Correlation between the Charge of Polymer Particles in Solution and

Article pubs.acs.org/Langmuir

Correlation between the Charge of Polymer Particles in Solution and in the Gas Phase Investigated by Zeta-Potential Measurements and Electrospray Ionization Mass Spectrometry. Nesrine Ouadah,†,‡ Tristan Doussineau,†,‡ Thomas Hamada,†,‡ Philippe Dugourd,†,‡ Claire Bordes,†,§ and Rodolphe Antoine*,†,‡ †

Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne cedex, France UMR5306, Institut Lumière Matière, Villeurbanne, France § UMR5180, Sciences Analytiques, Villeurbanne, France ‡

S Supporting Information *

ABSTRACT: The relationship between the effective charge of polymer nanoparticles (PNP) in solution and the charge states of ionized particles produced in the gas phase by electrospray ionization was investigated. Charge detection mass spectrometry was used to measure both the mass and charge of individual electrosprayed ions. The effective charges extracted from the measured zeta-potential of PNPs in solution are partially correlated with the average values of charge of PNPs in the gas phase. The correlation between the magnitude of charging of PNPs ions produced in the gas phase with the PNPs surface charge in solution demonstrates that the mass spectrometry-based analysis described in this work is an alternative and promising way for a fast and systematic characterization of charges on colloidal particles.

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the literature.15,16 The analytical expressions developed by Ohshima15 were found to be accurate for determining the effective charge number on colloidal particles17,18 and in particular on latex nanoparticles.19 Light scattering, especially dynamic light scattering, and electrophoretic light scattering are now the standard techniques for measuring the size and the zeta-potential of dispersed nanoparticles.20 Techniques using nanopores at the single particle level have recently emerged as alternative methods for measuring these values.21,22 All these techniques are performed in the liquid phase and the analysis of data to extract charges requires appropriate theoretical models. On the other hand, nanoparticles can be ionized and transferred to the gas phase thanks to electrospray ionization routes.23−25 Electrospray ionization (ESI) is an aerosolization method that generates highly charged droplets from solutions or suspensions and after a series of solvent evaporation−droplet fission cycles it results in solvent-free particles carrying multiple charges.26,27 Because of its properties, electrospraying is considered as an effective route to nanotechnology, for gas phase dispersion and deposition of nanoparticles on substrates,28,29 in-spray nanoparticle synthesis,30,31 and agglomeration.32 The generation of highly charged monodisperse aerosol

INTRODUCTION Engineered nanoparticles require for many applications an extensive physicochemical characterization in order to evidence their functionality, their stability, and so forth, or to relate these physicochemical properties to their toxicity.1−3 In particular, the interaction of nanoparticles with biological or synthetic objects is critical and requires a firm control over nanoparticle− object interplays, which are mainly governed by surface properties, for example, interfacial (bio)chemical composition and/or surface charge, of nanoparticles.4−6 Among nanoparticles, polymer nanoparticles (PNP) are interesting objects because of their high engineerability (e.g., size control and tunability of the physicochemical properties). They play a pivotal role in a wide spectrum of fields ranging from sensorics, biotechnology,7,8 environmental technology9 to textiles.10 One of the most important parameters used to evaluate surface properties of a particle is its electrostatic surface potential, which is often characterized through the so-called zeta-potential.11,12 The zeta-potential is usually defined as the electrical potential between the inner Helmholtz layer near a particle’s surface and the bulk liquid in which the particle is suspended.13 It is thus related to the effective charge of the particle. However, for nanoparticles, there is no simple analytical formula available for the calculation of an effective charge. On the basis of the solution of the spherical Poisson− Boltzmann equation,14 approximate analytic expressions of the surface charge/surface potential relationship were proposed in © 2013 American Chemical Society

Received: September 11, 2013 Revised: October 19, 2013 Published: October 21, 2013 14074

dx.doi.org/10.1021/la403516y | Langmuir 2013, 29, 14074−14081

14075

64.4

81.1

106.4 107.1

112.6 139.2 135.1

101.6

110.1 116.8

121.4 125.2

129.2 43.4

47.9

44.4

sample

L2

L3

L4 L5

L6 L 11 L 12

L 14

L 15 L 16

L 17 L 18

L 19 L 23

L 24

L 25

4.6

5.0

13.4 4.5

12.6 13.0

11.4 12.1

10.5

11.7 14.4 14.0

11.0 11.1

8.4

6.7

κRh

−3.994

−3.946

−4.802 −3.275

−4.615 −4.764

−5.891 −4.932

−4.531

3.438 4.146 2.316

2.585 3.965

3.506

4.223

electrophoretic mobility (μep) (μm.cm/V·s) + − + − + + − + + + − + − + + − + + − + + − + − + −

