A Monte Carlo Study of Flexible Polymer Chain Conformations in Restricted Volumes. I. A Model for Insoluble Blocks Conformations in Swollen Cores of Multimolecular Spherical Block Copolymer Micelles

1993 ◽  
Vol 58 (10) ◽  
pp. 2290-2304 ◽  
Author(s):  
Zuzana Limpouchová ◽  
Karel Procházka
Keyword(s):  
Monte Carlo ◽  
Block Copolymer ◽  
Monte Carlo Study ◽  
Volume Effect ◽  
Micellar Systems ◽  
Flexible Polymer ◽  
Block Copolymer Micelles ◽  
Copolymer Micelles ◽  
Chain Conformations ◽  
Chain Lengths

Monte Carlo simulations of chain conformations in a restricted spherical volume at relatively high densities of segments were performed for various numbers of chains, N, and chain lengths (number of segments), L, on a tetrahedral lattice. All chains are randomly end-tethered to the surface of the sphere. A relatively uniform surface density of the tethered ends is guaranteed in our simulations. A simultaneous self-avoiding walk of all chains creates starting conformations for a subsequent equilibration. A modified algorithm similar to that of Siepmann and Frenkel is used for the equilibration of the chain conformations. In this paper, only a geometrical excluded volume effect of segments is considered. Various structural and conformational characteristics, e.g. segment densities gS(r), free end densities gF(r) as functions of the position in the sphere (a distance from the center), distributions of the tethered-to-free end distances, ρTF(rTF), etc. are calculated and their physical meaning is discussed. The model is suitable for studies of chain conformations is swollen cores of multimolecular block copolymer micelles and for interpretation of non-radiative excitation energy migration in polymeric micellar systems.

A Monte Carlo Study of Insoluble Block Orientations in Swollen Cores of Multimolecular Block Copolymer Micelles

1994 ◽  
Vol 59 (4) ◽  
pp. 803-819 ◽  
Author(s):  
Zuzana Limpouchová ◽  
Karel Procházka
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Volume Effect ◽  
Distribution Functions ◽  
Excluded Volume Effect ◽  
Block Copolymer Micelles ◽  
Copolymer Micelles ◽  
End To End ◽  
Tethered Chains ◽  
Self Avoiding Walk

Conformations of tethered chains in restricted spherical volumes with an increasing radius were studied by Monte Carlo simulations. Simulations were performed on a tetrahedral lattice at relatively high densities of the occupied lattice sites. A simultaneous self-avoiding walk of all tethered chains creates the starting conformations of the multi-chain system which are futher equilibrated by a modified algorithm similar to that of Siepmann and Frenkel. In this paper, only a geometric excluded volume effect of segments is considered. Selectively chosen series of data for changing numbers of chains, N, their lengths, L, and radii of the sphere, R, give information on the system behavior under various conditions. In this part of our systematic study of tethered chains in constrained volumes, we present angular distribution functions of the end-to-end, end-to-gravity center distances, etc. for system studied in previous paper. The second class of studied conformational characteristics are the distributions of projections of the end-to-end vectors into the selected directions (i.e. the radial direction and the direction of the first-to-second polymer segment connection).

Donnan Equilibria in Polymeric Micellar Systems with Weak Polyelectrolyte Shells: The Lowering of the pH Value

1997 ◽  
Vol 62 (11) ◽  
pp. 1730-1736 ◽  
Author(s):  
Petr Munk ◽  
Zdeněk Tuzar ◽  
Karel Procházka
Keyword(s):  
Ionic Strength ◽  
Block Copolymer ◽  
Ph Value ◽  
Electrolyte Solutions ◽  
Hydrogen Ions ◽  
Micellar Systems ◽  
Weak Electrolytes ◽  
Block Copolymer Micelles ◽  
Copolymer Micelles ◽  
Polyelectrolyte Solutions

When two electrolyte solutions are separated and only some of the ions can cross the boundary, the concentrations of these ions are different on both sides of the boundary. This is the well-known Donnan effect. When weak electrolytes are involved, the imbalance includes also hydrogen ions: there is a difference of pH across the boundary and the dissociation of nondiffusible weak electrolytes is suppressed. The effect is very pronounced when the concentration of the weak electrolyte is high and ionic strength is low. The significance of this phenomenon is discussed for polyelectrolyte solutions, and particularly for block copolymer micelles with weak polyelectrolyte shells. The effect is quite dramatic in the latter case.

