Poly(alkyl methacrylate)-Grafted Polyolefins as Viscosity Modifiers for

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Poly(alkyl methacrylate)-Grafted Polyolefins as Viscosity Modifiers for Engine Oil: A New Mechanism for Improved Performance Mohammad T. Savoji,† Dan Zhao,† Richard J. Muisener,§ Klaus Schimossek,∥ Katrin Schoeller,∥ Timothy P. Lodge,*,†,‡ and Marc A. Hillmyer*,† †

Department of Chemistry and ‡Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, United States § Evonik Corporation, 299 Jefferson Road, Parsippany, New Jersey 07054, United States ∥ Evonik Resource Efficiency GmbH, Kirschenallee, Darmstadt 64293, Germany S Supporting Information *

ABSTRACT: Lubricant additives based on graft copolymers with polyolefin backbones and poly(alkyl methacrylate) side chains were examined for their viscosity modifying behavior in base oil. A combination of ring-opening metathesis polymerization, atom transfer radical polymerization of alkyl methacrylates, and hydrogenation was used to prepare the target materials. Viscometric measurements reveal that larger side chain molar mass provides better thickening efficiency. More importantly, increasing the side chain polarity favorably impacts the performance of these graft copolymers as viscosity modifiers. While competitive modifiers must simultaneously meet several technical requirements, the most promising graft copolymer exhibits similar or larger viscosity index at a lower concentration (treat rate) compared to state-of-the-art polymeric additives. This feature bodes well for future additive design. Dynamic light scattering and pulsed field gradient NMR on dilute solutions of the graft copolymer in dodecane (a model oil) consistently show a significant (∼30 nm) decrease in the hydrodynamic radius of the copolymer upon heating from 40 to 100 °C, in conflict with the prevailing assumed viscosification mechanism of coil expansion upon heating. Small angle neutron scattering experiments suggest that the graft copolymer chains may associate to give clusters containing methacrylate-rich domains at lower temperatures due to the solubility of the hydrocarbon backbone and insolubility of the polymethacrylate side chains. We posit that, at elevated temperatures, deaggregation into single chains occurs due to the increased solubility of the side chains. This declustering process results in an overall increase in the hydrodynamic volume of the dispersed polymers, which presumably leads to an improved viscosity modification behavior in engine oil.

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INTRODUCTION Polymeric materials have been used in the lubricant industry for decades to improve the oil performance under various working conditions.1,2 The first “all season” engine oil for passenger cars was introduced in 1949, which was modified with oil soluble polymethacrylates.3 These viscosity modifiers are typically the largest molecules in the oil formulation, and they are generally believed to undergo coil expansion with increasing temperature.4 Incorporation of polymeric additives naturally thickens the oil at all temperatures but decreases the oil viscosity variation over the working temperature of the engine; i.e., additives are more effective at increasing the oil viscosity at higher temperatures than at lower temperatures.2 The performance of these polymers has been evaluated through the viscosity index (VI).5 This method involves comparing the kinematic viscosity (KV) of the sample fluid to that of a reference fluid at both 40 and 100 °C. These polymeric additives raise the VI above that of the base oil at low polymer concentrations (socalled “treat rates”) that are typically less than 10 wt %. Therefore, one can expect less wear of the metallic parts of the © XXXX American Chemical Society

engine at elevated temperatures and easier engine startup at cold temperatures. Moreover, all season engine oils containing polymeric VI improvers do not necessarily require seasonal oil changes.5 Polymeric oil additives with various compositions and structures have been produced. Polyisobutylene, predominantly used in the early 1960s, exhibits proper load bearing characteristics and shear stability (i.e., resistance to chain degradation in use). However, it acts as more of an oil thickener (an additive that evenly thickens the oil at all temperatures) than a viscosity modifier at low temperatures.6 This prompted the use of poly(alkyl methacrylate) (PAMA), which offers improved properties over a wide temperature range. PAMA chains also interfere with the formation of wax crystals in the oil and enable a relatively lower oil viscosity in cold weather Received: November 7, 2017 Revised: January 10, 2018 Accepted: January 16, 2018

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DOI: 10.1021/acs.iecr.7b04634 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

mechanism for VI improvement. We suggest that the copolymer chains may form aggregates at lower temperatures due to the imbalanced solubility of the olefin backbone and methacrylate side chains. At elevated temperatures, the solubility of the side chains increases, thus leading to declustering of the chain aggregates into single chains. This thermally driven structural evolution in the graft copolymer may give rise to an overall increase in the effective hydrodynamic volume of the system, which leads to an enhanced performance of these graft copolymers as engine oil additives.

environments but are more expensive than olefinic copolymers and thus limited to high performance engine oils. Olefinic copolymers (OCPs) have made a breakthrough for their low cost and satisfactory performance. However, linear OCPs are susceptible to chain breakage under high shear conditions in an automobile engine, resulting in shorter lifetimes.7 To overcome this, comb-like PAMAs have been prepared by free radical copolymerization of olefin-based macromonomers and alkyl methacrylates to integrate the advantages of both OCPs and PAMAs as viscosity modifiers.8 With the advent of efficient and controlled polymerization techniques, polymers with more well-defined architectures can also be used to investigate the impact of structural characteristics on their viscosity modifying performance. For example, hyper-branched, 9,10 starshaped,11−13 and dendritic polymers14,15 have shown improved mechanical stability and reduced permanent shear thinning compared to linear polymeric additives. As far as we are aware, there is no report in the literature combining polyolefins and PAMAs in a graft copolymer architecture as VI improvers, except some statistically grafted OCPs. Graft copolymers are of particular interest due to their typically high molar mass, resulting in high VI values, combined with low sensitivity to mechanical degradation, i.e., improved shear stability. We prepared a series of graft copolymers with different molecular compositions based on polyolefin backbones and PAMA side chains. Polyolefin backbones were synthesized by ring opening metathesis (co)polymerization (ROMP) of cis-cyclooctene (COE), 3-ethyl COE, and αbromoisobutyrate functionalized cis-cyclooctene (BrICOE). Activator regenerated by electron transfer (ARGET) atom transfer radical polymerization (ATRP) was then used to grow butyl and lauryl methacrylate statistical copolymer side chains from the functionalized moieties along the backbone.16 Hydrogenation of these graft polymers yielded the corresponding polyolefin backbones. Given the precise control over molar mass, composition and grafting density accessible, we explored the effect of these molecular parameters on viscosification behavior. Although VI improvement by viscosity modifiers is commonly attributed to polymer coil expansion with increasing temperature, first proposed by Selby in 1958,4 several studies suggest that this mechanism is not always necessary to explain the elevation of VI. For example, Müller measured the temperature dependence of the intrinsic viscosity ([η], proportional to the hydrodynamic volume of the chain) and found that, although the viscosity modifiers containing PAMAs show an increase in [η] with increasing temperature, [η] becomes smaller at elevated temperatures for those made of aliphatic and aromatic copolymers.17 Similar findings were also reported by Gao and co-workers18 and Sen and Rubin.19 More recently, Covitch and Trickett combined rheology and small angle neutron scattering (SANS) experiments to study the variation of polymer coil size with changing temperature and also concluded that the coil expansion mechanism is not always valid.20 Accordingly, to better understand the mechanism responsible for the viscosity modification behavior of the graft copolymers synthesized in this work, we studied the variation in size with temperature for our most promising sample in a model oil, dodecane, using a suite of techniques including dynamic light scattering (DLS), static light scattering (SLS), pulsed field gradient NMR (PFG-NMR), and SANS. These results show a significant size decrease in the graft copolymer with temperature, which is in direct conflict with the prevailing

