Streaming potential studies of the adsorption of fluorescently-labeled poly(ethylene imine) onto mica

Colloids and Surfaces A: Physicochem. Eng. Aspects 494 (2016) 256–265

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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa

Review

Streaming potential studies of the adsorption of fluorescently-labeled poly(ethylene imine) onto mica Aneta Michna a,∗ , Zbigniew Adamczyk a , Mark Williams b , Steven P. Armes b a b

Jerzy Haber Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, Niezapominajek 8, 30-239 Cracow, Poland Department of Chemistry, University of Sheffield, Brook Hill, Sheffield, South Yorkshire S3 7HF, United Kingdom

h i g h l i g h t s

g r a p h i c a l

a b s t r a c t

• Fluorescent PEIR was synthesized and characterized in the bulk.

• The variations of zeta potential of PEIR monolayers on mica were determined by in situ streaming potential measurements. • The stability of PEIR monolayers was determined.

a r t i c l e

i n f o

Article history: Received 30 October 2015 Received in revised form 15 December 2015 Accepted 17 December 2015 Available online 29 December 2015 Keywords: Rhodamine B-labeled poly(ethylene imine) Absorption Fluorescence Poly(ethylene imine) Electrostatic adsorption Electrokinetics Streaming potential of PEIR monolayers

a b s t r a c t Rhodamine B-labeled poly(ethylene imine) (PEIR) was synthesized and characterized using UV–vis spectroscopy, dynamic light scattering (DLS) and combining electrophoresis with laser Doppler velocimetry (LDV). DLS studies indicated a mean hydrodynamic diameter of 8.3 nm in the presence of 10−2 M NaCl. Electrophoretic mobility studies confirmed that PEIR remained cationic for pH below 10. The kinetics of PEIR adsorption and desorption onto mica was determined by in situ streaming potential measurements. The variations of zeta potential of PEIR-coated mica were quantitatively interpreted using a 3D electrokinetic model. In contrast, a mean-field (Gouy–Chapman) model proved inadequate. The acid–base characteristics of adsorbed PEIR layers were determined via streaming potential measurements over a broad pH range. The kinetics of PEIR desorption was also assessed. The deposition of well-defined adsorbed layers of PEIR onto planar substrates can be utilized to assess the kinetics of binding of various ligands. © 2015 Elsevier B.V. All rights reserved.

∗ Corresponding author. Fax: +48 124251923. E-mail addresses: [email protected] (A. Michna), [email protected] (Z. Adamczyk), [email protected] (M. Williams), s.p.armes@sheffield.ac.uk (S.P. Armes). http://dx.doi.org/10.1016/j.colsurfa.2015.12.019 0927-7757/© 2015 Elsevier B.V. All rights reserved.

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Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 2.1. Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 2.2. Synthesis of rhodamine B-conjugated PEI (PEIR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 2.3. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 3.1. Characterization of PEIR in bulk aqueous solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 3.2. PEIR adsorption on mica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

1. Introduction Poly(ethylene imine) (PEI) is a cationic polyelectrolyte that has many commercial applications. It is used in biotechnology as a vector to deliver plasmid DNA to mammalian cells [1,2]. In this context, PEI acts as a “proton sponge” [3], since its buffering capacity leads to osmotic swelling and rupture of endosomes, resulting in the release of the oligonucleotide payload into the cytoplasm. Moreover, PEI conferred greater protection toward enzymatic degradation compared to other polyamines [4]. PEI has also been used as a complexing agent for water treatment [5], in paper manufacture [6], as an adsorbent for CO2 [7], or for the production of detergents and cosmetics [8]. PEI is a weak polybase comprising primary, secondary and tertiary amines in a 1:2:1 molar ratio. These amines become protonated at different pH. According to the literature, PEI is not fully protonated under physiological conditions (pH 7.4) and is not fully protonated even at pH 2; its mean degree of protonation decreases significantly with increasing pH [9,10]. Various techniques were applied to determine the acid–base properties of branched PEI. Borkovec and Koper [11], used Ising mean field models with short-range interactions in order to theoretically analyze its protonation behavior. The acid–base properties of PEI have been studied by conductometric and potentiometric titration by Nagaya et al. [12]. Crea et al. [13] used calorimetric and potentiometric measurements to investigate the protonation equilibria of 750 kDa branched PEI over a wide range of ionic strength. In this approach, it was assumed that branched PEI possessed four types of amine sites that could be independently protonated, with only the third protonation step being analyzed as a function of the degree of protonation. Interesting results concerning the degree of protonation of comblike poly(ethyleneimine) (PEI) were obtained by Koper et al. [14] using potentiometric titration method. The workers found that PEI protonates in three steps. At pH around 9.0–9.5 only the primary groups situated on the side chains are protonated. In the second step (at pH 4.5–5.0) all primary groups and only every second tertiary amine group protonate. At the end, the remaining tertiary groups protonate at pH range near 0. This very low pH point as well as detailed protonation mechanism were concluded from a site-binding model. The site-binding model was also applied to describe the experimental results of potentiometric titration of poly(amidoamine) (PAMAM) dendrimers of generations G0- G6 [15]. Cakara et al. suggested that at high pH, the primary amine groups at the outer part of the dendrimer protonate, while the tertiary amine groups in the dendrimer core only protonate at lower pH. Under appropriate pH and ionic strength conditions, PEI interacts strongly with anionic silver sols [16] and colloidal silica particles [17], surfactants [18], and proteins [19]. This cationic polyelectrolytealso enables preparation of multilayer films on macroscopic substrates such as stainless steel [20], silicon wafers

