Journal of Chromatography A, 1370 (2014) 255–262

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Generalized polymer effective charge measurement by capillary isotachophoresis Joseph Chamieh a,1 , Duˇsan Koval b,1 , Adeline Besson a , Václav Kaˇsiˇcka b , Hervé Cottet a,∗ a Institut des Biomolécules Max Mousseron (UMR 5247 CNRS—Université de Montpellier 1—Université de Montpellier 2), place Eugène Bataillon CC 1706, 34095 Montpellier Cedex 5, France b Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, v.v.i., Flemingovo n. 2, 166 10 Prague 6, Czech Republic

a r t i c l e

i n f o

Article history: Received 14 June 2014 Received in revised form 3 October 2014 Accepted 9 October 2014 Available online 18 October 2014 Keywords: Polymer effective charge Polyelectrolyte Isotachophoresis Counter-ion condensation Capillary electrophoresis

a b s t r a c t In this work, we have generalized the use of capillary isotachophoresis as a universal method for determination of effective charge of anionic and cationic (co)polymers on ordinary capillary electrophoresis instruments. This method is applicable to a broad range of strong or weak polyelectrolytes with good repeatability. Experimental parameters (components and concentrations of leading and terminating electrolytes, capillary diameters, constant electric current intensity) were optimized for implementation in 100 ␮m i.d. capillaries for both polyanions and polycations. Determined values of polymer effective charge were in a very good agreement with those obtained by capillary electrophoresis with indirect UV detection. Uncertainty of the effective charge measurement using isotachophoresis was addressed and estimated to be ∼5–10% for solutes with mobilities in the 20–50 × 10−9 m2 V−1 s−1 range. © 2014 Elsevier B.V. All rights reserved.

1. Introduction The effective charge of a macromolecule can be defined as the real charge of the macromolecule entity taking into account all the ionized groups and any ionic species tightly associated with it [1]. This parameter has a primary role in the control of interactions between charged species in solution [2–6]. It sets the strength of the relatively long-range electrostatic force between charged compounds. It also plays a great role in entropic effects such as those observed during the formation of polyelectrolyte complexes [7] due to counter-ion release. The determination of polymer effective charge remains a challenging issue because it depends on multiple parameters such as pH (dissociation or protonation of ionogenic moieties), counter-ion condensation [8,9] and possibly on specific interactions such as hydrophobic effects [10–12] and weak interactions [13]. Different methods have been investigated for polymer effective charge determination including conductivity measurements [14], osmotic pressure [15], scattering techniques [16] and electrophoretic techniques [17–25]. Conductivity and osmotic pressure measurements are generally performed in the absence of additional salts (or at very low ionic strength), while neutron scattering

∗ Corresponding author. Tel.: +33 4 6714 3427; fax: +33 4 6763 1046. E-mail address: [email protected] (H. Cottet). 1 These authors contributed equally. http://dx.doi.org/10.1016/j.chroma.2014.10.025 0021-9673/© 2014 Elsevier B.V. All rights reserved.

techniques requires specific and restricted-access source of radiations. Electrophoretic techniques can be applied at a given ionic strength in the typical 5–100 mM range. Regarding electrophoretic methods, one can distinguish two kinds of approaches. A first group is based on electrophoretic mobility measurement combined to electrophoretic modeling, as described, e.g. in ref [25]. These approaches are generally based on the experimental determination of the electrophoretic mobility and size (hydrodynamic radius) in combination with a theoretical model. This approach is well suited for small ions and nanoparticles (hardcore charged spheres) but is not yet applicable to polyelectrolytes due to the lack of suitable theoretical model. Numerical simulations can also be used [26–31] but these approaches are computationally time consuming and, as a consequence, limited so far to the study of oligomeric chains. A second group is basically relying on the Kohlrausch regulating function (KRF) [19] or on electroneutrality and electric current conservation [12,17,20], allowing a direct determination of the effective charge by capillary electrophoresis using indirect UV detection mode (IUV) [19] or by capillary isotachophoresis (ITP) using conductometric or UV-absorption detection [12,17,20]. The IUV method consists in determining the effective charge from the transfer ratio (i.e. the quantity of chromophore displaced per mole of analyte), which is measured from the sensitivity of detection (i.e. from the peak area of solute knowing its injected concentration). Applicability of the IUV method relies on the availability of a chromophore that absorbs UV radiation at the wavelength, at which the

