Schematic representation of a cylindrical unit cell of radius and unit length . The cell is centered about a DNA segment of radius and negative charges per unit length . The aqueous region of the cell contains pointlike mobile salt ions and cationic polymer.
Excess free energy per unit cell, , as function of cell radius . The polyplex coexists with cationic polymer of fixed volume fraction in the bulk. The charge fraction of the cationic polymer in the bulk is . The inset shows the corresponding amount (volume per unit cell) of cationic polymer, . The dashed lines in the inset mark the equilibrium values for and .
The free energy per unit cell of a polyplex as function of cell radius , plotted for different values of . Note that (in contrast to Fig. 2) the amount of cationic polymer is fixed.
Local volume fraction of cationic polymer, , for various choices of , ranging from to . In all cases, and . The inset shows the corresponding dimensionless potentials .
Local fraction of charge, , for various choices of , ranging from to . In all cases, and .
The total amount of charge per unit cell carried by the cationic polymer according to Eq. (7). Different curves correspond to different as indicated. In all cases, .
The osmotic pressure exerted by a polyplex as function of cell volume for and . The osmotic pressure is calculated according to Eq. (8) using the data given in Fig. 3. The critical osmotic pressure and the corresponding cell volumes for and are indicated. In all cases, .
The pressure exerted by free (uncomplexed) cationic polymer as a function of monomer concentration displayed for and . The horizontal dashed line marks the critical osmotic pressure , beyond which a lipid vesicle of radius is expected to rupture.
The relation according to Eq. (14) at which the osmotic pressure is equal to the critical pressure needed for rupture of a vesicle of radius . Here, is the total volume of free (uncomplexed) cationic polymer present in the vesicle and is the total length of DNA. The two straight lines correspond to and . Within the hatched region vesicle instability is induced by increasing from to . The inset replots the relation in terms of the ratio of free polymer to adsorbed polymer, , as function of the volume fraction of DNA in the vesicle.
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