POx as an Alternative to PEG? A Hydrodynamic ... - ACS Publications

Feb 22, 2018 - molar masses show an overarching good correlation to that of the hydrodynamic analysis utilizing the ultracentrifuge and viscometry. ...
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Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

POx as an Alternative to PEG? A Hydrodynamic and Light Scattering Study Mandy Grube,†,‡ Meike N. Leiske,†,‡ Ulrich S. Schubert,*,†,‡ and Ivo Nischang*,†,‡ †

Laboratory of Organic and Macromolecular Chemistry (IOMC), Friedrich Schiller University Jena, Humboldtstraße 10, 07743 Jena, Germany ‡ Jena Center for Soft Matter (JCSM), Friedrich Schiller University Jena, Philosophenweg 7, 07743 Jena, Germany S Supporting Information *

ABSTRACT: Poly(ethylene glycol)s (PEG) are widely and intensely used in the pharmaceutical industry and biomedical applications, and due to this fact, antibodies have recently been reported. Poly(2oxazoline)s (POx) are promising candidates for potential replacement of PEG in related applications, and as such, their hydrodynamic properties and characteristics derived from light scattering experiments are important to reconcile their behavior in solution. In this study, we have investigated the molecular hydrodynamic characteristics of poly(2-methyl-2-oxazoline)s and poly(2-ethyl-2-oxazoline)s in the pharmaceutical molar mass range as base candidates for such applications, prepared by cationic ring-opening polymerization in a microwave reactor. A combined viscometry and sedimentation−diffusion analysis by using sedimentation velocity experiments in an analytical ultracentrifuge includes (i) the study of intrinsic viscosities, (ii) sedimentation coefficients, and (iii) derived translational diffusion coefficients. These characteristics are then interrelated through hydrodynamic invariants that showed consistency between all these hydrodynamic parameters and, consequently, adequate values of derived absolute molar masses. The established scaling relationships of POx could as well be related quantitatively to that of pharmaceutical PEG from a recent study. Complementary, the molar masses were estimated by asymmetrical flow field-flow fractionation (AF4) and size exclusion chromatography (SEC) in conjunction with multiangle laser light scattering (MALLS). Thus, the obtained results of molar masses show an overarching good correlation to that of the hydrodynamic analysis utilizing the ultracentrifuge and viscometry. However, we demonstrate as well that AF4-/SEC-MALLS experiments of macromolecules below 10 000 g mol−1 may provide erroneous information on their molar mass, identified and discussed by the hydrodynamic invariant concept interrelating three independent experimental approaches on the same sample, i.e., (i) intrinsic viscosities, (ii) intrinsic sedimentation coefficients, and (iii) molar masses from light scattering. Our results open the gate for the replacement of pharmaceutical PEG by POx on a physicochemical basis with key first-principles hydrodynamic parameters of interest, all associated with values of the molar mass.

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INTRODUCTION Poly(ethylene glycol)s (PEG), and poly(ethylene oxide)s depending on the classification used, have gained major interest in the pharmaceutical industry.1 This is because standard PEG is inexpensive, has a low toxicity, shows stealth behavior, and is known for its biocompatibility.2 It is well established that the covalent attachment of PEG derivatives, in particular methoxyPEG (mPEG), to proteins and therapeutic entries (i.e., PEGylation) as approved by the Federal Drug Administration (FDA), maintains appreciable water solubility, biocompatibility, and function of the PEGylated substance. As a consequence, PEG is useful for drug development purposes.2,3 It is possible to prolong the blood circulation time of pharmaceutical entries as well as by reducing the renal ultrafiltration.2,4,5 In addition to that, a PEGylated composition may reduce the possibility of antibody generation, consequently preventing reticuloendothelial system (RES) uptake through opsonization.6 PEGylation is a widely applied methodology in the pharmaceutical industry and in biopharmaceutical research © XXXX American Chemical Society

by modulating the half-life and tailored plasma clearance time scales. Moreover, PEG has an enhanced permeability and retention effect.2 The chain-end chemistry of PEG is as well diversified, finding applications in diagnostics,7 formation of hydrogels,8,9 medical devices, regenerative medicine, cell culture, surface modification,10 and wound sealing and wound healing.3 Because of the wide and intense use of PEG in biomedical applications, unsurprisingly PEG antibodies have recently been reported.11 Thus, research in academia and pharmaceutical companies is also focused to find alternative macromolecules in a potential sought for PEG replacements.4,12 To this end, water-soluble poly(2-alkyl-2-oxazoline)s could be considered as potential biocompatible hydrophilic polymer alternatives to PEG.13−15 Poly(2-methyl-2-oxazoline)s (PMeOx) and, in Received: December 16, 2017 Revised: January 31, 2018

A

DOI: 10.1021/acs.macromol.7b02665 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

exclusion chromatography (SEC).36 Both solution-based molecular hydrodynamic analysis and solution light scattering are the arguably most powerful techniques in the estimation of molar masses of synthetic macromolecules.37−39 In this study, two series of POx with molar masses covering the pharmaceutical range of only a few thousand to 30 000 g mol−1, prepared by the CROP of 2-alkyl-2-oxazolines in a microwave reactor, were studied in depth via both of the aforementioned approaches. For physicochemical studies of solution properties, we employ sedimentation−diffusion analysis on sedimentation velocity experiments in an analytical ultracentrifuge in combination with viscometry as key absolute and interrelated methods based on first-principles measurements.33,40 Though this combination of hydrodynamic techniques is arguably slow, their unprecedented power emanates from a complementary assessment of macromolecular characteristics, apart from the molar mass. In a search for quicker alternatives, an independent study of molar masses of POx by AF4 and SEC coupled to multiangle laser light scattering (MALLS) has been utilized, exploring coverage of the lower molar mass end below 10 000 g mol−1, found in many typical applications, and possible to cover by analytical ultracentrifugation.33 Finally, solution properties of POx are confined, and molar mass values from these analytical tools are compared and discussed in view of the hydrodynamic invariants.

particular, poly(2-ethyl-2-oxazoline)s (PEtOx) are frequently compared to PEG because of the known stealth behavior toward plasmatic proteins.15−17 It has been shown already that poly(2-oxazoline)s (POx) can potentially be used in biological systems in combination also with other biomaterials.16 Next to their observed thermoresponsive properties,18 experimental explorations have shown desirable drug loading capabilities of tailored systems. The possibilities offered by macromolecular science enable the modulation of solubility, variation of size, architecture, and chemical functionalities.2,17 In the past years it could be shown that POx have the desired drug delivery properties for new biological applications.13,18,19 This includes recent research reports in areas that were dominated by the use of PEG, e.g., POxylation instead of PEGylation.18,20 Typically, the polymerization of (functional) 2-oxazolines is performed by cationic ring-opening polymerization (CROP) at high temperatures or for rather long time scales.21,22 By the very slow nature of the polymerization process it, however, could lead to a desirable molar mass range with decent dispersity. Alongside, the dispersity typically increases with the attempt to create higher molar masses.23,24 This may originate from the well-described chain transfer reactions, taking place at higher degrees of polymerization.25 Notwithstanding, recent attempts suggest to create high molar mass POx (>100 000 g mol−1) at prolonged time scales.26 In order to accelerate polymerization reactions, remediating attempts have been undertaken. A key role should here be reserved for the microwave reactor, allowing to perform polymerizations in the time scale of a few minutes instead of days to weeks,27,28 unfortunately not preventing all possible side reactions.25,28 In order for POx to be used as a potential replacement for PEG, an exact knowledge of its molar mass and the associated solution properties, in particular aqueous, is highly desirable. The chemical structures of most commonly known POx (PMeOx, PEtOx) and PEG are shown in Scheme 1. We note that POx typically do not exhibit diol content, a well-known and often raised issue in the pharmaceutically used mPEG.19

