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Publicly Available Published by De Gruyter March 12, 2015

Solvent screening for the fractionation of industrial kraft lignin

Antoine Duval, Francisco Vilaplana, Claudia Crestini and Martin Lawoko
From the journal Holzforschung


The polydispersity of commercially available kraft lignins (KLs) is one of the factors limiting their applications in polymer-based materials. A prerequisite is thus to develop lignin fractionation strategies compatible with industrial requirements and restrictions. For this purpose, a solvent-based lignin fractionation technique has been addressed. The partial solubility of KL in common industrial solvents compliant with the requirements of sustainable chemistry was studied, and the results were discussed in relation to Hansen solubility parameters. Based on this screening, a solvent sequence is proposed, which is able to separate well-defined KL fractions with low polydispersity.


Lignin is the second most abundant biopolymer on Earth. The total amount of native lignins in woody plants is estimated to be in the range of 5×108–36×108 t year-1 (Gellerstedt and Henriksson 2008). To date, most of the technical lignins produced originate from paper pulp processes. Among them, the kraft process is predominant, with approximately 120 Mt year-1 of pulp produced, corresponding to a total amount of lignin processed close to 70 Mt year-1 (Lora 2008; Sixta 2008). Most of the kraft lignin (KL) is burnt in plants to generate energy and recover the pulping chemicals. Consequently, the commercially available fraction is only approximately 100 000 t year-1 (Strassberger et al. 2014). However, new processes for KL isolation have been developed in recent years, such as the Lignoboost process (Tomani 2010). The second generation of biorefinery projects developing around the world also contributes to the expectation that lignin availability will be increased in the near future, with a high potential for value-added applications, for example, in polymer science (Duval and Lawoko 2014).

KL is recovered after the alkaline treatment of wood chips in the presence of sulfur-containing reagents. The numerous reactions occurring during the process include the cleavage of β-O-4 ether bonds between lignin subunits, which release small lignin fragments and create new free phenolic OH groups. Condensation reactions (i.e., the formation of new C-C linkages) also occur, especially in the case of softwood lignins (Chakar and Ragauskas 2004). The degree of heterogeneity of native lignins is thus further increasing during kraft pulping both in terms of molar mass distribution and chemical structure. On the contrary, industrial applications of KL require high homogeneity, which can only be achieved by fractionations either by membrane filtration or solvent fractionation. The fractionation of KL by ultrafiltration is facilitated by the development of ceramic membranes able to work at high pH and temperatures (Wallberg and Jönsson 2006). The literature reports on KL membrane fractions with low polydispersity and high yields (Brodin et al. 2009; Toledano et al. 2010; Helander et al. 2013; Sevastyanova et al. 2014).

The solvent-based fractionation of lignin was first described in the 1980s. Mörck et al. (1986) successively applied dichloromethane, isopropanol, methanol (MeOH), and a mixture of MeOH and dichloromethane to extract fractions of increasing molecular weights (MWs). Later on, many authors implemented similar strategies, with different solvents including hexane (Wang et al. 2010; Cui et al. 2014), diethyl ether (Vanderlaan and Thring 1998; Yuan et al. 2009; Wang et al. 2010; Ropponen et al. 2011; Li et al. 2012), ethyl acetate (EtOAc; Li et al. 2012), propan-1-ol (Sun et al. 2000; Yuan et al. 2009; Gosselink et al. 2010), acetone (Ropponen et al. 2011; Li et al. 2012; Boeriu et al. 2014; Cui et al. 2014), or dioxane (Yuan et al. 2009; Wang et al. 2010; Li et al. 2012). Lignin fractions obtained by sequential solvent extractions have been tested for various applications, including the elaboration of polymer blends (Pouteau et al. 2003; Yue et al. 2012), the preparation of polyurethanes (Vanderlaan and Thring 1998) or adhesives (Gosselink et al. 2010), or the use as antioxidants (Li et al. 2012; Arshanitsa et al. 2013) or dispersants for carbon nanotubes (Teng et al. 2013).

In the present study, common industrial solvents should be screened for their ability to partially solubilize KL. The results will be evaluated in terms of the Hansen solubility parameter (HSP) theory (Hansen 2007). The expectation is to be able to rationalize the solvent fractionation process and to obtain KL fractions with low polydispersity.

