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High temperature quadruple-detector size exclusion chromatography for topological characterization of polyethylene Laura Plüschke, Robert Mundil, Anatolij Sokolohorskyj, Jan Merna, Jens Uwe Sommer, and Albena Lederer Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b00619 • Publication Date (Web): 30 Apr 2018 Downloaded from http://pubs.acs.org on May 4, 2018

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Analytical Chemistry

High temperature quadruple-detector size exclusion chromatography for topological characterization of polyethylene Laura Plüschke†,‡, Robert Mundil§, Anatolij Sokolohorskyj§, Jan Merna§, Jens-Uwe Sommer†,‡, Albena Lederer*,†,‡ †

Leibniz-Institut für Polymerforschung Dresden, e.V., Hohe Str. 6, 01069 Dresden, Germany Technische Universität Dresden, 01062 Dresden, Germany § Department of Polymers, University of Chemistry and Technology, Prague, Technická 5, 166 28 Prague 6, Czech Republic

‡

ABSTRACT: Modifying material properties in simple macromolecules like polyethylene (PE) is achieved by different connection modes of ethylene monomers resulting in a plurality of possible topologies - from highly linear to dendritic species. However, the challenge still lies within the experimental identification of the topology and conformation of the isolated macromolecules because of their low solubility, which demands methods with specific solvents and high operating temperatures. Additionally, a separation technique has to be coupled to different detection methods to meet the specific demands of the respective characterization goal. In this paper, we report a quadruple-detector high temperature size exclusion chromatography (HT-SEC) system which contains online multi-angle laser light scattering (MALLS), dynamic light scattering (DLS), differential viscometry (VISC) and differential refractometry (dRI) detectors. Quadruple-detector HT-SEC was successfully applied to explore the full range of physical parameters of various PE samples with different branching topologies ranging from highly linear macromolecules, polymers with moderate level of branching to highly branched PEs with hyperbranched structure. This method is not only a useful tool to investigate molecular weight, mass distribution and size but enables the access to important factors which describe the conformation in dilute solution and branching density.

The synthesis of novel polymer architectures has significantly developed in the course of the 20th century and has still not reached limitations with regard to numerous reports and publications concerning innovative molecular topologies. Starting with primarily linear macromolecules in the 1930s, the diversity of polymer structures rapidly expanded towards intramolecular linking and branching as the industrial demand focused on more complex materials.1 The utilization of stars, brushes, combs or dendritic polymers as engineering substances established them in the market on a commercial level.2 However, the development of polyolefins started hesitatingly in the early days as materials lacked not only in terms of polymer properties but also in an effective technology for large scale production. With the invention of powerful catalysts like Ziegler-Natta or MgCl2-supported structures, polyolefins and especially polyethylene (PE) manifested as unique and industrially attractive within the diversity of plastic materials due to their physical and mechanical properties associated with an economic and profitable production.3,4 The diversity of PE is indicated by various molecular topologies ranging from classical structures such as linear (high density polyethylene, HDPE), linear with short chain branching (linear low density polyethylene, LLDPE), linear with long chain branching (low density polyethylene, LDPE) and crosslinked PE (XLPE) to very recently developed, highly branched or hyperbranched PE (HBPE).5–7 The latter represents a unique class of branched PE. More than two decades ago, Brookhart

et al. described a pathway to synthesize well-defined polyolefins from living coordination polymerization by using -diimine ligands incorporated in nickel and palladium complexes.8 These catalysts benefit from a high controllability delivering polymers with precisely adjustable structural parameters. Unlike common metallocenes, diimine catalysts characteristically perform the so called chain walking mechanism (CWM), a movement process where the catalyst reaction center migrates on the polymer chain.9 The key to success is given by the possibility to tune chain walking to propagation ratio by varying reaction conditions and catalyst structure.10–12 The superior outcome is homopolymerisation of polyethylene with tunable structural parameters by adjusting synthesis parameters.13 This diversity allows a vast field of potential applications packaging or insulating materials, pipes, fibers, films etc.4 However, the popularity of PE on the basis of the high chemical resistance is consequently accompanied by an elaborate analysis of solution properties. Yet, this information is highly valuable in terms of selecting and evaluating appropriate materials for specific purposes. Conventional methods for the investigation of solution properties are numerous such as static light scattering (SLS), dynamic light scattering (DLS), small angle scattering experiments (SANS & SAXS) as well as capillary viscometry. Yet, those methods are commonly applied in batch mode, which will solely deliver an average of a certain molecular property. Chromatographic or fractionation techniques allow the separation of molecules