[21], graphite electrodes [22] or on colloidal substrates such as soft microgels [23]. In principle, such composite films can be used as chemical sensors [24]. Functionalised branched PEI derivatives deposited onto contact lenses improved their optical properties, and reduced biofouling when exposed to various pathogens [25]. Adsorption of 70 kDa branched poly(ethylene imine) onto mica in the presence of either 10−2 M KBr or 0.05 M carbonate buffer (NaHCO3 , Na2 CO3 ) at pH 6.6–9.9 was studied by Claesson et al. [26] using surface forces apparatus, electro-osmotic measurements and XPS. The polyelectrolyte layer density depended strongly on the initial pH. At pH 9.9, high adsorbed amounts were observed. In contrast, the PEI was weakly adsorbed at pH 6.6, since it is protonated and hence has appreciable cationic character. The surface force data for 10−2 M KBr were theoretically analysed by applying DLVO theory. However, the experimental results obtained at higher pH and ionic strengths were not amenable to quantitative analysis. Mészáros et al. studied the adsorption kinetics of 750 kDa branched PEI on silicon wafers and the stability of the resulting layers using a commercial electrokinetic analyser [9], and a stagnation-point flow reflectometer [27]. Similar to Claessons et al. [26], the adsorbed layer thickness was found to depend strongly on the solution pH and ionic strength. Moreover, a relatively compact PEI layer was formed on adsorption at lower pH and low ionic strength, whereas a more extended layer was produced at higher pH. Mészáros et al. suggested that the PEI chains rearrange in order to maximize the number of surface contacts [9]. These workers also studied the kinetics of PEI desorption at pH 3.3, 5.8 and 9.7 [27]. No desorption occurred at pH 5.8–9.7. However, desorption was observed after a pH jump from pH 5.8 (or pH 9.7) to pH 3.3, with the initial high adsorbed mass of PEI being rapidly reduced to the same value as that obtained for adsorption at pH 3.3. The results were interpreted as overcoming the kinetic barrier to desorption via reduction of the number of surface contact points per PEI chain with concomitant greater electrostatic repulsion between cationic PEI segments. However, no quantitative analysis of the experimental data was attempted. Previously, we have studied the adsorption of 75 kDa branched PEI on mica at pH 6 [28]. More specifically, streaming potential measurements were performed at two ionic strengths (10−3 and 10−2 M) and relatively low PEI concentrations (0.01–0.20 mg L−1 ). The results revealed that the PEI chains adsorbed onto mica without any significant change in conformation. Moreover, the maximum coverage of PEI was close to 0.25 at an ionic strength of 10−2 M. This is consistent with AFM studies of the adsorption behavior of dendrimers of similar size performed by Pericet-Camara et al. [29]. Furthermore, variation of the zeta potential of the PEI-covered mica with PEI coverage was in agreement with a 3D electrokinetic model. Rhodamine B possesses strong fluorescence and is zwitterionic over a wide range of pH [30]. Its molecular diameter is approximately 1.6 nm [31]. Over the last decade, this dye label has been used to modify PEI: the carboxylic acid group of the

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former is reacted with some of the primary amine groups on the latter to form hydrolytically stable amide linkages [32]. Such rhodamine B-labelled PEI (PEIR) chains were used to study interactions with graphene oxide [32] or for encapsulation within polymeric nanoparticles [33]. However, as far as we are aware, there are no studies focused on the formation and stability of adsorbed PEIR monolayers under well-defined transport conditions. Moreover, there is insufficient information concerning the relatively broad molecular weight distribution of PEI. This leads to a wide range of diffusion coefficients, which may influence both initial monolayer formation and its stability. Moreover, there is no information regarding the stability of fluorescently-labelled PEI monolayers at various ionic strengths and solution pH. In the present work, we examined the pH-dependent adsorption of PEIR on mica using the streaming potential technique. In addition, the kinetics of desorption is determined as a function of pH under various conditions. The results are compared to conventional mean-field approaches in order to provide greater insights into the adsorption/desorption mechanisms. 2. Experimental 2.1. Materials Branched PEI (Mw = 25 000 Da and Mw /Mn = 2.50) was purchased from BASF, Germany. Given that the molar mass of the monomer repeat unit, Mwm , is 43 g mol−1 , the average number of monomers per chain, Nm , was calculated to be 580 [34]. Rhodamine B isothiocyanate (536.08 g mol−1 ) was purchased from Aldrich (UK) and was used as received. Natural ruby mica was purchased from Continental Trade (Poland) and was used as a model planar substrate for polyelectrolyte adsorption experiments. The solid pieces of mica were freshly cleaved into thin sheets of desired size and used in adsorption/deposition experiments without any pretreatment. Ultrapure water (Milli-Q Elix & Simplicity 185 purification system, supplied by Millipore SAS Molsheim, France) was used to prepare all solutions. A constant ionic strength of 10−2 M NaCl was employed for all measurements. The solution pH was adjusted using HCl and carbonate-free NaOH. All reagents were of analytical grade and were purchased from Sigma–Aldrich. Care was taken to avoid PEIR adsorption onto the cell and glass walls. This was achieved by exposing all glass containers to the PEIR stock solutions used in this work prior to the adsorption experiments. This ‘conditioning’ ensured that all available surface sites were already saturated, hence any reduction in the PEIR solution concentration could be solely attributed to its adsorption onto the mica substrate. 2.2. Synthesis of rhodamine B-conjugated PEI (PEIR) Poly(ethylene imine) (0.50 g) was dissolved in a sodium carbonate buffer (80 mL, pH 9). Rhodamine B isothiocyanate (8.0 mg, Aldrich) was dissolved in DMSO (1.0 mL) and then added to the PEI/buffer solution. The copolymer solution was stirred for 24 h at 4 ◦ C and then dialyzed against water prior to freeze-drying overnight. The final aqueous solution concentration of the labeled PEI was 25 wt.%.

