k ˚ ε  ˚ ˚ z n

n

+

+

=1 =1

 1  ε X4,k ˚k ˚ ε ˚ z n

n

=1

k=1 =1

 2  ε X5,k ˚k ˚ ˚ (ε − 2εk )˚ ˚ z n

n

−

n

n

k=1 =1

n

n

k=1 =1 =1

−

n

=1 =1

 1 ε X6,k ˚k (ε  − 2εk )˚ ˚ 2 n

n

=1 =1

k=1

−

=1

1 16 26 + 2 − 3 3Mk Mk

(8)

 1  ε X2,k ˚k ˚ εk ˚ z n

+

z  ε  ˚ ˚ 4 n

S X5,k  ˚k ˚ ˚ ˚



k=1 =1 =1

=1

(4) XiS

1 1 1 1 2 − − − 2 + M M M M Mk Mk



(7)



2Mk

n

S X3,k ˚k ˚



1 (2 − b3, − 3b4, ) M

E1 1  ε X1,k εk ˚k ˚ ˚ = NL RT z

n

where the first term on the right hand side of (3) is the contribution of the classical Flory–Huggins entropy [14] term, S is the correction term to the entropy, E1 and E2 are the energy contributions of first and second order. The entropy contributions S are calculated as follows:



(2 − b3,k − 3b4,k ) −

(M + M − 1)Mk + M M



1 (2b3, + 6b4, − 3) M (6)

Similar as shown in [17,20,25,29] the coefficients in Eq. (5)–(9) vanish, if z tends to infinity. This means, that the LCT-entropy contribution is reduced to the classical Flory–Huggins entropy contribution. The entropy contributions have also no adjusted parameter. They depend only on the structural parameters of the molecules. The energy contributions of first order can be calculated as follows:

(3)

i=1

S 1 = NL R z

+

Mk

(2b3,k + 6b4,k − 3) −

Mk2 − 5Mk − 2b3,k − 6b4,k + 6

×

3M M M

˚ S FLCT E1 E2 i ln (˚i ) − = − − NL RT Mi NL R NL RT NL RT

Mk



 (3 − 3M − 10M )M + (3 − 10M )M + 10M − 3    

lattice. In this work it is assumed that each water molecule occupies one lattice site. In order to describe the chain architecture of the polymer two additional structure parameters to Mi , namely the number of branching points of three b3,i and the number of branching points of four b4,i , are introduced. In contrast to earlier works, the structural parameters Ki [20,22–26] are not used in this work. For this reason the short chain branching cannot be described by this equation, as it is assumed, that there are at least two segments between two branching points. But for the used hyperbranched polymer this assumption is fulfilled. To consider the short chain branching the equations given in [27–29,34] have to be used. The advantage of the equations of this work is the simple way of describing the architecture and the reduced number of parameters. Using the Tables I–III in [17] with the correction given in [18] the Helmholtz free energy contribution of the LCT FLCT for an incompressible multicomponent LCT can be calculated as follows:

 1

 S X4,k

 1

b3,k 3b4,k 2 1− + + Mk Mk Mk

×

where Mi is the chain length of the polymer i (segment number of molecules) and ni is the number of molecules of kind i and NL is the number of lattice sites of the incompressible S X5,k  =

1 Mk

S X2,k = 1−

n

(10)

=1 =1

where the coefficient Xiε of (10) are calculated as follows: are calculated as follows:

1 − Mk M

 (5)

ε = X1,k

1 M



1−

1 Mk

 2M − 2  M

+ 2b3, + 6b4, − M − 1

(11)

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Fig. 1. Sketch of Hybrane DEO 750 8500.

ε X2,k =

+



1−

1 Mk



ε X4,k =

[2M − b3, − 3b4, − Mk M + Mk − 1]

2b3,k + 6b4,k − 3 +1 Mk

ε X3,k

+

2 M

1 = M



1 1− Mk



2 M



(12) ε X5,k

1 = M

1−



1 Mk



1 1− Mk

[4 − b3, − 3b4, + M2 − 4M ]

 1 − M − M  M

(14)

+ M

(15)

[2b3, + 6b4, − Mk + (Mk − M + 2)M − 3]

3 − 2b3,k − 6b4,k 1 − 2Mk 2

(13)

ε X6,k =



1−

1 Mk

 (16)

