The retention behavior of diblock copolymers in gradient chromatography; Similarities of diblock copolymers and homopolymers

Journal of Chromatography A, 1593 (2019) 17–23

Contents lists available at ScienceDirect

Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

The retention behavior of diblock copolymers in gradient chromatography; Similarities of diblock copolymers and homopolymers Wolfgang Radke PSS Polymer Standards Service GmbH, 55128, Mainz, Germany

a r t i c l e

i n f o

Article history: Received 11 November 2018 Received in revised form 26 December 2018 Accepted 15 January 2019 Available online 15 January 2019 Keywords: Gradient chromatography Block copolymers Limiting conditions Poly(methy methacrylate)-block-poly(styrene) Theory

a b s t r a c t The retention of binary diblock copolymers in solvent gradient interaction chromatography (SGIC) was investigated theoretically and compared with experimental results. The isocratic and gradient elution behavior of binary block copolymers can be described by the equations of an equivalent homopolymer having a suitable critical eluent composition and size to pore size ratio. For diblock copolymers the adsorption-desorption transition occurs at a limiting interaction energy, which is characterized by a limiting interaction parameter cA,lim , like the critical interaction parameter of homopolymers. Both, the limiting interaction parameter and the critical interaction parameter are independent of pore size. However, while for homopolymers the critical energy is also independent of molecular size, the limiting interaction parameter of block copolymers depends on the size and composition of the macromolecule. Therefore, even for block copolymers of a fixed composition a molar mass independent elution cannot be realized at isocratic conditions. Since binary block copolymers in solvent gradients elute very close to the stronger adsorbing homopolymer, separation of the block copolymer from the stronger adsorbing homopolymer becomes difficult. A slightly better separation is expected to occur in larger pores. The close elution of block copolymers and homopolymers in gradient elution was confirmed for poly(methy methacrylate)-block-poly(styrene)s in chloroform-THF gradients on a bare silica column. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Liquid chromatography can separate polymers according to molecular size, chemical composition, functionality and other structural features [1–33]. This allows obtaining detailed information on the molecular heterogeneity of complex polymer mixtures. In ideal size exclusion chromatography (SEC) no enthalpic interaction between the stationary phase and the polymer molecules exists, resulting in separations according to the hydrodynamic size of the polymer molecules. In SEC larger molecules elute at lower elution volume than smaller ones. SEC allows determining molar masses and molar mass distributions by correlating the elution volume with molar mass via a calibration curve. If separations by chemical composition or end-group functionality are aimed for, methods of interaction polymer chromatography (IPC) are more appropriate. In IPC specific interactions of the repeating units with the stationary phase are tuned to achieve the desired

E-mail address: [email protected] https://doi.org/10.1016/j.chroma.2019.01.043 0021-9673/© 2019 Elsevier B.V. All rights reserved.

separations. For homopolymers the interaction strength increases with molar mass resulting in an increasing elution volume with increasing molar mass [34]. Such a molar mass dependence of elution volume characterizes the mode of liquid adsorption chromatography (LAC). If the adsorptive interactions of the repeating units are exactly compensated by the size exclusion effect the retention of a homopolymer becomes molar mass independent. Under these conditions non-functionalized linear homopolymers elute at the void volume of the column. Chromatography at these conditions is termed liquid chromatography at critical conditions (LCCC) or critical chromatography (CC). Critical conditions for a given homopolymer on a specified stationary phase correspond to a specific eluent composition and temperature. Hunkeler and Macko compiled a large number of critical conditions for different polymers [35]. Since molar mass does not longer influence retention, LCCC allows separating polymer molecules by small structural differences e.g. functional end-groups or block length in block copolymers [28]. The strong molar mass dependency in LAC rapidly results in elution times inappropriate for most practical applications.

18

W. Radke / J. Chromatogr. A 1593 (2019) 17–23

Therefore, the eluent strength is often varied during the chromatographic experiment, to systematically lower the interaction strength between the macromolecules repeating units and the stationary phase. Variations of eluent strength are required especially if polymers of different polarity and thus widely different adsorption strength are to be separated. Such alterations in eluent strength can be realized in a solvent gradient, which varies systematically eluent composition (solvent gradient interaction chromatography, SGIC) or by temperature variations (temperature gradient interaction chromatography TGIC) [36,37]. Brun [38,39] as well as Bashir [40,41] showed that in SGIC the elution volume of a homopolymer initially increases with increasing molar mass. However, for very high masses the molar mass dependence vanishes and the homopolymer elutes irrespective of molar mass at an eluent composition, which is very close to the critical one. In addition, Brun was able to show that chemically homogeneous statistical copolymers exhibit a critical point, which is characterized by an effective interaction energy for a statistical segment [42,43]. Since SGIC elutes high molar mass polymers in order of their critical points, separations of blends and statistical copolymers according to chemical composition can be realized, allowing determination of chemical composition distributions. However, for block structures an effective interaction energy does not exist anymore. That is why for block copolymers of a given composition critical conditions do not exist [42]. While for homopolymers SGIC results in an elution volume which first increases with molar mass and becomes constant for high molar masses, TGIC allows to obtain an elution order of either increasing or decreasing elution volume with molar mass. Even a nearly molar mass independent elution can be achieved, depending on the ratio of flow rate to the steepness of the temperature gradient [44]. While the elution behavior of various polymer structures in the different isocratic elution has been calculated theoretically, allowing predicting chromatograms and separations for given structures in the various isocratic modes, less understanding exists on the elution in SGIC. Therefore, the present manuscript investigates the retention of diblock copolymers in SGIC. 2. Theory Let us first recall some basics of the theory describing homopolymer elution. The elution volume of a polymer is given by the general chromatographic equation. VR = Vi + K × VP