and tungsten- halogen lamps. Ultrapure water was used as a reference sample. The diffusion coefficient of PEIR was determined by dynamic light scattering (DLS) using a Malvern Zetasizer Nano ZS instrument. Using the same apparatus, electrophoretic mobilities were determined for various pH at a fixed ionic strength of 10−2 M by combining aqueous electrophoresis with laser Doppler velocimetry (LDV) [35]. The pH of polycation solutions were measured using a CPC-500 (Elmetron) pH meter. Zeta potentials were determined for both bare mica and PEIR-coated mica via streaming potential measurements using a home-made cell, as described previously [28,36,37]. The streaming potential, Es , was determined using a pair of Ag/AgCl electrodes as a function of the hydrostatic pressure difference P, which drives the background buffer (pure electrolyte) through the channel. In order to determine the streaming potential of PEIR-coated mica, the following experiments were undertaken: (i) the streaming potential of bare mica was measured at various solution pH in 10−2 M background electrolyte; (ii) the adsorption of PEIR at an initial concentration of 0–10 mg L−1 was studied at various solution pH for 10 min. in the presence of 10−2 M electrolyte under diffusion-controlled transport conditions; (iii) the cell channel was flushed with background electrolyte; (iv) streaming potential measurements were made for PEIR-coated mica. Subsequently, the stability of the adsorbed PEIR layers was assessed by rinsing with background electrolyte at a flow rate of 1.20 mL min−1 for 24 h. The streaming potential was measured at defined time intervals. The zeta potential of the mica () was then calculated using the Smoluchowski equation, as described previously [28,36,37]. 3. Results and discussion 3.1. Characterization of PEIR in bulk aqueous solution Initially, the physicochemical behavior of PEIR in bulk aqueous solution was assessed. More specifically, its UV–vis extinction spectra, size and electrophoretic mobility in solution were determined at various solution pH. Moreover, the self-buffering effect of this weak polybase in aqueous solution was studied over a wide range of PEIR concentration (0–2000 mg L−1 ). Addition of PEIR to water significantly increases the solution pH. For example, the initial pH of pure water (pH 5.8) increases to pH 9.8 on addition of PEIR at a concentration of 1266 mg L−1 , respectively. Moreover, dilute aqueous solutions of PEIR exhibited an intensive pink color. A representative UV–vis extinction spectrum recorded for PEIR at pH 9.8 is shown in Fig. 1. As indicated in Fig. 1, the three absorption bands are observed. The lowest energy absorption band exhibits a maximum at 555 nm and a shoulder at max2 523 nm. The former feature is assigned to the S1 state, whereas the latter indicates the presence of rhodamine dimer. A third band observed in the near-UV region (max3 353 nm) is attributed to the S2 state. Similar two-photon absorption spectra for rhodamine B in various solvents were reported by Nag and Goswami [38]. Rhodamine B is a non-centrosymmetric dye, hence the single-photon absorption (SPA) peaks and two-photon absorption (TPA) peaks may coincide as a result of symmetry relaxation [38]. The DLS diffusion coefficient D was used to calculate the hydrodynamic radius (rH ) via the well-known Stokes–Einstein relationship [39]: kT 6rH

2.3. Methods

D=

The PEIR extinction spectrum was recorded using a doublebeam Shimadzu UV-1800 spectrometer equipped with deuterium

k is the Boltzmann constant equal to where 1.38065 × 10−16 erg K−1 , T is the absolute temperature (T of

(1)

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259

Fig. 1. UV–vis extinction spectrum recorded for a dilute aqueous solution of Rhodamine B-conjugated PEI (PEIR) at pH 9.8.

