Molecular Weight Dependence of Deuterium ... - ACS Publications

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Molecular Weight Dependence of Deuterium Exchange on Polyethylene: Direct Measurement and SANS Model Brian M. Habersberger,* Kyle E. Hart, David Gillespie, and Tianzi Huang The Dow Chemical Company, 2301 North Brazosport Boulevard, Freeport, Texas 77541, United States

Downloaded by FLORIDA ATLANTIC UNIV on August 28, 2015 | http://pubs.acs.org Publication Date (Web): August 13, 2015 | doi: 10.1021/acs.macromol.5b01075

S Supporting Information *

ABSTRACT: Following a hydrogen−deuterium exchange reaction, size-exclusion chromatography with infrared detection (SECIR) was used to measure the distribution of deuterium with respect to molecular weight on a polyethylene resin. The SEC-IR method reveals significant heterogeneity in the distribution of deuterium across molecular weight, including a fraction of high molecular weight chains that are nearly or completely unlabeled. Small-angle neutron scattering (SANS) was performed on the labeled polymer and an isotopic blend; the random phase approximation model prediction for the scattering from an ncomponent blend was successfully used to model the measured SANS data. Additionally, a Monte Carlo algorithm was used to fit the measured SANS data to a deuterium distribution, yielding a measurement consistent with that obtained from SEC-IR. The methods are compared to literature approaches for describing nonideal deuterium labeling. These results demonstrate the value of including detailed information about the distribution of deuterium in a scattering model and provide methods for probing the structure and interactions of complex polyolefin resins that have been labeled via heterogeneous catalysis.

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INTRODUCTION

of microstructures not available through typical controlled polymerization techniques. The wealth of physical properties available from combining ethylene, propylene, and a small number of other α-olefins in free radical and catalytic polymerizations have led polyolefins to become the largest synthetic polymer market by volume. Properties can be tuned by varying the type, amount, distribution, and blockiness of comonomer as well as by the molecular weight and long-chain branching content and distribution.15,16 More sophisticated resins, produced by the use of multiple catalysts, contain multimodal distributions of species that have different architectural characteristics.17 Furthermore, different types of commercial polyethylene resins are often blended together to obtain a balance of desired processing and performance properties.18,19 A great deal of effort has been expended to elucidate the relationship between polyolefin microstructure, rheology, and mechanical performance.15,20−24 Because of the structural diversity of polyolefin systems, and because the chemical identity of all components is (CH2)N, it is difficult to identify the role of a particular subset of chains in a resin or blend. For example, comonomer heterogeneity (produced via Ziegler−Natta catalysts) can cause a fraction of chains to phase-separate.25 Deuterium exchange offers a method for labeling such chains, and, in combination with SANS or other deuterium-sensitive experiments, for elucidating

Isotopic labeling is widely used throughout the chemical and physical sciences to reveal reaction pathways,1,2 measure dynamic properties such as diffusion,3,4 probe the structure of proteins,5,6 and provide contrast to scattering or imaging techniques.7−9 Deuterium-labeled polymers are frequently used in conjunction with small-angle neutron scattering (SANS) to measure the conformational structure of amorphous or crystalline chains,10 the morphology of self-assembled block polymer structures,11 and the thermodynamic interactions of different polymer species.12−14 Precise control and understanding of the location of deuterium on macromolecules allows for the design of powerful experiments that isolate a particular structural or dynamic element in a multicomponent system. Three strategies are available for creating a deuterium-labeled polymer: synthesis incorporating deuterium-labeled monomer, saturation of a precursor polymer with D2, and hydrogen− deuterium exchange. Polymerization of labeled monomer offers the most control over the structural distribution of deuterium, but is by far the most expensive of the three methods. Saturation of a precursor polymer such as poly(butadiene) yields a model poly(ethylene-co-butene); this method has the advantage of easily preparing structurally matched pairs of labeled and unlabeled polymers at relatively low expense, but is limited to polymer chemistries and microstructures that can be prepared from a small set of unsaturated precursors. Deuterium exchange similarly can produce matched pairs of polymers at low cost, but can be performed on polymers with a broad range © 2015 American Chemical Society