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according to their size, conformation or even chemical composition. Column chromatography is still the most common method to study solution properties of polyolefins including classical size exclusion chromatography (SEC) and interaction chromatography, commonly known as high performance liquid chromatography (HPLC).14,15 The coupling of both separation principles (HPLC x SEC or SEC x HPLC) was subsequently introduced as two-dimensional liquid chromatography (2D-LC).16 This technique enables a complementary separation according to chemical composition and molar mass, which is particularly suitable for the characterization of PE-containing copolymers.17 Other fractionation techniques have been developed in the past decades to study solution properties of polyolefins such as temperature rising elution fractionation (TREF) and crystallization analysis fractionation (CRYSTAF).18,19 Both use the principle of fractionating polymers according to their crystallization from solution and therefore deliver information about their chemical composition. These approaches provide valuable insights into the composition and the physical properties of semi-crystalline materials, even though they are highly time-consuming with measuring times up to 20 h. SEC coupled to a series of various detectors gives access to a broad range of molar mass dependent molecular parameters. The conventional method to study solution properties of olefins is based on high temperatures between 130 and 160 °C as well as specific solvents such as 1,2,4-trichlorobenzene (TCB).15 Although TCB exhibits a high toxicity based on a restrained biodegradability,20 TCB remains the classical solvent as it allows a complete dissolution of even poorly soluble polymers such as linear PEs. Values from literature state TCB as a good solvent for PE with Kuhn-Mark Houwink parameter =0.725.21 The typical and most common applied set up is the triple detector system of SEC coupled to SLS, viscometry (VISC) and dRI. It gives access to significant data of the molecule in solution concerning size and topology including molar mass, radius of gyration as well as viscosity and therefore allows identification of the topological properties of the polymer. However, the supplementation by DLS enables the possibility of measuring three different radii, namely the radius of gyration (RG), the hydrodynamic radius (RH) and the viscometric radius (R) and hence permits the deployment of topological factors e.g. -parameter (RG/RH), all depending on the molar mass. Here, we present a unique study of high temperature SEC coupled to a fourfold detecting system containing MALLS, DLS, VISC and dRI as an efficient method to investigate size, molar mass, branching, solution properties, molecular density etc. of polyethylene with different architectures. Quadruple detection has been applied occasionally in the past, yet, in most cases an UVdetector for analyzing aggregation behavior was used in those studies.22–24 Among numerous articles concerning multipledetector chromatography Striegel et al. presented a fivefold detecting system including MALLS, DLS, VISC, dRI and UV.25 However, the principle was applied to study polyacrylamide copolymers and blends at room temperature. Yau et al. demonstrated a hybrid SEC-TREF system including fourfold detection (dRI/MALLS/VISC and Infrared spectrometry) to study polyolefins for the first time.26,27 To our knowledge this is the first study on high temperature quadruple detection including SEC-MALLS/DLS/VISC/dRI (HT-SEC, Figure S1 in the Supporting Information, SI).

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The simultaneous determination of static and dynamic light scattering as well as viscometry justifies the introduction of the ratios 𝜌=

𝑅𝐺 𝑅𝐻

(1)

𝜅=

𝑅𝜂 𝑅𝐺

(2)

Here, topological information is obtained from the relationship between the radius of the isolated macromolecule and the radius of the solvated analogue taking contributions from the solvent into account. In literature, values for hard spheres (= 0.78, = 1.23), linear coils (= 1.5-1.8, = 0.5-0.7) and rigid rods (= 2.36, = 0.3) can be found.28–30 In PEs, branching plays a significant role because bulk properties e.g. melt rheology and crystallinity as well as solution properties are tremendously influenced by the degree of branching (DB). Moreover, the type of branching is important for material properties.31 For polyolefins (PO), we distinguish short-chain branching and long-chain branching.32 Short-chain branches possess length up to 6 carbons and affects properties of the crystalline state. Branches containing more than 6 carbons count as long chain branching and mainly affect rheological features.33 To determine the branching density it is common to quote the contraction factor. This value is based on the logical concept that a branched molecule at a given molar mass is incontrovertibly denser compared to the linear analogue. The more pronounced the branching density, the higher the contraction and hence, the lower the contraction factor. One can differentiate the contraction factor based on the radii of gyration as expressed in eq. (3) and the contraction factor calculated from intrinsic viscosity expressed in eq. (4). 𝑔 = 𝑅𝐺2 𝐵𝑅𝐴 ⁄𝑅𝐺2 𝐿𝐼𝑁

(3)