the measurements is equal to 293 K),  is the dynamic viscosity of the fluid and  = 0.01 g cm−1 s−1 , and rH = 1/2 dH where dH is hydrodynamic diameter. In Fig. 2, five typical PEIR hydrodynamic diameter distributions derived form DLS: by intensity (2a) and by number (2b) are given. These data were obtained in 10−2 M NaCl at pH 5.8. As indicated, the DLS measurements confirmed that the PEIR molecules possessed a relatively broad size distribution, which was not unexpected given the manufacturer’s GPC Mw /Mn value of 2.50. Similar results were obtained in 10−2 M NaCl at pH 8.0 and 10.3. However, there were no significant differences in values of hydrodynamic diameters by intensity or by number. For example, the PEIR hydrodynamic diameter was 8.3 ± 2.4 nm (number-average) and 14.4 ± 4.4 nm (intensity-average) over a PEIR concentration range of 1000–10 000 mg L−1 in 10−2 M NaCl at pH 5.8. On the other hand, the PEIR hydrodynamic diameters of PEIR by number-average were 8.4 ± 3.6 nm and 7.6 ± 1.2 nm at pH 8.0 and 10.3, respectively. By intensity-average, the hydrodynamic diameters were equal to 14.6 ± 3.4 nm and 11.9 ± 3.2 nm at pH 8.0 and 10.3, respectively. For branched PEIR with the same molecular weight distribution, Sunoqrot et al. reported a hydrodynamic diameter of 11.2 ± 5.3 nm [33]. On the other hand, for branched PEI Andersson et al. determined a hydrodynamic diameter of 13.2 nm at pH 7.2 [40], and von Klitzing and Kolaric´ calculated a diameter of 12 nm using a thin film pressure balance technique [34]. The measurements of electrophoretic mobility can deliver relevant information about molecule stability and their interactions with interfaces under various conditions. The pH-dependence of the electrophoretic mobility (e ) was determined for PEIR in aqueous solution, as shown in Fig. 3. As can be seen, the electrophoretic mobility is positive over the entire pH range, indicating that the PEIR chains remain cationic. However, lower mobilities were observed at higher pH, especially above pH 8. For example, at pH 3.0 the mobility was 3.5 ␮m cm (Vs)−1 , whereas the mobility was 0.15 ␮m cm (Vs)−1 at pH 10.6. A similar pH dependence for unlabeled PEI of the same MW was determined via electrophoretic NMR experiments by Griffiths et al [10]. and also in our previous paper for branched unlabeled PEI with a higher molar mass of 75 kDa [28]. However, at pH lower than 5.8, the pHs of the PEIR solutions were adjusted with HCl. Therefore, the measured values of

electrophoretic mobility are less accurate because of a potential pH drift during the measurement. More reliable results can be obtained by using streaming potential measurements. Additionally, the streaming potential measurements require less than 10 mg L−1 bulk solutions of the polyelectrolyte, therefore, the pH changes are insignificant [41]. Additionally, the polyelectrolyte concentration exceeding 500 mg L−1 is necessary to perform reliable electrophoretic measurements [42], which generates considerable costs. The zeta potential can be calculated for a given electrophoretic mobility by using Henry’s equation for arbitrary a and lower  p [43]: e =

ε p f (a) 

with

(2)

⎡ f (a) =

2 3

⎤

⎢ ⎣1 + 

2 1+

1 2.5 a{1+2 exp(−a)}

⎥ 3 ⎦

here  p is the zeta potential of PEIR molecules, −1 is the thickness of the electrical double layer (−1 = 3.048 nm), ε is the electric permittivity of the solution (ε=80.2 in 293 K),  is dynamic viscosity of the fluid and it is equal to 0.01 g cm−1 s−1 , a is the dimensionless parameter, and f(a) is called Henry’s function which is equal to 0.697 for a = 1.361. Moreover, in our calculations of the zeta potential, the O’Brien and White model was used [44] which includes the relaxation effect of double layer around particles especially for low ionic strengths when the parameter a attains lower values. The electrophoretic mobilities (e ) and zeta potentials: ( p ) and ( BW ) calculated from two models and determined for PEIR in dilute aqueous solution are summarized in Table 1. Inspecting Table 1, one can notice that the zeta potentials decrease monotonically with pH. For example, zeta potentials of 71, 63, 39 or 3 mV were calculated using Henry’s equation at pH 3.0, 7.5, 9.4 or 10.6. A similar trend with pH is observed for zeta potentials determined by applying O’Brien and White theory. On the other hand, O’Brien and White model fails at pH range 3.0–4.8.

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Fig. 2. Typical PEIR size distributions by intensity (a) and by number (b) obtained in dilute aqueous solution at an ionic strength of 10−2 M at pH 5.8. All measurements were performed at 293 K. The measurements were completed on a Nano ZS instrument using backscatter detection.

where  is equal to 0.01 g cm−1 s−1 , rH = 4.15 nm and e values at various pH are summarized in Table 1. The mean number of elementary charges per molecule (Nc ) can be calculated as qc /e (where e = 1.602 × 10−19 C is the elementary charge) [45]. In principle, Eq. (3) is valid for molecules of arbitrary shape. However, its accuracy is reduced at higher ionic strength. On the other hand, in the low zeta potential limit the following formula can be applied to spherical molecules for arbitrary ionic strength [46,47]. qc1 = 2␲␩dH Nc1

Fig. 3. The pH dependence of the electrophoretic mobility for PEIR in dilute aqueous solution at an ionic strength of 10−2 M. All measurements were performed at 293 K. The solid line is a guide to the eye.

Moreover, these electrophoretic mobilities and hydrodynamic diameters enable calculation of the charge qc per PEIR chain by applying the relationship [45]: qc0 = 6␲␩rH e Nc0 =

qc0 e

(3)

1 + dH e = 2␲␧dH (1 + dH ) p f (dH )

(4)

qc1 = e

where  p values at various pH are summarized in Table 1. As indicated in Table 1, Nc0 is reduced from 17 e at pH 3.0 to 0.7 e at pH 10.6, whereas Nc1 calculated from Eq. (4) decreases from 39 e at pH 3.0 to 1.6 e at pH 10.6. The lower levels of uncompensated charge at higher pH confirm that there is a reduction in the mean degree of protonation of the PEIR chains, which become neutral at around pH 11. Similar findings have been previously reported for unlabeled 75 kDa PEI [28]. It is also noteworthy that this uncompensated charge is considerably lower than the nominal number of charges per one PEIR molecule which is equal to 580 (assuming full ionization). This is due to charge neutralization caused by the condensation of the counterions