Materials and methods

Softwood KL was obtained from the Lignoboost process (Tomani 2010). Before use, it was washed with acidic water (pH 2) to remove impurities and dried in a vacuum oven (24 h at 40°C). All solvents (analytical grade, >99.9%) were purchased from Fischer, VWR, Scharlau, or Sigma-Aldrich and used as received without further purification.

All solubility tests were conducted at room temperature (r.t.), except in the case of tert-butanol (t-buOH), when the mixture was heated to 40°C in an oil bath to maintain the solvent in the liquid state. Two grams of lignin were suspended in 20 ml solvent and gently stirred for 2 h. Then, the soluble and insoluble fractions were separated by filtration on grade 3 filter paper (Munktell, Sweden), and the insoluble fraction was resuspended again in the same solvent and stirred for 2 h. After filtration, the filtrates from both extractions were combined. The solvent was then removed under reduced pressure in a rotary evaporator to recover the soluble fraction. After full solvent evaporation, the fraction was removed from the flask with small amount of water and freeze dried. The insoluble fractions were left to dry overnight under a fume hood at r.t. All yields were calculated based on the dry mass of the recovered fractions.

Sequential solvent fractionation was performed twice with 10 and 20 g lignin, respectively. The protocol was similar to the solubility tests, except that the solvent volume was increased to maintain a concentration of 100 g l-1. At the end of the first step, the insoluble fraction was suspended in the following solvent and treated as before.

Size-exclusion chromatography (SEC) was performed on a SECcurity 1260 system (Polymer Standards Services, Mainz, Germany) coupled to a UV detector and a RI detector thermostated at 45°C. The separations were carried out through a GRAM PreColumn and two GRAM 1000 analytical columns in series (Polymer Standards Services, Mainz, Germany) with dimethylsulfoxide [DMSO; high-performance liquid chromatography (HPLC) grade, Scharlab, Sweden] with 0.5% (w/w) lithium bromide (LiBr; ReagentPlus (R), Sigma-Aldrich) as eluent, with a flow rate of 0.5 ml min-1 at 60°C. The lignin fractions were dissolved in native form (without derivatization) at r.t. in the SEC eluent (5 mg ml-1) and filtered through a 0.45 μm polytetrafluoroethylene syringe filter before injection. Standard calibration was performed with a set of narrow polydispersity pullulan standards (MW range, 342×105–3.44×105 g mol-1).

Before SEC in tetrahydrofuran (THF), the lignin samples were acetobrominated as reported elsewhere to ensure complete solubilization (Asikkala et al. 2012). Briefly, 5 mg lignin was suspended in 1 ml glacial acetic acid/acetyl bromide (9:1, v/v) for 2 h. The solvent was then removed under reduced pressure, and the residue was dissolved in THF and filtered over 0.45 μm syringe filter. SEC was performed on a Shimadzu LC 20AT chromatograph coupled to an SPD M20A UV diode array detector (280 nm). The separation was carried out through a set of columns connected in series (Varian PL gel MIXED-D 5 μm, 1–40K and PL gel MIXED-D 5 μm, 500–20K) with THF (Chromasolv®, HPLC grade, Sigma-Aldrich) as eluent (0.5 ml min-1 at 40°C). Standard calibration was performed with polystyrene standards (MW range, 162×106–5×106 g mol-1).

Klason lignin and carbohydrate analyses were performed according to TAPPI 222 om-02 and SCAN-CM 71:09. The analysis of sugar contents was performed on a Dionex ICS-3000 high-performance anion-exchange chromatography equipped with pulsed amperometric detector and a Dionex PA1 column. The column was calibrated with arabinose, galactose, glucose, xylose, and mannose. The acid-soluble lignin content was determined by UV spectrophotometry (Shimdazu dual-beam UV-2550 UV-visible instrument), assuming a lignin extinction coefficient of 128 l g-1 cm-1 (Dence 1992).

Results and discussion

Selection of solvents

Hexane, diethyl ether, dichloromethane, and dioxane are undesirable solvents for lignin fractionation in an industrial scale because of safety, environmental, and regulatory considerations. Alkanes, ethers, aromatic and chlorinated solvents were also excluded from the study for similar reasons (Curzons et al. 1999; Jiménez-González et al. 2004; Alfonsi et al. 2008). Polar aprotic solvents, such as dimethylformamide (DMF), dimethylacetamide (DMAc), or DMSO, are known to be good solvents for lignin, which are able to fully solubilize even highly polydisperse samples. These solvents are of great interest for analytical purposes, for example, as SEC eluents (Sjöholm et al. 1999a,b; Cathala et al. 2003; Ringena et al. 2006), but do not match the target criteria for lignin fractionation in industrial processes.