Received: May 19, 2015 Revised: July 21, 2015 Published: August 13, 2015 5951

DOI: 10.1021/acs.macromol.5b01075 Macromolecules 2015, 48, 5951−5958

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Macromolecules

volume was computed via the examination of a narrow polystyrene standard. Viscosity (Malvern) and light scattering (Agilent) detectors were also present on the system, and were calibrated via a homopolymer polyethylene reference (traceable to NBS 1475). Data processing was performed using GPC One Software from PolymerChar. Infrared Spectroscopy. The infrared spectrum of the deuteriumlabeled polymer was acquired on a Thermo 6700 FTIR spectrometer equipped with a Durascope single bounce diamond ATR. The FTIR bandpass filter reflectance spectrum was acquired on a Nexus-470 FTIR spectrometer equipped with a continuum Microscope. Data were acquired in reflectance mode, using a gold mirror as reference. Nuclear Magnetic Resonance Spectroscopy. 1H spectra were acquired on a Bruker AVANCE 400 MHz spectrometer equipped with a Bruker Dual DUL high-temperature CryoProbe and a sample temperature of 120 °C. 1,1,2,2-Tetrachloroethane-d2 (Cambridge Isotope Laboratories) was used as the NMR solvent, and paradichlorobenzene (Aldrich) was used as an internal standard. SANS. SANS was performed on the labeled product of the exchange reaction, a 50/50 volumetric blend of the labeled polymer and the unlabeled precursor polymer, and a background sample of unlabeled polymer. The blend was prepared by dissolving an appropriate amount of the two components in TCB with 200 ppm BHT at 150 °C, then precipitating into excess methanol at room temperature under stirring. The precipitate was filtered and rinsed with methanol, then dried in a vacuum oven at 80 °C for 48 h. After drying, samples were pressed into 15 mm diameter, 1.5 mm thickness discs and sealed between two quartz plates. Scattering experiments were performed at the 10 m NG-B nSoft beamline at the NIST Center for Neutron Research (NCNR). Exposures were collected in the melt state at 200 °C, and the isotropic patterns were azimuthally averaged to yield intensity as a function of the wave vector q = 4πλ−1 sin(θ/2). Samples were visually inspected in the heated sample rack to confirm that no bubbles were present in the beam intersection. Data reduction was performed using Igor Pro and the SANS package provided by NCNR; the data were corrected for background and empty cell scattering, detector sensitivity, sample transmission, and sample thickness.

their role in the morphology and behavior of a resin. However, in order for such experiments to be successful, the location and distribution of deuterium must be well-understood, and, ideally, incorporated into the scattering model used to interpret data. A facile method of performing hydrogen−deuterium exchange on polyethylene and ethylene-propylene copolymers using a Pt−Re catalyst on a wide-pore silica support was recently described by Habersberger et al.26 The amount of exchange was shown to be sensitive to comonomer content in a coarse way; polyethylene exchanged most significantly, little to no exchange was observed on polypropylene, and an alternating ethylene−propylene copolymer showed an intermediate amount of exchange, indicating that comonomers retard the H−D exchange reaction rate relative to ethylene homopolymer. Because some commercial polyolefins have molecular-weightdependent distributions of comonomer, exchange reactions performed on such resins should produce polymers with more deuterium on ethylene-rich molecular weight fractions.27 Additionally, the kinetics of hydrogenation reactions on a similar catalyst have been shown to be molecular-weight dependent, so homopolymers may also exhibit some molecularweight dependence in exchange reactions.28 When performing SANS experiments on systems incorporating such nonuniformly labeled polymers, the distribution of deuterium must be well understood in order to interpret the measured SANS patterns. In this report, the distribution of deuterium with respect to molecular weight on a polyethylene resin is investigated directly using size-exclusion chromatography. The effect of this distribution on SANS measurements is modeled, and the model is compared to measured SANS data. Additionally, a Monte Carlo algorithm is used in conjunction with the SANS model to fit a deuterium distribution to the SANS data. These results are placed within the context of the literature by applying the techniques presented here to previously described reports of heterogeneously labeled polymers.