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EXPERIMENTAL SECTION Materials. Cyclooctene (COE, 95%) and cis-4-octene (97%) were purchased from Acros Organics and GFS Chemicals, respectively, and were purified by vacuum distillation. Chloroform (CHCl3) for polymerization was purified by distillation over CaH2. Ethyl- and α-bromoisobutyrate functionalized COE were synthesized using a reported procedure.21 Toluene for ATRP was obtained from a solvent purification system. Base oil (NexBase 3043) and comb-like PAMA viscosity modifier (ES35) were donated by Evonik. All other chemicals were purchased from Sigma-Aldrich and used as received. Synthesis of Functionalized Polyolefin Backbones by ROMP. A previously reported method was used to prepare the polyolefin multifunctional macroinitiators using ring-opening metathesis polymerization (ROMP).22 A solution of COE, 3ethyl COE (EtCOE), and α-bromoisobutyrate functionalized cis-cyclooctene (BrICOE) was used as the monomer mixture in CHCl3 (1 M). The monomer solution was degassed by three freeze−pump−thaw cycles, and a solution of Grubbs’ second generation catalyst (G2) in 0.2 mL of dry CHCl3 was transferred to the reaction flask using a syringe. The appropriate amount of cis-4-octene as the chain transfer agent (CTA) was then added to the reaction mixture with a [monomer]/[CTA]/[G2] final molar ratio of 4000:30:1. The reaction was allowed to stir at 50 °C for 18 h before quenching by 0.1 mL of ethyl vinyl ether at room temperature. The polymer was precipitated from cold methanol and dried in vacuo. Grafting Polymethacrylate Arms from the Polyolefin Backbone. In a three-necked flask, a solution of polyolefin precursor (PO-Br), butyl methacrylate (BuMA), lauryl methacrylate (LMA), tin(II) 2-ethylhexanoate (Sn(EH)2), and N,N,N′,N″,N′′-pentamethyldiethylenetriamine (PMDETA) was degassed thoroughly by bubbling argon for 30 min prior to adding CuBr2. The final molar ratio of the reactant [monomer]/[PO-Br]/[CuBr2]/[Sn(EH)2]/[PMDETA] mixture was 2000:1:0.1:0.5:0.1 for atom transfer radical polymerization (ARGET ATRP). The reaction mixture was stirred at 70 °C for 16 h before cooling in an ice bath and opening to air. The polymer was then precipitated from methanol, dried in air, dissolved again in CHCl3, and passed through a basic alumina column to remove residual copper catalyst. The final polymer was obtained by another precipitation from a large excess of methanol and drying overnight in vacuo. Chemical Hydrogenation. A mixture of graft copolymer, p-tosyl hydrazide, tributylamine, and a trace amount of butylated hydroxytoluene was reacted in xylene for 5 h at 120 °C and then allowed to cool to room temperature. The hydrogenated polymer was recovered by precipitation from a large excess of methanol and dried overnight in vacuo. B


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Industrial & Engineering Chemistry Research Polymer Characterization. Proton nuclear magnetic resonance (1H NMR) spectra of the monomers and polymers were recorded on Bruker AV500 and HD500 spectrometers in deuterated chloroform (CDCl3). The chemical shifts are given compared to the solvent peak at 7.26 ppm as an internal standard. Molar mass and dispersity (Đ) of the polymers were obtained by size exclusion chromatography (SEC) on an Agilent 1100 series equipped with three PLgel 5 μm Mixed-C columns and a refractive index detector (Hewlett Packard 1047A) at 35 °C. CHCl3 was employed as the mobile phase at a flow rate of 1 mL/min, and the sample concentration was 1 mg/mL. The columns were calibrated with polystyrene standards. Thermogravimetric analysis (TGA) was performed on a TA Instruments Q500 under a nitrogen flow of 20 mL/ min. A 10−15 mg sample was heated at a heating rate of 10 °C/min from 20 to 380 °C. In isothermal TGA experiments, samples were heated at a rate of 20 °C/min to the desired temperature and then held there for 6 h. Viscosity Measurements. Temperature-dependent viscosities of the polymer-thickened base oil were measured on a TA Instruments AR-G2 rheometer with concentric cylinder geometry and equipped with Peltier temperature controller in series with a water bath. Prior to measurements, the graft copolymer additives were dissolved in base oil by stirring overnight at 90 °C. The outer cylinder of the rheometer was loaded with ca. 12 mL of oil solution, and the gap between outer and inner conical cylinders was set to 2.0 mm. Frequency was swept between 1 ≤ ω ≤ 100 rad/s in a rotational mode at chosen temperatures over the range from 0 to 140 °C at intervals of 20 °C. The obtained dynamic viscosity data were converted into kinematic viscosity (KV) by dividing the density of the polymer solution, which is assumed to be equal to that of the base oil (e.g., 0.837 g/mL at 15 °C). The viscosities at 40 and 100 °C were used to calculate viscosity index (VI) values through the Evonik online calculator.23 To simulate the performance of the polymeric viscosity modifiers, a preliminary study on high-temperature high-shear (HTHS) properties of the base oil modified by graft copolymers was also performed, and the results are presented in Table S1 (for more details, see the Supporting Information). Static and Dynamic Light Scattering. SLS measurements were conducted on a Brookhaven Instruments BI-200SM light scattering system using a 637 nm laser on at least four different dilute concentrations. The temperature was scanned between 4 and 60 °C, and the scattering angle was varied from 50° to 130° at 5° or 10° intervals. The dn/dc value of each solution was measured using an SEC RI detector (Wyatt Optilab DSP). Weight-averaged molar mass, Mw, radius of gyration, Rg, and second virial coefficient, A2, were calculated on the basis of the Berry-modified Zimm analysis,24,25 which is especially helpful for large polymers and was thus used in this work. DLS studies were conducted on a home-built apparatus with a 488 nm laser capable of measurements up to 200 °C with a range of scattering angles from 50° to 130°. All solutions were filtered through 0.2 μm filters to remove dust and were heated in a silicon oil bath with 20 min equilibration at each temperature prior to measurement. Intensity autocorrelation functions at various scattering angles between 50° and 130° were measured and further analyzed by the cumulant method to obtain the mean decay rate (Γ) in dodecane. The mutual diffusion coefficient (Dm) was extracted from a linear fit of Γ vs q2, where the wavevector q = 4πnsin(θ/2)/λ; n, θ, and λ are the refractive index of the solution, the scattering angle, and the