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solute is transparent, and that does not interact with the solute (no specific interaction or adsorption). For instance, in the case of linear and dendritic polylysines, it was difficult to find such a suitable chromophore and the ITP method was used instead of IUV [12]. The ITP method [12,17,20] is based on the linear dependence of the ITP zone length on the solute effective charge and concentration. It does not require any chromophore and seems thus more general than IUV. Nevertheless, the ITP mode requires the definition and the use of discontinuous electrolyte system composed of leading and terminating electrolytes, respectively, noted LE and TE. Specific equipments dedicated to ITP were developed in the past [32], especially for small ion analysis, and can of course be used for effective charge determination. However, to develop the wide applicability of the ITP method for polymer charge determination, it would be helpful to use ordinary capillary electrophoresis instruments that are much more common than ITP apparatus. Also, CE equipment would allow the automation and miniaturization (nL injected compared to ␮L) of the ITP method. This work aims to broaden application range of ITP based measurement of effective charge of various types of cationic and anionic polymers. Then, accessibility of this approach has been addressed by method transfer from specific ITP instrument to more common CE devices. To this end, experimental conditions in terms of electrolyte systems and operating conditions were studied, for both types of instruments, according to the characteristics of the polymers, having different charge densities, with strong or weak acidobasic moieties. This work also investigates the role of the operating experimental conditions and of the solute characteristics on the precision of the polymer effective charge determination.

interval and that polymer ionogenic groups are totally dissociated or protonated. Further, it is presumed in Eq. (1) that internal standard and polymer are mixed together and injected concomitantly. 2.2. Precision of the effective charge determined by ITP To get a better insight on the precision obtained for the determination of the effective charge zi of a given solute, it is convenient to differentiate Eq. (1) relative to all the experimental parameters: dzi dti dtref dc dc = + + i + ref + d ln zi ci cref ti tref

dlnzi =

2.1. Effective charge determination by ITP

(1)

where subscripts i, ref, and c refer to the species of interest, internal standard, and counter ion in corresponding ITP electrolyte system, respectively. Then, z stands for the charge number, t the zone length in time units, c the molar concentration, and  is the actual ionic mobility, i.e. mobility of fully dissociated ion at actual ionic strength and temperature. Note that absolute value of mobilities is used for effective charge calculation according to Eq. (1). For clear interpretation of effective charge, it is convenient to express concentration of polymer to be used in Eq. (1) as molar concentration of a monomer unit c1 . In the case of copolymers, concentration of charged monomer c1 is given by: c1 =

fcm,polymer fM1 + (1 − f )M2

(2)

where cm,polymer is the mass concentration in copolymer, M1 the molar mass of a charged monomer, M2 the molar mass of the uncharged monomer and f is the molar fraction of charged monomers in the copolymer [19]. Further, f, also called the chemical charge density, is expressed as: f =

N1 N1 + N2

ref



(4) Setting A = d ln A =

dA = A + +

 

i (ref +c ) , ref (i +c )

1

i



one gets:

1 i + c

 di

1 i − ref + c ref (i + c ) 1 i − ref + c i + c

 dref



dc

(5)

The overall uncertainty on the zi calculation is finally given by: zi (ti ) (tref ) ci cref = + + + zi ci cref ti tref

    1  1 1      −  +   i +   +  −  ( i+  )  ref c c c ref ref i i i   1 1   + − (6)  c  +  + ref

In our previous report [12], we developed a procedure for calculation of effective charge zi of charged species i as: ti cref i,z (ref,z + c,z ) tref ci ref,z (i,z + c,z )