ESI mode 0.38 0.45 0.90 1.04 1.95 2.40 3.79 2.64 5.53 4.77 4.21 1.62 3.10 3.15 3.75 4.51 4.38 4.36 3.92 5.41 0.14 0.20 1.08 0.63 0.99 0.53

MW(CDMS) (GDa) 0.36 0.42 0.86 1.00 1.91 2.33 3.45 2.55 5.43 4.63 4.00 1.58 3.00 3.04 3.43 4.14 4.31 4.27 3.58 5.30 0.13 0.18 0.72 0.38 0.65 0.31

Mn(CDMS) (GDa) 1.06 1.07 1.05 1.04 1.02 1.03 1.10 1.04 1.02 1.03 1.03 1.03 1.16 1.04 1.09 1.09 1.02 1.02 1.09 1.02 1.05 1.09 1. 5 1.66 1.53 1.70

PdICDMS (Mw/ Mn) 49.3 51.6 66.0 69.4 86.0 92.6 93.8 95.4 127.2 113.3 114.7 80.9 93.9 102.3 102.3 109.3 113.0 113.6 112.6 121.3 34.9 37.8 44.5 41.3 42.6 37.3

RCDMS (nm) 31% 25% 23% 17% 24% 16% 14% 18% 9% 19% 18% 26% 8% 8% 14% 7% 7% 10% 11% 6% 24% 15% 8% 16% 4% 19%

(Rh − RCDMS)/ RCDMS 867 854 1175 1243 1555 1891 1788 1822 2697 2138 2185 1380 1481 2142 2180 2463 2449 2452 2635 2712 650 770 750 829 750 705

||

2125 ± 24 2578 ± 145 4307 ± 67 4004 ± 33 7697 ± 458 3344 ± 31

44.70 ± 0.43 33.00 ± 1.67 50.60 ± 0.63 43.90 ± 0.30 52.90 ± 2.47 29.55 ± 0.24

−51.30 ± 2.90

−50.30 ± 1.76

−61.30 ± 1.15 −41.80 ± 1.41

−58.90 ± 0.75 −60.80 ± 0.93

−75.10 ± 2.64 −62.90 ± 2.49

706 ± 51

807 ± 36

8053 ± 207 529 ± 21

6865 ± 115 7484 ± 156

7849 ± 426 6819 ± 374

4254 ± 444

1687 ± 65

53.90 ± 1.61

−56.83 ± 4.41

|Zeff| Smoluchowski and Ohshima relationsa

zeta potential (mV) Smoluchowski’s relation

N/A

N/A

−89 ± 2 −63 ± 1

−87 ± 2 −89 ± 2

N/A N/A

N/A

57 ± 1 68 ± 1 36 ± 1

41 ± 1 68 ± 1

62 ± 1

N/A

zeta potential (mV) Ohshima’s relation

N/A

N/A

13980 ± 325 980 ± 40

11700 ± 230 12880 ± 310

N/A N/A

N/A

5300 ± 53 10500 ± 600 4300 ± 42

3130 ± 170 6140 ± 97

3070 ± 40

N/A

|Zeff| Ohshima and Ohshima relationsb

a Zeta-potential (ζ) extracted from electrophoretic mobility, using the Smoluchowski’s relation, as currently proposed by default in the commercial Malvern software47,48 was then directly converted into an effective charge (zeff) using eq 4. bZeta-potential (ζ) extracted from electrophoretic mobility, using the graphical determination given in Ohshima49 (see Figure S1 in Supporting Information) was then directly converted into an effective charge (zeff) using eq 4.

