Article Cite This: Langmuir 2019, 35, 9521−9528
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Counterion Exchange in Peptide-Complexed Core−Shell Microgels Jing Liang, Xixi Xiao, Tseng-Ming Chou, and Matthew Libera* Department of Chemical Engineering & Materials Science, Stevens Institute of Technology, Hoboken, New Jersey 07030, United States
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S Supporting Information *
ABSTRACT: The complexation of polyvalent macroions with oppositely charged polyelectrolyte microgels can lead to core−shell structures. The shell is believed to be highly deswollen with a high concentration of counter-macroions. The core is believed to be relatively free of macroions but under a uniform compressive stress due to the deswollen shell. We use cryo-scanning electron microscopy (SEM) with X-ray microanalysis to confirm this understanding. We study poly(acrylic acid) (PAA) microgels which form a core−shell structure when complexed with a small cationic antimicrobial peptide (L5). We follow the spatial distribution of polymer, water, Na counterions, and peptide based on the characteristic X-ray intensities of C, O, Na, and N, respectively. Frozen-hydrated microgel suspensions include buffers of known composition from which calibration curves can be generated and used to quantify both the microgel water and sodium concentrations, the latter with a minimum quantifiable concentration less than 0.048 M. We find that as-synthesized PAA microgels are enriched in Na relative to the surrounding buffer as anticipated from established ideas of counterion shielding of electrostatic charge. The shell in L5-complexed microgels is depleted in Na and enriched in peptide and contains relatively little water. Our measurements furthermore show that shell/core interface is diffuse over a length scale of a few micrometers. Within the limits of detection, the core Na concentration is the same as that in as-synthesized microgels, and the core is free of peptide. The core has a slightly lower water concentration than as-synthesized controls, consistent with the hypothesis that the core is under compression from the shell.
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INTRODUCTION
the microgel leads to local deswelling until a dense shell is formed around a central swollen core. Complexation-driven shell formation has been observed experimentally in several systems.6−11 There is, however, ongoing debate about whether and under what conditions the shell is a thermodynamically stable phase or is instead kinetically trapped in either a metastable or an unstable state. The deswelling associated with shell formation can reduce the local mesh size to the extent that subsequent macroion in-diffusion is either hindered or entirely prevented, thus creating a kinetic constraint on growth of the shell toward the microgel center. One can also argue that the network structure within the shell must be highly anisotropic to maintain mesh continuity at the interface between the swollen core and deswollen shell.12,13 In a spherical microgel the collapsing shell would lead to compression of the core. Despite the fact that shell formation has been observed and characterized by fluorescence optical microscopy,8,9,14,15 relatively little is known regarding the concentration and spatial distribution of counterions and macroions. Several techniques, such as electrophoresis,16 23Na NMR,17 X-ray scattering,18 neutron reflectometry,19 fluorescent dye staining,20 and electrical conductivity measurements,21 have been
Polyelectrolyte microgels have dimensions ranging from about 0.1 to 100 μm and are composed of cross-linked networks of ionizable polymer. Because of their electrostatic charge, polyelectrolyte microgels are responsive to pH changes and can swell extensively. They can carry a significant amount of oppositely charged and polyvalent macroions, such as drugs, peptides, proteins, nucleic acids, or polyvalent electrolytes. They are thus of particular interest for delivery applications.1−3 The electrostatic loading of oppositely charged macroions into polyelectrolyte gels and microgels is nevertheless complicated. It involves both enthalpic and entropic changes as counterions condensed around the polyelectrolyte chains are released and macroions complex with the gel network in their place. Significantly, complexation leads to collapse of the network and microgel deswelling.4 The morphology of an electrostatically loaded microgel often consists of a deswollen network with complexed macroions uniformly distributed throughout the microgel. However, core−shell structures have frequently been observed. These are distinct from microgels synthesized to intentionally have a core with one set of properties and a shell with another set of properties.5 Instead, a core−shell structure can form in a uniform microgel (Figure 1) when the rate of deswelling due to complexation exceeds the rate of macroion in-diffusion. In this case, macroion complexation within the outer regions of © 2019 American Chemical Society
