Article pubs.acs.org/Macromolecules
Associative and Entanglement Contributions to the Solution Rheology of a Bacterial Polysaccharide Mahesh Ganesan,† Steven Knier,† John G. Younger,‡ and Michael J. Solomon*,† †
Department of Chemical Engineering and ‡Department of Emergency Medicine, University of Michigan, Ann Arbor, Michigan 48109, United States S Supporting Information *
ABSTRACT: We report the viscosity of semidilute solutions of a bacterially synthesized polysaccharidea partially deacetylated poly-N-acetylglucosamineas measured by microrheology. This polymer, commonly called polysaccharide intercellular adhesin (PIA), is synthesized by Staphylococcal strains; it is a principal component of the biofilms of these bacteria. We show that the concentration-dependent viscosity of PIA at a pH in which it is associated can be predicted using the Heo−Larson equation for entangled polymers [J. Rheol. 2005, 49 (5), 1117−1128], if the molecular parameters of the equation are measured in its associated state. This agreement is consistent with PIA adopting a concentration-dependent scaling of the viscosity that is dominated by entanglements and intermolecular associations, as described in the theory of Rubinstein and Semenov [Macromolecules 2001, 34 (4), 1058−1068]. The zero-shear specific viscosity, ηsp, measured in the concentration range, cPIA = 0.1−13 wt %, scales as ηsp ∼ cPIA1.27±0.15 up to an entanglement concentration, ce = 3.2 wt %, after which ηsp ∼ cPIA4.25±0.30. In the presence of urea, a known disruptor of associations, these scaling shifts to ηsp ∼ cPIA1.02±0.2 and ηsp ∼ cPIA2.57±0.6, respectively; no shift in ce is observed. The urea effect is consistent with an associative contribution to viscosity in the aqueous solution case. The invariance of ce suggests that the rheology of this polymer−solvent system also includes an entanglement contribution. With independent estimates of the PIA weight-average molar mass, Mw, entanglement molecular weight, Me, hydrodynamic radius, RH, and excluded volume, ν, we use the Heo−Larson equation to predict ηsp as a function of cPIA. With the use of parameters from the associated stateparticularly the hydrodynamic radiuswe find good agreement between the model and data for aqueous PIA solutions. This study offers a means to predict the rheology of associating polysaccharides using correlations for nonassociating polymers adjusted with minimal a priori data from their associated state.
1. INTRODUCTION Polysaccharides are water-soluble, long chain sugar molecules capable of exhibiting intermolecular associative interactions.1 Associations in polysaccharides commonly arise due to sticky moieties such as hydroxyl and alkyl groups that contribute hydrogen bonding and hydrophobic attraction, respectively.1 Among their many occurrences, polysaccharides are integral constituents of the extracellular matrix of biofilms2,3surfaceattached bacterial consortia encapsulated in a matrix of extracellular polysaccharides.4 At in situ concentrations, in addition to entanglements, associations are known to strongly impact the polysaccharide’s viscoelastic properties.4−8 While these functional features are clearly germane to the microstructure and viscoelasticity of biofilms,5,6 there is limited understanding of how the rheology of the extracellular polysaccharide depends on its associative character and concentration. That is, the ability to predict the solution viscosity as a function of polymer concentration, solely from molecular properties, is current lacking for microbial synthesized polysaccharides. While semiempirical expressions for viscosity versus concentrationsuch as that of Martin, Fedors, and Lyons-Tobolskyhave been used to fit viscosity data of polysaccharides,9−12 such equations do not take molecular level © XXXX American Chemical Society
information on the polymer as the sole parameters. Instead, they also contain empirical parameters derived from fits to the rheology data itself. In this article, we consider the self-associating polysaccharide intercellular adhesin (PIA), synthesized by Staphylococcus epidermidis biofilms.13 PIA is a linear poly-β-(1,6)-N-acetyl-Dglucosamine with a degree of deacetylation of ∼20%.13 There is interest in understanding the concentration dependent viscosity of PIA, as well as its a priori prediction, because recent studies indicate that its rheology, mediated by associations, contributes to the spreading, elasticity, and eradication of staphylococcal biofilms.6 More broadly, prediction of bacterial polysaccharide rheological properties is of interest in a variety of areas, including foods,14 consumer products,15 and pharmaceuticals.15 Previous measurements of PIA7 show that it has a weightaverage molar mass, Mw = 201 ± 1.2 kDa, polydispersity of 2.8 ± 0.1, and excluded volume exponent, ν = 0.6 ± 0.01; pHdependent shifts in absorbance indicate that PIA associates in the range 3 < pH < 5.5.6 Received: July 26, 2016 Revised: October 8, 2016
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role of associations and entanglementsin contributing to solution viscosity.