wavelength, respectively. The hydrodynamic radius (Rh) was then obtained from Dm (or Dt, the translational diffusion coefficient in a diluted limit) using the Stokes−Einstein equation, Rh = kT/6πηDt, where k is Boltzmann constant, T is absolute temperature, and η is the viscosity of dodecane, assuming that the solutions were sufficiently dilute. Pulsed Field Gradient NMR. PFG-NMR measurements for selected protons were taken on a Bruker AV500 spectrometer in deuterated dodecane (d26). The diffusion coefficient (Dt) of the polymer at different temperatures was calculated by standard exponential fitting of the signal decay curve 2 2 2

I = I0e−Dt γ g

δ (Δ− δ /3)

(1)

where I is the observed intensity, I0 is the unattenuated reference intensity, γ is the gyromagnetic ratio of the proton (42.6 MHz/T), g is the gradient strength, Δ is the diffusion time, and δ is the gradient length. As with DLS, the hydrodynamic radius was calculated from the diffusion coefficient Dt using the Stokes−Einstein equation. Small Angle Neutron Scattering. The SANS experiments were performed on the NG-7 30m SANS beamline at the Center for Neutron Research of the National Institute of Standards and Technology (NIST). 26 Two instrument configurations (wavelength λ of 8.09 Å with a spread of 0.14, sample-to-detector distances of 4 and 13 m) were combined to provide a q range of 0.003−0.08 Å −1 . A calibrated thermocouple was used to monitor the actual sample temperature. Scattering data were acquired at each temperature after thermal equilibration for at least 5 min. The obtained 2-D scattering patterns were then reduced and converted to the 1-D data (I(q) vs q on an absolute scale) using the Igor Pro package developed by NIST.27

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RESULTS AND DISCUSSION Preparation of Polymeric Additives. Successive ROMP and ARGET ATRP were performed to graft alkyl methacrylate monomers onto an unsaturated polyolefin backbone, followed by chemical hydrogenation of the backbone (Scheme 1). The ATRP macroinitiators were synthesized from ROMP of COE, BrICOE, and EtCOE. Two ATRP macroinitiators were prepared containing 8 mol % BrICOE, one with a [COE]/ [EtCOE] molar ratio of 100:0 (C50, Mn = 50 kDa) and the other with a ratio of 25:75 (CE150, Mn = 150 kDa). This level of BrICOE corresponds to an average of one side chain per 100 carbon atoms of the polyolefin backbone. The molar mass of the backbone polymers was tuned by the incorporation of cis-4octene as a chain transfer agent (CTA). The detailed molecular characteristics of the two macroinitiators are given in Table S2 and Figures S1−S3. The unsaturated polyolefin precursor was then used in a “grafting-from” reaction of the methacrylate monomers through ARGET ATRP, prior to chemical hydrogenation. This modification from a previous procedure22 is critical; we recently reported28 that high temperature hydrogenation of the unsaturated precursor results in the thermal degradation of α-bromoisobutyrate functional groups along the backbone (Figures S4−S6). In this work, two alkyl methacrylate monomers were selected to prepare the side chains by statistical copolymerization: butyl methacrylate (C4) and lauryl methacrylate (C12). The methacrylate monomers were then grafted onto the backbones through ARGET ATRP using tin ethyl hexanoate C


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Viscosity Measurements for Base Oil Containing Graft Copolymers. Figure 1a shows the KV as a function of shear rate for 5 wt % P3 in base oil at two representative temperatures, 40 and 100 °C. At low shear rates (10 s−1 at 40 °C), the viscosity drops with increasing shear rate. This nonlinear behavior in dilute solution is typically attributed to the distortion of polymer chain conformations. Figure 1b shows the zero shear KV of P3 modified base oil at various temperatures (0−140 °C) and concentrations (0−5 wt %). As expected, the viscosity decreases with temperature; the modified solutions are always more viscous than the base oil, and the viscosity increases with increasing polymer concentration. Interestingly, both the intrinsic viscosity of P3 in base oil (inset of Figure 1b), obtained from fitting the KV data to the Huggins equation,31 and the specific viscosity (Figure S16d) first increase with temperature but then level off at ∼80 °C. This suggests that the graft copolymer increases the oil viscosity more at higher temperatures than at lower, making it a promising candidate as a viscosity modifier. To facilitate comparison of the viscosity modification performance among different polymeric additives, the polymer concentration was adjusted in each case to give a KV at 100 °C (KV100) in the range from 8.1 to 8.4 cSt (Table 2). We first examined the effect of the PAMA side chain length on viscosity modifier performance using P1, P2, and P3 (Table 1). The viscometric results are presented in Table 2 and Figure 2a. The treat rate required to achieve a KV100 of 8.4 cSt decreases as the PAMA side chain becomes longer (P1 > P2 > P3). This is due to the fact that the hydrodynamic volume will be larger for polymers with larger molar mass, thus giving rise to higher thickening efficiency. Interestingly, for the given treat rate of P1−P3 in Table 2, the KV40 follows the order P1 > P2 > P3 while the KV140 values are in the reverse order (i.e., P1 ≈ P2 < P3, Figure 2a). This implies that P3 increases the viscosity of the base oil relatively more at high temperatures, resulting in a higher VI than P1 or P2 (Table 2). Apparently, the longer PAMA side chains induce more thermally driven structural changes in the graft copolymer over the temperature range tested, which subsequently gives rise to reduced temperature dependence of the lubricant viscosity. To explore the effect of alkyl chain length in the side chains, four graft copolymers (P3−P6 in Table 1) were prepared from the same polyolefin backbone (CE150) but with varying fraction of the BuMA units in the side chains (ranging from 0 to 80%). Notably, P6 could not be dissolved in the base oil at room temperature, presumably due to the higher content of the relatively polar BuMA.32 The temperature-dependent viscosity of P3−P5 graft copolymer solutions in base oil is plotted in Figure 2b and summarized in Table 2. For these measurements, the polymer concentration was again tuned so that the formulated lubricants exhibit a KV100 value in the range of 8.1−8.4 cSt. The viscosity thickening power at 100 °C is in the order of P5 > P3 > P4, which correlates well with the molar mass (Mn) of the PAMA side chains; i.e., the higher the Mn of the side chain, the larger is the intrinsic viscosity and thus the larger is the thickening efficiency. More interestingly, the low temperature viscosity (KV0 in Figure 2b and KV40 in Table 2) decreases as the side chains become more polar. For example, P5 with the most polar side chain (60 mol % BuMA) in the series provides the smallest KV0 and KV40 values. On the other hand, the KV100