(1)

where VR , Vi and VP are the elution volume, interstitial and pore volume of the column under investigation, while K is the distribution coefficient of the polymer. The distribution coefficient is defined as the ratio of the analyte concentration in the stationary phase to that in the mobile phase. The distribution coefficient of a homopolymer is determined by the two parameters R/D and R × c, with R being the mean square radius of the polymer molecule, D the pore diameter and c an interaction parameter describing the interaction strength between the repeating unit and the stationary phase. For LAC conditions c > 0 and the elution volume increases with molar mass, while c < 0 if a SEClike elution order is observed. At critical conditions of adsorption c = 0. The value of c depends on eluent composition. At critical conditions the distribution coefficient K = 1, meaning that the polymer molecule migrates through the column at the same average velocity as the eluent molecules. In SEC K < 1 and under adsorbing conditions K > 1, indicating a faster and slower velocity, respectively, of the polymer molecules as compared to the eluent. In SGIC strong adsorption (c > 0) of the homopolymer

molecules onto the stationary phase takes place upon injection, due to the weak initial eluent composition. With increasing eluent strength desorption occurs. The polymer molecules start moving when an eluent composition of sufficient strength reaches them. Due to the strong molar mass dependence of the retention coefficient desorption occurs only in a narrow range of eluent compositions close to the critical one. Lower molar mass polymer molecules, being relatively weakly adsorbed, might start migrating at eluent compositions well below the critical one, while the higher molar mass molecules require a stronger eluent to desorb. As the polymer becomes desorbed it will be surrounded by an eluent below the critical composition, i.e. the polymer moves with a velocity lower than that of the eluent. Consequently, compositions of increasing eluent strength will surpass the macromolecule, resulting in its acceleration. This acceleration continues as long as the eluent molecules are faster than the polymer. The condition of the polymer velocity being equal to the eluent velocity corresponds to the critical conditions K = 1. Therefore, in SGIC polymer molecules will elute at a composition below or equal to the critical one. The composition at elution of a gradient experiment therefore provides a lower bound for the critical composition of a homopolymer. Higher molar mass molecules are more strongly adsorbed than lower molar mass one. Therefore, the composition at elution of high molar mass polymers will be closer to the critical composition than for lower molar mass molecules [38,40–42,45]. To a first approximation the elution process of a high molar mass diblock copolymer in gradient chromatography can be described as follows: Upon injection, both blocks A and B may become adsorbed to the stationary phase. With increasing eluent strength, the repeating units of the weaker adsorbed block (block B) will desorb, while block A remains in the adsorbed state, preventing migration of the copolymer molecule. With further increase in eluent strength adsorption of block A decreases until at a specific eluent composition, which corresponds to a limiting adsorption strength (characterized by a specific interaction parameter cA,lim ) desorption of block A occurs, allowing elution of the molecule. If block B would not be bound to block A, this limiting interaction strength, cA,lim, would correspond to the critical interaction parameter cA = 0, as explained in the previous paragraph. However, the already desorbed B segments support desorption of the A block by a “pulling effect”, resulting in block copolymer elution at cA,lim >cA = 0. cA,lim corresponds to the value of cA which fulfills the equation KAB =K(cA = cA,lim ) = 1. This results from the fact that the molecule cannot move faster than the surrounding solvent, i.e. K < 1, as the molecule would experience conditions reestablishing adsorption. However, the molecule also cannot fall behind the eluent composition corresponding to K(cA,lim ) = 1 as the block copolymer would experience SEC conditions, forcing the molecule to elute faster than the surrounding solvent. Consequently, the polymer moves with the same velocity than the solvent only at K=1 and will experience varying surrounding solvents of varying interaction strength. Therefore, it is informative evaluating at which conditions K = 1. Based on the Gaussian chain statistics Gorbunov and Vakhrushev [46] derived for the distribution coefficient KAB of an diblock copolymer in a wide (RA , RB
 KAB

2 1 2 = 1 − √ gB + − g 2 A arctan  B 



 A B

−



where gi =Ri /d, ␭i =-ci ×d, i = Ri2 /R2 with R2 = RA2 + RB2 .

