Polymer Diffusion in the Interphase Between Surface and Solution

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Polymer diffusion in the interphase between surface and solution Lukas Weger, Monika Weidmann, Wael Ali, Marcus Hildebrandt, Jochen Stefan Gutmann, and Kerstin Hoffmann-Jacobsen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00660 • Publication Date (Web): 22 May 2018 Downloaded from http://pubs.acs.org on May 22, 2018

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Polymer diffusion in the interphase between surface and solution Lukas Weger a,b, Monika Weidmann a, Wael Ali c, Marcus Hildebrandt c, Jochen S. Gutmann c and Kerstin Hoffmann-Jacobsen a* a

Niederrhein University of Applied Sciences, Department of Chemistry, Adlerstr. 32, 47798 Krefeld, Germany b

c

Physikalische Chemie, Universität Duisburg-Essen, Essen, Germany

Physikalische Chemie and CENIDE (Center for Nanointegration), Universität Duisburg-Essen, Essen, Germany

ACS Paragon Plus Environment

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ABSTRACT: Total internal reflection fluorescence correlation spectroscopy (TIR-FCS) is applied to study the self-diffusion of polyethylene glycol solutions in the presence of weakly attractive interfaces. Glass coverslips modified with aminopropyl- and propyl-terminated silanes are used to study the influence of solid surfaces on polymer diffusion. A model of three phases of polymer diffusion allows to describe the experimental fluorescence autocorrelation functions. Besides the two-dimensional diffusion of adsorbed polymer on the substrate and threedimensional free diffusion in bulk solution, a third diffusion time scale is observed with intermediate diffusion times. This retarded three-dimensional diffusion in solution is assigned to long range effects of solid surfaces on diffusional dynamics of polymers. The respective diffusion constants show Rouse scaling (D~N-1) indicating a screening of hydrodynamic interactions by the presence of the surface. Hence, the presented TIR-FCS method proves to be a valuable tool to investigate the effect of surfaces on polymer diffusion beyond the first adsorbed polymer layer on the 100 nm length scale.


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INTRODUCTION Polymers do not only find application as bulk materials, but are often used in conjunction with solid surfaces. Thin polymer layers are used as protective coatings of solid surfaces and fillers are introduced into polymer composites for reinforcement. It has long been suggested that the reinforcement results from altered polymer dynamics in the vicinity of filler surfaces.1,2 However, a microscopic understanding of the influence of solid surfaces on polymer dynamics and the acquisition of unambiguous experimental evidence is still a challenge in scientific research. A broad variety of experimental and simulation techniques have been applied to study the impact of solid surfaces on polymer dynamics.3 One matter of debate is the existence of long range effects of solid surfaces on polymer dynamics. It has been suggested that polymers form a glassy layer in the nanometer vicinity of solid surfaces4 whereas this idea has been rejected by other.5 Recently, the presence of a bound rubber layer in the vicinity of carbon black filler in rubber matrixes could be visualized by atomic force microscopy in terms of loss tangent images.6 In contrast, the number of techniques to address polymer dynamics directly in the presence of solid surfaces is limited. NMR7,8 as well as scattering techniques5 have been applied to study segmental dynamics. Confocal fluorescence correlation spectroscopy (FCS) has been used to study the diffusive dynamics of polymer solutions9 and in the adsorbed state.10–14 Here, polyethylene glycol (PEG) layers were prepared on glass surfaces and autocorrelation data were analyzed in terms of two-dimensional (2D) diffusion of adsorbed PEG. The scaling of the center of mass diffusion coefficient D with the molar mass was found to be either D~N-3/2 for polyethylene glycol on glass13 or N-1 for polystyrene adsorbed on a smooth quartz surface.14 The latter coincides with the theoretical prediction of Rouse diffusion due to the screening of


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hydrodynamic interaction in the presence of solid surfaces. The former was assigned to reptation-type diffusion as a result of surface roughness.14 Confocal FCS does not provide inherent surface sensitivity. Using total internal reflection (TIR) excitation in FCS, the normal dimension of the observation volume is restricted to 100 nm due to the limited penetration depth of the evanescent wave. TIR-FCS has been applied in a number of studies on interfacial diffusion in biological systems.15,16 Recently it was applied to analyze liquid flow in confined geometries.17 In the present study, we show that TIR-FCS is a powerful tool to monitor the diffusive dynamics of polymer solutions at the solid/liquid interface in equilibrium. Aqueous PEG solutions (3-20 kDa) in the presence of chemically modified glass surfaces are studied. Using a home-built TIR-FCS set-up18 we reveal the existence of polymer chains showing intermediate self-diffusion dynamics as compared to bulk solution and the adsorbed state. A global model describing the adsorbed, intermediate and bulk polymer dynamics is implemented to fit the autocorrelation data. It allows to deduce the scaling behavior of the diffusion constants of all dynamic phases.