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EXPERIMENTAL SECTION

Synthesis of the Poly(2-alkyl-2-oxazoline)s. POx were synthesized via CROP of 2-alkyl-2-oxazolines in a microwave reactor, similar to a procedure reported recently.27,41 Details on the adapted synthetic procedure, product isolation, purification, spectroscopic characterization by proton nuclear magnetic resonance spectroscopy (NMR, Figure S1), and standard size exclusion chromatography analysis (SEC, Figure S2) calibrated against polystyrene standards can be found in the Supporting Information (see also Table S1). Hydrodynamic Characterization. Viscometry. The relative viscosities of macromolecule solutions, ηr, were determined with an Automated Microviscometer (AMVn, Anton Paar, Graz, Austria) at T = 20 °C via a capillary/ball combination and the subsequent determination of the ball times in the solvent water, t0, and macromolecule solutions of specific concentrations, tc, at a tilting angle of the capillary of 50°. The measurements were performed in a range of macromolecule solution concentrations, c, that resulted in values of relative viscosities ηr = tc/t0 = 1.2−2.5. Extrapolations of linear fits to viscometric data were performed via both the Huggins and Kraemer relations42,43 (eqs 1 and 2) to zero concentration, which resulted in estimates of intrinsic viscosity, [η].

Scheme 1. Schematic Representation of the Structures of Poly(2-ethyl-2-oxazoline) (PEtOx), Poly(2-methyl-2oxazoline) (PMeOx), and Methoxypoly(ethylene glycol) (MPEG), All with the α-Methyl and the ω-Hydroxyl Terminus

ηr − 1 c

Classical and modern macromolecular characterization science offers two eminent attempts in solution characterization of macromolecules. Analytical ultracentrifugation, pioneered by Svedberg at the beginning of the past century,29−31 is the method of choice for absolute characterization of (bio)macromolecules through both sedimentation velocity and sedimentation equilibrium experiments.32 A combination of this technique with viscometry has as well been shown to provide fundamental insight into solution hydrodynamics and absolute properties of synthetic macromolecules.33 Next, light scattering in its multiplicity of implementations and recent advancements in instrumentation emerged as a practical and viable alternative.34,35 This includes upstream processing by fractionation/separation techniques applied on samples, such as asymmetrical flow field-flow fractionation (AF4) or size

ln ηr c

= [η] + kH[η]2 c + ...

= [η] + kK[η]2 c + ...

(1)

(2)

The average values of the resultant [η], that was typically very close, was considered as appropriate value of the intrinsic viscosity. Equations 1 and 2 as well allow determination of the Huggins, kH, and Kraemer constants, kK, for a particular macromolecule sample from dilutions of each individual macromolecular solution, simply by dividing the slope of the curves by [η]2. kH indicates the quality of the solvent, and based on mathematical origin of these equations, the following relation should hold between kH and kK: kH − kK = 0.5.44−47 Analytical Ultracentrifugation. Partial Specific Volume. The partial specific volume, υ, is an important parameter in macromolecular characterization science through centrifugation experiments. It describes the increase in volume of a solution when macromolecules B

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Macromolecules are added to a solvent at constant temperature and pressure.48,49 The partial specific volume, υ, of each individual POx in aqueous solution was determined with a DMA4100 density meter (Anton Paar, Graz, Austria) at T = 20 °C, as reported previously.33 This allowed for a cumulative view on each series of the POx macromolecules. The density measurements were performed in a concentration range of 0.1 ≤ c ≤ 1.4%. Sedimentation Velocity Experiments. Sedimentation velocity experiments were performed using a ProteomeLab XL-I analytical ultracentrifuge (Beckman Coulter Instruments, Brea, CA) with an An60 Ti four-hole rotor, using double-sector aluminum centerpieces with a 12 mm optical path length. The cells were filled with 420 μL of the sample in water and with 440 μL of water as the reference. Interference optics detection was used for observation of the sedimentation boundary with respect to time. All experiments were performed at a rotor speed of 50 000 rpm for 24 h and at a temperature of T = 20 °C. Scans were acquired at 3 min intervals. Every fifth or tenth scan was used for data evaluation. Sedimentation−Diffusion Analysis. The fundamental description of transport processes in the sector-shaped cell volume can be rationalized by the Lamm equation (eq 3).50,51 In this partial differential equation, a component originating from sedimentation (imposed by the centrifugal field ω2r) and a component of diffusion (imposed by developed concentration gradients ∂c/∂r) can be identified: ⎤ dc 1 ∂ ⎡⎛⎜ ∂c 2 ⎞ = ⎢⎝D − ω rs⎟⎠r ⎥ ⎣ ⎦ ∂r dt r ∂r

Figure 1. Differential distributions of sedimentation coefficients, s, for three descending concentrations of PEtOx 1 (c = 0.3 × 10−2, 0.15 × 10−2, and 0.05 × 10−2 g cm−3) (solid lines) and PEtOx 9 (c = 0.3 × 10−2, 0.2 × 10−2, and 0.1 × 10−2 g cm−3) (dotted lines). The continuous c(s) distribution model accounting for the numerical solution of the Lamm equation (eq 3) on sedimentation velocity data was employed. Further details of the macromolecules can be found in Table S1.

the term (1 − υρ0) the buoyancy factor, obtained from the density increment method (vide supra).33,49 Similarly to s0, the translational frictional ratio at infinite dilution, ( f/fsph)0, was determined from weight-average f/fsph values at different concentrations via the following relationship: f/fsph = ( f/fsph)0(1 + kfc), where kf is the concentration−frictional ratio coefficient. In cases where there was no apparent dependence of f/fsph on macromolecule solution concentrations, average values were taken as an estimate. With the knowledge of the essential numerical values of υ, ( f/fsph)0, and s0 from the sedimentation-diffusion analysis, the translational diffusion coefficient, D0, can be estimated:

(3)