Scheme 1. Successive ROMP, ARGET ATRP, and Chemical Hydrogenation To Prepare Polyolefins Grafted with Butyl and Lauryl Methacrylate

(Sn(EH) 2 ) as the reducing agent and degassed with argon.29,16,30 The final graft copolymers obtained after chemical hydrogenation are listed in Table 1; representative 1H NMR spectra are presented in Figures S7−S14. Two series of copolymers were synthesized, one based on CE150 and the other on C50. In each series, the molar ratio of the two methacrylate monomers was systematically varied. Moreover, the excess monomer ([M]/[initiator] = 2000:1) and, subsequently, low methacrylate monomer conversion (≤50%, Table 1) were utilized to minimize cross-linking of the polymer chains through radical−radical termination reactions. D


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Industrial & Engineering Chemistry Research Table 1. Molecular Characteristics, Conversion, and Yield of the Graft Copolymers graft copolymer P1 P2 P3 P4 P5 P6 P7 P8 P9 P10

methacrylate side chains from ATRP

polymeric additivea

Mnb (kDa)

Đb

LMA unitsc

BuMA unitsc

[LMA]/[BuMA]c

conv.d (%)

yielde (%)

Mnf (kDa)

L210-CE150 L290-CE150 L760-CE150 L60B40-CE150 L40B60-CE150 L20B80-CE150 L260-C50 L60B40-C50 L40B60-C50 L20B80-C50

215 300 750 610 600 780 290 260 660 520

2.2 2.1 2.4 3.6 2.7 2.4 2.1 2.1 2.2 2.1

210 290 760 530 480 150 260 180 470 360

0 0 0 330 740 690

100:0 100:0 100:0 62:38 40:60 18:82 100:0 65:35 39:61 19:81

9 11 29 29 25 22 46 50 24 21

85 79 75 74 86 92 86 79 82 88

53 74 190 180 230 140 65 60 220 310

95 710 1530

a

The general formula is poly(COEx-stat-EtCOEy-stat-BrICOE0.08)-graf t-poly(LMAn-stat-BuMAm), which is abbreviated as LnBm-C50 or LnBmCE150, where n and m are the rounded molar ratio of LMA and BuMA monomers in the side chain, respectively. For P1−3 and P7, the subscripted values indicate the number of LMA repeating units, calculated from 1H NMR spectroscopy. bDetermined by SEC in chloroform with polystyrene standards. cCalculated from 1H NMR spectroscopy dMethacrylate monomer conversion in the ATRP grafting process, determined by comparing the methylene proton signal from the residual monomers at 4.2−4.3 ppm with that of the polymer at 3.9−4.1 ppm in the 1H NMR spectra of the reaction mixture prior to precipitation (see Figure S15). eYield of the ATRP reaction calculated from the comparison of the actual and theoretical amount of dried polymer after precipitation. fMn = (LMA units) × 254 + (BuMA units) × 142 + 166, where 254, 142, and 166 are molecular weights of LMA, BuMA, and bromoisobutyrate, respectively.

Figure 1. (a) Flow curve of base oil formulated with 5 wt % P3 at two temperatures, 40 and 100 °C. (b) Zero shear viscosity vs temperature of the lubricant modified by P3 with different concentrations (“treat rates”), as indicated. The solid lines are drawn as guides to the eye. The inset shows the average intrinsic viscosity ⟨[η]⟩ obtained from three different fittings as a function of temperature. Here, the exact values of ⟨[η]⟩ should be viewed with some caution as different fittings do not converge to a single value. Nonetheless, the direction of change of ⟨[η]⟩ with temperature is the same. For more details, see Figure S16.

Table 2. Viscosity Modification Performance of Graft Copolymers (P1−5) in Base Oil additive P1 P2 P3 P4 P5 a

base oil L210-CE150 L290-CE150 L760-CE150 L60B40-CE150 L40B60-CE150

treat ratea (wt %) 1.3 1.2 0.8 1.0 0.7

side chain monomer unitsb 210 290 760 860 1220

side chain Mn (kDa)

KV40 (cSt)

KV100 (cSt)

viscosity index

53 74 190 180 230

22 41 40 38 37 34

4.4 8.4 8.4 8.4 8.4 8.1

109 187 193 207 214 225

The dose or concentration of polymeric additives in oil. bTotal number of LMA and BuMA units in the side chain.

investigation due to the same insolubility issue observed for P6. The viscosity results for base oil modified with P7−P9 are presented in Table 3 and Figure 2c for selected treat rates at which KV100 falls between 8.1 and 8.4 cSt. First, as shown in Table 3, P7 and P8 with comparable side chain length exhibit very similar VI behavior. Apparently, the performance of the polymeric additives was not significantly affected by incorporating up to 40% BuMA monomers in the side chains grafted to C50. However, interestingly, P9 with longer and more polar pendant chains (with 60% BuMA in the side chain) reduces the temperature dependence of the base oil viscosity and therefore

is almost constant at the given treat rates in Table 2; therefore, the VI increases with the polarity of the graft copolymers (i.e., P5 > P4 > P3) and is only limited by the solubility of the polymers at low temperatures. To explore the influence of branching in the backbone of these graft polymers on the viscosity modification, another series was produced on the basis of the C50 polyolefin backbone with no ethyl branches (P7−P10 in Table 1). Without ethyl branches, these polymers would have a higher propensity to crystallize than those synthesized from CE150 macroinitiators (P3−P6). P10 was eliminated from further E


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Figure 2. Zero shear viscosity vs temperature of the lubricant modified by graft copolymers (a) P1, P2, and P3, (b) P3, P4, and P5, and (c) P7, P8, and P9 at treat rates that give nearly identical KV values at 100 °C, as indicated inside the graph. The insets highlight the difference in the viscosity of base oil modified by these three copolymers at 0 and 140 °C. The solid lines are drawn as guides to the eye.