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RESULTS The polymer chosen for study is a high density polyethylene (hHDPE) resin with number-average and weight-average molecular weights of 14.6 kDa and 244 kDa, respectively. Figure 1 compares the refractometer-detection SEC chromatograms of the hHDPE before and after the deuterium exchange reaction, confirming that minimal degradation or other alteration to the molecular weight occurs. The average

EXPERIMENTAL PROCEDURES

Exchange Reactions. The exchange reaction was conducted using a Pt−Re catalyst on a wide-pore silica support.26 Three grams of polymer, 1.2 g of supported catalyst, and 270 mL of 2,2,4trimethylpentane were loaded into a 600 mL Parr reactor with 600 psi of D2 gas. Reactions were carried out at 170 °C for 16 h with stirring. Following reaction, the remaining solvent was evaporated. The dried polymer/catalyst mixture was redissolved in 1,2,4 trichlorobenzene (TCB) (Fisher, HPLC grade) containing 200 ppm of 2,6-ditert-butyl-4-methylphenol (BHT) (Sigma-Aldrich) (used as an antioxidant) at 150 °C, filtered using pearlite, then the hot filtrate was poured into an excess of room temperature methanol to precipitate the polymer. The methanol was removed via vacuum filtration and the polymer was dried in a vacuum oven for at least 24 h at 80 °C. Size Exclusion Chromatography. Size exclusion chromatography (SEC) was performed using a Polymer Laboratories Model 220 high temperature liquid chromatograph in TCB with 200 ppm BHT at 150 °C. Four 10-μm mixed-porosity analytical columns from Agilent (Mixed B) were used as the separation media. Molecular weight calibration was done against a series of 21 narrow polystyrene standards converted to polyethylene-equivalent molecular weight, referenced against linear homopolymer PE NIST NBS 1475. Then 200 μL of a 2.0 mg/mL polymer solution was injected using a flow rate of 1.0 mL/min. A fixed-wavelength infrared detector from PolymerChar (IR4) was coupled in series to the internal refractometer of the chromatograph for simultaneous measurement. The interdetector

Figure 1. Comparison of SEC with refractometer-detection on hHDPE measured before and after the exchange reaction. 5952


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Macromolecules deuterium fraction of the labeled polymer (hereafter denoted dHDPE), ⟨y⟩, measured via 1H NMR, is 0.36. Measurement of the Deuterium Distribution via SEC. Information about the distribution of deuterium with respect to molecular weight is available from SEC with IR detection (SEC-IR). In typical use, IR detection provides a concentration measurement for polyolefins and is often used in conjunction with a complementary light scattering detector to measure absolute molecular weight.29,30 The absorbance of the carbon− hydrogen stretching vibrations from 2750 to 3000 cm−1 is monitored as a function of elution volume; other vibrations are excluded from the detector by a filter. Calibration is performed to relate the absorbance (A2900), to the concentration of fully hydrogenous polyethylene (cPE‑H):

provides a semiquantitative measurement of the deuterium fraction as a function of molecular weight. Figure 3 compares cPE‑H, cPE, and ỹ*(MW), illustrating this measurement.

cPE − H = kA 2900


where k is an empirically measured calibration constant. Figure 2 illustrates the measured spectral range of the filter and

Figure 3. SEC traces measured with refractometer and IR detection and calculated ỹ*.

