Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Correlation between Comprehensive 2D Liquid Chromatography and Monte Carlo Simulations for Branched Polymers Nico Apel,† Vaidyanath Ramakrishnan,‡ Elena Uliyanchenko,‡ Stephan Moyses,§ Christian Wold,‡ Tibor Macko,† and Robert Brüll*,† †
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Division Plastics, Group Material Analytics, Fraunhofer Institute for Structural Durability and System Reliability (LBF), Schlossgartenstr. 6, 64289 Darmstadt, Germany ‡ SABIC, Plasticslaan 1, 4612 PX Bergen op Zoom, The Netherlands § SABIC, 1600 Industrial Blvd., Sugar Land, Texas 77478, United States S Supporting Information *
ABSTRACT: Detailed knowledge on structural information is required to derive the rheological properties of branched polymers. Size-exclusion chromatography with triple-detection (TD-SEC), comprising a concentration, a light scattering, and a viscosity detector, is a powerful tool to analyze the degree of branching of polymers as a function of their molar masses. However, TD-SEC alone is incapable of fully deconvoluting complex polymer systems. In this study we discuss a more sophisticated approach that includes coupling of TD to our recently described novel online twodimensional liquid chromatography method (2D-LC), based on solvent gradient at near-critical conditions in the first dimension. Thus, a contour plot of the branching ratio is presented, and unique detailed information on the degree of branching can be derived for branched polycarbonate (PC) sample. Furthermore, the molar mass distributions of separated linear and branched PC chains as well as their fractions in the polymer are quantified. The corresponding data are correlated to Monte Carlo simulations of the polycondensation process of a branched PC, and both methods show a high level of agreement in the determined molar mass distributions of the linear and branched PC chains as well as their fractions. Finally, the influence of chemical structure on rheological properties is demonstrated.
1. INTRODUCTION Poly(bisphenol A carbonate) (PC) is a polycondensation polymer, and it has excellent optical transparency, mechanical toughness, and good electrical insulating properties, which are exploited in a wide variety of applications ranging from data storage (CD, DVD) to automotive, electrical, and electronical industries.1 PC is commercially produced by two different polymerization processes. The interfacial process yields mainly fully end-capped PC, which is prepared in a two-phase liquid− liquid (methylene chloride−aqueous) system from phosgene and bisphenol A (BPA).2 Contrary to that, a partially uncapped PC is obtained in the melt process, where diphenyl carbonate (DPC) and BPA are reacted via transesterification.2 Thus, the polymer chains might be phenolic-end-capped or contain free hydroxyl end-groups.3 In addition to the heterogeneity with regard to end-groups, PC also reveals distributions in other molecular metrics such as molar mass or sometimes branching, which affect the macroscopic properties.4−6 Branching may be intentionally obtained by adding a tri-OH functional monomer such as 1,1,1-tris(p-hydroxyphenyl)ethane (THPE). The branching influences the rheological properties of the melt; i.e., higher © XXXX American Chemical Society
degrees of long chain branching yield higher melt elasticity at low shear rates and shear thinning at high shear rates.4,6,7 Thus, the branching directly affects the processing conditions of PC and allows new applications such as blow molding. Consequently, although material end-properties may be available, detailed information on the actual chemical microstructure of PC is highly desired to understand and control final processing and mechanical properties. To this end, the combination of characterization methods, which provide information on the material composition, with simulation, which allows correlating the material composition with their rheological properties, has gained popularity. Especially the combination of chromatography, which enables a sensitive separation of model branched samples, with viscoelastic simulations was reported in the literature and demonstrated promising outcomes.7−11 However, exactly establishing branching characteristics is generally not an easy task due to the high complexity of the Received: March 29, 2018 Revised: June 16, 2018
