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Polyelectrolytes in dilute solutions (0.01 mmol/L) adsorb in a two-dimensional lamellar phase to oppositely charged lipid monolayers at the air/water interface. The interchain separation is monitored by Grazing Incidence X-ray Diffraction. On monolayer compression, the interchain separation decreases to a factor of two. To investigate the influence of the electrostatic interaction, either the line charge density of the polymer is reduced (a statistic copolymer with 90% and 50% charged monomers) or mixtures between charged and uncharged lipids are used (dipalmitoylphosphatidylcholine (DPPC)/dioctadecyldimethylammonium bromide (DODAB)) On decrease of the surface charge density, the interchain separation increases, while on decrease of the linear charge density, the interchain separation decreases. The ratio between charged monomers and charged lipid molecules is fairly constant; it decreases up to 30% when the lipids are in the fluid phase. With decreasing surface charge or linear charge density, the correlation length of the lamellar order decreases.

Traditional Langmuir monolayers at the air/water interface are formed from amphiphilic, mostly lipid-like molecules. They contain hydrophilic heads that anchor onto the water subphase and hydrophobic tails that point toward the air. These monolayers have gained interest in the field of chemistry, physics and life science [

Most water-soluble polymers are charged,

This description is very qualitative. One cannot predict, when flatly adsorbed PEs are in a disordered or in a lamellar conformation [

Side view of the monolayer with adsorbed polyelectrolyte (PE) at the air-water interface (

Recently, we investigated polystyrene sulfonate (PSS) in a lamellar phase adsorbed onto an oppositely charged lipid monolayer. The lipids were dioctadecyldimethylammonium (DODA) with a positively charged head group [_{K} is smaller than the persistence length _{P} (_{K} ≤ _{P}) then the polymer is approximated as an elastic rod. Only if the contour length exceeds the persistence length (_{K} ≥ _{P}), then the chain can be described as a flexible polymer.

The lateral pressure π_{c}, which marks the LE/LC phase transition of lipid monolayers, does depend very strongly on the molecular weight. In the past, a reduction of the transition pressure π_{c} due to decreased electrostatic repulsion between the lipid head groups has been observed [_{c} with the molecular weight of PSS has been observed. It cannot be attributed to electrostatic forces as described by the DLVO theory [_{c} decreases on increase of the molecular weight, until the contour length corresponds to the persistence length, then π_{c} is independent of the molecular weight. For polystyrene sulfonate (PSS) a persistence length of _{P} = 210 Å was found (molecular weight 16 kDa) [_{P,steric} = 30 Å) [_{c}, the temperature dependence of the transition enthalpy ∆_{K} exceeds the persistence length _{P}. Then the temperature dependence of the phase transition enthalpy is low and constant. The lipids in the LE phase are partially immobilized by binding to a flexible rod; they loose entropy in the LE phase. The longer the flexible rod, the lower are transition pressure und transition enthalpy. If _{K} ≥ _{P}, polymer length is no longer important.

Now, we want to decrease the influence of the electrostatic forces. We use two different approaches. First, the line charge density of the PE is reduced (see

Polyelectrolytes adsorbed to oppositely charged monolayers: (_{x}_{1−}_{x}

We use PEs with large molecular weight, to actually adsorb a flexible polymer, and not an elastic rod. The PE concentration is low and leads to PE adsorption in a lamellar manner, 0.01 mmol/L with respect to the monomer concentration [

The cationic lipid dioctadecyldimethylammonium bromide (DODAB) and the zwitterionic DPPC are from Avanti, Alabaster, AL, USA. The strong polyanions are PSS sodium salt with molecular weight _{w} = 16 and 75.6 kDa, respectively and with polydispersity index PDI ≤ 1.1 and degree of sulfonation 97% (Polymer Standards Service, Mainz, Germany). The random copolymers are P–TrisAA_{x}_{1−}_{x}

Surface pressure isotherms (π-A isotherms) are measured on a Teflon trough (Riegler and Kirstein, Potsdam, Germany). The surface pressure is recorded with a Wilhelmy-type pressure measuring system using filter paper as plate with an accuracy of 0.1 mN/m. The area of the trough is 3.0 × 30 cm^{2}. DODA or DODA/DPPC, respectively, is spread from 0.14 mmol/L chloroform/methanol (3:1) [volume] solutions, using a 100 µL syringe.