Sedimentation velocity data were analyzed with SEDFIT (version 15.01b) and the c(s) model with a maximum entropy regularization procedure. This model accounts for a numerical solution of the Lamm equation based on sedimentation velocity profiles, assuming the same apparent weight-average translational frictional ratio, f/fsph, for the population of sedimenting macromolecules. f describes the translational friction coefficient of the macromolecule and fsph the translational friction coefficient of a spherical particle of the same anhydrous volume and mass.52 The c(s) analyses were carried out using a range of sedimentation coefficients s = 0−2S (with S representing the unit Svedberg). The maximum entropy regularization confidence levels (F-ratios) were set to 0.95. Density, ρ0, and viscosity, η0, of the solvent, as well as the partial specific volume of the macromolecules, υ, were estimated as described above. Results of numerical analysis led to distributions of s and numerical weightaverage values of f/fsph. Example sedimentation profiles of PEtOx samples are shown in Figure S3 for a relatively small (Figure S3a) and a larger molar mass (Figure S3b). It is clear that the relatively small molar mass (Figure S3a) resembles sedimentation profiles that are strongly influenced by back-diffusion. In turn, the sedimentation profiles for the macromolecule with a larger molar mass (Figure S3b) are less diffuse. The distributions of sedimentation coefficients for the small molar mass PEtOx and larger molar mass PEtOx clearly reveal concentrationdependent intensities and are readily narrow (Figure 1). Seen also is an apparent increase of sedimentation coefficients with descending solution concentration for the larger PEtOx (dotted lines in Figure 1), while distributions of sedimentation coefficients for the smaller PEtOx appear invariant (solid lines in Figure 1). In the here presented approach, different concentrations of macromolecules were centrifuged to indicate the dependence of derived distributions of sedimentation coefficients, s, against macromolecule solution concentrations. The sedimentation coefficient at infinite dilution, s0, was consequently determined via linear fits of individual weight (signal) averages of sedimentation coefficients determined at varying macromolecule solution concentrations to s−1 = s0−1(1 + ksc), where ks is the concentration−sedimentation coefficient (Gralen coefficient).33,52 Obtained values for s0 were afterward used to calculate the intrinsic sedimentation coefficient [s] = s0η0/(1 − υρ0) with η0 being the dynamic viscosity of the solvent and

D0 =

kT (1 − υρ0 )1/2 η0 3/2 9π 2 ((f /fsph )0 )3/2 (s0υ)1/2

(4)

with k being the Boltzmann constant. Consequently, the intrinsic diffusion coefficient [D] = D0η0/T can be calculated, with the temperature T in Kelvin. Consistency of the Experimental Results: Hydrodynamic Invariants. The interrelation of the basic hydrodynamic characteristics is considered important for indicating the suitability of the here provided analysis in the estimation of adequate values of the molar mass. This was done by calculating the hydrodynamic invariants, A0 (in g cm2 s−2 K−1 mol−1/3), for all populations of macromolecules in solution in the present work:53 A 0 = (R[η][s][D]2 )1/3 = R[η]1/3 [s]M −2/3

(5)

with R being the universal gas constant. This equation interrelates values of [η] (in numerical values dL g−1) from viscometry, as a measure for rotational friction, and estimates for [s] and [D] as a measure for translational friction, obtained from the sedimentation− diffusion analysis of sedimentation velocity experiments in the ultracentrifuge. Alternatively, A0 values can be calculated by utilization of the determined molar mass, M, provided by any other method. This will be an important part of our later discussion. Molar Mass and Hydrodynamic Diameter Estimations. Equation 6 shows the modified Svedberg equation, where the translational frictional ratio, ( f/fsph)0, values of the intrinsic sedimentation coefficients, [s], and partial specific volume, υ, are used directly to calculate values of the molar mass, Ms,f:

Ms,f = 9π 2 Na([s](f /fsph )0 )3/2 υ C

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In this equation, R is the excess Rayleigh ratio of the solution as the function of the scattering angle θ. It is proportional to the intensity of scattered light in excess to the light scattered by the solvent only. c is the sample concentration, and K is a constant for a given polymer− solvent system in the detector. rg is the radius of gyration and is expected very small, λ0 is the incident laser wavelength in vacuum, and n is the refractive index of the solvent. The optical constant, K, is expressed with the following equation:

with Na being the Avogadro constant. This equation should lead to adequate values of the molar mass, once the adequacy of estimations of (f/fsph)0 values and of the determined D0 (eq 4) is checked for by the invariants (eq 5).33,53 Similarly, the hydrodynamic diameter, dH, based on the equivalent hydrodynamic sphere concept and ( f/fsph)0 can be defined as dH = 3 2 [s]υ (f /fsph )0 3/2 . We note that the real shape and therefore specific dimensions of the macromolecules may differ substantially from this estimate.54 Asymmetrical Flow Field-Flow Fractionation/Size Exclusion Chromatography Coupled to Multiangle Laser Light Scattering. Asymmetrical Flow Field-Flow Fractionation (AF4). AF4 measurements were performed on an AF2000 MT System from Postnova Analytics GmbH (Landsberg, Germany), equipped with a tip and focus pump (PN1130), an autosampler (PN5300), and a channel oven unit (PN4020) with the channel coupled to a multiangle laser light scattering (MALLS) detector (PN3621) equipped with a 532 nm laser, and a refractive index (RI) detector (PN3150). The MALLS device can utilize an overall of 21 angles. The channel had a trapezoidal geometry with an overall footprint of 31.6 cm2. The nominal height of the spacer was 500 μm, and a regenerated cellulose (RC) membrane from Postnova Analytics GmbH (1 kDa RC membrane) with a molar mass cutoff of 1 kDa was used as accumulation wall, particularly used because of the relatively small molar masses of some of the POx investigated here. The channel oven temperature was set to T = 25 °C, and a mobile phase of 0.9% (w/w) aqueous sodium chloride solution was used as eluent and sample solvent. 20 μL of POx sample at a concentration of 15 mg mL−1 was injected with an injection flow rate of 0.2 mL min−1, a focus flow rate of 2.3 mL min−1, and a cross-flow rate of 2 mL min−1, resulting in a detector flow rate of 0.5 mL min−1. The focusing time was 4 min before switching to elution at a constant cross-flow of 2 mL min−1 for 60 min. After a linear decrease to 0 mL min−1 cross-flow within 5 min, the elution was monitored for a further 5 min. Alternatively, another elution method was used. For such measurements again a 1 kDa RC membrane, a 500 μm spacer and a mobile phase of 0.9% (w/w) aqueous sodium chloride solution were used. For the measurements, 20 μL of sample (15 mg mL−1) was injected with an injection flow rate of 0.2 mL min−1, a focus flow rate of 1.3 mL min−1, and a cross-flow rate of 1.2 mL min−1, resulting in a detector flow rate of 0.3 mL min−1. The focusing time was 4 min before switching to elution at a constant cross-flow of 1.2 mL min−1 for 1.5 min, followed by an exponential decay (with an exponent of 0.1) to 0.5 mL min−1 within 20 min. After a linear decrease to 0 mL min−1 within 1 min, the system was run for a further 40 min before conditioning for the next run. Size Exclusion Chromatography (SEC). Alternatively to AF4, the fractionation channel in the AF4 system was replaced by a SEC column (PSS, SUPREMA MAX column, 10 μm particle size, 30 nm pore size, dimensions: 300 mm length × 8 mm i.d.). Here, a suitable mobile phase of 0.1 M NaCl + 0.3% trifluoroacetic acid (TFA) was used for elution experiments. The oven temperature was set to T = 25 °C, and 50 μL of a 2 mg mL−1 concentrated polymer solution was injected. The isocratic flow of 1 mL min−1 was controlled with the tip pump. The SEC and AF4 runs were detailed postelution via RI as a concentration-sensitive detector and MALLS as a mass-sensitive detector. Multiangle Laser Light Scattering (MALLS). In MALLS, an incident beam of laser light enters the sample solution volume in the cell. The intensity of scattered light of the macromolecules is proportional to the product of concentration times the weight-average molar mass, Mw, of the sample. In this study, we implemented light scattering according to the following equation:35,55,56