Received: April 10, 2019 Revised: June 19, 2019 Published: June 26, 2019 9521
DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
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Langmuir
50 °C for 3 days. Each dried gel was then soaked for 3 days in buffer with a given ionic strength, after which time the hydrated mass, mhyd, was measured. The swell ratio Q is defined as mhyd Q= mdry (1) and the concentration of water in the gel (wt %), wwater, is calculated by mhyd − mdry wwater = × 100 mhyd (2) Microgels were synthesized by dispersing 1 mL of precursor solution into a round-bottom flask containing 10 mL of cyclohexane with 50 mg of Span 80 under continuous magnetic stirring at 1000 rpm. The precursor solution for microgel synthesis was the same formulation as that described above for gel synthesis. The emulsion was exposed to flowing nitrogen for 15 min and photopolymerized by UV exposure (15 min, 450 W). The resulting colloidal mixture was dispersed in deionized (DI) water, and the cyclohexane was removed by reduced-pressure distillation. The microgels were washed by repeated centrifugation and resuspension (10 times each) in ethanol and then in DI water. The microgels were equilibrated by repeated centrifugation and resuspension in phosphate buffer ([Na] = 0.019 M) or in phosphate buffer whose [Na] was varied from 0.019 to 0.532 M using NaCl. After a final centrifugation, the microgel pellet was dispersed to make a 25 vol % suspension. The average diameter of microgel hydrated in 0.01 M phosphate buffer was ∼100 μm (Figure S1 shows a size-distribution histogram). Complexation with Cationic Peptide. A subset of the microgels was loaded with the cationic peptide L5 (PAWRKAFRWAWRMLKKAA, Genscript).25 This peptide is of interest because of its antimicrobial and anticancer properties. L5 has a molecular weight of 2274 Da. It has +6 charges at pH 7.4. Peptide loading was followed by measuring microgel deswelling (n = 5 microgels) in situ by optical microscopy (Nikon E-1000) equipped with a SensiCam highsensitivity CCD Camera (Cooke) and a Fluor 20× dipping lens (NA = 0.5, WD = 2 mm). An HPF planchette was filled with colloidal microgel solution. The buffer was then replaced with a peptide solution (1 mg/mL in phosphate buffer). Bright-field images were collected in situ at 30 s intervals for periods as long as 100 min. After loading, the L5 was stained by exposing the microgels to a solution of 0.5 mg/mL FITC in phosphate buffer for 60 min, rinsing in buffer, and then imaging by confocal laser scanning microscopy (Nikon C1, 488 nm excitation). Cryo-Sample Preparation. All samples for cryo-SEM were prepared by using a Leica EM HPM100 high pressure freezing (HPF) system. Prior to use, the HPF planchettes were washed by ethanol and exposed to an oxygen plasma (10 min). As-synthesized microgels were equilibrated in phosphate buffers with various [Na]. A subset of microgels equilibrated in phosphate buffer were further exposed (2 h) to the same buffer containing L5 solution (1 mg/mL). Prior to HPF, these were washed (5×) using phosphate buffer. The resulting frozenhydrated samples were stored in liquid nitrogen. Subsequent cryotransfer and cryo-imaging were done by using a Leica VCT-100 system. Sample fracturing, transfer, and coating with sputtered Au (2.5 nm) were done under cryogenic conditions (T < −135 °C) by using a Leica EM MED020 system. Sublimation was used to create topographic contrast prior to SEM imaging by slightly warming frozen-hydrated samples. Cryo-SEM and X-ray Microanalysis. SEM imaging and energydispersive X-ray spectroscopy (EDS) used a Zeiss Auriga Cross-Beam FIB-SEM equipped with a Schottky field-emission electron gun (FEG) and an Oxford Max-80 ultrathin window (UTW) silicon-drift detector (SDD) interfaced to an Oxford INCA EDS system. Secondary electron imaging (Everhart-Thornley detector) was done by using 1 keV electrons and no Au coating. X-ray spectra were collected from Au-coated samples by using 5 keV electrons with a typical incident beam current of ∼200 pA and a working distance of 5 mm. To distribute the incident electron dose, unless otherwise
Figure 1. (A) An as-synthesized polyelectrolyte microgel with oppositely charged counterions from the surrounding buffer. (B) Deswollen shell formation around a swollen core due to counterion exchange with polyvalent macroions.
