Two different approaches to XPS quantitative analysis of polyelectrolyte adsorption layers

X‐ray photoelectron spectroscopy (XPS) was employed to quantify adsorption of polyelectrolytes from aqueous solutions of low ionic strength onto mica, glass, and silica. Silica surfaces were conditioned in base or in acid media as last pre‐treatment step (silica‐base last or silica‐acid last, respectively). Consistency in the determined adsorbed amount, Γ, was obtained independent of the choice of XPS mode and with the two quantification approaches used in the data evaluation. Under the same adsorption conditions, the adsorbed amount, Γ, varied as Γmica > Γsilica‐base last ≈ Γglass > Γsilica‐acid last. In addition, the adsorbed amount increased with decreasing polyelectrolyte charge density (100% to 1% of segments being charged) for all substrates. Large adsorbed amount was measured for low‐charge density polyelectrolytes, but the number of charged segments per square nanometer was low due to steric repulsion between polyelectrolyte chains that limited the adsorption. The adsorbed amount of highly charged polyelectrolytes was controlled by electrostatic interactions and thus limited to that needed to neutralize the substrate surface charge density. For silica, the adsorbed amount depended on the cleaning method, suggesting that this process influenced surface concentration and fraction of different silanol groups. Our results demonstrate that for silica, a higher density and/or more acidic silanol groups are formed using base, rather than acid, treatment in the last step.

X-ray photoelectron spectroscopy (XPS) was employed to quantify adsorption of polyelectrolytes from aqueous solutions of low ionic strength onto mica, glass, and silica. Silica surfaces were conditioned in base or in acid media as last pre-treatment step (silica-base last or silica-acid last, respectively). Consistency in the determined adsorbed amount, Γ, was obtained independent of the choice of XPS mode and with the two quantification approaches used in the data evaluation. Under the same adsorption conditions, the adsorbed amount, Γ, varied as Γ mica > Γ silica-base last ≈ Γ glass > Γ silica-acid last . In addition, the adsorbed amount increased with decreasing polyelectrolyte charge density (100% to 1% of segments being charged) for all substrates. Large adsorbed amount was measured for low-charge density polyelectrolytes, but the number of charged segments per square nanometer was low due to steric repulsion between polyelectrolyte chains that limited the adsorption. The adsorbed amount of highly charged polyelectrolytes was controlled by electrostatic interactions and thus limited to that needed to neutralize the substrate surface charge density. For silica, the adsorbed amount depended on the cleaning method, suggesting that this process influenced surface concentration and fraction of different silanol groups. Our results demonstrate that for silica, a higher density and/or more acidic silanol groups are formed using base, rather than acid, treatment in the last step.