Table 3. Viscosity Modification Performance of Graft Copolymers (P7, P8, and P9) in Base Oil

P7 P8 P9

additive

conc. (wt %)

monomer unitsb

KV40 (cSt)

KV100 (cSt)

viscosity index

L260-C50a L60B40-C50 L40B60-C50

1.3 1.0 0.8

260 275 1180

39 39 34

8.3 8.2 8.2

196 192 229

a

The subscript indicates the number of LMA repeating units, calculated from 1H NMR spectroscopy. bTotal number of LMA and BuMA units in the side chain.

gives a larger VI (Table 3). Further, the role of backbone branching on the viscometric performance can be examined by comparing P5 and P9, which have very similar side chain molar mass and polarity. It is evident that the unbranched P9 provides slightly improved VI than ethyl branch-containing P5 (229 vs 225, Tables 2 and 3). We have shown that higher side chain molar mass and polarity provide larger VI values or enhance viscometric performance. We found that P5 and P9 are the most promising viscosity modifiers based on the high VI values and low treat rates, with a slightly better performance for P9. To further benchmark the performance of P9, we performed the same viscometric testing on a comb polymer additive (ES35) provided by Evonik (Figure S17), which consists of a PAMA backbone and polyolefin side chains. The results are summarized in Figure 3. As shown, the KV of base oil modified by these two additives is very comparable over the entire temperature range measured. In fact, the calculated VI for ES35 is 228, which is approximately the same as that of P9 (VI = 229). However, it is important to note that, to achieve the same level of viscosity modification, the concentration of ES35 (3.4%) is four times higher than that of P9 (0.8%). Solution Behavior of P9 and ES35 in Model Oil. We performed systematic structural characterization on dilute solutions of P9 and ES35 in a model oil, dodecane, as a function of temperature, using a suite of techniques including DLS, PFG-NMR, SLS, and SANS (see Figures S18−S33). The temperature-dependent hydrodynamic radius of 2 mg/mL P9 and ES35 in dodecane measured by DLS is presented in Figure 4, and the corresponding diffusion coefficients are listed in Table S3. Note that, at this concentration, the hydrodynamic size of the species in both systems is essentially independent of

Figure 3. Zero shear viscosity vs temperature of the lubricant modified by the graft copolymer P9 and the comb polymer additive ES35 with different treat rates, as indicated inside the graph. The solid lines are drawn as guides to the eye.

Figure 4. Hydrodynamic radius (Rh) of 2 mg/mL P9 and ES35 in dodecane measured by DLS and in dodecane-d26 measured by PFGNMR as a function of temperature. The error bars in the DLS data represent 10% deviation of the mean size and those in PFG-NMR come from the fits to eq 1 (most of the error bars are smaller than the symbol size).

the polymer concentration (Figure S18), justifying that dilute solution behavior is being probed. At each temperature, the intensity correlation functions at various scattering angles were well-described with cumulant fits (Figure S19), indicating a monomodal size distribution. These correlation functions were F


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Figure 5. (a) The SANS scattering intensity I(q) as a function of the scattering vector q for 2 mg/mL P9 in dodecane-d26 at varying temperatures. The incoherent scattering background has been subtracted, which was obtained from the fits and is comparable to the scattering level of dodecaned26. The symbols are experimental data, and the solid lines represent best fits to a graft copolymer form factor. (b) The same data as in (a) plotted in the Kratky format, i.e., I(q)q2 vs q. The data are vertically shifted for clarity, as indicated inside the graph.

measured from SLS at room temperature is ∼10 times larger than that from SEC (Tables 1 and S4), again suggesting clustering of polymer chains. These polymer clusters are apparently stable against further aggregation, at least over the experimental time scale, as evidenced by the positive values of second virial coefficient (A2) measured by SLS (Table S3). Additionally, these low-temperature structures seem to be less dense or adopt some more expanded conformation compared to the single copolymer chains, as indicated by the increase in Rg/Rh with decreasing temperature (Figure S31). On the other hand, in contrast to P9, the DLS hydrodynamic size of ES35 barely changes with temperature, while that probed by PFG-NMR initially increases modestly up to 60 °C and then levels off (Figure 4). This result could possibly be consistent with the Selby mechanism; i.e., the polymer chain expands with an increase in temperature. In fact, as this polymer has a PAMA backbone and polyolefin side chains (opposite to P9), it should be stable on the single chain level, with the polar methacrylate groups already shielded by the polyolefin side chains from the nonpolar dodecane environment. As temperature increases, the solvent quality is improved, thus leading to an increase in the polymer chain dimension. This indirectly supports the aggregation picture we proposed for P9, in which case the side chain methacrylate groups are mostly located on the peripheral region of the copolymer; thus, they can easily interact with methacrylate groups from other chains and form aggregates at lower temperatures. Simple dissolution experiments are consistent with this inference; we observed that ES35 can be dissolved up to 25 wt % in base oil while P9 precipitates from solution at a concentration of ca. 5 wt %. Therefore, we conclude that the difference in structural arrangements of these two polymeric additives gives rise to their significantly different solubility behavior with temperature in the base oil, which ultimately results in different mechanisms for their viscosity modification behavior. Small-Angle Neutron Scattering. We have shown that the commonly accepted mechanism for VI improvers cannot explain the viscosity modification behavior of the P9 graft copolymer. In fact, the size decrease of polymeric VI improvers with increasing temperature has also been reported for OCPs in mineral oils and other hydrocarbon solvents.17,19,20 To gain better insight into this behavior, we performed SANS measurements on dilute solutions of P9 graft copolymer (2 mg/mL, or volume fraction ϕp = 0.002) in dodecane-d26 as a surrogate aliphatic oil (Figure 5). Note that here dodecane-d26

also analyzed by the REPES Laplace inversion algorithm to obtain the size distribution (Figure S20),33 and again, a single population of species in solution was confirmed. Therefore, the cumulant method was used to fit the correlation functions, and a linear dependence of the mean decay rate Γ vs q2 was verified (Figure S21). The hydrodynamic size of these two polymers in solution was also measured by PFG-NMR (Figure S15b and Table S3) in dodecane-d26 with varying temperatures and field gradient strengths (Figures S22 and S23). As shown in Figure 4, the hydrodynamic radius of P9 in dodecane measured by both DLS and PFG-NMR significantly decreases as the temperature is raised. In fact, there is a drop of ∼30 nm when the temperature increases from 40 to 100 °C. Note that the difference in size probed by these two techniques (e.g., for P9 at 40 °C, Rh,DLS ≈ 70 nm > Rh,NMR ≈ 50 nm) lies in the fact that DLS is more biased to particles with a larger size while PFG-NMR measures a number-averaged inverse size distribution. Consistently, the Rg measured from SLS also decreases from 55 nm at 40 °C to 31 nm at 60 °C (Table S4). Importantly, these findings are inconsistent with the dominant mechanism for VI improvers proposed by Selby in 1958.4 According to this mechanism, the polymeric additives increase the oil viscosity proportionately more at higher temperatures as a result of polymer coil expansion. Consequently, this thermally driven size change in polymeric additives counteracts the viscosity drop of the solvent, leading to a weaker dependence of oil viscosity on temperature. Clearly, this mechanism cannot explain the viscosity modification behavior of P9. Alternatively, here we speculate that the P9 polymer chains may associate into larger structures below 80 °C, possibly due to the imbalanced solubility of the polyolefin backbone and PAMA side chains in dodecane. The BuMA polar groups in the copolymer arms should be less soluble than the polyolefin backbone in nonpolar dodecane. As a result, these “surfactant-like” graft copolymers may form aggregates containing methacrylate-rich domains at lower temperatures. Two additional pieces of evidence support this interpretation. First, solutions consisting of even more polar P10 molecules in dodecane are clear at 90 °C but become opaque at room temperature, indicating formation of larger aggregates and phase separation. On this basis, it is conceivable that P9, which is less polar than P10, might associate into smaller clusters that do not strongly scatter visible light while suspended in solution at lower temperatures. Second, the molecular weight of P9 G


