# Formation of Uni-Lamellar Vesicles in Mixtures of DPPC with PEO-b-PCL Amphiphilic Diblock Copolymers

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

_{2}O) 99.90% was purchased from Euriso-top. The diblock copolymers poly(ethylene oxide)-block-poly(ε-caprolactone) (PEO-b-PCL) were synthesized via ring opening polymerization using PEO as the macroinitiator as described extensively elsewhere [23].

_{PEO}= 113 and N

_{PCL}= 49 and N

_{PEO}= 113 and N

_{PCL}= 20 respectively. PEO-b-PCL1 and PEO-b-PCL2 have molar masses of 10,600 and 7700 g mol

^{−1}, polydispersity (M

_{w}/M

_{n}) 1.43 and 1.18 and hydrophobic content (PCL) 53 and 30 % wt. respectively. In the mixtures of the polymers with DPPC, the DPPC/block copolymer molar ratio was 9/1.

#### 2.2. Sample Preparation

^{−1}, while dilution of stock solutions by the proper amount of water was performed for lower concentrations (10 and 3 mg mL

^{−1}). Samples were prepared in D

_{2}O unless otherwise stated. A Julabo thermostat was used to control sample temperature (accuracy 0.01 °C). A time period longer than half an hour at the desired temperature was allowed for equilibration. The temperatures 25, 37 and 45 °C were selected for the experiments. This way there was one temperature below (25 °C) and one above (45 °C) the gel-to-liquid crystalline phase transition [24,25,26,27] of DPPC tail-region bilayers, expected at 41–42 °C. The temperature 37 °C was chosen as it is the physiologically relevant body temperature.

#### 2.3. Small Angle Neutron Scattering Experiments

^{−1}was covered by three separate detection configurations (2, 8 and 20 m detection length) and neutron wavelength λ = 4.5 Å. The two-dimensional isotropic scattering data was treated by standard correction and reduction procedures and azimuthally integrated into 1-D scattered intensity $I\left(q\right)$. The flat background in the scattering profiles was subtracted from the experimental data. The instrumental resolution function [28,29] $\mathsf{\Delta}q\left(q\right)$ was introduced by a Gaussian function and was convoluted [30] with the theoretical SANS profiles ${I}^{th}\left(q\right)$ i.e., ${I}^{conv}\left(q\right)=\frac{1}{\sqrt{2\pi}\Delta q\left(q\right)}{{\displaystyle \int}}_{-\infty}^{+\infty}d{q}^{\prime}\xb7exp\left(-{\left(\frac{{q}^{\prime}-q}{\sqrt{2}\Delta q\left(q\right)}\right)}^{2}\right)\xb7{I}^{th}\left({q}^{\prime}\right)$. A Schultz distribution of vesicular internal radii was employed to treat polydispersity [31] as ${I}^{poly}\left(q;R\right)=\frac{{\left(\frac{z+1}{R}\right)}^{z+1}}{\Gamma \left(z+1\right)}{{\displaystyle \int}}_{0}^{+\infty}dr\xb7{r}^{z}\xb7exp\left(-\frac{z+1}{R}\xb7r\right)\xb7{I}^{conv}\left(q;r\right)$ where R is the mean internal radius (Results and Discussion). The polydispersity index is defined as $PDI={\left(z+1\right)}^{-1/2}$ with as $PDI=\frac{{\sigma}_{R}}{R}$ with ${\sigma}_{R}$ the root-mean-square deviation from the mean radius. In the fitting procedure ${I}^{poly}\left(q\right)$ was calculated in iterations and the sum of the weighted square differences ${\chi}^{2}={\displaystyle \sum}_{i=1}^{N}{\left(\frac{{I}^{poly}\left({q}_{i}\right)-{I}^{exp}\left({q}_{i}\right)}{\delta {I}^{exp}\left({q}_{i}\right)}\right)}^{2}$ between N theoretical and experimental intensities was minimized. Experimentally obtained intensities and their uncertainty are ${I}^{exp}\left({q}_{i}\right)$ and $\delta {I}^{exp}\left({q}_{i}\right)$ respectively. A custom made MATLAB code was used for ${I}^{poly}\left(q\right)$ calculations and for the application of a minimization algorithm based on a Monte Carlo simulated annealing scheme [32]. In the Results and Discussion section the fitting functions ${I}^{poly}\left(q\right)$ are referred to as $I\left(q\right)$.