A B

 (2)

W. Radke / J. Chromatogr. A 1593 (2019) 17–23

For fully established SEC conditions of B segments, i.e. for B →∞, the third term vanishes resulting in

 KAB

2 2 ≈ 1 − √ gB − g 2 A arctan  



 A B

−



 A B

(3)

Changing eluent composition might alter the sizes of the individual blocks and thus of the whole macromolecule (RA , RB , R) but it will clearly affect the interaction of A units with the stationary phase (cA ). In the following we will discuss the transition from adsorbed to desorbed state, which usually occurs in a rather narrow window of eluent composition. Thus, the change of the molecular size is expected not to be large and will be ignored on the following. Solving Eq. (3) for cA at the condition KAB = 1 yields

 cA,lim =

× B

 R arctan

   A

B

−



where for the correlation between A and B with composition, we took advantage of the scaling relation of the mean squared radii of the blocks RA2 and RB2 with the number of the respective monomer units. According to Eq. (4) cA,lim depends on composition via A and B and on molar mass via R. With increasing size R, and thus with increasing total molar mass, cA,lim approaches zero, irrespective of the composition of the block copolymer. Consequently, based on the above approximate theory, high molar mass block polymers will elute close to the homopolymer A, irrespective of their composition. The composition related term and therefore cA,lim is always positive, indicating that the molecule will always elute at an eluent composition, which if applied isocratically, would result in adsorbing conditions, i.e. in elution after the solvent. cA,lim defines the transition from adsorption to exclusion, which for a homopolymer corresponds to the critical point. However, at a given block copolymer composition cA,lim decreases with R and thus with molar mass. Consequently, block copolymers of a given composition do not exhibit critical behavior and cannot elute irrespective of molar mass, as already stated by Brun [42,43]. The above simplified model assumes a true on-off mechanism operative in SGIC. However, a more realistic model requires considering the slow migration at eluent strength below the limiting one. Assuming that the effect of eluent composition on cA is much stronger than on molecular size, the following equation is valid for a gradient exhibiting a linear variation of cA with time: [40] B × tP dcA dcA = [K − 1] L d˚ dx

(5)

with dcA /d˚ < 0. Here dcA /d˚ describes the time rate of change of the interaction parameter of A segments, cA , with eluent composition, ˚. B is the gradient slope. L and tP are the length and the pore volume of the chromatographic column. According to Eq. (3) the distribution coefficient of the block copolymer can be written KAB ≈ 1 + A + c A ,    √ A 2 arctan −   . where A = −2gB /  and  = 2d B A  g  B

Inserting Eq. (3) into Eq. (5) and solving for cA results in A A + (cA0 + ) × exp{ × }  

 = B × tP

dcA d˚

Table 1 Characteristics of samples used. Sample Name

Mp /gmol−1

% Styrene

PMMA1 PMMA2 PMMA3 PMMA4 PMMA5 PMMA6 BC1 BC2 BC3 BC4 BC5 BC6 BC7 BC8 BC9 BC10

386000 93300 44500 23500 5090 2200 20500 50000 85000 184000 407000 81000 136000 99700 108000 100000

– – – – – – 48 44 50 48 50 33 31 26 50 12

(4)

A B

cA,final = −

19

(6)

Here cA ◦ is the value of the interaction coefficient at the start of the gradient. By comparing the definitions of A and  with Eq. (4) one identifies cA,lim = −

A = 

Thus,



 R arctan

B

   A

B

−





(7)

A B





cA,final = cA,lim + cA0 − cA,lim × exp  ×  Since cA =

dcA d

(8)

(˚ − ˚c ) the composition at elution becomes





˚ = ˚lim + (˚0 − ˚lim ) × exp  × 

(9)

where ˚0 and ˚lim are the composition at gradient start and the composition corresponding to the limiting eluent composition, respectively. The distribution  coefficient of a homopolymer close to the critical conditions (cR ≤ 0.4) can be described by [47]: KA ≈ 1 +

R cA R = 1 + dcA g 2 d

(10)

Note that in [47] the pore size is characterized via the pore diameter D = 2d. Inserting Eq. (10) into Eq. (2) and solving the differential equation one finds for the eluent composition of a homopolymer at the time of elution in a linear solvent gradient:



˚ = ˚c + (˚0 − ˚c ) × exp  × g 2



(11)