Rh (nm)

Table 1. Characteristics of the PNPs Determined from DLS (Dynamic Light Scattering) and CDMS (Charge Detection Mass Spectrometry (a Density of 1.188 (of PMMA) Is Used to Calculate RCDMS from MW)

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bearing anionic persulfate groups, was added immediately (from 0.5 to 2% of monomer depending on the expected surface charge density). Polymerization reactions were run for about 5 h. The synthesis protocol was slightly modified for small nanoparticles (L23−25, see Table 1). The principle is the same as above except that water and acetone were mixed prior to introduction into the reactor. The cosolvent was added to increase the solubility of the monomer.45,46 Acetone was added at different ratio (between 30 and 50%) and we modified the concentration of MMA and/or initiator (APS), the temperature (75 to 80 °C) and the reaction time (between 3 and 5 h). Emulsion polymerization with acetone requires a system with a refrigerant to limit acetone evaporation and was carried out at 75 °C. Size Distribution and Zeta Potential of Latex Particles. PMMA particle size distributions were measured by dynamic light scattering (DLS) and the electrophoretic mobility was measured by laser Doppler velocimetry (with 10−3 M NaCl) using a Zetasizer Nano ZS (Malvern Instruments Ltd.). The measured electrophoretic mobility μep was then directly converted by the software into zetapotential (ζ) using the Smoluchowski’s relation, as currently proposed by default in the commercial Malvern software.47,48 However, this relation is only valid for large solutes compared to the Debye length (i.e., κRh ≫ 10). For finite solute sizes (Rh) in the range studied in this work (40−140 nm), this equation may lead to some errors. Numerical approachs or graphical determinations using the equation given in Ohshima49 (that takes into account relaxation and electrophoretic effects) could be used instead. Example of such graphical representations is given in Figure S1 in Supporting Information. However the graphical determination using equations given in Ohshima49 is only applicable for ζ < 100 mV.19,49 PNPs samples L2, L14, L15, L16, L24, and L25 exhibit (μep, κRh) values for which the graphical determination using equations given in Ohshima49 is not applicable. Zeta-potential (ζ) values extracted using the Smoluchowski’s relation and the Ohshima approach are reported in Table 1. Reported values for size and zeta-potential were averaged over respectively three and four measurements. Charge Detection Mass Spectrometry of Latex Particles. Experiments were performed on a custom-built charge detection-mass spectrometer with an electrospray source which is described in details in previous works.43,44 Briefly, PMMA latexes were obtained from synthesis as described above and were diluted in (water/methanol 50:50, v/v) to a concentration of around 1014 NPs/L. Samples were gently vortexed (1 min, 10 Hz) before injection to the electrospray source. Solutions were injected at flow rates of typically 200 μL/h and entered the electrospray chamber through a 0.1 mm internal diameter stainless steel capillary tube located inside the needle tip. Nitrogen drying gas was injected between the end-cap and the transfer glass capillary and flew through a heater typically set at 200 °C. The vacuum interface was composed of a glass transfer capillary that transferred the ions to the first stage of the vacuum system, an end-cap, a skimmer between the first and second vacuum stages, a hexapole ion guide, and an exit lens. The charge detection device measures the charge of individual ions on a electrode as they pass near this electrode (tube). The charge and the m/z ratio of the ions are determined from the image charge. It was used in a single pass mode.50 The signal induced by the charge on the tube was picked up by a JFET transistor and was amplified by a low-noise, charge-sensitive preamplifier and then shaped and differentiated by a home-built amplifier. The signal was recorded with a waveform digitizer card that recorded the entire waveform for each ion passing through the detector tube. The data were transferred to a desktop computer where they were analyzed to compute the charge and mass of each ion. Calibration in charge was performed using a test capacitor that allowed a known amount of charge to be pulsed onto the pick-up tube. The test pulses were generated with a shaping-pulse generator so that the time dependent signal response could be determined as well. The charge of a particle was then directly deduced from this calibration and from the average value of the voltage intensity of the two pulses generated by the particle on the detector. The mass-to-charge m/z ratio of an ion is determined from the time-of-flight Δt (time delay between the positive and negative pulses that correspond to the