The second order energy contributions to the Helmholtz energy are calculated as follows:

 2  εk  2  εk ε  E2 ε ε X1,k ˚k X2,k ˚k ˚ = ˚ + ˚ ˚ NL RT 4 2 n

n

k=1

=1 n

n n  

+

2

ε X3,k ˚k ˚



+

2

ε X5,k ˚k ˚



2

ε X7,k ˚k ˚



4

  ε2

=1 =1 k=1 =1 n n n 2 ε  ε2 ˚ ˚ + X8,k ˚k 8 =1 =1 k=1



=1 =1

˚ ˚ +

n  ε  εω =1 =1 ω=1 n n

k=1 =1 n n

+

4

k

4

n n   k=1 =1

˚ ˚ ˚ω +

2

ε X4,k ˚k ˚ n n  

n n n n     εω ε  =1 =1 ω=1 =1 n n

2

ε X6,k ˚k ˚

− εk εk + εk ε −

z  4 n

n

n

=1 =1 ω=1 =1



4

εk ε 2

˚ ˚ ˚ω ˚

n  εk εω

2

=1 =1 ω=1

k=1 =1

n

+

n

n

k=1 =1

n  εk εk =1 =1 n n

k=1 =1 n n

n

n

2

+

εk ε  2

ε2  ε  εω ε  εω − + 4 2 4

˚ ˚ ˚ω

(17)

 ˚ ˚

 ˚ ˚ ˚ω ˚

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where the coefficients in (18) are calculated as follows: 2

ε X1,k =

1 (b + 3b4,k − 1) Mk 3,k

2

ε X2,k =

Mk

2

ε X4,k =

1 Mk

2

1 Mk

2

1 Mk

2

1 Mk

ε X5,k = ε X6,k = ε X7,k = 2

ε X8,k =

 2

 1

2

ε X3,k =

1 Mk

M

(18)

  

M

(19)

2Mk 2 + −1 M M

(20)



2Mk − b3,k − 3b4,k −

 3



2Mk + 2Mk − 1 M

− b3,k − 3b4,k −

− b3,k − 3b4,k −

b3,k + 3b4,k +

 (21)



2Mk 2 − − 3Mk + 2 M M

(22)

4Mk 4 − +3 M M

(23)

b3,k + 3b4,k − 4Mk + Mk −

3Mk 7Mk 5 + − M 2 2

Mk + M − 1 M





(24)

1 (Mk − 1) Mk

(25)

Similar as the entropy contribution also the first and second order energy contributions reduce in the case z → ∞ and εij → 0 to the Flory–Huggins -parameter. In this work it should be proved, if it is possible to calculate the ATPS by the knowledge of the binary liquid–liquid phase behavior. As the PEG8000–water and HB–water subsystems show a lower critical solution temperature, the LCTEOS [27–29] is used to calculate this phase behavior. The LCT-EOS is derived by introducing holes in the lattice. Moreover, the pressure has to be calculated as follows: P=−

1



v0

ıFLCT ınv





=− T,ni = / v

1

v0

FLCT − NL

  n−1  ı(FLCT /N) ˚i

i=1

ı˚i

T

(26)

where P is the system pressure, v0 is the volume of a cell and nv is the number of holes in the lattice. In (26) it is assumed, that the nth component is the hole. By using the LCT-EOS, it has to be considered, that the interaction energy between a hole and another segment vanishes. For this reason the interaction energy (1) reduces to a pure component interaction in the case of interaction between a hole segment and one component segment. The mass fraction can be calculated using the molar mass MM,i and the chain length Mi as follows: wi =

MM,i ˚i Mi

n

MM,j ˚j j=1 Mj

(27)

As the LCT does not consider the associative interactions, it will be combined with the Wertheim theory. 2.2. Wertheim theory In this work three different polymers are used, carrying different polar functional groups; whereas the Dextran T40 has three OH-groups per glucose unit and PEG/HB have the association sites on the oxygen. In principal there are two different ways describing the association [35]. One way is the assumption of the formation of hydrogen bondings as a chemical reaction, this is called the “chemical theory”. Another possibility is the “physical theory”, where the association contributions are calculated with the help of integral equations including an interaction potential, describing the association interactions. The Wertheim theory [30,31] is a physical theory, treating an associative bond as a directional force between two association sites. In the framework of the Wertheim approach it is possible to consider the self-association between two molecules