A
DOI: 10.1021/acs.macromol.8b00667 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules molecular metrics of the polymer.12−14 Most of the commonly applied analytical approaches, such as nuclear magnetic resonance (NMR) spectroscopy or triple-detection sizeexclusion chromatography (TD-SEC), suffer from codetermination of linear and branched species and therefore may lead to a misinterpretation of the results.15 In a TD-SEC experiment downstream to a SEC column, which separates a polymer according to its hydrodynamic volume, a TD system is installed consisting of a light-scattering (LS) detector, a concentration-sensitive detector (usually refractive index, RI), and a viscometer (VI). 16 The combination of LS and RI detector allows a determination of the molar masses (Mw,LS) in each elution slice of the SEC experiment. Furthermore, the mean-square radius of gyration (Rg2) can be determined using a multiangle LS detector.16,17 As Rg2 is highly affected by branching present in the polymer chain, the comparison of Rg2 at a determined molar mass (Rg2Br,M) with Rg2 of an absolute linear reference sample at the same molar mass (Rg2Lin,M) enables quantification of branching, as was outlined by Zimm and Stockmayer.18 Rg2 g=
Rg
In the present paper, we describe a chromatographic setup, which amplifies the power of our new 2D-LC method by employing TD. The aim is to overcome issues in TD-SEC with regard to the discussed coelution and in that way accessing detailed information about branching for complex synthetic polymers. To the best of our knowledge there have been only very few publications dealing with the implementation of multiple-detection in 2D-LC, and none of these presented a contour plot of the branching ratio g or g′.20,24 The structural information, which is derived from the 2D-LC with TD, is then correlated to Monte Carlo (MC) simulations of the PC polycondensation reaction and with rheological properties of the materials.
2. EXPERIMENTAL SECTION 2.1. Samples. PC samples were obtained from SABIC, Bergen op Zoom, The Netherlands. The number-average (Mn) and weightaverage (Mw) molar masses, as determined by SEC with TD, are listed in Table 1. The experimental setup and details of the analyses are
Table 1. Average Molar Masses, End-Capping Level, and THPE Content of the Analyzed PC Samples
Br,M
2 Lin,M
From the branching ratio (g) information on the architecture of the branched materials can be derived. As a precise determination of Rg2 via LS is limited to Rg > 10 nm due to a loss of angular scattering dependence for smaller polymer chains, the VI is frequently applied to determine the intrinsic viscosity ([η]) of the SEC slices.16 Similar to Rg2, [η] is also affected by branching in the chain, as described by Zimm and Kilb.19 Therefore, the branching ratio in the case of [η] can be established similarly to the one of Rg2. g′ =
sample
Mn [kDa]
Mw [kDa]
fully end-capped
content THPE
PC1 PC3
12.2 15.1
29.0 43.8
yes no
− (linear) 0.86% (branched)
stated in section 2.2. End-capping of the sample was analyzed by 1H NMR spectroscopy according to the method described by Kim et al.25 2.2. 2D-LC with TD-SEC. In the first dimension (SG-NCC), an Agilent 1100 series HPLC system from Agilent, Waldbronn, Germany, consisting of a vacuum degasser, a quaternary gradient pump, an autosampler, and a column oven was used. A normal-phase Nucleosil column 250 × 4.0 mm (L × i.d.), ϕ 7 μm, 1000 Å, obtained from Macherey-Nagel (Düren, Germany), was thermostated in the column oven at 45 °C. Chloroform (CHCl3) stabilized with 0.002% 2-methyl-2-butene, which served as adsorption promoting eluent, and methyl tert-butyl ether (MTBE), which served as desorption promoting eluent, were purchased from Merck, Darmstadt, Germany. As the content of MTBE, which was required to completely desorb the PC from the silica column, was very low, a 97.5/2.5 vol % CHCl3/ MTBE solution was used as desorption promoting eluent, which was premixed before its application. This allowed exploiting higher flow rates of the gradient pump and therefore improving the accuracy and reliability of the applied eluent composition. A flow rate of 0.01 mL/min and a mobile phase gradient CHCl3 → 97.5/2.5 vol % CHCl3/MTBE over 3000 min were applied. In the second dimension a 1260 series HPLC system from Agilent, consisting of a vacuum