Because ỹ*(MW) is calculated from the ratio of the IR and refractometer signals, it is highly sensitive to error when those signals are weak. The weak signal associated with the high and low molecular weight limits results in both negative and highly fluctuating values of ỹ*(MW). For the purpose of analysis, the data at the edges of the molecular weight distribution have been trimmed (ỹ*(MW > 4 × 106 Da) and ỹ*(MW < 600 Da) set to 0), and any negative values of ỹ*(MW) are interpreted as 0. If the measured values of ỹ*(MW) corresponded to quantitatively accurate deuterium fractions for the various molecular weight slices, then the total amount of deuterium could be calculated via the weighted sum of ỹ*(MW) across all chains. However, such a calculation yields ⟨ỹ*⟩ = 0.28, significantly less than the value obtained from NMR (⟨y⟩ = 0.36). The origin of this discrepancy is not clear, but may be related to detector sensitivity. If we assume that the error in ỹ*(MW) is independent of molecular weight, then the measured values of ỹ*(MW) can be adjusted to yield a corrected value ỹ(MW):

Figure 2. FTIR spectra of dHDPE (attenuated total reflection) and the bandpass filter used with the SEC-IR (reflectance).

compares it to the deuterium-labeled hHDPE. Because carbondeuterium stretching vibrations are at lower wavenumber (approximately 2050−2250 cm−1), the IR response from a labeled polymer is less than that from a fully hydrogenous polymer at equal concentration. To normalize the IR signal, a second, deuterium-insensitive concentration detector is required. While Strazielle and Benoit report a difference in the polymer solution refractive index increment (dns/dc) of as much as 18% between polystyrene and poly(perdeuterostyrene) in a variety of solvents,31 SEC mass recovery measurements performed on many deuteriumexchanged polyolefins were consistent with a value of dns/dc for polyethylene in TCB that is, within weighing error, independent of deuterium content. Thus, a refractometer allows for measurement of the actual polymer concentration (cPE):

y ̃(MW) =

⟨y⟩ y ̃*(MW) ⟨y ̃*⟩

The SEC-IR method reveals significant heterogeneity in the distribution of deuterium across molecular weight, including a fraction of high molecular weight chains that are nearly or completely unlabeled. To our knowledge, this is the first reported measurement of the distribution of isotopes across molecular weight fractions. The effect of this distribution on SANS measurements is described in the following section, and the findings are compared to literature reports of nonideal labeling in the Discussion. Measurement and modeling of SANS. SANS experiments can be used to measure chain statistics and thermodynamic parameters in polymer blends containing a deuterium-labeled component, but typically, only ⟨y⟩ is known (from NMR or density measurements) and is assumed to be the deuterium fraction of all chains. Uniformly labeled polymers of any isotopic composition do not cause coherent

⎡ dn ⎤−1 cPE = ⎢ s ⎥ Δns ⎣ dc ⎦

For a hydrogenous polymer, the ratio cPE−H/cPE is unity. For a labeled polymer, the complement of this ratio, c y ̃*(MW) = 1 − PE − H cPE 5953


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Macromolecules scattering. In a common SANS measurement, binary blends of labeled and unlabeled polymers are prepared, and the scattering from these blends is modeled using the Random Phase Approximation (RPA) applied to the Flory−Huggins model for the free energy of mixing of an incompressible blend of Gaussian coils.12,13,26,32−35 The heterogeneity in ỹ(MW) results in scattering from dHDPE that a two-component model cannot predict. Instead, the generalized n-component RPA model (n-RPA) was used to predict the scattering from dHDPE and a binary blend of hHDPE and dHDPE. The labeled polymer was divided into n slices, each with molecular weight Mi and deuterium fraction yi, and the slices were treated as nondisperse components of a blend. The equations used in the n-RPA scattering prediction, as derived and described elsewhere, are reproduced without alteration here:33,36

Figure 4. SANS data for dHDPE and the 50/50 hHDPE/dHDPE blend. Blend data are shifted vertically by a factor of 3. Solid curves show the prediction of the n-RPA model. Inset shows the unshifted SANS data. Error bars fall within the size of the symbols.

