Kai Langenbach

Influence of different alcohols on the swelling behaviour of hydrogels

The swelling equilibrium of cross-linked poly(N-isopropylacrylamide) (PNIPAAm) hydrogels in alcohol solutions as a function of temperature, alcohol concentration, kind of alcohol (C1OH–C3OH) and gel properties was investigated experimentally. Additionally, the swelling degree as a function of the alcohol concentration was modelled with the UNIQUAC-Free Volume model in combination with the Phantom Network theory. The experiments show that, in pure water, the transition temperature is between 303.15 and 308.15 K depending on the properties of the gel and hence on the polymerization conditions. The transition from a swollen to a shrunken state is caused by the polymeric network and the change of polymer chain localization. In a system with hydrogel + water + alcohol, the swelling degree decreases with increasing alcohol concentration until the shrunken state is reached and increases again by further addition of alcohol at constant temperature. With increasing carbon number of the alcohols, the transition from a swollen to a shrunken state and vice versa shifts to lower concentrations at constant temperature. The use of the UNIQUAC-Free Volume model with Phantom Network theory leads to results in good agreement with the experimental data.

Cross-association of multi-component systems

The design and optimization of equipment in chemical industry (e.g. heat exchanger) and also process simulations require the knowledge of physical properties of mixtures, for instance the involved phase equilibria, enthalpies and the heat capacities. Most experimental data on these properties exists for pure compounds (e.g. water) and for binary mixtures (e.g. water ethanol). The database is however, very limited for mixtures of more than two species. Physically sound equations of state, like the Perturbed-Chain Statistical Associating Theory (PC-SAFT) have been used successfully to provide information about these thermodynamic properties for a wide variety of substances including systems of associating and non-associating or systems of associating and cross-associating species. One of the main challenges using this Wertheim-type equation of state is the mathematically implicit form of the underlying nonlinear system of equations, if association occurs. This article provides in depth information about our recently developed fast and stable algorithm to solve this system of equations numerically for multi-component systems, as well as a new method to find good initial values for the numerical algorithm. Furthermore, the numerical results are compared to experimental data on several properties of interest and found to be in good to excellent agreement.

Prediction of the solid–liquid–liquid equilibria of linear and branched semi-crystalline poly-ethylene in solutions of diphenyl ether by Lattice Cluster Theory

ABSTRACT Recently, Lattice Cluster Theory has been applied to predict liquid–liquid equilibria and solid–liquid equilibria of low and high molecular weight mixtures taking into account the molecular architecture and the nature of crystallinity of the respective component. Herein, an LCT-based theory is applied to calculate solid–liquid–liquid equilibrium of a polyethylene + diphenyl ether system, depending on branching and degree of crystallinity of the polymeric component. Understanding the role that branching number, branching type and degree of polymer crystallinity play in the behaviour of triple and triple critical points is focused on. Insight is given here into constitution and properties of triple and triple critical points in binary polymer solvent systems depending on the molecular architecture of both components, polymer and solvent respectively, and the semi-crystalline nature of the polymer.

Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory

A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO2). The molecular model of CO2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

Three-dimensional phase field modeling of inhomogeneous gas-liquid systems using the PeTS equation of state

Recently, an equation of state (EoS) for the Lennard-Jones truncated and shifted (LJTS) fluid has become available. As it describes metastable and unstable states well, it is suited for predicting density profiles in vapor-liquid interfaces in combination with density gradient theory (DGT). DGT is usually applied to describe interfaces in Cartesian one-dimensional scenarios. In the present work, the perturbed LJ truncated and shifted (PeTS) EoS is implemented into a three-dimensional phase field (PF) model which can be used for studying inhomogeneous gas-liquid systems in a more general way. The results are compared with the results from molecular dynamics simulations for the LJTS fluid that are carried out in the present work and good agreement is observed. The PF model can therefore be used to overcome the scale limit of molecular simulations. A finite element approach is applied for the implementation of the PF model. This requires the first and second derivatives of the PeTS EoS which are calculated using hyper-dual numbers. Several tests and examples of applications of the new PeTS PF model are discussed.