For semidilute polymers without associations, two scaling regimes for viscosity can be identified. Below the entanglement concentration, Rouse dynamics16,17 hold and ηp = ηRouse with the concentration scaling ηRouse ∼ c1/(3ν−1). For ν = 0.6, the Rouse theory predicts ηp ∼ c1.25. Above the entanglement concentration, based on the theoretical scaling ηp/ηRouse ∼ (c/ ce)2.4/(3ν−1), Heo and Larson18 show that the empirical equation ηp/ηRouse = 45(c/ce)2.95 is quantitatively correct for many polymers. For ν = 0.6, the Heo−Larson relation predicts ηp ∼ c4.2. Here, ηp = η0 − ηs and η0, ηs, and ηRouse are the zero-shear, solvent, and theoretical Rouse viscosity, respectively, and ce is the entanglement concentration. Molecular information enters the relations through the expression ηRouse = ηs([η]0c)1/(3ν−1) and ce = c*ne(3ν−1). Here, c* = 3Mw/(4πrg3NA) and ne = Me/M0 where [η]0 is the intrinsic viscosity, rg is the radius of gyration, NA is the Avogadro’s constant, and Me and M0 are the entanglement and monomer molecular weight, respectively. The concentration dependence of viscosity in semidilute solutions of associating polymers is given by Rubinstein and Semenov.19 Their model identifies multiple regimes, depending on whether or not associations are predominantly intra- or intermolecular and depending on whether or not chains are unentangled or entangled between associations. For semidilute unentangled solutions in which intermolecular associations dominatecalled the sticky Rouse regimethe scaling η ∼ c1+[0.225/(2(3ν−1))] holds. For ν = 0.6, the sticky Rouse regime predicts η ∼ c1.14. For semidilute entangled solutions with intermolecular associations, η ∼ c(7/4+3ν+0.1125)/(3ν−1), which yields η ∼ c4.6 for ν = 0.6. The difference between the above two regimes is the onset of entanglements. Other association regimes yield different viscosity scaling with concentration, depending on the degree to which associative bonds are transitioning from predominantly intramolecular to predominantly intermolecular. Although the Rubinstein−Semenov scaling reveals the physical effects of associations on solution rheology, they are not quantitative without a priori knowledge of the lifetime of sticking events, the fraction of associated stickers per chain, and the binding energy. These parameters are not easily measurable for polysaccharides such as PIA. However, the unentangled and entangled dynamics in their model, even with associations, lead to η versus c scaling that are nearly functionally equivalent to that of the Rouse model (for unentangled polymers) and the Heo−Larson relation (for entangled polymers), respectively. Therefore, the aim of this paper is to establish whether the Rouse and Heo−Larson equations can be used to quantify the concentration dependent viscosity of associating polysaccharides if the molecular parameters defined in the equations are measured in the associated state of the polymer. By using microrheology to measure the concentration dependent viscosity, we show that the Heo−Larson relation for entangled polymers can be used to predict the viscosity of the bacterially synthesized polysaccharide poly-β-(1,6)-Nacetyl-D-glucosamine (PIA)even given the presence of associationsprovided that suitable measures of molecular parameters of the polysaccharide in its associated state are available. Viscosity measurements were made in the absence and presence of urea, an agent that disrupts hydrogen-bonding and hydrophobic interactions.20−22 The effects of urea on the viscosity scaling and molecular parameter estimation further support the role of associations in this system. The study therefore provides a pathway to quantitatively understand fundamental features of polysaccharide rheologynamely, the