EXPERIMENTALS. The inverted fluorescence microscope setup used for fluorescence correlation spectroscopy was described in detail elsewhere.18 Briefly, the sample was illuminated by a 488 nm diode laser (LDH P-C-485, Picoquant, Berlin, Germany) at a power level of 2 mW and focused through the oil immersion objective alpha Plan-Apochromat 63x/1.46 Oil Corr M27 / NA 1.46 (Zeiss, Jena, Germany). Fluorescence was collected through the objective, and filtered by a dichroic mirror (H 488 LPXR superflat Vers.2, AHF Analysentechnik, Tübingen, Germany) and a fluorescence


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filter (10XM20-485, Newport Corporation, Irvine, CA). The fluorescence is then focused by a tube lens onto a 50 µm pinhole to a single-photon counting hybrid photodiode detector (PMA Hybrid-06, Picoquant, Berlin, Germany). Data collection and generation of FCS curves were carried out using a hardware correlator (PicoHarp 300, Picoquant, Berlin, Germany). Confocal FCS is measured with a calibrated confocal volume of (1.13 ± 0.01) fl. In order to change the setup into the TIR-FCS mode, a focusing lens is added in the excitation pathway. By laterally shifting this lens the laser angle of incidence at the cover slip/sample interface is set to total reflection. The resulting evanescent wave protrudes (115 ± 8) nm into the sample and provides surface sensitivity. α-ω-Diamine-poly(ethylene glycol) of different molecular weight were purchased from RAPP Polymere (Tübingen, Germany). These polymers have a very narrow polydispersity of 1.03 or below. The PEG polymers were fluorescently labeled with Atto 488 NHS ester (Atto-tec, Siegen, Germany). For labelling 18.3 nmol polymer were mixed with 2.74 nmol dye in 200 µL phosphate buffer pH 7.1 and allowed to react overnight at room temperature. 20 mM sodium phosphate solution was used for all buffers. Unreacted dye was removed via size exclusion chromatography. Polymer diffusion in diluted solution was assessed using the confocal FCS mode of the microscope set-up with 3 nM PEG in phosphate buffer (pH 8.3). The diffusion constants were determined by fitting the autocorrelation function to 3D bulk diffusion as described previously.18,19 The autocorrelation functions were generated by the SymPhoTime 64 Software (PicoQuant, Berlin, Germany) and the fitting was performed with the PyCorrFit© software developed by P. Müller.20


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Propyltriethoxysilane

(PTES),

aminopropyltriethoxysilane

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(APTES),

and

3-

[Methoxy(polyethyleneoxy)-propyl]trimethoxysilane (PEG-TMS) were purchased from abcr Chemie (Karlsruhe, Germany). The cover slips were cleaned before modification according to a protocol.21 The cover slips were modified overnight in a 1% solution of silane in methanol (for PEG-TMS) or ethanol (for PTES and APTES) containing 5% acetic acid. Contact angle measurements of the prepared surfaces have been performed with an aqueous polyethylene glycol solution of 100 g/L (Mw 9000 g/mol, Merck, Darmstadt, Germany). The cover slips were blow dried with compressed air prior to use. For the analysis of polymer diffusion in the presence of surfaces the set-up was transferred into the TIR-FCS mode and a solution of 30 nM PEG in phosphate buffer (pH 8.3) was applied to the covers slip. Routinely, three different covers slips were analyzed at five different positions. For the analysis of adsorbed polymer, the cover slip was subjected for three minutes to the same solution and rinsed extensively before analysis. To determine the surface roughness, the modified cover slips where analysed by scanning probe microscopy. SPM measurements were done in AC imaging mode (tapping mode) using Agilent Technologies model 5500 beam deflection AFM. Nanosensors tapping-mode cantilevers with silicon tips (AC frequency 146-236 kHz, force constant 21-98 N m–1, length 225 ± 10 µm, width 38 ± 7.5 µm and thickness of 7 ± 1 µm, tip height 10-15 µm) were used. The sampling resolution of all images was set at 1024 data points with scanning speed of 0.5 lines per second. All captured images (3 µm x 3 µm) were processed by the open-source Gwyddion software as follows: after data levelling, the polynomial background was subtracted to remove the curvature using the second order polynomial (for both horizontal and vertical). The roughness parameters


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Rq (RMS) were obtained by the average of row/column roughness statistics of the whole image at maximum resolution.

Figure 1. Autocorrelation curves of 6 kDa PEG-NH2-Atto 488 in solution acquired with confocal FCS (red) and in the vicinity of PEG-terminated glass surface (PEGylated, green), propyl-terminated (PTES, blue) and aminopropyl-terminated surfaces (APTES, black) as determined by TIR-FCS.