⎛ ⎤2 ⎞ Kc 1 ⎜ 2 2 ⎡ 4πn r sin( /2) = ⟨ ⟩ θ ⎢ ⎥ ⎟⎟ g R(θ) M w ⎜⎝ 3! ⎣ λ0 ⎦⎠

K=

4π 2n2(dn/dc)2 λ 0 4Na

(8)

In this equation, dn/dc is the refractive index increment of the macromolecules and Na is the Avogadro constant. For this study, we used a Zimm plot of Kc/R(θ) against sin2(θ/2) (eq 7). This allowed for determination of the resultant intercept from extrapolation to sin2(θ/2) = 0 and, by its inverse, Mw (eq 7). Refractive Index Increment (dn/dc). We note that the accuracy of the dn/dc is pivotal for appropriately estimated values of the molar mass due to its quadratic appearance in eq 8.57,58 Accurate values of the dn/dc were determined independently with an Optilab rEX system with a 658 nm laser (Wyatt, Germany) by manual delivery of six known concentrations, within c = 0.1−10 mg cm−3, of the POx in respective mobile phases used in AF4-/SEC-MALLS experiments, via a plastic syringe at a temperature of T = 25 °C. The dn/dc values were calculated by the slope of the plot from the refractive index against the concentration. This procedure was performed for the largest and smallest molar mass of each series of the POx. This was done in order to ensure validity of the dn/dc of each polymer series59 and to resolve expected differences in the dn/dc between the PMeOx and PEtOx. For the calculation of the molar masses the average values of the dn/dc for the low and high molar mass POx were utilized. System Performance. Beforehand, the AF4-MALLS system was calibrated with bovine serum albumin (BSA) of a monomer molar mass of ∼66 000 g mol−1, utilizing 0.9% (w/w) aqueous sodium chloride as sample and system run solvent to ensure acceptable separation and scattering performance (see Supporting Information for details). The AF4 analysis allowed separation of the BSA monomer from aggregates (Figure S4a). After the following POx measurements via AF4, a final run with BSA was carried out in order to see if the analysis of the POx altered separation and scattering performance. Virtually, identical separation performance of BSA and its aggregates was obtained, and the accurate molar mass of the BSA monomer was determined (Figure S4b). An evaluation of the two smallest POx in the AF4-MALLS (constant cross-flow) measurements was not possibe due to their high diffusion coefficients, poor separation from the void peak, and low recoveries, accompanied by small signal-to-noise ratios of the MALLS as a mass-sensitive detector. AF4-MALLS with an exponential decay in the cross-flow and SEC-MALLS was suitable to elute all POx, including estimation of molar masses of only a few thousand g moL−1. Depending on sensitivity, the highest and lowest detection angles have typically not been utilized due to their low signal-to-noise ratio and suitability for molar mass estimations via the Zimm plot.

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RESULTS AND DISCUSSION For a desired replacement of PEG by POx in biomedical applications, fundamental physicochemical properties in solution centered on the molar mass and derived from key first-principles experiments are deemed important. Overarching, we use a combined and self-sufficient hydrodynamic approach utilizing an analytical ultracentrifuge and viscometry33,52 as well as an independent approach based on the hydrodynamic separation principles of AF4/SEC coupled to MALLS for the characterization of the POx in aqueous solutions. For our hydrodynamic approach, we first report on the primary data of intrinsic viscosity, [η], and partial specific volume, υ. Then we estimate values for sedimentation coefficients, s0, frictional ratios, (f/fsph)0, diffusion coefficients,

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Macromolecules D0, and their interrelation for estimation of adequate values of molar masses, Ms,f. All parameters are consequently used for establishment of Kuhn−Mark−Houwink−Sakurada scaling relationships, reconciling a complete solution picture of the POx, quantitatively set in context to mPEG.33 In the second part of this paper, results from the hydrodynamic separation principle of AF4, based on differences of diffusion coefficients, and the hydrodynamic volume based separation principle of SEC are reported. Here, RI and MALLS were used to determine the weight-average molar mass, Mw, the values of which being compared to the purely hydrodynamic analysis. Particular emphasis is placed to also cover smaller molar masses below 10 000 g mol−1. Viscometry. Figure S5a,b shows dependences of viscosities for the set of the PEtOx 1−9 (Figure S5a) and PMeOx 1−7 (Figure S5b) against solution concentration after the Huggins and Kraemer equations (eqs 1 and 2). It is clear that the intercept of both curves for each of the POx is readily similar. Average values of intrinsic viscosities [η] are found in a range from [η] = 6−39 cm3 g−1 for the PEtOx 1−9 and [η] = 6−33 cm3 g−1 for the PMeOx 1−7. [η] values for each individual macromolecular solute population can be found in Table S1. Analytical Ultracentrifugation−Sedimentation−Diffusion Analysis. Partial Specific Volume. Figure S6 shows cumulative plots of density increment measurements, Δρ, against concentration, c, for the set of the PEtOx 1−9 (Figure S6a) and PMeOx 1−7 (Figure S6b). The slopes of these curves, also known as the buoyancy factor (1 − ρ0υ), obtained from linear fits to the cumulative data of each set, were used to determine the partial specific volume, υ, by the measured solvent density, ρ0. The partial specific volumes of the PEtOx 1−9 and PMeOx 1−7 were found being on average υ = 0.84 ± 0.007 cm3 g−1 and υ = 0.81 ± 0.008 cm3 g−1, respectively. As well, each individually calculated υ value is seen to fluctuate around each POx series mean without a significant trend (Figure S6c). The obtained estimates of υ for the PEtOx are slightly smaller than that reported in the literature, with reported values from Ye et al.60 of υ = 0.85 cm3 g−1 and υ = 0.87 cm3 g−1 from Chen et al.61 The values of υ for the PEtOx were found tractably higher on average than that of the PMeOx (Figure S6c), a situation having its origin in the existence of the ethyl instead of the methyl substituent on the carbonyl C (Scheme 1). Therefore, also, the PEtOx shows slightly lower densities than the PMeOx. A similar effect was also observed for that of methacrylic polymers in a nonrelated study.62 Sedimentation Coefficients. Figure 2 shows differential distributions of sedimentation coefficients, s, of each of the here investigated PEtOx 1−9 (Figure 2a) and PMeOx 1−7 (Figure 2b) macromolecule populations at the same macromolecule solution concentration of c = 0.3 × 10−2 g cm−3. It is apparent that the distributions of s are narrowest for that of the smaller molar mass POx. An increase in the apparently larger targeted molar mass results in broader and in some cases more asymmetric distributions, in instances showing fronting toward smaller values of s (Figure 2). For consideration of further estimations, we utilized the weight (signal) average of the resultant distributions of s and their dependence on solution concentration for the PEtOx 1−9 in Figure S7a and the PMeOx 1−7 in Figure S7b. Values of determined estimates of s0 in the present study range from s0 = 0.26−1S (Table S1). Translational Frictional Ratios. The data of numerical estimates of the weight-average ( f/fsph)0 values from plots of the f/fsph values against solution concentration for PEtOx 1−9