+ c ) ref (i + c ) i

+

2. Theory

zi = zref

  (

(3)

where N1 is the number of moles of charged monomers and N2 is the number of moles of uncharged monomers in the copolymer sample. As pointed out previously [12], validity conditions of Eq. (1) are that pH of the ITP electrolytic system lies inside the “safe” 4–10

c

i

c

Three different terms can be distinguished in Eq. (6): (i) the uncertainty relative to the determination of the time of the solute and reference ITP zone length; (ii) the uncertainty relative to the sample concentrations of the solute and the reference; and (iii) the uncertainty relative to the actual ionic mobilities of the solute, the reference and the counter-ion. The relative importance of these terms according to the experimental conditions is discussed in Section 4.4. 3. Experimental 3.1. Chemicals and materials Linear poly-␣-l-lysine (PLL) hydrochloride, Mn 9000 (Lot number: KC050-102) and poly-␣-l-glutamic acid (PGlu) sodium salt, Mn 15,900 (Lot number: E100-104) were obtained from Alamanda Polymers (Huntsville, AL, USA). Poly(2-acrylamido-2methyl-1-propanesulfonic acid) (PAMPS) and statistical copolymer poly(acrylamide-co-2-acrylamido-2-methyl-1-propanesulfonic acid), f (chemical charge density) = 10% (PAMAMPS 10%) were prepared in laboratory as described in supplementary information (SI) and [33–35]. The polymers were re-lyophylised prior to sample preparation in order to limit moisture content in the solid product. Internal standards benzoic acid, 5-sulfosalicylic acid, 2-amino-2-methyl-1,3-propanediol (Ammediol) as well as electrolyte components were obtained from major chemical vendors at the best available purity to prevent formation of interfering zones in ITP (see SI for product specification). Standard 18 M cm deionized water was used for preparation of the solutions. Fused silica capillaries of 100/375 ␮m i.d./o.d. with polyimide outer coating (cat. no. TSP100375) were from Polymicro Technologies

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(Phoenix, AZ, USA). For suppression of electroosmotic flow (EOF), capillaries were modified with hydroxypropylcellulose (HPC) as described elsewhere [36–38].

3.2. ITP experimental conditions Capillary electrophoresis analyzer Agilent 1600 (hereafter referred as CE apparatus) with built-in UV–vis diode array detection module was in addition equipped with the TraceDec contactless conductivity detector (Innovative Sensor Technologies, Strasshof, Austria). Total length of 100 ␮m i.d. capillaries was 58.5 cm. Detection points were 44.5 and 50.0 cm from capillary inlet for the conductivity and the UV–vis detectors, respectively. The capillary was rinsed with leading electrolyte at 1 bar for 1 min between runs; samples were introduced into the capillary hydrodynamically. Temperature of the capillary cartridge was set at 25 ◦ C. UV traces were monitored at 200 nm. C4 D detector parameters were adjusted in order to have a signal between 100 and 2000 mV for all buffer solutions (see SI for all parameters). Isotachophoretic analyzer (hereafter referred as ITP apparatus) was a coupled column EA101 model from Villa Labeco

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(Spiˇsská Nová Ves, Slovakia) equipped with contactless conductivity detection. Column material was fluorinated ethylene propylene copolymer (FEP). Samples were introduced with Hamilton syringes (model 7102 and 701). Separations were carried out at ambient temperature. This ITP device allows preseparation of the sample in larger column (800 ␮m i.d., 16 cm length) and subsequent inline transfer of selected zones to narrow bore analytical column (300 ␮m i.d., 16 cm length) (see Fig. 1a). However, this functionality was not employed and injected sample was in fact entirely transferred into the narrow bore column in all ITP experiments used to effective charge determination.

4. Results and discussion 4.1. Isotachophoretic systems for effective charge measurement of cationic and anionic polymers The ITP method for measurement of polymer effective charge relies on the following conditions: (i) the polymer is totally dissociated or protonated; (ii) it forms a stable zone that is well separated from other migrating components; (iii) a contribution of hydrogen

Fig. 1. Schematic representation of a dedicated ITP apparatus (a) and a CE apparatus (b). Both analyzers were used in this work for measurement of effective charge of selected polymers (c) by capillary ITP. Description: (a) ITP apparatus; C1, preseparation column; C2, analytical column; D1 and D2, on-column conductivity detectors; M1 and M2, semipermeable membranes allowing a closed system by shielding the separation capillaries from the electrode compartments; LE1 and LE2, leading electrolyte compartments for preseparation and analytical columns, respectively; TE, terminating electrolyte compartment; HV, high-voltage supply; S, septum for injection with a syringe; V, sampling and rinsing valve; (b) CE apparatus; C; separation capillary; D, on-column conductivity detector; LE, leading electrolyte compartment; TE, terminating electrolyte compartment; HV, high-voltage supply.