K E Y W O R D S
adsorption, ESCA, glass, mica, polyelectrolyte, quantification, silica, surface conditioning, XPS 1 | INTRODUCTION X-ray photoelectron spectroscopy, XPS, also known as ESCA (electron spectroscopy for chemical analysis), is a very powerful technique for characterizing surfaces and adsorbed layers because it is highly surface sensitive with analysis depth of the order of a few nanometers and provides quantitative chemical information. 1,2 It is of interest in a large range of scientific areas, and it has been noted that this technique was utilized in more than 9000 scientific publications in 2017, 3 and the interest remains equally high today. XPS finds use in areas ranging from adsorption of gas molecules 4,5 and proteins 6,7 to characterization of spray-dried food powders, 8 wood and pulp fibers, 9,10 functional coatings, [11][12][13] plasma polymer surfaces, 14 homogeneous bulk materials, 15 and even microbial surfaces. 16 The standard output from XPS analysis is the relative surface chemical composition expressed in atomic percent. However, it is possible to take the quantification a step further for absolute quantification of adsorbed amount, for instance, expressed as a surface density (atoms/nm 2 or mg/m 2 ).
In the quantitative analysis, a model for the adsorption layer needs to be considered, for example, the substrate/overlayer model. 1,2,17,18 This model was used in the present investigation, and the polyelectrolyte was treated as a homogenous overlayer with thickness t o residing on a smooth surface. The adsorbed amount per unit surface area was calculated using two approaches. The first, applicable to mica, is based on the known number of exchangeable ions located on the mica basal plane, which is used as an internal calibration standard. [19][20][21][22] In a similar procedure, the amount of polyelectrolytes adsorbed on cellulose and gold has been evaluated by comparing the N 1s signal intensities of the adsorbed polyelectrolyte with that obtained for the same type of polyelectrolytes adsorbed on mica. 19,21 The second approach makes use of the volume atomic density of one element present in the surface region of the substrate as internal calibration standard. This approach has previously been applied for quantification of the adsorption of fatty amine on quartz powder. 18,23 In this work, we compare the outcome of these two analysis approaches, and we also evaluate the consequences of considering only inelastic scattering of photoelectrons, as done in previous works, 18,23 or also considering elastic scattering of photoelectrons in the overlayer.
Adsorption of polymers and polyelectrolytes is an attractively simple method for surface modification, and it has received renewed interest because of the strive to increase the use of renewable materials such as, for example, cellulose in new applications. 24 Polyelectrolyte adsorption is also an efficient way to control colloidal stability. 25 In the present investigation, we compare the two approaches mentioned above to quantitatively analyze polyelectrolyte adsorption layers by XPS on mica, glass, and silica. These systems were chosen for three reasons (i) polyelectrolytes adsorb strongly as monolayers to oppositely charged surfaces, which renders sample preparation easy and reproducible. (ii) It is well established that highly charged polyelectrolytes under low ionic strength conditions adsorb to oppositely charged surfaces in a quantity that closely corresponds to the surface charge density. [26][27][28] This feature allows for an estimate of the surface charge density of the substrates used. 29 (iii) All the chosen substrates are common in surface chemical studies using devices such as ellipsometry, optical reflectometry, neutron reflectivity, AFM imaging, and surface force measurements. In particular, silica substrates are often used, but different surface conditioning procedures are adopted by different research communities. It is thus of interest to elucidate how the cleaning procedure affects adsorption and how silica compares to glass. In the present study, the silica surfaces were therefore pretreated in two ways, in base or in acid media as the last cleaning step (denoted as silica-base last or silica-acid last, respectively).
The effect of the silica surface conditioning on adsorption has been addressed in only a few studies. For instance, Atkin et al. investigated the adsorption of cationic surfactants on two types of silica surfaces: pyrogenic silica with a low density of silanol groups but a large fraction of isolated silanols that readily deprotonate in water, and hydroxylated silica that contains more silanol groups but the majority of these are less acidic than the isolated silanols. 30 They noted higher adsorption at high surfactant concentration on the pyrogenic silica and attributed this to a higher hydrophobicity of pyrogenic silica compared to hydroxylated silica. Chorro et al. also investigated cationic surfactant adsorption to silica, employing amorphous silica particles.
They found that the adsorbed amount on acid-washed silica was about half of that found on the unwashed silica. Thus, acid treatment was concluded to reduce the surface charge density of the silica substrate. 31 From adsorption enthalpy data, Ernstsson and Larsson noted a reduction in the number of adsorption sites on quartz powder that interacted strongly with fatty amines when the quartz sample was acid washed with hydrochloric acid. 23 The nature of the silica surface also strongly affects adsorption of non-ionic surfactants as demonstrated in the neutron reflectivity study by Penfold et al. 32 They cleaned their surfaces with mild acidic Pirhana and demonstrated a marked hysteresis in adsorption of the non-ionic surfactant C 12 E 6 during pH-cycling from 7 to 2.4 and back to 7 again. This was attributed to a change in the state of the silica surface.   Table 2). The ion-exchanged mica was obtained by immersion of a freshly cleaved mica sheet in water, which leads to replacement of K + and Na + ions on the top surface by protons. 33 Atomic-resolution AFM images of mica has reported the root-mean-square (RMS) roughness 0.25 Å. 34 Silica. Large silicon wafers (Okmetic, Finland) that had been oxidized in pure oxygen at 920 C for 1 h before being annealed in flowing argon were used as substrates. As a result of the treatment, the silicon wafers carry a 30-nm thick oxide layer. The wafers were cut to smaller silica slides, each with a width and length of ca. 10 and 15 mm, respectively, followed by cleaning of each slide using one of the following two sequences that differed in the order in which the solutions were applied: Silica-base last. The silica slides were first treated in a mixture of HCl:

| XPS procedure
The XPS spectra were recorded using a Kratos AXIS HS X-ray photoelectron spectrometer (Kratos Analytical, Manchester, UK). The samples were analyzed in fixed analyzer transmission (FAT) mode using three XPS modes of operation that will be referred to as Mg, Al-mono, and Al-elstat. Details of the three XPS modes as utilized in this work are summarized in Table 1.
The three XPS modes generate different signal intensities.
Because of the short distance between the dual anode and sample,  and C 1s peaks were baseline adjusted followed by curve-fitting the K 2p signal (to obtain the correct amount of K 2p, from the expected area ratio 2/1 between the K 2p 3/2 and K 2p 1/2 peaks). This was needed because the K 2p and C 1s peaks are not fully separated in the Al-elstat and Mg modes. If baseline correction is not considered, the K 2p peak area would be underestimated. 37 In some cases, a ghost peak from the O 1s signal at 531 eV was observed in Mg mode at ca. 298 eV. This ghost peak arises from Al impurity in the Mg anode because of wear of the Mg layer with usage. If present, the ghost peak is located close to the K 2p line, but it is easily accounted for by curve-fitting.

| Quantification of the adsorbed amount by XPS-the basis of the two approaches
The adsorbed amount of polyelectrolyte was quantified using the substrate/overlayer model, where the nitrogen atoms are considered as being distributed uniformly in the polyelectrolyte overlayer. In the first approach, the known number of exchangeable K + and Na + ions located on the mica basal plane was used as an internal standard in the calculation. The internal reference used in the second approach was instead the volume atomic density of one element present in the surface region of the substrate (Si in this study). We note that for an adsorbed layer of polyelectrolytes, the adsorbed layer is never completely homogeneous and thus the substrate/overlayer model adopted here is an approximation. If instead a patch wise model would have been adopted, a slightly higher adsorbed amount would have been obtained at low surface densities, as previously reported for surfactant adsorption on mica. 33 The difference is however small and (close to) negligible at high surface coverage, as in this work.