The monolayers are compressed at a rate of 3 Å^{2}/(molecule·min) after allowing 10 min for the evaporation of the solvent. Ultrapure water from a Milli-Q system with a resistance above 18 MΩ is used. Always, the subphase contains PE. The PE concentration is set to 0.01 mmol/L (with respect to the monomer concentration) and kept constant, leading to a pH value slightly below 6. The temperature is controlled by a thermostat (DC-30 Thermo-Haake, Haake-Technik, Karlsruhe, Germany). All isotherms shown are obtained during the first compression of the monolayer.

Grazing-incidence diffraction measurements were performed at the _{i} =_{c}_{c}_{f}

According to the geometry of diffraction, the scattering vector _{xy}^{2}α_{i} + cos^{2}α_{f} - 2cosα_{i} cosα_{f} cos2θ)^{1/2} and an out-of-plane component Q_{z} = 2π/λ(sinα_{i} + sinα_{f}). The positional correlation length ξ can be determined from the full width half maximum (_{whm}). For an exponential decay of positional correlation as observed in liquid crystals, corresponding to a Lorentzian as a Bragg profile, one obtains ξ = 2/_{whm}(_{xy}).

The position-resolved scans were corrected for illuminated area. Model peaks are assumed to be Lorentzians in the in-plane direction and Gaussians in the out-of-plane direction, and are fitted to corrected intensities. The lattice spacing is obtained from the in-plane diffraction data.

_{x}_{1−x}, for _{c}_{c}_{c}_{c} is assigned to the intersection. At the end of the coexistence region, the lipids are in the LC phase and π increases steeply.

Surface pressure—area isotherms of lipid monolayers on 0.01 mmol/L PE solution (with respect to the monomer concentration). (_{x}_{1−x} at temperatures indicated. ((_{c} marks the onset of the LE/LC phase transition. The temperature dependence of π_{c} is shown in the insets. (_{w} = 77 kDa) in the subphase. The composition of the monolayer is varied. The inset shows the average area per molecule at 30 mN/m.

For each system the temperature is varied. As expected, the phase transition pressure π_{c} increases on heating. However, the temperature dependence of π_{c} depends on the composition of the statistical copolymer: if the charged monomers AMPS form 90% of the statistical copolymer, the temperature dependence is strong (∂π_{c} / ∂_{c} / ∂^{2}/molecule, suggesting some fluid lipids. However, the decrease of the transition pressure π_{c} is attributed to the changed head group interactions of the mixed lipid monolayer. Note that DODA, DPPC and dipamitoylphosphatidylehtanolamine (DPPE) have the same saturated alkyl tails with 16 C-atoms (note that for DODA two C-atoms of each hydrocarbon chain are attributed to the head group). DPPE shows no fluid phase at 20 °C [

The repulsion between the head groups of DODA and DPPC have different physical origins. Therefore, mixing the two lipids reduces both the DODA–DODA and DPPC–DPPC repulsion. In the LC phase, the average distance between the charged DODA head groups is increased compared to a pure DODA monolayer. Therefore, the electrostatic repulsion of the DODA head groups is reduced.