## 3. Results and Discussion

^{−1}. It has to be noted that scattering from planar interfaces [36] follows $I\left(q\right)~{q}^{-2}$. In the case of DPPC/PEO-b-PCL1 (Figure 1) the situation is completely different. The power-law of $I\left(q\right)~{q}^{-3.33}$ cannot be followed by using a combination of uni- and multi-lamellar vesicles as in previous study [36]. Uni-lamellar vesicles introduce a trend $I\left(q\right)~{q}^{-2.23}$. In addition, multi-lamellar form factors introduce pronounced oscillations that are evidently not present in the data of DPPC/PEO-b-PCL1. In this case the form factor of vesicles had to be combined with the form factor of objects of different morphology. As it is demonstrated in Figure 1a the form factor of uni-lamellar vesicles is adequate to fit the data for $q>3\times {10}^{-2}{\mathrm{\AA}}^{-1}$. In order to fit the data at lower q the superposition with scattering from aggregates and clusters is employed. The presence of aggregates and clusters possibly corresponds to self-associations of PEO-b-PCL copolymers, associations of the copolymers with DPPC phospholipids in a random manner or combination of the two effects. Additionally, it may contain contributions of vesicle-vesicle associations.

_{2}O ($6.4\xb7{10}^{-6}{\mathrm{\AA}}^{-2}$) and H

_{2}O (−0.56$\xb7{10}^{-6}{\mathrm{\AA}}^{-2}$). The scattering amplitude of a single shell is ${A}_{shell}\left(q,B,R,{R}^{\prime}\right)=\frac{4\pi B}{{q}^{3}}\xb7\left(\left(sinq{R}^{\prime}-q{R}^{\prime}cosq{R}^{\prime}\right)-\left(sinqR-qRcosqR\right)\right)$. It has to be noted that the outer shells are identical in terms of thickness and SLD.

^{−1}and with high uncertainty. Therefore, the SLD profile cannot be resolved to the finest detail at the near sub-nm scale. This way the presence of the copolymer within the DPPC bilayers is not measurable. This is accompanied by the fact that the SLD of the copolymer blocks is between the values of the inner and outer layers of the bilayers, which would not lead to significant changes in the scattering contrast.

_{out}and d

_{in}do not seem to change as a function of temperature or concentration within experimental uncertainty (see following discussion on parameter uncertainties) in both PEO-b-PCL1 and PEO-b-PCL2 containing liposomes. In the case of pure DPPC a systematic decrease of the internal thickness was found and attributed to the gel-to-liquid crystalline phase transition of the lipid tail region [17,47].

_{B}T [51]. The vesicle distributions showed a sharp rise at sizes higher than a minimum critical size which is followed by a long tail at higher sizes. Increasing bending stiffness distribution maximum shifted to higher sizes and to more symmetric shapes. This is similar to the behavior observed here as a function of increasing temperature. Remarkably, PDI is found to drop as temperature increases in both polymers which in combination with the size increase can be thought of as an increase of bending stiffness (Table 1). Therefore, incorporation of PEO-b-PCL diblock copolymer chains enhances the rigidity of the bilayers and at the same time it increases their mean diameter.

^{−1}a drop is observed from 37 to 45 °C that does not agree with the rest of the results. It could be due to some partial precipitation in this particular sample. Mass percentages in PEO-b-PCL2 are higher than the ones of PEO-b-PCL signifying the higher hydrophobicity of this copolymer.

^{−1}at different temperatures (Figure 3 and Figure 4). Small, but clear change is found at 2.5 × 10

^{−2}−1.0 × 10

^{−1}× Å

^{−1}. The uncertainty of the measured SANS intensity is smaller than the size of data points at this q range (not shown). Additionally, the fitting model follows the different data sets showing that fitting procedure distinguishes the small differences induced by temperature. In the q range from 2.5 × 10

^{−2}to about 1 × 10

^{−1}× Å

^{−1}contributions from both aggregates and vesicles are significant. They are roughly equal (${I}_{agg}\approx {I}_{ves}$) at about 2 × 10

^{−2}× Å

^{−1}and at q > 2 × 10

^{−2}× Å

^{−1}${I}_{ves}$ gradually dominates scattered intensity. Any interdependency between parameters within or between the two form factors or any overlap of parameters within experimental uncertainty would not allow the extraction of conclusions regarding to which parameters really change by the temperature increase.

^{−1}are plotted as a function of temperature for the sake of discussion in Figure 5. It is evident that there is a clear increase from 25 °C to 37 °C and an apparent increase from 37 °C to 45 °C which is however within the experimental error in the case of $R$ and $D$. For ${R}_{g,agg}$ this is true only for PEO-b-PCL2 while for PEO-b-PCL1 it occurs from 37 °C to 45 °C. Actually, the significant change on the SANS profiles (Figure 2 and Figure 3b) are in the first temperature interval. In the second interval SANS profiles change only at the highest q values of the magnified region.