3. Experimental Commercial poly(methyl methacrylate) standards and commercial poly(methyl methacrylate)-block-poly(styrene)s (some samples were partially deuterated) of different molar masses were used (PSS Polymer Standards Service GmbH, Mainz, Germany). The sample characteristics are given in Table 1. For the gradient experiments a PSS SECcurity system equipped with a quarternary low-pressure gradient pump, an autosampler, column oven and a PSS SECcurity 1400 ELS detector (spray chamber temperature = 40 ◦ C, drift tube temperature = 60 ◦ C) was applied. The flow rate was set to 1 mL/min. Data were acquired and evaluated using PSS WINGPC Unity Software with Chrompilot for instrument control. The applied column was a Macherey & Nagel (Düren, Germany) 5␮ 100 Å Nucleosil column (250 × 4.6 mm length x ID). Column temperature was 35 ◦ C. The samples were dissolved at a concentration of 1 mg/mL in chloroform (VWR, Germany). The injection volume was 10 ␮L A lin-

20

W. Radke / J. Chromatogr. A 1593 (2019) 17–23

Fig. 1. Dependence of R x cA,lim on composition for diblock copolymers according to Eq. (7).

Fig. 2. Dependencies of cA,lim on composition ( B =0.1 (black), 0.25 (red), 0.5 (green), 0.75 (blue)) and molecular size for diblock copolymers. d = 100 (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

ear 10 min gradient starting at 100% chloroform and ending in pure tetrahydrofuran (THF, BASF Germany) was applied. 4. Results and discussion In the following discussion, all sizes (R, d) are given in multiples of the length of the repeating unit. For a given size R, the dependence of cA,lim on composition  B according to Eq. (4) is shown in Fig. 1, which shows a strong non-linearity. As expected, the larger the fraction of B, the stronger the adsorptivity (the larger cA,lim ) of the adsorbing block required to compensate the” pulling” steric exclusion effect of the non-adsorbed B block. Furthermore, at a given composition, cA,lim decreases with increasing size R, or equivalent with increasing molar mass (Fig. 2). This indicates that at a given composition shorter A blocks require larger cA values, i.e. stronger interaction per monomer unit, to compensate the SEC effect of the B block. cA,lim defines the transition from adsorbing to desorbing conditions for the block copolymer and corresponds to a specific eluent composition. At eluent compositions corresponding to cA < cA,lim the block copolymer would experience SEC conditions in isocratic elution and would elute before the column void volume, while the opposite is true for cA > cA,lim . For  B approaching zero, i.e. for the limiting case of a homopolymer of type A, cA,lim approaches zero, i.e. the transition occurs at critical conditions of the A block.

The dependencies of cA,lim on composition and molecular size are depicted in Fig. 2. With increasing molar mass cA,lim approaches zero, irrespective of composition. Although in the figure cA,lim is plotted versus R/d, the pore size has no effect on cA,lim within the limits of the model (cf. Eq. (7)). In other words, cA,lim , i.e. the transition from adsorption to desorption cannot be influenced by varying the pore size. This behavior equals the fact that the critical eluent composition, which defines the transition from adsorption to desorption of a homopolymer, is also independent of pore size. However, the extent of deviation from K = 1 at slightly off-limiting conditions, depends on pore size. If at the start of the gradient the eluent composition corresponds to cA < cA,lim , the block copolymer is not adsorbed at all. Berek introduced a chromatographic technique named chromatography at limiting condition of desorption (LC LDC) for macromolecular separation [48–51]. In LC LCD a good solvent favoring SEC conditions for the sample components is applied as sample solvent and as eluent. Immediately before the injection of the sample, a barrier liquid is introduced into the column. Due to the strong eluent conditions experienced by the sample components at the time of injection, the polymer components migrate faster than the surrounding solvent. Consequently, the macromolecules catch up with the previous introduced solvent barrier. Macromolecules for which the solvent barrier present a strong eluent penetrate and surpass the barrier, while macromolecules for which the barrier presents adsorbing conditions will be retarded and will elute immediately after the barrier, due to the strong eluent following the barrier. Thus, a separation of components adsorbed by the barrier from components penetrating the barrier is achieved. Attempts have been undertaken to separate diblock copolymers from homopolymer impurities [52–57]. However, these studies revealed that no generic LC LCD conditions could be established but the barrier conditions need to be adjusted to the specific composition and molar mass of the block copolymer to achieve the desired separation. This is easily understood based on the limiting interaction strength cA,lim defined in Eq. (4). As discussed above, cA,lim defines the transition of adsorption to desorption for diblock copolymers. For the diblock copolymer to penetrate the barrier cA ≤ cA,lim is required within the barrier. For the homopolymer A to not penetrate the barrier, the condition cA ≥ 0 needs to be fulfilled. Thus, a successful separation of homopolymer A from the diblock copolymer requires to adjust the solvent strength (as expressed by cA ) of the barrier to fulfill the condition 0≤ cA ≤ cA,lim . Looking into Fig. 2 it becomes clear that this requires extreme careful adjustment of the barrier composition even for polymers of moderate size. A molar mass and composition independent separation of homopolymer from the block copolymer is achieved only, if the barrier composition equals exactly the critical eluent composition of homopolymer A, i.e. if cA = 0 within the barrier. Keeping in mind that in a real chromatographic system some mixing of barrier solvent and eluent will take place, it becomes clear that establishing a generic LC LCD separation of block copolymer from homopolymer irrespective of molar mass and composition will be very hard to achieve. As discussed above cA,lim defines the transition from adsorption to desorption of block copolymers like the critical interaction of homopolymers. cA,lim allows estimating the elution behavior for a strict “on-off” elution mechanism, as it is approximately encountered for very high molar masses or in steep gradients. A more realistic description of the elution process in gradients is obtained from cA,final , however. Therefore, it is useful to have a closer look onto cA,final . Typical dependencies of cA,final as function of molecular size and composition for a given pore size d are shown in Fig. 3. As predicted above, for large molar masses cA,final approaches cA = 0, i.e. high molar mass diblock copolymers elute at eluent compositions, which are very close to the critical composition of

