**3. Results and Discussion**

The results of surface pressure (π) and electric surface potential changes (∆V) versus area per molecule (A) measurements for the investigated lipids are presented in Figures 1 and 2. Experimental π–A isotherms for all the studied phospholipids are in good agreement with those already published ([33] for DPPC, [34] for DSPC, [35] for DAPC, [36] for DOPC, [37] for DPPE and [38] for SM). Experimental <sup>∆</sup><sup>V</sup> − <sup>A</sup> curves can be characterized by two important parameters: critical area (Ac, which corresponds to the area at which ∆V is triggered off) and maximum value of surface potential (∆Vmax). The change in surface potential, observed at A<sup>c</sup> occurs at much earlier stages of monolayer compression

compared to the surface pressure lift-off area (Alift–off) [10]. The onset areas of both surface pressure (Alift–off) and surface potential (Ac) occur at the largest areas for the unsaturated phospholipid DOPC. This is due to the steric requirements for molecules with cis unsaturated bonds in their chains, having a coiled conformation, in contrast to saturated all-trans chains. For uncharged compounds, ∆V is approximately constant and close to zero at large areas per molecule. Upon compression, a sharp change (increase or decrease) is observed at the critical area. Changes in the slope of ∆V–A dependence reflect molecular orientation and/or conformational changes in the layer, as ∆V is proportional to the magnitude of the electrostatic field gradient normal to the subphase surface [1]. The maximum of the surface potential, ∆Vmax, is defined as the value corresponding to the most vertical orientation of molecules, which usually coincides with the maximum condensation of the monolayer, characterized by the maximum compressibility modulus: C −1 <sup>s</sup> = −A dπ dA [39]. Finally, at a collapse point, ∆V becomes approximately constant. The maximum value of the surface potential, ∆Vmax, is used to calculate the apparent dipole moment µ exp A of film molecules, using the following equation:

$$
\mu\_{\rm A}^{\rm exp} = \frac{\mu\_{\perp}}{\varepsilon} = \varepsilon\_0 \cdot \mathbf{A} \cdot \Delta \mathbf{V}\_{\rm max} \tag{3}
$$

wherein ε<sup>0</sup> is the vacuum permittivity, ε is the monolayer permittivity (unknown) and A and ∆Vmax are values extracted from experimental curves corresponding to the maximum compressibility modulus. The values of µ exp A for all the investigated phospholipids, together with other characteristic parameters for their monolayers, such as Alift–off, Ac, ∆Vmax and A, are summarized in Table 1.

**Figure 2.** Electric surface potential change and surface pressure isotherms, together with calculated compressional moduli curves for selected phosphatidylcholines: (**A**) DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine), (**B**) DSPC (1,2 distearoyl-sn-glycero-3-phosphocholine), (**C**) DAPC (1,2-diarachidoyl-sn-glycero-3-phosphocholine) and (**D**) DOPC (1,2 dioleoyl-sn-glycero-3-phosphocholine).

–

−

ΔV– A

ΔV– A


**Table 1.** Selected data read from surface pressure–area (π–A) and electric surface potential–area (∆V–A) experimental curves measured at 20 ◦C, together with experimental apparent dipole moments µ exp A values (uncertainty of ±∆<sup>µ</sup> exp <sup>A</sup> was obtained by exact differential method)—explanation in the text.

<sup>1</sup> 1,2-dipalmitoyl-sn-glycero-3-phosphocholine; <sup>2</sup> 1,2-distearoyl-sn-glycero-3-phosphocholine; <sup>3</sup> 1,2-diarachidoyl-sn-glycero-3 phosphocholine; <sup>4</sup> 1,2-dioleoyl-sn-glycero-3-phosphocholine; <sup>5</sup> 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine; <sup>6</sup> N-(hexadecanoyl) sphing-4-enine-1-phosphocholine.

> Let us first discuss the surface potential change curves recorded for phosphatidylcholine derivatives (Figure 2), in which the length of the apolar acyl chain or unsaturation degree is varied.