used to study counterions in 2D polyelectrolyte systems. These approaches, however, either provide averaged information or rely on fitting to assumed models of structure. Real-space imaging of hydrated microgels using transmission X-ray microscopy has been able to show size, shape, and swelling/ deswelling behavior as a function of pH and ionic strength22,23 but has not yet quantified counterions in microgels or core− shell structure microgels. Electron microscopy and its associated spectroscopies can access the relevant length scales and resolve the core−shell morphology without labeling or fitting to assumed models of structure. Here we use cryo-SEM to quantify the concentration and spatial distribution of counterions and macroions in poly(acrylic acid) (PAA) microgels complexed with a cationic peptide (L5). We use high-pressure freezing (HPF) to prepare cryo-fixed specimens while minimizing water crystallization.24 Imaging using 1 keV electrons avoids charging in uncoated frozen-hydrated specimens, and a thin gold coating enables the use of 5 keV electrons, which are sufficiently energetic to excite characteristic X-rays from C, N, O, Na, and Cl. These X-rays can follow the local polymer, complexed peptide, counterion, and water contents. Significantly, the fact that the frozenhydrated microgels are surrounded by buffer of known ionic strength provides internal standards with which to quantify the local Na and water concentrations.
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MATERIALS AND METHODS
Gel and Microgel Synthesis. Poly(acrylic acid) gels were synthesized by free-radical photopolymerization. An aqueous precursor solution was made using 20 vol % acrylic acid, 2 vol % poly(ethylene glycol diacrylate) (Mn 575 g/mol) as cross-linker, and 2 wt % lithium phenyl-2,4,6-trimethylbenzoylphosphinate as photoinitiator. This solution was exposed to flowing N2 gas for 15 min to remove oxygen and then polymerized by UV exposure (15 min, 450 W). The resulting gels were soaked in 0.01 M sodium phosphate buffer (pH 7.4) (referred to here as phosphate buffer) for 1 week, with daily buffer changes, to remove unreacted monomer and reach swelling equilibrium. Samples (∼1 cm × 1 cm × 5 mm) were cut from the resulting gels. The dry mass, mdry, was determined after holding at 9522
DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
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Langmuir indicated, X-ray spectra from the buffers and from the microgel interiors were acquired for 120 s from a square area of 5 μm × 5 μm. We typically used light sublimation conditions (−110 °C, 3 × 10−6 mbar, 10 min) to minimize topographic differences within specimens used for collecting X-ray spectra. Spectra from each buffer and its corresponding microgel were collected from five different locations within a specimen (n = 5). The X-ray peak intensities for C, N, O, Na, and Cl were extracted from each spectrum by using well-established methods of digital filtering and peak fitting provided within the INCA Energy (Oxford) software interfaced to the detector. In addition to collecting data from the microgel centers and the adjacent buffer, linear profiles of X-ray intensity were collected radially to study the composition in the outer portions of the microgels. These profiles were collected by integrating 1000 linear scans each using 128 pixels with a 0.5 μm interpixel spacing and a pixel dwell time 0.002 s. The minimum detectable and minimum quantifiable Na concentrations were calculated by following Currie.26−28 This approach uses the criterion that the minimum detectable Na concentration, CDL, corresponds to the Na characteristic X-ray intensity, INa, which exceeds the variation in background intensity, Ibg, by a factor of 3. Similarly, the minimum quantifiable composition, CMQ, corresponds to the INa that exceeds the variation in Ibg by a factor of 10. These criteria lead to the following expressions for CDL and CMQ: C DL
ÄÅ ÉÑ ÅÅ 3(I )1/2 ÑÑ ÅÅ bg ÑÑ 1 = ÅÅÅ ÑÑC Na ÅÅ INa n ÑÑÑÑ ÅÅÇ ÑÖ
and
C MQ
ÄÅ ÉÑ ÅÅ 10(I )1/2 ÑÑ ÅÅ ÑÑ bg 1 = ÅÅÅ ÑÑC Na ÅÅ INa n ÑÑÑÑ ÅÅÇ ÑÖ
(3) where CNa is the known concentration associated with a measurement giving the X-ray intensity INa and n corresponds to the number of times the measurement was repeated.