degasser, an isocratic pump, an autosampler, and a column oven, was used. A UV detector (254 nm) and an Agilent 1260 Infinity Multidetector suite (MDS) were applied as detectors. The MDS was equipped with a differential RI detector (λ = 658 nm), a dual angle (15°, 90°) LS detector (λ = 658 nm), and a four-capillary VI. The detectors were arranged in series. A specific refractive index increment (dn/dc) of 0.155 mL/g was determined for PC at λ = 658 nm and 30 °C in CHCl3. A flow rate of 1.5 mL/min was applied with CHCl3 as eluent in the second dimension. A PSS SDV column, 300 × 8 mm (L × i.d.), 5 μm, 10 000 Å, obtained from Polymer Standards Services (PSS), Mainz, Germany, was installed. The instrument calibration was performed with a PS standard (Mw = 98 kDa, ĐM = 1.02). The performance of the VI was confirmed analyzing a linear PC sample. The Mark−Houwink parameters αexp = 0.74 and Kexp = 0.0291 mL/g were obtained at 30 °C in CHCl3, which were in line with literature values (αlit = 0.74 and Klit = 0.0301 mL/ g).26 An electronically controlled 8-port VICI valve from Valco Instruments, Houston, TX, equipped with two loops of 200 μL
[η]Br,M [η]Lin,M
The determined values for g′ can be related to g; however, conversion requires knowledge of the viscosity shielding ratio (ϵ), which depends on a number of variables such as solvent, temperature, and molar mass.17 A further problem in all TDSEC measurements is the fact that polymer chains with different degree of branching but same hydrodynamic volume coelute and therefore are simultaneously detected, which may lead to misinterpretation of the calculated structural information.15,20−22 Recently, we published a chromatographic approach that might help to overcome these issues.23 By applying twodimensional liquid chromatography (2D-LC) with a solvent gradient at near-critical conditions (SG-NCC) in the first dimension and SEC in the second dimension, we were able to separate PC chains with different branching levels. This could be achieved as the applied solvent gradient in the first dimension was in a very narrow range around the critical point of adsorption and, thus, enabled an end-group separation. As branching results in additional end-groups to the polymer chain, we could separate PC branched structures based on differences in end-capping. Furthermore, since the hydrodynamic volumes of linear PC chains differ from the one of branched PC chains, hyphenation of the SG-NCC separation with SEC as second dimension also allowed separating linear and branched PCs with the same number of end-groups. B
DOI: 10.1021/acs.macromol.8b00667 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules
Figure 1. Color-coded contour plots of sample PC3 recorded with (a) RI detector, (b) LS detector, (c) VI detector (DP = differential pressure), and (d) UV detector. The corresponding scales in mV and Pa for the detector responses are presented in the figure. each, was installed to hyphenate the two chromatographic dimensions. The switching operation of the valve was triggered by an output relay, which was controlled by WinGPC software from PSS. Samples were dissolved in CHCl3 at a concentration of 100 mg/ mL. Signals were collected after the second dimension and processed using Agilent GPC/SEC software and OriginPro 9.1.0G from OriginLab Co., Northampton, MA. The delimitation of the spots in the contour plots that were obtained with 2D-LC was performed with software MATLAB 2012, while the minimum value between two adjacent spots was used for setting the borderline between the spots. 2.3. Linear Viscoelastic Measurements. The rheological response of the PC samples was measured with the commercial strain-controlled Advanced Rheometric Expansion System (ARES-G2, TA Instruments). Small-amplitude oscillatory shear tests were carried out using a 25 mm parallel plate geometry to determine the linear viscoelastic flow properties. The tests were carried out in a temperature range of 150−250 °C, frequency range of 0.1−100 rad/s, and a gap of 1 mm. Specimens for the tests were compressionmolded to 25 mm disks from the granulate material at 250 °C. Special care was taken to avoid degradation during the experiments by providing a nitrogen gas atmosphere and imposing a minimal heat induction time to the samples. All tests were done in triplicate and gave identical results within 1% system error.