| Substrate/overlayer method based on exchangeable ions on mica as standard
The amount of polyelectrolyte adsorbed on mica can be calculated according to Equation 1, which was derived in detail by Rojas et al. 19 Briefly, the adsorbed amount of polyelectrolyte on mica is calculated from the intensities of the N 1s and K 2p signals. The total number of exchangeable ions, K + (90-95%) and Na + (5-10%), located on the mica basal plane is used as the internal standard, and together they equal the number of negative surface charges that originates from the aluminosilicate lattice structure. This quantity amounts to 2.1 charges per square nanometer. 38,39 The nitrogen atom density per unit area, N N1s /A (atoms/nm 2 ), is calculated from 19 where I N1s and I K2p are the photoelectron signal intensities (counts/s), that is, the experimentally determined peak areas, for the overlayer (polyelectrolyte) and the substrate (mica), respectively, and S N1s and S K2p are the relative sensitivity factors. Note that these four quantities combined are the same as the atomic ratio between the N 1s and K 2p signals, that is, atomic% N/atomic% K.
Further, E N1s and E K2p are the kinetic energies (eV) of the ejected photoelectrons, t o is the overlayer thickness, λ o K2p is the photoelectron inelastic mean free path (IMFP) and describes the attenuation of the photoelectron signal in the overlayer, and θ is the photoelectron takeoff angle (defined with respect to the sample plane, 90 in the present F I G U R E 3 Nitrogen 1s detail spectra for polyelectrolytes of different charge densities adsorbed on mica: (A) polyMAPTAC (100% charge density) and (B) AM-MAPTAC-10 (10% charge density). For spectra of AM-MAPTAC-1 (1% charge density), see Figure 2B. All spectra were collected using the Mg XPS mode of operation  . The factor f(1+R) has to be determined experimentally for each XPS mode (see Table 2). In the expression f(1+R), the factor f is defined as the ratio of the K 2p signal intensities that originates from the exchangeable K + ions located at the mica surface to the K + ions inside the bulk of the mica crystal lattice. The factor (1+R) is used to account for the small amount of Na + ions that substitute for K + ions in the mica crystal lattice. For details on how to experimentally determine the factor f(1+R), we refer to previous publications. 19,33 The reduced thickness obtained from the ratio between two K 2p signal intensities; mica without an overlayer (I K2p,ref using ion-exchanged mica as the reference) is divided with that for mica with an overlayer: The nitrogen density per unit area obtained from Equation (1), N N1s /A (atoms/nm 2 ), is then used to calculate the adsorbed amount Γ (mg/m 2 ) by using Equation (3).
where M N is the molecular weight per nitrogen atom in the polyelectrolyte structure, N A is Avogadros number, and the factor of 10 21 arises because of conversion of the result into the unit of mg/m 2 .
The amount adsorbed on substrates different than mica, here exemplified by silica, is obtained by comparing the N 1s signal intensities for the adsorbed polyelectrolyte on silica, with the adsorbed amount of the same polyelectrolyte on mica according to As discussed in one of our previous work, 19 (5)). Alternatively, averaged values of atomic number and atomic size for organic materials can be used with Equations (6), (7).
The internal reference used is in this case was the volume atomic density of Si in the substrate surface region, which is assumed to have a homogeneous composition within the analysis depth. 18 The adsorbed amount of polyelectrolyte on the substrate is then calculated from the intensities of the N 1s signal from the polyelectrolyte, and the Si 2p signal from the substrate, that is, using the atomic ratios N/Si. To calculate the adsorbed amount of polyelectrolyte, we used Equation (10), the calculated photoelectron IMFP, or alternatively, the effective attenuation length (EAL) for elemental signals in the polyelectrolyte overlayer (Equations 5-7) and the experimentally determined overlayer thickness (Equation 9).
The volume atomic density of one element present in the surface region of the substrate is calculated from the density and molecular weight and using XPS data for the substrate without adsorbed polyelectrolyte. This accounts for possible chemical deviations between the measured substrate surface and the theoretical composition of the same substrate.
Unlike in the mica method where the ratio t o /λ ο was experimentally determined, we here need to consider the value of λ o . This can be done by calculating either the IMFP from Equation (5) or Equation (6), or the EAL from Equation (7), for the different photoelectron signals in the overlayer. We note that the difference between IMFP and EAL is that the IMFP only considers inelastic photoelectron scattering, whereas EAL considers both inelastic and elastic scattering. 2 Equation (5) where λ o is the IMFP (nm), 0 χ v is the zero-order valence index, and where λ o is the IMFP (nm), Z is the numbered averaged atomic number (Z ≈ 4 for organic materials), and a is the atomic size in nanometer, which is typically 0.25 nm.
where L o is the EAL (nm).
For light elements, such as in the polyelectrolyte overlayer, the elastic photoelectron scattering is small and one thus only expect small differences between IMFP and EAL values. 42 In Equations (8-10) we keep the notion λ o , but we have performed the calculations using both IMFP values and EAL values to consider possible discrepancies.
The substrate signal intensity is damped by photoelectron absorption when passing through the overlayer, according to the exponential term of Equation (8), and for Si 2p signal we obtain 18 where n Si2p is the volume atomic density (atoms/nm 3 ) in the surface region of the silica substrate.
The overlayer thickness can then be calculated from Equation (9), by combining two photoelectron signals from the substrate surface with a polyelectrolyte overlayer. In our study, the substrate signals Si 2p and O 1s were used in Equation (8) and combined to give Equation (9) 18 : From XPS analysis, the atomic ratio O/Si was calculated from the determined atomic% of oxygen and silicon. The atomic ratio O/Si, in Equation (9) n O1s ∕ n Si 2p À Á , was found to be 2.02 for silica-base last and silica-acid last, 2.04 for glass and 3.93 for mica. These ratios are reasonable because the theoretical O/Si atomic ratio for silica is 2.0, and for mica it is 4.0.
In the present work, the adsorbed amount of the polyelectrolyte was obtained by using the nitrogen signal from the overlayer and the silicon signal from the substrate. Clearly, in order to utilize Equation (10), one needs to know the volume atomic densities for silicon (n Si2p ) present in the surface region for mica, glass, silica-base last, and silica-acid last.
Muscovite mica with the structural unit KAl 2 (OH) 2 (AlSi 3 O 10 ) has a density of 2.8 g/cm 3 , and the structural unit has a molecular weight of 398.3 g/mol. 43  The nitrogen density per unit volume in the polyelectrolyte overlayer, n N1s (atoms/nm 3 ), was then calculated from Equation (10) 18 n N1s ¼ By multiplying the nitrogen density per unit volume n N1s (atoms/nm 3 ) with the overlayer thickness t o (nm), the surface density of nitrogen atoms (N atoms/nm 2 ) was calculated and thus the adsorbed amount Γ (mg/m 2 ) was obtained by using Equation (11): 3 | RESULTS AND DISCUSSION