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RESULTS AND DISCUSSION Imaging and Analysis of As-Synthesized Microgels in Buffer. Figure 2A schematically illustrates the geometry of the imaging and analysis experiment. The water sublimation rate from the buffer is slightly higher than that from the microgel and produces a small topographic offset between the two.29 Figure 2B presents a representative cryo-SEM image of two assynthesized PAA microgels in phosphate buffer. A typical X-ray spectrum is shown in Figure 2C. The 5 keV electrons only penetrate ∼500 nm into the specimen, so the X-rays are primarily generated within the near-surface regions. The carbon X-rays come exclusively from the polymer network while oxygen X-rays (note the change in scale) come from both the PAA acid groups and the buffer (H2O). The fact that the C intensity is much less than the O intensity in Figure 2C indicates that the microgel is highly hydrated. X-ray peaks characteristic of both Na and Cl are present. The Au signal comes from the conductive surface coating. The microgels are surrounded by buffer of known Na concentration (Figure 2A), and that buffer can be used to create a calibration curve with which to quantify X-ray intensity measurements from samples with unknown Na concentrations. Figure 3 shows the total X-ray intensities, Itot, collected from the Na window (0.97−1.11 keV) as a function of the Na concentration in the buffer. This concentration includes Na from both the phosphate and the NaCl. The X-ray intensity at each buffer composition represents the average of five different measurements, each of which corresponds to the sum of the X-ray counts characteristic of Na and the Bremsstrahlung background: Itot = INa + Ibg. The total Na X-ray intensity data in Figure 3 increase linearly with increasing Na concentration in the buffer, and the resulting linear least-squares fit can be used as a calibration line to establish the [Na] in an unknown sample. In the case of an
Figure 2. (A) Cross-sectional schematic of the cryo-imaging and analysis experiment. (B) Cryo-SEM image of PAA microgels suspended in frozen 0.01 M phosphate buffer (sublimated at −95 °C for 10 min). (C) An X-ray spectrum from a frozen-hydrated assynthesized PAA microgel in phosphate buffer with 0.21 M NaCl (sublimated at −110 °C for 10 min).
as-synthesized microgel fully equilibrated in phosphate buffer ([Na] = 0.019 M), the Na concentration within the microgel is 0.10 ± 0.01 M (Table 1). We can have confidence in this value because eqs 3 indicate that the minimum detectable and quantifiable Na concentrations are CDL = 0.014 M and CMQ = 0.048 M, respectively. Notably, the [Na] concentration within the microgel is substantially higher than that in the surrounding buffer and is consistent with the well-established understanding that a polyelectrolyte gel becomes enriched in counterions to partially neutralize its electrostatic charge.30,31 L5 Complexation and Core−Shell Formation. The microgels deswell when exposed to phosphate buffer that contains L5 peptide. Figure 4 follows the microgel diameter decrease, measured by in situ bright-field optical microscopy and normalized to the diameter at time t = 0, as a function of time during deswelling. The diameter decreases to ∼55% of its initial diameter over about 80 min with little change thereafter. 9523
DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
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Figure 3. Total X-ray intensity, Itotal = INa + Ibk, collected from frozen buffer increases linearly with increasing Na concentration. Each point and error bar represent the average and standard deviation of n = 5 measurements. The line represents a least-squares fit to the data.