Figure 2. Normalized differential distributions of sedimentation coefficients, s, of each of the here investigated (a) PEtOx 1−9 (from left to right) and (b) PMeOx 1−7 (from left to right) macromolecule populations at the same macromolecule solution concentration of c = 0.3 × 10−2 g cm−3. Further details on the macromolecules can be found in Table S1.

in Figure S8a and PMeOx 1−7 in Figure S8b are listed as well in Table S1. The numerical values cover a range of (f/fsph)0 = 1.26−2.25. Increased (f/fsph)0 values have their origin in an increased asymmetry of the macromolecular solutes and/or an increased solvation (vide infra).33 Apparent also is an increase in the concentration dependence of f/fsph values with larger molar mass POx (Figure S8). Translational Diffusion Coefficients. In the here presented analysis, estimates of s0, ( f/fsph)0, and υ were used for calculation of the translational diffusion coefficients, D0 (eq 4). These estimates are listed for PEtOx 1−9 and PMeOx 1−7 in Table S1. The adequacy of ( f/fsph)0 estimates for the calculation of values D0 (eq 4) and Ms,f (eq 6) was checked for by the hydrodynamic invariant approach.53 Consistency of Hydrodynamic Results: Hydrodynamic Invariants. Calculated values of A0 (in 10−10 g cm2 s−2 K−1 mol−1/3) (eq 5) in the present work are seen to assume an overall of averages of A0 = 3.45 ± 0.09 for the PEtOx 1−9 and A0 = 3.51 ± 0.23 for the PMeOx 1−7, without an apparent trend in each series and among the series of POx (Figure S9). This gross analysis indicates the flexible backbone structure of linear chain macromoleculesa result very similar to recently studied mPEG macromolecules.33 More importantly, such E

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displayed in Table 1. Known interrelations of the estimated exponents, i.e., bD0 = b( f/fsph)0 + 1/3, bD0 = (1 + bη)/3, and |bD0| + bs0 = 1, are found within the experimental error. The order of magnitude and numerical values of exponents from scaling relationships all indicate a random coil conformation of the macromolecules.63 The here presented analysis can do more. Figure 3 details that an increase in the molar mass, Ms,f, leads to an expected increase in [η], s0, and ( f/fsph)0. Expectedly also, an increase in Ms,f leads to a decrease in the diffusion coefficient, D0, with the exponent from the scaling relationship (eq 9) being opposite in sign to that of the calculated hydrodynamic diameter, dH (Table 1 and Figure S10). PMeOx as opposed to PEtOx is seen to feature slightly higher exponents bη and bs0. Apparent also, the PMeOx macromolecules sediment at a consistently higher rate, having its origin in smaller partial specific volumes, υ (Figure S6). This originates from the fact that υ is inversely proportional to the density of macromolecules in solution, and more dense objects sediment faster. The here provided data from Figure 3 and Table 1 can straightforwardly be compared to that of scaling relationships of pharmaceutical mPEG in a similar molar mass range, as reported in our previous study.33 The numerical values of scaling exponents s0, (f/fsph)0, D0, and dH vs Ms,f from eq 9 are readily similar when comparing PEtOx and PMeOx with mPEG, as can be seen in Table 1. A comparison of the actual magnitude of values at comparable molar masses shows that [η] and (f/fsph)0 for the POx are smaller as compared to mPEG, while D0 and s0 are generally larger. The dH values are consequently also smaller for the POx as opposed to the mPEG of similar molar masses (Figure S10). Summarizing, this suggests a more compact shape of POx vs mPEG at the same molar mass, a situation further resolved in the forthcoming section (vide infra). Hydrodynamic Volumes. The hydrodynamic volumes of the macromolecules are a useful estimate, last but not least because these can be utilized for the “absolute” calibration of SEC systems as established by Grubisic, Rempp, and Benoit.64 Key to access hydrodynamic volumes is the Flory equation (eq 10), parametrically describing the intrinsic viscosity [η]:

values support that adequate values of the determined molar masses, Ms,f, from eq 6 are obtained.53 This justifies the here presented methodology as a practical absolute method for determination of molar masses and estimation of the associated hydrodynamic characteristics (vide infra).53 Scaling Relationships and Gross Conformation in Solution. Estimates of particular hydrodynamic characteristics can straightforwardly be used to establish scaling relationships of the Kuhn−Mark−Houwink−Sakurada type that take the following general form: b

Pi = K i , jP j i ,j

(9)

In eq 9, the index i represents intrinsic viscosities, [η], sedimentation coefficients, s0, translational frictional ratios, ( f/ fsph)0, the translational diffusion coefficients, D0, or the hydrodynamic diameter, dH. In this study, the index j represents absolute values of the molar mass, Ms,f. Double-logarithmic plots of such dependences are shown in Figure 3.