Thus, the solvents tested in the present study are classified as “preferred” according to industrial guidelines. Moreover, the focus was on solvents with low boiling points (b.p.) because of the energy-saving recovery and to avoid thermal modification of the lignin fractions (Table 1). Three classes of solvents were tested, including alcohols, ketones, and esters. Primary alcohols were tested up to a chain length of three carbons. Above this limit, the b.p. becomes too high for easy removal by evaporation (b.p. of butan-1-ol is 117°C). In addition, the simplest secondary and tertiary alcohols [iso-propanol (i-propOH) and t-buOH] were considered. The simplest ketones [acetone and methyl ethyl ketone (MEK)] were also evaluated. Longer ketones, such as methyl isobutyl ketone (MIBK), have recently been reported for the fractionation of biomass (Brudecki et al. 2012; Katahira et al. 2014), but the b.p. (116°C for MIBK) is too high for industrial processes. Among esters, only EtOAc was evaluated, mainly because of its higher industrial significance.

Table 1:

Properties of the solvents used for lignin fractionation.

TypeSolventAbbreviationb.p. (°C)Hansen solubility parameter
Methyl ethyl ketoneMEK79.616.09.05.1
EsterEthyl acetateEtOAc7715.85.37.2

Yields and MW of soluble fractions

The yields of the soluble fractions, collected after the removal of the solvents by evaporation under reduced pressure, are listed in Table 2. The yields have been plotted against the solvent chain length in Figure 1. For homologous series, an increase in the carbon chain length lowers the lignin solubility (Schuerch 1952; Horvath 2006). For a comparable solvent chain length, the solubility increases in the following order: alcohol<acetate<ketone.

Figure 1: Yields of the soluble fraction as a function of solvent chain length.

Figure 1:

Yields of the soluble fraction as a function of solvent chain length.

Table 2:

Yields of the soluble fraction (xsol) and average MW and polydispersity of the soluble and insoluble fractions in the different solvents, as measured by SEC in DMSO/LiBr.




Soluble fractionInsoluble fraction

(g mol-1)

(g mol-1)

(g mol-1)

(g mol-1)

AlcoholMeOH61.258020403.52386014 1203.66
EtOH46.846014003.04320010 7103.35
KetoneAcetone66.562024503.95407015 7603.87
MEK55.432013004.06187010 3905.56

All KL fractions were analyzed by SEC with DMSO/LiBr (0.5%) as eluent. SEC separates macromolecules based on their hydrodynamic size (i.e., the hydrodynamic volume, Vh) according to the “universal calibration” principle and not by molar mass (Grubisic et al. 1967; Hamielec and Ouano 1978; Vilaplana and Gilbert 2010). Therefore, all MW distributions (MWDs) reported in this article are relative to the linear molar mass of pullulans. This theoretical divergence, however, does not hinder to draw conclusions about the effect of solvent extraction on the lignins’ polydispersity. The MWDs of the soluble fractions are presented in Figure 2, and the Mn, Mw, and polydispersity index (PDI) data are listed in Table 2.

Figure 2: MWDs measured by SEC in DMSO/LiBr of the soluble fractions in alcohols (a), ketones, and ester (b).The MWD of the fraction soluble in 1-propOH was similar to the one in i-propOH and is not represented on (a) for the sake of clarity.

Figure 2:

MWDs measured by SEC in DMSO/LiBr of the soluble fractions in alcohols (a), ketones, and ester (b).

The MWD of the fraction soluble in 1-propOH was similar to the one in i-propOH and is not represented on (a) for the sake of clarity.

The MWDs of the soluble fractions in 1-propanol (1-propOH), i-propOH, t-buOH, and EtOAc are very similar and correspond to low MW lignin fragments, approximately from dimers to tetramers. Indeed, Schuerch (1952) already noted that low MW lignin fragments could be dissolved in a wide range of organic solvents. However, based on the yields of the soluble fractions, EtOAc seems to be the most selective among the tested solvents in terms of separating low MW lignin fragments.