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261

Table 1 Electrophoretic mobility (e ), zeta potential ( p ) calculated from Henry’s equation Eq. (2), zeta potential ( BW ) calculated from O’Brien and White theory, and number of









uncompensated charges calculated at various pH either from Eq. (3) Nc0 or Eq. (4) Nc1 for PEIR molecules at 293 K for a fixed ionic strength of 10−2 M. The hydrodynamic number-average diameter remained constant at 8.3 nm, D = 5.16 × 10−7 cm2 s−1 , −1 = 3.048 nm, dH /2 = 1.361. pH

e [␮m cm (Vs)−1 ]

 p [mV]

 BW [mV] O’Brien and White

Nc0 [e]

Nc1 [e]

3.0 3.5 4.8 5.8 6.6 7.5 8.0 8.3 9.4 10.3 10.6

3.50 ± 0.02 3.70 ± 0.22 3.40 ± 0.05 3.30 ± 0.02 3.30 ± 0.05 3.10 ± 0.06 3.00 ± 0.05 2.80 ± 0.12 1.90 ± 0.09 0.41 ± 0.09 0.15 ± 0.04

71 74 68 66 66 63 61 56 39 8 3

a

17 18 16 16 16 15 15 14 9.4 2.0 0.70

39 41 37 36 36 34 33 31 21 4.5 1.6

a

a a

90 90 77 73 65 40 8 3

O’Brien and White model fails.

onto the polyelectrolyte chain (Manning counterion condensation) [48]. Our results confirm that the net PEIR protonation degree is very low, and varies between 2.9% at pH 3.0, 2.6% at pH 7.5 and only 0.1% at pH 10.6. Except for the ionization degree, the dependence of pH on PEIR solution concentration was determined for the supporting electrolyte 10−2 M NaCl (see Fig. 4). As can be seen, the solution pH increases significantly with PEIR concentration. For example, the pH increased from 5.6 in the absence of any PEIR to pH 7.0, 9.8 or 10.1 at a PEIR concentration of 10, 100 or 500 mg L−1 , respectively. Similar behavior was observed by Claesson et al. for unlabeled PEI [26]. These authors stated that addition of 50 mg L−1 PEI into the solution caused the increase in pH to 8.8. However, to the best of our knowledge, this is the first time that systematic studies of the effect of PEIR concentration on solution pH have been performed. Moreover, such an information is essential for developing procedures of preparation of well-defined PEI monolayers or multilayers. 3.2. PEIR adsorption on mica Streaming potential measurements provide direct information about the electric state of adsorbed layers of molecules or particles at the solid/liquid interfaces [41,47].

Fig. 4. The dependence of PEIR solution pH on its bulk concentration in 10−2 M NaCl solutions. The solid lines are a guide to the eye.

In the present study, this method was used to investigate PEIR adsorption on mica. The freshly cleaved mica sheets possess negative charge over a wide range of pH and ionic strength. For example, its zeta potential is −40 mV at an ionic strength of 10−2 M and pH 3 that decreases up to −70 mV at pH 7 [49]. In view of the positive zeta potential of PEIR between pH 3.5 and pH 9.0 and the negative zeta potential of mica, one should expect efficient PEIR adsorption. In order to confirm this hypothesis, the kinetics of PEIR adsorption was examined at pH 8.0 in 10−2 M NaCl at an initial PEIR concentration of 2 mg L−1 . The extent of PEIR adsorption was regulated by adjusting the adsorption time from 0 to 100 min. The streaming potential of PEIR-coated mica was determined and the zeta potential was calculated using the Smoluchowski equation [28,36,37]: =

L 4εbc cc Re

 E  s

P

=

Ke ε

 E  s

P

(5)

where Ke is the overall cell electric conductivity, L = 4 cm, 2bc = 0.027 cm and 2cc = 0.29 cm are the channel length, depth, and width, respectively. The adsorption was carried out under diffusion-controlled conditions (i.e., diffusion dominates convection). The results are presented in Fig. 5, which shows the change in zeta potential of PEIR-coated mica as a function of the square root of the adsorption time. Inspecting Fig. 5, one can observe that the zeta potential increases abruptly from −70 mV to +17 mV within approximately 1 min at pH 8. Thereafter, the zeta potential asymptotically approached its final value of 26 mV. However, this is significantly lower than the zeta potential of +61 mV determined for PEIR in dilute aqueous solution. It is interesting to mention that similar results were obtained in previous studies focused on the adsorption of polyelectrolytes, proteins or nanoparticles [28,36,47,49]. In the present work, the experimental data were quantitatively analyzed using a three-dimensional (3D) electrokinetic model and the Gouy–Chapman model [50,51]. The electrokinetic model is based on two complementary effects: (i) damping of the flow by adsorbed molecules, which reduces the ion flux from the double layer adjacent to the substrate surface and (ii) enhancement of the ion flux from the double layer adjacent to the adsorbed molecules. By considering these two effects, the following analytical expression was derived for the zeta potential of an interface coated with a molecule of arbitrary size and shape [52]:







  = Fi  i + Fp  p

(6)

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in Eq. (6). For example, for thin double layers, Fi ( ) and Fp ( ) can be expressed as [52]: Fi () = e−ci  (9)