Figure 5. Cryo-SEM image of frozen-hydrated L5-complexed (120 min) PAA microgels in 0.01 M phosphate buffer (10 min sublimation at −95 °C).
Table 1. Na Concentrations in As-Synthesized Microgels and in the L5-Complexed Microgel Corea Itot (counts) [Na] (M)
as-synthesized
complexed core
4268 ± 62 0.10 ± 0.01
4375 ± 90 0.12 ± 0.02
microgels (Figure 2B), again indicating that L5 complexation is responsible for shell formation. The spatial distribution of polymer, peptide, water, and counterion can be followed by monitoring the carbon, nitrogen, oxygen, and sodium X-ray signals. Figure 6 shows X-ray intensity profiles mapped along a line from the buffer across the shell and then into the core. Additional profiles are included as Figures S2 and S3, and these are qualitatively similar to Figure 6. The carbon signal follows the distribution of organic materialPAA and peptide. Because the buffer contains no organic material, the C intensity from the buffer is very low. It is slightly higher in the core since this region corresponds to highly hydrated polymer. The carbon intensity is highest in the shell where the O X-ray intensity simultaneously drops substantially. This indicates that the shell has a much lower water content than the core. The nitrogen X-ray intensity is exclusive to the L5 peptide. However, the nitrogen X-ray intensity is relatively low, and the data are noisy, even in the shell where the peptide concentration is highest. Nevertheless, the N profile (Figure 6) makes clear that the shell is enriched in peptide. The black lines on the N profile represent average intensity values in the buffer (n = 56), the core (n = 41), and the shell (n = 13). Oneway ANOVA testing (p = 0.05) confirms that the nitrogen intensity in the shell is significantly different from that in the core. It furthermore shows that there is no significant difference between the core and the surrounding buffer, indicating that if any L5 has diffused into the core, its concentration is at a level undetectable by the present experiments. Na is distributed in a manner opposite to that of N. Again, the absolute intensities are low, and the data are noisy, but the Na X-ray intensity profile shows that the microgel core is enriched in Na relative to both the shell and surrounding buffer. The black lines on the Na profile represent average INa values in the core (n = 41) and in the shell (n = 13), and a oneway ANOVA test confirms that difference between these average intensities is statistically significant (p = 0.05). The fact that the shell is depleted in Na is consistent with the counterion release theory of polyelectrolyte complexation.33−36
a
Each value and its uncertainty correspond to the average and standard deviation (n = 5).
Figure 4. Microgel deswelling due to L5 complexation. Each data point and error bar represent the average and standard deviation, respectively, from at least five different microgels. The inset is a confocal image of a FITC-stained microgel after 100 min.
The inset shows a fluorescence image of a microgel after 100 min of L5 loading. Such imaging shows that the L5 is localized around the perimeter of the microgel forming a peptide-rich shell around a less loaded core. This morphology is consistent with other peptide-complexed microgel systems.8,32 Figure 5 shows a typical cryo-SEM image of L5-complexed microgels. The inset shows the near-surface region of one microgel. Because of the different sublimation rates, there is topographic contrast not only between the microgel and the surrounding buffer but also within the microgel itself. Consistent with the optical imaging (Figure 4, inset), there is a shell surrounding a core that has lost more water. No such shell is observed in the cryo-SEM imaging of the as-synthesized 9524
DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
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distributed over a 25 μm2 area, is sufficient to confirm this prediction. The water concentration within a gel can be quantified by following the C:O X-ray intensity ratio (IC/IO). We first measured the swell ratio of macroscopic gels as a function of NaCl content within the buffer (eq 1). Increasing [Na] decreases the swell ratio (Figure 7). The water concentration within the gel can be determined by using eq 2.