The dissolution of higher MW lignin fragments is required to achieve higher yields. With this respect, MeOH and acetone are the most powerful among the solvents tested, judged by the yields of the collected fractions. A general correlation between the yield of the soluble fraction and its average MW is observed (Figure 3).

Figure 3: Correlation between the yield of the soluble fractions (xsol) and their average MWs (Mn, Mw) measured by SEC in DMSO/LiBr.

Figure 3:

Correlation between the yield of the soluble fractions (xsol) and their average MWs (Mn, Mw) measured by SEC in DMSO/LiBr.


The description of the solubility of solutes as a function of solvent properties has long been a subject of interest for both theoretical and practical reasons. Hildebrand was the first to introduce the term of solubility parameter, noted δ, defined as the square root of the cohesive energy density:

(1)δ=(EVm)1/2 (1)

where E is the solvent energy of vaporization and Vm is its molar volume (Hildebrand and Scott 1950).

According to this approach, a solute will likely to be dissolved in a solvent having δ close to its own. Schuerch (1952) tested a large number of solvents for their ability to dissolve lignin, which he related to their Hildebrand solubility parameters: solvents with δ close to 22.5 MPa1/2 were good solvents for lignin. Later on, group contribution models were developed to calculate δ for polymers based on their repetition motif. The literature data on δ of lignins are generally in the range of 28.0–29.9 MPa1/2 (Ni and Hu 1995; Quesada-Medina et al. 2010; Wang et al. 2011; Boeriu et al. 2014; Ye et al. 2014). Indeed, the solubility of lignin in mixtures of water and different organic solvents, such as 1,4-butanediol, ethanol (EtOH), THF, 1,4-dioxane, or acetone, was found to be the best with δ values of the mixture close to that of lignin (Ni and Hu 1995; Wang et al. 2011; Boeriu et al. 2014; Ye et al. 2014).

Theoretically, Hildebrand solubility parameters are, however, only applicable to strictly nonpolar systems (Hansen 2007). As an extension of Hildebrand’s approach, Hansen showed that the cohesive energy E results from three major interactions: dispersion forces, permanent dipole-permanent dipole interactions (i.e., polar forces), and hydrogen bonding (Hansen 1969). Based on this formalism, a solvent is characterized by a set of three parameters, called HSPs, related to dispersion forces (δD), polar interactions (δP), and hydrogen bonding (δH). HSPs are related to δ by the formula (Hansen 1969):

(2)δ2=δD2+δP2+δH2 (2)

Schuerch (1952) already noted that, for solvents of similar δ, the solubility increased with the hydrogen bonding ability. This can explain the partial solubility of lignin in alcohols of varying chain length (Table 2): the hydrogen bonding capacity (δH) decreases when the aliphatic hydrocarbon side chain becomes longer. However, this cannot explain the good solubility of KL in ketones, which have the lowest δH values (Table 1). The solvent polarity (δP) seems to be a good parameter to describe the partial solubility of KL in organic solvents, because a linear relationship is observed with the soluble yield (Figure 4a). The full solubility of KL in polar aprotic solvents, such as DMAc, DMF, or DMSO, is in accordance with this observation, because they all have high polarity (δP are 11.5, 13.7, and 16.4 MPa1/2, respectively). Nevertheless, the partial solubility in MeOH appears lower than expected (Figure 4a). The high association in alcohols through hydrogen bonding can indeed reduce the solvent power (Schuerch 1952), and similar observations apply to H2O/1,4-butanediol and H2O/EtOH solvent mixtures (Wang et al. 2011; Ye et al. 2014). However, the solvent polarity alone cannot describe properly lignin solubility, as visible on the unexpectedly high solubility in EtOAc (Figure 4a) or on the full solubility in pyridine or 1,4-dioxane, which have rather low δP (8.8 and 1.8 MPa1/2, respectively).

Figure 4: Yields of the soluble fractions as a function of solvent polarity, as expressed by HSP δP (a), or of the RED, as defined in Equation (4) (b).

Figure 4:

Yields of the soluble fractions as a function of solvent polarity, as expressed by HSP δP (a), or of the RED, as defined in Equation (4) (b).