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Industrial & Engineering Chemistry Research was used as the solvent to enhance the scattering contrast. As shown in Figure 5a, in each SANS curve, there exists a shoulder in the lower scattering vector regime (q < 0.01 Å−1), reflecting the internal structure of the graft copolymer. Also, in this q regime, the shape of the intensity trace changes with temperature (especially from 70 to 100 °C), indicating some change in copolymer structure. At higher q, the I(q) approximately scales as q−2, suggesting approximately Gaussian statistics. Additionally, as the temperature decreases, the scattering intensity at lower q increases monotonically. Qualitatively, this could be due to an upper critical solution temperature (UCST) behavior of P9 in dodecane, assuming the polymer chains are always individually dispersed in the solution over the entire temperature range studied. Alternatively, as we proposed earlier, this could also result from aggregation of polymer chains at lower temperatures. To better understand the molecular-level thermal response, we first fit the SANS data using a graft copolymer form factor coupled with the random phase approximation (RPA, eqs A8 and A10 in the Appendix). The fitting results are presented in Figure S32. As shown there, all the SANS traces at different temperatures are reasonably well represented by the proposed model, with three fitting parameters (the radius of gyration of one side chain, Rg,A, the backbone, Rg,B, and the effective Flory− Huggins interaction parameter, χeff). For these fittings, ϕp = 0.002, νp = 294 Å3, νs = 376 Å3, and the total number of monomers in P9 N = nANA + nBNB = 19 456 (nA and nB are the number of side chains and backbone blocks in P9. NA and NB are degree of polymerization of one side chain and one backbone block, respectively; see the Appendix for more details; from Table 1, we know nA = 25, NA = 720, nB = 26, and NB = 56). First, it is found that χeff decreases with increasing temperature, while both Rg,A and Rg,B increase with temperature. These results collectively suggest the P9−dodecane system displays a UCST phase behavior. However, they do not agree well with the DLS and PFG-NMR results (Figure 4), which show that the hydrodynamic size of P9 in dodecane decreases with temperature. This suggests that the RPA might not be the most appropriate way to describe the SANS data. In fact, the extracted χeff from the RPA fitting and the extrapolated reciprocal forward scattering intensity do not show a linear dependence on the reciprocal temperature (Figure S33). This likely indicates there might be some other changes in the system with temperature, such as chain clustering at lower temperatures. To examine this interpretation, we refit the SANS data using the model described in eq A9 in the Appendix. Here, the copolymers are assumed to interact athermally with the solvent, which does not significantly change within the temperature range studied. As shown in Figure 5, the SANS data are also well represented by this model, with the fitting parameters (Rg,A, Rg,B, and nagg) summarized in Figure 6. First, there is indeed a monotonic increase in nagg (here, nagg is the number of graft copolymer chains in one scattering object) as the temperature is reduced, consistent with the clustering hypothesis. Specifically, if the copolymers are assumed to be individually dispersed at 100 °C, they form clusters of ∼6 chains at 25 °C. On the other hand, Rg,B increases with temperature (∼30% from 25 to 100 °C), again reflecting the UCST phase behavior. In contrast, surprisingly, Rg,A becomes progressively smaller as the temperature increases. On the basis of these results, a possible picture emerges: at higher temperatures, the copolymer chains are individually dissolved,

Figure 6. Extracted parameters from Figure 5, radius of gyration (Rg,A and Rg,B) and the degree of polymerization normalized by that at 100 °C (nagg/nagg,100 °C) as a function of temperature.

but as the temperature decreases, chains aggregate into small clusters. As the copolymers could act as surfactants, i.e., the PAMA side chains prefer to be embedded inside the cluster while the polyolefin backbone provides a miscible interface with the solvent, and the PAMA side chains could stretch to avoid contacts with the solvent molecules as well as the polyolefin backbone. Accordingly, Rg,A increases as the polymer chains become more clustered (i.e., as the temperature is reduced). At this moment, we do not have direct evidence for this interpretation, and therefore, further investigation is needed. For example, the backbone or the side chain conformation could be selectively probed by the contrast matching method via tuning the hydrogenated and deuterated solvent composition; graft copolymers with deuterated side chains or backbones would be required. In summary, the chain aggregation hypothesis provides a more consistent overall picture of the SANS, SLS, DLS, and PFG-NMR results. Additionally, multiple results suggest that the P9−dodecane system displays a UCST phase behavior. As a result, the graft copolymer chains could expand with increasing temperature and, therefore, be partly responsible for the viscosity improving behavior of the graft copolymer in base oil. The increase of intrinsic viscosity with temperature is gradual, spanning from 0 to 80 °C which is due to the progressive chain clustering at lower temperatures that leads to gradual reduction in the overall hydrodynamic volume of the system, which ultimately gives a smaller increase in oil viscosity at reduced temperatures.

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CONCLUSIONS A library of lubricant additives based on graft copolymers with polyolefin backbones and PAMA side chains was synthesized by sequential ROMP of cyclic monomers and ARGET ATRP of butyl and lauryl methacrylate, followed by chemical hydrogenation. These graft copolymers were examined for their performance as viscosity modifiers over the temperature range of 0 to 140 °C. The side chain molar mass and polarity have been studied to optimize the VI value of the graft copolymer additives. The molecular weight of the PAMA side chains can be readily controlled by ATRP reaction conversion, while the side chain polarity was tailored by introducing alkyl methacrylate monomers with short alkyl chains. Viscometric tests reveal that, the higher the side chain molar mass, the larger is the thickening power of the graft copolymers. Additionally, larger side chain polarity can increase the VI value of the lubricants formulated with graft copolymers. Size measureH


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Figure A1. (a) A schematic for a graft copolymer, where the black line denotes the backbone. It is divided into nB blocks, with NB monomers for each block. The light blue lines represent the side chains (here, we have nA arms, with NA monomers per arm). The i’s and j’s are the representative monomers in the copolymer. (b) A similar schematic as in (a) used to demonstrate the correlations between the side chains and the backbone.

ments by DLS, SLS, and PFG-NMR indicated that coil expansion upon increasing temperature is not the mechanism for the viscosity improving behavior of these graft copolymers in oil. Instead, the SANS results suggest that the chain clustering with decreasing temperature should reduce the overall hydrodynamic volume of the system, thus weakening the temperature dependence of the base oil viscosity. The tunable chemistry given by this synthetic approach opens the door to further optimization to meet all the requirements of VI improvers, including permanent shear stability, high temperature, and high shear behavior.