2. EXPERIMENTAL SECTION 2.1. PIA Purification and Solution Preparation. Surface attached PIA was harvested from S. epidermidis biofilms. It was separated from the biofilm bacteria and other in situ macromolecules in sufficient quantities for rheological characterization. Four purification methods were compared based on yield and average molar mass− sonication,23 ultracentrifugation,24 EDTA extraction,25 and heat treatment.26 The molar mass of purified PIA was quantified using size exclusion chromatography and compared against a literature value.7 The yield of PIA from the EDTA extraction protocol was the maximum90% higher than the other protocols on averageand the molar mass of PIA purified by this method was 2.13 × 105 ± 4600 g/ mol (polydispersity = 3.1 ± 0.5) which deviates from the literature value by 6%.7 Details of biofilm culture, PIA purification protocol, and the measurement of yield and molar mass are in the Supporting Information (Figures S1 and S2). The EDTA extraction method was used to produce the PIA for microrheology and DLS. Purified PIA was dialyzed (2 × 12 h against DI water, 6 kDa cutoff membranes, Spectrum Laboratories, Compton, CA) and washed in filtered HPLC water and concentrated using 10 kDa cutoff centrifugal filters (Amicon Ultra, Millipore, Bedford, MA). 2.2. Diffusing Wave Spectroscopy (DWS) Microrheology. The viscosity of PIA was determined by DWS microrheology. Point source transmission mode DWS was performed using a compact goniometer (ALV GmbH, Langen, Germany) with a mode controlled laser source (488 nm, Innova 70 C, Coherent Inc., Santa Clara, CA) as per Lu and Solomon.27 Colloidal latex probes (0.5 μm, sulfate modified, Invitrogen, Carlsbad, CA) at 2% (v/v) were mixed with the PIA solutions and rolled for 1 h prior to measurement. A probe size and chemistry study was conducted to ensure DWS experiments are independent of probe choice (cf. Figure S4). Rectangular cuvettes of path length L = 1 mm (Starna Cells, Atascadero, CA) were chosen so that L/l* ∼ 8, ensuring multiple scattering.28 l* is the photon mean free path, calculated using Mie theory.29 The normalized intensity autocorrelation function, g2(t) = ⟨I(t) I(0)⟩/⟨I⟩2, of scattered light was constructed by pseudo-crosscorrelation with a minimum delay time of 12.5 ns (ALV 5000-E, ALV GmbH, Langen, Germany). Here, I(t) is the intensity of scattered light at time t, and ⟨ ⟩ denotes a time average. Measurements of g2(t) were taken for 3−6 h with frequent (∼15 min) resuspension of probes. Results are the average of 3−5 independent measurements. The contribution of fluctuations in laser intensity to g2(t) was subtracted. This subtraction was performed by fitting the long time correlation in the g2(t) of colloidal probes in water to an exponential decay which was then subtracted from the PIA g2(t) data (cf. Figure S3).30 The g2(t) was converted to the field autocorrelation function, g1(t), via the Siegert relation27 g1(t) = ((g2(t) − 1)/β)0.5. β is an instrument constant evaluated by fitting the first 20 data points of g2(t) to a thirdorder polynomial, where β = g2(t) at t → 0. g1(t) was converted to probe mean-squared displacement (MSD), ⟨Δr2(t)⟩, following Pine et al.28 To extract the viscosity of PIA, we apply and compare the following two forms of the generalized Stokes−Einstein equation to the measurements of probe MSD. First, the frequency-dependent loss modulus, G″(ω), of PIA was extracted from the Fourier transform of MSD as described in Dasgupta et al.31 The zero-shear viscosity, η0, was then obtained as the zero frequency limit of the complex viscosity, η″(ω) = [G″(ω)/ω].32 Second, the linear creep compliance, J(t), was πa directly obtained from the MSD following J(t ) = k T ⟨Δr 2(t )⟩.33 B