| Influence of X-ray irradiation time
Exposure of surfaces to X-ray irradiation may lead to chemical changes, as documented for polymers and other organic surface layers. [46][47][48] However, reducing the X-ray exposure time reduces or even eliminates this issue. 49 The reduction of signal intensity because of irradiation-induced degradation/desorption was investigated by monitoring the N 1s peak  Figure 4). The results presented in Figure 4 illustrate the importance of the order in which the different spectra are collected, and we recommend to start with signals from the elements that are used in the quantification. Therefore, we adopted the following measuring sequence. First, the polyelectrolyte specific signal (N 1s) was recorded, followed by the substrate specific signals (K 2p for mica only, Si 2p and O 1s). Finally, all other elements of interest and the wide spectra were collected. This protocol is in contrast to typical XPS procedures that start with the wide scan to detect the elements present on the surface of the sample.

| Adsorbed amount on mica
The three XPS modes described previously (Table 1) were used in the analysis, followed by calculation of the amount of polyelectrolyte adsorbed on mica (Equations (1-4)). We note that the factor f(1+R) used in Equation (1) depends on the XPS mode, and especially whether the X-rays were generated by Mg or Al anodes (see Table 2).
This factor has not previously been determined for the Mg mode. XPS data for the K 2p, Si 2p, and Na 1s signal intensities of ion-exchanged and freshly cleaved mica samples were used in these calculations.
For the Al-elstat mode, the f(1+R) value obtained was 0.21, which is the same as that reported by Herder et al. 33 (n.b. the factor is called FR in that study), and similar to the 0.197 reported by Rojas et al. 19 For the Al-mono mode, Rojas et al. 19 report The f(1+R) factor obtained for the Mg mode, 0.27, is higher than for the two Al X-ray based modes. This is reasonable because the surface sensitivity is higher due to the lower kinetic energies of the photoelectrons when using Mg X-rays (1253.6 eV) instead of Al X-rays (1486.6 eV). Thus, in the Mg mode, the exchangeable ions present on the freshly cleaved mica surface contribute to a larger degree to the measured K 2p signal and this increases the factor f.
In Table 3, the adsorbed amounts of the polyelectrolytes on mica obtained by using the three different XPS modes are shown, and the agreement between the results is satisfactory.
Compared to our earlier reports, larger adsorption of the low charge density polyelectrolytes was observed in the present study. This is likely due to larger irradiation-induced material loss during X-