F(βA NA ) =

1 − exp(−βA NA ) βA NA

(A3)

And the correlation between the anchoring points (i′ and j′ in Figure A1a is given by E(βBNB) = exp[−βB(NB − 1)]

(A4)

With this, we obtain PAA,inter(q) = 2(NAηA )2 F(βA NA )2

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nA

∑ (nA − k + 1)E(βBkNB) k=2

(A5)

APPENDIX Derivation of the Graft Copolymer Form Factor and Fitting Model for SANS Data. Here, we consider a graft copolymer consisting of the backbone (polyolefin) and side chains (or arms, PAMA). As shown in Figure A1a, there are nA arms, with NA monomers for each arm (monomer volume, vA, scattering length density, ρA, and the corresponding monomeric excess scattering length, ηA = (ρs − ρA)vA, where ρs is the scattering length density of the solvent). For simplicity, we assume the side chains are uniformly distributed along the backbone and thus divide the backbone into nB blocks (NB monomers per block, monomer volume, vB, and excess scattering length, ηB = (ρs − ρB)vB, where ρB is the scattering length density of the backbone). Clearly, the following relation holds: nB = nA + 1. The form factor of the graft copolymer has four terms:34,35 (I) The correlation of the backbone monomers (iB and jB in Figure A1a), as given by PBB(q) = (nBNBηB)2 P(βBnBNB)

where k − 1 represents the number of backbone blocks between two anchoring points, and we know that there are nA − k + 1 pairs of the same correlations described by E(βBkNB). This equation can be rewritten as PAA,inter(q) = 2(NAηA )2 F(βA NA )2 e(1 − 2NB)βB(e−nA βBNB + nA − nA e−βBNB − 1) (1 − e−βBNB)2

(IV) The cross-correlations between the side chains and the backbone blocks (iA and jB) are in Figure A1a. Starting from the first arm (solid light blue in Figure A1b), the correlation with the backbone has two parts separated by the first anchoring point; i.e., one block on its left-hand side (highlighted in yellow, given as NAηAF(βANA)NBηBF(βBNB)) and nB − 1 blocks on the right-hand side (highlighted in green, given as NAηAF(βANA)(nB − 1)NBηBF(βB(nB − 1)NB)). Note that the first and last side chains have the same correlations with the backbone due to chain symmetry. Similarly, for the second or the second to last one, the correlations will be that between the side chain with 2 and nB − 2 backbone blocks and so on. In other words, for any k blocks in the backbone, the correlation would be NAηAF(βANA)kNBηBF(βBkNB). Therefore, we have

(A1)

where βBnBNB = q2Rg,B2, q is the scattering vector, and P(βBnBNB) is the Debye function. (II) The intra-arm correlation or the correlation of monomers within the same side chain (iA and jA in Figure A1a), written as 2

PAA,intra = nA (NAηA ) P(βA NA )

(A6)

nB − 1

PAB(q) = 2NAηA F(βA NA )

∑ kNBηBF(βBkNB) k=1

(A7)

where k is the number of blocks; the factor of 2 comes from the fact that, for any k blocks, there are two side chains sharing the same correlation (symmetry along the backbone). Finally, the form factor of the graft copolymer is given by

(A2)

Similarly, βANA = q2Rg,A2 and P(βANA) again assumes the Debye function. (III) The interarm correlation (iA and jA′ in Figure A1a) can be treated as a series of triblock copolymers. In such a case, the correlations between the anchoring monomer (the one connected to the backbone) and the rest of the side chain monomers (i′ and iA; j′ and jA′ in Figure A1a) can be described by

P(q) = [PBB(q) + PAA,intra(q) + PAA,inter(q) + 2PAB(q)] /(nA NAηA + nBNBηB)2

(A8)

This form factor can be directly used to describe the SANS data if we assume the interaction between the copolymer and I



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the solvent is close to the theta condition, i.e., χ ≈ 0.5, as given by I(q) = ϕpP(q)nagg (nA NAηA + nBNBηB)2 /Vp

I(q)

=

2χeff 1 1 + − NvpϕpP(q) vs(1 − ϕp) vpvs

(A9)

(A10)

where ρp is the average scattering length density of the graft polymer, νp and νs are the average monomer volume of the graft polymer and solvent, respectively, N is the total degree of polymerization of the graft polymer, and χeff is the effective Flory-Huggins interaction parameter between the copolymer and the solvent. Here, the graft copolymer is effectively considered as one molecule (this is reasonable as the scattering length density of the backbone and the side chain are very similar compared to that of the solvent; see Table S5).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b04634. Characterization of the polyolefin backbone, thermal degradation of the polymer precursor, NMR spectra of the graft copolymers, intrinsic viscosity, Huggins coefficient and specific viscosity of P3 in base oil, zero shear viscosity of ES35, concentration dependence of hydrodynamic size for P9 and ES35, DLS correlation functions and size distribution, PFG-NMR decay curves, SLS Berry plots, Rg and Mw from SLS, neutron scattering length density of the graft copolymer and solvent, and modeling SANS data based on RPA (PDF)

