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| 2. |
- Jönsson, Bo, et al.
(författare)
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Titrating polyelectrolytes - Variational calculations and Monte Carlo simulations
- 1996
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Ingår i: Journal of Physical Chemistry. - : American Chemical Society (ACS). - 0022-3654 .- 1541-5740. ; 100:1, s. 409-417
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Tidskriftsartikel (refereegranskat)abstract
- Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. In the variational treatment, the Coulomb potentials are emulated by harmonic repulsive forces between all monomers; the force constants are used as variational parameters. The accuracy of the variational approach is tested against Monte Carlo data. Excellent agreement is obtained for the end-to-end separation and the apparent dissociation constant for the unscreened Coulomb chain. The short-range screened Coulomb potential is more difficult to handle variationally, and its structural features are less well described, although the thermodynamic properties are predicted with the same accuracy as for the unscreened chain. The number of variational parameters is on the order of N2, where N is the number of monomers, and the computational effort scales like N3. In addition, a simplified variational procedure with only two parameters is pursued, based on a rigid-rod approximation of the polymer. It gives surprisingly good accuracy for certain physical properties.
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| 3. |
- Jönsson, Bo, et al.
(författare)
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Variational approach to correlations in charged polymers
- 1993
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Ingår i: Physical Review Letters. - 0031-9007. ; 71:3, s. 376-379
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Tidskriftsartikel (refereegranskat)abstract
- A deterministic algorithm for calculating polymer properties is presented. It is based on a variational approach where the bond and Coulomb potentials are approximated by a quadratic trial energy. The parameters which describe average atom positions and Gaussian fluctuations, are the solutions of matrix equations. By a judicious choice of parameter representations and the use of incremental matrix inversion, an efficient iterative algorithm is constructed that is several orders of magnitude faster than Monte Carlo methods. The method is explored numerically at realistic temperatures with results that agree within 5% with those of Monte Carlo calculations.
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| 4. |
- Jönsson, Bo, et al.
(författare)
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Variational approach to the structure and thermodynamics of linear polyelectrolytes with Coulomb and screened Coulomb interactions
- 1995
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Ingår i: Journal of Physical Chemistry. - : American Chemical Society (ACS). - 0022-3654 .- 1541-5740. ; 99:4, s. 1251-1266
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Tidskriftsartikel (refereegranskat)abstract
- A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between all monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N3 rather than N4, as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed. An analysis of the high- and low-temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities. The accuracy of the approximations introduced is tested against Monte Carlo simulations for problem sizes ranging from N = 20 to 1024. Very good accuracy is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the harmonic variational Ansatz becomes less efficient with shorter range interactions. As a byproduct a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes-2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on low-T approximations to end-end and monomer-monomer separations. It is argued that the former increases faster than linearly with the number of bonds.
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| 5. |
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| 6. |
- Ullner, Magnus, et al.
(författare)
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A Monte Carlo study of titrating polyelectrolytes
- 1996
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 104:8, s. 3048-3057
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Tidskriftsartikel (refereegranskat)abstract
- Monte Carlo simulations have been used to study three different models for linear, titrating polyelectrolytes in a salt-free environment: (i) a rigid polymer with rigid bonds (rigid rod); (ii) a flexible polymer with rigid bonds; and (iii) a flexible polymer with flexible bonds. The use of a very efficient pivot algorithm has made it possible to simulate very long chains, with up to several thousand titrating groups. The results have been compared to a mean field approximation for a rigid rod and variational results emanating from a Flory type approach. It is found that the rigid rod mean field model gives a qualitatively correct description for the apparent dissociation constant for all three models. At room temperature, the energy contribution to the apparent dissociation constant often dominates over the entropic term, which partly explains the relative success of this approach. In the case of flexible bonds, both the conformational behavior and the behavior of the apparent dissociation constant are well described by a variational ansatz with a quadratic term, largely thanks to the harmonicity of the bonds themselves. The approach is less successful for rigid bonds, which becomes evident for highly charged chains where a harmonic entropy term is incorrect. This can be remedied by replacing it with an expression valid in the strong coupling regime. Empirical scaling expressions have also been found, primarily for the end-to-end distance.
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| 7. |
- Ullner, Magnus, et al.
(författare)
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The electrostatic persistence length calculated from Monte Carlo, variational and perturbation methods
- 1997
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Ingår i: Journal of Chemical Physics. - 0021-9606. ; 107:4, s. 1279-1287
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Tidskriftsartikel (refereegranskat)abstract
- Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-Hückel screening length, κ-1. As long as the salt content is low and κ-1 is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with κ-1. Decreasing the screening length, a controversial region is entered. We find that the electrostatic persistence length scales as √ξp/κ, in agreement with experiment on flexible polyelectrolytes, where ξp is a strength parameter measuring the electrostatic interactions within the polyelectrolyte. For screening lengths much shorter than the bond length, the κ-1 dependence becomes quadratic in the variational calculation. The simulations suffer from numerical problems in this regime, but seem to give a relationship half-way between linear and quadratic. A low temperature expansion only reproduces the first regime and a high temperature expansion, which treats the electrostatic interactions as a perturbation to a Gaussian chain, gives a quadratic dependence on the Debye length. For a sufficiently stiff chain, the persistence length varies quadratically with κ-1 in agreement with earlier theories.
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| 8. |
- Andersson, Bo, et al.
(författare)
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Implications of a large vector meson production on quark jet fragmentation and large p T reactions
- 1978
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Ingår i: Physica Scripta. - : IOP Publishing. - 0031-8949 .- 1402-4896. ; 18:4, s. 193-195
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Tidskriftsartikel (refereegranskat)abstract
- A large vector meson production in quark jet fragmentation implies characteristic differences between the kaon and pion spectra. This prediction is verified in a recent SLAC-MIT experiment. Similar considerations are relevant for the c-quark fragmentation into D-mesons, as observed in ν scattering experiments.The difference in kaon and pion spectra provides a test of the hard quark-quark scattering description of large p T events. In particular the K+/π+ ratio (∼ 1/2 for single particle triggers) should be around 0.1-0.2 for jet triggers.
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| 9. |
- Andersson, Bo, et al.
(författare)
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Quark Jet Fragmentation
- 1979
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Ingår i: Physica Scripta. - : IOP Publishing. - 0031-8949 .- 1402-4896. ; 19:2, s. 184-190
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Tidskriftsartikel (refereegranskat)abstract
- A semiclassical model is presented for the way the energy of a fast quark is transformed into observable hadrons. It reproduces the features of 1 + 1 dimensional QED (the Schwinger model) concerning a flat rapidity distribution in the central region. In particular the model predicts that the probability to find a meson containing a leading quark is independent of the Feynman scaling variable. Also a quark jet interpretation of low PT jets in hadronic interactions is discussed shortly.
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| 10. |
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