𝑔′ = [𝜂]𝐵𝑅𝐴 ⁄[𝜂]𝐿𝐼𝑁

(4)

Both parameters can be correlated using an exponent as expressed in eq. (5). Recent studies show that this so called drainage parameter  shows structurally characteristic values and hence can be additionally used for topological investigations of macromolecules.34 𝑔′ = 𝑔𝜀

(5)

 Experimental section Detailed information on theoretical background, instrumentation, chemicals and description of the investigated polymers is given in the supporting information (SI).  Results and discussion We analyzed six samples of PE with different topologies ranging from linear with a low amount of SCB up to compact dendritic PE. The broad spectrum of different architectures in PE is a result of using various synthesis approaches, including catalyst variation. Each catalyst is driven by a specific sequence of movement patterns and monomer insertions which leads to differences in the local and global structure of


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RI signal [a.u.]

the molecule.35 LLDPE and NIST SRM1484 (N IST) are both commercially available linear PE samples. NIST is a linear PE standard with narrow molecular weight distribution. As a standard reference material it is intended for calibration and evaluation of instruments.36 LLDPEs have a linear topology with an increased percentage of SCB compared to classical HDPE. As LLDPE is produced in a copolymerization process from ethylene and -olefins, the degree of branching is very well controllable. LDPEs are characterized by a high content of short and long chain branches, which results from the free radical polymerization processes in their synthesis. The high DB causes a loose packing of the bulk material leading to a decreased crystallinity compared to HDPE and the eponymous low density. LINPE, BPE and HBPE were synthesized using diimine complexes as catalysts and different reaction conditions to achieve different molecular topologies (see Table S1). LINPE is a linear PE with very low content of short branches and semi-crystallinity. BPE and HBPE have been produced at p = 7 and 0.09 bar, respectively. Both are expected to give dendritic PE with an approximate number of 100 branches per 1000 C atoms (determined by 1H NMR).9 However, different temperatures were applied during reaction with 0 and 35 °C for BPE and HBPE, respectively. Ye et al. clearly demonstrated that polymerization temperature is an effective tool to navigate branching density. Thereby, an increase in temperature shifts topologies towards hyperbranched or even dendritic architectures as an elevated chain walking activity of the catalyst at higher temperatures is supposed.37 At this point it should be mentioned that HT-SEC is not necessarily needed for the analysis of denritic PE (such as BPE and HBPE). Cotts et al. clearly demonstrated their solubility in THF at room temperature and the extensive characterization of these materials by e.g. SEC and NMR. 9,38 Yet, applying high temperature analyis on this materials enabled a straight comparison to linear PE.

1,00 0,75 0,50 0,25 0,00

LS (90°) signal [a.u.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


LLDPE NIST LDPE LINPE BPE HBPE

1,00

0,75

0,50

0,25

0,00 8

10

12

14

16

Elution time [min]

Figure 1. HT-SEC chromatograms of the different samples as detected by RI (normalized) and MALLS (90°) detector.

Measurements with fourfold HT-SEC were performed to determine dilute solution properties and characterize

branching topologies of all six PE samples (LLDPE, NIST, LDPE, LINPE, BPE and HBPE). In general, SEC enables a fractionation according to the hydrodynamic volume of the macromolecules. With a defined temporal rate the detectors constantly collect momentary “snapshots” of these eluting fractions. Hence, every elution slice corresponds to a polymer fraction, which is defined by four different measured quantities. Figure 1 shows an overlay of the chromatograms of all samples as detected by RI and MALLS detector. Based on this information and considering the viscosity and DLS signal, the development of RG, RH and R as a function of the elution time can be calculated (Figure S2 and S3, SI). In accordance to the principle of SEC large molecules elute first and the respective radii decrease with progressing retention time. It is clearly visible that RG is significantly larger than RH and R which results from the extended conformation of a linear coil as measured for LLDPE. The difference in size is almost 100 % resulting in a structure parameter ~ 2 (eq.(1)), which is typical for a polydispers linear chain in a good solvent.30 As expected the deviation of RH values is larger than for RG and R as the common sample concentration of approx. 4 mg/ml is marginally low for online DLS experiments. The molecular parameters of the PE samples are shown in Table 1. The Mw ranges from approximately 100-500 kg/mol. The dispersity is comparatively low for all PE samples except for LDPE and depends on the controllability of the reaction type used for their preparation. The broadest distribution is expectedly given by LDPE with Ð = 6.6, which can be explained by the conditions of free radical polymerization which limits the possibility of controlling molar mass ranges. Within the synthesized PEs the dispersity is slightly larger for HBPE with Ð = 1.30. This results from the occurrence of side reactions like chain transfer or chain termination which will significantly intensify with elevated temperatures.39 A molar mass distribution overlay of all PE samples is displayed in Figure S4, SI. The RG values range between 16-58 nm, for RH values between 12-30 nm and for R between 11-40 nm were calculated. Both absolute sizes and size range are largest for RG. This results from the different definition of these parameters as RG is the average value of all distances between the macromolecular center of mass and the chain segments whereas RH and R are values for hypothetical hard spheres showing the same diffusion or viscosity properties as the measured sample. For extended molecules this deviation is rather severe than for compact structures which explains the difference in the radii for linear and densely branched PEs. The measured intrinsic viscosity [] of PE samples ranges between 29-325 mL/g. Just as expected, the value of [] increases with decreasing branching density (see Figure 2b). The [] of the dendritic sample HBPE is the lowest and this value grows constantly for BPE and LDPE, both having highly branched but more open structure than HBPE. Within the linear samples (LLDPE, NIST and LINPE), LLDPE has the lowest value with 141 mL/g, while, [] of LINPE is the highest one. In the same order the number average molar mass of these samples increases. Though, the reason for this behavior is mainly the different molar mass distribution of the samples. LLDPE is broadly distributed containing molecules with polymerization degrees much lower (~50 kDa) than the