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and hydroxide ions to electric current in analyte zone is marginal, which in fact limits pH range to 4–10; (iv) intermolecular interactions of the polymer with components of ITP electrolyte system are negligible. In our previous report [12], we utilized ITP system for effective charge measurement of cationic polymers. The leading ion was ammonium, hydrogen ion was terminator and acetate served as buffering counter-ion. The working pH of 4.6 was appropriate for determination of effective charge of a series of linear and branched polylysines. In the present work, we slightly modified the ITP system by lowering its pH in order to favor the complete protonation of cationic polymers. Specifically, a LE composed from 10 mM ammonium hydroxide + 40 mM acetic acid stabilizes pH in the polymer zone to 4.0–4.1. The effective mobility of leading ammonium ion is ∼76.1 × 10−9 m2 V−1 s−1 in the corresponding LE and the effective mobility of trailing hydrogen ion is ∼23 × 10−9 m2 V−1 s−1 in the corresponding acetate TE (see Fig. 2 and SI for details). As for the characterization of polyanions, and in contrast to cationic ITP, migration of carbonates needs to be considered in development of anionic ITP system. In fact, carbon dioxide from air is absorbed by the electrolytes of pH ∼6.5 and higher (see Fig. S2). The (hydrogen)carbonate ions are then continuously focused between LE and TE during the ITP run and can interfere with analyzed charged polymers. To circumvent, we used one ITP system for strong polyelectrolytes at pH 4.9 composed of 10 mM hydrochloric acid + 20 mM creatinine as leading electrolyte, in which carbonate zone is not formed (see Fig. 3). TE was composed of 10 mM MES + 20 mM creatinine pH 5.6. However, weak polyelectrolytes require pH sufficiently high to assure complete ionization. Thus, ITP electrolyte system needs to be carefully selected to avoid interference of the polymer with carbonates. It turned out that for weak polyelectrolyte such as PGlu, suitable ITP system is 10 mM hydrochloric acid + 30 mM 4-hydroxyethylmorpholine (HEM) LE at pH 7.2 and 10 mM HEPES + 10 mM HEM TE at pH 7.6 (see Fig. 4). In the latter case, creatinine was replaced by HEM to increase the pH ensuring full ionization of the weak polyelectrolyte and separation with carbonates (see Fig. S2 for the choice of electrolytes).

4.2. Comparison of instrumentation and choice of the experimental conditions according to solute characteristics ITP and CE are electromigration methods based on the same electrochemical principles, but differing in terms of experimental setup, application range, and also instrumentation. As emphasized in Table 1, a principal difference between typical instruments for ITP and CE can be noted in higher level of miniaturization of CE instruments. Dedicated ITP apparatus used here and in our previous work [12] comprise two coupled capillary tubes of i.d. of 800 and 300 ␮m. The columns are in vertical arrangement and hydrodynamic flow due to gravity is eliminated by semipermeable membranes placed between electrolyte compartments and capillary tubes (see Fig. 1a). In contrast, thin capillaries of i.d. typically below 100 ␮m are used in CE. Hydrodynamically open arrangement is employed with equal level of electrolyte in the vials to avoid siphoning effect (see Fig. 1b). Consequently, larger i.d. capillaries used in ITP apparatus allow for microliter range injection volumes vs ∼50 nL in the case of CE (see Table 1 for comparison). Traditionally, ITP instruments are run with FEP capillaries which generate rather slow EOF. CE relies heavily on fused silica capillaries and, for ITP experiments, neutral coatings are generally used to suppress EOF. Contact or contactless conductivity is universal detection mode in ITP instruments. In CE apparatus, analytes are mainly detected by UV absorption. However, optional contactless conductivity detector can be integrated to enable full ITP experiments.