5

of the same kind and the cross association between different kinds of molecules. This theory has been widely used in the SAFT-EOS family [36]. The use of this theory requires the identification of association sites on the molecules [31,32]. The substances in the mixture are classified according to the groups to which bonds can be assigned. Such groups include OH, amine and carbonyl groups. This work focuses on the bonding between water and the functional groups of the HB, dextran and PEG. Water is modeled using the 4C model, which means that there is an association site on each lone electron pair of the oxygen and on each hydrogen atom. It is assumed, that the polar groups of the polymers carry just two association sites, because of steric reasons. For this reason the OH groups of the dextran are described by the 2B model. This model assumes that there are two different association sites on the OH group. For the same reason the HB and the PEG can also be described by a 2B model with two association sites on the oxygen. In this work the incompressible form of the LCT in combination with Wertheim theory is used to calculate the phase behavior of the ATPS. As this form of the LCT has no information of the density, the modified lattice Wertheim theory of Van Durme et al. [32,33] is used to calculate the ATPS. Because the binary subsystems of PEG–water and HB–water show a lower critical solution temperature, the LCTEOS has to be used to calculate this phase behavior. In combination with Wertheim theory the holes in the lattice were considered as a third component, which do not form hydrogen bonds. The association strength between two interacting molecules is calculated as follows:



ij =

Kijasso



exp

εasso ij kB T





−1

(28)

The two parameters Kijasso and εasso are the association volume and ij the association energy between two segments of component i and j. Within the framework of the Wertheim association theory six types of association in the ternary system, namely the self-association of each component and the cross-association between the different components, are considered. The association parameters have to be fitted on experimental data. Because of the cross-association combining rules have to be introduced to account for the association interaction between different kinds of molecules. Kijasso =

Kiiasso + Kjjasso 2

(29)



εasso = (1 − kij ) ij

εasso εasso ii jj

(30)

Similar as in [26] the parameter kij is introduced to consider the deviation of the association energy from the geometrical mixing rule. By using (30), (29), (28) the non-bonded segment fractions XAi can be calculated as follows:

⎡ XAi = ⎣1 +

 j

⎤−1 ˚j XBj ij ⎦

(31)

Bj

Eq. (31) is a non-linear equation system which has to be solved numerically. If all XAi are known, the associative contributions to the Helmholtz free energy can be calculated as follows:

⎡



    XA Fasso ˚i ⎣ ln XAi − i = NL RT 2 i

Ai



⎤ 1 + Niasso ⎦ 2

(32)

where Niasso is the number of association sites per segments of component i.

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The total Helmholtz energy when the architecture of the polymer and the association phenomena are taken into account is determined as: Fmix Fasso FLCT = + NL RT NL RT NL RT

(33)

The ATPS and binary liquid–liquid phase equilibria are calculated using chemical potentials, which can be calculated using standard thermodynamics. 3. Experimental 3.1. Materials Hyperbranched polymer Hybrane DEO 750 8500 (HB) (Fig. 1) investigated in the present study was commercially obtained from Polymer Factory Sweden AB and it was used without further purification. GPC analysis by the manufacturer shows that the HB has a molecular weight of 5417 g/mol and a MW/MN ratio of 1.47. Regarding the structure of this polymer the molar mass should be 8500 g/mol. One reason could be, that not all endgroups of the core carry a PEG-chain. For the theoretical modeling the molar mass of 8500 g/mol is used for the HB. Dextran from Leuconostoc spp. was purchased from Sigma–Aldrich Chemie GmbH and was used as obtained. The molar mass of dextran specified by producer is between 35,000 and 45,000 g/mol. The polyethylene glycol with the molar mass 8000 g/mol was purchased from Alfa Aesar GmbH & Co KG. and was used without further purification. To prepare the aqueous polymer solutions deionized water was used filtered by a millipore water purification system. 3.2. Liquid–liquid equilibrium of binary polymer solution Aqueous solution of hyperbranched polymer was prepared gravimetrically by weighing required amount of water and polymer in a flask. The flask was closed and the solution was mixed at ambient temperature until it became homogenous. For the measurement the flask with the homogenous polymer solution was put in the water bath and tempered at a chosen temperature for 30 min. If the solution remained clear and stable at this temperature, it was heated up with a heating rate of 0.5 ◦ C per 15 min until the first cloudiness due to the phase separation became visible. If the phase separation occurred after 30 min in water bath, this temperature was lowered and the search for a cloud point had to be begun at a lower temperature. To avoid possible errors the cloud point was also found by cooling down the polymer solution. In this case the measurements were begun in the two-phase region, and the polymer solution was cooled down with a cooling rate of 0.5 ◦ C per 30 min until the cloudiness disappeared. The results obtained by heating up and cooling down were averaged and this temperature is the cloud point temperature at a given polymer concentration. Repeating this procedure for different polymer concentrations gives the cloud point curve for the investigated polymer solution. 3.3. Liquid–liquid equilibrium of ternary polymer solution At first aqueous polymer solutions containing dextran and HB in different concentrations were necessary. They were prepared gravimetrically by weighing required amount of water, dextran and hyperbranched polymer in a flask. The flask was closed and the solution was stirred at room temperature for 1 h. Afterwards the samples were put in the water bath and tempered at 25 ◦ C for 30 min. Because the chosen polymer concentrations lay within a two-phase region a decomposition of the prepared polymer solutions into two liquid phases occurred, and these coexisting phases