W. Radke / J. Chromatogr. A 1593 (2019) 17–23

Fig. 3. Dependence of cA,final on size to pore size ratio (R/d) of diblock copolymers for different fractions of comonomer B.  B = 0.01, 0.25, 0.5 and 0.75. Calculation details: d = 100, tP = 2 mL, B = 0.1 min−1 , dc/d˚ = -3, cA ◦ = 3.

Fig. 4. a) Elution profiles of PMMAs. PMMA1 (pink), PMMA 2 (light blue), PMMA 3 (green), PMMA 4 (dark blue), PMMA 5 (red), PMMA 6 (black). b) Elution profiles of poly(methyl methacrylate)-block-poly(styrene)s. BC1 (black), BC2 (red), BC3 (green), BC4 (dark blue), BC5 (light blue), BC6 (pink), BC7 (orange), BC8 (brown), BC9 (navy), BC10 (purple) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

homopolymer A, irrespective of copolymer composition. Since high molar mass homopolymers also elute at eluent compositions close to the critical one, it follows that the elution volume of homopolymer A is very close to the elution volume of the diblock copolymer. To verify above predictions a series of poly(methyl methacrylate)-block-poly(styrene)s of different molar mass and composition as well as a series PMMA standards of different molar masses were analyzed in a CHCl3 /THF gradient. In Fig. 4 the chromatograms of narrowly distributed PMMA standards are compared with the chromatograms of poly(methyl methacrylate)block-poly(styrene)s. While the two lowest molar mass standards (M < 6000 g/mol) elute significantly before the higher molar masses, the elution volumes of the high molar PMMAs are very close to each other. The composition at the time of elution is very close to the critical eluent composition [38,40–42,45]. The elution volumes of the block copolymers are very close to each other and they elute only slightly before the high molar mass PMMAs, which confirms the theoretical predictions. The small peak at approx. 3 mL corresponds to a polystyrene impurity in sample BC1. The poly(methyl methacrylate)-block-poly(styrene)s seem to reveal two slightly separated peak groups, which are split at approximately 9.5 mL. The earlier eluting peaks correspond to poly(methyl methacrylate)-block-poly(styrene)s containing

21

Fig. 5. Dependence of cA,final on pore size d and molecular size of diblock copolymers for different fractions of comonomer B.  B = 0.01, 0.25, 0.5 and 0.75. Calculation details: solid lines d = 100, broken lines d = 200. tP = 2 mL, B = 0.1 min−1 , dc/d˚ = -3, cA ◦ = 3.

approximately 50% polystyrene. Apart from the highest molar mass block copolymer the polystyrene contents in later eluting peak group are significantly lower (styrene contents 12–33%), which also fits to the expectations. However, when plotting the elution volumes of the poly(methyl methacrylate)-block-poly(styrene)s versus composition or versus molar mass, no reasonable correlation was observed, indicating that neither useful separations by composition nor according to molar mass can be achieved for the block copolymers. While the limiting interaction parameter cA,lim was found to be independent of pore size d, the question arises, whether the separation of block copolymers of different composition can be enhanced by variation of the pore size d. Since cA,lim does not depend on pore size, d, a potential dependence on pore size can only result from the exponential part of Eq. (8). Because g = R/d,  varies as 1/d for a given size of the macromolecule. Thus, the smaller the pore size, the faster cA,final approaches cA,lim for a given size and composition of the block copolymer. In Fig. 5 the dependencies on composition and molecular size are depicted for two different pore sizes. At a given molecular size (molar mass), the lines corresponding to different compositions are slightly better separated from each other at larger pore sizes (broken lined). Thus, based on this observation it follows that the separation of block copolymers by composition can be slightly enhanced by application of large pore size columns. As an example, the diblock copolymer of size R = 75 containing 1% B elutes nearly at cA = 0, irrespective of pore radius. A block copolymer of  B = 0.5 elutes in the calculated gradient at cA = 0.18 and cA = 0.035 for pores sizes of d = 200 and d = 100, respectively. By comparing the equations of homopolymers and block copolymers in isocratic mode (Eqs. (3), (10)) and in SGIC (Eqs. (9) and (11)) one recognizes that at the specified conditions retention of diblock copolymers and homopolymers follow the same equations in gradient and in isocratic chromatography. Thus, the elution behavior of a diblock copolymer with one block in SEC mode and the second block close to critical conditions can be well described by an equivalent homopolymer having a critical eluent composition ˚c,equiv = ˚lim = ˚c −