Fig. 2. ITPgrams of a polycation PLL in a cationic electrolyte system at pH 4.2 obtained with a CE apparatus (a) or a dedicated ITP analyzer (b). Displayed ITPgrams are that of PLL and ammediol (black trace), its 1st derivative (red trace) used for determination of zone start and end, and a blank run (blue trace). Experimental conditions: LE, 10 mM NH4 OH + 40 mM AcOH, pH 4.2; TE, 40 mM AcOH, pH 3.1; sample, 5 g L−1 PLL (i.e. 30.4 mM in Lys monomer) + 15 mM ammediol in water; specifically for the CE apparatus: capillary, HPC coated fused silica, 100 ␮m i.d., 58.5 cm total length; current 10 ␮A; hydrodynamic injection 8 mbar for 10 s, temperature 25 ◦ C; specifically for the ITP apparatus: preseparation column, FEP, 800 ␮m i.d., 16 cm length; analytical column, FEP, 300 ␮m i.d., 16 cm length; current, preseparation 250 ␮A, analytical step 30 ␮A; syringe injection 1 ␮L; temperature, ambient (23 ◦ C). Electrophoretic actual ionic mobilities used for effective charge calculations: ref (Ammediol) = 28.5 × 10−9 m2 V−1 s−1 ; i (PLL) = 45.4 × 10−9 m2 V−1 s−1 , and c (acetate) = 38.8 × 10−9 m2 V−1 s−1 For interpretation of the color information in this figure legend, the reader is referred to the web version of the article.

In order to convert an ITP method from the ITP dedicated instrument to the CE device, technical aspects summarized in Table 1 should be taken in account. Notably, one must find the adequate combination between the applied constant electric current, the electrolyte concentrations and the capillary i.d. Then, higher driving current can be applied in large bore while corresponding voltage achieves moderate values. In narrow CE capillaries, constant current in ITP experiments needs to be lower as the voltage instrument limit can be easily reached. Concentration of LE is a straightforward way to tune electric conductivity of the ITP electrolyte system. In

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Fig. 3. ITPgrams obtained on a CE apparatus (a) or on a dedicated ITP system (b) for the analysis of weakly charged (PAMAMPS, f = 10%) (green trace) or highly charged (PAMPS, f = 100%) (black trace) strong polyacids at pH 5 accompanied by a blank run (blue trace). Experimental conditions: LE, 10 mM HCl + 20 mM creatinine pH 4.9; TE, 10 mM MES + 20 mM creatinine pH 5.7. Specifically for the CE apparatus: current −5 ␮A; hydrodynamic injection: 8 mbar for 10 s; injected polymer concentration: 3.97 g L−1 PAMPS 100% (i.e. 17 mM in AMPS monomer) + 2 mM sulfosalicylate and 4.27 g L−1 PAMAMPS 10% (i.e. 4.9 mM in AMPS monomer) + 2 mM sulfosalicylate; temperature 25 ◦ C; specifically for the ITP apparatus: current, preseparation −250 ␮A, analytical step −40 ␮A; injected polymer concentrations: 14 mM of AMPS monomer in PAMPS + 2.3 mM sulfosalicylate and 3.9 mM of AMPS monomer in PAMPAMPS copolymer + 2.3 mM sulfosalicylate; syringe injection, 5 ␮L. Samples were dissolved in water. Electrophoretic actual ionic mobilities used for effective charge calculations: ref (sulfosalicylate) = 50.9 × 10−9 m2 V−1 s−1 ; i (PAMPS) = 40.4 × 10−9 m2 V−1 s−1 , i (PAMAMPS, f = 10%) = 23.1 × 10−9 m2 V−1 s−1 and c (creatinine) = 37.2 × 10−9 m2 V−1 s−1 . Other experimental conditions for CE and ITP are the same as in Fig. 2 For interpretation of the color information in this figure legend, the reader is referred to the web version of the article.

addition, concentration of the leading ion cL governs the concentration of the solute in its ITP zone ci [39]: ci = cL

i L + c i + c L

(7)

Note that absolute value of mobilities is used in Eq. (7). It means that for constant amount of the solute injected, shorter zone length is obtained for more concentrated LE. Therefore, an increase in cL tends to decrease the solute zone length for a given injected