were titrated with water. Water was added to the sample stepwise in small amounts, and between two steps the sample was tempered in the water bath at 25 ◦ C for 15 min to get into equilibrium. The procedure was repeated until the cloudiness disappeared. The amount of added water was determined by weighing the sample before and after the experiment. For the determination of polymer concentrations in coexisting phases new aqueous polymer solutions were prepared. The polymer solutions were also prepared gravimetrically by weighing required amount of water, dextran and hyperbranched polymer in a flask. Afterwards the flask was closed and the solution was stirred at room temperature for 2 h. Subsequently, the samples were put in the water bath and held at 25 ◦ C for 72 h to get into equilibrium. After this time the phases were separated by means of a syringe, diluted and used for the measurement. The concentration of HB and dextran in coexisting phases was determined by use of size-exclusion, high-performance liquid chromatography. The used chromatographic system consisted of an auto sampler AS 4000, an interface D6000A, a pump L6200 from Hitachi/Merck, a column oven from Shimadzu, a refractive index detector K2301 from Herbert Knauer GmbH and one SUPREMA 100 A˚ column. The chromatographic measurements were carried out at 40 ◦ C, and deionized water was used as mobile phase which was pumped through the HPLC system with a flow rate of 1.0 ml/min. To integrate the peaks and evaluate experimental data the built-in peak analyzer from OriginPro 8.6 was used. 3.4. Viscosity measurements Polymer solutions at different demixing points were prepared gravimetrically by weighing required amount of water and polymer with an accuracy of 0.1 mg. After mixing the polymer solutions were stirred for 1 h at ambient temperature. During the phase separation the flasks with the prepared polymer solutions were put in water bath and were tempered at 25 ◦ C for 72 h. After this time the phases were separated by means of a syringe and were used for the measurements of viscosity and density. The viscosity was measured with a KPG-Ubbelohde Viscometer (DIN 51562) from SCHOTT Instruments GmbH, Mainz, Germany. As the viscosity depends strongly on temperature the sample was also tempered at 25 ◦ C during the measurement. In order to raise the accuracy of measurement an automated measuring system from MGW Lauda Dr. R. Wobser KG, Lauda, Germany was used. In the experiment the flowtime was measured twice for each sample to avoid random errors. Both values were averaged and the kinematic viscosity in mm2 /s can be calculated as follows: = K(t − ϑ)

(34)

where t is the average flow time, K is a constant specified by producer for a capillary and ϑ is Hagenbach correction, which depends on the flow time and the tube capillary number. According to the producer the viscosity can be measured with the used apparatus with an accuracy of ±1%. If the density of solution is known, the dynamic viscosity can readily be calculated:  =

(35)

3.5. Density measurements The polymer solutions that were prepared for the viscosity measurements were also used for density measurements. Density of aqueous polymer solutions was determined by means of a vibrating-tube densimeter DMA 46 from Anton Paar KG, Graz, Austria. Before the beginning of measurements the apparatus was calibrated with deionized water and air. The calibration gave two