Conformations of Insoluble Blocks in Swollen Micellar Cores of Multimolecular Block Copolymer Micelles Studied by Monte Carlo Simulation Technique

1994 ◽  
Vol 59 (4) ◽  
pp. 782-802 ◽  
Author(s):  
Karel Procházka ◽  
Zuzana Limpouchová
Keyword(s):  
Monte Carlo ◽  
Chain Flexibility ◽  
Monte Carlo Simulation Technique ◽  
Geometrical Constraints ◽  
Lattice Distance ◽  
Block Copolymer Micelles ◽  
Chain Conformations ◽  
Chain Lengths ◽  
Self Avoiding Walk ◽  
Physical Quantities

Monte Carlo simulations of chain conformations in restricted spherical volumes with an increasing radius were performed on a tetrahedral lattice (ca 2 700 to 9 200 lattice sites) at relatively high densities of the occupied lattice sites. A simultaneous self-avoiding walk together with the equilibration algorithm similar to that of Siepmann and Frenkel were used to create the equilibrated multi-chain conformations. (a) A series of simulations was carried out for a constant average segment density, <gS> = 0.52, together with the three values of the radius of the sphere, R = 10 l, 12.5 l and 15 l (l is the lattice distance), and various numbers of chains, N ∈ <15, 86>, and chain lengths, L ∈ <31, 163>. The results give information on the system behavior and on the effects of: (i) multi-chain conformational correlations, which depend both on N and L, (ii) the L-dependent chain flexibility, and (iii) R-dependent external geometrical constraints. Another two series of data: (b) for a constant average segment density, <gS> = 0.36, a constant N = 21, and L proportional to R3, and (c) for <gS> = 0.36, L = 47 and N proportional to R3, are shown to give a supplementary detailed information on conformational behavior of individual chains. Various physical quantities (e.g. the densities of chain free ends, gF(r), or distributions of the tethered end-to-the free end distances, ρTF(rTF), etc.) were calculated in the course of computer simulations and their shapes and physical significance is discussed with respect to the changing values of N, L and R.

Tethered Chains in Concave Volumes. A Monte Carlo Study

1994 ◽  
Vol 59 (10) ◽  
pp. 2166-2189 ◽  
Author(s):  
Karel Procházka ◽  
Zuzana Limpouchová
Keyword(s):  
Monte Carlo ◽  
Spherical Cavity ◽  
Monte Carlo Study ◽  
Volume Effect ◽  
Distribution Functions ◽  
Spherical Cavities ◽  
Chain Conformations ◽  
Tethered Chains ◽  
Self Avoiding Walk ◽  
Tethered Chain

Monte Carlo study of tethered chain conformations in spherical cavities was performed in a relatively broad range of average segment densities (i.e. numbers of tethered chains with increasing length in the sphere). Simulations were performed on a tetrahedral lattice using (i) an equilibrated self-avoiding walk for systems containing a single tethered chain with increasing length, and (ii) a simultaneous self-avoiding walk of many tethered chains in the spherical cavity together with equilibration of the system which was performed by a modified algorithm similar to that of Siepmann and Frenkel. Only a geometric excluded volume effect of segments was considered (i.e. the prohibition principle of a double occupancy of one lattice site by two different segments). Various distribution functions (e.g. distribution of the end-to-end and the end-to-gravity center distances and their orientations with respect either to the radial direction, or to the direction of the first-to-second segment connection, etc.) were calculated and the effect of increasing average segment density in the sphere on conformational characteristics of individual chains was studied. It was found that conformational and orientational properties of relatively short tethered chains are only little affected by increasing segment density (i.e. by the number of chains in the spherical cavity), whereas arrangements of long tethered chains are significantly influenced by the density of the system.

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