nanoparticles by means of electrospray of gold colloidal suspension was demonstrated by Suh et al.33 We recently conducted by electrospray ionization charge detection mass spectrometry (CDMS)34,35 a thorough study on the charging of micellar nanoparticles.36 Charge detection mass spectrometry is an emerging field of mass spectrometry37,38 that offers an alternative to time-of-flight MS (TOF-MS)39 and Fourier transform ion cyclotron resonance MS (FTICR-MS)40 for measuring high mass ions. CDMS directly measures the charge and the m/z of individual ions as they pass near an electrode inducing an image charge on the electrode. The charge of micellar nanoparticles electrosprayed from water solution (z) was compared to the Rayleigh’s limiting charge (zR) of charged water droplet of same dimensions and an average ratio (z/zR) of 0.6−0.65 was found.36 The charge level on electrosprayed particles continues to inspire debate and controversy and may result from a combination of charged residue evaporation and field emission processes.41 Some works tried to correlate charges of macromolecules observed in solution and in the gas phase. In particular, by using protein charge ladders combined to capillary electrophoresis and online electrospray ionization mass spectrometry, Smith and co-workers42 showed that charge states for proteins produced in the gas phase by ESI do not necessarily reflect the net charge of the protein in solution or the number of amino groups on the protein. The net charge of ions of a protein produced by ESI is mainly determined by the protein contour area and the Coulombic repulsion between charged sites on its surface. This outlines the role of gas-phase and liquid-phase protein conformations on its net charge. Nevertheless, it is expected that such conformational effects would be less important for rigid spherical colloids. To our knowledge, due in particular to the difficulty to measure the charge state of ions with molecular weight superior to hundreds of megadalton, no in-depth correlation between the charge of nanoparticles in solution and in the gas phase was investigated. In this work, we study the relationship between the effective charge of polymer nanoparticles in solution and the charge states of ions of particles produced in the gas phase by ESI. The charge detection mass spectrometry was used to measure both the mass and the charge of individual electrosprayed ions obtained from PNP.43,44 The charge states observed in the gas phase were then compared to the effective charges of PNP in solution determined from classical zetapotential measurements.

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EXPERIMENTAL SECTION

Materials. Methyl methacrylate (MMA) was purchased from Acrôs Organics and was used as such. The compound 2,2′-azobis (2methylpropionamidine) dihydrochloride (V50) was from Aldrich with a 97% purity and was used as such. Ammonium persulfate (APS) was purchased from Sigma Aldrich with a 98.0% purity and was used as received. Water was deionized before use. All solutions were prepared fresh before use. Preparation of Latex Nanoparticles. Anionic or cationic poly(methyl methacrylate) (PMMA) latexes were synthetized by radical emulsifier-free emulsion polymerization. The polymerization reactions were carried out at 80 °C in a glass jacketed reactor equipped with a paddle stirrer and containing about 150 mL water. The stirrer speed was adjusted to 200−500 rpm and kept stable along the reaction. The required amount of MMA monomer (from 5 to 25% of water depending on the expected size of particles) was introduced into the reactor when the temperature reached 80 °C. Then the initiator, V50 for latexes bearing cationic amidino groups or APS for latexes 14076


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entrance and the exit from the detector tube). The ion velocity vm is given by vm = L/Δt and m/z = 2 eV/(v2m − v2g) where L is the length of the detector tube (i.e., 3.75 cm), m is the mass, z is the number of charges, and V is the electrostatic acceleration voltage. vg is the ion velocity due to the free gas expansion, which takes into account the initial kinetic energy imparted to the ion by the free jet expansion of the gas prior to acceleration by the electric field. It is determined by grounding all electrostatic lenses and timing the passage of the ion through the detector. These procedures allow the internal calibration of the charge detection mass spectrometer. An external calibration was performed using NIST traceable size standards (70, 100, 150, 200, and 300 nm polystyrene nanospheres supplied by Polysciences Europe GmbH). In charge detection mass spectrometry, the mass m of nanoobjects is calculated using m/z = (2 eV/(v2m − v2g) × z. Mass histograms are built from the collection of a statistically relevant number N of single mass measurements for each sample (N > 5000 typically).