3. RESULTS AND DISCUSSION 3.1. 2D-LC with Triple Detection. As outlined in the Introduction, coupling of the 2D-LC method with TD holds great potential for the characterization of branched polymers, since it enables the elucidation of structural information as well as the determination of absolute molar masses. Furthermore, the hyphenation can solve coelution issues of linear and branched species, which occur in the case of TD-SEC. However, only very few studies have been published describing the augmentation of 2D-LC by multiple detection.20,24 This might be explained by the complexity and high number of experimental parameters that need to be optimized (e.g., flow rates of the individual dimensions, measurement times, and the detector sensitivities). For that purpose, we provide a detailed description on the determination of the experimental parameters for the augmentation of 2D-LC by TD in the Supporting Information. Besides, the experimental parameters for the 2D-LC setup coupled with TD are summarized in section 2.2. For a detailed method development of the basic 2D-LC setup, a systematic assignment of the spots separated by the 2D-LC, and an explanation of the underlying separation C
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Macromolecules Table 2. Assignment of the Spots Delimited in Figure 1a to the Corresponding PC Structures
sequently, the VI is regularly used to determine [η] and to derive the degree of branching, since it can be more accurately established for lower molar masses compared with the LS.16 Hence, based on the LS response Mw,LS and based on the VI response, [η] of each analyzed elution slice can be determined. As the function of [η] in dependence of the molar mass for an absolute linear polycarbonate is given by the Mark−Houwink equation, detected deviations from these curve characteristics indicate the presence of branching. Thus, as stated in the Introduction, the branching ratio g′ is a measure of the degree of branching in an analyzed sample, while g′ = 1 corresponds to linear and g′ < 1 corresponds to branched structures. The determined contour plot of g′ resulting from the contour plots of the RI, LS, and VI responses is presented in Figure 2. To the authors’ best knowledge, this represents the first reported contour plot of the branching ratio. An initial assignment of the spots to the structures based on matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and HPLC data was given in the previous study.23 The peaks eluting early in the first dimension corresponded to linear chains, while later eluting
mechanism, we refer the interested readers to our recently published paper.23 To summarize, the developed separation in the first dimension allows for a separation according to endgroups. As branching results in additional end-groups to the polymer chain, we could separate PC branched structures based on differences in end-capping. As the separation principle (according to end-groups) is superimposed by a separation according to molar mass, a hyphenation of the setup to 2D-LC applying SEC (separation according to molar mass) in the second dimension enabled a significant improvement in the separation of the single end-capping and branching structure types. We notice that the contour plot of sample PC1 with an UV detector was published recently.23 The sample PC1 was fully end-capped and contained only linear macromolecules; i.e., its contour plot contained only one spot. The corresponding color-coded contour plots of the RI, LS, and VI responses for the sample PC3, which contains linear as well as branched macromolecules, are shown in Figures 1a, 1b, and 1c, respectively. Furthermore, Figure 1d shows the UV response. Although both the RI and UV detectors are directly proportional to the concentration of the PC in the eluate and, thus, the contour plots provide the identical information, the response of the UV detector revealed a much higher sensitivity than the RI response in the present case (compare maximum responses in Figures 1a and 1d: RI: 28 mV compared with UV: 500 mV). As result, the UV detector manifests the presence of spot 3 at an elution volume of about 1400 min in the first dimension (Figure 1a), which is less clear in RI as will be discussed later. Based on our previous study, the delimited spots in Figure 1a can be assigned to specific end-group structures as presented in Table 2. As expected, differences in the intensity progression can be observed in the contour plots of UV and RI detector responses compared with those of LS and VI, as the latter are more sensitive toward higher molar masses; i.e., they show higher intensities in that range. PC, as a polycondensation product, typically reveals weightaverage molar masses of several tens-of-thousand daltons, and thus, an accurate measurement of Rg2 by LS in a TD-SEC experiment to analyze the degree of branching is complicated. It has to be mentioned that, contrary to Rg2, the molar masses (Mw,LS) are precisely obtained by the LS detector. Con-
Figure 2. Color-coded contour plot of g′ resulting from the contour plots of the RI, LS, and VI responses. Also shown is the grid for the spot delimitation (as obtained from the RI plot). D
DOI: 10.1021/acs.macromol.8b00667 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 3. Molar Ratios of the Single Monomers in the Recipes Used in the MC Simulations of PC1 and PC3