Here, kB, T, and a are the Boltzmann constant, temperature, and probe radius, respectively. η0 was then computed as η0 = [t/J(t)]t→∞.32 Both methods of extrapolation yield η0 that differ by less than 6% (cf. Figures S5−S7). We discuss the first method in the Results section; equivalent results extracted by second method are in the Supporting Information. For microrheology, the concentration of PIA, cPIA, ranged from 0.1 to 13 wt %. Microrheology was performed at pH = 5.0 in B
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Macromolecules solutions of HPLC water; this condition has previously been identified as one at which PIA self-associates.6,7 2.3. Dynamic Light Scattering (DLS) of PIA Solutions. The hydrodynamic radius, RH, of PIA was measured using DLS. Experiments were performed using an ALV-CGS3 (ALV GmbH, Langen, Germany) compact goniometer unit equipped with a laser source of wavelength λ0 = 632.8 nm and an ALV-LSE 5004 multitau digital correlator (ALV GmbH, Langen, Germany). Measurements were made with 0.2 wt % PIA solutions in the angular range 30° < θ < 130°, corresponding to 6.8 μm−1 < q < 23.9 μm−1. Here, q is the scattering vector, q = 4πn sin(θ/2)/λ0. Samples were filtered through a 1.5 μm filter, and experiments were done in cylindrical glass cuvettes that were doubly cleaned with acetone, water bath sonication, and UV ozone treatment. 2.4. Effect of Urea on the Rheology of PIA. To measure the concentration-dependent viscosity of PIA in the absence of associative interactions, we performed microrheology and DLS in solutions containing 4 M urea. Urea added at this concentration is known to decrease hydrogen and hydrophobic interactions.20,21 The concentration of urea was chosen in the following way: the viscosity of PIA at a fixed concentration of 5.0 wt % was studied with increasing amounts of urea added between the range of 0.25−6 M. The point at which we observed a less than 5% drop in solution viscosity with increasing urea was chosen as the concentration of urea to be added for further studies (cf. Figure S8).
curve nearly overlays that of the aqueous solvent, indicating minimal influence of PIA on probe dynamics. With increasing PIA concentration, the g2(t) decay shifts to longer times. This shift indicates retardation in probe dynamics. Following Pine et al.,28 g2(t) was converted to the probe MSD, ⟨Δr2(t)⟩. Results are plotted in Figure 2. Consistent with
3. RESULTS AND DISCUSSION The objective of this article is to study the concentration dependence of the viscosity of PIA and to develop a method to predict its viscosity over a broad concentration range. In section 3.1, we present DWS measurements of probe MSD in PIA solutions of varying concentrations. The viscosity extracted from the MSD data is discussed in section 3.2. In section 3.3 the DLS measurements of PIA hydrodynamic radius are discussed. In section 3.4, using molecular parameters as the only inputs, the Rouse and Heo−Larson equations are used to predict the viscosity of PIA and compared against the measured data. 3.1. Colloidal Probe Motion in PIA Solutions. Figure 1 reports the intensity autocorrelation function, g2(t), corrected for the contribution from laser intensity fluctuations, of 0.5 μm colloidal probes embedded in PIA solutions for cPIA from 0.1 to 13 wt %. At low concentrations (cPIA < 0.6 wt %), the g2(t)
Figure 2. Mean-squared displacement (MSD), ⟨Δr2(t)⟩, versus time of 0.5 μm probes at 2% (v/v) in solutions of varying PIA concentration. The dashed lines are best fit lines to the power law ⟨Δr2(t)⟩ ∼ tα. (inset) The power law exponent, α, as a function of PIA concentration, cPIA.