NIST sample (~100 kDa) and the LINPE (~300 kDa), which are both rather narrowly distributed. For the linear sample NIST, the values can be compared to data reported by Sun et al. Here, Mw of 122.1 kg/mol and [] of 201 mL/g were found.40 Values obtained by fourfold HT-SEC are slightly deviating with Mw=108.4 kg/mol and []=172.3 mL/g, corresponding to 12-15 % lower values. While average values (Table 1) give a useful overview on the molecular parameters it is more reasonable to compare respective molar mass dependencies. The empirical relationship between RG and Mw is given by a power law 𝑅𝐺 = 𝐾 ∙ 𝑀𝜐 with the exponent  showing structure characteristic values: = 0.33 for a hard sphere, = 0.3-0.5 for hyperbranched structures, = 0.5-0.6 for a random linear coil and = 1 for a rod.2,41 The graphical visualization is referred to conformation plot and is given in Figure 2a for all PE samples. Thereby a double logarithmic scaling enables to receive  directly from the slope of the data. We note that dendrimers are not expected to display a pure power-law but a combination of logarithmic and power-law behavior with an asymptotic exponent of = 0.2 for very large dendrimers.42 In this case effective exponents which are fitted from empirical data might be missinterpreted. Beside the conformation plots of the PEs obtained from HT-SEC a theoretical model of linear PE (see eq. (6)), dashed line in Figure 2a) was added for evaluation of topology and calculation of the contraction factor g eq.(3). The linear PE model can be described by −2

𝑅𝐺 = 2.3 ∙ 10 𝑀𝑊

0.58

(6)

with model parameters taken from Sun et al.40 First of all, one can identify a qualitative agreement between  and presumed topologies of PEs. The highly branched samples BPE and HBPE possess slopes of 0.43 and 0.48, respectively. Contrary to the expectations (BPE) is marginally lower than (HBPE) although HBPE is supposed to be denser. However, for BPE and HBPE the slope slightly increases at higher molar mass (M > 400 kg/mol). This could be an outcome of the catalytic working principle. The mechanism of the catalyst enables either monomer insertion or a random walk along the macromolecular chain and therefore limits a homogenous growth towards a spherical shape as we know it from classical hyperbranched (hb) polymers from AB2-monomers.43 Consequently, we suspect that the polymer is more worm-like on global scale but contains a highly branched structure on the segmental level. This phenomenon was recently described by Patil et al.44 Here, they suggested that PE synthesized at low ethylene pressure produces macromolecules with a densely branched local structure, which forms a linear structure on a large scale since the catalysts performance is limited to a certain walking distance and only adds monomers to one side of the molecule. As a result, there is a distinct difference between highly branched PEs and conventional hb polymers concerning structure and solution properties.

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Most likely, an increase of LCB mainly contributes to this alteration.45 Interestingly, the curve of LLDPE shows the same behavior even though the radii are significantly larger.

Figure 2. Conformation plots (a) and KMHS plots (b) of PE samples determined by fourfold HT-SEC. The insets in section (a) and (b) display the power law exponents and , respectively. The dotted line in (a) and (b) denote linear PE model.