T


I(q) = Δρ ·S (q) ·Δρ

Δρi = ρi − ρn

scattering model was applied using the measured SEC data and ỹ(MW) as inputs by dividing the molecular weight distribution into 35 slices. Above a certain number of slicesin this case, about 20the system was adequately described such that additional slices gave similar results, as shown in Figure SI1. The model prediction, shown in the solid curves in Figure 4, yields an excellent fit. Note that no adjustable parameters were used in this calculation. Determining ỹ(MW) from SANS: Monte Carlo Algorithm. The n-RPA model confirms that the measured ỹ(MW) and measured SANS patterns are consistent, but it does not identify if the SANS patterns are uniquely characteristic of ỹ(MW). To determine what information can be extracted from the SANS pattern, a Monte Carlo method was used to perform a fit with the scattering model. The method takes only the standard SEC data and ⟨y⟩ as inputs along with the SANS patterns from dHDPE and the 50/50 hHDPE/dHDPE blend. Randomly generated polynomials are used as trial distributions for ỹ(MW), then the n-RPA model is used to calculate the corresponding SANS patterns. Other functionalities for the trial distributions were tested and yielded similar results to those described here, but polynomials were found to be more computationally efficient. The relative difference between the modeled and measured SANS at some set of q values is taken as the error. Both SANS patterns are fit simultaneously. The process is repeated an arbitrary number of times while always retaining the set of ỹ(MW) guesses associated with the m lowest error values (denoted ỹMC(MW)). The algorithm is illustrated in Scheme 1, and a Mathematica implementation is included in the Supporting Information. Figure 5 shows the results of the Monte Carlo method after 107 trials. The five best-fitting ỹMC(MW) profiles are compared to ỹ(MW) as measured via SEC-IR, and the corresponding SANS predictions are compared to the measured SANS data. Above 10 kg/mol, ỹMC(MW) and ỹ(MW) are quite similar, with ỹMC(MW) indicating a sharper peak with a lower molecular weight cutoff above which no exchange was observed. At lower molecular weights, the various ỹMC(MW) curves differ significantly from each other and from ỹ(MW). However, this is an artifact caused by the relatively weak scattering from low molecular weight chains and the polynomial functionality of ỹMC(MW); the deuterium concentration of these chains could be changed to any arbitrary value

ρi = [8yb + 8(1 − yi )bH ]v0−1 i D −1

−1

S (q) = S0 (q) + V (q) Sii0(q) = ϕiNv i 0P(zi) −1

0 Vii(q) = Snn (q) − 2

−1

0 Vij(q) = Snn (q) +

P(zi) =

zi =

χin v0

χij v0

−

χin v0

−

χjn v0

2 (z i − 1 + e − zi ) zi 2

q2a2Ni 6

Here, bD and bH are the scattering lengths of deuterium and hydrogen, respectively,37 and v0 is a reference volume of approximately four (CH2) units, equal to 123 Å3 at 200 °C.38,39 The scattering length density of a slice, ρi, is calculated based on the number of protons and deuterons in this reference volume. Ni and φi are the volumetric degree of polymerization and volume fraction of component i, and a is the statistical segment length of linear polyethylene, adjusted to the 200 °C experiment temperature.38,40 The Flory−Huggins interaction parameter, χij, was estimated using the measurement of Londono et al. (for fully labeled and unlabeled chains) combined with the random mixing hypothesis to adjust for partial labeling.34,41−44 Component n is arbitrarily used as a reference component. In our implementation, component n is the unlabeled polymer, which is described as a single component using the weight-averaged product ⟨NP(q,Rg)⟩w; to model the scattering from dHDPE, this component is set to a minute volume fraction.33,45 The off-diagonal elements of the matrix S 0 are zero since no block architectures are present in the system. SANS patterns for dHDPE and a 50/50 volumetric blend of hHDPE and dHDPE are shown in Figure 4. The scattering intensity of dHDPE is comparable to that of the blend, consistent with significantly heterogeneous labeling. The 5954