branching on molar mass, which is important to understand and predict the material properties. 3.2. Comparison with Monte Carlo Simulations. The results presented in the previous section are further strengthened using Monte Carlo (MC) simulations. MC simulations have been widely used to describe the polymerization statistics not only of polycondensation polymers such as PC and polyamides but also of polyolefins.7,28,29 The chain structures of these materials could be derived from the polymerization statistics, which allowed to predict their rheological properties. These were in good agreement with experimental results.30−32 However, only bulk samples of branched PC have been considered in the previous study.7 With the newly developed method presented in section 3.1 the possibility arises to compare the statistically formed chain structures with experimental results which enables a better validation of MC simulation accuracy for the synthesis of branched PC. To this end, we simulate the growth of a linear (PC1) and a branched (PC3) polymer as listed in Table 1 using a method and algorithm described by Hillegers et al.28,33−35 For the sake of clarity mathematical details are skipped, and the reader is referred to the above references. The chain growth of PC is assumed to follow an “Af iBgi” type step growth polymerization, where “A” and “B” are the reactive end-groups and “f i” and “gi” are the number of such groups in each monomer. In the present case, the PC is built up from a mixture of monomers bearing reactive hydroxyl (denoted as type “A”) and phenyl end-groups (denoted as type “B”). As the BPA as well as the DPC units have two groups of type “A” or” B”, they are referred to as A2 and B2, respectively. The branched polymer is simulated by adding a tri-OH functional comonomer bearing three “A” groups (A3) to the monomer mixture. It is assumed that (1) all reactions occur with equal probability, independent of the size of the molecules involved and independent of the status of other functional groups on the same monomeric unit, (2) cycles do not form, i.e., no reaction takes place between functional groups on the same molecule, (3) only reactions between “A” and “B” groups take
chains represented branched structures (cf. Figure 1a and Table 2). These assignments can fully be confirmed and further extended by the contour plot of the branching ratio g′ (Figure 2). Spots 1, 2, and 4 (linear) reveal g′ equal or close to 1 in the corresponding elution range, as linear chains should prevail, which generally corresponds to our observations. However, it can be recognized that g′ is slightly shifted toward lower values in the center of the peaks while g′ exceeds 1 (gray scale) at the exterior areas. This observation might be explained by interdetector band broadening effects, which frequently occur in multidetector analyses.27 As the analyzed chain species, which are detected in the corresponding elution range are almost equimolar, band broadening influences the determined g′. A drop in g′ can be observed for spot 3, suggesting the presence of branched structures. Thus, referring to previous studies spot 3 can be assigned to branched structures with high levels of end-capping, which were not noticed as a separated spot before.23 That outcome demonstrates the high potential of coupling TD to 2D-LC, since it allows for an isolated TD analysis of individual peaks, which helps to deepen the knowledge on the composition of branched PC samples. The progress of g′ (increase in the degree of branching) for individual branched species can be particularly well observed for spots 5−7 (branched), which correspond to different branched PC structures (cf. Table 2). Thus, hyphenation of 2D-LC with TD enables observing the differences of g′ for these specific linear and branched species, while conventional TD-SEC only provides information on the overall degree of branching for distinct hydrodynamic volumes, where linear and branched species overlap. As evident from the contour plot of the sample described here, TD-SEC results would be highly inaccurate because the sample contains a large fraction of linear chains eluting in the same SEC volume as the branched species. 2D-LC-TD, on the other hand, allows individual analysis of each spot and quantification of linear and branched fractions in the sample (see next section). Hence, the approach shown here provides detailed knowledge on the dependence of E
DOI: 10.1021/acs.macromol.8b00667 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules place, and (4) when “A” and “B” react, one molecule of the condensation byproduct is formed. The removal of this byproduct controls the conversion of the reaction. Simulation for building one molecule runs until all sites have been accessed. The polymers mentioned in Table 1 are generated using the monomers and the molar ratios stated in Table 3. These are converted into units with specific mass and functionalities. In this way, a representative ensemble of virtual polymer molecules is generated according to the reaction mechanism of step-growth polymerization. Typically, in our simulation, the ensemble comprised 10 000−100 000 polymer chains. A schematic drawing of the single formed molecules is shown in Figure 3.