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REFERENCES

(1) Bruson, H. A. Process for preparing esters and products. U.S. Patent 2,100,993, Nov. 30, 1937. (2) Srivastava, S. P. Developments in lubricant technology; John Wiley & Sons: Hoboken, NJ, 2014. (3) Horne, W. V. Polymethacrylates as viscosity index improvers and pour point depressants. Ind. Eng. Chem. 1949, 41, 952−959. (4) Selby, T. The non-Newtonian characteristics of lubricating oils. ASLE Trans. 1958, 1, 68−81. (5) Torbacke, M.; Rudolphi, Å. K.; Kassfeldt, E. Lubricants: introduction to properties and performance; John Wiley & Sons: Chichester, 2014. (6) Rudnick, L. R. Lubricant additives: chemistry and applications; Marcel Dekker: New York, 2003. (7) Ver Strate, G.; Struglinski, M. J. Polymers as lubricating-oil viscosity modifiers. In Polymers as rhelogy modifiers; Schulz, D. N., Glass, J. E., Eds.; American Chemical Society: Washington, D.C., 1991; pp 256−272. (8) Stöhr, T.; Eisenberg, B.; Müller, M. A new generation of high performance viscosity modifiers based on comb polymers. SAE Int. J. Fuels Lubr. 2009, 1, 1511−1516. (9) Wang, J.; Ye, Z.; Zhu, S. Topology-engineered hyperbranched high-molecular-weight polyethylenes as lubricant viscosity-index improvers of high shear stability. Ind. Eng. Chem. Res. 2007, 46, 1174− 1178. (10) Gao, C.; Yan, D. Hyperbranched polymers: from synthesis to applications. Prog. Polym. Sci. 2004, 29, 183−275. (11) Eckert, R. J. Hydrogenated star-shaped polymer. U.S. Patent 4,116,917, Sep. 26, 1978. (12) Wang, T. Y.; Tsiang, R. C. C.; Liou, J. S.; Wu, J.; Sheu, H. C. Preparation and characterization of a star-shaped polystyrene-b-poly (ethylene-co-propylene) block copolymer as a viscosity index improver of lubricant. J. Appl. Polym. Sci. 2001, 79, 1838−1846. (13) Xue, L.; Agarwal, U.; Lemstra, P. Shear degradation resistance of star polymers during elongational flow. Macromolecules 2005, 38, 8825−8832. (14) Hawker, C. J.; Farrington, P. J.; Mackay, M. E.; Wooley, K. L.; Frechet, J. M. Molecular ball bearings: the unusual melt viscosity behavior of dendritic macromolecules. J. Am. Chem. Soc. 1995, 117, 4409−4410. (15) Bosman, A.; Janssen, H.; Meijer, E. About dendrimers: structure, physical properties, and applications. Chem. Rev. 1999, 99, 1665−1688. (16) Jakubowski, W.; Min, K.; Matyjaszewski, K. Activators regenerated by electron transfer for atom transfer radical polymerization of styrene. Macromolecules 2006, 39, 39−45. (17) Müller, H. Mechanism of action of viscosity index improvers. Tribol. Int. 1978, 11, 189−192. (18) Lariviere, D.; Asfour, A.-F. A.; Hage, A.; Gao, J. Z. Viscometric Properties of Viscosity Index Improvers in Lubricant Base Oil over a Wide Temperature Range. Part I: Group II Base Oil. Lubr. Sci. 2000, 12, 133−143. (19) Sen, A.; Rubin, I. D. Molecular structures and solution viscosities of ethylene-propylene copolymers. Macromolecules 1990, 23, 2519−2524. (20) Covitch, M. J.; Trickett, K. J. How polymers behave as viscosity index improvers in lubricating oils. Adv. Chem. Eng. Sci. 2015, 5, 134− 151. (21) Pitet, L. M. Functional Materials from Nanostructured Block Polymers Prepared via Ring-opening Metathesis Polymerization. Ph.D. Dissertation, University of Minnesota, 2011. (22) Xu, Y.; Thurber, C. M.; Lodge, T. P.; Hillmyer, M. A. Synthesis and remarkable efficacy of model polyethylene-graf t-poly (methyl methacrylate) copolymers as compatibilizers in polyethylene/poly (methyl methacrylate) blends. Macromolecules 2012, 45, 9604−9610. (23) EVONIK. Blending Tool Page; http://oil-additives.evonik.com/ product/oil-additives/en/blending-tools/Pages/default.aspx (accessed November 2016).

where I(q) is the scattering intensity, ϕp is the polymer volume fraction in solution, nagg is the aggregation number of the graft polymer chains in one cluster, and Vp = nANAνA + nBNBνB is the copolymer volume. Note that here P(q) could be the form factor of one graft copolymer or one cluster. Alternatively, the form factor can be combined with the random phase approximation (RPA) to model the SANS data if we assume the polymer chains are individually distributed in the solution, as given by (ρp − ρs )2

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (M.A.H.). *E-mail [email protected] (T.P.L.). ORCID

Timothy P. Lodge: 0000-0001-5916-8834 Marc A. Hillmyer: 0000-0001-8255-3853 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Evonik Resource Efficiency GmbH is acknowledged for the support of base oil and commercial additives. This work was funded by the Evonik Resource Efficiency GmbH. We acknowledge the support of the National Institute of Standards and Technology (NIST), U.S. Department of Commerce, for providing the neutron research facilities used in this work. We thank Dr. Paul Butler and Dr. Yimin Mao at NIST for assistance with SANS measurements. J


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Industrial & Engineering Chemistry Research (24) Berry, G. Thermodynamic and Conformational Properties of Polystyrene. I. Light-Scattering Studies on Dilute Solutions of Linear Polystyrenes. J. Chem. Phys. 1966, 44, 4550−4564. (25) Zimm, B. H. Apparatus and methods for measurement and interpretation of the angular variation of light scattering; preliminary results on polystyrene solutions. J. Chem. Phys. 1948, 16, 1099−1116. (26) Glinka, C.; Barker, J.; Hammouda, B.; Krueger, S.; Moyer, J.; Orts, W. The 30 m small-angle neutron scattering instruments at the National Institute of Standards and Technology. J. Appl. Crystallogr. 1998, 31, 430−445. (27) Kline, S. R. Reduction and analysis of SANS and USANS data using IGOR Pro. J. Appl. Crystallogr. 2006, 39, 895−900. (28) Savoji, M. T.; Xu, Y.; Thurber, C. M.; Lodge, T. P.; Hillmyer, M. A. Correction to Synthesis and Remarkable Efficacy of Model Polyethylene-graf t-poly (methyl methacrylate) Copolymers as Compatibilizers in Polyethylene/Poly (methyl methacrylate) Blends. Macromolecules 2016, 49, 432−432. (29) Matyjaszewski, K.; Dong, H.; Jakubowski, W.; Pietrasik, J.; Kusumo, A. Grafting from surfaces for “everyone”: ARGET ATRP in the presence of air. Langmuir 2007, 23, 4528−4531. (30) Matyjaszewski, K.; Jakubowski, W.; Min, K.; Tang, W.; Huang, J.; Braunecker, W. A.; Tsarevsky, N. V. Diminishing catalyst concentration in atom transfer radical polymerization with reducing agents. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 15309−15314. (31) Huggins, M. L. The viscosity of dilute solutions of long-chain molecules. J. Am. Chem. Soc. 1942, 64, 2716−2718. (32) Yorulmaz, Y. Alkylated polymers as lube oil additives. J. Mater. Sci. 1983, 18, 1638−1644. (33) Jakeš, J. Regularized positive exponential sum (REPES) program-A way of inverting laplace transform data obtained by dynamic light scattering. Collect. Czech. Chem. Commun. 1995, 60, 1781−1797. (34) Benoit, H.; Hadziioannou, G. Scattering theory and properties of block copolymers with various architectures in the homogeneous bulk state. Macromolecules 1988, 21, 1449−1464. (35) Hammouda, B. SANS from homogeneous polymer mixtures: a unified overview. Adv. Polym. Sci. 1993, 106, 87−133.

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Poly(alkyl methacrylate)-Grafted Polyolefins as Viscosity Modifiers for

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