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The fact that the higher molecular weight portion of ỹMC(MW) converge into a single curve indicates that the measured SANS patterns uniquely identify a deuterium distribution very similar to that measured via SEC-IR. While only 5 ỹMC(MW) curves are shown in Figure 5 for clarity, comparison of the 500 best-fitting ỹMC(MW) curves (shown in Figure SI-2) demonstrates that they all have essentially the same profile. It was necessary to minimize the error using SANS patterns from both dHDPE and the 50/50 hHDPE/ dHDPE blend in order to obtain this unique fit of ỹMC(MW); performing the fit on just the dHDPE scattering yields multiple solutions. Considering the general space of all molecular weight and deuterium distributions, it is unlikely that the SANS patterns from a labeled polymer and a 50/50 isotopic blend will always yield a unique solution as seen here. In some cases, scattering from additional blend compositions may be necessary to eliminate a family of ỹMC(MW) solutions. In other cases, the scattering from a labeled polymer may be adequately described by a statistical distribution of deuterium without regard for molecular weight, as described by Balsara et al.32 The advantages and limitations of this and other approaches are considered in the Discussion.


Scheme 1. Illustration of Monte Carlo algorithm

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DISCUSSION The measured deuterium distributions from both SEC-IR and the Monte Carlo fit to the SANS data confirm the presence of high molecular weight chains that have experienced little to no deuterium exchange. The Pt−Re catalyst used for the exchange reaction is on a wide-pore silica support with a mean pore diameter of 380 nm.46 Using melt chain statistics for estimations,38 the peak in the deuterium distribution occurs at an Rg of approximately 16 nm, and above 40 nm essentially no exchange has occurred. These estimations are well below the pore diameter, so pore exclusion effects are not the likely origin of the observed deuterium distribution. A Pt catalyst on the same silica support was used by Ness et al. to investigate the kinetics of polystyrene hydrogenation as a function of molecular weight.28 In this case, a significant drop in the initial reaction rate was observed for chains with Rg > 17 nm. The peak in ỹ(MW) is roughly coincident with this Rg, though the polymer described in the current report contains a significant fraction of chains of much larger size than those considered by Ness et al. The authors considered many hypotheses and argued that the origin of the decline in reaction rate was related to the dimensions of the catalyst sites, which were approximately 10 nm in diameter. Chains of sufficient size cannot interface as efficiently with catalyst sites as smaller chains, leading to a reduction in reaction rate. The H2 pressure was held constant in this kinetic study, while in the current report the amount of D2 available for exchange declined over the course of the reaction (the total pressure remained constant as D2 was replaced by H2). As a result, a molecular-weight dependent reaction rate of this origin could partially explain the observed deuterium distribution, as lower molecular weight chains exchange rapidly and consume the available D2. However, this mechanism suggests that low molecular weight chains should have the largest amount of exchange, which is inconsistent with the measured peak in ỹ(MW) at intermediate molecular weight. Understanding the kinetics of exchange would require further experiments that are beyond the scope of this report, but the methods introduced here provide valuable tools for elucidating the mechanism of polymer adsorption and exchange.

Figure 5. (a) Five best-fitting ỹMC(MW) curves from the Monte Carlo fit and (b) corresponding SANS patterns using the n-RPA model.

without affecting the quality of the fit, and the polynomial form imposes some curvature constraints on the solutions. 5955


