Simulating polydispersity effect

Clearly there is much to be done by using more realistic models, by doing Brownian dynamics simulations, by considering polydispersity effects, and ex-... 

In this experiment, the LLDPEs were simulated by hydrogenated (or deuterated) polybutadienes, because they can be prepared as monodisperse molecules (with a ratio of weight- and number-averaged molecular weights, Mw/M < 1.1) and a homogenous branch distribution within the chains. Such studies are therefore unaffected by polydispersity effects, either in the branch content or molecular... 

The increase of the corrected simulated relative extinction cross sections, with larger widths of the particle size distribution, tends to increase slightly with an increasing transmission. This effect appears for all theoretical relative extinction cross sections and principally can be explained by a dependence of polydispersity effect of other effects. Therefore, a correction of the polydispersity effect must be carried out as a function of the mean value of the transmission. 

Basically, the simulations can be performed for a variety of particle size distributions with different widths and shapes to determine the SE-Function. In this case, the correction of the polydispersity effect is carried out together with the correction of the boundary layer and the overlapping effect in one step by piecewise linear 3D interpolation. Thereby, a corrected particle size distribution is determined with an advanced PSD-SE-Method, which requires the measurement of enough independent transmission signals of tight beams with different geometries. 

FTIR, NMR, and EXAFS and ex situ methodologies such as electron microscopy (SEM and TEM) are also powerful and important tools in the investigation of the mechanisms by which materials form. Combination of experimental approaches not only facilitates their interpretation but also enables cross-correlation between experimental phenomena. This is especially important because SAXS provides information on reciprocal space. The estimation of the structure of a scatterer from its scattering profiles is called the inverse scattering problem, and this problem cannot be solved uniquely [1]. Scattering profiles are complicated further when polydispersity effects are operative, which is usually to some extent the case for sol-gel systems. In practice, the interpretation of SAXS patterns therefore depends heavily on the development of hypothetical structural models and on comparison of the simulated scattering profile, which can be calculated from a given structure, with the experimental profile. Hence, additional independent structural or chemical information may aid in the interpretation of SAXS profiles. 

Computationally, polydispersity is best handled within a grand canonical (GCE) or semi-grand canonical ensemble in which the density distribution p(a) is controlled by a conjugate chemical potential distribution p(cr). Use of such an ensemble is attractive because it allows p(a) to fluctuate as a whole, thereby sampling many different realizations of the disorder and hence reducing finite-size effects. Within such a framework, the case of variable polydispersity is considerably easier to tackle than fixed polydispersity The phase behavior is simply obtained as a function of the width of the prescribed p(cr) distribution. Perhaps for this reason, most simulation studies of phase behavior in polydisperse systems have focused on the variable case [90, 101-103]. 

Recently, Chu et al. [41,42] and Chu and Wasan [43] have made simulation and MSA studies of the structure and forces in thin films and colloidal dispersions. They include the effect of polydispersity. They also find oscillatory forces. 

T. L. Farias, U. O. Koylil, and M. G. Carvalho, Effects of Polydispersity of Aggregates and Primary Particles on Radiative Properties of Simulated Soot, Journal of Quant. Spectrosc. Radiative Transfer, 55, p. 357,1995. 

We have investigated theoretically film-thickness stability and structure formation inside a liquid film by Monte Carlo numerical simulations and analytical methods, using the Omstein-Zemicke (0-Z) statistical mechanics theory (21-24). The formation of longrange, ordered microstructures (giving rise to an oscillating force) within the liquid film leads to a new mechanism of stabilization of emulsions (3,4,25). In addition to the effective volume of micelles or other colloidal particles and polydispersity in micelle size, the film size is also found to be flic main parameter governing emulsion stability (15). 

Serra and coworkers studied the outstanding effect of mixing on conversion, molecular weight and polydispersity in free-radical polymerizations of styrene by a numerical simulation using different micromixer geometries [170, 171]. 

This paper proposes a phenomenological analysis, based on laboratory experimental work, of the effects of adsorption properties on pol3nner slug propagation. The adsorption properties studied include kinetic aspects, i.e. instantaneous adsorption, reorganization of macromolecules inside adsorbed layer, exchanges between free and adsorbed polymer, desorption as well as properties at thermodynamic equilibrium which can be described by a partially reversible adsorption isotherm. The conditions for hydro-dynamic retention are also discussed. In addition, an analysis of the effects of polymer polydispersity on each of these adsorption phenomena shows that these effects cannot be neglected in a predictive simulator. 

In a study (29) of differences in signals from two detectors, using the same tof instrument, equimass blends of narrow PMMA standards were used to simulate a wide polydispersity polymer and it was shown that different detection systems produced different MMD for the poljmier blend using the same sample preparation method and the same analyzer conditions. The differences arose from detection mechanisms, saturation effects in the detector, and signal to noise problems. 

An imderstanding of the influence of polydispersity on chain dynamics in the melt was achieved by Baschnagel and co-workers (177) in a simulation using BFM. These dynamic Monte Carlo simulations showed that long chains move more rapidly in the presence of short chains, and the short ones move more slowly in the presence of the long ones. The net effect is that the dsniamics of a polydis-perse melt is close to Rouse theory predictions, ie, the chains act as if they are not entangled An indirect approach to reptation dynamics was described by Byutner... 

---