Unlike LDPE, LCB does not occur in LLDPE as it is synthesized through copolymerization of ethylene and other olefins giving solely linear PE with short branches. However, the number of longer side chains is obviously increasing for M > 700 kg/mol. With = 0.70 NIST deviates slightly from theory, even though, it is a standard reference material. Nevertheless, the radius/molar mass dependency corresponds very well to the ones from the theoretical PE. We emphasize, that the extraction of an effective exponent in a certain window of molar mass should not be necessarily related with a scaling behavior. It should be rather taken here as a qualitative classification of different structures. This will be analyzed in more detail using computer simulations in future work. More information concerning molar mass dependencies are given by KMHS-plot. Similar to RG, [] is related to MW by a power law [𝜂] = 𝐾𝜂 ∙ 𝑀𝛼 where exponent has values depending on topological properties: = 0 for a hard sphere, = 0.3-0.5 hyperbranched structures, = 0.5-0.8 for a linear coil and = 1 for a rigid rod.2,41 The KMHS plots of PE samples are shown in Figure 2b including all power law exponents  taken from the respective slopes. Here we added a theoretical model of linear PE for comparison which can be mathematically described by [𝜂] = 5.3 ∙ 10−4 𝑀𝑊 0.7

With = 0.58 LINPE corresponds very well to the theoretical value of a random linear coil. While (LINPE) perfectly matches with (MODEL), lgK is slightly larger. For LDPE,  decreases with increasing molar mass from initially 0.65 to 0.35, which indicates a structural conversion from a primarily linear coil to a more compact topology at higher molar masses.


(7)

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Table 1. Number-,weight and z-average molar mass, molar mass distribution (Mw/Mn), radius of gyration, hydrodynamic radius, viscometric radius and intrinsic viscosity of PE samples determined using fourfold HT-SEC (error estimations included in SI).

Sample LLDPE

Mn [kg/mol] 54.8

Mw [kg/mol] 123.7

Mz [kg/mol] 217.8

Ð 2.26

RG [nm]a 35

RH [nm] b 16

R [nm]a 22

[] [mL/g]c 140.7

NIST LDPE

105.5 75.9

108.4 492.5

111 2928.2

1.03 6.62

30 58

14 30

15 40

172.3 97

LINPE BPE HBPE

257.3 320.8 161.3

295.8 376.3 210

401.7 426.7 272

1.15 1.17 1.30

47 24 16

26 18 12

28 18 11

325.4 74.9 28.9

All values stated as followed: Average ± standard error (standard deviation). All averages and uncertainties calculated from triple determination as stated in experimental section. az-average value, buncertainty-weighted average, cweight-average value.

with model parameters taken from Wood-Adams et al.46 The order of the curves with regard to [] is consistent with the expected topologies. The lowest intrinsic viscosities are given by highly branched samples HBPE and BPE. In the low molar mass range = 0.47 and 0.60 for HBPE and BPE, respectively. The slopes increase with increasing MW, showing a relatively high overall slope with = 0.56 (HBPE) and 0.68 (BPE). Once more, that points to a distinct structural difference on global and local scale of these highly branched PEs. However, the behavior of the highly branched samples strongly deviates from the expected K and  values as it is given by literature. Most likely, not only the amount of branches, but also the conformation and the topological variations on different size scales are crucial to solution properties e.g. viscosity. For HBPE and BPE, various facts linked to the working principle of the Pd-based -diimine catalyst lead to highly branched PE and consequently to a reduction in [] and RG compared to the linear PE analytes: (a) slow rates of chain transfer reaction due to the bulky substituents of the catalyst; (b) migration of metal along the polymer chain causes branching; (c) severe energetic priority of catalyst migration over monomer insertion.47 While HBPE and BPE show an almost steady KMHS behaviour,  of LDPE and LLDPE decreases at high MW down to = 0.15 and 0.31, respectively, indicating a structural transition close to hard sphere. Branched molecules possess a higher molecular density compared to linear analogues at the same molar mass and consequently a reduced intrinsic viscosity.2 LDPE contains an elevated amount of SCB and LCB. The intrinsic viscosity of LDPE is therefore significantly smaller in comparison to linear PE. LLDPE contains a small percentage of SCB. Its intrinsic viscosity therefore ranges between LDPE and linear PE analytes. For both polymers, the further reduction of [] at high molar mass range results most likely from intramolecular entanglement or interpenetration of the polymer chains. The linear samples NIST and LINPE show a good agreement with the theoretical model not only concerning values for [] but too. When comparing molecules with different types of branching as it is present in various types of PE (e.g. only methyl-groups, SCB or LCB), it is challenging to find an appropriate indicator that quantifies the branching density. Traditionally, hb molecules with ABX-monomers (x ≥ 2) were characterized by the concepts of Fréchet48 and Kim49, which was revised shortly afterwards by Hölter et al.50 This approach is based on the quantification of the different units (linear, dendritic and