^{−1}at 45 °C for PEO-b-PCL1) the relative mass concentration of vesicles decreases as concentration decreases. This shows that there is an amount of material (either PEO-b-PCL or DPPC phospholipids or both) that leaves the vesicular state. Possibly this material is incorporated in clusters or causes stronger clustering of the initially formed aggregates.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) SANS profiles from DPPC/PEO-b-PCL1 at 30 (black) mg mL

^{−1}at 25 °C. Red line is the best fit with equation 1. Light gray and dark gray lines correspond to contributions from aggregates ${I}_{agg}$ and vesicles ${I}_{ves}$ respectively. Characteristic power-law trends are indicated by dashed lines. (

**b**) Fitting the data of (

**a**) using the additional term ${I}_{clust}$ (dashed line).

**Figure 2.**Number of vesicles per unit volume (

**a**) and aggregates’ forward scattering (

**b**) in solutions of DPPC/PEO-b-PCL1 (circles) and DPPC/PEO-b-PCL2 (squares) at 25 °C (black), 37 °C (red) and 45 °C (blue). Data from DPPC/PEO-b-PCL2 are multiplied by 2 for clarity. Gray dashed lines have slope equal to 1 and differ by a factor of 2.

**Figure 3.**(

**a**) SANS profiles from DPPC/PEO-b-PCL1 at 30 mg mL

^{−1}at 25 °C (black), 37 °C (red) and 45 °C (blue). (

**b**) Magnification of the region in rectangular from (

**a**). Fitting lines are shown with the same color as the corresponding experimental data.

**Figure 4.**(

**a**) SANS profiles from DPPC/PEO-b-PCL2 at 30 mg mL

^{−1}at 25 °C (black), 37 °C (red) and 45 °C (blue). (

**b**) Magnification of the region in rectangular from (

**a**). Fitting lines are shown with the same color as the corresponding experimental data.

**Figure 5.**SANS-extracted $R$ (closed circles) and $D$ (open circles) (

**a**) and ${R}_{g,agg}$ (

**b**) from DPPC/PEO-b-PCL1 (black) and DPPC/PEO-b-PCL2 (red) at 30 mg mL

^{−1}. Horizontal lines are used as a guide to the eye.

**Figure 6.**Corner plots of fitted parameters from DPPC/PEO-b-PCL1 at 30 mg mL

^{−1}at 25 °C. Interdependencies are shown as “n” for negligible, “w” for weak and “m” for moderate.

**Figure 7.**Concentration-normalized SANS profiles from DPPC/PEO-b-PCL1 at 3 (blue), 10 (red) and 30 (black) mg mL

^{−1}at different temperatures i.e., (

**a**) 25 °C, (

**b**) 37 °C and (

**c**) 45 °C.

**Figure 8.**Concentration-normalized SANS profiles from DPPC/PEO-b-PCL2 at 3 (blue), 10 (red) and 30 (black) mg mL

^{−1}at different temperatures i.e., (

**a**) 25 °C, (

**b**) 37 °C and (

**c**) 45 °C.

**Table 1.**SANS parameters extracted for DPPC/PEO-b-PCL1 solutions. Including number of vesicles per unit volume (N

_{ves}), vesicles’ diameter (D), vesicles’ polydispersity (PDI), forward scattering from aggregates (G

_{agg}), aggregates’ radius of gyration (R

_{g,agg}), aggregates’ fractal dimension (D

_{agg}), aggregates’ cut-off length (R

_{cut,agg}) and clusters’ scattering at the lowest q (I

_{0,clust}).

T (°C) | 25 | 37 | 45 | $\%\mathit{\delta}{\mathit{P}}_{\mathit{i}}/{\mathit{P}}_{\mathit{i}}*$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|

c (mg mL^{−1}) | 3 | 10 | 30 | 3 | 10 | 30 | 3 | 10 | 30 | |

DPPC/PEO-b-PCL1 | ||||||||||

N_{ves} (10^{−9} nm^{−3}) | 0.432 | 1.80 | 5.45 | 0.409 | 1.60 | 4.84 | 0.386 | 1.70 | 4.98 | 10 |

d_{out} (nm) | 0.61 | 0.64 | 0.60 | 0.59 | 0.62 | 0.58 | 0.62 | 0.63 | 0.60 | 29 |

d_{in} (nm) | 2.86 | 3.16 | 2.88 | 3.03 | 2.93 | 3.13 | 2.74 | 2.94 | 2.91 | 9.6 |

R (nm) | 8.66 | 8.66 | 8.83 | 9.95 | 9.98 | 10.2 | 10.5 | 10.8 | 10.8 | 3.7 |

D (nm) | 25.6 | 25.6 | 25.9 | 28.5 | 28.5 | 29.1 | 29.4 | 29.9 | 30.0 | 2.7 |

PDI | 0.853 | 0.853 | 0.827 | 0.760 | 0.760 | 0.730 | 0.705 | 0.696 | 0.695 | 5.9 |

G_{agg} (cm^{−1}) | 18.8 | 83.0 | 260 | 16.00 | 81.0 | 246 | 16.6 | 83.8 | 258 | 6.3 |