further react with A3 that allows for higher order branched structures to be created on a reasonable time scale. The molar mass in simulations are controlled using either degree of conversion or the amount of byproduct still present in the system. Besides, the dispersity index (Đ) could be affected using either of those approaches. In order to facilitate comparison and to mimic the polymerization of the samples mentioned, we decided to control the molar masses using the degree of conversion. In case of the branched PC, there are no end-cappers or chain stoppers added to the simulation and the simulation was stopped at a conversion of 0.9857, while for the linear PC the simulation was run to a conversion of 0.9998. This resulted in the simulated polymers having the same average molar mass as that of the samples given in Table 1. The generated ensemble comprises the structure of each molecule. With such detailed information not only several statistical quantities can be calculated, but also structural information can be obtained, which is not accessible by other approaches and can be used to predict macroscopic properties, such as the rheological and mechanical behavior. We first look at the MMD and then discuss the topology of the simulated PC chains. Figure 4 shows the MMD of PC
Figure 3. Schematic representation of the molecules (a: linear PC1; b: branched PC3) produced from the MC simulations.
For the simulation the conversion of “A” or “B” groups is 0 ≤ p[A or B] ≤ 1, defined as the fraction of “A” or “B” groups that has reacted. Since each reaction involves one “A” group and one “B” group, the relation holds, where f tot and gtot are the total number of “A” and “B”, respectively. For instance, the conversion of group “B” (p[B]) is as follows: p[B] = rp[A], where r is the molar ratio of groups “A” and “B”. It is further assumed that the system is below its gel point, given by the Durand and Bruneau formula.36 It must be noted that the probability of generating a molecule in the MC algorithm is directly proportional to its size defined as the number of monomer units constituting the molecule. Hence, there is an overestimation of the molecules of larger sizes. Therefore, in the ensemble of polymer structures generated a molecule of size X is over-represented by a factor. Consequently, it is normalized by factor X. In order to speed up the calculations, which take up to 1 day to finish in the case of branched PC, a Flory distribution of linear chains consisting exclusively of repeating units of type -[-A2-B2-]- is created. This is critical as it affects the polydispersity index and the subsequent rheology predictions. As the polycarbonate kinetics are known to follow Flory statistics, the pooling of larger chains used to speed up the simulations. In this context the assumption and condition of equal end group reactivity also holds. These resulting linear chains are then drawn to
Figure 4. MMD of linear (PC1) and branched (PC3) PC, determined by TD-SEC and MC simulation. The solid lines are experimental data and the symbols are from simulations.
(linear and branched) obtained from TD-SEC and calculated using the MC simulation. It can be seen that the MMDs from both the simulation and SEC match quite well. As expected, the Đ as well as the molar masses increase upon branching. It should be noted that for a given conversion both Đ and molar masses of a branched polymer exceed those of the linear one. The branch density, length, and distribution along the segments play a very important role in the rheological behavior.32,37−41 The molecular size increases exponentially with the different branched structures. Figure 5a, obtained from the simulations, shows the weight fraction of all molecules having a particular molar mass and a particular number of branching points. The plot suggests that the molecules with the highest number of branching points are present at the high end of the MMD (though the mass fraction of these molecules is less than ∼5%), and the majority is concentrated in a very narrow window of molar masses and number of branches (i.e.,