RESULTS AND DISCUSSION Preceding the measurements at surfaces, the diffusion dynamics of PEG in dilute solutions were investigated with confocal FCS. Figure 1 (red curve) depicts exemplarily the autocorrelation function of 6 kDa PEG. Figure 2 shows the dependence of the deduced diffusion constant D on the molar mass. In solution the diffusion constant is found to obey a N-0.45±0,05 dependence (Table 1). A scaling exponent of 0.5 is in line with the ideal self-avoiding chain undergoing hydrodynamic interactions.22


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Figure 2. Dependence of the diffusion constant D of PEG-NH2-Atto 488 on the number of monomers N. PEG-NH2-Atto 488 in solution was measured by confocal FCS (red). The diffusion in the presence of PEG-terminated glass surface was determined by TIR-FCS (green). Second, the TIR-FCS mode was used to study diffusion in the vicinity of modified glass surface. No fluorescence signal of adsorbed PEG was detected on the PEGylated glass proving that the PEG-silane prevents adsorption. The autocorrelation function of PEG in the presence of the PEGylated glass surface as measured by TIR FCS (Figure 1) could be fitted with a TIR 3D diffusion model derived by Hassler et al. 23

〈〉

⁄ ²

²

√ !"# $1 &

'(

)*⁄*+,-.

'

/

(1)

with 〈0〉 being the number of particles in the observed volume, κ the reciprocal of the evanescent wave penetration depth, R0 the lateral extend of the pinhole and w(z) stating the Faddeevafunction 1 2 3 25671 depending on the distance z from the surface. Triplet excitation 4

is described by the triplet fraction T and the triplet lifetime τtrip.


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As shown in Figure 2, the fitted diffusion constants are only marginally lower than those acquired with confocal FCS in bulk solution. Hence, the PEGylated surface allows to analyze PEG diffusion in the presence of a non-interactive surface. Third, the diffusion of adsorbed polymers was analyzed. Glass silanized with a hydrophobic silane, propyltriethoxysilane (PTES) and a polar H-bonding silane, aminopropyltriethoxysilane (APTES) represent weakly attractive surfaces. Here, fluorescence signals of adsorbed polymer were obtained. As adsorbed polymer can only diffuse in the surface plane the autocorrelation functions of PEG were fitted to the model of 2D diffusion16 using the PyCorrFit software. Figure 3 depicts the diffusion constants of PEG adsorbed to APTES and PTES surfaces. A scaling of N-1 to N-3/2 is observed as found previously for unmodified silica and mica surfaces.13,14 A strict analysis of the scaling behavior of PEG adsorbed on the APTES surface is hampered by the large relative experimental error of the respective diffusion constants. This is a result of the small mean square displacements close to the resolution limit of FCS analysis.24

Figure 3. Diffusion constants of PEG-NH2-Atto 488 adsorbed on the PTES surface (blue) and the APTES surfaces (black).


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Yet, APTES readily adsorbs in multilayers.25 Laterally inhomogeneous multilayer adsorption would explain the tendency of a higher scaling exponent of PEG as an inhomogeneous multilayer structure also represents a rough surface. Thus, the surface roughness of the differently modified cover slips was assed via scanning probe microscopy (SPM). The obtained root-mean-square roughness Rq of the analyzed surfaces is shown in Figure 4. Detailed data and SPM images are provided in the Supporting Information in Table S1 and Figures S1-S4. With Rq ranging from 0.25 to 0.3 nm all surfaces can be considered as very smooth.26 Moreover, all roughness variations between the surfaces are within the experimental error. Hence, we can exclude the surface roughness as major parameter determining polymer diffusion on the surface. The experimentally clearly distinguishable different diffusion coefficients of PEG adsorbed to surfaces of varied chemistry are not a result of surface topography. However, we cannot exclude that minor variations of the surface roughness between the APTES and the PTES surface lead to slightly different scaling exponents.

Figure 4. Root mean square surface roughness Rq of modified cover slip surfaces as measured by SPM.


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TIR-FCS does not only allow the analysis of the diffusion of the adsorbed layer but also the investigation of the overall diffusion dynamics of PEG solutions in contact with the respective surface. The observation volume of TIR-FCS includes the adsorbed layer and extends on the nanometer scale into the bulk. Yet, the 3D model failed to describe the data of PEG diffusion in the presence of the PTES as well as the APTES surface. The additional consideration of 2D diffusion of adsorbed polymer did still not lead to a satisfactory description of the experimental autocorrelation function, as intermediate correlation times were not well described.

Figure 5. Illustration of the fitting model of the fluorescence autocorrelation function in the presence of an interactive surface. The correlation function comprises a fraction of 2D diffusion on the surface and two 3D phases of different diffusion constants; corresponding to diffusion in solution and diffusion in the interface between surface and solution. Hence, the fitting model was expended as sketched in Figure 5. A third 3D diffusion term with an intermediate diffusion constant between surface and bulk was added to the fitting equation for the autocorrelation function G(τ) (Eq. 1). The first term of G(τ) accounts for 2D diffusion of the adsorbed layer (D2D), the second term describes 3D diffusion with intermediate diffusion


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constants (Di) and the third term represents 3D bulk diffusion (Db). The sum of the fractions F of these terms is constrained to unity.

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Polymer Diffusion in the Interphase Between Surface and Solution

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