Indeed, all three parameters δD, δP, and δH play a synergistic role in solubility and should be considered together rather than individually. In this context, a useful representation uses a space whose axes are the HSPs, called Hansen’s space. A solvent is then represented by a single point of coordinates (δD, δP, δH), whereas a solute is represented by a sphere, thus requiring a fourth parameter, the interaction radius (R0). For a given solute, the good solvents should be included in the sphere, whereas the nonsolvents should lie outside. The “solubility parameter difference” (Ra) is used to compare two substances within Hansen’s space (Hansen 2007):

(3)Ra=4(δD1-δD2)2+(δP1-δP2)2+(δH1-δH2)2 (3)

As solubility theoretically requires Ra<R0, it can be helpful for solubility prediction to consider the relative energy difference (RED), defined as:

(4)RED=RaR0 (4)

In this case, solubility should be achieved for RED<1.

Recently, genetic algorithms were applied for calculating lignin HSPs (Vebber et al. 2014), and the obtained values (21.7, 14.2, 16.9, and 13.5 MPa1/2 for δD, δP, δH, and R0) are in good agreement with previously published data (Hansen and Björkman 1998). Based on these values, the REDs were calculated for each of the aforementioned solvents and compared with the amount of lignin solubilized xsol. However, as seen in Figure 4b, no correlation was found.

HSPs thus partly fail to describe the partial solubility of KL in organic solvents. They are, however, powerful when it comes to the full solubility, as good solvents for KL have RED values smaller than 1 (e.g., DMAc, DMSO, DMF, or pyridine). The HSPs of lignin used for the calculation could be the source of error. Lignin HSPs calculated by Hansen (1969) were referred to milled wood lignin (MWL), whereas Vebber et al. (2014) gave no hints to the type of lignin considered. In view of the structural differences between KL and MWL, significant differences in terms of solubility parameters are expectable. In addition, the lignin structure is dependent on the MW. In particular, the content in phenolic OH groups, whose contribution to the HSPs δP and δH is high (Hansen and Björkman 1998), is inversely correlated to the MW (Mörck et al. 1988; Brodin et al. 2009; Cui et al. 2014; Sevastyanova et al. 2014).

From solvent screening to sequential fractionation

Based on the yields and MWDs, a solvent sequence has been defined for the fractionation of KL. Only common industrial solvents were chosen, whereas the solvent power within the sequence must be in increasing order. The fractionation scheme is represented in Figure 5. From the results of the solubility tests, the predicted yields for the sequential fractionation were calculated as follows:

Figure 5: Scheme of the sequential solvent fractionation applied to KL.

Figure 5:

Scheme of the sequential solvent fractionation applied to KL.


where y is the predicted yield of the fraction and x is the measured dissolved mass fraction, as reported in Table 2.

Two distinct sets of extractions have been performed, starting from 10 and 20 g KL, respectively. The yields of the fractions were found to vary by <2% between the sets. The highest yields are obtained for the fraction soluble in EtOAc (KL2) and the insoluble one (KL6), with 27–28% yield of the initial material. The fractions soluble in EtOH (KL3) and MeOH (KL4) present yields in the range of 13–20%. In this particular sequence, the yield of the soluble fraction in acetone (KL5) is low (6%), which makes it less attractive for further applications.

The yield plots “experimental vs. predicted data” (Figure 6a) show a very good correlation. However, for the insoluble fraction, the experimental yield is clearly lower than the expected one (27.1% vs. 33.5%). This difference corresponds to the losses during the process, which account for 4–5% of the starting material. Therefore, simple solubility tests are useful to define a sequential solvent fractionation of KL and to predict the corresponding yields.

Figure 6: Experimental yields of the sequential solvent fractionation, plotted against the predicted yields based on solubility tests (a) and MWDs of the corresponding fractions measured by SEC in DMSO/LiBr (b).

Figure 6:

Experimental yields of the sequential solvent fractionation, plotted against the predicted yields based on solubility tests (a) and MWDs of the corresponding fractions measured by SEC in DMSO/LiBr (b).

The MWDs of the different fractions are presented in Figure 6b, and the corresponding data are listed in Table 3. The average MWs are increasing gradually from KL2 to KL6. PDIs of 2 or lower are seen for all fractions, whereas the initial index of the unfractionated KL was higher than 6. The sequential membrane fractionation of lignins (Toledano et al. 2010; Sevastyanova et al. 2014) and other solvent-based fractionations (Mörck et al. 1988; Sun et al. 2000; Yuan et al. 2009; Wang et al. 2010) led to similar data.

Table 3:

Average MWs and polydispersity from SEC in DMSO/LiBr and composition of the lignin fractions.