> The ∆V–A curve recorded for DPPC shows a characteristic sharp increase starting at the molecular area ca. 139.0 Å<sup>2</sup> from −30 to ca. 168 mV, where there is a visible inflection. Then, the surface potential rise is continued, albeit with a much smaller slope. Starting from ca. 68 Å2/molecule and 283 mV, the curve slope increases again. A similar sequence is observed in the π–A isotherm and can be attributed to a change in physical surface states in DPPC, i.e., a phase transition from a liquid-expanded (LE) to a liquid-condensed (LC) phase. As is well known, the LC state is more ordered than the LE state due to (i) closer molecular packing (resulting from the increased conformational order of hydrocarbon chains), and (ii) the smaller tilt angle of molecules in the surface layer [40]. The most condensed DPPC monolayer is characterized by a surface potential change equal to 509 mV, which is in agreement with previous studies (527 mV [23], 551 mV [24] and 544 mV [41]). Further elongation of acyl chains to 18 (DSPC) and 20 (DAPC) carbons influence the electrical properties of the formed monolayers. The critical area becomes shifted to smaller values: 96.2 and 82.6 Å2/molecule for DSPC and DAPC, respectively. This suggests that phosphatidylcholines with longer hydrocarbon chains form more tightly packed and more condensed films compared to the DPPC monolayer. The curve for DSPC is characterized by one inflection appearing at ca. 77 Å2/molecule and 466 mV, which suggests changes in molecular orientation in the monolayer (understood as a change in molecular angle in respect to the surface) [42]. On the other hand, the ∆V–A isotherm for DAPC shows a gradual rise without noticeable slope changes until the film collapse. The maximum surface potential values are equal to 684 mV and 614 mV for DSPC and DAPC, respectively. The DOPC molecule possesses one double bond in each of the octadecyl chains and can be compared to DSPC, which has hydrophobic chains of the same length, but both are saturated. As can be noticed, the ∆V–A curves of both phospholipids are characterized by the same shape (with one inflection). However, some differences should also be noted. Firstly, the critical area for DOPC is approximately 66 Å2/molecule larger as compared to DSPC. This suggests lower packing of the DOPC film, which is also confirmed by the values of the compressibility moduli. Secondly, the maximum value of the surface potential ∆Vmax is equal to 358 mV. Since the surface potential is proportional to the component of the electrostatic field vertical to the surface, it can be concluded that DOPC acyl chains in the monolayer are more disordered in comparison to DSPC. The molecular basis of this issue is due to the presence of double bonds in the cis configuration in DOPC. The configuration of unsaturated bonds affects the conformation of entire hydrocarbon chains, causing disorders (gauche defects, etc.). In contrast, the DSPC hydrocarbon backbone exists mainly in an all-trans zig-zag conformation. To sum up, the participation of hydrocarbon chains in the surface potential change of phosphatidylcholines is mainly steric, related to packing density and order, which is in agreement with previous work [43].

ΔV୫ୟ୶

In the next step of our studies, we examined the influence of the interfacial area and polar group modification on surface potential isotherms (Figure 3).

ΔV– A

**Figure 3.** Electric surface potential change and surface pressure isotherms, together with calculated compressional moduli curves for (**A**) DPPE and (**B**) SM.

π– A ΔV– A The SM molecule contains the same polar group as the PCs (the phosphocholine group), however, its structure is different in the region of the sphingosine backbone. The π–A and ∆V–A isotherms measured for SM show an analogical course to DPPC and suggest the existence of stable liquid-expanded and liquid-condensed phases. Despite this fact, the values of the critical area (92.9 Å<sup>2</sup> per molecule) and the maximum of surface potential (295 mV) for SM are significantly lower than for DPPC. Values read from the measured ∆V–A isotherm of SM are in agreement with the literature [24].

ΔV– A ΔV– A In the next part of our studies, we examined the electrical properties of monolayers composed of a representative of phosphatidylethanolamines—DPPE. The ∆V–A curve is characterized by a gradual increase, without any visible inflections, starting from molecular area 144 Å<sup>2</sup> and reaching a maximum value of surface potential equal to 573 mV (in agreement with the literature data, reporting values ranging from 520 mV [18] to 589 mV [23]).

μ୲୭୲ To enrich and interpret the results obtained from our experiments, theoretical DFT calculations of molecular conformations were performed. The values of the total dipole moments of free molecules in a vacuum (µtot) are compiled in Table 2. To determine the magnitude of the normal component of the electrical dipole moment, µ<sup>z</sup> , two different approaches were applied. Firstly, the values µ<sup>z</sup> were directly read from the total dipole moment µtot of the molecule in a vacuum (ε = 1). Additionally, the component of the dipole moment in the plane of the interface (µx−<sup>y</sup> ) has also been provided. However, it should be emphasized that the calculated dipole moment corresponds to the free molecule, and not to the molecule adsorbed at the interface. Therefore µ<sup>z</sup> cannot be directly compared to µ exp A values obtained from experimental ∆V–A dependencies. In this approach, the molecule is treated as a single entity, without distinguishing its local parts (polar/apolar). As a result, differences in dielectric permittivity between polar and apolar parts are not taken into consideration. In the second approach, we separated the normal component of the dielectric dipole moment of a free molecule into contributions from the polar head (µ p ⊥ ) and hydrocarbon chains (µ a ⊥ ) individually (see Figure 4). The results of these theoretical calculations (µtot, <sup>µ</sup>x−<sup>y</sup> , µ<sup>z</sup> , µ p , µ a ⊥ ) are collected in Table 2.