Figure 1, for cPIA < 0.6 wt % the behavior of probe MSD in the PIA solutions is similar to their MSD in the absence of any polymer. At concentrations greater than 0.6 wt %, the displacement of the probes decreased with increasing polymer concentration. The curves in Figure 2 can be modeled as a power law:33 ⟨Δr2(t)⟩ ∼ tα. For a Brownian probe fluctuating in a viscoelastic medium, motion is subdiffusive, with 0 < α < 1. For PIA, at cPIA < 0.6 wt %, α ∼ 1, indicating a purely viscous response (inset, Figure 2). For cPIA > 0.6 wt %, α decreases with increasing concentration. At these concentrations, the subdiffusive motion is characterized by α decreasing from 0.9 to 0.6 as cPIA increases from 0.6 to 13 wt % (inset, Figure 2). The decreasing value of α indicates increasing viscoelasticity. The smallest value of α observed for PIA is about 0.6. The lack of a plateau in any of the MSD curves indicates that PIA behaves as a viscoelastic liquid in the concentration range studied. When the MSD measurements of Figure 2 were converted into the frequency domain, the ratio G″(ω)/G′(ω) was greater than 1 at all frequencies over the concentration range studied. Thus, the time scale of the measurement is in the terminal region, below the longest viscoelastic relaxation time of the system.32 3.2. Concentration Dependent Zero-Shear Rate Viscosity. 3.2.1. Extracting Viscosity from MSD Measurements. Figure 3 plots G″(ω) obtained from the MSD measurements of Figure 2, using the generalized Stokes− Einstein equation, following Dasgupta et al.31 The modulus scales as ω1 at all frequencies for PIA concentrations less than 1 wt %, and for higher concentrations, the slope of G″(ω) varies continuously with frequency. The log−log slope, γ, for the first 30 data points of G″(ω) versus ω is plotted in the inset. γ decreases from 1 (cPIA = 0.1−1.0 wt %) to an average value of 0.84 (cPIA ≥ 3.2 wt %). The apparent increase in γ at cPIA = 11.2
Figure 1. DWS intensity autocorrelation function, g2(t), of 0.5 μm probes at 2% (v/v) in solutions of varying PIA concentration as a function of time. C
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limited sample volume available (∼50 μL). The frequency range probed represents what is possible for the diffusing wave spectroscopy technique for this bacterial polysaccharide; an extrapolation to measure the low-frequency limit is therefore necessary. We obtain η0 by extrapolating to ω = 0 using an empirical exponential function of the form η″(ω) = C1 exp(−ωC2), where C2 > 0 and η0 = C1 as ω → 0 (Figure 4, dashed lines). Using a third-order polynomial of the form η″(ω) = C1ω3 + C2ω2 + C3ω + C4, where η0 = C4 as ω → 0, resulted in ce) and that the viscosity scaling of these regime agrees respectively with the Rouse (semidilute, unentangled) and with the Heo−Larson (semidilute, entangled) scaling. We therefore explore whether the Rouse and Heo−Larson equations, with parameters taken from measurements in which associations are present, accurately model the data of Figure 5 in the unentangled and entangled regimes. 3.4.1. Predicting the Viscosity of Aqueous PIA Solutions. 3.4.1.1. Rouse Theory Prediction in the Regime cPIA ≪ ce. For cPIA < ce, the Rouse viscosity as a function of concentration is16−18 (ηsp)Rouse = ([η]0 c PIA )1/(3ν− 1)
(1)
In this equation, the intrinsic viscosity, [η]0, is calculated following Heo and Larson as18 [η]0 = (4πNArg 3/3M w )
(2)
Here, rg is the radius of gyration. For random coil linear polydisperse polymers in good solvents, rg = 2.05RH.46 The values of the molecular parameters in eqs 1 and 2 are reported in Table 1. The effect of associations is incorporated through the increased value of the hydrodynamic radius that enters eq 2 through the radius of gyration. Table 1. PIA Molecular Parameters Used To Predict Its Viscosity Behavior parameter weight-average molar mass, Mw monomer molar mass, M0 entanglement molar mass, Me hydrodynamic radius, RH excluded volume exponent, n
value 2.13 × 10 g/mol (cf. Supporting Information) 221.21 g/mol 1.9 × 104 g/mol (refer text) 22 ± 1.5 nm (Figure 6) 0.6 (ref 5) 5