(g mol-1)

(g mol-1)


Klason lignin

Acid-soluble lignin

KL1 initial101065006.441.7±0.186.5±0.04.1±0.2
KL2 EtOAc3507502.140.1±0.176.3±0.59.6±0.4
KL3 EtOH101020602.040.8±0.187.8±0.44.0±0.4
KL4 MeOH211037401.771.0±0.092.8±0.90.8±0.3
KL5 acetone299051501.720.1±0.194.2±0.40.3±0.3
KL6 insoluble640017 7402.773.4±0.186.1±0.40.3±0.3

Yields are based on weight (dry basis).

For comparison, the MWDs of the fractions were also determined in THF as eluent after acetobromination (Asikkala et al. 2012), as those conditions were recommended from the results of a round-robin analysis (Baumberger et al. 2007). The comparison of the MWDs in DMSO and in THF is given in Figure 7, and the correlations between the average MW values thus obtained are presented in Figure 8. As expected, the data of the two systems correlate fairly well in the intermediate MW range but show certain divergences in some of the fractions studied. These may be due to the differences in the hydrodynamic volume of the standards used for calibration (pullulan vs. polystyrene), solute affinity to column matrices, or possible aggregation phenomena (Gellerstedt 1992; Fredheim et al. 2002; Ringena et al. 2006; Baumberger et al. 2007). In addition, side reactions such as bromination, hydrolysis, or condensation can be promoted by the acidic environment and the release of HBr during acetobromination, and may also contribute to the observed discrepancies.

Figure 7: Comparison of the MWDs of the fractions KL1 to KL6 (a–f) measured, respectively, in DMSO/LiBr (nonderivatized lignins) or in THF (acetobrominated lignins).

Figure 7:

Comparison of the MWDs of the fractions KL1 to KL6 (a–f) measured, respectively, in DMSO/LiBr (nonderivatized lignins) or in THF (acetobrominated lignins).

Figure 8: Correlation between MW values obtained by SEC in DMSO (nonderivatized lignins) and in THF (acetobrominated lignins).

Figure 8:

Correlation between MW values obtained by SEC in DMSO (nonderivatized lignins) and in THF (acetobrominated lignins).

The results of carbohydrate analysis conducted on the initial lignin and the isolated fractions are presented in Table 3. The unfractionated KL contains 1.7% carbohydrates. The highest carbohydrate content was found in the highest MW fraction KL6 (3.4%). The residual carbohydrates are likely to exist as lignin-carbohydrate complexes, in which the components are chemically bound and the carbohydrates thus contribute to the MW of the fraction. All other fractions are relatively pure with total carbohydrate content below 1%. The Klason lignin content increases with the fraction’s MW, except for the less pure KL6 fraction. This can be explained by the high content of low MW fractions in acid-soluble lignin, up to almost 10% for the EtOAc soluble fraction KL2.


Common industrial solvents were screened for their capacity to solubilize KL. Low MW fragments were found to be soluble in all solvents, but the selectivity of EtOAc for this fraction was the best. HSPs failed to describe accurately the observed results. Further analysis focusing especially on the HSPs of lignin in relation to the chemical structure and molar mass are needed to enhance the predictability of lignin solubility according to Hansen’s theory.

The results were finally exploited to define a solvent sequence composed of only common industrial solvents. These were able to separate five lignin fractions with polydispersity reduced below 2 and with good reproducibility. Of particular interest could be the EtOAc soluble fraction, which was found to be free from sugar and had Mn and Mw values of 350 and 750 g mol-1, respectively. This fraction contains phenolic fragments up to tetramers, which could find interest as prepolymers for the synthesis of several kinds of thermosets or thermoplastics. A detailed structural analysis of the lignin fractions is currently under investigation and will be the subject of a forthcoming paper.

Corresponding author: Martin Lawoko, Wallenberg Wood Science Center (WWSC), KTH Royal Institute of Technology, Department of Fiber and Polymer Technology, SE-100 44 Stockholm, Sweden, e-mail:


The Knut and Alice Wallenberg Foundation is acknowledged for funding. Dr. Heiko Lange (Tor Vergata University) is thanked for his help and fruitful discussions.


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Received: 2014-11-28
Accepted: 2015-2-17
Published Online: 2015-3-12
Published in Print: 2016-1-1

©2016 by De Gruyter