| Polyelectrolyte adsorption evaluated by using mica as calibration standard
The calculated adsorbed amounts of the three polyelectrolytes on the four substrates are shown in Figure 5 and Table 4, using mica as a calibration standard (Equations (1-4)). For all substrates, the adsorbed amount decreases with increasing polyelectrolyte charge density, as expected theoretically 26,27 and observed experimentally. [19][20][21] We also note that for each polyelectrolyte, the adsorbed amount decreases according to the following order: mica > silica-base last ≈ glass > silica-acid last. However, if electrostatic interactions were the only forces of importance for polyelectrolyte adsorption, one would expect the number of charged groups in the adsorbed layer to be independent of the polyelectrolyte charge density. This is clearly not the case as illustrated in Table 4 and Figure 6. Instead, it is found that even though the adsorbed amount increases with decreasing polyelectrolyte charge density, the number of charged segments within the adsorbed layer decreases. The reason is that for low charge density polyelectrolytes the steric repulsion between the adsorbed polyelectrolyte chains, rather than electrostatic repulsion, limits the adsorption. [26][27][28] Thus, the increase in adsorbed mass with decreasing polyelectrolyte charge density is less than could be expected if only electrostatic interactions were of importance.
T A B L E 4 The average adsorbed amount Γ (mg/m 2 or segments/nm 2 ), number density of adsorbed charged segments (charged segments/ nm 2 ), and surface area occupied per adsorbed charged segment (nm 2 ), for AM-MAPTAC-1, AM-MAPTAC-10, and polyMAPTAC on mica, glass, silica-base last, and silica-acid last  For the highly charged polyMAPTAC, adsorption is largely controlled by electrostatic interactions, and the adsorbed amount thus reflects the charge density of the substrate. This fact is used in the polyelectrolyte titration of surfaces as a method to determine the surface charge density. 29 Therefore, the data in Table 4 and Figure 6 for the number of charged segments per nm 2 in the adsorbed layer give an estimate of the number density of charged surface sites, σ. We obtain the following trend in surface charge density: σ mica > σ silica-base last ≈ σ glass > σ silica-acid last . It is clear that the cleaning process of the silica substrate strongly affected the surface charge density. In order to rationalize this, we need to consider the surface chemistry of silica.

| The surface chemistry of silica and its relevance for polyelectrolyte adsorption
The surface chemistry of silica has attracted attention for a long time.
One notable early work is that by Iler, 44 and there is also a comprehensive review paper that summarizes much of the current understanding. 50 Silica and glass surfaces are negatively charged above their isoelectric point of about 2-4, depending on the type of silica and cleaning method. 44,51,52 The negative charges are due to the dissociation of surface hydroxyl (silanol) groups according to The ionization of surface silanol groups, and hence the surface charge density of silica, increases with pH and ionic strength of the aqueous solution, 44,45,53 and also with increasing temperature in the range of 10-75 C. 54 In our case, the pH (5.5-6.0), temperature (≈ 22 C), and ionic strength (0.1-mM NaCl background electrolyte) were the same in all cases. The concentration of silanol groups on a fully hydroxylated silica surface has been estimated to be 4-5 silanol groups/nm 2 . 44,50,55 This quantity is gradually reduced by thermal treatment and is found to be about 1 silanol group/nm 2 after heating to 700-800 C. 44,55 The current understanding is that the silanol groups on silica is not all equal but can be divided into isolated single, geminal, and vicinal groups, as illustrated in Figure 7. The geminal groups are formed when two hydroxyls bind to one surface silicon atom. If the surface density of silanol groups is high enough, they may form hydrogen bonds to each other, and such groups are called vicinal silanol groups. The different silanol groups also form hydrogen bonds to water, 50  The dissociation degree of the silanol groups depends on the pKa values of the dissociation reaction described by Equation (12). It has been suggested that isolated single silanol groups dissociate most easily, that is, they are more acidic than the other silanol groups (because isolated groups cannot form hydrogen bonds with their neighbor). 45  It is also worthwhile briefly mentioning the ongoing discussion about the presence of a silica gel on silica surfaces. It is well known that the solubility of silica increases with pH and temperature as for example reported in the paper by Fleming and Crerar. 59 It is less established if a gel layer forms on the surface of silica as a result of treatment in alkaline solution for a short time (10 min at 75-78 C in our case). In our own neutron reflectivity measurements, we did not find evidence for formation of a silica gel layer after 30 min in NaOH solution pH 10. 52 Surface force measurements between silica surfaces prepared by E-beam evaporation noted a short-range repulsion that initially was interpreted as being due to the presence of a ≈ 2 nm thick silica gel layer. 60 However, in later work, the preferred interpretation of this short-range repulsion is rather that it is due to strongly bound water, that is, a hydration force. 56 Further, no evidence for a gel layer was found in studies of surface forces between glass surfaces at pH 10. 61 Considering these reports, we conclude that it is unlikely that the presence of a silica gel layer on alkaline-last treated silica is the reason for the higher adsorbed amount seen on these surfaces compared to on acid-last treated samples. For the highly charged polyMAPTAC, the data in Table 4    surface. For a surface with adsorbed polyelectrolyte, the degree of dissociation of silanol groups will therefore be higher than for a reference sample in a polyelectrolyte-free salt solution, jσj ads PE > jσj ref .
This effect has been explained theoretically 27,28 and observed experimentally, for example, in a potentiometric titration study 53 (11), one needs to estimate the overlayer thickness (t o ), Equation (9), and for the different elemental signals in the polyelectrolyte overlayer determine either the IMFP (λ ) or the EAL (L o ) (Equations (5-7)). In

