Polymer mean particle displacement

If the penetrant enters the glassy matrix faster than the polymer can adapt itself by volume relaxation, the solvent front advances linearly with time. This behaviour is called case-II diffusion or relaxation-controlled diffusion. It is a special case of anomalous diffusion, where the mean square particle displacement is proportional to t. It commonly applies to polymers in the glassy state [Wei2]. Here the system 1,4-dioxane/PVC is an example (Fig. 10.1.8(b)). Due to the softening of the material behind the diffusion front, the polymer relaxation in the already swollen matrix is fast enough to adapt to a new situation created by further solvent uptake. Therefore, solvent ingress as well as swelling behind the diffusion front is Fickian. 

Latex Drying. Film formation from latexes poses a special problem in that one is not dealing with a continuum until a stage is reached at which most of the water has evaporated, the solid particles have undergone considerable distortion, and polymer begins to displace water at the interface. The residual stresses in this case are directed outward from the center of each particle in tiny domains. In the past, pigmentation and other means of achieving opacity exacerbated the problem (78). 

Another contribution to the correlation function, which cannot be neglected for large particles, is their rotational motion. This problem has not been treated theoretically so far but intuitively one can expect that when a large particle rotates, the mean-square displacement of embedded flurophores would be larger than that without rotation. Hence, a higher apparent diffusion coefficient than that for a pure translational diffusion should be observed. Recently, we also addressed this problem in our computer simulations. Because the use of PCS in polymer science is very limited, we will describe its advantageous features in Sect. 3.5. 

If particle motion were observed over times shorter than the viscoelastic relaxation times Particle displacements in successive moments would be correlated. Equation 12 would not be correct. log[g (q, r)]/ would not be proportional to the mean-square particle displacement during r. With respect to polymer dynamics, the interest in eqs 9-12 has been the short time regime in which viscoelastic effects are apparent in D(r), but in the short time regime eq 12 does not describe probe motion in solution. 

Concerning PCS, the most interesting observables from the simulations are the trajectories of single diffusion molecules or particles, respectively. From these trajectories, the mean square displacements and the autocorrelation functions can be calculated. This way, it can be analyzed how heterogeneity expresses itself in the PCS results, i.e., how anomalous diffusion is averaged over the relevant PCS time and length scales. Also, the question how interactions between dye and polymer chains influence PCS results has been recently addressed using a combination of PCS experiments with simulations [46] (Fig. 14). 

According to generally accepted theories (42, 43) the self-diffusion coefficient D of polymer melts is inversely proportional to the square of the chain length. For long chains, this leads to extremely low values of D. Since th mean square displacement of a particle in a specified direction, measure small D values is limited by the spatial resolution of the experimental technique. For instance, the first data on self-diffusion in a polymer melt were obtained following the diffusion of deuterated polyethylene into normal polyethylene by IR spectroscopy (44) and this technique could resolve only distances of 0.1 mm thus, experiments extending over a day could... 

Later authors (37) have studied extensively the preparation of polycaprolac-tone nanopanicles by solvent displacement. Rive factors of formulation affecting the particle size characteristics and the percentage of drug entrapment were studied aqueous medium temperature, diameter of the needle employed to inject the organic into the aqueous phase, organic phase volume, amounts of both polymer and surfactant. In ihi.s CCD, the authors specified that the results were the mean... 

The structure of foams and filled polymers was eharacterized by means of MRI. It is also possible to observe the deformation behavior of the structure of foams and filled polymers in situ. The NMR images were analyzed by image processing. Average distances between particles were estimated by the spectrum of the autocorrelation function. The displacement field was calculated by the cross-correlation function. Information about particle distances and micromechanical deformation can be obtained by NMR imaging methods by combining autocorrelation and cross-correlation. 

---