Figure 3. Double-logarithmic plots of hydrodynamic parameters Pi (eq 9) where the index i refers to [η] (black symbols), s0 (blue symbols), (f/fsph)0 (green symbols), and D0 (red symbols) and Pj, where the index j refers to absolute values of the molar mass, Ms,f (eq 6). Symbol assignment: PEtOx (filled symbols); PMeOx (empty symbols). The data in plots were fitted linearly to determine the resultant constants Ki,j and exponents bi,j from eq 9 (see footnote of Table 1). Data points of the same symbol type in filled gray, including the linear fits, refer to mPEG from a recent study performed at the exactly same temperature, use of same solvent, and instrumentation.33

[η] = ϕ

⟨h2⟩3/2 Ms,f

(10)

where ϕ is a parameter for a given polymer system (Flory parameter). The term ⟨h2⟩ is the mean-square chain end-to-end distance of the population of the macromolecules. It follows from eq 10 that the product [η]Ms,f ∼ ⟨h2⟩3/2. In other words

At first glance all plots among the series of the PEtOx 1−9 and PMeOx 1−7 are reasonably similar and show typical linear dependences. Exponents from a linear fit to each of these double-logarithmic plots and values of estimated constants are

Table 1. Constants Ki,j and Exponents bi,j (Eq 9) with Standard Error in Parentheses (Index i Refers to [η], s0, (f/fsph)0, D0, or dH and Index j Refers to Ms,f) Polymera

b[η]

bs0

b( f/fsph)0

bD0

bdH

PEtOxb PMeOxc mPEGd

0.63 (±0.02) 0.68 (±0.04) 0.63 (±0.03)

0.46 (±0.01) 0.48 (±0.02) 0.41 (±0.02)

0.20 (±0.01) 0.18 (±0.02) 0.21 (±0.01)

−0.53 (±0.01) −0.52 (±0.02) −0.52 (±0.01)

0.53 (±0.01) 0.52 (±0.02) 0.55 (±0.01)

Structure of the macromolecules is shown in Scheme 1. bConstants: K[η] = 5.0 × 10−2 cm3 g−1; Ks0 = 0.8 × 10−2 S; K(f/fsph)0 = 27.1 × 10−2; KD0 = 112.3 × 10−6 cm2 s−1; KdH = 3.8 × 10−2 nm. cConstants: K[η] = 3.6 × 10−2 cm3 g−1; Ks0 = 0.8 × 10−2 S; K(f/fsph)0 = 32.2 × 10−2; KD0 = 96.9 × 10−6 cm2 s−1; KdH = 4.4 × 10−2 nm. dData from a previous study of mPEG macromolecules establishing scaling relationships over a comparable molar mass range.33 a

F

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Macromolecules [η]Ms,f represents an estimate of the hydrodynamic volume, VH. Estimates [η]Ms,f are plotted against Ms,f in Figure 4 and detail

Figure 4. Double-logarithmic plots of hydrodynamic volume estimates [η]Ms,f (eq 10) of PEtOx 1−9 (black squares and fitted black line) and PMeOx 1−7 (blue circles and fitted blue line) against Ms,f. Further details on the macromolecules can be found in Table S1. Shown also are hydrodynamic volume estimates of mPEG from a recent study in filled gray symbols and the fitted gray line.33

that the hydrodynamic volume among POx macromolecules is readily similar but systematically smaller than that of the mPEG of similar molar masses as shown by the respective gray symbols and line in Figure 4.33 Viscometric studies (Figure S5, eqs 1 and 2) allow for further insight into macromolecules in solution by studying numerical values of the Huggins constant, kH (Figure 5a). As well, systematically seen is an increase of the numerical values of kH with a decrease in the molar mass for each series of the POx, with PEtOx developing larger values of kH than the PMeOx. The apparent origin is the ethyl substituent as opposed to that of the methyl substituent on the carbonyl C present in the repeating unit of the macromolecules (Scheme 1). This observed increase in kH values, for both PEtOx and PMeOx, may indicate poorer solvation of the macromolecules at decreased molar masses.33 This appears similar to that of the recently studied mPEG macromolecules (gray data points and lines), additionally showing end-group specific characteristics at identical backbone chemistry.33 The larger molar mass POx appear to approach values of kH ≈ 0.3, virtually the same value as of typical PEG macromolecules at molar masses of 20 000 g mol−1.33 Here, results demonstrate water being an equally good solvent for POx as well as PEG. As seen in Figure 5b, the difference between the Huggins, kH, and Kraemer constant, kK, assumes relatively large values that however asymptotically approach kH − kK = 0.5 at the increase of molar masses, a situation common to all macromolecules. Though the difference between kH and kK is seldom reported in the literature, such behavior indicates molar mass dependent viscometric behavior,33 in this case modulated by the polymer backbone chemistry. This difference vanishes at higher molar masses. AF4/SEC Coupled to MALLS. The main objective of the MALLS experiments is the investigation of the weight-average molar mass (Mw). For this to happen, it is desirable to create a separation of the population of macromolecules in solution and its forthcoming characterization by suitable detection technology. A priori, we optimized the separation conditions in AF4

Figure 5. (a) Semilogarithmic plot of the Huggins constants, kH (eq 1), derived from intrinsic viscosity, [η], measurements shown in Figure S5, in dependence of the absolute molar mass, Ms,f (eq 6). The dotted line at a value of kH = 0.3 is shown as a guide to the eye. (b) Semilogarithmic plot of the difference of kH (eq 1) and kK (eq 2), kH − kK, in dependence of Ms,f (eq 6). The dotted line at a value of kH − kK = 0.5 is shown as a guide to the eye. Symbols: PEtOx (black squares and line); PMeOx (blue circles and line). Gray squares and solid lines refer to mPEG from a recent study performed at exactly same temperature, same solvent, and utilized instrumentation.33

with the aim of a maximum resolution of different molar masses within a given sample. Based on the separation principle of AF4, macromolecules with high diffusion coefficients (consequently smallest molar mass and hydrodynamic size) elute first, followed by the more slowly diffusing macromolecules of larger molar masses and hydrodynamic size. This “stretching” of the population is highly useful because that way it allows the efficient prefractionation of disperse and complex samples, later detailed by MALLS experiments on individual elution slices and consideration of the elution window of distinct populations. In SEC, separation is strongly dependent on the porous properties of the column and elution as well is expected to generate a good representation of the molar mass distribution. Here, larger molar masses show smaller elution times since they permeate a smaller overall stationary phase pore volume due to their larger hydrodynamic volume. Smaller molar masses show larger elution times since they permeate a larger overall stationary phase pore volume due to their smaller hydrodynamic volume. The respective values for the refractive index increment in the AF4 run solvent were dn/dc = 0.1657 ± 0.0004 mL g−1 for G