259

Fig. 4. ITPgrams of a weak polyanion PGlu in an anionic electrolyte system at pH 7.2 obtained with a CE apparatus (a) or a dedicated ITP analyzer (b). Displayed ITPgrams are that of PGlu and benzoate (black trace), and a blank run (blue trace). Experimental conditions: LE, 10 mM HCl + 30 mM 4-(2-hydroxyethyl)morpholine, pH 7.2; TE, 10 mM HEPES + 30 mM 4-(2-hydroxyethyl)morpholine, pH 7.6; specifically for the CE apparatus: current, −8 ␮A; sample, 11.4 g L−1 PGlu (i.e. 75.2 mM in Glu monomer) + 18.9 mM sodium benzoate in water; hydrodynamic injection 20 mbar for 10 s; specifically for the ITP apparatus: current, preseparation, −250 ␮A, analytical step, −40 ␮A; sample, 1.65 g L−1 PGlu (i.e. 10.9 mM in Glu monomer) + 3.5 mM sodium benzoate in water; syringe injection, 5 ␮L. Electrophoretic actual ionic mobilities used for effective charge calculations: ref (benzoate) = 29.9 × 10−9 m2 V−1 s−1 ; i (PGlu) = 41.0 × 10−9 m2 V−1 s−1 , and c (HEM) = 32.1 × 10−9 m2 V−1 s−1 . Other experimental conditions for CE and ITP are the same as in Fig. 2 For interpretation of the color information in this figure legend, the reader is referred to the web version of the article.

amount. It is, however, necessary to keep reasonable zone lengths in order to control uncertainty of effective charge measurement (see the following Section 4.3). Concentration of LE should then be set appropriately since limitation exists for injected amount: (i) viscosity of concentrated polymer solutions can hamper sample handling, hydrodynamic injection, and ITP process, (ii) excessive injection volume compromises separation resolution. In addition, experimental conditions have to be selected so as to assure steadystate formation in ITP process (see the SI for details), which is fundamental for validity of the presented method for effective charge measurement.

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Table 1 Main characteristics of ITP experiments on ITP or CE apparatus used in this work. Apparatus

ITP

CE

Injected volume Injection mode

1–5 ␮L

∼50 nL

Syringe (manual)

Hydrodynamic (automatic) Rinsing/injection/ separation/detection

Rinsing/injection/ preseparation/separation/ detection Fluorinated ethylene propylene (FEP) Preseparation: 800 ␮m × 16 cm Separation: 300 ␮m × 16 cm Closed capillaries (with membranes) 200–250 ␮A (preseparation step) 30–40 ␮A (separation step) 1–7 kV in pre separation step 2–11 kV in separation step Contactless conductivity (2 detection points) Ambient (23 ◦ C) 20–30 min

Method

Capillary material Capillary dimensions

Hydrodynamic system Constant current intensity Voltage range

Detector(s)

Temperature Analysis time

Hydroxypropylcellulose coated fused silica 100 ␮m × 58.5 cm (44.5/50 cm to the conductivity/UV detector, respectively) Open capillaries 5–8 ␮A

5–30 kV

UV-absorption and contactless conductivity Air cooled at 25 ◦ C 10–20 min

To this end, to carry out ITP measurements on the CE analyzer, LEs comprising 10 mM leading ion concentration were used with 100 ␮m i.d. capillaries of approx. 60 cm of total length (see Table 1). It allowed decent driving constant current of 5–8 ␮A to keep analysis time short and not to exceed the 30 kV instrument voltage limit. 4.3. Determination of the polymer effective charge A set of synthetic polymers for demonstration of the ITP method for effective charge calculation comprised weak polycation PLL 50, weak polyanion PGlu, and strong polyanions with high and low charge density PAMPS 100% and PAMAMPS 10%, respectively (see Fig. 1c). ITP analyses of polymers and internal standards (see Table 2 for details) are summarized in Figs. 2–4. Electrophoretic mobilities for effective charge calculation according to Eq. 1 were mostly determined experimentally by CE with double UV and conductivity detectors (see SI and [40–42]). In part, electrophoretic mobilities of some of electrolyte components were obtained from PeakMaster simulations (http://web.natur.cuni.cz/∼gas/). The polymers were analyzed in parallel using CE and ITP analyzers according to Table 2 Electrolyte systems and internal standards used for measurement of polymer effective charge by capillary ITP. Sample

LE

TE

Internal standard

PGlu (weak polyacid)