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350.75 351.35 350.25 349.22 349.15 349.65 351.32 353.58 354.58

0.00808 0.01131 0.05206 0.07293 0.16146 0.20197 0.25314 0.29784 0.35823

420 410 400

TH2

2O

2 − Tair

H2 O − air

380 370 360

constants A and B that are necessary to calculate the density are given as: A=

LCT-EO OS+ Wertheiim Exp. Daata HB- watter Exp. Daata PEG80000- water

390

T[K]

T [K]

7

350 0 0.0

0.1

0.2

0.3

0.4

wPolymer

= 15.3915

(36)

2 −A· B = Tair air = 19.2486

where H2 O and air are the density at desired temperature of water and air, respectively. Tair and TH2 O are the displayed values of the densimeter in calibration mode for water and air. For the measurements a vibrating tube is filled with the desired liquid and the density is obtained by setting the tube into oscillation by an electromagnetic field. The eigenfrequency of the filled tube is a measure for the density of liquid. Both constants A and B have to be entered into the densimeter and in measurement mode the displayed value is the density of liquid of interest at desired temperature. In the experiment the density of polymer solutions was investigated at 25 ◦ C. According to the manufacturer of the densimeter the density can be measured with an accuracy of 10−4 g/cm3 . 4. Results and discussion Similar as shown in former articles [22–26,29] the polymer architecture will not be considered as an adjustable parameter, but it will be determined by the chemical structure of the polymer. At first the structure characteristics of the HB will be analyzed. All Hybrane polymers consist of a similar core with different functional groups. The functional groups of this HB are PEG chains. The core will be divided into 142 segments with 16 branching points of three. Moreover, the HB polymer carries 7 PEG chains, which are divided into 7 segments. So the whole HB is divided into 191 segments with 16 branching points of three. In addition to the HB the architecture of Dextran T40 is analyzed. Each dextran ring is considered as a solely monomer which is divided into 7 segments. By the division of each ring into segments it was considered, that a ring has a higher volume, than the single segment. As the PEG8000 (PEG10000) is a simple linear polymer it was divided as it would be divided applying the Flory–Huggins [14] theory, so it has 445 (556) segments. In addition to the architecture, the coordination number z has to be fixed. It determines the number of next segments in the fluid. As this number is experimentally challenging to estimate, it has to be fixed to a certain value for the calculation. Originally, the LCT was derived on the basis of a primitive cubic lattice (z = 6), but it was also shown by molecular simulation, that the LCT can also describe the behavior of other lattice structures [15]. In this work a coordination number of z = 6 as used by Dudowicz and Freed [17] is chosen. Fig. 2 shows the LLE of the binary subsystems PEG8000–water and HB–water. In contrast to the liquid–liquid equilibrium of PEG8000 + water, the LLE of HB + water is broader and the critical point is shifted to higher polymer concentrations and a lower temperature. The experimental data can be found in Table 1. The LCT-EOS in combination with Wertheim association theory was used to model the LCST behavior of both solutions; where the

Fig. 2. Binary liquid–liquid phase behavior of HB + water and PEG8000 + water. The solid lines are the calculated using the combination of LCT-EOS and Wertheim theory. The triangles are experimental data estimated by Saeki et al. [37]. Table 2 Binary interaction parameter. εij

Components

kB

PEG–water PEG–Dextran Water–Dextran HB–Dextran HB–water

[K]

kij

3 21.7 −6 60 1

0 0.0245 0 0.04 0

model parameters can be found in Tables 2 and 3. Similar as in [27], the interaction parameters of the pure solvent were fitted on a pure component property. Here the liquid density of water in the relevant temperature range was used. So the volume of the cell v0 was determined as 16.5 cm3 /mol. By calculating the binary LLE, the kij was set to zero, as for both polymers the association energy was fitted on the experimental data. It can be seen that this model describes the low concentrated polymer branch in good agreement with experimental data in both cases, but the phase behavior of the high concentrated branch in the HB solution cannot be described in accordance with experimental data. One reason could be the higher polydispersity of the HB. Another improvement of the calculation could be achieved by using the Wertheim approach of the SAFT-EOS [36], which was developed for compressible systems or another approach for compressible systems as CALM [38]. But this fit on the binary LLE is used to determine the binary interaction parameters to calculate the ternary ATPS. Fig. 3 shows the ATPS PEG8000–Dextran T40–water at 295.15 K calculated by the introduced model. As the binary subsystem Dextran T40–water shows no demixing behavior, the interaction parameter of Dextran T40–water has to be fitted on the ternary LLE. In addition to the interaction parameters of Dextran T40–water, the binary interaction parameters of the subsystem Dextran T40–PEG8000 were also adjusted to the ATPS. The interaction parameters for the calculation of the ATPS can be found in Tables 2 and 3. In Fig. 3 a good accordance between the experimental data and the calculations with the used model can be seen. Table 3 Association parameters and LCT-EOS parameter. Components