⊥ In the next step of our calculations, we were interested in relating theoretical and experimental values, using the following equation [16], introducing the values of local dielectric permittivities (εp, εa) to the theoretically calculated normal dipole moments of

the polar and apolar groups (µ p ⊥ , µ a ⊥ ) as well as the contribution from the reorientation of water molecules (µ w ⊥ /εw):

$$
\mu\_{\rm A}^{\rm calc} = \frac{\mu\_{\perp}^{\rm w}}{\varepsilon\_{\rm W}} + \frac{\mu\_{\perp}^{\rm P}}{\varepsilon\_{\rm p}} + \frac{\mu\_{\perp}^{\rm a}}{\varepsilon\_{\rm a}} \tag{4}
$$

In Equation (4), there are three unknown parameters: (µ w ⊥ /εw), ε<sup>p</sup> and εa. Therefore, initially, we took these values from other works [16,18,19] to see which set of values best fits the value µ exp A obtained experimentally. The obtained results are presented in Table 3.

**Table 2.** Values of dipole moments and their contributions, calculated using Gaussian software for entire molecules and their selected parts in vacuum.


μୄ ୮ μୄ ୟ **Figure 4.** Molecular structure of selected phospholipids: DPPC (**A**), DPPE (**B**) and SM (**C**) with the directions of normal components of electrical dipole moment visualized separately for the polar group (µ p ⊥ ) and hydrocarbon chains (µ a ⊥ ). Carbon atoms are visualized in dark gray, hydrogen in bright gray, oxygen in red, nitrogen in blue and phosphorus in orange.

ε<sup>୮</sup> ε<sup>ୟ</sup> μୄ ୮ μୄ ୟ μୄ <sup>୵</sup>/ε<sup>୵</sup> μ ୡୟ୪ୡ = μୄ ୵ ε୵ + μୄ ୮ ε୮ + μୄ ୟ εୟ As can be seen, the results obtained using the literature values of parameters do not agree with the experimentally determined µ exp A . Therefore, in the second step, we developed a new methodology. For a series of phosphatidylcholines DPPC, DSPC, DAPC and DOPC, multiple linear regression was used to find a model describing the relationship between the normal components of the calculated dipole moments of the polar and apolar parts of molecules and their experimental values µ exp A . The equation of the fitted model has the following form:

$$
\mu\_{\rm A}^{\rm calc(4)} = -1.8 + 0.098 \cdot \mu\_{\perp}^{\rm P} + 1.05 \cdot \mu\_{\perp}^{\rm a} \tag{5}
$$

μୄ

ࣆ ()

−

μ <sup>୵</sup>/ε<sup>୵</sup> ε<sup>୮</sup> ε<sup>ୟ</sup> which means that the determined parameters are equal to: µ w ⊥ /ε<sup>w</sup> = −1.8 ± 1.4 *D*; ε<sup>p</sup> = 10.2 ± 7.0 and ε<sup>a</sup> = 0.95 ± 0.52. The predicted parameters show good agreement with

> ࣆ ()

ࣆ

ୣ୶୮

ࣆ ()

−

−

the observed parameters, as shown in Figure 5. The R-squared statistic indicates that the fitted model explains 86% of the variability in µA.

**Table 3.** Values of apparent dipole moments calculated from Equation (4) using the set of values of (µ w ⊥ /εw), ε<sup>p</sup> and ε<sup>a</sup> equal to (1) 0.04; 7.6 and 5.3 (according to [16]); (2) −0.065; 6.4 and 2.8 (according to [18]); (3) 0.04; 7.6; 4.2 (according to [19]); (4) −1.8; 10.2; 0.95 (according to our model). μ ୣ୶୮ .


μ ୡୟ୪ୡ(ସ) μ ୣ୶୮ **Figure 5.** Predicted µ calc(4) A versus experimental µ exp A values for the studied phosphatidylcholines with the line of identity.

ε<sup>ୟ</sup> ε<sup>୮</sup> − − − μୄ <sup>୵</sup>/ε<sup>୵</sup> As can be seen, the second value (εa) is about ten times smaller compared to εp, which indicates that the contribution of non-polar groups to the apparent dipole moment is more significant. A similar relationship was found by other authors [16,18,19], however, this effect was not so pronounced. This can result from the fact that literature models were based on homological series of compounds with small, simple polar groups (such as −COOH, −OH, −NH2), whereas our approach involves bulky, zwitterionic systems. The obtained contribution from the reorientation of water molecules µ w ⊥ /ε<sup>w</sup> is high, which can be explained by the ability of phosphatidylcholines to form hydrogen bonds with surrounding water dipoles. It is known that the hydration of the polar PC head groups is very high (even 11 water molecules per DPPC [44]), which may result in the formation of an organized water "quasi ice" lattice in the vicinity of a phosphocholine moiety [45]. The model developed in this paper for phosphatidylcholines cannot be applied to other phospholipids due to different hydration of polar groups (i.e., hydration for PC was determined to be 11.3 water molecules per lipid, whereas for PE it is 6.6). Although SM possesses the same polar group as PC, the presence of the hydroxyl group in the interfacial region may affect its hydration [46].