10 mM HCl + 30 mM HEM, pH 7.2 10 mM HCl + 20 mM creatinine, pH 4.9

10 mM HEPES + 30 mM HEM, pH 7.6 10 mM MES + 20 mM creatinine, pH 5.7

Benzoate

10 mM NH4 OH + 40 mM AcOH, pH 4.2

40 mM AcOH, pH 3.1

Ammediol

PAMPS 100% and PAMAMPS 10% (highly or weakly charged strong polyacid) PLL (polybase)

Sulfosalicylate

specifications provided in Table 1 (see Figs. 2–4 for corresponding ITPgrams). Apparently, effective charge values measured with the CE instrument match those obtained with the ITP analyzer for all analyzed polymers with an average difference between measurements in the two instruments of about ∼5% (see Table 3). In addition, effective charge of PGlu, PAMPS 100%, and PAMAMPS 10% from the ITP experiments are in a good agreement with data obtained previously by CE with IUV detection. As for PLL 50, IUV method was not applicable since no suitable chromophore could be found, as previously discussed [12]. On the whole, the three methods (CE, ITP and IUV) lead to similar results. Regarding the comparison of the effective charge values with the theoretical value predicted by Manning theory (see the last column in Table 3), a very good agreement was obtained for PLL and PAMPS samples with different values for the two samples due to different charge spacing for polypeptide and vinylic polymers. For PGlu and PAMAMPS 10%, lower effective charges were obtained compared with the expected theoretical values. In the case of PAMAMPS copolymer, the lower experimental effective charge (z1 ∼0.73–0.79 vs 1) was explained by a non-perfect statistical repartition of the charged groups [19] leading to rich AMPS sequences monomers within the polymer chain. This explanation was supported by the differences between reactivity ratios for the two monomers [33,43]. For PGlu, slightly lower experimental effective charges z1 (0.36–0.39) compared with the expected Manning theoretical value (0.50) can be explained by incomplete dissociation of some glutamic acid residues at pH ∼7.4 [44]. Repeatability of the method with CE and ITP devices was evaluated for all samples on the basis of 7 successive injections. Repeatability was slightly better for CE (average RSD of ∼2%) than for ITP (average RSD of ∼5%). In the next section, the uncertainty of the effective charge measurement is discussed. 4.4. Uncertainty on the effective charge determination To shed more light on the contribution of experimental parameters to the error of effective mobility measurement using Eq. (1), we will rely on Eq. (6) derived in Section 3.2. Thus, assuming absolute uncertainty of 1 s on the determination of the temporal zone lengths (ti ) and (tref ), we obtain error of zi /zi of 1% for each zone (solute and reference). Note that temporal zone lengths, ti and tref , are in the order of 100 s. Similarly, a 1% relative error of injected concentrations ci and cref translates to the same value of relative error on the effective charge zi . Then, the contribution relative to the uncertainty on the electrophoretic mobilities (A/A given by the last three terms in Eq. (6)) highly depends on the mobility of the solute i. Assumption of an uncertainty of 1 × 10−9 m2 V−1 s−1 on the determination of the actual ionic mobilities i , ref , and c , leads to a relative A/A uncertainty of 1.5%, 3.8%, and 0.9% for PAMPS, PAMAMPS 10%, and PGlu, respectively. It can be noted that the contributions of time, concentration, and mobility to the total uncertainty as presented in Eq. (6) are in the same order of magnitude. Finally, one can estimate the overall precision on the effective charge determination to be 5%, 8%, and 6%, for PAMPS, PAMAMPS 10%, and PGlu, respectively. If the uncertainty is supposed to be constant whatever the solute for the terms relative to time and concentration, the uncertainty relative to the mobility term (A/A) highly depends on i and strongly diverges when the uncertainty of the mobility  increases. This is presented in Fig. 5 giving A/A as a function of i for three different absolute uncertainties on mobilities (0.5, 1 and 2 in 10−9 m2 V−1 s−1 units). Fig. 5 points out two important trends regarding the measurement of effective charge by ITP: (i) when the uncertainty on the mobilities is higher than 1 × 10−9 m2 V−1 s−1 unit, A/A becomes the most important source of uncertainty with

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Table 3 Figures of merits of the effective charge for anionic (PGlu, PAMPS 100%, PAMAMPS 10%) or cationic (PLL) polymer samples obtained by ITP performed on a CE apparatus or on a dedicated ITP device (in both cases n = 7). Sample

z1 (ITPCE )

z1 (ITPITP )

