11 Integration of Modelling at Various Length and Time Scales 229 EIJ PI(r)pJ(r）dn (11.2) Which assumes a local mean-field.However,the mean-field must account for the interchain interactions a non-local mean-field is preferred.A suitable choice leads to: Fmid[= EIJ (Ir-r'l)pr(r)pj(r')dr dr' (11.3) where s(r-r')is a cohesive interaction defined by the same Gaussian kernel as in the ideal chain Hamiltonian.This parameter is then directly related to a calculable property,namely the Flory-Huggins interaction pa- rameter X. -DPD DPD is a particle based method that uses soft-spheres to represent groups of atoms,and incorporates hydrodynamic behavior via a random noise, which is coupled to a pair-wise dissipation.These terms are coupled so as to obey the fluctuation-dissipation theorem.Groot and Warren [11.12 established the connection between a DPD fluid and a real fluid again re- lating the bead-bead interaction potential to the Flory-Huggins parameter X.For a full description of DPD and some of its applications see [11.14] and[11.15. The two methods overlap,but DPD is preferred where concentrations are low,and MesoDyn is ideal for systems,which comprise polymer melts and blends. 11.3.3 Applications of Mesoscale Modeling The mesoscale techniques have been used to rationalize complex behaviour of latex emulsions for the paints,coatings and lubricants industries [11.16. A series of simulations was undertaken to establish the link between latex- particle size distribution and the hydrophilic chain length of the non-ionic surfactants used to stabilize the emulsion.The more uniform the size dis- tribution the more reliable the paint appearance and application rheology. Several MesoDyn calculations were performed with various chain lengths and a system,which led to optimal distribution of the latex particles was found. This was then taken to the laboratory where an improved formulation was established. In the area of drug delivery DPD and MesoDyn have found many appli- cations including formulation stability,active release profiles,compatibiliza- tion,effect of hydrophobic drugs on micelle sizes in a pluronic solution and the role of excipients.These complex problems are difficult to conceptualize, are poorly served by static theories and are critical to the efficacy of a novel drug formulation.11 Integration of Modelling at Various Length and Time Scales 229 Fnid RPA[ρ] = 1 2  IJ  V εIJ ρI (r)ρJ (r) dr (11.2) Which assumes a local mean-field. However, the mean-field must account for the interchain interactions a non-local mean-field is preferred. A suitable choice leads to: Fnid[ρ] = 1 2  V  V εIJ (|r − r |) ρI (r)ρJ (r ) dr dr (11.3) where εIJ (|r − r |) is a cohesive interaction defined by the same Gaussian kernel as in the ideal chain Hamiltonian. This parameter is then directly related to a calculable property, namely the Flory-Huggins interaction pa￾rameter χ. – DPD DPD is a particle based method that uses soft-spheres to represent groups of atoms, and incorporates hydrodynamic behavior via a random noise, which is coupled to a pair-wise dissipation. These terms are coupled so as to obey the fluctuation-dissipation theorem. Groot and Warren [11.12] established the connection between a DPD fluid and a real fluid again re￾lating the bead-bead interaction potential to the Flory-Huggins parameter χ. For a full description of DPD and some of its applications see [11.14] and [11.15]. The two methods overlap, but DPD is preferred where concentrations are low, and MesoDyn is ideal for systems, which comprise polymer melts and blends. 11.3.3 Applications of Mesoscale Modeling The mesoscale techniques have been used to rationalize complex behaviour of latex emulsions for the paints, coatings and lubricants industries [11.16]. A series of simulations was undertaken to establish the link between latex￾particle size distribution and the hydrophilic chain length of the non-ionic surfactants used to stabilize the emulsion. The more uniform the size dis￾tribution the more reliable the paint appearance and application rheology. Several MesoDyn calculations were performed with various chain lengths and a system, which led to optimal distribution of the latex particles was found. This was then taken to the laboratory where an improved formulation was established. In the area of drug delivery DPD and MesoDyn have found many appli￾cations including formulation stability, active release profiles, compatibiliza￾tion, effect of hydrophobic drugs on micelle sizes in a pluronic solution and the role of excipients. These complex problems are difficult to conceptualize, are poorly served by static theories and are critical to the efficacy of a novel drug formulation.