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RESULTS AND DISCUSSION Several polymerization reactions were carried out by varying the amount of the monomer and/or the initiator in order to synthesize anionic or cationic nanolatexes with relatively monodisperse sizes (diameters ranging between ∼80 and ∼300 nm) and with various surface charges (see Table 1). Average molecular weights obtained from CDMS measurements were converted into volumes (for which a radius can be defined) assuming perfectly spherical nanoobjects and a homogeneous density of 1.188 (density of PMMA). The radii extracted by CDMS are systematically lower than those extracted by DLS, as expected (see Table 1). Indeed, the hydrodynamic volume accessible by dynamic light scattering, overestimates the real size.43 Convergence between radii measured by DLS and extracted by CDMS is observed for heavier samples. The surface charges of all the nanoparticles produced were investigated both by charge detection mass spectrometry and zeta potential measurements. Charge versus Mass Dependence z(m) on Electrosprayed Polymer Nanoparticles. CDMS allows detection at the single ion level. Thus, for each ion the value of the charge can be plotted as a function of the mass. Data obtained for two different samples (samples L2 and L3, see Table 1) are plotted in the graphs displayed in Figure 1 in both positive and negative modes. The mass to charge plots show that each sample displays a broad distribution both in mass and in charge. The broadness is due to the dispersion in the degree of polymerization. The charging capacity of each sample is similar in both polarity mode of ionization, as also observed for biomolecular macromolecules51 and micellar particles.43 However, for several samples the ion efficiency in ESI negative mode was severely reduced (by at least 1 order of magnitude). Furthermore, the spray conditions under negative ion mode using the standard electrospray inlet were much more difficult to reproduce and maintain than those under positive ion mode. Especially, in the negative ionization mode the source is prone to discharges. Concerning the nature of charges, in positive mode and for cationic latexes, the charges are certainly due to amidino groups. On the other hand, for anionic latexes the charges are certainly due to SO4− groups in ESI negative mode. Amidino and SO4− groups come from the initiator molecules used for the synthesis of cationic and anionic PNPs. To better address the nature of charges, we perfomed MS analysis with a quadrupole linear ion trap (LTQ, Thermo Fisher Scientific, San Jose, CA). Both cationic and anionic latexes were synthesized in order to perform a kinetic follow out using the LTQ mass

Figure 1. Mass to charge plot for L2 and L3 polymer nanoparticles (see Table 1) in positive and negative ESI modes. The solid curve gives the predicted Rayleigh’s limit based on eq 1 for water/methanol mixture (50:50, v/v).

spectrometer. During the synthesis, samples were taken at 10 min, 20 min, and 1 h of reaction and the polymerization was stopped by cooling in the fridge at around 6 °C. Samples were then analyzed by our MS instrument. For cationic and anionic samples at early step of polymerization (between 10 nm and 1 h), distributions of polymer ions are clearly observed and have permitted to confirm the nature of charges observed in electrospray ionization (Figure 2) (e.g., amidino and SO4− groups, see Figures S2 and S3 in Supporting Information). However, the nature of charges, in positive (negative) mode and for anionic (cationic) latexes, is less clear. The assignment of peaks in mass spectra is less evident. For cationic samples in negative ESI mode, the isotopic pattern of MS peaks show the presence of chlorine atoms present in V50, (see Figure S2 in

Figure 2. Schematic representation of the structure of (a) anionic and (b) cationic polymer nanoparticles bearing sulfate and amidino groups, respectively. 14077


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Supporting Information). We propose that chlorine adducts contribute to negative charges in MS spectra of latexes. In the same way, for anionic samples in positive ESI mode the positive charges are assigned to ammonium adducts (present in APS). Note that both zeta potential in solution and the charging of PNPs in the gas phase are little sensitive to pH and salt concentration (i.e., NaCl) as exemplified with L5 in Figures S4 and S5 in Supporting Information. As intuitively expected, the number of charges on a particle increases with the size of the particle. Experimental results are compared with the Rayleigh charge zR, which corresponds to the maximum charge that a spherical droplet can hold. The Rayleigh’s limiting charge depends on the size and surface tension γ of the droplet and can be expressed as a function of the mass m (assuming spherical geometries) by 3 ⎞1/2

⎛ γε R z R = 8π ⎜ 02 ⎟ ⎝ e ⎠

⎛ 3γε π ⎞ = 4⎜ 2 0 ⎟ ⎝ e NAρ ⎠

σ=

⎡ ⎢ 2 ⎢1 + 1 κR h cosh2 eζ ⎢ 4kBT ⎢⎣

( )

+

1 κ 2R h2

⎡ 8 ln⎢cosh ⎣

⎤1/2

( )⎤⎥⎦ ⎥⎥ sinh ( ) ⎥⎥⎦ 2

eζ 4kBT

eζ 2kBT

(3)

where κ is the Debye−Hückel parameter. From σ and Rh, one can calculate the effective charge number zeff of the particle by zeff =

8πεrε0 e

2

⎛ eζ ⎞ κkBTR h2 sinh⎜ ⎟ ⎝ 2kBT ⎠

⎡ ⎢ 2 ⎢1 + 1 κR h cosh2 eζ ⎢ 4kBT ⎢⎣

( )

1/2

+

1 κ 2R h2

⎡ 8 ln⎢cosh ⎣

⎤1/2

( )⎤⎥⎦ ⎥⎥ sinh ( ) ⎥⎥⎦ 2

eζ 4kBT

eζ 2kBT

(4)