B



dcA /d˚ × R[arctan(

A )− B



(12) A B ]

22

W. Radke / J. Chromatogr. A 1593 (2019) 17–23

The change of interaction parameter with eluent composition of the equivalent homopolymer is identical to dcA /d˚ (dcA,equiv. /d˚ = dcA /d˚) while size of the equivalent homopolymer is given by



2 gequi v.

2 = /d = g 2 arctan 





A B

−



A B



(13)

The fact that the elution behavior of an block copolymer can be described via the behavior of a corresponding homopolymer significantly eases predicting separations by virtual chromatography approaches [40,45], as no separate equations need to be programmed. References [1] H. Pasch, Chromatographic investigations of macromolecules in the critical range of liquid chromatography: 3. Analysis of polymer blends, Polymer 34 (1993) 4095–4099. [2] H. Pasch, M. Augenstein, Chromatographic investigations of macromolecules in the critical range of liquid chromatography. 5. Characterization of block copolymers of decyl and methyl methacrylate, Makromol. Chem. 194 (1993) 2533–2541. [3] H. Pasch, H. Much, G. Schulz, Characterization of functional homopolymers and block copolymers by chromatographic methods, J. Appl. Polym. Sci. Symp. 52 (1993) 79–90. [4] H. Pasch, A. Deffieux, I. Henze, M. Schappacher, L. Rique-Lurbet, Analysis of macrocyclic polystyrenes. 1. Liquid chromatographic investigations, Macromolecules 29 (1996) 8776–8782. [5] D. Braun, I. Henze, H. Pasch, Functionality type analysis of carboxy-terminated oligostyrenes by gradient high-performance liquid chromatography, Macromol. Chem. Phys. 198 (1997) 3365–3376. [6] H. Pasch, B. Trathnigg, HPLC of Polymers., Springer, Berlin, 1997. [7] D. Braun, I. Kramer, H. Pasch, S. Mori, Phase separation in random copolymers from high conversion free radical polymerization. Part 2. Chemical heterogeneity analysis of poly(styrene-co-ethyl acrylate) by gradient HPLC, Macromol. Chem. Phys. 200 (1999) 949–954. [8] I. Krämer, H. Pasch, H. Handel, K. Albert, Chemical heterogeneity analysis of high-conversion poly[styrene-co-(ethyl acrylate)]s by NMR and online coupled SEC-NMR, Macromol. Chem. Phys. 200 (1999) 1734–1744. [9] W. Radke, Polymer separations by liquid interaction chromatography: principles–prospects–limitations, J. Chromatogr. A 1335 (2014) 62–79. [10] W. Radke, J. Falkenhagen, Liquid interaction chromatography of polymers, in: S. Fanali, P.R. Haddad, C. Poole, P. Schoenmakers, D. Lloyd (Eds.), Liquid Chromatography Applications, Elsevier, 2013, pp. 93–129. [11] H.O. Ghareeb, W. Radke, Separation of cellulose acetates by degree of substitution, Polymer 54 (2013) 2632–2638. [12] T. Li, S. Strunz, W. Radke, R. Klein, T. Hofe, Chromatographic separation of polylactides by stereochemical composition, Polymer 52 (2011) 40–45. [13] M. AlSamman, W. Radke, A. Khalyavina, A. Lederer, Retention behavior of linear, branched, and hyperbranched polyesters in interaction liquid chromatography, Macromolecules 43 (2010) 3215–3220. [14] W. Radke, Chromatography of polymers, in: Y. K.G. Matyjaszewski, L. Leibler (Eds.), Macromolecular Engineering, Wiley-VCH, Weinheim, 2007, pp. 1881–1936. [15] W. Radke, K. Rode, A.V. Gorshkov, T. Biela, Chromatographic behavior of functionalized star-shaped poly(lactide)s under critical conditions of adsorption. Comparison of theory and experiment, Polymer 46 (2005) 5456–5465. [16] J. Gerber, W. Radke, Separation of linear and star-shaped polystyrenes by 2-Dimensional chromatography, ePolymers 045 (2005). [17] T. Chang, Chromatographic separation of polymers, e. al., in: Y.W (Ed.), Recent Progress in Separation of Macromolecules and Particulates, ACS, Washington, 2018, pp. 1–17. [18] S. Banerjee, P.N. Shah, Y. Jeong, T. Chang, K. Seethamraju, R. Faust, Structural characterization of telechelic polyisobutylene diol, J. Chromatogr. B Analyt. Technol. Biomed. Life Sci. 1376 (2014) 98–104. [19] W. Lee, T. Chang, Non-size-exclusion chromatography analysis of synthetic polymers, in: R.A. Meyers (Ed.), Encyclopedia of Analytical Chemistry, Wiley, Chichester, 2010, pp. 1–23. [20] T. Chang, Polymer characterization by interaction chromatography, J. Polym. Sci. Part B: Polym. Phys. 43 (2005) 1591. [21] I. Park, S. Park, D. Cho, T. Chang, E. Kim, K. Lee, Y.J. Kim, Effect of block copolymer chain architecture on chromatographic retention, Macromolecules 36 (2003) 8539–8543. [22] P. Schoenmakers, P. Aarnoutse, Multi-dimensional separations of polymers, Anal. Chem. 86 (2014) 6172–6179. [23] Mv. Hulst, Avd. Horst, W.T. Kok, P.J. Schoenmakers, Comprehensive 2-D chromatography of random and block methacrylate copolymers, J. Sep. Sci. 33 (2010) 1414–1420. [24] X. Jiang, A. van der Horst, V. Limac, S.P. J, Comprehensive two-dimensional liquid chromatography for the characterization of functional acrylate polymers, J. Chromatogr. A 1076 (2005) 51–61.