The temperature dependence of the phase transition pressure dπ_{c}/d_{c}/d_{w} (PSS) = 16 kDa is reached (superscript “1” indicates data from [_{x}_{1−x} influences dπ_{c}/d

DODA monolayer | |
---|---|

PSS (4 kDa)^{1} |
1.58 |

PSS (6.5 kDa)^{1} |
1.28 |

PSS (8.6 kDa)^{1} |
1.04 |

PSS (16, 33, 77, 168, 1330 kDa)^{1} |
0.85 ± 0.05 |

P–trisAA_{0.1}–rand–AMPS_{0.9} |
1.76 |

P–trisAA_{0.5}–rand–AMPS_{0.5} |
0.68 |

Furthermore, the steric repulsion of the DPPC head-groups is decreased, due to the incorporation of small DODA head groups in the monolayer. The decreased head group repulsion solidifies the lipid monolayer, and the LE/LC phase transition pressure π_{c} of the lipid mixtures is reduced.

To better understand the LE/LC phase transition of the monolayers, the transition enthalpy ∆

_{A} the Avogradro constant. _{fl}_{s}

Transition Enthalpy ∆_{x}_{1−x} (_{x}_{1−x} is 0.01mmol/L in monomer units.

_{w} = 16 kDa, _{K}_{PE}. On monolayer compression the low-angle peak shifts to larger _{xy}^{−1}), indicating a decrease of the interchain separation _{PE}. In the coexistence region, the low-angle peak observed in the fluid phase exhibits a constant position [_{xy}_{z}_{xy}_{z}^{−1} ≤ _{xy}^{−1}) [_{z}_{z}_{xy}_{z}

The surface charge of the monolayer is reduced by mixing DODA with increasing proportions of DPPC, mixtures of 90%, 75% and 50% DODA are used. Small angle GID peaks due to aligned PSS chains are only observed, when the mixtures contain 90% or 75% DODA (see

When the DODA proportion is reduced to 75%, the onset of the surface pressure increase at 75 Å^{2} suggests a LE phase. No clear LE/LC phase transition can be discerned. However, above 3–5 mN/m wide angle peaks are observed which indicate that at least some lipids are in the LC phase. These wide angle peaks are similar to those obtained with pure DODA monolayers, yet the peak at low _{z}_{xy}_{z}_{0.5}DPPC_{0.5} is similar: it is orthorhombic with a tilt towards the next neighbor (data not shown).

Small and wide angle Grazing Incidence X-ray Diffraction (GID) measurements along DODA_{y}_{1−}_{y}_{w} (PSS) = 16 kDa). (_{0.9}DPPC_{0.1} (_{w} (PSS) = 76 kDa). (_{0.75}DPPC_{0.25} (_{w} (PSS) = 76 kDa). For the small angle peaks, background is subtracted. Contour plots are calculated from least square fits to appropriate models.

_{diffr} measured by diffraction correlates with the tilt angle _{diffr} = _{tail}/cos(_{tail} is the average area of the tails, measured perpendicular to the long axis. One obtains _{tail} = 20 Å^{2}. This value is very similar to the 19.8 Å^{2} known from phospholipid monolayers [

The liquid condensed (LC) phase of DODA_{y}_{1−y} monolayers with different proportions of DODA. The tilt angle _{diffr} (_{diffr}/20). (_{w} (PSS) = 76 kDa, _{PSS} = 0.01 mmol/L with respect to the monomer concentration).

Additionally, _{tilt,┴} perpendicular to the tilt angle (≈30 Å) [_{tilt,┴} is larger (≈150 Å). _{tilt,┴} on the film composition. ξ_{tilt,┴} increases on decrease of the DODA proportion. When the DODA proportion is 50%, the correlation length is almost as large as for pure DPPC monolayers. The dependence of the tilt angle and of the correlation length on the monolayer composition confirms our assumption that DODA and DPPC form homogeneous mixtures.

In the next step, PSS is replaced by the statistical copolymer P–trisAA_{x}_{1−x} with a reduced line charge. DODA monolayers with their large surface charge are used. Again, small-angle diffraction peaks due to aligned PE chains are observed (_{0.1}–rand–AMPS_{0.9}, peaks are observed along the whole isotherm, when the lipids are in the LE and the LC phase (see wide-angle diffraction peaks). However, for P–trisAA_{0.5}–rand–AMPS_{0.5} with its reduced line charge, small angle peaks are observed only when DODA is in the LE phase. In the LC phase, wide angle GID peaks due to ordered alkyl tails are found, but there are no low angle peaks due to aligned PSS chains.