19

It was demonstrated by Ibrahim et al. that eq 4 was the most suitable equation for the effective charge determination of nanoparticles from electrophoretic mobility and Rh values at a given ionic strength. The zeta-potential (ζ) extracted from electrophoretic mobility, using the graphical determination given in Ohshima49 (see Figure S1 in Supporting Information) was then directly converted into an effective charge (zeff) using eq 4. Results are given in Table 1. Correlation between the Charge of Polymer Particles in Solution and in the Gas Phase. The effective charges (zeff) extracted from the measured zeta-potential (ζ) of PNPs in solution were compared with the average values of charge ⟨zCDMS⟩ of the same particles extracted from gas phase measurements by CDMS. For sake of simplicity, we compared absolute values for zeff and ⟨zCDMS⟩. Results for PNPs (in both positive and negative ESI modes) are displayed in Figure 3a). They show a good correlation between zeff and for both latexes. The correlation coefficient is defined as

m1/2 (1)

In eq 1, ε0 is the vacuum permittivity, NA is the Avogadro constant, ρ, R, and m are respectively the density, the radius, and the mass of droplet, and e is the electron charge. We used ρ = 1 g/cm3 and γ = 0.0473 N/m. The solid curve in Figure 1 gives the evolution of the charge versus the mass z(m) based on eq 1. The trend of the experimental values follows the Rayleigh’s prediction, while the absolute values are lower. From the charge versus mass z(m) distributions, an average value of charge ⟨zCDMS⟩ was extracted for each sample. These values are reported in Table 1. Zeta-Potential and Effective Charges of Polymer Nanoparticles. The zeta-potential is related to the surface charge of a particle. However, for nanoparticles, there is no simple analytical formula available for the calculation of an effective charge from the zeta potential measurements. Considering a spherical colloidal particle of radius Rh in a symmetrical 1−1 type electrolyte solution, the electric potential ψ(r) at a distance r (r ≥ Rh) from the center of the particle satisfies the spherical Poisson−Boltzmann (PB) equation (in SI units):14 ⎛ eψ ⎞ d2ψ 2 dψ 2en + = sinh⎜ ⎟ 2 εrε0 r dr dr ⎝ kBT ⎠

⎛ eζ ⎞ 2εrε0 κkBT sinh⎜ ⎟ e ⎝ 2kBT ⎠

n

rZCDMS, Zeff =

∑i = 1 (ZCDMS, i − ZCDMS )(Zeff, i − Zeff ̅ ̅ ) n

n

2 ∑i = 1 (ZCDMS, i − ZCDMS )2 ∑i = 1 (Zeff, i − Zeff ̅ ̅ )

(5)

where the summation is performed over the n PNP batches of polymer used for this work. The corresponding rZCDMS,Zeff value is equal to 0.89. In this work however, the molecular weight of latexes is not constant and it is well-known that the number of charges on a particle increases with the size of the particle (thus the molecular weight MW). In Figure 3b,c), the charges of PNPs in solution (zeff) and in the gas phase (⟨zCDMS⟩) are plotted as a function of their molecular weight. Charges are correlated to the molecular weight with a stronger correlation in the gas phase (rZCDMS,MW = 0.94) than in solution (rZeff,MWrZeff,MW = 0.79). To overcome this dependence, one can perform partial correlation. Partial correlation is a procedure that allows determining what the correlation between any two of the variables would be (hypothetically) if they were not each correlated with the third variable. The partial correlation coefficient can be defined as

(2)

where e is the elementary electric charge, n is the electrolyte concentration, εr is the relative permittivity of the solution, ε0 is the vacuum permittivity, kB is the Boltzmann constant, and T is the absolute temperature. Ohshima et al. approximated the spherical PB equation by another readily solvable differential equation.15 They obtained analytic expressions of remarkable accuracy for the surface charge density/surface potential relationship and double-layer potential distribution of a spherical colloidal particle. Assuming a spherical geometry of the particle and a uniform charge distribution on its surface, the electric charge density (σ) at the plane of shear for a given ζ and a given Rh can be calculated using the following empirical equation derived by Ohshima et al.15

rzCDMSzeff ,MW =

rzCDMS,zeff − (rzCDMS,MW )(rzeff ,MW ) (1 − (rzCDMS,MW )2 ) (1 − (rzeff ,MW )2 )

(6)

The partial correlation rZCDMSZeff,MW then turns out smaller (0.70) than the original correlation rZCDMS,Zeff (0.89). The two 14078


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the limited correlation in charging between gas phase and solution.