The predicted viscosity using eqs 1 and 2 is plotted in Figure 7 (dotted line). In this concentration regime, we find good agreement between the predicted and the measured viscosity. Overall, the Rouse viscosity predicts the viscosity of semidilute unentangled PIA solutions within a factor of 1.13 ± 0.1 in magnitude. 3.4.1.2. Heo−Larson Prediction in the Regime cPIA ≥ ce. In the semidilute entangled regime, the solution viscosity, following Heo and Larson,18 is given as ⎡η ⎛ c ⎞2.95⎤ (ηsp)HL = 45⎢ Rouse ⎜ PIA ⎟ ⎥ ⎢⎣ ηs ⎝ ce ⎠ ⎥⎦
(3)
The authors obtain the proportionality factor 45 and the power law exponent 2.95 through a nonlinear regression applied to viscosity data sets of several semidilute, entangled polymer− solvent systems of varying molecular properties.18 The entanglement concentration, ce, is given as ce = c*(Me /M 0)3ν− 1
(4)
Here, the coil overlap concentration, c*, is c* = F
3M w 4πrg 3NA
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The performance of the Rouse model and the Heo−Larson scaling suggests that the viscosity behavior of associating polysaccharides can potentially be predicted, within acceptable accuracy, using quantitative equations developed for nonassociating polymers, where the impact of associations are incorporated by measuring the polymer molecular properties, specifically the RH, in the associated conformation of the polymer. 3.4.2. Viscosity Prediction in Urea-Containing PIA Solutions. We also apply eqs 1−6 to the case of PIA in 4 M urea solution. Here, the value of the hydrodynamic radius is RH = 11.6 nm as measured by dynamic light scattering. The predictions in the unentangled and entangled regimes are compared to the experimental data in Figure 8. In the
Figure 7. Prediction of PIA viscosity in aqueous solutions. The dotted and dashed line represents the individual Rouse (eq 1) and Heo− Larson (eq 3) contributions, respectively, while the red line is the sum of both the models (eqs 1−6), and the inset is a plot of the fit residuals. The dot-dot-dashed line is the viscosity calculated from eqs 1−6 by taking the value of rg of PIA in its unassociated state.
We take take rg = 2.05RH as earlier. The Rouse viscosity, ηRouse, is as in eq 1. The entanglement molecular weight, Me (g/mol), is estimated using the empirical relation of Fetters and coworkers:47 Me = (188.3 × 1024)p3 ρ
(6)
Here, p is a packing parameter given by p = Mw/(6rg ρNA), and ρ (kg/m3) is the polymer density. Assuming the density to be equal to that of chitosan, a β-(1,4) isomer of PIA, and again taking rg = 2.05RH, the calculated value for Me is reported in Table 1. The ce calculated in this method is equal to 5.2 wt %, which differs by a factor of 1.6 from the experimental value of ce obtained from Figure 5. The effect of associations enters the correlation through its effect on ηRouse and rg. Figure 7 compares the prediction of eqs 3−6 (dashed line) against the measured data from Figure 5. The Heo−Larson prediction shows good agreement with the experimental data. The predictions are higher than the measured value by a factor of 1.3 ± 0.1. The combined performance of the models is very good, as seen by the red curve in Figure 7, the sum of the Rouse and Heo−Larson contributions (eqs 1−6). The overall prediction is within a factor of 1.3 of the measured data. The inset in Figure 7 plots the residual difference between the fit and the data. The maximum residuals are about 9% and over the concentration range studied; the average residual is ≈7%. The fit residuals quantify that the Rouse and Heo−Larson equations predicts the viscosity of PIA with good accuracy. There are no adjustable parameters in the prediction. Moreover, no rheological data were used for parameter estimation. Instead, equation parameters are estimated from molecular properties in the associated state. The quality of the prediction is strongly dependent on using the hydrodynamic radius in the associated state. For example, if we apply the unassociated rg of 29 nm from ref 7, then the discrepancy between the model prediction and the data is significantwith the model underpredicting the measured value by a factor of ∼7 (Figure 7, double dot-dashed line). 2
Figure 8. Prediction of PIA viscosity in the presence of urea. The dotted and dashed line represents the individual Rouse (eq 1) and Heo−Larson (eq 3) contributions, respectively, while the red line is the sum of both the models (eqs 1−6). The dot-dot-dashed line is the viscosity calculated from eqs 1−6 by taking the value of rg of PIA in its unassociated state.