PGlu PAMPS 100% PAMAMPS 10% PLL 50

0.362 ± 0.003 (RSD = 1.0%) 0.33 ± 0.01 (RSD = 1.3%) 0.74 ± 0.03 (RSD = 4.7%) 0.491 ± 0.002 (RSD = 0.5%)

0.37 ± 0.02 (RSD = 4.1%) 0.35 ± 0.03 (RSD = 7.2%) 0.75 ± 0.04 (RSD = 5.7%) 0.55 ± 0.02 (RSD = 4.2%)

z1 a (IUV) 0.39 [6] 0.35 [19] 0.79 [19] –c

z1 ,theo b (Manning) 0.50 0.36 1.00 0.50

a

Effective charge per charged monomer was determined in previous works by indirect UV detection in CE (see refs. [6,19]). The theoretical effective charge per charged monomer z1,theo is given by the Manning theory as follows: z1,theo is equal to b/lb , where b is the average charge spacing (in nm), lb is the Bjerrum length (0.713 nm at 298 K), when b/lb is lower than 1. z1,theo = 1 when b/lb is higher than 1. c Effective charge of PLL could not be measured by indirect UV detection in CE due to interactions between the PLL and the chromophore [12]. b

apparatus were consistent with those determined by CE with indirect UV detection. Uncertainty of the measurement using CE or ITP was estimated to be ∼5–10% for solutes with mobilities in the 20–50 × 10−9 m2 V−1 s−1 range. We believe that this work will facilitate implementation of isotachophoresis based effective charge measurement in research laboratories. Acknowledgements This work was supported by Ministry of Education, Youth and Sports of the Czech Republic (FR-CZE bilateral Barrande Project No. 26521RB, 7AMB12FR012), the Academy of Sciences of the Czech Republic (M200551207 and RVO 61388963), and the Czech Science Foundation (13-17224S). H.C. gratefully acknowledges the support from the Institut Universitaire de France and from the Region Languedoc-Roussillon for the fellowship “Chercheurs d’Avenir”. Appendix A. Supplementary data Fig. 5. Variation of the A/A contribution to the overall relative uncertainty on the effective charge determination given by Eq. (3) as a function of the solute mobility, for different absolute errors of the mobilities (as stated on the graph). For calculations, we retained c = 37.2 × 10−9 m2 V−1 s−1 (as for creatinine) and ref = 50.9 × 10−9 m2 V−1 s−1 (sulfosalicylate). The absolute error on mobilities  is supposed to be the same for all mobilities.

values higher than 5% for i < 30 × 10−9 m2 V−1 s−1 ; (ii) for i < 10 × 10−9 m2 V−1 s−1 the A/A uncertainty becomes critical, even for  = 0.5 × 10−9 m2 V−1 s−1 . In conclusion, the ITP method for effective charge determination leads to overall relative uncertainty about 5–10% for solutes with mobilities in the 20–50 × 10−9 m2 V−1 s−1 range, as estimated for different polymers in this work. For polymer solutes having mobility ranging between 10 and 20 × 10−9 m2 V−1 s−1 a special attention should be paid to the estimation/calculation of the solute/reference/counter-ion mobilities. In that case, absolute error on the mobilities should be kept below 0.5 × 10−9 m2 V−1 s−1 to keep the overall relative uncertainty in the 5–10% range. For polymer solutes having mobility < 10 × 10−9 m2 V−1 s−1 , the overall uncertainty is expected to increase rapidly which may limit the application of the ITP method in that case. 5. Conclusions To summarize, we present here capillary ITP as universal method for determination of effective charge of broad range of polymers. ITP electrolyte systems were developed to address analysis of weak and strong polycations and polyanions. It was demonstrated that effective charge measurement can be carried out in ordinary CE instruments with typical RSD as low as ∼2%. It was verified for several polymers that effective charges obtained by ITP using either specific ITP instrument or CE

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Generalized polymer effective charge measurement by capillary isotachophoresis.

In this work, we have generalized the use of capillary isotachophoresis as a universal method for determination of effective charge of anionic and cat...
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