√ 1 Fp () = √ (1 − e− 2Cp  ) 2

where Ci and Cp approach the limiting values of Ci0 = 10.2 and Cp0 = 6.51, respectively [51]. The constants Ci and Cp depend on ␬a [51], which is equal to 1.36 for PEIR in 10−2 M NaCl. Thus Ci and Cp were calculated to be 9.0 and 6.5, respectively [51]. The Fi () function vanishes in the limit of higher coverage, and √ the function Fp () approaches a limiting value of 1/ 2 [36,49]. Thus, for this case, Eq. (6) simplifies to the form [54]: 1  → √ p 2

Fig. 5. Change in zeta potential of PEIR-coated mica as a function of the square root of the adsorption time under diffusion-controlled conditions at 293 K. The adsorption conditions were as follows: initial PEIR concentration = 2.0 mg L−1 , 10−2 M NaCl, pH 8.0. The solid line represents the non-linear fit to the experimental data.

where  p determined for PEIR at various pH presented as as in Table 1. It is interesting to mention that by using Eqs. (6)–(9) one can determine the zeta potential of polyelectrolyte in the bulk if it is not known from the formula: p =

Here () is the zeta potential of the substrate coated with adsorbed molecules (e.g., PEIR),  i is the zeta potential of bare mica,  p is the zeta potential of molecules in dilute aqueous solution (see Table 2) and Fi (), Fp () are dimensionless correction functions for the coverage and the electrical double layer thicknes, respectively.  is the dimensionless coverage of molecules defined as [50]:  = NSg

(7)

where N is the surface concentration of macro molecules and Sg is the geometric cross-sectional area of the macro molecule. Pfau et al. stated that branched PEI chains adopt a spherical conformation in solution and become only slightly flattened after adsorption at an interface [53]. Therefore, the cross-section of branched PEIR molecules can be calculated using Eq. (8) [50]: Sg =

2 dH

(8)

4

where dH is the hydrodynamic diameter of the PEIR chains. By considering the hydrodynamic diameter of PEIR macro(molecule) equal to 8.3 nm, the cross-sectional molecular area calculated from Eq. (8) was 54 nm2 . It should be emphasized that the functions Fi ( ) and Fp ( ) are theoretically determined, hence no fitting parameters are involved

Table 2 Zeta potential data obtained for PEIR in dilute aqueous solution in the presence of 10−2 M NaCl for various pHs at 293 K.  p was calculated from Eq. (2) using electrophoretic mobilities.  s was calculated from Eq. (11) using correction functions Fi and Fp of 0.105 and 0.636, respectively over the range pH 3.5–pH 10.6. Nominal PEIR sublayer coverage was 0.25. pH

 p [mV]

 s [mV]

3.5 4.8 5.8 6.6 7.5 8.0 8.3 9.4 10.3 10.6

74 68 66 66 63 61 56 39 8 3

84 83 75 66 55 53 41 37 10 −9

(10)

(max ) − Fi (max )i Fp (max )

(11)

On the other hand, according to the Gouy–Chapman mean field model, the zeta potential of the surface covered by macromolecules is described by the formula [28],



2

1/2

| | + | | + 4 2kT () = ± ln 2 e

(12)

where the upper sign denotes positive surface charge, ¯ =

/ i , i is the charge density of mica equal to −0.064 e/nm2 and −0.138 e/nm2 for  i −40 mV and −70 mV, respectively, and

= Nc /Sg is the charge density of the PEIR, and e.g., at pH 5.8 it is equal to 0.296 e/nm2 and 0.667 e/nm2 for Nc0 /Sg and Nc1 /Sg , respectively. The nominal coverage of PEIR () is calculated from the following formula valid for diffusion-controlled transport [55,56]  = 2Sg

 Dt 1/2 

nb

(13)

where nb = 10−6 MAvw cb is the number concentration of PEIR molecules in aqueous solution expressed in number of PEIR molecules that are contained in cm−3 , cb is the PEIR concentration in aqueous solution expressed in mg L−1 (0–10 mg L−1 ), Av is Avogadro constant equal to 6.022 × 1023 mol−1 , and Mw is molar mass expressed in g mol −1 . Using Eq. (13), the experimental data expressed as  vs. t1/2 plots can be transformed to the  vs.  relationships presented in Fig. 6a–b for 10−2 M NaCl and pH 5.6 (red triangles) and pH 8.0 (dark blue circles), respectively. The zeta potential increased almost linearly for  < 0.1 at both pH 5.8 and pH 8.0. Moreover, zeta potential inversion occurred at a surface coverage slightly above this limiting value. It is noteworthy that limiting zeta potentials of 43 mV and 26 mV were determined at pH 5.8 and 8.0, respectively. These experimental values are lower than the theoretical values of 47 and 43 mV, respectively, that are predicted by Eq. (10). These experimental results were interpreted in terms of both the 3D electrokinetic model and the mean-field GC model. It is clear that the agreement between the experimental data and theoretical predictions calculated from Eq. (6) is reasonable for PEIR nominal coverage below 0.3 for both pH 5.8 and 8.0. One can estimate that the maximum coverage of PEIR was 0.26 for pH 5.8 and 0.25 for pH 8.0.