terminal) occurring in hb molecules and the calculation of the degree of branching (DB) (see eq.(S8), SI). Although this parameter has been very well established in the field of dendrimers and hb polymers,51 it is not useful for all branched systems, since the degree of branching is not a topological measure. However, material properties of PEs are not only sensitive to the degree of branching but also to the type of branching.7,52 PEs synthesized using -diimine catalysts with diverse reaction conditions differ significantly in rheological and thermal behavior from polymers synthesized by ZieglerNatta catalysts or metallocenes. Yet, NMR-studies revealed that despite having different types of branching, the total amount of branches per 1000 carbon atoms is constant.9 Another possibility to evaluate branching is the contraction factor. The contraction factor quantifies the size reduction of a branched molecule respective to its linear analogue. It enables a suitable comparison of PEs with different topologies and is therefore used to evaluate the branching density. Regularly, g and g’ start at a value of 1.0 since there is no significant difference between a linear and a branched molecule at very low polymerisation degrees. However, with increasing molar mass the topological deviation of the branched molecule from the linear grows causing increased contraction. The molar mass dependencies of g and g’ of all PE samples are given in Figure 3a and b. The theoretical models eq. (6) and (7) were taken as linear reference for g and g’, respectively. Since the molar mass ranges of the PEs differ significantly only the lower molar mass region (MW ≤ 700 kg/mol) is displayed although some samples have much higher MW. Generally, one can see a clear difference between PEs with linear (LLDPE, NIST, LINPE) and branched topology (LDPE, BPE, HBPE). While linear PEs show only small contraction (g = 0.8-1.0), branched PEs have values of g = 0.2-0.5. Indeed, LLDPE and LINPE show branching ratio of 1.1 and 1.2, respectively, pointing out a topology that is more linear than the theoretical model. Unlike g(LLDPE) which decreases with MW down to g = 0.8, g(LINPE) varies between 1.1-1.2 over the whole molar mass range. As it is entirely constant over the whole molar mass range it was additionally taken as linear reference for subsequent calculations. For a better comparison it is useful to calculate g and g’ at specific molar mass, which was performed at MW = 150 kg/mol. The respective values are given in Table S3 (SI). It can be seen that the accuracy of g’ is higher than for g, which results from the lower error of [] values compared to RG. The highest contraction is given by HBPE with g = 0.23 followed by LDPE and BPE with g = 0.41 and 0.43, respectively. It should be mentioned that g(BPE) further



decreases to 0.35 while g(LDPE) remains constant. The difference is much more distinct for g’. The linear samples show expectedly much higher values with g = 0.86 and 0.74 for LLDPE and NIST, respectively. However, g’ behaves differently for NIST as it is supposed to show a lower contraction and hence a higher g then LLDPE due to less branching.

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0.0021 g/cm³. The density obviously reaches a limit with approx. 0.001 g/cm³ for the linear PE samples. However, regarding absolute values dAPP(PEs) are very small compared to known dendritic systems. For example, aliphatic-aromatic polyester pseudo-dendrimers range between 0.014-0.2 g/cm³, whereas aliphatic polyamide dendrimers have dAPP of 1.01.5 g/cm³ depending on the generation number.43,55 The comparatively low density of branched PE results from its linear topology on global scale, which inhibits such compactness as known from dendrimers.

Figure 3. Contraction factor g vs. molar mass (a) and contraction factor g’ vs. molar mass (b).

Furthermore, the drainage parameter  which expresses the mathematical relation between g and g’ according to eq.(5) was calculated. It usually ranges between 0.5-1.5 where the lower limit corresponds to linear molecules and the upper limit to molecules with a high DB.34,53 Generally, this tendency was confirmed by the studied PE samples. The lowest value is given by NIST with = 0.47 followed by LDPE with 0.77. The highly branched samples HBPE and BPE have considerably high  with 1.52 and 2.42, respectively. Although the order should be reverse it is obvious that these values are in the range of compact structures. With = 1.36 the value of LLDPE is higher than expected, which probably results from the lower sensitivity of g to differences in the branching type. The molar mass dependency of  is displayed in Figure S6, SI for samples LLDPE, LDPE, BPE and HBPE. Samples LINPE and NIST could not be visualized as contraction factors g, g’ ≥ 1 deliver mathematical errors for . Here, it can be seen that  is not constant but increases with molar mass in a range between 0.5–3. This behavior has been previously reported by Beer et al. who studied branching properties in low-density PE.54 For further visualization g’ was therefore used as a branching ratio. Another helpful parameter to evaluate the compactness of branched samples is the apparent density dAPP according to eq.(S7). Naturally, the contraction should be directly proportional to a high apparent density. Figure 4a shows the relation between dAPP and g’ for different PEs. Just as expected, HBPE has the highest density with dAPP = 0.021 g/cm³ followed by BPE and LDPE with dAPP = 0.01 and

Figure 4. Apparent density (a), topology factor  (b) and topology factor  vs. contraction factor g’ of PE samples.