εii kB

Water PEG Dextran HB

270 + 13000K/T 190 – 280

[K]

εasso ii

kB

1512 750 869 790

Kiiasso 0.01 0.09 0.012 0.09

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8

0.7 70

0.30

0.75

0.25 5 0.20

r w Wa te

5 0.85

0.15

an xtr

0.90

0.20

w De

0.15

0.25 5

0.80

an xtr

0.85 5

LCT+ Werrtheim Exp. Data

0.30

0.75

w De

w Wa ter

0.80

0.7 70

Exp. Daata (Diamonnd und Hsu) LCT+ W Wertheim

0.1 10

0.90 0 0.95

0.1 10

0.05

0 0.95 1.00

0.05

0.00

0.0 00

0.05

0.10

0 0.15

0.20 0

0.25

0.30

1.00

wP PEG8000

0.0 00

0.00 0.05

0.10

Fig. 3. ATPS PEG8000–Dextran T40–water at T = 295.15 K. Experimental data are taken from Diamond and Hsu [39].

0 0.15 wHB

0.20 0

0.25

0.30

Fig. 5. ATPS HB–Dextran T40–water at T = 298.15 K.

Moreover, the tie lines can be described in good agreement with experimental estimated tie lines. Using the interaction parameters fitted on the ATPS (Fig. 3) the ATPS water–Dextran T40–PEG10000 can be predicted (Fig. 4). Similar as shown in Fig. 3 the binodal curve of the investigated system can be described in good accordance with experimental data (Fig. 4). But there is a higher deviation between the experimental and the calculated tie lines. Fig. 5 shows the ATPS consisting of HB + Dextran T40 and water. Comparing the ATPS based on the HB and the ATPS including the PEG8000, it can be seen that the PEG8000 containing ATPS has steeper tie lines. One disadvantage of the ATPS based on HB is that the weight fraction of HB polymer of the top (HB-rich) phase is quite higher, than in the PEG8000 containing ATPS, which results in a higher requirement of HB to form an ATPS. The experimental data of the ATPS HB–Dextran T40 can be found in Table 4 (tie lines) and Table 5 (titrated binodal curve). Moreover, Fig. 5 shows the modeling of the ATPS based on the HB. The parameters of the calculation can be found in Tables 2 and 3; whereas the interaction parameters of HB–Dextran T40 kij and εij /kB have to be fitted on the ternary phase behavior, as no data on the subsystem HB–Dextran T40 is experimental accessible. Comparing the experimental data with the calculations with

0.7 70 0.75

0.25 5

0.15

0.90

n tra

0.85 5

0.1 10

0 0.95

0.05

1.00 0.0 00

0.00 0.05

0.10

0 0.15

0.20 0

0.25

Top phase

Bottom phase

wHB

wDextran

wHB

wDextran

0.1629 0.22459 0.27539

0.02483 0.01206 0.00859

0.01943 2.5E−3 1.4E−3

0.10936 0.15848 0.19413

LCT combined with Wertheim theory, there are deviations of the dextran-rich phase and the HB-rich phase. But the used model describes the gradient of the tie lines in accordance with experimental data. One reason for the deviation between experimental data and experimental data could be the polydispersity of the HB and the dextran. In addition to the phase behavior of ATPS, the kinematic viscosity of each system plays an important role for the industrial use in an extraction setup. In Fig. 6 the kinematic viscosity of the ATPS phases in the systems PEG8000 + Dextran T40 and HB + Dextran T40 in water at 298.15 K is shown. On the y-axis the kinematic viscosity is plotted over the dextran and the PEG/HB mass fraction at the demixing point; whereas the mass fractions of both phases forming polymers are chosen equal. As expected the viscosity of both systems increases with increasing polymer concentration. By comparing the dextran-rich phase in both systems, it is obvious, that the viscosity of this phase in the PEG8000 containing system is higher and increases quite faster than the viscosity of the dextran-rich phase in the ATPS based on a HB. One reason is the lower dextran concentration in the HB Table 5 ATPS HB–Dextran T40–water titration data at 298.15 K.

