On the equation of state for thermal polymer solutions and melts with attractive interaction

We perform Monte Carlo simulations of a lattice model for polymer melts, i. e., the bond fluctuation model in three dimensions. By using an energy parameter that prefers relatively long bonds, the model exhibits a glass transition at low temperatures, in close qualitative similarity to experiment. We modify this model by adding an attractive interaction of variable strength. We demonstrate that a small interaction strength has only a very small effect on the static properties of the melt. For a fixed strength of the potential, the chemical potential is measured by a modified particle-insertion method over a large range of temperatures and densities. The osmotic pressure is obtained by thermodynamic integration. In contrast to the original version our extended model exhibits a positive thermal expansion.     

Brownian dynamics simulation of grafted polymer brushes

We present results of computer simulations by the method of Brownian dynamics of polymeric brushes attached to impenetrable planes. For testing both model and method we have used one polymer brush attached to a repulsive plane and compare some results with Monte Carlo results of Lai and Binder on the bond fluctuation model. We have also studied two polymeric brushes attached to two parallel planes at different distances between planes, and investigate the interplay between the interpenetration of the brushes and the configurational properties of the grafted chains.     

Experimental investigation of the strength of structural plastics in multiple pulsed bending

Strip-beams of molded fabric-reinforced plastic, unidirectional wound glass-reinforced plastic, and polystyrene and syntactic foam have been tested in pulse bending in a modified electrodynamic testing device. The main stages of the failure process and the nature of the relation between the peak load and the number of cycles to failure have been established. For all the materials tested these relations are similar to the cyclic strength curves obtained at low loading rates. It is shown that for glass-reinforced plastics there is a correlation between the various stages of the failure process.Translated from Mekhanika Polimerov, No. 2, pp. 337–341, March–April, 1971.     

Dynamic percolation transition induced by phase separation: A Monte Carlo analysis

The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider quenching experiments, where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki spinexchange dynamics. Analyzing the distributionn _l(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly lower than the percolation concentration of the initial random state. This dynamic percolation transition is analyzed with finite-size scaling methods. While at zero temperature, where the system settles down at a frozen-in cluster distribution and further phase separation stops, the critical exponents associated with this percolation transition are consistent with the universality class of random percolation, the critical behavior of the transient time-dependent percolation occurring at nonzero temperature possibly belongs to a different, new universality class.     

Finite-size scaling in a microcanonical ensemble

The finite-size scaling technique is extended to a microcanonical ensemble. As an application, equilibrium magnetic properties of anL×L square lattice Ising model are computed using the microcanonical ensemble simulation technique of Creutz, and the results are analyzed using the microcanonical ensemble finite-size scaling. The computations were done on the multitransputer system of the Condensed Matter Theory Group at the University of Mainz.     

Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis

The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionP _L (ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities <ρ>. Particular attention is paid to the question whether accurate estimates of critical temperatureT _c and critical density ρ _c can be obtained. In the lattice gas model these critical parameters are known exactly and the limitations of the approach can thus be definitively asserted. The final estimates for the Lennard Jones problem areT _c =0.47±0.01 (in units of the Lennard Jones energy ε) and ρ _c (in units of σ²), a comparison with previous estimates is made.     

Synthesis and characterization of polymer linked copper(I) bis(N‐heterocyclic carbene) mechanocatalysts

In this paper, the synthesis and characterization of a series of latent polymeric bis(N‐heterocyclic carbene) (NHC) copper(I) complexes is reported, which can be activated for the copper(I)‐catalyzed azide/alkyne cycloaddition (CuAAC) via ultrasound. To prove the influence of chain length and nature of the polymer towards the activation, poly(isobutylene) (PIB), poly(styrene) (PS) and poly(tetrahydrofuran) (PTHF) are synthesized via living polymerization techniques (LCCP, ATRP, CROP) obtaining different chain lengths (from 2500 to 9000 g/mol), followed by quaternization with N‐methylimidazole, generating the corresponding N‐methylimidazolium‐telechelic polymers. The deprotonation of these macroligands via strong bases like sodium tert‐butoxide (NaO^tBu) or potassium hexamethyldisilazide (KHMDS) yields the free N‐heterocyclic carbenes (NHCs), which are used to coordinate to tetrakis(acetonitrile)copper(I) hexafluorophosphate, forming the final polymer‐based mono‐ and bis(N‐methylimidazole‐2‐ylidene) copper(I)X complexes. The structural proof of these complexes is accomplished via ¹H‐NMR spectroscopy, MALDI‐TOF‐MS and GPC‐techniques. The activation of the copper(I) biscarbene catalysts by ultrasound is studied by GPC, revealing the cleavage of one shielding NHC‐ligand. The initial catalytic latency and the via ultrasound introduced catalytic activation is successfully demonstrated monitoring a CuAAC “click” reaction of benzyl azide and phenylacetylene by in situ ¹H‐NMR spectroscopy introducing thus “click” conversions up to 97%. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3893–3907     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.     

Analysis of the cluster formation in two-component cylindrical bottle-brush polymers under poor solvent conditions. A simulation study

Two-component bottle-brush polymers, where flexible side chains containing N = 20, 35 and 50 effective monomers are grafted alternatingly to a rigid backbone, are studied by Molecular Dynamics simulations, varying the grafting density s \sigma and the solvent quality. Whereas for poor solvents and large enough s \sigma the molecular brush is a cylindrical object with monomers of different type occupying locally the two different halves of the cylinder, for intermediate values of s \sigma an axially inhomogeneous structure of “pearl-necklace” type is formed, where microphase separation between monomers of different type within a cluster takes place. These “pearls” have a strongly non-spherical ellipsoidal shape, due to the fact that several side chains cluster together in one “pearl”. We discuss the resulting structures in detail and we present a comparison with the single-component bottle-brush case.