Small and wide angle GID measurements along DODA isotherms at the molecular areas indicated. The subphase contains 0.01 mmol/L P–trisAA_{x}_{1−x} (with respect to the monomer concentration), _{0.1}–rand–AMPS_{0.9}. (_{0.5}–rand–AMPS_{0.5}. Always, background is subtracted and contour plots are calculated from least square fits to appropriate models.

_{PE} as deduced from the low angle GID peaks is plotted for the different systems. On monolayer compression, it decreases at most by a factor of two, provided the monolayer shows both a LE and a LC phase. Also shown is the ratio of lipid molecules to PE monomers, _{PE}/_{Lipid}. To get further insight into electrostatic interactions, the ratio between charged PE monomers and charged lipid molecules is given, ch_{PE}/ch_{Lipid}. For these calculations, the average molecular area _{PE} (_{monomer} = 2.5 Å _{PE}; 2.5 Å is the monomer length of all PEs, see _{x}_{1−x}.

Top row: The dependence of the interchain separation _{PE} on the molecular area _{x}_{1−x} adsorbed to DODA. Center row: the ratio between PE monomers and lipid molecules, _{PE}/_{Lipid}. Bottom row: ratio of charged PE monomers to charged lipid molecules, ch_{PE}/ch_{Lipid}.

For the mixed DODA/DPPC monolayers with adsorbed PSS, _{PE} increases with decreasing surface charge. This observation is valid when the lipids are in the LC phase, in the LE phase, or the coexistence region of the LE and LC phase. A comparison of the three monolayers shows that a decrease of the fraction of the charged lipids causes a decrease in the ratio _{PE}/_{Lipid} (see _{PE}/ch_{Lipid}, is between 0.5 and 0.8. Expected are values below 1, reversal of the surface charge hinders the formation of the lamellar phase. ch_{PE}/ch_{Lipid} is largest for the system with the highest surface and linear charge density, DODA monolayers (see _{PE}/ch_{Lipid} = 0.74 and 0.67). In the LC phase, ch_{PE}/ch_{Lipid} increases to about 0.8. However, in the LE phase, ch_{PE}/ch_{Lipid} decreases with decreasing fraction of charge lipids.

Next, pure DODA monolayers with adsorbed PSS and statistical copolymer P–TrisAA_{x}_{1−x}, are compared (see _{PE} coincides within resolution for all phases of the lipid monolayer. When 50% of the monomers are charged, _{PE} is drastically decreased. The interchain separation is smaller, _{0.5}–rand–AMPS_{0.5}, Bragg peaks can only be observed when the DODA monolayer is in the LE phase. _{PE}/_{Lipid} shows that for this copolymer with the low line charge about one monomer per lipid molecule is adsorbed. This ratio between PE monomers and lipid molecules suggests that in the LC phase the interchain separation is 20 Å or less,

Nevertheless, when we consider the ratio between charged monomers and lipid molecules, we get again values below 1. ch_{PE}/ch_{Lipid} depends on the phase of the lipids. When the lipid phase is unchanged, ch_{PE}/ch_{Lipid} changes little during monolayer compression (see _{PE}/ch_{Lipid} for each lipid phase (see _{PE}/ch_{Lipid} is larger in the LC phase than in the LE phase. When the surface charge is varied, ch_{PE}/ch_{Lipid} is fairly constant, suggesting that the adsorption is mainly due to electrostatic forces. However, with decreasing linear charge, ch_{PE}/ch_{Lipid} decreases. The neutral monomers seem to interact strongly with the DODA monolayer; other interactions besides electrostatic forces have to be considered.