Figure 6. X-ray intensity profiles of C (black), O (blue), N (red), and Na (green) across the cross section of an L5-complexed microgel (∗ indicates a statistically significant difference; see text). The sample was sublimated at −110 °C for 10 min. Figure 7. (A) Gel swell ratio decreases with increasing ionic strength. (B) Linear calibration curve relating the IC/IO to the microgel water content (derived from the Q data in (A)).
The X-ray intensity profiles furthermore suggest that the shell is not uniform in composition. The profiles are all asymmetric, with gradients less steep on the core side of the shell than on the buffer side. While these variations in X-ray intensity are clear, we note that composition of the shell is substantially different from that in the buffer or in the assynthesized microgels, and using the calibration curves generated from highly hydrated structures whose composition is substantially different (e.g., Figure 3) to quantify the shell composition may not be appropriate. Core Composition. Because water has clearly been rejected from the shell due to L5 complexation, the effective mesh size there must be much less than that of the assynthesized microgel. As a consequence, the shell is believed to exert a compressive force on the core that is absent in the assynthesized microgel.10,11 Such compression can be expected to reduce the mesh size within the core and thus reduce the water content there relative to a microgel with no shell. The spatial resolution of the SEM, even when the incident dose is
Assuming that microgels manifest the same swelling properties as macroscopic gels of identical average composition and under identical buffering conditions,29 a calibration curve can be generated that relates the ratio of characteristic X-ray intensities of carbon and oxygen (IC/IO) to gel water content. Figure 7B shows IC/IO data collected from as-synthesized microgels equilibrated in buffers with varying [Na] and, hence, varying wwater. The relation is linear and can be used to establish the water content of an unknown sample. A comparison between an as-synthesized microgel and the core of an L5-complexed microgel, both immersed in phosphate buffer with [Na] = 0.019 M, is given in Table 2. The IC/IO ratio is higher in the core, indicating that the core has a lower water concentration, and thus a higher polymer content, than the as-synthesized microgel with no shell. This finding is 9525
DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
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L5 would occupy a spherical space with a diameter below 2 nm.47,48 We can thus expect that any effects of tortuosity on peptide diffusion through core should be relatively small. In short, except for the slightly lower mesh size, which we attribute to compression from the shell, the gel core appears to be very similar to the as-synthesized microgels, except perhaps in the immediate vicinity of the core−shell interface itself where network continuity between the deswollen shell and the swollen core must be maintained. We note, however, that the asymmetry of the composition profiles within the shell (Figure 6, Figures S2 and S3)with a sharp shell/buffer interface but with a more gradual shell/core interfacesuggests that the transition of the mesh size in the radial direction from the shell toward the core is not abrupt. We can have particular confidence in the oxygen and carbon intensity profiles at the shell/core interface, since their X-ray intensities are relatively high. These indicate that the C/O intensity ratio decreases substantially over a length scale of a few micrometers before plateauing at a minimum (average) associated with the core (Table 2). The fact that the core is similar to the assynthesized microgels suggests that complexation within the core remains thermodynamically possible but does not occur perhaps because of constraints imposed by the shell on transport of L5 peptides into the core.
Table 2. H2O Concentrations within As-Synthesized Microgels and within the Core of L5-Complexed Microgelsa IC/IO [H2O] (wt %)
as-synthesized
complexed core
0.0135 ± 0.0011 97.1 ± 0.6
0.0160 ± 0.0007 95.8 ± 0.4
a
Each datum and its uncertainty correspond to the average and standard deviation of n = 5 measurements. A one-way ANOVA test (p = 0.05) indicates that the water concentrations within the assynthesized microgel and L5-complexed core are not significantly different.