The key advantage of quadruple-detector HT-SEC is the simultaneous online-determination of three radii, namely RG, RH and R. At this point it seems necessary to emphasize the different definition of these parameters. RG is the root mean square of the average distance of any scattering point (e.g. atom, group of atoms etc.) from the center of mass. RH is the radius of a hard sphere with the same translational diffusion coefficient as the sample molecule. R is the radius of a hard sphere that affects the fluid viscosity in the same way as the investigated molecule.56 From threefold radii determination we are able to obtain values that describe the size of a macromolecule in solution differently, for example taking solvation or diffusion behavior into account. Secondly, we have the possibility to describe different radius averages (number-, mass- or z-averaged radius). Moreover, by putting


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them in relation, ratios  and  give valuable information about structure and dissolution behavior. And finally, we can obtain insights into conformational transitions depending on the molar mass and receive topological information from the power law relationships of radii and molar mass. Figure S5 displays the molar mass dependencies of RG, RH and R of highly branched sample HBPE and linear sample LINPE. Generally, the slopes of the three different conformation plots within one sample can differ marginally. For HBPE  varies between 0.47-0.52. The values are all in the range of hb molecules. The range for (LINPE) is significantly broader with 0.45-0.58 where the lower limit does not correspond to linear molecules. The scattering of the RH-data complicates a comparison. Therefore, one should focus more on RG and R data as they reflect differences in structural properties more reliably. The relation between RG and RH or RG and R is dependent on topology and conformation and is given by  eq.(1) and  eq.(2), respectively. Theoretical values are known for hard spheres (= 0.78, = 1.3), linear coils (= 1.5-1.8, = 0.5-0.7) and rigid rods (= 2.36, = 0.3). Additionally, literature describes hb species with = 1.23 (accounts for hb polymers from AB2monomers).28–30 However, no references are given for  values of hb structures. Following the tendency of the structures described above with (sphere) < (hb) < (linear) one could rank  in the same way by proposing (sphere) > (hb) > (linear) leading to a potential range of  = 0.8-1.2 for hb structures with AB2-monomers where the upper limit would correspond to dendrimers and the lower limit to highly branched structures. For LINPE, RH is in a good accordance with R, whereas for HBPE a small difference between the two radii is notable. In particular RH is slightly larger than R pointing out that the diffusion behavior might be more sensitive to changes in branching than the fluid viscosity. For both samples, RG is considerably higher than RH or R leading consequently to topology factors > 1 and < 1 which is evident for molecules with a rather isotropically extended topology. The structure parameters can also give valuable information about potential topology changes between individual polymer fractions. Figiure 5a and b display the molar mass dependency of  and  for branched sample HBPE and linear sample LINPE, respectively. For both samples one can record a shift of  and  with increasing molar mass. For LINPE, = 1.4 on average at low molar mass. With increasing mass  slightly increases to > 1.6. Although the variance is high for the data points at high molar mass, one can clearly indicate the increase of  which corresponds to a minor structural transition. Supposedly, LINPE forms rather extended coils at higher molar mass which will not allow a dense formation of the linear chain. The same tendency can be noticed from the molar mass dependency of . At low molare mass = 0.69 and drops down to 0.62 with increasing molar mass. While both values are in the range of a random coil, the structure changes towards a more extended molecule. For HBPE, the structural change is more pronounced regarding structure parameter . At low molar mass = 1.48 on average and decreases down to 1.25 with increasing molar mass indicating a transition to more compact structures at high molar masses.

This assumption can be supported by the behavior of , which ranges between 0.65 and 0.73 for low and high M, respectively. The slight increase of  indicates one more time the change to a more densely branched topology for HBPE. Although for both samples the changes are not significant, they are still well detectable and confirm structural differences of highly branched and coil-like polymers.

Figure 5. Topology factor  (blue) and  (red) vs. molar mass of samples HBPE (a) and LINPE (b). The dashed lines mark range for hard sphere. The dotted lines mark range of linear coil.