| IMFP and EAL values
The results provided in Table 5 demonstrate that the IMFP values calculated from Equations (5) and (6) are similar and also similar to the EAL values calculated from Equation (7). The similarity between the IMFP and EAL is a consequence of the low importance of elastic scattering for light elements. 42 However, we note slightly higher values for polyMAPTAC when Equation (5) (5), because we know the molecular structure of the polyelectrolytes. This is preferred instead of Equations (6) and (7) where average values of atomic number and atomic size for organic layers are utilized. For a few samples, we have also compared the result with those obtained by using Equation (6) or Equation (7)

| Overlayer thickness
The overlayer thicknesses obtained are shown in Figure 8. The thickness is found to decrease with increasing charge density of the polyelectrolyte, and for a given polyelectrolyte, it scales with the adsorbed amount (see below). Hence, the highest thickness is obtained on mica and the lowest on silica-acid last. Numerically, the overlayer thicknesses on mica calculated from Equation (9), while using IMFP values from Equation (5) The overlayer thickness values shown in Table 6 compare the values obtained when the thickness calculations employed either the values of IMFP from Equation (5) or Equation (6), or EAL from Equation (7). The results are similar, and the only slight variation is noted for AM-MAPTAC-1.

| Adsorbed amount
The calculated adsorbed amounts according to the two approaches for quantification are shown in Table 7. The agreement between the two approaches is satisfactory, suggesting that both methods are inherently sound.

| CONCLUSIONS
We have shown that the two XPS quantification approaches presented in this report provide consistent data on the adsorbed amount per unit surface area independent of the XPS mode utilized.
It is proposed that the atomic density approach is more convenient because only one set of measurement is necessary, instead of two as required in the mica calibration method. In our case, with an overlayer of light elements, the IMFP is close to the EAL as the effect of elastic scattering of photoelectrons is small. Thus, overlayer thickness and adsorbed amount calculated based on IMFP values are similar to those calculated by employing EAL values. Our data also demonstrate that X-ray-induced degradation/desorption occurs, and this effect cannot be ignored for the low charge density polyelectrolytes. To minimize the consequences of this effect, the detail spectra used for quantification should be recorded first, followed by the other spectra of interest.
For highly charged polyelectrolytes in dilute ionic strength solutions, electrostatic interactions dictate the adsorption and the adsorbed amount can be used to estimate the surface charge density of the substrate. By considering the adsorbed amount of highly charged polyMAPTAC, we obtained the following trend in surface charge density σ mica > σ silica-base last ≈ σ glass > σ silica-acid last . The adsorbed amount of polyMAPTAC on mica was found to be slightly less than expected from the known number of negative sites. For silica and glass, the surface charge density depends on the density and type of silanol groups present on the surface. We have demonstrated that the choice of cleaning method for the silica surface is very important for the extent of adsorption, and base treatment in the last step increases the adsorption of a highly charged cationic polyelectrolyte by a factor of 2 compared to silica treated with acid as the last step.
The glass surface is similar to the silica-base last surface.
For low charge density, polyelectrolytes steric repulsion between the adsorbed polyelectrolyte chains, rather than electrostatic repulsion, limits the adsorption. However, also in this case, the adsorbed amount (Γ) depends on the substrate: Γ mica > Γ silica-base last ≈ Γ-