R_{g.agg} (nm) | 16.4 | 16.8 | 16.6 | 17.5 | 17.5 | 17.2 | 18.5 | 18.5 | 18.0 | 2.6 |

D_{agg} | 2.93 | 2.91 | 2.94 | 2.95 | 2.94 | 2.77 | 3.07 | 3.09 | 2.95 | 26 |

R_{cut.agg} (nm) | 7.61 | 6.60 | 6.52 | 6.86 | 6.86 | 6.68 | 6.58 | 6.58 | 6.33 | 19 |

I_{0,clust} (cm ^{−1}) | 231 | 164 | 162 | 210 | 171 | 241 | 159 | 236 | 127 | 8.0–30 |

DPPC/PEO-b-PCL2 | ||||||||||

N (10^{−9}nm^{−3}) | 0.567 | 1.99 | 6.14 | 0.523 | 1.67 | 5.00 | 0.479 | 1.60 | 5.18 | 10 |

d_{out} (nm) | 0.64 | 0.60 | 0.62 | 0.61 | 0.59 | 0.64 | 0.60 | 0.62 | 0.58 | 29 |

d_{in} (nm) | 2.87 | 2.96 | 2.86 | 3.15 | 3.08 | 2.89 | 2.94 | 2.97 | 2.91 | 9.6 |

R (nm) | 8.28 | 8.72 | 9.24 | 9.87 | 10.7 | 10.6 | 11.7 | 11.8 | 11.5 | 3.7 |

D (nm) | 24.8 | 25.7 | 26.8 | 28.4 | 29.9 | 29.9 | 31.7 | 32.0 | 31.3 | 2.7 |

PDI | 0.900 | 0.838 | 0.790 | 0.729 | 0.700 | 0.700 | 0.649 | 0.643 | 0.663 | 5.9 |

G_{agg} (cm^{−1}) | 24.1 | 86.5 | 261 | 29.3 | 91.00 | 273 | 23.4 | 79.1 | 264 | 6.3 |

R_{g.agg} (nm) | 16.8 | 16.7 | 16.5 | 19.3 | 18.4 | 18.4 | 18.8 | 18.7 | 18.1 | 2.6 |

D_{agg} | 2.85 | 2.98 | 2.94 | 3.30 | 3.14 | 3.14 | 3.19 | 3.17 | 3.07 | 26 |

R_{cut.agg} (nm) | 6.87 | 6.67 | 6.58 | 6.04 | 5.88 | 5.88 | 6.29 | 6.25 | 6.20 | 19 |

I_{0,clust} (cm^{−1}) | 384 | 633 | 262 | 463 | 581 | 304 | 373 | 670 | 269 | 8.0–30 ** |

**Table 2.**Percentage of mass concentration of vesicles relative to the nominal DPPC mass concentration (c

_{ves}/c · 100). The uncertainty δc/c on the presented concentrations is about 12%.

T (°C) | 25 | 37 | 45 | ||||||
---|---|---|---|---|---|---|---|---|---|

c (mg mL)^{−1} | 3 | 10 | 30 | 3 | 10 | 30 | 3 | 10 | 30 |

DPPC/PEO-b-PCL1 | 23.8 | 29.7 | 30.5 | 29.0 | 33.8 | 35.0 | 28.4 | 39.3 | 38.3 |

DPPC/PEO-b-PCL2 | 29.4 | 32.9 | 37.0 | 35.0 | 38.4 | 38.3 | 41.7 | 42.6 | 44.0 |

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**MDPI and ACS Style**

Papagiannopoulos, A.; Pippa, N.; Demetzos, C.; Pispas, S.; Radulescu, A.
Formation of Uni-Lamellar Vesicles in Mixtures of DPPC with PEO-b-PCL Amphiphilic Diblock Copolymers. *Polymers* **2021**, *13*, 4.
https://doi.org/10.3390/polym13010004

**AMA Style**

Papagiannopoulos A, Pippa N, Demetzos C, Pispas S, Radulescu A.
Formation of Uni-Lamellar Vesicles in Mixtures of DPPC with PEO-b-PCL Amphiphilic Diblock Copolymers. *Polymers*. 2021; 13(1):4.
https://doi.org/10.3390/polym13010004

**Chicago/Turabian Style**

Papagiannopoulos, Aristeidis, Natassa Pippa, Costas Demetzos, Stergios Pispas, and Aurel Radulescu.
2021. "Formation of Uni-Lamellar Vesicles in Mixtures of DPPC with PEO-b-PCL Amphiphilic Diblock Copolymers" *Polymers* 13, no. 1: 4.
https://doi.org/10.3390/polym13010004