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Macromolecules the PEtOx 1 and 0.1724 ± 0.0025 mL g−1 for the PEtOx 9. The determined dn/dc for the PMeOx 1 was dn/dc = 0.1556 ± 0.0006 mL g−1and for the PMeOx 7 dn/dc = 0.1592 ± 0.0009 mL g−1. In the SEC run solvent, values of dn/dc = 0.1621 ± 0.0011 mL g−1 for the PEtOx 1 and dn/dc = 0.1607 ± 0.0012 mL g−1 for the PEtOx 9 have been determined. The determined dn/dc for the PMeOx 1 was dn/dc = 0.1602 ± 0.0018 mL g−1and for the PMeOx 7 dn/dc = 0.1454 ± 0.0009 mL g−1. In each case, averages of the large and small molar mass for each series have been used for data evaluation. Comparing the dn/dc estimates for PEtOx with literature data shows good agreement despite the different solvents used.60,65 Normalized RI and MALLS AF4-/SEC-elugrams for PEtOx 3 are shown in Figure 6. Accurately determined dn/dc values in identical solution composition than used for the AF4-/SECMALLS experiments with the light scattering data at various angles were used to construct Zimm plots at discrete elution points. Example Zimm plots from elution slices of the three elution methods utilized are shown in Figure S11 for PEtOx 3. The results show that the macromolecules can be considered as isotropic scatterers due to their readily small size. Also, synthetic macromolecules are always disperse, but in the case of a small elution slice (i.e., a narrow subpopulation, individual blue data points in Figure 6), we can assume identity of the different molar mass averages, i.e., number-average molar mass, Mn, weight-average molar mass, Mw, and the z-average molar mass, Mz. This is because there is negligible dispersity in this subpopulation. Calling this a molar mass component Mi of the entire population, via the well-known relation, the weightaverage molar mass, Mw = ∑NiMi2/∑NiMi with Ni being the number of macromolecules from the concentration-sensitive RI detector, can be estimated. It can be seen in Figure 6a that with AF4 utilizing a constant cross-flow the molar mass population is separated with a clear tendency to increased molar masses across the elution peak (from ca. 6 200−8 200 g mol−1). This represents the elution principle of AF4. The recovery appears readily poor with only a 25% supported by the noisy MALLS signal. The method using an exponential decay in the cross-flow (Figure 6b) unsurprisingly leads to higher signal-to-noise ratios, while the overall population of macromolecules becomes narrowed to a negligibly smaller elution window (from ca. 6 200 to 8 100 g mol−1). In this case the recovery significantly increased to 97%. For SEC (Figure 6c), a relatively narrow elution peak (when compared to the AF4 data) is observed, and the molar mass within the elution peak decreases (from ca. 7 400 to 5 400 g mol−1), congruent with the expected principle of SEC, accompanied by a recovery of 92%. In any case, for determination of the Mw estimates of the populations of macromolecules, the appropriate elution fractions (e.g., region of the blue trace in Figure 6) utilizing RI data and MALLS data of individual elution slices were considered. All Mw estimates can be found in Table S1. Interrelation of AUC and AF4-/SEC-MALLS. In this study, we attempt the investigation of the molecular properties of POx macromolecules by two overarching independent methods based on (i) solution hydrodynamics utilizing viscometry and sedimentation velocity experiments with their interrelation and (ii) MALLS to determine the molar mass of POx macromolecules from a priori separation enabled by AF4 and SEC. The prime common parameter of interest from all these substantially different physical principles (hydrodynamics vs

Figure 6. Normalized time-based RI and MALLS elugrams for PEtOx 3 from (a) AF4 under constant cross-flow conditions, (b) AF4 with an exponential decay in the cross-flow, and (c) SEC elution. Identical scattering conditions have been used for all elution methods. The black line is the RI trace, and the gray line is the 90° MALLS scattering trace. The corresponding molar mass traces Mi based on Zimm plots (e.g., Figure S11) of individual slices are shown in blue circles. Further details on the macromolecule sample can be found in Table S1.

light scattering), the determined molar mass is used to check for overarching consistency. In addition, SEC data with a relative calibration of typically used narrow dispersity polystyrene standards66,67 have also been included in this comparison to gauge manifestation of errors implied by this most commonly used technique for polymer characterization (see Supporting Information for details). Individual elution profiles are shown in Figure S2a for the PEtOx and Figure S2b for the PMeOx as well as molar mass estimates are shown in Table S1. H

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7 200 g mol−1. The same trend can be seen for the PMeOx data (see Figure S12). This is a point in our discussion where we wish to refer to the hydrodynamic invariant concept from eq 5 in the form A0 = R[η]1/3[s]M−2/3. Our experiments and established data set now enable a view on the macromolecules in solution via essentially three independent methods, i.e., viscometry via the capillary/ ball combination to obtain [η], sedimentation velocity experiments in the ultracentrifuge to obtain [s], molar masses from the hydrodynamic analysis, Ms,f = Mw, or most crude from the PS-calibrated SEC. For hydrodynamic analysis, numerical values of A0 (eq 5) are identical when using the intrinsic diffusion coefficient [D] (eq 4) or Ms,f = Mw (eq 6).53 The obtained Mw from light scattering could as well be used to calculate numerical values of A0 in combination with [η] from viscometry and [s] from sedimentation velocity experiments. For completeness, the data of Mw estimations from SEC with the polystyrene reference standard are plotted as well in estimations of A0. The data are shown in Figure 8 for the PEtOx 1−9 and Figure S13 for the PMeOx 1−7.

Figure 7 shows plots of the weight-average molar mass, Mw, from AF4-/SEC-MALLS experiments and SEC with a

Figure 7. Plots of the weight-average molar mass, Mw, from AF4-/ SEC-MALLS experiments against the absolute molar masses, Ms,f, obtained from sedimentation−diffusion analysis on sedimentation velocity analytical ultracentrifugation experiments for PEtOx 1−9 (i.e., the entire molar mass range investigated in this study) (top) and the gray shaded zoom area focusing on molar masses below 10 000 g mol−1 (bottom). The black dotted line shows hypothetical equivalence of the molar masses.

Figure 8. Semilogarithmic plots of hydrodynamic invariants, A0, against molar mass estimates for PEtOx 1−9 calculated by eq 5 using [η] (eqs 1 and 2) together with [s] and [D] from sedimentation− diffusion analysis (being identical when utilizing Ms,f = Mw obtained via the modified Svedberg equation (eq 6) shown with filled black squares and line. Alternatively, A0 was calculated from eq 5 using [η] and [s] only from sedimentation velocity analysis and Mw from MALLS experiments (filled blue circles and line: AF4-MALLS with constant cross-flow; half-filled blue circles and line: AF4-MALLS with crossflow decay; empty blue circles and line: SEC-MALLS). For comparison, invariant estimates with Mw determinations from SEC analysis (calibrated with polystyrene standards) are also shown (black stars). Region (a) in the graph refers to a statistical estimate of invariants of linear, flexible-chain macromolecules and region (b) to a statistical estimate of invariants of synthetic macromolecules with high chain rigidity, all extracted from the literature and comprehended by Tsvetkov et al.53 For comparison, data of mPEG from a recent hydrodynamic study are also shown (filled gray squares and line).33

calibration standard against Ms,f (from sedimentation−diffusion analysis using the ultracentrifuge). Values of Ms,f obtained from sedimentation−diffusion analysis should closely relate to the Mw of the macromolecules.51,68 Overarching, both AF4-/SECMALLS data and sedimentation−diffusion analysis data show consistency of the obtained molar masses. All absolute methods deviate significantly from that of the SEC data that appear to overestimate molar masses substantially. This situation is not surprising, since a reference standard, different in its physicochemical properties, consequently hydrodynamic volume, is utilized for the SEC calibration.67 Again, deviations between molar mass estimations for PEtOx in the AF4-/SEC-MALLS and analytical ultracentrifugation analysis are seen minimal within a global view. However, systematically seen in the zoom area is a significant deviation between the ultracentrifugation and MALLS data, i.e., Mws from the MALLS data appear to be larger than that of hydrodynamic analysis (Figure 7). For example, a molar mass of Mw = 6 000 g mol−1 from hydrodynamic analysis leads to Mws calculated from populations of light scattering data in the range of 6 800 to