consistent with the prediction that the core is compressed by the deswollen shell.37 Na X-ray intensity data can be used in conjunction with the [Na] calibration curve (Figure 3) to quantify the [Na] within the core. The results are summarized in Table 1. A one-way ANOVA test (p = 0.05) indicates that the [Na] of the assynthesized microgel and L5-complexed core are not significantly different. We used the Peppas−Merrill modification38 of the Flory− Rehner equation to estimate the average distance between cross-links (mesh size), ξ, and address the question of whether the mesh size has decreased to a point that the peptide transport through the network is inhibited: ÄÅ ÉÑ 1/2 Ñ ÅÅ ÅÅ 1/2ijj M̅ c yzz ÑÑÑ −1/3 ξ = ÅÅÅCn jj2 zz l ÑÑÑν2,s j M̅ z ÑÑ ÅÅ r{ k ÅÅÇ ÑÑÖ (4)
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CONCLUSIONS We have used cryo-SEM imaging and its associated technique of energy-dispersive X-ray microanalysis to quantify the morphology of the core−shell structure within an anionic microgel (PAA) complexed with a small-molecule polycation (L5 macroion). The X-ray data are consistent with the general understanding that macroions from the buffer exchange with Na counterions at and near the microgel surface. Because the macroions are polyvalent, they introduce an additional set of cross-links that substantially deswell the outer portion of the microgel with the concomitant release of water there. This process forms the shell. However, X-ray intensity profiles across the shell indicate that it is not homogeneous but instead manifests a gradient in water content, and hence mesh size, in the radial direction at the shell/core interface. We used buffers of known concentration together with as-synthesized microgels of known water contents to generate calibration curves to quantify both the water content and the Na counterion content within the core. The core has a slightly lower water content than an as-synthesized microgel equilibrated within the same buffer but Na counterion concentrations that within the resolution limit of the spectroscopic technique are the same.
where 1 2 = − M̅ c M̅ n
− ν2,s) + υ2,s + χν2,s 2] ÄÅ ÉÑ ÅÅ ν2,s 1/3 Ñ 1 ν2, s Ñ Å ν2,rÅÅÅ ν − 2 ν ÑÑÑÑ 2,r Ñ ÅÅÇ 2,r ÑÖ
ν̅ [ln(1 V1̅
( )
( )
(5)
and ρp i mhyd
y jj − 1zzz (6) k { 39−42 In these expressions, Cn is the characteristic ratio (6.7), Mc is the average molecular weight between cross-links, Mr is the molecular weight of the repeat unit (72 g/mol), Mn is taken as 75000 g/mol,43,44 l is the bond length along the polymer chain (0.154 nm), χ is the Flory−Huggins interaction parameter between the polymer and the solvent (0.5),40,43,45 v̅1 is the molar volume of the solvent (18.1 cm3/mol), M is the specific volume of the polymer in the amorphous state (0.951 cm3/g), and v2,r is the polymer volume fraction immediately after synthesis (0.20). The water contents (Table 2) can be converted to polymer volume fraction in the fully swollen state v2,s by eq 6, assuming a water density, ρs, and polymer density, ρp, of 1.00 and 1.05 g/cm3, respectively. This model estimates the mesh size of an as-synthesized microgel as 39 nm and of an L5-complexed microgel core as 31 nm. Even when considering uncertainties in some parameters, most notably in Mn, and that the Peppas−Merrill model ignores electrostatic interactions within the gel,42,44 both of these values substantially exceed the dimensions of an L5 peptide. A Chou−Fasman model of secondary structure46 indicates that L5 is an α helix with a diameter of ∼1 nm and a length of ∼2.7 nm, while a random-coil model indicates that 1
ν2,s =
1+
ρs j mdry
∼
1 Q
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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.langmuir.9b01058. Figure S1: the microgel size distribution histogram; Figure S2 and S3: examples of X-ray intensity line profiles that map O, C, N, and Na along a line from the buffer, across the shell, and into the core (they complement Figure 6) (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. 9526
DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
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Matthew Libera: 0000-0001-5026-802X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work has been supported by the United States National Science Foundation (Grant DMR-1608406) and used microscopy resources supported by the National Science Foundation (Grants DMR-1428296 and DMR-0922522). The authors are grateful to Dr. Nicholas Ritchie for his helpful comments regarding trace-element X-ray microanalysis.
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DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
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DOI: 10.1021/acs.langmuir.9b01058 Langmuir 2019, 35, 9521−9528
