How to derive and parameterize effective potentials in colloid-polymer mixtures

Polymer chains in colloid-polymer mixtures can be coarse-grained by replacing them with single soft particles interacting via effective polymer-polymer and polymer-colloid pair potentials. Here we describe in detail how Ornstein-Zernike inversion techniques, originally developed for atomic and molecular fluids, can be generalized to complex fluids and used to derive effective potentials from computer simulations on a microscopic level. In particular, we consider polymer solutions for which we derive effective potentials between the centers of mass, and also between mid-points or end-points from simulations of self-avoiding walk polymers. In addition, we derive effective potentials for polymers near a hard wall or a hard sphere. We emphasize the importance of including both structural and thermodynamic information (through sum-rules) from the underlying simulations. In addition we develop a simple numerical scheme to optimize the parameterization of the density dependent polymer-polymer, polymer-wall and polymer-sphere potentials for dilute and semi-dilute polymer densities, thus opening up the possibility of performing large-scale simulations of colloid-polymer mixtures. The methods developed here should be applicable to a much wider range effective potentials in complex fluids.Comment: uses revtex4.cls; submitted for archival purpose

Effects of dietary fibre on behaviour and satiety in pigs

During the past decades there has been considerable interest in the use of dietary fibre in both animal and human nutrition. In human subjects dietary fibre has been studied intensively for possible effects on body-weight management and health. In animal nutrition the interest in dietary fibre has increased because it can be used as a cheap source of energy and because of its potential to improve animal welfare and reduce abnormal (mainly stereotypic) behaviour. Animal welfare is impaired if the diet does not provide sufficient satiety, combined with an environment that does not meet specific behavioural requirements related to natural feeding habits (e.g. rooting in pigs). A considerable proportion of the behavioural effects of dietary fibre are thought to be related to reduced feeding motivation. It has been hypothesized that: (1) bulky fibres increase satiety and thereby decrease physical activity and stereotypic behaviours immediately following a meal in pigs; (2) fermentable fibres prolong postprandial satiety and thereby reduce physical activity and appetitive behaviours for many hours after a meal. The validity of these hypotheses is examined by considering published data. In sows dietary fibres (irrespective of source) reduce stereotypic self-directed behaviours and substrate-directed behaviours, and to a lesser extent overall physical activity, indicating enhanced satiety shortly after a meal. Furthermore, fermentable dietary fibre reduces substrate-directed behaviour in sows and physical activity in sows and growing pigs for many hours after a meal. Evidence of long-term effects of poorly-fermentable fibre sources is inconclusive. The findings suggest that highly-fermentable dietary fibres have a higher potential to prolong postprandial satiet

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions

We calculate the two, three, four, and five-body (state independent) effective potentials between the centers of mass (CM) of self avoiding walk polymers by Monte-Carlo simulations. For full overlap, these coarse-grained n-body interactions oscillate in sign as (-1)^n, and decrease in absolute magnitude with increasing n. We find semi-quantitative agreement with a scaling theory, and use this to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many-body potentials. We also derive effective {\em density dependent} 2-body potentials which exactly reproduce the pair-correlations between the CM of the self avoiding walk polymers. The density dependence of these pair potentials can be largely understood from the effects of the {\em density independent} 3-body potential. Triplet correlations between the CM of the polymers are surprisingly well, but not exactly, described by our coarse-grained effective pair potential picture. In fact, we demonstrate that a pair-potential cannot simultaneously reproduce the two and three body correlations in a system with many-body interactions. However, the deviations that do occur in our system are very small, and can be explained by the direct influence of 3-body potentials.Comment: 11 pages, 1 table, 9 figures, RevTeX (revtex.cls

Rare events via multiple reaction channels sampled by path replica exchange

Transition path sampling (TPS) was developed for studying activated processes in complex systems with unknown reaction coordinate. Transition interface sampling (TIS) allows efficient evaluation of the rate constants. However, when the transition can occur via more than one reaction channel separated by a high barrier, TPS and TIS are ineffective in sampling both channels. The combination of replica exchange with TIS can overcome this problem. This work shows how, by including both the backward and forward reactions, the corresponding rate constants, as well as the free energy barrier can be computed in a single simulation. The method is illustrated on a two dimensional potential using the Langevin dynamics. In addition, a simpler algorithm based on only forward shooting from the interfaces is shown to give equally accurate results, and forms a bridge between the transition interface and the forward flux sampling methods. The diffusive behavior of the replicas can be used to assess the quality of the choice of the order parameter used for the interfaces

Investigating Rare Events by Transition Interface Sampling

We briefly review simulation schemes for the investigation of rare transitions and we resume the recently introduced Transition Interface Sampling, a method in which the computation of rate constants is recast into the computation of fluxes through interfaces dividing the reactant and product state.Comment: 12 pages, 1 figure, contributed paper to the proceedings of NEXT 2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, 21-28 Sep 2003, Cagliari (Italy

A Novel Path Sampling Method for the Calculation of Rate Constants

We derive a novel efficient scheme to measure the rate constant of transitions between stable states separated by high free energy barriers in a complex environment within the framework of transition path sampling. The method is based on directly and simultaneously measuring the fluxes through many phase space interfaces and increases the efficiency with at least a factor of two with respect to existing transition path sampling rate constant algorithms. The new algorithm is illustrated on the isomerization of a diatomic molecule immersed in a simple fluid.Comment: 14 pages, including 13 figures, RevTeX

Rate constants for diffusive processes by partial path sampling

We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the efficiency by sampling only parts of complete transition trajectories confined within a certain region. The algorithm assumes the loss of memory for highly diffusive progression along the reaction coordinate. We compare the new technique to the TIS method for a simple diatomic system and show that the computation time of the new method scales linearly, instead of quadraticaly, with the length of the diffusive barrier. The validity of the memory loss assumption is also discussed.Comment: 12 pages, including 8 figures, RevTeX

Evaluation of effect of the primary particle size on compactibility of spray-dried lactoses

Spray-dried lactose is one of the most used filler-binders in direct compaction of tablets. Spray-dried lactose is produced by spray-drying a suspension of α-lactose monohydrate crystals in a saturated aqueous solution of lactoses. The resulting product is composed of spherical particles, containing 80-85% crystals of α-lactose monohydrate (primary particles) and 15-20% amorphous lactose The compactibility of two commercial spray-dried lactoses, Pharmatose® DCL 11 (DCL11), prepared from α-lactose monohydrate with a median primary particle size of 34 µm and a new product, Pharmatose® DCL 14 (DCL14), prepared from 20 µm primary particles, were investigated