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CONCLUSION Surface charges of anionic and cationic PNP have been investigated both in gas phase by charge detection mass spectrometry combined to electrospray ionization source and in solution by zeta potential measurements. The correlation between the magnitude of charging of PNPs ions produced in the gas phase with the PNPs surface charge in solution demonstrates that the mass spectrometry-based analysis described in this work is an alternative and promising way for a fast and systematic characterization of charges of colloidal particles. The effective charges (zeff) extracted from the measured zeta-potential (ζ) of PNPs in solution are partially correlated with the average values of charge ⟨zCDMS⟩ of PNPs in the gas phase. Also, a more thorough study with colloidal objects for which molecular weight are the same and surface charging would be changed using different ligand-coated NPs is required to enable the universality of this correlation. Particularly, it should be emphasized that the present ESICDMS study characterizes dispersion properties on an objectby-object basis and represents a new approach for understanding and investigating dispersity in biological and synthetic colloids, which is not possible by current ensemble analysis techniques. Indeed, information gained at the single-molecule level is richer than the mere averages, as it provides insight into the charging mechanism through the correlation between various observables (e.g., molecular weight and charge) for a given PNP sample.

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Figure 3. (a) Absolute values of effective charges (zeff) extracted from the measured zeta-potential (ζ) of PNPs in solution compared with the average absolute values of charge ⟨zCDMS⟩ of the same particles extracted from gas phase measurements by CDMS. Results for (black square) positive and (red square) negative ESI modes. Plots of absolute values of (zeff) (b) and ⟨zCDMS⟩ (c) as a function of the mass of the PNPs. The zeta-potential (ζ) extracted from electrophoretic mobility, using the graphical determination given in Ohshima49 (see Figure S1 in Supporting Information) was then directly converted into an effective charge (zeff) using eq 4.

ASSOCIATED CONTENT

S Supporting Information *

Electrophoretic mobility μ as a function of κRh for different zeta potential (ζ) values according to Ohshima (J. Colloid Interface Sci. 2001, 239, 587). MS spectra of cationic and anionic polymer samples at early step of polymerization. Evolution of the absolute average charge obtained by CDMS, zeta potential, and the hydrodynamic radius for sample L5 as a function of the pH and salt concentration in solution. Absolute values of effective charges (zeff) extracted from the measured zetapotential (ζ) using the Smoluchowski’s relation of PNPs in solution compared with the average absolute values of charge ⟨zCDMS⟩. This material is available free of charge via the Internet at http://pubs.acs.org.

other partial correlations (i.e., rZCDMSMW,Zeff and rZeffMW,ZCDMS) are 0.84 and −0.30 respectively. A decrease from 79 to 50% in covariation (rZCDMSZeff2 and rZMSZeff,MW2) means that the correlation between charging in solution and in the gas phase remains, even after removing the influence of molecular weight. Similar correlations are obtained if the effective charges (zeff) are calculated using eq 4, from zeta-potentials (ζ) extracted from electrophoretic mobility, using the Smoluchowski’s relation, as currently proposed by default in the commercial Malvern software (see Figure S6 in Supporting Information). So, the important result here is that partial correlation shows that charge distributions in solution and in the gas phase are correlated independently of the size of the particle. The main difference between the charging in the gas phase and in solution is the presence of counterions in solution. The consequence of this is that charging in the gas phase is limited by the Coulombic repulsion (Rayleigh limit) while in solution, it is mainly related to the number of ionizable groups. This explains why molecular weight and charges are strongly correlated in the gas phase (rZCDMSMW,Zeff = 0.84) while this is not the case in solution (rZeffMW,ZCDMS = −0.30). This also certainly accounts for

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to the ANR for financial support of this work (ANR-11-PDOC-032-01). REFERENCES

(1) Rivera-Gil, P.; Jimenez De Aberasturi, D.; Wulf, V.; Pelaz, B.; Del Pino, P.; Zhao, Y.; De La Fuente, J. M.; Ruiz De Larramendi, I.; Rojo, T. F.; Liang, X.-J.; Parak, W. J. The Challenge To Relate the Physicochemical Properties of Colloidal Nanoparticles to Their Cytotoxicity. Acc. Chem. Res. 2013, 46, 743−749.

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