Three key features can be seen in Figure 8 for the PEtOx 1− 9 data. First, Mws from SEC data are unphysical based on values of [η] and [s], i.e., simple knowledge of these independently determined parameters by hydrodynamic first-principles, combined with the molar mass derived by SEC, leads to values of A0 that have neither been reported and lie very much below the approximate region for flexible chain macromolecules (region b in Figure 8), even below the theoretical limit for a rigid impermeable sphere.69 This as well highlights that I

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Macromolecules estimated Mws by SEC in this study are overestimated; smaller values would move invariants into a more physically sound range of values (eq 5). Qualitatively, this situation does not change for any of the molar masses. Second, with molar masses of 10 000 g mol−1 and higher, for both hydrodynamic analysis and MALLS, the invariants basically assume values typical for flexible chain macromolecules. This is indicative of the fact that either method reported here can be considered an accurate method for molar mass estimations of synthetic macromolecules (Figure 8).53 Invariants, A0, for molar masses ≥10 000 g mol−1 assume average values of 3.61 ± 0.37 for AF4-MALLS at constant cross-flow, 3.39 ± 0.17 for AF4-MALLS with the cross-flow gradient, 3.60 ± 0.14 for SEC-MALLS, and 3.53 ± 0.11 for exclusive hydrodynamic analysis. In fact, despite fluctuations with individual estimations, they are mathematically readily similar within calculated errors. Third, and most important, systematic differences seem apparent for a molar mass range below 10 000 g mol−1. While data from hydrodynamic analysis remain invariant as compared to the larger molar masses (as well observed in a recent study for PEG with varying α-end identity),33 any of the MALLS data and invariants calculated (eq 5) appear to systematically decrease for the POx. In fact, invariants, A0, enter a region clearly below the theoretical limit of an impermeable solid sphere.69 These data suggest that the molar mass of these populations of macromolecules show tendency for being overestimated by AF4-/SEC-MALLS, based on existing hydrodynamic theory (eq 5).53 Similar observations can be made for the PMeOx 1−7 as shown in Figure S13. This situation as well indicates that establishment of scaling relationships (eq 9 and Figure 3) over a limited and rather small molar mass range for the PEtOx 1−9 and PMeOx 1−7 would potentially be biased as compared to the centrifuge by molar masses obtained from MALLS experiments. In order to explain this apparent obstacle for the desired congruence of methods used in this article, we note that the MALLS detector is a mass-sensitive detector and RI a concentration-sensitive detector, both utilized for the estimation of molar masses (eq 7) by either here utilized elution method of AF4-/SEC-MALLS. In all cases reported in this study, RI represents an essentially noise free signal (Figure 6). This is different for the MALLS that returns a mass-sensitive signal, together with a significantly higher noise level (e.g., Figure 6), as well depending on the scattering angle. This noise level, in instances entering critical signal-to-noise ratios under conditions where the RI essentially returns a noise-free signal, is particularly problematic for “weighing” small molar masses of an inherently disperse population. When considering populations of macromolecules such way, a bias toward larger molar masses of a population is possible. Particularly for low molar mass POx sample populations, only the “largest” molar masses of the population are reliably identified. Such a situation bears potential to systematically overestimate the true molar masses of a particularly small molar mass POx population eluted via AF4 or SEC. In other words, the MALLS starts being “blind” for the low molar masses of the population. This is in contrast to ultracentrifugation experiments in which RI detection is utilized for observation of the sedimentation boundary with respect to time. Because of the conserved mass balance in the sector-shaped cell volume, including the entire population of macromolecules with detection not discriminating molar masses, ultracentrifugation

enables an accurate determination of the distribution of sedimentation coefficients from the entire population of macromolecules and, in the present case, physically sound weight-average translational frictional ratios utilized for molar mass estimations.

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CONCLUSIONS We have reported on the solution properties of POx in water by a detailed hydrodynamic study, concerning measurements performed under translational and rotational friction. The hydrodynamic, molecular, and conformational characteristics of the POx macromolecules clearly resemble their random coil conformation in solution and quantitative consistency between each series of the POx. Our study showed that POx of similar molar mass than PEG are physically more compact in shape and are solvated to a smaller extent than PEG. This became quantitatively tractable by the estimation of apparent hydrodynamic sizes and hydrodynamic volumes. Associated to these properties, POx sediment at a significantly higher rate, additionally modulated by differences in their partial specific volumes, i.e. considering molecular densities in solution. All of the characteristics of the POx, i.e. the intrinsic sedimentation, intrinsic viscosity, and intrinsic diffusion coefficient, were used to establish hydrodynamic invariants. Despite all of the quantitative differences in the individual hydrodynamic prime parameters shown for these macromolecules, the hydrodynamic invariants practically assume same average values as that for PEG. This, together with practically similar scaling exponents from scaling relationships, nurtures the idea that POx are a suitable candidate for replacement of PEG on a profound and informed physicochemical basis. The here provided data as well can be used to replace PEG by POx with essentially the same absolute physicochemical properties such as intrinsic viscosity, friction, diffusion, sedimentation, effective hydrodynamic diameter, hydrodynamic volume, or combinations of these. Last, but not least, our study shows for the first time an attempt for quantitative interrelation of two major and highend macromolecular characterization techniques that under proper physical assumptions, led to a similarity in estimated macromolecular characteristics, of prime interest being the molar mass. Care, however, should be taken when approaching small molar mass estimations of disperse macromolecule populations via AF4-/SEC-light scattering. In this case, an independent correlation with intrinsic sedimentation and intrinsic viscosity data is highly recommended, if not mandatory.

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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.macromol.7b02665. Experimental details; Figures S1−S13 and Table S1 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (U.S.S.). *E-mail: [email protected] (I.N.). ORCID

Ulrich S. Schubert: 0000-0003-4978-4670 Ivo Nischang: 0000-0001-6182-5215 J

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Macromolecules Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge support of this study from the Thüringer Ministerium für Wirtschaft, Wissenschaft und Digitale Gesellschaft (TMWWDG, ProExzellenz II, NanoPolar) for funding the Solution Characterization Group (SCG) at the Jena Center for Soft Matter (JCSM), Friedrich Schiller University Jena. M.N.L. further acknowledges the Bundesministerium für Bildung und Forschung (BMBF # 13N13416 smart-dye-livery) for financial support. This work was supported by the DFG-funded Collaborative Research Centre PolyTarget (SFB 1278, project Z01).

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DOI: 10.1021/acs.macromol.7b02665 Macromolecules XXXX, XXX, XXX−XXX