0.20

w De x

wa ter

0.80

w

Ex xp. Data (F Forciniti et aal.) LC CT+ Wertheeim

0.30

Table 4 ATPS HB–Dextran T40–water tie lines at 298.15 K.

0.30

W PEG10000 Fig. 4. ATPS PEG10000–Dextran T40–water at 298.15 K. Experimental data are taken from Forciniti et al. [40].

WHB

wDextran

0.07066 0.06501 0.01034 0.03264 0.04879 0.05874 0.07374 0.08966 0.10781 0.13226 0.15554 0.19786 0.04695 0.12859

0.07208 0.07622 0.12676 0.10441 0.08847 0.07951 0.07003 0.05906 0.04817 0.03538 0.02151 0.00652 0.08745 0.03397

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220 200 180 160

DexT40 - PEG8000 - water; PEG-enriched phase Dex T40 - PEG8000 - water; Dex-enriched phase Dex T40 - HB - water; HB-enriched phase Dex T40 - HB - water; Dex-enriched phase T=298.15K

120

2

ν [mm /s]

140

100 80 60 40 20 0 0,06

0,08

0,10

0,12

0,14

Dex T40 respect. PEG/HB at the demixing point Fig. 6. Comparison of kinematic viscosity of ATPS Dextran T40 + PEG8000/HB in water. Table 6 Density, kinematic viscosity and dynamic viscosity of the ATPS PEG8000 + Dextran T40 + water at 298.15 K. Phase

PEG-enriched PEG-enriched PEG-enriched PEG-enriched PEG-enriched PEG-enriched Dex-enriched Dex-enriched Dex-enriched Dex-enriched Dex-enriched Dex-enriched

wDextran = wPEG8000 at demixing point

[mm2 /s]

[g/cm3 ]

0.0625 0.0775 0.0925 0.1075 0.1225 0.1375 0.0625 0.0775 0.0925 0.1075 0.1225 0.1375

5.1019 6.3613 8.5946 11.4634 15.2189 20.2553 15.1498 26.8903 44.8999 71.5640 114.7948 182.1328

1.0209 1.0213 1.0238 1.0273 1.0313 1.0356 1.0630 1.0845 1.1035 1.1211 1.1380 1.1552

 [mPa s]

5.2085 6.4967 8.7991 11.7763 15.6952 20.9764 16.1043 29.1625 49.5471 80.2304 130.6365 210.3998

Table 7 Density, kinematic viscosity and dynamic viscosity of the ATPS HB + Dextran T40 + water at 298.15 K. Phase HB-enriched HB-enriched HB-enriched HB-enriched Dex-enriched Dex-enriched Dex-enriched Dex-enriched

wDextran = wHB at demixing point

[mm2 /s]

[g/cm3 ]

0.0775 0.0975 0.1175 0.1375 0.0775 0.0975 0.1175 0.1375

6.8360 17.3299 52.6236 198.4708 6.6765 11.1477 18.4326 31.4070

1.0225 1.0236 1.0266 1.0300 1.0411 1.0596 1.0761 1.0937

 [mPa s] 6.9898 17.7389 54.0234 204.4250 6.9510 11.8121 19.8353 34.3499

based ATPS. The viscosity of the PEG-rich phase is in the same order as the viscosity of the HB-rich phase, but the increase of the viscosity of the PEG-rich phase is much smaller than the increase of the HB-rich phase. By regarding Figs. 3 and 5, it is obvious, that this increase can be explained, by the higher polymer concentration of the HB in the ATPS (Fig. 5) compared to the PEG8000 concentration in the ATPS (Fig. 3). This concentration differences compensate the structural effect of the branched structure compared to the linear structure. The viscosity data can be found in Tables 6 and 7. 5. Conclusion In this work a novel ATPS based on a hyperbranched polymer is presented. This ATPS consists of a PEG-functionalized