Ratio of charged adsorbed PE monomers to charged lipid molecules ch_{PE}/ch_{Lipid} as function of the surface charge or linear charge density, respectively. Each value of ch_{PE}/ch_{Lipid} shown is the average of all GID measurements taken from the lipid phase indicated. (_{y}_{1−y} monolayers with adsorbed PSS. (_{x}_{1−x} with

The correlation length is a measure of the extension of lateral order. _{PE}, the correlation length of the domains consisting of aligned PEs. ξ_{PE} depends on the phase of the lipids. When the monolayer is compressed within a lipid phase, ξ_{PE} does not change [_{PE} for each lipid phase (see _{PE}/_{PE} (see _{PE} is found for PSS adsorbed to DODA in the LC phase, it corresponds to three times _{PE}.

Left: DODA_{y}_{1−y} monolayers with adsorbed PSS (76 kDa). Right: DODA monolayers with adsorbed PE (PSS, P–TrisAA_{x}_{1−x} with _{PE} of adsorbed PEs as function of the surface charge density or linear charge density, respectively. Bottom: Ratio between correlation length ξ_{PE} and interchain separation _{PE} and ξ_{PE}/d_{PE} are the average of all GID measurements taken from the lipid phase indicated. Symbol assignment and color code is the same as

For all DODA_{y}_{1−y} monolayers, we find a larger correlation length ξ_{PE} when PSS adsorbs to the LC phase than to the LE phase. This finding was attributed to a larger mobility of PSS adsorbed to lipids in the LE phase [_{PE} decreases. If PSS adsorbs to lipids in the LC phase, the ratio ξ_{PE}/d_{PE} decreases from 3 to 2. However, if the lipids are in the LE phase, the decrease is more drastic, from 1.3 to 0.6. The small value of ξ_{PE}/d_{PE} suggests that on further decrease of the surface charge density PSS will adsorb no longer in the 2-D lamellar phase, but in a flatly disordered phase.

For the statistic copolymer adsorbed to DODA, the picture is more complex. Already for the strongly charged P–TrisAA_{0.1}–rand–AMPS_{0.9}, we obtain ξ_{PE}/d_{PE} = 1, independent of the lipid phase. The order of the aligned PE chains is very short-ranged. When the proportion of charged monomers is decreased (P–TrisAA_{0.5}–rand–AMPS_{0.5}), Bragg peaks due to aligned PE molecules are only found when the lipids are in the LE phase. ξ_{PE}/d_{PE} is small, only 0.6. When the lipids are in the LC phase, d_{PE} decreases further. Now, the positional broadening of the PE chain (in the direction perpendicular to the chain) exceeds the distance between adjacent PE chains, no diffraction peaks can form. This is indeed observed.

Actually, we developed a model of the density distribution of the adsorbed PE chains beneath the lipids described in [_{total} is the sum of a laterally homogeneous part, ρ(_{diff}(_{diff}(x, y, z) = 0. The molecular form factor is given by the Fourier transformation, |_{mol}(_{z})|^{2} = |∫∫∫dxdydz ρ·_{diff}(x, y, z) ·exp(_{x}x_{y}y_{z}z^{2}. When a Bragg peak in _{xy}_{PE}, consisting of a chain with a diameter _{chain} and electron density ρ_{PE} embedded in water (width _{PE}_{chain}, electron density ρ_{H2O}). Focusing on the in-plane integration at the peak position, one has _{peak} yields _{0.1}–rand–AMPS_{0.9}, one obtains ρ_{PE} = 0.372 e^{−}/Å^{3}, which decreases for P–TrisAA_{0.}_{5}–rand–AMPS_{0.}_{5} to 0.356 e^{−}/Å^{3}. When the lipids are in the fluid phase, one obtains for ^{−}/Å^{2}, respectively. In the gel phase, _{PE} is decreased, and so is ^{−}/Å^{2}, respectively. The latter number is an estimate, since below the lipids in the gel phase, no peak of P–TrisAA_{0.}_{5}–rand–AMPS_{0.}_{5} is observed (see _{PE} = 15 Å. Note that _{0.}_{5}–rand–AMPS_{0.}_{5} has an electron density more similar to water than the random copolymer with the larger linear charge density and (b) _{PE} approaches the diameter of P–TrisAA_{0.}_{5}–rand–AMPS_{0.}_{5} (15 and 12 Å, respectively).