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Balsara et al. observed scattering from labeled polymers prepared via saturation of precursor polydienes with D2.32 In this case, the amount of scattering was relatively slight (coherent I(q = 0) ≈ 1−5 cm−1) as compared to that described here (I(q = 0) ≈ 100 cm−1), though the deuterium concentrations are comparable. The RPA model was extended to include a statistical distribution of deuterium in the labeled polymer; that is, ⟨y⟩ represents the average of some distribution of deuterium across the chains. As in the Tanzer and Crist model, all chains have the same molecular weight. The result of this extension is an additional term in the scattering model that predicts quantifiable coherent scattering from the labeled polymer and excess scattering in an isotopic blend; both of these contributions are proportional to the standard deviation of the deuterium distribution. The authors infer this standard deviation using measured SANS data. Interestingly, this analysis, when applied to the SANS data reported by Tanzer and Crist, yields a value for the standard deviation that is consistent with the proposed binary distribution of chains initially used to explain their observations (see Figure SI-3). This reveals that the Tanzer and Crist model is a specific case included within the more general approach used by Balsara et al. The n-RPA model described in the current study, which considers a blend of chains with varying molecular weight and deuterium fractions, can easily be adapted to describe a blend of chains with uniform length and nonuniform labeling, as in the analysis used by Tanzer and Crist and Balsara et al. When adapted in this fashion, the model leads to the same conclusions as described in the respective reports. However, it is clear that as chain length dispersity is introduced, this approach will fail to accurately describe SANS data, and as a result, neither of the literature models are capable of describing the scattering reported here. The results of Tanzer and Crist and Balsara et al. can also be analyzed by including chain length dispersity. In both cases, Đ = MW/MN is less than 1.06. The n-RPA model can divide such a molecular weight distribution into an arbitrary number of slices, but because Đ is so low, the slices do not represent significantly different molecular weights. In effect, for sufficiently low Đ, the n-RPA model reflects scattering of the origin described by Balsara et al.; i.e. molecular weight dispersity, while included in the model, does not play any role in the predicted scattering. To assess the impact of Đ, the predicted scattering from the nRPA model and from the Balsara el al. model at q = 0 was compared using a Monte Carlo method; for this comparison χ was set to zero. Log-normal distributions with a range of Đ values were generated, and random polynomials were used as deuterium distributions. Because the deuterium distribution is explicitly defined in this way, the true standard deviation (σD) of the distribution is readily calculable. The method described by Balsara et al. (eq 18 in ref 32) was used to measure the standard deviation (σmeas) from the modeled scattering. For a given value of Đ, 5000 trials were measured, and then the relative error of σmeas with respect to σD per trial was calculated. The results are shown in Figure 6. This figure demonstrates that the “uniform chain length approximation” is only reasonable for Đ < 1.1, as relative error accumulates rapidly with increasing Đ. In practice, the error in σmeas obtained from applying the method of Balsara et al. to experimental SANS data is likely less than Figure 6 suggests, since the calculated error is based on arbitrary polynomial distributions, many of which are not physically plausible. Nevertheless, it is clear that

While it is evident from the SANS patterns that both dHDPE and the isotopic blend form a single homogeneous phase, the heterogeneous nature of the exchange chemistry combined with the isotopic interaction parameter raises the possibility for high extents of exchange to induce phase separation. As above, we will treat the labeled polymer as a blend of 35 nondisperse components in order to calculate the stability of the system. Nesarikar et al. used a similar approach to estimate the stability of a linear low-density polyethylene resin with a broad distribution of butene comonomer, revealing that the resin forms two phases in the melt.47 In this case, the authors used a simplified form of the generalized Flory−Huggins free energy of mixing, as outlined by Scott,48 in conjunction with the random mixing hypothesis to calculate the spinodal surface. However, they included only comonomer dispersity, ignoring molecular weight dispersity. We return to Scott’s general result for the spinodal surface of an n-component blend of random AB copolymers, simplified only by the random mixing hypothesis: ⎡ ⎛ ⎞⎤ ∑j φjNy j j ⎟⎥ = 1 χAB ⎢∑ φiNi⎜⎜yi − ⎟⎥ ⎢ N 2 w ⎝ ⎠⎦ ⎣ i