9

hyperbranched polyesteramide + Dextran T40 + water and it is compared with an ATPS consisting of PEG8000 + Dextran T40 + water. In addition to the experimental validation both ATPS were modeled using the LCT combined with Wertheim association theory. The LCT was used to take especially the branched architecture of the hyperbranched polymer into account. But with the LCT also the Dextran T40 and the PEG can be modeled. By the incorporation of the Wertheim theory, the influence of polar groups is considered. With help of the binary phase behavior of PEG8000 + water and of HB + water the binary interaction parameters of the used model were determined. Using these parameters the ATPS PEG8000 + Dextran T40 + water and the ATPS hyperbranched polyesteramide + Dextran T40 + water could be modeled; whereas the binary parameters of Dextran T40–water were adjusted on the ATPS PEG8000 + Dextran T40 + water and the binary interaction parameters of the polymers have to be adjusted on each ATPS. With the introduced model both ATPS were calculated in good accordance with experimental data. Comparing the investigated ATPS, the dextran concentration in the dextran-rich phase is in the PEG8000 based ATPS higher than in the hyperbranched polymer based ATPS. On the other hand a higher hyperbranched polymer concentration is needed to form an ATPS. Moreover, the HB concentration is higher than the PEG8000 concentration in the corresponding systems. Additionally to the phase behavior also the kinematic viscosity of both investigated ATPS was experimentally estimated. It could be shown that the dextran-rich phase in the HB based system shows a lower kinematic viscosity than in the PEG8000 based ATPS and the viscosity of the HB-rich phase in one ATPS increases more rapidly than the viscosity of PEG-rich phase in the other ATPS. This depends on the higher HB polymer concentration. Concluding it can be summarized, that hyperbranched polymer ATPS represents a promising application of hyperbranched polymers, but the basis of the suitable hyperbranched polymers has to be broadened and the distribution of a target product depending on the functional groups of the hyperbranched polymer has to be investigated. Acknowledgements For financial support the authors thank the German Science Foundation (DFG, ZE 990/1-1). We also would like to thank Gerhard Schaldach from the department of mechanical process engineering for his help with viscosity measurements. References [1] U. Gottschalk, K.D.J. Mundt, Modern biopharmaceuticals: design, development and optimization, in: Knäblein (Ed.), Thirty Years of Monoclonal Antibodies, Wiley-VCH, Weinheim, 2005, pp. 1105–1145. [2] G. Walsh, Biopharmaceuticals: recent approvals and likely directions, Trends Biotechnol. 23 (2005) 553–558. [3] Y. Liu, Y.L. Yu, M.Z. Chen, X. Xiao, Advances in aqueous two-phase systems and applications in protein separation and purification, Can. J. Chem. Eng. Technol. 2 (2011) 1–7. [4] M.W. Beijerinck, Ueber Emulsionsbildung bei der Vermischung wässriger Lösungen gewisser gelatinierender Kolloide, Colloid Polym. Sci. 7 (1910) 16–20. [5] P.A. Albertsson, Partition of Cell Particles and Macromolecules, John Wiley & Sons, New York, United States, 1985. [6] P.A.J. Rosa, I.F. Ferreira, A.M. Azevedo, M.R. Aires-Barros, Aqueous two-phase systems: a viable platform in the manufacturing of biopharmaceuticals, J. Chromatogr., A 1217 (2010) 2296–2305. [7] J. Persson, H.O. Johansson, I. Galaev, B. Mattiasson, F. Tjerneld, Aqueous polymer two-phase systems formed by new thermoseparating polymers, Bioseparation 9 (2000) 105–116. [8] S. Sturesson, F. Tjerneld, G. Johansson, Partition of macromolecules and cell particles in aqueous two-phase systems based on hydroxypropyl starch and poly(ethylene glycol), Appl. Biochem. Biotechnol. 26 (1990) 281–295. [9] M. van Berlo, K.C.A.M. Luyben, L.A.M. van der Wielen, Poly(ethylene glycol)–salt aqueous two-phase systems with easily recyclable volatile salts, J. Chromatogr., B 711 (1998) 61–68.

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Please cite this article in press as: A. Kulaguin-Chicaroux, T. Zeiner, Novel aqueous two-phase system based on a hyperbranched polymer, Fluid Phase Equilib. (2013), http://dx.doi.org/10.1016/j.fluid.2013.07.059