The description of the adsorbed PEs helps to understand the transition enthalpy ∆_{0.5}–rand–AMPS_{0.5} highlights the importance of not-electrostatic interactions between polyelectrolytes and model membranes.

A combination of thermodynamic analysis and Grazing Incidence X-ray Diffraction (GID) is used to investigate the adsorption of PEs to oppositely charged lipid monolayers. The shed some light on the role of electrostatic forces in PE adsorption, lipid monolayers of different composition (mixtures of DPPC and DODA) and PEs with different linear charge density (the statistic copolymer P–TrisAA_{x}_{1−x} with

In most cases we find the 2-dimensional lamellar phase. The ratio of charged PE monomers to charged lipid molecules, ch_{PE}/ch_{Lipid}, is always smaller one. The adsorbed PEs decrease but do not inverse the surface charge of the monolayer, as predicted theoretically [_{PE}/ch_{Lipid} is larger when the lipids are in the LC phase. ch_{PE}/ch_{Lipid} decreases by 30% or less, when the line charge density or the surface charge density is decreased and the lipids are in the LE phase. The ratio of charged monomers to lipid molecules, ch_{PE}/ch_{Lipid} depends on the phase of the lipids, it is not changed during compression of the respective lipid phase. This observation suggests that the PE/lipid interaction depends weakly on the lipid phase. ch_{PE}/ch_{Lipid} is largest for DODA/PSS, the system with the highest surface charge density and the highest linear charge density.

(

ch_{PE}/ch_{Lipid} varies, by 30%. For all DODA_{y}_{1−y} monolayers, ch_{PE}/ch_{Lipid} is larger when the lipids are in the LC phase. Nevertheless, some features are obvious: On decreasing the surface charge density, less PE adsorbs, to keep ch_{PE}/ch_{Lipid} more or less constant. Conversely, on decreasing the line charge, more PE adsorbs, and ch_{PE}/ch_{Lipid} shows a small decrease. Therefore, mainly electrostatic forces determine how much PE adsorbs in the two-dimensional lamellar phase. Actually, with decreasing surface charge or linear charge density, the extension of the lamellar order decreases. The smallest values of the correlation length observed are about half a chain separation.

Concluding, the combination of structural and thermodynamic data is a very powerful approach. Grazing Incidence Diffraction allows determining the surface coverage and especially the phase of the adsorbed polyelectrolyte. Thus, insight into the polyelectrolyte-monolayer interaction and the relative importance of electrostatic interactions is possible.

We thank Hamburger Synchrotron laboratory (HASYLAB) at Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany for beam time and for providing all necessary facilities. Discussions with Burkhard Dünweg were helpful. Financial support of the Deutsche Forschungsgemeinschaft (DFG) (He 1616/14-1) is appreciated.

This collaboration between Potsdam and Greifswald University has been directed at understanding and modifying the phases of PEs at interfaces. Thomas Ortmann is a doctoral student, supervised by Christiane A. Helm. He is responsible for the characterization of PEs adsorbed to lipid monolayers. Heiko Ahrens, Andreas Gröning and Frank Lawrenz helped with the experiments at the synchrotron; Heiko Ahrens was also instrumental in the analysis of the diffraction peaks. Sven Milewski was a Bachelor student who worked on lipid mixtures. Sebastian Garnier and André Laschewsky designed, synthesized and characterized the polyelectrolyte random copolymers of varying charge at Universität Potsdam.

The authors declare no conflict of interest.

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