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263

Fig. 7. Change in zeta potential for PEIR-coated mica with rinsing time at pH 5.8. The flow rate of NaCl was 1.2 cm3 min−1 , 10−2 M at 293 K. 1 (dark blue circles) initial coverage  = 0.32, 2 (green squares) initial coverage  = 0.16, 3 (red triangles) initial coverage  = 0.08. The solid lines are non-linear interpolations of the experimental data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

Fig. 6. Variation of zeta potential of PEIR-coated mica with the nominal surface coverage at 293 K, 10−2 M NaCl. Measurement conditions were as follows: (a) pH 5.8 (red triangles), (b) pH 8.0 (dark blue circles). The solid lines show the theoretical curves calculated using the 3D electrokinetic model. The dashed lines show the theoretical curves calculated using the Gouy–Chapman model. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

The desorption of PEIR from mica was studied under convectioncontrolled conditions at a flow rate of 1.2 cm3 min−1 at pH 5.8 for 10−2 M NaCl at 293 K. The change in zeta potential with rinsing time is presented in Fig. 7 for initial fractional PEIR coverages of 0.32, 0.16 and 0.08, respectively. The zeta potential decreases monotonically with rinsing time for initial coverages of 0.32 and 0.16, as indicated by curves 1 and 2. Under these conditions, the final zeta potential recorded after 24 h rinsing was reduced from an initial 38 mV to 30 mV (dark blue circles) and from 27 mV to 17 mV (green squares), respectively. These results suggested that only a modest amount of PEIR became desorbed within 2 h. Moreover, there was almost no difference between the initial and final zeta potential when such rinsing experiments were performed at an initial coverage of 0.08. The streaming potential data enable precise monitoring of the PEIR coverage under in situ conditions. Thus, this technique was exploited to determine the acid-base properties of adsorbed PEIR layers, with the results shown in Fig. 8. The pH dependence of the zeta potential of PEIR-coated mica was determined at an initial fractional surface coverage of 0.25. Then the PEIR solution was replaced by an electrolyte solution at the desired pH (within the range of pH 3.8–10.6) by judicious addition of either HCl (for pH < 5.8) or NaOH (for pH > 5.8). The background electrolyte concentration was fixed

Fig. 8. The pH-dependence of the zeta potential for PEIR-coated mica for an initial surface coverage  of 0.25, 10−2 M NaCl at 293 K. The red filled circles denote the experimental data calculated from streaming potential measurements (2), the open √ circles represent the multiplied by 1/ 2 data obtained from microelectrophoretic measurements (1) and the pH-dependence of the zeta potential for bare mica is indicated by yellow triangles [49] (3). The solid lines are a guide to the eye. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

at 10−2 M NaCl in all experiments. The zeta potential was calculated from the streaming potential using the Smoluchowski equation. In Fig. 8, experimental data are presented for the pHdependence of the √ zeta potential of PEIR-coated mica (filled circles), multiplied by 1/ 2 data obtained from microelectrophoretic measurements (open circles), and the pH-dependence of the zeta potential for bare mica (triangles). As shown in Fig. 8, the zeta potential for PEIR-coated mica decreases with pH, from 52 mV at pH 3.8, to 42 mV at pH 5.8 and 11 mV at pH 9.0. This pH-dependence was compared with zeta potential behavior determined by electrophoresis in dilute aqueous √ solution after multiplied by a factor of 1/ 2. As shown in Fig. 8, the streaming potential results (filled circles) only agree with the electrophoretic data set (open circles) below pH 5.8 and above pH 10.0.

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Fig. 9. The pH-dependence of zeta potential of PEIR at 293 K, 10−2 M NaCl. Open circles denote the data set calculated from Eq. (2) using electrophoretic mobilities, the full circles represent the data set calculated from Eq. (11) using correction functions Fi and Fp of 0.105 and 0.636, respectively. For comparison, the pH-dependence of the zeta potential for bare mica is indicated by triangles [49]. The solid lines are a guide to the eye. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

At intermediate pH, streaming potentials were considerably lower than the corresponding multiplied by values obtained from electrophoresis. This discrepancy is attributed to a reliability low PEIR coverage and high negative zeta potential of mica. √ Therefore, an exact relationship between the multiplied by 1/ 2 zeta potential determined by electrophoresis in dilute aqueous solution and the apparent zeta potential for PEIR-coated surfaces should be determined for a nominal PEIR coverage of less than 0.50. This can be achieved using the Eq. (11). For a PEIR coverage of 0.25 Fi () and Fp () were equal to 0.105 and 0.636, respectively. For the sake of convenience, the calculated ( s ) data are presented in Table 2 together with suitable zeta potentials ( p ) for PEIR in dilute aqueous solution, as determined by electrophoresis. The zeta potentials ( s ) calculated from Eq. (11) and the zeta potentials calculated from Eq. (2) using electrophoretic mobilities are shown as a function of pH in Fig. 9. Comparing the data from Fig. 9 with that presented in Table 2, the bulk zeta potentials calculated from Eq. (11) using streaming potential method furnished reliable bulk zeta potential for a wide range of pH. Therefore, the streaming potential measurements allow one to precisely determined the zeta potential of PEIR in aqueous solution for a wide range of pH. This is advantageous compared to the bulk electrophoretic mobility measurements involving high PEIR concentration that creates problems with pH stabilization. 4. Conclusions Rhodamine B-labeled poly(ethylene imine) (PEIR) was synthesized and its diffusion coefficient and electrophoretic mobility were determined for various pHs by combining DLS and electrophoresis. Regardless of the solution pH, DLS studies indicated that the PEIR molecules had a hydrodynamic diameter of 8.3 nm. At a fixed ionic strength of 10−2 M, the calculated number of uncompensated charges per PEIR chain decreased from 39 e to 1.6 e over the pH range 3.0–10.6. This gives a very low ionization degree of 2.9–0.1%. Addition of PEIR to pure deionized water resulted in a significant increase in pH, which is consistent with the well-known self-buffering behavior for this weak polybase. Optimum conditions for the adsorption of PEIR onto mica were determined by

