**6.1.3 Effects of the shear rate on the liposome properties**

*Mean diameter -* Additional data allowed the construction of the curve presented in Figure 8A. The curve shows a clear relationship between liposome comminution and shear rate, with the mean diameter exponentially decaying with applied shear rate. The error bars are higher at lower shear rates due to the poor homogenization of liposomes provided by the lower pumping capabilities of the mechanical systems.

The microchannel microfluidizer, working in the pressure range of 200 to 1500 bars, provided shear rates in the range of 2×105 to 6×105 s-1 .The data from the microchannel microfluidizer were obtained for pre-treated liposomes using Ultra-Turrax at shear and feed flow rates of 5600 to 24000 s-1 and 0.09 to 0.96 mL.s-1, respectively. The results show that the pre-formed liposomes reached the nanometric range (100 nm) in only one passage using Ultra-Turrax and the high shear rate range of the microchannel microfluidizer.

This comminution behavior agrees with the results reported by Diat et al. (1993a). Through a balance between elastic and viscous forces in the liposomes, the mean diameter is reduced according to the square root of the applied shear rate (Equation 21).

Technological Aspects of Scalable Processes for the

0.0 0.2 0.4 0.6

q [Å-1]

**Sample Period[Å] Bilayer** 

η

various shear treatments compared to control (Bangham's method).

A B C

Fig. 10. Transmission electronic microscopy of liposomes obtained using (A) Bangham's method followed by extrusion in membranes, (B) ultra-turrax under a shear rate of 21430 s-1, (C) microchannel microfluidizer under a shear rate 6 961 000 s-1. Bars :200nm

liposomes.

I(q) [arb. u.]

*N is the average number of bilayers and* 

**6.1.3.3 Morphology** 

Production of Functional Liposomes for Gene Therapy 285

lipids, and stiffness is an extensive property dependent on the structure and packing of the aggregate. Therefore, we associated the changes in the slope of the straight lines in Figure 8B with changes in the elastic constants as a consequence of the changes in packing in the

> -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Δρ [arb. u.]


 no shear extrusion microfluid turrax

**thickness[Å] <sup>N</sup>**<sup>η</sup>

r[Å]

turrax microfluid

extrusion

no shear

Fig. 9. Left: Small angle X-ray scattering (SAXS) profiles determined for the liposomes treated under moderate shear (extruded through polycarbonate membranes) and high shear produced by Ultra-Turrax*®* (21430 s-1) and microchannel microfluidizer devices (6 961 000 s-1).

Right: Electron density profile across the bilayer obtained from the fitting (see Table 3).

*no shear* 76.7±0.2 59,9±0.1 3.2±0.1 0.18±0.02 *Extrusion* 73.4±0.1 59,3±0.1 3.4±0.1 0.26±0.01 *Turrax* 72.5±0.2 59,1±0.1 4.1±0.1 0.26±0.01 *Microfluid* 72.3±0.1 59,2±0.2 2.3±0.1 0.09±0.01

 *is the Caillé parameter.* 

Figure 10 presents transmission electronic microscope images of the liposomes under

Table 3. Structural parameters obtained from full curve modeling of SAXS data.

Fig. 8. Cumulative hydrodynamic mean diameter as a function of the shear rate provided by Caules stirrer, Ultra-Turrax®, or microchannel microfluidizer. (A) Z-average values obtained from light scattering measurements. (B) Linear relationship from Equation 21 proposed by Diat et al. (1993a).

$$R = \sqrt{\frac{4.\pi.\left(2.k + \overline{k}\right)}{\mu.d.\dot{\gamma}}}\tag{21}$$

Where R is the liposome radius at equilibrium, k and k are the average and Gaussian elastic constant of the membrane, respectively, µ is the viscosity of the liposome dispersion, ߛሶ is the shear rate, and d is the interlamellar distance. The different slopes for the straight lines in Figure 9B were obtained for the shear rate ranges of the devices used, agreeing with the mass balance between elastic and viscous forces in the liposomes described by Diat et al. (1993b). Higher shear rates produce higher slopes, indicating the presence of liposomes with higher elastic constant, lower viscosity, and shorter interlamellar distance.

#### **6.1.3.1 Viscosity, surface tension, and zeta potential**

The shear rate also reduced the viscosity of the liposome dispersion from 5 to 2 mPa, but no significant changes were observed in the surface tension as a consequence of the reduction in size. However, the reduction in size also resulted in rearrangement of the lipids in the external layer, changing the zeta potential from -50 to -40 mV.

