Macromolecular Theory and Simulations

Summary: Monte Carlo method was used to simulate the degradation of porous PLA scaffolds. The simulated volume was assumed to be divided homogeneously between the pore and solid PLA with the ratio equal to the bulk porosity of the scaffold. The volume was divided into surface and bulk elements where the surface elements were in direct contact with the aqueous degradation medium, while the bulk elements were surrounded by the pore and solid PLA. The effect of degradation time on PLA ester groups and carboxylic acid end‐groups for surface and bulk elements, pH, PLA degradation rate and mass loss, and PLA molecular weight distribution was simulated. For surface elements, pH remained constant at 7.4 over the entire time of degradation, while for bulk elements its value decreased significantly to as low as 5.8. The highest drop in pH within the scaffold was observed for the highest porosity of 90%. There was a lag time of at least 7 weeks in the mass loss for surface as well as bulk elements for porosities ranging from 70 to 90%. The mass loss for bulk elements was considerably faster than the surface elements. This difference in the rate of mass loss between the surface and bulk elements could affect the 3D morphology and dimensional stability of the scaffold in vivo as degradation proceeds. The simulation predicts that, due to differences in the rate of bulk and surface degradation, hollow structures could form inside the scaffold after 19, 17, and 15 weeks for initial porosities of 70, 80, and 90%, respectively.

A schematic diagram illustrating the degradation of an element on the outer surface of the scaffold (surface element) versus an element within the volume of the scaffold (bulk element).

The full moment equations and equations using pseudo‐kinetic rate constants for binary copolymerization with chain transfer to polymer in the context of the terminal model have been developed and solved numerically for a batch reactor operating over a wide range of conditions. Calculated number‐ and weight‐average molecular weights (M̄_n and M̄_w) were compared with those found using the pseudo‐kinetic rate constant method (PKRCM). The results show that the weight‐average molecular weights calculated using PKRCM are in agreement with those found using the method of full moments for binary copolymerization when polymeric radical fractions φ₁^˙ and φ₂^˙ of type 1 and 2 (radical centers are on monomer types 1 and 2 for a binary copolymerization) are calculated accounting for chain transfer to small molecules and polymer reactions in addition to propagation reactions. Errors in calculating M̄_w using PKRCM are not always negligible when polymer radical fractions are calculated neglecting chain transfer to small molecules and polymer. In this case, the relative error in M̄_w by PKRCM increases with increase in monomer conversion, extent of copolymer compositional drift and chain transfer to polymer rates. The errors in calculating M̄_w, however, vanish over the entire monomer conversion range for all polymerization conditions when chain transfer reactions are properly taken into account. It is theoretically proven that the pseudo‐kinetic rate constant for chain transfer to polymer is valid for copolymerizations. One can therefore conclude that the pseudo‐kinetic rate constant method is a valid method for molecular weight modelling for binary and multicomponent polymerizations.

The moment equations for binary copolymerization in the context of the terminal model have been solved numerically for a batch reactor operating over a wide range of conditions. Calculated number‐ and weight‐average molecular weights were compared with those found using pseudo‐kinetic rate constants with the method of moments and with the instantaneous property method for homopolymerization. With the pseudo‐kinetic rate constant method under polymerization conditions where number‐average molecular weights (M̄_n) are below about 10³ the error in calculating M̄_n exceeds 5%. The error increases rapidly with decrease in molecular weight for M̄_n < 10³. M̄_n measured experimentally for polymer chains (homo‐ and copolymers) have error limits of greater than ±5% at the 95% confidence level. Therefore, for all practical purposes, the pseudo‐kinetic rate constant method is valid for M̄_n greater than 10³. Errors in calculating weight‐average molecular weights (M̄_w) or higher averages are always smaller than those for M̄_n when applying the pseudo‐kinetic rate constant method. The assumptions involved in molecular weight modelling using the pseudo‐kinetic rate constant approach are thus proven to be valid, and therefore it is recommended that the pseudo‐kinetic rate constant method be employed with the instantaneous property method to calculate the full molecular weight distribution and averages for linear chains synthesized by multicomponent chain growth polymerization.

Free radical addition reactions in the presence of cobaloximes and related compounds have been modelled. Several mechanisms are presented and similarities with the “persistent radical effect” noted by Daikh and Finke are discussed. Cobaloximes and salophen

System. name: N‐acetyl‐p‐aminophenyl salicylate.

The nucleation of cavities in a homogeneous polymer under tensile strain is studied in a coarse‐grained MD simulation. To establish a causal relation between local microstructure and the onset of cavitation, a detailed analysis of some local properties is presented. In contrast to common assumptions, the nucleation of a cavity is neither correlated to a local loss of density nor to stress at the atomic scale or the chain‐end density in the nondeformed state. Instead, a cavity in glassy polymers nucleates in regions that display a low bulk elastic modulus. Even if the localization of a cavity is not directly predictable from the initial configuration, the elastically weak zones identified in the initial state emerge as favorite spots for cavity formation.magnified image

A general model for all kinds of size‐dependent melting points, free of any adjustable parameter, is extended to illustrate the size‐dependence of the melting temperature of polyethylene (PE). The model prediction for the depression of the melting temperature of PE is consistent with the calorimetric experimental results as shown in the Figure where the melting temperature of lamellae PE crystals as a function of the thickness of the crystals is presented.

The T_m(D) function of PE shown as a solid line in terms of Equation (4). The necessary parameters for use of Equation (4) are shown in Table 1. The symbols ○ and • denote the experimental evidence of T_m(D) of linear alkanes14b and cyclic alkanes,14c respectively. The values of D are determined by D = 0.1273n6 with 0.1273 nm being the orthorhombic CC lattice distance in the c‐direction.5 The symbol □ denotes the experimental evidence of chain‐extended PE.6

With the help of a simple reaction‐diffusion model with constant striation thickness the influence of micromixing on free‐radical polymerization was investigated for several test reactions with discontinuous prepolymerization and jerky addition of selected reactants. Monomer conversion or mean values of molar mass and chemical composition cannot be expected to be very sensitive to micromixing effects. If molar mass distributions are to be used, problems will arise from the fact that the distribution of the polymer accumulated during prepolymerization covers mixing influences occurring after reactant feed. The instantaneous molar mass distribution would be more suitable. Time‐integral distributions of chemical composition or sequence length in combination with appropriate test reactions proved to be feasible indicators for the effects of micromixing as it becomes possible to separate the distribution of the prepolymer from that of the polymer which is formed after addition when micromixing is to be investigated.