considering both the uncompensated (electrokinetic) charge on the PEIR chains and the electrophoretic behavior of mica as a function of pH. This approach indicated that PEIR should be strongly adsorbed onto mica at pH 5.8 to 8.0. This hypothesis was confirmed by streaming potential measurements. Such experiments were quantitatively interpreted in terms of an electrokinetic 3D model, whereas an mean-field model proved to be inadequate. It was also confirmed that the PEIR monolayers were quite stable for rinsing times of up to 24 h. Moreover, streaming potential measurements enable precise in situ control over the extent of PEIR adsorption. In particular, welldefined PEIR submonolayers were deposited onto mica that could be exploited for studies of acid-base properties or kinetics of binding of various ligands. Additionally, using the bulk zeta potential for PEIR and the correction functions Fi (), Fp (), the zeta potential of PEIR-coated mica was calculated over the pH range 3.5–10.6. It is emphasised that the streaming potential measurements of PEIR monolayer adsorbed at mica proved to be advantageous compared to bulk studies over this pH range. Acknowledgement This work was financially supported by the Grant POIG. 01.01.02.-12-028/09. References [1] A. Kichler, C. Leborgne, E. Coeytaux, O. Danos, Polyethylenimine-mediated gene delivery: a mechanistic study, J. Gene Med. 3 (2001) 135–144. [2] J.D. Ziebarth, Y. Wang, Understanding the protonation behavior of linear polyethylenimine in solutions through Monte Carlo simulations, Biomacromolecules 11 (2010) 29–38. [3] T. Merdan, K. Kunath, D. Fischer, J. Kopecek, T. Kissel, Intracellular processing of poly(ethylene imine)/ribozyme complexes can be observed in living cells by using confocal laser scanning microscopy and inhibitor experiments, Pharm. Res. 19 (2002) 140–146. [4] W.T. Godbey, M.A. Barry, P. Saggau, K.K. Wu, A.G. Mikos, Poly(ethylenimine)-mediated transfection: a new paradigm for gene delivery, J. Biomed. Mater. Res. 51 (2000) 321–328. [5] A.P. Kryvoruchko, L. Yu Yurlova, I.D. Atamanenko, B. Yu Kornilovich, Ultrafiltration removal of U(VI) from contaminated water, Desalination 162 (2004) 229–236. [6] H. Xiao, G.L. Zhao, J.R. Li, B.H. He, Hydrophobically associating polyethylenimine for controlling dissolved and colloidal substances of alkaline peroxide mechanical pulp, Bioresources 9 (2014) 1121–1131. [7] R. Sanz, G. Calleja, A. Arencibia, E.S. Sanz-Pérez, Development of high efficiency adsorbents for CO2 capture based on a double-functionalization method of grafting and impregnation, J. Mater. Chem. A 1 (2013) 1956–1962. [8] I.C. Constantinides et al, Personal care compositions comprising responsive particles, U.S. Patent No 8865144 B2, 21 Oct (2014). [9] R. Mészáros, L. Thompson, M. Bos, P. de Groot, Adsorption and electrokinetic properties of polyethylenimine on silica surfaces, Langmuir 18 (2002) 6164–6169. [10] P.C. Griffiths, A. Paul, P. Stilbs, E. Petterson, Charge on poly(ethylene imine): comparing electrophoretic NMR measurements and pH titrations, Macromolecules 38 (2005) 3539–3542. [11] M. Borkovec, G.J.M. Koper, Proton binding characteristics of branched polyelectrolytes, Macromolecules 30 (1997) 2151–2158. [12] J. Nagaya, M. Homma, A. Tanioka, A. Minakata, Relationship between protonation and ion condensation for branched poly (ethylenimine), Biophys. Chem. 60 (1996) 45–51. [13] F. Crea, P. Crea, A. de Robertis, S. Sammartano, Thermodynamic study for the protonation of branched poly(ethylenimine) in NaCl (aq) and its dependence on ionic strength, J. Chem. Eng. Data 52 (2007) 279–285. [14] G.J.M. Koper, R.C. van Duijvenbode, D.D.P.W. Stam, U. Steuerle, M. Borkovec, Synthesis and protonation behavior of comblike poly(ethyleneimine) hesis and protonation behavior of comblike poly(ethyleneimine), Macromolecules 36 (2003) 2500–2507. [15] D. Cakara, J. Kleimann, M. Borkovec, Microscopic protonation equilibria of poly (amidoamine) dendrimers from macroscopic titrations, Macromolecules 36 (2003) 4201–4207. [16] S. Sanchez-Cortes, R. Marsal Berenguel, A. Madejón, M. Pérez-Méndez, Adsorption of polyethyleneimine on silver nanoparticles and its interaction with a plasmid DNA: a surface-enhanced Raman scattering study, Biomacromolecules 3 (2002) 655–660. [17] L. Avadiar, Y.-K. Leong, Interactions of PEI (polyethylenimine)–silica particles with citric acid in dispersions, Colloid Polym. Sci. 289 (2011) 237–245.

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