unentangled regime, the Rouse viscosity (Figure 8, dotted line) quantifies the experimental data well; however, beyond ce, the Heo−Larson prediction (Figure 8, dashed line) diverges significantly from the data. The viscosity scaling exponent of 2.57 in the semidilute, entangled regime for PIA containing solutions of urea is much lower than commonly measured. For example, for nonassociating, entangled polymers, the scaling exponent reported for the polymers used in the Heo and Larson correlation varies from about 3.9 to 4.7.18 The Heo−Larson correlation itself predicts an exponent of 4.2 in a good solvent and 4.95 in a theta solvent.18 Likewise, the lowest scaling exponent of the different associating regimes in concentrated solutions predicted by Rubinstein and Semenov is 3.75.19 Alternatively, other approaches for understanding the solution viscosity measured here, such as polyelectrolyte rheology,48 do not appear consistent with the measurements given the presence of a high concentration of urea.
4. DISCUSSION AND CONCLUSION We constructed a simple method, using pre-existing viscosity relations, parametrized by molecular properties of the polymer, to predict the viscosity as a function of concentration for a partially deacetylated poly-N-acetylglucosamine, over a broad concentration range, in its associated state. This polymer, also G
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called polysaccharide intercellular adhesin (PIA), is synthesized by the biofilm forming bacteria Staphylococcus epidermidis.13 The method uses simple relations for polymer viscosity in the unentangled and entangled regimes but accounts for associations through their effect on the polymer hydrodynamic radius, as measured by dynamic light scattering. We discuss the following limitations of the analysis and directions for future work related to them. First, the entanglement molecular weight for PIA was estimated using a general empirical relationship. Measurement of the plateau modulus in a concentrated solution would allow a characterization of this property specific to PIA; more generally, the approach employed here could be extended to address the linear viscoelastic spectrum of this bacterial polysaccharide at high concentrations. Second, because PIA is a polydisperse polymer (Mw/Mn ∼ 3), the effect of polydispersity should be better incorporated into the analysis. In the present case, Mw was used to estimate properties needed in the correlation, and polydispersity was incorporated into the conversion between RH and rg. Third, the viscosity scaling for aqueous solutions of PIA with added urea was anomalous, with an exponent much lower than could be understood by available theory. Urea might potentially affect the solution rheology through multiple pathways, including (i) disrupting intermolecular associative interactions that are based on either hydrophobic or hydrogenbonding interactions and (ii) affecting single-chain conformation, through properties such as the polymer persistence length or excluded volume exponent. Further investigation of these conditions is warranted. For example, measurement of the coil size under dilute conditions in urea could reveal changes in both persistence length and excluded volume exponent. Fourth, the viscosity of PIA solutions was measured only in the semidilute regime. Accessing the dilute solution behavior would require a precision method such as Ubbelohde viscometry. However, this measurement requires an ∼15 mL sample volumean amount of material that cannot easily be produced for this bacterially synthesized polysaccharide. Finally, further studies could establish the degree to which this method can be extended to predict the viscosity of other associated polysaccharides, such as chitosan, hyaluronan, pectin, etc., all of which show similar scaling exponents in dilute and concentrated solutions as reported here. In conclusion, by direct measurement of the effect of associations on coil size, the present work extends the range of viscosity correlations developed for semidilute entangled polymer solutions to include an associated polysaccharide, a class of material that is broadly used in a range of fields, including consumer products and foods and as biomaterials.
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AUTHOR INFORMATION
Corresponding Author
*(M.J.S.) E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by NSF DMR 1408817. REFERENCES
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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.6b01598. Procedure for biofilm culture, PIA extraction and molar mass measurement, correcting for laser fluctuations in DWS data, alternative methods for calculating viscosity, DWS results for PIA solutions containing urea (Figures S1−S9) (PDF) H
DOI: 10.1021/acs.macromol.6b01598 Macromolecules XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.macromol.6b01598 Macromolecules XXXX, XXX, XXX−XXX