where χAB is the interaction parameter between homopolymers A and B, yi is the fraction of B monomers on chain i, and Nw is the weight or volume average degree of polymerization across all chains. In the present case, A and B refer to unlabeled and fully labeled monomer units, respectively. Evaluation of the left side of the equation using the same parameters as the scattering model yields a value of 0.15. This equation outlines the limit of stability: if the quantity of the left side of the equation is greater than 1/2, the blend is unstable; if it is less, the blend may be stable or unstable. Calculation of the binodal surface is much more difficult and is beyond the scope of the present report, but has been outlined in the literature only with certain simplifying assumptions. Bauer allowed comonomer dispersity but limited all chains to a single molecular weight,49 while Vanhee et al. allowed molecular weight dispersity but used a single interaction parameter.50 Researchers should bear these issues in mind when preparing labeled polymers with a high extent of exchange. Uniformly labeled polymers should not cause coherent smallangle neutron scattering, yet labeled polymers prepared via saturation of an unsaturated precursor with D2 and exchange reactions often result in observable scattering.26,32,35 Two methods have been used in the literature to explain such scattering. Tanzer and Crist prepared labeled polyethylene via deuterium exchange chemistry and observed a greater amount of scattering from the labeled polymer than from a 50/50 isotopic blend.35 They hypothesized that the exchange reaction had occurred only on a fraction of the chains, and that as a result, the reaction product was essentially a binary isotopic blend of an unknown composition. Using SANS data and a value of ⟨y⟩ obtained from density measurements, they determined that a small fraction of the chains had been labeled to a significant extent, while the remainder were unmodified by the exchange reaction. Because all the chains in this model are of the same molecular weight, this requires that the scattering patterns from the blend and labeled polymer are proportional (IdHDPE(q) = K·Iblend(q)). The SANS patterns in the present study are not consistent with this hypothesis (see inset of Figure 4). 5956


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AUTHOR INFORMATION

Corresponding Author

*(B.M.H.) E-mail: [email protected]. Telephone: 979 238 9852. Fax: 979 238 0235. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank Daniel Baugh III for performing the NMR measurement, Rajesh Paradkar for performing the FTIR reflectance measurement, Steve Ueligger and Tom Castille for performing the deuterium exchange reactions, and Peter Shimeall for filtering and drying the reaction products. SANS experiments were conducted through Dow’s membership in the NIST nSoft Consortium for the advancement of neutron-based measurements for manufacturing of soft materials. We thank the Dow Chemical High Performance Computing Center for computational resources.


Figure 6. Error in σmeas as a function of Đ. Inset highlights the region of data from Đ = 1.0 to 1.3.

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nonuniformity of labeling with respect to molecular weight should be considered when performing SANS experiments on any labeled polymer prepared via heterogeneous catalysis.

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SUMMARY AND CONCLUSIONS A deuterium exchange reaction was performed on an ethylene homopolymer with a broad molecular weight distribution. SEC with IR and refractometer detection was adapted to measure the distribution of deuterium across molecular weight, revealing significantly nonuniform labeling. The RPA prediction for scattering from an n-component polymer blend was adapted to model the SANS patterns measured from the labeled polymer and a 50/50 labeled/unlabeled blend, yielding excellent agreement. A Monte Carlo method was used in conjunction with this SANS model to provide a second, independent measurement of the deuterium distribution that is remarkably consistent with that measured via SEC. The results apply to polymers prepared via deuterium exchange as well as polymers prepared by saturation with D2 on a heterogeneous catalyst, since some amount of exchange typically occurs during such reactions. Detailed models that are coupled to information obtained from SEC are needed to probe the structure and thermodynamics of labeled commercial polymer resins, which often have complex distributions of molecular weight, comonomer, and long chain branching. Because of the scale of the chemical processes used to synthesize such resins, deuterium labeling can only practically be accomplished through exchange. Additionally, deuterium exchange reactions and methods for characterizing labeled polymers provide powerful tools for probing the interactions between polymer, solvent, and catalyst in heterogeneous reaction systems and potentially in broader polymer adsorption applications.

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REFERENCES

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b01075. More detailed results of the Monte Carlo method and a comparison of literature data analysis methods (PDF) Mathematica implementation of the Monte Carlo deuterium distribution fitting algorithm (ZIP) 5957


Article


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Molecular Weight Dependence of Deuterium ... - ACS Publications

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