The correlation between topology factor  and branching ratio g’ for all PE samples is displayed in Figure 4b. Here,  was calculated from the respective radii given in Table 1. As previously mentioned, the contraction factor g’ was determined at MW = 150 kg/mol for a suitable comparison. For , densely branched sample HBPE and BPE shows values of 1.32 and 1.36, respectively, which corresponds to hb structures according to literature. With increasing g’ one can clearly indicate an increase of  values. With 1.82 (LINPE) is very well located within the range of a linear coil. Yet, LDPE, NIST and LLDPE show  values much higher than expected with 1.90, 2.04 and 2.24, respectively. This would mean that these PE samples form structures which are closer to linear polydisperse coils or coils with anisotric shape. However, the values probably occur due to a higher error of RH caused by an elevated variance of DLS data. On the contrary, the structure parameter  corresponds much better to theoretical values of a linear coil. This becomes evident when we focus on the correlation between g’ and  (see Figure 4c). PE samples with low g’ show the highest topology factors  with 0.70 and 0.72 for HBPE and BPE, respectively. Less branched sample LDPE follows with = 0.70. The linear samples show much lower  with LLDPE = 0.65, LINPE = 0.59 and NIST = 0.50. All PEs correspond to theoretical values in the range of linear chains even the hb samples that can be found at the upper limit (= 0.70). Nevertheless, an obvious reduction of  with increasing g’ is notable which proofs the correlation between branching density and structural conformation. This dependency is much



better pronounced than for  since the order of  corresponds very well to expected branching topology of the samples: Highly branched PEs (HBPE & BPE) show compact topology followed by PE with linear topology but LCB and SCB (LDPE). Next in order is PE with linear chains but methyl groups as branches (LLDPE). Finally, PE samples with lower amount of branching, NIST & LINPE, follow corresponding to random linear coils. It should be stated that  seems rather less sensitive to minor changes in branching. For example a dramatic increase of g’ from 0.1 to 0.5 leads to a reduction =0.02 whereas the difference between branched and linear PEs is much more pronounced (= 0.2). Setting a statement for  is controversial. The difference of  between branched and linear samples is more distinct with = 0.9, yet the statistical variation of RH-data is higher leading to a higher uncertainty of . 

Conclusions

In this study we investigate the physical properties of various PE samples as a function of branching density using fourfold detection HT-SEC. The observed results give an interesting overview of the architectural pluralism of PE. Whereas linear PE has an open structure forming random coils in dilute solution state, non-linear PE species are rather compact corresponding to the branching density. Hyperbranched PEs with dendritic branching even tend to spherical shapes. We clearly showed that this method is helpful to characterize physical parameters such as molar mass and mass distributions, radii, intrinsic viscosity and that qudruple detection HT-SEC is able to simultaneously determine molecular conformation and topology properties. We successfully evaluate the necessity of this coupling techniques by showing that conventional data obtained by classical tripledetector HT-SEC consisting of MALLS, VISCO and DRI, is not always sufficient to clearly distinguish polymer architectures, especially regarding polyethylene. For example, power law exponents  and  gave sometimes similar values for PEs with distinctively different branching properties. We assume that in those cases the differences in local structure are much more severe than on global scale. This causes analogous arrangement of polymer chains even though their topologies significantly differ, which cannot be distinguished by power law relations. We emphasize that the extraction of exponents from certain windows in the molar mass of polymers has to be interpreted by a scaling model. Only for self-similar conformations such as linear chains or for randomly branched polymers with a self-similar topology such an exponent has a physical meaning. Dendrimers and disordered dendritic topologies are described by simple power-law. Our results are ment for a first classification of the polymer architectures and more information about the branching topology is necessary. The extension of HT-SEC by the DLS-detector enables the online determination of hydrodynamic radius related to molar mass as well as radii moments and therefore allows the calculation of the structure parameter . Combined with the structure parameter  and the apparent density dAPP one can record the topological variations in more detail. The contraction factor g or g’ has emerged as a valuable measure to rate and compare branching densities of different PEs when the total number of branching points is equal and can therefore function as an alternative branching quantification measure.

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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. brief description (file type, i.e., PDF)

AUTHOR INFORMATION Corresponding Author * [email protected]

ACKNOWLEDGMENT We would like to express our gratitude to Petra Treppe for her technical assistance. Deutsche Forschungsgemeinschaft (DFG) and Czech Science Foundation are greatly acknowledged for financial support of this work which is part of the BraCat projects DFG LE 1424/7 and CSF 15-15887J.

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