[25] X. Jiang, P.J. Schoenmakers, X. Lou, V. Lima, J.L.J. van Dongen, J. Brokken-Zijp, Separation and characterization of functional poly(n-butyl acrylate) by critical liquid chromatography, J. Chromatogr. A 1055 (2004) 123–133. [26] S.M. Weidner, J. Falkenhagen, K. Knop, A. Thünemann, Structure and end-group analysis of complex hexanediol-neopentylglycol-adipic acid copolyesters by matrix-assisted laser desorption/ionization collision-induced dissociation tandem mass spectrometry, Rapid Commun. Mass Spectrom. 23 (2009) 2768–2774. [27] J. Falkenhagen, G. Schulz, R.P. Krüger, H. Much, St. Weidner, Liquid adsorption chromatography near critical conditions of adsorption coupled with matrix-assisted laser Desorption/Ionization mass spectrometry, Int. J. Polym. Anal. Charact. 5 (2000) 549–562. [28] J. Falkenhagen, H. Much, W. Stauf, A.H.E. Müller, Characterization of block copolymers by liquid adsorption chromatography at critical conditions. 1. Diblock copolymers, Macromolecules 33 (2000) 3687–3693. [29] N. Apel, E. Uliyanchenko, S. Moyses, S. Rommens, C. Wold, T. Macko, K. Rode, R. Brüll, Selective chromatographic separation of polycarbonate according to hydroxyl end-groups using a porous graphitic carbon column, J. Chromatogr. A 1488 (2017) 77–84. [30] T. Macko, R. Brüll, Y.T. Zhu, Y.M. Wang, A review on the development of liquid chromatography systems for polyolefins, J. Sep. Sci. 33 (2010) 3446–3454. [31] A. Ginzburg, T. Macko, V. Dolle, R. Brull, High-temperature two-dimensional liquid chromatography of ethylene-vinylacetate copolymers, J. Chromatogr. A 1217 (2010) 6867–6874. [32] R. Chitta, R. Brüll, T. Macko, V. Monteil, C. Boisson, E. Grau, A. Leblanc, Characterization of ethylene-methyl methacrylate and ethylene-butylacrylate copolymers with interactive liquid chromatography, Macromol. Symp. 298 (2010) 191–199. [33] T. Macko, H. Pasch, Separation of linear polyethylene from isotactic, atactic, and syndiotactic polypropylene by high-temperature adsorption liquid chromatography, Macromolecules 42 (2009) 6063–6067. [34] G. Glöckner, Gradient HPLC of Copolymers and Chromatographic Cross-Fractionation, Springer, Berlin, 1991. [35] T. Macko, D. Hunkeler, Liquid chromatography under critical and limiting conditions: a survey of exp.system for synthetic polymers, Adv. Polym. Sci. 163 (2003) 62–136. [36] H.C. Lee, T. Chang, Polymer molecular weight characterization by temperature gradient high performance liquid chromatography, Polymer 37 (1996) 5747–5749. [37] W. Lee, H.C. Lee, S. Park, T. Chang, J.Y. Chang, Temperature gradient interaction chromatography of low molecular weight polystyrene, Polymer 40 (1999) 7227–7231. [38] Y. Brun, Y. Alden, Gradient separation of polymers at critical point of adsorption, J. Chromatogr. A 966 (2002) 25–40. [39] Y. Brun, The mechanism of copolymer retention in interactive polymer chromatography. II. Gradient separation, J. Liq. Chromatogr. Relat. Technol. 22 (1999) 3067–3090. [40] M.A. Bashir, W. Radke, Comparison of retention models for polymers. 1. Poly(ethylene glycol)s, J. Chromatogr. A 1131 (2006) 130–141. [41] M.A. Bashir, A. Brüll, W. Radke, Fast determination of critical eluent composition for polymers by gradient chromatography, Polymer 46 (2005) 3223–3229. [42] Y. Brun, P. Foster, Characterization of synthetic copolymers by interaction polymer chromatography: separation by microstructure, J. Sep. Sci. 33 (2010) 3501–3510. [43] Y. Brun, The mechanism of copolymer retention in interactive polymer chromatography. I. Critical point of adsorption for statistical copolymers, J. Liq. Chromatogr. Relat. Technol. 22 (1999) 3027–3065. [44] W. Radke, S. Lee, T. Chang, Temperature gradient interaction chromatography of polymers: a molecular statistical model, J. Sep. Sci. 33 (2010) 3578–3583. [45] M.A. Bashir, W. Radke, Predicting the chromatographic retention of polymers; Poly(methyl methacrylate)s and polyacryate blends, J. Chromatogr. A 1163 (2007) 86–95. [46] A.A. Gorbunov, A.V. Vakhrushev, Theory of chromatographic separation of linear and star-shaped binary block-copolymers, J. Chromatogr. A 1064 (2005) 169–181. [47] A.M. Skvortsov, J.G. Fleer, End-functionalized polymer as a tool to determine the pore size and the interaction parameters in liquid chromatography, Macromolecules 35 (2002) 8609–8620. [48] D. Berek, Liquid chromatography of macromolecules under limiting conditions of desorption. 1. Principles of the method, Macromolecules 31 (1998) 8517–8521. [49] D. Berek, T. Kitayama, K. Hatada, H. Ihara, I. Capek, E. Borsig, Liquid chromatography under limiting conditions of desorption IV. Separation of macromolecules according to their stereoregularity, Polym. J. (Tokyo, Japan) 41 (2009) 1144–1151. [50] D. Berek, Separation of minor macromolecular constituents from multicomponent polymer systems by means of liquid chromatography under limiting conditions of enthalpic interactions, Eur. Polym. J. 45 (2009) 1798–1810. [51] D. Berek, E. Macova, Liquid chromatography under limiting conditions of desorption 6: separation of a four-component polymer blend, J. Sep. Sci. 38 (2015) 543–549. [52] M. Rollet, B. Pelletier, A. Altounian, D. Berek, Sb. Maria, E. Beaudoin, D. Gigmes, Separation of parent homopolymers from polystyrene-b-poly(ethylene oxide)-b-polystyrene triblock copolymers by