#### **6.1.3.2 Lamellar packing**

Small angle X-ray scattering (SAXS) characterization showed changes in the interlamellar distances for the applied shear rate ranges (Figure 9). The distance decreased with higher shear rates. The decreasing interlamellar distance was a consequence of the loss of interlamellar water, calculated to be up to 12% for the highest level of shear rate, as well as of lipid packing in the liposome, found to be less than 2%. The water layer is calculated as the difference between the full period and the bilayer thickness (see Table 4). These factors may explain the observed changes in zeta potential and the different slopes of the straight lines obtained for the studied shear rate ranges. In addition to the interlamellar distance and packing, the elasticity of the bilayer may also be influenced by the shear rate and changes in the elastic constants determined. In general, elastic modulus is not the same as stiffness. Elastic modulus is a property of the constituent material, whereas stiffness is a property of the structure. In the case of liposomes, the elastic modulus is an intensive property of the

A B

Cumulative mean hydrodynamic diameter (nm)

Fig. 8. Cumulative hydrodynamic mean diameter as a function of the shear rate provided by Caules stirrer, Ultra-Turrax®, or microchannel microfluidizer. (A) Z-average values obtained from light scattering measurements. (B) Linear relationship from Equation 21

π

*R*

higher elastic constant, lower viscosity, and shorter interlamellar distance.

**6.1.3.1 Viscosity, surface tension, and zeta potential** 

0 5000 10000150002000025000 2500000 5000000 7500000

 Ultra-Turrax Cowles Microfluidizer

Shear rate (s-1 )

external layer, changing the zeta potential from -50 to -40 mV.

4. . 2. ( ) . . *k k*

*d*

<sup>+</sup> <sup>=</sup> (21)

0,000 0,005 0,010 0,015 0,020 0,025 0,030

(Shear rate)-1/2 (s1/2)

 Ultra-Turrax Cowles Microfluidizer

μ γ

Where R is the liposome radius at equilibrium, k and k are the average and Gaussian elastic constant of the membrane, respectively, µ is the viscosity of the liposome dispersion, ߛሶ is the shear rate, and d is the interlamellar distance. The different slopes for the straight lines in Figure 9B were obtained for the shear rate ranges of the devices used, agreeing with the mass balance between elastic and viscous forces in the liposomes described by Diat et al. (1993b). Higher shear rates produce higher slopes, indicating the presence of liposomes with

The shear rate also reduced the viscosity of the liposome dispersion from 5 to 2 mPa, but no significant changes were observed in the surface tension as a consequence of the reduction in size. However, the reduction in size also resulted in rearrangement of the lipids in the

Small angle X-ray scattering (SAXS) characterization showed changes in the interlamellar distances for the applied shear rate ranges (Figure 9). The distance decreased with higher shear rates. The decreasing interlamellar distance was a consequence of the loss of interlamellar water, calculated to be up to 12% for the highest level of shear rate, as well as of lipid packing in the liposome, found to be less than 2%. The water layer is calculated as the difference between the full period and the bilayer thickness (see Table 4). These factors may explain the observed changes in zeta potential and the different slopes of the straight lines obtained for the studied shear rate ranges. In addition to the interlamellar distance and packing, the elasticity of the bilayer may also be influenced by the shear rate and changes in the elastic constants determined. In general, elastic modulus is not the same as stiffness. Elastic modulus is a property of the constituent material, whereas stiffness is a property of the structure. In the case of liposomes, the elastic modulus is an intensive property of the

proposed by Diat et al. (1993a).

Cumulative mean hydrodynamic diameter (nm)

**6.1.3.2 Lamellar packing** 

lipids, and stiffness is an extensive property dependent on the structure and packing of the aggregate. Therefore, we associated the changes in the slope of the straight lines in Figure 8B with changes in the elastic constants as a consequence of the changes in packing in the liposomes.

Fig. 9. Left: Small angle X-ray scattering (SAXS) profiles determined for the liposomes treated under moderate shear (extruded through polycarbonate membranes) and high shear produced by Ultra-Turrax*®* (21430 s-1) and microchannel microfluidizer devices (6 961 000 s-1). Right: Electron density profile across the bilayer obtained from the fitting (see Table 3).


*N is the average number of bilayers and* η *is the Caillé parameter.* 

Table 3. Structural parameters obtained from full curve modeling of SAXS data.