W. Radke / J. Chromatogr. A 1593 (2019) 17–23 means of liquid chromatography: 1. Comparison of different methods, Anal. Chem. 86 (2014) 2694–2702. [53] M. Rollet, B. Pelletier, D. Berek, S. Maria, T.N.T. Phan, D. Gigmes, Separation of parent homopolymers from poly(ethylene oxide) and polystyrene based block copolymers by liquid chromatography under limiting conditions of desorption−2. Studies of samples obtained from ATRP and NMP, in: Controlled Radical Polymerization: Materials, ACS, 2015, pp. 327–347. [54] M. Rollet, B. Pelletier, A. Altounian, D. Berek, S. Maria, T.N.T. Phan, D. Gigmes, Separation of parent homopolymers from poly(ethylene oxide) and polystyrene-based block copolymers by liquid chromatography under limiting conditions of desorption – 1. Determination of the suitable molar mass range and optimization of chromatographic conditions, J. Chromatogr. A 1392 (2015) 37–47.

[55] D. Berek, Separation of parent homopolymers from diblock copolymers by liquid chromatography under limiting conditions of desorption 3. Role of column packing, Polymer 51 (2010) 587–596. [56] D. Berek, Separation of parent homopolymers from diblock copolymers by liquid chromatography under limiting conditions of desorption 4. Role of eluent and temperature, J. Sep. Sci. 33 (2010) 3476–3493. [57] Y. Li, E. Pearce, J.W. Lyons, D. Murray, T. Chatterjeec, D.M. Meunier, Fundamental study of the separation of homopolymers from blockcopolymers by liquid chromatography with preloaded adsorption promoting barriers, J. Chromatogr. A 1475 (2016) 41–54.

23